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Antonin Portelli 2013-05-01 09:35:30 -04:00
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# binaries
*.o
*.a
*.so
*.dylib
examples/ex_test
sandbox/*
# Apple stuffs
*.xcodeproj
.DS_Store
# VIM
*.swp
# debug
*.dSYM
# autotools
*.la
*.lo
*.Plo
autom4te.cache/*
config.h*
Makefile.in
Makefile
configure
libtool
.buildutils/m4/*
.buildutils/*
latan/.libs/*
latan/.deps/*
examples/.deps/*
examples/.libs/*
utils/.deps/*
utils/.libs/*
aclocal.m4
config.log
config.status
stamp-h1
myconfig.sh

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under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, your program's commands
might be different; for a GUI interface, you would use an "about box".
You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
<http://www.gnu.org/licenses/>.
The GNU General Public License does not permit incorporating your program
into proprietary programs. If your program is a subroutine library, you
may consider it more useful to permit linking proprietary applications with
the library. If this is what you want to do, use the GNU Lesser General
Public License instead of this License. But first, please read
<http://www.gnu.org/philosophy/why-not-lgpl.html>.

0
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370
INSTALL Normal file
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Installation Instructions
*************************
Copyright (C) 1994-1996, 1999-2002, 2004-2012 Free Software Foundation,
Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved. This file is offered as-is,
without warranty of any kind.
Basic Installation
==================
Briefly, the shell commands `./configure; make; make install' should
configure, build, and install this package. The following
more-detailed instructions are generic; see the `README' file for
instructions specific to this package. Some packages provide this
`INSTALL' file but do not implement all of the features documented
below. The lack of an optional feature in a given package is not
necessarily a bug. More recommendations for GNU packages can be found
in *note Makefile Conventions: (standards)Makefile Conventions.
The `configure' shell script attempts to guess correct values for
various system-dependent variables used during compilation. It uses
those values to create a `Makefile' in each directory of the package.
It may also create one or more `.h' files containing system-dependent
definitions. Finally, it creates a shell script `config.status' that
you can run in the future to recreate the current configuration, and a
file `config.log' containing compiler output (useful mainly for
debugging `configure').
It can also use an optional file (typically called `config.cache'
and enabled with `--cache-file=config.cache' or simply `-C') that saves
the results of its tests to speed up reconfiguring. Caching is
disabled by default to prevent problems with accidental use of stale
cache files.
If you need to do unusual things to compile the package, please try
to figure out how `configure' could check whether to do them, and mail
diffs or instructions to the address given in the `README' so they can
be considered for the next release. If you are using the cache, and at
some point `config.cache' contains results you don't want to keep, you
may remove or edit it.
The file `configure.ac' (or `configure.in') is used to create
`configure' by a program called `autoconf'. You need `configure.ac' if
you want to change it or regenerate `configure' using a newer version
of `autoconf'.
The simplest way to compile this package is:
1. `cd' to the directory containing the package's source code and type
`./configure' to configure the package for your system.
Running `configure' might take a while. While running, it prints
some messages telling which features it is checking for.
2. Type `make' to compile the package.
3. Optionally, type `make check' to run any self-tests that come with
the package, generally using the just-built uninstalled binaries.
4. Type `make install' to install the programs and any data files and
documentation. When installing into a prefix owned by root, it is
recommended that the package be configured and built as a regular
user, and only the `make install' phase executed with root
privileges.
5. Optionally, type `make installcheck' to repeat any self-tests, but
this time using the binaries in their final installed location.
This target does not install anything. Running this target as a
regular user, particularly if the prior `make install' required
root privileges, verifies that the installation completed
correctly.
6. You can remove the program binaries and object files from the
source code directory by typing `make clean'. To also remove the
files that `configure' created (so you can compile the package for
a different kind of computer), type `make distclean'. There is
also a `make maintainer-clean' target, but that is intended mainly
for the package's developers. If you use it, you may have to get
all sorts of other programs in order to regenerate files that came
with the distribution.
7. Often, you can also type `make uninstall' to remove the installed
files again. In practice, not all packages have tested that
uninstallation works correctly, even though it is required by the
GNU Coding Standards.
8. Some packages, particularly those that use Automake, provide `make
distcheck', which can by used by developers to test that all other
targets like `make install' and `make uninstall' work correctly.
This target is generally not run by end users.
Compilers and Options
=====================
Some systems require unusual options for compilation or linking that
the `configure' script does not know about. Run `./configure --help'
for details on some of the pertinent environment variables.
You can give `configure' initial values for configuration parameters
by setting variables in the command line or in the environment. Here
is an example:
./configure CC=c99 CFLAGS=-g LIBS=-lposix
*Note Defining Variables::, for more details.
Compiling For Multiple Architectures
====================================
You can compile the package for more than one kind of computer at the
same time, by placing the object files for each architecture in their
own directory. To do this, you can use GNU `make'. `cd' to the
directory where you want the object files and executables to go and run
the `configure' script. `configure' automatically checks for the
source code in the directory that `configure' is in and in `..'. This
is known as a "VPATH" build.
With a non-GNU `make', it is safer to compile the package for one
architecture at a time in the source code directory. After you have
installed the package for one architecture, use `make distclean' before
reconfiguring for another architecture.
On MacOS X 10.5 and later systems, you can create libraries and
executables that work on multiple system types--known as "fat" or
"universal" binaries--by specifying multiple `-arch' options to the
compiler but only a single `-arch' option to the preprocessor. Like
this:
./configure CC="gcc -arch i386 -arch x86_64 -arch ppc -arch ppc64" \
CXX="g++ -arch i386 -arch x86_64 -arch ppc -arch ppc64" \
CPP="gcc -E" CXXCPP="g++ -E"
This is not guaranteed to produce working output in all cases, you
may have to build one architecture at a time and combine the results
using the `lipo' tool if you have problems.
Installation Names
==================
By default, `make install' installs the package's commands under
`/usr/local/bin', include files under `/usr/local/include', etc. You
can specify an installation prefix other than `/usr/local' by giving
`configure' the option `--prefix=PREFIX', where PREFIX must be an
absolute file name.
You can specify separate installation prefixes for
architecture-specific files and architecture-independent files. If you
pass the option `--exec-prefix=PREFIX' to `configure', the package uses
PREFIX as the prefix for installing programs and libraries.
Documentation and other data files still use the regular prefix.
In addition, if you use an unusual directory layout you can give
options like `--bindir=DIR' to specify different values for particular
kinds of files. Run `configure --help' for a list of the directories
you can set and what kinds of files go in them. In general, the
default for these options is expressed in terms of `${prefix}', so that
specifying just `--prefix' will affect all of the other directory
specifications that were not explicitly provided.
The most portable way to affect installation locations is to pass the
correct locations to `configure'; however, many packages provide one or
both of the following shortcuts of passing variable assignments to the
`make install' command line to change installation locations without
having to reconfigure or recompile.
The first method involves providing an override variable for each
affected directory. For example, `make install
prefix=/alternate/directory' will choose an alternate location for all
directory configuration variables that were expressed in terms of
`${prefix}'. Any directories that were specified during `configure',
but not in terms of `${prefix}', must each be overridden at install
time for the entire installation to be relocated. The approach of
makefile variable overrides for each directory variable is required by
the GNU Coding Standards, and ideally causes no recompilation.
However, some platforms have known limitations with the semantics of
shared libraries that end up requiring recompilation when using this
method, particularly noticeable in packages that use GNU Libtool.
The second method involves providing the `DESTDIR' variable. For
example, `make install DESTDIR=/alternate/directory' will prepend
`/alternate/directory' before all installation names. The approach of
`DESTDIR' overrides is not required by the GNU Coding Standards, and
does not work on platforms that have drive letters. On the other hand,
it does better at avoiding recompilation issues, and works well even
when some directory options were not specified in terms of `${prefix}'
at `configure' time.
Optional Features
=================
If the package supports it, you can cause programs to be installed
with an extra prefix or suffix on their names by giving `configure' the
option `--program-prefix=PREFIX' or `--program-suffix=SUFFIX'.
Some packages pay attention to `--enable-FEATURE' options to
`configure', where FEATURE indicates an optional part of the package.
They may also pay attention to `--with-PACKAGE' options, where PACKAGE
is something like `gnu-as' or `x' (for the X Window System). The
`README' should mention any `--enable-' and `--with-' options that the
package recognizes.
For packages that use the X Window System, `configure' can usually
find the X include and library files automatically, but if it doesn't,
you can use the `configure' options `--x-includes=DIR' and
`--x-libraries=DIR' to specify their locations.
Some packages offer the ability to configure how verbose the
execution of `make' will be. For these packages, running `./configure
--enable-silent-rules' sets the default to minimal output, which can be
overridden with `make V=1'; while running `./configure
--disable-silent-rules' sets the default to verbose, which can be
overridden with `make V=0'.
Particular systems
==================
On HP-UX, the default C compiler is not ANSI C compatible. If GNU
CC is not installed, it is recommended to use the following options in
order to use an ANSI C compiler:
./configure CC="cc -Ae -D_XOPEN_SOURCE=500"
and if that doesn't work, install pre-built binaries of GCC for HP-UX.
HP-UX `make' updates targets which have the same time stamps as
their prerequisites, which makes it generally unusable when shipped
generated files such as `configure' are involved. Use GNU `make'
instead.
On OSF/1 a.k.a. Tru64, some versions of the default C compiler cannot
parse its `<wchar.h>' header file. The option `-nodtk' can be used as
a workaround. If GNU CC is not installed, it is therefore recommended
to try
./configure CC="cc"
and if that doesn't work, try
./configure CC="cc -nodtk"
On Solaris, don't put `/usr/ucb' early in your `PATH'. This
directory contains several dysfunctional programs; working variants of
these programs are available in `/usr/bin'. So, if you need `/usr/ucb'
in your `PATH', put it _after_ `/usr/bin'.
On Haiku, software installed for all users goes in `/boot/common',
not `/usr/local'. It is recommended to use the following options:
./configure --prefix=/boot/common
Specifying the System Type
==========================
There may be some features `configure' cannot figure out
automatically, but needs to determine by the type of machine the package
will run on. Usually, assuming the package is built to be run on the
_same_ architectures, `configure' can figure that out, but if it prints
a message saying it cannot guess the machine type, give it the
`--build=TYPE' option. TYPE can either be a short name for the system
type, such as `sun4', or a canonical name which has the form:
CPU-COMPANY-SYSTEM
where SYSTEM can have one of these forms:
OS
KERNEL-OS
See the file `config.sub' for the possible values of each field. If
`config.sub' isn't included in this package, then this package doesn't
need to know the machine type.
If you are _building_ compiler tools for cross-compiling, you should
use the option `--target=TYPE' to select the type of system they will
produce code for.
If you want to _use_ a cross compiler, that generates code for a
platform different from the build platform, you should specify the
"host" platform (i.e., that on which the generated programs will
eventually be run) with `--host=TYPE'.
Sharing Defaults
================
If you want to set default values for `configure' scripts to share,
you can create a site shell script called `config.site' that gives
default values for variables like `CC', `cache_file', and `prefix'.
`configure' looks for `PREFIX/share/config.site' if it exists, then
`PREFIX/etc/config.site' if it exists. Or, you can set the
`CONFIG_SITE' environment variable to the location of the site script.
A warning: not all `configure' scripts look for a site script.
Defining Variables
==================
Variables not defined in a site shell script can be set in the
environment passed to `configure'. However, some packages may run
configure again during the build, and the customized values of these
variables may be lost. In order to avoid this problem, you should set
them in the `configure' command line, using `VAR=value'. For example:
./configure CC=/usr/local2/bin/gcc
causes the specified `gcc' to be used as the C compiler (unless it is
overridden in the site shell script).
Unfortunately, this technique does not work for `CONFIG_SHELL' due to
an Autoconf limitation. Until the limitation is lifted, you can use
this workaround:
CONFIG_SHELL=/bin/bash ./configure CONFIG_SHELL=/bin/bash
`configure' Invocation
======================
`configure' recognizes the following options to control how it
operates.
`--help'
`-h'
Print a summary of all of the options to `configure', and exit.
`--help=short'
`--help=recursive'
Print a summary of the options unique to this package's
`configure', and exit. The `short' variant lists options used
only in the top level, while the `recursive' variant lists options
also present in any nested packages.
`--version'
`-V'
Print the version of Autoconf used to generate the `configure'
script, and exit.
`--cache-file=FILE'
Enable the cache: use and save the results of the tests in FILE,
traditionally `config.cache'. FILE defaults to `/dev/null' to
disable caching.
`--config-cache'
`-C'
Alias for `--cache-file=config.cache'.
`--quiet'
`--silent'
`-q'
Do not print messages saying which checks are being made. To
suppress all normal output, redirect it to `/dev/null' (any error
messages will still be shown).
`--srcdir=DIR'
Look for the package's source code in directory DIR. Usually
`configure' can determine that directory automatically.
`--prefix=DIR'
Use DIR as the installation prefix. *note Installation Names::
for more details, including other options available for fine-tuning
the installation locations.
`--no-create'
`-n'
Run the configure checks, but stop before creating any output
files.
`configure' also accepts some other, not widely useful, options. Run
`configure --help' for more details.

67
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// !$*UTF8*$!
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archiveVersion = 1;
classes = {
};
objectVersion = 46;
objects = {
/* Begin PBXGroup section */
69C93A9E172FFBC00041B3C8 = {
isa = PBXGroup;
children = (
);
sourceTree = "<group>";
};
/* End PBXGroup section */
/* Begin PBXProject section */
69C93A9F172FFBC00041B3C8 /* Project object */ = {
isa = PBXProject;
attributes = {
LastUpgradeCheck = 0460;
};
buildConfigurationList = 69C93AA2172FFBC00041B3C8 /* Build configuration list for PBXProject "LatAnalyze3" */;
compatibilityVersion = "Xcode 3.2";
developmentRegion = English;
hasScannedForEncodings = 0;
knownRegions = (
en,
);
mainGroup = 69C93A9E172FFBC00041B3C8;
projectDirPath = "";
projectRoot = "";
targets = (
);
};
/* End PBXProject section */
/* Begin XCBuildConfiguration section */
69C93AA3172FFBC00041B3C8 /* Debug */ = {
isa = XCBuildConfiguration;
buildSettings = {
};
name = Debug;
};
69C93AA4172FFBC00041B3C8 /* Release */ = {
isa = XCBuildConfiguration;
buildSettings = {
};
name = Release;
};
/* End XCBuildConfiguration section */
/* Begin XCConfigurationList section */
69C93AA2172FFBC00041B3C8 /* Build configuration list for PBXProject "LatAnalyze3" */ = {
isa = XCConfigurationList;
buildConfigurations = (
69C93AA3172FFBC00041B3C8 /* Debug */,
69C93AA4172FFBC00041B3C8 /* Release */,
);
defaultConfigurationIsVisible = 0;
defaultConfigurationName = Release;
};
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rootObject = 69C93A9F172FFBC00041B3C8 /* Project object */;
}

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SUBDIRS = latan examples
ACLOCAL_AMFLAGS = -I .buildutils/m4

0
NEWS Normal file
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0
README Normal file
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94
acinclude.m4 Normal file
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AC_DEFUN([AX_GCC_OPTION], [
AC_REQUIRE([AC_PROG_CC])
AC_MSG_CHECKING([if gcc accepts $1 option])
AS_IF([ test "x$GCC" = "xyes" ],[
AS_IF([ test -z "$3" ],[
ax_gcc_option_test="int main()
{
return 0;
}"
],[
ax_gcc_option_test="$3"
])
# Dump the test program to file
cat <<EOF > conftest.c
$ax_gcc_option_test
EOF
# Dump back the file to the log, useful for debugging purposes
AC_TRY_COMMAND(cat conftest.c 1>&AS_MESSAGE_LOG_FD)
AS_IF([ AC_TRY_COMMAND($CC $2 $1 -c conftest.c 1>&AS_MESSAGE_LOG_FD) ],[
AC_MSG_RESULT([yes])
$4
],[
AC_MSG_RESULT([no])
$5
])
],[
AC_MSG_RESULT([no gcc available])
])
])
AC_DEFUN([AX_GCC_VERSION], [
GCC_VERSION=""
AX_GCC_OPTION([-dumpversion],[],[],[
ax_gcc_version_option=yes
],[
ax_gcc_version_option=no
])
AS_IF([test "x$GCC" = "xyes"],[
AS_IF([test "x$ax_gcc_version_option" != "xno"],[
AC_CACHE_CHECK([gcc version],[ax_cv_gcc_version],[
ax_cv_gcc_version="`$CC -dumpversion`"
AS_IF([test "x$ax_cv_gcc_version" = "x"],[
ax_cv_gcc_version=""
])
])
GCC_VERSION=$ax_cv_gcc_version
])
])
AC_SUBST([GCC_VERSION])
])
AC_DEFUN([AX_GXX_VERSION], [
GXX_VERSION=""
AX_GCC_OPTION([-dumpversion],[],[],[
ax_gcc_version_option=yes
],[
ax_gcc_version_option=no
])
AS_IF([test "x$GXX" = "xyes"],[
AS_IF([test "x$ax_gxx_version_option" != "no"],[
AC_CACHE_CHECK([gxx version],[ax_cv_gxx_version],[
ax_cv_gxx_version="`$CXX -dumpversion`"
AS_IF([test "x$ax_cv_gxx_version" = "x"],[
ax_cv_gxx_version=""
])
])
GXX_VERSION=$ax_cv_gxx_version
])
])
AC_SUBST([GXX_VERSION])
])
AC_DEFUN([AX_COMPILER_VENDOR],
[
AC_CACHE_CHECK([for _AC_LANG compiler vendor], ax_cv_[]_AC_LANG_ABBREV[]_compiler_vendor,
[ax_cv_[]_AC_LANG_ABBREV[]_compiler_vendor=unknown
# note: don't check for gcc first since some other compilers define __GNUC__
for ventest in intel:__ICC,__ECC,__INTEL_COMPILER ibm:__xlc__,__xlC__,__IBMC__,__IBMCPP__ pathscale:__PATHCC__,__PATHSCALE__ gnu:__GNUC__ sun:__SUNPRO_C,__SUNPRO_CC hp:__HP_cc,__HP_aCC dec:__DECC,__DECCXX,__DECC_VER,__DECCXX_VER borland:__BORLANDC__,__TURBOC__ comeau:__COMO__ cray:_CRAYC kai:__KCC lcc:__LCC__ metrowerks:__MWERKS__ sgi:__sgi,sgi microsoft:_MSC_VER watcom:__WATCOMC__ portland:__PGI; do
vencpp="defined("`echo $ventest | cut -d: -f2 | sed 's/,/) || defined(/g'`")"
AC_COMPILE_IFELSE([AC_LANG_PROGRAM(,[
#if !($vencpp)
thisisanerror;
#endif
])], [ax_cv_]_AC_LANG_ABBREV[_compiler_vendor=`echo $ventest | cut -d: -f1`; break])
done
])
])

5
bootstrap.sh Executable file
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#!/usr/bin/env bash
rm -rf .buildutils
mkdir -p .buildutils/m4
autoreconf -fvi

22
build.sh Executable file
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#!/bin/bash
PREFIX=`cat Makefile | grep '^prefix =' | awk '{print $3}'`
case $1 in
'')
echo '-- building...'
make -j3
echo '-- installing...'
make uninstall 1>/dev/null
make install 1>/dev/null
if [[ `basename \`pwd\`` == "latan" ]]
then
echo '-- creating debug symbols...'
dsymutil .libs/liblatan.0.dylib -o ${PREFIX}/lib/liblatan.0.dylib.dSYM
fi;;
'clean')
echo '-- cleaning...'
make -j3 clean;;
*)
echo 'error: unknown action' 1>&2
exit 1;;
esac

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# Process this file with autoconf to produce a configure script.
# Initialization
AC_PREREQ([2.64])
AC_INIT([LatAnalyze],[3.0alpha1],[antonin.portelli@me.com],[latan])
AC_CONFIG_AUX_DIR([.buildutils])
AC_CONFIG_SRCDIR([latan/Global.cpp])
AC_CONFIG_SRCDIR([examples/ex_test.cpp])
AC_CONFIG_MACRO_DIR([.buildutils/m4])
AM_INIT_AUTOMAKE([-Wall -Werror])
AM_SILENT_RULES([yes])
AC_CONFIG_HEADERS([config.h])
# Checks for programs.
AC_PROG_CXX
AC_PROG_AWK
AC_PROG_CC
AC_PROG_CPP
AC_PROG_INSTALL
AC_PROG_LN_S
AC_PROG_MAKE_SET
m4_ifdef([AM_PROG_AR],[AM_PROG_AR])
LT_INIT
# Get compilers informations
AX_COMPILER_VENDOR
AC_DEFINE_UNQUOTED([C_COMP_VENDOR],["$ax_cv_c_compiler_vendor"],
[vendor of C compiler that will compile the code])
AM_CONDITIONAL([CC_GNU],[test $ax_cv_c_compiler_vendor = "gnu"])
AM_CONDITIONAL([CC_INTEL],[test $ax_cv_c_compiler_vendor = "intel"])
AC_LANG([C++])
AX_COMPILER_VENDOR
AC_DEFINE_UNQUOTED([CXX_COMP_VENDOR],["$ax_cv_cxx_compiler_vendor"],
[vendor of C++ compiler that will compile the code])
AM_CONDITIONAL([CXX_GNU],[test $ax_cv_cxx_compiler_vendor = "gnu"])
AM_CONDITIONAL([CXX_INTEL],[test $ax_cv_cxx_compiler_vendor = "intel"])
AC_LANG([C])
AX_GCC_VERSION
AC_DEFINE_UNQUOTED([GCC_VERSION],["$GCC_VERSION"],
[version of gcc that will compile the code])
AX_GXX_VERSION
AC_DEFINE_UNQUOTED([GXX_VERSION],["$GXX_VERSION"],
[version of g++ that will compile the code])
# Checks for libraries.
AC_LANG([C++])
AC_CHECK_LIB([m],[cos],[],[AC_MSG_ERROR([libm library not found])])
AC_CHECK_LIB([stdc++],[main],[LIBS="-lstdc++ $LIBS"],[AC_MSG_ERROR([libstdc++ library not found])])
# Checks for header files.
AC_HEADER_STDC
AC_SUBST([LIBS])
AC_SUBST([AM_CFLAGS])
AC_SUBST([AM_LDFLAGS])
AC_CONFIG_FILES([Makefile latan/Makefile examples/Makefile])
AC_OUTPUT

24
examples/Makefile.am Normal file
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@ -0,0 +1,24 @@
if CC_GNU
COM_CFLAGS = -Wall -W -pedantic
else
if CC_INTEL
COM_CFLAGS = -Wall
endif
endif
if CXX_GNU
COM_CXXFLAGS = -Wall -W -pedantic
else
if CXX_INTEL
COM_CXXFLAGS = -Wall
endif
endif
noinst_PROGRAMS = \
ex_test
ex_test_SOURCES = ex_test.cpp
ex_test_CFLAGS = -g -O2
ex_test_LDFLAGS = -L../latan/.libs -llatan
ACLOCAL_AMFLAGS = -I .buildutils/m4

20
examples/ex_test.cpp Normal file
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@ -0,0 +1,20 @@
#include <iostream>
#include <latan/Global.h>
using namespace std;
using namespace Latan;
int main(void)
{
DMat m(2,2);
m(0,6) = 3;
m(1,0) = 2.5;
m(0,1) = -1;
m(1,1) = m(1,0) + m(0,1);
cout << "Here is the matrix m:\n" << m << endl;
DVec v(2);
v(0) = 4;
v(1) = v(0) - 1;
cout << "Here is the vector v:\n" << v << endl;
}

1
examples/latan Symbolic link
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@ -0,0 +1 @@
../latan

11
latan/Eigen/Array Normal file
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@ -0,0 +1,11 @@
#ifndef EIGEN_ARRAY_MODULE_H
#define EIGEN_ARRAY_MODULE_H
// include Core first to handle Eigen2 support macros
#include "Core"
#ifndef EIGEN2_SUPPORT
#error The Eigen/Array header does no longer exist in Eigen3. All that functionality has moved to Eigen/Core.
#endif
#endif // EIGEN_ARRAY_MODULE_H

32
latan/Eigen/Cholesky Normal file
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#ifndef EIGEN_CHOLESKY_MODULE_H
#define EIGEN_CHOLESKY_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Cholesky_Module Cholesky module
*
*
*
* This module provides two variants of the Cholesky decomposition for selfadjoint (hermitian) matrices.
* Those decompositions are accessible via the following MatrixBase methods:
* - MatrixBase::llt(),
* - MatrixBase::ldlt()
*
* \code
* #include <Eigen/Cholesky>
* \endcode
*/
#include "src/misc/Solve.h"
#include "src/Cholesky/LLT.h"
#include "src/Cholesky/LDLT.h"
#ifdef EIGEN_USE_LAPACKE
#include "src/Cholesky/LLT_MKL.h"
#endif
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_CHOLESKY_MODULE_H
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

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latan/Eigen/CholmodSupport Normal file
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#ifndef EIGEN_CHOLMODSUPPORT_MODULE_H
#define EIGEN_CHOLMODSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
extern "C" {
#include <cholmod.h>
}
/** \ingroup Support_modules
* \defgroup CholmodSupport_Module CholmodSupport module
*
* This module provides an interface to the Cholmod library which is part of the <a href="http://www.cise.ufl.edu/research/sparse/SuiteSparse/">suitesparse</a> package.
* It provides the two following main factorization classes:
* - class CholmodSupernodalLLT: a supernodal LLT Cholesky factorization.
* - class CholmodDecomposiiton: a general L(D)LT Cholesky factorization with automatic or explicit runtime selection of the underlying factorization method (supernodal or simplicial).
*
* For the sake of completeness, this module also propose the two following classes:
* - class CholmodSimplicialLLT
* - class CholmodSimplicialLDLT
* Note that these classes does not bring any particular advantage compared to the built-in
* SimplicialLLT and SimplicialLDLT factorization classes.
*
* \code
* #include <Eigen/CholmodSupport>
* \endcode
*
* In order to use this module, the cholmod headers must be accessible from the include paths, and your binary must be linked to the cholmod library and its dependencies.
* The dependencies depend on how cholmod has been compiled.
* For a cmake based project, you can use our FindCholmod.cmake module to help you in this task.
*
*/
#include "src/misc/Solve.h"
#include "src/misc/SparseSolve.h"
#include "src/CholmodSupport/CholmodSupport.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_CHOLMODSUPPORT_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2007-2011 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CORE_H
#define EIGEN_CORE_H
// first thing Eigen does: stop the compiler from committing suicide
#include "src/Core/util/DisableStupidWarnings.h"
// then include this file where all our macros are defined. It's really important to do it first because
// it's where we do all the alignment settings (platform detection and honoring the user's will if he
// defined e.g. EIGEN_DONT_ALIGN) so it needs to be done before we do anything with vectorization.
#include "src/Core/util/Macros.h"
#include <complex>
// this include file manages BLAS and MKL related macros
// and inclusion of their respective header files
#include "src/Core/util/MKL_support.h"
// if alignment is disabled, then disable vectorization. Note: EIGEN_ALIGN is the proper check, it takes into
// account both the user's will (EIGEN_DONT_ALIGN) and our own platform checks
#if !EIGEN_ALIGN
#ifndef EIGEN_DONT_VECTORIZE
#define EIGEN_DONT_VECTORIZE
#endif
#endif
#ifdef _MSC_VER
#include <malloc.h> // for _aligned_malloc -- need it regardless of whether vectorization is enabled
#if (_MSC_VER >= 1500) // 2008 or later
// Remember that usage of defined() in a #define is undefined by the standard.
// a user reported that in 64-bit mode, MSVC doesn't care to define _M_IX86_FP.
#if (defined(_M_IX86_FP) && (_M_IX86_FP >= 2)) || defined(_M_X64)
#define EIGEN_SSE2_ON_MSVC_2008_OR_LATER
#endif
#endif
#else
// Remember that usage of defined() in a #define is undefined by the standard
#if (defined __SSE2__) && ( (!defined __GNUC__) || (defined __INTEL_COMPILER) || EIGEN_GNUC_AT_LEAST(4,2) )
#define EIGEN_SSE2_ON_NON_MSVC_BUT_NOT_OLD_GCC
#endif
#endif
#ifndef EIGEN_DONT_VECTORIZE
#if defined (EIGEN_SSE2_ON_NON_MSVC_BUT_NOT_OLD_GCC) || defined(EIGEN_SSE2_ON_MSVC_2008_OR_LATER)
// Defines symbols for compile-time detection of which instructions are
// used.
// EIGEN_VECTORIZE_YY is defined if and only if the instruction set YY is used
#define EIGEN_VECTORIZE
#define EIGEN_VECTORIZE_SSE
#define EIGEN_VECTORIZE_SSE2
// Detect sse3/ssse3/sse4:
// gcc and icc defines __SSE3__, ...
// there is no way to know about this on msvc. You can define EIGEN_VECTORIZE_SSE* if you
// want to force the use of those instructions with msvc.
#ifdef __SSE3__
#define EIGEN_VECTORIZE_SSE3
#endif
#ifdef __SSSE3__
#define EIGEN_VECTORIZE_SSSE3
#endif
#ifdef __SSE4_1__
#define EIGEN_VECTORIZE_SSE4_1
#endif
#ifdef __SSE4_2__
#define EIGEN_VECTORIZE_SSE4_2
#endif
// include files
// This extern "C" works around a MINGW-w64 compilation issue
// https://sourceforge.net/tracker/index.php?func=detail&aid=3018394&group_id=202880&atid=983354
// In essence, intrin.h is included by windows.h and also declares intrinsics (just as emmintrin.h etc. below do).
// However, intrin.h uses an extern "C" declaration, and g++ thus complains of duplicate declarations
// with conflicting linkage. The linkage for intrinsics doesn't matter, but at that stage the compiler doesn't know;
// so, to avoid compile errors when windows.h is included after Eigen/Core, ensure intrinsics are extern "C" here too.
// notice that since these are C headers, the extern "C" is theoretically needed anyways.
extern "C" {
#include <emmintrin.h>
#include <xmmintrin.h>
#ifdef EIGEN_VECTORIZE_SSE3
#include <pmmintrin.h>
#endif
#ifdef EIGEN_VECTORIZE_SSSE3
#include <tmmintrin.h>
#endif
#ifdef EIGEN_VECTORIZE_SSE4_1
#include <smmintrin.h>
#endif
#ifdef EIGEN_VECTORIZE_SSE4_2
#include <nmmintrin.h>
#endif
} // end extern "C"
#elif defined __ALTIVEC__
#define EIGEN_VECTORIZE
#define EIGEN_VECTORIZE_ALTIVEC
#include <altivec.h>
// We need to #undef all these ugly tokens defined in <altivec.h>
// => use __vector instead of vector
#undef bool
#undef vector
#undef pixel
#elif defined __ARM_NEON__
#define EIGEN_VECTORIZE
#define EIGEN_VECTORIZE_NEON
#include <arm_neon.h>
#endif
#endif
#if (defined _OPENMP) && (!defined EIGEN_DONT_PARALLELIZE)
#define EIGEN_HAS_OPENMP
#endif
#ifdef EIGEN_HAS_OPENMP
#include <omp.h>
#endif
// MSVC for windows mobile does not have the errno.h file
#if !(defined(_MSC_VER) && defined(_WIN32_WCE)) && !defined(__ARMCC_VERSION)
#define EIGEN_HAS_ERRNO
#endif
#ifdef EIGEN_HAS_ERRNO
#include <cerrno>
#endif
#include <cstddef>
#include <cstdlib>
#include <cmath>
#include <cassert>
#include <functional>
#include <iosfwd>
#include <cstring>
#include <string>
#include <limits>
#include <climits> // for CHAR_BIT
// for min/max:
#include <algorithm>
// for outputting debug info
#ifdef EIGEN_DEBUG_ASSIGN
#include <iostream>
#endif
// required for __cpuid, needs to be included after cmath
#if defined(_MSC_VER) && (defined(_M_IX86)||defined(_M_X64))
#include <intrin.h>
#endif
#if defined(_CPPUNWIND) || defined(__EXCEPTIONS)
#define EIGEN_EXCEPTIONS
#endif
#ifdef EIGEN_EXCEPTIONS
#include <new>
#endif
/** \brief Namespace containing all symbols from the %Eigen library. */
namespace Eigen {
inline static const char *SimdInstructionSetsInUse(void) {
#if defined(EIGEN_VECTORIZE_SSE4_2)
return "SSE, SSE2, SSE3, SSSE3, SSE4.1, SSE4.2";
#elif defined(EIGEN_VECTORIZE_SSE4_1)
return "SSE, SSE2, SSE3, SSSE3, SSE4.1";
#elif defined(EIGEN_VECTORIZE_SSSE3)
return "SSE, SSE2, SSE3, SSSE3";
#elif defined(EIGEN_VECTORIZE_SSE3)
return "SSE, SSE2, SSE3";
#elif defined(EIGEN_VECTORIZE_SSE2)
return "SSE, SSE2";
#elif defined(EIGEN_VECTORIZE_ALTIVEC)
return "AltiVec";
#elif defined(EIGEN_VECTORIZE_NEON)
return "ARM NEON";
#else
return "None";
#endif
}
} // end namespace Eigen
#define STAGE10_FULL_EIGEN2_API 10
#define STAGE20_RESOLVE_API_CONFLICTS 20
#define STAGE30_FULL_EIGEN3_API 30
#define STAGE40_FULL_EIGEN3_STRICTNESS 40
#define STAGE99_NO_EIGEN2_SUPPORT 99
#if defined EIGEN2_SUPPORT_STAGE40_FULL_EIGEN3_STRICTNESS
#define EIGEN2_SUPPORT
#define EIGEN2_SUPPORT_STAGE STAGE40_FULL_EIGEN3_STRICTNESS
#elif defined EIGEN2_SUPPORT_STAGE30_FULL_EIGEN3_API
#define EIGEN2_SUPPORT
#define EIGEN2_SUPPORT_STAGE STAGE30_FULL_EIGEN3_API
#elif defined EIGEN2_SUPPORT_STAGE20_RESOLVE_API_CONFLICTS
#define EIGEN2_SUPPORT
#define EIGEN2_SUPPORT_STAGE STAGE20_RESOLVE_API_CONFLICTS
#elif defined EIGEN2_SUPPORT_STAGE10_FULL_EIGEN2_API
#define EIGEN2_SUPPORT
#define EIGEN2_SUPPORT_STAGE STAGE10_FULL_EIGEN2_API
#elif defined EIGEN2_SUPPORT
// default to stage 3, that's what it's always meant
#define EIGEN2_SUPPORT_STAGE30_FULL_EIGEN3_API
#define EIGEN2_SUPPORT_STAGE STAGE30_FULL_EIGEN3_API
#else
#define EIGEN2_SUPPORT_STAGE STAGE99_NO_EIGEN2_SUPPORT
#endif
#ifdef EIGEN2_SUPPORT
#undef minor
#endif
// we use size_t frequently and we'll never remember to prepend it with std:: everytime just to
// ensure QNX/QCC support
using std::size_t;
// gcc 4.6.0 wants std:: for ptrdiff_t
using std::ptrdiff_t;
/** \defgroup Core_Module Core module
* This is the main module of Eigen providing dense matrix and vector support
* (both fixed and dynamic size) with all the features corresponding to a BLAS library
* and much more...
*
* \code
* #include <Eigen/Core>
* \endcode
*/
/** \defgroup Support_modules Support modules [category]
* Category of modules which add support for external libraries.
*/
#include "src/Core/util/Constants.h"
#include "src/Core/util/ForwardDeclarations.h"
#include "src/Core/util/Meta.h"
#include "src/Core/util/XprHelper.h"
#include "src/Core/util/StaticAssert.h"
#include "src/Core/util/Memory.h"
#include "src/Core/NumTraits.h"
#include "src/Core/MathFunctions.h"
#include "src/Core/GenericPacketMath.h"
#if defined EIGEN_VECTORIZE_SSE
#include "src/Core/arch/SSE/PacketMath.h"
#include "src/Core/arch/SSE/MathFunctions.h"
#include "src/Core/arch/SSE/Complex.h"
#elif defined EIGEN_VECTORIZE_ALTIVEC
#include "src/Core/arch/AltiVec/PacketMath.h"
#include "src/Core/arch/AltiVec/Complex.h"
#elif defined EIGEN_VECTORIZE_NEON
#include "src/Core/arch/NEON/PacketMath.h"
#include "src/Core/arch/NEON/Complex.h"
#endif
#include "src/Core/arch/Default/Settings.h"
#include "src/Core/Functors.h"
#include "src/Core/DenseCoeffsBase.h"
#include "src/Core/DenseBase.h"
#include "src/Core/MatrixBase.h"
#include "src/Core/EigenBase.h"
#ifndef EIGEN_PARSED_BY_DOXYGEN // work around Doxygen bug triggered by Assign.h r814874
// at least confirmed with Doxygen 1.5.5 and 1.5.6
#include "src/Core/Assign.h"
#endif
#include "src/Core/util/BlasUtil.h"
#include "src/Core/DenseStorage.h"
#include "src/Core/NestByValue.h"
#include "src/Core/ForceAlignedAccess.h"
#include "src/Core/ReturnByValue.h"
#include "src/Core/NoAlias.h"
#include "src/Core/PlainObjectBase.h"
#include "src/Core/Matrix.h"
#include "src/Core/Array.h"
#include "src/Core/CwiseBinaryOp.h"
#include "src/Core/CwiseUnaryOp.h"
#include "src/Core/CwiseNullaryOp.h"
#include "src/Core/CwiseUnaryView.h"
#include "src/Core/SelfCwiseBinaryOp.h"
#include "src/Core/Dot.h"
#include "src/Core/StableNorm.h"
#include "src/Core/MapBase.h"
#include "src/Core/Stride.h"
#include "src/Core/Map.h"
#include "src/Core/Block.h"
#include "src/Core/VectorBlock.h"
#include "src/Core/Transpose.h"
#include "src/Core/DiagonalMatrix.h"
#include "src/Core/Diagonal.h"
#include "src/Core/DiagonalProduct.h"
#include "src/Core/PermutationMatrix.h"
#include "src/Core/Transpositions.h"
#include "src/Core/Redux.h"
#include "src/Core/Visitor.h"
#include "src/Core/Fuzzy.h"
#include "src/Core/IO.h"
#include "src/Core/Swap.h"
#include "src/Core/CommaInitializer.h"
#include "src/Core/Flagged.h"
#include "src/Core/ProductBase.h"
#include "src/Core/GeneralProduct.h"
#include "src/Core/TriangularMatrix.h"
#include "src/Core/SelfAdjointView.h"
#include "src/Core/products/GeneralBlockPanelKernel.h"
#include "src/Core/products/Parallelizer.h"
#include "src/Core/products/CoeffBasedProduct.h"
#include "src/Core/products/GeneralMatrixVector.h"
#include "src/Core/products/GeneralMatrixMatrix.h"
#include "src/Core/SolveTriangular.h"
#include "src/Core/products/GeneralMatrixMatrixTriangular.h"
#include "src/Core/products/SelfadjointMatrixVector.h"
#include "src/Core/products/SelfadjointMatrixMatrix.h"
#include "src/Core/products/SelfadjointProduct.h"
#include "src/Core/products/SelfadjointRank2Update.h"
#include "src/Core/products/TriangularMatrixVector.h"
#include "src/Core/products/TriangularMatrixMatrix.h"
#include "src/Core/products/TriangularSolverMatrix.h"
#include "src/Core/products/TriangularSolverVector.h"
#include "src/Core/BandMatrix.h"
#include "src/Core/BooleanRedux.h"
#include "src/Core/Select.h"
#include "src/Core/VectorwiseOp.h"
#include "src/Core/Random.h"
#include "src/Core/Replicate.h"
#include "src/Core/Reverse.h"
#include "src/Core/ArrayBase.h"
#include "src/Core/ArrayWrapper.h"
#ifdef EIGEN_USE_BLAS
#include "src/Core/products/GeneralMatrixMatrix_MKL.h"
#include "src/Core/products/GeneralMatrixVector_MKL.h"
#include "src/Core/products/GeneralMatrixMatrixTriangular_MKL.h"
#include "src/Core/products/SelfadjointMatrixMatrix_MKL.h"
#include "src/Core/products/SelfadjointMatrixVector_MKL.h"
#include "src/Core/products/TriangularMatrixMatrix_MKL.h"
#include "src/Core/products/TriangularMatrixVector_MKL.h"
#include "src/Core/products/TriangularSolverMatrix_MKL.h"
#endif // EIGEN_USE_BLAS
#ifdef EIGEN_USE_MKL_VML
#include "src/Core/Assign_MKL.h"
#endif
#include "src/Core/GlobalFunctions.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#ifdef EIGEN2_SUPPORT
#include "Eigen2Support"
#endif
#endif // EIGEN_CORE_H

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#include "Core"
#include "LU"
#include "Cholesky"
#include "QR"
#include "SVD"
#include "Geometry"
#include "Eigenvalues"

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#include "Dense"
//#include "Sparse"

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN2SUPPORT_H
#define EIGEN2SUPPORT_H
#if (!defined(EIGEN2_SUPPORT)) || (!defined(EIGEN_CORE_H))
#error Eigen2 support must be enabled by defining EIGEN2_SUPPORT before including any Eigen header
#endif
#include "src/Core/util/DisableStupidWarnings.h"
/** \ingroup Support_modules
* \defgroup Eigen2Support_Module Eigen2 support module
* This module provides a couple of deprecated functions improving the compatibility with Eigen2.
*
* To use it, define EIGEN2_SUPPORT before including any Eigen header
* \code
* #define EIGEN2_SUPPORT
* \endcode
*
*/
#include "src/Eigen2Support/Macros.h"
#include "src/Eigen2Support/Memory.h"
#include "src/Eigen2Support/Meta.h"
#include "src/Eigen2Support/Lazy.h"
#include "src/Eigen2Support/Cwise.h"
#include "src/Eigen2Support/CwiseOperators.h"
#include "src/Eigen2Support/TriangularSolver.h"
#include "src/Eigen2Support/Block.h"
#include "src/Eigen2Support/VectorBlock.h"
#include "src/Eigen2Support/Minor.h"
#include "src/Eigen2Support/MathFunctions.h"
#include "src/Core/util/ReenableStupidWarnings.h"
// Eigen2 used to include iostream
#include<iostream>
#define EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \
using Eigen::Matrix##SizeSuffix##TypeSuffix; \
using Eigen::Vector##SizeSuffix##TypeSuffix; \
using Eigen::RowVector##SizeSuffix##TypeSuffix;
#define EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(TypeSuffix) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 2) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 3) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 4) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X) \
#define EIGEN_USING_MATRIX_TYPEDEFS \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(i) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(f) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(d) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(cf) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(cd)
#define USING_PART_OF_NAMESPACE_EIGEN \
EIGEN_USING_MATRIX_TYPEDEFS \
using Eigen::Matrix; \
using Eigen::MatrixBase; \
using Eigen::ei_random; \
using Eigen::ei_real; \
using Eigen::ei_imag; \
using Eigen::ei_conj; \
using Eigen::ei_abs; \
using Eigen::ei_abs2; \
using Eigen::ei_sqrt; \
using Eigen::ei_exp; \
using Eigen::ei_log; \
using Eigen::ei_sin; \
using Eigen::ei_cos;
#endif // EIGEN2SUPPORT_H

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#ifndef EIGEN_EIGENVALUES_MODULE_H
#define EIGEN_EIGENVALUES_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
#include "Cholesky"
#include "Jacobi"
#include "Householder"
#include "LU"
#include "Geometry"
/** \defgroup Eigenvalues_Module Eigenvalues module
*
*
*
* This module mainly provides various eigenvalue solvers.
* This module also provides some MatrixBase methods, including:
* - MatrixBase::eigenvalues(),
* - MatrixBase::operatorNorm()
*
* \code
* #include <Eigen/Eigenvalues>
* \endcode
*/
#include "src/Eigenvalues/Tridiagonalization.h"
#include "src/Eigenvalues/RealSchur.h"
#include "src/Eigenvalues/EigenSolver.h"
#include "src/Eigenvalues/SelfAdjointEigenSolver.h"
#include "src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h"
#include "src/Eigenvalues/HessenbergDecomposition.h"
#include "src/Eigenvalues/ComplexSchur.h"
#include "src/Eigenvalues/ComplexEigenSolver.h"
#include "src/Eigenvalues/MatrixBaseEigenvalues.h"
#ifdef EIGEN_USE_LAPACKE
#include "src/Eigenvalues/RealSchur_MKL.h"
#include "src/Eigenvalues/ComplexSchur_MKL.h"
#include "src/Eigenvalues/SelfAdjointEigenSolver_MKL.h"
#endif
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_EIGENVALUES_MODULE_H
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

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#ifndef EIGEN_GEOMETRY_MODULE_H
#define EIGEN_GEOMETRY_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
#include "SVD"
#include "LU"
#include <limits>
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
/** \defgroup Geometry_Module Geometry module
*
*
*
* This module provides support for:
* - fixed-size homogeneous transformations
* - translation, scaling, 2D and 3D rotations
* - quaternions
* - \ref MatrixBase::cross() "cross product"
* - \ref MatrixBase::unitOrthogonal() "orthognal vector generation"
* - some linear components: parametrized-lines and hyperplanes
*
* \code
* #include <Eigen/Geometry>
* \endcode
*/
#include "src/Geometry/OrthoMethods.h"
#include "src/Geometry/EulerAngles.h"
#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
#include "src/Geometry/Homogeneous.h"
#include "src/Geometry/RotationBase.h"
#include "src/Geometry/Rotation2D.h"
#include "src/Geometry/Quaternion.h"
#include "src/Geometry/AngleAxis.h"
#include "src/Geometry/Transform.h"
#include "src/Geometry/Translation.h"
#include "src/Geometry/Scaling.h"
#include "src/Geometry/Hyperplane.h"
#include "src/Geometry/ParametrizedLine.h"
#include "src/Geometry/AlignedBox.h"
#include "src/Geometry/Umeyama.h"
#if defined EIGEN_VECTORIZE_SSE
#include "src/Geometry/arch/Geometry_SSE.h"
#endif
#endif
#ifdef EIGEN2_SUPPORT
#include "src/Eigen2Support/Geometry/All.h"
#endif
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_GEOMETRY_MODULE_H
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

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#ifndef EIGEN_HOUSEHOLDER_MODULE_H
#define EIGEN_HOUSEHOLDER_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Householder_Module Householder module
* This module provides Householder transformations.
*
* \code
* #include <Eigen/Householder>
* \endcode
*/
#include "src/Householder/Householder.h"
#include "src/Householder/HouseholderSequence.h"
#include "src/Householder/BlockHouseholder.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_HOUSEHOLDER_MODULE_H
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

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#ifndef EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
#define EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
#include "SparseCore"
#include "OrderingMethods"
#include "src/Core/util/DisableStupidWarnings.h"
/** \ingroup Sparse_modules
* \defgroup IterativeLinearSolvers_Module IterativeLinearSolvers module
*
* This module currently provides iterative methods to solve problems of the form \c A \c x = \c b, where \c A is a squared matrix, usually very large and sparse.
* Those solvers are accessible via the following classes:
* - ConjugateGradient for selfadjoint (hermitian) matrices,
* - BiCGSTAB for general square matrices.
*
* These iterative solvers are associated with some preconditioners:
* - IdentityPreconditioner - not really useful
* - DiagonalPreconditioner - also called JAcobi preconditioner, work very well on diagonal dominant matrices.
* - IncompleteILUT - incomplete LU factorization with dual thresholding
*
* Such problems can also be solved using the direct sparse decomposition modules: SparseCholesky, CholmodSupport, UmfPackSupport, SuperLUSupport.
*
* \code
* #include <Eigen/IterativeLinearSolvers>
* \endcode
*/
#include "src/misc/Solve.h"
#include "src/misc/SparseSolve.h"
#include "src/IterativeLinearSolvers/IterativeSolverBase.h"
#include "src/IterativeLinearSolvers/BasicPreconditioners.h"
#include "src/IterativeLinearSolvers/ConjugateGradient.h"
#include "src/IterativeLinearSolvers/BiCGSTAB.h"
#include "src/IterativeLinearSolvers/IncompleteLUT.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_ITERATIVELINEARSOLVERS_MODULE_H

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#ifndef EIGEN_JACOBI_MODULE_H
#define EIGEN_JACOBI_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Jacobi_Module Jacobi module
* This module provides Jacobi and Givens rotations.
*
* \code
* #include <Eigen/Jacobi>
* \endcode
*
* In addition to listed classes, it defines the two following MatrixBase methods to apply a Jacobi or Givens rotation:
* - MatrixBase::applyOnTheLeft()
* - MatrixBase::applyOnTheRight().
*/
#include "src/Jacobi/Jacobi.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_JACOBI_MODULE_H
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

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#ifndef EIGEN_LU_MODULE_H
#define EIGEN_LU_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup LU_Module LU module
* This module includes %LU decomposition and related notions such as matrix inversion and determinant.
* This module defines the following MatrixBase methods:
* - MatrixBase::inverse()
* - MatrixBase::determinant()
*
* \code
* #include <Eigen/LU>
* \endcode
*/
#include "src/misc/Solve.h"
#include "src/misc/Kernel.h"
#include "src/misc/Image.h"
#include "src/LU/FullPivLU.h"
#include "src/LU/PartialPivLU.h"
#ifdef EIGEN_USE_LAPACKE
#include "src/LU/PartialPivLU_MKL.h"
#endif
#include "src/LU/Determinant.h"
#include "src/LU/Inverse.h"
#if defined EIGEN_VECTORIZE_SSE
#include "src/LU/arch/Inverse_SSE.h"
#endif
#ifdef EIGEN2_SUPPORT
#include "src/Eigen2Support/LU.h"
#endif
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_LU_MODULE_H
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

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#ifndef EIGEN_REGRESSION_MODULE_H
#define EIGEN_REGRESSION_MODULE_H
#ifndef EIGEN2_SUPPORT
#error LeastSquares is only available in Eigen2 support mode (define EIGEN2_SUPPORT)
#endif
// exclude from normal eigen3-only documentation
#ifdef EIGEN2_SUPPORT
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
#include "Eigenvalues"
#include "Geometry"
/** \defgroup LeastSquares_Module LeastSquares module
* This module provides linear regression and related features.
*
* \code
* #include <Eigen/LeastSquares>
* \endcode
*/
#include "src/Eigen2Support/LeastSquares.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN2_SUPPORT
#endif // EIGEN_REGRESSION_MODULE_H

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#ifndef EIGEN_ORDERINGMETHODS_MODULE_H
#define EIGEN_ORDERINGMETHODS_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
/** \ingroup Sparse_modules
* \defgroup OrderingMethods_Module OrderingMethods module
*
* This module is currently for internal use only.
*
*
* \code
* #include <Eigen/OrderingMethods>
* \endcode
*/
#include "src/OrderingMethods/Amd.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_ORDERINGMETHODS_MODULE_H

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#ifndef EIGEN_PASTIXSUPPORT_MODULE_H
#define EIGEN_PASTIXSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
#include <complex.h>
extern "C" {
#include <pastix_nompi.h>
#include <pastix.h>
}
#ifdef complex
#undef complex
#endif
/** \ingroup Support_modules
* \defgroup PaStiXSupport_Module PaStiXSupport module
*
* This module provides an interface to the <a href="http://pastix.gforge.inria.fr/">PaSTiX</a> library.
* PaSTiX is a general \b supernodal, \b parallel and \b opensource sparse solver.
* It provides the two following main factorization classes:
* - class PastixLLT : a supernodal, parallel LLt Cholesky factorization.
* - class PastixLDLT: a supernodal, parallel LDLt Cholesky factorization.
* - class PastixLU : a supernodal, parallel LU factorization (optimized for a symmetric pattern).
*
* \code
* #include <Eigen/PaStiXSupport>
* \endcode
*
* In order to use this module, the PaSTiX headers must be accessible from the include paths, and your binary must be linked to the PaSTiX library and its dependencies.
* The dependencies depend on how PaSTiX has been compiled.
* For a cmake based project, you can use our FindPaSTiX.cmake module to help you in this task.
*
*/
#include "src/misc/Solve.h"
#include "src/misc/SparseSolve.h"
#include "src/PaStiXSupport/PaStiXSupport.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_PASTIXSUPPORT_MODULE_H

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#ifndef EIGEN_PARDISOSUPPORT_MODULE_H
#define EIGEN_PARDISOSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
#include <mkl_pardiso.h>
#include <unsupported/Eigen/SparseExtra>
/** \ingroup Support_modules
* \defgroup PardisoSupport_Module PardisoSupport module
*
* This module brings support for the Intel(R) MKL PARDISO direct sparse solvers.
*
* \code
* #include <Eigen/PardisoSupport>
* \endcode
*
* In order to use this module, the MKL headers must be accessible from the include paths, and your binary must be linked to the MKL library and its dependencies.
* See this \ref TopicUsingIntelMKL "page" for more information on MKL-Eigen integration.
*
*/
#include "src/PardisoSupport/PardisoSupport.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_PARDISOSUPPORT_MODULE_H

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#ifndef EIGEN_QR_MODULE_H
#define EIGEN_QR_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
#include "Cholesky"
#include "Jacobi"
#include "Householder"
/** \defgroup QR_Module QR module
*
*
*
* This module provides various QR decompositions
* This module also provides some MatrixBase methods, including:
* - MatrixBase::qr(),
*
* \code
* #include <Eigen/QR>
* \endcode
*/
#include "src/misc/Solve.h"
#include "src/QR/HouseholderQR.h"
#include "src/QR/FullPivHouseholderQR.h"
#include "src/QR/ColPivHouseholderQR.h"
#ifdef EIGEN_USE_LAPACKE
#include "src/QR/HouseholderQR_MKL.h"
#include "src/QR/ColPivHouseholderQR_MKL.h"
#endif
#ifdef EIGEN2_SUPPORT
#include "src/Eigen2Support/QR.h"
#endif
#include "src/Core/util/ReenableStupidWarnings.h"
#ifdef EIGEN2_SUPPORT
#include "Eigenvalues"
#endif
#endif // EIGEN_QR_MODULE_H
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

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#ifndef EIGEN_QTMALLOC_MODULE_H
#define EIGEN_QTMALLOC_MODULE_H
#include "Core"
#if (!EIGEN_MALLOC_ALREADY_ALIGNED)
#include "src/Core/util/DisableStupidWarnings.h"
void *qMalloc(size_t size)
{
return Eigen::internal::aligned_malloc(size);
}
void qFree(void *ptr)
{
Eigen::internal::aligned_free(ptr);
}
void *qRealloc(void *ptr, size_t size)
{
void* newPtr = Eigen::internal::aligned_malloc(size);
memcpy(newPtr, ptr, size);
Eigen::internal::aligned_free(ptr);
return newPtr;
}
#include "src/Core/util/ReenableStupidWarnings.h"
#endif
#endif // EIGEN_QTMALLOC_MODULE_H
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

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#ifndef EIGEN_SVD_MODULE_H
#define EIGEN_SVD_MODULE_H
#include "QR"
#include "Householder"
#include "Jacobi"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup SVD_Module SVD module
*
*
*
* This module provides SVD decomposition for matrices (both real and complex).
* This decomposition is accessible via the following MatrixBase method:
* - MatrixBase::jacobiSvd()
*
* \code
* #include <Eigen/SVD>
* \endcode
*/
#include "src/misc/Solve.h"
#include "src/SVD/JacobiSVD.h"
#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)
#include "src/SVD/JacobiSVD_MKL.h"
#endif
#include "src/SVD/UpperBidiagonalization.h"
#ifdef EIGEN2_SUPPORT
#include "src/Eigen2Support/SVD.h"
#endif
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SVD_MODULE_H
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

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#ifndef EIGEN_SPARSE_MODULE_H
#define EIGEN_SPARSE_MODULE_H
/** \defgroup Sparse_modules Sparse modules
*
* Meta-module including all related modules:
* - SparseCore
* - OrderingMethods
* - SparseCholesky
* - IterativeLinearSolvers
*
* \code
* #include <Eigen/Sparse>
* \endcode
*/
#include "SparseCore"
#include "OrderingMethods"
#include "SparseCholesky"
#include "IterativeLinearSolvers"
#endif // EIGEN_SPARSE_MODULE_H

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#ifndef EIGEN_SPARSECHOLESKY_MODULE_H
#define EIGEN_SPARSECHOLESKY_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
/** \ingroup Sparse_modules
* \defgroup SparseCholesky_Module SparseCholesky module
*
* This module currently provides two variants of the direct sparse Cholesky decomposition for selfadjoint (hermitian) matrices.
* Those decompositions are accessible via the following classes:
* - SimplicialLLt,
* - SimplicialLDLt
*
* Such problems can also be solved using the ConjugateGradient solver from the IterativeLinearSolvers module.
*
* \code
* #include <Eigen/SparseCholesky>
* \endcode
*/
#include "src/misc/Solve.h"
#include "src/misc/SparseSolve.h"
#include "src/SparseCholesky/SimplicialCholesky.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SPARSECHOLESKY_MODULE_H

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#ifndef EIGEN_SPARSECORE_MODULE_H
#define EIGEN_SPARSECORE_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
#include <vector>
#include <map>
#include <cstdlib>
#include <cstring>
#include <algorithm>
/** \ingroup Sparse_modules
* \defgroup SparseCore_Module SparseCore module
*
* This module provides a sparse matrix representation, and basic associatd matrix manipulations
* and operations.
*
* See the \ref TutorialSparse "Sparse tutorial"
*
* \code
* #include <Eigen/SparseCore>
* \endcode
*
* This module depends on: Core.
*/
namespace Eigen {
/** The type used to identify a general sparse storage. */
struct Sparse {};
}
#include "src/SparseCore/SparseUtil.h"
#include "src/SparseCore/SparseMatrixBase.h"
#include "src/SparseCore/CompressedStorage.h"
#include "src/SparseCore/AmbiVector.h"
#include "src/SparseCore/SparseMatrix.h"
#include "src/SparseCore/MappedSparseMatrix.h"
#include "src/SparseCore/SparseVector.h"
#include "src/SparseCore/CoreIterators.h"
#include "src/SparseCore/SparseBlock.h"
#include "src/SparseCore/SparseTranspose.h"
#include "src/SparseCore/SparseCwiseUnaryOp.h"
#include "src/SparseCore/SparseCwiseBinaryOp.h"
#include "src/SparseCore/SparseDot.h"
#include "src/SparseCore/SparsePermutation.h"
#include "src/SparseCore/SparseAssign.h"
#include "src/SparseCore/SparseRedux.h"
#include "src/SparseCore/SparseFuzzy.h"
#include "src/SparseCore/ConservativeSparseSparseProduct.h"
#include "src/SparseCore/SparseSparseProductWithPruning.h"
#include "src/SparseCore/SparseProduct.h"
#include "src/SparseCore/SparseDenseProduct.h"
#include "src/SparseCore/SparseDiagonalProduct.h"
#include "src/SparseCore/SparseTriangularView.h"
#include "src/SparseCore/SparseSelfAdjointView.h"
#include "src/SparseCore/TriangularSolver.h"
#include "src/SparseCore/SparseView.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SPARSECORE_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_STDDEQUE_MODULE_H
#define EIGEN_STDDEQUE_MODULE_H
#include "Core"
#include <deque>
#if (defined(_MSC_VER) && defined(_WIN64)) /* MSVC auto aligns in 64 bit builds */
#define EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(...)
#else
#include "src/StlSupport/StdDeque.h"
#endif
#endif // EIGEN_STDDEQUE_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_STDLIST_MODULE_H
#define EIGEN_STDLIST_MODULE_H
#include "Core"
#include <list>
#if (defined(_MSC_VER) && defined(_WIN64)) /* MSVC auto aligns in 64 bit builds */
#define EIGEN_DEFINE_STL_LIST_SPECIALIZATION(...)
#else
#include "src/StlSupport/StdList.h"
#endif
#endif // EIGEN_STDLIST_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_STDVECTOR_MODULE_H
#define EIGEN_STDVECTOR_MODULE_H
#include "Core"
#include <vector>
#if (defined(_MSC_VER) && defined(_WIN64)) /* MSVC auto aligns in 64 bit builds */
#define EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(...)
#else
#include "src/StlSupport/StdVector.h"
#endif
#endif // EIGEN_STDVECTOR_MODULE_H

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#ifndef EIGEN_SUPERLUSUPPORT_MODULE_H
#define EIGEN_SUPERLUSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
#ifdef EMPTY
#define EIGEN_EMPTY_WAS_ALREADY_DEFINED
#endif
typedef int int_t;
#include <slu_Cnames.h>
#include <supermatrix.h>
#include <slu_util.h>
// slu_util.h defines a preprocessor token named EMPTY which is really polluting,
// so we remove it in favor of a SUPERLU_EMPTY token.
// If EMPTY was already defined then we don't undef it.
#if defined(EIGEN_EMPTY_WAS_ALREADY_DEFINED)
# undef EIGEN_EMPTY_WAS_ALREADY_DEFINED
#elif defined(EMPTY)
# undef EMPTY
#endif
#define SUPERLU_EMPTY (-1)
namespace Eigen { struct SluMatrix; }
/** \ingroup Support_modules
* \defgroup SuperLUSupport_Module SuperLUSupport module
*
* This module provides an interface to the <a href="http://crd-legacy.lbl.gov/~xiaoye/SuperLU/">SuperLU</a> library.
* It provides the following factorization class:
* - class SuperLU: a supernodal sequential LU factorization.
* - class SuperILU: a supernodal sequential incomplete LU factorization (to be used as a preconditioner for iterative methods).
*
* \warning When including this module, you have to use SUPERLU_EMPTY instead of EMPTY which is no longer defined because it is too polluting.
*
* \code
* #include <Eigen/SuperLUSupport>
* \endcode
*
* In order to use this module, the superlu headers must be accessible from the include paths, and your binary must be linked to the superlu library and its dependencies.
* The dependencies depend on how superlu has been compiled.
* For a cmake based project, you can use our FindSuperLU.cmake module to help you in this task.
*
*/
#include "src/misc/Solve.h"
#include "src/misc/SparseSolve.h"
#include "src/SuperLUSupport/SuperLUSupport.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SUPERLUSUPPORT_MODULE_H

