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Lanczos untested/partially tested additions. In middle of shake out but at least compiles
This commit is contained in:
Peter Boyle
parent
44fecd4d8d
commit
2d95dac6b6
106
lib/algorithms/iterative/DenseMatrix.h
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106
lib/algorithms/iterative/DenseMatrix.h
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@ -0,0 +1,106 @@
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#ifndef GRID_DENSE_MATRIX_H
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#define GRID_DENSE_MATRIX_H
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namespace Grid {
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/////////////////////////////////////////////////////////////
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// Matrix untils
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/////////////////////////////////////////////////////////////
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template<class T> using DenseVector = std::vector<T>;
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template<class T> using DenseMatrix = DenseVector<DenseVector<T> >;
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template<class T> void Size(DenseVector<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(DenseMatrix<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(DenseMatrix<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 Resize(DenseMatrix<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 Fill(DenseMatrix<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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template<class T> DenseMatrix<T> Transpose(DenseMatrix<T> & mat){
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int N,M;
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Size(mat,N,M);
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DenseMatrix<T> 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 DenseMatrix to unit matrix **/
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template<class T> void Unity(DenseMatrix<T> &A){
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int N; SizeSquare(A,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(DenseMatrix<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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template<class T>
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DenseMatrix<T> HermitianConj(DenseMatrix<T> &mat){
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int dim; SizeSquare(mat,dim);
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DenseMatrix<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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/**Get a square submatrix**/
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template <class T>
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DenseMatrix<T> GetSubMtx(DenseMatrix<T> &A,int row_st, int row_end, int col_st, int col_end)
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{
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DenseMatrix<T> H; Resize(H,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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}
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#include <algorithms/iterative/Householder.h>
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#include <algorithms/iterative/Francis.h>
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#endif
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52
lib/algorithms/iterative/EigenSort.h
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52
lib/algorithms/iterative/EigenSort.h
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@ -0,0 +1,52 @@
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#ifndef GRID_EIGENSORT_H
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#define GRID_EIGENSORT_H
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namespace Grid {
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/////////////////////////////////////////////////////////////
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// Eigen sorter to begin with
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/////////////////////////////////////////////////////////////
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template<class Field>
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class SortEigen {
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private:
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static bool less_lmd(RealD left,RealD right){
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return fabs(left) < fabs(right);
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}
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static bool less_pair(std::pair<RealD,Field>& left,
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std::pair<RealD,Field>& right){
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return fabs(left.first) < fabs(right.first);
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}
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public:
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void push(DenseVector<RealD>& lmd,
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DenseVector<Field>& evec,int N) {
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DenseVector<std::pair<RealD, Field> > emod;
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typename DenseVector<std::pair<RealD, Field> >::iterator it;
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for(int i=0;i<lmd.size();++i){
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emod.push_back(std::pair<RealD,Field>(lmd[i],evec[i]));
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}
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partial_sort(emod.begin(),emod.begin()+N,emod.end(),less_pair);
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it=emod.begin();
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for(int i=0;i<N;++i){
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lmd[i]=it->first;
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evec[i]=it->second;
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++it;
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}
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}
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void push(DenseVector<RealD>& lmd,int N) {
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std::partial_sort(lmd.begin(),lmd.begin()+N,lmd.end(),less_lmd);
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}
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bool saturated(RealD lmd, RealD thrs) {
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return fabs(lmd) > fabs(thrs);
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}
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};
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}
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#endif
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498
lib/algorithms/iterative/Francis.h
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498
lib/algorithms/iterative/Francis.h
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@ -0,0 +1,498 @@
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#ifndef FRANCIS_H
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#define FRANCIS_H
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#include <cstdlib>
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#include <string>
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#include <cmath>
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#include <iostream>
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#include <sstream>
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#include <stdexcept>
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#include <fstream>
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#include <complex>
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#include <algorithm>
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//#include <timer.h>
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//#include <lapacke.h>
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//#include <Eigen/Dense>
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namespace Grid {
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template <class T> int SymmEigensystem(DenseMatrix<T > &Ain, DenseVector<T> &evals, DenseMatrix<T> &evecs, RealD small);
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template <class T> int Eigensystem(DenseMatrix<T > &Ain, DenseVector<T> &evals, DenseMatrix<T> &evecs, RealD small);
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/**
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Find the eigenvalues of an upper hessenberg matrix using the Francis QR algorithm.
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H =
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x x x x x x x x x
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x x x x x x x x x
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0 x x x x x x x x
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0 0 x x x x x x x
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0 0 0 x x x x x x
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0 0 0 0 x x x x x
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0 0 0 0 0 x x x x
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0 0 0 0 0 0 x x x
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0 0 0 0 0 0 0 x x
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Factorization is P T P^H where T is upper triangular (mod cc blocks) and P is orthagonal/unitary.
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**/
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template <class T>
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int QReigensystem(DenseMatrix<T> &Hin, DenseVector<T> &evals, DenseMatrix<T> &evecs, RealD small)
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{
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DenseMatrix<T> H = Hin;
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int N ; SizeSquare(H,N);
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int M = N;
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Fill(evals,0);
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Fill(evecs,0);
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T s,t,x=0,y=0,z=0;
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T u,d;
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T apd,amd,bc;
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DenseVector<T> p(N,0);
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T nrm = Norm(H); ///DenseMatrix Norm
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int n, m;
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int e = 0;
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int it = 0;
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int tot_it = 0;
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int l = 0;
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int r = 0;
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DenseMatrix<T> P; Resize(P,N,N); Unity(P);
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DenseVector<int> trows(N,0);
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/// Check if the matrix is really hessenberg, if not abort
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RealD sth = 0;
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for(int j=0;j<N;j++){
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for(int i=j+2;i<N;i++){
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sth = abs(H[i][j]);
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if(sth > small){
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std::cout << "Non hessenberg H = " << sth << " > " << small << std::endl;
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exit(1);
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}
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}
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}
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do{
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std::cout << "Francis QR Step N = " << N << std::endl;
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/** Check for convergence
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x x x x x
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0 x x x x
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0 0 x x x
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0 0 x x x
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0 0 0 0 x
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for this matrix l = 4
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**/
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do{
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l = Chop_subdiag(H,nrm,e,small);
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r = 0; ///May have converged on more than one eval
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///Single eval
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if(l == N-1){
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evals[e] = H[l][l];
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N--; e++; r++; it = 0;
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}
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///RealD eval
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if(l == N-2){
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trows[l+1] = 1; ///Needed for UTSolve
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apd = H[l][l] + H[l+1][l+1];
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amd = H[l][l] - H[l+1][l+1];
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bc = (T)4.0*H[l+1][l]*H[l][l+1];
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evals[e] = (T)0.5*( apd + sqrt(amd*amd + bc) );
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evals[e+1] = (T)0.5*( apd - sqrt(amd*amd + bc) );
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N-=2; e+=2; r++; it = 0;
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}
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} while(r>0);
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if(N ==0) break;
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DenseVector<T > ck; Resize(ck,3);
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DenseVector<T> v; Resize(v,3);
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for(int m = N-3; m >= l; m--){
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///Starting vector essentially random shift.
