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WIP Dealing with the Beyn clusterfuck (compiles now). 

TODO inverse M -matrix


Former-commit-id: eb2a37128c04c10406dc65eca7d47152b4d93db9
This commit is contained in:
Marek Nečada 2019-08-22 17:02:53 +03:00
parent b52942a5e5
commit 6e875d65ae
2 changed files with 104 additions and 120 deletions
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191
qpms/beyn.c
View File

@ -1,6 +1,6 @@
/* Copyright (C) 2005-2011 M. T. Homer Reid /*
* * This file was originally part of SCUFF-EM by M. T. Homer Reid.
* This file is part of SCUFF-EM. * Modified by Kristian Arjas and Marek Nečada to work without libhmat and libhrutil.
* *
* SCUFF-EM is free software; you can redistribute it and/or modify * SCUFF-EM is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by * it under the terms of the GNU General Public License as published by
@ -17,19 +17,15 @@
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/ */
/* #define STATIC_ASSERT(COND,MSG) typedef char static_assertion_##MSG[(COND)?1:-1]
* libBeyn.cc -- implementation of Beyn's method for
* -- nonlinear eigenvalue problems #include <complex.h>
* #include <lapacke.h>
* Homer Reid -- 6/2016
*
*/
#include <stdio.h> #include <stdio.h>
#include <stdlib.h> #include <stdlib.h>
#include <math.h> #include <math.h>
#include <time.h> #include <time.h>
#include "qpms_error.h"
#include <complex.h>
// Maybe GSL works? // Maybe GSL works?
#include <gsl/gsl_matrix.h> #include <gsl/gsl_matrix.h>
@ -40,6 +36,8 @@
#include <beyn.h> #include <beyn.h>
STATIC_ASSERT((sizeof(lapack_complex_double) == sizeof(gsl_complex)), lapack_and_gsl_complex_must_be_consistent);
// Uniformly random number between -2 and 2 // Uniformly random number between -2 and 2
gsl_complex zrandN(){ gsl_complex zrandN(){
double a = (rand()*4.0/RAND_MAX) - 2; double a = (rand()*4.0/RAND_MAX) - 2;
@ -56,14 +54,17 @@ BeynSolver *CreateBeynSolver(int M, int L)
Solver->M = M; Solver->M = M;
Solver->L = L; Solver->L = L;
QPMS_ENSURE(L <= M, "We expect L <= M, but we got L = %d, M = %d ", L, M);
#if 0
int MLMax = (M>L) ? M : L; int MLMax = (M>L) ? M : L;
#endif
int MLMin = (M<L) ? M : L; int MLMin = (M<L) ? M : L;
// storage for eigenvalues and eigenvectors // storage for eigenvalues and eigenvectors
Solver->Eigenvalues = gsl_vector_complex_calloc(L); Solver->Eigenvalues = gsl_vector_complex_calloc(L);
Solver->EVErrors = gsl_vector_complex_calloc(L); Solver->EVErrors = gsl_vector_complex_calloc(L);
Solver->Residuals = gsl_vector_complex_calloc(L); Solver->Residuals = gsl_vector_calloc(L);
Solver->Eigenvectors = gsl_matrix_complex_calloc(M, L); Solver->Eigenvectors = gsl_matrix_complex_calloc(M, L);
// storage for singular values, random VHat matrix, etc. used in algorithm // storage for singular values, random VHat matrix, etc. used in algorithm
@ -76,14 +77,13 @@ BeynSolver *CreateBeynSolver(int M, int L)
Solver->Sigma = gsl_vector_calloc(MLMin); Solver->Sigma = gsl_vector_calloc(MLMin);
ReRandomize(Solver,(unsigned)time(NULL)); ReRandomize(Solver,(unsigned)time(NULL));
#if 0
// internal workspace: need storage for 2 MxL matrices // internal workspace: need storage for 2 MxL matrices
// plus 3 LxL matrices // plus 3 LxL matrices
#define MLBUFFERS 2 #define MLBUFFERS 2
#define LLBUFFERS 3 #define LLBUFFERS 3
size_t ML = MLMax*L, LL = L*L; size_t ML = MLMax*L, LL = L*L;
size_t WorkspaceSize = (MLBUFFERS*ML + LLBUFFERS*LL)*sizeof(double complex); #endif
