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Grid/lib/Grid_math_arith.h
Peter Boyle cffad66894 Reorganise to keep files smaller
2015-04-18 18:36:48 +01:00

746 lines
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#ifndef GRID_MATH_ARITH_H
#define GRID_MATH_ARITH_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> 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> 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> 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> 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++){
add(&ret->_internal[c1][c2],&lhs->_internal,&rhs->_internal[c1][c2]);
}}
return;
}
template<class vtype,class ltype,class rtype, int N> 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;
}
// Need to figure multi-precision.
template<class Mytype> Mytype timesI(Mytype &r)
{
iScalar<Complex> i;
i._internal = Complex(0,1);
return r*i;
}
// + operator for scalar, vector, matrix
template<class ltype,class rtype>
//inline auto operator + (iScalar<ltype>& lhs,iScalar<rtype>&& rhs) -> iScalar<decltype(lhs._internal + rhs._internal)>
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>
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>
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>
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>
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;
}
///////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////// 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> 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> 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> 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> 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> 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;
}
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]);
}}
}
// - operator for scalar, vector, matrix
template<class ltype,class rtype> 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>
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>
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>
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>
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;
}
///////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////// 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>
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>
inline void mac(iMatrix<rrtype,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++){
for(int c3=0;c3<N;c3++){
mac(&ret->_internal[c1][c2],&lhs->_internal[c1][c3],&rhs->_internal[c3][c2]);
}}}
return;
}
template<class rrtype,class ltype,class rtype,int N>
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>
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>
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>
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>
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;
}
///////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////// MUL ///////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////
template<class rtype,class vtype,class mtype>
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>
inline void mult(iMatrix<rrtype,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++){
mult(&ret->_internal[c1][c2],&lhs->_internal[c1][0],&rhs->_internal[0][c2]);
for(int c3=1;c3<N;c3++){
mac(&ret->_internal[c1][c2],&lhs->_internal[c1][c3],&rhs->_internal[c3][c2]);
}
}}
return;
}
template<class rrtype,class ltype,class rtype,int N>
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>
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>
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>
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>
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> 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> 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> 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>
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> 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> 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> 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> 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> 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> 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;
}
//////////////////////////////////////////////////////////////////////////////////////////
// Must support native C++ types Integer, Complex, Real
//////////////////////////////////////////////////////////////////////////////////////////
// multiplication by fundamental scalar type
template<class l,int N> inline iScalar<l> operator * (const iScalar<l>& lhs,const typename iScalar<l>::scalar_type rhs)
{
typename iScalar<l>::tensor_reduced srhs(rhs);
return lhs*srhs;
}
template<class l,int N> inline iScalar<l> operator * (const typename iScalar<l>::scalar_type lhs,const iScalar<l>& rhs) { return rhs*lhs; }
template<class l,int N> inline iVector<l,N> operator * (const iVector<l,N>& lhs,const typename iScalar<l>::scalar_type rhs)
{
typename iVector<l,N>::tensor_reduced srhs(rhs);
return lhs*srhs;
}
template<class l,int N> 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> inline iMatrix<l,N> operator * (const iMatrix<l,N>& lhs,const typename iScalar<l>::scalar_type &rhs)
{
typename iMatrix<l,N>::tensor_reduced srhs(rhs);
return lhs*srhs;
}
template<class l,int N> 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> inline iScalar<l> operator * (const iScalar<l>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs*srhs;
}
template<class l> inline iScalar<l> operator * (double lhs,const iScalar<l>& rhs) { return rhs*lhs; }
