LA_library/mat.cc

#include "mat.h"
#include <stdlib.h>
#include <sys/types.h>
#include <sys/stat.h>
#include <fcntl.h>
#include <errno.h>
extern "C" {
extern ssize_t read(int, void *, size_t);
extern ssize_t write(int, const void *, size_t);
}
// TODO :
//


/*
 *  Templates first, specializations for BLAS next
*/

//row of
template <typename T>
const NRVec<T> NRMat<T>::row(const int i, int l) const
{
#ifdef DEBUG
if(i<0||i>=nn) laerror("illegal index in row()");
#endif
if(l < 0) l=mm;
NRVec<T> r(l);
LA_traits<T>::copy(&r[0],
#ifdef MATPTR
        v[i]
#else
        v+i*l
#endif
,l);
return r;
}


//raw I/O
template <typename T>
void NRMat<T>::put(int fd, bool dim, bool transp) const
{
errno=0;
if(dim)
{
if(sizeof(int) != write(fd,&(transp?mm:nn),sizeof(int))) laerror("cannot write");
if(sizeof(int) != write(fd,&(transp?nn:mm),sizeof(int))) laerror("cannot write");
}

if(transp)  //not particularly efficient
        {
        for(int j=0; j<mm; ++j)
                for(int i=0; i<nn; ++i)
                        LA_traits<T>::put(fd, 
#ifdef MATPTR
                                v[i][j]
#else
                                v[i*mm+j]
#endif
                        ,dim,transp); 
        }
else 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, bool transp)
{
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");
if(transp) resize(mm0,nn0); else resize(nn0,mm0);
}
else
copyonwrite();
if(transp)  //not particularly efficient
	{
	for(int j=0; j<mm; ++j)
		for(int i=0; i<nn; ++i)
			LA_traits<T>::get(fd,
#ifdef MATPTR
				v[i][j]
#else
				v[i*mm+j]
#endif
			,dim,transp);
	}
else 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
	 memset(v[0],0,nn*nn*sizeof(T));
	 for (int i=0; i< nn; i++) v[i][i] = a;
#else
	 memset(v,0,nn*nn*sizeof(T));
	 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;
}

//block submatrix
template <typename T>
const NRMat<T> NRMat<T>::submatrix(const int fromrow, const int torow, const int fromcol, const int tocol) const
{
#ifdef DEBUG
if(fromrow <0 ||fromrow >=nn||torow <0 ||torow >=nn ||fromcol<0||fromcol>=mm||tocol<0||tocol>=mm||fromrow>torow||fromcol>tocol) laerror("bad indices in submatrix");
#endif
int n=torow-fromrow+1;
int m=tocol-fromcol+1;
NRMat<T> r(n,m);
for(int i=fromrow; i<=torow; ++i)
#ifdef MATPTR
	memcpy(r.v[i-fromrow],v[i]+fromcol,m*sizeof(T));
#else
	memcpy(r.v+(i-fromrow)*m,v+i*mm+fromcol,m*sizeof(T));
#endif
return r;
}


// 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>
 */

template<>
const NRSMat<double>  NRMat<double>::transposedtimes() const
{
NRSMat<double> r(mm,mm);
int i,j;
for(i=0; i<mm; ++i) for(j=0; j<=i; ++j)
#ifdef MATPTR
	r(i,j) = cblas_ddot(nn,v[0]+i,mm,v[0]+j,mm);
#else
	r(i,j) = cblas_ddot(nn,v+i,mm,v+j,mm);
#endif
return r;
}

template<>
const NRSMat<complex<double> >  NRMat<complex<double> >::transposedtimes() const
{
NRSMat<complex<double> > r(mm,mm);
int i,j;
for(i=0; i<mm; ++i) for(j=0; j<=i; ++j)
#ifdef MATPTR
	cblas_zdotc_sub(nn, v[0]+i , mm,v[0]+j, mm, (void *)(&r(i,j)));
#else
	cblas_zdotc_sub(nn, v+i , mm,v+j, mm, (void *)(&r(i,j)));
#endif
return r;
}