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#ifndef EIGEN_UMFPACKSUPPORT_MODULE_H
#define EIGEN_UMFPACKSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
extern "C" {
#include <umfpack.h>
}
/** \ingroup Support_modules
* \defgroup UmfPackSupport_Module UmfPackSupport module
*
* This module provides an interface to the UmfPack library which is part of the <a href="http://www.cise.ufl.edu/research/sparse/SuiteSparse/">suitesparse</a> package.
* It provides the following factorization class:
* - class UmfPackLU: a multifrontal sequential LU factorization.
*
* \code
* #include <Eigen/UmfPackSupport>
* \endcode
*
* In order to use this module, the umfpack headers must be accessible from the include paths, and your binary must be linked to the umfpack library and its dependencies.
* The dependencies depend on how umfpack has been compiled.
* For a cmake based project, you can use our FindUmfPack.cmake module to help you in this task.
*
*/
#include "src/misc/Solve.h"
#include "src/misc/SparseSolve.h"
#include "src/UmfPackSupport/UmfPackSupport.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_UMFPACKSUPPORT_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Keir Mierle <mierle@gmail.com>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2011 Timothy E. Holy <tim.holy@gmail.com >
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_LDLT_H
#define EIGEN_LDLT_H
namespace Eigen {
namespace internal {
template<typename MatrixType, int UpLo> struct LDLT_Traits;
}
/** \ingroup Cholesky_Module
*
* \class LDLT
*
* \brief Robust Cholesky decomposition of a matrix with pivoting
*
* \param MatrixType the type of the matrix of which to compute the LDL^T Cholesky decomposition
* \param UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
* The other triangular part won't be read.
*
* Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite
* matrix \f$ A \f$ such that \f$ A = P^TLDL^*P \f$, where P is a permutation matrix, L
* is lower triangular with a unit diagonal and D is a diagonal matrix.
*
* The decomposition uses pivoting to ensure stability, so that L will have
* zeros in the bottom right rank(A) - n submatrix. Avoiding the square root
* on D also stabilizes the computation.
*
* Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky
* decomposition to determine whether a system of equations has a solution.
*
* \sa MatrixBase::ldlt(), class LLT
*/
template<typename _MatrixType, int _UpLo> class LDLT
{
public:
typedef _MatrixType MatrixType;
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
Options = MatrixType::Options & ~RowMajorBit, // these are the options for the TmpMatrixType, we need a ColMajor matrix here!
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
UpLo = _UpLo
};
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef typename MatrixType::Index Index;
typedef Matrix<Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1> TmpMatrixType;
typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
typedef internal::LDLT_Traits<MatrixType,UpLo> Traits;
/** \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via LDLT::compute(const MatrixType&).
*/
LDLT() : m_matrix(), m_transpositions(), m_isInitialized(false) {}
/** \brief Default Constructor with memory preallocation
*
* Like the default constructor but with preallocation of the internal data
* according to the specified problem \a size.
* \sa LDLT()
*/
LDLT(Index size)
: m_matrix(size, size),
m_transpositions(size),
m_temporary(size),
m_isInitialized(false)
{}
/** \brief Constructor with decomposition
*
* This calculates the decomposition for the input \a matrix.
* \sa LDLT(Index size)
*/
LDLT(const MatrixType& matrix)
: m_matrix(matrix.rows(), matrix.cols()),
m_transpositions(matrix.rows()),
m_temporary(matrix.rows()),
m_isInitialized(false)
{
compute(matrix);
}
/** Clear any existing decomposition
* \sa rankUpdate(w,sigma)
*/
void setZero()
{
m_isInitialized = false;
}
/** \returns a view of the upper triangular matrix U */
inline typename Traits::MatrixU matrixU() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return Traits::getU(m_matrix);
}
/** \returns a view of the lower triangular matrix L */
inline typename Traits::MatrixL matrixL() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return Traits::getL(m_matrix);
}
/** \returns the permutation matrix P as a transposition sequence.
*/
inline const TranspositionType& transpositionsP() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_transpositions;
}
/** \returns the coefficients of the diagonal matrix D */
inline Diagonal<const MatrixType> vectorD() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_matrix.diagonal();
}
/** \returns true if the matrix is positive (semidefinite) */
inline bool isPositive() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_sign == 1;
}
#ifdef EIGEN2_SUPPORT
inline bool isPositiveDefinite() const
{
return isPositive();
}
#endif
/** \returns true if the matrix is negative (semidefinite) */
inline bool isNegative(void) const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_sign == -1;
}
/** \returns a solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* This function also supports in-place solves using the syntax <tt>x = decompositionObject.solve(x)</tt> .
*
* \note_about_checking_solutions
*
* More precisely, this method solves \f$ A x = b \f$ using the decomposition \f$ A = P^T L D L^* P \f$
* by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$,
* \f$ L^* y_4 = y_3 \f$ and \f$ P x = y_4 \f$ in succession. If the matrix \f$ A \f$ is singular, then
* \f$ D \f$ will also be singular (all the other matrices are invertible). In that case, the
* least-square solution of \f$ D y_3 = y_2 \f$ is computed. This does not mean that this function
* computes the least-square solution of \f$ A x = b \f$ is \f$ A \f$ is singular.
*
* \sa MatrixBase::ldlt()
*/
template<typename Rhs>
inline const internal::solve_retval<LDLT, Rhs>
solve(const MatrixBase<Rhs>& b) const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
eigen_assert(m_matrix.rows()==b.rows()
&& "LDLT::solve(): invalid number of rows of the right hand side matrix b");
return internal::solve_retval<LDLT, Rhs>(*this, b.derived());
}
#ifdef EIGEN2_SUPPORT
template<typename OtherDerived, typename ResultType>
bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const
{
*result = this->solve(b);
return true;
}
#endif
template<typename Derived>
bool solveInPlace(MatrixBase<Derived> &bAndX) const;
LDLT& compute(const MatrixType& matrix);
template <typename Derived>
LDLT& rankUpdate(const MatrixBase<Derived>& w,RealScalar alpha=1);
/** \returns the internal LDLT decomposition matrix
*
* TODO: document the storage layout
*/
inline const MatrixType& matrixLDLT() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_matrix;
}
MatrixType reconstructedMatrix() const;
inline Index rows() const { return m_matrix.rows(); }
inline Index cols() const { return m_matrix.cols(); }
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was succesful,
* \c NumericalIssue if the matrix.appears to be negative.
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return Success;
}
protected:
/** \internal
* Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
* The strict upper part is used during the decomposition, the strict lower
* part correspond to the coefficients of L (its diagonal is equal to 1 and
* is not stored), and the diagonal entries correspond to D.
*/
MatrixType m_matrix;
TranspositionType m_transpositions;
TmpMatrixType m_temporary;
int m_sign;
bool m_isInitialized;
};
namespace internal {
template<int UpLo> struct ldlt_inplace;
template<> struct ldlt_inplace<Lower>
{
template<typename MatrixType, typename TranspositionType, typename Workspace>
static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, int* sign=0)
{
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::Index Index;
eigen_assert(mat.rows()==mat.cols());
const Index size = mat.rows();
if (size <= 1)
{
transpositions.setIdentity();
if(sign)
*sign = real(mat.coeff(0,0))>0 ? 1:-1;
return true;
}
RealScalar cutoff(0), biggest_in_corner;
for (Index k = 0; k < size; ++k)
{
// Find largest diagonal element
Index index_of_biggest_in_corner;
biggest_in_corner = mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
index_of_biggest_in_corner += k;
if(k == 0)
{
// The biggest overall is the point of reference to which further diagonals
// are compared; if any diagonal is negligible compared
// to the largest overall, the algorithm bails.
cutoff = abs(NumTraits<Scalar>::epsilon() * biggest_in_corner);
if(sign)
*sign = real(mat.diagonal().coeff(index_of_biggest_in_corner)) > 0 ? 1 : -1;
}
// Finish early if the matrix is not full rank.
if(biggest_in_corner < cutoff)
{
for(Index i = k; i < size; i++) transpositions.coeffRef(i) = i;
break;
}
transpositions.coeffRef(k) = index_of_biggest_in_corner;
if(k != index_of_biggest_in_corner)
{
// apply the transposition while taking care to consider only
// the lower triangular part
Index s = size-index_of_biggest_in_corner-1; // trailing size after the biggest element
mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));
mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));
std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner));
for(int i=k+1;i<index_of_biggest_in_corner;++i)
{
Scalar tmp = mat.coeffRef(i,k);
mat.coeffRef(i,k) = conj(mat.coeffRef(index_of_biggest_in_corner,i));
mat.coeffRef(index_of_biggest_in_corner,i) = conj(tmp);
}
if(NumTraits<Scalar>::IsComplex)
mat.coeffRef(index_of_biggest_in_corner,k) = conj(mat.coeff(index_of_biggest_in_corner,k));
}
// partition the matrix:
// A00 | - | -
// lu = A10 | A11 | -
// A20 | A21 | A22
Index rs = size - k - 1;
Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
if(k>0)
{
temp.head(k) = mat.diagonal().head(k).asDiagonal() * A10.adjoint();
mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();
if(rs>0)
A21.noalias() -= A20 * temp.head(k);
}
if((rs>0) && (abs(mat.coeffRef(k,k)) > cutoff))
A21 /= mat.coeffRef(k,k);
}
return true;
}
// Reference for the algorithm: Davis and Hager, "Multiple Rank
// Modifications of a Sparse Cholesky Factorization" (Algorithm 1)
// Trivial rearrangements of their computations (Timothy E. Holy)
// allow their algorithm to work for rank-1 updates even if the
// original matrix is not of full rank.
// Here only rank-1 updates are implemented, to reduce the
// requirement for intermediate storage and improve accuracy
template<typename MatrixType, typename WDerived>
static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w, typename MatrixType::RealScalar sigma=1)
{
using internal::isfinite;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::Index Index;
const Index size = mat.rows();
eigen_assert(mat.cols() == size && w.size()==size);
RealScalar alpha = 1;
// Apply the update
for (Index j = 0; j < size; j++)
{
// Check for termination due to an original decomposition of low-rank
if (!(isfinite)(alpha))
break;
// Update the diagonal terms
RealScalar dj = real(mat.coeff(j,j));
Scalar wj = w.coeff(j);
RealScalar swj2 = sigma*abs2(wj);
RealScalar gamma = dj*alpha + swj2;
mat.coeffRef(j,j) += swj2/alpha;
alpha += swj2/dj;
// Update the terms of L
Index rs = size-j-1;
w.tail(rs) -= wj * mat.col(j).tail(rs);
if(gamma != 0)
mat.col(j).tail(rs) += (sigma*conj(wj)/gamma)*w.tail(rs);
}
return true;
}
template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
static bool update(MatrixType& mat, const TranspositionType& transpositions, Workspace& tmp, const WType& w, typename MatrixType::RealScalar sigma=1)
{
// Apply the permutation to the input w
tmp = transpositions * w;
return ldlt_inplace<Lower>::updateInPlace(mat,tmp,sigma);
}
};
template<> struct ldlt_inplace<Upper>
{
template<typename MatrixType, typename TranspositionType, typename Workspace>
static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, int* sign=0)
{
Transpose<MatrixType> matt(mat);
return ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);
}
template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w, typename MatrixType::RealScalar sigma=1)
{
Transpose<MatrixType> matt(mat);
return ldlt_inplace<Lower>::update(matt, transpositions, tmp, w.conjugate(), sigma);
}
};
template<typename MatrixType> struct LDLT_Traits<MatrixType,Lower>
{
typedef const TriangularView<const MatrixType, UnitLower> MatrixL;
typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitUpper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return m; }
static inline MatrixU getU(const MatrixType& m) { return m.adjoint(); }
};
template<typename MatrixType> struct LDLT_Traits<MatrixType,Upper>
{
typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitLower> MatrixL;
typedef const TriangularView<const MatrixType, UnitUpper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return m.adjoint(); }
static inline MatrixU getU(const MatrixType& m) { return m; }
};
} // end namespace internal
/** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \a matrix
*/
template<typename MatrixType, int _UpLo>
LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const MatrixType& a)
{
eigen_assert(a.rows()==a.cols());
const Index size = a.rows();
m_matrix = a;
m_transpositions.resize(size);
m_isInitialized = false;
m_temporary.resize(size);
internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, &m_sign);
m_isInitialized = true;
return *this;
}
/** Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.
* \param w a vector to be incorporated into the decomposition.
* \param sigma a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column vectors. Optional; default value is +1.
* \sa setZero()
*/
template<typename MatrixType, int _UpLo>
template<typename Derived>
LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Derived>& w,typename NumTraits<typename MatrixType::Scalar>::Real sigma)
{
const Index size = w.rows();
if (m_isInitialized)
{
eigen_assert(m_matrix.rows()==size);
}
else
{
m_matrix.resize(size,size);
m_matrix.setZero();
m_transpositions.resize(size);
for (Index i = 0; i < size; i++)
m_transpositions.coeffRef(i) = i;
m_temporary.resize(size);
m_sign = sigma>=0 ? 1 : -1;
m_isInitialized = true;
}
internal::ldlt_inplace<UpLo>::update(m_matrix, m_transpositions, m_temporary, w, sigma);
return *this;
}
namespace internal {
template<typename _MatrixType, int _UpLo, typename Rhs>
struct solve_retval<LDLT<_MatrixType,_UpLo>, Rhs>
: solve_retval_base<LDLT<_MatrixType,_UpLo>, Rhs>
{
typedef LDLT<_MatrixType,_UpLo> LDLTType;
EIGEN_MAKE_SOLVE_HELPERS(LDLTType,Rhs)
template<typename Dest> void evalTo(Dest& dst) const
{
eigen_assert(rhs().rows() == dec().matrixLDLT().rows());
// dst = P b
dst = dec().transpositionsP() * rhs();
// dst = L^-1 (P b)
dec().matrixL().solveInPlace(dst);
// dst = D^-1 (L^-1 P b)
// more precisely, use pseudo-inverse of D (see bug 241)
using std::abs;
using std::max;
typedef typename LDLTType::MatrixType MatrixType;
typedef typename LDLTType::Scalar Scalar;
typedef typename LDLTType::RealScalar RealScalar;
const Diagonal<const MatrixType> vectorD = dec().vectorD();
RealScalar tolerance = (max)(vectorD.array().abs().maxCoeff() * NumTraits<Scalar>::epsilon(),
RealScalar(1) / NumTraits<RealScalar>::highest()); // motivated by LAPACK's xGELSS
for (Index i = 0; i < vectorD.size(); ++i) {
if(abs(vectorD(i)) > tolerance)
dst.row(i) /= vectorD(i);
else
dst.row(i).setZero();
}
// dst = L^-T (D^-1 L^-1 P b)
dec().matrixU().solveInPlace(dst);
// dst = P^-1 (L^-T D^-1 L^-1 P b) = A^-1 b
dst = dec().transpositionsP().transpose() * dst;
}
};
}
/** \internal use x = ldlt_object.solve(x);
*
* This is the \em in-place version of solve().
*
* \param bAndX represents both the right-hand side matrix b and result x.
*
* \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
*
* This version avoids a copy when the right hand side matrix b is not
* needed anymore.
*
* \sa LDLT::solve(), MatrixBase::ldlt()
*/
template<typename MatrixType,int _UpLo>
template<typename Derived>
bool LDLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
eigen_assert(m_matrix.rows() == bAndX.rows());
bAndX = this->solve(bAndX);
return true;
}
/** \returns the matrix represented by the decomposition,
* i.e., it returns the product: P^T L D L^* P.
* This function is provided for debug purpose. */
template<typename MatrixType, int _UpLo>
MatrixType LDLT<MatrixType,_UpLo>::reconstructedMatrix() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
const Index size = m_matrix.rows();
MatrixType res(size,size);
// P
res.setIdentity();
res = transpositionsP() * res;
// L^* P
res = matrixU() * res;
// D(L^*P)
res = vectorD().asDiagonal() * res;
// L(DL^*P)
res = matrixL() * res;
// P^T (LDL^*P)
res = transpositionsP().transpose() * res;
return res;
}
/** \cholesky_module
* \returns the Cholesky decomposition with full pivoting without square root of \c *this
*/
template<typename MatrixType, unsigned int UpLo>
inline const LDLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
SelfAdjointView<MatrixType, UpLo>::ldlt() const
{
return LDLT<PlainObject,UpLo>(m_matrix);
}
/** \cholesky_module
* \returns the Cholesky decomposition with full pivoting without square root of \c *this
*/
template<typename Derived>
inline const LDLT<typename MatrixBase<Derived>::PlainObject>
MatrixBase<Derived>::ldlt() const
{
return LDLT<PlainObject>(derived());
}
} // end namespace Eigen
#endif // EIGEN_LDLT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_LLT_H
#define EIGEN_LLT_H
namespace Eigen {
namespace internal{
template<typename MatrixType, int UpLo> struct LLT_Traits;
}
/** \ingroup Cholesky_Module
*
* \class LLT
*
* \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features
*
* \param MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition
* \param UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
* The other triangular part won't be read.
*
* This class performs a LL^T Cholesky decomposition of a symmetric, positive definite
* matrix A such that A = LL^* = U^*U, where L is lower triangular.
*
* While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b,
* for that purpose, we recommend the Cholesky decomposition without square root which is more stable
* and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other
* situations like generalised eigen problems with hermitian matrices.
*
* Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices,
* use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations
* has a solution.
*
* Example: \include LLT_example.cpp
* Output: \verbinclude LLT_example.out
*
* \sa MatrixBase::llt(), class LDLT
*/
/* HEY THIS DOX IS DISABLED BECAUSE THERE's A BUG EITHER HERE OR IN LDLT ABOUT THAT (OR BOTH)
* Note that during the decomposition, only the upper triangular part of A is considered. Therefore,
* the strict lower part does not have to store correct values.
*/
template<typename _MatrixType, int _UpLo> class LLT
{
public:
typedef _MatrixType MatrixType;
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
Options = MatrixType::Options,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
};
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef typename MatrixType::Index Index;
enum {
PacketSize = internal::packet_traits<Scalar>::size,
AlignmentMask = int(PacketSize)-1,
UpLo = _UpLo
};
typedef internal::LLT_Traits<MatrixType,UpLo> Traits;
/**
* \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via LLT::compute(const MatrixType&).
*/
LLT() : m_matrix(), m_isInitialized(false) {}
/** \brief Default Constructor with memory preallocation
*
* Like the default constructor but with preallocation of the internal data
* according to the specified problem \a size.
* \sa LLT()
*/
LLT(Index size) : m_matrix(size, size),
m_isInitialized(false) {}
LLT(const MatrixType& matrix)
: m_matrix(matrix.rows(), matrix.cols()),
m_isInitialized(false)
{
compute(matrix);
}
/** \returns a view of the upper triangular matrix U */
inline typename Traits::MatrixU matrixU() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return Traits::getU(m_matrix);
}
/** \returns a view of the lower triangular matrix L */
inline typename Traits::MatrixL matrixL() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return Traits::getL(m_matrix);
}
/** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* Since this LLT class assumes anyway that the matrix A is invertible, the solution
* theoretically exists and is unique regardless of b.
*
* Example: \include LLT_solve.cpp
* Output: \verbinclude LLT_solve.out
*
* \sa solveInPlace(), MatrixBase::llt()
*/
template<typename Rhs>
inline const internal::solve_retval<LLT, Rhs>
solve(const MatrixBase<Rhs>& b) const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(m_matrix.rows()==b.rows()
&& "LLT::solve(): invalid number of rows of the right hand side matrix b");
return internal::solve_retval<LLT, Rhs>(*this, b.derived());
}
#ifdef EIGEN2_SUPPORT
template<typename OtherDerived, typename ResultType>
bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const
{
*result = this->solve(b);
return true;
}
bool isPositiveDefinite() const { return true; }
#endif
template<typename Derived>
void solveInPlace(MatrixBase<Derived> &bAndX) const;
LLT& compute(const MatrixType& matrix);
/** \returns the LLT decomposition matrix
*
* TODO: document the storage layout
*/
inline const MatrixType& matrixLLT() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return m_matrix;
}
MatrixType reconstructedMatrix() const;
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was succesful,
* \c NumericalIssue if the matrix.appears to be negative.
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return m_info;
}
inline Index rows() const { return m_matrix.rows(); }
inline Index cols() const { return m_matrix.cols(); }
template<typename VectorType>
LLT rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);
protected:
/** \internal
* Used to compute and store L
* The strict upper part is not used and even not initialized.
*/
MatrixType m_matrix;
bool m_isInitialized;
ComputationInfo m_info;
};
namespace internal {
template<typename Scalar, int UpLo> struct llt_inplace;
template<typename MatrixType, typename VectorType>
static typename MatrixType::Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma)
{
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::Index Index;
typedef typename MatrixType::ColXpr ColXpr;
typedef typename internal::remove_all<ColXpr>::type ColXprCleaned;
typedef typename ColXprCleaned::SegmentReturnType ColXprSegment;
typedef Matrix<Scalar,Dynamic,1> TempVectorType;
typedef typename TempVectorType::SegmentReturnType TempVecSegment;
int n = mat.cols();
eigen_assert(mat.rows()==n && vec.size()==n);
TempVectorType temp;
if(sigma>0)
{
// This version is based on Givens rotations.
// It is faster than the other one below, but only works for updates,
// i.e., for sigma > 0
temp = sqrt(sigma) * vec;
for(int i=0; i<n; ++i)
{
JacobiRotation<Scalar> g;
g.makeGivens(mat(i,i), -temp(i), &mat(i,i));
int rs = n-i-1;
if(rs>0)
{
ColXprSegment x(mat.col(i).tail(rs));
TempVecSegment y(temp.tail(rs));
apply_rotation_in_the_plane(x, y, g);
}
}
}
else
{
temp = vec;
RealScalar beta = 1;
for(int j=0; j<n; ++j)
{
RealScalar Ljj = real(mat.coeff(j,j));
RealScalar dj = abs2(Ljj);
Scalar wj = temp.coeff(j);
RealScalar swj2 = sigma*abs2(wj);
RealScalar gamma = dj*beta + swj2;
RealScalar x = dj + swj2/beta;
if (x<=RealScalar(0))
return j;
RealScalar nLjj = sqrt(x);
mat.coeffRef(j,j) = nLjj;
beta += swj2/dj;
// Update the terms of L
Index rs = n-j-1;
if(rs)
{
temp.tail(rs) -= (wj/Ljj) * mat.col(j).tail(rs);
if(gamma != 0)
mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*conj(wj)/gamma)*temp.tail(rs);
}
}
}
return -1;
}
template<typename Scalar> struct llt_inplace<Scalar, Lower>
{
typedef typename NumTraits<Scalar>::Real RealScalar;
template<typename MatrixType>
static typename MatrixType::Index unblocked(MatrixType& mat)
{
typedef typename MatrixType::Index Index;
eigen_assert(mat.rows()==mat.cols());
const Index size = mat.rows();
for(Index k = 0; k < size; ++k)
{
Index rs = size-k-1; // remaining size
Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
RealScalar x = real(mat.coeff(k,k));
if (k>0) x -= A10.squaredNorm();
if (x<=RealScalar(0))
return k;
mat.coeffRef(k,k) = x = sqrt(x);
if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint();
if (rs>0) A21 *= RealScalar(1)/x;
}
return -1;
}
template<typename MatrixType>
static typename MatrixType::Index blocked(MatrixType& m)
{
typedef typename MatrixType::Index Index;
eigen_assert(m.rows()==m.cols());
Index size = m.rows();
if(size<32)
return unblocked(m);
Index blockSize = size/8;
blockSize = (blockSize/16)*16;
blockSize = (std::min)((std::max)(blockSize,Index(8)), Index(128));
for (Index k=0; k<size; k+=blockSize)
{
// partition the matrix:
// A00 | - | -
// lu = A10 | A11 | -
// A20 | A21 | A22
Index bs = (std::min)(blockSize, size-k);
Index rs = size - k - bs;
Block<MatrixType,Dynamic,Dynamic> A11(m,k, k, bs,bs);
Block<MatrixType,Dynamic,Dynamic> A21(m,k+bs,k, rs,bs);
Block<MatrixType,Dynamic,Dynamic> A22(m,k+bs,k+bs,rs,rs);
Index ret;
if((ret=unblocked(A11))>=0) return k+ret;
if(rs>0) A11.adjoint().template triangularView<Upper>().template solveInPlace<OnTheRight>(A21);
if(rs>0) A22.template selfadjointView<Lower>().rankUpdate(A21,-1); // bottleneck
}
return -1;
}
template<typename MatrixType, typename VectorType>
static typename MatrixType::Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
{
return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
}
};
template<typename Scalar> struct llt_inplace<Scalar, Upper>
{
typedef typename NumTraits<Scalar>::Real RealScalar;
template<typename MatrixType>
static EIGEN_STRONG_INLINE typename MatrixType::Index unblocked(MatrixType& mat)
{
Transpose<MatrixType> matt(mat);
return llt_inplace<Scalar, Lower>::unblocked(matt);
}
template<typename MatrixType>
static EIGEN_STRONG_INLINE typename MatrixType::Index blocked(MatrixType& mat)
{
Transpose<MatrixType> matt(mat);
return llt_inplace<Scalar, Lower>::blocked(matt);
}
template<typename MatrixType, typename VectorType>
static typename MatrixType::Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
{
Transpose<MatrixType> matt(mat);
return llt_inplace<Scalar, Lower>::rankUpdate(matt, vec.conjugate(), sigma);
}
};
template<typename MatrixType> struct LLT_Traits<MatrixType,Lower>
{
typedef const TriangularView<const MatrixType, Lower> MatrixL;
typedef const TriangularView<const typename MatrixType::AdjointReturnType, Upper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return m; }
static inline MatrixU getU(const MatrixType& m) { return m.adjoint(); }
static bool inplace_decomposition(MatrixType& m)
{ return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m)==-1; }
};
template<typename MatrixType> struct LLT_Traits<MatrixType,Upper>
{
typedef const TriangularView<const typename MatrixType::AdjointReturnType, Lower> MatrixL;
typedef const TriangularView<const MatrixType, Upper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return m.adjoint(); }
static inline MatrixU getU(const MatrixType& m) { return m; }
static bool inplace_decomposition(MatrixType& m)
{ return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m)==-1; }
};
} // end namespace internal
/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix
*
* \returns a reference to *this
*
* Example: \include TutorialLinAlgComputeTwice.cpp
* Output: \verbinclude TutorialLinAlgComputeTwice.out
*/
template<typename MatrixType, int _UpLo>
LLT<MatrixType,_UpLo>& LLT<MatrixType,_UpLo>::compute(const MatrixType& a)
{
eigen_assert(a.rows()==a.cols());
const Index size = a.rows();
m_matrix.resize(size, size);
m_matrix = a;
m_isInitialized = true;
bool ok = Traits::inplace_decomposition(m_matrix);
m_info = ok ? Success : NumericalIssue;
return *this;
}
/** Performs a rank one update (or dowdate) of the current decomposition.
* If A = LL^* before the rank one update,
* then after it we have LL^* = A + sigma * v v^* where \a v must be a vector
* of same dimension.
*/
template<typename _MatrixType, int _UpLo>
template<typename VectorType>
LLT<_MatrixType,_UpLo> LLT<_MatrixType,_UpLo>::rankUpdate(const VectorType& v, const RealScalar& sigma)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType);
eigen_assert(v.size()==m_matrix.cols());
eigen_assert(m_isInitialized);
if(internal::llt_inplace<typename MatrixType::Scalar, UpLo>::rankUpdate(m_matrix,v,sigma)>=0)
m_info = NumericalIssue;
else
m_info = Success;
return *this;
}
namespace internal {
template<typename _MatrixType, int UpLo, typename Rhs>
struct solve_retval<LLT<_MatrixType, UpLo>, Rhs>
: solve_retval_base<LLT<_MatrixType, UpLo>, Rhs>
{
typedef LLT<_MatrixType,UpLo> LLTType;
EIGEN_MAKE_SOLVE_HELPERS(LLTType,Rhs)
template<typename Dest> void evalTo(Dest& dst) const
{
dst = rhs();
dec().solveInPlace(dst);
}
};
}
/** \internal use x = llt_object.solve(x);
*
* This is the \em in-place version of solve().
*
* \param bAndX represents both the right-hand side matrix b and result x.
*
* \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
*
* This version avoids a copy when the right hand side matrix b is not
* needed anymore.
*
* \sa LLT::solve(), MatrixBase::llt()
*/
template<typename MatrixType, int _UpLo>
template<typename Derived>
void LLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(m_matrix.rows()==bAndX.rows());
matrixL().solveInPlace(bAndX);
matrixU().solveInPlace(bAndX);
}
/** \returns the matrix represented by the decomposition,
* i.e., it returns the product: L L^*.
* This function is provided for debug purpose. */
template<typename MatrixType, int _UpLo>
MatrixType LLT<MatrixType,_UpLo>::reconstructedMatrix() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return matrixL() * matrixL().adjoint().toDenseMatrix();
}
/** \cholesky_module
* \returns the LLT decomposition of \c *this
*/
template<typename Derived>
inline const LLT<typename MatrixBase<Derived>::PlainObject>
MatrixBase<Derived>::llt() const
{
return LLT<PlainObject>(derived());
}
/** \cholesky_module
* \returns the LLT decomposition of \c *this
*/
template<typename MatrixType, unsigned int UpLo>
inline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
SelfAdjointView<MatrixType, UpLo>::llt() const
{
return LLT<PlainObject,UpLo>(m_matrix);
}
} // end namespace Eigen
#endif // EIGEN_LLT_H

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/*
Copyright (c) 2011, Intel Corporation. All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* Neither the name of Intel Corporation nor the names of its contributors may
be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
********************************************************************************
* Content : Eigen bindings to Intel(R) MKL
* LLt decomposition based on LAPACKE_?potrf function.
********************************************************************************
*/
#ifndef EIGEN_LLT_MKL_H
#define EIGEN_LLT_MKL_H
#include "Eigen/src/Core/util/MKL_support.h"
#include <iostream>
namespace Eigen {
namespace internal {
template<typename Scalar> struct mkl_llt;
#define EIGEN_MKL_LLT(EIGTYPE, MKLTYPE, MKLPREFIX) \
template<> struct mkl_llt<EIGTYPE> \
{ \
template<typename MatrixType> \
static inline typename MatrixType::Index potrf(MatrixType& m, char uplo) \
{ \
lapack_int matrix_order; \
lapack_int size, lda, info, StorageOrder; \
EIGTYPE* a; \
eigen_assert(m.rows()==m.cols()); \
/* Set up parameters for ?potrf */ \
size = m.rows(); \
StorageOrder = MatrixType::Flags&RowMajorBit?RowMajor:ColMajor; \
matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \
a = &(m.coeffRef(0,0)); \
lda = m.outerStride(); \
\
info = LAPACKE_##MKLPREFIX##potrf( matrix_order, uplo, size, (MKLTYPE*)a, lda ); \
info = (info==0) ? Success : NumericalIssue; \
return info; \
} \
}; \
template<> struct llt_inplace<EIGTYPE, Lower> \
{ \
template<typename MatrixType> \
static typename MatrixType::Index blocked(MatrixType& m) \
{ \
return mkl_llt<EIGTYPE>::potrf(m, 'L'); \
} \
template<typename MatrixType, typename VectorType> \
static typename MatrixType::Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \
{ return Eigen::internal::llt_rank_update_lower(mat, vec, sigma); } \
}; \
template<> struct llt_inplace<EIGTYPE, Upper> \
{ \
template<typename MatrixType> \
static typename MatrixType::Index blocked(MatrixType& m) \
{ \
return mkl_llt<EIGTYPE>::potrf(m, 'U'); \
} \
template<typename MatrixType, typename VectorType> \
static typename MatrixType::Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \
{ \
Transpose<MatrixType> matt(mat); \
return llt_inplace<EIGTYPE, Lower>::rankUpdate(matt, vec.conjugate(), sigma); \
} \
};
EIGEN_MKL_LLT(double, double, d)
EIGEN_MKL_LLT(float, float, s)
EIGEN_MKL_LLT(dcomplex, MKL_Complex16, z)
EIGEN_MKL_LLT(scomplex, MKL_Complex8, c)
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_LLT_MKL_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CHOLMODSUPPORT_H
#define EIGEN_CHOLMODSUPPORT_H
namespace Eigen {
namespace internal {
template<typename Scalar, typename CholmodType>
void cholmod_configure_matrix(CholmodType& mat)
{
if (internal::is_same<Scalar,float>::value)
{
mat.xtype = CHOLMOD_REAL;
mat.dtype = CHOLMOD_SINGLE;
}
else if (internal::is_same<Scalar,double>::value)
{
mat.xtype = CHOLMOD_REAL;
mat.dtype = CHOLMOD_DOUBLE;
}
else if (internal::is_same<Scalar,std::complex<float> >::value)
{
mat.xtype = CHOLMOD_COMPLEX;
mat.dtype = CHOLMOD_SINGLE;
}
else if (internal::is_same<Scalar,std::complex<double> >::value)
{
mat.xtype = CHOLMOD_COMPLEX;
mat.dtype = CHOLMOD_DOUBLE;
}
else
{
eigen_assert(false && "Scalar type not supported by CHOLMOD");
}
}
} // namespace internal
/** Wraps the Eigen sparse matrix \a mat into a Cholmod sparse matrix object.
* Note that the data are shared.
*/
template<typename _Scalar, int _Options, typename _Index>
cholmod_sparse viewAsCholmod(SparseMatrix<_Scalar,_Options,_Index>& mat)
{
typedef SparseMatrix<_Scalar,_Options,_Index> MatrixType;
cholmod_sparse res;
res.nzmax = mat.nonZeros();
res.nrow = mat.rows();;
res.ncol = mat.cols();
res.p = mat.outerIndexPtr();
res.i = mat.innerIndexPtr();
res.x = mat.valuePtr();
res.sorted = 1;
if(mat.isCompressed())
{
res.packed = 1;
}
else
{
res.packed = 0;
res.nz = mat.innerNonZeroPtr();
}
res.dtype = 0;
res.stype = -1;
if (internal::is_same<_Index,int>::value)
{
res.itype = CHOLMOD_INT;
}
else
{
eigen_assert(false && "Index type different than int is not supported yet");
}
// setup res.xtype
internal::cholmod_configure_matrix<_Scalar>(res);
res.stype = 0;
return res;
}
template<typename _Scalar, int _Options, typename _Index>
const cholmod_sparse viewAsCholmod(const SparseMatrix<_Scalar,_Options,_Index>& mat)
{
cholmod_sparse res = viewAsCholmod(mat.const_cast_derived());
return res;
}
/** Returns a view of the Eigen sparse matrix \a mat as Cholmod sparse matrix.
* The data are not copied but shared. */
template<typename _Scalar, int _Options, typename _Index, unsigned int UpLo>
cholmod_sparse viewAsCholmod(const SparseSelfAdjointView<SparseMatrix<_Scalar,_Options,_Index>, UpLo>& mat)
{
cholmod_sparse res = viewAsCholmod(mat.matrix().const_cast_derived());
if(UpLo==Upper) res.stype = 1;
if(UpLo==Lower) res.stype = -1;
return res;
}
/** Returns a view of the Eigen \b dense matrix \a mat as Cholmod dense matrix.
* The data are not copied but shared. */
template<typename Derived>
cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat)
{
EIGEN_STATIC_ASSERT((internal::traits<Derived>::Flags&RowMajorBit)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
typedef typename Derived::Scalar Scalar;
cholmod_dense res;
res.nrow = mat.rows();
res.ncol = mat.cols();
res.nzmax = res.nrow * res.ncol;
res.d = Derived::IsVectorAtCompileTime ? mat.derived().size() : mat.derived().outerStride();
res.x = mat.derived().data();
res.z = 0;
internal::cholmod_configure_matrix<Scalar>(res);
return res;
}
/** Returns a view of the Cholmod sparse matrix \a cm as an Eigen sparse matrix.
* The data are not copied but shared. */
template<typename Scalar, int Flags, typename Index>
MappedSparseMatrix<Scalar,Flags,Index> viewAsEigen(cholmod_sparse& cm)
{
return MappedSparseMatrix<Scalar,Flags,Index>
(cm.nrow, cm.ncol, reinterpret_cast<Index*>(cm.p)[cm.ncol],
reinterpret_cast<Index*>(cm.p), reinterpret_cast<Index*>(cm.i),reinterpret_cast<Scalar*>(cm.x) );
}
enum CholmodMode {
CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt
};
/** \ingroup CholmodSupport_Module
* \class CholmodBase
* \brief The base class for the direct Cholesky factorization of Cholmod
* \sa class CholmodSupernodalLLT, class CholmodSimplicialLDLT, class CholmodSimplicialLLT
*/
template<typename _MatrixType, int _UpLo, typename Derived>
class CholmodBase : internal::noncopyable
{
public:
typedef _MatrixType MatrixType;
enum { UpLo = _UpLo };
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef MatrixType CholMatrixType;
typedef typename MatrixType::Index Index;
public:
CholmodBase()
: m_cholmodFactor(0), m_info(Success), m_isInitialized(false)
{
cholmod_start(&m_cholmod);
}
CholmodBase(const MatrixType& matrix)
: m_cholmodFactor(0), m_info(Success), m_isInitialized(false)
{
cholmod_start(&m_cholmod);
compute(matrix);
}
~CholmodBase()
{
if(m_cholmodFactor)
cholmod_free_factor(&m_cholmodFactor, &m_cholmod);
cholmod_finish(&m_cholmod);
}
inline Index cols() const { return m_cholmodFactor->n; }
inline Index rows() const { return m_cholmodFactor->n; }
Derived& derived() { return *static_cast<Derived*>(this); }
const Derived& derived() const { return *static_cast<const Derived*>(this); }
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was succesful,
* \c NumericalIssue if the matrix.appears to be negative.
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "Decomposition is not initialized.");
return m_info;
}
/** Computes the sparse Cholesky decomposition of \a matrix */
Derived& compute(const MatrixType& matrix)
{
analyzePattern(matrix);
factorize(matrix);
return derived();
}
/** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* \sa compute()
*/
template<typename Rhs>
inline const internal::solve_retval<CholmodBase, Rhs>
solve(const MatrixBase<Rhs>& b) const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(rows()==b.rows()
&& "CholmodDecomposition::solve(): invalid number of rows of the right hand side matrix b");
return internal::solve_retval<CholmodBase, Rhs>(*this, b.derived());
}
/** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* \sa compute()
*/
template<typename Rhs>
inline const internal::sparse_solve_retval<CholmodBase, Rhs>
solve(const SparseMatrixBase<Rhs>& b) const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(rows()==b.rows()
&& "CholmodDecomposition::solve(): invalid number of rows of the right hand side matrix b");
return internal::sparse_solve_retval<CholmodBase, Rhs>(*this, b.derived());
}
/** Performs a symbolic decomposition on the sparcity of \a matrix.
*
* This function is particularly useful when solving for several problems having the same structure.
*
* \sa factorize()
*/
void analyzePattern(const MatrixType& matrix)
{
if(m_cholmodFactor)
{
cholmod_free_factor(&m_cholmodFactor, &m_cholmod);
m_cholmodFactor = 0;
}
cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
m_cholmodFactor = cholmod_analyze(&A, &m_cholmod);
this->m_isInitialized = true;
this->m_info = Success;
m_analysisIsOk = true;
m_factorizationIsOk = false;
}
/** Performs a numeric decomposition of \a matrix
*
* The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
*
* \sa analyzePattern()
*/
void factorize(const MatrixType& matrix)
{
eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
cholmod_factorize(&A, m_cholmodFactor, &m_cholmod);
this->m_info = Success;
m_factorizationIsOk = true;
}
/** Returns a reference to the Cholmod's configuration structure to get a full control over the performed operations.
* See the Cholmod user guide for details. */
cholmod_common& cholmod() { return m_cholmod; }
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal */
template<typename Rhs,typename Dest>
void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
{
eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
const Index size = m_cholmodFactor->n;
eigen_assert(size==b.rows());
// note: cd stands for Cholmod Dense
cholmod_dense b_cd = viewAsCholmod(b.const_cast_derived());
cholmod_dense* x_cd = cholmod_solve(CHOLMOD_A, m_cholmodFactor, &b_cd, &m_cholmod);
if(!x_cd)
{
this->m_info = NumericalIssue;
}
// TODO optimize this copy by swapping when possible (be carreful with alignment, etc.)
dest = Matrix<Scalar,Dest::RowsAtCompileTime,Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),b.rows(),b.cols());
cholmod_free_dense(&x_cd, &m_cholmod);
}
/** \internal */
template<typename RhsScalar, int RhsOptions, typename RhsIndex, typename DestScalar, int DestOptions, typename DestIndex>
void _solve(const SparseMatrix<RhsScalar,RhsOptions,RhsIndex> &b, SparseMatrix<DestScalar,DestOptions,DestIndex> &dest) const
{
eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
const Index size = m_cholmodFactor->n;
eigen_assert(size==b.rows());
// note: cs stands for Cholmod Sparse
cholmod_sparse b_cs = viewAsCholmod(b);
cholmod_sparse* x_cs = cholmod_spsolve(CHOLMOD_A, m_cholmodFactor, &b_cs, &m_cholmod);
if(!x_cs)
{
this->m_info = NumericalIssue;
}
// TODO optimize this copy by swapping when possible (be carreful with alignment, etc.)
dest = viewAsEigen<DestScalar,DestOptions,DestIndex>(*x_cs);
cholmod_free_sparse(&x_cs, &m_cholmod);
}
#endif // EIGEN_PARSED_BY_DOXYGEN
template<typename Stream>
void dumpMemory(Stream& s)
{}
protected:
mutable cholmod_common m_cholmod;
cholmod_factor* m_cholmodFactor;
mutable ComputationInfo m_info;
bool m_isInitialized;
int m_factorizationIsOk;
int m_analysisIsOk;
};
/** \ingroup CholmodSupport_Module
* \class CholmodSimplicialLLT
* \brief A simplicial direct Cholesky (LLT) factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization
* using the Cholmod library.
* This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Thefore, it has little practical interest.
* The sparse matrix A must be selfajoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
*
* \sa \ref TutorialSparseDirectSolvers, class CholmodSupernodalLLT, class SimplicialLLT
*/
template<typename _MatrixType, int _UpLo = Lower>
class CholmodSimplicialLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT<_MatrixType, _UpLo> >
{
typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT> Base;
using Base::m_cholmod;
public:
typedef _MatrixType MatrixType;
CholmodSimplicialLLT() : Base() { init(); }
CholmodSimplicialLLT(const MatrixType& matrix) : Base()
{
init();
compute(matrix);
}
~CholmodSimplicialLLT() {}
protected:
void init()
{
m_cholmod.final_asis = 0;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
m_cholmod.final_ll = 1;
}
};
/** \ingroup CholmodSupport_Module
* \class CholmodSimplicialLDLT
* \brief A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization
* using the Cholmod library.
* This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Thefore, it has little practical interest.
* The sparse matrix A must be selfajoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
*
* \sa \ref TutorialSparseDirectSolvers, class CholmodSupernodalLLT, class SimplicialLDLT
*/
template<typename _MatrixType, int _UpLo = Lower>
class CholmodSimplicialLDLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT<_MatrixType, _UpLo> >
{
typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT> Base;
using Base::m_cholmod;
public:
typedef _MatrixType MatrixType;
CholmodSimplicialLDLT() : Base() { init(); }
CholmodSimplicialLDLT(const MatrixType& matrix) : Base()
{
init();
compute(matrix);
}
~CholmodSimplicialLDLT() {}
protected:
void init()
{
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
}
};
/** \ingroup CholmodSupport_Module
* \class CholmodSupernodalLLT
* \brief A supernodal Cholesky (LLT) factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a supernodal LL^T Cholesky factorization
* using the Cholmod library.
* This supernodal variant performs best on dense enough problems, e.g., 3D FEM, or very high order 2D FEM.
* The sparse matrix A must be selfajoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
*
* \sa \ref TutorialSparseDirectSolvers
*/
template<typename _MatrixType, int _UpLo = Lower>
class CholmodSupernodalLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT<_MatrixType, _UpLo> >
{
typedef CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT> Base;
using Base::m_cholmod;
public:
typedef _MatrixType MatrixType;
CholmodSupernodalLLT() : Base() { init(); }
CholmodSupernodalLLT(const MatrixType& matrix) : Base()
{
init();
compute(matrix);
}
~CholmodSupernodalLLT() {}
protected:
void init()
{
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
}
};
/** \ingroup CholmodSupport_Module
* \class CholmodDecomposition
* \brief A general Cholesky factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a LL^T or LDL^T Cholesky factorization
* using the Cholmod library. The sparse matrix A must be selfajoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* This variant permits to change the underlying Cholesky method at runtime.
* On the other hand, it does not provide access to the result of the factorization.
* The default is to let Cholmod automatically choose between a simplicial and supernodal factorization.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
*
* \sa \ref TutorialSparseDirectSolvers
*/
template<typename _MatrixType, int _UpLo = Lower>
class CholmodDecomposition : public CholmodBase<_MatrixType, _UpLo, CholmodDecomposition<_MatrixType, _UpLo> >
{
typedef CholmodBase<_MatrixType, _UpLo, CholmodDecomposition> Base;
using Base::m_cholmod;
public:
typedef _MatrixType MatrixType;
CholmodDecomposition() : Base() { init(); }
CholmodDecomposition(const MatrixType& matrix) : Base()
{
init();
compute(matrix);
}
~CholmodDecomposition() {}
void setMode(CholmodMode mode)
{
switch(mode)
{
case CholmodAuto:
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_AUTO;
break;
case CholmodSimplicialLLt:
m_cholmod.final_asis = 0;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
m_cholmod.final_ll = 1;
break;
case CholmodSupernodalLLt:
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
break;
case CholmodLDLt:
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
break;
default:
break;
}
}
protected:
void init()
{
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_AUTO;
}
};
namespace internal {
template<typename _MatrixType, int _UpLo, typename Derived, typename Rhs>
struct solve_retval<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs>
: solve_retval_base<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs>
{
typedef CholmodBase<_MatrixType,_UpLo,Derived> Dec;
EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
template<typename Dest> void evalTo(Dest& dst) const
{
dec()._solve(rhs(),dst);
}
};
template<typename _MatrixType, int _UpLo, typename Derived, typename Rhs>
struct sparse_solve_retval<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs>
: sparse_solve_retval_base<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs>
{
typedef CholmodBase<_MatrixType,_UpLo,Derived> Dec;
EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
template<typename Dest> void evalTo(Dest& dst) const
{
dec()._solve(rhs(),dst);
}
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_CHOLMODSUPPORT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ARRAY_H
#define EIGEN_ARRAY_H
namespace Eigen {
/** \class Array
* \ingroup Core_Module
*
* \brief General-purpose arrays with easy API for coefficient-wise operations
*
* The %Array class is very similar to the Matrix class. It provides
* general-purpose one- and two-dimensional arrays. The difference between the
* %Array and the %Matrix class is primarily in the API: the API for the
* %Array class provides easy access to coefficient-wise operations, while the
* API for the %Matrix class provides easy access to linear-algebra
* operations.
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_ARRAY_PLUGIN.
*
* \sa \ref TutorialArrayClass, \ref TopicClassHierarchy
*/
namespace internal {
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
struct traits<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > : traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
{
typedef ArrayXpr XprKind;
typedef ArrayBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > XprBase;
};
}
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
class Array
: public PlainObjectBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
{
public:
typedef PlainObjectBase<Array> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Array)
enum { Options = _Options };
typedef typename Base::PlainObject PlainObject;
protected:
template <typename Derived, typename OtherDerived, bool IsVector>
friend struct internal::conservative_resize_like_impl;
using Base::m_storage;
public:
using Base::base;
using Base::coeff;
using Base::coeffRef;
/**
* The usage of
* using Base::operator=;
* fails on MSVC. Since the code below is working with GCC and MSVC, we skipped
* the usage of 'using'. This should be done only for operator=.
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE Array& operator=(const EigenBase<OtherDerived> &other)
{
return Base::operator=(other);
}
/** Copies the value of the expression \a other into \c *this with automatic resizing.
*
* *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
* it will be initialized.
*
* Note that copying a row-vector into a vector (and conversely) is allowed.
* The resizing, if any, is then done in the appropriate way so that row-vectors
* remain row-vectors and vectors remain vectors.
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE Array& operator=(const ArrayBase<OtherDerived>& other)
{
return Base::_set(other);
}
/** This is a special case of the templated operator=. Its purpose is to
* prevent a default operator= from hiding the templated operator=.
*/
EIGEN_STRONG_INLINE Array& operator=(const Array& other)
{
return Base::_set(other);
}
/** Default constructor.
*
* For fixed-size matrices, does nothing.
*
* For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
* is called a null matrix. This constructor is the unique way to create null matrices: resizing
* a matrix to 0 is not supported.
*
* \sa resize(Index,Index)
*/
EIGEN_STRONG_INLINE explicit Array() : Base()
{
Base::_check_template_params();
EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
// FIXME is it still needed ??
/** \internal */
Array(internal::constructor_without_unaligned_array_assert)
: Base(internal::constructor_without_unaligned_array_assert())
{
Base::_check_template_params();
EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
}
#endif
/** Constructs a vector or row-vector with given dimension. \only_for_vectors
*
* Note that this is only useful for dynamic-size vectors. For fixed-size vectors,
* it is redundant to pass the dimension here, so it makes more sense to use the default
* constructor Matrix() instead.
*/
EIGEN_STRONG_INLINE explicit Array(Index dim)
: Base(dim, RowsAtCompileTime == 1 ? 1 : dim, ColsAtCompileTime == 1 ? 1 : dim)
{
Base::_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Array)
eigen_assert(dim >= 0);
eigen_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == dim);
EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename T0, typename T1>
EIGEN_STRONG_INLINE Array(const T0& x, const T1& y)
{
Base::_check_template_params();
this->template _init2<T0,T1>(x, y);
}
#else
/** constructs an uninitialized matrix with \a rows rows and \a cols columns.
*
* This is useful for dynamic-size matrices. For fixed-size matrices,
* it is redundant to pass these parameters, so one should use the default constructor
* Matrix() instead. */
Array(Index rows, Index cols);
/** constructs an initialized 2D vector with given coefficients */
Array(const Scalar& x, const Scalar& y);
#endif
/** constructs an initialized 3D vector with given coefficients */
EIGEN_STRONG_INLINE Array(const Scalar& x, const Scalar& y, const Scalar& z)
{
Base::_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 3)
m_storage.data()[0] = x;
m_storage.data()[1] = y;
m_storage.data()[2] = z;
}
/** constructs an initialized 4D vector with given coefficients */
EIGEN_STRONG_INLINE Array(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w)
{
Base::_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 4)
m_storage.data()[0] = x;
m_storage.data()[1] = y;
m_storage.data()[2] = z;
m_storage.data()[3] = w;
}
explicit Array(const Scalar *data);
/** Constructor copying the value of the expression \a other */
template<typename OtherDerived>
EIGEN_STRONG_INLINE Array(const ArrayBase<OtherDerived>& other)
: Base(other.rows() * other.cols(), other.rows(), other.cols())
{
Base::_check_template_params();
Base::_set_noalias(other);
}
/** Copy constructor */
EIGEN_STRONG_INLINE Array(const Array& other)
: Base(other.rows() * other.cols(), other.rows(), other.cols())
{
Base::_check_template_params();
Base::_set_noalias(other);
}
/** Copy constructor with in-place evaluation */
template<typename OtherDerived>
EIGEN_STRONG_INLINE Array(const ReturnByValue<OtherDerived>& other)
{
Base::_check_template_params();
Base::resize(other.rows(), other.cols());
other.evalTo(*this);
}
/** \sa MatrixBase::operator=(const EigenBase<OtherDerived>&) */
template<typename OtherDerived>
EIGEN_STRONG_INLINE Array(const EigenBase<OtherDerived> &other)
: Base(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
{
Base::_check_template_params();
Base::resize(other.rows(), other.cols());
*this = other;
}
/** Override MatrixBase::swap() since for dynamic-sized matrices of same type it is enough to swap the
* data pointers.
*/
template<typename OtherDerived>
void swap(ArrayBase<OtherDerived> const & other)
{ this->_swap(other.derived()); }
inline Index innerStride() const { return 1; }
inline Index outerStride() const { return this->innerSize(); }
#ifdef EIGEN_ARRAY_PLUGIN
#include EIGEN_ARRAY_PLUGIN
#endif
private:
template<typename MatrixType, typename OtherDerived, bool SwapPointers>
friend struct internal::matrix_swap_impl;
};
/** \defgroup arraytypedefs Global array typedefs
* \ingroup Core_Module
*
* Eigen defines several typedef shortcuts for most common 1D and 2D array types.
*
* The general patterns are the following:
*
* \c ArrayRowsColsType where \c Rows and \c Cols can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
* and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
* for complex double.
*
* For example, \c Array33d is a fixed-size 3x3 array type of doubles, and \c ArrayXXf is a dynamic-size matrix of floats.
*
* There are also \c ArraySizeType which are self-explanatory. For example, \c Array4cf is
* a fixed-size 1D array of 4 complex floats.
*
* \sa class Array
*/
#define EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
/** \ingroup arraytypedefs */ \
typedef Array<Type, Size, Size> Array##SizeSuffix##SizeSuffix##TypeSuffix; \
/** \ingroup arraytypedefs */ \
typedef Array<Type, Size, 1> Array##SizeSuffix##TypeSuffix;
#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
/** \ingroup arraytypedefs */ \
typedef Array<Type, Size, Dynamic> Array##Size##X##TypeSuffix; \
/** \ingroup arraytypedefs */ \
typedef Array<Type, Dynamic, Size> Array##X##Size##TypeSuffix;
#define EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 2, 2) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 3, 3) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 4, 4) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(int, i)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(float, f)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(double, d)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<float>, cf)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
#undef EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES
#undef EIGEN_MAKE_ARRAY_TYPEDEFS
#undef EIGEN_MAKE_ARRAY_TYPEDEFS_LARGE
#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \
using Eigen::Matrix##SizeSuffix##TypeSuffix; \
using Eigen::Vector##SizeSuffix##TypeSuffix; \
using Eigen::RowVector##SizeSuffix##TypeSuffix;
#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(TypeSuffix) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 2) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 3) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 4) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X) \
#define EIGEN_USING_ARRAY_TYPEDEFS \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(i) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(f) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(d) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cf) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cd)
} // end namespace Eigen
#endif // EIGEN_ARRAY_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ARRAYBASE_H
#define EIGEN_ARRAYBASE_H
namespace Eigen {
template<typename ExpressionType> class MatrixWrapper;
/** \class ArrayBase
* \ingroup Core_Module
*
* \brief Base class for all 1D and 2D array, and related expressions
*
* An array is similar to a dense vector or matrix. While matrices are mathematical
* objects with well defined linear algebra operators, an array is just a collection
* of scalar values arranged in a one or two dimensionnal fashion. As the main consequence,
* all operations applied to an array are performed coefficient wise. Furthermore,
* arrays support scalar math functions of the c++ standard library (e.g., std::sin(x)), and convenient
* constructors allowing to easily write generic code working for both scalar values
* and arrays.
*
* This class is the base that is inherited by all array expression types.
*
* \tparam Derived is the derived type, e.g., an array or an expression type.
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_ARRAYBASE_PLUGIN.
*
* \sa class MatrixBase, \ref TopicClassHierarchy
*/
template<typename Derived> class ArrayBase
: public DenseBase<Derived>
{
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** The base class for a given storage type. */
typedef ArrayBase StorageBaseType;
typedef ArrayBase Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl;
using internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
typename NumTraits<typename internal::traits<Derived>::Scalar>::Real>::operator*;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Index Index;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef DenseBase<Derived> Base;
using Base::RowsAtCompileTime;
using Base::ColsAtCompileTime;
using Base::SizeAtCompileTime;
using Base::MaxRowsAtCompileTime;
using Base::MaxColsAtCompileTime;
using Base::MaxSizeAtCompileTime;
using Base::IsVectorAtCompileTime;
using Base::Flags;
using Base::CoeffReadCost;
using Base::derived;
using Base::const_cast_derived;
using Base::rows;
using Base::cols;
using Base::size;
using Base::coeff;
using Base::coeffRef;
using Base::lazyAssign;
using Base::operator=;
using Base::operator+=;
using Base::operator-=;
using Base::operator*=;
using Base::operator/=;
typedef typename Base::CoeffReturnType CoeffReturnType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal the plain matrix type corresponding to this expression. Note that is not necessarily
* exactly the return type of eval(): in the case of plain matrices, the return type of eval() is a const
* reference to a matrix, not a matrix! It is however guaranteed that the return type of eval() is either
* PlainObject or const PlainObject&.
*/
typedef Array<typename internal::traits<Derived>::Scalar,
internal::traits<Derived>::RowsAtCompileTime,
internal::traits<Derived>::ColsAtCompileTime,
AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),
internal::traits<Derived>::MaxRowsAtCompileTime,
internal::traits<Derived>::MaxColsAtCompileTime
> PlainObject;
/** \internal Represents a matrix with all coefficients equal to one another*/
typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Derived> ConstantReturnType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::ArrayBase
# include "../plugins/CommonCwiseUnaryOps.h"
# include "../plugins/MatrixCwiseUnaryOps.h"
# include "../plugins/ArrayCwiseUnaryOps.h"
# include "../plugins/CommonCwiseBinaryOps.h"
# include "../plugins/MatrixCwiseBinaryOps.h"
# include "../plugins/ArrayCwiseBinaryOps.h"
# ifdef EIGEN_ARRAYBASE_PLUGIN
# include EIGEN_ARRAYBASE_PLUGIN
# endif
#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
/** Special case of the template operator=, in order to prevent the compiler
* from generating a default operator= (issue hit with g++ 4.1)
*/
Derived& operator=(const ArrayBase& other)
{
return internal::assign_selector<Derived,Derived>::run(derived(), other.derived());
}
Derived& operator+=(const Scalar& scalar)
{ return *this = derived() + scalar; }
Derived& operator-=(const Scalar& scalar)
{ return *this = derived() - scalar; }
template<typename OtherDerived>
Derived& operator+=(const ArrayBase<OtherDerived>& other);
template<typename OtherDerived>
Derived& operator-=(const ArrayBase<OtherDerived>& other);
template<typename OtherDerived>
Derived& operator*=(const ArrayBase<OtherDerived>& other);
template<typename OtherDerived>
Derived& operator/=(const ArrayBase<OtherDerived>& other);
public:
ArrayBase<Derived>& array() { return *this; }
const ArrayBase<Derived>& array() const { return *this; }
/** \returns an \link MatrixBase Matrix \endlink expression of this array
* \sa MatrixBase::array() */
MatrixWrapper<Derived> matrix() { return derived(); }
const MatrixWrapper<const Derived> matrix() const { return derived(); }
// template<typename Dest>
// inline void evalTo(Dest& dst) const { dst = matrix(); }
protected:
ArrayBase() : Base() {}
private:
explicit ArrayBase(Index);
ArrayBase(Index,Index);
template<typename OtherDerived> explicit ArrayBase(const ArrayBase<OtherDerived>&);
protected:
// mixing arrays and matrices is not legal
template<typename OtherDerived> Derived& operator+=(const MatrixBase<OtherDerived>& )
{EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
// mixing arrays and matrices is not legal
template<typename OtherDerived> Derived& operator-=(const MatrixBase<OtherDerived>& )
{EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
};
/** replaces \c *this by \c *this - \a other.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived &
ArrayBase<Derived>::operator-=(const ArrayBase<OtherDerived> &other)
{
SelfCwiseBinaryOp<internal::scalar_difference_op<Scalar>, Derived, OtherDerived> tmp(derived());
tmp = other.derived();
return derived();
}
/** replaces \c *this by \c *this + \a other.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived &
ArrayBase<Derived>::operator+=(const ArrayBase<OtherDerived>& other)
{
SelfCwiseBinaryOp<internal::scalar_sum_op<Scalar>, Derived, OtherDerived> tmp(derived());
tmp = other.derived();
return derived();
}
/** replaces \c *this by \c *this * \a other coefficient wise.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived &
ArrayBase<Derived>::operator*=(const ArrayBase<OtherDerived>& other)
{
SelfCwiseBinaryOp<internal::scalar_product_op<Scalar>, Derived, OtherDerived> tmp(derived());
tmp = other.derived();
return derived();
}
/** replaces \c *this by \c *this / \a other coefficient wise.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived &
ArrayBase<Derived>::operator/=(const ArrayBase<OtherDerived>& other)
{
SelfCwiseBinaryOp<internal::scalar_quotient_op<Scalar>, Derived, OtherDerived> tmp(derived());
tmp = other.derived();
return derived();
}
} // end namespace Eigen
#endif // EIGEN_ARRAYBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ARRAYWRAPPER_H
#define EIGEN_ARRAYWRAPPER_H
namespace Eigen {
/** \class ArrayWrapper
* \ingroup Core_Module
*
* \brief Expression of a mathematical vector or matrix as an array object
*
* This class is the return type of MatrixBase::array(), and most of the time
* this is the only way it is use.
*
* \sa MatrixBase::array(), class MatrixWrapper
*/
namespace internal {
template<typename ExpressionType>
struct traits<ArrayWrapper<ExpressionType> >
: public traits<typename remove_all<typename ExpressionType::Nested>::type >
{
typedef ArrayXpr XprKind;
};
}
template<typename ExpressionType>
class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
{
public:
typedef ArrayBase<ArrayWrapper> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(ArrayWrapper)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ArrayWrapper)
typedef typename internal::conditional<
internal::is_lvalue<ExpressionType>::value,
Scalar,
const Scalar
>::type ScalarWithConstIfNotLvalue;
typedef typename internal::nested<ExpressionType>::type NestedExpressionType;
inline ArrayWrapper(ExpressionType& matrix) : m_expression(matrix) {}
inline Index rows() const { return m_expression.rows(); }
inline Index cols() const { return m_expression.cols(); }
inline Index outerStride() const { return m_expression.outerStride(); }
inline Index innerStride() const { return m_expression.innerStride(); }
inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
inline const Scalar* data() const { return m_expression.data(); }
inline CoeffReturnType coeff(Index row, Index col) const
{
return m_expression.coeff(row, col);
}
inline Scalar& coeffRef(Index row, Index col)
{
return m_expression.const_cast_derived().coeffRef(row, col);
}
inline const Scalar& coeffRef(Index row, Index col) const
{
return m_expression.const_cast_derived().coeffRef(row, col);
}
inline CoeffReturnType coeff(Index index) const
{
return m_expression.coeff(index);
}
inline Scalar& coeffRef(Index index)
{
return m_expression.const_cast_derived().coeffRef(index);
}
inline const Scalar& coeffRef(Index index) const
{
return m_expression.const_cast_derived().coeffRef(index);
}
template<int LoadMode>
inline const PacketScalar packet(Index row, Index col) const
{
return m_expression.template packet<LoadMode>(row, col);
}
template<int LoadMode>
inline void writePacket(Index row, Index col, const PacketScalar& x)
{
m_expression.const_cast_derived().template writePacket<LoadMode>(row, col, x);
}
template<int LoadMode>
inline const PacketScalar packet(Index index) const
{
return m_expression.template packet<LoadMode>(index);
}
template<int LoadMode>
inline void writePacket(Index index, const PacketScalar& x)
{
m_expression.const_cast_derived().template writePacket<LoadMode>(index, x);
}
template<typename Dest>
inline void evalTo(Dest& dst) const { dst = m_expression; }
const typename internal::remove_all<NestedExpressionType>::type&
nestedExpression() const
{
return m_expression;
}
/** Forwards the resizing request to the nested expression
* \sa DenseBase::resize(Index) */
void resize(Index newSize) { m_expression.const_cast_derived().resize(newSize); }
/** Forwards the resizing request to the nested expression
* \sa DenseBase::resize(Index,Index)*/
void resize(Index nbRows, Index nbCols) { m_expression.const_cast_derived().resize(nbRows,nbCols); }
protected:
NestedExpressionType m_expression;
};
/** \class MatrixWrapper
* \ingroup Core_Module
*
* \brief Expression of an array as a mathematical vector or matrix
*
* This class is the return type of ArrayBase::matrix(), and most of the time
* this is the only way it is use.
*
* \sa MatrixBase::matrix(), class ArrayWrapper
*/
namespace internal {
template<typename ExpressionType>
struct traits<MatrixWrapper<ExpressionType> >
: public traits<typename remove_all<typename ExpressionType::Nested>::type >
{
typedef MatrixXpr XprKind;
};
}
template<typename ExpressionType>
class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
{
public:
typedef MatrixBase<MatrixWrapper<ExpressionType> > Base;
EIGEN_DENSE_PUBLIC_INTERFACE(MatrixWrapper)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(MatrixWrapper)
typedef typename internal::conditional<
internal::is_lvalue<ExpressionType>::value,
Scalar,
const Scalar
>::type ScalarWithConstIfNotLvalue;
typedef typename internal::nested<ExpressionType>::type NestedExpressionType;
inline MatrixWrapper(ExpressionType& matrix) : m_expression(matrix) {}
inline Index rows() const { return m_expression.rows(); }
inline Index cols() const { return m_expression.cols(); }
inline Index outerStride() const { return m_expression.outerStride(); }
inline Index innerStride() const { return m_expression.innerStride(); }
inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
inline const Scalar* data() const { return m_expression.data(); }
inline CoeffReturnType coeff(Index row, Index col) const
{
return m_expression.coeff(row, col);
}
inline Scalar& coeffRef(Index row, Index col)
{
return m_expression.const_cast_derived().coeffRef(row, col);
}
inline const Scalar& coeffRef(Index row, Index col) const
{
return m_expression.derived().coeffRef(row, col);
}
inline CoeffReturnType coeff(Index index) const
{
return m_expression.coeff(index);
}
inline Scalar& coeffRef(Index index)
{
return m_expression.const_cast_derived().coeffRef(index);
}
inline const Scalar& coeffRef(Index index) const
{
return m_expression.const_cast_derived().coeffRef(index);
}
template<int LoadMode>
inline const PacketScalar packet(Index row, Index col) const
{
return m_expression.template packet<LoadMode>(row, col);
}
template<int LoadMode>
inline void writePacket(Index row, Index col, const PacketScalar& x)
{
m_expression.const_cast_derived().template writePacket<LoadMode>(row, col, x);
}
template<int LoadMode>
inline const PacketScalar packet(Index index) const
{
return m_expression.template packet<LoadMode>(index);
}
template<int LoadMode>
inline void writePacket(Index index, const PacketScalar& x)
{
m_expression.const_cast_derived().template writePacket<LoadMode>(index, x);
}
const typename internal::remove_all<NestedExpressionType>::type&
nestedExpression() const
{
return m_expression;
}
/** Forwards the resizing request to the nested expression
* \sa DenseBase::resize(Index) */
void resize(Index newSize) { m_expression.const_cast_derived().resize(newSize); }
/** Forwards the resizing request to the nested expression
* \sa DenseBase::resize(Index,Index)*/
void resize(Index nbRows, Index nbCols) { m_expression.const_cast_derived().resize(nbRows,nbCols); }
protected:
NestedExpressionType m_expression;
};
} // end namespace Eigen
#endif // EIGEN_ARRAYWRAPPER_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007 Michael Olbrich <michael.olbrich@gmx.net>
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ASSIGN_H
#define EIGEN_ASSIGN_H
namespace Eigen {
namespace internal {
/***************************************************************************
* Part 1 : the logic deciding a strategy for traversal and unrolling *
***************************************************************************/
template <typename Derived, typename OtherDerived>
struct assign_traits
{
public:
enum {
DstIsAligned = Derived::Flags & AlignedBit,
DstHasDirectAccess = Derived::Flags & DirectAccessBit,
SrcIsAligned = OtherDerived::Flags & AlignedBit,
JointAlignment = bool(DstIsAligned) && bool(SrcIsAligned) ? Aligned : Unaligned
};
private:
enum {
InnerSize = int(Derived::IsVectorAtCompileTime) ? int(Derived::SizeAtCompileTime)
: int(Derived::Flags)&RowMajorBit ? int(Derived::ColsAtCompileTime)
: int(Derived::RowsAtCompileTime),
InnerMaxSize = int(Derived::IsVectorAtCompileTime) ? int(Derived::MaxSizeAtCompileTime)
: int(Derived::Flags)&RowMajorBit ? int(Derived::MaxColsAtCompileTime)
: int(Derived::MaxRowsAtCompileTime),
MaxSizeAtCompileTime = Derived::SizeAtCompileTime,
PacketSize = packet_traits<typename Derived::Scalar>::size
};
enum {
StorageOrdersAgree = (int(Derived::IsRowMajor) == int(OtherDerived::IsRowMajor)),
MightVectorize = StorageOrdersAgree
&& (int(Derived::Flags) & int(OtherDerived::Flags) & ActualPacketAccessBit),
MayInnerVectorize = MightVectorize && int(InnerSize)!=Dynamic && int(InnerSize)%int(PacketSize)==0
&& int(DstIsAligned) && int(SrcIsAligned),
MayLinearize = StorageOrdersAgree && (int(Derived::Flags) & int(OtherDerived::Flags) & LinearAccessBit),
MayLinearVectorize = MightVectorize && MayLinearize && DstHasDirectAccess
&& (DstIsAligned || MaxSizeAtCompileTime == Dynamic),
/* If the destination isn't aligned, we have to do runtime checks and we don't unroll,
so it's only good for large enough sizes. */
MaySliceVectorize = MightVectorize && DstHasDirectAccess
&& (int(InnerMaxSize)==Dynamic || int(InnerMaxSize)>=3*PacketSize)
/* slice vectorization can be slow, so we only want it if the slices are big, which is
indicated by InnerMaxSize rather than InnerSize, think of the case of a dynamic block
in a fixed-size matrix */
};
public:
enum {
Traversal = int(MayInnerVectorize) ? int(InnerVectorizedTraversal)
: int(MayLinearVectorize) ? int(LinearVectorizedTraversal)
: int(MaySliceVectorize) ? int(SliceVectorizedTraversal)
: int(MayLinearize) ? int(LinearTraversal)
: int(DefaultTraversal),
Vectorized = int(Traversal) == InnerVectorizedTraversal
|| int(Traversal) == LinearVectorizedTraversal
|| int(Traversal) == SliceVectorizedTraversal
};
private:
enum {
UnrollingLimit = EIGEN_UNROLLING_LIMIT * (Vectorized ? int(PacketSize) : 1),
MayUnrollCompletely = int(Derived::SizeAtCompileTime) != Dynamic
&& int(OtherDerived::CoeffReadCost) != Dynamic
&& int(Derived::SizeAtCompileTime) * int(OtherDerived::CoeffReadCost) <= int(UnrollingLimit),
MayUnrollInner = int(InnerSize) != Dynamic
&& int(OtherDerived::CoeffReadCost) != Dynamic
&& int(InnerSize) * int(OtherDerived::CoeffReadCost) <= int(UnrollingLimit)
};
public:
enum {
Unrolling = (int(Traversal) == int(InnerVectorizedTraversal) || int(Traversal) == int(DefaultTraversal))
? (
int(MayUnrollCompletely) ? int(CompleteUnrolling)
: int(MayUnrollInner) ? int(InnerUnrolling)
: int(NoUnrolling)
)
: int(Traversal) == int(LinearVectorizedTraversal)
? ( bool(MayUnrollCompletely) && bool(DstIsAligned) ? int(CompleteUnrolling) : int(NoUnrolling) )
: int(Traversal) == int(LinearTraversal)
? ( bool(MayUnrollCompletely) ? int(CompleteUnrolling) : int(NoUnrolling) )
: int(NoUnrolling)
};
#ifdef EIGEN_DEBUG_ASSIGN
static void debug()
{
EIGEN_DEBUG_VAR(DstIsAligned)
EIGEN_DEBUG_VAR(SrcIsAligned)
EIGEN_DEBUG_VAR(JointAlignment)
EIGEN_DEBUG_VAR(InnerSize)
EIGEN_DEBUG_VAR(InnerMaxSize)
EIGEN_DEBUG_VAR(PacketSize)
EIGEN_DEBUG_VAR(StorageOrdersAgree)
EIGEN_DEBUG_VAR(MightVectorize)
EIGEN_DEBUG_VAR(MayLinearize)
EIGEN_DEBUG_VAR(MayInnerVectorize)
EIGEN_DEBUG_VAR(MayLinearVectorize)
EIGEN_DEBUG_VAR(MaySliceVectorize)
EIGEN_DEBUG_VAR(Traversal)
EIGEN_DEBUG_VAR(UnrollingLimit)
EIGEN_DEBUG_VAR(MayUnrollCompletely)
EIGEN_DEBUG_VAR(MayUnrollInner)
EIGEN_DEBUG_VAR(Unrolling)
}
#endif
};
/***************************************************************************
* Part 2 : meta-unrollers
***************************************************************************/
/************************
*** Default traversal ***
************************/
template<typename Derived1, typename Derived2, int Index, int Stop>
struct assign_DefaultTraversal_CompleteUnrolling
{
enum {
outer = Index / Derived1::InnerSizeAtCompileTime,
inner = Index % Derived1::InnerSizeAtCompileTime
};
static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
{
dst.copyCoeffByOuterInner(outer, inner, src);
assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, Index+1, Stop>::run(dst, src);
}
};
template<typename Derived1, typename Derived2, int Stop>
struct assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
{
static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &) {}
};
template<typename Derived1, typename Derived2, int Index, int Stop>
struct assign_DefaultTraversal_InnerUnrolling
{
static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src, int outer)
{
dst.copyCoeffByOuterInner(outer, Index, src);
assign_DefaultTraversal_InnerUnrolling<Derived1, Derived2, Index+1, Stop>::run(dst, src, outer);
}
};
template<typename Derived1, typename Derived2, int Stop>
struct assign_DefaultTraversal_InnerUnrolling<Derived1, Derived2, Stop, Stop>
{
static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &, int) {}
};
/***********************
*** Linear traversal ***
***********************/
template<typename Derived1, typename Derived2, int Index, int Stop>
struct assign_LinearTraversal_CompleteUnrolling
{
static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
{
dst.copyCoeff(Index, src);
assign_LinearTraversal_CompleteUnrolling<Derived1, Derived2, Index+1, Stop>::run(dst, src);
}
};
template<typename Derived1, typename Derived2, int Stop>
struct assign_LinearTraversal_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
{
static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &) {}
};
/**************************
*** Inner vectorization ***
**************************/
template<typename Derived1, typename Derived2, int Index, int Stop>
struct assign_innervec_CompleteUnrolling
{
enum {
outer = Index / Derived1::InnerSizeAtCompileTime,
inner = Index % Derived1::InnerSizeAtCompileTime,
JointAlignment = assign_traits<Derived1,Derived2>::JointAlignment
};
static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
{
dst.template copyPacketByOuterInner<Derived2, Aligned, JointAlignment>(outer, inner, src);
assign_innervec_CompleteUnrolling<Derived1, Derived2,
Index+packet_traits<typename Derived1::Scalar>::size, Stop>::run(dst, src);
}
};
template<typename Derived1, typename Derived2, int Stop>
struct assign_innervec_CompleteUnrolling<Derived1, Derived2, Stop, Stop>
{
static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &) {}
};
template<typename Derived1, typename Derived2, int Index, int Stop>
struct assign_innervec_InnerUnrolling
{
static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src, int outer)
{
dst.template copyPacketByOuterInner<Derived2, Aligned, Aligned>(outer, Index, src);
assign_innervec_InnerUnrolling<Derived1, Derived2,
Index+packet_traits<typename Derived1::Scalar>::size, Stop>::run(dst, src, outer);
}
};
template<typename Derived1, typename Derived2, int Stop>
struct assign_innervec_InnerUnrolling<Derived1, Derived2, Stop, Stop>
{
static EIGEN_STRONG_INLINE void run(Derived1 &, const Derived2 &, int) {}
};
/***************************************************************************
* Part 3 : implementation of all cases
***************************************************************************/
template<typename Derived1, typename Derived2,
int Traversal = assign_traits<Derived1, Derived2>::Traversal,
int Unrolling = assign_traits<Derived1, Derived2>::Unrolling,
int Version = Specialized>
struct assign_impl;
/************************
*** Default traversal ***
************************/
template<typename Derived1, typename Derived2, int Unrolling, int Version>
struct assign_impl<Derived1, Derived2, InvalidTraversal, Unrolling, Version>
{
static inline void run(Derived1 &, const Derived2 &) { }
};
template<typename Derived1, typename Derived2, int Version>
struct assign_impl<Derived1, Derived2, DefaultTraversal, NoUnrolling, Version>
{
typedef typename Derived1::Index Index;
static inline void run(Derived1 &dst, const Derived2 &src)
{
const Index innerSize = dst.innerSize();
const Index outerSize = dst.outerSize();
for(Index outer = 0; outer < outerSize; ++outer)
for(Index inner = 0; inner < innerSize; ++inner)
dst.copyCoeffByOuterInner(outer, inner, src);
}
};
template<typename Derived1, typename Derived2, int Version>
struct assign_impl<Derived1, Derived2, DefaultTraversal, CompleteUnrolling, Version>
{
static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
{
assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, 0, Derived1::SizeAtCompileTime>
::run(dst, src);
}
};
template<typename Derived1, typename Derived2, int Version>
struct assign_impl<Derived1, Derived2, DefaultTraversal, InnerUnrolling, Version>
{
typedef typename Derived1::Index Index;
static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
{
const Index outerSize = dst.outerSize();
for(Index outer = 0; outer < outerSize; ++outer)
assign_DefaultTraversal_InnerUnrolling<Derived1, Derived2, 0, Derived1::InnerSizeAtCompileTime>
::run(dst, src, outer);
}
};
/***********************
*** Linear traversal ***
***********************/
template<typename Derived1, typename Derived2, int Version>
struct assign_impl<Derived1, Derived2, LinearTraversal, NoUnrolling, Version>
{
typedef typename Derived1::Index Index;
static inline void run(Derived1 &dst, const Derived2 &src)
{
const Index size = dst.size();
for(Index i = 0; i < size; ++i)
dst.copyCoeff(i, src);
}
};
template<typename Derived1, typename Derived2, int Version>
struct assign_impl<Derived1, Derived2, LinearTraversal, CompleteUnrolling, Version>
{
static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
{
assign_LinearTraversal_CompleteUnrolling<Derived1, Derived2, 0, Derived1::SizeAtCompileTime>
::run(dst, src);
}
};
/**************************
*** Inner vectorization ***
**************************/
template<typename Derived1, typename Derived2, int Version>
struct assign_impl<Derived1, Derived2, InnerVectorizedTraversal, NoUnrolling, Version>
{
typedef typename Derived1::Index Index;
static inline void run(Derived1 &dst, const Derived2 &src)
{
const Index innerSize = dst.innerSize();
const Index outerSize = dst.outerSize();
const Index packetSize = packet_traits<typename Derived1::Scalar>::size;
for(Index outer = 0; outer < outerSize; ++outer)
for(Index inner = 0; inner < innerSize; inner+=packetSize)
dst.template copyPacketByOuterInner<Derived2, Aligned, Aligned>(outer, inner, src);
}
};
template<typename Derived1, typename Derived2, int Version>
struct assign_impl<Derived1, Derived2, InnerVectorizedTraversal, CompleteUnrolling, Version>
{
static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
{
assign_innervec_CompleteUnrolling<Derived1, Derived2, 0, Derived1::SizeAtCompileTime>
::run(dst, src);
}
};
template<typename Derived1, typename Derived2, int Version>
struct assign_impl<Derived1, Derived2, InnerVectorizedTraversal, InnerUnrolling, Version>
{
typedef typename Derived1::Index Index;
static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
{
const Index outerSize = dst.outerSize();
for(Index outer = 0; outer < outerSize; ++outer)
assign_innervec_InnerUnrolling<Derived1, Derived2, 0, Derived1::InnerSizeAtCompileTime>
::run(dst, src, outer);
}
};
/***************************
*** Linear vectorization ***
***************************/
template <bool IsAligned = false>
struct unaligned_assign_impl
{
template <typename Derived, typename OtherDerived>
static EIGEN_STRONG_INLINE void run(const Derived&, OtherDerived&, typename Derived::Index, typename Derived::Index) {}
};
template <>
struct unaligned_assign_impl<false>
{
// MSVC must not inline this functions. If it does, it fails to optimize the
// packet access path.
#ifdef _MSC_VER
template <typename Derived, typename OtherDerived>
static EIGEN_DONT_INLINE void run(const Derived& src, OtherDerived& dst, typename Derived::Index start, typename Derived::Index end)
#else
template <typename Derived, typename OtherDerived>
static EIGEN_STRONG_INLINE void run(const Derived& src, OtherDerived& dst, typename Derived::Index start, typename Derived::Index end)
#endif
{
for (typename Derived::Index index = start; index < end; ++index)
dst.copyCoeff(index, src);
}
};
template<typename Derived1, typename Derived2, int Version>
struct assign_impl<Derived1, Derived2, LinearVectorizedTraversal, NoUnrolling, Version>
{
typedef typename Derived1::Index Index;
static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
{
const Index size = dst.size();
typedef packet_traits<typename Derived1::Scalar> PacketTraits;
enum {
packetSize = PacketTraits::size,
dstAlignment = PacketTraits::AlignedOnScalar ? Aligned : int(assign_traits<Derived1,Derived2>::DstIsAligned) ,
srcAlignment = assign_traits<Derived1,Derived2>::JointAlignment
};
const Index alignedStart = assign_traits<Derived1,Derived2>::DstIsAligned ? 0
: internal::first_aligned(&dst.coeffRef(0), size);
const Index alignedEnd = alignedStart + ((size-alignedStart)/packetSize)*packetSize;
unaligned_assign_impl<assign_traits<Derived1,Derived2>::DstIsAligned!=0>::run(src,dst,0,alignedStart);
for(Index index = alignedStart; index < alignedEnd; index += packetSize)
{
dst.template copyPacket<Derived2, dstAlignment, srcAlignment>(index, src);
}
unaligned_assign_impl<>::run(src,dst,alignedEnd,size);
}
};
template<typename Derived1, typename Derived2, int Version>
struct assign_impl<Derived1, Derived2, LinearVectorizedTraversal, CompleteUnrolling, Version>
{
typedef typename Derived1::Index Index;
static EIGEN_STRONG_INLINE void run(Derived1 &dst, const Derived2 &src)
{
enum { size = Derived1::SizeAtCompileTime,
packetSize = packet_traits<typename Derived1::Scalar>::size,
alignedSize = (size/packetSize)*packetSize };
assign_innervec_CompleteUnrolling<Derived1, Derived2, 0, alignedSize>::run(dst, src);
assign_DefaultTraversal_CompleteUnrolling<Derived1, Derived2, alignedSize, size>::run(dst, src);
}
};
/**************************
*** Slice vectorization ***
***************************/
template<typename Derived1, typename Derived2, int Version>
struct assign_impl<Derived1, Derived2, SliceVectorizedTraversal, NoUnrolling, Version>
{
typedef typename Derived1::Index Index;
static inline void run(Derived1 &dst, const Derived2 &src)
{
typedef packet_traits<typename Derived1::Scalar> PacketTraits;
enum {
packetSize = PacketTraits::size,
alignable = PacketTraits::AlignedOnScalar,
dstAlignment = alignable ? Aligned : int(assign_traits<Derived1,Derived2>::DstIsAligned) ,
srcAlignment = assign_traits<Derived1,Derived2>::JointAlignment
};
const Index packetAlignedMask = packetSize - 1;
const Index innerSize = dst.innerSize();
const Index outerSize = dst.outerSize();
const Index alignedStep = alignable ? (packetSize - dst.outerStride() % packetSize) & packetAlignedMask : 0;
Index alignedStart = ((!alignable) || assign_traits<Derived1,Derived2>::DstIsAligned) ? 0
: internal::first_aligned(&dst.coeffRef(0,0), innerSize);
for(Index outer = 0; outer < outerSize; ++outer)
{
const Index alignedEnd = alignedStart + ((innerSize-alignedStart) & ~packetAlignedMask);
// do the non-vectorizable part of the assignment
for(Index inner = 0; inner<alignedStart ; ++inner)
dst.copyCoeffByOuterInner(outer, inner, src);
// do the vectorizable part of the assignment
for(Index inner = alignedStart; inner<alignedEnd; inner+=packetSize)
dst.template copyPacketByOuterInner<Derived2, dstAlignment, Unaligned>(outer, inner, src);
// do the non-vectorizable part of the assignment
for(Index inner = alignedEnd; inner<innerSize ; ++inner)
dst.copyCoeffByOuterInner(outer, inner, src);
alignedStart = std::min<Index>((alignedStart+alignedStep)%packetSize, innerSize);
}
}
};
} // end namespace internal
/***************************************************************************
* Part 4 : implementation of DenseBase methods
***************************************************************************/
template<typename Derived>
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived& DenseBase<Derived>
::lazyAssign(const DenseBase<OtherDerived>& other)
{
enum{
SameType = internal::is_same<typename Derived::Scalar,typename OtherDerived::Scalar>::value
};
EIGEN_STATIC_ASSERT_LVALUE(Derived)
EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
EIGEN_STATIC_ASSERT(SameType,YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
#ifdef EIGEN_DEBUG_ASSIGN
internal::assign_traits<Derived, OtherDerived>::debug();
#endif
eigen_assert(rows() == other.rows() && cols() == other.cols());
internal::assign_impl<Derived, OtherDerived, int(SameType) ? int(internal::assign_traits<Derived, OtherDerived>::Traversal)
: int(InvalidTraversal)>::run(derived(),other.derived());
#ifndef EIGEN_NO_DEBUG
checkTransposeAliasing(other.derived());
#endif
return derived();
}
namespace internal {
template<typename Derived, typename OtherDerived,
bool EvalBeforeAssigning = (int(OtherDerived::Flags) & EvalBeforeAssigningBit) != 0,
bool NeedToTranspose = Derived::IsVectorAtCompileTime
&& OtherDerived::IsVectorAtCompileTime
&& ((int(Derived::RowsAtCompileTime) == 1 && int(OtherDerived::ColsAtCompileTime) == 1)
| // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".
// revert to || as soon as not needed anymore.
(int(Derived::ColsAtCompileTime) == 1 && int(OtherDerived::RowsAtCompileTime) == 1))
&& int(Derived::SizeAtCompileTime) != 1>
struct assign_selector;
template<typename Derived, typename OtherDerived>
struct assign_selector<Derived,OtherDerived,false,false> {
static EIGEN_STRONG_INLINE Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.derived()); }
};
template<typename Derived, typename OtherDerived>
struct assign_selector<Derived,OtherDerived,true,false> {
static EIGEN_STRONG_INLINE Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.eval()); }
};
template<typename Derived, typename OtherDerived>
struct assign_selector<Derived,OtherDerived,false,true> {
static EIGEN_STRONG_INLINE Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.transpose()); }
};
template<typename Derived, typename OtherDerived>
struct assign_selector<Derived,OtherDerived,true,true> {
static EIGEN_STRONG_INLINE Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.transpose().eval()); }
};
} // end namespace internal
template<typename Derived>
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase<OtherDerived>& other)
{
return internal::assign_selector<Derived,OtherDerived>::run(derived(), other.derived());
}
template<typename Derived>
EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase& other)
{
return internal::assign_selector<Derived,Derived>::run(derived(), other.derived());
}
template<typename Derived>
EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const MatrixBase& other)
{
return internal::assign_selector<Derived,Derived>::run(derived(), other.derived());
}
template<typename Derived>
template <typename OtherDerived>
EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const DenseBase<OtherDerived>& other)
{
return internal::assign_selector<Derived,OtherDerived>::run(derived(), other.derived());
}
template<typename Derived>
template <typename OtherDerived>
EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const EigenBase<OtherDerived>& other)
{
other.derived().evalTo(derived());
return derived();
}
template<typename Derived>
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
{
other.evalTo(derived());
return derived();
}
} // end namespace Eigen
#endif // EIGEN_ASSIGN_H

