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Addedd Ta functionality to the tensor types

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Merge remote-tracking branch 'upstream/master'

Conflicts:
	configure
This commit is contained in:
neo
2015-06-04 18:11:32 +09:00
parent ff9340d4d5 37aa74dfd2
commit b9edadc53e
149 changed files with 4367 additions and 1150 deletions
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38
lib/tensors/Tensor_Ta.h Normal file
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#ifndef GRID_MATH_TA_H
#define GRID_MATH_TA_H
namespace Grid {
///////////////////////////////////////////////
// Ta function for scalar, vector, matrix
///////////////////////////////////////////////
/* inline ComplexF Ta( const ComplexF &arg){ return arg;} */
/* inline ComplexD Ta( const ComplexD &arg){ return arg;} */
/* inline RealF Ta( const RealF &arg){ return arg;} */
/* inline RealD Ta( const RealD &arg){ return arg;} */
template<class vtype> inline iScalar<vtype> Ta(const iScalar<vtype>&r)
{
iScalar<vtype> ret;
ret._internal = Ta(r._internal);
return ret;
}
template<class vtype,int N> inline iVector<vtype,N> Ta(const iVector<vtype,N>&r)
{
iVector<vtype,N> ret;
for(int i=0;i<N;i++){
ret._internal[i] = Ta(r._internal[i]);
}
return ret;
}
template<class vtype,int N> inline iMatrix<vtype,N> Ta(const iMatrix<vtype,N> &arg)
{
iMatrix<vtype,N> ret(arg);
vtype factor = (1/(double)N);
ret = (ret - adj(arg))*0.5;
ret -= trace(ret)*factor;
return ret;
}
}
#endif

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#ifndef GRID_MATH_ARITH_H
#define GRID_MATH_ARITH_H
#include <tensors/Tensor_arith_add.h>
#include <tensors/Tensor_arith_sub.h>
#include <tensors/Tensor_arith_mac.h>
#include <tensors/Tensor_arith_mul.h>
#include <tensors/Tensor_arith_scalar.h>
#endif

118
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#ifndef GRID_MATH_ARITH_ADD_H
#define GRID_MATH_ARITH_ADD_H
namespace Grid {
///////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////// ADD ///////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////
// ADD is simple for now; cannot mix types and straightforward template
// Scalar +/- Scalar
// Vector +/- Vector
// Matrix +/- Matrix
template<class vtype,class ltype,class rtype> strong_inline void add(iScalar<vtype> * __restrict__ ret,
const iScalar<ltype> * __restrict__ lhs,
const iScalar<rtype> * __restrict__ rhs)
{
add(&ret->_internal,&lhs->_internal,&rhs->_internal);
}
template<class vtype,class ltype,class rtype,int N> strong_inline void add(iVector<vtype,N> * __restrict__ ret,
const iVector<ltype,N> * __restrict__ lhs,
const iVector<rtype,N> * __restrict__ rhs)
{
for(int c=0;c<N;c++){
ret->_internal[c]=lhs->_internal[c]+rhs->_internal[c];
}
return;
}
template<class vtype,class ltype,class rtype, int N> strong_inline void add(iMatrix<vtype,N> * __restrict__ ret,
const iMatrix<ltype,N> * __restrict__ lhs,
const iMatrix<rtype,N> * __restrict__ rhs)
{
for(int c2=0;c2<N;c2++){
for(int c1=0;c1<N;c1++){
add(&ret->_internal[c1][c2],&lhs->_internal[c1][c2],&rhs->_internal[c1][c2]);
}}
return;
}
template<class vtype,class ltype,class rtype, int N> strong_inline void add(iMatrix<vtype,N> * __restrict__ ret,
const iScalar<ltype> * __restrict__ lhs,
const iMatrix<rtype,N> * __restrict__ rhs)
{
for(int c2=0;c2<N;c2++){
for(int c1=0;c1<N;c1++){
if ( c1==c2)
add(&ret->_internal[c1][c2],&lhs->_internal,&rhs->_internal[c1][c2]);
else
ret->_internal[c1][c2]=lhs->_internal[c1][c2];
}}
return;
}
template<class vtype,class ltype,class rtype, int N> strong_inline void add(iMatrix<vtype,N> * __restrict__ ret,
const iMatrix<ltype,N> * __restrict__ lhs,
const iScalar<rtype> * __restrict__ rhs)
{
for(int c2=0;c2<N;c2++){
for(int c1=0;c1<N;c1++){
if ( c1==c2)
add(&ret->_internal[c1][c2],&lhs->_internal[c1][c2],&rhs->_internal);
else
ret->_internal[c1][c2]=lhs->_internal[c1][c2];
}}
return;
}
// + operator for scalar, vector, matrix
template<class ltype,class rtype>
//strong_inline auto operator + (iScalar<ltype>& lhs,iScalar<rtype>&& rhs) -> iScalar<decltype(lhs._internal + rhs._internal)>
strong_inline auto operator + (const iScalar<ltype>& lhs,const iScalar<rtype>& rhs) -> iScalar<decltype(lhs._internal + rhs._internal)>
{
typedef iScalar<decltype(lhs._internal+rhs._internal)> ret_t;
ret_t ret;
add(&ret,&lhs,&rhs);
return ret;
}
template<class ltype,class rtype,int N>
strong_inline auto operator + (const iVector<ltype,N>& lhs,const iVector<rtype,N>& rhs) ->iVector<decltype(lhs._internal[0]+rhs._internal[0]),N>
{
typedef iVector<decltype(lhs._internal[0]+rhs._internal[0]),N> ret_t;
ret_t ret;
add(&ret,&lhs,&rhs);
return ret;
}
template<class ltype,class rtype,int N>
strong_inline auto operator + (const iMatrix<ltype,N>& lhs,const iMatrix<rtype,N>& rhs) ->iMatrix<decltype(lhs._internal[0][0]+rhs._internal[0][0]),N>
{
typedef iMatrix<decltype(lhs._internal[0][0]+rhs._internal[0][0]),N> ret_t;
ret_t ret;
add(&ret,&lhs,&rhs);
return ret;
}
template<class ltype,class rtype,int N>
strong_inline auto operator + (const iScalar<ltype>& lhs,const iMatrix<rtype,N>& rhs)->iMatrix<decltype(lhs._internal+rhs._internal[0][0]),N>
{
typedef iMatrix<decltype(lhs._internal+rhs._internal[0][0]),N> ret_t;
ret_t ret;
add(&ret,&lhs,&rhs);
return ret;
}
template<class ltype,class rtype,int N>
strong_inline auto operator + (const iMatrix<ltype,N>& lhs,const iScalar<rtype>& rhs)->iMatrix<decltype(lhs._internal[0][0]+rhs._internal),N>
{
typedef iMatrix<decltype(lhs._internal[0][0]+rhs._internal),N> ret_t;
ret_t ret;
add(&ret,&lhs,&rhs);
return ret;
}
}
#endif

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#ifndef GRID_MATH_ARITH_MAC_H
#define GRID_MATH_ARITH_MAC_H
namespace Grid {
///////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////// MAC ///////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////
///////////////////////////
// Legal multiplication table
///////////////////////////
// scal x scal = scal
// mat x mat = mat
// mat x scal = mat
// scal x mat = mat
// mat x vec = vec
// vec x scal = vec
// scal x vec = vec
///////////////////////////
template<class rtype,class vtype,class mtype>
strong_inline void mac(iScalar<rtype> * __restrict__ ret,const iScalar<vtype> * __restrict__ lhs,const iScalar<mtype> * __restrict__ rhs)
{
mac(&ret->_internal,&lhs->_internal,&rhs->_internal);
}
template<class rrtype,class ltype,class rtype,int N>
strong_inline void mac(iMatrix<rrtype,N> * __restrict__ ret,const iMatrix<ltype,N> * __restrict__ lhs,const iMatrix<rtype,N> * __restrict__ rhs){
for(int c3=0;c3<N;c3++){
for(int c1=0;c1<N;c1++){
for(int c2=0;c2<N;c2++){
mac(&ret->_internal[c1][c2],&lhs->_internal[c1][c3],&rhs->_internal[c3][c2]);
}}}
return;
}
template<class rrtype,class ltype,class rtype,int N>
strong_inline void mac(iMatrix<rrtype,N> * __restrict__ ret,const iMatrix<ltype,N> * __restrict__ lhs,const iScalar<rtype> * __restrict__ rhs){
for(int c1=0;c1<N;c1++){
for(int c2=0;c2<N;c2++){
mac(&ret->_internal[c1][c2],&lhs->_internal[c1][c2],&rhs->_internal);
}}
return;
}
template<class rrtype,class ltype,class rtype,int N>
strong_inline void mac(iMatrix<rrtype,N> * __restrict__ ret,const iScalar<ltype> * __restrict__ lhs,const iMatrix<rtype,N> * __restrict__ rhs){
for(int c1=0;c1<N;c1++){
for(int c2=0;c2<N;c2++){
mac(&ret->_internal[c1][c2],&lhs->_internal,&rhs->_internal[c1][c2]);
}}
return;
}
template<class rrtype,class ltype,class rtype,int N>
strong_inline void mac(iVector<rrtype,N> * __restrict__ ret,const iMatrix<ltype,N> * __restrict__ lhs,const iVector<rtype,N> * __restrict__ rhs)
{
for(int c1=0;c1<N;c1++){
for(int c2=0;c2<N;c2++){
mac(&ret->_internal[c1],&lhs->_internal[c1][c2],&rhs->_internal[c2]);
}}
return;
}
template<class rrtype,class ltype,class rtype,int N>
strong_inline void mac(iVector<rrtype,N> * __restrict__ ret,const iScalar<ltype> * __restrict__ lhs,const iVector<rtype,N> * __restrict__ rhs)
{
for(int c1=0;c1<N;c1++){
mac(&ret->_internal[c1],&lhs->_internal,&rhs->_internal[c1]);
}
return;
}
template<class rrtype,class ltype,class rtype,int N>
strong_inline void mac(iVector<rrtype,N> * __restrict__ ret,const iVector<ltype,N> * __restrict__ lhs,const iScalar<rtype> * __restrict__ rhs)
{
for(int c1=0;c1<N;c1++){
mac(&ret->_internal[c1],&lhs->_internal[c1],&rhs->_internal);
}
return;
}
}
#endif

