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Grid/lib/algorithms/iterative/Householder.h

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/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./lib/algorithms/iterative/Householder.h
Copyright (C) 2015
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
See the full license in the file "LICENSE" in the top level distribution directory
*************************************************************************************/
/* END LEGAL */
#ifndef HOUSEHOLDER_H
#define HOUSEHOLDER_H
#define TIMER(A) std::cout << GridLogMessage << __FUNC__ << " file "<< __FILE__ <<" line " << __LINE__ << std::endl;
#define ENTER() std::cout << GridLogMessage << "ENTRY "<<__FUNC__ << " file "<< __FILE__ <<" line " << __LINE__ << std::endl;
#define LEAVE() std::cout << GridLogMessage << "EXIT "<<__FUNC__ << " file "<< __FILE__ <<" line " << __LINE__ << std::endl;
#include <cstdlib>
#include <string>
#include <cmath>
#include <iostream>
#include <sstream>
#include <stdexcept>
#include <fstream>
#include <complex>
#include <algorithm>
namespace Grid {
/** Comparison function for finding the max element in a vector **/
template <class T> bool cf(T i, T j) {
return abs(i) < abs(j);
}
/**
Calculate a real Givens angle
**/
template <class T> inline void Givens_calc(T y, T z, T &c, T &s){
RealD mz = (RealD)abs(z);
if(mz==0.0){
c = 1; s = 0;
}
if(mz >= (RealD)abs(y)){
T t = -y/z;
s = (T)1.0 / sqrt ((T)1.0 + t * t);
c = s * t;
} else {
T t = -z/y;
c = (T)1.0 / sqrt ((T)1.0 + t * t);
s = c * t;
}
}
template <class T> inline void Givens_mult(DenseMatrix<T> &A, int i, int k, T c, T s, int dir)
{
int q ; SizeSquare(A,q);
if(dir == 0){
for(int j=0;j<q;j++){
T nu = A[i][j];
T w = A[k][j];
A[i][j] = (c*nu + s*w);
A[k][j] = (-s*nu + c*w);
}
}
if(dir == 1){
for(int j=0;j<q;j++){
T nu = A[j][i];
T w = A[j][k];
A[j][i] = (c*nu - s*w);
A[j][k] = (s*nu + c*w);
}
}
}
/**
from input = x;
Compute the complex Householder vector, v, such that
P = (I - b v transpose(v) )
b = 2/v.v
P | x | | x | k = 0
| x | | 0 |
| x | = | 0 |
| x | | 0 | j = 3
| x | | x |
These are the "Unreduced" Householder vectors.
**/
template <class T> inline void Householder_vector(DenseVector<T> input, int k, int j, DenseVector<T> &v, T &beta)
{
int N ; Size(input,N);
T m = *max_element(input.begin() + k, input.begin() + j + 1, cf<T> );
if(abs(m) > 0.0){
T alpha = 0;
for(int i=k; i<j+1; i++){
v[i] = input[i]/m;
alpha = alpha + v[i]*conj(v[i]);
}
alpha = sqrt(alpha);
beta = (T)1.0/(alpha*(alpha + abs(v[k]) ));
if(abs(v[k]) > 0.0) v[k] = v[k] + (v[k]/abs(v[k]))*alpha;
else v[k] = -alpha;
} else{
for(int i=k; i<j+1; i++){
v[i] = 0.0;
}
}
}
/**
from input = x;
Compute the complex Householder vector, v, such that
P = (I - b v transpose(v) )
b = 2/v.v
Px = alpha*e_dir
These are the "Unreduced" Householder vectors.
**/
template <class T> inline void Householder_vector(DenseVector<T> input, int k, int j, int dir, DenseVector<T> &v, T &beta)
{
int N = input.size();
T m = *max_element(input.begin() + k, input.begin() + j + 1, cf);
if(abs(m) > 0.0){
T alpha = 0;
for(int i=k; i<j+1; i++){
v[i] = input[i]/m;
alpha = alpha + v[i]*conj(v[i]);
}
alpha = sqrt(alpha);
beta = 1.0/(alpha*(alpha + abs(v[dir]) ));
if(abs(v[dir]) > 0.0) v[dir] = v[dir] + (v[dir]/abs(v[dir]))*alpha;
else v[dir] = -alpha;
}else{
for(int i=k; i<j+1; i++){
v[i] = 0.0;
}
}
}
/**
Compute the product PA if trans = 0
AP if trans = 1
P = (I - b v transpose(v) )
b = 2/v.v
start at element l of matrix A
v is of length j - k + 1 of v are nonzero
**/
template <class T> inline void Householder_mult(DenseMatrix<T> &A , DenseVector<T> v, T beta, int l, int k, int j, int trans)
{
int N ; SizeSquare(A,N);
if(abs(beta) > 0.0){
for(int p=l; p<N; p++){
T s = 0;
if(trans==0){
for(int i=k;i<j+1;i++) s += conj(v[i-k])*A[i][p];
s *= beta;
for(int i=k;i<j+1;i++){ A[i][p] = A[i][p]-s*conj(v[i-k]);}
} else {
for(int i=k;i<j+1;i++){ s += conj(v[i-k])*A[p][i];}
s *= beta;
for(int i=k;i<j+1;i++){ A[p][i]=A[p][i]-s*conj(v[i-k]);}
}
}
}
}
/**
Compute the product PA if trans = 0
AP if trans = 1
P = (I - b v transpose(v) )
b = 2/v.v
start at element l of matrix A
v is of length j - k + 1 of v are nonzero
A is tridiagonal
**/
template <class T> inline void Householder_mult_tri(DenseMatrix<T> &A , DenseVector<T> v, T beta, int l, int M, int k, int j, int trans)
{
if(abs(beta) > 0.0){
int N ; SizeSquare(A,N);
DenseMatrix<T> tmp; Resize(tmp,N,N); Fill(tmp,0);
T s;
for(int p=l; p<M; p++){
s = 0;
if(trans==0){
for(int i=k;i<j+1;i++) s = s + conj(v[i-k])*A[i][p];
}else{
for(int i=k;i<j+1;i++) s = s + v[i-k]*A[p][i];
}
s = beta*s;
if(trans==0){
for(int i=k;i<j+1;i++) tmp[i][p] = tmp(i,p) - s*v[i-k];
}else{
for(int i=k;i<j+1;i++) tmp[p][i] = tmp[p][i] - s*conj(v[i-k]);
}
}
for(int p=l; p<M; p++){
if(trans==0){
for(int i=k;i<j+1;i++) A[i][p] = A[i][p] + tmp[i][p];
}else{
for(int i=k;i<j+1;i++) A[p][i] = A[p][i] + tmp[p][i];
}
}
}
}
}
#endif
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