Solver->Workspace = (double complex*)malloc( WorkspaceSize );
return Solver; return Solver;
@ -104,10 +104,9 @@ void DestroyBeynSolver(BeynSolver *Solver)
gsl_matrix_complex_free(Solver->A1Coarse); gsl_matrix_complex_free(Solver->A1Coarse);
gsl_matrix_complex_free(Solver->MInvVHat); gsl_matrix_complex_free(Solver->MInvVHat);
gsl_vector_free(Solver->Sigma); gsl_vector_free(Solver->Sigma);
gsl_vector_free(Solver->Residuals);
gsl_matrix_complex_free(Solver->VHat); gsl_matrix_complex_free(Solver->VHat);
free(Solver->Workspace);
free(Solver); free(Solver);
} }
@ -134,7 +133,7 @@ void ReRandomize(BeynSolver *Solver, unsigned int RandSeed)
/* eigenvalues and eigenvectors */ /* eigenvalues and eigenvectors */
/***************************************************************/ /***************************************************************/
int ProcessAMatrices(BeynSolver *Solver, BeynFunction UserFunc, int ProcessAMatrices(BeynSolver *Solver, beyn_function_M_t M_function,
void *Params, void *Params,
gsl_matrix_complex *A0, gsl_matrix_complex *A1, double complex z0, gsl_matrix_complex *A0, gsl_matrix_complex *A1, double complex z0,
gsl_vector_complex *Eigenvalues, gsl_matrix_complex *Eigenvectors) gsl_vector_complex *Eigenvalues, gsl_matrix_complex *Eigenvectors)
@ -155,15 +154,27 @@ int ProcessAMatrices(BeynSolver *Solver, BeynFunction UserFunc,
gsl_matrix_complex* W0TFull = gsl_matrix_complex_calloc(L,L); gsl_matrix_complex* W0TFull = gsl_matrix_complex_calloc(L,L);
//A0->SVD(Sigma, &V0Full, &W0TFull); //A0->SVD(Sigma, &V0Full, &W0TFull);
gsl_vector_complex *work = gsl_vector_complex_alloc(M);
QPMS_ENSURE(Sigma->stride == 1, "Sigma vector stride must be 1 for LAPACKE_zgesdd, got %zd.", Sigma->stride);
// FIXME not supported by GSL; use LAPACKE_zgesdd // FIXME not supported by GSL; use LAPACKE_zgesdd
gsl_linalg_complex_SV_decomp(V0Full, W0TFull, Sigma, work); //gsl_linalg_complex_SV_decomp(V0Full, W0TFull, Sigma, work);
QPMS_ENSURE_SUCCESS(LAPACKE_zgesdd(LAPACK_ROW_MAJOR, // A = U*Σ*conjg(V')
'O' /*jobz, 'O' overwrites a with U and saves conjg(V') in vt if m >= n, i.e. if M >= L, which holds*/,
V0Full->size1 /* m, number of rows */,
V0Full->size2 /* n, number of columns */,
(lapack_complex_double *)(V0Full->data) /*a*/,
V0Full->tda /*lda*/,
Sigma->data /*s*/,
NULL /*u; not used*/,
0 /*ldu; not used*/,
(lapack_complex_double *)W0TFull->data /*vt*/,
W0TFull->tda /*ldvt*/
));
// compute effective rank K (number of eigenvalue candidates) // compute effective rank K (number of eigenvalue candidates)
int K=0; int K=0;
for(int k=0; k<Sigma->size; k++) for(int k=0; k<Sigma->size /* this is L, actually */; k++)
{ if (Verbose) printf("Beyn: SV(%i)=%e",k,gsl_vector_get(Sigma, k)); { if (Verbose) printf("Beyn: SV(%i)=%e",k,gsl_vector_get(Sigma, k));
if (gsl_vector_get(Sigma, k) > RankTol ) if (gsl_vector_get(Sigma, k) > RankTol )
K++; K++;
@ -191,7 +202,6 @@ int ProcessAMatrices(BeynSolver *Solver, BeynFunction UserFunc,
gsl_matrix_complex_free(V0Full); gsl_matrix_complex_free(V0Full);
gsl_matrix_complex_free(W0TFull); gsl_matrix_complex_free(W0TFull);
gsl_vector_complex_free(work);
gsl_vector_complex_free(TempM); gsl_vector_complex_free(TempM);
gsl_vector_complex_free(TempL); gsl_vector_complex_free(TempL);
@ -202,8 +212,8 @@ int ProcessAMatrices(BeynSolver *Solver, BeynFunction UserFunc,
printf(" Multiplying V0*A1->TM...\n"); printf(" Multiplying V0*A1->TM...\n");