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#ifndef GRID_MATH_ARITH_MUL_H
#define GRID_MATH_ARITH_MUL_H
namespace Grid {
///////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////// MUL ///////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////
template<class rtype,class vtype,class mtype>
strong_inline void mult(iScalar<rtype> * __restrict__ ret,const iScalar<mtype> * __restrict__ lhs,const iScalar<vtype> * __restrict__ rhs){
mult(&ret->_internal,&lhs->_internal,&rhs->_internal);
}
template<class rrtype,class ltype,class rtype,int N>
strong_inline void mult(iMatrix<rrtype,N> * __restrict__ ret,const iMatrix<ltype,N> * __restrict__ lhs,const iMatrix<rtype,N> * __restrict__ rhs){
for(int c1=0;c1<N;c1++){
for(int c2=0;c2<N;c2++){
mult(&ret->_internal[c1][c2],&lhs->_internal[c1][0],&rhs->_internal[0][c2]);
}
}
for(int c1=0;c1<N;c1++){
for(int c3=1;c3<N;c3++){
for(int c2=0;c2<N;c2++){
mac(&ret->_internal[c1][c2],&lhs->_internal[c1][c3],&rhs->_internal[c3][c2]);
}
}
}
return;
}
template<class rrtype,class ltype,class rtype,int N>
strong_inline void mult(iMatrix<rrtype,N> * __restrict__ ret,const iMatrix<ltype,N> * __restrict__ lhs,const iScalar<rtype> * __restrict__ rhs){
for(int c2=0;c2<N;c2++){
for(int c1=0;c1<N;c1++){
mult(&ret->_internal[c1][c2],&lhs->_internal[c1][c2],&rhs->_internal);
}}
return;
}
template<class rrtype,class ltype,class rtype, int N>
strong_inline void mult(iMatrix<rrtype,N> * __restrict__ ret,const iScalar<ltype> * __restrict__ lhs,const iMatrix<rtype,N> * __restrict__ rhs){
for(int c2=0;c2<N;c2++){
for(int c1=0;c1<N;c1++){
mult(&ret->_internal[c1][c2],&lhs->_internal,&rhs->_internal[c1][c2]);
}}
return;
}
// Matrix left multiplies vector
template<class rtype,class vtype,class mtype,int N>
strong_inline void mult(iVector<rtype,N> * __restrict__ ret,const iMatrix<mtype,N> * __restrict__ lhs,const iVector<vtype,N> * __restrict__ rhs)
{
for(int c1=0;c1<N;c1++){
mult(&ret->_internal[c1],&lhs->_internal[c1][0],&rhs->_internal[0]);
for(int c2=1;c2<N;c2++){
mac(&ret->_internal[c1],&lhs->_internal[c1][c2],&rhs->_internal[c2]);
}
}
return;
}
template<class rtype,class vtype,class mtype,int N>
strong_inline void mult(iVector<rtype,N> * __restrict__ ret,
const iScalar<mtype> * __restrict__ lhs,
const iVector<vtype,N> * __restrict__ rhs){
for(int c1=0;c1<N;c1++){
mult(&ret->_internal[c1],&lhs->_internal,&rhs->_internal[c1]);
}
}
template<class rtype,class vtype,class mtype,int N>
strong_inline void mult(iVector<rtype,N> * __restrict__ ret,
const iVector<vtype,N> * __restrict__ rhs,
const iScalar<mtype> * __restrict__ lhs){
mult(ret,lhs,rhs);
}
template<class rtype,class vtype,class mtype,int N> strong_inline
iVector<rtype,N> operator * (const iMatrix<mtype,N>& lhs,const iVector<vtype,N>& rhs)
{
iVector<rtype,N> ret;
mult(&ret,&lhs,&rhs);
return ret;
}
template<class rtype,class vtype,class mtype,int N> strong_inline
iVector<rtype,N> operator * (const iScalar<mtype>& lhs,const iVector<vtype,N>& rhs)
{
iVector<rtype,N> ret;
mult(&ret,&lhs,&rhs);
return ret;
}
template<class rtype,class vtype,class mtype,int N> strong_inline
iVector<rtype,N> operator * (const iVector<mtype,N>& lhs,const iScalar<vtype>& rhs)
{
iVector<rtype,N> ret;
mult(&ret,&lhs,&rhs);
return ret;
}
//////////////////////////////////////////////////////////////////
// Glue operators to mult routines. Must resolve return type cleverly from typeof(internal)
// since nesting matrix<scalar> x matrix<matrix>-> matrix<matrix>
// while matrix<scalar> x matrix<scalar>-> matrix<scalar>
// so return type depends on argument types in nasty way.
//////////////////////////////////////////////////////////////////
// scal x scal = scal
// mat x mat = mat
// mat x scal = mat
// scal x mat = mat
// mat x vec = vec
// vec x scal = vec
// scal x vec = vec
//
// We can special case scalar_type ??
template<class l,class r>
strong_inline auto operator * (const iScalar<l>& lhs,const iScalar<r>& rhs) -> iScalar<decltype(lhs._internal * rhs._internal)>
{
typedef iScalar<decltype(lhs._internal*rhs._internal)> ret_t;
ret_t ret;
mult(&ret,&lhs,&rhs);
return ret;
}
template<class l,class r,int N> strong_inline
auto operator * (const iMatrix<l,N>& lhs,const iMatrix<r,N>& rhs) -> iMatrix<decltype(lhs._internal[0][0]*rhs._internal[0][0]),N>
{
typedef decltype(lhs._internal[0][0]*rhs._internal[0][0]) ret_t;
iMatrix<ret_t,N> ret;
mult(&ret,&lhs,&rhs);
return ret;
}
template<class l,class r, int N> strong_inline
auto operator * (const iMatrix<r,N>& lhs,const iScalar<l>& rhs) -> iMatrix<decltype(lhs._internal[0][0]*rhs._internal),N>
{
typedef decltype(lhs._internal[0][0]*rhs._internal) ret_t;
iMatrix<ret_t,N> ret;
for(int c1=0;c1<N;c1++){
for(int c2=0;c2<N;c2++){
mult(&ret._internal[c1][c2],&lhs._internal[c1][c2],&rhs._internal);
}}
return ret;
}
template<class l,class r,int N> strong_inline
auto operator * (const iScalar<l>& lhs,const iMatrix<r,N>& rhs) -> iMatrix<decltype(lhs._internal*rhs._internal[0][0]),N>
{
typedef decltype(lhs._internal*rhs._internal[0][0]) ret_t;
iMatrix<ret_t,N> ret;
for(int c1=0;c1<N;c1++){
for(int c2=0;c2<N;c2++){
mult(&ret._internal[c1][c2],&lhs._internal,&rhs._internal[c1][c2]);
}}
return ret;
}
template<class l,class r,int N> strong_inline
auto operator * (const iMatrix<l,N>& lhs,const iVector<r,N>& rhs) -> iVector<decltype(lhs._internal[0][0]*rhs._internal[0]),N>
{
typedef decltype(lhs._internal[0][0]*rhs._internal[0]) ret_t;
iVector<ret_t,N> ret;
for(int c1=0;c1<N;c1++){
mult(&ret._internal[c1],&lhs._internal[c1][0],&rhs._internal[0]);
for(int c2=1;c2<N;c2++){
mac(&ret._internal[c1],&lhs._internal[c1][c2],&rhs._internal[c2]);
}
}
return ret;
}
template<class l,class r,int N> strong_inline
auto operator * (const iScalar<l>& lhs,const iVector<r,N>& rhs) -> iVector<decltype(lhs._internal*rhs._internal[0]),N>
{
typedef decltype(lhs._internal*rhs._internal[0]) ret_t;
iVector<ret_t,N> ret;
for(int c1=0;c1<N;c1++){
mult(&ret._internal[c1],&lhs._internal,&rhs._internal[c1]);
}
return ret;
}
template<class l,class r,int N> strong_inline
auto operator * (const iVector<l,N>& lhs,const iScalar<r>& rhs) -> iVector<decltype(lhs._internal[0]*rhs._internal),N>
{
typedef decltype(lhs._internal[0]*rhs._internal) ret_t;
iVector<ret_t,N> ret;
for(int c1=0;c1<N;c1++){
mult(&ret._internal[c1],&lhs._internal[c1],&rhs._internal);
}
return ret;
}
}
#endif