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if(it%10 == 0 && N >= 3 && it > 0){
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s = (T)1.618033989*( abs( H[N-1][N-2] ) + abs( H[N-2][N-3] ) );
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t = (T)0.618033989*( abs( H[N-1][N-2] ) + abs( H[N-2][N-3] ) );
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x = H[m][m]*H[m][m] + H[m][m+1]*H[m+1][m] - s*H[m][m] + t;
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y = H[m+1][m]*(H[m][m] + H[m+1][m+1] - s);
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z = H[m+1][m]*H[m+2][m+1];
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}
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///Starting vector implicit Q theorem
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else{
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s = (H[N-2][N-2] + H[N-1][N-1]);
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t = (H[N-2][N-2]*H[N-1][N-1] - H[N-2][N-1]*H[N-1][N-2]);
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x = H[m][m]*H[m][m] + H[m][m+1]*H[m+1][m] - s*H[m][m] + t;
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y = H[m+1][m]*(H[m][m] + H[m+1][m+1] - s);
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z = H[m+1][m]*H[m+2][m+1];
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}
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ck[0] = x; ck[1] = y; ck[2] = z;
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if(m == l) break;
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/** Some stupid thing from numerical recipies, seems to work**/
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// PAB.. for heaven's sake quote page, purpose, evidence it works.
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// what sort of comment is that!?!?!?
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u=abs(H[m][m-1])*(abs(y)+abs(z));
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d=abs(x)*(abs(H[m-1][m-1])+abs(H[m][m])+abs(H[m+1][m+1]));
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if ((T)abs(u+d) == (T)abs(d) ){
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l = m; break;
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}
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//if (u < small){l = m; break;}
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}
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if(it > 100000){
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std::cout << "QReigensystem: bugger it got stuck after 100000 iterations" << std::endl;
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std::cout << "got " << e << " evals " << l << " " << N << std::endl;
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exit(1);
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}
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normalize(ck); ///Normalization cancels in PHP anyway
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T beta;
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Householder_vector<T >(ck, 0, 2, v, beta);
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Householder_mult<T >(H,v,beta,0,l,l+2,0);
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Householder_mult<T >(H,v,beta,0,l,l+2,1);
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///Accumulate eigenvector
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Householder_mult<T >(P,v,beta,0,l,l+2,1);
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int sw = 0; ///Are we on the last row?
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for(int k=l;k<N-2;k++){
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x = H[k+1][k];
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y = H[k+2][k];
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z = (T)0.0;
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if(k+3 <= N-1){
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z = H[k+3][k];
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} else{
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sw = 1;
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v[2] = (T)0.0;
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}
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ck[0] = x; ck[1] = y; ck[2] = z;
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normalize(ck);
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Householder_vector<T >(ck, 0, 2-sw, v, beta);
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Householder_mult<T >(H,v, beta,0,k+1,k+3-sw,0);
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Householder_mult<T >(H,v, beta,0,k+1,k+3-sw,1);
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///Accumulate eigenvector
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Householder_mult<T >(P,v, beta,0,k+1,k+3-sw,1);
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}
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it++;
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tot_it++;
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}while(N > 1);
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N = evals.size();
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///Annoying - UT solves in reverse order;
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DenseVector<T> tmp; Resize(tmp,N);
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for(int i=0;i<N;i++){
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tmp[i] = evals[N-i-1];
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}
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evals = tmp;
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UTeigenvectors(H, trows, evals, evecs);
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for(int i=0;i<evals.size();i++){evecs[i] = P*evecs[i]; normalize(evecs[i]);}
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return tot_it;
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}
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template <class T>
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int my_Wilkinson(DenseMatrix<T> &Hin, DenseVector<T> &evals, DenseMatrix<T> &evecs, RealD small)
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{
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/**
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Find the eigenvalues of an upper Hessenberg matrix using the Wilkinson QR algorithm.
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H =
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x x 0 0 0 0
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x x x 0 0 0
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0 x x x 0 0
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0 0 x x x 0
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0 0 0 x x x
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0 0 0 0 x x
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Factorization is P T P^H where T is upper triangular (mod cc blocks) and P is orthagonal/unitary. **/
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return my_Wilkinson(Hin, evals, evecs, small, small);
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}
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template <class T>
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int my_Wilkinson(DenseMatrix<T> &Hin, DenseVector<T> &evals, DenseMatrix<T> &evecs, RealD small, RealD tol)
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{
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int N; SizeSquare(Hin,N);
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int M = N;
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///I don't want to modify the input but matricies must be passed by reference
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//Scale a matrix by its "norm"
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//RealD Hnorm = abs( Hin.LargestDiag() ); H = H*(1.0/Hnorm);
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DenseMatrix<T> H; H = Hin;
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RealD Hnorm = abs(Norm(Hin));
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H = H * (1.0 / Hnorm);
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// TODO use openmp and memset
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Fill(evals,0);
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Fill(evecs,0);
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T s, t, x = 0, y = 0, z = 0;
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T u, d;
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T apd, amd, bc;
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DenseVector<T> p; Resize(p,N); Fill(p,0);
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T nrm = Norm(H); ///DenseMatrix Norm
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int n, m;
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int e = 0;
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int it = 0;
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int tot_it = 0;
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int l = 0;
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int r = 0;
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DenseMatrix<T> P; Resize(P,N,N);
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Unity(P);
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DenseVector<int> trows(N, 0);
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/// Check if the matrix is really symm tridiag
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RealD sth = 0;
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for(int j = 0; j < N; ++j)
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{
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for(int i = j + 2; i < N; ++i)
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{
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if(abs(H[i][j]) > tol || abs(H[j][i]) > tol)
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{
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std::cout << "Non Tridiagonal H(" << i << ","<< j << ") = |" << Real( real( H[j][i] ) ) << "| > " << tol << std::endl;
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std::cout << "Warning tridiagonalize and call again" << std::endl;
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// exit(1); // see what is going on
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//return;
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}
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}
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}
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do{
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do{
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//Jasper
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//Check if the subdiagonal term is small enough (<small)
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//if true then it is converged.
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//check start from H.dim - e - 1
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//How to deal with more than 2 are converged?
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//What if Chop_symm_subdiag return something int the middle?
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//--------------
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l = Chop_symm_subdiag(H,nrm, e, small);
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r = 0; ///May have converged on more than one eval
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//Jasper
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//In this case
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// x x 0 0 0 0
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// x x x 0 0 0
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// 0 x x x 0 0
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// 0 0 x x x 0
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// 0 0 0 x x 0
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// 0 0 0 0 0 x <- l
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//--------------
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///Single eval
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if(l == N - 1)
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||||
{
|
||||
evals[e] = H[l][l];
|
||||
N--;
|
||||
e++;
|
||||
r++;
|
||||
it = 0;
|
||||
}
|
||||
//Jasper
|
||||
// x x 0 0 0 0
|
||||
// x x x 0 0 0
|
||||
// 0 x x x 0 0
|
||||
// 0 0 x x 0 0
|
||||
// 0 0 0 0 x x <- l
|
||||
// 0 0 0 0 x x
|
||||
//--------------
|
||||
///RealD eval
|
||||
if(l == N - 2)
|
||||
{
|
||||
trows[l + 1] = 1; ///Needed for UTSolve
|
||||
apd = H[l][l] + H[l + 1][ l + 1];
|
||||
amd = H[l][l] - H[l + 1][l + 1];
|
||||
bc = (T) 4.0 * H[l + 1][l] * H[l][l + 1];
|
||||
evals[e] = (T) 0.5 * (apd + sqrt(amd * amd + bc));
|
||||
evals[e + 1] = (T) 0.5 * (apd - sqrt(amd * amd + bc));
|
||||
N -= 2;
|
||||
e += 2;
|
||||
r++;
|
||||
it = 0;
|
||||
}
|
||||
}while(r > 0);
|
||||
//Jasper
|
||||
//Already converged
|
||||
//--------------
|
||||
if(N == 0) break;
|
||||
|
||||
DenseVector<T> ck,v; Resize(ck,2); Resize(v,2);
|
||||
|
||||
for(int m = N - 3; m >= l; m--)
|
||||
{
|
||||
///Starting vector essentially random shift.