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/*
Copyright (c) 2011, Intel Corporation. All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* Neither the name of Intel Corporation nor the names of its contributors may
be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
********************************************************************************
* Content : Eigen bindings to Intel(R) MKL
* MKL VML support for coefficient-wise unary Eigen expressions like a=b.sin()
********************************************************************************
*/
#ifndef EIGEN_ASSIGN_VML_H
#define EIGEN_ASSIGN_VML_H
namespace Eigen {
namespace internal {
template<typename Op> struct vml_call
{ enum { IsSupported = 0 }; };
template<typename Dst, typename Src, typename UnaryOp>
class vml_assign_traits
{
private:
enum {
DstHasDirectAccess = Dst::Flags & DirectAccessBit,
SrcHasDirectAccess = Src::Flags & DirectAccessBit,
StorageOrdersAgree = (int(Dst::IsRowMajor) == int(Src::IsRowMajor)),
InnerSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::SizeAtCompileTime)
: int(Dst::Flags)&RowMajorBit ? int(Dst::ColsAtCompileTime)
: int(Dst::RowsAtCompileTime),
InnerMaxSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::MaxSizeAtCompileTime)
: int(Dst::Flags)&RowMajorBit ? int(Dst::MaxColsAtCompileTime)
: int(Dst::MaxRowsAtCompileTime),
MaxSizeAtCompileTime = Dst::SizeAtCompileTime,
MightEnableVml = vml_call<UnaryOp>::IsSupported && StorageOrdersAgree && DstHasDirectAccess && SrcHasDirectAccess
&& Src::InnerStrideAtCompileTime==1 && Dst::InnerStrideAtCompileTime==1,
MightLinearize = MightEnableVml && (int(Dst::Flags) & int(Src::Flags) & LinearAccessBit),
VmlSize = MightLinearize ? MaxSizeAtCompileTime : InnerMaxSize,
LargeEnough = VmlSize==Dynamic || VmlSize>=EIGEN_MKL_VML_THRESHOLD,
MayEnableVml = MightEnableVml && LargeEnough,
MayLinearize = MayEnableVml && MightLinearize
};
public:
enum {
Traversal = MayLinearize ? LinearVectorizedTraversal
: MayEnableVml ? InnerVectorizedTraversal
: DefaultTraversal
};
};
template<typename Derived1, typename Derived2, typename UnaryOp, int Traversal, int Unrolling,
int VmlTraversal = vml_assign_traits<Derived1, Derived2, UnaryOp>::Traversal >
struct vml_assign_impl
: assign_impl<Derived1, Eigen::CwiseUnaryOp<UnaryOp, Derived2>,Traversal,Unrolling,BuiltIn>
{
};
template<typename Derived1, typename Derived2, typename UnaryOp, int Traversal, int Unrolling>
struct vml_assign_impl<Derived1, Derived2, UnaryOp, Traversal, Unrolling, InnerVectorizedTraversal>
{
typedef typename Derived1::Scalar Scalar;
typedef typename Derived1::Index Index;
static inline void run(Derived1& dst, const CwiseUnaryOp<UnaryOp, Derived2>& src)
{
// in case we want to (or have to) skip VML at runtime we can call:
// assign_impl<Derived1,Eigen::CwiseUnaryOp<UnaryOp, Derived2>,Traversal,Unrolling,BuiltIn>::run(dst,src);
const Index innerSize = dst.innerSize();
const Index outerSize = dst.outerSize();
for(Index outer = 0; outer < outerSize; ++outer) {
const Scalar *src_ptr = src.IsRowMajor ? &(src.nestedExpression().coeffRef(outer,0)) :
&(src.nestedExpression().coeffRef(0, outer));
Scalar *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer));
vml_call<UnaryOp>::run(src.functor(), innerSize, src_ptr, dst_ptr );
}
}
};
template<typename Derived1, typename Derived2, typename UnaryOp, int Traversal, int Unrolling>
struct vml_assign_impl<Derived1, Derived2, UnaryOp, Traversal, Unrolling, LinearVectorizedTraversal>
{
static inline void run(Derived1& dst, const CwiseUnaryOp<UnaryOp, Derived2>& src)
{
// in case we want to (or have to) skip VML at runtime we can call:
// assign_impl<Derived1,Eigen::CwiseUnaryOp<UnaryOp, Derived2>,Traversal,Unrolling,BuiltIn>::run(dst,src);
vml_call<UnaryOp>::run(src.functor(), dst.size(), src.nestedExpression().data(), dst.data() );
}
};
// Macroses
#define EIGEN_MKL_VML_SPECIALIZE_ASSIGN(TRAVERSAL,UNROLLING) \
template<typename Derived1, typename Derived2, typename UnaryOp> \
struct assign_impl<Derived1, Eigen::CwiseUnaryOp<UnaryOp, Derived2>, TRAVERSAL, UNROLLING, Specialized> { \
static inline void run(Derived1 &dst, const Eigen::CwiseUnaryOp<UnaryOp, Derived2> &src) { \
vml_assign_impl<Derived1,Derived2,UnaryOp,TRAVERSAL,UNROLLING>::run(dst, src); \
} \
};
EIGEN_MKL_VML_SPECIALIZE_ASSIGN(DefaultTraversal,NoUnrolling)
EIGEN_MKL_VML_SPECIALIZE_ASSIGN(DefaultTraversal,CompleteUnrolling)
EIGEN_MKL_VML_SPECIALIZE_ASSIGN(DefaultTraversal,InnerUnrolling)
EIGEN_MKL_VML_SPECIALIZE_ASSIGN(LinearTraversal,NoUnrolling)
EIGEN_MKL_VML_SPECIALIZE_ASSIGN(LinearTraversal,CompleteUnrolling)
EIGEN_MKL_VML_SPECIALIZE_ASSIGN(InnerVectorizedTraversal,NoUnrolling)
EIGEN_MKL_VML_SPECIALIZE_ASSIGN(InnerVectorizedTraversal,CompleteUnrolling)
EIGEN_MKL_VML_SPECIALIZE_ASSIGN(InnerVectorizedTraversal,InnerUnrolling)
EIGEN_MKL_VML_SPECIALIZE_ASSIGN(LinearVectorizedTraversal,CompleteUnrolling)
EIGEN_MKL_VML_SPECIALIZE_ASSIGN(LinearVectorizedTraversal,NoUnrolling)
EIGEN_MKL_VML_SPECIALIZE_ASSIGN(SliceVectorizedTraversal,NoUnrolling)
#if !defined (EIGEN_FAST_MATH) || (EIGEN_FAST_MATH != 1)
#define EIGEN_MKL_VML_MODE VML_HA
#else
#define EIGEN_MKL_VML_MODE VML_LA
#endif
#define EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE) \
template<> struct vml_call< scalar_##EIGENOP##_op<EIGENTYPE> > { \
enum { IsSupported = 1 }; \
static inline void run( const scalar_##EIGENOP##_op<EIGENTYPE>& /*func*/, \
int size, const EIGENTYPE* src, EIGENTYPE* dst) { \
VMLOP(size, (const VMLTYPE*)src, (VMLTYPE*)dst); \
} \
};
#define EIGEN_MKL_VML_DECLARE_UNARY_CALL_LA(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE) \
template<> struct vml_call< scalar_##EIGENOP##_op<EIGENTYPE> > { \
enum { IsSupported = 1 }; \
static inline void run( const scalar_##EIGENOP##_op<EIGENTYPE>& /*func*/, \
int size, const EIGENTYPE* src, EIGENTYPE* dst) { \
MKL_INT64 vmlMode = EIGEN_MKL_VML_MODE; \
VMLOP(size, (const VMLTYPE*)src, (VMLTYPE*)dst, vmlMode); \
} \
};
#define EIGEN_MKL_VML_DECLARE_POW_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE) \
template<> struct vml_call< scalar_##EIGENOP##_op<EIGENTYPE> > { \
enum { IsSupported = 1 }; \
static inline void run( const scalar_##EIGENOP##_op<EIGENTYPE>& func, \
int size, const EIGENTYPE* src, EIGENTYPE* dst) { \
EIGENTYPE exponent = func.m_exponent; \
MKL_INT64 vmlMode = EIGEN_MKL_VML_MODE; \
VMLOP(&size, (const VMLTYPE*)src, (const VMLTYPE*)&exponent, \
(VMLTYPE*)dst, &vmlMode); \
} \
};
#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, vs##VMLOP, float, float) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, vd##VMLOP, double, double)
#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_COMPLEX(EIGENOP, VMLOP) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, vc##VMLOP, scomplex, MKL_Complex8) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, vz##VMLOP, dcomplex, MKL_Complex16)
#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS(EIGENOP, VMLOP) \
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP) \
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_COMPLEX(EIGENOP, VMLOP)
#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL_LA(EIGENOP, VMLOP) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL_LA(EIGENOP, vms##VMLOP, float, float) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL_LA(EIGENOP, vmd##VMLOP, double, double)
#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_COMPLEX_LA(EIGENOP, VMLOP) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL_LA(EIGENOP, vmc##VMLOP, scomplex, MKL_Complex8) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL_LA(EIGENOP, vmz##VMLOP, dcomplex, MKL_Complex16)
#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(EIGENOP, VMLOP) \
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL_LA(EIGENOP, VMLOP) \
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_COMPLEX_LA(EIGENOP, VMLOP)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(sin, Sin)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(asin, Asin)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(cos, Cos)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(acos, Acos)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(tan, Tan)
//EIGEN_MKL_VML_DECLARE_UNARY_CALLS(abs, Abs)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(exp, Exp)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(log, Ln)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(sqrt, Sqrt)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(square, Sqr)
// The vm*powx functions are not avaibale in the windows version of MKL.
#ifdef _WIN32
EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmspowx_, float, float)
EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmdpowx_, double, double)
EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmcpowx_, scomplex, MKL_Complex8)
EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmzpowx_, dcomplex, MKL_Complex16)
#endif
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_ASSIGN_VML_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_BANDMATRIX_H
#define EIGEN_BANDMATRIX_H
namespace Eigen {
namespace internal {
template<typename Derived>
class BandMatrixBase : public EigenBase<Derived>
{
public:
enum {
Flags = internal::traits<Derived>::Flags,
CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
Supers = internal::traits<Derived>::Supers,
Subs = internal::traits<Derived>::Subs,
Options = internal::traits<Derived>::Options
};
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> DenseMatrixType;
typedef typename DenseMatrixType::Index Index;
typedef typename internal::traits<Derived>::CoefficientsType CoefficientsType;
typedef EigenBase<Derived> Base;
protected:
enum {
DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic))
? 1 + Supers + Subs
: Dynamic,
SizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime)
};
public:
using Base::derived;
using Base::rows;
using Base::cols;
/** \returns the number of super diagonals */
inline Index supers() const { return derived().supers(); }
/** \returns the number of sub diagonals */
inline Index subs() const { return derived().subs(); }
/** \returns an expression of the underlying coefficient matrix */
inline const CoefficientsType& coeffs() const { return derived().coeffs(); }
/** \returns an expression of the underlying coefficient matrix */
inline CoefficientsType& coeffs() { return derived().coeffs(); }
/** \returns a vector expression of the \a i -th column,
* only the meaningful part is returned.
* \warning the internal storage must be column major. */
inline Block<CoefficientsType,Dynamic,1> col(Index i)
{
EIGEN_STATIC_ASSERT((Options&RowMajor)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
Index start = 0;
Index len = coeffs().rows();
if (i<=supers())
{
start = supers()-i;
len = (std::min)(rows(),std::max<Index>(0,coeffs().rows() - (supers()-i)));
}
else if (i>=rows()-subs())
len = std::max<Index>(0,coeffs().rows() - (i + 1 - rows() + subs()));
return Block<CoefficientsType,Dynamic,1>(coeffs(), start, i, len, 1);
}
/** \returns a vector expression of the main diagonal */
inline Block<CoefficientsType,1,SizeAtCompileTime> diagonal()
{ return Block<CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
/** \returns a vector expression of the main diagonal (const version) */
inline const Block<const CoefficientsType,1,SizeAtCompileTime> diagonal() const
{ return Block<const CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
template<int Index> struct DiagonalIntReturnType {
enum {
ReturnOpposite = (Options&SelfAdjoint) && (((Index)>0 && Supers==0) || ((Index)<0 && Subs==0)),
Conjugate = ReturnOpposite && NumTraits<Scalar>::IsComplex,
ActualIndex = ReturnOpposite ? -Index : Index,
DiagonalSize = (RowsAtCompileTime==Dynamic || ColsAtCompileTime==Dynamic)
? Dynamic
: (ActualIndex<0
? EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime, RowsAtCompileTime + ActualIndex)
: EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime - ActualIndex))
};
typedef Block<CoefficientsType,1, DiagonalSize> BuildType;
typedef typename internal::conditional<Conjugate,
CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>,BuildType >,
BuildType>::type Type;
};
/** \returns a vector expression of the \a N -th sub or super diagonal */
template<int N> inline typename DiagonalIntReturnType<N>::Type diagonal()
{
return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
}
/** \returns a vector expression of the \a N -th sub or super diagonal */
template<int N> inline const typename DiagonalIntReturnType<N>::Type diagonal() const
{
return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
}
/** \returns a vector expression of the \a i -th sub or super diagonal */
inline Block<CoefficientsType,1,Dynamic> diagonal(Index i)
{
eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
return Block<CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
}
/** \returns a vector expression of the \a i -th sub or super diagonal */
inline const Block<const CoefficientsType,1,Dynamic> diagonal(Index i) const
{
eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
return Block<const CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
}
template<typename Dest> inline void evalTo(Dest& dst) const
{
dst.resize(rows(),cols());
dst.setZero();
dst.diagonal() = diagonal();
for (Index i=1; i<=supers();++i)
dst.diagonal(i) = diagonal(i);
for (Index i=1; i<=subs();++i)
dst.diagonal(-i) = diagonal(-i);
}
DenseMatrixType toDenseMatrix() const
{
DenseMatrixType res(rows(),cols());
evalTo(res);
return res;
}
protected:
inline Index diagonalLength(Index i) const
{ return i<0 ? (std::min)(cols(),rows()+i) : (std::min)(rows(),cols()-i); }
};
/**
* \class BandMatrix
* \ingroup Core_Module
*
* \brief Represents a rectangular matrix with a banded storage
*
* \param _Scalar Numeric type, i.e. float, double, int
* \param Rows Number of rows, or \b Dynamic
* \param Cols Number of columns, or \b Dynamic
* \param Supers Number of super diagonal
* \param Subs Number of sub diagonal
* \param _Options A combination of either \b #RowMajor or \b #ColMajor, and of \b #SelfAdjoint
* The former controls \ref TopicStorageOrders "storage order", and defaults to
* column-major. The latter controls whether the matrix represents a selfadjoint
* matrix in which case either Supers of Subs have to be null.
*
* \sa class TridiagonalMatrix
*/
template<typename _Scalar, int _Rows, int _Cols, int _Supers, int _Subs, int _Options>
struct traits<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >
{
typedef _Scalar Scalar;
typedef Dense StorageKind;
typedef DenseIndex Index;
enum {
CoeffReadCost = NumTraits<Scalar>::ReadCost,
RowsAtCompileTime = _Rows,
ColsAtCompileTime = _Cols,
MaxRowsAtCompileTime = _Rows,
MaxColsAtCompileTime = _Cols,
Flags = LvalueBit,
Supers = _Supers,
Subs = _Subs,
Options = _Options,
DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
};
typedef Matrix<Scalar,DataRowsAtCompileTime,ColsAtCompileTime,Options&RowMajor?RowMajor:ColMajor> CoefficientsType;
};
template<typename _Scalar, int Rows, int Cols, int Supers, int Subs, int Options>
class BandMatrix : public BandMatrixBase<BandMatrix<_Scalar,Rows,Cols,Supers,Subs,Options> >
{
public:
typedef typename internal::traits<BandMatrix>::Scalar Scalar;
typedef typename internal::traits<BandMatrix>::Index Index;
typedef typename internal::traits<BandMatrix>::CoefficientsType CoefficientsType;
inline BandMatrix(Index rows=Rows, Index cols=Cols, Index supers=Supers, Index subs=Subs)
: m_coeffs(1+supers+subs,cols),
m_rows(rows), m_supers(supers), m_subs(subs)
{
}
/** \returns the number of columns */
inline Index rows() const { return m_rows.value(); }
/** \returns the number of rows */
inline Index cols() const { return m_coeffs.cols(); }
/** \returns the number of super diagonals */
inline Index supers() const { return m_supers.value(); }
/** \returns the number of sub diagonals */
inline Index subs() const { return m_subs.value(); }
inline const CoefficientsType& coeffs() const { return m_coeffs; }
inline CoefficientsType& coeffs() { return m_coeffs; }
protected:
CoefficientsType m_coeffs;
internal::variable_if_dynamic<Index, Rows> m_rows;
internal::variable_if_dynamic<Index, Supers> m_supers;
internal::variable_if_dynamic<Index, Subs> m_subs;
};
template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
class BandMatrixWrapper;
template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
struct traits<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
{
typedef typename _CoefficientsType::Scalar Scalar;
typedef typename _CoefficientsType::StorageKind StorageKind;
typedef typename _CoefficientsType::Index Index;
enum {
CoeffReadCost = internal::traits<_CoefficientsType>::CoeffReadCost,
RowsAtCompileTime = _Rows,
ColsAtCompileTime = _Cols,
MaxRowsAtCompileTime = _Rows,
MaxColsAtCompileTime = _Cols,
Flags = LvalueBit,
Supers = _Supers,
Subs = _Subs,
Options = _Options,
DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
};
typedef _CoefficientsType CoefficientsType;
};
template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
class BandMatrixWrapper : public BandMatrixBase<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
{
public:
typedef typename internal::traits<BandMatrixWrapper>::Scalar Scalar;
typedef typename internal::traits<BandMatrixWrapper>::CoefficientsType CoefficientsType;
typedef typename internal::traits<BandMatrixWrapper>::Index Index;
inline BandMatrixWrapper(const CoefficientsType& coeffs, Index rows=_Rows, Index cols=_Cols, Index supers=_Supers, Index subs=_Subs)
: m_coeffs(coeffs),
m_rows(rows), m_supers(supers), m_subs(subs)
{
EIGEN_UNUSED_VARIABLE(cols);
//internal::assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows());
}
/** \returns the number of columns */
inline Index rows() const { return m_rows.value(); }
/** \returns the number of rows */
inline Index cols() const { return m_coeffs.cols(); }
/** \returns the number of super diagonals */
inline Index supers() const { return m_supers.value(); }
/** \returns the number of sub diagonals */
inline Index subs() const { return m_subs.value(); }
inline const CoefficientsType& coeffs() const { return m_coeffs; }
protected:
const CoefficientsType& m_coeffs;
internal::variable_if_dynamic<Index, _Rows> m_rows;
internal::variable_if_dynamic<Index, _Supers> m_supers;
internal::variable_if_dynamic<Index, _Subs> m_subs;
};
/**
* \class TridiagonalMatrix
* \ingroup Core_Module
*
* \brief Represents a tridiagonal matrix with a compact banded storage
*
* \param _Scalar Numeric type, i.e. float, double, int
* \param Size Number of rows and cols, or \b Dynamic
* \param _Options Can be 0 or \b SelfAdjoint
*
* \sa class BandMatrix
*/
template<typename Scalar, int Size, int Options>
class TridiagonalMatrix : public BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor>
{
typedef BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor> Base;
typedef typename Base::Index Index;
public:
TridiagonalMatrix(Index size = Size) : Base(size,size,Options&SelfAdjoint?0:1,1) {}
inline typename Base::template DiagonalIntReturnType<1>::Type super()
{ return Base::template diagonal<1>(); }
inline const typename Base::template DiagonalIntReturnType<1>::Type super() const
{ return Base::template diagonal<1>(); }
inline typename Base::template DiagonalIntReturnType<-1>::Type sub()
{ return Base::template diagonal<-1>(); }
inline const typename Base::template DiagonalIntReturnType<-1>::Type sub() const
{ return Base::template diagonal<-1>(); }
protected:
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_BANDMATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_BLOCK_H
#define EIGEN_BLOCK_H
namespace Eigen {
/** \class Block
* \ingroup Core_Module
*
* \brief Expression of a fixed-size or dynamic-size block
*
* \param XprType the type of the expression in which we are taking a block
* \param BlockRows the number of rows of the block we are taking at compile time (optional)
* \param BlockCols the number of columns of the block we are taking at compile time (optional)
* \param _DirectAccessStatus \internal used for partial specialization
*
* This class represents an expression of either a fixed-size or dynamic-size block. It is the return
* type of DenseBase::block(Index,Index,Index,Index) and DenseBase::block<int,int>(Index,Index) and
* most of the time this is the only way it is used.
*
* However, if you want to directly maniputate block expressions,
* for instance if you want to write a function returning such an expression, you
* will need to use this class.
*
* Here is an example illustrating the dynamic case:
* \include class_Block.cpp
* Output: \verbinclude class_Block.out
*
* \note Even though this expression has dynamic size, in the case where \a XprType
* has fixed size, this expression inherits a fixed maximal size which means that evaluating
* it does not cause a dynamic memory allocation.
*
* Here is an example illustrating the fixed-size case:
* \include class_FixedBlock.cpp
* Output: \verbinclude class_FixedBlock.out
*
* \sa DenseBase::block(Index,Index,Index,Index), DenseBase::block(Index,Index), class VectorBlock
*/
namespace internal {
template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool HasDirectAccess>
struct traits<Block<XprType, BlockRows, BlockCols, InnerPanel, HasDirectAccess> > : traits<XprType>
{
typedef typename traits<XprType>::Scalar Scalar;
typedef typename traits<XprType>::StorageKind StorageKind;
typedef typename traits<XprType>::XprKind XprKind;
typedef typename nested<XprType>::type XprTypeNested;
typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;
enum{
MatrixRows = traits<XprType>::RowsAtCompileTime,
MatrixCols = traits<XprType>::ColsAtCompileTime,
RowsAtCompileTime = MatrixRows == 0 ? 0 : BlockRows,
ColsAtCompileTime = MatrixCols == 0 ? 0 : BlockCols,
MaxRowsAtCompileTime = BlockRows==0 ? 0
: RowsAtCompileTime != Dynamic ? int(RowsAtCompileTime)
: int(traits<XprType>::MaxRowsAtCompileTime),
MaxColsAtCompileTime = BlockCols==0 ? 0
: ColsAtCompileTime != Dynamic ? int(ColsAtCompileTime)
: int(traits<XprType>::MaxColsAtCompileTime),
XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0,
IsRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
: (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
: XprTypeIsRowMajor,
HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),
InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
InnerStrideAtCompileTime = HasSameStorageOrderAsXprType
? int(inner_stride_at_compile_time<XprType>::ret)
: int(outer_stride_at_compile_time<XprType>::ret),
OuterStrideAtCompileTime = HasSameStorageOrderAsXprType
? int(outer_stride_at_compile_time<XprType>::ret)
: int(inner_stride_at_compile_time<XprType>::ret),
MaskPacketAccessBit = (InnerSize == Dynamic || (InnerSize % packet_traits<Scalar>::size) == 0)
&& (InnerStrideAtCompileTime == 1)
? PacketAccessBit : 0,
MaskAlignedBit = (InnerPanel && (OuterStrideAtCompileTime!=Dynamic) && (((OuterStrideAtCompileTime * int(sizeof(Scalar))) % 16) == 0)) ? AlignedBit : 0,
FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1) ? LinearAccessBit : 0,
FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
Flags0 = traits<XprType>::Flags & ( (HereditaryBits & ~RowMajorBit) |
DirectAccessBit |
MaskPacketAccessBit |
MaskAlignedBit),
Flags = Flags0 | FlagsLinearAccessBit | FlagsLvalueBit | FlagsRowMajorBit
};
};
}
template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool HasDirectAccess> class Block
: public internal::dense_xpr_base<Block<XprType, BlockRows, BlockCols, InnerPanel, HasDirectAccess> >::type
{
public:
typedef typename internal::dense_xpr_base<Block>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Block)
class InnerIterator;
/** Column or Row constructor
*/
inline Block(XprType& xpr, Index i)
: m_xpr(xpr),
// It is a row if and only if BlockRows==1 and BlockCols==XprType::ColsAtCompileTime,
// and it is a column if and only if BlockRows==XprType::RowsAtCompileTime and BlockCols==1,
// all other cases are invalid.
// The case a 1x1 matrix seems ambiguous, but the result is the same anyway.
m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),
m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0),
m_blockRows(BlockRows==1 ? 1 : xpr.rows()),
m_blockCols(BlockCols==1 ? 1 : xpr.cols())
{
eigen_assert( (i>=0) && (
((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && i<xpr.rows())
||((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && i<xpr.cols())));
}
/** Fixed-size constructor
*/
inline Block(XprType& xpr, Index startRow, Index startCol)
: m_xpr(xpr), m_startRow(startRow), m_startCol(startCol),
m_blockRows(BlockRows), m_blockCols(BlockCols)
{
EIGEN_STATIC_ASSERT(RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic,THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)
eigen_assert(startRow >= 0 && BlockRows >= 1 && startRow + BlockRows <= xpr.rows()
&& startCol >= 0 && BlockCols >= 1 && startCol + BlockCols <= xpr.cols());
}
/** Dynamic-size constructor
*/
inline Block(XprType& xpr,
Index startRow, Index startCol,
Index blockRows, Index blockCols)
: m_xpr(xpr), m_startRow(startRow), m_startCol(startCol),
m_blockRows(blockRows), m_blockCols(blockCols)
{
eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==blockRows)
&& (ColsAtCompileTime==Dynamic || ColsAtCompileTime==blockCols));
eigen_assert(startRow >= 0 && blockRows >= 0 && startRow + blockRows <= xpr.rows()
&& startCol >= 0 && blockCols >= 0 && startCol + blockCols <= xpr.cols());
}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
inline Index rows() const { return m_blockRows.value(); }
inline Index cols() const { return m_blockCols.value(); }
inline Scalar& coeffRef(Index row, Index col)
{
EIGEN_STATIC_ASSERT_LVALUE(XprType)
return m_xpr.const_cast_derived()
.coeffRef(row + m_startRow.value(), col + m_startCol.value());
}
inline const Scalar& coeffRef(Index row, Index col) const
{
return m_xpr.derived()
.coeffRef(row + m_startRow.value(), col + m_startCol.value());
}
EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index row, Index col) const
{
return m_xpr.coeff(row + m_startRow.value(), col + m_startCol.value());
}
inline Scalar& coeffRef(Index index)
{
EIGEN_STATIC_ASSERT_LVALUE(XprType)
return m_xpr.const_cast_derived()
.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
}
inline const Scalar& coeffRef(Index index) const
{
return m_xpr.const_cast_derived()
.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
}
inline const CoeffReturnType coeff(Index index) const
{
return m_xpr
.coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
}
template<int LoadMode>
inline PacketScalar packet(Index row, Index col) const
{
return m_xpr.template packet<Unaligned>
(row + m_startRow.value(), col + m_startCol.value());
}
template<int LoadMode>
inline void writePacket(Index row, Index col, const PacketScalar& x)
{
m_xpr.const_cast_derived().template writePacket<Unaligned>
(row + m_startRow.value(), col + m_startCol.value(), x);
}
template<int LoadMode>
inline PacketScalar packet(Index index) const
{
return m_xpr.template packet<Unaligned>
(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
}
template<int LoadMode>
inline void writePacket(Index index, const PacketScalar& x)
{
m_xpr.const_cast_derived().template writePacket<Unaligned>
(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0), x);
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \sa MapBase::data() */
inline const Scalar* data() const;
inline Index innerStride() const;
inline Index outerStride() const;
#endif
const typename internal::remove_all<typename XprType::Nested>::type& nestedExpression() const
{
return m_xpr;
}
Index startRow() const
{
return m_startRow.value();
}
Index startCol() const
{
return m_startCol.value();
}
protected:
const typename XprType::Nested m_xpr;
const internal::variable_if_dynamic<Index, XprType::RowsAtCompileTime == 1 ? 0 : Dynamic> m_startRow;
const internal::variable_if_dynamic<Index, XprType::ColsAtCompileTime == 1 ? 0 : Dynamic> m_startCol;
const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_blockRows;
const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_blockCols;
};
/** \internal */
template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
class Block<XprType,BlockRows,BlockCols, InnerPanel,true>
: public MapBase<Block<XprType, BlockRows, BlockCols, InnerPanel, true> >
{
public:
typedef MapBase<Block> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Block)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
/** Column or Row constructor
*/
inline Block(XprType& xpr, Index i)
: Base(internal::const_cast_ptr(&xpr.coeffRef(
(BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0,
(BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0)),
BlockRows==1 ? 1 : xpr.rows(),
BlockCols==1 ? 1 : xpr.cols()),
m_xpr(xpr)
{
eigen_assert( (i>=0) && (
((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && i<xpr.rows())
||((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && i<xpr.cols())));
init();
}
/** Fixed-size constructor
*/
inline Block(XprType& xpr, Index startRow, Index startCol)
: Base(internal::const_cast_ptr(&xpr.coeffRef(startRow,startCol))), m_xpr(xpr)
{
eigen_assert(startRow >= 0 && BlockRows >= 1 && startRow + BlockRows <= xpr.rows()
&& startCol >= 0 && BlockCols >= 1 && startCol + BlockCols <= xpr.cols());
init();
}
/** Dynamic-size constructor
*/
inline Block(XprType& xpr,
Index startRow, Index startCol,
Index blockRows, Index blockCols)
: Base(internal::const_cast_ptr(&xpr.coeffRef(startRow,startCol)), blockRows, blockCols),
m_xpr(xpr)
{
eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==blockRows)
&& (ColsAtCompileTime==Dynamic || ColsAtCompileTime==blockCols));
eigen_assert(startRow >= 0 && blockRows >= 0 && startRow + blockRows <= xpr.rows()
&& startCol >= 0 && blockCols >= 0 && startCol + blockCols <= xpr.cols());
init();
}
const typename internal::remove_all<typename XprType::Nested>::type& nestedExpression() const
{
return m_xpr;
}
/** \sa MapBase::innerStride() */
inline Index innerStride() const
{
return internal::traits<Block>::HasSameStorageOrderAsXprType
? m_xpr.innerStride()
: m_xpr.outerStride();
}
/** \sa MapBase::outerStride() */
inline Index outerStride() const
{
return m_outerStride;
}
#ifndef __SUNPRO_CC
// FIXME sunstudio is not friendly with the above friend...
// META-FIXME there is no 'friend' keyword around here. Is this obsolete?
protected:
#endif
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal used by allowAligned() */
inline Block(XprType& xpr, const Scalar* data, Index blockRows, Index blockCols)
: Base(data, blockRows, blockCols), m_xpr(xpr)
{
init();
}
#endif
protected:
void init()
{
m_outerStride = internal::traits<Block>::HasSameStorageOrderAsXprType
? m_xpr.outerStride()
: m_xpr.innerStride();
}
typename XprType::Nested m_xpr;
Index m_outerStride;
};
} // end namespace Eigen
#endif // EIGEN_BLOCK_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ALLANDANY_H
#define EIGEN_ALLANDANY_H
namespace Eigen {
namespace internal {
template<typename Derived, int UnrollCount>
struct all_unroller
{
enum {
col = (UnrollCount-1) / Derived::RowsAtCompileTime,
row = (UnrollCount-1) % Derived::RowsAtCompileTime
};
static inline bool run(const Derived &mat)
{
return all_unroller<Derived, UnrollCount-1>::run(mat) && mat.coeff(row, col);
}
};
template<typename Derived>
struct all_unroller<Derived, 1>
{
static inline bool run(const Derived &mat) { return mat.coeff(0, 0); }
};
template<typename Derived>
struct all_unroller<Derived, Dynamic>
{
static inline bool run(const Derived &) { return false; }
};
template<typename Derived, int UnrollCount>
struct any_unroller
{
enum {
col = (UnrollCount-1) / Derived::RowsAtCompileTime,
row = (UnrollCount-1) % Derived::RowsAtCompileTime
};
static inline bool run(const Derived &mat)
{
return any_unroller<Derived, UnrollCount-1>::run(mat) || mat.coeff(row, col);
}
};
template<typename Derived>
struct any_unroller<Derived, 1>
{
static inline bool run(const Derived &mat) { return mat.coeff(0, 0); }
};
template<typename Derived>
struct any_unroller<Derived, Dynamic>
{
static inline bool run(const Derived &) { return false; }
};
} // end namespace internal
/** \returns true if all coefficients are true
*
* Example: \include MatrixBase_all.cpp
* Output: \verbinclude MatrixBase_all.out
*
* \sa any(), Cwise::operator<()
*/
template<typename Derived>
inline bool DenseBase<Derived>::all() const
{
enum {
unroll = SizeAtCompileTime != Dynamic
&& CoeffReadCost != Dynamic
&& NumTraits<Scalar>::AddCost != Dynamic
&& SizeAtCompileTime * (CoeffReadCost + NumTraits<Scalar>::AddCost) <= EIGEN_UNROLLING_LIMIT
};
if(unroll)
return internal::all_unroller<Derived,
unroll ? int(SizeAtCompileTime) : Dynamic
>::run(derived());
else
{
for(Index j = 0; j < cols(); ++j)
for(Index i = 0; i < rows(); ++i)
if (!coeff(i, j)) return false;
return true;
}
}
/** \returns true if at least one coefficient is true
*
* \sa all()
*/
template<typename Derived>
inline bool DenseBase<Derived>::any() const
{
enum {
unroll = SizeAtCompileTime != Dynamic
&& CoeffReadCost != Dynamic
&& NumTraits<Scalar>::AddCost != Dynamic
&& SizeAtCompileTime * (CoeffReadCost + NumTraits<Scalar>::AddCost) <= EIGEN_UNROLLING_LIMIT
};
if(unroll)
return internal::any_unroller<Derived,
unroll ? int(SizeAtCompileTime) : Dynamic
>::run(derived());
else
{
for(Index j = 0; j < cols(); ++j)
for(Index i = 0; i < rows(); ++i)
if (coeff(i, j)) return true;
return false;
}
}
/** \returns the number of coefficients which evaluate to true
*
* \sa all(), any()
*/
template<typename Derived>
inline typename DenseBase<Derived>::Index DenseBase<Derived>::count() const
{
return derived().template cast<bool>().template cast<Index>().sum();
}
} // end namespace Eigen
#endif // EIGEN_ALLANDANY_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_COMMAINITIALIZER_H
#define EIGEN_COMMAINITIALIZER_H
namespace Eigen {
/** \class CommaInitializer
* \ingroup Core_Module
*
* \brief Helper class used by the comma initializer operator
*
* This class is internally used to implement the comma initializer feature. It is
* the return type of MatrixBase::operator<<, and most of the time this is the only
* way it is used.
*
* \sa \ref MatrixBaseCommaInitRef "MatrixBase::operator<<", CommaInitializer::finished()
*/
template<typename XprType>
struct CommaInitializer
{
typedef typename XprType::Scalar Scalar;
typedef typename XprType::Index Index;
inline CommaInitializer(XprType& xpr, const Scalar& s)
: m_xpr(xpr), m_row(0), m_col(1), m_currentBlockRows(1)
{
m_xpr.coeffRef(0,0) = s;
}
template<typename OtherDerived>
inline CommaInitializer(XprType& xpr, const DenseBase<OtherDerived>& other)
: m_xpr(xpr), m_row(0), m_col(other.cols()), m_currentBlockRows(other.rows())
{
m_xpr.block(0, 0, other.rows(), other.cols()) = other;
}
/* inserts a scalar value in the target matrix */
CommaInitializer& operator,(const Scalar& s)
{
if (m_col==m_xpr.cols())
{
m_row+=m_currentBlockRows;
m_col = 0;
m_currentBlockRows = 1;
eigen_assert(m_row<m_xpr.rows()
&& "Too many rows passed to comma initializer (operator<<)");
}
eigen_assert(m_col<m_xpr.cols()
&& "Too many coefficients passed to comma initializer (operator<<)");
eigen_assert(m_currentBlockRows==1);
m_xpr.coeffRef(m_row, m_col++) = s;
return *this;
}
/* inserts a matrix expression in the target matrix */
template<typename OtherDerived>
CommaInitializer& operator,(const DenseBase<OtherDerived>& other)
{
if(other.cols()==0 || other.rows()==0)
return *this;
if (m_col==m_xpr.cols())
{
m_row+=m_currentBlockRows;
m_col = 0;
m_currentBlockRows = other.rows();
eigen_assert(m_row+m_currentBlockRows<=m_xpr.rows()
&& "Too many rows passed to comma initializer (operator<<)");
}
eigen_assert(m_col<m_xpr.cols()
&& "Too many coefficients passed to comma initializer (operator<<)");
eigen_assert(m_currentBlockRows==other.rows());
if (OtherDerived::SizeAtCompileTime != Dynamic)
m_xpr.template block<OtherDerived::RowsAtCompileTime != Dynamic ? OtherDerived::RowsAtCompileTime : 1,
OtherDerived::ColsAtCompileTime != Dynamic ? OtherDerived::ColsAtCompileTime : 1>
(m_row, m_col) = other;
else
m_xpr.block(m_row, m_col, other.rows(), other.cols()) = other;
m_col += other.cols();
return *this;
}
inline ~CommaInitializer()
{
eigen_assert((m_row+m_currentBlockRows) == m_xpr.rows()
&& m_col == m_xpr.cols()
&& "Too few coefficients passed to comma initializer (operator<<)");
}
/** \returns the built matrix once all its coefficients have been set.
* Calling finished is 100% optional. Its purpose is to write expressions
* like this:
* \code
* quaternion.fromRotationMatrix((Matrix3f() << axis0, axis1, axis2).finished());
* \endcode
*/
inline XprType& finished() { return m_xpr; }
XprType& m_xpr; // target expression
Index m_row; // current row id
Index m_col; // current col id
Index m_currentBlockRows; // current block height
};
/** \anchor MatrixBaseCommaInitRef
* Convenient operator to set the coefficients of a matrix.
*
* The coefficients must be provided in a row major order and exactly match
* the size of the matrix. Otherwise an assertion is raised.
*
* Example: \include MatrixBase_set.cpp
* Output: \verbinclude MatrixBase_set.out
*
* \sa CommaInitializer::finished(), class CommaInitializer
*/
template<typename Derived>
inline CommaInitializer<Derived> DenseBase<Derived>::operator<< (const Scalar& s)
{
return CommaInitializer<Derived>(*static_cast<Derived*>(this), s);
}
/** \sa operator<<(const Scalar&) */
template<typename Derived>
template<typename OtherDerived>
inline CommaInitializer<Derived>
DenseBase<Derived>::operator<<(const DenseBase<OtherDerived>& other)
{
return CommaInitializer<Derived>(*static_cast<Derived *>(this), other);
}
} // end namespace Eigen
#endif // EIGEN_COMMAINITIALIZER_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_BINARY_OP_H
#define EIGEN_CWISE_BINARY_OP_H
namespace Eigen {
/** \class CwiseBinaryOp
* \ingroup Core_Module
*
* \brief Generic expression where a coefficient-wise binary operator is applied to two expressions
*
* \param BinaryOp template functor implementing the operator
* \param Lhs the type of the left-hand side
* \param Rhs the type of the right-hand side
*
* This class represents an expression where a coefficient-wise binary operator is applied to two expressions.
* It is the return type of binary operators, by which we mean only those binary operators where
* both the left-hand side and the right-hand side are Eigen expressions.
* For example, the return type of matrix1+matrix2 is a CwiseBinaryOp.
*
* Most of the time, this is the only way that it is used, so you typically don't have to name
* CwiseBinaryOp types explicitly.
*
* \sa MatrixBase::binaryExpr(const MatrixBase<OtherDerived> &,const CustomBinaryOp &) const, class CwiseUnaryOp, class CwiseNullaryOp
*/
namespace internal {
template<typename BinaryOp, typename Lhs, typename Rhs>
struct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
{
// we must not inherit from traits<Lhs> since it has
// the potential to cause problems with MSVC
typedef typename remove_all<Lhs>::type Ancestor;
typedef typename traits<Ancestor>::XprKind XprKind;
enum {
RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,
ColsAtCompileTime = traits<Ancestor>::ColsAtCompileTime,
MaxRowsAtCompileTime = traits<Ancestor>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = traits<Ancestor>::MaxColsAtCompileTime
};
// even though we require Lhs and Rhs to have the same scalar type (see CwiseBinaryOp constructor),
// we still want to handle the case when the result type is different.
typedef typename result_of<
BinaryOp(
typename Lhs::Scalar,
typename Rhs::Scalar
)
>::type Scalar;
typedef typename promote_storage_type<typename traits<Lhs>::StorageKind,
typename traits<Rhs>::StorageKind>::ret StorageKind;
typedef typename promote_index_type<typename traits<Lhs>::Index,
typename traits<Rhs>::Index>::type Index;
typedef typename Lhs::Nested LhsNested;
typedef typename Rhs::Nested RhsNested;
typedef typename remove_reference<LhsNested>::type _LhsNested;
typedef typename remove_reference<RhsNested>::type _RhsNested;
enum {
LhsCoeffReadCost = _LhsNested::CoeffReadCost,
RhsCoeffReadCost = _RhsNested::CoeffReadCost,
LhsFlags = _LhsNested::Flags,
RhsFlags = _RhsNested::Flags,
SameType = is_same<typename _LhsNested::Scalar,typename _RhsNested::Scalar>::value,
StorageOrdersAgree = (int(Lhs::Flags)&RowMajorBit)==(int(Rhs::Flags)&RowMajorBit),
Flags0 = (int(LhsFlags) | int(RhsFlags)) & (
HereditaryBits
| (int(LhsFlags) & int(RhsFlags) &
( AlignedBit
| (StorageOrdersAgree ? LinearAccessBit : 0)
| (functor_traits<BinaryOp>::PacketAccess && StorageOrdersAgree && SameType ? PacketAccessBit : 0)
)
)
),
Flags = (Flags0 & ~RowMajorBit) | (LhsFlags & RowMajorBit),
CoeffReadCost = LhsCoeffReadCost + RhsCoeffReadCost + functor_traits<BinaryOp>::Cost
};
};
} // end namespace internal
// we require Lhs and Rhs to have the same scalar type. Currently there is no example of a binary functor
// that would take two operands of different types. If there were such an example, then this check should be
// moved to the BinaryOp functors, on a per-case basis. This would however require a change in the BinaryOp functors, as
// currently they take only one typename Scalar template parameter.
// It is tempting to always allow mixing different types but remember that this is often impossible in the vectorized paths.
// So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to
// add together a float matrix and a double matrix.
#define EIGEN_CHECK_BINARY_COMPATIBILIY(BINOP,LHS,RHS) \
EIGEN_STATIC_ASSERT((internal::functor_allows_mixing_real_and_complex<BINOP>::ret \
? int(internal::is_same<typename NumTraits<LHS>::Real, typename NumTraits<RHS>::Real>::value) \
: int(internal::is_same<LHS, RHS>::value)), \
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
template<typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>
class CwiseBinaryOpImpl;
template<typename BinaryOp, typename Lhs, typename Rhs>
class CwiseBinaryOp : internal::no_assignment_operator,
public CwiseBinaryOpImpl<
BinaryOp, Lhs, Rhs,
typename internal::promote_storage_type<typename internal::traits<Lhs>::StorageKind,
typename internal::traits<Rhs>::StorageKind>::ret>
{
public:
typedef typename CwiseBinaryOpImpl<
BinaryOp, Lhs, Rhs,
typename internal::promote_storage_type<typename internal::traits<Lhs>::StorageKind,
typename internal::traits<Rhs>::StorageKind>::ret>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseBinaryOp)
typedef typename internal::nested<Lhs>::type LhsNested;
typedef typename internal::nested<Rhs>::type RhsNested;
typedef typename internal::remove_reference<LhsNested>::type _LhsNested;
typedef typename internal::remove_reference<RhsNested>::type _RhsNested;
EIGEN_STRONG_INLINE CwiseBinaryOp(const Lhs& lhs, const Rhs& rhs, const BinaryOp& func = BinaryOp())
: m_lhs(lhs), m_rhs(rhs), m_functor(func)
{
EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp,typename Lhs::Scalar,typename Rhs::Scalar);
// require the sizes to match
EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs, Rhs)
eigen_assert(lhs.rows() == rhs.rows() && lhs.cols() == rhs.cols());
}
EIGEN_STRONG_INLINE Index rows() const {
// return the fixed size type if available to enable compile time optimizations
if (internal::traits<typename internal::remove_all<LhsNested>::type>::RowsAtCompileTime==Dynamic)
return m_rhs.rows();
else
return m_lhs.rows();
}
EIGEN_STRONG_INLINE Index cols() const {
// return the fixed size type if available to enable compile time optimizations
if (internal::traits<typename internal::remove_all<LhsNested>::type>::ColsAtCompileTime==Dynamic)
return m_rhs.cols();
else
return m_lhs.cols();
}
/** \returns the left hand side nested expression */
const _LhsNested& lhs() const { return m_lhs; }
/** \returns the right hand side nested expression */
const _RhsNested& rhs() const { return m_rhs; }
/** \returns the functor representing the binary operation */
const BinaryOp& functor() const { return m_functor; }
protected:
LhsNested m_lhs;
RhsNested m_rhs;
const BinaryOp m_functor;
};
template<typename BinaryOp, typename Lhs, typename Rhs>
class CwiseBinaryOpImpl<BinaryOp, Lhs, Rhs, Dense>
: public internal::dense_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type
{
typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> Derived;
public:
typedef typename internal::dense_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE( Derived )
EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
{
return derived().functor()(derived().lhs().coeff(row, col),
derived().rhs().coeff(row, col));
}
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet(Index row, Index col) const
{
return derived().functor().packetOp(derived().lhs().template packet<LoadMode>(row, col),
derived().rhs().template packet<LoadMode>(row, col));
}
EIGEN_STRONG_INLINE const Scalar coeff(Index index) const
{
return derived().functor()(derived().lhs().coeff(index),
derived().rhs().coeff(index));
}
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
{
return derived().functor().packetOp(derived().lhs().template packet<LoadMode>(index),
derived().rhs().template packet<LoadMode>(index));
}
};
/** replaces \c *this by \c *this - \a other.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived &
MatrixBase<Derived>::operator-=(const MatrixBase<OtherDerived> &other)
{
SelfCwiseBinaryOp<internal::scalar_difference_op<Scalar>, Derived, OtherDerived> tmp(derived());
tmp = other.derived();
return derived();
}
/** replaces \c *this by \c *this + \a other.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived &
MatrixBase<Derived>::operator+=(const MatrixBase<OtherDerived>& other)
{
SelfCwiseBinaryOp<internal::scalar_sum_op<Scalar>, Derived, OtherDerived> tmp(derived());
tmp = other.derived();
return derived();
}
} // end namespace Eigen
#endif // EIGEN_CWISE_BINARY_OP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_NULLARY_OP_H
#define EIGEN_CWISE_NULLARY_OP_H
namespace Eigen {
/** \class CwiseNullaryOp
* \ingroup Core_Module
*
* \brief Generic expression of a matrix where all coefficients are defined by a functor
*
* \param NullaryOp template functor implementing the operator
* \param PlainObjectType the underlying plain matrix/array type
*
* This class represents an expression of a generic nullary operator.
* It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods,
* and most of the time this is the only way it is used.
*
* However, if you want to write a function returning such an expression, you
* will need to use this class.
*
* \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr()
*/
namespace internal {
template<typename NullaryOp, typename PlainObjectType>
struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectType>
{
enum {
Flags = (traits<PlainObjectType>::Flags
& ( HereditaryBits
| (functor_has_linear_access<NullaryOp>::ret ? LinearAccessBit : 0)
| (functor_traits<NullaryOp>::PacketAccess ? PacketAccessBit : 0)))
| (functor_traits<NullaryOp>::IsRepeatable ? 0 : EvalBeforeNestingBit),
CoeffReadCost = functor_traits<NullaryOp>::Cost
};
};
}
template<typename NullaryOp, typename PlainObjectType>
class CwiseNullaryOp : internal::no_assignment_operator,
public internal::dense_xpr_base< CwiseNullaryOp<NullaryOp, PlainObjectType> >::type
{
public:
typedef typename internal::dense_xpr_base<CwiseNullaryOp>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(CwiseNullaryOp)
CwiseNullaryOp(Index rows, Index cols, const NullaryOp& func = NullaryOp())
: m_rows(rows), m_cols(cols), m_functor(func)
{
eigen_assert(rows >= 0
&& (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
&& cols >= 0
&& (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
}
EIGEN_STRONG_INLINE Index rows() const { return m_rows.value(); }
EIGEN_STRONG_INLINE Index cols() const { return m_cols.value(); }
EIGEN_STRONG_INLINE const Scalar coeff(Index rows, Index cols) const
{
return m_functor(rows, cols);
}
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet(Index row, Index col) const
{
return m_functor.packetOp(row, col);
}
EIGEN_STRONG_INLINE const Scalar coeff(Index index) const
{
return m_functor(index);
}
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
{
return m_functor.packetOp(index);
}
/** \returns the functor representing the nullary operation */
const NullaryOp& functor() const { return m_functor; }
protected:
const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
const NullaryOp m_functor;
};
/** \returns an expression of a matrix defined by a custom functor \a func
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this MatrixBase type.
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
* instead.
*
* The template parameter \a CustomNullaryOp is the type of the functor.
*
* \sa class CwiseNullaryOp
*/
template<typename Derived>
template<typename CustomNullaryOp>
EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, Derived>
DenseBase<Derived>::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func)
{
return CwiseNullaryOp<CustomNullaryOp, Derived>(rows, cols, func);
}
/** \returns an expression of a matrix defined by a custom functor \a func
*
* The parameter \a size is the size of the returned vector.
* Must be compatible with this MatrixBase type.
*
* \only_for_vectors
*
* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
* it is redundant to pass \a size as argument, so Zero() should be used
* instead.
*
* The template parameter \a CustomNullaryOp is the type of the functor.
*
* \sa class CwiseNullaryOp
*/
template<typename Derived>
template<typename CustomNullaryOp>
EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, Derived>
DenseBase<Derived>::NullaryExpr(Index size, const CustomNullaryOp& func)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, Derived>(1, size, func);
else return CwiseNullaryOp<CustomNullaryOp, Derived>(size, 1, func);
}
/** \returns an expression of a matrix defined by a custom functor \a func
*
* This variant is only for fixed-size DenseBase types. For dynamic-size types, you
* need to use the variants taking size arguments.
*
* The template parameter \a CustomNullaryOp is the type of the functor.
*
* \sa class CwiseNullaryOp
*/
template<typename Derived>
template<typename CustomNullaryOp>
EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, Derived>
DenseBase<Derived>::NullaryExpr(const CustomNullaryOp& func)
{
return CwiseNullaryOp<CustomNullaryOp, Derived>(RowsAtCompileTime, ColsAtCompileTime, func);
}
/** \returns an expression of a constant matrix of value \a value
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this DenseBase type.
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
* instead.
*
* The template parameter \a CustomNullaryOp is the type of the functor.
*
* \sa class CwiseNullaryOp
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value)
{
return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_constant_op<Scalar>(value));
}
/** \returns an expression of a constant matrix of value \a value
*
* The parameter \a size is the size of the returned vector.
* Must be compatible with this DenseBase type.
*
* \only_for_vectors
*
* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
* it is redundant to pass \a size as argument, so Zero() should be used
* instead.
*
* The template parameter \a CustomNullaryOp is the type of the functor.
*
* \sa class CwiseNullaryOp
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
DenseBase<Derived>::Constant(Index size, const Scalar& value)
{
return DenseBase<Derived>::NullaryExpr(size, internal::scalar_constant_op<Scalar>(value));
}
/** \returns an expression of a constant matrix of value \a value
*
* This variant is only for fixed-size DenseBase types. For dynamic-size types, you
* need to use the variants taking size arguments.
*
* The template parameter \a CustomNullaryOp is the type of the functor.
*
* \sa class CwiseNullaryOp
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
DenseBase<Derived>::Constant(const Scalar& value)
{
EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_constant_op<Scalar>(value));
}
/**
* \brief Sets a linearly space vector.
*
* The function generates 'size' equally spaced values in the closed interval [low,high].
* This particular version of LinSpaced() uses sequential access, i.e. vector access is
* assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization
* and yields faster code than the random access version.
*
* When size is set to 1, a vector of length 1 containing 'high' is returned.
*
* \only_for_vectors
*
* Example: \include DenseBase_LinSpaced_seq.cpp
* Output: \verbinclude DenseBase_LinSpaced_seq.out
*
* \sa setLinSpaced(Index,const Scalar&,const Scalar&), LinSpaced(Index,Scalar,Scalar), CwiseNullaryOp
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::SequentialLinSpacedReturnType
DenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,false>(low,high,size));
}
/**
* \copydoc DenseBase::LinSpaced(Sequential_t, Index, const Scalar&, const Scalar&)
* Special version for fixed size types which does not require the size parameter.
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::SequentialLinSpacedReturnType
DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,false>(low,high,Derived::SizeAtCompileTime));
}
/**
* \brief Sets a linearly space vector.
*
* The function generates 'size' equally spaced values in the closed interval [low,high].
* When size is set to 1, a vector of length 1 containing 'high' is returned.
*
* \only_for_vectors
*
* Example: \include DenseBase_LinSpaced.cpp
* Output: \verbinclude DenseBase_LinSpaced.out
*
* \sa setLinSpaced(Index,const Scalar&,const Scalar&), LinSpaced(Sequential_t,Index,const Scalar&,const Scalar&,Index), CwiseNullaryOp
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
DenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,true>(low,high,size));
}
/**
* \copydoc DenseBase::LinSpaced(Index, const Scalar&, const Scalar&)
* Special version for fixed size types which does not require the size parameter.
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
DenseBase<Derived>::LinSpaced(const Scalar& low, const Scalar& high)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,true>(low,high,Derived::SizeAtCompileTime));
}
/** \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
template<typename Derived>
bool DenseBase<Derived>::isApproxToConstant
(const Scalar& value, RealScalar prec) const
{
for(Index j = 0; j < cols(); ++j)
for(Index i = 0; i < rows(); ++i)
if(!internal::isApprox(this->coeff(i, j), value, prec))
return false;
return true;
}
/** This is just an alias for isApproxToConstant().
*
* \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
template<typename Derived>
bool DenseBase<Derived>::isConstant
(const Scalar& value, RealScalar prec) const
{
return isApproxToConstant(value, prec);
}
/** Alias for setConstant(): sets all coefficients in this expression to \a value.
*
* \sa setConstant(), Constant(), class CwiseNullaryOp
*/
template<typename Derived>
EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& value)
{
setConstant(value);
}
/** Sets all coefficients in this expression to \a value.
*
* \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& value)
{
return derived() = Constant(rows(), cols(), value);
}
/** Resizes to the given \a size, and sets all coefficients in this expression to the given \a value.
*
* \only_for_vectors
*
* Example: \include Matrix_setConstant_int.cpp
* Output: \verbinclude Matrix_setConstant_int.out
*
* \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived&
PlainObjectBase<Derived>::setConstant(Index size, const Scalar& value)
{
resize(size);
return setConstant(value);
}
/** Resizes to the given size, and sets all coefficients in this expression to the given \a value.
*
* \param rows the new number of rows
* \param cols the new number of columns
* \param value the value to which all coefficients are set
*
* Example: \include Matrix_setConstant_int_int.cpp
* Output: \verbinclude Matrix_setConstant_int_int.out
*
* \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived&
PlainObjectBase<Derived>::setConstant(Index rows, Index cols, const Scalar& value)
{
resize(rows, cols);
return setConstant(value);
}
/**
* \brief Sets a linearly space vector.
*
* The function generates 'size' equally spaced values in the closed interval [low,high].
* When size is set to 1, a vector of length 1 containing 'high' is returned.
*
* \only_for_vectors
*
* Example: \include DenseBase_setLinSpaced.cpp
* Output: \verbinclude DenseBase_setLinSpaced.out
*
* \sa CwiseNullaryOp
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index size, const Scalar& low, const Scalar& high)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return derived() = Derived::NullaryExpr(size, internal::linspaced_op<Scalar,false>(low,high,size));
}
/**
* \brief Sets a linearly space vector.
*
* The function fill *this with equally spaced values in the closed interval [low,high].
* When size is set to 1, a vector of length 1 containing 'high' is returned.
*
* \only_for_vectors
*
* \sa setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(const Scalar& low, const Scalar& high)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return setLinSpaced(size(), low, high);
}
// zero:
/** \returns an expression of a zero matrix.
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this MatrixBase type.
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
* instead.
*
* Example: \include MatrixBase_zero_int_int.cpp
* Output: \verbinclude MatrixBase_zero_int_int.out
*
* \sa Zero(), Zero(Index)
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
DenseBase<Derived>::Zero(Index rows, Index cols)
{
return Constant(rows, cols, Scalar(0));
}
/** \returns an expression of a zero vector.
*
* The parameter \a size is the size of the returned vector.
* Must be compatible with this MatrixBase type.
*
* \only_for_vectors
*
* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
* it is redundant to pass \a size as argument, so Zero() should be used
* instead.
*
* Example: \include MatrixBase_zero_int.cpp
* Output: \verbinclude MatrixBase_zero_int.out
*
* \sa Zero(), Zero(Index,Index)
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
DenseBase<Derived>::Zero(Index size)
{
return Constant(size, Scalar(0));
}
/** \returns an expression of a fixed-size zero matrix or vector.
*
* This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
* need to use the variants taking size arguments.
*
* Example: \include MatrixBase_zero.cpp
* Output: \verbinclude MatrixBase_zero.out
*
* \sa Zero(Index), Zero(Index,Index)
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
DenseBase<Derived>::Zero()
{
return Constant(Scalar(0));
}
/** \returns true if *this is approximately equal to the zero matrix,
* within the precision given by \a prec.
*
* Example: \include MatrixBase_isZero.cpp
* Output: \verbinclude MatrixBase_isZero.out
*
* \sa class CwiseNullaryOp, Zero()
*/
template<typename Derived>
bool DenseBase<Derived>::isZero(RealScalar prec) const
{
for(Index j = 0; j < cols(); ++j)
for(Index i = 0; i < rows(); ++i)
if(!internal::isMuchSmallerThan(this->coeff(i, j), static_cast<Scalar>(1), prec))
return false;
return true;
}
/** Sets all coefficients in this expression to zero.
*
* Example: \include MatrixBase_setZero.cpp
* Output: \verbinclude MatrixBase_setZero.out
*
* \sa class CwiseNullaryOp, Zero()
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero()
{
return setConstant(Scalar(0));
}
/** Resizes to the given \a size, and sets all coefficients in this expression to zero.
*
* \only_for_vectors
*
* Example: \include Matrix_setZero_int.cpp
* Output: \verbinclude Matrix_setZero_int.out
*
* \sa DenseBase::setZero(), setZero(Index,Index), class CwiseNullaryOp, DenseBase::Zero()
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived&
PlainObjectBase<Derived>::setZero(Index size)
{
resize(size);
return setConstant(Scalar(0));
}
/** Resizes to the given size, and sets all coefficients in this expression to zero.
*
* \param rows the new number of rows
* \param cols the new number of columns
*
* Example: \include Matrix_setZero_int_int.cpp
* Output: \verbinclude Matrix_setZero_int_int.out
*
* \sa DenseBase::setZero(), setZero(Index), class CwiseNullaryOp, DenseBase::Zero()
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived&
PlainObjectBase<Derived>::setZero(Index rows, Index cols)
{
resize(rows, cols);
return setConstant(Scalar(0));
}
// ones:
/** \returns an expression of a matrix where all coefficients equal one.
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this MatrixBase type.
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so Ones() should be used
* instead.
*
* Example: \include MatrixBase_ones_int_int.cpp
* Output: \verbinclude MatrixBase_ones_int_int.out
*
* \sa Ones(), Ones(Index), isOnes(), class Ones
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
DenseBase<Derived>::Ones(Index rows, Index cols)
{
return Constant(rows, cols, Scalar(1));
}
/** \returns an expression of a vector where all coefficients equal one.
*
* The parameter \a size is the size of the returned vector.
* Must be compatible with this MatrixBase type.
*
* \only_for_vectors
*
* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
* it is redundant to pass \a size as argument, so Ones() should be used
* instead.
*
* Example: \include MatrixBase_ones_int.cpp
* Output: \verbinclude MatrixBase_ones_int.out
*
* \sa Ones(), Ones(Index,Index), isOnes(), class Ones
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
DenseBase<Derived>::Ones(Index size)
{
return Constant(size, Scalar(1));
}
/** \returns an expression of a fixed-size matrix or vector where all coefficients equal one.
*
* This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
* need to use the variants taking size arguments.
*
* Example: \include MatrixBase_ones.cpp
* Output: \verbinclude MatrixBase_ones.out
*
* \sa Ones(Index), Ones(Index,Index), isOnes(), class Ones
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
DenseBase<Derived>::Ones()
{
return Constant(Scalar(1));
}
/** \returns true if *this is approximately equal to the matrix where all coefficients
* are equal to 1, within the precision given by \a prec.
*
* Example: \include MatrixBase_isOnes.cpp
* Output: \verbinclude MatrixBase_isOnes.out
*
* \sa class CwiseNullaryOp, Ones()
*/
template<typename Derived>
bool DenseBase<Derived>::isOnes
(RealScalar prec) const
{
return isApproxToConstant(Scalar(1), prec);
}
/** Sets all coefficients in this expression to one.
*
* Example: \include MatrixBase_setOnes.cpp
* Output: \verbinclude MatrixBase_setOnes.out
*
* \sa class CwiseNullaryOp, Ones()
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setOnes()
{
return setConstant(Scalar(1));
}
/** Resizes to the given \a size, and sets all coefficients in this expression to one.
*
* \only_for_vectors
*
* Example: \include Matrix_setOnes_int.cpp
* Output: \verbinclude Matrix_setOnes_int.out
*
* \sa MatrixBase::setOnes(), setOnes(Index,Index), class CwiseNullaryOp, MatrixBase::Ones()
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived&
PlainObjectBase<Derived>::setOnes(Index size)
{
resize(size);
return setConstant(Scalar(1));
}
/** Resizes to the given size, and sets all coefficients in this expression to one.
*
* \param rows the new number of rows
* \param cols the new number of columns
*
* Example: \include Matrix_setOnes_int_int.cpp
* Output: \verbinclude Matrix_setOnes_int_int.out
*
* \sa MatrixBase::setOnes(), setOnes(Index), class CwiseNullaryOp, MatrixBase::Ones()
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived&
PlainObjectBase<Derived>::setOnes(Index rows, Index cols)
{
resize(rows, cols);
return setConstant(Scalar(1));
}
// Identity:
/** \returns an expression of the identity matrix (not necessarily square).
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this MatrixBase type.
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so Identity() should be used
* instead.
*
* Example: \include MatrixBase_identity_int_int.cpp
* Output: \verbinclude MatrixBase_identity_int_int.out
*
* \sa Identity(), setIdentity(), isIdentity()
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
MatrixBase<Derived>::Identity(Index rows, Index cols)
{
return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_identity_op<Scalar>());
}
/** \returns an expression of the identity matrix (not necessarily square).
*
* This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
* need to use the variant taking size arguments.
*
* Example: \include MatrixBase_identity.cpp
* Output: \verbinclude MatrixBase_identity.out
*
* \sa Identity(Index,Index), setIdentity(), isIdentity()
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
MatrixBase<Derived>::Identity()
{
EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
return MatrixBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_identity_op<Scalar>());
}
/** \returns true if *this is approximately equal to the identity matrix
* (not necessarily square),
* within the precision given by \a prec.
*
* Example: \include MatrixBase_isIdentity.cpp
* Output: \verbinclude MatrixBase_isIdentity.out
*
* \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()
*/
template<typename Derived>
bool MatrixBase<Derived>::isIdentity
(RealScalar prec) const
{
for(Index j = 0; j < cols(); ++j)
{
for(Index i = 0; i < rows(); ++i)
{
if(i == j)
{
if(!internal::isApprox(this->coeff(i, j), static_cast<Scalar>(1), prec))
return false;
}
else
{
if(!internal::isMuchSmallerThan(this->coeff(i, j), static_cast<RealScalar>(1), prec))
return false;
}
}
}
return true;
}
namespace internal {
template<typename Derived, bool Big = (Derived::SizeAtCompileTime>=16)>
struct setIdentity_impl
{
static EIGEN_STRONG_INLINE Derived& run(Derived& m)
{
return m = Derived::Identity(m.rows(), m.cols());
}
};
template<typename Derived>
struct setIdentity_impl<Derived, true>
{
typedef typename Derived::Index Index;
static EIGEN_STRONG_INLINE Derived& run(Derived& m)
{
m.setZero();
const Index size = (std::min)(m.rows(), m.cols());
for(Index i = 0; i < size; ++i) m.coeffRef(i,i) = typename Derived::Scalar(1);
return m;
}
};
} // end namespace internal
/** Writes the identity expression (not necessarily square) into *this.
*
* Example: \include MatrixBase_setIdentity.cpp
* Output: \verbinclude MatrixBase_setIdentity.out
*
* \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity()
{
return internal::setIdentity_impl<Derived>::run(derived());
}
/** \brief Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
*
* \param rows the new number of rows
* \param cols the new number of columns
*
* Example: \include Matrix_setIdentity_int_int.cpp
* Output: \verbinclude Matrix_setIdentity_int_int.out
*
* \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(Index rows, Index cols)
{
derived().resize(rows, cols);
return setIdentity();
}
/** \returns an expression of the i-th unit (basis) vector.
*
* \only_for_vectors
*
* \sa MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index size, Index i)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return BasisReturnType(SquareMatrixType::Identity(size,size), i);
}
/** \returns an expression of the i-th unit (basis) vector.
*
* \only_for_vectors
*
* This variant is for fixed-size vector only.
*
* \sa MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index i)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return BasisReturnType(SquareMatrixType::Identity(),i);
}
/** \returns an expression of the X axis unit vector (1{,0}^*)
*
* \only_for_vectors
*
* \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX()
{ return Derived::Unit(0); }
/** \returns an expression of the Y axis unit vector (0,1{,0}^*)
*
* \only_for_vectors
*
* \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY()
{ return Derived::Unit(1); }
/** \returns an expression of the Z axis unit vector (0,0,1{,0}^*)
*
* \only_for_vectors
*
* \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ()
{ return Derived::Unit(2); }
/** \returns an expression of the W axis unit vector (0,0,0,1)
*
* \only_for_vectors
*
* \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
*/
template<typename Derived>
EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW()
{ return Derived::Unit(3); }
} // end namespace Eigen
#endif // EIGEN_CWISE_NULLARY_OP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_UNARY_OP_H
#define EIGEN_CWISE_UNARY_OP_H
namespace Eigen {
/** \class CwiseUnaryOp
* \ingroup Core_Module
*
* \brief Generic expression where a coefficient-wise unary operator is applied to an expression
*
* \param UnaryOp template functor implementing the operator
* \param XprType the type of the expression to which we are applying the unary operator
*
* This class represents an expression where a unary operator is applied to an expression.
* It is the return type of all operations taking exactly 1 input expression, regardless of the
* presence of other inputs such as scalars. For example, the operator* in the expression 3*matrix
* is considered unary, because only the right-hand side is an expression, and its
* return type is a specialization of CwiseUnaryOp.
*
* Most of the time, this is the only way that it is used, so you typically don't have to name
* CwiseUnaryOp types explicitly.
*
* \sa MatrixBase::unaryExpr(const CustomUnaryOp &) const, class CwiseBinaryOp, class CwiseNullaryOp
*/
namespace internal {
template<typename UnaryOp, typename XprType>
struct traits<CwiseUnaryOp<UnaryOp, XprType> >
: traits<XprType>
{
typedef typename result_of<
UnaryOp(typename XprType::Scalar)
>::type Scalar;
typedef typename XprType::Nested XprTypeNested;
typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;
enum {
Flags = _XprTypeNested::Flags & (
HereditaryBits | LinearAccessBit | AlignedBit
| (functor_traits<UnaryOp>::PacketAccess ? PacketAccessBit : 0)),
CoeffReadCost = _XprTypeNested::CoeffReadCost + functor_traits<UnaryOp>::Cost
};
};
}
template<typename UnaryOp, typename XprType, typename StorageKind>
class CwiseUnaryOpImpl;
template<typename UnaryOp, typename XprType>
class CwiseUnaryOp : internal::no_assignment_operator,
public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal::traits<XprType>::StorageKind>
{
public:
typedef typename CwiseUnaryOpImpl<UnaryOp, XprType,typename internal::traits<XprType>::StorageKind>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryOp)
inline CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())
: m_xpr(xpr), m_functor(func) {}
EIGEN_STRONG_INLINE Index rows() const { return m_xpr.rows(); }
EIGEN_STRONG_INLINE Index cols() const { return m_xpr.cols(); }
/** \returns the functor representing the unary operation */
const UnaryOp& functor() const { return m_functor; }
/** \returns the nested expression */
const typename internal::remove_all<typename XprType::Nested>::type&
nestedExpression() const { return m_xpr; }
/** \returns the nested expression */
typename internal::remove_all<typename XprType::Nested>::type&
nestedExpression() { return m_xpr.const_cast_derived(); }
protected:
typename XprType::Nested m_xpr;
const UnaryOp m_functor;
};
// This is the generic implementation for dense storage.
// It can be used for any expression types implementing the dense concept.
template<typename UnaryOp, typename XprType>
class CwiseUnaryOpImpl<UnaryOp,XprType,Dense>
: public internal::dense_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type
{
public:
typedef CwiseUnaryOp<UnaryOp, XprType> Derived;
typedef typename internal::dense_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
{
return derived().functor()(derived().nestedExpression().coeff(row, col));
}
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet(Index row, Index col) const
{
return derived().functor().packetOp(derived().nestedExpression().template packet<LoadMode>(row, col));
}
EIGEN_STRONG_INLINE const Scalar coeff(Index index) const
{
return derived().functor()(derived().nestedExpression().coeff(index));
}
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
{
return derived().functor().packetOp(derived().nestedExpression().template packet<LoadMode>(index));
}
};
} // end namespace Eigen
#endif // EIGEN_CWISE_UNARY_OP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_UNARY_VIEW_H
#define EIGEN_CWISE_UNARY_VIEW_H
namespace Eigen {
/** \class CwiseUnaryView
* \ingroup Core_Module
*
* \brief Generic lvalue expression of a coefficient-wise unary operator of a matrix or a vector
*
* \param ViewOp template functor implementing the view
* \param MatrixType the type of the matrix we are applying the unary operator
*
* This class represents a lvalue expression of a generic unary view operator of a matrix or a vector.
* It is the return type of real() and imag(), and most of the time this is the only way it is used.
*
* \sa MatrixBase::unaryViewExpr(const CustomUnaryOp &) const, class CwiseUnaryOp
*/
namespace internal {
template<typename ViewOp, typename MatrixType>
struct traits<CwiseUnaryView<ViewOp, MatrixType> >
: traits<MatrixType>
{
typedef typename result_of<
ViewOp(typename traits<MatrixType>::Scalar)
>::type Scalar;
typedef typename MatrixType::Nested MatrixTypeNested;
typedef typename remove_all<MatrixTypeNested>::type _MatrixTypeNested;
enum {
Flags = (traits<_MatrixTypeNested>::Flags & (HereditaryBits | LvalueBit | LinearAccessBit | DirectAccessBit)),
CoeffReadCost = traits<_MatrixTypeNested>::CoeffReadCost + functor_traits<ViewOp>::Cost,
MatrixTypeInnerStride = inner_stride_at_compile_time<MatrixType>::ret,
// need to cast the sizeof's from size_t to int explicitly, otherwise:
// "error: no integral type can represent all of the enumerator values
InnerStrideAtCompileTime = MatrixTypeInnerStride == Dynamic
? int(Dynamic)
: int(MatrixTypeInnerStride) * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar)),
OuterStrideAtCompileTime = outer_stride_at_compile_time<MatrixType>::ret == Dynamic
? int(Dynamic)
: outer_stride_at_compile_time<MatrixType>::ret * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar))
};
};
}
template<typename ViewOp, typename MatrixType, typename StorageKind>
class CwiseUnaryViewImpl;
template<typename ViewOp, typename MatrixType>
class CwiseUnaryView : internal::no_assignment_operator,
public CwiseUnaryViewImpl<ViewOp, MatrixType, typename internal::traits<MatrixType>::StorageKind>
{
public:
typedef typename CwiseUnaryViewImpl<ViewOp, MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryView)
inline CwiseUnaryView(const MatrixType& mat, const ViewOp& func = ViewOp())
: m_matrix(mat), m_functor(func) {}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryView)
EIGEN_STRONG_INLINE Index rows() const { return m_matrix.rows(); }
EIGEN_STRONG_INLINE Index cols() const { return m_matrix.cols(); }
/** \returns the functor representing unary operation */
const ViewOp& functor() const { return m_functor; }
/** \returns the nested expression */
const typename internal::remove_all<typename MatrixType::Nested>::type&
nestedExpression() const { return m_matrix; }
/** \returns the nested expression */
typename internal::remove_all<typename MatrixType::Nested>::type&
nestedExpression() { return m_matrix.const_cast_derived(); }
protected:
// FIXME changed from MatrixType::Nested because of a weird compilation error with sun CC
typename internal::nested<MatrixType>::type m_matrix;
ViewOp m_functor;
};
template<typename ViewOp, typename MatrixType>
class CwiseUnaryViewImpl<ViewOp,MatrixType,Dense>
: public internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type
{
public:
typedef CwiseUnaryView<ViewOp, MatrixType> Derived;
typedef typename internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
inline Index innerStride() const
{
return derived().nestedExpression().innerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);
}
inline Index outerStride() const
{
return derived().nestedExpression().outerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);
}
EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const
{
return derived().functor()(derived().nestedExpression().coeff(row, col));
}
EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
{
return derived().functor()(derived().nestedExpression().coeff(index));
}
EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)
{
return derived().functor()(const_cast_derived().nestedExpression().coeffRef(row, col));
}
EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)
{
return derived().functor()(const_cast_derived().nestedExpression().coeffRef(index));
}
};
} // end namespace Eigen
#endif // EIGEN_CWISE_UNARY_VIEW_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DENSEBASE_H
#define EIGEN_DENSEBASE_H
namespace Eigen {
/** \class DenseBase
* \ingroup Core_Module
*
* \brief Base class for all dense matrices, vectors, and arrays
*
* This class is the base that is inherited by all dense objects (matrix, vector, arrays,
* and related expression types). The common Eigen API for dense objects is contained in this class.
*
* \tparam Derived is the derived type, e.g., a matrix type or an expression.
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_DENSEBASE_PLUGIN.
*
* \sa \ref TopicClassHierarchy
*/
template<typename Derived> class DenseBase
#ifndef EIGEN_PARSED_BY_DOXYGEN
: public internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
typename NumTraits<typename internal::traits<Derived>::Scalar>::Real>
#else
: public DenseCoeffsBase<Derived>
#endif // not EIGEN_PARSED_BY_DOXYGEN
{
public:
using internal::special_scalar_op_base<Derived,typename internal::traits<Derived>::Scalar,
typename NumTraits<typename internal::traits<Derived>::Scalar>::Real>::operator*;
class InnerIterator;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
/** \brief The type of indices
* \details To change this, \c \#define the preprocessor symbol \c EIGEN_DEFAULT_DENSE_INDEX_TYPE.
* \sa \ref TopicPreprocessorDirectives.
*/
typedef typename internal::traits<Derived>::Index Index;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef DenseCoeffsBase<Derived> Base;
using Base::derived;
using Base::const_cast_derived;
using Base::rows;
using Base::cols;
using Base::size;
using Base::rowIndexByOuterInner;
using Base::colIndexByOuterInner;
using Base::coeff;
using Base::coeffByOuterInner;
using Base::packet;
using Base::packetByOuterInner;
using Base::writePacket;
using Base::writePacketByOuterInner;
using Base::coeffRef;
using Base::coeffRefByOuterInner;
using Base::copyCoeff;
using Base::copyCoeffByOuterInner;
using Base::copyPacket;
using Base::copyPacketByOuterInner;
using Base::operator();
using Base::operator[];
using Base::x;
using Base::y;
using Base::z;
using Base::w;
using Base::stride;
using Base::innerStride;
using Base::outerStride;
using Base::rowStride;
using Base::colStride;
typedef typename Base::CoeffReturnType CoeffReturnType;
enum {
RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
/**< The number of rows at compile-time. This is just a copy of the value provided
* by the \a Derived type. If a value is not known at compile-time,
* it is set to the \a Dynamic constant.
* \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
/**< The number of columns at compile-time. This is just a copy of the value provided
* by the \a Derived type. If a value is not known at compile-time,
* it is set to the \a Dynamic constant.
* \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,
internal::traits<Derived>::ColsAtCompileTime>::ret),
/**< This is equal to the number of coefficients, i.e. the number of
* rows times the number of columns, or to \a Dynamic if this is not
* known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
/**< This value is equal to the maximum possible number of rows that this expression
* might have. If this expression might have an arbitrarily high number of rows,
* this value is set to \a Dynamic.
*
* This value is useful to know when evaluating an expression, in order to determine
* whether it is possible to avoid doing a dynamic memory allocation.
*
* \sa RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime
*/
MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
/**< This value is equal to the maximum possible number of columns that this expression
* might have. If this expression might have an arbitrarily high number of columns,
* this value is set to \a Dynamic.
*
* This value is useful to know when evaluating an expression, in order to determine
* whether it is possible to avoid doing a dynamic memory allocation.
*
* \sa ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
*/
MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,
internal::traits<Derived>::MaxColsAtCompileTime>::ret),
/**< This value is equal to the maximum possible number of coefficients that this expression
* might have. If this expression might have an arbitrarily high number of coefficients,
* this value is set to \a Dynamic.
*
* This value is useful to know when evaluating an expression, in order to determine
* whether it is possible to avoid doing a dynamic memory allocation.
*
* \sa SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
*/
IsVectorAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime == 1
|| internal::traits<Derived>::MaxColsAtCompileTime == 1,
/**< This is set to true if either the number of rows or the number of
* columns is known at compile-time to be equal to 1. Indeed, in that case,
* we are dealing with a column-vector (if there is only one column) or with
* a row-vector (if there is only one row). */
Flags = internal::traits<Derived>::Flags,
/**< This stores expression \ref flags flags which may or may not be inherited by new expressions
* constructed from this one. See the \ref flags "list of flags".
*/
IsRowMajor = int(Flags) & RowMajorBit, /**< True if this expression has row-major storage order. */
InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)
: int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
/**< This is a rough measure of how expensive it is to read one coefficient from
* this expression.
*/
InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret,
OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret
};
enum { ThisConstantIsPrivateInPlainObjectBase };
/** \returns the number of nonzero coefficients which is in practice the number
* of stored coefficients. */
inline Index nonZeros() const { return size(); }
/** \returns true if either the number of rows or the number of columns is equal to 1.
* In other words, this function returns
* \code rows()==1 || cols()==1 \endcode
* \sa rows(), cols(), IsVectorAtCompileTime. */
/** \returns the outer size.
*
* \note For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension
* with respect to the \ref TopicStorageOrders "storage order", i.e., the number of columns for a
* column-major matrix, and the number of rows for a row-major matrix. */
Index outerSize() const
{
return IsVectorAtCompileTime ? 1
: int(IsRowMajor) ? this->rows() : this->cols();
}
/** \returns the inner size.
*
* \note For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension
* with respect to the \ref TopicStorageOrders "storage order", i.e., the number of rows for a
* column-major matrix, and the number of columns for a row-major matrix. */
Index innerSize() const
{
return IsVectorAtCompileTime ? this->size()
: int(IsRowMajor) ? this->cols() : this->rows();
}
/** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are
* Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does
* nothing else.
*/
void resize(Index size)
{
EIGEN_ONLY_USED_FOR_DEBUG(size);
eigen_assert(size == this->size()
&& "DenseBase::resize() does not actually allow to resize.");
}
/** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are
* Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does
* nothing else.
*/
void resize(Index rows, Index cols)
{
EIGEN_ONLY_USED_FOR_DEBUG(rows);
EIGEN_ONLY_USED_FOR_DEBUG(cols);
eigen_assert(rows == this->rows() && cols == this->cols()
&& "DenseBase::resize() does not actually allow to resize.");
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal Represents a matrix with all coefficients equal to one another*/
typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Derived> ConstantReturnType;
/** \internal Represents a vector with linearly spaced coefficients that allows sequential access only. */
typedef CwiseNullaryOp<internal::linspaced_op<Scalar,false>,Derived> SequentialLinSpacedReturnType;
/** \internal Represents a vector with linearly spaced coefficients that allows random access. */
typedef CwiseNullaryOp<internal::linspaced_op<Scalar,true>,Derived> RandomAccessLinSpacedReturnType;
/** \internal the return type of MatrixBase::eigenvalues() */
typedef Matrix<typename NumTraits<typename internal::traits<Derived>::Scalar>::Real, internal::traits<Derived>::ColsAtCompileTime, 1> EigenvaluesReturnType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
/** Copies \a other into *this. \returns a reference to *this. */
template<typename OtherDerived>
Derived& operator=(const DenseBase<OtherDerived>& other);
/** Special case of the template operator=, in order to prevent the compiler
* from generating a default operator= (issue hit with g++ 4.1)
*/
Derived& operator=(const DenseBase& other);
template<typename OtherDerived>
Derived& operator=(const EigenBase<OtherDerived> &other);
template<typename OtherDerived>
Derived& operator+=(const EigenBase<OtherDerived> &other);
template<typename OtherDerived>
Derived& operator-=(const EigenBase<OtherDerived> &other);
template<typename OtherDerived>
Derived& operator=(const ReturnByValue<OtherDerived>& func);
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** Copies \a other into *this without evaluating other. \returns a reference to *this. */
template<typename OtherDerived>
Derived& lazyAssign(const DenseBase<OtherDerived>& other);
#endif // not EIGEN_PARSED_BY_DOXYGEN
CommaInitializer<Derived> operator<< (const Scalar& s);
template<unsigned int Added,unsigned int Removed>
const Flagged<Derived, Added, Removed> flagged() const;
template<typename OtherDerived>
CommaInitializer<Derived> operator<< (const DenseBase<OtherDerived>& other);
Eigen::Transpose<Derived> transpose();
typedef const Transpose<const Derived> ConstTransposeReturnType;
ConstTransposeReturnType transpose() const;
void transposeInPlace();
#ifndef EIGEN_NO_DEBUG
protected:
template<typename OtherDerived>
void checkTransposeAliasing(const OtherDerived& other) const;
public:
#endif
typedef VectorBlock<Derived> SegmentReturnType;
typedef const VectorBlock<const Derived> ConstSegmentReturnType;
template<int Size> struct FixedSegmentReturnType { typedef VectorBlock<Derived, Size> Type; };
template<int Size> struct ConstFixedSegmentReturnType { typedef const VectorBlock<const Derived, Size> Type; };
// Note: The "DenseBase::" prefixes are added to help MSVC9 to match these declarations with the later implementations.
SegmentReturnType segment(Index start, Index size);
typename DenseBase::ConstSegmentReturnType segment(Index start, Index size) const;
SegmentReturnType head(Index size);
typename DenseBase::ConstSegmentReturnType head(Index size) const;
SegmentReturnType tail(Index size);
typename DenseBase::ConstSegmentReturnType tail(Index size) const;
template<int Size> typename FixedSegmentReturnType<Size>::Type head();
template<int Size> typename ConstFixedSegmentReturnType<Size>::Type head() const;
template<int Size> typename FixedSegmentReturnType<Size>::Type tail();
template<int Size> typename ConstFixedSegmentReturnType<Size>::Type tail() const;
template<int Size> typename FixedSegmentReturnType<Size>::Type segment(Index start);
template<int Size> typename ConstFixedSegmentReturnType<Size>::Type segment(Index start) const;
static const ConstantReturnType
Constant(Index rows, Index cols, const Scalar& value);
static const ConstantReturnType
Constant(Index size, const Scalar& value);
static const ConstantReturnType
Constant(const Scalar& value);
static const SequentialLinSpacedReturnType
LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high);
static const RandomAccessLinSpacedReturnType
LinSpaced(Index size, const Scalar& low, const Scalar& high);
static const SequentialLinSpacedReturnType
LinSpaced(Sequential_t, const Scalar& low, const Scalar& high);
static const RandomAccessLinSpacedReturnType
LinSpaced(const Scalar& low, const Scalar& high);
template<typename CustomNullaryOp>
static const CwiseNullaryOp<CustomNullaryOp, Derived>
NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func);
template<typename CustomNullaryOp>
static const CwiseNullaryOp<CustomNullaryOp, Derived>
NullaryExpr(Index size, const CustomNullaryOp& func);
template<typename CustomNullaryOp>
static const CwiseNullaryOp<CustomNullaryOp, Derived>
NullaryExpr(const CustomNullaryOp& func);
static const ConstantReturnType Zero(Index rows, Index cols);
static const ConstantReturnType Zero(Index size);
static const ConstantReturnType Zero();
static const ConstantReturnType Ones(Index rows, Index cols);
static const ConstantReturnType Ones(Index size);
static const ConstantReturnType Ones();
void fill(const Scalar& value);
Derived& setConstant(const Scalar& value);
Derived& setLinSpaced(Index size, const Scalar& low, const Scalar& high);
Derived& setLinSpaced(const Scalar& low, const Scalar& high);
Derived& setZero();
Derived& setOnes();
Derived& setRandom();
template<typename OtherDerived>
bool isApprox(const DenseBase<OtherDerived>& other,
RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
bool isMuchSmallerThan(const RealScalar& other,
RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
template<typename OtherDerived>
bool isMuchSmallerThan(const DenseBase<OtherDerived>& other,
RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
bool isApproxToConstant(const Scalar& value, RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
bool isConstant(const Scalar& value, RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
bool isZero(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
bool isOnes(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
inline Derived& operator*=(const Scalar& other);
inline Derived& operator/=(const Scalar& other);
typedef typename internal::add_const_on_value_type<typename internal::eval<Derived>::type>::type EvalReturnType;
/** \returns the matrix or vector obtained by evaluating this expression.
*
* Notice that in the case of a plain matrix or vector (not an expression) this function just returns
* a const reference, in order to avoid a useless copy.
*/
EIGEN_STRONG_INLINE EvalReturnType eval() const
{
// Even though MSVC does not honor strong inlining when the return type
// is a dynamic matrix, we desperately need strong inlining for fixed
// size types on MSVC.
return typename internal::eval<Derived>::type(derived());
}
/** swaps *this with the expression \a other.
*
*/
template<typename OtherDerived>
void swap(const DenseBase<OtherDerived>& other,
int = OtherDerived::ThisConstantIsPrivateInPlainObjectBase)
{
SwapWrapper<Derived>(derived()).lazyAssign(other.derived());
}
/** swaps *this with the matrix or array \a other.
*
*/
template<typename OtherDerived>
void swap(PlainObjectBase<OtherDerived>& other)
{
SwapWrapper<Derived>(derived()).lazyAssign(other.derived());
}
inline const NestByValue<Derived> nestByValue() const;
inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
inline ForceAlignedAccess<Derived> forceAlignedAccess();
template<bool Enable> inline const typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf() const;
template<bool Enable> inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf();
Scalar sum() const;
Scalar mean() const;
Scalar trace() const;
Scalar prod() const;
typename internal::traits<Derived>::Scalar minCoeff() const;
typename internal::traits<Derived>::Scalar maxCoeff() const;
template<typename IndexType>
typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const;
template<typename IndexType>
typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const;
template<typename IndexType>
typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const;
template<typename IndexType>
typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const;
template<typename BinaryOp>
typename internal::result_of<BinaryOp(typename internal::traits<Derived>::Scalar)>::type
redux(const BinaryOp& func) const;
template<typename Visitor>
void visit(Visitor& func) const;
inline const WithFormat<Derived> format(const IOFormat& fmt) const;
/** \returns the unique coefficient of a 1x1 expression */
CoeffReturnType value() const
{
EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
eigen_assert(this->rows() == 1 && this->cols() == 1);
return derived().coeff(0,0);
}
/////////// Array module ///////////
bool all(void) const;
bool any(void) const;
Index count() const;
typedef VectorwiseOp<Derived, Horizontal> RowwiseReturnType;
typedef const VectorwiseOp<const Derived, Horizontal> ConstRowwiseReturnType;
typedef VectorwiseOp<Derived, Vertical> ColwiseReturnType;
typedef const VectorwiseOp<const Derived, Vertical> ConstColwiseReturnType;
ConstRowwiseReturnType rowwise() const;
RowwiseReturnType rowwise();
ConstColwiseReturnType colwise() const;
ColwiseReturnType colwise();
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Derived> Random(Index rows, Index cols);
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Derived> Random(Index size);
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Derived> Random();
template<typename ThenDerived,typename ElseDerived>
const Select<Derived,ThenDerived,ElseDerived>
select(const DenseBase<ThenDerived>& thenMatrix,
const DenseBase<ElseDerived>& elseMatrix) const;
template<typename ThenDerived>
inline const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>
select(const DenseBase<ThenDerived>& thenMatrix, typename ThenDerived::Scalar elseScalar) const;
template<typename ElseDerived>
inline const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >
select(typename ElseDerived::Scalar thenScalar, const DenseBase<ElseDerived>& elseMatrix) const;
template<int p> RealScalar lpNorm() const;
template<int RowFactor, int ColFactor>
const Replicate<Derived,RowFactor,ColFactor> replicate() const;
const Replicate<Derived,Dynamic,Dynamic> replicate(Index rowFacor,Index colFactor) const;
typedef Reverse<Derived, BothDirections> ReverseReturnType;
typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType;
ReverseReturnType reverse();
ConstReverseReturnType reverse() const;
void reverseInPlace();
#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::DenseBase
# include "../plugins/BlockMethods.h"
# ifdef EIGEN_DENSEBASE_PLUGIN
# include EIGEN_DENSEBASE_PLUGIN
# endif
#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
#ifdef EIGEN2_SUPPORT
Block<Derived> corner(CornerType type, Index cRows, Index cCols);
const Block<Derived> corner(CornerType type, Index cRows, Index cCols) const;
template<int CRows, int CCols>
Block<Derived, CRows, CCols> corner(CornerType type);
template<int CRows, int CCols>
const Block<Derived, CRows, CCols> corner(CornerType type) const;
#endif // EIGEN2_SUPPORT
// disable the use of evalTo for dense objects with a nice compilation error
template<typename Dest> inline void evalTo(Dest& ) const
{
EIGEN_STATIC_ASSERT((internal::is_same<Dest,void>::value),THE_EVAL_EVALTO_FUNCTION_SHOULD_NEVER_BE_CALLED_FOR_DENSE_OBJECTS);
}
protected:
/** Default constructor. Do nothing. */
DenseBase()
{
/* Just checks for self-consistency of the flags.
* Only do it when debugging Eigen, as this borders on paranoiac and could slow compilation down
*/
#ifdef EIGEN_INTERNAL_DEBUGGING
EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, int(IsRowMajor))
&& EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, int(!IsRowMajor))),
INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION)
#endif
}
private:
explicit DenseBase(int);
DenseBase(int,int);
template<typename OtherDerived> explicit DenseBase(const DenseBase<OtherDerived>&);
};
} // end namespace Eigen
#endif // EIGEN_DENSEBASE_H