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#ifndef GRID_MATH_ARITH_SCALAR_H
#define GRID_MATH_ARITH_SCALAR_H
namespace Grid {
//////////////////////////////////////////////////////////////////////////////////////////
// Must support native C++ types Integer, Complex, Real
//////////////////////////////////////////////////////////////////////////////////////////
// multiplication by fundamental scalar type
template<class l,int N> strong_inline iScalar<l> operator * (const iScalar<l>& lhs,const typename iScalar<l>::scalar_type rhs)
{
typename iScalar<l>::tensor_reduced srhs; srhs=rhs;
return lhs*srhs;
}
template<class l,int N> strong_inline iScalar<l> operator * (const typename iScalar<l>::scalar_type lhs,const iScalar<l>& rhs) { return rhs*lhs; }
template<class l,int N> strong_inline iVector<l,N> operator * (const iVector<l,N>& lhs,const typename iScalar<l>::scalar_type rhs)
{
typename iVector<l,N>::tensor_reduced srhs; srhs=rhs;
return lhs*srhs;
}
template<class l,int N> strong_inline iVector<l,N> operator * (const typename iScalar<l>::scalar_type lhs,const iVector<l,N>& rhs) { return rhs*lhs; }
template<class l,int N> strong_inline iMatrix<l,N> operator * (const iMatrix<l,N>& lhs,const typename iScalar<l>::scalar_type &rhs)
{
typename iMatrix<l,N>::tensor_reduced srhs; srhs=rhs;
return lhs*srhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator * (const typename iScalar<l>::scalar_type & lhs,const iMatrix<l,N>& rhs) { return rhs*lhs; }
////////////////////////////////////////////////////////////////////
// Double support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> strong_inline iScalar<l> operator * (const iScalar<l>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t; t=rhs;
typename iScalar<l>::tensor_reduced srhs;srhs=t;
return lhs*srhs;
}
template<class l> strong_inline iScalar<l> operator * (double lhs,const iScalar<l>& rhs) { return rhs*lhs; }
template<class l,int N> strong_inline iVector<l,N> operator * (const iVector<l,N>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t;t=rhs;
typename iScalar<l>::tensor_reduced srhs;srhs=t;
return lhs*srhs;
}
template<class l,int N> strong_inline iVector<l,N> operator * (double lhs,const iVector<l,N>& rhs) { return rhs*lhs; }
template<class l,int N> strong_inline iMatrix<l,N> operator * (const iMatrix<l,N>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t;t=rhs;
typename iScalar<l>::tensor_reduced srhs;srhs=t;
return lhs*srhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator * (double lhs,const iMatrix<l,N>& rhs) { return rhs*lhs; }
////////////////////////////////////////////////////////////////////
// Complex support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> strong_inline iScalar<l> operator * (const iScalar<l>& lhs,ComplexD rhs)
{
typename iScalar<l>::scalar_type t;t=rhs;
typename iScalar<l>::tensor_reduced srhs;srhs=t;
return lhs*srhs;
}
template<class l> strong_inline iScalar<l> operator * (ComplexD lhs,const iScalar<l>& rhs) { return rhs*lhs; }
template<class l,int N> strong_inline iVector<l,N> operator * (const iVector<l,N>& lhs,ComplexD rhs)
{
typename iScalar<l>::scalar_type t;t=rhs;
typename iScalar<l>::tensor_reduced srhs;srhs=t;
return lhs*srhs;
}
template<class l,int N> strong_inline iVector<l,N> operator * (ComplexD lhs,const iVector<l,N>& rhs) { return rhs*lhs; }
template<class l,int N> strong_inline iMatrix<l,N> operator * (const iMatrix<l,N>& lhs,ComplexD rhs)
{
typename iScalar<l>::scalar_type t;t=rhs;
typename iScalar<l>::tensor_reduced srhs;srhs=t;
return lhs*srhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator * (ComplexD lhs,const iMatrix<l,N>& rhs) { return rhs*lhs; }
////////////////////////////////////////////////////////////////////
// Integer support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> strong_inline iScalar<l> operator * (const iScalar<l>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t; t=rhs;
typename iScalar<l>::tensor_reduced srhs; srhs=t;
return lhs*srhs;
}
template<class l> strong_inline iScalar<l> operator * (Integer lhs,const iScalar<l>& rhs) { return rhs*lhs; }
template<class l,int N> strong_inline iVector<l,N> operator * (const iVector<l,N>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t;t=rhs;
typename iScalar<l>::tensor_reduced srhs;srhs=t;
return lhs*srhs;
}
template<class l,int N> strong_inline iVector<l,N> operator * (Integer lhs,const iVector<l,N>& rhs) { return rhs*lhs; }
template<class l,int N> strong_inline iMatrix<l,N> operator * (const iMatrix<l,N>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t;t=rhs;
typename iScalar<l>::tensor_reduced srhs;srhs=t;
return lhs*srhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator * (Integer lhs,const iMatrix<l,N>& rhs) { return rhs*lhs; }
///////////////////////////////////////////////////////////////////////////////////////////////
// addition by fundamental scalar type applies to matrix(down diag) and scalar
///////////////////////////////////////////////////////////////////////////////////////////////
template<class l,int N> strong_inline iScalar<l> operator + (const iScalar<l>& lhs,const typename iScalar<l>::scalar_type rhs)
{
typename iScalar<l>::tensor_reduced srhs; srhs=rhs;
return lhs+srhs;
}
template<class l,int N> strong_inline iScalar<l> operator + (const typename iScalar<l>::scalar_type lhs,const iScalar<l>& rhs) { return rhs+lhs; }
template<class l,int N> strong_inline iMatrix<l,N> operator + (const iMatrix<l,N>& lhs,const typename iScalar<l>::scalar_type rhs)
{
typename iMatrix<l,N>::tensor_reduced srhs; srhs=rhs;
return lhs+srhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator + (const typename iScalar<l>::scalar_type lhs,const iMatrix<l,N>& rhs) { return rhs+lhs; }
////////////////////////////////////////////////////////////////////
// Double support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> strong_inline iScalar<l> operator + (const iScalar<l>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t; t=rhs;
typename iScalar<l>::tensor_reduced srhs; srhs=t;
return lhs+srhs;
}
template<class l> strong_inline iScalar<l> operator + (double lhs,const iScalar<l>& rhs) { return rhs+lhs; }
template<class l,int N> strong_inline iMatrix<l,N> operator + (const iMatrix<l,N>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t;t=rhs;
typename iScalar<l>::tensor_reduced srhs;srhs=t;
return lhs+srhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator + (double lhs,const iMatrix<l,N>& rhs) { return rhs+lhs; }
// Integer support cast to scalar type through constructor
template<class l> strong_inline iScalar<l> operator + (const iScalar<l>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t; t=rhs;
typename iScalar<l>::tensor_reduced srhs; srhs=t;
return lhs+srhs;
}
template<class l> strong_inline iScalar<l> operator + (Integer lhs,const iScalar<l>& rhs) { return rhs+lhs; }
template<class l,int N> strong_inline iMatrix<l,N> operator + (const iMatrix<l,N>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t;t=rhs;
typename iScalar<l>::tensor_reduced srhs;srhs=t;
return lhs+srhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator + (Integer lhs,const iMatrix<l,N>& rhs) { return rhs+lhs; }
///////////////////////////////////////////////////////////////////////////////////////////////
// subtraction of fundamental scalar type applies to matrix(down diag) and scalar
///////////////////////////////////////////////////////////////////////////////////////////////
template<class l,int N> strong_inline iScalar<l> operator - (const iScalar<l>& lhs,const typename iScalar<l>::scalar_type rhs)
{
typename iScalar<l>::tensor_reduced srhs; srhs=rhs;
return lhs-srhs;
}
template<class l,int N> strong_inline iScalar<l> operator - (const typename iScalar<l>::scalar_type lhs,const iScalar<l>& rhs)
{
typename iScalar<l>::tensor_reduced slhs;slhs=lhs;
return slhs-rhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator - (const iMatrix<l,N>& lhs,const typename iScalar<l>::scalar_type rhs)
{
typename iScalar<l>::tensor_reduced srhs; srhs=rhs;
return lhs-srhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator - (const typename iScalar<l>::scalar_type lhs,const iMatrix<l,N>& rhs)
{
typename iScalar<l>::tensor_reduced slhs;slhs=lhs;
return slhs-rhs;
}
////////////////////////////////////////////////////////////////////
// Double support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> strong_inline iScalar<l> operator - (const iScalar<l>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t; t=rhs;
typename iScalar<l>::tensor_reduced srhs; srhs=t;
return lhs-srhs;
}
template<class l> strong_inline iScalar<l> operator - (double lhs,const iScalar<l>& rhs)
{
typename iScalar<l>::scalar_type t(lhs);
typename iScalar<l>::tensor_reduced slhs;slhs=t;
return slhs-rhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator - (const iMatrix<l,N>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t;t=rhs;
typename iScalar<l>::tensor_reduced srhs;srhs=t;
return lhs-srhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator - (double lhs,const iMatrix<l,N>& rhs)
{
typename iScalar<l>::scalar_type t(lhs);
typename iScalar<l>::tensor_reduced slhs;slhs=t;
return slhs-rhs;
}
////////////////////////////////////////////////////////////////////
// Integer support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> strong_inline iScalar<l> operator - (const iScalar<l>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t; t=rhs;
typename iScalar<l>::tensor_reduced srhs; srhs=t;
return lhs-srhs;
}
template<class l> strong_inline iScalar<l> operator - (Integer lhs,const iScalar<l>& rhs)
{
typename iScalar<l>::scalar_type t;t=lhs;
typename iScalar<l>::tensor_reduced slhs;slhs=t;
return slhs-rhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator - (const iMatrix<l,N>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t;t=rhs;
typename iScalar<l>::tensor_reduced srhs;srhs=t;
return lhs-srhs;
}
template<class l,int N> strong_inline iMatrix<l,N> operator - (Integer lhs,const iMatrix<l,N>& rhs)
{
typename iScalar<l>::scalar_type t;t=lhs;
typename iScalar<l>::tensor_reduced slhs;slhs=t;
return slhs-rhs;
}
}
#endif

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#ifndef GRID_MATH_ARITH_SUB_H
#define GRID_MATH_ARITH_SUB_H
namespace Grid {
///////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////// SUB ///////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////
// SUB is simple for now; cannot mix types and straightforward template
// Scalar +/- Scalar
// Vector +/- Vector
// Matrix +/- Matrix
// Matrix /- scalar
template<class vtype,class ltype,class rtype> strong_inline void sub(iScalar<vtype> * __restrict__ ret,
const iScalar<ltype> * __restrict__ lhs,
const iScalar<rtype> * __restrict__ rhs)
{
sub(&ret->_internal,&lhs->_internal,&rhs->_internal);
}
template<class vtype,class ltype,class rtype,int N> strong_inline void sub(iVector<vtype,N> * __restrict__ ret,
const iVector<ltype,N> * __restrict__ lhs,
const iVector<rtype,N> * __restrict__ rhs)
{
for(int c=0;c<N;c++){
ret->_internal[c]=lhs->_internal[c]-rhs->_internal[c];
}
return;
}
template<class vtype,class ltype,class rtype, int N> strong_inline void sub(iMatrix<vtype,N> * __restrict__ ret,
const iMatrix<ltype,N> * __restrict__ lhs,
const iMatrix<rtype,N> * __restrict__ rhs){
for(int c2=0;c2<N;c2++){
for(int c1=0;c1<N;c1++){
sub(&ret->_internal[c1][c2],&lhs->_internal[c1][c2],&rhs->_internal[c1][c2]);
}}
return;
}
template<class vtype,class ltype,class rtype, int N> strong_inline void sub(iMatrix<vtype,N> * __restrict__ ret,
const iScalar<ltype> * __restrict__ lhs,
const iMatrix<rtype,N> * __restrict__ rhs){
for(int c2=0;c2<N;c2++){
for(int c1=0;c1<N;c1++){
if ( c1==c2) {
sub(&ret->_internal[c1][c2],&lhs->_internal,&rhs->_internal[c1][c2]);
} else {
// Fails -- need unary minus. Catalogue other unops?
ret->_internal[c1][c2]=zero;
ret->_internal[c1][c2]=ret->_internal[c1][c2]-rhs->_internal[c1][c2];
}
}}
return;
}
template<class vtype,class ltype,class rtype, int N> strong_inline void sub(iMatrix<vtype,N> * __restrict__ ret,
const iMatrix<ltype,N> * __restrict__ lhs,
const iScalar<rtype> * __restrict__ rhs){
for(int c2=0;c2<N;c2++){
for(int c1=0;c1<N;c1++){
if ( c1==c2)
sub(&ret->_internal[c1][c2],&lhs->_internal[c1][c2],&rhs->_internal);
else
ret->_internal[c1][c2]=lhs->_internal[c1][c2];
}}
return;
}
// - operator for scalar, vector, matrix
template<class ltype,class rtype> strong_inline auto
operator - (const iScalar<ltype>& lhs, const iScalar<rtype>& rhs) -> iScalar<decltype(lhs._internal - rhs._internal)>
{
typedef iScalar<decltype(lhs._internal-rhs._internal)> ret_t;
ret_t ret;
sub(&ret,&lhs,&rhs);
return ret;
}
template<class ltype,class rtype,int N>
strong_inline auto operator - (const iVector<ltype,N>& lhs,const iVector<rtype,N>& rhs) ->iVector<decltype(lhs._internal[0]-rhs._internal[0]),N>
{
typedef iVector<decltype(lhs._internal[0]-rhs._internal[0]),N> ret_t;
ret_t ret;
sub(&ret,&lhs,&rhs);
return ret;
}
template<class ltype,class rtype,int N>
strong_inline auto operator - (const iMatrix<ltype,N>& lhs,const iMatrix<rtype,N>& rhs) ->iMatrix<decltype(lhs._internal[0][0]-rhs._internal[0][0]),N>
{
typedef iMatrix<decltype(lhs._internal[0][0]-rhs._internal[0][0]),N> ret_t;
ret_t ret;
sub(&ret,&lhs,&rhs);
return ret;
}
template<class ltype,class rtype,int N>
strong_inline auto operator - (const iScalar<ltype>& lhs,const iMatrix<rtype,N>& rhs)->iMatrix<decltype(lhs._internal-rhs._internal[0][0]),N>
{
typedef iMatrix<decltype(lhs._internal-rhs._internal[0][0]),N> ret_t;
ret_t ret;
sub(&ret,&lhs,&rhs);
return ret;
}
template<class ltype,class rtype,int N>
strong_inline auto operator - (const iMatrix<ltype,N>& lhs,const iScalar<rtype>& rhs)->iMatrix<decltype(lhs._internal[0][0]-rhs._internal),N>
{
typedef iMatrix<decltype(lhs._internal[0][0]-rhs._internal),N> ret_t;
ret_t ret;
sub(&ret,&lhs,&rhs);
return ret;
}
}
#endif