|
||||
if(it%10 == 0 && N >= 3 && it > 0)
|
||||
{
|
||||
t = abs(H[N - 1][N - 2]) + abs(H[N - 2][N - 3]);
|
||||
x = H[m][m] - t;
|
||||
z = H[m + 1][m];
|
||||
} else {
|
||||
///Starting vector implicit Q theorem
|
||||
d = (H[N - 2][N - 2] - H[N - 1][N - 1]) * (T) 0.5;
|
||||
t = H[N - 1][N - 1] - H[N - 1][N - 2] * H[N - 1][N - 2]
|
||||
/ (d + sign(d) * sqrt(d * d + H[N - 1][N - 2] * H[N - 1][N - 2]));
|
||||
x = H[m][m] - t;
|
||||
z = H[m + 1][m];
|
||||
}
|
||||
//Jasper
|
||||
//why it is here????
|
||||
//-----------------------
|
||||
if(m == l)
|
||||
break;
|
||||
|
||||
u = abs(H[m][m - 1]) * (abs(y) + abs(z));
|
||||
d = abs(x) * (abs(H[m - 1][m - 1]) + abs(H[m][m]) + abs(H[m + 1][m + 1]));
|
||||
if ((T)abs(u + d) == (T)abs(d))
|
||||
{
|
||||
l = m;
|
||||
break;
|
||||
}
|
||||
}
|
||||
//Jasper
|
||||
if(it > 1000000)
|
||||
{
|
||||
std::cout << "Wilkinson: bugger it got stuck after 100000 iterations" << std::endl;
|
||||
std::cout << "got " << e << " evals " << l << " " << N << std::endl;
|
||||
exit(1);
|
||||
}
|
||||
//
|
||||
T s, c;
|
||||
Givens_calc<T>(x, z, c, s);
|
||||
Givens_mult<T>(H, l, l + 1, c, -s, 0);
|
||||
Givens_mult<T>(H, l, l + 1, c, s, 1);
|
||||
Givens_mult<T>(P, l, l + 1, c, s, 1);
|
||||
//
|
||||
for(int k = l; k < N - 2; ++k)
|
||||
{
|
||||
x = H.A[k + 1][k];
|
||||
z = H.A[k + 2][k];
|
||||
Givens_calc<T>(x, z, c, s);
|
||||
Givens_mult<T>(H, k + 1, k + 2, c, -s, 0);
|
||||
Givens_mult<T>(H, k + 1, k + 2, c, s, 1);
|
||||
Givens_mult<T>(P, k + 1, k + 2, c, s, 1);
|
||||
}
|
||||
it++;
|
||||
tot_it++;
|
||||
}while(N > 1);
|
||||
|
||||
N = evals.size();
|
||||
///Annoying - UT solves in reverse order;
|
||||
DenseVector<T> tmp(N);
|
||||
for(int i = 0; i < N; ++i)
|
||||
tmp[i] = evals[N-i-1];
|
||||
evals = tmp;
|
||||
//
|
||||
UTeigenvectors(H, trows, evals, evecs);
|
||||
//UTSymmEigenvectors(H, trows, evals, evecs);
|
||||
for(int i = 0; i < evals.size(); ++i)
|
||||
{
|
||||
evecs[i] = P * evecs[i];
|
||||
normalize(evecs[i]);
|
||||
evals[i] = evals[i] * Hnorm;
|
||||
}
|
||||
// // FIXME this is to test
|
||||
// Hin.write("evecs3", evecs);
|
||||
// Hin.write("evals3", evals);
|
||||
// // check rsd
|
||||
// for(int i = 0; i < M; i++) {
|
||||
// vector<T> Aevec = Hin * evecs[i];
|
||||
// RealD norm2(0.);
|
||||
// for(int j = 0; j < M; j++) {
|
||||
// norm2 += (Aevec[j] - evals[i] * evecs[i][j]) * (Aevec[j] - evals[i] * evecs[i][j]);
|
||||
// }
|
||||
// }
|
||||
return tot_it;
|
||||
}
|
||||
|
||||
template <class T>
|
||||
void Hess(DenseMatrix<T > &A, DenseMatrix<T> &Q, int start){
|
||||
|
||||
/**
|
||||
turn a matrix A =
|
||||
x x x x x
|
||||
x x x x x
|
||||
x x x x x
|
||||
x x x x x
|
||||
x x x x x
|
||||
into
|
||||
x x x x x
|
||||
x x x x x
|
||||
0 x x x x
|
||||
0 0 x x x
|
||||
0 0 0 x x
|
||||
with householder rotations
|
||||
Slow.
|
||||
*/
|
||||
int N ; SizeSquare(A,N);
|
||||
DenseVector<T > p; Resize(p,N); Fill(p,0);
|
||||
|
||||
for(int k=start;k<N-2;k++){
|
||||
//cerr << "hess" << k << std::endl;
|
||||
DenseVector<T > ck,v; Resize(ck,N-k-1); Resize(v,N-k-1);
|
||||
for(int i=k+1;i<N;i++){ck[i-k-1] = A(i,k);} ///kth column
|
||||
normalize(ck); ///Normalization cancels in PHP anyway
|
||||
T beta;
|
||||
Householder_vector<T >(ck, 0, ck.size()-1, v, beta); ///Householder vector
|
||||
Householder_mult<T>(A,v,beta,start,k+1,N-1,0); ///A -> PA
|
||||
Householder_mult<T >(A,v,beta,start,k+1,N-1,1); ///PA -> PAP^H
|
||||
///Accumulate eigenvector
|
||||
Householder_mult<T >(Q,v,beta,start,k+1,N-1,1); ///Q -> QP^H
|
||||
}
|
||||
/*for(int l=0;l<N-2;l++){
|
||||
for(int k=l+2;k<N;k++){
|
||||
A(0,k,l);
|
||||
}
|
||||
}*/
|
||||
}
|
||||
|
||||
template <class T>
|
||||
void Tri(DenseMatrix<T > &A, DenseMatrix<T> &Q, int start){
|
||||
///Tridiagonalize a matrix
|
||||
int N; SizeSquare(A,N);
|
||||
Hess(A,Q,start);
|
||||
/*for(int l=0;l<N-2;l++){
|
||||
for(int k=l+2;k<N;k++){
|
||||
A(0,l,k);
|
||||
}
|
||||
}*/
|
||||
}
|
||||
|
||||
template <class T>
|
||||
void ForceTridiagonal(DenseMatrix<T> &A){
|
||||
///Tridiagonalize a matrix
|
||||
int N ; SizeSquare(A,N);
|
||||
for(int l=0;l<N-2;l++){
|
||||
for(int k=l+2;k<N;k++){
|
||||
A[l][k]=0;
|
||||
A[k][l]=0;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
template <class T>
|
||||
int my_SymmEigensystem(DenseMatrix<T > &Ain, DenseVector<T> &evals, DenseVector<DenseVector<T> > &evecs, RealD small){
|
||||
///Solve a symmetric eigensystem, not necessarily in tridiagonal form
|
