1266 lines
28 KiB
C++
1266 lines
28 KiB
C++
/*
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LA: linear algebra C++ interface library
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Copyright (C) 2008 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
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complex versions written by Roman Curik <roman.curik@jh-inst.cas.cz>
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "mat.h"
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#include <stdlib.h>
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#include <sys/types.h>
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#include <sys/stat.h>
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#include <fcntl.h>
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#include <errno.h>
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extern "C" {
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extern ssize_t read(int, void *, size_t);
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extern ssize_t write(int, const void *, size_t);
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}
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// TODO :
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//
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namespace LA {
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/*
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* Templates first, specializations for BLAS next
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*/
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//direct sum
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template <typename T>
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const NRMat<T> NRMat<T>::oplus(const NRMat<T> &rhs) const
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{
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if(nn==0 && mm == 0) return rhs;
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if(rhs.nn==0 && rhs.mm== 0) return *this;
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NRMat<T> r((T)0,nn+rhs.nn,mm+rhs.mm);
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#ifdef oldversion
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int i,j;
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for(i=0;i<nn;i++) for(j=0;j<mm;j++) r(i,j)=(*this)(i,j);
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for(i=0;i<nn;i++) for(j=mm;j<mm+rhs.mm;j++) r(i,j)= (T)0;
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for(i=nn;i<nn+rhs.nn;i++) for(j=0;j<mm;j++) r(i,j)= (T)0;
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for(i=nn;i<nn+rhs.nn;i++) for(j=mm;j<mm+rhs.mm;j++) r(i,j)= rhs(i-nn,j-mm);
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#else
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r.storesubmatrix(0,0,*this);
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r.storesubmatrix(nn,mm,rhs);
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#endif
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return r;
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}
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//direct product
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template <typename T>
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const NRMat<T> NRMat<T>::otimes(const NRMat<T> &rhs, bool reversecolumns) const
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{
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if(nn==0 && mm == 0) return *this;
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if(rhs.nn==0 && rhs.mm== 0) return rhs;
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NRMat<T> r((T)0,nn*rhs.nn,mm*rhs.mm);
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int i,j,k,l;
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if(reversecolumns)
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{
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for(i=0;i<nn;i++) for(j=0;j<mm;j++)
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{
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T c=(*this)(i,j);
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for(k=0;k<rhs.mm;k++) for(l=0;l<rhs.mm;l++)
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r( i*rhs.nn+k , l*nn+j ) = c *rhs(k,l);
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}
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}
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else
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{
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for(i=0;i<nn;i++) for(j=0;j<mm;j++)
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{
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T c=(*this)(i,j);
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for(k=0;k<rhs.mm;k++) for(l=0;l<rhs.mm;l++)
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r( i*rhs.nn+k , j*rhs.nn+l ) = c *rhs(k,l);
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}
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}
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return r;
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}
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//row of
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template <typename T>
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const NRVec<T> NRMat<T>::row(const int i, int l) const
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{
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#ifdef DEBUG
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if(i<0||i>=nn) laerror("illegal index in row()");
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#endif
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if(l < 0) l=mm;
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NRVec<T> r(l);
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LA_traits<T>::copy(&r[0],
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#ifdef MATPTR
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v[i]
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#else
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v+i*l
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#endif
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,l);
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return r;
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}
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//raw I/O
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template <typename T>
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void NRMat<T>::put(int fd, bool dim, bool transp) const
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{
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errno=0;
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if(dim)
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{
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if(sizeof(int) != write(fd,&(transp?mm:nn),sizeof(int))) laerror("cannot write");
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if(sizeof(int) != write(fd,&(transp?nn:mm),sizeof(int))) laerror("cannot write");
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}
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if(transp) //not particularly efficient
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{
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for(int j=0; j<mm; ++j)
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for(int i=0; i<nn; ++i)
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LA_traits<T>::put(fd,
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#ifdef MATPTR