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#ifndef GRID_MATH_TENSORS_H
#define GRID_MATH_TENSORS_H
namespace Grid {
///////////////////////////////////////////////////
// Scalar, Vector, Matrix objects.
// These can be composed to form tensor products of internal indices.
///////////////////////////////////////////////////
// It is useful to NOT have any constructors
// so that these classes assert "is_pod<class> == true"
// because then the standard C++ valarray container eliminates fill overhead on new allocation and
// non-move copying.
//
// However note that doing this eliminates some syntactical sugar such as
// calling the constructor explicitly or implicitly
//
class GridTensorBase {};
template<class vtype> class iScalar
{
public:
vtype _internal;
typedef typename GridTypeMapper<vtype>::scalar_type scalar_type;
typedef typename GridTypeMapper<vtype>::vector_type vector_type;
typedef typename GridTypeMapper<vtype>::tensor_reduced tensor_reduced_v;
typedef iScalar<tensor_reduced_v> tensor_reduced;
typedef typename GridTypeMapper<vtype>::scalar_object recurse_scalar_object;
typedef iScalar<recurse_scalar_object> scalar_object;
enum { TensorLevel = GridTypeMapper<vtype>::TensorLevel + 1};
// Scalar no action
// template<int Level> using tensor_reduce_level = typename iScalar<GridTypeMapper<vtype>::tensor_reduce_level<Level> >;
iScalar() = default;
/*
iScalar(const iScalar<vtype> &copyme)=default;
iScalar(iScalar<vtype> &&copyme)=default;
iScalar<vtype> & operator= (const iScalar<vtype> &copyme) = default;
iScalar<vtype> & operator= (iScalar<vtype> &&copyme) = default;
*/
iScalar(scalar_type s) : _internal(s) {};// recurse down and hit the constructor for vector_type
iScalar(const Zero &z){ *this = zero; };
iScalar<vtype> & operator= (const Zero &hero){
zeroit(*this);
return *this;
}
friend strong_inline void vstream(iScalar<vtype> &out,const iScalar<vtype> &in){
vstream(out._internal,in._internal);
}
friend strong_inline void zeroit(iScalar<vtype> &that){
zeroit(that._internal);
}
friend strong_inline void prefetch(iScalar<vtype> &that){
prefetch(that._internal);
}
friend strong_inline void permute(iScalar<vtype> &out,const iScalar<vtype> &in,int permutetype){
permute(out._internal,in._internal,permutetype);
}
// Unary negation
friend strong_inline iScalar<vtype> operator -(const iScalar<vtype> &r) {
iScalar<vtype> ret;
ret._internal= -r._internal;
return ret;
}
// *=,+=,-= operators inherit from corresponding "*,-,+" behaviour
strong_inline iScalar<vtype> &operator *=(const iScalar<vtype> &r) {
*this = (*this)*r;
return *this;
}
strong_inline iScalar<vtype> &operator -=(const iScalar<vtype> &r) {
*this = (*this)-r;
return *this;
}
strong_inline iScalar<vtype> &operator +=(const iScalar<vtype> &r) {
*this = (*this)+r;
return *this;
}
strong_inline vtype & operator ()(void) {
return _internal;
}
strong_inline const vtype & operator ()(void) const {
return _internal;
}
operator ComplexD () const { return(TensorRemove(_internal)); };
operator RealD () const { return(real(TensorRemove(_internal))); }
// convert from a something to a scalar
template<class T,typename std::enable_if<!isGridTensor<T>::value, T>::type* = nullptr > strong_inline auto operator = (T arg) -> iScalar<vtype>
{
_internal = vtype(arg);
return *this;
}
friend std::ostream& operator<< (std::ostream& stream, const iScalar<vtype> &o){
stream<< "S {"<<o._internal<<"}";
return stream;
};
};
///////////////////////////////////////////////////////////
// Allows to turn scalar<scalar<scalar<double>>>> back to double.
///////////////////////////////////////////////////////////
template<class T> strong_inline typename std::enable_if<!isGridTensor<T>::value, T>::type TensorRemove(T arg) { return arg;}
template<class vtype> strong_inline auto TensorRemove(iScalar<vtype> arg) -> decltype(TensorRemove(arg._internal))
{
return TensorRemove(arg._internal);
}
template<class vtype,int N> class iVector
{
public:
vtype _internal[N];
typedef typename GridTypeMapper<vtype>::scalar_type scalar_type;
typedef typename GridTypeMapper<vtype>::vector_type vector_type;
typedef typename GridTypeMapper<vtype>::tensor_reduced tensor_reduced_v;
typedef typename GridTypeMapper<vtype>::scalar_object recurse_scalar_object;
typedef iScalar<tensor_reduced_v> tensor_reduced;
typedef iVector<recurse_scalar_object,N> scalar_object;
enum { TensorLevel = GridTypeMapper<vtype>::TensorLevel + 1};
iVector(const Zero &z){ *this = zero; };
iVector() =default;
/*
iVector(const iVector<vtype,N> &copyme)=default;
iVector(iVector<vtype,N> &&copyme)=default;
iVector<vtype,N> & operator= (const iVector<vtype,N> &copyme) = default;
iVector<vtype,N> & operator= (iVector<vtype,N> &&copyme) = default;
*/
iVector<vtype,N> & operator= (const Zero &hero){
zeroit(*this);
return *this;
}
friend strong_inline void zeroit(iVector<vtype,N> &that){
for(int i=0;i<N;i++){
zeroit(that._internal[i]);
}
}
friend strong_inline void prefetch(iVector<vtype,N> &that){
for(int i=0;i<N;i++) prefetch(that._internal[i]);
}
friend strong_inline void vstream(iVector<vtype,N> &out,const iVector<vtype,N> &in){
for(int i=0;i<N;i++){
vstream(out._internal[i],in._internal[i]);
}
}
friend strong_inline void permute(iVector<vtype,N> &out,const iVector<vtype,N> &in,int permutetype){
for(int i=0;i<N;i++){
permute(out._internal[i],in._internal[i],permutetype);
}
}
// Unary negation
friend strong_inline iVector<vtype,N> operator -(const iVector<vtype,N> &r) {
iVector<vtype,N> ret;
for(int i=0;i<N;i++) ret._internal[i]= -r._internal[i];
return ret;
}
// *=,+=,-= operators inherit from corresponding "*,-,+" behaviour
strong_inline iVector<vtype,N> &operator *=(const iScalar<vtype> &r) {
*this = (*this)*r;
return *this;
}
strong_inline iVector<vtype,N> &operator -=(const iVector<vtype,N> &r) {
*this = (*this)-r;
return *this;
}
strong_inline iVector<vtype,N> &operator +=(const iVector<vtype,N> &r) {
*this = (*this)+r;
return *this;
}
strong_inline vtype & operator ()(int i) {
return _internal[i];
}
strong_inline const vtype & operator ()(int i) const {
return _internal[i];
}
friend std::ostream& operator<< (std::ostream& stream, const iVector<vtype,N> &o){
stream<< "V<"<<N<<">{";
for(int i=0;i<N;i++) {
stream<<o._internal[i];
if (i<N-1) stream<<",";
}
stream<<"}";
return stream;
};
// strong_inline vtype && operator ()(int i) {
// return _internal[i];
// }
};
template<class vtype,int N> class iMatrix
{
public:
vtype _internal[N][N];
typedef typename GridTypeMapper<vtype>::scalar_type scalar_type;
typedef typename GridTypeMapper<vtype>::vector_type vector_type;
typedef typename GridTypeMapper<vtype>::tensor_reduced tensor_reduced_v;
typedef typename GridTypeMapper<vtype>::scalar_object recurse_scalar_object;
typedef iScalar<tensor_reduced_v> tensor_reduced;
typedef iMatrix<recurse_scalar_object,N> scalar_object;
enum { TensorLevel = GridTypeMapper<vtype>::TensorLevel + 1};
iMatrix(const Zero &z){ *this = zero; };
iMatrix() =default;
iMatrix& operator=(const iMatrix& rhs){
for(int i=0;i<N;i++)
for(int j=0;j<N;j++)
vstream(_internal[i][j],rhs._internal[i][j]);
return *this;
};
iMatrix(scalar_type s) { (*this) = s ;};// recurse down and hit the constructor for vector_type
/*
iMatrix(const iMatrix<vtype,N> &copyme)=default;
iMatrix(iMatrix<vtype,N> &&copyme)=default;
iMatrix<vtype,N> & operator= (const iMatrix<vtype,N> &copyme) = default;
iMatrix<vtype,N> & operator= (iMatrix<vtype,N> &&copyme) = default;
*/
iMatrix<vtype,N> & operator= (const Zero &hero){
zeroit(*this);
return *this;
}
template<class T,typename std::enable_if<!isGridTensor<T>::value, T>::type* = nullptr > strong_inline auto operator = (T arg) -> iMatrix<vtype,N>
{
zeroit(*this);
for(int i=0;i<N;i++)
_internal[i][i] = arg;
return *this;
}
friend strong_inline void zeroit(iMatrix<vtype,N> &that){
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
zeroit(that._internal[i][j]);
}}
}
friend strong_inline void prefetch(iMatrix<vtype,N> &that){
for(int i=0;i<N;i++)
for(int j=0;j<N;j++)
prefetch(that._internal[i][j]);
}
friend strong_inline void vstream(iMatrix<vtype,N> &out,const iMatrix<vtype,N> &in){
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
vstream(out._internal[i][j],in._internal[i][j]);
}}
}
friend strong_inline void permute(iMatrix<vtype,N> &out,const iMatrix<vtype,N> &in,int permutetype){
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
permute(out._internal[i][j],in._internal[i][j],permutetype);
}}
}
// Unary negation
friend strong_inline iMatrix<vtype,N> operator -(const iMatrix<vtype,N> &r) {
iMatrix<vtype,N> ret;
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
ret._internal[i][j]= -r._internal[i][j];
}}
return ret;
}
// *=,+=,-= operators inherit from corresponding "*,-,+" behaviour
template<class T>
strong_inline iMatrix<vtype,N> &operator *=(const T &r) {
*this = (*this)*r;
return *this;
}
template<class T>
strong_inline iMatrix<vtype,N> &operator -=(const T &r) {
*this = (*this)-r;
return *this;
}
template<class T>
strong_inline iMatrix<vtype,N> &operator +=(const T &r) {
*this = (*this)+r;
return *this;
}
// returns an lvalue reference
strong_inline vtype & operator ()(int i,int j) {
return _internal[i][j];
}
strong_inline const vtype & operator ()(int i,int j) const {
return _internal[i][j];
}
friend std::ostream& operator<< (std::ostream& stream, const iMatrix<vtype,N> &o){
stream<< "M<"<<N<<">{";
for(int i=0;i<N;i++) {
stream<< "{";
for(int j=0;j<N;j++) {
stream<<o._internal[i][j];
if (i<N-1) stream<<",";
}
stream<<"}\n\t\t";
}
stream<<"}";
return stream;
};
// strong_inline vtype && operator ()(int i,int j) {
// return _internal[i][j];
// }
};
template<class v> void vprefetch(const iScalar<v> &vv)
{
vprefetch(vv._internal);
}
template<class v,int N> void vprefetch(const iVector<v,N> &vv)
{
for(int i=0;i<N;i++){
vprefetch(vv._internal[i]);
}
}
template<class v,int N> void vprefetch(const iMatrix<v,N> &vv)
{
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
vprefetch(vv._internal[i][j]);
}}
}
}
#endif