||||
int N; SizeSquare(Ain,N);
|
||||
DenseMatrix<T > A; A = Ain;
|
||||
DenseMatrix<T > Q; Resize(Q,N,N); Unity(Q);
|
||||
Tri(A,Q,0);
|
||||
int it = my_Wilkinson<T>(A, evals, evecs, small);
|
||||
for(int k=0;k<N;k++){evecs[k] = Q*evecs[k];}
|
||||
return it;
|
||||
}
|
||||
|
||||
|
||||
template <class T>
|
||||
int Wilkinson(DenseMatrix<T> &Ain, DenseVector<T> &evals, DenseVector<DenseVector<T> > &evecs, RealD small){
|
||||
return my_Wilkinson(Ain, evals, evecs, small);
|
||||
}
|
||||
|
||||
template <class T>
|
||||
int SymmEigensystem(DenseMatrix<T> &Ain, DenseVector<T> &evals, DenseVector<DenseVector<T> > &evecs, RealD small){
|
||||
return my_SymmEigensystem(Ain, evals, evecs, small);
|
||||
}
|
||||
|
||||
template <class T>
|
||||
int Eigensystem(DenseMatrix<T > &Ain, DenseVector<T> &evals, DenseVector<DenseVector<T> > &evecs, RealD small){
|
||||
///Solve a general eigensystem, not necessarily in tridiagonal form
|
||||
int N = Ain.dim;
|
||||
DenseMatrix<T > A(N); A = Ain;
|
||||
DenseMatrix<T > Q(N);Q.Unity();
|
||||
Hess(A,Q,0);
|
||||
int it = QReigensystem<T>(A, evals, evecs, small);
|
||||
for(int k=0;k<N;k++){evecs[k] = Q*evecs[k];}
|
||||
return it;
|
||||
}
|
||||
|
||||
}
|
||||
#endif
|
||||
215
lib/algorithms/iterative/Householder.h
Normal file
215
lib/algorithms/iterative/Householder.h
Normal file
@ -0,0 +1,215 @@
|
||||
#ifndef HOUSEHOLDER_H
|
||||
#define HOUSEHOLDER_H
|
||||
|
||||
#define TIMER(A) std::cout << GridLogMessage << __FUNC__ << " file "<< __FILE__ <<" line " << __LINE__ << std::endl;
|
||||
#define ENTER() std::cout << GridLogMessage << "ENTRY "<<__FUNC__ << " file "<< __FILE__ <<" line " << __LINE__ << std::endl;
|
||||
#define LEAVE() std::cout << GridLogMessage << "EXIT "<<__FUNC__ << " file "<< __FILE__ <<" line " << __LINE__ << std::endl;
|
||||
|
||||
#include <cstdlib>
|
||||
#include <string>
|
||||
#include <cmath>
|
||||
#include <iostream>
|
||||
#include <sstream>
|
||||
#include <stdexcept>
|
||||
#include <fstream>
|
||||
#include <complex>
|
||||
#include <algorithm>
|
||||
|
||||
namespace Grid {
|
||||
/** Comparison function for finding the max element in a vector **/
|
||||
template <class T> bool cf(T i, T j) {
|
||||
return abs(i) < abs(j);
|
||||
}
|
||||
|
||||
/**
|
||||
Calculate a real Givens angle
|
||||
**/
|
||||
template <class T> inline void Givens_calc(T y, T z, T &c, T &s){
|
||||
|
||||
RealD mz = (RealD)abs(z);
|
||||
|
||||
if(mz==0.0){
|
||||
c = 1; s = 0;
|
||||
}
|
||||
if(mz >= (RealD)abs(y)){
|
||||
T t = -y/z;
|
||||
s = (T)1.0 / sqrt ((T)1.0 + t * t);
|
||||
c = s * t;
|
||||
} else {
|
||||
T t = -z/y;
|
||||
c = (T)1.0 / sqrt ((T)1.0 + t * t);
|
||||
s = c * t;
|
||||
}
|
||||
}
|
||||
|
||||
template <class T> inline void Givens_mult(DenseMatrix<T> &A, int i, int k, T c, T s, int dir)
|
||||
{
|
||||
int q ; SizeSquare(A,q);
|
||||
|
||||
if(dir == 0){
|
||||
for(int j=0;j<q;j++){
|
||||
T nu = A[i][j];
|
||||
T w = A[k][j];
|
||||
A[i][j] = (c*nu + s*w);
|
||||
A[k][j] = (-s*nu + c*w);
|
||||
}
|
||||
}
|
||||
|
||||
if(dir == 1){
|
||||
for(int j=0;j<q;j++){
|
||||
T nu = A[j][i];
|
||||
T w = A[j][k];
|
||||
A[j][i] = (c*nu - s*w);
|
||||
A[j][k] = (s*nu + c*w);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
from input = x;
|
||||
Compute the complex Householder vector, v, such that
|
||||
P = (I - b v transpose(v) )
|
||||
b = 2/v.v
|
||||
|
||||
P | x | | x | k = 0
|
||||
| x | | 0 |
|
||||
| x | = | 0 |
|
||||
| x | | 0 | j = 3
|
||||
| x | | x |
|
||||
|
||||
These are the "Unreduced" Householder vectors.
|
||||
|
||||
**/
|
||||
template <class T> inline void Householder_vector(DenseVector<T> input, int k, int j, DenseVector<T> &v, T &beta)
|
||||
{
|
||||
int N ; Size(input,N);
|
||||
T m = *max_element(input.begin() + k, input.begin() + j + 1, cf<T> );
|
||||
|
||||
if(abs(m) > 0.0){
|
||||
T alpha = 0;
|
||||
|
||||
for(int i=k; i<j+1; i++){
|
||||
v[i] = input[i]/m;
|
||||
alpha = alpha + v[i]*conj(v[i]);
|
||||
}
|
||||
alpha = sqrt(alpha);
|
||||
beta = (T)1.0/(alpha*(alpha + abs(v[k]) ));
|
||||
|
||||
if(abs(v[k]) > 0.0) v[k] = v[k] + (v[k]/abs(v[k]))*alpha;
|
||||
else v[k] = -alpha;
|
||||
} else{
|
||||
for(int i=k; i<j+1; i++){
|
||||
v[i] = 0.0;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
from input = x;
|
||||
Compute the complex Householder vector, v, such that
|
||||
P = (I - b v transpose(v) )
|
||||
b = 2/v.v
|
||||
|
||||
Px = alpha*e_dir
|
||||
|
||||
These are the "Unreduced" Householder vectors.