//V0.Multiply(A1, &TM2, "--transA C"); // TM2 <- V0' * A1 //V0.Multiply(A1, &TM2, "--transA C"); // TM2 <- V0' * A1
gsl_complex one = gsl_complex_rect(1,0); const gsl_complex one = gsl_complex_rect(1,0);
gsl_complex zero = gsl_complex_rect(0,0); const gsl_complex zero = gsl_complex_rect(0,0);
gsl_blas_zgemm(CblasConjTrans, CblasNoTrans, one, gsl_blas_zgemm(CblasConjTrans, CblasNoTrans, one,
V0, A1, zero, TM2); V0, A1, zero, TM2);
@ -234,94 +244,72 @@ int ProcessAMatrices(BeynSolver *Solver, BeynFunction UserFunc,
// B -> S*Lambda*S' // B -> S*Lambda*S'
printf(" Eigensolving (%i,%i)\n",K,K); printf(" Eigensolving (%i,%i)\n",K,K);
gsl_vector_complex *Lambda = gsl_vector_complex_calloc(K); // Eigenvalues gsl_vector_complex *Lambda = gsl_vector_complex_alloc(K); // Eigenvalues
gsl_matrix_complex *S = gsl_matrix_complex_calloc(K,K); // Eigenvectors gsl_matrix_complex *S = gsl_matrix_complex_alloc(K,K); // Eigenvectors
gsl_matrix_complex *Eye = gsl_matrix_complex_alloc(K,K);
gsl_vector_complex *alph = gsl_vector_complex_calloc(K);
gsl_vector_complex *beta = gsl_vector_complex_calloc(K);
gsl_matrix_complex_set_identity(Eye);
// FIXME general complex eigensystems not supported by GSL (use LAPACKE_zgee?) // FIXME general complex eigensystems not supported by GSL (use LAPACKE_zgee?)
gsl_eigen_genv_workspace * W = gsl_eigen_genv_alloc(K); //gsl_eigen_genv_workspace * W = gsl_eigen_genv_alloc(K);
gsl_eigen_genv(B, Eye, alph, beta, S,W); //gsl_eigen_genv(B, Eye, alph, beta, S,W);
gsl_eigen_genv_free(W); //gsl_eigen_genv_free(W);
QPMS_ENSURE(Sigma->stride == 1, "Sigma vector stride must be 1 for LAPACKE_zgesdd, got %zd.", Sigma->stride);
QPMS_ENSURE(Lambda->stride == 1, "Lambda vector stride must be 1 for LAPACKE_zgesdd, got %zd.", Sigma->stride);
QPMS_ENSURE_SUCCESS(LAPACKE_zgeev(
LAPACK_ROW_MAJOR,
'N' /* jobvl; don't compute left eigenvectors */,
'V' /* jobvr; do compute right eigenvectors */,
K /* n */,
(lapack_complex_double *)(S->data) /* a */,
S->tda /* lda */,
(lapack_complex_double *) Lambda->data /* w */,
NULL /* vl */,
0 /* ldvl */,
(lapack_complex_double *)(B->data)/* vr */,
B->tda/* ldvr */
));
gsl_complex tmpa;
gsl_complex tmpb;
for(int i = 0; i < K; i++){
tmpb = gsl_vector_complex_get(beta,i);
tmpa = gsl_vector_complex_get(alph,i);
if(gsl_complex_abs(tmpb)){
gsl_vector_complex_set(Lambda, i, gsl_complex_div(tmpa,tmpb));
printf("Eigenvalue %e + %e i found\n",GSL_REAL(gsl_complex_div(tmpa,tmpb)), GSL_IMAG(gsl_complex_div(tmpa,tmpb)));
} else{
printf("Beta %d is zero \n",i);
}
if(!gsl_complex_abs(tmpa)){
printf("Alpha %d is zero \n",i);
}
}
gsl_vector_complex_free(alph);
gsl_vector_complex_free(beta);
gsl_matrix_complex_free(Eye);
//B.NSEig(&Lambda, &S); //B.NSEig(&Lambda, &S);
// V0S <- V0*S // V0S <- V0*S
printf("Multiplying V0*S...\n"); printf("Multiplying V0*S...\n");
gsl_matrix_complex *V0S = gsl_matrix_complex_alloc(M, K);
gsl_vector_complex *V = gsl_vector_complex_alloc(K); QPMS_ENSURE_SUCCESS(gsl_blas_zgemm(CblasNoTrans, CblasNoTrans,
gsl_vector_complex *s = gsl_vector_complex_alloc(K); one, V0, S, zero, V0S));
printf("Evaluating retained values \n");
int KRetained=0;
gsl_vector_complex * om = gsl_vector_complex_alloc(1);
for(int k=0; k<K; k++)
{
if(gsl_complex_abs(gsl_vector_complex_get(Lambda,k))){
gsl_complex tmp_c = gsl_vector_complex_get(Lambda, k);
double complex z = z0 + GSL_REAL(tmp_c) + GSL_IMAG(tmp_c)*I;
//gsl_matrix_get_col(V, V0S, k);
gsl_matrix_complex_get_col(s, S, k);
gsl_blas_zgemv(CblasNoTrans, one, V0, s, zero, V);