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@ -0,0 +1,754 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DENSECOEFFSBASE_H
#define EIGEN_DENSECOEFFSBASE_H
namespace Eigen {
namespace internal {
template<typename T> struct add_const_on_value_type_if_arithmetic
{
typedef typename conditional<is_arithmetic<T>::value, T, typename add_const_on_value_type<T>::type>::type type;
};
}
/** \brief Base class providing read-only coefficient access to matrices and arrays.
* \ingroup Core_Module
* \tparam Derived Type of the derived class
* \tparam #ReadOnlyAccessors Constant indicating read-only access
*
* This class defines the \c operator() \c const function and friends, which can be used to read specific
* entries of a matrix or array.
*
* \sa DenseCoeffsBase<Derived, WriteAccessors>, DenseCoeffsBase<Derived, DirectAccessors>,
* \ref TopicClassHierarchy
*/
template<typename Derived>
class DenseCoeffsBase<Derived,ReadOnlyAccessors> : public EigenBase<Derived>
{
public:
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Index Index;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
// Explanation for this CoeffReturnType typedef.
// - This is the return type of the coeff() method.
// - The LvalueBit means exactly that we can offer a coeffRef() method, which means exactly that we can get references
// to coeffs, which means exactly that we can have coeff() return a const reference (as opposed to returning a value).
// - The is_artihmetic check is required since "const int", "const double", etc. will cause warnings on some systems
// while the declaration of "const T", where T is a non arithmetic type does not. Always returning "const Scalar&" is
// not possible, since the underlying expressions might not offer a valid address the reference could be referring to.
typedef typename internal::conditional<bool(internal::traits<Derived>::Flags&LvalueBit),
const Scalar&,
typename internal::conditional<internal::is_arithmetic<Scalar>::value, Scalar, const Scalar>::type
>::type CoeffReturnType;
typedef typename internal::add_const_on_value_type_if_arithmetic<
typename internal::packet_traits<Scalar>::type
>::type PacketReturnType;
typedef EigenBase<Derived> Base;
using Base::rows;
using Base::cols;
using Base::size;
using Base::derived;
EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner) const
{
return int(Derived::RowsAtCompileTime) == 1 ? 0
: int(Derived::ColsAtCompileTime) == 1 ? inner
: int(Derived::Flags)&RowMajorBit ? outer
: inner;
}
EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner) const
{
return int(Derived::ColsAtCompileTime) == 1 ? 0
: int(Derived::RowsAtCompileTime) == 1 ? inner
: int(Derived::Flags)&RowMajorBit ? inner
: outer;
}
/** Short version: don't use this function, use
* \link operator()(Index,Index) const \endlink instead.
*
* Long version: this function is similar to
* \link operator()(Index,Index) const \endlink, but without the assertion.
* Use this for limiting the performance cost of debugging code when doing
* repeated coefficient access. Only use this when it is guaranteed that the
* parameters \a row and \a col are in range.
*
* If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
* function equivalent to \link operator()(Index,Index) const \endlink.
*
* \sa operator()(Index,Index) const, coeffRef(Index,Index), coeff(Index) const
*/
EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const
{
eigen_internal_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
return derived().coeff(row, col);
}
EIGEN_STRONG_INLINE CoeffReturnType coeffByOuterInner(Index outer, Index inner) const
{
return coeff(rowIndexByOuterInner(outer, inner),
colIndexByOuterInner(outer, inner));
}
/** \returns the coefficient at given the given row and column.
*
* \sa operator()(Index,Index), operator[](Index)
*/
EIGEN_STRONG_INLINE CoeffReturnType operator()(Index row, Index col) const
{
eigen_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
return derived().coeff(row, col);
}
/** Short version: don't use this function, use
* \link operator[](Index) const \endlink instead.
*
* Long version: this function is similar to
* \link operator[](Index) const \endlink, but without the assertion.
* Use this for limiting the performance cost of debugging code when doing
* repeated coefficient access. Only use this when it is guaranteed that the
* parameter \a index is in range.
*
* If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
* function equivalent to \link operator[](Index) const \endlink.
*
* \sa operator[](Index) const, coeffRef(Index), coeff(Index,Index) const
*/
EIGEN_STRONG_INLINE CoeffReturnType
coeff(Index index) const
{
eigen_internal_assert(index >= 0 && index < size());
return derived().coeff(index);
}
/** \returns the coefficient at given index.
*
* This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
*
* \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
* z() const, w() const
*/
EIGEN_STRONG_INLINE CoeffReturnType
operator[](Index index) const
{
#ifndef EIGEN2_SUPPORT
EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
#endif
eigen_assert(index >= 0 && index < size());
return derived().coeff(index);
}
/** \returns the coefficient at given index.
*
* This is synonymous to operator[](Index) const.
*
* This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
*
* \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
* z() const, w() const
*/
EIGEN_STRONG_INLINE CoeffReturnType
operator()(Index index) const
{
eigen_assert(index >= 0 && index < size());
return derived().coeff(index);
}
/** equivalent to operator[](0). */
EIGEN_STRONG_INLINE CoeffReturnType
x() const { return (*this)[0]; }
/** equivalent to operator[](1). */
EIGEN_STRONG_INLINE CoeffReturnType
y() const { return (*this)[1]; }
/** equivalent to operator[](2). */
EIGEN_STRONG_INLINE CoeffReturnType
z() const { return (*this)[2]; }
/** equivalent to operator[](3). */
EIGEN_STRONG_INLINE CoeffReturnType
w() const { return (*this)[3]; }
/** \internal
* \returns the packet of coefficients starting at the given row and column. It is your responsibility
* to ensure that a packet really starts there. This method is only available on expressions having the
* PacketAccessBit.
*
* The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
* the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
* starting at an address which is a multiple of the packet size.
*/
template<int LoadMode>
EIGEN_STRONG_INLINE PacketReturnType packet(Index row, Index col) const
{
eigen_internal_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
return derived().template packet<LoadMode>(row,col);
}
/** \internal */
template<int LoadMode>
EIGEN_STRONG_INLINE PacketReturnType packetByOuterInner(Index outer, Index inner) const
{
return packet<LoadMode>(rowIndexByOuterInner(outer, inner),
colIndexByOuterInner(outer, inner));
}
/** \internal
* \returns the packet of coefficients starting at the given index. It is your responsibility
* to ensure that a packet really starts there. This method is only available on expressions having the
* PacketAccessBit and the LinearAccessBit.
*
* The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
* the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
* starting at an address which is a multiple of the packet size.
*/
template<int LoadMode>
EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
{
eigen_internal_assert(index >= 0 && index < size());
return derived().template packet<LoadMode>(index);
}
protected:
// explanation: DenseBase is doing "using ..." on the methods from DenseCoeffsBase.
// But some methods are only available in the DirectAccess case.
// So we add dummy methods here with these names, so that "using... " doesn't fail.
// It's not private so that the child class DenseBase can access them, and it's not public
// either since it's an implementation detail, so has to be protected.
void coeffRef();
void coeffRefByOuterInner();
void writePacket();
void writePacketByOuterInner();
void copyCoeff();
void copyCoeffByOuterInner();
void copyPacket();
void copyPacketByOuterInner();
void stride();
void innerStride();
void outerStride();
void rowStride();
void colStride();
};
/** \brief Base class providing read/write coefficient access to matrices and arrays.
* \ingroup Core_Module
* \tparam Derived Type of the derived class
* \tparam #WriteAccessors Constant indicating read/write access
*
* This class defines the non-const \c operator() function and friends, which can be used to write specific
* entries of a matrix or array. This class inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which
* defines the const variant for reading specific entries.
*
* \sa DenseCoeffsBase<Derived, DirectAccessors>, \ref TopicClassHierarchy
*/
template<typename Derived>
class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
{
public:
typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Index Index;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
using Base::coeff;
using Base::rows;
using Base::cols;
using Base::size;
using Base::derived;
using Base::rowIndexByOuterInner;
using Base::colIndexByOuterInner;
using Base::operator[];
using Base::operator();
using Base::x;
using Base::y;
using Base::z;
using Base::w;
/** Short version: don't use this function, use
* \link operator()(Index,Index) \endlink instead.
*
* Long version: this function is similar to
* \link operator()(Index,Index) \endlink, but without the assertion.
* Use this for limiting the performance cost of debugging code when doing
* repeated coefficient access. Only use this when it is guaranteed that the
* parameters \a row and \a col are in range.
*
* If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
* function equivalent to \link operator()(Index,Index) \endlink.
*
* \sa operator()(Index,Index), coeff(Index, Index) const, coeffRef(Index)
*/
EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)
{
eigen_internal_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
return derived().coeffRef(row, col);
}
EIGEN_STRONG_INLINE Scalar&
coeffRefByOuterInner(Index outer, Index inner)
{
return coeffRef(rowIndexByOuterInner(outer, inner),
colIndexByOuterInner(outer, inner));
}
/** \returns a reference to the coefficient at given the given row and column.
*
* \sa operator[](Index)
*/
EIGEN_STRONG_INLINE Scalar&
operator()(Index row, Index col)
{
eigen_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
return derived().coeffRef(row, col);
}
/** Short version: don't use this function, use
* \link operator[](Index) \endlink instead.
*
* Long version: this function is similar to
* \link operator[](Index) \endlink, but without the assertion.
* Use this for limiting the performance cost of debugging code when doing
* repeated coefficient access. Only use this when it is guaranteed that the
* parameters \a row and \a col are in range.
*
* If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
* function equivalent to \link operator[](Index) \endlink.
*
* \sa operator[](Index), coeff(Index) const, coeffRef(Index,Index)
*/
EIGEN_STRONG_INLINE Scalar&
coeffRef(Index index)
{
eigen_internal_assert(index >= 0 && index < size());
return derived().coeffRef(index);
}
/** \returns a reference to the coefficient at given index.
*
* This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
*
* \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
*/
EIGEN_STRONG_INLINE Scalar&
operator[](Index index)
{
#ifndef EIGEN2_SUPPORT
EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
#endif
eigen_assert(index >= 0 && index < size());
return derived().coeffRef(index);
}
/** \returns a reference to the coefficient at given index.
*
* This is synonymous to operator[](Index).
*
* This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
*
* \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
*/
EIGEN_STRONG_INLINE Scalar&
operator()(Index index)
{
eigen_assert(index >= 0 && index < size());
return derived().coeffRef(index);
}
/** equivalent to operator[](0). */
EIGEN_STRONG_INLINE Scalar&
x() { return (*this)[0]; }
/** equivalent to operator[](1). */
EIGEN_STRONG_INLINE Scalar&
y() { return (*this)[1]; }
/** equivalent to operator[](2). */
EIGEN_STRONG_INLINE Scalar&
z() { return (*this)[2]; }
/** equivalent to operator[](3). */
EIGEN_STRONG_INLINE Scalar&
w() { return (*this)[3]; }
/** \internal
* Stores the given packet of coefficients, at the given row and column of this expression. It is your responsibility
* to ensure that a packet really starts there. This method is only available on expressions having the
* PacketAccessBit.
*
* The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
* the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
* starting at an address which is a multiple of the packet size.
*/
template<int StoreMode>
EIGEN_STRONG_INLINE void writePacket
(Index row, Index col, const typename internal::packet_traits<Scalar>::type& x)
{
eigen_internal_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
derived().template writePacket<StoreMode>(row,col,x);
}
/** \internal */
template<int StoreMode>
EIGEN_STRONG_INLINE void writePacketByOuterInner
(Index outer, Index inner, const typename internal::packet_traits<Scalar>::type& x)
{
writePacket<StoreMode>(rowIndexByOuterInner(outer, inner),
colIndexByOuterInner(outer, inner),
x);
}
/** \internal
* Stores the given packet of coefficients, at the given index in this expression. It is your responsibility
* to ensure that a packet really starts there. This method is only available on expressions having the
* PacketAccessBit and the LinearAccessBit.
*
* The \a LoadMode parameter may have the value \a Aligned or \a Unaligned. Its effect is to select
* the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
* starting at an address which is a multiple of the packet size.
*/
template<int StoreMode>
EIGEN_STRONG_INLINE void writePacket
(Index index, const typename internal::packet_traits<Scalar>::type& x)
{
eigen_internal_assert(index >= 0 && index < size());
derived().template writePacket<StoreMode>(index,x);
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal Copies the coefficient at position (row,col) of other into *this.
*
* This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
* with usual assignments.
*
* Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE void copyCoeff(Index row, Index col, const DenseBase<OtherDerived>& other)
{
eigen_internal_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
derived().coeffRef(row, col) = other.derived().coeff(row, col);
}
/** \internal Copies the coefficient at the given index of other into *this.
*
* This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
* with usual assignments.
*
* Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE void copyCoeff(Index index, const DenseBase<OtherDerived>& other)
{
eigen_internal_assert(index >= 0 && index < size());
derived().coeffRef(index) = other.derived().coeff(index);
}
template<typename OtherDerived>
EIGEN_STRONG_INLINE void copyCoeffByOuterInner(Index outer, Index inner, const DenseBase<OtherDerived>& other)
{
const Index row = rowIndexByOuterInner(outer,inner);
const Index col = colIndexByOuterInner(outer,inner);
// derived() is important here: copyCoeff() may be reimplemented in Derived!
derived().copyCoeff(row, col, other);
}
/** \internal Copies the packet at position (row,col) of other into *this.
*
* This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
* with usual assignments.
*
* Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
*/
template<typename OtherDerived, int StoreMode, int LoadMode>
EIGEN_STRONG_INLINE void copyPacket(Index row, Index col, const DenseBase<OtherDerived>& other)
{
eigen_internal_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
derived().template writePacket<StoreMode>(row, col,
other.derived().template packet<LoadMode>(row, col));
}
/** \internal Copies the packet at the given index of other into *this.
*
* This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
* with usual assignments.
*
* Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
*/
template<typename OtherDerived, int StoreMode, int LoadMode>
EIGEN_STRONG_INLINE void copyPacket(Index index, const DenseBase<OtherDerived>& other)
{
eigen_internal_assert(index >= 0 && index < size());
derived().template writePacket<StoreMode>(index,
other.derived().template packet<LoadMode>(index));
}
/** \internal */
template<typename OtherDerived, int StoreMode, int LoadMode>
EIGEN_STRONG_INLINE void copyPacketByOuterInner(Index outer, Index inner, const DenseBase<OtherDerived>& other)
{
const Index row = rowIndexByOuterInner(outer,inner);
const Index col = colIndexByOuterInner(outer,inner);
// derived() is important here: copyCoeff() may be reimplemented in Derived!
derived().template copyPacket< OtherDerived, StoreMode, LoadMode>(row, col, other);
}
#endif
};
/** \brief Base class providing direct read-only coefficient access to matrices and arrays.
* \ingroup Core_Module
* \tparam Derived Type of the derived class
* \tparam #DirectAccessors Constant indicating direct access
*
* This class defines functions to work with strides which can be used to access entries directly. This class
* inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which defines functions to access entries read-only using
* \c operator() .
*
* \sa \ref TopicClassHierarchy
*/
template<typename Derived>
class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
{
public:
typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
typedef typename internal::traits<Derived>::Index Index;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
using Base::rows;
using Base::cols;
using Base::size;
using Base::derived;
/** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
*
* \sa outerStride(), rowStride(), colStride()
*/
inline Index innerStride() const
{
return derived().innerStride();
}
/** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
* in a column-major matrix).
*
* \sa innerStride(), rowStride(), colStride()
*/
inline Index outerStride() const
{
return derived().outerStride();
}
// FIXME shall we remove it ?
inline Index stride() const
{
return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
}
/** \returns the pointer increment between two consecutive rows.
*
* \sa innerStride(), outerStride(), colStride()
*/
inline Index rowStride() const
{
return Derived::IsRowMajor ? outerStride() : innerStride();
}
/** \returns the pointer increment between two consecutive columns.
*
* \sa innerStride(), outerStride(), rowStride()
*/
inline Index colStride() const
{
return Derived::IsRowMajor ? innerStride() : outerStride();
}
};
/** \brief Base class providing direct read/write coefficient access to matrices and arrays.
* \ingroup Core_Module
* \tparam Derived Type of the derived class
* \tparam #DirectWriteAccessors Constant indicating direct access
*
* This class defines functions to work with strides which can be used to access entries directly. This class
* inherits DenseCoeffsBase<Derived, WriteAccessors> which defines functions to access entries read/write using
* \c operator().
*
* \sa \ref TopicClassHierarchy
*/
template<typename Derived>
class DenseCoeffsBase<Derived, DirectWriteAccessors>
: public DenseCoeffsBase<Derived, WriteAccessors>
{
public:
typedef DenseCoeffsBase<Derived, WriteAccessors> Base;
typedef typename internal::traits<Derived>::Index Index;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
using Base::rows;
using Base::cols;
using Base::size;
using Base::derived;
/** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
*
* \sa outerStride(), rowStride(), colStride()
*/
inline Index innerStride() const
{
return derived().innerStride();
}
/** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
* in a column-major matrix).
*
* \sa innerStride(), rowStride(), colStride()
*/
inline Index outerStride() const
{
return derived().outerStride();
}
// FIXME shall we remove it ?
inline Index stride() const
{
return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
}
/** \returns the pointer increment between two consecutive rows.
*
* \sa innerStride(), outerStride(), colStride()
*/
inline Index rowStride() const
{
return Derived::IsRowMajor ? outerStride() : innerStride();
}
/** \returns the pointer increment between two consecutive columns.
*
* \sa innerStride(), outerStride(), rowStride()
*/
inline Index colStride() const
{
return Derived::IsRowMajor ? innerStride() : outerStride();
}
};
namespace internal {
template<typename Derived, bool JustReturnZero>
struct first_aligned_impl
{
static inline typename Derived::Index run(const Derived&)
{ return 0; }
};
template<typename Derived>
struct first_aligned_impl<Derived, false>
{
static inline typename Derived::Index run(const Derived& m)
{
return internal::first_aligned(&m.const_cast_derived().coeffRef(0,0), m.size());
}
};
/** \internal \returns the index of the first element of the array that is well aligned for vectorization.
*
* There is also the variant first_aligned(const Scalar*, Integer) defined in Memory.h. See it for more
* documentation.
*/
template<typename Derived>
static inline typename Derived::Index first_aligned(const Derived& m)
{
return first_aligned_impl
<Derived, (Derived::Flags & AlignedBit) || !(Derived::Flags & DirectAccessBit)>
::run(m);
}
template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
struct inner_stride_at_compile_time
{
enum { ret = traits<Derived>::InnerStrideAtCompileTime };
};
template<typename Derived>
struct inner_stride_at_compile_time<Derived, false>
{
enum { ret = 0 };
};
template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
struct outer_stride_at_compile_time
{
enum { ret = traits<Derived>::OuterStrideAtCompileTime };
};
template<typename Derived>
struct outer_stride_at_compile_time<Derived, false>
{
enum { ret = 0 };
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_DENSECOEFFSBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MATRIXSTORAGE_H
#define EIGEN_MATRIXSTORAGE_H
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN EIGEN_DENSE_STORAGE_CTOR_PLUGIN;
#else
#define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
#endif
namespace Eigen {
namespace internal {
struct constructor_without_unaligned_array_assert {};
/** \internal
* Static array. If the MatrixOrArrayOptions require auto-alignment, the array will be automatically aligned:
* to 16 bytes boundary if the total size is a multiple of 16 bytes.
*/
template <typename T, int Size, int MatrixOrArrayOptions,
int Alignment = (MatrixOrArrayOptions&DontAlign) ? 0
: (((Size*sizeof(T))%16)==0) ? 16
: 0 >
struct plain_array
{
T array[Size];
plain_array() {}
plain_array(constructor_without_unaligned_array_assert) {}
};
#if defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT)
#define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask)
#elif EIGEN_GNUC_AT_LEAST(4,7)
// GCC 4.7 is too aggressive in its optimizations and remove the alignement test based on the fact the array is declared to be aligned.
// See this bug report: http://gcc.gnu.org/bugzilla/show_bug.cgi?id=53900
// Hiding the origin of the array pointer behind a function argument seems to do the trick even if the function is inlined:
template<typename PtrType>
EIGEN_ALWAYS_INLINE PtrType eigen_unaligned_array_assert_workaround_gcc47(PtrType array) { return array; }
#define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \
eigen_assert((reinterpret_cast<size_t>(eigen_unaligned_array_assert_workaround_gcc47(array)) & sizemask) == 0 \
&& "this assertion is explained here: " \
"http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html" \
" **** READ THIS WEB PAGE !!! ****");
#else
#define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \
eigen_assert((reinterpret_cast<size_t>(array) & sizemask) == 0 \
&& "this assertion is explained here: " \
"http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html" \
" **** READ THIS WEB PAGE !!! ****");
#endif
template <typename T, int Size, int MatrixOrArrayOptions>
struct plain_array<T, Size, MatrixOrArrayOptions, 16>
{
EIGEN_USER_ALIGN16 T array[Size];
plain_array() { EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(0xf) }
plain_array(constructor_without_unaligned_array_assert) {}
};
template <typename T, int MatrixOrArrayOptions, int Alignment>
struct plain_array<T, 0, MatrixOrArrayOptions, Alignment>
{
EIGEN_USER_ALIGN16 T array[1];
plain_array() {}
plain_array(constructor_without_unaligned_array_assert) {}
};
} // end namespace internal
/** \internal
*
* \class DenseStorage
* \ingroup Core_Module
*
* \brief Stores the data of a matrix
*
* This class stores the data of fixed-size, dynamic-size or mixed matrices
* in a way as compact as possible.
*
* \sa Matrix
*/
template<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseStorage;
// purely fixed-size matrix
template<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseStorage
{
internal::plain_array<T,Size,_Options> m_data;
public:
inline explicit DenseStorage() {}
inline DenseStorage(internal::constructor_without_unaligned_array_assert)
: m_data(internal::constructor_without_unaligned_array_assert()) {}
inline DenseStorage(DenseIndex,DenseIndex,DenseIndex) {}
inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); }
static inline DenseIndex rows(void) {return _Rows;}
static inline DenseIndex cols(void) {return _Cols;}
inline void conservativeResize(DenseIndex,DenseIndex,DenseIndex) {}
inline void resize(DenseIndex,DenseIndex,DenseIndex) {}
inline const T *data() const { return m_data.array; }
inline T *data() { return m_data.array; }
};
// null matrix
template<typename T, int _Rows, int _Cols, int _Options> class DenseStorage<T, 0, _Rows, _Cols, _Options>
{
public:
inline explicit DenseStorage() {}
inline DenseStorage(internal::constructor_without_unaligned_array_assert) {}
inline DenseStorage(DenseIndex,DenseIndex,DenseIndex) {}
inline void swap(DenseStorage& ) {}
static inline DenseIndex rows(void) {return _Rows;}
static inline DenseIndex cols(void) {return _Cols;}
inline void conservativeResize(DenseIndex,DenseIndex,DenseIndex) {}
inline void resize(DenseIndex,DenseIndex,DenseIndex) {}
inline const T *data() const { return 0; }
inline T *data() { return 0; }
};
// more specializations for null matrices; these are necessary to resolve ambiguities
template<typename T, int _Options> class DenseStorage<T, 0, Dynamic, Dynamic, _Options>
: public DenseStorage<T, 0, 0, 0, _Options> { };
template<typename T, int _Rows, int _Options> class DenseStorage<T, 0, _Rows, Dynamic, _Options>
: public DenseStorage<T, 0, 0, 0, _Options> { };
template<typename T, int _Cols, int _Options> class DenseStorage<T, 0, Dynamic, _Cols, _Options>
: public DenseStorage<T, 0, 0, 0, _Options> { };
// dynamic-size matrix with fixed-size storage
template<typename T, int Size, int _Options> class DenseStorage<T, Size, Dynamic, Dynamic, _Options>
{
internal::plain_array<T,Size,_Options> m_data;
DenseIndex m_rows;
DenseIndex m_cols;
public:
inline explicit DenseStorage() : m_rows(0), m_cols(0) {}
inline DenseStorage(internal::constructor_without_unaligned_array_assert)
: m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0), m_cols(0) {}
inline DenseStorage(DenseIndex, DenseIndex rows, DenseIndex cols) : m_rows(rows), m_cols(cols) {}
inline void swap(DenseStorage& other)
{ std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); std::swap(m_cols,other.m_cols); }
inline DenseIndex rows(void) const {return m_rows;}
inline DenseIndex cols(void) const {return m_cols;}
inline void conservativeResize(DenseIndex, DenseIndex rows, DenseIndex cols) { m_rows = rows; m_cols = cols; }
inline void resize(DenseIndex, DenseIndex rows, DenseIndex cols) { m_rows = rows; m_cols = cols; }
inline const T *data() const { return m_data.array; }
inline T *data() { return m_data.array; }
};
// dynamic-size matrix with fixed-size storage and fixed width
template<typename T, int Size, int _Cols, int _Options> class DenseStorage<T, Size, Dynamic, _Cols, _Options>
{
internal::plain_array<T,Size,_Options> m_data;
DenseIndex m_rows;
public:
inline explicit DenseStorage() : m_rows(0) {}
inline DenseStorage(internal::constructor_without_unaligned_array_assert)
: m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0) {}
inline DenseStorage(DenseIndex, DenseIndex rows, DenseIndex) : m_rows(rows) {}
inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }
inline DenseIndex rows(void) const {return m_rows;}
inline DenseIndex cols(void) const {return _Cols;}
inline void conservativeResize(DenseIndex, DenseIndex rows, DenseIndex) { m_rows = rows; }
inline void resize(DenseIndex, DenseIndex rows, DenseIndex) { m_rows = rows; }
inline const T *data() const { return m_data.array; }
inline T *data() { return m_data.array; }
};
// dynamic-size matrix with fixed-size storage and fixed height
template<typename T, int Size, int _Rows, int _Options> class DenseStorage<T, Size, _Rows, Dynamic, _Options>
{
internal::plain_array<T,Size,_Options> m_data;
DenseIndex m_cols;
public:
inline explicit DenseStorage() : m_cols(0) {}
inline DenseStorage(internal::constructor_without_unaligned_array_assert)
: m_data(internal::constructor_without_unaligned_array_assert()), m_cols(0) {}
inline DenseStorage(DenseIndex, DenseIndex, DenseIndex cols) : m_cols(cols) {}
inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }
inline DenseIndex rows(void) const {return _Rows;}
inline DenseIndex cols(void) const {return m_cols;}
inline void conservativeResize(DenseIndex, DenseIndex, DenseIndex cols) { m_cols = cols; }
inline void resize(DenseIndex, DenseIndex, DenseIndex cols) { m_cols = cols; }
inline const T *data() const { return m_data.array; }
inline T *data() { return m_data.array; }
};
// purely dynamic matrix.
template<typename T, int _Options> class DenseStorage<T, Dynamic, Dynamic, Dynamic, _Options>
{
T *m_data;
DenseIndex m_rows;
DenseIndex m_cols;
public:
inline explicit DenseStorage() : m_data(0), m_rows(0), m_cols(0) {}
inline DenseStorage(internal::constructor_without_unaligned_array_assert)
: m_data(0), m_rows(0), m_cols(0) {}
inline DenseStorage(DenseIndex size, DenseIndex rows, DenseIndex cols)
: m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(rows), m_cols(cols)
{ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
inline ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, m_rows*m_cols); }
inline void swap(DenseStorage& other)
{ std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); std::swap(m_cols,other.m_cols); }
inline DenseIndex rows(void) const {return m_rows;}
inline DenseIndex cols(void) const {return m_cols;}
inline void conservativeResize(DenseIndex size, DenseIndex rows, DenseIndex cols)
{
m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, m_rows*m_cols);
m_rows = rows;
m_cols = cols;
}
void resize(DenseIndex size, DenseIndex rows, DenseIndex cols)
{
if(size != m_rows*m_cols)
{
internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, m_rows*m_cols);
if (size)
m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);
else
m_data = 0;
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
}
m_rows = rows;
m_cols = cols;
}
inline const T *data() const { return m_data; }
inline T *data() { return m_data; }
};
// matrix with dynamic width and fixed height (so that matrix has dynamic size).
template<typename T, int _Rows, int _Options> class DenseStorage<T, Dynamic, _Rows, Dynamic, _Options>
{
T *m_data;
DenseIndex m_cols;
public:
inline explicit DenseStorage() : m_data(0), m_cols(0) {}
inline DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_cols(0) {}
inline DenseStorage(DenseIndex size, DenseIndex, DenseIndex cols) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_cols(cols)
{ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
inline ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Rows*m_cols); }
inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }
static inline DenseIndex rows(void) {return _Rows;}
inline DenseIndex cols(void) const {return m_cols;}
inline void conservativeResize(DenseIndex size, DenseIndex, DenseIndex cols)
{
m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, _Rows*m_cols);
m_cols = cols;
}
EIGEN_STRONG_INLINE void resize(DenseIndex size, DenseIndex, DenseIndex cols)
{
if(size != _Rows*m_cols)
{
internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Rows*m_cols);
if (size)
m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);
else
m_data = 0;
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
}
m_cols = cols;
}
inline const T *data() const { return m_data; }
inline T *data() { return m_data; }
};
// matrix with dynamic height and fixed width (so that matrix has dynamic size).
template<typename T, int _Cols, int _Options> class DenseStorage<T, Dynamic, Dynamic, _Cols, _Options>
{
T *m_data;
DenseIndex m_rows;
public:
inline explicit DenseStorage() : m_data(0), m_rows(0) {}
inline DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_rows(0) {}
inline DenseStorage(DenseIndex size, DenseIndex rows, DenseIndex) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(rows)
{ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN }
inline ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Cols*m_rows); }
inline void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }
inline DenseIndex rows(void) const {return m_rows;}
static inline DenseIndex cols(void) {return _Cols;}
inline void conservativeResize(DenseIndex size, DenseIndex rows, DenseIndex)
{
m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, m_rows*_Cols);
m_rows = rows;
}
EIGEN_STRONG_INLINE void resize(DenseIndex size, DenseIndex rows, DenseIndex)
{
if(size != m_rows*_Cols)
{
internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Cols*m_rows);
if (size)
m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);
else
m_data = 0;
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
}
m_rows = rows;
}
inline const T *data() const { return m_data; }
inline T *data() { return m_data; }
};
} // end namespace Eigen
#endif // EIGEN_MATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DIAGONAL_H
#define EIGEN_DIAGONAL_H
namespace Eigen {
/** \class Diagonal
* \ingroup Core_Module
*
* \brief Expression of a diagonal/subdiagonal/superdiagonal in a matrix
*
* \param MatrixType the type of the object in which we are taking a sub/main/super diagonal
* \param DiagIndex the index of the sub/super diagonal. The default is 0 and it means the main diagonal.
* A positive value means a superdiagonal, a negative value means a subdiagonal.
* You can also use Dynamic so the index can be set at runtime.
*
* The matrix is not required to be square.
*
* This class represents an expression of the main diagonal, or any sub/super diagonal
* of a square matrix. It is the return type of MatrixBase::diagonal() and MatrixBase::diagonal(Index) and most of the
* time this is the only way it is used.
*
* \sa MatrixBase::diagonal(), MatrixBase::diagonal(Index)
*/
namespace internal {
template<typename MatrixType, int DiagIndex>
struct traits<Diagonal<MatrixType,DiagIndex> >
: traits<MatrixType>
{
typedef typename nested<MatrixType>::type MatrixTypeNested;
typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
typedef typename MatrixType::StorageKind StorageKind;
enum {
RowsAtCompileTime = (int(DiagIndex) == Dynamic || int(MatrixType::SizeAtCompileTime) == Dynamic) ? Dynamic
: (EIGEN_PLAIN_ENUM_MIN(MatrixType::RowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0),
MatrixType::ColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))),
ColsAtCompileTime = 1,
MaxRowsAtCompileTime = int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic
: DiagIndex == Dynamic ? EIGEN_SIZE_MIN_PREFER_FIXED(MatrixType::MaxRowsAtCompileTime,
MatrixType::MaxColsAtCompileTime)
: (EIGEN_PLAIN_ENUM_MIN(MatrixType::MaxRowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0),
MatrixType::MaxColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))),
MaxColsAtCompileTime = 1,
MaskLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
Flags = (unsigned int)_MatrixTypeNested::Flags & (HereditaryBits | LinearAccessBit | MaskLvalueBit | DirectAccessBit) & ~RowMajorBit,
CoeffReadCost = _MatrixTypeNested::CoeffReadCost,
MatrixTypeOuterStride = outer_stride_at_compile_time<MatrixType>::ret,
InnerStrideAtCompileTime = MatrixTypeOuterStride == Dynamic ? Dynamic : MatrixTypeOuterStride+1,
OuterStrideAtCompileTime = 0
};
};
}
template<typename MatrixType, int DiagIndex> class Diagonal
: public internal::dense_xpr_base< Diagonal<MatrixType,DiagIndex> >::type
{
public:
typedef typename internal::dense_xpr_base<Diagonal>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Diagonal)
inline Diagonal(MatrixType& matrix, Index index = DiagIndex) : m_matrix(matrix), m_index(index) {}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Diagonal)
inline Index rows() const
{ return m_index.value()<0 ? (std::min)(m_matrix.cols(),m_matrix.rows()+m_index.value()) : (std::min)(m_matrix.rows(),m_matrix.cols()-m_index.value()); }
inline Index cols() const { return 1; }
inline Index innerStride() const
{
return m_matrix.outerStride() + 1;
}
inline Index outerStride() const
{
return 0;
}
typedef typename internal::conditional<
internal::is_lvalue<MatrixType>::value,
Scalar,
const Scalar
>::type ScalarWithConstIfNotLvalue;
inline ScalarWithConstIfNotLvalue* data() { return &(m_matrix.const_cast_derived().coeffRef(rowOffset(), colOffset())); }
inline const Scalar* data() const { return &(m_matrix.const_cast_derived().coeffRef(rowOffset(), colOffset())); }
inline Scalar& coeffRef(Index row, Index)
{
EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
return m_matrix.const_cast_derived().coeffRef(row+rowOffset(), row+colOffset());
}
inline const Scalar& coeffRef(Index row, Index) const
{
return m_matrix.const_cast_derived().coeffRef(row+rowOffset(), row+colOffset());
}
inline CoeffReturnType coeff(Index row, Index) const
{
return m_matrix.coeff(row+rowOffset(), row+colOffset());
}
inline Scalar& coeffRef(Index index)
{
EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
return m_matrix.const_cast_derived().coeffRef(index+rowOffset(), index+colOffset());
}
inline const Scalar& coeffRef(Index index) const
{
return m_matrix.const_cast_derived().coeffRef(index+rowOffset(), index+colOffset());
}
inline CoeffReturnType coeff(Index index) const
{
return m_matrix.coeff(index+rowOffset(), index+colOffset());
}
const typename internal::remove_all<typename MatrixType::Nested>::type&
nestedExpression() const
{
return m_matrix;
}
int index() const
{
return m_index.value();
}
protected:
typename MatrixType::Nested m_matrix;
const internal::variable_if_dynamic<Index, DiagIndex> m_index;
private:
// some compilers may fail to optimize std::max etc in case of compile-time constants...
EIGEN_STRONG_INLINE Index absDiagIndex() const { return m_index.value()>0 ? m_index.value() : -m_index.value(); }
EIGEN_STRONG_INLINE Index rowOffset() const { return m_index.value()>0 ? 0 : -m_index.value(); }
EIGEN_STRONG_INLINE Index colOffset() const { return m_index.value()>0 ? m_index.value() : 0; }
// triger a compile time error is someone try to call packet
template<int LoadMode> typename MatrixType::PacketReturnType packet(Index) const;
template<int LoadMode> typename MatrixType::PacketReturnType packet(Index,Index) const;
};
/** \returns an expression of the main diagonal of the matrix \c *this
*
* \c *this is not required to be square.
*
* Example: \include MatrixBase_diagonal.cpp
* Output: \verbinclude MatrixBase_diagonal.out
*
* \sa class Diagonal */
template<typename Derived>
inline typename MatrixBase<Derived>::DiagonalReturnType
MatrixBase<Derived>::diagonal()
{
return derived();
}
/** This is the const version of diagonal(). */
template<typename Derived>
inline const typename MatrixBase<Derived>::ConstDiagonalReturnType
MatrixBase<Derived>::diagonal() const
{
return ConstDiagonalReturnType(derived());
}
/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
*
* \c *this is not required to be square.
*
* The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
* and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
*
* Example: \include MatrixBase_diagonal_int.cpp
* Output: \verbinclude MatrixBase_diagonal_int.out
*
* \sa MatrixBase::diagonal(), class Diagonal */
template<typename Derived>
inline typename MatrixBase<Derived>::template DiagonalIndexReturnType<Dynamic>::Type
MatrixBase<Derived>::diagonal(Index index)
{
return typename DiagonalIndexReturnType<Dynamic>::Type(derived(), index);
}
/** This is the const version of diagonal(Index). */
template<typename Derived>
inline typename MatrixBase<Derived>::template ConstDiagonalIndexReturnType<Dynamic>::Type
MatrixBase<Derived>::diagonal(Index index) const
{
return typename ConstDiagonalIndexReturnType<Dynamic>::Type(derived(), index);
}
/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
*
* \c *this is not required to be square.
*
* The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
* and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
*
* Example: \include MatrixBase_diagonal_template_int.cpp
* Output: \verbinclude MatrixBase_diagonal_template_int.out
*
* \sa MatrixBase::diagonal(), class Diagonal */
template<typename Derived>
template<int Index>
inline typename MatrixBase<Derived>::template DiagonalIndexReturnType<Index>::Type
MatrixBase<Derived>::diagonal()
{
return derived();
}
/** This is the const version of diagonal<int>(). */
template<typename Derived>
template<int Index>
inline typename MatrixBase<Derived>::template ConstDiagonalIndexReturnType<Index>::Type
MatrixBase<Derived>::diagonal() const
{
return derived();
}
} // end namespace Eigen
#endif // EIGEN_DIAGONAL_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DIAGONALMATRIX_H
#define EIGEN_DIAGONALMATRIX_H
namespace Eigen {
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename Derived>
class DiagonalBase : public EigenBase<Derived>
{
public:
typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;
typedef typename DiagonalVectorType::Scalar Scalar;
typedef typename DiagonalVectorType::RealScalar RealScalar;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Index Index;
enum {
RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
IsVectorAtCompileTime = 0,
Flags = 0
};
typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;
typedef DenseMatrixType DenseType;
typedef DiagonalMatrix<Scalar,DiagonalVectorType::SizeAtCompileTime,DiagonalVectorType::MaxSizeAtCompileTime> PlainObject;
inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
inline Derived& derived() { return *static_cast<Derived*>(this); }
DenseMatrixType toDenseMatrix() const { return derived(); }
template<typename DenseDerived>
void evalTo(MatrixBase<DenseDerived> &other) const;
template<typename DenseDerived>
void addTo(MatrixBase<DenseDerived> &other) const
{ other.diagonal() += diagonal(); }
template<typename DenseDerived>
void subTo(MatrixBase<DenseDerived> &other) const
{ other.diagonal() -= diagonal(); }
inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
inline DiagonalVectorType& diagonal() { return derived().diagonal(); }
inline Index rows() const { return diagonal().size(); }
inline Index cols() const { return diagonal().size(); }
template<typename MatrixDerived>
const DiagonalProduct<MatrixDerived, Derived, OnTheLeft>
operator*(const MatrixBase<MatrixDerived> &matrix) const;
inline const DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType> >
inverse() const
{
return diagonal().cwiseInverse();
}
inline const DiagonalWrapper<const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DiagonalVectorType> >
operator*(const Scalar& scalar) const
{
return diagonal() * scalar;
}
friend inline const DiagonalWrapper<const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DiagonalVectorType> >
operator*(const Scalar& scalar, const DiagonalBase& other)
{
return other.diagonal() * scalar;
}
#ifdef EIGEN2_SUPPORT
template<typename OtherDerived>
bool isApprox(const DiagonalBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
{
return diagonal().isApprox(other.diagonal(), precision);
}
template<typename OtherDerived>
bool isApprox(const MatrixBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
{
return toDenseMatrix().isApprox(other, precision);
}
#endif
};
template<typename Derived>
template<typename DenseDerived>
void DiagonalBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const
{
other.setZero();
other.diagonal() = diagonal();
}
#endif
/** \class DiagonalMatrix
* \ingroup Core_Module
*
* \brief Represents a diagonal matrix with its storage
*
* \param _Scalar the type of coefficients
* \param SizeAtCompileTime the dimension of the matrix, or Dynamic
* \param MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults
* to SizeAtCompileTime. Most of the time, you do not need to specify it.
*
* \sa class DiagonalWrapper
*/
namespace internal {
template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
struct traits<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
: traits<Matrix<_Scalar,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
{
typedef Matrix<_Scalar,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1> DiagonalVectorType;
typedef Dense StorageKind;
typedef DenseIndex Index;
enum {
Flags = LvalueBit
};
};
}
template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
class DiagonalMatrix
: public DiagonalBase<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
{
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename internal::traits<DiagonalMatrix>::DiagonalVectorType DiagonalVectorType;
typedef const DiagonalMatrix& Nested;
typedef _Scalar Scalar;
typedef typename internal::traits<DiagonalMatrix>::StorageKind StorageKind;
typedef typename internal::traits<DiagonalMatrix>::Index Index;
#endif
protected:
DiagonalVectorType m_diagonal;
public:
/** const version of diagonal(). */
inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
/** \returns a reference to the stored vector of diagonal coefficients. */
inline DiagonalVectorType& diagonal() { return m_diagonal; }
/** Default constructor without initialization */
inline DiagonalMatrix() {}
/** Constructs a diagonal matrix with given dimension */
inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}
/** 2D constructor. */
inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {}
/** 3D constructor. */
inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {}
/** Copy constructor. */
template<typename OtherDerived>
inline DiagonalMatrix(const DiagonalBase<OtherDerived>& other) : m_diagonal(other.diagonal()) {}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** copy constructor. prevent a default copy constructor from hiding the other templated constructor */
inline DiagonalMatrix(const DiagonalMatrix& other) : m_diagonal(other.diagonal()) {}
#endif
/** generic constructor from expression of the diagonal coefficients */
template<typename OtherDerived>
explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other)
{}
/** Copy operator. */
template<typename OtherDerived>
DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other)
{
m_diagonal = other.diagonal();
return *this;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** This is a special case of the templated operator=. Its purpose is to
* prevent a default operator= from hiding the templated operator=.
*/
DiagonalMatrix& operator=(const DiagonalMatrix& other)
{
m_diagonal = other.diagonal();
return *this;
}
#endif
/** Resizes to given size. */
inline void resize(Index size) { m_diagonal.resize(size); }
/** Sets all coefficients to zero. */
inline void setZero() { m_diagonal.setZero(); }
/** Resizes and sets all coefficients to zero. */
inline void setZero(Index size) { m_diagonal.setZero(size); }
/** Sets this matrix to be the identity matrix of the current size. */
inline void setIdentity() { m_diagonal.setOnes(); }
/** Sets this matrix to be the identity matrix of the given size. */
inline void setIdentity(Index size) { m_diagonal.setOnes(size); }
};
/** \class DiagonalWrapper
* \ingroup Core_Module
*
* \brief Expression of a diagonal matrix
*
* \param _DiagonalVectorType the type of the vector of diagonal coefficients
*
* This class is an expression of a diagonal matrix, but not storing its own vector of diagonal coefficients,
* instead wrapping an existing vector expression. It is the return type of MatrixBase::asDiagonal()
* and most of the time this is the only way that it is used.
*
* \sa class DiagonalMatrix, class DiagonalBase, MatrixBase::asDiagonal()
*/
namespace internal {
template<typename _DiagonalVectorType>
struct traits<DiagonalWrapper<_DiagonalVectorType> >
{
typedef _DiagonalVectorType DiagonalVectorType;
typedef typename DiagonalVectorType::Scalar Scalar;
typedef typename DiagonalVectorType::Index Index;
typedef typename DiagonalVectorType::StorageKind StorageKind;
enum {
RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
MaxRowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
MaxColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
Flags = traits<DiagonalVectorType>::Flags & LvalueBit
};
};
}
template<typename _DiagonalVectorType>
class DiagonalWrapper
: public DiagonalBase<DiagonalWrapper<_DiagonalVectorType> >, internal::no_assignment_operator
{
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef _DiagonalVectorType DiagonalVectorType;
typedef DiagonalWrapper Nested;
#endif
/** Constructor from expression of diagonal coefficients to wrap. */
inline DiagonalWrapper(DiagonalVectorType& diagonal) : m_diagonal(diagonal) {}
/** \returns a const reference to the wrapped expression of diagonal coefficients. */
const DiagonalVectorType& diagonal() const { return m_diagonal; }
protected:
typename DiagonalVectorType::Nested m_diagonal;
};
/** \returns a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients
*
* \only_for_vectors
*
* Example: \include MatrixBase_asDiagonal.cpp
* Output: \verbinclude MatrixBase_asDiagonal.out
*
* \sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
**/
template<typename Derived>
inline const DiagonalWrapper<const Derived>
MatrixBase<Derived>::asDiagonal() const
{
return derived();
}
/** \returns true if *this is approximately equal to a diagonal matrix,
* within the precision given by \a prec.
*
* Example: \include MatrixBase_isDiagonal.cpp
* Output: \verbinclude MatrixBase_isDiagonal.out
*
* \sa asDiagonal()
*/
template<typename Derived>
bool MatrixBase<Derived>::isDiagonal(RealScalar prec) const
{
if(cols() != rows()) return false;
RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
for(Index j = 0; j < cols(); ++j)
{
RealScalar absOnDiagonal = internal::abs(coeff(j,j));
if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
}
for(Index j = 0; j < cols(); ++j)
for(Index i = 0; i < j; ++i)
{
if(!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
if(!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
}
return true;
}
} // end namespace Eigen
#endif // EIGEN_DIAGONALMATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DIAGONALPRODUCT_H
#define EIGEN_DIAGONALPRODUCT_H
namespace Eigen {
namespace internal {
template<typename MatrixType, typename DiagonalType, int ProductOrder>
struct traits<DiagonalProduct<MatrixType, DiagonalType, ProductOrder> >
: traits<MatrixType>
{
typedef typename scalar_product_traits<typename MatrixType::Scalar, typename DiagonalType::Scalar>::ReturnType Scalar;
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
_StorageOrder = MatrixType::Flags & RowMajorBit ? RowMajor : ColMajor,
_PacketOnDiag = !((int(_StorageOrder) == RowMajor && int(ProductOrder) == OnTheLeft)
||(int(_StorageOrder) == ColMajor && int(ProductOrder) == OnTheRight)),
_SameTypes = is_same<typename MatrixType::Scalar, typename DiagonalType::Scalar>::value,
// FIXME currently we need same types, but in the future the next rule should be the one
//_Vectorizable = bool(int(MatrixType::Flags)&PacketAccessBit) && ((!_PacketOnDiag) || (_SameTypes && bool(int(DiagonalType::Flags)&PacketAccessBit))),
_Vectorizable = bool(int(MatrixType::Flags)&PacketAccessBit) && _SameTypes && ((!_PacketOnDiag) || (bool(int(DiagonalType::Flags)&PacketAccessBit))),
Flags = (HereditaryBits & (unsigned int)(MatrixType::Flags)) | (_Vectorizable ? PacketAccessBit : 0),
CoeffReadCost = NumTraits<Scalar>::MulCost + MatrixType::CoeffReadCost + DiagonalType::DiagonalVectorType::CoeffReadCost
};
};
}
template<typename MatrixType, typename DiagonalType, int ProductOrder>
class DiagonalProduct : internal::no_assignment_operator,
public MatrixBase<DiagonalProduct<MatrixType, DiagonalType, ProductOrder> >
{
public:
typedef MatrixBase<DiagonalProduct> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(DiagonalProduct)
inline DiagonalProduct(const MatrixType& matrix, const DiagonalType& diagonal)
: m_matrix(matrix), m_diagonal(diagonal)
{
eigen_assert(diagonal.diagonal().size() == (ProductOrder == OnTheLeft ? matrix.rows() : matrix.cols()));
}
inline Index rows() const { return m_matrix.rows(); }
inline Index cols() const { return m_matrix.cols(); }
const Scalar coeff(Index row, Index col) const
{
return m_diagonal.diagonal().coeff(ProductOrder == OnTheLeft ? row : col) * m_matrix.coeff(row, col);
}
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet(Index row, Index col) const
{
enum {
StorageOrder = Flags & RowMajorBit ? RowMajor : ColMajor
};
const Index indexInDiagonalVector = ProductOrder == OnTheLeft ? row : col;
return packet_impl<LoadMode>(row,col,indexInDiagonalVector,typename internal::conditional<
((int(StorageOrder) == RowMajor && int(ProductOrder) == OnTheLeft)
||(int(StorageOrder) == ColMajor && int(ProductOrder) == OnTheRight)), internal::true_type, internal::false_type>::type());
}
protected:
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet_impl(Index row, Index col, Index id, internal::true_type) const
{
return internal::pmul(m_matrix.template packet<LoadMode>(row, col),
internal::pset1<PacketScalar>(m_diagonal.diagonal().coeff(id)));
}
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet_impl(Index row, Index col, Index id, internal::false_type) const
{
enum {
InnerSize = (MatrixType::Flags & RowMajorBit) ? MatrixType::ColsAtCompileTime : MatrixType::RowsAtCompileTime,
DiagonalVectorPacketLoadMode = (LoadMode == Aligned && ((InnerSize%16) == 0)) ? Aligned : Unaligned
};
return internal::pmul(m_matrix.template packet<LoadMode>(row, col),
m_diagonal.diagonal().template packet<DiagonalVectorPacketLoadMode>(id));
}
typename MatrixType::Nested m_matrix;
typename DiagonalType::Nested m_diagonal;
};
/** \returns the diagonal matrix product of \c *this by the diagonal matrix \a diagonal.
*/
template<typename Derived>
template<typename DiagonalDerived>
inline const DiagonalProduct<Derived, DiagonalDerived, OnTheRight>
MatrixBase<Derived>::operator*(const DiagonalBase<DiagonalDerived> &diagonal) const
{
return DiagonalProduct<Derived, DiagonalDerived, OnTheRight>(derived(), diagonal.derived());
}
/** \returns the diagonal matrix product of \c *this by the matrix \a matrix.
*/
template<typename DiagonalDerived>
template<typename MatrixDerived>
inline const DiagonalProduct<MatrixDerived, DiagonalDerived, OnTheLeft>
DiagonalBase<DiagonalDerived>::operator*(const MatrixBase<MatrixDerived> &matrix) const
{
return DiagonalProduct<MatrixDerived, DiagonalDerived, OnTheLeft>(matrix.derived(), derived());
}
} // end namespace Eigen
#endif // EIGEN_DIAGONALPRODUCT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DOT_H
#define EIGEN_DOT_H
namespace Eigen {
namespace internal {
// helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot
// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE
// looking at the static assertions. Thus this is a trick to get better compile errors.
template<typename T, typename U,
// the NeedToTranspose condition here is taken straight from Assign.h
bool NeedToTranspose = T::IsVectorAtCompileTime
&& U::IsVectorAtCompileTime
&& ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1)
| // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".
// revert to || as soon as not needed anymore.
(int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))
>
struct dot_nocheck
{
typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
{
return a.template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
}
};
template<typename T, typename U>
struct dot_nocheck<T, U, true>
{
typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
{
return a.transpose().template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
}
};
} // end namespace internal
/** \returns the dot product of *this with other.
*
* \only_for_vectors
*
* \note If the scalar type is complex numbers, then this function returns the hermitian
* (sesquilinear) dot product, conjugate-linear in the first variable and linear in the
* second variable.
*
* \sa squaredNorm(), norm()
*/
template<typename Derived>
template<typename OtherDerived>
typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;
EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar);
eigen_assert(size() == other.size());
return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other);
}
#ifdef EIGEN2_SUPPORT
/** \returns the dot product of *this with other, with the Eigen2 convention that the dot product is linear in the first variable
* (conjugating the second variable). Of course this only makes a difference in the complex case.
*
* This method is only available in EIGEN2_SUPPORT mode.
*
* \only_for_vectors
*
* \sa dot()
*/
template<typename Derived>
template<typename OtherDerived>
typename internal::traits<Derived>::Scalar
MatrixBase<Derived>::eigen2_dot(const MatrixBase<OtherDerived>& other) const
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
eigen_assert(size() == other.size());
return internal::dot_nocheck<OtherDerived,Derived>::run(other,*this);
}
#endif
//---------- implementation of L2 norm and related functions ----------
/** \returns, for vectors, the squared \em l2 norm of \c *this, and for matrices the Frobenius norm.
* In both cases, it consists in the sum of the square of all the matrix entries.
* For vectors, this is also equals to the dot product of \c *this with itself.
*
* \sa dot(), norm()
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
{
return internal::real((*this).cwiseAbs2().sum());
}
/** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm.
* In both cases, it consists in the square root of the sum of the square of all the matrix entries.
* For vectors, this is also equals to the square root of the dot product of \c *this with itself.
*
* \sa dot(), squaredNorm()
*/
template<typename Derived>
inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
{
return internal::sqrt(squaredNorm());
}
/** \returns an expression of the quotient of *this by its own norm.
*
* \only_for_vectors
*
* \sa norm(), normalize()
*/
template<typename Derived>
inline const typename MatrixBase<Derived>::PlainObject
MatrixBase<Derived>::normalized() const
{
typedef typename internal::nested<Derived>::type Nested;
typedef typename internal::remove_reference<Nested>::type _Nested;
_Nested n(derived());
return n / n.norm();
}
/** Normalizes the vector, i.e. divides it by its own norm.
*
* \only_for_vectors
*
* \sa norm(), normalized()
*/
template<typename Derived>
inline void MatrixBase<Derived>::normalize()
{
*this /= norm();
}
//---------- implementation of other norms ----------
namespace internal {
template<typename Derived, int p>
struct lpNorm_selector
{
typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
static inline RealScalar run(const MatrixBase<Derived>& m)
{
return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);
}
};
template<typename Derived>
struct lpNorm_selector<Derived, 1>
{
static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
{
return m.cwiseAbs().sum();
}
};
template<typename Derived>
struct lpNorm_selector<Derived, 2>
{
static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
{
return m.norm();
}
};
template<typename Derived>
struct lpNorm_selector<Derived, Infinity>
{
static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
{
return m.cwiseAbs().maxCoeff();
}
};
} // end namespace internal
/** \returns the \f$ \ell^p \f$ norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values
* of the coefficients of *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$
* norm, that is the maximum of the absolute values of the coefficients of *this.
*
* \sa norm()
*/
template<typename Derived>
template<int p>
inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
MatrixBase<Derived>::lpNorm() const
{
return internal::lpNorm_selector<Derived, p>::run(*this);
}
//---------- implementation of isOrthogonal / isUnitary ----------
/** \returns true if *this is approximately orthogonal to \a other,
* within the precision given by \a prec.
*
* Example: \include MatrixBase_isOrthogonal.cpp
* Output: \verbinclude MatrixBase_isOrthogonal.out
*/
template<typename Derived>
template<typename OtherDerived>
bool MatrixBase<Derived>::isOrthogonal
(const MatrixBase<OtherDerived>& other, RealScalar prec) const
{
typename internal::nested<Derived,2>::type nested(derived());
typename internal::nested<OtherDerived,2>::type otherNested(other.derived());
return internal::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
}
/** \returns true if *this is approximately an unitary matrix,
* within the precision given by \a prec. In the case where the \a Scalar
* type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
*
* \note This can be used to check whether a family of vectors forms an orthonormal basis.
* Indeed, \c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an
* orthonormal basis.
*
* Example: \include MatrixBase_isUnitary.cpp
* Output: \verbinclude MatrixBase_isUnitary.out
*/
template<typename Derived>
bool MatrixBase<Derived>::isUnitary(RealScalar prec) const
{
typename Derived::Nested nested(derived());
for(Index i = 0; i < cols(); ++i)
{
if(!internal::isApprox(nested.col(i).squaredNorm(), static_cast<RealScalar>(1), prec))
return false;
for(Index j = 0; j < i; ++j)
if(!internal::isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec))
return false;
}
return true;
}
} // end namespace Eigen
#endif // EIGEN_DOT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_EIGENBASE_H
#define EIGEN_EIGENBASE_H
namespace Eigen {
/** Common base class for all classes T such that MatrixBase has an operator=(T) and a constructor MatrixBase(T).
*
* In other words, an EigenBase object is an object that can be copied into a MatrixBase.
*
* Besides MatrixBase-derived classes, this also includes special matrix classes such as diagonal matrices, etc.
*
* Notice that this class is trivial, it is only used to disambiguate overloaded functions.
*
* \sa \ref TopicClassHierarchy
*/
template<typename Derived> struct EigenBase
{
// typedef typename internal::plain_matrix_type<Derived>::type PlainObject;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Index Index;
/** \returns a reference to the derived object */
Derived& derived() { return *static_cast<Derived*>(this); }
/** \returns a const reference to the derived object */
const Derived& derived() const { return *static_cast<const Derived*>(this); }
inline Derived& const_cast_derived() const
{ return *static_cast<Derived*>(const_cast<EigenBase*>(this)); }
inline const Derived& const_derived() const
{ return *static_cast<const Derived*>(this); }
/** \returns the number of rows. \sa cols(), RowsAtCompileTime */
inline Index rows() const { return derived().rows(); }
/** \returns the number of columns. \sa rows(), ColsAtCompileTime*/
inline Index cols() const { return derived().cols(); }
/** \returns the number of coefficients, which is rows()*cols().
* \sa rows(), cols(), SizeAtCompileTime. */
inline Index size() const { return rows() * cols(); }
/** \internal Don't use it, but do the equivalent: \code dst = *this; \endcode */
template<typename Dest> inline void evalTo(Dest& dst) const
{ derived().evalTo(dst); }
/** \internal Don't use it, but do the equivalent: \code dst += *this; \endcode */
template<typename Dest> inline void addTo(Dest& dst) const
{
// This is the default implementation,
// derived class can reimplement it in a more optimized way.
typename Dest::PlainObject res(rows(),cols());
evalTo(res);
dst += res;
}
/** \internal Don't use it, but do the equivalent: \code dst -= *this; \endcode */
template<typename Dest> inline void subTo(Dest& dst) const
{
// This is the default implementation,
// derived class can reimplement it in a more optimized way.
typename Dest::PlainObject res(rows(),cols());
evalTo(res);
dst -= res;
}
/** \internal Don't use it, but do the equivalent: \code dst.applyOnTheRight(*this); \endcode */
template<typename Dest> inline void applyThisOnTheRight(Dest& dst) const
{
// This is the default implementation,
// derived class can reimplement it in a more optimized way.
dst = dst * this->derived();
}
/** \internal Don't use it, but do the equivalent: \code dst.applyOnTheLeft(*this); \endcode */
template<typename Dest> inline void applyThisOnTheLeft(Dest& dst) const
{
// This is the default implementation,
// derived class can reimplement it in a more optimized way.
dst = this->derived() * dst;
}
};
/***************************************************************************
* Implementation of matrix base methods
***************************************************************************/
/** \brief Copies the generic expression \a other into *this.
*
* \details The expression must provide a (templated) evalTo(Derived& dst) const
* function which does the actual job. In practice, this allows any user to write
* its own special matrix without having to modify MatrixBase
*
* \returns a reference to *this.
*/
template<typename Derived>
template<typename OtherDerived>
Derived& DenseBase<Derived>::operator=(const EigenBase<OtherDerived> &other)
{
other.derived().evalTo(derived());
return derived();
}
template<typename Derived>
template<typename OtherDerived>
Derived& DenseBase<Derived>::operator+=(const EigenBase<OtherDerived> &other)
{
other.derived().addTo(derived());
return derived();
}
template<typename Derived>
template<typename OtherDerived>
Derived& DenseBase<Derived>::operator-=(const EigenBase<OtherDerived> &other)
{
other.derived().subTo(derived());
return derived();
}
/** replaces \c *this by \c *this * \a other.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
inline Derived&
MatrixBase<Derived>::operator*=(const EigenBase<OtherDerived> &other)
{
other.derived().applyThisOnTheRight(derived());
return derived();
}
/** replaces \c *this by \c *this * \a other. It is equivalent to MatrixBase::operator*=() */
template<typename Derived>
template<typename OtherDerived>
inline void MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived> &other)
{
other.derived().applyThisOnTheRight(derived());
}
/** replaces \c *this by \c *this * \a other. */
template<typename Derived>
template<typename OtherDerived>
inline void MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived> &other)
{
other.derived().applyThisOnTheLeft(derived());
}
} // end namespace Eigen
#endif // EIGEN_EIGENBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_FLAGGED_H
#define EIGEN_FLAGGED_H
namespace Eigen {
/** \class Flagged
* \ingroup Core_Module
*
* \brief Expression with modified flags
*
* \param ExpressionType the type of the object of which we are modifying the flags
* \param Added the flags added to the expression
* \param Removed the flags removed from the expression (has priority over Added).
*
* This class represents an expression whose flags have been modified.
* It is the return type of MatrixBase::flagged()
* and most of the time this is the only way it is used.
*
* \sa MatrixBase::flagged()
*/
namespace internal {
template<typename ExpressionType, unsigned int Added, unsigned int Removed>
struct traits<Flagged<ExpressionType, Added, Removed> > : traits<ExpressionType>
{
enum { Flags = (ExpressionType::Flags | Added) & ~Removed };
};
}
template<typename ExpressionType, unsigned int Added, unsigned int Removed> class Flagged
: public MatrixBase<Flagged<ExpressionType, Added, Removed> >
{
public:
typedef MatrixBase<Flagged> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Flagged)
typedef typename internal::conditional<internal::must_nest_by_value<ExpressionType>::ret,
ExpressionType, const ExpressionType&>::type ExpressionTypeNested;
typedef typename ExpressionType::InnerIterator InnerIterator;
inline Flagged(const ExpressionType& matrix) : m_matrix(matrix) {}
inline Index rows() const { return m_matrix.rows(); }
inline Index cols() const { return m_matrix.cols(); }
inline Index outerStride() const { return m_matrix.outerStride(); }
inline Index innerStride() const { return m_matrix.innerStride(); }
inline CoeffReturnType coeff(Index row, Index col) const
{
return m_matrix.coeff(row, col);
}
inline CoeffReturnType coeff(Index index) const
{
return m_matrix.coeff(index);
}
inline const Scalar& coeffRef(Index row, Index col) const
{
return m_matrix.const_cast_derived().coeffRef(row, col);
}
inline const Scalar& coeffRef(Index index) const
{
return m_matrix.const_cast_derived().coeffRef(index);
}
inline Scalar& coeffRef(Index row, Index col)
{
return m_matrix.const_cast_derived().coeffRef(row, col);
}
inline Scalar& coeffRef(Index index)
{
return m_matrix.const_cast_derived().coeffRef(index);
}
template<int LoadMode>
inline const PacketScalar packet(Index row, Index col) const
{
return m_matrix.template packet<LoadMode>(row, col);
}
template<int LoadMode>
inline void writePacket(Index row, Index col, const PacketScalar& x)
{
m_matrix.const_cast_derived().template writePacket<LoadMode>(row, col, x);
}
template<int LoadMode>
inline const PacketScalar packet(Index index) const
{
return m_matrix.template packet<LoadMode>(index);
}
template<int LoadMode>
inline void writePacket(Index index, const PacketScalar& x)
{
m_matrix.const_cast_derived().template writePacket<LoadMode>(index, x);
}
const ExpressionType& _expression() const { return m_matrix; }
template<typename OtherDerived>
typename ExpressionType::PlainObject solveTriangular(const MatrixBase<OtherDerived>& other) const;
template<typename OtherDerived>
void solveTriangularInPlace(const MatrixBase<OtherDerived>& other) const;
protected:
ExpressionTypeNested m_matrix;
};
/** \returns an expression of *this with added and removed flags
*
* This is mostly for internal use.
*
* \sa class Flagged
*/
template<typename Derived>
template<unsigned int Added,unsigned int Removed>
inline const Flagged<Derived, Added, Removed>
DenseBase<Derived>::flagged() const
{
return derived();
}
} // end namespace Eigen
#endif // EIGEN_FLAGGED_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_FORCEALIGNEDACCESS_H
#define EIGEN_FORCEALIGNEDACCESS_H
namespace Eigen {
/** \class ForceAlignedAccess
* \ingroup Core_Module
*
* \brief Enforce aligned packet loads and stores regardless of what is requested
*
* \param ExpressionType the type of the object of which we are forcing aligned packet access
*
* This class is the return type of MatrixBase::forceAlignedAccess()
* and most of the time this is the only way it is used.
*
* \sa MatrixBase::forceAlignedAccess()
*/
namespace internal {
template<typename ExpressionType>
struct traits<ForceAlignedAccess<ExpressionType> > : public traits<ExpressionType>
{};
}
template<typename ExpressionType> class ForceAlignedAccess
: public internal::dense_xpr_base< ForceAlignedAccess<ExpressionType> >::type
{
public:
typedef typename internal::dense_xpr_base<ForceAlignedAccess>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(ForceAlignedAccess)
inline ForceAlignedAccess(const ExpressionType& matrix) : m_expression(matrix) {}
inline Index rows() const { return m_expression.rows(); }
inline Index cols() const { return m_expression.cols(); }
inline Index outerStride() const { return m_expression.outerStride(); }