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v[i][j]
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#else
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v[i*mm+j]
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#endif
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,dim,transp);
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}
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else LA_traits<T>::multiput(nn*mm,fd,
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#ifdef MATPTR
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v[0]
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#else
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v
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#endif
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,dim);
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}
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template <typename T>
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void NRMat<T>::get(int fd, bool dim, bool transp)
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{
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int nn0,mm0;
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errno=0;
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if(dim)
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{
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if(sizeof(int) != read(fd,&nn0,sizeof(int))) laerror("cannot read");
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if(sizeof(int) != read(fd,&mm0,sizeof(int))) laerror("cannot read");
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if(transp) resize(mm0,nn0); else resize(nn0,mm0);
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}
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else
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copyonwrite();
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if(transp) //not particularly efficient
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{
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for(int j=0; j<mm; ++j)
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for(int i=0; i<nn; ++i)
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LA_traits<T>::get(fd,
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#ifdef MATPTR
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v[i][j]
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#else
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v[i*mm+j]
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#endif
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,dim,transp);
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}
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else LA_traits<T>::multiget(nn*mm,fd,
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#ifdef MATPTR
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v[0]
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#else
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v
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#endif
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,dim);
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}
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// Assign diagonal
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template <typename T>
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NRMat<T> & NRMat<T>::operator=(const T &a)
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{
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copyonwrite();
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#ifdef DEBUG
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if (nn != mm) laerror("RMat.operator=scalar on non-square matrix");
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#endif
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#ifdef MATPTR
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memset(v[0],0,nn*nn*sizeof(T));
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for (int i=0; i< nn; i++) v[i][i] = a;
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#else
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memset(v,0,nn*nn*sizeof(T));
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for (int i=0; i< nn*nn; i+=nn+1) v[i] = a;
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#endif
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return *this;
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}
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// M += a
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template <typename T>
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NRMat<T> & NRMat<T>::operator+=(const T &a)
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{
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copyonwrite();
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#ifdef DEBUG
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if (nn != mm) laerror("Mat.operator+=scalar on non-square matrix");
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#endif
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#ifdef MATPTR
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for (int i=0; i< nn; i++) v[i][i] += a;
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#else
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for (int i=0; i< nn*nn; i+=nn+1) v[i] += a;
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#endif
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return *this;
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}
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// M -= a
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template <typename T>
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NRMat<T> & NRMat<T>::operator-=(const T &a)
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{
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copyonwrite();
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#ifdef DEBUG
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if (nn != mm) laerror("Mat.operator-=scalar on non-square matrix");
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#endif
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#ifdef MATPTR
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for (int i=0; i< nn; i++) v[i][i] -= a;
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#else
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for (int i=0; i< nn*nn; i+=nn+1) v[i] -= a;
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#endif
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return *this;
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}
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// unary minus
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template <typename T>
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const NRMat<T> NRMat<T>::operator-() const
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{
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NRMat<T> result(nn, mm);
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#ifdef MATPTR
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for (int i=0; i<nn*mm; i++) result.v[0][i]= -v[0][i];
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#else
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for (int i=0; i<nn*mm; i++) result.v[i]= -v[i];
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#endif
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return result;
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}
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// direct sum