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#ifndef GRID_EXTRACT_H
#define GRID_EXTRACT_H
/////////////////////////////////////////////////////////////////
// Generic extract/merge/permute
/////////////////////////////////////////////////////////////////
namespace Grid{
////////////////////////////////////////////////////////////////////////////////////////////////
// Extract/merge a fundamental vector type, to pointer array with offset
////////////////////////////////////////////////////////////////////////////////////////////////
template<class vsimd,class scalar>
inline void extract(typename std::enable_if<!isGridTensor<vsimd>::value, const vsimd >::type * y,
std::vector<scalar *> &extracted,int offset){
// FIXME: bounce off memory is painful
int Nextr=extracted.size();
int Nsimd=vsimd::Nsimd();
int s=Nsimd/Nextr;
scalar*buf = (scalar *)y;
for(int i=0;i<Nextr;i++){
extracted[i][offset] = buf[i*s];
}
};
////////////////////////////////////////////////////////////////////////
// Merge simd vector from array of scalars to pointer array with offset
////////////////////////////////////////////////////////////////////////
template<class vsimd,class scalar>
inline void merge(typename std::enable_if<!isGridTensor<vsimd>::value, vsimd >::type * y,
std::vector<scalar *> &extracted,int offset){
int Nextr=extracted.size();
int Nsimd=vsimd::Nsimd();
int s=Nsimd/Nextr;
scalar *buf =(scalar *) y;
for(int i=0;i<Nextr;i++){
for(int ii=0;ii<s;ii++){
buf[i*s+ii]=extracted[i][offset];
}
}
};
////////////////////////////////////////////////////////////////////////////////////////////////
// Extract a fundamental vector type to scalar array
////////////////////////////////////////////////////////////////////////////////////////////////
template<class vsimd,class scalar>
inline void extract(typename std::enable_if<!isGridTensor<vsimd>::value, const vsimd >::type &y,std::vector<scalar> &extracted){
int Nextr=extracted.size();
int Nsimd=vsimd::Nsimd();
int s=Nsimd/Nextr;
scalar *buf = (scalar *)&y;
for(int i=0;i<Nextr;i++){
for(int ii=0;ii<s;ii++){
extracted[i]=buf[i*s+ii];
}
}
};
////////////////////////////////////////////////////////////////////////
// Merge simd vector from array of scalars
////////////////////////////////////////////////////////////////////////
template<class vsimd,class scalar>
inline void merge(typename std::enable_if<!isGridTensor<vsimd>::value, vsimd >::type &y,std::vector<scalar> &extracted){
int Nextr=extracted.size();
int Nsimd=vsimd::Nsimd();
int s=Nsimd/Nextr;
scalar *buf = (scalar *)&y;
for(int i=0;i<Nextr;i++){
for(int ii=0;ii<s;ii++){
buf[i*s+ii]=extracted[i];
}
}
};
template<class vsimd,class scalar>
inline void AmergeA(typename std::enable_if<!isGridTensor<vsimd>::value, vsimd >::type &y,std::vector<scalar> &extracted){
int Nextr=extracted.size();
int Nsimd=vsimd::Nsimd();
int s=Nsimd/Nextr;
scalar *buf = (scalar *)&y;
for(int i=0;i<Nextr;i++){
for(int ii=0;ii<s;ii++){
buf[i*s+ii]=extracted[i];
}
}
};
////////////////////////////////////////////////////////////////////////
// Extract to contiguous array scalar object
////////////////////////////////////////////////////////////////////////
template<class vobj> inline void extract(const vobj &vec,std::vector<typename vobj::scalar_object> &extracted)
{
typedef typename vobj::scalar_type scalar_type ;
typedef typename vobj::vector_type vector_type ;
const int Nsimd=vobj::vector_type::Nsimd();
const int words=sizeof(vobj)/sizeof(vector_type);
extracted.resize(Nsimd);
std::vector<scalar_type *> pointers(Nsimd);
for(int i=0;i<Nsimd;i++)
pointers[i] =(scalar_type *)& extracted[i];
vector_type *vp = (vector_type *)&vec;
for(int w=0;w<words;w++){
extract<vector_type,scalar_type>(&vp[w],pointers,w);
}
}
////////////////////////////////////////////////////////////////////////
// Extract to a bunch of scalar object pointers, with offset
////////////////////////////////////////////////////////////////////////
template<class vobj> inline
void extract(const vobj &vec,std::vector<typename vobj::scalar_object *> &extracted, int offset)
{
typedef typename vobj::scalar_type scalar_type ;
typedef typename vobj::vector_type vector_type ;
const int words=sizeof(vobj)/sizeof(vector_type);
const int Nsimd=vobj::vector_type::Nsimd();
assert(extracted.size()==Nsimd);
std::vector<scalar_type *> pointers(Nsimd);
for(int i=0;i<Nsimd;i++) {
pointers[i] =(scalar_type *)& extracted[i][offset];
}
vector_type *vp = (vector_type *)&vec;
for(int w=0;w<words;w++){
extract<vector_type,scalar_type>(&vp[w],pointers,w);
}
}
////////////////////////////////////////////////////////////////////////
// Merge a contiguous array of scalar objects
////////////////////////////////////////////////////////////////////////
template<class vobj> inline
void merge(vobj &vec,std::vector<typename vobj::scalar_object> &extracted)
{
typedef typename vobj::scalar_type scalar_type ;
typedef typename vobj::vector_type vector_type ;
const int Nsimd=vobj::vector_type::Nsimd();
const int words=sizeof(vobj)/sizeof(vector_type);
assert(extracted.size()==Nsimd);
std::vector<scalar_type *> pointers(Nsimd);
for(int i=0;i<Nsimd;i++)
pointers[i] =(scalar_type *)& extracted[i];
vector_type *vp = (vector_type *)&vec;
for(int w=0;w<words;w++){
merge<vector_type,scalar_type>(&vp[w],pointers,w);
}
}
////////////////////////////////////////////////////////////////////////
// Merge a bunch of different scalar object pointers, with offset
////////////////////////////////////////////////////////////////////////
template<class vobj> inline
void merge(vobj &vec,std::vector<typename vobj::scalar_object *> &extracted,int offset)
{
typedef typename vobj::scalar_type scalar_type ;
typedef typename vobj::vector_type vector_type ;
const int Nsimd=vobj::vector_type::Nsimd();
const int words=sizeof(vobj)/sizeof(vector_type);
assert(extracted.size()==Nsimd);
std::vector<scalar_type *> pointers(Nsimd);
for(int i=0;i<Nsimd;i++)
pointers[i] =(scalar_type *)& extracted[i][offset];
vector_type *vp = (vector_type *)&vec;
assert((void *)vp!=NULL);
for(int w=0;w<words;w++){
merge<vector_type,scalar_type>(&vp[w],pointers,w);
}
}
}
#endif