inline Index innerStride() const { return m_expression.innerStride(); }
inline const CoeffReturnType coeff(Index row, Index col) const
{
return m_expression.coeff(row, col);
}
inline Scalar& coeffRef(Index row, Index col)
{
return m_expression.const_cast_derived().coeffRef(row, col);
}
inline const CoeffReturnType coeff(Index index) const
{
return m_expression.coeff(index);
}
inline Scalar& coeffRef(Index index)
{
return m_expression.const_cast_derived().coeffRef(index);
}
template<int LoadMode>
inline const PacketScalar packet(Index row, Index col) const
{
return m_expression.template packet<Aligned>(row, col);
}
template<int LoadMode>
inline void writePacket(Index row, Index col, const PacketScalar& x)
{
m_expression.const_cast_derived().template writePacket<Aligned>(row, col, x);
}
template<int LoadMode>
inline const PacketScalar packet(Index index) const
{
return m_expression.template packet<Aligned>(index);
}
template<int LoadMode>
inline void writePacket(Index index, const PacketScalar& x)
{
m_expression.const_cast_derived().template writePacket<Aligned>(index, x);
}
operator const ExpressionType&() const { return m_expression; }
protected:
const ExpressionType& m_expression;
private:
ForceAlignedAccess& operator=(const ForceAlignedAccess&);
};
/** \returns an expression of *this with forced aligned access
* \sa forceAlignedAccessIf(),class ForceAlignedAccess
*/
template<typename Derived>
inline const ForceAlignedAccess<Derived>
MatrixBase<Derived>::forceAlignedAccess() const
{
return ForceAlignedAccess<Derived>(derived());
}
/** \returns an expression of *this with forced aligned access
* \sa forceAlignedAccessIf(), class ForceAlignedAccess
*/
template<typename Derived>
inline ForceAlignedAccess<Derived>
MatrixBase<Derived>::forceAlignedAccess()
{
return ForceAlignedAccess<Derived>(derived());
}
/** \returns an expression of *this with forced aligned access if \a Enable is true.
* \sa forceAlignedAccess(), class ForceAlignedAccess
*/
template<typename Derived>
template<bool Enable>
inline typename internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type
MatrixBase<Derived>::forceAlignedAccessIf() const
{
return derived();
}
/** \returns an expression of *this with forced aligned access if \a Enable is true.
* \sa forceAlignedAccess(), class ForceAlignedAccess
*/
template<typename Derived>
template<bool Enable>
inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type
MatrixBase<Derived>::forceAlignedAccessIf()
{
return derived();
}
} // end namespace Eigen
#endif // EIGEN_FORCEALIGNEDACCESS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_FUNCTORS_H
#define EIGEN_FUNCTORS_H
namespace Eigen {
namespace internal {
// associative functors:
/** \internal
* \brief Template functor to compute the sum of two scalars
*
* \sa class CwiseBinaryOp, MatrixBase::operator+, class VectorwiseOp, MatrixBase::sum()
*/
template<typename Scalar> struct scalar_sum_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_sum_op)
EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a + b; }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
{ return internal::padd(a,b); }
template<typename Packet>
EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
{ return internal::predux(a); }
};
template<typename Scalar>
struct functor_traits<scalar_sum_op<Scalar> > {
enum {
Cost = NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasAdd
};
};
/** \internal
* \brief Template functor to compute the product of two scalars
*
* \sa class CwiseBinaryOp, Cwise::operator*(), class VectorwiseOp, MatrixBase::redux()
*/
template<typename LhsScalar,typename RhsScalar> struct scalar_product_op {
enum {
// TODO vectorize mixed product
Vectorizable = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasMul && packet_traits<RhsScalar>::HasMul
};
typedef typename scalar_product_traits<LhsScalar,RhsScalar>::ReturnType result_type;
EIGEN_EMPTY_STRUCT_CTOR(scalar_product_op)
EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a * b; }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
{ return internal::pmul(a,b); }
template<typename Packet>
EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const
{ return internal::predux_mul(a); }
};
template<typename LhsScalar,typename RhsScalar>
struct functor_traits<scalar_product_op<LhsScalar,RhsScalar> > {
enum {
Cost = (NumTraits<LhsScalar>::MulCost + NumTraits<RhsScalar>::MulCost)/2, // rough estimate!
PacketAccess = scalar_product_op<LhsScalar,RhsScalar>::Vectorizable
};
};
/** \internal
* \brief Template functor to compute the conjugate product of two scalars
*
* This is a short cut for conj(x) * y which is needed for optimization purpose; in Eigen2 support mode, this becomes x * conj(y)
*/
template<typename LhsScalar,typename RhsScalar> struct scalar_conj_product_op {
enum {
Conj = NumTraits<LhsScalar>::IsComplex
};
typedef typename scalar_product_traits<LhsScalar,RhsScalar>::ReturnType result_type;
EIGEN_EMPTY_STRUCT_CTOR(scalar_conj_product_op)
EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const
{ return conj_helper<LhsScalar,RhsScalar,Conj,false>().pmul(a,b); }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
{ return conj_helper<Packet,Packet,Conj,false>().pmul(a,b); }
};
template<typename LhsScalar,typename RhsScalar>
struct functor_traits<scalar_conj_product_op<LhsScalar,RhsScalar> > {
enum {
Cost = NumTraits<LhsScalar>::MulCost,
PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMul
};
};
/** \internal
* \brief Template functor to compute the min of two scalars
*
* \sa class CwiseBinaryOp, MatrixBase::cwiseMin, class VectorwiseOp, MatrixBase::minCoeff()
*/
template<typename Scalar> struct scalar_min_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_min_op)
EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { using std::min; return (min)(a, b); }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
{ return internal::pmin(a,b); }
template<typename Packet>
EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
{ return internal::predux_min(a); }
};
template<typename Scalar>
struct functor_traits<scalar_min_op<Scalar> > {
enum {
Cost = NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasMin
};
};
/** \internal
* \brief Template functor to compute the max of two scalars
*
* \sa class CwiseBinaryOp, MatrixBase::cwiseMax, class VectorwiseOp, MatrixBase::maxCoeff()
*/
template<typename Scalar> struct scalar_max_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_max_op)
EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { using std::max; return (max)(a, b); }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
{ return internal::pmax(a,b); }
template<typename Packet>
EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
{ return internal::predux_max(a); }
};
template<typename Scalar>
struct functor_traits<scalar_max_op<Scalar> > {
enum {
Cost = NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasMax
};
};
/** \internal
* \brief Template functor to compute the hypot of two scalars
*
* \sa MatrixBase::stableNorm(), class Redux
*/
template<typename Scalar> struct scalar_hypot_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_hypot_op)
// typedef typename NumTraits<Scalar>::Real result_type;
EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& _x, const Scalar& _y) const
{
using std::max;
using std::min;
Scalar p = (max)(_x, _y);
Scalar q = (min)(_x, _y);
Scalar qp = q/p;
return p * sqrt(Scalar(1) + qp*qp);
}
};
template<typename Scalar>
struct functor_traits<scalar_hypot_op<Scalar> > {
enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess=0 };
};
/** \internal
* \brief Template functor to compute the pow of two scalars
*/
template<typename Scalar, typename OtherScalar> struct scalar_binary_pow_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_binary_pow_op)
inline Scalar operator() (const Scalar& a, const OtherScalar& b) const { return internal::pow(a, b); }
};
template<typename Scalar, typename OtherScalar>
struct functor_traits<scalar_binary_pow_op<Scalar,OtherScalar> > {
enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
};
// other binary functors:
/** \internal
* \brief Template functor to compute the difference of two scalars
*
* \sa class CwiseBinaryOp, MatrixBase::operator-
*/
template<typename Scalar> struct scalar_difference_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_difference_op)
EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a - b; }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
{ return internal::psub(a,b); }
};
template<typename Scalar>
struct functor_traits<scalar_difference_op<Scalar> > {
enum {
Cost = NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasSub
};
};
/** \internal
* \brief Template functor to compute the quotient of two scalars
*
* \sa class CwiseBinaryOp, Cwise::operator/()
*/
template<typename Scalar> struct scalar_quotient_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_quotient_op)
EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a / b; }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
{ return internal::pdiv(a,b); }
};
template<typename Scalar>
struct functor_traits<scalar_quotient_op<Scalar> > {
enum {
Cost = 2 * NumTraits<Scalar>::MulCost,
PacketAccess = packet_traits<Scalar>::HasDiv
};
};
/** \internal
* \brief Template functor to compute the and of two booleans
*
* \sa class CwiseBinaryOp, ArrayBase::operator&&
*/
struct scalar_boolean_and_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_and_op)
EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a && b; }
};
template<> struct functor_traits<scalar_boolean_and_op> {
enum {
Cost = NumTraits<bool>::AddCost,
PacketAccess = false
};
};
/** \internal
* \brief Template functor to compute the or of two booleans
*
* \sa class CwiseBinaryOp, ArrayBase::operator||
*/
struct scalar_boolean_or_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_or_op)
EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a || b; }
};
template<> struct functor_traits<scalar_boolean_or_op> {
enum {
Cost = NumTraits<bool>::AddCost,
PacketAccess = false
};
};
// unary functors:
/** \internal
* \brief Template functor to compute the opposite of a scalar
*
* \sa class CwiseUnaryOp, MatrixBase::operator-
*/
template<typename Scalar> struct scalar_opposite_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_opposite_op)
EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return -a; }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
{ return internal::pnegate(a); }
};
template<typename Scalar>
struct functor_traits<scalar_opposite_op<Scalar> >
{ enum {
Cost = NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasNegate };
};
/** \internal
* \brief Template functor to compute the absolute value of a scalar
*
* \sa class CwiseUnaryOp, Cwise::abs
*/
template<typename Scalar> struct scalar_abs_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_abs_op)
typedef typename NumTraits<Scalar>::Real result_type;
EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return internal::abs(a); }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
{ return internal::pabs(a); }
};
template<typename Scalar>
struct functor_traits<scalar_abs_op<Scalar> >
{
enum {
Cost = NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasAbs
};
};
/** \internal
* \brief Template functor to compute the squared absolute value of a scalar
*
* \sa class CwiseUnaryOp, Cwise::abs2
*/
template<typename Scalar> struct scalar_abs2_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_abs2_op)
typedef typename NumTraits<Scalar>::Real result_type;
EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return internal::abs2(a); }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
{ return internal::pmul(a,a); }
};
template<typename Scalar>
struct functor_traits<scalar_abs2_op<Scalar> >
{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasAbs2 }; };
/** \internal
* \brief Template functor to compute the conjugate of a complex value
*
* \sa class CwiseUnaryOp, MatrixBase::conjugate()
*/
template<typename Scalar> struct scalar_conjugate_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_conjugate_op)
EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return internal::conj(a); }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const { return internal::pconj(a); }
};
template<typename Scalar>
struct functor_traits<scalar_conjugate_op<Scalar> >
{
enum {
Cost = NumTraits<Scalar>::IsComplex ? NumTraits<Scalar>::AddCost : 0,
PacketAccess = packet_traits<Scalar>::HasConj
};
};
/** \internal
* \brief Template functor to cast a scalar to another type
*
* \sa class CwiseUnaryOp, MatrixBase::cast()
*/
template<typename Scalar, typename NewType>
struct scalar_cast_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_cast_op)
typedef NewType result_type;
EIGEN_STRONG_INLINE const NewType operator() (const Scalar& a) const { return cast<Scalar, NewType>(a); }
};
template<typename Scalar, typename NewType>
struct functor_traits<scalar_cast_op<Scalar,NewType> >
{ enum { Cost = is_same<Scalar, NewType>::value ? 0 : NumTraits<NewType>::AddCost, PacketAccess = false }; };
/** \internal
* \brief Template functor to extract the real part of a complex
*
* \sa class CwiseUnaryOp, MatrixBase::real()
*/
template<typename Scalar>
struct scalar_real_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_real_op)
typedef typename NumTraits<Scalar>::Real result_type;
EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return internal::real(a); }
};
template<typename Scalar>
struct functor_traits<scalar_real_op<Scalar> >
{ enum { Cost = 0, PacketAccess = false }; };
/** \internal
* \brief Template functor to extract the imaginary part of a complex
*
* \sa class CwiseUnaryOp, MatrixBase::imag()
*/
template<typename Scalar>
struct scalar_imag_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_op)
typedef typename NumTraits<Scalar>::Real result_type;
EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return internal::imag(a); }
};
template<typename Scalar>
struct functor_traits<scalar_imag_op<Scalar> >
{ enum { Cost = 0, PacketAccess = false }; };
/** \internal
* \brief Template functor to extract the real part of a complex as a reference
*
* \sa class CwiseUnaryOp, MatrixBase::real()
*/
template<typename Scalar>
struct scalar_real_ref_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_real_ref_op)
typedef typename NumTraits<Scalar>::Real result_type;
EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return internal::real_ref(*const_cast<Scalar*>(&a)); }
};
template<typename Scalar>
struct functor_traits<scalar_real_ref_op<Scalar> >
{ enum { Cost = 0, PacketAccess = false }; };
/** \internal
* \brief Template functor to extract the imaginary part of a complex as a reference
*
* \sa class CwiseUnaryOp, MatrixBase::imag()
*/
template<typename Scalar>
struct scalar_imag_ref_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_ref_op)
typedef typename NumTraits<Scalar>::Real result_type;
EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return internal::imag_ref(*const_cast<Scalar*>(&a)); }
};
template<typename Scalar>
struct functor_traits<scalar_imag_ref_op<Scalar> >
{ enum { Cost = 0, PacketAccess = false }; };
/** \internal
*
* \brief Template functor to compute the exponential of a scalar
*
* \sa class CwiseUnaryOp, Cwise::exp()
*/
template<typename Scalar> struct scalar_exp_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_exp_op)
inline const Scalar operator() (const Scalar& a) const { return internal::exp(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::pexp(a); }
};
template<typename Scalar>
struct functor_traits<scalar_exp_op<Scalar> >
{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasExp }; };
/** \internal
*
* \brief Template functor to compute the logarithm of a scalar
*
* \sa class CwiseUnaryOp, Cwise::log()
*/
template<typename Scalar> struct scalar_log_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_log_op)
inline const Scalar operator() (const Scalar& a) const { return internal::log(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::plog(a); }
};
template<typename Scalar>
struct functor_traits<scalar_log_op<Scalar> >
{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasLog }; };
/** \internal
* \brief Template functor to multiply a scalar by a fixed other one
*
* \sa class CwiseUnaryOp, MatrixBase::operator*, MatrixBase::operator/
*/
/* NOTE why doing the pset1() in packetOp *is* an optimization ?
* indeed it seems better to declare m_other as a Packet and do the pset1() once
* in the constructor. However, in practice:
* - GCC does not like m_other as a Packet and generate a load every time it needs it
* - on the other hand GCC is able to moves the pset1() outside the loop :)
* - simpler code ;)
* (ICC and gcc 4.4 seems to perform well in both cases, the issue is visible with y = a*x + b*y)
*/
template<typename Scalar>
struct scalar_multiple_op {
typedef typename packet_traits<Scalar>::type Packet;
// FIXME default copy constructors seems bugged with std::complex<>
EIGEN_STRONG_INLINE scalar_multiple_op(const scalar_multiple_op& other) : m_other(other.m_other) { }
EIGEN_STRONG_INLINE scalar_multiple_op(const Scalar& other) : m_other(other) { }
EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a * m_other; }
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
{ return internal::pmul(a, pset1<Packet>(m_other)); }
typename add_const_on_value_type<typename NumTraits<Scalar>::Nested>::type m_other;
};
template<typename Scalar>
struct functor_traits<scalar_multiple_op<Scalar> >
{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
template<typename Scalar1, typename Scalar2>
struct scalar_multiple2_op {
typedef typename scalar_product_traits<Scalar1,Scalar2>::ReturnType result_type;
EIGEN_STRONG_INLINE scalar_multiple2_op(const scalar_multiple2_op& other) : m_other(other.m_other) { }
EIGEN_STRONG_INLINE scalar_multiple2_op(const Scalar2& other) : m_other(other) { }
EIGEN_STRONG_INLINE result_type operator() (const Scalar1& a) const { return a * m_other; }
typename add_const_on_value_type<typename NumTraits<Scalar2>::Nested>::type m_other;
};
template<typename Scalar1,typename Scalar2>
struct functor_traits<scalar_multiple2_op<Scalar1,Scalar2> >
{ enum { Cost = NumTraits<Scalar1>::MulCost, PacketAccess = false }; };
/** \internal
* \brief Template functor to divide a scalar by a fixed other one
*
* This functor is used to implement the quotient of a matrix by
* a scalar where the scalar type is not necessarily a floating point type.
*
* \sa class CwiseUnaryOp, MatrixBase::operator/
*/
template<typename Scalar>
struct scalar_quotient1_op {
typedef typename packet_traits<Scalar>::type Packet;
// FIXME default copy constructors seems bugged with std::complex<>
EIGEN_STRONG_INLINE scalar_quotient1_op(const scalar_quotient1_op& other) : m_other(other.m_other) { }
EIGEN_STRONG_INLINE scalar_quotient1_op(const Scalar& other) : m_other(other) {}
EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a / m_other; }
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
{ return internal::pdiv(a, pset1<Packet>(m_other)); }
typename add_const_on_value_type<typename NumTraits<Scalar>::Nested>::type m_other;
};
template<typename Scalar>
struct functor_traits<scalar_quotient1_op<Scalar> >
{ enum { Cost = 2 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasDiv }; };
// nullary functors
template<typename Scalar>
struct scalar_constant_op {
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_STRONG_INLINE scalar_constant_op(const scalar_constant_op& other) : m_other(other.m_other) { }
EIGEN_STRONG_INLINE scalar_constant_op(const Scalar& other) : m_other(other) { }
template<typename Index>
EIGEN_STRONG_INLINE const Scalar operator() (Index, Index = 0) const { return m_other; }
template<typename Index>
EIGEN_STRONG_INLINE const Packet packetOp(Index, Index = 0) const { return internal::pset1<Packet>(m_other); }
const Scalar m_other;
};
template<typename Scalar>
struct functor_traits<scalar_constant_op<Scalar> >
// FIXME replace this packet test by a safe one
{ enum { Cost = 1, PacketAccess = packet_traits<Scalar>::Vectorizable, IsRepeatable = true }; };
template<typename Scalar> struct scalar_identity_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_identity_op)
template<typename Index>
EIGEN_STRONG_INLINE const Scalar operator() (Index row, Index col) const { return row==col ? Scalar(1) : Scalar(0); }
};
template<typename Scalar>
struct functor_traits<scalar_identity_op<Scalar> >
{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = false, IsRepeatable = true }; };
template <typename Scalar, bool RandomAccess> struct linspaced_op_impl;
// linear access for packet ops:
// 1) initialization
// base = [low, ..., low] + ([step, ..., step] * [-size, ..., 0])
// 2) each step (where size is 1 for coeff access or PacketSize for packet access)
// base += [size*step, ..., size*step]
//
// TODO: Perhaps it's better to initialize lazily (so not in the constructor but in packetOp)
// in order to avoid the padd() in operator() ?
template <typename Scalar>
struct linspaced_op_impl<Scalar,false>
{
typedef typename packet_traits<Scalar>::type Packet;
linspaced_op_impl(Scalar low, Scalar step) :
m_low(low), m_step(step),
m_packetStep(pset1<Packet>(packet_traits<Scalar>::size*step)),
m_base(padd(pset1<Packet>(low), pmul(pset1<Packet>(step),plset<Scalar>(-packet_traits<Scalar>::size)))) {}
template<typename Index>
EIGEN_STRONG_INLINE const Scalar operator() (Index i) const
{
m_base = padd(m_base, pset1<Packet>(m_step));
return m_low+i*m_step;
}
template<typename Index>
EIGEN_STRONG_INLINE const Packet packetOp(Index) const { return m_base = padd(m_base,m_packetStep); }
const Scalar m_low;
const Scalar m_step;
const Packet m_packetStep;
mutable Packet m_base;
};
// random access for packet ops:
// 1) each step
// [low, ..., low] + ( [step, ..., step] * ( [i, ..., i] + [0, ..., size] ) )
template <typename Scalar>
struct linspaced_op_impl<Scalar,true>
{
typedef typename packet_traits<Scalar>::type Packet;
linspaced_op_impl(Scalar low, Scalar step) :
m_low(low), m_step(step),
m_lowPacket(pset1<Packet>(m_low)), m_stepPacket(pset1<Packet>(m_step)), m_interPacket(plset<Scalar>(0)) {}
template<typename Index>
EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return m_low+i*m_step; }
template<typename Index>
EIGEN_STRONG_INLINE const Packet packetOp(Index i) const
{ return internal::padd(m_lowPacket, pmul(m_stepPacket, padd(pset1<Packet>(i),m_interPacket))); }
const Scalar m_low;
const Scalar m_step;
const Packet m_lowPacket;
const Packet m_stepPacket;
const Packet m_interPacket;
};
// ----- Linspace functor ----------------------------------------------------------------
// Forward declaration (we default to random access which does not really give
// us a speed gain when using packet access but it allows to use the functor in
// nested expressions).
template <typename Scalar, bool RandomAccess = true> struct linspaced_op;
template <typename Scalar, bool RandomAccess> struct functor_traits< linspaced_op<Scalar,RandomAccess> >
{ enum { Cost = 1, PacketAccess = packet_traits<Scalar>::HasSetLinear, IsRepeatable = true }; };
template <typename Scalar, bool RandomAccess> struct linspaced_op
{
typedef typename packet_traits<Scalar>::type Packet;
linspaced_op(Scalar low, Scalar high, int num_steps) : impl((num_steps==1 ? high : low), (num_steps==1 ? Scalar() : (high-low)/(num_steps-1))) {}
template<typename Index>
EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return impl(i); }
// We need this function when assigning e.g. a RowVectorXd to a MatrixXd since
// there row==0 and col is used for the actual iteration.
template<typename Index>
EIGEN_STRONG_INLINE const Scalar operator() (Index row, Index col) const
{
eigen_assert(col==0 || row==0);
return impl(col + row);
}
template<typename Index>
EIGEN_STRONG_INLINE const Packet packetOp(Index i) const { return impl.packetOp(i); }
// We need this function when assigning e.g. a RowVectorXd to a MatrixXd since
// there row==0 and col is used for the actual iteration.
template<typename Index>
EIGEN_STRONG_INLINE const Packet packetOp(Index row, Index col) const
{
eigen_assert(col==0 || row==0);
return impl.packetOp(col + row);
}
// This proxy object handles the actual required temporaries, the different
// implementations (random vs. sequential access) as well as the
// correct piping to size 2/4 packet operations.
const linspaced_op_impl<Scalar,RandomAccess> impl;
};
// all functors allow linear access, except scalar_identity_op. So we fix here a quick meta
// to indicate whether a functor allows linear access, just always answering 'yes' except for
// scalar_identity_op.
// FIXME move this to functor_traits adding a functor_default
template<typename Functor> struct functor_has_linear_access { enum { ret = 1 }; };
template<typename Scalar> struct functor_has_linear_access<scalar_identity_op<Scalar> > { enum { ret = 0 }; };
// in CwiseBinaryOp, we require the Lhs and Rhs to have the same scalar type, except for multiplication
// where we only require them to have the same _real_ scalar type so one may multiply, say, float by complex<float>.
// FIXME move this to functor_traits adding a functor_default
template<typename Functor> struct functor_allows_mixing_real_and_complex { enum { ret = 0 }; };
template<typename LhsScalar,typename RhsScalar> struct functor_allows_mixing_real_and_complex<scalar_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
template<typename LhsScalar,typename RhsScalar> struct functor_allows_mixing_real_and_complex<scalar_conj_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
/** \internal
* \brief Template functor to add a scalar to a fixed other one
* \sa class CwiseUnaryOp, Array::operator+
*/
/* If you wonder why doing the pset1() in packetOp() is an optimization check scalar_multiple_op */
template<typename Scalar>
struct scalar_add_op {
typedef typename packet_traits<Scalar>::type Packet;
// FIXME default copy constructors seems bugged with std::complex<>
inline scalar_add_op(const scalar_add_op& other) : m_other(other.m_other) { }
inline scalar_add_op(const Scalar& other) : m_other(other) { }
inline Scalar operator() (const Scalar& a) const { return a + m_other; }
inline const Packet packetOp(const Packet& a) const
{ return internal::padd(a, pset1<Packet>(m_other)); }
const Scalar m_other;
};
template<typename Scalar>
struct functor_traits<scalar_add_op<Scalar> >
{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasAdd }; };
/** \internal
* \brief Template functor to compute the square root of a scalar
* \sa class CwiseUnaryOp, Cwise::sqrt()
*/
template<typename Scalar> struct scalar_sqrt_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_sqrt_op)
inline const Scalar operator() (const Scalar& a) const { return internal::sqrt(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::psqrt(a); }
};
template<typename Scalar>
struct functor_traits<scalar_sqrt_op<Scalar> >
{ enum {
Cost = 5 * NumTraits<Scalar>::MulCost,
PacketAccess = packet_traits<Scalar>::HasSqrt
};
};
/** \internal
* \brief Template functor to compute the cosine of a scalar
* \sa class CwiseUnaryOp, ArrayBase::cos()
*/
template<typename Scalar> struct scalar_cos_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_cos_op)
inline Scalar operator() (const Scalar& a) const { return internal::cos(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::pcos(a); }
};
template<typename Scalar>
struct functor_traits<scalar_cos_op<Scalar> >
{
enum {
Cost = 5 * NumTraits<Scalar>::MulCost,
PacketAccess = packet_traits<Scalar>::HasCos
};
};
/** \internal
* \brief Template functor to compute the sine of a scalar
* \sa class CwiseUnaryOp, ArrayBase::sin()
*/
template<typename Scalar> struct scalar_sin_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_sin_op)
inline const Scalar operator() (const Scalar& a) const { return internal::sin(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::psin(a); }
};
template<typename Scalar>
struct functor_traits<scalar_sin_op<Scalar> >
{
enum {
Cost = 5 * NumTraits<Scalar>::MulCost,
PacketAccess = packet_traits<Scalar>::HasSin
};
};
/** \internal
* \brief Template functor to compute the tan of a scalar
* \sa class CwiseUnaryOp, ArrayBase::tan()
*/
template<typename Scalar> struct scalar_tan_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_tan_op)
inline const Scalar operator() (const Scalar& a) const { return internal::tan(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::ptan(a); }
};
template<typename Scalar>
struct functor_traits<scalar_tan_op<Scalar> >
{
enum {
Cost = 5 * NumTraits<Scalar>::MulCost,
PacketAccess = packet_traits<Scalar>::HasTan
};
};
/** \internal
* \brief Template functor to compute the arc cosine of a scalar
* \sa class CwiseUnaryOp, ArrayBase::acos()
*/
template<typename Scalar> struct scalar_acos_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_acos_op)
inline const Scalar operator() (const Scalar& a) const { return internal::acos(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::pacos(a); }
};
template<typename Scalar>
struct functor_traits<scalar_acos_op<Scalar> >
{
enum {
Cost = 5 * NumTraits<Scalar>::MulCost,
PacketAccess = packet_traits<Scalar>::HasACos
};
};
/** \internal
* \brief Template functor to compute the arc sine of a scalar
* \sa class CwiseUnaryOp, ArrayBase::asin()
*/
template<typename Scalar> struct scalar_asin_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_asin_op)
inline const Scalar operator() (const Scalar& a) const { return internal::asin(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::pasin(a); }
};
template<typename Scalar>
struct functor_traits<scalar_asin_op<Scalar> >
{
enum {
Cost = 5 * NumTraits<Scalar>::MulCost,
PacketAccess = packet_traits<Scalar>::HasASin
};
};
/** \internal
* \brief Template functor to raise a scalar to a power
* \sa class CwiseUnaryOp, Cwise::pow
*/
template<typename Scalar>
struct scalar_pow_op {
// FIXME default copy constructors seems bugged with std::complex<>
inline scalar_pow_op(const scalar_pow_op& other) : m_exponent(other.m_exponent) { }
inline scalar_pow_op(const Scalar& exponent) : m_exponent(exponent) {}
inline Scalar operator() (const Scalar& a) const { return internal::pow(a, m_exponent); }
const Scalar m_exponent;
};
template<typename Scalar>
struct functor_traits<scalar_pow_op<Scalar> >
{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false }; };
/** \internal
* \brief Template functor to compute the quotient between a scalar and array entries.
* \sa class CwiseUnaryOp, Cwise::inverse()
*/
template<typename Scalar>
struct scalar_inverse_mult_op {
scalar_inverse_mult_op(const Scalar& other) : m_other(other) {}
inline Scalar operator() (const Scalar& a) const { return m_other / a; }
template<typename Packet>
inline const Packet packetOp(const Packet& a) const
{ return internal::pdiv(pset1<Packet>(m_other),a); }
Scalar m_other;
};
/** \internal
* \brief Template functor to compute the inverse of a scalar
* \sa class CwiseUnaryOp, Cwise::inverse()
*/
template<typename Scalar>
struct scalar_inverse_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_inverse_op)
inline Scalar operator() (const Scalar& a) const { return Scalar(1)/a; }
template<typename Packet>
inline const Packet packetOp(const Packet& a) const
{ return internal::pdiv(pset1<Packet>(Scalar(1)),a); }
};
template<typename Scalar>
struct functor_traits<scalar_inverse_op<Scalar> >
{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasDiv }; };
/** \internal
* \brief Template functor to compute the square of a scalar
* \sa class CwiseUnaryOp, Cwise::square()
*/
template<typename Scalar>
struct scalar_square_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_square_op)
inline Scalar operator() (const Scalar& a) const { return a*a; }
template<typename Packet>
inline const Packet packetOp(const Packet& a) const
{ return internal::pmul(a,a); }
};
template<typename Scalar>
struct functor_traits<scalar_square_op<Scalar> >
{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
/** \internal
* \brief Template functor to compute the cube of a scalar
* \sa class CwiseUnaryOp, Cwise::cube()
*/
template<typename Scalar>
struct scalar_cube_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_cube_op)
inline Scalar operator() (const Scalar& a) const { return a*a*a; }
template<typename Packet>
inline const Packet packetOp(const Packet& a) const
{ return internal::pmul(a,pmul(a,a)); }
};
template<typename Scalar>
struct functor_traits<scalar_cube_op<Scalar> >
{ enum { Cost = 2*NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
// default functor traits for STL functors:
template<typename T>
struct functor_traits<std::multiplies<T> >
{ enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::divides<T> >
{ enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::plus<T> >
{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::minus<T> >
{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::negate<T> >
{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::logical_or<T> >
{ enum { Cost = 1, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::logical_and<T> >
{ enum { Cost = 1, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::logical_not<T> >
{ enum { Cost = 1, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::greater<T> >
{ enum { Cost = 1, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::less<T> >
{ enum { Cost = 1, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::greater_equal<T> >
{ enum { Cost = 1, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::less_equal<T> >
{ enum { Cost = 1, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::equal_to<T> >
{ enum { Cost = 1, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::not_equal_to<T> >
{ enum { Cost = 1, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::binder2nd<T> >
{ enum { Cost = functor_traits<T>::Cost, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::binder1st<T> >
{ enum { Cost = functor_traits<T>::Cost, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::unary_negate<T> >
{ enum { Cost = 1 + functor_traits<T>::Cost, PacketAccess = false }; };
template<typename T>
struct functor_traits<std::binary_negate<T> >
{ enum { Cost = 1 + functor_traits<T>::Cost, PacketAccess = false }; };
#ifdef EIGEN_STDEXT_SUPPORT
template<typename T0,typename T1>
struct functor_traits<std::project1st<T0,T1> >
{ enum { Cost = 0, PacketAccess = false }; };
template<typename T0,typename T1>
struct functor_traits<std::project2nd<T0,T1> >
{ enum { Cost = 0, PacketAccess = false }; };
template<typename T0,typename T1>
struct functor_traits<std::select2nd<std::pair<T0,T1> > >
{ enum { Cost = 0, PacketAccess = false }; };
template<typename T0,typename T1>
struct functor_traits<std::select1st<std::pair<T0,T1> > >
{ enum { Cost = 0, PacketAccess = false }; };
template<typename T0,typename T1>
struct functor_traits<std::unary_compose<T0,T1> >
{ enum { Cost = functor_traits<T0>::Cost + functor_traits<T1>::Cost, PacketAccess = false }; };
template<typename T0,typename T1,typename T2>
struct functor_traits<std::binary_compose<T0,T1,T2> >
{ enum { Cost = functor_traits<T0>::Cost + functor_traits<T1>::Cost + functor_traits<T2>::Cost, PacketAccess = false }; };
#endif // EIGEN_STDEXT_SUPPORT
// allow to add new functors and specializations of functor_traits from outside Eigen.
// this macro is really needed because functor_traits must be specialized after it is declared but before it is used...
#ifdef EIGEN_FUNCTORS_PLUGIN
#include EIGEN_FUNCTORS_PLUGIN
#endif
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_FUNCTORS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_FUZZY_H
#define EIGEN_FUZZY_H
namespace Eigen {
namespace internal
{
template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
struct isApprox_selector
{
static bool run(const Derived& x, const OtherDerived& y, typename Derived::RealScalar prec)
{
using std::min;
typename internal::nested<Derived,2>::type nested(x);
typename internal::nested<OtherDerived,2>::type otherNested(y);
return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * (min)(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());
}
};
template<typename Derived, typename OtherDerived>
struct isApprox_selector<Derived, OtherDerived, true>
{
static bool run(const Derived& x, const OtherDerived& y, typename Derived::RealScalar)
{
return x.matrix() == y.matrix();
}
};
template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
struct isMuchSmallerThan_object_selector
{
static bool run(const Derived& x, const OtherDerived& y, typename Derived::RealScalar prec)
{
return x.cwiseAbs2().sum() <= abs2(prec) * y.cwiseAbs2().sum();
}
};
template<typename Derived, typename OtherDerived>
struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true>
{
static bool run(const Derived& x, const OtherDerived&, typename Derived::RealScalar)
{
return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
}
};
template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
struct isMuchSmallerThan_scalar_selector
{
static bool run(const Derived& x, const typename Derived::RealScalar& y, typename Derived::RealScalar prec)
{
return x.cwiseAbs2().sum() <= abs2(prec * y);
}
};
template<typename Derived>
struct isMuchSmallerThan_scalar_selector<Derived, true>
{
static bool run(const Derived& x, const typename Derived::RealScalar&, typename Derived::RealScalar)
{
return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
}
};
} // end namespace internal
/** \returns \c true if \c *this is approximately equal to \a other, within the precision
* determined by \a prec.
*
* \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
* are considered to be approximately equal within precision \f$ p \f$ if
* \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
* For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm
* L2 norm).
*
* \note Because of the multiplicativeness of this comparison, one can't use this function
* to check whether \c *this is approximately equal to the zero matrix or vector.
* Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
* or vector. If you want to test whether \c *this is zero, use internal::isMuchSmallerThan(const
* RealScalar&, RealScalar) instead.
*
* \sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const
*/
template<typename Derived>
template<typename OtherDerived>
bool DenseBase<Derived>::isApprox(
const DenseBase<OtherDerived>& other,
RealScalar prec
) const
{
return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
}
/** \returns \c true if the norm of \c *this is much smaller than \a other,
* within the precision determined by \a prec.
*
* \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
* considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
* \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
*
* For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason,
* the value of the reference scalar \a other should come from the Hilbert-Schmidt norm
* of a reference matrix of same dimensions.
*
* \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
*/
template<typename Derived>
bool DenseBase<Derived>::isMuchSmallerThan(
const typename NumTraits<Scalar>::Real& other,
RealScalar prec
) const
{
return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec);
}
/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
* within the precision determined by \a prec.
*
* \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
* considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
* \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
* For matrices, the comparison is done using the Hilbert-Schmidt norm.
*
* \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
*/
template<typename Derived>
template<typename OtherDerived>
bool DenseBase<Derived>::isMuchSmallerThan(
const DenseBase<OtherDerived>& other,
RealScalar prec
) const
{
return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
}
} // end namespace Eigen
#endif // EIGEN_FUZZY_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_GENERAL_PRODUCT_H
#define EIGEN_GENERAL_PRODUCT_H
namespace Eigen {
/** \class GeneralProduct
* \ingroup Core_Module
*
* \brief Expression of the product of two general matrices or vectors
*
* \param LhsNested the type used to store the left-hand side
* \param RhsNested the type used to store the right-hand side
* \param ProductMode the type of the product
*
* This class represents an expression of the product of two general matrices.
* We call a general matrix, a dense matrix with full storage. For instance,
* This excludes triangular, selfadjoint, and sparse matrices.
* It is the return type of the operator* between general matrices. Its template
* arguments are determined automatically by ProductReturnType. Therefore,
* GeneralProduct should never be used direclty. To determine the result type of a
* function which involves a matrix product, use ProductReturnType::Type.
*
* \sa ProductReturnType, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
*/
template<typename Lhs, typename Rhs, int ProductType = internal::product_type<Lhs,Rhs>::value>
class GeneralProduct;
enum {
Large = 2,
Small = 3
};
namespace internal {
template<int Rows, int Cols, int Depth> struct product_type_selector;
template<int Size, int MaxSize> struct product_size_category
{
enum { is_large = MaxSize == Dynamic ||
Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD,
value = is_large ? Large
: Size == 1 ? 1
: Small
};
};
template<typename Lhs, typename Rhs> struct product_type
{
typedef typename remove_all<Lhs>::type _Lhs;
typedef typename remove_all<Rhs>::type _Rhs;
enum {
MaxRows = _Lhs::MaxRowsAtCompileTime,
Rows = _Lhs::RowsAtCompileTime,
MaxCols = _Rhs::MaxColsAtCompileTime,
Cols = _Rhs::ColsAtCompileTime,
MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::MaxColsAtCompileTime,
_Rhs::MaxRowsAtCompileTime),
Depth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::ColsAtCompileTime,
_Rhs::RowsAtCompileTime),
LargeThreshold = EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
};
// the splitting into different lines of code here, introducing the _select enums and the typedef below,
// is to work around an internal compiler error with gcc 4.1 and 4.2.
private:
enum {
rows_select = product_size_category<Rows,MaxRows>::value,
cols_select = product_size_category<Cols,MaxCols>::value,
depth_select = product_size_category<Depth,MaxDepth>::value
};
typedef product_type_selector<rows_select, cols_select, depth_select> selector;
public:
enum {
value = selector::ret
};
#ifdef EIGEN_DEBUG_PRODUCT
static void debug()
{
EIGEN_DEBUG_VAR(Rows);
EIGEN_DEBUG_VAR(Cols);
EIGEN_DEBUG_VAR(Depth);
EIGEN_DEBUG_VAR(rows_select);
EIGEN_DEBUG_VAR(cols_select);
EIGEN_DEBUG_VAR(depth_select);
EIGEN_DEBUG_VAR(value);
}
#endif
};
/* The following allows to select the kind of product at compile time
* based on the three dimensions of the product.
* This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
// FIXME I'm not sure the current mapping is the ideal one.
template<int M, int N> struct product_type_selector<M,N,1> { enum { ret = OuterProduct }; };
template<int Depth> struct product_type_selector<1, 1, Depth> { enum { ret = InnerProduct }; };
template<> struct product_type_selector<1, 1, 1> { enum { ret = InnerProduct }; };
template<> struct product_type_selector<Small,1, Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<1, Small,Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<Small,Small,Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<Small, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
template<> struct product_type_selector<Small, Large, 1> { enum { ret = LazyCoeffBasedProductMode }; };
template<> struct product_type_selector<Large, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
template<> struct product_type_selector<1, Large,Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<1, Large,Large> { enum { ret = GemvProduct }; };
template<> struct product_type_selector<1, Small,Large> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<Large,1, Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<Large,1, Large> { enum { ret = GemvProduct }; };
template<> struct product_type_selector<Small,1, Large> { enum { ret = CoeffBasedProductMode }; };
template<> struct product_type_selector<Small,Small,Large> { enum { ret = GemmProduct }; };
template<> struct product_type_selector<Large,Small,Large> { enum { ret = GemmProduct }; };
template<> struct product_type_selector<Small,Large,Large> { enum { ret = GemmProduct }; };
template<> struct product_type_selector<Large,Large,Large> { enum { ret = GemmProduct }; };
template<> struct product_type_selector<Large,Small,Small> { enum { ret = GemmProduct }; };
template<> struct product_type_selector<Small,Large,Small> { enum { ret = GemmProduct }; };
template<> struct product_type_selector<Large,Large,Small> { enum { ret = GemmProduct }; };
} // end namespace internal
/** \class ProductReturnType
* \ingroup Core_Module
*
* \brief Helper class to get the correct and optimized returned type of operator*
*
* \param Lhs the type of the left-hand side
* \param Rhs the type of the right-hand side
* \param ProductMode the type of the product (determined automatically by internal::product_mode)
*
* This class defines the typename Type representing the optimized product expression
* between two matrix expressions. In practice, using ProductReturnType<Lhs,Rhs>::Type
* is the recommended way to define the result type of a function returning an expression
* which involve a matrix product. The class Product should never be
* used directly.
*
* \sa class Product, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
*/
template<typename Lhs, typename Rhs, int ProductType>
struct ProductReturnType
{
// TODO use the nested type to reduce instanciations ????
// typedef typename internal::nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
// typedef typename internal::nested<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
typedef GeneralProduct<Lhs/*Nested*/, Rhs/*Nested*/, ProductType> Type;
};
template<typename Lhs, typename Rhs>
struct ProductReturnType<Lhs,Rhs,CoeffBasedProductMode>
{
typedef typename internal::nested<Lhs, Rhs::ColsAtCompileTime, typename internal::plain_matrix_type<Lhs>::type >::type LhsNested;
typedef typename internal::nested<Rhs, Lhs::RowsAtCompileTime, typename internal::plain_matrix_type<Rhs>::type >::type RhsNested;
typedef CoeffBasedProduct<LhsNested, RhsNested, EvalBeforeAssigningBit | EvalBeforeNestingBit> Type;
};
template<typename Lhs, typename Rhs>
struct ProductReturnType<Lhs,Rhs,LazyCoeffBasedProductMode>
{
typedef typename internal::nested<Lhs, Rhs::ColsAtCompileTime, typename internal::plain_matrix_type<Lhs>::type >::type LhsNested;
typedef typename internal::nested<Rhs, Lhs::RowsAtCompileTime, typename internal::plain_matrix_type<Rhs>::type >::type RhsNested;
typedef CoeffBasedProduct<LhsNested, RhsNested, NestByRefBit> Type;
};
// this is a workaround for sun CC
template<typename Lhs, typename Rhs>
struct LazyProductReturnType : public ProductReturnType<Lhs,Rhs,LazyCoeffBasedProductMode>
{};
/***********************************************************************
* Implementation of Inner Vector Vector Product
***********************************************************************/
// FIXME : maybe the "inner product" could return a Scalar
// instead of a 1x1 matrix ??
// Pro: more natural for the user
// Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix
// product ends up to a row-vector times col-vector product... To tackle this use
// case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);
namespace internal {
template<typename Lhs, typename Rhs>
struct traits<GeneralProduct<Lhs,Rhs,InnerProduct> >
: traits<Matrix<typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> >
{};
}
template<typename Lhs, typename Rhs>
class GeneralProduct<Lhs, Rhs, InnerProduct>
: internal::no_assignment_operator,
public Matrix<typename internal::scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1>
{
typedef Matrix<typename internal::scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> Base;
public:
GeneralProduct(const Lhs& lhs, const Rhs& rhs)
{
EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
Base::coeffRef(0,0) = (lhs.transpose().cwiseProduct(rhs)).sum();
}
/** Convertion to scalar */
operator const typename Base::Scalar() const {
return Base::coeff(0,0);
}
};
/***********************************************************************
* Implementation of Outer Vector Vector Product
***********************************************************************/
namespace internal {
template<int StorageOrder> struct outer_product_selector;
template<typename Lhs, typename Rhs>
struct traits<GeneralProduct<Lhs,Rhs,OuterProduct> >
: traits<ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs> >
{};
}
template<typename Lhs, typename Rhs>
class GeneralProduct<Lhs, Rhs, OuterProduct>
: public ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs>
{
public:
EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
{
EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
}
template<typename Dest> void scaleAndAddTo(Dest& dest, Scalar alpha) const
{
internal::outer_product_selector<(int(Dest::Flags)&RowMajorBit) ? RowMajor : ColMajor>::run(*this, dest, alpha);
}
};
namespace internal {
template<> struct outer_product_selector<ColMajor> {
template<typename ProductType, typename Dest>
static EIGEN_DONT_INLINE void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha) {
typedef typename Dest::Index Index;
// FIXME make sure lhs is sequentially stored
// FIXME not very good if rhs is real and lhs complex while alpha is real too
const Index cols = dest.cols();
for (Index j=0; j<cols; ++j)
dest.col(j) += (alpha * prod.rhs().coeff(j)) * prod.lhs();
}
};
template<> struct outer_product_selector<RowMajor> {
template<typename ProductType, typename Dest>
static EIGEN_DONT_INLINE void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha) {
typedef typename Dest::Index Index;
// FIXME make sure rhs is sequentially stored
// FIXME not very good if lhs is real and rhs complex while alpha is real too
const Index rows = dest.rows();
for (Index i=0; i<rows; ++i)
dest.row(i) += (alpha * prod.lhs().coeff(i)) * prod.rhs();
}
};
} // end namespace internal
/***********************************************************************
* Implementation of General Matrix Vector Product
***********************************************************************/
/* According to the shape/flags of the matrix we have to distinghish 3 different cases:
* 1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
* 2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
* 3 - all other cases are handled using a simple loop along the outer-storage direction.
* Therefore we need a lower level meta selector.
* Furthermore, if the matrix is the rhs, then the product has to be transposed.
*/
namespace internal {
template<typename Lhs, typename Rhs>
struct traits<GeneralProduct<Lhs,Rhs,GemvProduct> >
: traits<ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs> >
{};
template<int Side, int StorageOrder, bool BlasCompatible>
struct gemv_selector;
} // end namespace internal
template<typename Lhs, typename Rhs>
class GeneralProduct<Lhs, Rhs, GemvProduct>
: public ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs>
{
public:
EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
typedef typename Lhs::Scalar LhsScalar;
typedef typename Rhs::Scalar RhsScalar;
GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
{
// EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::Scalar, typename Rhs::Scalar>::value),
// YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
}
enum { Side = Lhs::IsVectorAtCompileTime ? OnTheLeft : OnTheRight };
typedef typename internal::conditional<int(Side)==OnTheRight,_LhsNested,_RhsNested>::type MatrixType;
template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const
{
eigen_assert(m_lhs.rows() == dst.rows() && m_rhs.cols() == dst.cols());
internal::gemv_selector<Side,(int(MatrixType::Flags)&RowMajorBit) ? RowMajor : ColMajor,
bool(internal::blas_traits<MatrixType>::HasUsableDirectAccess)>::run(*this, dst, alpha);
}
};
namespace internal {
// The vector is on the left => transposition
template<int StorageOrder, bool BlasCompatible>
struct gemv_selector<OnTheLeft,StorageOrder,BlasCompatible>
{
template<typename ProductType, typename Dest>
static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
{
Transpose<Dest> destT(dest);
enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
gemv_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
::run(GeneralProduct<Transpose<const typename ProductType::_RhsNested>,Transpose<const typename ProductType::_LhsNested>, GemvProduct>
(prod.rhs().transpose(), prod.lhs().transpose()), destT, alpha);
}
};
template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
template<typename Scalar,int Size,int MaxSize>
struct gemv_static_vector_if<Scalar,Size,MaxSize,false>
{
EIGEN_STRONG_INLINE Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; }
};
template<typename Scalar,int Size>
struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
{
EIGEN_STRONG_INLINE Scalar* data() { return 0; }
};
template<typename Scalar,int Size,int MaxSize>
struct gemv_static_vector_if<Scalar,Size,MaxSize,true>
{
#if EIGEN_ALIGN_STATICALLY
internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize),0> m_data;
EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; }
#else
// Some architectures cannot align on the stack,
// => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
enum {
ForceAlignment = internal::packet_traits<Scalar>::Vectorizable,
PacketSize = internal::packet_traits<Scalar>::size
};
internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize)+(ForceAlignment?PacketSize:0),0> m_data;
EIGEN_STRONG_INLINE Scalar* data() {
return ForceAlignment
? reinterpret_cast<Scalar*>((reinterpret_cast<size_t>(m_data.array) & ~(size_t(15))) + 16)
: m_data.array;
}
#endif
};
template<> struct gemv_selector<OnTheRight,ColMajor,true>
{
template<typename ProductType, typename Dest>
static inline void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
{
typedef typename ProductType::Index Index;
typedef typename ProductType::LhsScalar LhsScalar;
typedef typename ProductType::RhsScalar RhsScalar;
typedef typename ProductType::Scalar ResScalar;
typedef typename ProductType::RealScalar RealScalar;
typedef typename ProductType::ActualLhsType ActualLhsType;
typedef typename ProductType::ActualRhsType ActualRhsType;
typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
typedef Map<Matrix<ResScalar,Dynamic,1>, Aligned> MappedDest;
ActualLhsType actualLhs = LhsBlasTraits::extract(prod.lhs());
ActualRhsType actualRhs = RhsBlasTraits::extract(prod.rhs());
ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
* RhsBlasTraits::extractScalarFactor(prod.rhs());
enum {
// FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
// on, the other hand it is good for the cache to pack the vector anyways...
EvalToDestAtCompileTime = Dest::InnerStrideAtCompileTime==1,
ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
MightCannotUseDest = (Dest::InnerStrideAtCompileTime!=1) || ComplexByReal
};
gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
bool alphaIsCompatible = (!ComplexByReal) || (imag(actualAlpha)==RealScalar(0));
bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
evalToDest ? dest.data() : static_dest.data());
if(!evalToDest)
{
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
int size = dest.size();
EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#endif
if(!alphaIsCompatible)
{
MappedDest(actualDestPtr, dest.size()).setZero();
compatibleAlpha = RhsScalar(1);
}
else
MappedDest(actualDestPtr, dest.size()) = dest;
}
general_matrix_vector_product
<Index,LhsScalar,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsBlasTraits::NeedToConjugate>::run(
actualLhs.rows(), actualLhs.cols(),
actualLhs.data(), actualLhs.outerStride(),
actualRhs.data(), actualRhs.innerStride(),
actualDestPtr, 1,
compatibleAlpha);
if (!evalToDest)
{
if(!alphaIsCompatible)
dest += actualAlpha * MappedDest(actualDestPtr, dest.size());
else
dest = MappedDest(actualDestPtr, dest.size());
}
}
};
template<> struct gemv_selector<OnTheRight,RowMajor,true>
{
template<typename ProductType, typename Dest>
static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
{
typedef typename ProductType::LhsScalar LhsScalar;
typedef typename ProductType::RhsScalar RhsScalar;
typedef typename ProductType::Scalar ResScalar;
typedef typename ProductType::Index Index;
typedef typename ProductType::ActualLhsType ActualLhsType;
typedef typename ProductType::ActualRhsType ActualRhsType;
typedef typename ProductType::_ActualRhsType _ActualRhsType;
typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
* RhsBlasTraits::extractScalarFactor(prod.rhs());
enum {
// FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
// on, the other hand it is good for the cache to pack the vector anyways...
DirectlyUseRhs = _ActualRhsType::InnerStrideAtCompileTime==1
};
gemv_static_vector_if<RhsScalar,_ActualRhsType::SizeAtCompileTime,_ActualRhsType::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
if(!DirectlyUseRhs)
{
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
int size = actualRhs.size();
EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#endif
Map<typename _ActualRhsType::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
}
general_matrix_vector_product
<Index,LhsScalar,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsBlasTraits::NeedToConjugate>::run(
actualLhs.rows(), actualLhs.cols(),
actualLhs.data(), actualLhs.outerStride(),
actualRhsPtr, 1,
dest.data(), dest.innerStride(),
actualAlpha);
}
};
template<> struct gemv_selector<OnTheRight,ColMajor,false>
{
template<typename ProductType, typename Dest>
static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
{
typedef typename Dest::Index Index;
// TODO makes sure dest is sequentially stored in memory, otherwise use a temp
const Index size = prod.rhs().rows();
for(Index k=0; k<size; ++k)
dest += (alpha*prod.rhs().coeff(k)) * prod.lhs().col(k);
}
};
template<> struct gemv_selector<OnTheRight,RowMajor,false>
{
template<typename ProductType, typename Dest>
static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
{
typedef typename Dest::Index Index;
// TODO makes sure rhs is sequentially stored in memory, otherwise use a temp
const Index rows = prod.rows();
for(Index i=0; i<rows; ++i)
dest.coeffRef(i) += alpha * (prod.lhs().row(i).cwiseProduct(prod.rhs().transpose())).sum();
}
};
} // end namespace internal
/***************************************************************************
* Implementation of matrix base methods
***************************************************************************/
/** \returns the matrix product of \c *this and \a other.
*
* \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
*
* \sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
*/
template<typename Derived>
template<typename OtherDerived>
inline const typename ProductReturnType<Derived, OtherDerived>::Type
MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
{
// A note regarding the function declaration: In MSVC, this function will sometimes
// not be inlined since DenseStorage is an unwindable object for dynamic
// matrices and product types are holding a member to store the result.
// Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
enum {
ProductIsValid = Derived::ColsAtCompileTime==Dynamic
|| OtherDerived::RowsAtCompileTime==Dynamic
|| int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
};
// note to the lost user:
// * for a dot product use: v1.dot(v2)
// * for a coeff-wise product use: v1.cwiseProduct(v2)
EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
#ifdef EIGEN_DEBUG_PRODUCT
internal::product_type<Derived,OtherDerived>::debug();
#endif
return typename ProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
}
/** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation.
*
* The returned product will behave like any other expressions: the coefficients of the product will be
* computed once at a time as requested. This might be useful in some extremely rare cases when only
* a small and no coherent fraction of the result's coefficients have to be computed.
*
* \warning This version of the matrix product can be much much slower. So use it only if you know
* what you are doing and that you measured a true speed improvement.
*
* \sa operator*(const MatrixBase&)
*/
template<typename Derived>
template<typename OtherDerived>
const typename LazyProductReturnType<Derived,OtherDerived>::Type
MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const
{
enum {
ProductIsValid = Derived::ColsAtCompileTime==Dynamic
|| OtherDerived::RowsAtCompileTime==Dynamic
|| int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
};
// note to the lost user:
// * for a dot product use: v1.dot(v2)
// * for a coeff-wise product use: v1.cwiseProduct(v2)
EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
return typename LazyProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
}
} // end namespace Eigen
#endif // EIGEN_PRODUCT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_GENERIC_PACKET_MATH_H
#define EIGEN_GENERIC_PACKET_MATH_H
namespace Eigen {
namespace internal {
/** \internal
* \file GenericPacketMath.h
*
* Default implementation for types not supported by the vectorization.
* In practice these functions are provided to make easier the writing
* of generic vectorized code.
*/
#ifndef EIGEN_DEBUG_ALIGNED_LOAD
#define EIGEN_DEBUG_ALIGNED_LOAD
#endif
#ifndef EIGEN_DEBUG_UNALIGNED_LOAD
#define EIGEN_DEBUG_UNALIGNED_LOAD
#endif
#ifndef EIGEN_DEBUG_ALIGNED_STORE
#define EIGEN_DEBUG_ALIGNED_STORE
#endif
#ifndef EIGEN_DEBUG_UNALIGNED_STORE
#define EIGEN_DEBUG_UNALIGNED_STORE
#endif
struct default_packet_traits
{
enum {
HasAdd = 1,
HasSub = 1,
HasMul = 1,
HasNegate = 1,
HasAbs = 1,
HasAbs2 = 1,
HasMin = 1,
HasMax = 1,
HasConj = 1,
HasSetLinear = 1,
HasDiv = 0,
HasSqrt = 0,
HasExp = 0,
HasLog = 0,
HasPow = 0,
HasSin = 0,
HasCos = 0,
HasTan = 0,
HasASin = 0,
HasACos = 0,
HasATan = 0
};
};
template<typename T> struct packet_traits : default_packet_traits
{
typedef T type;
enum {
Vectorizable = 0,
size = 1,
AlignedOnScalar = 0
};
enum {
HasAdd = 0,
HasSub = 0,
HasMul = 0,
HasNegate = 0,
HasAbs = 0,
HasAbs2 = 0,
HasMin = 0,
HasMax = 0,
HasConj = 0,
HasSetLinear = 0
};
};
/** \internal \returns a + b (coeff-wise) */
template<typename Packet> inline Packet
padd(const Packet& a,
const Packet& b) { return a+b; }
/** \internal \returns a - b (coeff-wise) */
template<typename Packet> inline Packet
psub(const Packet& a,
const Packet& b) { return a-b; }
/** \internal \returns -a (coeff-wise) */
template<typename Packet> inline Packet
pnegate(const Packet& a) { return -a; }
/** \internal \returns conj(a) (coeff-wise) */
template<typename Packet> inline Packet
pconj(const Packet& a) { return conj(a); }
/** \internal \returns a * b (coeff-wise) */
template<typename Packet> inline Packet
pmul(const Packet& a,
const Packet& b) { return a*b; }
/** \internal \returns a / b (coeff-wise) */
template<typename Packet> inline Packet
pdiv(const Packet& a,
const Packet& b) { return a/b; }
/** \internal \returns the min of \a a and \a b (coeff-wise) */
template<typename Packet> inline Packet
pmin(const Packet& a,
const Packet& b) { using std::min; return (min)(a, b); }
/** \internal \returns the max of \a a and \a b (coeff-wise) */
template<typename Packet> inline Packet
pmax(const Packet& a,
const Packet& b) { using std::max; return (max)(a, b); }
/** \internal \returns the absolute value of \a a */
template<typename Packet> inline Packet
pabs(const Packet& a) { return abs(a); }
/** \internal \returns the bitwise and of \a a and \a b */
template<typename Packet> inline Packet
pand(const Packet& a, const Packet& b) { return a & b; }
/** \internal \returns the bitwise or of \a a and \a b */
template<typename Packet> inline Packet
por(const Packet& a, const Packet& b) { return a | b; }
/** \internal \returns the bitwise xor of \a a and \a b */
template<typename Packet> inline Packet
pxor(const Packet& a, const Packet& b) { return a ^ b; }
/** \internal \returns the bitwise andnot of \a a and \a b */
template<typename Packet> inline Packet
pandnot(const Packet& a, const Packet& b) { return a & (!b); }
/** \internal \returns a packet version of \a *from, from must be 16 bytes aligned */
template<typename Packet> inline Packet
pload(const typename unpacket_traits<Packet>::type* from) { return *from; }
/** \internal \returns a packet version of \a *from, (un-aligned load) */
template<typename Packet> inline Packet
ploadu(const typename unpacket_traits<Packet>::type* from) { return *from; }
/** \internal \returns a packet with elements of \a *from duplicated, e.g.: (from[0],from[0],from[1],from[1]) */
template<typename Packet> inline Packet
ploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; }
/** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */
template<typename Packet> inline Packet
pset1(const typename unpacket_traits<Packet>::type& a) { return a; }
/** \internal \brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */
template<typename Scalar> inline typename packet_traits<Scalar>::type
plset(const Scalar& a) { return a; }
/** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
template<typename Scalar, typename Packet> inline void pstore(Scalar* to, const Packet& from)
{ (*to) = from; }
/** \internal copy the packet \a from to \a *to, (un-aligned store) */
template<typename Scalar, typename Packet> inline void pstoreu(Scalar* to, const Packet& from)
{ (*to) = from; }
/** \internal tries to do cache prefetching of \a addr */
template<typename Scalar> inline void prefetch(const Scalar* addr)
{
#if !defined(_MSC_VER)
__builtin_prefetch(addr);
#endif
}
/** \internal \returns the first element of a packet */
template<typename Packet> inline typename unpacket_traits<Packet>::type pfirst(const Packet& a)
{ return a; }
/** \internal \returns a packet where the element i contains the sum of the packet of \a vec[i] */
template<typename Packet> inline Packet
preduxp(const Packet* vecs) { return vecs[0]; }
/** \internal \returns the sum of the elements of \a a*/
template<typename Packet> inline typename unpacket_traits<Packet>::type predux(const Packet& a)
{ return a; }
/** \internal \returns the product of the elements of \a a*/
template<typename Packet> inline typename unpacket_traits<Packet>::type predux_mul(const Packet& a)
{ return a; }
/** \internal \returns the min of the elements of \a a*/
template<typename Packet> inline typename unpacket_traits<Packet>::type predux_min(const Packet& a)
{ return a; }
/** \internal \returns the max of the elements of \a a*/
template<typename Packet> inline typename unpacket_traits<Packet>::type predux_max(const Packet& a)
{ return a; }
/** \internal \returns the reversed elements of \a a*/
template<typename Packet> inline Packet preverse(const Packet& a)
{ return a; }
/** \internal \returns \a a with real and imaginary part flipped (for complex type only) */
template<typename Packet> inline Packet pcplxflip(const Packet& a)
{ return Packet(imag(a),real(a)); }
/**************************
* Special math functions
***************************/
/** \internal \returns the sine of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet psin(const Packet& a) { return sin(a); }
/** \internal \returns the cosine of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet pcos(const Packet& a) { return cos(a); }
/** \internal \returns the tan of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet ptan(const Packet& a) { return tan(a); }
/** \internal \returns the arc sine of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet pasin(const Packet& a) { return asin(a); }
/** \internal \returns the arc cosine of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet pacos(const Packet& a) { return acos(a); }
/** \internal \returns the exp of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet pexp(const Packet& a) { return exp(a); }
/** \internal \returns the log of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet plog(const Packet& a) { return log(a); }
/** \internal \returns the square-root of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet psqrt(const Packet& a) { return sqrt(a); }
/***************************************************************************
* The following functions might not have to be overwritten for vectorized types
***************************************************************************/
/** \internal copy a packet with constant coeficient \a a (e.g., [a,a,a,a]) to \a *to. \a to must be 16 bytes aligned */
// NOTE: this function must really be templated on the packet type (think about different packet types for the same scalar type)
template<typename Packet>
inline void pstore1(typename unpacket_traits<Packet>::type* to, const typename unpacket_traits<Packet>::type& a)
{
pstore(to, pset1<Packet>(a));
}
/** \internal \returns a * b + c (coeff-wise) */
template<typename Packet> inline Packet
pmadd(const Packet& a,
const Packet& b,
const Packet& c)
{ return padd(pmul(a, b),c); }
/** \internal \returns a packet version of \a *from.
* If LoadMode equals #Aligned, \a from must be 16 bytes aligned */
template<typename Packet, int LoadMode>
inline Packet ploadt(const typename unpacket_traits<Packet>::type* from)
{
if(LoadMode == Aligned)
return pload<Packet>(from);
else
return ploadu<Packet>(from);
}
/** \internal copy the packet \a from to \a *to.
* If StoreMode equals #Aligned, \a to must be 16 bytes aligned */
template<typename Scalar, typename Packet, int LoadMode>
inline void pstoret(Scalar* to, const Packet& from)
{
if(LoadMode == Aligned)
pstore(to, from);
else
pstoreu(to, from);
}
/** \internal default implementation of palign() allowing partial specialization */
template<int Offset,typename PacketType>
struct palign_impl
{
// by default data are aligned, so there is nothing to be done :)
static inline void run(PacketType&, const PacketType&) {}
};
/** \internal update \a first using the concatenation of the \a Offset last elements
* of \a first and packet_size minus \a Offset first elements of \a second */
template<int Offset,typename PacketType>
inline void palign(PacketType& first, const PacketType& second)
{
palign_impl<Offset,PacketType>::run(first,second);
}
/***************************************************************************
* Fast complex products (GCC generates a function call which is very slow)
***************************************************************************/
template<> inline std::complex<float> pmul(const std::complex<float>& a, const std::complex<float>& b)
{ return std::complex<float>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
template<> inline std::complex<double> pmul(const std::complex<double>& a, const std::complex<double>& b)
{ return std::complex<double>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_GENERIC_PACKET_MATH_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_GLOBAL_FUNCTIONS_H
#define EIGEN_GLOBAL_FUNCTIONS_H
#define EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(NAME,FUNCTOR) \
template<typename Derived> \
inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
NAME(const Eigen::ArrayBase<Derived>& x) { \
return x.derived(); \
}
#define EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(NAME,FUNCTOR) \
\
template<typename Derived> \
struct NAME##_retval<ArrayBase<Derived> > \
{ \
typedef const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> type; \
}; \
template<typename Derived> \
struct NAME##_impl<ArrayBase<Derived> > \
{ \
static inline typename NAME##_retval<ArrayBase<Derived> >::type run(const Eigen::ArrayBase<Derived>& x) \