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template <typename T>
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const NRMat<T> NRMat<T>::operator&(const NRMat<T> & b) const
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{
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NRMat<T> result((T)0, nn+b.nn, mm+b.mm);
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for (int i=0; i<nn; i++) memcpy(result[i], (*this)[i], sizeof(T)*mm);
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for (int i=0; i<b.nn; i++) memcpy(result[nn+i]+nn, b[i], sizeof(T)*b.mm);
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return result;
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}
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// direct product
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template <typename T>
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const NRMat<T> NRMat<T>::operator|(const NRMat<T> &b) const
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{
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NRMat<T> result(nn*b.nn, mm*b.mm);
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for (int i=0; i<nn; i++)
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for (int j=0; j<mm; j++)
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for (int k=0; k<b.nn; k++)
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for (int l=0; l<b.mm; l++)
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result[i*b.nn+k][j*b.mm+l] = (*this)[i][j]*b[k][l];
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return result;
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}
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// sum of columns
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template <typename T>
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const NRVec<T> NRMat<T>::csum() const
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{
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NRVec<T> result(nn);
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T sum;
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for (int i=0; i<nn; i++) {
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sum = (T)0;
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for(int j=0; j<mm; j++) sum += (*this)[i][j];
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result[i] = sum;
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}
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return result;
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}
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// sum of rows
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template <typename T>
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const NRVec<T> NRMat<T>::rsum() const
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{
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NRVec<T> result(nn);
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T sum;
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for (int i=0; i<mm; i++) {
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sum = (T)0;
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for(int j=0; j<nn; j++) sum += (*this)[j][i];
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result[i] = sum;
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}
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return result;
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}
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//block submatrix
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template <typename T>
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const NRMat<T> NRMat<T>::submatrix(const int fromrow, const int torow, const int fromcol, const int tocol) const
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{
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#ifdef DEBUG
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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");
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#endif
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int n=torow-fromrow+1;
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int m=tocol-fromcol+1;
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NRMat<T> r(n,m);
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for(int i=fromrow; i<=torow; ++i)
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#ifdef MATPTR
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memcpy(r.v[i-fromrow],v[i]+fromcol,m*sizeof(T));
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#else
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memcpy(r.v+(i-fromrow)*m,v+i*mm+fromcol,m*sizeof(T));
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#endif
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return r;
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}
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template <typename T>
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void NRMat<T>::storesubmatrix(const int fromrow, const int fromcol, const NRMat &rhs)
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{
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int tocol=fromcol+rhs.ncols()-1;
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int torow=fromrow+rhs.nrows()-1;
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#ifdef DEBUG
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if(fromrow <0 ||fromrow >=nn||torow >=nn ||fromcol<0||fromcol>=mm||tocol>=mm) laerror("bad indices in storesubmatrix");
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#endif
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int m=tocol-fromcol+1;
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for(int i=fromrow; i<=torow; ++i)
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#ifdef MATPTR
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memcpy(v[i]+fromcol,rhs.v[i-fromrow],m*sizeof(T));
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#else
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memcpy(v+i*mm+fromcol,rhs.v+(i-fromrow)*m,m*sizeof(T));
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#endif
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}
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// transpose Mat
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template <typename T>
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NRMat<T> & NRMat<T>::transposeme(int n)
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{
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if(n==0) n=nn;
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#ifdef DEBUG
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if (n==nn && nn != mm || n>mm || n>nn) laerror("transpose of non-square Mat");
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#endif
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copyonwrite();
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for(int i=1; i<n; i++)
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for(int j=0; j<i; j++) {
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#ifdef MATPTR
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T tmp = v[i][j];
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v[i][j] = v[j][i];
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v[j][i] = tmp;
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#else
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register int a;
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register int b;
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a = i*mm+j;