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#ifndef GRID_MATH_INNER_H
#define GRID_MATH_INNER_H
namespace Grid {
///////////////////////////////////////////////////////////////////////////////////////
// innerProduct Scalar x Scalar -> Scalar
// innerProduct Vector x Vector -> Scalar
// innerProduct Matrix x Matrix -> Scalar
///////////////////////////////////////////////////////////////////////////////////////
template<class sobj> inline RealD norm2(const sobj &arg){
typedef typename sobj::scalar_type scalar;
decltype(innerProduct(arg,arg)) nrm;
nrm = innerProduct(arg,arg);
return real(nrm);
}
template<class l,class r,int N> inline
auto innerProduct (const iVector<l,N>& lhs,const iVector<r,N>& rhs) -> iScalar<decltype(innerProduct(lhs._internal[0],rhs._internal[0]))>
{
typedef decltype(innerProduct(lhs._internal[0],rhs._internal[0])) ret_t;
iScalar<ret_t> ret;
ret=zero;
for(int c1=0;c1<N;c1++){
ret._internal += innerProduct(lhs._internal[c1],rhs._internal[c1]);
}
return ret;
}
template<class l,class r,int N> inline
auto innerProduct (const iMatrix<l,N>& lhs,const iMatrix<r,N>& rhs) -> iScalar<decltype(innerProduct(lhs._internal[0][0],rhs._internal[0][0]))>
{
typedef decltype(innerProduct(lhs._internal[0][0],rhs._internal[0][0])) ret_t;
iScalar<ret_t> ret;
iScalar<ret_t> tmp;
ret=zero;
for(int c1=0;c1<N;c1++){
for(int c2=0;c2<N;c2++){
ret._internal+=innerProduct(lhs._internal[c1][c2],rhs._internal[c1][c2]);
}}
return ret;
}
template<class l,class r> inline
auto innerProduct (const iScalar<l>& lhs,const iScalar<r>& rhs) -> iScalar<decltype(innerProduct(lhs._internal,rhs._internal))>
{
typedef decltype(innerProduct(lhs._internal,rhs._internal)) ret_t;
iScalar<ret_t> ret;
ret._internal = innerProduct(lhs._internal,rhs._internal);
return ret;
}
}
#endif

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#ifndef GRID_MATH_OUTER_H
#define GRID_MATH_OUTER_H
namespace Grid {
///////////////////////////////////////////////////////////////////////////////////////
// outerProduct Scalar x Scalar -> Scalar
// Vector x Vector -> Matrix
///////////////////////////////////////////////////////////////////////////////////////
template<class l,class r,int N> inline
auto outerProduct (const iVector<l,N>& lhs,const iVector<r,N>& rhs) -> iMatrix<decltype(outerProduct(lhs._internal[0],rhs._internal[0])),N>
{
typedef decltype(outerProduct(lhs._internal[0],rhs._internal[0])) ret_t;
iMatrix<ret_t,N> ret;
for(int c1=0;c1<N;c1++){
for(int c2=0;c2<N;c2++){
ret._internal[c1][c2] = outerProduct(lhs._internal[c1],rhs._internal[c2]);
}}
return ret;
}
template<class l,class r> inline
auto outerProduct (const iScalar<l>& lhs,const iScalar<r>& rhs) -> iScalar<decltype(outerProduct(lhs._internal,rhs._internal))>
{
typedef decltype(outerProduct(lhs._internal,rhs._internal)) ret_t;
iScalar<ret_t> ret;
ret._internal = outerProduct(lhs._internal,rhs._internal);
return ret;
}
inline ComplexF outerProduct(const ComplexF &l, const ComplexF& r)
{
return l*r;
}
inline ComplexD outerProduct(const ComplexD &l, const ComplexD& r)
{
return l*r;
}
inline RealF outerProduct(const RealF &l, const RealF& r)
{
return l*r;
}
inline RealD outerProduct(const RealD &l, const RealD& r)
{
return l*r;
}
}
#endif

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#ifndef GRID_MATH_PEEK_H
#define GRID_MATH_PEEK_H
namespace Grid {
//////////////////////////////////////////////////////////////////////////////
// Peek on a specific index; returns a scalar in that index, tensor inherits rest
//////////////////////////////////////////////////////////////////////////////
// If we hit the right index, return scalar with no further recursion
//template<int Level> inline ComplexF peekIndex(const ComplexF arg) { return arg;}
//template<int Level> inline ComplexD peekIndex(const ComplexD arg) { return arg;}
//template<int Level> inline RealF peekIndex(const RealF arg) { return arg;}
//template<int Level> inline RealD peekIndex(const RealD arg) { return arg;}
// Scalar peek, no indices
template<int Level,class vtype,typename std::enable_if< iScalar<vtype>::TensorLevel == Level >::type * =nullptr> inline
auto peekIndex(const iScalar<vtype> &arg) -> iScalar<vtype>
{
return arg;
}
// Vector peek, one index
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel == Level >::type * =nullptr> inline
auto peekIndex(const iVector<vtype,N> &arg,int i) -> iScalar<vtype> // Index matches
{
iScalar<vtype> ret; // return scalar
ret._internal = arg._internal[i];
return ret;
}
// Matrix peek, two indices
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel == Level >::type * =nullptr> inline
auto peekIndex(const iMatrix<vtype,N> &arg,int i,int j) -> iScalar<vtype>
{
iScalar<vtype> ret; // return scalar
ret._internal = arg._internal[i][j];
return ret;
}
/////////////
// No match peek for scalar,vector,matrix must forward on either 0,1,2 args. Must have 9 routines with notvalue
/////////////
// scalar
template<int Level,class vtype,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
auto peekIndex(const iScalar<vtype> &arg) -> iScalar<decltype(peekIndex<Level>(arg._internal))>
{
iScalar<decltype(peekIndex<Level>(arg._internal))> ret;
ret._internal= peekIndex<Level>(arg._internal);
return ret;
}
template<int Level,class vtype, typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
auto peekIndex(const iScalar<vtype> &arg,int i) -> iScalar<decltype(peekIndex<Level>(arg._internal,i))>
{
iScalar<decltype(peekIndex<Level>(arg._internal,i))> ret;
ret._internal=peekIndex<Level>(arg._internal,i);
return ret;
}
template<int Level,class vtype, typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
auto peekIndex(const iScalar<vtype> &arg,int i,int j) -> iScalar<decltype(peekIndex<Level>(arg._internal,i,j))>
{
iScalar<decltype(peekIndex<Level>(arg._internal,i,j))> ret;
ret._internal=peekIndex<Level>(arg._internal,i,j);
return ret;
}
// vector
template<int Level,class vtype,int N, typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
auto peekIndex(const iVector<vtype,N> &arg) -> iVector<decltype(peekIndex<Level>(arg._internal[0])),N>
{
iVector<decltype(peekIndex<Level>(arg._internal[0])),N> ret;
for(int ii=0;ii<N;ii++){
ret._internal[ii]=peekIndex<Level>(arg._internal[ii]);
}
return ret;
}
template<int Level,class vtype,int N, typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
auto peekIndex(const iVector<vtype,N> &arg,int i) -> iVector<decltype(peekIndex<Level>(arg._internal[0],i)),N>
{
iVector<decltype(peekIndex<Level>(arg._internal[0],i)),N> ret;
for(int ii=0;ii<N;ii++){
ret._internal[ii]=peekIndex<Level>(arg._internal[ii],i);
}
return ret;
}
template<int Level,class vtype,int N, typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
auto peekIndex(const iVector<vtype,N> &arg,int i,int j) -> iVector<decltype(peekIndex<Level>(arg._internal[0],i,j)),N>
{
iVector<decltype(peekIndex<Level>(arg._internal[0],i,j)),N> ret;
for(int ii=0;ii<N;ii++){
ret._internal[ii]=peekIndex<Level>(arg._internal[ii],i,j);
}
return ret;
}
// matrix
template<int Level,class vtype,int N, typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
auto peekIndex(const iMatrix<vtype,N> &arg) -> iMatrix<decltype(peekIndex<Level>(arg._internal[0][0])),N>
{
iMatrix<decltype(peekIndex<Level>(arg._internal[0][0])),N> ret;
for(int ii=0;ii<N;ii++){
for(int jj=0;jj<N;jj++){
ret._internal[ii][jj]=peekIndex<Level>(arg._internal[ii][jj]);// Could avoid this because peeking a scalar is dumb
}}
return ret;
}
template<int Level,class vtype,int N, typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
auto peekIndex(const iMatrix<vtype,N> &arg,int i) -> iMatrix<decltype(peekIndex<Level>(arg._internal[0][0],i)),N>
{
iMatrix<decltype(peekIndex<Level>(arg._internal[0][0],i)),N> ret;
for(int ii=0;ii<N;ii++){
for(int jj=0;jj<N;jj++){
ret._internal[ii][jj]=peekIndex<Level>(arg._internal[ii][jj],i);
}}
return ret;
}
template<int Level,class vtype,int N, typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
auto peekIndex(const iMatrix<vtype,N> &arg,int i,int j) -> iMatrix<decltype(peekIndex<Level>(arg._internal[0][0],i,j)),N>
{
iMatrix<decltype(peekIndex<Level>(arg._internal[0][0],i,j)),N> ret;
for(int ii=0;ii<N;ii++){
for(int jj=0;jj<N;jj++){
ret._internal[ii][jj]=peekIndex<Level>(arg._internal[ii][jj],i,j);
}}
return ret;
}
}
#endif

