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https://github.com/paboyle/Grid.git
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454 lines
11 KiB
C++
454 lines
11 KiB
C++
/*************************************************************************************
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Grid physics library, www.github.com/paboyle/Grid
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Source file: ./lib/algorithms/iterative/Matrix.h
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Copyright (C) 2015
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Author: Peter Boyle <paboyle@ph.ed.ac.uk>
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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 2 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 along
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with this program; if not, write to the Free Software Foundation, Inc.,
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51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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See the full license in the file "LICENSE" in the top level distribution directory
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*************************************************************************************/
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/* END LEGAL */
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#ifndef MATRIX_H
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#define MATRIX_H
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#include <cstdlib>
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#include <string>
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#include <cmath>
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#include <vector>
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#include <iostream>
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#include <iomanip>
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#include <complex>
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#include <typeinfo>
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#include <Grid.h>
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/** Sign function **/
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template <class T> T sign(T p){return ( p/abs(p) );}
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/////////////////////////////////////////////////////////////////////////////////////////////////////////
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///////////////////// Hijack STL containers for our wicked means /////////////////////////////////////////
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/////////////////////////////////////////////////////////////////////////////////////////////////////////
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template<class T> using Vector = Vector<T>;
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template<class T> using Matrix = Vector<Vector<T> >;
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template<class T> void Resize(Vector<T > & vec, int N) { vec.resize(N); }
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template<class T> void Resize(Matrix<T > & mat, int N, int M) {
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mat.resize(N);
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for(int i=0;i<N;i++){
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mat[i].resize(M);
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}
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}
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template<class T> void Size(Vector<T> & vec, int &N)
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{
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N= vec.size();
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}
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template<class T> void Size(Matrix<T> & mat, int &N,int &M)
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{
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N= mat.size();
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M= mat[0].size();
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}
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template<class T> void SizeSquare(Matrix<T> & mat, int &N)
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{
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int M; Size(mat,N,M);
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assert(N==M);
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}
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template<class T> void SizeSame(Matrix<T> & mat1,Matrix<T> &mat2, int &N1,int &M1)
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{
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int N2,M2;
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Size(mat1,N1,M1);
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Size(mat2,N2,M2);
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assert(N1==N2);
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assert(M1==M2);
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}
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//*****************************************
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//* (Complex) Vector operations *
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//*****************************************
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/**Conj of a Vector **/
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template <class T> Vector<T> conj(Vector<T> p){
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Vector<T> q(p.size());
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for(int i=0;i<p.size();i++){q[i] = conj(p[i]);}
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return q;
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}
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/** Norm of a Vector**/
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template <class T> T norm(Vector<T> p){
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T sum = 0;
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for(int i=0;i<p.size();i++){sum = sum + p[i]*conj(p[i]);}
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return abs(sqrt(sum));
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}
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/** Norm squared of a Vector **/
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template <class T> T norm2(Vector<T> p){
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T sum = 0;
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for(int i=0;i<p.size();i++){sum = sum + p[i]*conj(p[i]);}
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return abs((sum));
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}
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/** Sum elements of a Vector **/
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template <class T> T trace(Vector<T> p){
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T sum = 0;
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for(int i=0;i<p.size();i++){sum = sum + p[i];}
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return sum;
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}
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/** Fill a Vector with constant c **/
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template <class T> void Fill(Vector<T> &p, T c){
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for(int i=0;i<p.size();i++){p[i] = c;}
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}
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/** Normalize a Vector **/
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template <class T> void normalize(Vector<T> &p){
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T m = norm(p);
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if( abs(m) > 0.0) for(int i=0;i<p.size();i++){p[i] /= m;}
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}
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/** Vector by scalar **/
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template <class T, class U> Vector<T> times(Vector<T> p, U s){
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for(int i=0;i<p.size();i++){p[i] *= s;}
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return p;
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}
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template <class T, class U> Vector<T> times(U s, Vector<T> p){
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for(int i=0;i<p.size();i++){p[i] *= s;}
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return p;
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}
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/** inner product of a and b = conj(a) . b **/
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template <class T> T inner(Vector<T> a, Vector<T> b){
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T m = 0.;
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for(int i=0;i<a.size();i++){m = m + conj(a[i])*b[i];}
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return m;
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}
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/** sum of a and b = a + b **/
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template <class T> Vector<T> add(Vector<T> a, Vector<T> b){
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Vector<T> m(a.size());
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for(int i=0;i<a.size();i++){m[i] = a[i] + b[i];}
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return m;
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}
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/** sum of a and b = a - b **/
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template <class T> Vector<T> sub(Vector<T> a, Vector<T> b){
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Vector<T> m(a.size());
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for(int i=0;i<a.size();i++){m[i] = a[i] - b[i];}
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return m;