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b = j*mm+i;
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T tmp = v[a];
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v[a] = v[b];
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v[b] = tmp;
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#endif
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}
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return *this;
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}
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//complex from real
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template<>
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NRMat<complex<double> >::NRMat(const NRMat<double> &rhs, bool imagpart)
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: nn(rhs.nrows()), mm(rhs.ncols()), count(new int(1))
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{
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#ifdef MATPTR
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v = new complex<double>*[n];
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v[0] = new complex<double>[mm*nn];
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for (int i=1; i<n; i++) v[i] = v[i-1] + m;
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memset(v[0], 0, nn*mm*sizeof(complex<double>));
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cblas_dcopy(nn*mm,&rhs[0][0],1,((double *)v[0]) + (imagpart?1:0),2);
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#else
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v = new complex<double>[mm*nn];
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memset(v, 0, nn*mm*sizeof(complex<double>));
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cblas_dcopy(nn*mm,&rhs[0][0],1,((double *)v) + (imagpart?1:0),2);
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#endif
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}
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// Output of Mat
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template <typename T>
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void NRMat<T>::fprintf(FILE *file, const char *format, const int modulo) const
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{
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lawritemat(file, (const T*)(*this), nn, mm, format, 2, modulo, 0);
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}
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// Input of Mat
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template <typename T>
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void NRMat<T>::fscanf(FILE *f, const char *format)
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{
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int n, m;
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if (std::fscanf(f, "%d %d", &n, &m) != 2)
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laerror("cannot read matrix dimensions in Mat::fscanf()");
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resize(n,m);
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T *p = *this;
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for(int i=0; i<n; i++)
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for(int j=0; j<n; j++)
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if(std::fscanf(f,format,p++) != 1)
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laerror("cannot read matrix element in Mat::fscanf()");
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}
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/*
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* BLAS specializations for double and complex<double>
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*/
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template<>
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const NRSMat<double> NRMat<double>::transposedtimes() const
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{
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NRSMat<double> r(mm,mm);
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int i,j;
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for(i=0; i<mm; ++i) for(j=0; j<=i; ++j)
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#ifdef MATPTR
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r(i,j) = cblas_ddot(nn,v[0]+i,mm,v[0]+j,mm);
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#else
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r(i,j) = cblas_ddot(nn,v+i,mm,v+j,mm);
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#endif
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return r;
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}
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template<>
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const NRSMat<complex<double> > NRMat<complex<double> >::transposedtimes() const
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{
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NRSMat<complex<double> > r(mm,mm);
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int i,j;
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for(i=0; i<mm; ++i) for(j=0; j<=i; ++j)
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#ifdef MATPTR
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cblas_zdotc_sub(nn, v[0]+i , mm,v[0]+j, mm, &r(i,j));
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#else
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cblas_zdotc_sub(nn, v+i , mm,v+j, mm, &r(i,j));
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#endif
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return r;
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}
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//and for general type
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template <typename T>
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const NRSMat<T> NRMat<T>::transposedtimes() const
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{
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NRSMat<T> r(mm,mm);
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int i,j;
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for(i=0; i<mm; ++i) for(j=0; j<=i; ++j)
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{
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T s =(T)0;
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for(int k=0; k<nn; ++k) s+= (*this)(k,i) * (*this)(k,j);
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r(i,j)=s;
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}
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return r;
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}
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template<>
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const NRSMat<double> NRMat<double>::timestransposed() const
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{
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NRSMat<double> r(nn,nn);
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int i,j;
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for(i=0; i<nn; ++i) for(j=0; j<=i; ++j)
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#ifdef MATPTR
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r(i,j) = cblas_ddot(mm,v[i],1,v[j],1);
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#else
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r(i,j) = cblas_ddot(mm,v+i*mm,1,v+j*mm,1);
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#endif