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#ifndef GRID_MATH_POKE_H
#define GRID_MATH_POKE_H
namespace Grid {
//////////////////////////////////////////////////////////////////////////////
// Poke a specific index;
//////////////////////////////////////////////////////////////////////////////
// Scalar poke
template<int Level,class vtype,typename std::enable_if< iScalar<vtype>::TensorLevel == Level >::type * =nullptr> inline
void pokeIndex(iScalar<vtype> &ret, const iScalar<vtype> &arg)
{
ret._internal = arg._internal;
}
// Vector poke, one index
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel == Level >::type * =nullptr> inline
void pokeIndex(iVector<vtype,N> &ret, const iScalar<vtype> &arg,int i)
{
ret._internal[i] = arg._internal;
}
// Vector poke, two indices
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel == Level >::type * =nullptr> inline
void pokeIndex(iMatrix<vtype,N> &ret, const iScalar<vtype> &arg,int i,int j)
{
ret._internal[i][j] = arg._internal;
}
/////////////
// No match poke for scalar,vector,matrix must forward on either 0,1,2 args. Must have 9 routines with notvalue
/////////////
// scalar
template<int Level,class vtype,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
void pokeIndex(iScalar<vtype> &ret, const iScalar<decltype(peekIndex<Level>(ret._internal))> &arg)
{
pokeIndex<Level>(ret._internal,arg._internal);
}
template<int Level,class vtype,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
void pokeIndex(iScalar<vtype> &ret, const iScalar<decltype(peekIndex<Level>(ret._internal,0))> &arg, int i)
{
pokeIndex<Level>(ret._internal,arg._internal,i);
}
template<int Level,class vtype,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
void pokeIndex(iScalar<vtype> &ret, const iScalar<decltype(peekIndex<Level>(ret._internal,0,0))> &arg,int i,int j)
{
pokeIndex<Level>(ret._internal,arg._internal,i,j);
}
// Vector
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
void pokeIndex(iVector<vtype,N> &ret, iVector<decltype(peekIndex<Level>(ret._internal)),N> &arg)
{
for(int ii=0;ii<N;ii++){
pokeIndex<Level>(ret._internal[ii],arg._internal[ii]);
}
}
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
void pokeIndex(iVector<vtype,N> &ret, const iVector<decltype(peekIndex<Level>(ret._internal,0)),N> &arg,int i)
{
for(int ii=0;ii<N;ii++){
pokeIndex<Level>(ret._internal[ii],arg._internal[ii],i);
}
}
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
void pokeIndex(iVector<vtype,N> &ret, const iVector<decltype(peekIndex<Level>(ret._internal,0,0)),N> &arg,int i,int j)
{
for(int ii=0;ii<N;ii++){
pokeIndex<Level>(ret._internal[ii],arg._internal[ii],i,j);
}
}
// Matrix
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
void pokeIndex(iMatrix<vtype,N> &ret, const iMatrix<decltype(peekIndex<Level>(ret._internal)),N> &arg)
{
for(int ii=0;ii<N;ii++){
for(int jj=0;jj<N;jj++){
pokeIndex<Level>(ret._internal[ii][jj],arg._internal[ii][jj]);
}}
}
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
void pokeIndex(iMatrix<vtype,N> &ret, const iMatrix<decltype(peekIndex<Level>(ret._internal,0)),N> &arg,int i)
{
for(int ii=0;ii<N;ii++){
for(int jj=0;jj<N;jj++){
pokeIndex<Level>(ret._internal[ii][jj],arg._internal[ii][jj],i);
}}
}
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
void pokeIndex(iMatrix<vtype,N> &ret, const iMatrix<decltype(peekIndex<Level>(ret._internal,0,0)),N> &arg, int i,int j)
{
for(int ii=0;ii<N;ii++){
for(int jj=0;jj<N;jj++){
pokeIndex<Level>(ret._internal[ii][jj],arg._internal[ii][jj],i,j);
}}
}
}
#endif

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#ifndef GRID_MATH_REALITY_H
#define GRID_MATH_REALITY_H
namespace Grid {
///////////////////////////////////////////////
// multiply by I; make recursive.
///////////////////////////////////////////////
template<class vtype> inline iScalar<vtype> timesI(const iScalar<vtype>&r)
{
iScalar<vtype> ret;
timesI(ret._internal,r._internal);
return ret;
}
template<class vtype,int N> inline iVector<vtype,N> timesI(const iVector<vtype,N>&r)
{
iVector<vtype,N> ret;
for(int i=0;i<N;i++){
timesI(ret._internal[i],r._internal[i]);
}
return ret;
}
template<class vtype,int N> inline iMatrix<vtype,N> timesI(const iMatrix<vtype,N>&r)
{
iMatrix<vtype,N> ret;
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
timesI(ret._internal[i][j],r._internal[i][j]);
}}
return ret;
}
template<class vtype> inline void timesI(iScalar<vtype> &ret,const iScalar<vtype>&r)
{
timesI(ret._internal,r._internal);
}
template<class vtype,int N> inline void timesI(iVector<vtype,N> &ret,const iVector<vtype,N>&r)
{
for(int i=0;i<N;i++){
timesI(ret._internal[i],r._internal[i]);
}
}
template<class vtype,int N> inline void timesI(iMatrix<vtype,N> &ret,const iMatrix<vtype,N>&r)
{
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
timesI(ret._internal[i][j],r._internal[i][j]);
}}
}
template<class vtype> inline iScalar<vtype> timesMinusI(const iScalar<vtype>&r)
{
iScalar<vtype> ret;
timesMinusI(ret._internal,r._internal);
return ret;
}
template<class vtype,int N> inline iVector<vtype,N> timesMinusI(const iVector<vtype,N>&r)
{
iVector<vtype,N> ret;
for(int i=0;i<N;i++){
timesMinusI(ret._internal[i],r._internal[i]);
}
return ret;
}
template<class vtype,int N> inline iMatrix<vtype,N> timesMinusI(const iMatrix<vtype,N>&r)
{
iMatrix<vtype,N> ret;
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
timesMinusI(ret._internal[i][j],r._internal[i][j]);
}}
return ret;
}
template<class vtype> inline void timesMinusI(iScalar<vtype> &ret,const iScalar<vtype>&r)
{
timesMinusI(ret._internal,r._internal);
}
template<class vtype,int N> inline void timesMinusI(iVector<vtype,N> &ret,const iVector<vtype,N>&r)
{
for(int i=0;i<N;i++){
timesMinusI(ret._internal[i],r._internal[i]);
}
}
template<class vtype,int N> inline void timesMinusI(iMatrix<vtype,N> &ret,const iMatrix<vtype,N>&r)
{
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
timesMinusI(ret._internal[i][j],r._internal[i][j]);
}}
}
///////////////////////////////////////////////
// Conj function for scalar, vector, matrix
///////////////////////////////////////////////
template<class vtype> inline iScalar<vtype> conjugate(const iScalar<vtype>&r)
{
iScalar<vtype> ret;
ret._internal = conjugate(r._internal);
return ret;
}
template<class vtype,int N> inline iVector<vtype,N> conjugate(const iVector<vtype,N>&r)
{
iVector<vtype,N> ret;
for(int i=0;i<N;i++){
ret._internal[i] = conjugate(r._internal[i]);
}
return ret;
}
template<class vtype,int N> inline iMatrix<vtype,N> conjugate(const iMatrix<vtype,N>&r)
{
iMatrix<vtype,N> ret;
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
ret._internal[i][j] = conjugate(r._internal[i][j]);
}}
return ret;
}
///////////////////////////////////////////////
// Adj function for scalar, vector, matrix
///////////////////////////////////////////////
template<class vtype> inline iScalar<vtype> adj(const iScalar<vtype>&r)
{
iScalar<vtype> ret;
ret._internal = adj(r._internal);
return ret;
}
template<class vtype,int N> inline iVector<vtype,N> adj(const iVector<vtype,N>&r)
{
iVector<vtype,N> ret;
for(int i=0;i<N;i++){
ret._internal[i] = adj(r._internal[i]);
}
return ret;
}
template<class vtype,int N> inline iMatrix<vtype,N> adj(const iMatrix<vtype,N> &arg)
{
iMatrix<vtype,N> ret;
for(int c1=0;c1<N;c1++){
for(int c2=0;c2<N;c2++){
ret._internal[c1][c2]=adj(arg._internal[c2][c1]);
}}
return ret;
}
/////////////////////////////////////////////////////////////////
// Can only take the real/imag part of scalar objects, since
// lattice objects of different complex nature are non-conformable.
/////////////////////////////////////////////////////////////////
template<class itype> inline auto real(const iScalar<itype> &z) -> iScalar<decltype(real(z._internal))>
{
iScalar<decltype(real(z._internal))> ret;
ret._internal = real(z._internal);
return ret;
}
template<class itype,int N> inline auto real(const iMatrix<itype,N> &z) -> iMatrix<decltype(real(z._internal[0][0])),N>
{
iMatrix<decltype(real(z._internal[0][0])),N> ret;
for(int c1=0;c1<N;c1++){
for(int c2=0;c2<N;c2++){
ret._internal[c1][c2] = real(z._internal[c1][c2]);
}}
return ret;
}
template<class itype,int N> inline auto real(const iVector<itype,N> &z) -> iVector<decltype(real(z._internal[0])),N>
{
iVector<decltype(real(z._internal[0])),N> ret;
for(int c1=0;c1<N;c1++){
ret._internal[c1] = real(z._internal[c1]);
}
return ret;
}
template<class itype> inline auto imag(const iScalar<itype> &z) -> iScalar<decltype(imag(z._internal))>
{
iScalar<decltype(imag(z._internal))> ret;
ret._internal = imag(z._internal);
return ret;
}
template<class itype,int N> inline auto imag(const iMatrix<itype,N> &z) -> iMatrix<decltype(imag(z._internal[0][0])),N>
{
iMatrix<decltype(imag(z._internal[0][0])),N> ret;
for(int c1=0;c1<N;c1++){
for(int c2=0;c2<N;c2++){
ret._internal[c1][c2] = imag(z._internal[c1][c2]);
}}
return ret;
}
template<class itype,int N> inline auto imag(const iVector<itype,N> &z) -> iVector<decltype(imag(z._internal[0])),N>
{
iVector<decltype(imag(z._internal[0])),N> ret;
for(int c1=0;c1<N;c1++){
ret._internal[c1] = imag(z._internal[c1]);
}
return ret;
}
}
#endif