double Residual=0.0;
if (ResTol>0.0) int KRetained = 0;
{ /*gsl_matrix_complex Vk(M,1,V); gsl_matrix_complex *Mmat = gsl_matrix_complex_alloc(M,L);
gsl_matrix_complex MVk(M,1,MLBuffers[0]); gsl_vector_complex *MVk = gsl_vector_complex_alloc(M);
UserFunc(z, Params, &Vk, &MVk); for (int k = 0; k < K; ++k) {
Residual=VecNorm(MVk.ZM, M); const gsl_complex zgsl = gsl_complex_add(gsl_complex_rect(creal(z0), cimag(z0)), gsl_vector_complex_get(Lambda, k));
*/ const complex double z = GSL_REAL(zgsl) + I*GSL_IMAG(zgsl);
gsl_vector_complex_set(om,1,tmp_c); gsl_vector_complex_const_view Vk = gsl_matrix_complex_const_column(V0S, k);
Residual = min_sing(om,Params); // in unitcell.c
if (1) printf("Beyn: Residual(%i)=%e\n",k,Residual); double residual = 0;
if(ResTol > 0) {
QPMS_ENSURE_SUCCESS(M_function(Mmat, z, Params));
QPMS_ENSURE_SUCCESS(gsl_blas_zgemv(CblasNoTrans, one, Mmat, &(Vk.vector), zero, MVk));
residual = gsl_blas_dznrm2(MVk);
if (Verbose) printf("Beyn: Residual(%i)=%e\n",k,residual);
} }
if (ResTol>0.0 && Residual>ResTol) continue; if (ResTol > 0 && residual > ResTol) continue;
//Eigenvalues->SetEntry(KRetained, z); gsl_vector_complex_set(Eigenvalues, KRetained, zgsl);
gsl_vector_complex_set(Eigenvalues, KRetained, tmp_c); if(Eigenvectors) {
gsl_matrix_complex_set_col(Eigenvectors, KRetained, V); gsl_matrix_complex_set_col(Eigenvectors, KRetained, &(Vk.vector));
/*if (Eigenvectors) gsl_vector_set(Solver->Residuals, KRetained, residual);
{
//Eigenvectors->SetEntries(":", KRetained, V);
//Solver->Residuals->SetEntry(KRetained,Residual);
}
*/
KRetained++;
} }
++KRetained;
} }
printf("%d eigenvalues found \n",KRetained); gsl_matrix_complex_free(V0S);
gsl_matrix_complex_free(Mmat);
gsl_vector_complex_free(MVk);
gsl_matrix_complex_free(S); gsl_matrix_complex_free(S);
gsl_matrix_complex_free(V0);
gsl_vector_complex_free(Lambda); gsl_vector_complex_free(Lambda);
gsl_vector_complex_free(om);
return KRetained; return KRetained;
} }
@ -329,8 +317,8 @@ int ProcessAMatrices(BeynSolver *Solver, BeynFunction UserFunc,
/***************************************************************/ /***************************************************************/
/***************************************************************/ /***************************************************************/
int BeynSolve(BeynSolver *Solver, int BeynSolve(BeynSolver *Solver, beyn_function_M_t M_function,
BeynFunction UserFunc, void *Params, beyn_function_M_inv_Vhat_t M_inv_Vhat_function, void *Params,
double complex z0, double Rx, double Ry, int N) double complex z0, double Rx, double Ry, int N)
{ {
/***************************************************************/ /***************************************************************/
@ -380,7 +368,12 @@ int BeynSolve(BeynSolver *Solver,
// Tän pitäis kutsua eval_WT // Tän pitäis kutsua eval_WT
// Output ilmeisesti tallentuun neljänteen parametriin // Output ilmeisesti tallentuun neljänteen parametriin
UserFunc(z0+zz, Params, VHat, MInvVHat); if(M_inv_Vhat_function) {
QPMS_ENSURE_SUCCESS(M_inv_Vhat_function(MInvVHat, VHat, z0+zz, Params));
} else {
QPMS_NOT_IMPLEMENTED("TODO");
}
//UserFunc(z0+zz, Params, VHat, MInvVHat);
gsl_matrix_complex_scale(MInvVHat, dz); gsl_matrix_complex_scale(MInvVHat, dz);
gsl_matrix_complex_add(A0, MInvVHat); gsl_matrix_complex_add(A0, MInvVHat);
@ -401,7 +394,7 @@ int BeynSolve(BeynSolver *Solver,
//gsl_vector_complex *EVErrors = Solver->EVErrors; //gsl_vector_complex *EVErrors = Solver->EVErrors;