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return r;
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}
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template<>
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const NRSMat<complex<double> > NRMat<complex<double> >::timestransposed() const
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{
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NRSMat<complex<double> > r(nn,nn);
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int i,j;
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for(i=0; i<nn; ++i) for(j=0; j<=i; ++j)
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#ifdef MATPTR
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cblas_zdotc_sub(mm, v[i] , 1,v[j], 1, &r(i,j));
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#else
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cblas_zdotc_sub(mm, v+i*mm , 1,v+j*mm, 1, &r(i,j));
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#endif
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return r;
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}
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//and for general type
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template <typename T>
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const NRSMat<T> NRMat<T>::timestransposed() const
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{
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NRSMat<T> r(nn,nn);
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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;
|
|
}
|
|
|
|
|
|
//randomize
|
|
template<>
|
|
void NRMat<double>::randomize(const double &x)
|
|
{
|
|
for(int i=0; i<nn; ++i)
|
|
for(int j=0; j<mm; ++j)
|
|
(*this)(i,j) = x*(2.*random()/(1.+RAND_MAX) -1.);
|
|
}
|
|
|
|
template<>
|
|
void NRMat<complex<double> >::randomize(const double &x)
|
|
{
|
|
for(int i=0; i<nn; ++i)
|
|
for(int j=0; j<mm; ++j)
|
|
{
|
|
(*this)(i,j).real() = x*(2.*random()/(1.+RAND_MAX) -1.);
|
|
(*this)(i,j).imag() = x*(2.*random()/(1.+RAND_MAX) -1.);
|
|
}
|
|
}
|
|
|
|
|
|
|
|
// 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, (*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, rhs[0], 1, (*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, rhs[0], 1, (*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, &CONE, p, 1, (*this)[i], 1);
|
|
p += i+1;
|
|
}
|
|
p = rhs; p++;
|
|
for (int i=1; i<nn; i++) {
|
|
cblas_zaxpy(i, &CONE, p, 1, (*this)[0]+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)[j]+i) += 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, &CMONE, p, 1, (*this)[i], 1);
|
|
p += i+1;
|
|
}
|
|
p = rhs; p++;
|
|
for (int i=1; i<nn; i++) {
|
|
cblas_zaxpy(i, &CMONE, p, 1, (*this)[0]+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)[j]+i) -= 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, (*this)[0], 1, rhs[0], 1,
|
|
&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");
|
|
if (rhs.mm <=0) laerror("illegal matrix dimension in gemm");
|
|
#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,
|
|
&CONE,(*this)[0], mm, rhs[0],
|
|
rhs.mm, &CZERO, 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)(0,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)(0,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, &CONE, &rhs[0],
|
|
(*this)[i], 1, &CZERO, result[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, (*this)[i], 1, (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()");
|
|
if(b.mm <=0 || mm<=0) laerror("illegal matrix dimension in 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 std::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 std::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, &alpha, mat, 1, (*this)[0], 1);
|
|
}
|
|
|
|
|
|
|
|
|
|
// trace of Mat
|
|
template <typename T>
|
|
const T NRMat<T>::trace() const
|
|
{
|
|
#ifdef DEBUG
|
|
if (nn != mm) laerror("no-square matrix in Mat::trace()");
|
|
#endif
|
|
T sum=0;
|
|
#ifdef MATPTR
|
|
for (int i=0; i<nn; ++i) sum += v[i][i];
|
|
#else
|
|
for (int i=0; i<nn*nn; i+=(nn+1)) 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
|
|
{
|
|
if (r.size() != nn) laerror("diagonalof() incompatible vector");
|
|
|
|
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];
|
|
}
|
|
|
|
|
|
//set diagonal
|
|
template<>
|
|
void NRMat<double>::diagonalset(const NRVec<double> &r)
|
|
{
|
|
if (r.size() != nn) laerror("diagonalset() incompatible vector");
|
|
if(nn!=mm) laerror("diagonalset only for square matrix");
|
|
|
|
copyonwrite();
|
|
|
|
#ifdef MATPTR
|
|
for (int i=0; i< nn; i++) v[i][i] = r[i];
|
|
#else
|
|
{int i,j; for (i=j=0; j< nn; ++j, i+=nn+1) v[i] = r[j];}
|
|
#endif
|
|
}
|
|
|
|
template<>
|
|
void NRMat<double>::orthonormalize(const bool rowcol, const NRSMat<double> *metric) //modified Gram-Schmidt
|
|
{
|
|
if(metric) //general metric
|
|
{
|
|
if(rowcol) //vectors are rows
|
|
{
|
|
if((*metric).nrows() != mm) laerror("incompatible metric in orthonormalize");
|
|
for(int j=0; j<nn; ++j)
|
|
{
|
|
for(int i=0; i<j; ++i)
|
|
{
|
|
NRVec<double> tmp = *metric * (*this).row(i);
|
|
double fact = cblas_ddot(mm,(*this)[j],1,tmp,1);
|
|
cblas_daxpy(mm,-fact,(*this)[i],1,(*this)[j],1);
|
|
}
|
|
NRVec<double> tmp = *metric * (*this).row(j);
|
|
double norm = cblas_ddot(mm,(*this)[j],1,tmp,1);
|
|
if(norm<=0.) laerror("zero vector in orthonormalize or nonpositive metric");
|
|
cblas_dscal(mm,1./std::sqrt(norm),(*this)[j],1);
|
|
}
|
|
}
|
|
else //vectors are columns
|
|
{
|
|
if((*metric).nrows() != nn) laerror("incompatible metric in orthonormalize");
|
|
for(int j=0; j<mm; ++j)
|
|
{
|
|
for(int i=0; i<j; ++i)
|
|
{
|
|
NRVec<double> tmp = *metric * (*this).column(i);
|
|
double fact = cblas_ddot(nn,&(*this)[0][j],mm,tmp,1);
|
|
cblas_daxpy(nn,-fact,&(*this)[0][i],mm,&(*this)[0][j],mm);
|
|
}
|
|
NRVec<double> tmp = *metric * (*this).column(j);
|
|
double norm = cblas_ddot(nn,&(*this)[0][j],mm,tmp,1);
|
|
if(norm<=0.) laerror("zero vector in orthonormalize or nonpositive metric");
|
|
cblas_dscal(nn,1./std::sqrt(norm),&(*this)[0][j],mm);
|
|
}
|
|
}
|
|
}
|
|
|
|
else //unit metric
|
|
|
|
{
|
|
if(rowcol) //vectors are rows
|
|
{
|
|
for(int j=0; j<nn; ++j)
|
|
{
|
|
for(int i=0; i<j; ++i)
|
|
{
|
|
double fact = cblas_ddot(mm,(*this)[j],1,(*this)[i],1);
|
|
cblas_daxpy(mm,-fact,(*this)[i],1,(*this)[j],1);
|
|
}
|
|
double norm = cblas_dnrm2(mm,(*this)[j],1);
|
|
if(norm==0.) laerror("zero vector in orthonormalize");
|
|
cblas_dscal(mm,1./norm,(*this)[j],1);
|
|
}
|
|
}
|
|
else //vectors are columns
|
|
{
|
|
for(int j=0; j<mm; ++j)
|
|
{
|
|
for(int i=0; i<j; ++i)
|
|
{
|
|
double fact = cblas_ddot(nn,&(*this)[0][j],mm,&(*this)[0][i],mm);
|
|
cblas_daxpy(nn,-fact,&(*this)[0][i],mm,&(*this)[0][j],mm);
|
|
}
|
|
double norm = cblas_dnrm2(nn,&(*this)[0][j],mm);
|
|
if(norm==0.) laerror("zero vector in orthonormalize");
|
|
cblas_dscal(nn,1./norm,&(*this)[0][j],mm);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
//////////////////////////////////////////////////////////////////////////////
|
|
//// forced instantization in the corresponding object file
|
|
template class NRMat<double>;
|
|
template class NRMat<complex<double> >;
|
|
template class NRMat<long long>;
|
|
template class NRMat<long>;
|
|
template class NRMat<int>;
|
|
template class NRMat<short>;
|
|
template class NRMat<char>;
|
|
template class NRMat<unsigned char>;
|
|
template class NRMat<unsigned short>;
|
|
template class NRMat<unsigned int>;
|
|
template class NRMat<unsigned long>;
|
|
template class NRMat<unsigned long long>;
|
|
|
|
}//namespace
|