LA_library/mat.cc
2005-02-18 22:08:15 +00:00

843 lines
20 KiB
C++

#include "mat.h"
#include <stdlib.h>
#include <sys/types.h>
#include <sys/stat.h>
#include <fcntl.h>
extern "C" {
extern ssize_t read(int, void *, size_t);
extern ssize_t write(int, const void *, size_t);
}
// TODO :
//
//////////////////////////////////////////////////////////////////////////////
//// forced instantization in the corresponding object file
template NRMat<double>;
template NRMat< complex<double> >;
template NRMat<int>;
template NRMat<char>;
/*
* Templates first, specializations for BLAS next
*/
//raw I/O
template <typename T>
void NRMat<T>::put(int fd, bool dim) const
{
errno=0;
if(dim)
{
if(sizeof(int) != write(fd,&nn,sizeof(int))) laerror("cannot write");
if(sizeof(int) != write(fd,&mm,sizeof(int))) laerror("cannot write");
}
LA_traits<T>::multiput(nn*mm,fd,
#ifdef MATPTR
v[0]
#else
v
#endif
,dim);
}
template <typename T>
void NRMat<T>::get(int fd, bool dim)
{
int nn0,mm0;
errno=0;
if(dim)
{
if(sizeof(int) != read(fd,&nn0,sizeof(int))) laerror("cannot read");
if(sizeof(int) != read(fd,&mm0,sizeof(int))) laerror("cannot read");
resize(nn0,mm0);
}
else
copyonwrite();
LA_traits<T>::multiget(nn*mm,fd,
#ifdef MATPTR
v[0]
#else
v
#endif
,dim);
}
// Assign diagonal
template <typename T>
NRMat<T> & NRMat<T>::operator=(const T &a)
{
copyonwrite();
#ifdef DEBUG
if (nn != mm) laerror("RMat.operator=scalar on non-square matrix");
#endif
#ifdef MATPTR
for (int i=0; i< nn; i++) v[i][i] = a;
#else
for (int i=0; i< nn*nn; i+=nn+1) v[i] = a;
#endif
return *this;
}
// M += a
template <typename T>
NRMat<T> & NRMat<T>::operator+=(const T &a)
{
copyonwrite();
#ifdef DEBUG
if (nn != mm) laerror("Mat.operator+=scalar on non-square matrix");
#endif
#ifdef MATPTR
for (int i=0; i< nn; i++) v[i][i] += a;
#else
for (int i=0; i< nn*nn; i+=nn+1) v[i] += a;
#endif
return *this;
}
// M -= a
template <typename T>
NRMat<T> & NRMat<T>::operator-=(const T &a)
{
copyonwrite();
#ifdef DEBUG
if (nn != mm) laerror("Mat.operator-=scalar on non-square matrix");
#endif
#ifdef MATPTR
for (int i=0; i< nn; i++) v[i][i] -= a;
#else
for (int i=0; i< nn*nn; i+=nn+1) v[i] -= a;
#endif
return *this;
}
// unary minus
template <typename T>
const NRMat<T> NRMat<T>::operator-() const
{
NRMat<T> result(nn, mm);
#ifdef MATPTR
for (int i=0; i<nn*mm; i++) result.v[0][i]= -v[0][i];
#else
for (int i=0; i<nn*mm; i++) result.v[i]= -v[i];
#endif
return result;
}
// direct sum
template <typename T>
const NRMat<T> NRMat<T>::operator&(const NRMat<T> & b) const
{
NRMat<T> result((T)0, nn+b.nn, mm+b.mm);
for (int i=0; i<nn; i++) memcpy(result[i], (*this)[i], sizeof(T)*mm);
for (int i=0; i<b.nn; i++) memcpy(result[nn+i]+nn, b[i], sizeof(T)*b.mm);
return result;
}
// direct product
template <typename T>
const NRMat<T> NRMat<T>::operator|(const NRMat<T> &b) const
{
NRMat<T> result(nn*b.nn, mm*b.mm);
for (int i=0; i<nn; i++)
for (int j=0; j<mm; j++)
for (int k=0; k<b.nn; k++)
for (int l=0; l<b.mm; l++)
result[i*b.nn+k][j*b.mm+l] = (*this)[i][j]*b[k][l];
return result;
}
// sum of columns
template <typename T>
const NRVec<T> NRMat<T>::csum() const
{
NRVec<T> result(nn);
T sum;