{ \
return x.derived(); \
} \
};
namespace std
{
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(real,scalar_real_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(imag,scalar_imag_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(sin,scalar_sin_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(cos,scalar_cos_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(asin,scalar_asin_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(acos,scalar_acos_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(tan,scalar_tan_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(exp,scalar_exp_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(log,scalar_log_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(abs,scalar_abs_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(sqrt,scalar_sqrt_op)
template<typename Derived>
inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar>, const Derived>
pow(const Eigen::ArrayBase<Derived>& x, const typename Derived::Scalar& exponent) {
return x.derived().pow(exponent);
}
template<typename Derived>
inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename Derived::Scalar>, const Derived, const Derived>
pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<Derived>& exponents)
{
return Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename Derived::Scalar>, const Derived, const Derived>(
x.derived(),
exponents.derived()
);
}
}
namespace Eigen
{
/**
* \brief Component-wise division of a scalar by array elements.
**/
template <typename Derived>
inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>
operator/(typename Derived::Scalar s, const Eigen::ArrayBase<Derived>& a)
{
return Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>(
a.derived(),
Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>(s)
);
}
namespace internal
{
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(imag,scalar_imag_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(sin,scalar_sin_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(cos,scalar_cos_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(asin,scalar_asin_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(acos,scalar_acos_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(tan,scalar_tan_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(exp,scalar_exp_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(log,scalar_log_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs,scalar_abs_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs2,scalar_abs2_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(sqrt,scalar_sqrt_op)
}
}
// TODO: cleanly disable those functions that are not supported on Array (internal::real_ref, internal::random, internal::isApprox...)
#endif // EIGEN_GLOBAL_FUNCTIONS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_IO_H
#define EIGEN_IO_H
namespace Eigen {
enum { DontAlignCols = 1 };
enum { StreamPrecision = -1,
FullPrecision = -2 };
namespace internal {
template<typename Derived>
std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt);
}
/** \class IOFormat
* \ingroup Core_Module
*
* \brief Stores a set of parameters controlling the way matrices are printed
*
* List of available parameters:
* - \b precision number of digits for floating point values, or one of the special constants \c StreamPrecision and \c FullPrecision.
* The default is the special value \c StreamPrecision which means to use the
* stream's own precision setting, as set for instance using \c cout.precision(3). The other special value
* \c FullPrecision means that the number of digits will be computed to match the full precision of each floating-point
* type.
* - \b flags an OR-ed combination of flags, the default value is 0, the only currently available flag is \c DontAlignCols which
* allows to disable the alignment of columns, resulting in faster code.
* - \b coeffSeparator string printed between two coefficients of the same row
* - \b rowSeparator string printed between two rows
* - \b rowPrefix string printed at the beginning of each row
* - \b rowSuffix string printed at the end of each row
* - \b matPrefix string printed at the beginning of the matrix
* - \b matSuffix string printed at the end of the matrix
*
* Example: \include IOFormat.cpp
* Output: \verbinclude IOFormat.out
*
* \sa DenseBase::format(), class WithFormat
*/
struct IOFormat
{
/** Default contructor, see class IOFormat for the meaning of the parameters */
IOFormat(int _precision = StreamPrecision, int _flags = 0,
const std::string& _coeffSeparator = " ",
const std::string& _rowSeparator = "\n", const std::string& _rowPrefix="", const std::string& _rowSuffix="",
const std::string& _matPrefix="", const std::string& _matSuffix="")
: matPrefix(_matPrefix), matSuffix(_matSuffix), rowPrefix(_rowPrefix), rowSuffix(_rowSuffix), rowSeparator(_rowSeparator),
coeffSeparator(_coeffSeparator), precision(_precision), flags(_flags)
{
rowSpacer = "";
int i = int(matSuffix.length())-1;
while (i>=0 && matSuffix[i]!='\n')
{
rowSpacer += ' ';
i--;
}
}
std::string matPrefix, matSuffix;
std::string rowPrefix, rowSuffix, rowSeparator, rowSpacer;
std::string coeffSeparator;
int precision;
int flags;
};
/** \class WithFormat
* \ingroup Core_Module
*
* \brief Pseudo expression providing matrix output with given format
*
* \param ExpressionType the type of the object on which IO stream operations are performed
*
* This class represents an expression with stream operators controlled by a given IOFormat.
* It is the return type of DenseBase::format()
* and most of the time this is the only way it is used.
*
* See class IOFormat for some examples.
*
* \sa DenseBase::format(), class IOFormat
*/
template<typename ExpressionType>
class WithFormat
{
public:
WithFormat(const ExpressionType& matrix, const IOFormat& format)
: m_matrix(matrix), m_format(format)
{}
friend std::ostream & operator << (std::ostream & s, const WithFormat& wf)
{
return internal::print_matrix(s, wf.m_matrix.eval(), wf.m_format);
}
protected:
const typename ExpressionType::Nested m_matrix;
IOFormat m_format;
};
/** \returns a WithFormat proxy object allowing to print a matrix the with given
* format \a fmt.
*
* See class IOFormat for some examples.
*
* \sa class IOFormat, class WithFormat
*/
template<typename Derived>
inline const WithFormat<Derived>
DenseBase<Derived>::format(const IOFormat& fmt) const
{
return WithFormat<Derived>(derived(), fmt);
}
namespace internal {
template<typename Scalar, bool IsInteger>
struct significant_decimals_default_impl
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static inline int run()
{
using std::ceil;
return cast<RealScalar,int>(ceil(-log(NumTraits<RealScalar>::epsilon())/log(RealScalar(10))));
}
};
template<typename Scalar>
struct significant_decimals_default_impl<Scalar, true>
{
static inline int run()
{
return 0;
}
};
template<typename Scalar>
struct significant_decimals_impl
: significant_decimals_default_impl<Scalar, NumTraits<Scalar>::IsInteger>
{};
/** \internal
* print the matrix \a _m to the output stream \a s using the output format \a fmt */
template<typename Derived>
std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt)
{
if(_m.size() == 0)
{
s << fmt.matPrefix << fmt.matSuffix;
return s;
}
typename Derived::Nested m = _m;
typedef typename Derived::Scalar Scalar;
typedef typename Derived::Index Index;
Index width = 0;
std::streamsize explicit_precision;
if(fmt.precision == StreamPrecision)
{
explicit_precision = 0;
}
else if(fmt.precision == FullPrecision)
{
if (NumTraits<Scalar>::IsInteger)
{
explicit_precision = 0;
}
else
{
explicit_precision = significant_decimals_impl<Scalar>::run();
}
}
else
{
explicit_precision = fmt.precision;
}
bool align_cols = !(fmt.flags & DontAlignCols);
if(align_cols)
{
// compute the largest width
for(Index j = 1; j < m.cols(); ++j)
for(Index i = 0; i < m.rows(); ++i)
{
std::stringstream sstr;
if(explicit_precision) sstr.precision(explicit_precision);
sstr << m.coeff(i,j);
width = std::max<Index>(width, Index(sstr.str().length()));
}
}
std::streamsize old_precision = 0;
if(explicit_precision) old_precision = s.precision(explicit_precision);
s << fmt.matPrefix;
for(Index i = 0; i < m.rows(); ++i)
{
if (i)
s << fmt.rowSpacer;
s << fmt.rowPrefix;
if(width) s.width(width);
s << m.coeff(i, 0);
for(Index j = 1; j < m.cols(); ++j)
{
s << fmt.coeffSeparator;
if (width) s.width(width);
s << m.coeff(i, j);
}
s << fmt.rowSuffix;
if( i < m.rows() - 1)
s << fmt.rowSeparator;
}
s << fmt.matSuffix;
if(explicit_precision) s.precision(old_precision);
return s;
}
} // end namespace internal
/** \relates DenseBase
*
* Outputs the matrix, to the given stream.
*
* If you wish to print the matrix with a format different than the default, use DenseBase::format().
*
* It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers.
* If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.
*
* \sa DenseBase::format()
*/
template<typename Derived>
std::ostream & operator <<
(std::ostream & s,
const DenseBase<Derived> & m)
{
return internal::print_matrix(s, m.eval(), EIGEN_DEFAULT_IO_FORMAT);
}
} // end namespace Eigen
#endif // EIGEN_IO_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MAP_H
#define EIGEN_MAP_H
namespace Eigen {
/** \class Map
* \ingroup Core_Module
*
* \brief A matrix or vector expression mapping an existing array of data.
*
* \tparam PlainObjectType the equivalent matrix type of the mapped data
* \tparam MapOptions specifies whether the pointer is \c #Aligned, or \c #Unaligned.
* The default is \c #Unaligned.
* \tparam StrideType optionally specifies strides. By default, Map assumes the memory layout
* of an ordinary, contiguous array. This can be overridden by specifying strides.
* The type passed here must be a specialization of the Stride template, see examples below.
*
* This class represents a matrix or vector expression mapping an existing array of data.
* It can be used to let Eigen interface without any overhead with non-Eigen data structures,
* such as plain C arrays or structures from other libraries. By default, it assumes that the
* data is laid out contiguously in memory. You can however override this by explicitly specifying
* inner and outer strides.
*
* Here's an example of simply mapping a contiguous array as a \ref TopicStorageOrders "column-major" matrix:
* \include Map_simple.cpp
* Output: \verbinclude Map_simple.out
*
* If you need to map non-contiguous arrays, you can do so by specifying strides:
*
* Here's an example of mapping an array as a vector, specifying an inner stride, that is, the pointer
* increment between two consecutive coefficients. Here, we're specifying the inner stride as a compile-time
* fixed value.
* \include Map_inner_stride.cpp
* Output: \verbinclude Map_inner_stride.out
*
* Here's an example of mapping an array while specifying an outer stride. Here, since we're mapping
* as a column-major matrix, 'outer stride' means the pointer increment between two consecutive columns.
* Here, we're specifying the outer stride as a runtime parameter. Note that here \c OuterStride<> is
* a short version of \c OuterStride<Dynamic> because the default template parameter of OuterStride
* is \c Dynamic
* \include Map_outer_stride.cpp
* Output: \verbinclude Map_outer_stride.out
*
* For more details and for an example of specifying both an inner and an outer stride, see class Stride.
*
* \b Tip: to change the array of data mapped by a Map object, you can use the C++
* placement new syntax:
*
* Example: \include Map_placement_new.cpp
* Output: \verbinclude Map_placement_new.out
*
* This class is the return type of PlainObjectBase::Map() but can also be used directly.
*
* \sa PlainObjectBase::Map(), \ref TopicStorageOrders
*/
namespace internal {
template<typename PlainObjectType, int MapOptions, typename StrideType>
struct traits<Map<PlainObjectType, MapOptions, StrideType> >
: public traits<PlainObjectType>
{
typedef traits<PlainObjectType> TraitsBase;
typedef typename PlainObjectType::Index Index;
typedef typename PlainObjectType::Scalar Scalar;
enum {
InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0
? int(PlainObjectType::InnerStrideAtCompileTime)
: int(StrideType::InnerStrideAtCompileTime),
OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
? int(PlainObjectType::OuterStrideAtCompileTime)
: int(StrideType::OuterStrideAtCompileTime),
HasNoInnerStride = InnerStrideAtCompileTime == 1,
HasNoOuterStride = StrideType::OuterStrideAtCompileTime == 0,
HasNoStride = HasNoInnerStride && HasNoOuterStride,
IsAligned = bool(EIGEN_ALIGN) && ((int(MapOptions)&Aligned)==Aligned),
IsDynamicSize = PlainObjectType::SizeAtCompileTime==Dynamic,
KeepsPacketAccess = bool(HasNoInnerStride)
&& ( bool(IsDynamicSize)
|| HasNoOuterStride
|| ( OuterStrideAtCompileTime!=Dynamic
&& ((static_cast<int>(sizeof(Scalar))*OuterStrideAtCompileTime)%16)==0 ) ),
Flags0 = TraitsBase::Flags & (~NestByRefBit),
Flags1 = IsAligned ? (int(Flags0) | AlignedBit) : (int(Flags0) & ~AlignedBit),
Flags2 = (bool(HasNoStride) || bool(PlainObjectType::IsVectorAtCompileTime))
? int(Flags1) : int(Flags1 & ~LinearAccessBit),
Flags3 = is_lvalue<PlainObjectType>::value ? int(Flags2) : (int(Flags2) & ~LvalueBit),
Flags = KeepsPacketAccess ? int(Flags3) : (int(Flags3) & ~PacketAccessBit)
};
private:
enum { Options }; // Expressions don't have Options
};
}
template<typename PlainObjectType, int MapOptions, typename StrideType> class Map
: public MapBase<Map<PlainObjectType, MapOptions, StrideType> >
{
public:
typedef MapBase<Map> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Map)
typedef typename Base::PointerType PointerType;
#if EIGEN2_SUPPORT_STAGE <= STAGE30_FULL_EIGEN3_API
typedef const Scalar* PointerArgType;
inline PointerType cast_to_pointer_type(PointerArgType ptr) { return const_cast<PointerType>(ptr); }
#else
typedef PointerType PointerArgType;
inline PointerType cast_to_pointer_type(PointerArgType ptr) { return ptr; }
#endif
inline Index innerStride() const
{
return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
}
inline Index outerStride() const
{
return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
: IsVectorAtCompileTime ? this->size()
: int(Flags)&RowMajorBit ? this->cols()
: this->rows();
}
/** Constructor in the fixed-size case.
*
* \param data pointer to the array to map
* \param stride optional Stride object, passing the strides.
*/
inline Map(PointerArgType data, const StrideType& stride = StrideType())
: Base(cast_to_pointer_type(data)), m_stride(stride)
{
PlainObjectType::Base::_check_template_params();
}
/** Constructor in the dynamic-size vector case.
*
* \param data pointer to the array to map
* \param size the size of the vector expression
* \param stride optional Stride object, passing the strides.
*/
inline Map(PointerArgType data, Index size, const StrideType& stride = StrideType())
: Base(cast_to_pointer_type(data), size), m_stride(stride)
{
PlainObjectType::Base::_check_template_params();
}
/** Constructor in the dynamic-size matrix case.
*
* \param data pointer to the array to map
* \param rows the number of rows of the matrix expression
* \param cols the number of columns of the matrix expression
* \param stride optional Stride object, passing the strides.
*/
inline Map(PointerArgType data, Index rows, Index cols, const StrideType& stride = StrideType())
: Base(cast_to_pointer_type(data), rows, cols), m_stride(stride)
{
PlainObjectType::Base::_check_template_params();
}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
protected:
StrideType m_stride;
};
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
inline Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>
::Array(const Scalar *data)
{
this->_set_noalias(Eigen::Map<const Array>(data));
}
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
inline Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>
::Matrix(const Scalar *data)
{
this->_set_noalias(Eigen::Map<const Matrix>(data));
}
} // end namespace Eigen
#endif // EIGEN_MAP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MAPBASE_H
#define EIGEN_MAPBASE_H
#define EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) \
EIGEN_STATIC_ASSERT((int(internal::traits<Derived>::Flags) & LinearAccessBit) || Derived::IsVectorAtCompileTime, \
YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT)
namespace Eigen {
/** \class MapBase
* \ingroup Core_Module
*
* \brief Base class for Map and Block expression with direct access
*
* \sa class Map, class Block
*/
template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
: public internal::dense_xpr_base<Derived>::type
{
public:
typedef typename internal::dense_xpr_base<Derived>::type Base;
enum {
RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
SizeAtCompileTime = Base::SizeAtCompileTime
};
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Index Index;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef typename internal::conditional<
bool(internal::is_lvalue<Derived>::value),
Scalar *,
const Scalar *>::type
PointerType;
using Base::derived;
// using Base::RowsAtCompileTime;
// using Base::ColsAtCompileTime;
// using Base::SizeAtCompileTime;
using Base::MaxRowsAtCompileTime;
using Base::MaxColsAtCompileTime;
using Base::MaxSizeAtCompileTime;
using Base::IsVectorAtCompileTime;
using Base::Flags;
using Base::IsRowMajor;
using Base::rows;
using Base::cols;
using Base::size;
using Base::coeff;
using Base::coeffRef;
using Base::lazyAssign;
using Base::eval;
using Base::innerStride;
using Base::outerStride;
using Base::rowStride;
using Base::colStride;
// bug 217 - compile error on ICC 11.1
using Base::operator=;
typedef typename Base::CoeffReturnType CoeffReturnType;
inline Index rows() const { return m_rows.value(); }
inline Index cols() const { return m_cols.value(); }
/** Returns a pointer to the first coefficient of the matrix or vector.
*
* \note When addressing this data, make sure to honor the strides returned by innerStride() and outerStride().
*
* \sa innerStride(), outerStride()
*/
inline const Scalar* data() const { return m_data; }
inline const Scalar& coeff(Index row, Index col) const
{
return m_data[col * colStride() + row * rowStride()];
}
inline const Scalar& coeff(Index index) const
{
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
return m_data[index * innerStride()];
}
inline const Scalar& coeffRef(Index row, Index col) const
{
return this->m_data[col * colStride() + row * rowStride()];
}
inline const Scalar& coeffRef(Index index) const
{
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
return this->m_data[index * innerStride()];
}
template<int LoadMode>
inline PacketScalar packet(Index row, Index col) const
{
return internal::ploadt<PacketScalar, LoadMode>
(m_data + (col * colStride() + row * rowStride()));
}
template<int LoadMode>
inline PacketScalar packet(Index index) const
{
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
return internal::ploadt<PacketScalar, LoadMode>(m_data + index * innerStride());
}
inline MapBase(PointerType data) : m_data(data), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
{
EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
checkSanity();
}
inline MapBase(PointerType data, Index size)
: m_data(data),
m_rows(RowsAtCompileTime == Dynamic ? size : Index(RowsAtCompileTime)),
m_cols(ColsAtCompileTime == Dynamic ? size : Index(ColsAtCompileTime))
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
eigen_assert(size >= 0);
eigen_assert(data == 0 || SizeAtCompileTime == Dynamic || SizeAtCompileTime == size);
checkSanity();
}
inline MapBase(PointerType data, Index rows, Index cols)
: m_data(data), m_rows(rows), m_cols(cols)
{
eigen_assert( (data == 0)
|| ( rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
&& cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)));
checkSanity();
}
protected:
void checkSanity() const
{
EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(internal::traits<Derived>::Flags&PacketAccessBit,
internal::inner_stride_at_compile_time<Derived>::ret==1),
PACKET_ACCESS_REQUIRES_TO_HAVE_INNER_STRIDE_FIXED_TO_1);
eigen_assert(EIGEN_IMPLIES(internal::traits<Derived>::Flags&AlignedBit, (size_t(m_data) % 16) == 0)
&& "data is not aligned");
}
PointerType m_data;
const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
};
template<typename Derived> class MapBase<Derived, WriteAccessors>
: public MapBase<Derived, ReadOnlyAccessors>
{
public:
typedef MapBase<Derived, ReadOnlyAccessors> Base;
typedef typename Base::Scalar Scalar;
typedef typename Base::PacketScalar PacketScalar;
typedef typename Base::Index Index;
typedef typename Base::PointerType PointerType;
using Base::derived;
using Base::rows;
using Base::cols;
using Base::size;
using Base::coeff;
using Base::coeffRef;
using Base::innerStride;
using Base::outerStride;
using Base::rowStride;
using Base::colStride;
typedef typename internal::conditional<
internal::is_lvalue<Derived>::value,
Scalar,
const Scalar
>::type ScalarWithConstIfNotLvalue;
inline const Scalar* data() const { return this->m_data; }
inline ScalarWithConstIfNotLvalue* data() { return this->m_data; } // no const-cast here so non-const-correct code will give a compile error
inline ScalarWithConstIfNotLvalue& coeffRef(Index row, Index col)
{
return this->m_data[col * colStride() + row * rowStride()];
}
inline ScalarWithConstIfNotLvalue& coeffRef(Index index)
{
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
return this->m_data[index * innerStride()];
}
template<int StoreMode>
inline void writePacket(Index row, Index col, const PacketScalar& x)
{
internal::pstoret<Scalar, PacketScalar, StoreMode>
(this->m_data + (col * colStride() + row * rowStride()), x);
}
template<int StoreMode>
inline void writePacket(Index index, const PacketScalar& x)
{
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
internal::pstoret<Scalar, PacketScalar, StoreMode>
(this->m_data + index * innerStride(), x);
}
explicit inline MapBase(PointerType data) : Base(data) {}
inline MapBase(PointerType data, Index size) : Base(data, size) {}
inline MapBase(PointerType data, Index rows, Index cols) : Base(data, rows, cols) {}
Derived& operator=(const MapBase& other)
{
Base::Base::operator=(other);
return derived();
}
using Base::Base::operator=;
};
} // end namespace Eigen
#endif // EIGEN_MAPBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MATHFUNCTIONS_H
#define EIGEN_MATHFUNCTIONS_H
namespace Eigen {
namespace internal {
/** \internal \struct global_math_functions_filtering_base
*
* What it does:
* Defines a typedef 'type' as follows:
* - if type T has a member typedef Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl, then
* global_math_functions_filtering_base<T>::type is a typedef for it.
* - otherwise, global_math_functions_filtering_base<T>::type is a typedef for T.
*
* How it's used:
* To allow to defined the global math functions (like sin...) in certain cases, like the Array expressions.
* When you do sin(array1+array2), the object array1+array2 has a complicated expression type, all what you want to know
* is that it inherits ArrayBase. So we implement a partial specialization of sin_impl for ArrayBase<Derived>.
* So we must make sure to use sin_impl<ArrayBase<Derived> > and not sin_impl<Derived>, otherwise our partial specialization
* won't be used. How does sin know that? That's exactly what global_math_functions_filtering_base tells it.
*
* How it's implemented:
* SFINAE in the style of enable_if. Highly susceptible of breaking compilers. With GCC, it sure does work, but if you replace
* the typename dummy by an integer template parameter, it doesn't work anymore!
*/
template<typename T, typename dummy = void>
struct global_math_functions_filtering_base
{
typedef T type;
};
template<typename T> struct always_void { typedef void type; };
template<typename T>
struct global_math_functions_filtering_base
<T,
typename always_void<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::type
>
{
typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;
};
#define EIGEN_MATHFUNC_IMPL(func, scalar) func##_impl<typename global_math_functions_filtering_base<scalar>::type>
#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename func##_retval<typename global_math_functions_filtering_base<scalar>::type>::type
/****************************************************************************
* Implementation of real *
****************************************************************************/
template<typename Scalar>
struct real_impl
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static inline RealScalar run(const Scalar& x)
{
return x;
}
};
template<typename RealScalar>
struct real_impl<std::complex<RealScalar> >
{
static inline RealScalar run(const std::complex<RealScalar>& x)
{
using std::real;
return real(x);
}
};
template<typename Scalar>
struct real_retval
{
typedef typename NumTraits<Scalar>::Real type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
}
/****************************************************************************
* Implementation of imag *
****************************************************************************/
template<typename Scalar>
struct imag_impl
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static inline RealScalar run(const Scalar&)
{
return RealScalar(0);
}
};
template<typename RealScalar>
struct imag_impl<std::complex<RealScalar> >
{
static inline RealScalar run(const std::complex<RealScalar>& x)
{
using std::imag;
return imag(x);
}
};
template<typename Scalar>
struct imag_retval
{
typedef typename NumTraits<Scalar>::Real type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
}
/****************************************************************************
* Implementation of real_ref *
****************************************************************************/
template<typename Scalar>
struct real_ref_impl
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static inline RealScalar& run(Scalar& x)
{
return reinterpret_cast<RealScalar*>(&x)[0];
}
static inline const RealScalar& run(const Scalar& x)
{
return reinterpret_cast<const RealScalar*>(&x)[0];
}
};
template<typename Scalar>
struct real_ref_retval
{
typedef typename NumTraits<Scalar>::Real & type;
};
template<typename Scalar>
inline typename add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)
{
return real_ref_impl<Scalar>::run(x);
}
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
}
/****************************************************************************
* Implementation of imag_ref *
****************************************************************************/
template<typename Scalar, bool IsComplex>
struct imag_ref_default_impl
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static inline RealScalar& run(Scalar& x)
{
return reinterpret_cast<RealScalar*>(&x)[1];
}
static inline const RealScalar& run(const Scalar& x)
{
return reinterpret_cast<RealScalar*>(&x)[1];
}
};
template<typename Scalar>
struct imag_ref_default_impl<Scalar, false>
{
static inline Scalar run(Scalar&)
{
return Scalar(0);
}
static inline const Scalar run(const Scalar&)
{
return Scalar(0);
}
};
template<typename Scalar>
struct imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
template<typename Scalar>
struct imag_ref_retval
{
typedef typename NumTraits<Scalar>::Real & type;
};
template<typename Scalar>
inline typename add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)
{
return imag_ref_impl<Scalar>::run(x);
}
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
}
/****************************************************************************
* Implementation of conj *
****************************************************************************/
template<typename Scalar>
struct conj_impl
{
static inline Scalar run(const Scalar& x)
{
return x;
}
};
template<typename RealScalar>
struct conj_impl<std::complex<RealScalar> >
{
static inline std::complex<RealScalar> run(const std::complex<RealScalar>& x)
{
using std::conj;
return conj(x);
}
};
template<typename Scalar>
struct conj_retval
{
typedef Scalar type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
}
/****************************************************************************
* Implementation of abs *
****************************************************************************/
template<typename Scalar>
struct abs_impl
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static inline RealScalar run(const Scalar& x)
{
using std::abs;
return abs(x);
}
};
template<typename Scalar>
struct abs_retval
{
typedef typename NumTraits<Scalar>::Real type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(abs, Scalar) abs(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(abs, Scalar)::run(x);
}
/****************************************************************************
* Implementation of abs2 *
****************************************************************************/
template<typename Scalar>
struct abs2_impl
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static inline RealScalar run(const Scalar& x)
{
return x*x;
}
};
template<typename RealScalar>
struct abs2_impl<std::complex<RealScalar> >
{
static inline RealScalar run(const std::complex<RealScalar>& x)
{
return real(x)*real(x) + imag(x)*imag(x);
}
};
template<typename Scalar>
struct abs2_retval
{
typedef typename NumTraits<Scalar>::Real type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
}
/****************************************************************************
* Implementation of norm1 *
****************************************************************************/
template<typename Scalar, bool IsComplex>
struct norm1_default_impl
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static inline RealScalar run(const Scalar& x)
{
return abs(real(x)) + abs(imag(x));
}
};
template<typename Scalar>
struct norm1_default_impl<Scalar, false>
{
static inline Scalar run(const Scalar& x)
{
return abs(x);
}
};
template<typename Scalar>
struct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
template<typename Scalar>
struct norm1_retval
{
typedef typename NumTraits<Scalar>::Real type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
}
/****************************************************************************
* Implementation of hypot *
****************************************************************************/
template<typename Scalar>
struct hypot_impl
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static inline RealScalar run(const Scalar& x, const Scalar& y)
{
using std::max;
using std::min;
RealScalar _x = abs(x);
RealScalar _y = abs(y);
RealScalar p = (max)(_x, _y);
RealScalar q = (min)(_x, _y);
RealScalar qp = q/p;
return p * sqrt(RealScalar(1) + qp*qp);
}
};
template<typename Scalar>
struct hypot_retval
{
typedef typename NumTraits<Scalar>::Real type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
{
return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
}
/****************************************************************************
* Implementation of cast *
****************************************************************************/
template<typename OldType, typename NewType>
struct cast_impl
{
static inline NewType run(const OldType& x)
{
return static_cast<NewType>(x);
}
};
// here, for once, we're plainly returning NewType: we don't want cast to do weird things.
template<typename OldType, typename NewType>
inline NewType cast(const OldType& x)
{
return cast_impl<OldType, NewType>::run(x);
}
/****************************************************************************
* Implementation of sqrt *
****************************************************************************/
template<typename Scalar, bool IsInteger>
struct sqrt_default_impl
{
static inline Scalar run(const Scalar& x)
{
using std::sqrt;
return sqrt(x);
}
};
template<typename Scalar>
struct sqrt_default_impl<Scalar, true>
{
static inline Scalar run(const Scalar&)
{
#ifdef EIGEN2_SUPPORT
eigen_assert(!NumTraits<Scalar>::IsInteger);
#else
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
#endif
return Scalar(0);
}
};
template<typename Scalar>
struct sqrt_impl : sqrt_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
template<typename Scalar>
struct sqrt_retval
{
typedef Scalar type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(sqrt, Scalar) sqrt(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(sqrt, Scalar)::run(x);
}
/****************************************************************************
* Implementation of standard unary real functions (exp, log, sin, cos, ... *
****************************************************************************/
// This macro instanciate all the necessary template mechanism which is common to all unary real functions.
#define EIGEN_MATHFUNC_STANDARD_REAL_UNARY(NAME) \
template<typename Scalar, bool IsInteger> struct NAME##_default_impl { \
static inline Scalar run(const Scalar& x) { using std::NAME; return NAME(x); } \
}; \
template<typename Scalar> struct NAME##_default_impl<Scalar, true> { \
static inline Scalar run(const Scalar&) { \
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar) \
return Scalar(0); \
} \
}; \
template<typename Scalar> struct NAME##_impl \
: NAME##_default_impl<Scalar, NumTraits<Scalar>::IsInteger> \
{}; \
template<typename Scalar> struct NAME##_retval { typedef Scalar type; }; \
template<typename Scalar> \
inline EIGEN_MATHFUNC_RETVAL(NAME, Scalar) NAME(const Scalar& x) { \
return EIGEN_MATHFUNC_IMPL(NAME, Scalar)::run(x); \
}
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(exp)
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(log)
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(sin)
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(cos)
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(tan)
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(asin)
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(acos)
/****************************************************************************
* Implementation of atan2 *
****************************************************************************/
template<typename Scalar, bool IsInteger>
struct atan2_default_impl
{
typedef Scalar retval;
static inline Scalar run(const Scalar& x, const Scalar& y)
{
using std::atan2;
return atan2(x, y);
}
};
template<typename Scalar>
struct atan2_default_impl<Scalar, true>
{
static inline Scalar run(const Scalar&, const Scalar&)
{
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
return Scalar(0);
}
};
template<typename Scalar>
struct atan2_impl : atan2_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
template<typename Scalar>
struct atan2_retval
{
typedef Scalar type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(atan2, Scalar) atan2(const Scalar& x, const Scalar& y)
{
return EIGEN_MATHFUNC_IMPL(atan2, Scalar)::run(x, y);
}
/****************************************************************************
* Implementation of pow *
****************************************************************************/
template<typename Scalar, bool IsInteger>
struct pow_default_impl
{
typedef Scalar retval;
static inline Scalar run(const Scalar& x, const Scalar& y)
{
using std::pow;
return pow(x, y);
}
};
template<typename Scalar>
struct pow_default_impl<Scalar, true>
{
static inline Scalar run(Scalar x, Scalar y)
{
Scalar res(1);
eigen_assert(!NumTraits<Scalar>::IsSigned || y >= 0);
if(y & 1) res *= x;
y >>= 1;
while(y)
{
x *= x;
if(y&1) res *= x;
y >>= 1;
}
return res;
}
};
template<typename Scalar>
struct pow_impl : pow_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
template<typename Scalar>
struct pow_retval
{
typedef Scalar type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y)
{
return EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y);
}
/****************************************************************************
* Implementation of random *
****************************************************************************/
template<typename Scalar,
bool IsComplex,
bool IsInteger>
struct random_default_impl {};
template<typename Scalar>
struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
template<typename Scalar>
struct random_retval
{
typedef Scalar type;
};
template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y);
template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();
template<typename Scalar>
struct random_default_impl<Scalar, false, false>
{
static inline Scalar run(const Scalar& x, const Scalar& y)
{
return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);
}
static inline Scalar run()
{
return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));
}
};
enum {
floor_log2_terminate,
floor_log2_move_up,
floor_log2_move_down,
floor_log2_bogus
};
template<unsigned int n, int lower, int upper> struct floor_log2_selector
{
enum { middle = (lower + upper) / 2,
value = (upper <= lower + 1) ? int(floor_log2_terminate)
: (n < (1 << middle)) ? int(floor_log2_move_down)
: (n==0) ? int(floor_log2_bogus)
: int(floor_log2_move_up)
};
};
template<unsigned int n,
int lower = 0,
int upper = sizeof(unsigned int) * CHAR_BIT - 1,
int selector = floor_log2_selector<n, lower, upper>::value>
struct floor_log2 {};
template<unsigned int n, int lower, int upper>
struct floor_log2<n, lower, upper, floor_log2_move_down>
{
enum { value = floor_log2<n, lower, floor_log2_selector<n, lower, upper>::middle>::value };
};
template<unsigned int n, int lower, int upper>
struct floor_log2<n, lower, upper, floor_log2_move_up>
{
enum { value = floor_log2<n, floor_log2_selector<n, lower, upper>::middle, upper>::value };
};
template<unsigned int n, int lower, int upper>
struct floor_log2<n, lower, upper, floor_log2_terminate>
{
enum { value = (n >= ((unsigned int)(1) << (lower+1))) ? lower+1 : lower };
};
template<unsigned int n, int lower, int upper>
struct floor_log2<n, lower, upper, floor_log2_bogus>
{
// no value, error at compile time
};
template<typename Scalar>
struct random_default_impl<Scalar, false, true>
{
typedef typename NumTraits<Scalar>::NonInteger NonInteger;
static inline Scalar run(const Scalar& x, const Scalar& y)
{
return x + Scalar((NonInteger(y)-x+1) * std::rand() / (RAND_MAX + NonInteger(1)));
}
static inline Scalar run()
{
#ifdef EIGEN_MAKING_DOCS
return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));
#else
enum { rand_bits = floor_log2<(unsigned int)(RAND_MAX)+1>::value,
scalar_bits = sizeof(Scalar) * CHAR_BIT,
shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits))
};
Scalar x = Scalar(std::rand() >> shift);
Scalar offset = NumTraits<Scalar>::IsSigned ? Scalar(1 << (rand_bits-1)) : Scalar(0);
return x - offset;
#endif
}
};
template<typename Scalar>
struct random_default_impl<Scalar, true, false>
{
static inline Scalar run(const Scalar& x, const Scalar& y)
{
return Scalar(random(real(x), real(y)),
random(imag(x), imag(y)));
}
static inline Scalar run()
{
typedef typename NumTraits<Scalar>::Real RealScalar;
return Scalar(random<RealScalar>(), random<RealScalar>());
}
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y)
{
return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
}
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
{
return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
}
/****************************************************************************
* Implementation of fuzzy comparisons *
****************************************************************************/
template<typename Scalar,
bool IsComplex,
bool IsInteger>
struct scalar_fuzzy_default_impl {};
template<typename Scalar>
struct scalar_fuzzy_default_impl<Scalar, false, false>
{
typedef typename NumTraits<Scalar>::Real RealScalar;
template<typename OtherScalar>
static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
{
return abs(x) <= abs(y) * prec;
}
static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
{
using std::min;
return abs(x - y) <= (min)(abs(x), abs(y)) * prec;
}
static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec)
{
return x <= y || isApprox(x, y, prec);
}
};
template<typename Scalar>
struct scalar_fuzzy_default_impl<Scalar, false, true>
{
typedef typename NumTraits<Scalar>::Real RealScalar;
template<typename OtherScalar>
static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&)
{
return x == Scalar(0);
}
static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&)
{
return x == y;
}
static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar&)
{
return x <= y;
}
};
template<typename Scalar>
struct scalar_fuzzy_default_impl<Scalar, true, false>
{
typedef typename NumTraits<Scalar>::Real RealScalar;
template<typename OtherScalar>
static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
{
return abs2(x) <= abs2(y) * prec * prec;
}
static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
{
using std::min;
return abs2(x - y) <= (min)(abs2(x), abs2(y)) * prec * prec;
}
};
template<typename Scalar>
struct scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
template<typename Scalar, typename OtherScalar>
inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
{
return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);
}
template<typename Scalar>
inline bool isApprox(const Scalar& x, const Scalar& y,
typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
{
return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);
}
template<typename Scalar>
inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y,
typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
{
return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);
}
/******************************************
*** The special case of the bool type ***
******************************************/
template<> struct random_impl<bool>
{
static inline bool run()
{
return random<int>(0,1)==0 ? false : true;
}
};
template<> struct scalar_fuzzy_impl<bool>
{
typedef bool RealScalar;
template<typename OtherScalar>
static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&)
{
return !x;
}
static inline bool isApprox(bool x, bool y, bool)
{
return x == y;
}
static inline bool isApproxOrLessThan(const bool& x, const bool& y, const bool&)
{
return (!x) || y;
}
};
/****************************************************************************
* Special functions *
****************************************************************************/
// std::isfinite is non standard, so let's define our own version,
// even though it is not very efficient.
template<typename T> bool (isfinite)(const T& x)
{
return x<NumTraits<T>::highest() && x>NumTraits<T>::lowest();
}
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_MATHFUNCTIONS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MATRIX_H
#define EIGEN_MATRIX_H
namespace Eigen {
/** \class Matrix
* \ingroup Core_Module
*
* \brief The matrix class, also used for vectors and row-vectors
*
* The %Matrix class is the work-horse for all \em dense (\ref dense "note") matrices and vectors within Eigen.
* Vectors are matrices with one column, and row-vectors are matrices with one row.
*
* The %Matrix class encompasses \em both fixed-size and dynamic-size objects (\ref fixedsize "note").
*
* The first three template parameters are required:
* \tparam _Scalar \anchor matrix_tparam_scalar Numeric type, e.g. float, double, int or std::complex<float>.
* User defined sclar types are supported as well (see \ref user_defined_scalars "here").
* \tparam _Rows Number of rows, or \b Dynamic
* \tparam _Cols Number of columns, or \b Dynamic
*
* The remaining template parameters are optional -- in most cases you don't have to worry about them.
* \tparam _Options \anchor matrix_tparam_options A combination of either \b #RowMajor or \b #ColMajor, and of either
* \b #AutoAlign or \b #DontAlign.
* The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter controls alignment, which is required
* for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size.
* \tparam _MaxRows Maximum number of rows. Defaults to \a _Rows (\ref maxrows "note").
* \tparam _MaxCols Maximum number of columns. Defaults to \a _Cols (\ref maxrows "note").
*
* Eigen provides a number of typedefs covering the usual cases. Here are some examples:
*
* \li \c Matrix2d is a 2x2 square matrix of doubles (\c Matrix<double, 2, 2>)
* \li \c Vector4f is a vector of 4 floats (\c Matrix<float, 4, 1>)
* \li \c RowVector3i is a row-vector of 3 ints (\c Matrix<int, 1, 3>)
*
* \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix<float, Dynamic, Dynamic>)
* \li \c VectorXf is a dynamic-size vector of floats (\c Matrix<float, Dynamic, 1>)
*
* \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix<float, 2, Dynamic>)
* \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix<double, Dynamic, 3>)
*
* See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs.
*
* You can access elements of vectors and matrices using normal subscripting:
*
* \code
* Eigen::VectorXd v(10);
* v[0] = 0.1;
* v[1] = 0.2;
* v(0) = 0.3;
* v(1) = 0.4;
*
* Eigen::MatrixXi m(10, 10);
* m(0, 1) = 1;
* m(0, 2) = 2;
* m(0, 3) = 3;
* \endcode
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_MATRIX_PLUGIN.
*
* <i><b>Some notes:</b></i>
*
* <dl>
* <dt><b>\anchor dense Dense versus sparse:</b></dt>
* <dd>This %Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the Sparse module.
*
* Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary contiguous array.
* This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero coefficients.</dd>
*
* <dt><b>\anchor fixedsize Fixed-size versus dynamic-size:</b></dt>
* <dd>Fixed-size means that the numbers of rows and columns are known are compile-time. In this case, Eigen allocates the array
* of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices, typically up to 4x4, sometimes up
* to 16x16. Larger matrices should be declared as dynamic-size even if one happens to know their size at compile-time.
*
* Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they are runtime
* variables, and the array of coefficients is allocated dynamically on the heap.
*
* Note that \em dense matrices, be they Fixed-size or Dynamic-size, <em>do not</em> expand dynamically in the sense of a std::map.
* If you want this behavior, see the Sparse module.</dd>
*
* <dt><b>\anchor maxrows _MaxRows and _MaxCols:</b></dt>
* <dd>In most cases, one just leaves these parameters to the default values.
* These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases
* when the exact numbers of rows and columns are not known are compile-time, but it is known at compile-time that they cannot
* exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case _MaxRows and _MaxCols
* are the dimensions of the original matrix, while _Rows and _Cols are Dynamic.</dd>
* </dl>
*
* \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy,
* \ref TopicStorageOrders
*/
namespace internal {
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
struct traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
{
typedef _Scalar Scalar;
typedef Dense StorageKind;
typedef DenseIndex Index;
typedef MatrixXpr XprKind;
enum {
RowsAtCompileTime = _Rows,
ColsAtCompileTime = _Cols,
MaxRowsAtCompileTime = _MaxRows,
MaxColsAtCompileTime = _MaxCols,
Flags = compute_matrix_flags<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret,
CoeffReadCost = NumTraits<Scalar>::ReadCost,
Options = _Options,
InnerStrideAtCompileTime = 1,
OuterStrideAtCompileTime = (Options&RowMajor) ? ColsAtCompileTime : RowsAtCompileTime
};
};
}
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
class Matrix
: public PlainObjectBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
{
public:
/** \brief Base class typedef.
* \sa PlainObjectBase
*/
typedef PlainObjectBase<Matrix> Base;
enum { Options = _Options };
EIGEN_DENSE_PUBLIC_INTERFACE(Matrix)
typedef typename Base::PlainObject PlainObject;
using Base::base;
using Base::coeffRef;
/**
* \brief Assigns matrices to each other.
*
* \note This is a special case of the templated operator=. Its purpose is
* to prevent a default operator= from hiding the templated operator=.
*
* \callgraph
*/
EIGEN_STRONG_INLINE Matrix& operator=(const Matrix& other)
{
return Base::_set(other);
}
/** \internal
* \brief Copies the value of the expression \a other into \c *this with automatic resizing.
*
* *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
* it will be initialized.
*
* Note that copying a row-vector into a vector (and conversely) is allowed.
* The resizing, if any, is then done in the appropriate way so that row-vectors
* remain row-vectors and vectors remain vectors.
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE Matrix& operator=(const MatrixBase<OtherDerived>& other)
{
return Base::_set(other);
}
/* Here, doxygen failed to copy the brief information when using \copydoc */
/**
* \brief Copies the generic expression \a other into *this.
* \copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other)
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE Matrix& operator=(const EigenBase<OtherDerived> &other)
{
return Base::operator=(other);
}
template<typename OtherDerived>
EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue<OtherDerived>& func)
{
return Base::operator=(func);
}
/** \brief Default constructor.
*
* For fixed-size matrices, does nothing.
*
* For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
* is called a null matrix. This constructor is the unique way to create null matrices: resizing
* a matrix to 0 is not supported.
*
* \sa resize(Index,Index)
*/
EIGEN_STRONG_INLINE explicit Matrix() : Base()
{
Base::_check_template_params();
EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
}
// FIXME is it still needed
Matrix(internal::constructor_without_unaligned_array_assert)
: Base(internal::constructor_without_unaligned_array_assert())
{ Base::_check_template_params(); EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED }
/** \brief Constructs a vector or row-vector with given dimension. \only_for_vectors
*
* Note that this is only useful for dynamic-size vectors. For fixed-size vectors,
* it is redundant to pass the dimension here, so it makes more sense to use the default
* constructor Matrix() instead.
*/
EIGEN_STRONG_INLINE explicit Matrix(Index dim)
: Base(dim, RowsAtCompileTime == 1 ? 1 : dim, ColsAtCompileTime == 1 ? 1 : dim)
{
Base::_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Matrix)
eigen_assert(dim >= 0);
eigen_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == dim);
EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename T0, typename T1>
EIGEN_STRONG_INLINE Matrix(const T0& x, const T1& y)
{
Base::_check_template_params();
Base::template _init2<T0,T1>(x, y);
}
#else
/** \brief Constructs an uninitialized matrix with \a rows rows and \a cols columns.
*
* This is useful for dynamic-size matrices. For fixed-size matrices,
* it is redundant to pass these parameters, so one should use the default constructor
* Matrix() instead. */
Matrix(Index rows, Index cols);
/** \brief Constructs an initialized 2D vector with given coefficients */
Matrix(const Scalar& x, const Scalar& y);
#endif
/** \brief Constructs an initialized 3D vector with given coefficients */
EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z)
{
Base::_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 3)
m_storage.data()[0] = x;
m_storage.data()[1] = y;
m_storage.data()[2] = z;
}
/** \brief Constructs an initialized 4D vector with given coefficients */
EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w)
{
Base::_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 4)
m_storage.data()[0] = x;
m_storage.data()[1] = y;
m_storage.data()[2] = z;
m_storage.data()[3] = w;
}
explicit Matrix(const Scalar *data);
/** \brief Constructor copying the value of the expression \a other */
template<typename OtherDerived>
EIGEN_STRONG_INLINE Matrix(const MatrixBase<OtherDerived>& other)
: Base(other.rows() * other.cols(), other.rows(), other.cols())
{
// This test resides here, to bring the error messages closer to the user. Normally, these checks
// are performed deeply within the library, thus causing long and scary error traces.
EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
Base::_check_template_params();
Base::_set_noalias(other);
}
/** \brief Copy constructor */
EIGEN_STRONG_INLINE Matrix(const Matrix& other)
: Base(other.rows() * other.cols(), other.rows(), other.cols())
{
Base::_check_template_params();
Base::_set_noalias(other);
}
/** \brief Copy constructor with in-place evaluation */
template<typename OtherDerived>
EIGEN_STRONG_INLINE Matrix(const ReturnByValue<OtherDerived>& other)
{
Base::_check_template_params();
Base::resize(other.rows(), other.cols());
other.evalTo(*this);
}
/** \brief Copy constructor for generic expressions.
* \sa MatrixBase::operator=(const EigenBase<OtherDerived>&)
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived> &other)
: Base(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
{
Base::_check_template_params();
Base::resize(other.rows(), other.cols());
// FIXME/CHECK: isn't *this = other.derived() more efficient. it allows to
// go for pure _set() implementations, right?
*this = other;
}
/** \internal
* \brief Override MatrixBase::swap() since for dynamic-sized matrices
* of same type it is enough to swap the data pointers.
*/
template<typename OtherDerived>
void swap(MatrixBase<OtherDerived> const & other)
{ this->_swap(other.derived()); }
inline Index innerStride() const { return 1; }
inline Index outerStride() const { return this->innerSize(); }
/////////// Geometry module ///////////
template<typename OtherDerived>
explicit Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
template<typename OtherDerived>
Matrix& operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
#ifdef EIGEN2_SUPPORT
template<typename OtherDerived>
explicit Matrix(const eigen2_RotationBase<OtherDerived,ColsAtCompileTime>& r);
template<typename OtherDerived>
Matrix& operator=(const eigen2_RotationBase<OtherDerived,ColsAtCompileTime>& r);
#endif
// allow to extend Matrix outside Eigen
#ifdef EIGEN_MATRIX_PLUGIN
#include EIGEN_MATRIX_PLUGIN
#endif
protected:
template <typename Derived, typename OtherDerived, bool IsVector>
friend struct internal::conservative_resize_like_impl;
using Base::m_storage;
};
/** \defgroup matrixtypedefs Global matrix typedefs
*
* \ingroup Core_Module
*
* Eigen defines several typedef shortcuts for most common matrix and vector types.
*
* The general patterns are the following:
*
* \c MatrixSizeType where \c Size can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
* and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
* for complex double.
*
* For example, \c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \c MatrixXf is a dynamic-size matrix of floats.
*
* There are also \c VectorSizeType and \c RowVectorSizeType which are self-explanatory. For example, \c Vector4cf is
* a fixed-size vector of 4 complex floats.
*
* \sa class Matrix
*/
#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, Size, 1> Vector##SizeSuffix##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, 1, Size> RowVector##SizeSuffix##TypeSuffix;
#define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, Dynamic, Size> Matrix##X##Size##TypeSuffix;
#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<float>, cf)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
#undef EIGEN_MAKE_TYPEDEFS
#undef EIGEN_MAKE_FIXED_TYPEDEFS
} // end namespace Eigen
#endif // EIGEN_MATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MATRIXBASE_H
#define EIGEN_MATRIXBASE_H
namespace Eigen {
/** \class MatrixBase
* \ingroup Core_Module
*
* \brief Base class for all dense matrices, vectors, and expressions
*
* This class is the base that is inherited by all matrix, vector, and related expression
* types. Most of the Eigen API is contained in this class, and its base classes. Other important
* classes for the Eigen API are Matrix, and VectorwiseOp.
*
* Note that some methods are defined in other modules such as the \ref LU_Module LU module
* for all functions related to matrix inversions.
*
* \tparam Derived is the derived type, e.g. a matrix type, or an expression, etc.
*
* When writing a function taking Eigen objects as argument, if you want your function
* to take as argument any matrix, vector, or expression, just let it take a
* MatrixBase argument. As an example, here is a function printFirstRow which, given
* a matrix, vector, or expression \a x, prints the first row of \a x.
*
* \code
template<typename Derived>
void printFirstRow(const Eigen::MatrixBase<Derived>& x)
{
cout << x.row(0) << endl;
}
* \endcode
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN.
*
* \sa \ref TopicClassHierarchy
*/
template<typename Derived> class MatrixBase
: public DenseBase<Derived>
{
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef MatrixBase StorageBaseType;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Index Index;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef DenseBase<Derived> Base;
using Base::RowsAtCompileTime;
using Base::ColsAtCompileTime;
using Base::SizeAtCompileTime;
using Base::MaxRowsAtCompileTime;
using Base::MaxColsAtCompileTime;
using Base::MaxSizeAtCompileTime;
using Base::IsVectorAtCompileTime;
using Base::Flags;
using Base::CoeffReadCost;
using Base::derived;
using Base::const_cast_derived;
using Base::rows;
using Base::cols;
using Base::size;
using Base::coeff;
using Base::coeffRef;
using Base::lazyAssign;
using Base::eval;
using Base::operator+=;
using Base::operator-=;
using Base::operator*=;
using Base::operator/=;
typedef typename Base::CoeffReturnType CoeffReturnType;
typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType;
typedef typename Base::RowXpr RowXpr;
typedef typename Base::ColXpr ColXpr;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** type of the equivalent square matrix */
typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime),
EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
/** \returns the size of the main diagonal, which is min(rows(),cols()).
* \sa rows(), cols(), SizeAtCompileTime. */
inline Index diagonalSize() const { return (std::min)(rows(),cols()); }
/** \brief The plain matrix type corresponding to this expression.
*
* This is not necessarily exactly the return type of eval(). In the case of plain matrices,
* the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed
* that the return type of eval() is either PlainObject or const PlainObject&.
*/
typedef Matrix<typename internal::traits<Derived>::Scalar,
internal::traits<Derived>::RowsAtCompileTime,
internal::traits<Derived>::ColsAtCompileTime,
AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),
internal::traits<Derived>::MaxRowsAtCompileTime,
internal::traits<Derived>::MaxColsAtCompileTime
> PlainObject;
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal Represents a matrix with all coefficients equal to one another*/
typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Derived> ConstantReturnType;
/** \internal the return type of MatrixBase::adjoint() */
typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,
ConstTransposeReturnType
>::type AdjointReturnType;
/** \internal Return type of eigenvalues() */
typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> EigenvaluesReturnType;
/** \internal the return type of identity */
typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>,Derived> IdentityReturnType;
/** \internal the return type of unit vectors */
typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>,
internal::traits<Derived>::RowsAtCompileTime,
internal::traits<Derived>::ColsAtCompileTime> BasisReturnType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase
# include "../plugins/CommonCwiseUnaryOps.h"
# include "../plugins/CommonCwiseBinaryOps.h"
# include "../plugins/MatrixCwiseUnaryOps.h"
# include "../plugins/MatrixCwiseBinaryOps.h"
# ifdef EIGEN_MATRIXBASE_PLUGIN
# include EIGEN_MATRIXBASE_PLUGIN
# endif
#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
/** Special case of the template operator=, in order to prevent the compiler
* from generating a default operator= (issue hit with g++ 4.1)
*/
Derived& operator=(const MatrixBase& other);
// We cannot inherit here via Base::operator= since it is causing
// trouble with MSVC.
template <typename OtherDerived>
Derived& operator=(const DenseBase<OtherDerived>& other);
template <typename OtherDerived>
Derived& operator=(const EigenBase<OtherDerived>& other);
template<typename OtherDerived>
Derived& operator=(const ReturnByValue<OtherDerived>& other);
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename ProductDerived, typename Lhs, typename Rhs>
Derived& lazyAssign(const ProductBase<ProductDerived, Lhs,Rhs>& other);
#endif // not EIGEN_PARSED_BY_DOXYGEN
template<typename OtherDerived>
Derived& operator+=(const MatrixBase<OtherDerived>& other);
template<typename OtherDerived>
Derived& operator-=(const MatrixBase<OtherDerived>& other);
template<typename OtherDerived>
const typename ProductReturnType<Derived,OtherDerived>::Type
operator*(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
const typename LazyProductReturnType<Derived,OtherDerived>::Type
lazyProduct(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
Derived& operator*=(const EigenBase<OtherDerived>& other);
template<typename OtherDerived>
void applyOnTheLeft(const EigenBase<OtherDerived>& other);
template<typename OtherDerived>
void applyOnTheRight(const EigenBase<OtherDerived>& other);
template<typename DiagonalDerived>
const DiagonalProduct<Derived, DiagonalDerived, OnTheRight>
operator*(const DiagonalBase<DiagonalDerived> &diagonal) const;
template<typename OtherDerived>
typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
dot(const MatrixBase<OtherDerived>& other) const;
#ifdef EIGEN2_SUPPORT
template<typename OtherDerived>
Scalar eigen2_dot(const MatrixBase<OtherDerived>& other) const;
#endif
RealScalar squaredNorm() const;
RealScalar norm() const;
RealScalar stableNorm() const;
RealScalar blueNorm() const;
RealScalar hypotNorm() const;
const PlainObject normalized() const;
void normalize();
const AdjointReturnType adjoint() const;
void adjointInPlace();
typedef Diagonal<Derived> DiagonalReturnType;
DiagonalReturnType diagonal();
typedef const Diagonal<const Derived> ConstDiagonalReturnType;
const ConstDiagonalReturnType diagonal() const;
template<int Index> struct DiagonalIndexReturnType { typedef Diagonal<Derived,Index> Type; };
template<int Index> struct ConstDiagonalIndexReturnType { typedef const Diagonal<const Derived,Index> Type; };
template<int Index> typename DiagonalIndexReturnType<Index>::Type diagonal();
template<int Index> typename ConstDiagonalIndexReturnType<Index>::Type diagonal() const;
// Note: The "MatrixBase::" prefixes are added to help MSVC9 to match these declarations with the later implementations.
// On the other hand they confuse MSVC8...
#if (defined _MSC_VER) && (_MSC_VER >= 1500) // 2008 or later
typename MatrixBase::template DiagonalIndexReturnType<Dynamic>::Type diagonal(Index index);
typename MatrixBase::template ConstDiagonalIndexReturnType<Dynamic>::Type diagonal(Index index) const;
#else
typename DiagonalIndexReturnType<Dynamic>::Type diagonal(Index index);
typename ConstDiagonalIndexReturnType<Dynamic>::Type diagonal(Index index) const;
#endif
#ifdef EIGEN2_SUPPORT
template<unsigned int Mode> typename internal::eigen2_part_return_type<Derived, Mode>::type part();
template<unsigned int Mode> const typename internal::eigen2_part_return_type<Derived, Mode>::type part() const;
// huuuge hack. make Eigen2's matrix.part<Diagonal>() work in eigen3. Problem: Diagonal is now a class template instead
// of an integer constant. Solution: overload the part() method template wrt template parameters list.
template<template<typename T, int N> class U>
const DiagonalWrapper<ConstDiagonalReturnType> part() const
{ return diagonal().asDiagonal(); }
#endif // EIGEN2_SUPPORT
template<unsigned int Mode> struct TriangularViewReturnType { typedef TriangularView<Derived, Mode> Type; };
template<unsigned int Mode> struct ConstTriangularViewReturnType { typedef const TriangularView<const Derived, Mode> Type; };
template<unsigned int Mode> typename TriangularViewReturnType<Mode>::Type triangularView();
template<unsigned int Mode> typename ConstTriangularViewReturnType<Mode>::Type triangularView() const;
template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SelfAdjointView<Derived, UpLo> Type; };
template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SelfAdjointView<const Derived, UpLo> Type; };
template<unsigned int UpLo> typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
template<unsigned int UpLo> typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
const SparseView<Derived> sparseView(const Scalar& m_reference = Scalar(0),
typename NumTraits<Scalar>::Real m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
static const IdentityReturnType Identity();
static const IdentityReturnType Identity(Index rows, Index cols);
static const BasisReturnType Unit(Index size, Index i);
static const BasisReturnType Unit(Index i);
static const BasisReturnType UnitX();
static const BasisReturnType UnitY();
static const BasisReturnType UnitZ();
static const BasisReturnType UnitW();
const DiagonalWrapper<const Derived> asDiagonal() const;
const PermutationWrapper<const Derived> asPermutation() const;
Derived& setIdentity();
Derived& setIdentity(Index rows, Index cols);
bool isIdentity(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
bool isDiagonal(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
bool isUpperTriangular(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
bool isLowerTriangular(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
template<typename OtherDerived>
bool isOrthogonal(const MatrixBase<OtherDerived>& other,
RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
bool isUnitary(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
/** \returns true if each coefficients of \c *this and \a other are all exactly equal.
* \warning When using floating point scalar values you probably should rather use a
* fuzzy comparison such as isApprox()
* \sa isApprox(), operator!= */
template<typename OtherDerived>
inline bool operator==(const MatrixBase<OtherDerived>& other) const
{ return cwiseEqual(other).all(); }
/** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other.
* \warning When using floating point scalar values you probably should rather use a
* fuzzy comparison such as isApprox()
* \sa isApprox(), operator== */
template<typename OtherDerived>
inline bool operator!=(const MatrixBase<OtherDerived>& other) const
{ return cwiseNotEqual(other).any(); }
NoAlias<Derived,Eigen::MatrixBase > noalias();
inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
inline ForceAlignedAccess<Derived> forceAlignedAccess();
template<bool Enable> inline typename internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type forceAlignedAccessIf() const;
template<bool Enable> inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf();
Scalar trace() const;
/////////// Array module ///////////
template<int p> RealScalar lpNorm() const;
MatrixBase<Derived>& matrix() { return *this; }
const MatrixBase<Derived>& matrix() const { return *this; }
/** \returns an \link ArrayBase Array \endlink expression of this matrix
* \sa ArrayBase::matrix() */
ArrayWrapper<Derived> array() { return derived(); }
const ArrayWrapper<const Derived> array() const { return derived(); }
/////////// LU module ///////////
const FullPivLU<PlainObject> fullPivLu() const;
const PartialPivLU<PlainObject> partialPivLu() const;
#if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
const LU<PlainObject> lu() const;
#endif
#ifdef EIGEN2_SUPPORT
const LU<PlainObject> eigen2_lu() const;
#endif
#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
const PartialPivLU<PlainObject> lu() const;
#endif
#ifdef EIGEN2_SUPPORT
template<typename ResultType>
void computeInverse(MatrixBase<ResultType> *result) const {
*result = this->inverse();
}
#endif
const internal::inverse_impl<Derived> inverse() const;
template<typename ResultType>
void computeInverseAndDetWithCheck(
ResultType& inverse,
typename ResultType::Scalar& determinant,
bool& invertible,
const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
) const;
template<typename ResultType>
void computeInverseWithCheck(
ResultType& inverse,
bool& invertible,
const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
) const;
Scalar determinant() const;
/////////// Cholesky module ///////////
const LLT<PlainObject> llt() const;
const LDLT<PlainObject> ldlt() const;
/////////// QR module ///////////
const HouseholderQR<PlainObject> householderQr() const;
const ColPivHouseholderQR<PlainObject> colPivHouseholderQr() const;
const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr() const;
#ifdef EIGEN2_SUPPORT
const QR<PlainObject> qr() const;
#endif
EigenvaluesReturnType eigenvalues() const;
RealScalar operatorNorm() const;
/////////// SVD module ///////////
JacobiSVD<PlainObject> jacobiSvd(unsigned int computationOptions = 0) const;
#ifdef EIGEN2_SUPPORT
SVD<PlainObject> svd() const;
#endif
/////////// Geometry module ///////////
#ifndef EIGEN_PARSED_BY_DOXYGEN
/// \internal helper struct to form the return type of the cross product
template<typename OtherDerived> struct cross_product_return_type {
typedef typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;
};
#endif // EIGEN_PARSED_BY_DOXYGEN
template<typename OtherDerived>
typename cross_product_return_type<OtherDerived>::type
cross(const MatrixBase<OtherDerived>& other) const;
template<typename OtherDerived>
PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
PlainObject unitOrthogonal(void) const;
Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
ScalarMultipleReturnType operator*(const UniformScaling<Scalar>& s) const;
// put this as separate enum value to work around possible GCC 4.3 bug (?)
enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1?Vertical:Horizontal };
typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
HomogeneousReturnType homogeneous() const;
#endif
enum {
SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
};
typedef Block<const Derived,
internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>,
const ConstStartMinusOne > HNormalizedReturnType;
const HNormalizedReturnType hnormalized() const;
////////// Householder module ///////////
void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
template<typename EssentialPart>
void makeHouseholder(EssentialPart& essential,
Scalar& tau, RealScalar& beta) const;
template<typename EssentialPart>
void applyHouseholderOnTheLeft(const EssentialPart& essential,
const Scalar& tau,
Scalar* workspace);
template<typename EssentialPart>
void applyHouseholderOnTheRight(const EssentialPart& essential,
const Scalar& tau,
Scalar* workspace);
///////// Jacobi module /////////
template<typename OtherScalar>
void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
template<typename OtherScalar>
void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
///////// MatrixFunctions module /////////
typedef typename internal::stem_function<Scalar>::type StemFunction;
const MatrixExponentialReturnValue<Derived> exp() const;
const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
const MatrixFunctionReturnValue<Derived> cosh() const;
const MatrixFunctionReturnValue<Derived> sinh() const;
const MatrixFunctionReturnValue<Derived> cos() const;
const MatrixFunctionReturnValue<Derived> sin() const;
const MatrixSquareRootReturnValue<Derived> sqrt() const;
const MatrixLogarithmReturnValue<Derived> log() const;
#ifdef EIGEN2_SUPPORT
template<typename ProductDerived, typename Lhs, typename Rhs>
Derived& operator+=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
EvalBeforeAssigningBit>& other);
template<typename ProductDerived, typename Lhs, typename Rhs>