|
||||
|
||||
**/
|
||||
|
||||
template <class T> inline void Householder_vector(DenseVector<T> input, int k, int j, int dir, DenseVector<T> &v, T &beta)
|
||||
{
|
||||
int N = input.size();
|
||||
T m = *max_element(input.begin() + k, input.begin() + j + 1, cf);
|
||||
|
||||
if(abs(m) > 0.0){
|
||||
T alpha = 0;
|
||||
|
||||
for(int i=k; i<j+1; i++){
|
||||
v[i] = input[i]/m;
|
||||
alpha = alpha + v[i]*conj(v[i]);
|
||||
}
|
||||
|
||||
alpha = sqrt(alpha);
|
||||
beta = 1.0/(alpha*(alpha + abs(v[dir]) ));
|
||||
|
||||
if(abs(v[dir]) > 0.0) v[dir] = v[dir] + (v[dir]/abs(v[dir]))*alpha;
|
||||
else v[dir] = -alpha;
|
||||
}else{
|
||||
for(int i=k; i<j+1; i++){
|
||||
v[i] = 0.0;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
Compute the product PA if trans = 0
|
||||
AP if trans = 1
|
||||
P = (I - b v transpose(v) )
|
||||
b = 2/v.v
|
||||
start at element l of matrix A
|
||||
v is of length j - k + 1 of v are nonzero
|
||||
**/
|
||||
|
||||
template <class T> inline void Householder_mult(DenseMatrix<T> &A , DenseVector<T> v, T beta, int l, int k, int j, int trans)
|
||||
{
|
||||
int N ; SizeSquare(A,N);
|
||||
|
||||
if(abs(beta) > 0.0){
|
||||
for(int p=l; p<N; p++){
|
||||
T s = 0;
|
||||
if(trans==0){
|
||||
for(int i=k;i<j+1;i++) s += conj(v[i-k])*A[i][p];
|
||||
s *= beta;
|
||||
for(int i=k;i<j+1;i++){ A[i][p] = A[i][p]-s*conj(v[i-k]);}
|
||||
} else {
|
||||
for(int i=k;i<j+1;i++){ s += conj(v[i-k])*A[p][i];}
|
||||
s *= beta;
|
||||
for(int i=k;i<j+1;i++){ A[p][i]=A[p][i]-s*conj(v[i-k]);}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
Compute the product PA if trans = 0
|
||||
AP if trans = 1
|
||||
P = (I - b v transpose(v) )
|
||||
b = 2/v.v
|
||||
start at element l of matrix A
|
||||
v is of length j - k + 1 of v are nonzero
|
||||
A is tridiagonal
|
||||
**/
|
||||
template <class T> inline void Householder_mult_tri(DenseMatrix<T> &A , DenseVector<T> v, T beta, int l, int M, int k, int j, int trans)
|
||||
{
|
||||
if(abs(beta) > 0.0){
|
||||
|
||||
int N ; SizeSquare(A,N);
|
||||
|
||||
DenseMatrix<T> tmp; Resize(tmp,N,N); Fill(tmp,0);
|
||||
|
||||
T s;
|
||||
for(int p=l; p<M; p++){
|
||||
s = 0;
|
||||
if(trans==0){
|
||||
for(int i=k;i<j+1;i++) s = s + conj(v[i-k])*A[i][p];
|
||||
}else{
|
||||
for(int i=k;i<j+1;i++) s = s + v[i-k]*A[p][i];
|
||||
}
|
||||
s = beta*s;
|
||||
if(trans==0){
|
||||
for(int i=k;i<j+1;i++) tmp[i][p] = tmp(i,p) - s*v[i-k];
|
||||
}else{
|
||||
for(int i=k;i<j+1;i++) tmp[p][i] = tmp[p][i] - s*conj(v[i-k]);
|
||||
}
|
||||
}
|
||||
for(int p=l; p<M; p++){
|
||||
if(trans==0){
|
||||
for(int i=k;i<j+1;i++) A[i][p] = A[i][p] + tmp[i][p];
|
||||
}else{
|
||||
for(int i=k;i<j+1;i++) A[p][i] = A[p][i] + tmp[p][i];
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
#endif
|
||||
File diff suppressed because it is too large
Load Diff
426
lib/algorithms/iterative/Matrix.h
Normal file
426
lib/algorithms/iterative/Matrix.h
Normal file
@ -0,0 +1,426 @@
|
||||
#ifndef MATRIX_H
|
||||
#define MATRIX_H
|
||||
|
||||
#include <cstdlib>
|
||||
#include <string>
|
||||
#include <cmath>
|
||||
#include <vector>
|
||||
#include <iostream>
|
||||
#include <iomanip>
|
||||
#include <complex>
|
||||
#include <typeinfo>
|
||||
#include <Grid.h>
|
||||
|
||||
|
||||
/** Sign function **/
|
||||
template <class T> T sign(T p){return ( p/abs(p) );}
|
||||
|
||||
/////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
///////////////////// Hijack STL containers for our wicked means /////////////////////////////////////////
|
||||
/////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
template<class T> using Vector = Vector<T>;
|
||||
template<class T> using Matrix = Vector<Vector<T> >;
|
||||
|
||||
template<class T> void Resize(Vector<T > & vec, int N) { vec.resize(N); }
|
||||
|
||||
template<class T> void Resize(Matrix<T > & mat, int N, int M) {
|
||||
mat.resize(N);
|
||||
for(int i=0;i<N;i++){
|
||||
mat[i].resize(M);
|
||||
}
|
||||
}
|
||||
template<class T> void Size(Vector<T> & vec, int &N)
|
||||
{
|
||||
N= vec.size();
|
||||
}
|
||||
template<class T> void Size(Matrix<T> & mat, int &N,int &M)
|
||||
{
|
||||
N= mat.size();
|
||||
M= mat[0].size();
|
||||
}
|
||||
template<class T> void SizeSquare(Matrix<T> & mat, int &N)
|
||||
{
|
||||
int M; Size(mat,N,M);
|
||||
assert(N==M);
|
||||
}
|
||||
template<class T> void SizeSame(Matrix<T> & mat1,Matrix<T> &mat2, int &N1,int &M1)
|
||||
{
|
||||
int N2,M2;
|
||||
Size(mat1,N1,M1);
|
||||
Size(mat2,N2,M2);
|
||||
assert(N1==N2);
|
||||
assert(M1==M2);
|
||||
}
|
||||
|
||||
//*****************************************
|
||||
//* (Complex) Vector operations *
|
||||
//*****************************************
|
||||
|
||||
/**Conj of a Vector **/
|
||||
template <class T> Vector<T> conj(Vector<T> p){
|
||||
Vector<T> q(p.size());
|
||||
for(int i=0;i<p.size();i++){q[i] = conj(p[i]);}
|
||||
return q;
|
||||
}
|
||||
|
||||
/** Norm of a Vector**/
|
||||
template <class T> T norm(Vector<T> p){
|
||||
T sum = 0;
|
||||
for(int i=0;i<p.size();i++){sum = sum + p[i]*conj(p[i]);}
|
||||
return abs(sqrt(sum));
|
||||
}
|
||||
|
||||
/** Norm squared of a Vector **/
|
||||
template <class T> T norm2(Vector<T> p){
|
||||
T sum = 0;
|
||||
for(int i=0;i<p.size();i++){sum = sum + p[i]*conj(p[i]);}
|
||||