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#ifndef GRID_MATH_TRACE_H
#define GRID_MATH_TRACE_H
namespace Grid {
//////////////////////////////////////////////////////////////////
// Traces: both all indices and a specific index
/////////////////////////////////////////////////////////////////
inline ComplexF trace( const ComplexF &arg){ return arg;}
inline ComplexD trace( const ComplexD &arg){ return arg;}
inline RealF trace( const RealF &arg){ return arg;}
inline RealD trace( const RealD &arg){ return arg;}
template<int Level> inline ComplexF traceIndex(const ComplexF arg) { return arg;}
template<int Level> inline ComplexD traceIndex(const ComplexD arg) { return arg;}
template<int Level> inline RealF traceIndex(const RealF arg) { return arg;}
template<int Level> inline RealD traceIndex(const RealD arg) { return arg;}
template<class vtype,int N>
inline auto trace(const iMatrix<vtype,N> &arg) -> iScalar<decltype(trace(arg._internal[0][0]))>
{
iScalar<decltype( trace(arg._internal[0][0] )) > ret;
zeroit(ret._internal);
for(int i=0;i<N;i++){
ret._internal=ret._internal+trace(arg._internal[i][i]);
}
return ret;
}
template<class vtype>
inline auto trace(const iScalar<vtype> &arg) -> iScalar<decltype(trace(arg._internal))>
{
iScalar<decltype(trace(arg._internal))> ret;
ret._internal=trace(arg._internal);
return ret;
}
////////////////////////////////////////////////////////////////////////////////////////////////////////
// Trace Specific indices.
////////////////////////////////////////////////////////////////////////////////////////////////////////
template<int Level,class vtype,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline auto
traceIndex (const iScalar<vtype> &arg) -> iScalar<decltype(traceIndex<Level>(arg._internal))>
{
iScalar<decltype(traceIndex<Level>(arg._internal))> ret;
ret._internal=traceIndex<Level>(arg._internal);
return ret;
}
template<int Level,class vtype,typename std::enable_if< iScalar<vtype>::TensorLevel == Level >::type * =nullptr> inline auto
traceIndex (const iScalar<vtype> &arg) -> iScalar<vtype>
{
return arg;
}
// If we hit the right index, return scalar and trace it with no further recursion
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel == Level >::type * =nullptr> inline
auto traceIndex(const iMatrix<vtype,N> &arg) -> iScalar<vtype>
{
iScalar<vtype> ret;
zeroit(ret._internal);
for(int i=0;i<N;i++){
ret._internal = ret._internal + arg._internal[i][i];
}
return ret;
}
// not this level, so recurse
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline
auto traceIndex(const iMatrix<vtype,N> &arg) -> iMatrix<decltype(traceIndex<Level>(arg._internal[0][0])),N>
{
iMatrix<decltype(traceIndex<Level>(arg._internal[0][0])),N> ret;
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
ret._internal[i][j] = traceIndex<Level>(arg._internal[i][j]);
}}
return ret;
}
}
#endif

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#ifndef GRID_MATH_TRAITS_H
#define GRID_MATH_TRAITS_H
#include <type_traits>
namespace Grid {
//////////////////////////////////////////////////////////////////////////////////
// Want to recurse: GridTypeMapper<Matrix<vComplexD> >::scalar_type == ComplexD.
// Use of a helper class like this allows us to template specialise and "dress"
// other classes such as RealD == double, ComplexD == std::complex<double> with these
// traits.
//
// It is possible that we could do this more elegantly if I introduced a
// queryable trait in iScalar, iMatrix and iVector and used the query on vtype in
// place of the type mapper?
//
// Not sure how to do this, but probably could be done with a research effort
// to study C++11's type_traits.h file. (std::enable_if<isGridTensorType<vtype> >)
//
//////////////////////////////////////////////////////////////////////////////////
template <class T> class GridTypeMapper {
public:
typedef typename T::scalar_type scalar_type;
typedef typename T::vector_type vector_type;
typedef typename T::tensor_reduced tensor_reduced;
typedef typename T::scalar_object scalar_object;
enum { TensorLevel = T::TensorLevel };
};
//////////////////////////////////////////////////////////////////////////////////
// Recursion stops with these template specialisations
//////////////////////////////////////////////////////////////////////////////////
template<> class GridTypeMapper<RealF> {
public:
typedef RealF scalar_type;
typedef RealF vector_type;
typedef RealF tensor_reduced ;
typedef RealF scalar_object;
enum { TensorLevel = 0 };
};
template<> class GridTypeMapper<RealD> {
public:
typedef RealD scalar_type;
typedef RealD vector_type;
typedef RealD tensor_reduced;
typedef RealD scalar_object;
enum { TensorLevel = 0 };
};
template<> class GridTypeMapper<ComplexF> {
public:
typedef ComplexF scalar_type;
typedef ComplexF vector_type;
typedef ComplexF tensor_reduced;
typedef ComplexF scalar_object;
enum { TensorLevel = 0 };
};
template<> class GridTypeMapper<ComplexD> {
public:
typedef ComplexD scalar_type;
typedef ComplexD vector_type;
typedef ComplexD tensor_reduced;
typedef ComplexD scalar_object;
enum { TensorLevel = 0 };
};
template<> class GridTypeMapper<Integer> {
public:
typedef Integer scalar_type;
typedef Integer vector_type;
typedef Integer tensor_reduced;
typedef Integer scalar_object;
enum { TensorLevel = 0 };
};
template<> class GridTypeMapper<vRealF> {
public:
typedef RealF scalar_type;
typedef vRealF vector_type;
typedef vRealF tensor_reduced;
typedef RealF scalar_object;
enum { TensorLevel = 0 };
};
template<> class GridTypeMapper<vRealD> {
public:
typedef RealD scalar_type;
typedef vRealD vector_type;
typedef vRealD tensor_reduced;
typedef RealD scalar_object;
enum { TensorLevel = 0 };
};
template<> class GridTypeMapper<vComplexF> {
public:
typedef ComplexF scalar_type;
typedef vComplexF vector_type;
typedef vComplexF tensor_reduced;
typedef ComplexF scalar_object;
enum { TensorLevel = 0 };
};
template<> class GridTypeMapper<vComplexD> {
public:
typedef ComplexD scalar_type;
typedef vComplexD vector_type;
typedef vComplexD tensor_reduced;
typedef ComplexD scalar_object;
enum { TensorLevel = 0 };
};
template<> class GridTypeMapper<vInteger> {
public:
typedef Integer scalar_type;
typedef vInteger vector_type;
typedef vInteger tensor_reduced;
typedef Integer scalar_object;
enum { TensorLevel = 0 };
};
// First some of my own traits
template<typename T> struct isGridTensor {
static const bool value = true;
static const bool notvalue = false;
};
template<> struct isGridTensor<int > {
static const bool value = false;
static const bool notvalue = true;
};
template<> struct isGridTensor<RealD > {
static const bool value = false;
static const bool notvalue = true;
};
template<> struct isGridTensor<RealF > {
static const bool value = false;
static const bool notvalue = true;
};
template<> struct isGridTensor<ComplexD > {
static const bool value = false;
static const bool notvalue = true;
};
template<> struct isGridTensor<ComplexF > {
static const bool value = false;
static const bool notvalue = true;
};
template<> struct isGridTensor<Integer > {
static const bool value = false;
static const bool notvalue = true;
};
template<> struct isGridTensor<vRealD > {
static const bool value = false;
static const bool notvalue = true;
};
template<> struct isGridTensor<vRealF > {
static const bool value = false;
static const bool notvalue = true;
};
template<> struct isGridTensor<vComplexD > {
static const bool value = false;
static const bool notvalue = true;
};
template<> struct isGridTensor<vComplexF > {
static const bool value = false;
static const bool notvalue = true;
};
template<> struct isGridTensor<vInteger > {
static const bool value = false;
static const bool notvalue = true;
};
// Match the index
template<typename T,int Level> struct matchGridTensorIndex {
static const bool value = (Level==T::TensorLevel);
static const bool notvalue = (Level!=T::TensorLevel);
};
// What is the vtype
template<typename T> struct isComplex {
static const bool value = false;
};
template<> struct isComplex<ComplexF> {
static const bool value = true;
};
template<> struct isComplex<ComplexD> {
static const bool value = true;
};
}
#endif

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#ifndef GRID_MATH_TRANSPOSE_H
#define GRID_MATH_TRANSPOSE_H
namespace Grid {
/////////////////////////////////////////////////////////////////
// Transpose all indices
/////////////////////////////////////////////////////////////////
inline ComplexD transpose(ComplexD &rhs){ return rhs;}
inline ComplexF transpose(ComplexF &rhs){ return rhs;}
inline RealD transpose(RealD &rhs){ return rhs;}
inline RealF transpose(RealF &rhs){ return rhs;}
template<class vtype,int N>
inline typename std::enable_if<isGridTensor<vtype>::value, iMatrix<vtype,N> >::type
transpose(iMatrix<vtype,N> arg)
{
iMatrix<vtype,N> ret;
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
ret._internal[i][j] = transpose(arg._internal[j][i]); // NB recurses
}}
return ret;
}
template<class vtype,int N>
inline typename std::enable_if<isGridTensor<vtype>::notvalue, iMatrix<vtype,N> >::type
transpose(iMatrix<vtype,N> arg)
{
iMatrix<vtype,N> ret;
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
ret._internal[i][j] = arg._internal[j][i]; // Stop recursion if not a tensor type
}}
return ret;
}
template<class vtype>
inline typename std::enable_if<isGridTensor<vtype>::value, iScalar<vtype> >::type
transpose(iScalar<vtype> arg)
{
iScalar<vtype> ret;
ret._internal = transpose(arg._internal); // NB recurses
return ret;
}
template<class vtype>
inline typename std::enable_if<isGridTensor<vtype>::notvalue, iScalar<vtype> >::type
transpose(iScalar<vtype> arg)
{
iScalar<vtype> ret;
ret._internal = arg._internal; // NB recursion stops
return ret;
}
////////////////////////////////////////////////////////////////////////////////////////////
// Transpose a specific index; instructive to compare this style of recursion termination
// to that of adj; which is easiers?
////////////////////////////////////////////////////////////////////////////////////////////
template<int Level,class vtype,int N> inline
typename std::enable_if<matchGridTensorIndex<iMatrix<vtype,N>,Level>::value, iMatrix<vtype,N> >::type
transposeIndex (const iMatrix<vtype,N> &arg)
{
iMatrix<vtype,N> ret;
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
ret._internal[i][j] = arg._internal[j][i];
}}
return ret;
}
// or not
template<int Level,class vtype,int N> inline
typename std::enable_if<matchGridTensorIndex<iMatrix<vtype,N>,Level>::notvalue, iMatrix<vtype,N> >::type
transposeIndex (const iMatrix<vtype,N> &arg)
{
iMatrix<vtype,N> ret;
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
ret._internal[i][j] = transposeIndex<Level>(arg._internal[i][j]);
}}
return ret;
}
template<int Level,class vtype> inline
typename std::enable_if<matchGridTensorIndex<iScalar<vtype>,Level>::notvalue, iScalar<vtype> >::type
transposeIndex (const iScalar<vtype> &arg)
{
iScalar<vtype> ret;
ret._internal=transposeIndex<Level>(arg._internal);
return ret;
}
template<int Level,class vtype> inline
typename std::enable_if<matchGridTensorIndex<iScalar<vtype>,Level>::value, iScalar<vtype> >::type
transposeIndex (const iScalar<vtype> &arg)
{
return arg;
}
}
#endif