gsl_matrix_complex *Eigenvectors = Solver->Eigenvectors; gsl_matrix_complex *Eigenvectors = Solver->Eigenvectors;
int K = ProcessAMatrices(Solver, UserFunc, Params, A0, A1, z0, Eigenvalues, Eigenvectors); int K = ProcessAMatrices(Solver, M_function, Params, A0, A1, z0, Eigenvalues, Eigenvectors);
//int KCoarse = ProcessAMatrices(Solver, UserFunc, Params, A0Coarse, A1Coarse, z0, EVErrors, Eigenvectors); //int KCoarse = ProcessAMatrices(Solver, UserFunc, Params, A0Coarse, A1Coarse, z0, EVErrors, Eigenvectors);
// Log("{K,KCoarse}={%i,%i}",K,KCoarse); // Log("{K,KCoarse}={%i,%i}",K,KCoarse);
/* /*

29
qpms/beyn.h
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@ -31,24 +31,15 @@
#ifndef BEYN_H #ifndef BEYN_H
#define BEYN_H #define BEYN_H
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <stdarg.h>
#include <fenv.h>
#include <complex.h> #include <complex.h>
// Needs to be changed to gsl or something
//#include <libhmat.h>
#include <gsl/gsl_matrix.h> #include <gsl/gsl_matrix.h>
/***************************************************************/
/* prototype for user-supplied function passed to BeynMethod. */ /// User-supplied function that provides the operator M(z) whose "roots" are to be found.
/* The user's function should replace VHat with */ typedef int (*beyn_function_M_t)(gsl_matrix_complex *target_M, complex double z, void *params);
/* Inverse[ M(z) ] * VHat. */
/***************************************************************/ /// (optional) User-supplied function that, given \f$ \hat V \f$, calculates \f$ M(z)^{-1} \hat V \f$.
typedef void (*BeynFunction)(double complex z, void *Params, gsl_matrix_complex *VHat, gsl_matrix_complex *MVHat); typedef int (*beyn_function_M_inv_Vhat_t)(gsl_matrix_complex *target_M_inv_Vhat,
const gsl_matrix_complex *Vhat, complex double z, void *params);
/***************************************************************/ /***************************************************************/
/***************************************************************/ /***************************************************************/
@ -58,11 +49,11 @@ typedef struct BeynSolver
int M; // dimension of matrices int M; // dimension of matrices
int L; // number of columns of VHat matrix int L; // number of columns of VHat matrix
gsl_vector_complex *Eigenvalues, *EVErrors, *Residuals; gsl_vector_complex *Eigenvalues, *EVErrors;
gsl_matrix_complex *Eigenvectors; gsl_matrix_complex *Eigenvectors;
gsl_matrix_complex *A0, *A1, *A0Coarse, *A1Coarse, *MInvVHat; gsl_matrix_complex *A0, *A1, *A0Coarse, *A1Coarse, *MInvVHat;
gsl_matrix_complex *VHat; gsl_matrix_complex *VHat;
gsl_vector *Sigma; gsl_vector *Sigma, *Residuals;
double complex *Workspace; double complex *Workspace;
} BeynSolver; } BeynSolver;
@ -89,7 +80,7 @@ void ReRandomize(BeynSolver *Solver, unsigned int RandSeed);
// Beyn method for elliptical contour of horizontal, vertical // Beyn method for elliptical contour of horizontal, vertical
// radii Rx, Ry, centered at z0, using N quadrature points // radii Rx, Ry, centered at z0, using N quadrature points
int BeynSolve(BeynSolver *Solver, int BeynSolve(BeynSolver *Solver,
BeynFunction UserFunction, void *Params, beyn_function_M_t M_function, beyn_function_M_inv_Vhat_t M_inv_Vhat_function, void *params,
double complex z0, double Rx, double Ry, int N); double complex z0, double Rx, double Ry, int N);
#endif // BEYN_H #endif // BEYN_H