return abs((sum));
|
||||
}
|
||||
|
||||
/** Sum elements of a Vector **/
|
||||
template <class T> T trace(Vector<T> p){
|
||||
T sum = 0;
|
||||
for(int i=0;i<p.size();i++){sum = sum + p[i];}
|
||||
return sum;
|
||||
}
|
||||
|
||||
/** Fill a Vector with constant c **/
|
||||
template <class T> void Fill(Vector<T> &p, T c){
|
||||
for(int i=0;i<p.size();i++){p[i] = c;}
|
||||
}
|
||||
/** Normalize a Vector **/
|
||||
template <class T> void normalize(Vector<T> &p){
|
||||
T m = norm(p);
|
||||
if( abs(m) > 0.0) for(int i=0;i<p.size();i++){p[i] /= m;}
|
||||
}
|
||||
/** Vector by scalar **/
|
||||
template <class T, class U> Vector<T> times(Vector<T> p, U s){
|
||||
for(int i=0;i<p.size();i++){p[i] *= s;}
|
||||
return p;
|
||||
}
|
||||
template <class T, class U> Vector<T> times(U s, Vector<T> p){
|
||||
for(int i=0;i<p.size();i++){p[i] *= s;}
|
||||
return p;
|
||||
}
|
||||
/** inner product of a and b = conj(a) . b **/
|
||||
template <class T> T inner(Vector<T> a, Vector<T> b){
|
||||
T m = 0.;
|
||||
for(int i=0;i<a.size();i++){m = m + conj(a[i])*b[i];}
|
||||
return m;
|
||||
}
|
||||
/** sum of a and b = a + b **/
|
||||
template <class T> Vector<T> add(Vector<T> a, Vector<T> b){
|
||||
Vector<T> m(a.size());
|
||||
for(int i=0;i<a.size();i++){m[i] = a[i] + b[i];}
|
||||
return m;
|
||||
}
|
||||
/** sum of a and b = a - b **/
|
||||
template <class T> Vector<T> sub(Vector<T> a, Vector<T> b){
|
||||
Vector<T> m(a.size());
|
||||
for(int i=0;i<a.size();i++){m[i] = a[i] - b[i];}
|
||||
return m;
|
||||
}
|
||||
|
||||
/**
|
||||
*********************************
|
||||
* Matrices *
|
||||
*********************************
|
||||
**/
|
||||
|
||||
template<class T> void Fill(Matrix<T> & mat, T&val) {
|
||||
int N,M;
|
||||
Size(mat,N,M);
|
||||
for(int i=0;i<N;i++){
|
||||
for(int j=0;j<M;j++){
|
||||
mat[i][j] = val;
|
||||
}}
|
||||
}
|
||||
|
||||
/** Transpose of a matrix **/
|
||||
Matrix<T> Transpose(Matrix<T> & mat){
|
||||
int N,M;
|
||||
Size(mat,N,M);
|
||||
Matrix C; Resize(C,M,N);
|
||||
for(int i=0;i<M;i++){
|
||||
for(int j=0;j<N;j++){
|
||||
C[i][j] = mat[j][i];
|
||||
}}
|
||||
return C;
|
||||
}
|
||||
/** Set Matrix to unit matrix **/
|
||||
template<class T> void Unity(Matrix<T> &mat){
|
||||
int N; SizeSquare(mat,N);
|
||||
for(int i=0;i<N;i++){
|
||||
for(int j=0;j<N;j++){
|
||||
if ( i==j ) A[i][j] = 1;
|
||||
else A[i][j] = 0;
|
||||
}
|
||||
}
|
||||
}
|
||||
/** Add C * I to matrix **/
|
||||
template<class T>
|
||||
void PlusUnit(Matrix<T> & A,T c){
|
||||
int dim; SizeSquare(A,dim);
|
||||
for(int i=0;i<dim;i++){A[i][i] = A[i][i] + c;}
|
||||
}
|
||||
|
||||
/** return the Hermitian conjugate of matrix **/
|
||||
Matrix<T> HermitianConj(Matrix<T> &mat){
|
||||
|
||||
int dim; SizeSquare(mat,dim);
|
||||
|
||||
Matrix<T> C; Resize(C,dim,dim);
|
||||
|
||||
for(int i=0;i<dim;i++){
|
||||
for(int j=0;j<dim;j++){
|
||||
C[i][j] = conj(mat[j][i]);
|
||||
}
|
||||
}
|
||||
return C;
|
||||
}
|
||||
|
||||
/** return diagonal entries as a Vector **/
|
||||
Vector<T> diag(Matrix<T> &A)
|
||||
{
|
||||
int dim; SizeSquare(A,dim);
|
||||
Vector<T> d; Resize(d,dim);
|
||||
|
||||
for(int i=0;i<dim;i++){
|
||||
d[i] = A[i][i];
|
||||
}
|
||||
return d;
|
||||
}
|
||||
|
||||
/** Left multiply by a Vector **/
|
||||
Vector<T> operator *(Vector<T> &B,Matrix<T> &A)
|
||||
{
|
||||
int K,M,N;
|
||||
Size(B,K);
|
||||
Size(A,M,N);
|
||||
assert(K==M);
|
||||
|
||||
Vector<T> C; Resize(C,N);
|
||||
|
||||
for(int j=0;j<N;j++){
|
||||
T sum = 0.0;
|
||||
for(int i=0;i<M;i++){
|
||||
sum += B[i] * A[i][j];
|
||||
}
|
||||
C[j] = sum;
|
||||
}
|
||||
return C;
|
||||
}
|
||||
|
||||
/** return 1/diagonal entries as a Vector **/
|
||||
Vector<T> inv_diag(Matrix<T> & A){
|
||||
int dim; SizeSquare(A,dim);
|
||||
Vector<T> d; Resize(d,dim);
|
||||
for(int i=0;i<dim;i++){
|
||||
d[i] = 1.0/A[i][i];
|
||||
}
|
||||
return d;
|
||||
}
|
||||
/** Matrix Addition **/
|
||||
inline Matrix<T> operator + (Matrix<T> &A,Matrix<T> &B)
|
||||
{
|
||||
int N,M ; SizeSame(A,B,N,M);
|
||||
Matrix C; Resize(C,N,M);
|
||||
for(int i=0;i<N;i++){
|
||||
for(int j=0;j<M;j++){
|
||||
C[i][j] = A[i][j] + B[i][j];
|
||||
}
|
||||
}
|
||||
return C;
|
||||
}
|
||||
/** Matrix Subtraction **/
|
||||
inline Matrix<T> operator- (Matrix<T> & A,Matrix<T> &B){
|
||||
int N,M ; SizeSame(A,B,N,M);
|
||||
Matrix C; Resize(C,N,M);
|
||||
for(int i=0;i<N;i++){
|
||||
for(int j=0;j<M;j++){
|
||||
C[i][j] = A[i][j] - B[i][j];
|
||||
}}
|
||||
return C;
|
||||
}
|
||||
|
||||
/** Matrix scalar multiplication **/
|
||||
inline Matrix<T> operator* (Matrix<T> & A,T c){
|
||||
int N,M; Size(A,N,M);
|
||||
Matrix C; Resize(C,N,M);
|
||||
for(int i=0;i<N;i++){
|
||||
for(int j=0;j<M;j++){
|
||||
C[i][j] = A[i][j]*c;
|
||||
}}
|
||||
return C;
|
||||
}
|
||||
/** Matrix Matrix multiplication **/
|
||||
inline Matrix<T> operator* (Matrix<T> &A,Matrix<T> &B){
|
||||
int K,L,N,M;
|
||||
Size(A,K,L);
|
||||
Size(B,N,M); assert(L==N);
|
||||
Matrix C; Resize(C,K,M);
|
||||
|
||||
for(int i=0;i<K;i++){
|
||||
for(int j=0;j<M;j++){
|
||||
T sum = 0.0;
|
||||
for(int k=0;k<N;k++) sum += A[i][k]*B[k][j];
|
||||
C[i][j] =sum;
|
||||
}
|
||||
}
|
||||
return C;
|
||||
}
|
||||
/** Matrix Vector multiplication **/
|
||||