Derived& operator-=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
EvalBeforeAssigningBit>& other);
/** \deprecated because .lazy() is deprecated
* Overloaded for cache friendly product evaluation */
template<typename OtherDerived>
Derived& lazyAssign(const Flagged<OtherDerived, 0, EvalBeforeAssigningBit>& other)
{ return lazyAssign(other._expression()); }
template<unsigned int Added>
const Flagged<Derived, Added, 0> marked() const;
const Flagged<Derived, 0, EvalBeforeAssigningBit> lazy() const;
inline const Cwise<Derived> cwise() const;
inline Cwise<Derived> cwise();
VectorBlock<Derived> start(Index size);
const VectorBlock<const Derived> start(Index size) const;
VectorBlock<Derived> end(Index size);
const VectorBlock<const Derived> end(Index size) const;
template<int Size> VectorBlock<Derived,Size> start();
template<int Size> const VectorBlock<const Derived,Size> start() const;
template<int Size> VectorBlock<Derived,Size> end();
template<int Size> const VectorBlock<const Derived,Size> end() const;
Minor<Derived> minor(Index row, Index col);
const Minor<Derived> minor(Index row, Index col) const;
#endif
protected:
MatrixBase() : Base() {}
private:
explicit MatrixBase(int);
MatrixBase(int,int);
template<typename OtherDerived> explicit MatrixBase(const MatrixBase<OtherDerived>&);
protected:
// mixing arrays and matrices is not legal
template<typename OtherDerived> Derived& operator+=(const ArrayBase<OtherDerived>& )
{EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
// mixing arrays and matrices is not legal
template<typename OtherDerived> Derived& operator-=(const ArrayBase<OtherDerived>& )
{EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
};
} // end namespace Eigen
#endif // EIGEN_MATRIXBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_NESTBYVALUE_H
#define EIGEN_NESTBYVALUE_H
namespace Eigen {
/** \class NestByValue
* \ingroup Core_Module
*
* \brief Expression which must be nested by value
*
* \param ExpressionType the type of the object of which we are requiring nesting-by-value
*
* This class is the return type of MatrixBase::nestByValue()
* and most of the time this is the only way it is used.
*
* \sa MatrixBase::nestByValue()
*/
namespace internal {
template<typename ExpressionType>
struct traits<NestByValue<ExpressionType> > : public traits<ExpressionType>
{};
}
template<typename ExpressionType> class NestByValue
: public internal::dense_xpr_base< NestByValue<ExpressionType> >::type
{
public:
typedef typename internal::dense_xpr_base<NestByValue>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(NestByValue)
inline NestByValue(const ExpressionType& matrix) : m_expression(matrix) {}
inline Index rows() const { return m_expression.rows(); }
inline Index cols() const { return m_expression.cols(); }
inline Index outerStride() const { return m_expression.outerStride(); }
inline Index innerStride() const { return m_expression.innerStride(); }
inline const CoeffReturnType coeff(Index row, Index col) const
{
return m_expression.coeff(row, col);
}
inline Scalar& coeffRef(Index row, Index col)
{
return m_expression.const_cast_derived().coeffRef(row, col);
}
inline const CoeffReturnType coeff(Index index) const
{
return m_expression.coeff(index);
}
inline Scalar& coeffRef(Index index)
{
return m_expression.const_cast_derived().coeffRef(index);
}
template<int LoadMode>
inline const PacketScalar packet(Index row, Index col) const
{
return m_expression.template packet<LoadMode>(row, col);
}
template<int LoadMode>
inline void writePacket(Index row, Index col, const PacketScalar& x)
{
m_expression.const_cast_derived().template writePacket<LoadMode>(row, col, x);
}
template<int LoadMode>
inline const PacketScalar packet(Index index) const
{
return m_expression.template packet<LoadMode>(index);
}
template<int LoadMode>
inline void writePacket(Index index, const PacketScalar& x)
{
m_expression.const_cast_derived().template writePacket<LoadMode>(index, x);
}
operator const ExpressionType&() const { return m_expression; }
protected:
const ExpressionType m_expression;
};
/** \returns an expression of the temporary version of *this.
*/
template<typename Derived>
inline const NestByValue<Derived>
DenseBase<Derived>::nestByValue() const
{
return NestByValue<Derived>(derived());
}
} // end namespace Eigen
#endif // EIGEN_NESTBYVALUE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_NOALIAS_H
#define EIGEN_NOALIAS_H
namespace Eigen {
/** \class NoAlias
* \ingroup Core_Module
*
* \brief Pseudo expression providing an operator = assuming no aliasing
*
* \param ExpressionType the type of the object on which to do the lazy assignment
*
* This class represents an expression with special assignment operators
* assuming no aliasing between the target expression and the source expression.
* More precisely it alloas to bypass the EvalBeforeAssignBit flag of the source expression.
* It is the return type of MatrixBase::noalias()
* and most of the time this is the only way it is used.
*
* \sa MatrixBase::noalias()
*/
template<typename ExpressionType, template <typename> class StorageBase>
class NoAlias
{
typedef typename ExpressionType::Scalar Scalar;
public:
NoAlias(ExpressionType& expression) : m_expression(expression) {}
/** Behaves like MatrixBase::lazyAssign(other)
* \sa MatrixBase::lazyAssign() */
template<typename OtherDerived>
EIGEN_STRONG_INLINE ExpressionType& operator=(const StorageBase<OtherDerived>& other)
{ return internal::assign_selector<ExpressionType,OtherDerived,false>::run(m_expression,other.derived()); }
/** \sa MatrixBase::operator+= */
template<typename OtherDerived>
EIGEN_STRONG_INLINE ExpressionType& operator+=(const StorageBase<OtherDerived>& other)
{
typedef SelfCwiseBinaryOp<internal::scalar_sum_op<Scalar>, ExpressionType, OtherDerived> SelfAdder;
SelfAdder tmp(m_expression);
typedef typename internal::nested<OtherDerived>::type OtherDerivedNested;
typedef typename internal::remove_all<OtherDerivedNested>::type _OtherDerivedNested;
internal::assign_selector<SelfAdder,_OtherDerivedNested,false>::run(tmp,OtherDerivedNested(other.derived()));
return m_expression;
}
/** \sa MatrixBase::operator-= */
template<typename OtherDerived>
EIGEN_STRONG_INLINE ExpressionType& operator-=(const StorageBase<OtherDerived>& other)
{
typedef SelfCwiseBinaryOp<internal::scalar_difference_op<Scalar>, ExpressionType, OtherDerived> SelfAdder;
SelfAdder tmp(m_expression);
typedef typename internal::nested<OtherDerived>::type OtherDerivedNested;
typedef typename internal::remove_all<OtherDerivedNested>::type _OtherDerivedNested;
internal::assign_selector<SelfAdder,_OtherDerivedNested,false>::run(tmp,OtherDerivedNested(other.derived()));
return m_expression;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename ProductDerived, typename Lhs, typename Rhs>
EIGEN_STRONG_INLINE ExpressionType& operator+=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
{ other.derived().addTo(m_expression); return m_expression; }
template<typename ProductDerived, typename Lhs, typename Rhs>
EIGEN_STRONG_INLINE ExpressionType& operator-=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
{ other.derived().subTo(m_expression); return m_expression; }
template<typename Lhs, typename Rhs, int NestingFlags>
EIGEN_STRONG_INLINE ExpressionType& operator+=(const CoeffBasedProduct<Lhs,Rhs,NestingFlags>& other)
{ return m_expression.derived() += CoeffBasedProduct<Lhs,Rhs,NestByRefBit>(other.lhs(), other.rhs()); }
template<typename Lhs, typename Rhs, int NestingFlags>
EIGEN_STRONG_INLINE ExpressionType& operator-=(const CoeffBasedProduct<Lhs,Rhs,NestingFlags>& other)
{ return m_expression.derived() -= CoeffBasedProduct<Lhs,Rhs,NestByRefBit>(other.lhs(), other.rhs()); }
#endif
protected:
ExpressionType& m_expression;
};
/** \returns a pseudo expression of \c *this with an operator= assuming
* no aliasing between \c *this and the source expression.
*
* More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag.
* Currently, even though several expressions may alias, only product
* expressions have this flag. Therefore, noalias() is only usefull when
* the source expression contains a matrix product.
*
* Here are some examples where noalias is usefull:
* \code
* D.noalias() = A * B;
* D.noalias() += A.transpose() * B;
* D.noalias() -= 2 * A * B.adjoint();
* \endcode
*
* On the other hand the following example will lead to a \b wrong result:
* \code
* A.noalias() = A * B;
* \endcode
* because the result matrix A is also an operand of the matrix product. Therefore,
* there is no alternative than evaluating A * B in a temporary, that is the default
* behavior when you write:
* \code
* A = A * B;
* \endcode
*
* \sa class NoAlias
*/
template<typename Derived>
NoAlias<Derived,MatrixBase> MatrixBase<Derived>::noalias()
{
return derived();
}
} // end namespace Eigen
#endif // EIGEN_NOALIAS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_NUMTRAITS_H
#define EIGEN_NUMTRAITS_H
namespace Eigen {
/** \class NumTraits
* \ingroup Core_Module
*
* \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
*
* \param T the numeric type at hand
*
* This class stores enums, typedefs and static methods giving information about a numeric type.
*
* The provided data consists of:
* \li A typedef \a Real, giving the "real part" type of \a T. If \a T is already real,
* then \a Real is just a typedef to \a T. If \a T is \c std::complex<U> then \a Real
* is a typedef to \a U.
* \li A typedef \a NonInteger, giving the type that should be used for operations producing non-integral values,
* such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
* \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
* take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
* only intended as a helper for code that needs to explicitly promote types.
* \li A typedef \a Nested giving the type to use to nest a value inside of the expression tree. If you don't know what
* this means, just use \a T here.
* \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex
* type, and to 0 otherwise.
* \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int,
* and to \c 0 otherwise.
* \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed
* to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers.
* Stay vague here. No need to do architecture-specific stuff.
* \li An enum value \a IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T is unsigned.
* \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must
* be called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1 otherwise.
* \li An epsilon() function which, unlike std::numeric_limits::epsilon(), returns a \a Real instead of a \a T.
* \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default
* value by the fuzzy comparison operators.
* \li highest() and lowest() functions returning the highest and lowest possible values respectively.
*/
template<typename T> struct GenericNumTraits
{
enum {
IsInteger = std::numeric_limits<T>::is_integer,
IsSigned = std::numeric_limits<T>::is_signed,
IsComplex = 0,
RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
ReadCost = 1,
AddCost = 1,
MulCost = 1
};
typedef T Real;
typedef typename internal::conditional<
IsInteger,
typename internal::conditional<sizeof(T)<=2, float, double>::type,
T
>::type NonInteger;
typedef T Nested;
static inline Real epsilon() { return std::numeric_limits<T>::epsilon(); }
static inline Real dummy_precision()
{
// make sure to override this for floating-point types
return Real(0);
}
static inline T highest() { return (std::numeric_limits<T>::max)(); }
static inline T lowest() { return IsInteger ? (std::numeric_limits<T>::min)() : (-(std::numeric_limits<T>::max)()); }
#ifdef EIGEN2_SUPPORT
enum {
HasFloatingPoint = !IsInteger
};
typedef NonInteger FloatingPoint;
#endif
};
template<typename T> struct NumTraits : GenericNumTraits<T>
{};
template<> struct NumTraits<float>
: GenericNumTraits<float>
{
static inline float dummy_precision() { return 1e-5f; }
};
template<> struct NumTraits<double> : GenericNumTraits<double>
{
static inline double dummy_precision() { return 1e-12; }
};
template<> struct NumTraits<long double>
: GenericNumTraits<long double>
{
static inline long double dummy_precision() { return 1e-15l; }
};
template<typename _Real> struct NumTraits<std::complex<_Real> >
: GenericNumTraits<std::complex<_Real> >
{
typedef _Real Real;
enum {
IsComplex = 1,
RequireInitialization = NumTraits<_Real>::RequireInitialization,
ReadCost = 2 * NumTraits<_Real>::ReadCost,
AddCost = 2 * NumTraits<Real>::AddCost,
MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
};
static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
};
template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
{
typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
typedef ArrayType & Nested;
enum {
IsComplex = NumTraits<Scalar>::IsComplex,
IsInteger = NumTraits<Scalar>::IsInteger,
IsSigned = NumTraits<Scalar>::IsSigned,
RequireInitialization = 1,
ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::ReadCost,
AddCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost,
MulCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost
};
};
} // end namespace Eigen
#endif // EIGEN_NUMTRAITS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PERMUTATIONMATRIX_H
#define EIGEN_PERMUTATIONMATRIX_H
namespace Eigen {
template<int RowCol,typename IndicesType,typename MatrixType, typename StorageKind> class PermutedImpl;
/** \class PermutationBase
* \ingroup Core_Module
*
* \brief Base class for permutations
*
* \param Derived the derived class
*
* This class is the base class for all expressions representing a permutation matrix,
* internally stored as a vector of integers.
* The convention followed here is that if \f$ \sigma \f$ is a permutation, the corresponding permutation matrix
* \f$ P_\sigma \f$ is such that if \f$ (e_1,\ldots,e_p) \f$ is the canonical basis, we have:
* \f[ P_\sigma(e_i) = e_{\sigma(i)}. \f]
* This convention ensures that for any two permutations \f$ \sigma, \tau \f$, we have:
* \f[ P_{\sigma\circ\tau} = P_\sigma P_\tau. \f]
*
* Permutation matrices are square and invertible.
*
* Notice that in addition to the member functions and operators listed here, there also are non-member
* operator* to multiply any kind of permutation object with any kind of matrix expression (MatrixBase)
* on either side.
*
* \sa class PermutationMatrix, class PermutationWrapper
*/
namespace internal {
template<typename PermutationType, typename MatrixType, int Side, bool Transposed=false>
struct permut_matrix_product_retval;
template<typename PermutationType, typename MatrixType, int Side, bool Transposed=false>
struct permut_sparsematrix_product_retval;
enum PermPermProduct_t {PermPermProduct};
} // end namespace internal
template<typename Derived>
class PermutationBase : public EigenBase<Derived>
{
typedef internal::traits<Derived> Traits;
typedef EigenBase<Derived> Base;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
enum {
Flags = Traits::Flags,
CoeffReadCost = Traits::CoeffReadCost,
RowsAtCompileTime = Traits::RowsAtCompileTime,
ColsAtCompileTime = Traits::ColsAtCompileTime,
MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
};
typedef typename Traits::Scalar Scalar;
typedef typename Traits::Index Index;
typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime,0,MaxRowsAtCompileTime,MaxColsAtCompileTime>
DenseMatrixType;
typedef PermutationMatrix<IndicesType::SizeAtCompileTime,IndicesType::MaxSizeAtCompileTime,Index>
PlainPermutationType;
using Base::derived;
#endif
/** Copies the other permutation into *this */
template<typename OtherDerived>
Derived& operator=(const PermutationBase<OtherDerived>& other)
{
indices() = other.indices();
return derived();
}
/** Assignment from the Transpositions \a tr */
template<typename OtherDerived>
Derived& operator=(const TranspositionsBase<OtherDerived>& tr)
{
setIdentity(tr.size());
for(Index k=size()-1; k>=0; --k)
applyTranspositionOnTheRight(k,tr.coeff(k));
return derived();
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** This is a special case of the templated operator=. Its purpose is to
* prevent a default operator= from hiding the templated operator=.
*/
Derived& operator=(const PermutationBase& other)
{
indices() = other.indices();
return derived();
}
#endif
/** \returns the number of rows */
inline Index rows() const { return Index(indices().size()); }
/** \returns the number of columns */
inline Index cols() const { return Index(indices().size()); }
/** \returns the size of a side of the respective square matrix, i.e., the number of indices */
inline Index size() const { return Index(indices().size()); }
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename DenseDerived>
void evalTo(MatrixBase<DenseDerived>& other) const
{
other.setZero();
for (int i=0; i<rows();++i)
other.coeffRef(indices().coeff(i),i) = typename DenseDerived::Scalar(1);
}
#endif
/** \returns a Matrix object initialized from this permutation matrix. Notice that it
* is inefficient to return this Matrix object by value. For efficiency, favor using
* the Matrix constructor taking EigenBase objects.
*/
DenseMatrixType toDenseMatrix() const
{
return derived();
}
/** const version of indices(). */
const IndicesType& indices() const { return derived().indices(); }
/** \returns a reference to the stored array representing the permutation. */
IndicesType& indices() { return derived().indices(); }
/** Resizes to given size.
*/
inline void resize(Index size)
{
indices().resize(size);
}
/** Sets *this to be the identity permutation matrix */
void setIdentity()
{
for(Index i = 0; i < size(); ++i)
indices().coeffRef(i) = i;
}
/** Sets *this to be the identity permutation matrix of given size.
*/
void setIdentity(Index size)
{
resize(size);
setIdentity();
}
/** Multiplies *this by the transposition \f$(ij)\f$ on the left.
*
* \returns a reference to *this.
*
* \warning This is much slower than applyTranspositionOnTheRight(int,int):
* this has linear complexity and requires a lot of branching.
*
* \sa applyTranspositionOnTheRight(int,int)
*/
Derived& applyTranspositionOnTheLeft(Index i, Index j)
{
eigen_assert(i>=0 && j>=0 && i<size() && j<size());
for(Index k = 0; k < size(); ++k)
{
if(indices().coeff(k) == i) indices().coeffRef(k) = j;
else if(indices().coeff(k) == j) indices().coeffRef(k) = i;
}
return derived();
}
/** Multiplies *this by the transposition \f$(ij)\f$ on the right.
*
* \returns a reference to *this.
*
* This is a fast operation, it only consists in swapping two indices.
*
* \sa applyTranspositionOnTheLeft(int,int)
*/
Derived& applyTranspositionOnTheRight(Index i, Index j)
{
eigen_assert(i>=0 && j>=0 && i<size() && j<size());
std::swap(indices().coeffRef(i), indices().coeffRef(j));
return derived();
}
/** \returns the inverse permutation matrix.
*
* \note \note_try_to_help_rvo
*/
inline Transpose<PermutationBase> inverse() const
{ return derived(); }
/** \returns the tranpose permutation matrix.
*
* \note \note_try_to_help_rvo
*/
inline Transpose<PermutationBase> transpose() const
{ return derived(); }
/**** multiplication helpers to hopefully get RVO ****/
#ifndef EIGEN_PARSED_BY_DOXYGEN
protected:
template<typename OtherDerived>
void assignTranspose(const PermutationBase<OtherDerived>& other)
{
for (int i=0; i<rows();++i) indices().coeffRef(other.indices().coeff(i)) = i;
}
template<typename Lhs,typename Rhs>
void assignProduct(const Lhs& lhs, const Rhs& rhs)
{
eigen_assert(lhs.cols() == rhs.rows());
for (int i=0; i<rows();++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));
}
#endif
public:
/** \returns the product permutation matrix.
*
* \note \note_try_to_help_rvo
*/
template<typename Other>
inline PlainPermutationType operator*(const PermutationBase<Other>& other) const
{ return PlainPermutationType(internal::PermPermProduct, derived(), other.derived()); }
/** \returns the product of a permutation with another inverse permutation.
*
* \note \note_try_to_help_rvo
*/
template<typename Other>
inline PlainPermutationType operator*(const Transpose<PermutationBase<Other> >& other) const
{ return PlainPermutationType(internal::PermPermProduct, *this, other.eval()); }
/** \returns the product of an inverse permutation with another permutation.
*
* \note \note_try_to_help_rvo
*/
template<typename Other> friend
inline PlainPermutationType operator*(const Transpose<PermutationBase<Other> >& other, const PermutationBase& perm)
{ return PlainPermutationType(internal::PermPermProduct, other.eval(), perm); }
protected:
};
/** \class PermutationMatrix
* \ingroup Core_Module
*
* \brief Permutation matrix
*
* \param SizeAtCompileTime the number of rows/cols, or Dynamic
* \param MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
* \param IndexType the interger type of the indices
*
* This class represents a permutation matrix, internally stored as a vector of integers.
*
* \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
*/
namespace internal {
template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType> >
: traits<Matrix<IndexType,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
{
typedef IndexType Index;
typedef Matrix<IndexType, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
};
}
template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
class PermutationMatrix : public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType> >
{
typedef PermutationBase<PermutationMatrix> Base;
typedef internal::traits<PermutationMatrix> Traits;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
#endif
inline PermutationMatrix()
{}
/** Constructs an uninitialized permutation matrix of given size.
*/
inline PermutationMatrix(int size) : m_indices(size)
{}
/** Copy constructor. */
template<typename OtherDerived>
inline PermutationMatrix(const PermutationBase<OtherDerived>& other)
: m_indices(other.indices()) {}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** Standard copy constructor. Defined only to prevent a default copy constructor
* from hiding the other templated constructor */
inline PermutationMatrix(const PermutationMatrix& other) : m_indices(other.indices()) {}
#endif
/** Generic constructor from expression of the indices. The indices
* array has the meaning that the permutations sends each integer i to indices[i].
*
* \warning It is your responsibility to check that the indices array that you passes actually
* describes a permutation, i.e., each value between 0 and n-1 occurs exactly once, where n is the
* array's size.
*/
template<typename Other>
explicit inline PermutationMatrix(const MatrixBase<Other>& indices) : m_indices(indices)
{}
/** Convert the Transpositions \a tr to a permutation matrix */
template<typename Other>
explicit PermutationMatrix(const TranspositionsBase<Other>& tr)
: m_indices(tr.size())
{
*this = tr;
}
/** Copies the other permutation into *this */
template<typename Other>
PermutationMatrix& operator=(const PermutationBase<Other>& other)
{
m_indices = other.indices();
return *this;
}
/** Assignment from the Transpositions \a tr */
template<typename Other>
PermutationMatrix& operator=(const TranspositionsBase<Other>& tr)
{
return Base::operator=(tr.derived());
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** This is a special case of the templated operator=. Its purpose is to
* prevent a default operator= from hiding the templated operator=.
*/
PermutationMatrix& operator=(const PermutationMatrix& other)
{
m_indices = other.m_indices;
return *this;
}
#endif
/** const version of indices(). */
const IndicesType& indices() const { return m_indices; }
/** \returns a reference to the stored array representing the permutation. */
IndicesType& indices() { return m_indices; }
/**** multiplication helpers to hopefully get RVO ****/
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename Other>
PermutationMatrix(const Transpose<PermutationBase<Other> >& other)
: m_indices(other.nestedPermutation().size())
{
for (int i=0; i<m_indices.size();++i) m_indices.coeffRef(other.nestedPermutation().indices().coeff(i)) = i;
}
template<typename Lhs,typename Rhs>
PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs)
: m_indices(lhs.indices().size())
{
Base::assignProduct(lhs,rhs);
}
#endif
protected:
IndicesType m_indices;
};
namespace internal {
template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess>
struct traits<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess> >
: traits<Matrix<IndexType,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
{
typedef IndexType Index;
typedef Map<const Matrix<IndexType, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, _PacketAccess> IndicesType;
};
}
template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess>
class Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess>
: public PermutationBase<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess> >
{
typedef PermutationBase<Map> Base;
typedef internal::traits<Map> Traits;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
typedef typename IndicesType::Scalar Index;
#endif
inline Map(const Index* indices)
: m_indices(indices)
{}
inline Map(const Index* indices, Index size)
: m_indices(indices,size)
{}
/** Copies the other permutation into *this */
template<typename Other>
Map& operator=(const PermutationBase<Other>& other)
{ return Base::operator=(other.derived()); }
/** Assignment from the Transpositions \a tr */
template<typename Other>
Map& operator=(const TranspositionsBase<Other>& tr)
{ return Base::operator=(tr.derived()); }
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** This is a special case of the templated operator=. Its purpose is to
* prevent a default operator= from hiding the templated operator=.
*/
Map& operator=(const Map& other)
{
m_indices = other.m_indices;
return *this;
}
#endif
/** const version of indices(). */
const IndicesType& indices() const { return m_indices; }
/** \returns a reference to the stored array representing the permutation. */
IndicesType& indices() { return m_indices; }
protected:
IndicesType m_indices;
};
/** \class PermutationWrapper
* \ingroup Core_Module
*
* \brief Class to view a vector of integers as a permutation matrix
*
* \param _IndicesType the type of the vector of integer (can be any compatible expression)
*
* This class allows to view any vector expression of integers as a permutation matrix.
*
* \sa class PermutationBase, class PermutationMatrix
*/
struct PermutationStorage {};
template<typename _IndicesType> class TranspositionsWrapper;
namespace internal {
template<typename _IndicesType>
struct traits<PermutationWrapper<_IndicesType> >
{
typedef PermutationStorage StorageKind;
typedef typename _IndicesType::Scalar Scalar;
typedef typename _IndicesType::Scalar Index;
typedef _IndicesType IndicesType;
enum {
RowsAtCompileTime = _IndicesType::SizeAtCompileTime,
ColsAtCompileTime = _IndicesType::SizeAtCompileTime,
MaxRowsAtCompileTime = IndicesType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = IndicesType::MaxColsAtCompileTime,
Flags = 0,
CoeffReadCost = _IndicesType::CoeffReadCost
};
};
}
template<typename _IndicesType>
class PermutationWrapper : public PermutationBase<PermutationWrapper<_IndicesType> >
{
typedef PermutationBase<PermutationWrapper> Base;
typedef internal::traits<PermutationWrapper> Traits;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
#endif
inline PermutationWrapper(const IndicesType& indices)
: m_indices(indices)
{}
/** const version of indices(). */
const typename internal::remove_all<typename IndicesType::Nested>::type&
indices() const { return m_indices; }
protected:
typename IndicesType::Nested m_indices;
};
/** \returns the matrix with the permutation applied to the columns.
*/
template<typename Derived, typename PermutationDerived>
inline const internal::permut_matrix_product_retval<PermutationDerived, Derived, OnTheRight>
operator*(const MatrixBase<Derived>& matrix,
const PermutationBase<PermutationDerived> &permutation)
{
return internal::permut_matrix_product_retval
<PermutationDerived, Derived, OnTheRight>
(permutation.derived(), matrix.derived());
}
/** \returns the matrix with the permutation applied to the rows.
*/
template<typename Derived, typename PermutationDerived>
inline const internal::permut_matrix_product_retval
<PermutationDerived, Derived, OnTheLeft>
operator*(const PermutationBase<PermutationDerived> &permutation,
const MatrixBase<Derived>& matrix)
{
return internal::permut_matrix_product_retval
<PermutationDerived, Derived, OnTheLeft>
(permutation.derived(), matrix.derived());
}
namespace internal {
template<typename PermutationType, typename MatrixType, int Side, bool Transposed>
struct traits<permut_matrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
{
typedef typename MatrixType::PlainObject ReturnType;
};
template<typename PermutationType, typename MatrixType, int Side, bool Transposed>
struct permut_matrix_product_retval
: public ReturnByValue<permut_matrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
{
typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned;
permut_matrix_product_retval(const PermutationType& perm, const MatrixType& matrix)
: m_permutation(perm), m_matrix(matrix)
{}
inline int rows() const { return m_matrix.rows(); }
inline int cols() const { return m_matrix.cols(); }
template<typename Dest> inline void evalTo(Dest& dst) const
{
const int n = Side==OnTheLeft ? rows() : cols();
if(is_same<MatrixTypeNestedCleaned,Dest>::value && extract_data(dst) == extract_data(m_matrix))
{
// apply the permutation inplace
Matrix<bool,PermutationType::RowsAtCompileTime,1,0,PermutationType::MaxRowsAtCompileTime> mask(m_permutation.size());
mask.fill(false);
int r = 0;
while(r < m_permutation.size())
{
// search for the next seed
while(r<m_permutation.size() && mask[r]) r++;
if(r>=m_permutation.size())
break;
// we got one, let's follow it until we are back to the seed
int k0 = r++;
int kPrev = k0;
mask.coeffRef(k0) = true;
for(int k=m_permutation.indices().coeff(k0); k!=k0; k=m_permutation.indices().coeff(k))
{
Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>(dst, k)
.swap(Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
(dst,((Side==OnTheLeft) ^ Transposed) ? k0 : kPrev));
mask.coeffRef(k) = true;
kPrev = k;
}
}
}
else
{
for(int i = 0; i < n; ++i)
{
Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
(dst, ((Side==OnTheLeft) ^ Transposed) ? m_permutation.indices().coeff(i) : i)
=
Block<const MatrixTypeNestedCleaned,Side==OnTheLeft ? 1 : MatrixType::RowsAtCompileTime,Side==OnTheRight ? 1 : MatrixType::ColsAtCompileTime>
(m_matrix, ((Side==OnTheRight) ^ Transposed) ? m_permutation.indices().coeff(i) : i);
}
}
}
protected:
const PermutationType& m_permutation;
typename MatrixType::Nested m_matrix;
};
/* Template partial specialization for transposed/inverse permutations */
template<typename Derived>
struct traits<Transpose<PermutationBase<Derived> > >
: traits<Derived>
{};
} // end namespace internal
template<typename Derived>
class Transpose<PermutationBase<Derived> >
: public EigenBase<Transpose<PermutationBase<Derived> > >
{
typedef Derived PermutationType;
typedef typename PermutationType::IndicesType IndicesType;
typedef typename PermutationType::PlainPermutationType PlainPermutationType;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef internal::traits<PermutationType> Traits;
typedef typename Derived::DenseMatrixType DenseMatrixType;
enum {
Flags = Traits::Flags,
CoeffReadCost = Traits::CoeffReadCost,
RowsAtCompileTime = Traits::RowsAtCompileTime,
ColsAtCompileTime = Traits::ColsAtCompileTime,
MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
};
typedef typename Traits::Scalar Scalar;
#endif
Transpose(const PermutationType& p) : m_permutation(p) {}
inline int rows() const { return m_permutation.rows(); }
inline int cols() const { return m_permutation.cols(); }
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename DenseDerived>
void evalTo(MatrixBase<DenseDerived>& other) const
{
other.setZero();
for (int i=0; i<rows();++i)
other.coeffRef(i, m_permutation.indices().coeff(i)) = typename DenseDerived::Scalar(1);
}
#endif
/** \return the equivalent permutation matrix */
PlainPermutationType eval() const { return *this; }
DenseMatrixType toDenseMatrix() const { return *this; }
/** \returns the matrix with the inverse permutation applied to the columns.
*/
template<typename OtherDerived> friend
inline const internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheRight, true>
operator*(const MatrixBase<OtherDerived>& matrix, const Transpose& trPerm)
{
return internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheRight, true>(trPerm.m_permutation, matrix.derived());
}
/** \returns the matrix with the inverse permutation applied to the rows.
*/
template<typename OtherDerived>
inline const internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheLeft, true>
operator*(const MatrixBase<OtherDerived>& matrix) const
{
return internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheLeft, true>(m_permutation, matrix.derived());
}
const PermutationType& nestedPermutation() const { return m_permutation; }
protected:
const PermutationType& m_permutation;
};
template<typename Derived>
const PermutationWrapper<const Derived> MatrixBase<Derived>::asPermutation() const
{
return derived();
}
} // end namespace Eigen
#endif // EIGEN_PERMUTATIONMATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DENSESTORAGEBASE_H
#define EIGEN_DENSESTORAGEBASE_H
#ifdef EIGEN_INITIALIZE_MATRICES_BY_ZERO
# define EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED for(int i=0;i<base().size();++i) coeffRef(i)=Scalar(0);
#else
# define EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
#endif
namespace Eigen {
namespace internal {
template<typename Index>
EIGEN_ALWAYS_INLINE void check_rows_cols_for_overflow(Index rows, Index cols)
{
// http://hg.mozilla.org/mozilla-central/file/6c8a909977d3/xpcom/ds/CheckedInt.h#l242
// we assume Index is signed
Index max_index = (size_t(1) << (8 * sizeof(Index) - 1)) - 1; // assume Index is signed
bool error = (rows < 0 || cols < 0) ? true
: (rows == 0 || cols == 0) ? false
: (rows > max_index / cols);
if (error)
throw_std_bad_alloc();
}
template <typename Derived, typename OtherDerived = Derived, bool IsVector = bool(Derived::IsVectorAtCompileTime)> struct conservative_resize_like_impl;
template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers> struct matrix_swap_impl;
} // end namespace internal
/** \class PlainObjectBase
* \brief %Dense storage base class for matrices and arrays.
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_PLAINOBJECTBASE_PLUGIN.
*
* \sa \ref TopicClassHierarchy
*/
#ifdef EIGEN_PARSED_BY_DOXYGEN
namespace internal {
// this is a warkaround to doxygen not being able to understand the inheritence logic
// when it is hidden by the dense_xpr_base helper struct.
template<typename Derived> struct dense_xpr_base_dispatcher_for_doxygen;// : public MatrixBase<Derived> {};
/** This class is just a workaround for Doxygen and it does not not actually exist. */
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
struct dense_xpr_base_dispatcher_for_doxygen<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
: public MatrixBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > {};
/** This class is just a workaround for Doxygen and it does not not actually exist. */
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
struct dense_xpr_base_dispatcher_for_doxygen<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
: public ArrayBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > {};
} // namespace internal
template<typename Derived>
class PlainObjectBase : public internal::dense_xpr_base_dispatcher_for_doxygen<Derived>
#else
template<typename Derived>
class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
#endif
{
public:
enum { Options = internal::traits<Derived>::Options };
typedef typename internal::dense_xpr_base<Derived>::type Base;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Index Index;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Derived DenseType;
using Base::RowsAtCompileTime;
using Base::ColsAtCompileTime;
using Base::SizeAtCompileTime;
using Base::MaxRowsAtCompileTime;
using Base::MaxColsAtCompileTime;
using Base::MaxSizeAtCompileTime;
using Base::IsVectorAtCompileTime;
using Base::Flags;
template<typename PlainObjectType, int MapOptions, typename StrideType> friend class Eigen::Map;
friend class Eigen::Map<Derived, Unaligned>;
typedef Eigen::Map<Derived, Unaligned> MapType;
friend class Eigen::Map<const Derived, Unaligned>;
typedef const Eigen::Map<const Derived, Unaligned> ConstMapType;
friend class Eigen::Map<Derived, Aligned>;
typedef Eigen::Map<Derived, Aligned> AlignedMapType;
friend class Eigen::Map<const Derived, Aligned>;
typedef const Eigen::Map<const Derived, Aligned> ConstAlignedMapType;
template<typename StrideType> struct StridedMapType { typedef Eigen::Map<Derived, Unaligned, StrideType> type; };
template<typename StrideType> struct StridedConstMapType { typedef Eigen::Map<const Derived, Unaligned, StrideType> type; };
template<typename StrideType> struct StridedAlignedMapType { typedef Eigen::Map<Derived, Aligned, StrideType> type; };
template<typename StrideType> struct StridedConstAlignedMapType { typedef Eigen::Map<const Derived, Aligned, StrideType> type; };
protected:
DenseStorage<Scalar, Base::MaxSizeAtCompileTime, Base::RowsAtCompileTime, Base::ColsAtCompileTime, Options> m_storage;
public:
enum { NeedsToAlign = SizeAtCompileTime != Dynamic && (internal::traits<Derived>::Flags & AlignedBit) != 0 };
EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
Base& base() { return *static_cast<Base*>(this); }
const Base& base() const { return *static_cast<const Base*>(this); }
EIGEN_STRONG_INLINE Index rows() const { return m_storage.rows(); }
EIGEN_STRONG_INLINE Index cols() const { return m_storage.cols(); }
EIGEN_STRONG_INLINE const Scalar& coeff(Index row, Index col) const
{
if(Flags & RowMajorBit)
return m_storage.data()[col + row * m_storage.cols()];
else // column-major
return m_storage.data()[row + col * m_storage.rows()];
}
EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const
{
return m_storage.data()[index];
}
EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)
{
if(Flags & RowMajorBit)
return m_storage.data()[col + row * m_storage.cols()];
else // column-major
return m_storage.data()[row + col * m_storage.rows()];
}
EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)
{
return m_storage.data()[index];
}
EIGEN_STRONG_INLINE const Scalar& coeffRef(Index row, Index col) const
{
if(Flags & RowMajorBit)
return m_storage.data()[col + row * m_storage.cols()];
else // column-major
return m_storage.data()[row + col * m_storage.rows()];
}
EIGEN_STRONG_INLINE const Scalar& coeffRef(Index index) const
{
return m_storage.data()[index];
}
/** \internal */
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet(Index row, Index col) const
{
return internal::ploadt<PacketScalar, LoadMode>
(m_storage.data() + (Flags & RowMajorBit
? col + row * m_storage.cols()
: row + col * m_storage.rows()));
}
/** \internal */
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
{
return internal::ploadt<PacketScalar, LoadMode>(m_storage.data() + index);
}
/** \internal */
template<int StoreMode>
EIGEN_STRONG_INLINE void writePacket(Index row, Index col, const PacketScalar& x)
{
internal::pstoret<Scalar, PacketScalar, StoreMode>
(m_storage.data() + (Flags & RowMajorBit
? col + row * m_storage.cols()
: row + col * m_storage.rows()), x);
}
/** \internal */
template<int StoreMode>
EIGEN_STRONG_INLINE void writePacket(Index index, const PacketScalar& x)
{
internal::pstoret<Scalar, PacketScalar, StoreMode>(m_storage.data() + index, x);
}
/** \returns a const pointer to the data array of this matrix */
EIGEN_STRONG_INLINE const Scalar *data() const
{ return m_storage.data(); }
/** \returns a pointer to the data array of this matrix */
EIGEN_STRONG_INLINE Scalar *data()
{ return m_storage.data(); }
/** Resizes \c *this to a \a rows x \a cols matrix.
*
* This method is intended for dynamic-size matrices, although it is legal to call it on any
* matrix as long as fixed dimensions are left unchanged. If you only want to change the number
* of rows and/or of columns, you can use resize(NoChange_t, Index), resize(Index, NoChange_t).
*
* If the current number of coefficients of \c *this exactly matches the
* product \a rows * \a cols, then no memory allocation is performed and
* the current values are left unchanged. In all other cases, including
* shrinking, the data is reallocated and all previous values are lost.
*
* Example: \include Matrix_resize_int_int.cpp
* Output: \verbinclude Matrix_resize_int_int.out
*
* \sa resize(Index) for vectors, resize(NoChange_t, Index), resize(Index, NoChange_t)
*/
EIGEN_STRONG_INLINE void resize(Index rows, Index cols)
{
#ifdef EIGEN_INITIALIZE_MATRICES_BY_ZERO
internal::check_rows_cols_for_overflow(rows, cols);
Index size = rows*cols;
bool size_changed = size != this->size();
m_storage.resize(size, rows, cols);
if(size_changed) EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
#else
internal::check_rows_cols_for_overflow(rows, cols);
m_storage.resize(rows*cols, rows, cols);
#endif
}
/** Resizes \c *this to a vector of length \a size
*
* \only_for_vectors. This method does not work for
* partially dynamic matrices when the static dimension is anything other
* than 1. For example it will not work with Matrix<double, 2, Dynamic>.
*
* Example: \include Matrix_resize_int.cpp
* Output: \verbinclude Matrix_resize_int.out
*
* \sa resize(Index,Index), resize(NoChange_t, Index), resize(Index, NoChange_t)
*/
inline void resize(Index size)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(PlainObjectBase)
eigen_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == size);
#ifdef EIGEN_INITIALIZE_MATRICES_BY_ZERO
bool size_changed = size != this->size();
#endif
if(RowsAtCompileTime == 1)
m_storage.resize(size, 1, size);
else
m_storage.resize(size, size, 1);
#ifdef EIGEN_INITIALIZE_MATRICES_BY_ZERO
if(size_changed) EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
#endif
}
/** Resizes the matrix, changing only the number of columns. For the parameter of type NoChange_t, just pass the special value \c NoChange
* as in the example below.
*
* Example: \include Matrix_resize_NoChange_int.cpp
* Output: \verbinclude Matrix_resize_NoChange_int.out
*
* \sa resize(Index,Index)
*/
inline void resize(NoChange_t, Index cols)
{
resize(rows(), cols);
}
/** Resizes the matrix, changing only the number of rows. For the parameter of type NoChange_t, just pass the special value \c NoChange
* as in the example below.
*
* Example: \include Matrix_resize_int_NoChange.cpp
* Output: \verbinclude Matrix_resize_int_NoChange.out
*
* \sa resize(Index,Index)
*/
inline void resize(Index rows, NoChange_t)
{
resize(rows, cols());
}
/** Resizes \c *this to have the same dimensions as \a other.
* Takes care of doing all the checking that's needed.
*
* Note that copying a row-vector into a vector (and conversely) is allowed.
* The resizing, if any, is then done in the appropriate way so that row-vectors
* remain row-vectors and vectors remain vectors.
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE void resizeLike(const EigenBase<OtherDerived>& _other)
{
const OtherDerived& other = _other.derived();
internal::check_rows_cols_for_overflow(other.rows(), other.cols());
const Index othersize = other.rows()*other.cols();
if(RowsAtCompileTime == 1)
{
eigen_assert(other.rows() == 1 || other.cols() == 1);
resize(1, othersize);
}
else if(ColsAtCompileTime == 1)
{
eigen_assert(other.rows() == 1 || other.cols() == 1);
resize(othersize, 1);
}
else resize(other.rows(), other.cols());
}
/** Resizes the matrix to \a rows x \a cols while leaving old values untouched.
*
* The method is intended for matrices of dynamic size. If you only want to change the number
* of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or
* conservativeResize(Index, NoChange_t).
*
* Matrices are resized relative to the top-left element. In case values need to be
* appended to the matrix they will be uninitialized.
*/
EIGEN_STRONG_INLINE void conservativeResize(Index rows, Index cols)
{
internal::conservative_resize_like_impl<Derived>::run(*this, rows, cols);
}
/** Resizes the matrix to \a rows x \a cols while leaving old values untouched.
*
* As opposed to conservativeResize(Index rows, Index cols), this version leaves
* the number of columns unchanged.
*
* In case the matrix is growing, new rows will be uninitialized.
*/
EIGEN_STRONG_INLINE void conservativeResize(Index rows, NoChange_t)
{
// Note: see the comment in conservativeResize(Index,Index)
conservativeResize(rows, cols());
}
/** Resizes the matrix to \a rows x \a cols while leaving old values untouched.
*
* As opposed to conservativeResize(Index rows, Index cols), this version leaves
* the number of rows unchanged.
*
* In case the matrix is growing, new columns will be uninitialized.
*/
EIGEN_STRONG_INLINE void conservativeResize(NoChange_t, Index cols)
{
// Note: see the comment in conservativeResize(Index,Index)
conservativeResize(rows(), cols);
}
/** Resizes the vector to \a size while retaining old values.
*
* \only_for_vectors. This method does not work for
* partially dynamic matrices when the static dimension is anything other
* than 1. For example it will not work with Matrix<double, 2, Dynamic>.
*
* When values are appended, they will be uninitialized.
*/
EIGEN_STRONG_INLINE void conservativeResize(Index size)
{
internal::conservative_resize_like_impl<Derived>::run(*this, size);
}
/** Resizes the matrix to \a rows x \a cols of \c other, while leaving old values untouched.
*
* The method is intended for matrices of dynamic size. If you only want to change the number
* of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or
* conservativeResize(Index, NoChange_t).
*
* Matrices are resized relative to the top-left element. In case values need to be
* appended to the matrix they will copied from \c other.
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE void conservativeResizeLike(const DenseBase<OtherDerived>& other)
{
internal::conservative_resize_like_impl<Derived,OtherDerived>::run(*this, other);
}
/** This is a special case of the templated operator=. Its purpose is to
* prevent a default operator= from hiding the templated operator=.
*/
EIGEN_STRONG_INLINE Derived& operator=(const PlainObjectBase& other)
{
return _set(other);
}
/** \sa MatrixBase::lazyAssign() */
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived& lazyAssign(const DenseBase<OtherDerived>& other)
{
_resize_to_match(other);
return Base::lazyAssign(other.derived());
}
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived& operator=(const ReturnByValue<OtherDerived>& func)
{
resize(func.rows(), func.cols());
return Base::operator=(func);
}
EIGEN_STRONG_INLINE explicit PlainObjectBase() : m_storage()
{
// _check_template_params();
// EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
// FIXME is it still needed ?
/** \internal */
PlainObjectBase(internal::constructor_without_unaligned_array_assert)
: m_storage(internal::constructor_without_unaligned_array_assert())
{
// _check_template_params(); EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
}
#endif
EIGEN_STRONG_INLINE PlainObjectBase(Index size, Index rows, Index cols)
: m_storage(size, rows, cols)
{
// _check_template_params();
// EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
}
/** \copydoc MatrixBase::operator=(const EigenBase<OtherDerived>&)
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived& operator=(const EigenBase<OtherDerived> &other)
{
_resize_to_match(other);
Base::operator=(other.derived());
return this->derived();
}
/** \sa MatrixBase::operator=(const EigenBase<OtherDerived>&) */
template<typename OtherDerived>
EIGEN_STRONG_INLINE PlainObjectBase(const EigenBase<OtherDerived> &other)
: m_storage(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
{
_check_template_params();
internal::check_rows_cols_for_overflow(other.derived().rows(), other.derived().cols());
Base::operator=(other.derived());
}
/** \name Map
* These are convenience functions returning Map objects. The Map() static functions return unaligned Map objects,
* while the AlignedMap() functions return aligned Map objects and thus should be called only with 16-byte-aligned
* \a data pointers.
*
* \see class Map
*/
//@{
static inline ConstMapType Map(const Scalar* data)
{ return ConstMapType(data); }
static inline MapType Map(Scalar* data)
{ return MapType(data); }
static inline ConstMapType Map(const Scalar* data, Index size)
{ return ConstMapType(data, size); }
static inline MapType Map(Scalar* data, Index size)
{ return MapType(data, size); }
static inline ConstMapType Map(const Scalar* data, Index rows, Index cols)
{ return ConstMapType(data, rows, cols); }
static inline MapType Map(Scalar* data, Index rows, Index cols)
{ return MapType(data, rows, cols); }
static inline ConstAlignedMapType MapAligned(const Scalar* data)
{ return ConstAlignedMapType(data); }
static inline AlignedMapType MapAligned(Scalar* data)
{ return AlignedMapType(data); }
static inline ConstAlignedMapType MapAligned(const Scalar* data, Index size)
{ return ConstAlignedMapType(data, size); }
static inline AlignedMapType MapAligned(Scalar* data, Index size)
{ return AlignedMapType(data, size); }
static inline ConstAlignedMapType MapAligned(const Scalar* data, Index rows, Index cols)
{ return ConstAlignedMapType(data, rows, cols); }
static inline AlignedMapType MapAligned(Scalar* data, Index rows, Index cols)
{ return AlignedMapType(data, rows, cols); }
template<int Outer, int Inner>
static inline typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, const Stride<Outer, Inner>& stride)
{ return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, stride); }
template<int Outer, int Inner>
static inline typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, const Stride<Outer, Inner>& stride)
{ return typename StridedMapType<Stride<Outer, Inner> >::type(data, stride); }
template<int Outer, int Inner>
static inline typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, Index size, const Stride<Outer, Inner>& stride)
{ return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, size, stride); }
template<int Outer, int Inner>
static inline typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, Index size, const Stride<Outer, Inner>& stride)
{ return typename StridedMapType<Stride<Outer, Inner> >::type(data, size, stride); }
template<int Outer, int Inner>
static inline typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
{ return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
template<int Outer, int Inner>
static inline typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
{ return typename StridedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
template<int Outer, int Inner>
static inline typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, const Stride<Outer, Inner>& stride)
{ return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, stride); }
template<int Outer, int Inner>
static inline typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, const Stride<Outer, Inner>& stride)
{ return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, stride); }
template<int Outer, int Inner>
static inline typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, Index size, const Stride<Outer, Inner>& stride)
{ return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, size, stride); }
template<int Outer, int Inner>
static inline typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, Index size, const Stride<Outer, Inner>& stride)
{ return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, size, stride); }
template<int Outer, int Inner>
static inline typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
{ return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
template<int Outer, int Inner>
static inline typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
{ return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
//@}
using Base::setConstant;
Derived& setConstant(Index size, const Scalar& value);
Derived& setConstant(Index rows, Index cols, const Scalar& value);
using Base::setZero;
Derived& setZero(Index size);
Derived& setZero(Index rows, Index cols);
using Base::setOnes;
Derived& setOnes(Index size);
Derived& setOnes(Index rows, Index cols);
using Base::setRandom;
Derived& setRandom(Index size);
Derived& setRandom(Index rows, Index cols);
#ifdef EIGEN_PLAINOBJECTBASE_PLUGIN
#include EIGEN_PLAINOBJECTBASE_PLUGIN
#endif
protected:
/** \internal Resizes *this in preparation for assigning \a other to it.
* Takes care of doing all the checking that's needed.
*
* Note that copying a row-vector into a vector (and conversely) is allowed.
* The resizing, if any, is then done in the appropriate way so that row-vectors
* remain row-vectors and vectors remain vectors.
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE void _resize_to_match(const EigenBase<OtherDerived>& other)
{
#ifdef EIGEN_NO_AUTOMATIC_RESIZING
eigen_assert((this->size()==0 || (IsVectorAtCompileTime ? (this->size() == other.size())
: (rows() == other.rows() && cols() == other.cols())))
&& "Size mismatch. Automatic resizing is disabled because EIGEN_NO_AUTOMATIC_RESIZING is defined");
EIGEN_ONLY_USED_FOR_DEBUG(other);
#else
resizeLike(other);
#endif
}
/**
* \brief Copies the value of the expression \a other into \c *this with automatic resizing.
*
* *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
* it will be initialized.
*
* Note that copying a row-vector into a vector (and conversely) is allowed.
* The resizing, if any, is then done in the appropriate way so that row-vectors
* remain row-vectors and vectors remain vectors.
*
* \sa operator=(const MatrixBase<OtherDerived>&), _set_noalias()
*
* \internal
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived& _set(const DenseBase<OtherDerived>& other)
{
_set_selector(other.derived(), typename internal::conditional<static_cast<bool>(int(OtherDerived::Flags) & EvalBeforeAssigningBit), internal::true_type, internal::false_type>::type());
return this->derived();
}
template<typename OtherDerived>
EIGEN_STRONG_INLINE void _set_selector(const OtherDerived& other, const internal::true_type&) { _set_noalias(other.eval()); }
template<typename OtherDerived>
EIGEN_STRONG_INLINE void _set_selector(const OtherDerived& other, const internal::false_type&) { _set_noalias(other); }
/** \internal Like _set() but additionally makes the assumption that no aliasing effect can happen (which
* is the case when creating a new matrix) so one can enforce lazy evaluation.
*
* \sa operator=(const MatrixBase<OtherDerived>&), _set()
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE Derived& _set_noalias(const DenseBase<OtherDerived>& other)
{
// I don't think we need this resize call since the lazyAssign will anyways resize
// and lazyAssign will be called by the assign selector.
//_resize_to_match(other);
// the 'false' below means to enforce lazy evaluation. We don't use lazyAssign() because
// it wouldn't allow to copy a row-vector into a column-vector.
return internal::assign_selector<Derived,OtherDerived,false>::run(this->derived(), other.derived());
}
template<typename T0, typename T1>
EIGEN_STRONG_INLINE void _init2(Index rows, Index cols, typename internal::enable_if<Base::SizeAtCompileTime!=2,T0>::type* = 0)
{
EIGEN_STATIC_ASSERT(bool(NumTraits<T0>::IsInteger) &&
bool(NumTraits<T1>::IsInteger),
FLOATING_POINT_ARGUMENT_PASSED__INTEGER_WAS_EXPECTED)
eigen_assert(rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
&& cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
internal::check_rows_cols_for_overflow(rows, cols);
m_storage.resize(rows*cols,rows,cols);
EIGEN_INITIALIZE_BY_ZERO_IF_THAT_OPTION_IS_ENABLED
}
template<typename T0, typename T1>
EIGEN_STRONG_INLINE void _init2(const Scalar& x, const Scalar& y, typename internal::enable_if<Base::SizeAtCompileTime==2,T0>::type* = 0)
{
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 2)
m_storage.data()[0] = x;
m_storage.data()[1] = y;
}
template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers>
friend struct internal::matrix_swap_impl;
/** \internal generic implementation of swap for dense storage since for dynamic-sized matrices of same type it is enough to swap the
* data pointers.
*/
template<typename OtherDerived>
void _swap(DenseBase<OtherDerived> const & other)
{
enum { SwapPointers = internal::is_same<Derived, OtherDerived>::value && Base::SizeAtCompileTime==Dynamic };
internal::matrix_swap_impl<Derived, OtherDerived, bool(SwapPointers)>::run(this->derived(), other.const_cast_derived());
}
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
static EIGEN_STRONG_INLINE void _check_template_params()
{
EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, (Options&RowMajor)==RowMajor)
&& EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, (Options&RowMajor)==0)
&& ((RowsAtCompileTime == Dynamic) || (RowsAtCompileTime >= 0))
&& ((ColsAtCompileTime == Dynamic) || (ColsAtCompileTime >= 0))
&& ((MaxRowsAtCompileTime == Dynamic) || (MaxRowsAtCompileTime >= 0))
&& ((MaxColsAtCompileTime == Dynamic) || (MaxColsAtCompileTime >= 0))
&& (MaxRowsAtCompileTime == RowsAtCompileTime || RowsAtCompileTime==Dynamic)
&& (MaxColsAtCompileTime == ColsAtCompileTime || ColsAtCompileTime==Dynamic)
&& (Options & (DontAlign|RowMajor)) == Options),
INVALID_MATRIX_TEMPLATE_PARAMETERS)
}
#endif
private:
enum { ThisConstantIsPrivateInPlainObjectBase };
};
template <typename Derived, typename OtherDerived, bool IsVector>
struct internal::conservative_resize_like_impl
{
typedef typename Derived::Index Index;
static void run(DenseBase<Derived>& _this, Index rows, Index cols)
{
if (_this.rows() == rows && _this.cols() == cols) return;
EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(Derived)
if ( ( Derived::IsRowMajor && _this.cols() == cols) || // row-major and we change only the number of rows
(!Derived::IsRowMajor && _this.rows() == rows) ) // column-major and we change only the number of columns
{
internal::check_rows_cols_for_overflow(rows, cols);
_this.derived().m_storage.conservativeResize(rows*cols,rows,cols);
}
else
{
// The storage order does not allow us to use reallocation.
typename Derived::PlainObject tmp(rows,cols);
const Index common_rows = (std::min)(rows, _this.rows());
const Index common_cols = (std::min)(cols, _this.cols());
tmp.block(0,0,common_rows,common_cols) = _this.block(0,0,common_rows,common_cols);
_this.derived().swap(tmp);
}
}
static void run(DenseBase<Derived>& _this, const DenseBase<OtherDerived>& other)
{
if (_this.rows() == other.rows() && _this.cols() == other.cols()) return;
// Note: Here is space for improvement. Basically, for conservativeResize(Index,Index),
// neither RowsAtCompileTime or ColsAtCompileTime must be Dynamic. If only one of the
// dimensions is dynamic, one could use either conservativeResize(Index rows, NoChange_t) or
// conservativeResize(NoChange_t, Index cols). For these methods new static asserts like
// EIGEN_STATIC_ASSERT_DYNAMIC_ROWS and EIGEN_STATIC_ASSERT_DYNAMIC_COLS would be good.
EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(Derived)
EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(OtherDerived)
if ( ( Derived::IsRowMajor && _this.cols() == other.cols()) || // row-major and we change only the number of rows
(!Derived::IsRowMajor && _this.rows() == other.rows()) ) // column-major and we change only the number of columns
{
const Index new_rows = other.rows() - _this.rows();
const Index new_cols = other.cols() - _this.cols();
_this.derived().m_storage.conservativeResize(other.size(),other.rows(),other.cols());
if (new_rows>0)
_this.bottomRightCorner(new_rows, other.cols()) = other.bottomRows(new_rows);
else if (new_cols>0)
_this.bottomRightCorner(other.rows(), new_cols) = other.rightCols(new_cols);
}
else
{
// The storage order does not allow us to use reallocation.
typename Derived::PlainObject tmp(other);
const Index common_rows = (std::min)(tmp.rows(), _this.rows());
const Index common_cols = (std::min)(tmp.cols(), _this.cols());
tmp.block(0,0,common_rows,common_cols) = _this.block(0,0,common_rows,common_cols);
_this.derived().swap(tmp);
}
}
};
namespace internal {
template <typename Derived, typename OtherDerived>
struct conservative_resize_like_impl<Derived,OtherDerived,true>
{
typedef typename Derived::Index Index;
static void run(DenseBase<Derived>& _this, Index size)
{
const Index new_rows = Derived::RowsAtCompileTime==1 ? 1 : size;
const Index new_cols = Derived::RowsAtCompileTime==1 ? size : 1;
_this.derived().m_storage.conservativeResize(size,new_rows,new_cols);
}
static void run(DenseBase<Derived>& _this, const DenseBase<OtherDerived>& other)
{
if (_this.rows() == other.rows() && _this.cols() == other.cols()) return;
const Index num_new_elements = other.size() - _this.size();
const Index new_rows = Derived::RowsAtCompileTime==1 ? 1 : other.rows();
const Index new_cols = Derived::RowsAtCompileTime==1 ? other.cols() : 1;
_this.derived().m_storage.conservativeResize(other.size(),new_rows,new_cols);
if (num_new_elements > 0)
_this.tail(num_new_elements) = other.tail(num_new_elements);
}
};
template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers>
struct matrix_swap_impl
{
static inline void run(MatrixTypeA& a, MatrixTypeB& b)
{
a.base().swap(b);
}
};
template<typename MatrixTypeA, typename MatrixTypeB>
struct matrix_swap_impl<MatrixTypeA, MatrixTypeB, true>
{
static inline void run(MatrixTypeA& a, MatrixTypeB& b)
{
static_cast<typename MatrixTypeA::Base&>(a).m_storage.swap(static_cast<typename MatrixTypeB::Base&>(b).m_storage);
}
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_DENSESTORAGEBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla Public
// License, v. 2.0. If a copy of the MPL was not distributed with this
// file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PRODUCT_H
#define EIGEN_PRODUCT_H
template<typename Lhs, typename Rhs> class Product;
template<typename Lhs, typename Rhs, typename StorageKind> class ProductImpl;
/** \class Product
* \ingroup Core_Module
*
* \brief Expression of the product of two arbitrary matrices or vectors
*
* \param Lhs the type of the left-hand side expression
* \param Rhs the type of the right-hand side expression
*
* This class represents an expression of the product of two arbitrary matrices.
*
*/
namespace internal {
template<typename Lhs, typename Rhs>
struct traits<Product<Lhs, Rhs> >
{
typedef MatrixXpr XprKind;
typedef typename remove_all<Lhs>::type LhsCleaned;
typedef typename remove_all<Rhs>::type RhsCleaned;
typedef typename scalar_product_traits<typename traits<LhsCleaned>::Scalar, typename traits<RhsCleaned>::Scalar>::ReturnType Scalar;
typedef typename promote_storage_type<typename traits<LhsCleaned>::StorageKind,
typename traits<RhsCleaned>::StorageKind>::ret StorageKind;
typedef typename promote_index_type<typename traits<LhsCleaned>::Index,
typename traits<RhsCleaned>::Index>::type Index;
enum {
RowsAtCompileTime = LhsCleaned::RowsAtCompileTime,
ColsAtCompileTime = RhsCleaned::ColsAtCompileTime,
MaxRowsAtCompileTime = LhsCleaned::MaxRowsAtCompileTime,
MaxColsAtCompileTime = RhsCleaned::MaxColsAtCompileTime,
Flags = (MaxRowsAtCompileTime==1 ? RowMajorBit : 0), // TODO should be no storage order
CoeffReadCost = 0 // TODO CoeffReadCost should not be part of the expression traits
};
};
} // end namespace internal
template<typename Lhs, typename Rhs>
class Product : public ProductImpl<Lhs,Rhs,typename internal::promote_storage_type<typename internal::traits<Lhs>::StorageKind,
typename internal::traits<Rhs>::StorageKind>::ret>
{
public:
typedef typename ProductImpl<
Lhs, Rhs,
typename internal::promote_storage_type<typename Lhs::StorageKind,
typename Rhs::StorageKind>::ret>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
typedef typename Lhs::Nested LhsNested;
typedef typename Rhs::Nested RhsNested;
typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;
typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;
Product(const Lhs& lhs, const Rhs& rhs) : m_lhs(lhs), m_rhs(rhs)
{
eigen_assert(lhs.cols() == rhs.rows()
&& "invalid matrix product"
&& "if you wanted a coeff-wise or a dot product use the respective explicit functions");
}
inline Index rows() const { return m_lhs.rows(); }
inline Index cols() const { return m_rhs.cols(); }
const LhsNestedCleaned& lhs() const { return m_lhs; }
const RhsNestedCleaned& rhs() const { return m_rhs; }
protected:
const LhsNested m_lhs;
const RhsNested m_rhs;
};
template<typename Lhs, typename Rhs>
class ProductImpl<Lhs,Rhs,Dense> : public internal::dense_xpr_base<Product<Lhs,Rhs> >::type
{
typedef Product<Lhs, Rhs> Derived;
public:
typedef typename internal::dense_xpr_base<Product<Lhs, Rhs> >::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
};
#endif // EIGEN_PRODUCT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PRODUCTBASE_H
#define EIGEN_PRODUCTBASE_H
namespace Eigen {
/** \class ProductBase
* \ingroup Core_Module
*
*/
namespace internal {
template<typename Derived, typename _Lhs, typename _Rhs>
struct traits<ProductBase<Derived,_Lhs,_Rhs> >
{
typedef MatrixXpr XprKind;
typedef typename remove_all<_Lhs>::type Lhs;
typedef typename remove_all<_Rhs>::type Rhs;
typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
typedef typename promote_storage_type<typename traits<Lhs>::StorageKind,
typename traits<Rhs>::StorageKind>::ret StorageKind;
typedef typename promote_index_type<typename traits<Lhs>::Index,
typename traits<Rhs>::Index>::type Index;
enum {
RowsAtCompileTime = traits<Lhs>::RowsAtCompileTime,
ColsAtCompileTime = traits<Rhs>::ColsAtCompileTime,
MaxRowsAtCompileTime = traits<Lhs>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = traits<Rhs>::MaxColsAtCompileTime,
Flags = (MaxRowsAtCompileTime==1 ? RowMajorBit : 0)
| EvalBeforeNestingBit | EvalBeforeAssigningBit | NestByRefBit,
// Note that EvalBeforeNestingBit and NestByRefBit
// are not used in practice because nested is overloaded for products
CoeffReadCost = 0 // FIXME why is it needed ?
};
};
}
#define EIGEN_PRODUCT_PUBLIC_INTERFACE(Derived) \
typedef ProductBase<Derived, Lhs, Rhs > Base; \
EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
typedef typename Base::LhsNested LhsNested; \
typedef typename Base::_LhsNested _LhsNested; \
typedef typename Base::LhsBlasTraits LhsBlasTraits; \
typedef typename Base::ActualLhsType ActualLhsType; \
typedef typename Base::_ActualLhsType _ActualLhsType; \
typedef typename Base::RhsNested RhsNested; \
typedef typename Base::_RhsNested _RhsNested; \
typedef typename Base::RhsBlasTraits RhsBlasTraits; \
typedef typename Base::ActualRhsType ActualRhsType; \
typedef typename Base::_ActualRhsType _ActualRhsType; \
using Base::m_lhs; \
using Base::m_rhs;
template<typename Derived, typename Lhs, typename Rhs>
class ProductBase : public MatrixBase<Derived>
{
public:
typedef MatrixBase<Derived> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(ProductBase)
typedef typename Lhs::Nested LhsNested;
typedef typename internal::remove_all<LhsNested>::type _LhsNested;
typedef internal::blas_traits<_LhsNested> LhsBlasTraits;
typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
typedef typename internal::remove_all<ActualLhsType>::type _ActualLhsType;
typedef typename internal::traits<Lhs>::Scalar LhsScalar;
typedef typename Rhs::Nested RhsNested;
typedef typename internal::remove_all<RhsNested>::type _RhsNested;
typedef internal::blas_traits<_RhsNested> RhsBlasTraits;
typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
typedef typename internal::remove_all<ActualRhsType>::type _ActualRhsType;
typedef typename internal::traits<Rhs>::Scalar RhsScalar;
// Diagonal of a product: no need to evaluate the arguments because they are going to be evaluated only once
typedef CoeffBasedProduct<LhsNested, RhsNested, 0> FullyLazyCoeffBaseProductType;
public:
typedef typename Base::PlainObject PlainObject;
ProductBase(const Lhs& lhs, const Rhs& rhs)
: m_lhs(lhs), m_rhs(rhs)
{
eigen_assert(lhs.cols() == rhs.rows()
&& "invalid matrix product"
&& "if you wanted a coeff-wise or a dot product use the respective explicit functions");
}
inline Index rows() const { return m_lhs.rows(); }
inline Index cols() const { return m_rhs.cols(); }
template<typename Dest>
inline void evalTo(Dest& dst) const { dst.setZero(); scaleAndAddTo(dst,Scalar(1)); }
template<typename Dest>
inline void addTo(Dest& dst) const { scaleAndAddTo(dst,Scalar(1)); }
template<typename Dest>
inline void subTo(Dest& dst) const { scaleAndAddTo(dst,Scalar(-1)); }
template<typename Dest>
inline void scaleAndAddTo(Dest& dst,Scalar alpha) const { derived().scaleAndAddTo(dst,alpha); }
const _LhsNested& lhs() const { return m_lhs; }
const _RhsNested& rhs() const { return m_rhs; }
// Implicit conversion to the nested type (trigger the evaluation of the product)
operator const PlainObject& () const
{
m_result.resize(m_lhs.rows(), m_rhs.cols());
derived().evalTo(m_result);
return m_result;
}
const Diagonal<const FullyLazyCoeffBaseProductType,0> diagonal() const
{ return FullyLazyCoeffBaseProductType(m_lhs, m_rhs); }
template<int Index>
const Diagonal<FullyLazyCoeffBaseProductType,Index> diagonal() const
{ return FullyLazyCoeffBaseProductType(m_lhs, m_rhs); }
const Diagonal<FullyLazyCoeffBaseProductType,Dynamic> diagonal(Index index) const
{ return FullyLazyCoeffBaseProductType(m_lhs, m_rhs).diagonal(index); }
// restrict coeff accessors to 1x1 expressions. No need to care about mutators here since this isnt a Lvalue expression
typename Base::CoeffReturnType coeff(Index row, Index col) const
{
#ifdef EIGEN2_SUPPORT
return lhs().row(row).cwiseProduct(rhs().col(col).transpose()).sum();
#else
EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
eigen_assert(this->rows() == 1 && this->cols() == 1);
Matrix<Scalar,1,1> result = *this;
return result.coeff(row,col);
#endif
}
typename Base::CoeffReturnType coeff(Index i) const
{
EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
eigen_assert(this->rows() == 1 && this->cols() == 1);
Matrix<Scalar,1,1> result = *this;
return result.coeff(i);
}
const Scalar& coeffRef(Index row, Index col) const
{
EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
eigen_assert(this->rows() == 1 && this->cols() == 1);
return derived().coeffRef(row,col);
}
const Scalar& coeffRef(Index i) const
{
EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
eigen_assert(this->rows() == 1 && this->cols() == 1);
return derived().coeffRef(i);
}
protected:
LhsNested m_lhs;
RhsNested m_rhs;
mutable PlainObject m_result;
};
// here we need to overload the nested rule for products
// such that the nested type is a const reference to a plain matrix
namespace internal {
template<typename Lhs, typename Rhs, int Mode, int N, typename PlainObject>
struct nested<GeneralProduct<Lhs,Rhs,Mode>, N, PlainObject>
{
typedef PlainObject const& type;
};
}
template<typename NestedProduct>
class ScaledProduct;
// Note that these two operator* functions are not defined as member
// functions of ProductBase, because, otherwise we would have to
// define all overloads defined in MatrixBase. Furthermore, Using
// "using Base::operator*" would not work with MSVC.
//
// Also note that here we accept any compatible scalar types
template<typename Derived,typename Lhs,typename Rhs>
const ScaledProduct<Derived>
operator*(const ProductBase<Derived,Lhs,Rhs>& prod, typename Derived::Scalar x)
{ return ScaledProduct<Derived>(prod.derived(), x); }
template<typename Derived,typename Lhs,typename Rhs>
typename internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value,
const ScaledProduct<Derived> >::type