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}
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/**
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*********************************
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* Matrices *
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*********************************
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**/
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template<class T> void Fill(Matrix<T> & mat, T&val) {
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int N,M;
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Size(mat,N,M);
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for(int i=0;i<N;i++){
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for(int j=0;j<M;j++){
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mat[i][j] = val;
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}}
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}
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/** Transpose of a matrix **/
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Matrix<T> Transpose(Matrix<T> & mat){
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int N,M;
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Size(mat,N,M);
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Matrix C; Resize(C,M,N);
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for(int i=0;i<M;i++){
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for(int j=0;j<N;j++){
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C[i][j] = mat[j][i];
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}}
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return C;
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}
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/** Set Matrix to unit matrix **/
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template<class T> void Unity(Matrix<T> &mat){
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int N; SizeSquare(mat,N);
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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 ( i==j ) A[i][j] = 1;
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else A[i][j] = 0;
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}
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}
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}
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/** Add C * I to matrix **/
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template<class T>
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void PlusUnit(Matrix<T> & A,T c){
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int dim; SizeSquare(A,dim);
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for(int i=0;i<dim;i++){A[i][i] = A[i][i] + c;}
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}
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/** return the Hermitian conjugate of matrix **/
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Matrix<T> HermitianConj(Matrix<T> &mat){
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int dim; SizeSquare(mat,dim);
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Matrix<T> C; Resize(C,dim,dim);
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for(int i=0;i<dim;i++){
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for(int j=0;j<dim;j++){
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C[i][j] = conj(mat[j][i]);
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}
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}
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return C;
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}
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/** return diagonal entries as a Vector **/
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Vector<T> diag(Matrix<T> &A)
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{
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int dim; SizeSquare(A,dim);
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Vector<T> d; Resize(d,dim);
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for(int i=0;i<dim;i++){
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d[i] = A[i][i];
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}
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return d;
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}
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/** Left multiply by a Vector **/
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Vector<T> operator *(Vector<T> &B,Matrix<T> &A)
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{
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int K,M,N;
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Size(B,K);
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Size(A,M,N);
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assert(K==M);
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Vector<T> C; Resize(C,N);
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for(int j=0;j<N;j++){
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T sum = 0.0;
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for(int i=0;i<M;i++){
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sum += B[i] * A[i][j];
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}
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C[j] = sum;
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}
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return C;
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}
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/** return 1/diagonal entries as a Vector **/
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Vector<T> inv_diag(Matrix<T> & A){
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int dim; SizeSquare(A,dim);
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Vector<T> d; Resize(d,dim);
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for(int i=0;i<dim;i++){
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d[i] = 1.0/A[i][i];
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}
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return d;
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}
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/** Matrix Addition **/
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inline Matrix<T> operator + (Matrix<T> &A,Matrix<T> &B)
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{
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int N,M ; SizeSame(A,B,N,M);
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Matrix C; Resize(C,N,M);
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for(int i=0;i<N;i++){
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for(int j=0;j<M;j++){
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C[i][j] = A[i][j] + B[i][j];
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}
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}
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return C;
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}
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/** Matrix Subtraction **/
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inline Matrix<T> operator- (Matrix<T> & A,Matrix<T> &B){
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int N,M ; SizeSame(A,B,N,M);
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Matrix C; Resize(C,N,M);
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for(int i=0;i<N;i++){
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for(int j=0;j<M;j++){
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C[i][j] = A[i][j] - B[i][j];
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}}
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return C;
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}
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/** Matrix scalar multiplication **/
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inline Matrix<T> operator* (Matrix<T> & A,T c){
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int N,M; Size(A,N,M);
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Matrix C; Resize(C,N,M);
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for(int i=0;i<N;i++){
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for(int j=0;j<M;j++){
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C[i][j] = A[i][j]*c;
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}}
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return C;
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}
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/** Matrix Matrix multiplication **/
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inline Matrix<T> operator* (Matrix<T> &A,Matrix<T> &B){
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int K,L,N,M;
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Size(A,K,L);
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Size(B,N,M); assert(L==N);
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Matrix C; Resize(C,K,M);
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for(int i=0;i<K;i++){
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for(int j=0;j<M;j++){
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T sum = 0.0;
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for(int k=0;k<N;k++) sum += A[i][k]*B[k][j];
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C[i][j] =sum;
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}
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}
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return C;
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}
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/** Matrix Vector multiplication **/
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inline Vector<T> operator* (Matrix<T> &A,Vector<T> &B){
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int M,N,K;
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Size(A,N,M);
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Size(B,K); assert(K==M);
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Vector<T> C; Resize(C,N);
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for(int i=0;i<N;i++){