inline Vector<T> operator* (Matrix<T> &A,Vector<T> &B){
|
||||
int M,N,K;
|
||||
Size(A,N,M);
|
||||
Size(B,K); assert(K==M);
|
||||
Vector<T> C; Resize(C,N);
|
||||
for(int i=0;i<N;i++){
|
||||
T sum = 0.0;
|
||||
for(int j=0;j<M;j++) sum += A[i][j]*B[j];
|
||||
C[i] = sum;
|
||||
}
|
||||
return C;
|
||||
}
|
||||
|
||||
/** Some version of Matrix norm **/
|
||||
/*
|
||||
inline T Norm(){ // this is not a usual L2 norm
|
||||
T norm = 0;
|
||||
for(int i=0;i<dim;i++){
|
||||
for(int j=0;j<dim;j++){
|
||||
norm += abs(A[i][j]);
|
||||
}}
|
||||
return norm;
|
||||
}
|
||||
*/
|
||||
|
||||
/** Some version of Matrix norm **/
|
||||
template<class T> T LargestDiag(Matrix<T> &A)
|
||||
{
|
||||
int dim ; SizeSquare(A,dim);
|
||||
|
||||
T ld = abs(A[0][0]);
|
||||
for(int i=1;i<dim;i++){
|
||||
T cf = abs(A[i][i]);
|
||||
if(abs(cf) > abs(ld) ){ld = cf;}
|
||||
}
|
||||
return ld;
|
||||
}
|
||||
|
||||
/** Look for entries on the leading subdiagonal that are smaller than 'small' **/
|
||||
template <class T,class U> int Chop_subdiag(Matrix<T> &A,T norm, int offset, U small)
|
||||
{
|
||||
int dim; SizeSquare(A,dim);
|
||||
for(int l = dim - 1 - offset; l >= 1; l--) {
|
||||
if((U)abs(A[l][l - 1]) < (U)small) {
|
||||
A[l][l-1]=(U)0.0;
|
||||
return l;
|
||||
}
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
||||
/** Look for entries on the leading subdiagonal that are smaller than 'small' **/
|
||||
template <class T,class U> int Chop_symm_subdiag(Matrix<T> & A,T norm, int offset, U small)
|
||||
{
|
||||
int dim; SizeSquare(A,dim);
|
||||
for(int l = dim - 1 - offset; l >= 1; l--) {
|
||||
if((U)abs(A[l][l - 1]) < (U)small) {
|
||||
A[l][l - 1] = (U)0.0;
|
||||
A[l - 1][l] = (U)0.0;
|
||||
return l;
|
||||
}
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
/**Assign a submatrix to a larger one**/
|
||||
template<class T>
|
||||
void AssignSubMtx(Matrix<T> & A,int row_st, int row_end, int col_st, int col_end, Matrix<T> &S)
|
||||
{
|
||||
for(int i = row_st; i<row_end; i++){
|
||||
for(int j = col_st; j<col_end; j++){
|
||||
A[i][j] = S[i - row_st][j - col_st];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**Get a square submatrix**/
|
||||
template <class T>
|
||||
Matrix<T> GetSubMtx(Matrix<T> &A,int row_st, int row_end, int col_st, int col_end)
|
||||
{
|
||||
Matrix<T> H; Resize(row_end - row_st,col_end-col_st);
|
||||
|
||||
for(int i = row_st; i<row_end; i++){
|
||||
for(int j = col_st; j<col_end; j++){
|
||||
H[i-row_st][j-col_st]=A[i][j];
|
||||
}}
|
||||
return H;
|
||||
}
|
||||
|
||||
/**Assign a submatrix to a larger one NB remember Vector Vectors are transposes of the matricies they represent**/
|
||||
template<class T>
|
||||
void AssignSubMtx(Matrix<T> & A,int row_st, int row_end, int col_st, int col_end, Matrix<T> &S)
|
||||
{
|
||||
for(int i = row_st; i<row_end; i++){
|
||||
for(int j = col_st; j<col_end; j++){
|
||||
A[i][j] = S[i - row_st][j - col_st];
|
||||
}}
|
||||
}
|
||||
|
||||
/** compute b_i A_ij b_j **/ // surprised no Conj
|
||||
template<class T> T proj(Matrix<T> A, Vector<T> B){
|
||||
int dim; SizeSquare(A,dim);
|
||||
int dimB; Size(B,dimB);
|
||||
assert(dimB==dim);
|
||||
T C = 0;
|
||||
for(int i=0;i<dim;i++){
|
||||
T sum = 0.0;
|
||||
for(int j=0;j<dim;j++){
|
||||
sum += A[i][j]*B[j];
|
||||
}
|
||||
C += B[i]*sum; // No conj?
|
||||
}
|
||||
return C;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
*************************************************************
|
||||
*
|
||||
* Matrix Vector products
|
||||
*
|
||||
*************************************************************
|
||||
*/
|
||||
// Instead make a linop and call my CG;
|
||||
|
||||
/// q -> q Q
|
||||
template <class T,class Fermion> void times(Vector<Fermion> &q, Matrix<T> &Q)
|
||||
{
|
||||
int M; SizeSquare(Q,M);
|
||||
int N; Size(q,N);
|
||||
assert(M==N);
|
||||
|
||||
times(q,Q,N);
|
||||
}
|
||||
|
||||
/// q -> q Q
|
||||
template <class T> void times(multi1d<LatticeFermion> &q, Matrix<T> &Q, int N)
|
||||
{
|
||||
GridBase *grid = q[0]._grid;
|
||||
int M; SizeSquare(Q,M);
|
||||
int K; Size(q,K);
|
||||
assert(N<M);
|
||||
assert(N<K);
|
||||
Vector<Fermion> S(N,grid );
|
||||
for(int j=0;j<N;j++){
|
||||
S[j] = zero;
|
||||
for(int k=0;k<N;k++){
|
||||
S[j] = S[j] + q[k]* Q[k][j];
|
||||
}
|
||||
}
|
||||
for(int j=0;j<q.size();j++){
|
||||
q[j] = S[j];
|
||||
}
|
||||
}
|
||||
#endif
|
||||
122
lib/algorithms/iterative/bisec.c
Normal file
122
lib/algorithms/iterative/bisec.c
Normal file
@ -0,0 +1,122 @@
|
||||
#include <math.h>
|
||||
#include <stdlib.h>
|
||||
#include <vector>
|
||||
|
||||
struct Bisection {
|
||||
|
||||
static void get_eig2(int row_num,std::vector<RealD> &ALPHA,std::vector<RealD> &BETA, std::vector<RealD> & eig)
|
||||
{
|
||||
int i,j;
|
||||
std::vector<RealD> evec1(row_num+3);
|
||||
std::vector<RealD> evec2(row_num+3);
|
||||
RealD eps2;
|
||||
ALPHA[1]=0.;
|
||||
BETHA[1]=0.;
|
||||
for(i=0;i<row_num-1;i++) {
|
||||
ALPHA[i+1] = A[i*(row_num+1)].real();
|
||||
BETHA[i+2] = A[i*(row_num+1)+1].real();
|
||||
}
|
||||
ALPHA[row_num] = A[(row_num-1)*(row_num+1)].real();
|
||||
bisec(ALPHA,BETHA,row_num,1,row_num,1e-10,1e-10,evec1,eps2);
|
||||
bisec(ALPHA,BETHA,row_num,1,row_num,1e-16,1e-16,evec2,eps2);
|
||||
|
||||
// Do we really need to sort here?