for (int i=0; i<nn; i++) {
sum = (T)0;
for(int j=0; j<mm; j++) sum += (*this)[i][j];
result[i] = sum;
}
return result;
}
// sum of rows
template <typename T>
const NRVec<T> NRMat<T>::rsum() const
{
NRVec<T> result(nn);
T sum;
for (int i=0; i<mm; i++) {
sum = (T)0;
for(int j=0; j<nn; j++) sum += (*this)[j][i];
result[i] = sum;
}
return result;
}
// transpose Mat
template <typename T>
NRMat<T> & NRMat<T>::transposeme(int n)
{
if(n==0) n=nn;
#ifdef DEBUG
if (n==nn && nn != mm || n>mm || n>nn) laerror("transpose of non-square Mat");
#endif
copyonwrite();
for(int i=1; i<n; i++)
for(int j=0; j<i; j++) {
#ifdef MATPTR
T tmp = v[i][j];
v[i][j] = v[j][i];
v[j][i] = tmp;
#else
register int a;
register int b;
a = i*mm+j;
b = j*mm+i;
T tmp = v[a];
v[a] = v[b];
v[b] = tmp;
#endif
}
return *this;
}
// Output of Mat
template <typename T>
void NRMat<T>::fprintf(FILE *file, const char *format, const int modulo) const
{
lawritemat(file, (const T*)(*this), nn, mm, format, 2, modulo, 0);
}
// Input of Mat
template <typename T>
void NRMat<T>::fscanf(FILE *f, const char *format)
{
int n, m;
if (std::fscanf(f, "%d %d", &n, &m) != 2)
laerror("cannot read matrix dimensions in Mat::fscanf()");
resize(n,m);
T *p = *this;
for(int i=0; i<n; i++)
for(int j=0; j<n; j++)
if(std::fscanf(f,format,p++) != 1)
laerror("cannot read matrix element in Mat::fscanf()");
}
/*
* BLAS specializations for double and complex<double>
*/
// Mat *= a
NRMat<double> & NRMat<double>::operator*=(const double &a)
{
copyonwrite();
cblas_dscal(nn*mm, a, *this, 1);
return *this;
}
NRMat< complex<double> > &
NRMat< complex<double> >::operator*=(const complex<double> &a)
{
copyonwrite();
cblas_zscal(nn*mm, &a, (void *)(*this)[0], 1);
return *this;
}
//and for general type
template <typename T>
NRMat<T> & NRMat<T>::operator*=(const T &a)
{
copyonwrite();
#ifdef MATPTR
for (int i=0; i< nn*nn; i++) v[0][i] *= a;
#else
for (int i=0; i< nn*nn; i++) v[i] *= a;
#endif
return *this;
}
// Mat += Mat
NRMat<double> & NRMat<double>::operator+=(const NRMat<double> &rhs)
{
#ifdef DEBUG
if (nn != rhs.nn || mm!= rhs.mm)
laerror("Mat += Mat of incompatible matrices");
#endif
copyonwrite();
cblas_daxpy(nn*mm, 1.0, rhs, 1, *this, 1);
return *this;
}
NRMat< complex<double> > &
NRMat< complex<double> >::operator+=(const NRMat< complex<double> > &rhs)
{
#ifdef DEBUG
if (nn != rhs.nn || mm!= rhs.mm)
laerror("Mat += Mat of incompatible matrices");
#endif
copyonwrite();
cblas_zaxpy(nn*mm, &CONE, (void *)rhs[0], 1, (void *)(*this)[0], 1);
return *this;
}
//and for general type
template <typename T>
NRMat<T> & NRMat<T>::operator+=(const NRMat<T> &rhs)
{
#ifdef DEBUG
if (nn != rhs.nn || mm!= rhs.mm)
laerror("Mat -= Mat of incompatible matrices");
#endif
copyonwrite();
#ifdef MATPTR
for (int i=0; i< nn*nn; i++) v[0][i] += rhs.v[0][i] ;
#else
for (int i=0; i< nn*nn; i++) v[i] += rhs.v[i] ;
#endif
return *this;
}
// Mat -= Mat
NRMat<double> & NRMat<double>::operator-=(const NRMat<double> &rhs)
{
#ifdef DEBUG
if (nn != rhs.nn || mm!= rhs.mm)
laerror("Mat -= Mat of incompatible matrices");
#endif
copyonwrite();
cblas_daxpy(nn*mm, -1.0, rhs, 1, *this, 1);
return *this;
}
NRMat< complex<double> > &