operator*(const ProductBase<Derived,Lhs,Rhs>& prod, typename Derived::RealScalar x)
{ return ScaledProduct<Derived>(prod.derived(), x); }
template<typename Derived,typename Lhs,typename Rhs>
const ScaledProduct<Derived>
operator*(typename Derived::Scalar x,const ProductBase<Derived,Lhs,Rhs>& prod)
{ return ScaledProduct<Derived>(prod.derived(), x); }
template<typename Derived,typename Lhs,typename Rhs>
typename internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value,
const ScaledProduct<Derived> >::type
operator*(typename Derived::RealScalar x,const ProductBase<Derived,Lhs,Rhs>& prod)
{ return ScaledProduct<Derived>(prod.derived(), x); }
namespace internal {
template<typename NestedProduct>
struct traits<ScaledProduct<NestedProduct> >
: traits<ProductBase<ScaledProduct<NestedProduct>,
typename NestedProduct::_LhsNested,
typename NestedProduct::_RhsNested> >
{
typedef typename traits<NestedProduct>::StorageKind StorageKind;
};
}
template<typename NestedProduct>
class ScaledProduct
: public ProductBase<ScaledProduct<NestedProduct>,
typename NestedProduct::_LhsNested,
typename NestedProduct::_RhsNested>
{
public:
typedef ProductBase<ScaledProduct<NestedProduct>,
typename NestedProduct::_LhsNested,
typename NestedProduct::_RhsNested> Base;
typedef typename Base::Scalar Scalar;
typedef typename Base::PlainObject PlainObject;
// EIGEN_PRODUCT_PUBLIC_INTERFACE(ScaledProduct)
ScaledProduct(const NestedProduct& prod, Scalar x)
: Base(prod.lhs(),prod.rhs()), m_prod(prod), m_alpha(x) {}
template<typename Dest>
inline void evalTo(Dest& dst) const { dst.setZero(); scaleAndAddTo(dst, Scalar(1)); }
template<typename Dest>
inline void addTo(Dest& dst) const { scaleAndAddTo(dst, Scalar(1)); }
template<typename Dest>
inline void subTo(Dest& dst) const { scaleAndAddTo(dst, Scalar(-1)); }
template<typename Dest>
inline void scaleAndAddTo(Dest& dst,Scalar alpha) const { m_prod.derived().scaleAndAddTo(dst,alpha * m_alpha); }
const Scalar& alpha() const { return m_alpha; }
protected:
const NestedProduct& m_prod;
Scalar m_alpha;
};
/** \internal
* Overloaded to perform an efficient C = (A*B).lazy() */
template<typename Derived>
template<typename ProductDerived, typename Lhs, typename Rhs>
Derived& MatrixBase<Derived>::lazyAssign(const ProductBase<ProductDerived, Lhs,Rhs>& other)
{
other.derived().evalTo(derived());
return derived();
}
} // end namespace Eigen
#endif // EIGEN_PRODUCTBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_RANDOM_H
#define EIGEN_RANDOM_H
namespace Eigen {
namespace internal {
template<typename Scalar> struct scalar_random_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_random_op)
template<typename Index>
inline const Scalar operator() (Index, Index = 0) const { return random<Scalar>(); }
};
template<typename Scalar>
struct functor_traits<scalar_random_op<Scalar> >
{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false, IsRepeatable = false }; };
} // end namespace internal
/** \returns a random matrix expression
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this MatrixBase type.
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so Random() should be used
* instead.
*
* Example: \include MatrixBase_random_int_int.cpp
* Output: \verbinclude MatrixBase_random_int_int.out
*
* This expression has the "evaluate before nesting" flag so that it will be evaluated into
* a temporary matrix whenever it is nested in a larger expression. This prevents unexpected
* behavior with expressions involving random matrices.
*
* \sa MatrixBase::setRandom(), MatrixBase::Random(Index), MatrixBase::Random()
*/
template<typename Derived>
inline const CwiseNullaryOp<internal::scalar_random_op<typename internal::traits<Derived>::Scalar>, Derived>
DenseBase<Derived>::Random(Index rows, Index cols)
{
return NullaryExpr(rows, cols, internal::scalar_random_op<Scalar>());
}
/** \returns a random vector expression
*
* The parameter \a size is the size of the returned vector.
* Must be compatible with this MatrixBase type.
*
* \only_for_vectors
*
* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
* it is redundant to pass \a size as argument, so Random() should be used
* instead.
*
* Example: \include MatrixBase_random_int.cpp
* Output: \verbinclude MatrixBase_random_int.out
*
* This expression has the "evaluate before nesting" flag so that it will be evaluated into
* a temporary vector whenever it is nested in a larger expression. This prevents unexpected
* behavior with expressions involving random matrices.
*
* \sa MatrixBase::setRandom(), MatrixBase::Random(Index,Index), MatrixBase::Random()
*/
template<typename Derived>
inline const CwiseNullaryOp<internal::scalar_random_op<typename internal::traits<Derived>::Scalar>, Derived>
DenseBase<Derived>::Random(Index size)
{
return NullaryExpr(size, internal::scalar_random_op<Scalar>());
}
/** \returns a fixed-size random matrix or vector expression
*
* This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
* need to use the variants taking size arguments.
*
* Example: \include MatrixBase_random.cpp
* Output: \verbinclude MatrixBase_random.out
*
* This expression has the "evaluate before nesting" flag so that it will be evaluated into
* a temporary matrix whenever it is nested in a larger expression. This prevents unexpected
* behavior with expressions involving random matrices.
*
* \sa MatrixBase::setRandom(), MatrixBase::Random(Index,Index), MatrixBase::Random(Index)
*/
template<typename Derived>
inline const CwiseNullaryOp<internal::scalar_random_op<typename internal::traits<Derived>::Scalar>, Derived>
DenseBase<Derived>::Random()
{
return NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_random_op<Scalar>());
}
/** Sets all coefficients in this expression to random values.
*
* Example: \include MatrixBase_setRandom.cpp
* Output: \verbinclude MatrixBase_setRandom.out
*
* \sa class CwiseNullaryOp, setRandom(Index), setRandom(Index,Index)
*/
template<typename Derived>
inline Derived& DenseBase<Derived>::setRandom()
{
return *this = Random(rows(), cols());
}
/** Resizes to the given \a size, and sets all coefficients in this expression to random values.
*
* \only_for_vectors
*
* Example: \include Matrix_setRandom_int.cpp
* Output: \verbinclude Matrix_setRandom_int.out
*
* \sa MatrixBase::setRandom(), setRandom(Index,Index), class CwiseNullaryOp, MatrixBase::Random()
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived&
PlainObjectBase<Derived>::setRandom(Index size)
{
resize(size);
return setRandom();
}
/** Resizes to the given size, and sets all coefficients in this expression to random values.
*
* \param rows the new number of rows
* \param cols the new number of columns
*
* Example: \include Matrix_setRandom_int_int.cpp
* Output: \verbinclude Matrix_setRandom_int_int.out
*
* \sa MatrixBase::setRandom(), setRandom(Index), class CwiseNullaryOp, MatrixBase::Random()
*/
template<typename Derived>
EIGEN_STRONG_INLINE Derived&
PlainObjectBase<Derived>::setRandom(Index rows, Index cols)
{
resize(rows, cols);
return setRandom();
}
} // end namespace Eigen
#endif // EIGEN_RANDOM_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_REDUX_H
#define EIGEN_REDUX_H
namespace Eigen {
namespace internal {
// TODO
// * implement other kind of vectorization
// * factorize code
/***************************************************************************
* Part 1 : the logic deciding a strategy for vectorization and unrolling
***************************************************************************/
template<typename Func, typename Derived>
struct redux_traits
{
public:
enum {
PacketSize = packet_traits<typename Derived::Scalar>::size,
InnerMaxSize = int(Derived::IsRowMajor)
? Derived::MaxColsAtCompileTime
: Derived::MaxRowsAtCompileTime
};
enum {
MightVectorize = (int(Derived::Flags)&ActualPacketAccessBit)
&& (functor_traits<Func>::PacketAccess),
MayLinearVectorize = MightVectorize && (int(Derived::Flags)&LinearAccessBit),
MaySliceVectorize = MightVectorize && int(InnerMaxSize)>=3*PacketSize
};
public:
enum {
Traversal = int(MayLinearVectorize) ? int(LinearVectorizedTraversal)
: int(MaySliceVectorize) ? int(SliceVectorizedTraversal)
: int(DefaultTraversal)
};
public:
enum {
Cost = ( Derived::SizeAtCompileTime == Dynamic
|| Derived::CoeffReadCost == Dynamic
|| (Derived::SizeAtCompileTime!=1 && functor_traits<Func>::Cost == Dynamic)
) ? Dynamic
: Derived::SizeAtCompileTime * Derived::CoeffReadCost
+ (Derived::SizeAtCompileTime-1) * functor_traits<Func>::Cost,
UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Traversal) == int(DefaultTraversal) ? 1 : int(PacketSize))
};
public:
enum {
Unrolling = Cost != Dynamic && Cost <= UnrollingLimit
? CompleteUnrolling
: NoUnrolling
};
};
/***************************************************************************
* Part 2 : unrollers
***************************************************************************/
/*** no vectorization ***/
template<typename Func, typename Derived, int Start, int Length>
struct redux_novec_unroller
{
enum {
HalfLength = Length/2
};
typedef typename Derived::Scalar Scalar;
static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func& func)
{
return func(redux_novec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
redux_novec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func));
}
};
template<typename Func, typename Derived, int Start>
struct redux_novec_unroller<Func, Derived, Start, 1>
{
enum {
outer = Start / Derived::InnerSizeAtCompileTime,
inner = Start % Derived::InnerSizeAtCompileTime
};
typedef typename Derived::Scalar Scalar;
static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func&)
{
return mat.coeffByOuterInner(outer, inner);
}
};
// This is actually dead code and will never be called. It is required
// to prevent false warnings regarding failed inlining though
// for 0 length run() will never be called at all.
template<typename Func, typename Derived, int Start>
struct redux_novec_unroller<Func, Derived, Start, 0>
{
typedef typename Derived::Scalar Scalar;
static EIGEN_STRONG_INLINE Scalar run(const Derived&, const Func&) { return Scalar(); }
};
/*** vectorization ***/
template<typename Func, typename Derived, int Start, int Length>
struct redux_vec_unroller
{
enum {
PacketSize = packet_traits<typename Derived::Scalar>::size,
HalfLength = Length/2
};
typedef typename Derived::Scalar Scalar;
typedef typename packet_traits<Scalar>::type PacketScalar;
static EIGEN_STRONG_INLINE PacketScalar run(const Derived &mat, const Func& func)
{
return func.packetOp(
redux_vec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
redux_vec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func) );
}
};
template<typename Func, typename Derived, int Start>
struct redux_vec_unroller<Func, Derived, Start, 1>
{
enum {
index = Start * packet_traits<typename Derived::Scalar>::size,
outer = index / int(Derived::InnerSizeAtCompileTime),
inner = index % int(Derived::InnerSizeAtCompileTime),
alignment = (Derived::Flags & AlignedBit) ? Aligned : Unaligned
};
typedef typename Derived::Scalar Scalar;
typedef typename packet_traits<Scalar>::type PacketScalar;
static EIGEN_STRONG_INLINE PacketScalar run(const Derived &mat, const Func&)
{
return mat.template packetByOuterInner<alignment>(outer, inner);
}
};
/***************************************************************************
* Part 3 : implementation of all cases
***************************************************************************/
template<typename Func, typename Derived,
int Traversal = redux_traits<Func, Derived>::Traversal,
int Unrolling = redux_traits<Func, Derived>::Unrolling
>
struct redux_impl;
template<typename Func, typename Derived>
struct redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>
{
typedef typename Derived::Scalar Scalar;
typedef typename Derived::Index Index;
static EIGEN_STRONG_INLINE Scalar run(const Derived& mat, const Func& func)
{
eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
Scalar res;
res = mat.coeffByOuterInner(0, 0);
for(Index i = 1; i < mat.innerSize(); ++i)
res = func(res, mat.coeffByOuterInner(0, i));
for(Index i = 1; i < mat.outerSize(); ++i)
for(Index j = 0; j < mat.innerSize(); ++j)
res = func(res, mat.coeffByOuterInner(i, j));
return res;
}
};
template<typename Func, typename Derived>
struct redux_impl<Func,Derived, DefaultTraversal, CompleteUnrolling>
: public redux_novec_unroller<Func,Derived, 0, Derived::SizeAtCompileTime>
{};
template<typename Func, typename Derived>
struct redux_impl<Func, Derived, LinearVectorizedTraversal, NoUnrolling>
{
typedef typename Derived::Scalar Scalar;
typedef typename packet_traits<Scalar>::type PacketScalar;
typedef typename Derived::Index Index;
static Scalar run(const Derived& mat, const Func& func)
{
const Index size = mat.size();
eigen_assert(size && "you are using an empty matrix");
const Index packetSize = packet_traits<Scalar>::size;
const Index alignedStart = internal::first_aligned(mat);
enum {
alignment = bool(Derived::Flags & DirectAccessBit) || bool(Derived::Flags & AlignedBit)
? Aligned : Unaligned
};
const Index alignedSize2 = ((size-alignedStart)/(2*packetSize))*(2*packetSize);
const Index alignedSize = ((size-alignedStart)/(packetSize))*(packetSize);
const Index alignedEnd2 = alignedStart + alignedSize2;
const Index alignedEnd = alignedStart + alignedSize;
Scalar res;
if(alignedSize)
{
PacketScalar packet_res0 = mat.template packet<alignment>(alignedStart);
if(alignedSize>packetSize) // we have at least two packets to partly unroll the loop
{
PacketScalar packet_res1 = mat.template packet<alignment>(alignedStart+packetSize);
for(Index index = alignedStart + 2*packetSize; index < alignedEnd2; index += 2*packetSize)
{
packet_res0 = func.packetOp(packet_res0, mat.template packet<alignment>(index));
packet_res1 = func.packetOp(packet_res1, mat.template packet<alignment>(index+packetSize));
}
packet_res0 = func.packetOp(packet_res0,packet_res1);
if(alignedEnd>alignedEnd2)
packet_res0 = func.packetOp(packet_res0, mat.template packet<alignment>(alignedEnd2));
}
res = func.predux(packet_res0);
for(Index index = 0; index < alignedStart; ++index)
res = func(res,mat.coeff(index));
for(Index index = alignedEnd; index < size; ++index)
res = func(res,mat.coeff(index));
}
else // too small to vectorize anything.
// since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
{
res = mat.coeff(0);
for(Index index = 1; index < size; ++index)
res = func(res,mat.coeff(index));
}
return res;
}
};
template<typename Func, typename Derived>
struct redux_impl<Func, Derived, SliceVectorizedTraversal, NoUnrolling>
{
typedef typename Derived::Scalar Scalar;
typedef typename packet_traits<Scalar>::type PacketScalar;
typedef typename Derived::Index Index;
static Scalar run(const Derived& mat, const Func& func)
{
eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
const Index innerSize = mat.innerSize();
const Index outerSize = mat.outerSize();
enum {
packetSize = packet_traits<Scalar>::size
};
const Index packetedInnerSize = ((innerSize)/packetSize)*packetSize;
Scalar res;
if(packetedInnerSize)
{
PacketScalar packet_res = mat.template packet<Unaligned>(0,0);
for(Index j=0; j<outerSize; ++j)
for(Index i=(j==0?packetSize:0); i<packetedInnerSize; i+=Index(packetSize))
packet_res = func.packetOp(packet_res, mat.template packetByOuterInner<Unaligned>(j,i));
res = func.predux(packet_res);
for(Index j=0; j<outerSize; ++j)
for(Index i=packetedInnerSize; i<innerSize; ++i)
res = func(res, mat.coeffByOuterInner(j,i));
}
else // too small to vectorize anything.
// since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
{
res = redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>::run(mat, func);
}
return res;
}
};
template<typename Func, typename Derived>
struct redux_impl<Func, Derived, LinearVectorizedTraversal, CompleteUnrolling>
{
typedef typename Derived::Scalar Scalar;
typedef typename packet_traits<Scalar>::type PacketScalar;
enum {
PacketSize = packet_traits<Scalar>::size,
Size = Derived::SizeAtCompileTime,
VectorizedSize = (Size / PacketSize) * PacketSize
};
static EIGEN_STRONG_INLINE Scalar run(const Derived& mat, const Func& func)
{
eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
Scalar res = func.predux(redux_vec_unroller<Func, Derived, 0, Size / PacketSize>::run(mat,func));
if (VectorizedSize != Size)
res = func(res,redux_novec_unroller<Func, Derived, VectorizedSize, Size-VectorizedSize>::run(mat,func));
return res;
}
};
} // end namespace internal
/***************************************************************************
* Part 4 : public API
***************************************************************************/
/** \returns the result of a full redux operation on the whole matrix or vector using \a func
*
* The template parameter \a BinaryOp is the type of the functor \a func which must be
* an associative operator. Both current STL and TR1 functor styles are handled.
*
* \sa DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()
*/
template<typename Derived>
template<typename Func>
EIGEN_STRONG_INLINE typename internal::result_of<Func(typename internal::traits<Derived>::Scalar)>::type
DenseBase<Derived>::redux(const Func& func) const
{
typedef typename internal::remove_all<typename Derived::Nested>::type ThisNested;
return internal::redux_impl<Func, ThisNested>
::run(derived(), func);
}
/** \returns the minimum of all coefficients of *this
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
DenseBase<Derived>::minCoeff() const
{
return this->redux(Eigen::internal::scalar_min_op<Scalar>());
}
/** \returns the maximum of all coefficients of *this
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
DenseBase<Derived>::maxCoeff() const
{
return this->redux(Eigen::internal::scalar_max_op<Scalar>());
}
/** \returns the sum of all coefficients of *this
*
* \sa trace(), prod(), mean()
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
DenseBase<Derived>::sum() const
{
if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
return Scalar(0);
return this->redux(Eigen::internal::scalar_sum_op<Scalar>());
}
/** \returns the mean of all coefficients of *this
*
* \sa trace(), prod(), sum()
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
DenseBase<Derived>::mean() const
{
return Scalar(this->redux(Eigen::internal::scalar_sum_op<Scalar>())) / Scalar(this->size());
}
/** \returns the product of all coefficients of *this
*
* Example: \include MatrixBase_prod.cpp
* Output: \verbinclude MatrixBase_prod.out
*
* \sa sum(), mean(), trace()
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
DenseBase<Derived>::prod() const
{
if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
return Scalar(1);
return this->redux(Eigen::internal::scalar_product_op<Scalar>());
}
/** \returns the trace of \c *this, i.e. the sum of the coefficients on the main diagonal.
*
* \c *this can be any matrix, not necessarily square.
*
* \sa diagonal(), sum()
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
MatrixBase<Derived>::trace() const
{
return derived().diagonal().sum();
}
} // end namespace Eigen
#endif // EIGEN_REDUX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_REPLICATE_H
#define EIGEN_REPLICATE_H
namespace Eigen {
/**
* \class Replicate
* \ingroup Core_Module
*
* \brief Expression of the multiple replication of a matrix or vector
*
* \param MatrixType the type of the object we are replicating
*
* This class represents an expression of the multiple replication of a matrix or vector.
* It is the return type of DenseBase::replicate() and most of the time
* this is the only way it is used.
*
* \sa DenseBase::replicate()
*/
namespace internal {
template<typename MatrixType,int RowFactor,int ColFactor>
struct traits<Replicate<MatrixType,RowFactor,ColFactor> >
: traits<MatrixType>
{
typedef typename MatrixType::Scalar Scalar;
typedef typename traits<MatrixType>::StorageKind StorageKind;
typedef typename traits<MatrixType>::XprKind XprKind;
enum {
Factor = (RowFactor==Dynamic || ColFactor==Dynamic) ? Dynamic : RowFactor*ColFactor
};
typedef typename nested<MatrixType,Factor>::type MatrixTypeNested;
typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
enum {
RowsAtCompileTime = RowFactor==Dynamic || int(MatrixType::RowsAtCompileTime)==Dynamic
? Dynamic
: RowFactor * MatrixType::RowsAtCompileTime,
ColsAtCompileTime = ColFactor==Dynamic || int(MatrixType::ColsAtCompileTime)==Dynamic
? Dynamic
: ColFactor * MatrixType::ColsAtCompileTime,
//FIXME we don't propagate the max sizes !!!
MaxRowsAtCompileTime = RowsAtCompileTime,
MaxColsAtCompileTime = ColsAtCompileTime,
IsRowMajor = MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1 ? 1
: MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1 ? 0
: (MatrixType::Flags & RowMajorBit) ? 1 : 0,
Flags = (_MatrixTypeNested::Flags & HereditaryBits & ~RowMajorBit) | (IsRowMajor ? RowMajorBit : 0),
CoeffReadCost = _MatrixTypeNested::CoeffReadCost
};
};
}
template<typename MatrixType,int RowFactor,int ColFactor> class Replicate
: public internal::dense_xpr_base< Replicate<MatrixType,RowFactor,ColFactor> >::type
{
typedef typename internal::traits<Replicate>::MatrixTypeNested MatrixTypeNested;
typedef typename internal::traits<Replicate>::_MatrixTypeNested _MatrixTypeNested;
public:
typedef typename internal::dense_xpr_base<Replicate>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Replicate)
template<typename OriginalMatrixType>
inline explicit Replicate(const OriginalMatrixType& matrix)
: m_matrix(matrix), m_rowFactor(RowFactor), m_colFactor(ColFactor)
{
EIGEN_STATIC_ASSERT((internal::is_same<typename internal::remove_const<MatrixType>::type,OriginalMatrixType>::value),
THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)
eigen_assert(RowFactor!=Dynamic && ColFactor!=Dynamic);
}
template<typename OriginalMatrixType>
inline Replicate(const OriginalMatrixType& matrix, Index rowFactor, Index colFactor)
: m_matrix(matrix), m_rowFactor(rowFactor), m_colFactor(colFactor)
{
EIGEN_STATIC_ASSERT((internal::is_same<typename internal::remove_const<MatrixType>::type,OriginalMatrixType>::value),
THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)
}
inline Index rows() const { return m_matrix.rows() * m_rowFactor.value(); }
inline Index cols() const { return m_matrix.cols() * m_colFactor.value(); }
inline Scalar coeff(Index row, Index col) const
{
// try to avoid using modulo; this is a pure optimization strategy
const Index actual_row = internal::traits<MatrixType>::RowsAtCompileTime==1 ? 0
: RowFactor==1 ? row
: row%m_matrix.rows();
const Index actual_col = internal::traits<MatrixType>::ColsAtCompileTime==1 ? 0
: ColFactor==1 ? col
: col%m_matrix.cols();
return m_matrix.coeff(actual_row, actual_col);
}
template<int LoadMode>
inline PacketScalar packet(Index row, Index col) const
{
const Index actual_row = internal::traits<MatrixType>::RowsAtCompileTime==1 ? 0
: RowFactor==1 ? row
: row%m_matrix.rows();
const Index actual_col = internal::traits<MatrixType>::ColsAtCompileTime==1 ? 0
: ColFactor==1 ? col
: col%m_matrix.cols();
return m_matrix.template packet<LoadMode>(actual_row, actual_col);
}
const _MatrixTypeNested& nestedExpression() const
{
return m_matrix;
}
protected:
MatrixTypeNested m_matrix;
const internal::variable_if_dynamic<Index, RowFactor> m_rowFactor;
const internal::variable_if_dynamic<Index, ColFactor> m_colFactor;
};
/**
* \return an expression of the replication of \c *this
*
* Example: \include MatrixBase_replicate.cpp
* Output: \verbinclude MatrixBase_replicate.out
*
* \sa VectorwiseOp::replicate(), DenseBase::replicate(Index,Index), class Replicate
*/
template<typename Derived>
template<int RowFactor, int ColFactor>
inline const Replicate<Derived,RowFactor,ColFactor>
DenseBase<Derived>::replicate() const
{
return Replicate<Derived,RowFactor,ColFactor>(derived());
}
/**
* \return an expression of the replication of \c *this
*
* Example: \include MatrixBase_replicate_int_int.cpp
* Output: \verbinclude MatrixBase_replicate_int_int.out
*
* \sa VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate
*/
template<typename Derived>
inline const Replicate<Derived,Dynamic,Dynamic>
DenseBase<Derived>::replicate(Index rowFactor,Index colFactor) const
{
return Replicate<Derived,Dynamic,Dynamic>(derived(),rowFactor,colFactor);
}
/**
* \return an expression of the replication of each column (or row) of \c *this
*
* Example: \include DirectionWise_replicate_int.cpp
* Output: \verbinclude DirectionWise_replicate_int.out
*
* \sa VectorwiseOp::replicate(), DenseBase::replicate(), class Replicate
*/
template<typename ExpressionType, int Direction>
const typename VectorwiseOp<ExpressionType,Direction>::ReplicateReturnType
VectorwiseOp<ExpressionType,Direction>::replicate(Index factor) const
{
return typename VectorwiseOp<ExpressionType,Direction>::ReplicateReturnType
(_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1);
}
} // end namespace Eigen
#endif // EIGEN_REPLICATE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_RETURNBYVALUE_H
#define EIGEN_RETURNBYVALUE_H
namespace Eigen {
/** \class ReturnByValue
* \ingroup Core_Module
*
*/
namespace internal {
template<typename Derived>
struct traits<ReturnByValue<Derived> >
: public traits<typename traits<Derived>::ReturnType>
{
enum {
// We're disabling the DirectAccess because e.g. the constructor of
// the Block-with-DirectAccess expression requires to have a coeffRef method.
// Also, we don't want to have to implement the stride stuff.
Flags = (traits<typename traits<Derived>::ReturnType>::Flags
| EvalBeforeNestingBit) & ~DirectAccessBit
};
};
/* The ReturnByValue object doesn't even have a coeff() method.
* So the only way that nesting it in an expression can work, is by evaluating it into a plain matrix.
* So internal::nested always gives the plain return matrix type.
*
* FIXME: I don't understand why we need this specialization: isn't this taken care of by the EvalBeforeNestingBit ??
*/
template<typename Derived,int n,typename PlainObject>
struct nested<ReturnByValue<Derived>, n, PlainObject>
{
typedef typename traits<Derived>::ReturnType type;
};
} // end namespace internal
template<typename Derived> class ReturnByValue
: public internal::dense_xpr_base< ReturnByValue<Derived> >::type
{
public:
typedef typename internal::traits<Derived>::ReturnType ReturnType;
typedef typename internal::dense_xpr_base<ReturnByValue>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(ReturnByValue)
template<typename Dest>
inline void evalTo(Dest& dst) const
{ static_cast<const Derived*>(this)->evalTo(dst); }
inline Index rows() const { return static_cast<const Derived*>(this)->rows(); }
inline Index cols() const { return static_cast<const Derived*>(this)->cols(); }
#ifndef EIGEN_PARSED_BY_DOXYGEN
#define Unusable YOU_ARE_TRYING_TO_ACCESS_A_SINGLE_COEFFICIENT_IN_A_SPECIAL_EXPRESSION_WHERE_THAT_IS_NOT_ALLOWED_BECAUSE_THAT_WOULD_BE_INEFFICIENT
class Unusable{
Unusable(const Unusable&) {}
Unusable& operator=(const Unusable&) {return *this;}
};
const Unusable& coeff(Index) const { return *reinterpret_cast<const Unusable*>(this); }
const Unusable& coeff(Index,Index) const { return *reinterpret_cast<const Unusable*>(this); }
Unusable& coeffRef(Index) { return *reinterpret_cast<Unusable*>(this); }
Unusable& coeffRef(Index,Index) { return *reinterpret_cast<Unusable*>(this); }
#endif
};
template<typename Derived>
template<typename OtherDerived>
Derived& DenseBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
{
other.evalTo(derived());
return derived();
}
} // end namespace Eigen
#endif // EIGEN_RETURNBYVALUE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009 Ricard Marxer <email@ricardmarxer.com>
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_REVERSE_H
#define EIGEN_REVERSE_H
namespace Eigen {
/** \class Reverse
* \ingroup Core_Module
*
* \brief Expression of the reverse of a vector or matrix
*
* \param MatrixType the type of the object of which we are taking the reverse
*
* This class represents an expression of the reverse of a vector.
* It is the return type of MatrixBase::reverse() and VectorwiseOp::reverse()
* and most of the time this is the only way it is used.
*
* \sa MatrixBase::reverse(), VectorwiseOp::reverse()
*/
namespace internal {
template<typename MatrixType, int Direction>
struct traits<Reverse<MatrixType, Direction> >
: traits<MatrixType>
{
typedef typename MatrixType::Scalar Scalar;
typedef typename traits<MatrixType>::StorageKind StorageKind;
typedef typename traits<MatrixType>::XprKind XprKind;
typedef typename nested<MatrixType>::type MatrixTypeNested;
typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
// let's enable LinearAccess only with vectorization because of the product overhead
LinearAccess = ( (Direction==BothDirections) && (int(_MatrixTypeNested::Flags)&PacketAccessBit) )
? LinearAccessBit : 0,
Flags = int(_MatrixTypeNested::Flags) & (HereditaryBits | LvalueBit | PacketAccessBit | LinearAccess),
CoeffReadCost = _MatrixTypeNested::CoeffReadCost
};
};
template<typename PacketScalar, bool ReversePacket> struct reverse_packet_cond
{
static inline PacketScalar run(const PacketScalar& x) { return preverse(x); }
};
template<typename PacketScalar> struct reverse_packet_cond<PacketScalar,false>
{
static inline PacketScalar run(const PacketScalar& x) { return x; }
};
} // end namespace internal
template<typename MatrixType, int Direction> class Reverse
: public internal::dense_xpr_base< Reverse<MatrixType, Direction> >::type
{
public:
typedef typename internal::dense_xpr_base<Reverse>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Reverse)
using Base::IsRowMajor;
// next line is necessary because otherwise const version of operator()
// is hidden by non-const version defined in this file
using Base::operator();
protected:
enum {
PacketSize = internal::packet_traits<Scalar>::size,
IsColMajor = !IsRowMajor,
ReverseRow = (Direction == Vertical) || (Direction == BothDirections),
ReverseCol = (Direction == Horizontal) || (Direction == BothDirections),
OffsetRow = ReverseRow && IsColMajor ? PacketSize : 1,
OffsetCol = ReverseCol && IsRowMajor ? PacketSize : 1,
ReversePacket = (Direction == BothDirections)
|| ((Direction == Vertical) && IsColMajor)
|| ((Direction == Horizontal) && IsRowMajor)
};
typedef internal::reverse_packet_cond<PacketScalar,ReversePacket> reverse_packet;
public:
inline Reverse(const MatrixType& matrix) : m_matrix(matrix) { }
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Reverse)
inline Index rows() const { return m_matrix.rows(); }
inline Index cols() const { return m_matrix.cols(); }
inline Index innerStride() const
{
return -m_matrix.innerStride();
}
inline Scalar& operator()(Index row, Index col)
{
eigen_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
return coeffRef(row, col);
}
inline Scalar& coeffRef(Index row, Index col)
{
return m_matrix.const_cast_derived().coeffRef(ReverseRow ? m_matrix.rows() - row - 1 : row,
ReverseCol ? m_matrix.cols() - col - 1 : col);
}
inline CoeffReturnType coeff(Index row, Index col) const
{
return m_matrix.coeff(ReverseRow ? m_matrix.rows() - row - 1 : row,
ReverseCol ? m_matrix.cols() - col - 1 : col);
}
inline CoeffReturnType coeff(Index index) const
{
return m_matrix.coeff(m_matrix.size() - index - 1);
}
inline Scalar& coeffRef(Index index)
{
return m_matrix.const_cast_derived().coeffRef(m_matrix.size() - index - 1);
}
inline Scalar& operator()(Index index)
{
eigen_assert(index >= 0 && index < m_matrix.size());
return coeffRef(index);
}
template<int LoadMode>
inline const PacketScalar packet(Index row, Index col) const
{
return reverse_packet::run(m_matrix.template packet<LoadMode>(
ReverseRow ? m_matrix.rows() - row - OffsetRow : row,
ReverseCol ? m_matrix.cols() - col - OffsetCol : col));
}
template<int LoadMode>
inline void writePacket(Index row, Index col, const PacketScalar& x)
{
m_matrix.const_cast_derived().template writePacket<LoadMode>(
ReverseRow ? m_matrix.rows() - row - OffsetRow : row,
ReverseCol ? m_matrix.cols() - col - OffsetCol : col,
reverse_packet::run(x));
}
template<int LoadMode>
inline const PacketScalar packet(Index index) const
{
return internal::preverse(m_matrix.template packet<LoadMode>( m_matrix.size() - index - PacketSize ));
}
template<int LoadMode>
inline void writePacket(Index index, const PacketScalar& x)
{
m_matrix.const_cast_derived().template writePacket<LoadMode>(m_matrix.size() - index - PacketSize, internal::preverse(x));
}
const typename internal::remove_all<typename MatrixType::Nested>::type&
nestedExpression() const
{
return m_matrix;
}
protected:
typename MatrixType::Nested m_matrix;
};
/** \returns an expression of the reverse of *this.
*
* Example: \include MatrixBase_reverse.cpp
* Output: \verbinclude MatrixBase_reverse.out
*
*/
template<typename Derived>
inline typename DenseBase<Derived>::ReverseReturnType
DenseBase<Derived>::reverse()
{
return derived();
}
/** This is the const version of reverse(). */
template<typename Derived>
inline const typename DenseBase<Derived>::ConstReverseReturnType
DenseBase<Derived>::reverse() const
{
return derived();
}
/** This is the "in place" version of reverse: it reverses \c *this.
*
* In most cases it is probably better to simply use the reversed expression
* of a matrix. However, when reversing the matrix data itself is really needed,
* then this "in-place" version is probably the right choice because it provides
* the following additional features:
* - less error prone: doing the same operation with .reverse() requires special care:
* \code m = m.reverse().eval(); \endcode
* - this API allows to avoid creating a temporary (the current implementation creates a temporary, but that could be avoided using swap)
* - it allows future optimizations (cache friendliness, etc.)
*
* \sa reverse() */
template<typename Derived>
inline void DenseBase<Derived>::reverseInPlace()
{
derived() = derived().reverse().eval();
}
} // end namespace Eigen
#endif // EIGEN_REVERSE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SELECT_H
#define EIGEN_SELECT_H
namespace Eigen {
/** \class Select
* \ingroup Core_Module
*
* \brief Expression of a coefficient wise version of the C++ ternary operator ?:
*
* \param ConditionMatrixType the type of the \em condition expression which must be a boolean matrix
* \param ThenMatrixType the type of the \em then expression
* \param ElseMatrixType the type of the \em else expression
*
* This class represents an expression of a coefficient wise version of the C++ ternary operator ?:.
* It is the return type of DenseBase::select() and most of the time this is the only way it is used.
*
* \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const
*/
namespace internal {
template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
struct traits<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >
: traits<ThenMatrixType>
{
typedef typename traits<ThenMatrixType>::Scalar Scalar;
typedef Dense StorageKind;
typedef typename traits<ThenMatrixType>::XprKind XprKind;
typedef typename ConditionMatrixType::Nested ConditionMatrixNested;
typedef typename ThenMatrixType::Nested ThenMatrixNested;
typedef typename ElseMatrixType::Nested ElseMatrixNested;
enum {
RowsAtCompileTime = ConditionMatrixType::RowsAtCompileTime,
ColsAtCompileTime = ConditionMatrixType::ColsAtCompileTime,
MaxRowsAtCompileTime = ConditionMatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = ConditionMatrixType::MaxColsAtCompileTime,
Flags = (unsigned int)ThenMatrixType::Flags & ElseMatrixType::Flags & HereditaryBits,
CoeffReadCost = traits<typename remove_all<ConditionMatrixNested>::type>::CoeffReadCost
+ EIGEN_SIZE_MAX(traits<typename remove_all<ThenMatrixNested>::type>::CoeffReadCost,
traits<typename remove_all<ElseMatrixNested>::type>::CoeffReadCost)
};
};
}
template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
class Select : internal::no_assignment_operator,
public internal::dense_xpr_base< Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >::type
{
public:
typedef typename internal::dense_xpr_base<Select>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Select)
Select(const ConditionMatrixType& conditionMatrix,
const ThenMatrixType& thenMatrix,
const ElseMatrixType& elseMatrix)
: m_condition(conditionMatrix), m_then(thenMatrix), m_else(elseMatrix)
{
eigen_assert(m_condition.rows() == m_then.rows() && m_condition.rows() == m_else.rows());
eigen_assert(m_condition.cols() == m_then.cols() && m_condition.cols() == m_else.cols());
}
Index rows() const { return m_condition.rows(); }
Index cols() const { return m_condition.cols(); }
const Scalar coeff(Index i, Index j) const
{
if (m_condition.coeff(i,j))
return m_then.coeff(i,j);
else
return m_else.coeff(i,j);
}
const Scalar coeff(Index i) const
{
if (m_condition.coeff(i))
return m_then.coeff(i);
else
return m_else.coeff(i);
}
const ConditionMatrixType& conditionMatrix() const
{
return m_condition;
}
const ThenMatrixType& thenMatrix() const
{
return m_then;
}
const ElseMatrixType& elseMatrix() const
{
return m_else;
}
protected:
typename ConditionMatrixType::Nested m_condition;
typename ThenMatrixType::Nested m_then;
typename ElseMatrixType::Nested m_else;
};
/** \returns a matrix where each coefficient (i,j) is equal to \a thenMatrix(i,j)
* if \c *this(i,j), and \a elseMatrix(i,j) otherwise.
*
* Example: \include MatrixBase_select.cpp
* Output: \verbinclude MatrixBase_select.out
*
* \sa class Select
*/
template<typename Derived>
template<typename ThenDerived,typename ElseDerived>
inline const Select<Derived,ThenDerived,ElseDerived>
DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
const DenseBase<ElseDerived>& elseMatrix) const
{
return Select<Derived,ThenDerived,ElseDerived>(derived(), thenMatrix.derived(), elseMatrix.derived());
}
/** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
* the \em else expression being a scalar value.
*
* \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
*/
template<typename Derived>
template<typename ThenDerived>
inline const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>
DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
typename ThenDerived::Scalar elseScalar) const
{
return Select<Derived,ThenDerived,typename ThenDerived::ConstantReturnType>(
derived(), thenMatrix.derived(), ThenDerived::Constant(rows(),cols(),elseScalar));
}
/** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
* the \em then expression being a scalar value.
*
* \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
*/
template<typename Derived>
template<typename ElseDerived>
inline const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >
DenseBase<Derived>::select(typename ElseDerived::Scalar thenScalar,
const DenseBase<ElseDerived>& elseMatrix) const
{
return Select<Derived,typename ElseDerived::ConstantReturnType,ElseDerived>(
derived(), ElseDerived::Constant(rows(),cols(),thenScalar), elseMatrix.derived());
}
} // end namespace Eigen
#endif // EIGEN_SELECT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SELFADJOINTMATRIX_H
#define EIGEN_SELFADJOINTMATRIX_H
namespace Eigen {
/** \class SelfAdjointView
* \ingroup Core_Module
*
*
* \brief Expression of a selfadjoint matrix from a triangular part of a dense matrix
*
* \param MatrixType the type of the dense matrix storing the coefficients
* \param TriangularPart can be either \c #Lower or \c #Upper
*
* This class is an expression of a sefladjoint matrix from a triangular part of a matrix
* with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()
* and most of the time this is the only way that it is used.
*
* \sa class TriangularBase, MatrixBase::selfadjointView()
*/
namespace internal {
template<typename MatrixType, unsigned int UpLo>
struct traits<SelfAdjointView<MatrixType, UpLo> > : traits<MatrixType>
{
typedef typename nested<MatrixType>::type MatrixTypeNested;
typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
typedef MatrixType ExpressionType;
typedef typename MatrixType::PlainObject DenseMatrixType;
enum {
Mode = UpLo | SelfAdjoint,
Flags = MatrixTypeNestedCleaned::Flags & (HereditaryBits)
& (~(PacketAccessBit | DirectAccessBit | LinearAccessBit)), // FIXME these flags should be preserved
CoeffReadCost = MatrixTypeNestedCleaned::CoeffReadCost
};
};
}
template <typename Lhs, int LhsMode, bool LhsIsVector,
typename Rhs, int RhsMode, bool RhsIsVector>
struct SelfadjointProductMatrix;
// FIXME could also be called SelfAdjointWrapper to be consistent with DiagonalWrapper ??
template<typename MatrixType, unsigned int UpLo> class SelfAdjointView
: public TriangularBase<SelfAdjointView<MatrixType, UpLo> >
{
public:
typedef TriangularBase<SelfAdjointView> Base;
typedef typename internal::traits<SelfAdjointView>::MatrixTypeNested MatrixTypeNested;
typedef typename internal::traits<SelfAdjointView>::MatrixTypeNestedCleaned MatrixTypeNestedCleaned;
/** \brief The type of coefficients in this matrix */
typedef typename internal::traits<SelfAdjointView>::Scalar Scalar;
typedef typename MatrixType::Index Index;
enum {
Mode = internal::traits<SelfAdjointView>::Mode
};
typedef typename MatrixType::PlainObject PlainObject;
inline SelfAdjointView(MatrixType& matrix) : m_matrix(matrix)
{}
inline Index rows() const { return m_matrix.rows(); }
inline Index cols() const { return m_matrix.cols(); }
inline Index outerStride() const { return m_matrix.outerStride(); }
inline Index innerStride() const { return m_matrix.innerStride(); }
/** \sa MatrixBase::coeff()
* \warning the coordinates must fit into the referenced triangular part
*/
inline Scalar coeff(Index row, Index col) const
{
Base::check_coordinates_internal(row, col);
return m_matrix.coeff(row, col);
}
/** \sa MatrixBase::coeffRef()
* \warning the coordinates must fit into the referenced triangular part
*/
inline Scalar& coeffRef(Index row, Index col)
{
Base::check_coordinates_internal(row, col);
return m_matrix.const_cast_derived().coeffRef(row, col);
}
/** \internal */
const MatrixTypeNestedCleaned& _expression() const { return m_matrix; }
const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }
MatrixTypeNestedCleaned& nestedExpression() { return *const_cast<MatrixTypeNestedCleaned*>(&m_matrix); }
/** Efficient self-adjoint matrix times vector/matrix product */
template<typename OtherDerived>
SelfadjointProductMatrix<MatrixType,Mode,false,OtherDerived,0,OtherDerived::IsVectorAtCompileTime>
operator*(const MatrixBase<OtherDerived>& rhs) const
{
return SelfadjointProductMatrix
<MatrixType,Mode,false,OtherDerived,0,OtherDerived::IsVectorAtCompileTime>
(m_matrix, rhs.derived());
}
/** Efficient vector/matrix times self-adjoint matrix product */
template<typename OtherDerived> friend
SelfadjointProductMatrix<OtherDerived,0,OtherDerived::IsVectorAtCompileTime,MatrixType,Mode,false>
operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView& rhs)
{
return SelfadjointProductMatrix
<OtherDerived,0,OtherDerived::IsVectorAtCompileTime,MatrixType,Mode,false>
(lhs.derived(),rhs.m_matrix);
}
/** Perform a symmetric rank 2 update of the selfadjoint matrix \c *this:
* \f$ this = this + \alpha u v^* + conj(\alpha) v u^* \f$
* \returns a reference to \c *this
*
* The vectors \a u and \c v \b must be column vectors, however they can be
* a adjoint expression without any overhead. Only the meaningful triangular
* part of the matrix is updated, the rest is left unchanged.
*
* \sa rankUpdate(const MatrixBase<DerivedU>&, Scalar)
*/
template<typename DerivedU, typename DerivedV>
SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, Scalar alpha = Scalar(1));
/** Perform a symmetric rank K update of the selfadjoint matrix \c *this:
* \f$ this = this + \alpha ( u u^* ) \f$ where \a u is a vector or matrix.
*
* \returns a reference to \c *this
*
* Note that to perform \f$ this = this + \alpha ( u^* u ) \f$ you can simply
* call this function with u.adjoint().
*
* \sa rankUpdate(const MatrixBase<DerivedU>&, const MatrixBase<DerivedV>&, Scalar)
*/
template<typename DerivedU>
SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, Scalar alpha = Scalar(1));
/////////// Cholesky module ///////////
const LLT<PlainObject, UpLo> llt() const;
const LDLT<PlainObject, UpLo> ldlt() const;
/////////// Eigenvalue module ///////////
/** Real part of #Scalar */
typedef typename NumTraits<Scalar>::Real RealScalar;
/** Return type of eigenvalues() */
typedef Matrix<RealScalar, internal::traits<MatrixType>::ColsAtCompileTime, 1> EigenvaluesReturnType;
EigenvaluesReturnType eigenvalues() const;
RealScalar operatorNorm() const;
#ifdef EIGEN2_SUPPORT
template<typename OtherDerived>
SelfAdjointView& operator=(const MatrixBase<OtherDerived>& other)
{
enum {
OtherPart = UpLo == Upper ? StrictlyLower : StrictlyUpper
};
m_matrix.const_cast_derived().template triangularView<UpLo>() = other;
m_matrix.const_cast_derived().template triangularView<OtherPart>() = other.adjoint();
return *this;
}
template<typename OtherMatrixType, unsigned int OtherMode>
SelfAdjointView& operator=(const TriangularView<OtherMatrixType, OtherMode>& other)
{
enum {
OtherPart = UpLo == Upper ? StrictlyLower : StrictlyUpper
};
m_matrix.const_cast_derived().template triangularView<UpLo>() = other.toDenseMatrix();
m_matrix.const_cast_derived().template triangularView<OtherPart>() = other.toDenseMatrix().adjoint();
return *this;
}
#endif
protected:
MatrixTypeNested m_matrix;
};
// template<typename OtherDerived, typename MatrixType, unsigned int UpLo>
// internal::selfadjoint_matrix_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >
// operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView<MatrixType,UpLo>& rhs)
// {
// return internal::matrix_selfadjoint_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >(lhs.derived(),rhs);
// }
// selfadjoint to dense matrix
namespace internal {
template<typename Derived1, typename Derived2, int UnrollCount, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), UnrollCount, ClearOpposite>
{
enum {
col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
row = (UnrollCount-1) % Derived1::RowsAtCompileTime
};
static inline void run(Derived1 &dst, const Derived2 &src)
{
triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), UnrollCount-1, ClearOpposite>::run(dst, src);
if(row == col)
dst.coeffRef(row, col) = real(src.coeff(row, col));
else if(row < col)
dst.coeffRef(col, row) = conj(dst.coeffRef(row, col) = src.coeff(row, col));
}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Upper, 0, ClearOpposite>
{
static inline void run(Derived1 &, const Derived2 &) {}
};
template<typename Derived1, typename Derived2, int UnrollCount, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), UnrollCount, ClearOpposite>
{
enum {
col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
row = (UnrollCount-1) % Derived1::RowsAtCompileTime
};
static inline void run(Derived1 &dst, const Derived2 &src)
{
triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), UnrollCount-1, ClearOpposite>::run(dst, src);
if(row == col)
dst.coeffRef(row, col) = real(src.coeff(row, col));
else if(row > col)
dst.coeffRef(col, row) = conj(dst.coeffRef(row, col) = src.coeff(row, col));
}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Lower, 0, ClearOpposite>
{
static inline void run(Derived1 &, const Derived2 &) {}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Upper, Dynamic, ClearOpposite>
{
typedef typename Derived1::Index Index;
static inline void run(Derived1 &dst, const Derived2 &src)
{
for(Index j = 0; j < dst.cols(); ++j)
{
for(Index i = 0; i < j; ++i)
{
dst.copyCoeff(i, j, src);
dst.coeffRef(j,i) = conj(dst.coeff(i,j));
}
dst.copyCoeff(j, j, src);
}
}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Lower, Dynamic, ClearOpposite>
{
static inline void run(Derived1 &dst, const Derived2 &src)
{
typedef typename Derived1::Index Index;
for(Index i = 0; i < dst.rows(); ++i)
{
for(Index j = 0; j < i; ++j)
{
dst.copyCoeff(i, j, src);
dst.coeffRef(j,i) = conj(dst.coeff(i,j));
}
dst.copyCoeff(i, i, src);
}
}
};
} // end namespace internal
/***************************************************************************
* Implementation of MatrixBase methods
***************************************************************************/
template<typename Derived>
template<unsigned int UpLo>
typename MatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type
MatrixBase<Derived>::selfadjointView() const
{
return derived();
}
template<typename Derived>
template<unsigned int UpLo>
typename MatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type
MatrixBase<Derived>::selfadjointView()
{
return derived();
}
} // end namespace Eigen
#endif // EIGEN_SELFADJOINTMATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SELFCWISEBINARYOP_H
#define EIGEN_SELFCWISEBINARYOP_H
namespace Eigen {
/** \class SelfCwiseBinaryOp
* \ingroup Core_Module
*
* \internal
*
* \brief Internal helper class for optimizing operators like +=, -=
*
* This is a pseudo expression class re-implementing the copyCoeff/copyPacket
* method to directly performs a +=/-= operations in an optimal way. In particular,
* this allows to make sure that the input/output data are loaded only once using
* aligned packet loads.
*
* \sa class SwapWrapper for a similar trick.
*/
namespace internal {
template<typename BinaryOp, typename Lhs, typename Rhs>
struct traits<SelfCwiseBinaryOp<BinaryOp,Lhs,Rhs> >
: traits<CwiseBinaryOp<BinaryOp,Lhs,Rhs> >
{
enum {
// Note that it is still a good idea to preserve the DirectAccessBit
// so that assign can correctly align the data.
Flags = traits<CwiseBinaryOp<BinaryOp,Lhs,Rhs> >::Flags | (Lhs::Flags&DirectAccessBit) | (Lhs::Flags&LvalueBit),
OuterStrideAtCompileTime = Lhs::OuterStrideAtCompileTime,
InnerStrideAtCompileTime = Lhs::InnerStrideAtCompileTime
};
};
}
template<typename BinaryOp, typename Lhs, typename Rhs> class SelfCwiseBinaryOp
: public internal::dense_xpr_base< SelfCwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type
{
public:
typedef typename internal::dense_xpr_base<SelfCwiseBinaryOp>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(SelfCwiseBinaryOp)
typedef typename internal::packet_traits<Scalar>::type Packet;
inline SelfCwiseBinaryOp(Lhs& xpr, const BinaryOp& func = BinaryOp()) : m_matrix(xpr), m_functor(func) {}
inline Index rows() const { return m_matrix.rows(); }
inline Index cols() const { return m_matrix.cols(); }
inline Index outerStride() const { return m_matrix.outerStride(); }
inline Index innerStride() const { return m_matrix.innerStride(); }
inline const Scalar* data() const { return m_matrix.data(); }
// note that this function is needed by assign to correctly align loads/stores
// TODO make Assign use .data()
inline Scalar& coeffRef(Index row, Index col)
{
EIGEN_STATIC_ASSERT_LVALUE(Lhs)
return m_matrix.const_cast_derived().coeffRef(row, col);
}
inline const Scalar& coeffRef(Index row, Index col) const
{
return m_matrix.coeffRef(row, col);
}
// note that this function is needed by assign to correctly align loads/stores
// TODO make Assign use .data()
inline Scalar& coeffRef(Index index)
{
EIGEN_STATIC_ASSERT_LVALUE(Lhs)
return m_matrix.const_cast_derived().coeffRef(index);
}
inline const Scalar& coeffRef(Index index) const
{
return m_matrix.const_cast_derived().coeffRef(index);
}
template<typename OtherDerived>
void copyCoeff(Index row, Index col, const DenseBase<OtherDerived>& other)
{
OtherDerived& _other = other.const_cast_derived();
eigen_internal_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
Scalar& tmp = m_matrix.coeffRef(row,col);
tmp = m_functor(tmp, _other.coeff(row,col));
}
template<typename OtherDerived>
void copyCoeff(Index index, const DenseBase<OtherDerived>& other)
{
OtherDerived& _other = other.const_cast_derived();
eigen_internal_assert(index >= 0 && index < m_matrix.size());
Scalar& tmp = m_matrix.coeffRef(index);
tmp = m_functor(tmp, _other.coeff(index));
}
template<typename OtherDerived, int StoreMode, int LoadMode>
void copyPacket(Index row, Index col, const DenseBase<OtherDerived>& other)
{
OtherDerived& _other = other.const_cast_derived();
eigen_internal_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
m_matrix.template writePacket<StoreMode>(row, col,
m_functor.packetOp(m_matrix.template packet<StoreMode>(row, col),_other.template packet<LoadMode>(row, col)) );
}
template<typename OtherDerived, int StoreMode, int LoadMode>
void copyPacket(Index index, const DenseBase<OtherDerived>& other)
{
OtherDerived& _other = other.const_cast_derived();
eigen_internal_assert(index >= 0 && index < m_matrix.size());
m_matrix.template writePacket<StoreMode>(index,
m_functor.packetOp(m_matrix.template packet<StoreMode>(index),_other.template packet<LoadMode>(index)) );
}
// reimplement lazyAssign to handle complex *= real
// see CwiseBinaryOp ctor for details
template<typename RhsDerived>
EIGEN_STRONG_INLINE SelfCwiseBinaryOp& lazyAssign(const DenseBase<RhsDerived>& rhs)
{
EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs,RhsDerived)
EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp,typename Lhs::Scalar,typename RhsDerived::Scalar);
#ifdef EIGEN_DEBUG_ASSIGN
internal::assign_traits<SelfCwiseBinaryOp, RhsDerived>::debug();
#endif
eigen_assert(rows() == rhs.rows() && cols() == rhs.cols());
internal::assign_impl<SelfCwiseBinaryOp, RhsDerived>::run(*this,rhs.derived());
#ifndef EIGEN_NO_DEBUG
this->checkTransposeAliasing(rhs.derived());
#endif
return *this;
}
// overloaded to honor evaluation of special matrices
// maybe another solution would be to not use SelfCwiseBinaryOp
// at first...
SelfCwiseBinaryOp& operator=(const Rhs& _rhs)
{
typename internal::nested<Rhs>::type rhs(_rhs);
return Base::operator=(rhs);
}
Lhs& expression() const
{
return m_matrix;
}
const BinaryOp& functor() const
{
return m_functor;
}
protected:
Lhs& m_matrix;
const BinaryOp& m_functor;
private:
SelfCwiseBinaryOp& operator=(const SelfCwiseBinaryOp&);
};
template<typename Derived>
inline Derived& DenseBase<Derived>::operator*=(const Scalar& other)
{
typedef typename Derived::PlainObject PlainObject;
SelfCwiseBinaryOp<internal::scalar_product_op<Scalar>, Derived, typename PlainObject::ConstantReturnType> tmp(derived());
tmp = PlainObject::Constant(rows(),cols(),other);
return derived();
}
template<typename Derived>
inline Derived& DenseBase<Derived>::operator/=(const Scalar& other)
{
typedef typename internal::conditional<NumTraits<Scalar>::IsInteger,
internal::scalar_quotient_op<Scalar>,
internal::scalar_product_op<Scalar> >::type BinOp;
typedef typename Derived::PlainObject PlainObject;
SelfCwiseBinaryOp<BinOp, Derived, typename PlainObject::ConstantReturnType> tmp(derived());
tmp = PlainObject::Constant(rows(),cols(), NumTraits<Scalar>::IsInteger ? other : Scalar(1)/other);
return derived();
}
} // end namespace Eigen
#endif // EIGEN_SELFCWISEBINARYOP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SOLVETRIANGULAR_H
#define EIGEN_SOLVETRIANGULAR_H
namespace Eigen {
namespace internal {
// Forward declarations:
// The following two routines are implemented in the products/TriangularSolver*.h files
template<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
struct triangular_solve_vector;
template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder, int OtherStorageOrder>
struct triangular_solve_matrix;
// small helper struct extracting some traits on the underlying solver operation
template<typename Lhs, typename Rhs, int Side>
class trsolve_traits
{
private:
enum {
RhsIsVectorAtCompileTime = (Side==OnTheLeft ? Rhs::ColsAtCompileTime : Rhs::RowsAtCompileTime)==1
};
public:
enum {
Unrolling = (RhsIsVectorAtCompileTime && Rhs::SizeAtCompileTime != Dynamic && Rhs::SizeAtCompileTime <= 8)
? CompleteUnrolling : NoUnrolling,
RhsVectors = RhsIsVectorAtCompileTime ? 1 : Dynamic
};
};
template<typename Lhs, typename Rhs,
int Side, // can be OnTheLeft/OnTheRight
int Mode, // can be Upper/Lower | UnitDiag
int Unrolling = trsolve_traits<Lhs,Rhs,Side>::Unrolling,
int RhsVectors = trsolve_traits<Lhs,Rhs,Side>::RhsVectors
>
struct triangular_solver_selector;
template<typename Lhs, typename Rhs, int Side, int Mode>
struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,1>
{
typedef typename Lhs::Scalar LhsScalar;
typedef typename Rhs::Scalar RhsScalar;
typedef blas_traits<Lhs> LhsProductTraits;
typedef typename LhsProductTraits::ExtractType ActualLhsType;
typedef Map<Matrix<RhsScalar,Dynamic,1>, Aligned> MappedRhs;
static void run(const Lhs& lhs, Rhs& rhs)
{
ActualLhsType actualLhs = LhsProductTraits::extract(lhs);
// FIXME find a way to allow an inner stride if packet_traits<Scalar>::size==1
bool useRhsDirectly = Rhs::InnerStrideAtCompileTime==1 || rhs.innerStride()==1;
ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhs,rhs.size(),
(useRhsDirectly ? rhs.data() : 0));
if(!useRhsDirectly)
MappedRhs(actualRhs,rhs.size()) = rhs;
triangular_solve_vector<LhsScalar, RhsScalar, typename Lhs::Index, Side, Mode, LhsProductTraits::NeedToConjugate,
(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor>
::run(actualLhs.cols(), actualLhs.data(), actualLhs.outerStride(), actualRhs);
if(!useRhsDirectly)
rhs = MappedRhs(actualRhs, rhs.size());
}
};
// the rhs is a matrix
template<typename Lhs, typename Rhs, int Side, int Mode>
struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,Dynamic>
{
typedef typename Rhs::Scalar Scalar;
typedef typename Rhs::Index Index;
typedef blas_traits<Lhs> LhsProductTraits;
typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType;
static void run(const Lhs& lhs, Rhs& rhs)
{
typename internal::add_const_on_value_type<ActualLhsType>::type actualLhs = LhsProductTraits::extract(lhs);
const Index size = lhs.rows();
const Index othersize = Side==OnTheLeft? rhs.cols() : rhs.rows();
typedef internal::gemm_blocking_space<(Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
Rhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxRowsAtCompileTime,4> BlockingType;
BlockingType blocking(rhs.rows(), rhs.cols(), size);
triangular_solve_matrix<Scalar,Index,Side,Mode,LhsProductTraits::NeedToConjugate,(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,
(Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor>
::run(size, othersize, &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &rhs.coeffRef(0,0), rhs.outerStride(), blocking);
}
};
/***************************************************************************
* meta-unrolling implementation
***************************************************************************/
template<typename Lhs, typename Rhs, int Mode, int Index, int Size,
bool Stop = Index==Size>
struct triangular_solver_unroller;
template<typename Lhs, typename Rhs, int Mode, int Index, int Size>
struct triangular_solver_unroller<Lhs,Rhs,Mode,Index,Size,false> {
enum {
IsLower = ((Mode&Lower)==Lower),
I = IsLower ? Index : Size - Index - 1,
S = IsLower ? 0 : I+1
};
static void run(const Lhs& lhs, Rhs& rhs)
{
if (Index>0)
rhs.coeffRef(I) -= lhs.row(I).template segment<Index>(S).transpose()
.cwiseProduct(rhs.template segment<Index>(S)).sum();
if(!(Mode & UnitDiag))
rhs.coeffRef(I) /= lhs.coeff(I,I);
triangular_solver_unroller<Lhs,Rhs,Mode,Index+1,Size>::run(lhs,rhs);
}
};
template<typename Lhs, typename Rhs, int Mode, int Index, int Size>
struct triangular_solver_unroller<Lhs,Rhs,Mode,Index,Size,true> {
static void run(const Lhs&, Rhs&) {}
};
template<typename Lhs, typename Rhs, int Mode>
struct triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,CompleteUnrolling,1> {
static void run(const Lhs& lhs, Rhs& rhs)
{ triangular_solver_unroller<Lhs,Rhs,Mode,0,Rhs::SizeAtCompileTime>::run(lhs,rhs); }
};
template<typename Lhs, typename Rhs, int Mode>
struct triangular_solver_selector<Lhs,Rhs,OnTheRight,Mode,CompleteUnrolling,1> {
static void run(const Lhs& lhs, Rhs& rhs)
{
Transpose<const Lhs> trLhs(lhs);
Transpose<Rhs> trRhs(rhs);
triangular_solver_unroller<Transpose<const Lhs>,Transpose<Rhs>,
((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
0,Rhs::SizeAtCompileTime>::run(trLhs,trRhs);
}
};
} // end namespace internal
/***************************************************************************
* TriangularView methods
***************************************************************************/
/** "in-place" version of TriangularView::solve() where the result is written in \a other
*
* \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
* This function will const_cast it, so constness isn't honored here.
*
* See TriangularView:solve() for the details.
*/
template<typename MatrixType, unsigned int Mode>
template<int Side, typename OtherDerived>
void TriangularView<MatrixType,Mode>::solveInPlace(const MatrixBase<OtherDerived>& _other) const
{
OtherDerived& other = _other.const_cast_derived();
eigen_assert( cols() == rows() && ((Side==OnTheLeft && cols() == other.rows()) || (Side==OnTheRight && cols() == other.cols())) );
eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit && OtherDerived::IsVectorAtCompileTime };
typedef typename internal::conditional<copy,
typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
OtherCopy otherCopy(other);
internal::triangular_solver_selector<MatrixType, typename internal::remove_reference<OtherCopy>::type,
Side, Mode>::run(nestedExpression(), otherCopy);
if (copy)
other = otherCopy;
}
/** \returns the product of the inverse of \c *this with \a other, \a *this being triangular.
*
* This function computes the inverse-matrix matrix product inverse(\c *this) * \a other if
* \a Side==OnTheLeft (the default), or the right-inverse-multiply \a other * inverse(\c *this) if
* \a Side==OnTheRight.
*
* The matrix \c *this must be triangular and invertible (i.e., all the coefficients of the
* diagonal must be non zero). It works as a forward (resp. backward) substitution if \c *this
* is an upper (resp. lower) triangular matrix.
*
* Example: \include MatrixBase_marked.cpp
* Output: \verbinclude MatrixBase_marked.out
*
* This function returns an expression of the inverse-multiply and can works in-place if it is assigned
* to the same matrix or vector \a other.
*
* For users coming from BLAS, this function (and more specifically solveInPlace()) offer
* all the operations supported by the \c *TRSV and \c *TRSM BLAS routines.
*
* \sa TriangularView::solveInPlace()
*/
template<typename Derived, unsigned int Mode>
template<int Side, typename Other>
const internal::triangular_solve_retval<Side,TriangularView<Derived,Mode>,Other>
TriangularView<Derived,Mode>::solve(const MatrixBase<Other>& other) const
{
return internal::triangular_solve_retval<Side,TriangularView,Other>(*this, other.derived());
}
namespace internal {
template<int Side, typename TriangularType, typename Rhs>
struct traits<triangular_solve_retval<Side, TriangularType, Rhs> >
{
typedef typename internal::plain_matrix_type_column_major<Rhs>::type ReturnType;
};
template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval
: public ReturnByValue<triangular_solve_retval<Side, TriangularType, Rhs> >
{
typedef typename remove_all<typename Rhs::Nested>::type RhsNestedCleaned;
typedef ReturnByValue<triangular_solve_retval> Base;
typedef typename Base::Index Index;
triangular_solve_retval(const TriangularType& tri, const Rhs& rhs)
: m_triangularMatrix(tri), m_rhs(rhs)
{}
inline Index rows() const { return m_rhs.rows(); }
inline Index cols() const { return m_rhs.cols(); }
template<typename Dest> inline void evalTo(Dest& dst) const
{
if(!(is_same<RhsNestedCleaned,Dest>::value && extract_data(dst) == extract_data(m_rhs)))
dst = m_rhs;
m_triangularMatrix.template solveInPlace<Side>(dst);
}
protected:
const TriangularType& m_triangularMatrix;
typename Rhs::Nested m_rhs;
};
} // namespace internal
} // end namespace Eigen
#endif // EIGEN_SOLVETRIANGULAR_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_STABLENORM_H
#define EIGEN_STABLENORM_H
namespace Eigen {
namespace internal {
template<typename ExpressionType, typename Scalar>
inline void stable_norm_kernel(const ExpressionType& bl, Scalar& ssq, Scalar& scale, Scalar& invScale)
{
Scalar max = bl.cwiseAbs().maxCoeff();
if (max>scale)
{
ssq = ssq * abs2(scale/max);
scale = max;
invScale = Scalar(1)/scale;
}
// TODO if the max is much much smaller than the current scale,
// then we can neglect this sub vector
ssq += (bl*invScale).squaredNorm();
}
}
/** \returns the \em l2 norm of \c *this avoiding underflow and overflow.
* This version use a blockwise two passes algorithm:
* 1 - find the absolute largest coefficient \c s
* 2 - compute \f$ s \Vert \frac{*this}{s} \Vert \f$ in a standard way
*
* For architecture/scalar types supporting vectorization, this version
* is faster than blueNorm(). Otherwise the blueNorm() is much faster.
*
* \sa norm(), blueNorm(), hypotNorm()
*/
template<typename Derived>
inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
MatrixBase<Derived>::stableNorm() const
{
using std::min;
const Index blockSize = 4096;
RealScalar scale(0);
RealScalar invScale(1);
RealScalar ssq(0); // sum of square
enum {
Alignment = (int(Flags)&DirectAccessBit) || (int(Flags)&AlignedBit) ? 1 : 0
};
Index n = size();
Index bi = internal::first_aligned(derived());
if (bi>0)
internal::stable_norm_kernel(this->head(bi), ssq, scale, invScale);
for (; bi<n; bi+=blockSize)
internal::stable_norm_kernel(this->segment(bi,(min)(blockSize, n - bi)).template forceAlignedAccessIf<Alignment>(), ssq, scale, invScale);
return scale * internal::sqrt(ssq);
}
/** \returns the \em l2 norm of \c *this using the Blue's algorithm.
* A Portable Fortran Program to Find the Euclidean Norm of a Vector,
* ACM TOMS, Vol 4, Issue 1, 1978.
*
* For architecture/scalar types without vectorization, this version
* is much faster than stableNorm(). Otherwise the stableNorm() is faster.
*
* \sa norm(), stableNorm(), hypotNorm()
*/
template<typename Derived>
inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
MatrixBase<Derived>::blueNorm() const
{
using std::pow;
using std::min;
using std::max;
static bool initialized = false;
static RealScalar b1, b2, s1m, s2m, overfl, rbig, relerr;
if(!initialized)
{
int ibeta, it, iemin, iemax, iexp;
RealScalar abig, eps;
// This program calculates the machine-dependent constants
// bl, b2, slm, s2m, relerr overfl
// from the "basic" machine-dependent numbers
// ibeta, it, iemin, iemax, rbig.
// The following define the basic machine-dependent constants.
// For portability, the PORT subprograms "ilmaeh" and "rlmach"
// are used. For any specific computer, each of the assignment
// statements can be replaced
ibeta = std::numeric_limits<RealScalar>::radix; // base for floating-point numbers
it = std::numeric_limits<RealScalar>::digits; // number of base-beta digits in mantissa
iemin = std::numeric_limits<RealScalar>::min_exponent; // minimum exponent
iemax = std::numeric_limits<RealScalar>::max_exponent; // maximum exponent
rbig = (std::numeric_limits<RealScalar>::max)(); // largest floating-point number
iexp = -((1-iemin)/2);
b1 = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp))); // lower boundary of midrange
iexp = (iemax + 1 - it)/2;
b2 = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp))); // upper boundary of midrange
iexp = (2-iemin)/2;
s1m = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp))); // scaling factor for lower range
iexp = - ((iemax+it)/2);
s2m = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp))); // scaling factor for upper range
overfl = rbig*s2m; // overflow boundary for abig
eps = RealScalar(pow(double(ibeta), 1-it));
relerr = internal::sqrt(eps); // tolerance for neglecting asml
abig = RealScalar(1.0/eps - 1.0);
initialized = true;
}
Index n = size();
RealScalar ab2 = b2 / RealScalar(n);
RealScalar asml = RealScalar(0);
RealScalar amed = RealScalar(0);
RealScalar abig = RealScalar(0);
for(Index j=0; j<n; ++j)
{
RealScalar ax = internal::abs(coeff(j));
if(ax > ab2) abig += internal::abs2(ax*s2m);
else if(ax < b1) asml += internal::abs2(ax*s1m);
else amed += internal::abs2(ax);
}
if(abig > RealScalar(0))
{
abig = internal::sqrt(abig);
if(abig > overfl)
{
return rbig;
}
if(amed > RealScalar(0))
{
abig = abig/s2m;
amed = internal::sqrt(amed);
}
else
return abig/s2m;
}
else if(asml > RealScalar(0))
{
if (amed > RealScalar(0))
{
abig = internal::sqrt(amed);
amed = internal::sqrt(asml) / s1m;
}
else
return internal::sqrt(asml)/s1m;
}
else
return internal::sqrt(amed);
asml = (min)(abig, amed);
abig = (max)(abig, amed);
if(asml <= abig*relerr)
return abig;
else
return abig * internal::sqrt(RealScalar(1) + internal::abs2(asml/abig));
}
/** \returns the \em l2 norm of \c *this avoiding undeflow and overflow.
* This version use a concatenation of hypot() calls, and it is very slow.
*
* \sa norm(), stableNorm()
*/
template<typename Derived>
inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
MatrixBase<Derived>::hypotNorm() const
{
return this->cwiseAbs().redux(internal::scalar_hypot_op<RealScalar>());
}
} // end namespace Eigen
#endif // EIGEN_STABLENORM_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_STRIDE_H
#define EIGEN_STRIDE_H
namespace Eigen {
/** \class Stride
* \ingroup Core_Module
*
* \brief Holds strides information for Map
*
* This class holds the strides information for mapping arrays with strides with class Map.
*
* It holds two values: the inner stride and the outer stride.
*
* The inner stride is the pointer increment between two consecutive entries within a given row of a
* row-major matrix or within a given column of a column-major matrix.
*
* The outer stride is the pointer increment between two consecutive rows of a row-major matrix or
* between two consecutive columns of a column-major matrix.
*
* These two values can be passed either at compile-time as template parameters, or at runtime as
* arguments to the constructor.
*
* Indeed, this class takes two template parameters:
* \param _OuterStrideAtCompileTime the outer stride, or Dynamic if you want to specify it at runtime.
* \param _InnerStrideAtCompileTime the inner stride, or Dynamic if you want to specify it at runtime.
*
* Here is an example:
* \include Map_general_stride.cpp
* Output: \verbinclude Map_general_stride.out
*
* \sa class InnerStride, class OuterStride, \ref TopicStorageOrders
*/
template<int _OuterStrideAtCompileTime, int _InnerStrideAtCompileTime>
class Stride
{
public:
typedef DenseIndex Index;
enum {
InnerStrideAtCompileTime = _InnerStrideAtCompileTime,
OuterStrideAtCompileTime = _OuterStrideAtCompileTime
};
/** Default constructor, for use when strides are fixed at compile time */
Stride()
: m_outer(OuterStrideAtCompileTime), m_inner(InnerStrideAtCompileTime)
{
eigen_assert(InnerStrideAtCompileTime != Dynamic && OuterStrideAtCompileTime != Dynamic);
}
/** Constructor allowing to pass the strides at runtime */
Stride(Index outerStride, Index innerStride)
: m_outer(outerStride), m_inner(innerStride)
{
eigen_assert(innerStride>=0 && outerStride>=0);
}
/** Copy constructor */
Stride(const Stride& other)
: m_outer(other.outer()), m_inner(other.inner())
{}
/** \returns the outer stride */
inline Index outer() const { return m_outer.value(); }
/** \returns the inner stride */
inline Index inner() const { return m_inner.value(); }
protected:
internal::variable_if_dynamic<Index, OuterStrideAtCompileTime> m_outer;
internal::variable_if_dynamic<Index, InnerStrideAtCompileTime> m_inner;
};
/** \brief Convenience specialization of Stride to specify only an inner stride
* See class Map for some examples */
template<int Value = Dynamic>
class InnerStride : public Stride<0, Value>
{
typedef Stride<0, Value> Base;
public:
typedef DenseIndex Index;
InnerStride() : Base() {}
InnerStride(Index v) : Base(0, v) {}
};
/** \brief Convenience specialization of Stride to specify only an outer stride
* See class Map for some examples */
template<int Value = Dynamic>
class OuterStride : public Stride<Value, 0>
{
typedef Stride<Value, 0> Base;
public:
typedef DenseIndex Index;
OuterStride() : Base() {}
OuterStride(Index v) : Base(v,0) {}
};
} // end namespace Eigen
#endif // EIGEN_STRIDE_H

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