|
||||
int begin=1;
|
||||
int end = row_num;
|
||||
int swapped=1;
|
||||
while(swapped) {
|
||||
swapped=0;
|
||||
for(i=begin;i<end;i++){
|
||||
if(mag(evec2[i])>mag(evec2[i+1])) {
|
||||
swap(evec2+i,evec2+i+1);
|
||||
swapped=1;
|
||||
}
|
||||
}
|
||||
end--;
|
||||
for(i=end-1;i>=begin;i--){
|
||||
if(mag(evec2[i])>mag(evec2[i+1])) {
|
||||
swap(evec2+i,evec2+i+1);
|
||||
swapped=1;
|
||||
}
|
||||
}
|
||||
begin++;
|
||||
}
|
||||
|
||||
for(i=0;i<row_num;i++){
|
||||
for(j=0;j<row_num;j++) {
|
||||
if(i==j) H[i*row_num+j]=evec2[i+1];
|
||||
else H[i*row_num+j]=0.;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
static void bisec(std::vector<RealD> &c,
|
||||
std::vector<RealD> &b,
|
||||
int n,
|
||||
int m1,
|
||||
int m2,
|
||||
RealD eps1,
|
||||
RealD relfeh,
|
||||
std::vector<RealD> &x,
|
||||
RealD &eps2)
|
||||
{
|
||||
std::vector<RealD> wu(n+2);
|
||||
|
||||
RealD h,q,x1,xu,x0,xmin,xmax;
|
||||
int i,a,k;
|
||||
|
||||
b[1]=0.0;
|
||||
xmin=c[n]-fabs(b[n]);
|
||||
xmax=c[n]+fabs(b[n]);
|
||||
for(i=1;i<n;i++){
|
||||
h=fabs(b[i])+fabs(b[i+1]);
|
||||
if(c[i]+h>xmax) xmax= c[i]+h;
|
||||
if(c[i]-h<xmin) xmin= c[i]-h;
|
||||
}
|
||||
xmax *=2.;
|
||||
|
||||
eps2=relfeh*((xmin+xmax)>0.0 ? xmax : -xmin);
|
||||
if(eps1<=0.0) eps1=eps2;
|
||||
eps2=0.5*eps1+7.0*(eps2);
|
||||
x0=xmax;
|
||||
for(i=m1;i<=m2;i++){
|
||||
x[i]=xmax;
|
||||
wu[i]=xmin;
|
||||
}
|
||||
|
||||
for(k=m2;k>=m1;k--){
|
||||
xu=xmin;
|
||||
i=k;
|
||||
do{
|
||||
if(xu<wu[i]){
|
||||
xu=wu[i];
|
||||
i=m1-1;
|
||||
}
|
||||
i--;
|
||||
}while(i>=m1);
|
||||
if(x0>x[k]) x0=x[k];
|
||||
while((x0-xu)>2*relfeh*(fabs(xu)+fabs(x0))+eps1){
|
||||
x1=(xu+x0)/2;
|
||||
|
||||
a=0;
|
||||
q=1.0;
|
||||
for(i=1;i<=n;i++){
|
||||
q=c[i]-x1-((q!=0.0)? b[i]*b[i]/q:fabs(b[i])/relfeh);
|
||||
if(q<0) a++;
|
||||
}
|
||||
// printf("x1=%e a=%d\n",x1,a);
|
||||
if(a<k){
|
||||
if(a<m1){
|
||||
xu=x1;
|
||||
wu[m1]=x1;
|
||||
}else {
|
||||
xu=x1;
|
||||
wu[a+1]=x1;
|
||||
if(x[a]>x1) x[a]=x1;
|
||||
}
|
||||
}else x0=x1;
|
||||
}
|
||||
x[k]=(x0+xu)/2;
|
||||
}
|
||||
}
|
||||
}
|
||||
1
lib/algorithms/iterative/get_eig.c
Normal file
1
lib/algorithms/iterative/get_eig.c
Normal file
@ -0,0 +1 @@
|
||||
|
||||
123
tests/Test_synthetic_lanczos.cc
Normal file
123
tests/Test_synthetic_lanczos.cc
Normal file
@ -0,0 +1,123 @@
|
||||
#include <fenv.h>
|
||||
#include <Grid.h>
|
||||
|
||||
using namespace std;
|
||||
using namespace Grid;
|
||||
using namespace Grid::QCD;
|
||||
|
||||
static int
|
||||
FEenableexcept (unsigned int excepts)
|
||||
{
|
||||
static fenv_t fenv;
|
||||
unsigned int new_excepts = excepts & FE_ALL_EXCEPT,
|
||||
old_excepts; // previous masks
|
||||
|
||||
if ( fegetenv (&fenv) ) return -1;
|
||||
old_excepts = fenv.__control & FE_ALL_EXCEPT;
|
||||
|
||||
// unmask
|
||||
fenv.__control &= ~new_excepts;
|
||||
fenv.__mxcsr &= ~(new_excepts << 7);
|
||||
|
||||
return ( fesetenv (&fenv) ? -1 : old_excepts );
|
||||
}
|
||||
|
||||
|
||||
template<class Field> class DumbOperator : public LinearOperatorBase<Field> {
|
||||
public:
|
||||
LatticeComplex scale;
|
||||
|
||||
DumbOperator(GridBase *grid) : scale(grid)
|
||||
{
|
||||
GridParallelRNG pRNG(grid);
|
||||
std::vector<int> seeds({5,6,7,8});
|
||||
pRNG.SeedFixedIntegers(seeds);
|
||||
|
||||
random(pRNG,scale);
|
||||
|
||||
scale = exp(-real(scale)*6.0);
|
||||
std::cout << " True matrix \n"<< scale <<std::endl;
|
||||
}
|
||||
|
||||
// Support for coarsening to a multigrid
|
||||
void OpDiag (const Field &in, Field &out) {};
|
||||
void OpDir (const Field &in, Field &out,int dir,int disp){};
|
||||
|
||||
void Op (const Field &in, Field &out){
|
||||
out = scale * in;
|
||||
}
|
||||
void AdjOp (const Field &in, Field &out){
|
||||
out = scale * in;
|
||||
}
|
||||
void HermOp(const Field &in, Field &out){
|
||||
double n1, n2;
|
||||
HermOpAndNorm(in,out,n1,n2);
|
||||
}
|
||||
void HermOpAndNorm(const Field &in, Field &out,double &n1,double &n2){
|
||||
ComplexD dot;
|
||||
|
||||
out = scale * in;
|
||||
|
||||
dot= innerProduct(in,out);
|
||||
n1=real(dot);
|
||||
|
||||
dot = innerProduct(out,out);
|
||||
n2=real(dot);
|
||||
}
|
||||
};
|
||||
|
||||
|
||||
int main (int argc, char ** argv)
|
||||
{
|
||||
|
||||
FEenableexcept(FE_ALL_EXCEPT & ~FE_INEXACT);
|
||||
|
||||
Grid_init(&argc,&argv);
|
||||
|
||||
GridCartesian *grid = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(),
|
||||
GridDefaultSimd(Nd,vComplex::Nsimd()),
|
||||
GridDefaultMpi());
|
||||
|
||||
GridParallelRNG RNG(grid);
|
||||
std::vector<int> seeds({1,2,3,4});
|
||||
RNG.SeedFixedIntegers(seeds);
|
||||
|
||||
|
||||
RealD alpha = 1.0;
|
||||
RealD beta = 0.03;
|
||||
RealD mu = 0.0;
|
||||
int order = 11;
|
||||
ChebyshevLanczos<LatticeComplex> Cheby(alpha,beta,mu,order);
|
||||
|
||||
std::ofstream file("pooh.dat");
|
||||
Cheby.csv(file);
|
||||
|
||||
HermOpOperatorFunction<LatticeComplex> X;
|
||||
DumbOperator<LatticeComplex> HermOp(grid);
|
||||
|
||||
const int Nk = 40;
|
||||
const int Nm = 80;
|
||||
const int Nit= 10000;
|
||||
|
||||
int Nconv;
|
||||
RealD eresid = 1.0e-8;
|
||||
|
||||
ImplicitlyRestartedLanczos<LatticeComplex> IRL(HermOp,X,Nk,Nm,eresid,Nit);
|
||||
|
||||
ImplicitlyRestartedLanczos<LatticeComplex> ChebyIRL(HermOp,Cheby,Nk,Nm,eresid,Nit);
|
||||
|
||||
LatticeComplex src(grid); gaussian(RNG,src);
|
||||
{
|
||||
std::vector<RealD> eval(Nm);
|
||||
std::vector<LatticeComplex> evec(Nm,grid);
|
||||
IRL.calc(eval,evec,src, Nconv);
|
||||
}
|
||||
|
||||
{
|
||||
std::vector<RealD> eval(Nm);
|
||||
std::vector<LatticeComplex> evec(Nm,grid);
|
||||
ChebyIRL.calc(eval,evec,src, Nconv);
|
||||
}
|
||||
|
||||
Grid_finalize();
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user