NRMat< complex<double> >::operator-=(const NRMat< complex<double> > &rhs)
{
#ifdef DEBUG
if (nn != rhs.nn || mm!= rhs.mm)
laerror("Mat -= Mat of incompatible matrices");
#endif
copyonwrite();
cblas_zaxpy(nn*mm, &CMONE, (void *)rhs[0], 1, (void *)(*this)[0], 1);
return *this;
}
//and for general type
template <typename T>
NRMat<T> & NRMat<T>::operator-=(const NRMat<T> &rhs)
{
#ifdef DEBUG
if (nn != rhs.nn || mm!= rhs.mm)
laerror("Mat -= Mat of incompatible matrices");
#endif
copyonwrite();
#ifdef MATPTR
for (int i=0; i< nn*nn; i++) v[0][i] -= rhs.v[0][i] ;
#else
for (int i=0; i< nn*nn; i++) v[i] -= rhs.v[i] ;
#endif
return *this;
}
// Mat += SMat
NRMat<double> & NRMat<double>::operator+=(const NRSMat<double> &rhs)
{
#ifdef DEBUG
if (nn!=mm || nn!=rhs.nrows()) laerror("incompatible matrix size in Mat+=SMat");
#endif
const double *p = rhs;
copyonwrite();
for (int i=0; i<nn; i++) {
cblas_daxpy(i+1, 1.0, p, 1, (*this)[i], 1);
p += i+1;
}
p = rhs; p++;
for (int i=1; i<nn; i++) {
cblas_daxpy(i, 1.0, p, 1, (*this)[0]+i, nn);
p += i+1;
}
return *this;
}
NRMat< complex<double> > &
NRMat< complex<double> >::operator+=(const NRSMat< complex<double> > &rhs)
{
#ifdef DEBUG
if (nn!=mm || nn!=rhs.nrows()) laerror("incompatible matrix size in Mat+=SMat");
#endif
const complex<double> *p = rhs;
copyonwrite();
for (int i=0; i<nn; i++) {
cblas_zaxpy(i+1, (void *)&CONE, (void *)p, 1, (void *)(*this)[i], 1);
p += i+1;
}
p = rhs; p++;
for (int i=1; i<nn; i++) {
cblas_zaxpy(i, (void *)&CONE, (void *)p, 1, (void *)((*this)[i]+i), nn);
p += i+1;
}
return *this;
}
//and for general type
template <typename T>
NRMat<T> & NRMat<T>::operator+=(const NRSMat<T> &rhs)
{
#ifdef DEBUG
if (nn!=mm || nn!=rhs.nrows()) laerror("incompatible matrix size in Mat+=SMat");
#endif
const T *p = rhs;
copyonwrite();
for (int i=0; i<nn; i++) {
for(int j=0; j<i+1; ++j) *((*this)[i]+j) += p[j];
p += i+1;
}
p = rhs; p++;
for (int i=1; i<nn; i++) {
for(int j=0; j<i; ++j) *((*this)[i]+i+nn*j) += p[j];
p += i+1;
}
return *this;
}
// Mat -= SMat
NRMat<double> & NRMat<double>::operator-=(const NRSMat<double> &rhs)
{
#ifdef DEBUG
if (nn!=mm || nn!=rhs.nrows()) laerror("incompatible matrix size in Mat-=SMat");
#endif
const double *p = rhs;
copyonwrite();
for (int i=0; i<nn; i++) {
cblas_daxpy(i+1, -1.0, p, 1, (*this)[i], 1);
p += i+1;
}
p = rhs; p++;
for (int i=1; i<nn; i++) {
cblas_daxpy(i, -1.0, p, 1, (*this)[0]+i, nn);
p += i+1;
}
return *this;
}
NRMat< complex<double> > &
NRMat< complex<double> >::operator-=(const NRSMat< complex<double> > &rhs)
{
#ifdef DEBUG
if (nn!=mm || nn!=rhs.nrows()) laerror("incompatible matrix size in Mat-=SMat");
#endif
const complex<double> *p = rhs;
copyonwrite();
for (int i=0; i<nn; i++) {
cblas_zaxpy(i+1, (void *)&CMONE, (void *)p, 1, (void *)(*this)[i], 1);
p += i+1;
}
p = rhs; p++;
for (int i=1; i<nn; i++) {
cblas_zaxpy(i, (void *)&CMONE, (void *)p, 1, (void *)((*this)[i]+i), nn);
p += i+1;
}
return *this;
}
//and for general type
template <typename T>
NRMat<T> & NRMat<T>::operator-=(const NRSMat<T> &rhs)
{
#ifdef DEBUG
if (nn!=mm || nn!=rhs.nrows()) laerror("incompatible matrix size in Mat+=SMat");
#endif