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T sum = 0.0;
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for(int j=0;j<M;j++) sum += A[i][j]*B[j];
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C[i] = sum;
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}
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return C;
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}
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/** Some version of Matrix norm **/
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/*
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inline T Norm(){ // this is not a usual L2 norm
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T norm = 0;
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for(int i=0;i<dim;i++){
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for(int j=0;j<dim;j++){
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norm += abs(A[i][j]);
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}}
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return norm;
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}
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*/
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/** Some version of Matrix norm **/
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template<class T> T LargestDiag(Matrix<T> &A)
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{
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int dim ; SizeSquare(A,dim);
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T ld = abs(A[0][0]);
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for(int i=1;i<dim;i++){
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T cf = abs(A[i][i]);
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if(abs(cf) > abs(ld) ){ld = cf;}
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}
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return ld;
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}
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/** Look for entries on the leading subdiagonal that are smaller than 'small' **/
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template <class T,class U> int Chop_subdiag(Matrix<T> &A,T norm, int offset, U small)
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{
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int dim; SizeSquare(A,dim);
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for(int l = dim - 1 - offset; l >= 1; l--) {
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if((U)abs(A[l][l - 1]) < (U)small) {
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A[l][l-1]=(U)0.0;
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return l;
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}
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}
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return 0;
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}
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/** Look for entries on the leading subdiagonal that are smaller than 'small' **/
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template <class T,class U> int Chop_symm_subdiag(Matrix<T> & A,T norm, int offset, U small)
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{
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int dim; SizeSquare(A,dim);
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for(int l = dim - 1 - offset; l >= 1; l--) {
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if((U)abs(A[l][l - 1]) < (U)small) {
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A[l][l - 1] = (U)0.0;
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A[l - 1][l] = (U)0.0;
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return l;
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}
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}
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return 0;
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}
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/**Assign a submatrix to a larger one**/
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template<class T>
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void AssignSubMtx(Matrix<T> & A,int row_st, int row_end, int col_st, int col_end, Matrix<T> &S)
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{
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for(int i = row_st; i<row_end; i++){
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for(int j = col_st; j<col_end; j++){
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A[i][j] = S[i - row_st][j - col_st];
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}
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}
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}
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/**Get a square submatrix**/
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template <class T>
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Matrix<T> GetSubMtx(Matrix<T> &A,int row_st, int row_end, int col_st, int col_end)
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{
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Matrix<T> H; Resize(row_end - row_st,col_end-col_st);
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for(int i = row_st; i<row_end; i++){
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for(int j = col_st; j<col_end; j++){
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H[i-row_st][j-col_st]=A[i][j];
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}}
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return H;
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}
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/**Assign a submatrix to a larger one NB remember Vector Vectors are transposes of the matricies they represent**/
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template<class T>
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void AssignSubMtx(Matrix<T> & A,int row_st, int row_end, int col_st, int col_end, Matrix<T> &S)
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{
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for(int i = row_st; i<row_end; i++){
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for(int j = col_st; j<col_end; j++){
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A[i][j] = S[i - row_st][j - col_st];
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}}
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}
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/** compute b_i A_ij b_j **/ // surprised no Conj
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template<class T> T proj(Matrix<T> A, Vector<T> B){
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int dim; SizeSquare(A,dim);
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int dimB; Size(B,dimB);
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assert(dimB==dim);
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T C = 0;
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for(int i=0;i<dim;i++){
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T sum = 0.0;
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for(int j=0;j<dim;j++){
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sum += A[i][j]*B[j];
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}
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C += B[i]*sum; // No conj?
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}
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return C;
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}
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/*
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*************************************************************
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*
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* Matrix Vector products
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*
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*************************************************************
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*/
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// Instead make a linop and call my CG;
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/// q -> q Q
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template <class T,class Fermion> void times(Vector<Fermion> &q, Matrix<T> &Q)
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{
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int M; SizeSquare(Q,M);
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int N; Size(q,N);
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assert(M==N);
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times(q,Q,N);
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}
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/// q -> q Q
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template <class T> void times(multi1d<LatticeFermion> &q, Matrix<T> &Q, int N)
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{
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GridBase *grid = q[0]._grid;
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int M; SizeSquare(Q,M);
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int K; Size(q,K);
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assert(N<M);
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assert(N<K);
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Vector<Fermion> S(N,grid );
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for(int j=0;j<N;j++){
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S[j] = zero;
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for(int k=0;k<N;k++){
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S[j] = S[j] + q[k]* Q[k][j];
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}
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}
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for(int j=0;j<q.size();j++){
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q[j] = S[j];
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}
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}
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#endif
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