//and for general type
template <typename T>
const NRSMat<T>  NRMat<T>::transposedtimes() const
{
NRSMat<T> r(mm,mm);
int i,j;
for(i=0; i<mm; ++i) for(j=0; j<=i; ++j)
	{
	T s =(T)0;
	for(int k=0; k<nn; ++k) s+= (*this)(k,i) * (*this)(k,j);
	r(i,j)=s;
	}
return r;
}



template<>
const NRSMat<double>  NRMat<double>::timestransposed() const
{
NRSMat<double> r(nn,nn);
int i,j;
for(i=0; i<nn; ++i) for(j=0; j<=i; ++j)
#ifdef MATPTR
	r(i,j) = cblas_ddot(mm,v[i],1,v[j],1);
#else
	r(i,j) = cblas_ddot(mm,v+i*mm,1,v+j*mm,1);
#endif
return r;
}

template<>
const NRSMat<complex<double> >  NRMat<complex<double> >::timestransposed() const
{
NRSMat<complex<double> > r(nn,nn);
int i,j;
for(i=0; i<nn; ++i) for(j=0; j<=i; ++j)
#ifdef MATPTR
	cblas_zdotc_sub(mm, v[i] , 1,v[j], 1, (void *)(&r(i,j)));
#else
	cblas_zdotc_sub(mm, v+i*mm , 1,v+j*mm, 1, (void *)(&r(i,j)));
#endif
return r;
}



//and for general type
template <typename T>
const NRSMat<T>  NRMat<T>::timestransposed() const
{
NRSMat<T> r(nn,nn);
int i,j;
for(i=0; i<nn; ++i) for(j=0; j<=i; ++j)
	{
	T s =(T)0;
	for(int k=0; k<mm; ++k) s+= (*this)(i,k) * (*this)(j,k);
	r(i,j)=s;
	}
return r;
}




// Mat *= a
template<>
NRMat<double> & NRMat<double>::operator*=(const double &a)
{
	copyonwrite();
	cblas_dscal(nn*mm, a, *this, 1);
	return *this;
}


template<>
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
template<>
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;
}


template<>
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
template<>
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;
}



template<>
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
template<>
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;
}



template<>
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
template<>
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;
}



template<>
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
template<>
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);
}



template<>
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
template<>
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;
}



template<>
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
template<>
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);
}



template<>
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
template<>
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);
}



template<>
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
//NOTE: dsymm is not appropriate as it works on UNPACKED symmetric matrix
template<>
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;
}



template<>
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
template<>
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
template<>
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
template<>
NRMat<double> &NRMat<double>::conjugateme() {return *this;}

template<>
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
template<>
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;
}
template<>
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
template<>
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 k(transa=='n'?a.mm:a.nn);

#ifdef DEBUG
	int l(transa=='n'?a.nn:a.mm);
	int kk(transb=='n'?b.nn:b.mm);
	int ll(transb=='n'?b.mm:b.nn);
	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);
}



template<>
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 k(transa=='n'?a.mm:a.nn);

#ifdef DEBUG
	int l(transa=='n'?a.nn:a.mm);
	int kk(transb=='n'?b.nn:b.mm);
	int ll(transb=='n'?b.mm:b.nn);
	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
template<>
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);
}



template<>
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
template<>
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);
}



template<>
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
template<>
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);


}



template<>
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 
template<>
const double * NRMat<double>::diagonalof(NRVec<double> &r, const bool divide, bool cache) 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;
	}
}

return divide?NULL:&r[0];
}



//////////////////////////////////////////////////////////////////////////////
//// 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(short)
INSTANTIZE(char)
INSTANTIZE(unsigned char)
INSTANTIZE(unsigned long)
INSTANTIZE(unsigned int)


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 << (typename LA_traits_io<T>::IOtype) 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);
		typename LA_traits_io<T>::IOtype tmp;
                for(i=0;i<n;i++) for(j=0; j<m;j++) { s>>tmp; x[i][j]=tmp;}
                return s;
                }

//direct sum and product (oplus, otimes) to be done














//////////////////////////////////////////////////////////////////////////////
//// forced instantization in the corresponding object file
template class NRMat<double>;
template class NRMat<complex<double> >;
template class NRMat<int>;
template class NRMat<short>;
template class NRMat<char>;
template class NRMat<unsigned char>;
template class NRMat<unsigned int>;
template class NRMat<unsigned long>;