const T *p = rhs;
copyonwrite();
for (int i=0; i<nn; i++) {
for(int j=0; j<i+1; ++j) *((*this)[i]+j) -= p[j];
p += i+1;
}
p = rhs; p++;
for (int i=1; i<nn; i++) {
for(int j=0; j<i; ++j) *((*this)[i]+i+nn*j) -= p[j];
p += i+1;
}
return *this;
}
// Mat.Mat - scalar product
const double NRMat<double>::dot(const NRMat<double> &rhs) const
{
#ifdef DEBUG
if(nn!=rhs.nn || mm!= rhs.mm) laerror("Mat.Mat incompatible matrices");
#endif
return cblas_ddot(nn*mm, (*this)[0], 1, rhs[0], 1);
}
const complex<double>
NRMat< complex<double> >::dot(const NRMat< complex<double> > &rhs) const
{
#ifdef DEBUG
if(nn!=rhs.nn || mm!= rhs.mm) laerror("Mat.Mat incompatible matrices");
#endif
complex<double> dot;
cblas_zdotc_sub(nn*mm, (void *)(*this)[0], 1, (void *)rhs[0], 1,
(void *)(&dot));
return dot;
}
// Mat * Mat
const NRMat<double> NRMat<double>::operator*(const NRMat<double> &rhs) const
{
#ifdef DEBUG
if (mm != rhs.nn) laerror("product of incompatible matrices");
#endif
NRMat<double> result(nn, rhs.mm);
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, nn, rhs.mm, mm, 1.0,
*this, mm, rhs, rhs.mm, 0.0, result, rhs.mm);
return result;
}
const NRMat< complex<double> >
NRMat< complex<double> >::operator*(const NRMat< complex<double> > &rhs) const
{
#ifdef DEBUG
if (mm != rhs.nn) laerror("product of incompatible matrices");
#endif
NRMat< complex<double> > result(nn, rhs.mm);
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, nn, rhs.mm, mm,
(const void *)(&CONE),(const void *)(*this)[0], mm, (const void *)rhs[0],
rhs.mm, (const void *)(&CZERO), (void *)result[0], rhs.mm);
return result;
}
// Multiply by diagonal from L
void NRMat<double>::diagmultl(const NRVec<double> &rhs)
{
#ifdef DEBUG
if (nn != rhs.size()) laerror("incompatible matrix dimension in diagmultl");
#endif
copyonwrite();
for(int i=0; i<nn; i++) cblas_dscal(mm, rhs[i], (*this)[i], 1);
}
void NRMat< complex<double> >::diagmultl(const NRVec< complex<double> > &rhs)
{
#ifdef DEBUG
if (nn != rhs.size()) laerror("incompatible matrix dimension in diagmultl");
#endif
copyonwrite();
for (int i=0; i<nn; i++) cblas_zscal(mm, &rhs[i], (*this)[i], 1);
}
// Multiply by diagonal from R
void NRMat<double>::diagmultr(const NRVec<double> &rhs)
{
#ifdef DEBUG
if (mm != rhs.size()) laerror("incompatible matrix dimension in diagmultr");
#endif
copyonwrite();
for (int i=0; i<mm; i++) cblas_dscal(nn, rhs[i], (*this)[i], mm);
}
void NRMat< complex<double> >::diagmultr(const NRVec< complex<double> > &rhs)
{
#ifdef DEBUG
if (mm != rhs.size()) laerror("incompatible matrix dimension in diagmultl");
#endif
copyonwrite();
for (int i=0; i<mm; i++) cblas_zscal(nn, &rhs[i], (*this)[i], mm);
}
// Mat * Smat, decomposed to nn x Vec * Smat
const NRMat<double>
NRMat<double>::operator*(const NRSMat<double> &rhs) const
{
#ifdef DEBUG
if (mm != rhs.nrows()) laerror("incompatible dimension in Mat*SMat");
#endif
NRMat<double> result(nn, rhs.ncols());
for (int i=0; i<nn; i++)
cblas_dspmv(CblasRowMajor, CblasLower, mm, 1.0, &rhs[0],
(*this)[i], 1, 0.0, result[i], 1);
return result;
}
const NRMat< complex<double> >
NRMat< complex<double> >::operator*(const NRSMat< complex<double> > &rhs) const
{