template<class l,int N> inline iVector<l,N> operator * (const iVector<l,N>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs*srhs;
}
template<class l,int N> inline iVector<l,N> operator * (double lhs,const iVector<l,N>& rhs) { return rhs*lhs; }
template<class l,int N> inline iMatrix<l,N> operator * (const iMatrix<l,N>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs*srhs;
}
template<class l,int N> 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> inline iScalar<l> operator * (const iScalar<l>& lhs,ComplexD rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs*srhs;
}
template<class l> inline iScalar<l> operator * (ComplexD lhs,const iScalar<l>& rhs) { return rhs*lhs; }
template<class l,int N> inline iVector<l,N> operator * (const iVector<l,N>& lhs,ComplexD rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs*srhs;
}
template<class l,int N> inline iVector<l,N> operator * (ComplexD lhs,const iVector<l,N>& rhs) { return rhs*lhs; }
template<class l,int N> inline iMatrix<l,N> operator * (const iMatrix<l,N>& lhs,ComplexD rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs*srhs;
}
template<class l,int N> 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> inline iScalar<l> operator * (const iScalar<l>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs*srhs;
}
template<class l> inline iScalar<l> operator * (Integer lhs,const iScalar<l>& rhs) { return rhs*lhs; }
template<class l,int N> inline iVector<l,N> operator * (const iVector<l,N>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs*srhs;
}
template<class l,int N> inline iVector<l,N> operator * (Integer lhs,const iVector<l,N>& rhs) { return rhs*lhs; }
template<class l,int N> inline iMatrix<l,N> operator * (const iMatrix<l,N>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs*srhs;
}
template<class l,int N> 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> inline iScalar<l> operator + (const iScalar<l>& lhs,const typename iScalar<l>::scalar_type rhs)
{
typename iScalar<l>::tensor_reduced srhs(rhs);
return lhs+srhs;
}
template<class l,int N> inline iScalar<l> operator + (const typename iScalar<l>::scalar_type lhs,const iScalar<l>& rhs) { return rhs+lhs; }
template<class l,int N> inline iMatrix<l,N> operator + (const iMatrix<l,N>& lhs,const typename iScalar<l>::scalar_type rhs)
{
typename iMatrix<l,N>::tensor_reduced srhs(rhs);
return lhs+srhs;
}
template<class l,int N> 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> inline iScalar<l> operator + (const iScalar<l>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs+srhs;
}
template<class l> inline iScalar<l> operator + (double lhs,const iScalar<l>& rhs) { return rhs+lhs; }
template<class l,int N> inline iMatrix<l,N> operator + (const iMatrix<l,N>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs+srhs;
}
template<class l,int N> 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> inline iScalar<l> operator + (const iScalar<l>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs+srhs;
}
template<class l> inline iScalar<l> operator + (Integer lhs,const iScalar<l>& rhs) { return rhs+lhs; }
template<class l,int N> inline iMatrix<l,N> operator + (const iMatrix<l,N>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs+srhs;
}
template<class l,int N> 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> inline iScalar<l> operator - (const iScalar<l>& lhs,const typename iScalar<l>::scalar_type rhs)
{
typename iScalar<l>::tensor_reduced srhs(rhs);
return lhs-srhs;
}
template<class l,int N> inline iScalar<l> operator - (const typename iScalar<l>::scalar_type lhs,const iScalar<l>& rhs)
{
typename iScalar<l>::tensor_reduced slhs(lhs);
return slhs-rhs;
}
template<class l,int N> inline iMatrix<l,N> operator - (const iMatrix<l,N>& lhs,const typename iScalar<l>::scalar_type rhs)
{
typename iScalar<l>::tensor_reduced srhs(rhs);
return lhs-srhs;
}
template<class l,int N> inline iMatrix<l,N> operator - (const typename iScalar<l>::scalar_type lhs,const iMatrix<l,N>& rhs)
{
typename iScalar<l>::tensor_reduced slhs(lhs);
return slhs-rhs;
}
////////////////////////////////////////////////////////////////////
// Double support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> inline iScalar<l> operator - (const iScalar<l>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs-srhs;
}
template<class l> inline iScalar<l> operator - (double lhs,const iScalar<l>& rhs)
{
typename iScalar<l>::scalar_type t(lhs);
typename iScalar<l>::tensor_reduced slhs(t);
return slhs-rhs;
}
template<class l,int N> inline iMatrix<l,N> operator - (const iMatrix<l,N>& lhs,double rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs-srhs;
}
template<class l,int N> 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(t);
return slhs-rhs;
}
////////////////////////////////////////////////////////////////////
// Integer support; cast to "scalar_type" through constructor
////////////////////////////////////////////////////////////////////
template<class l> inline iScalar<l> operator - (const iScalar<l>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs-srhs;
}
template<class l> inline iScalar<l> operator - (Integer lhs,const iScalar<l>& rhs)
{
typename iScalar<l>::scalar_type t(lhs);
typename iScalar<l>::tensor_reduced slhs(t);
return slhs-rhs;
}
template<class l,int N> inline iMatrix<l,N> operator - (const iMatrix<l,N>& lhs,Integer rhs)
{
typename iScalar<l>::scalar_type t(rhs);
typename iScalar<l>::tensor_reduced srhs(t);
return lhs-srhs;
}
template<class l,int N> inline iMatrix<l,N> operator - (Integer lhs,const iMatrix<l,N>& rhs)
{
typename iScalar<l>::scalar_type t(lhs);
typename iScalar<l>::tensor_reduced slhs(t);
return slhs-rhs;
}
}
#endif
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