#ifdef DEBUG
if (mm != rhs.nrows()) laerror("incompatible dimension in Mat*SMat");
#endif
NRMat< complex<double> > result(nn, rhs.ncols());
for (int i=0; i<nn; i++)
cblas_zhpmv(CblasRowMajor, CblasLower, mm, (void *)&CONE, (void *)&rhs[0],
(void *)(*this)[i], 1, (void *)&CZERO, (void *)result[i], 1);
return result;
}
// sum of rows
const NRVec<double> NRMat<double>::rsum() const
{
NRVec<double> result(mm);
for (int i=0; i<mm; i++) result[i] = cblas_dasum(nn,(*this)[0]+i,mm);
return result;
}
// sum of columns
const NRVec<double> NRMat<double>::csum() const
{
NRVec<double> result(nn);
for (int i=0; i<nn; i++) result[i] = cblas_dasum(mm, (*this)[i], 1);
return result;
}
// complex conjugate of Mat
NRMat<double> &NRMat<double>::conjugateme() {return *this;}
NRMat< complex<double> > & NRMat< complex<double> >::conjugateme()
{
copyonwrite();
cblas_dscal(mm*nn, -1.0, (double *)((*this)[0])+1, 2);
return *this;
}
// transpose and optionally conjugate
const NRMat<double> NRMat<double>::transpose(bool conj) const
{
NRMat<double> result(mm,nn);
for(int i=0; i<nn; i++) cblas_dcopy(mm, (*this)[i], 1, result[0]+i, nn);
return result;
}
const NRMat< complex<double> >
NRMat< complex<double> >::transpose(bool conj) const
{
NRMat< complex<double> > result(mm,nn);
for (int i=0; i<nn; i++)
cblas_zcopy(mm, (void *)(*this)[i], 1, (void *)(result[0]+i), nn);
if (conj) cblas_dscal(mm*nn, -1.0, (double *)(result[0])+1, 2);
return result;
}
// gemm : this = alpha*op( A )*op( B ) + beta*this
void NRMat<double>::gemm(const double &beta, const NRMat<double> &a,
const char transa, const NRMat<double> &b, const char transb,
const double &alpha)
{
int l(transa=='n'?a.nn:a.mm);
int k(transa=='n'?a.mm:a.nn);
int kk(transb=='n'?b.nn:b.mm);
int ll(transb=='n'?b.mm:b.nn);
#ifdef DEBUG
if (l!=nn || ll!=mm || k!=kk) laerror("incompatible matrices in Mat:gemm()");
#endif
if (alpha==0.0 && beta==1.0) return;
copyonwrite();
cblas_dgemm(CblasRowMajor, (transa=='n' ? CblasNoTrans : CblasTrans),
(transb=='n' ? CblasNoTrans : CblasTrans), nn, mm, k, alpha, a,
a.mm, b , b.mm, beta, *this , mm);
}
void NRMat< complex<double> >::gemm(const complex<double> & beta,
const NRMat< complex<double> > & a, const char transa,
const NRMat< complex<double> > & b, const char transb,
const complex<double> & alpha)
{
int l(transa=='n'?a.nn:a.mm);
int k(transa=='n'?a.mm:a.nn);
int kk(transb=='n'?b.nn:b.mm);
int ll(transb=='n'?b.mm:b.nn);
#ifdef DEBUG
if (l!=nn || ll!=mm || k!=kk) laerror("incompatible matrices in Mat:gemm()");
#endif
if (alpha==CZERO && beta==CONE) return;
copyonwrite();
cblas_zgemm(CblasRowMajor,
(transa=='n' ? CblasNoTrans : (transa=='c'?CblasConjTrans:CblasTrans)),
(transb=='n' ? CblasNoTrans : (transa=='c'?CblasConjTrans:CblasTrans)),
nn, mm, k, &alpha, a , a.mm, b , b.mm, &beta, *this , mm);
}
// norm of Mat
const double NRMat<double>::norm(const double scalar) const
{
if (!scalar) return cblas_dnrm2(nn*mm, (*this)[0], 1);
double sum = 0;
for (int i=0; i<nn; i++)
for (int j=0; j<mm; j++) {
register double tmp;
#ifdef MATPTR
tmp = v[i][j];
#else
tmp = v[i*mm+j];
#endif
if (i==j) tmp -= scalar;
sum += tmp*tmp;
}
return sqrt(sum);
}
const double NRMat< complex<double> >::norm(const complex<double> scalar) const
{
if (scalar == CZERO) return cblas_dznrm2(nn*mm, (*this)[0], 1);
double sum = 0;
for (int i=0; i<nn; i++)
for (int j=0; j<mm; j++) {
register complex<double> tmp;
#ifdef MATPTR
tmp = v[i][j];
#else
tmp = v[i*mm+j];
#endif
if (i==j) tmp -= scalar;
sum += tmp.real()*tmp.real()+tmp.imag()*tmp.imag();
}
return sqrt(sum);
}
// axpy: this = a * Mat
void NRMat<double>::axpy(const double alpha, const NRMat<double> &mat)
{
#ifdef DEBUG
if (nn!=mat.nn || mm!=mat.mm) laerror("daxpy of incompatible matrices");
#endif
copyonwrite();
cblas_daxpy(nn*mm, alpha, mat, 1, *this, 1);
}
void NRMat< complex<double> >::axpy(const complex<double> alpha,
const NRMat< complex<double> > & mat)
{
#ifdef DEBUG
if (nn!=mat.nn || mm!=mat.mm) laerror("zaxpy of incompatible matrices");
#endif
copyonwrite();
cblas_zaxpy(nn*mm, (void *)&alpha, mat, 1, (void *)(*this)[0], 1);
}
// trace of Mat
const double NRMat<double>::trace() const
{
#ifdef DEBUG
if (nn != mm) laerror("no-square matrix in Mat::trace()");
#endif
return cblas_dasum(nn, (*this)[0], nn+1);
}
const complex<double> NRMat< complex<double> >::trace() const
{
#ifdef DEBUG
if (nn != mm) laerror("no-square matrix in Mat::trace()");
#endif
register complex<double> sum = CZERO;
for (int i=0; i<nn*nn; i+=(nn+1))
#ifdef MATPTR
sum += v[0][i];
#else
sum += v[i];
#endif
return sum;
}
//get diagonal; for compatibility with large matrices do not return newly created object
//for non-square get diagonal of A^TA, will be used as preconditioner
void NRMat<double>::diagonalof(NRVec<double> &r, const bool divide) const
{
#ifdef DEBUG
if (r.size() != nn) laerror("diagonalof() incompatible vector");
#endif
double a;
r.copyonwrite();
if(nn==mm)
{
#ifdef MATPTR
if(divide) for (int i=0; i< nn; i++) if((a=v[i][i])) r[i]/=a;
else for (int i=0; i< nn; i++) r[i] = v[i][i];
#else
if(divide) {int i,j; for (i=j=0; j< nn; ++j, i+=nn+1) if((a=v[i])) r[j] /=a;}
else {int i,j; for (i=j=0; j< nn; ++j, i+=nn+1) r[j] = v[i];}
#endif
}
else //non-square
{
for (int i=0; i< mm; i++)
{
#ifdef MATPTR
a= cblas_ddot(nn,v[0]+i,mm,v[0]+i,mm);
#else
a=cblas_ddot(nn,v+i,mm,v+i,mm);
#endif
if(divide) {if(a) r[i]/=a;}
else r[i] = a;
}
}
}
//////////////////////////////////////////////////////////////////////////////
//// forced instantization in the corespoding object file
#define INSTANTIZE(T) \
template ostream & operator<<(ostream &s, const NRMat< T > &x); \
template istream & operator>>(istream &s, NRMat< T > &x); \
INSTANTIZE(double)
INSTANTIZE(complex<double>)
INSTANTIZE(int)
INSTANTIZE(char)
export template <typename T>
ostream& operator<<(ostream &s, const NRMat<T> &x)
{
int i,j,n,m;
n=x.nrows();
m=x.ncols();
s << n << ' ' << m << '\n';
for(i=0;i<n;i++)
{
for(j=0; j<m;j++) s << x[i][j] << (j==m-1 ? '\n' : ' '); // endl cannot be used in the conditional expression, since it is an overloaded function
}
return s;
}
export template <typename T>
istream& operator>>(istream &s, NRMat<T> &x)
{
int i,j,n,m;
s >> n >> m;
x.resize(n,m);
for(i=0;i<n;i++) for(j=0; j<m;j++) s>>x[i][j] ;
return s;
}
//direct sum and product (oplus, otimes) to be done