[WIP;BROKEN] Getting rid of gsl linear algebra in Beyn.
Segfaults in LAPACKE_zgesdd. Former-commit-id: 39ce2f70e214bfe2fba6f1ec2960139194dbc761
This commit is contained in:
Marek Nečada
parent
7e0d7639e8
commit
64f77557a7
405
qpms/beyn.c
405
qpms/beyn.c
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@ -10,30 +10,25 @@
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#include <math.h>
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#include <time.h>
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#include "qpms_error.h"
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// Maybe GSL works?
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#include <gsl/gsl_matrix.h>
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#include <gsl/gsl_complex_math.h>
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#include <gsl/gsl_linalg.h>
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#include <gsl/gsl_blas.h>
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#include <gsl/gsl_eigen.h>
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#include <string.h>
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#include <cblas.h>
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#include "beyn.h"
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#define SQ(x) ((x)*(x))
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STATIC_ASSERT((sizeof(lapack_complex_double) == sizeof(gsl_complex)), lapack_and_gsl_complex_must_be_consistent);
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// matrix access
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#define MAT(mat_, n_rows_, n_cols_, i_row_, i_col_) (mat_[(n_cols_) * (i_row_) + (i_col_)])
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typedef struct BeynSolver
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{
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int M; // dimension of matrices
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int L; // number of columns of VHat matrix
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gsl_vector_complex *eigenvalues, *eigenvalue_errors;
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gsl_matrix_complex *eigenvectors;
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gsl_matrix_complex *A0, *A1, *A0_coarse, *A1_coarse, *MInvVHat;
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gsl_matrix_complex *VHat;
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gsl_vector *Sigma, *residuals;
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complex double *eigenvalues, *eigenvalue_errors; // [L]
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complex double *eigenvectors; // [L][M] (!!!)
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complex double *A0, *A1, *A0_coarse, *A1_coarse, *MInvVHat; // [M][L]
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complex double *VHat; // [M][L]
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double *Sigma, *residuals; // [L]
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} BeynSolver;
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// constructor, destructor
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@ -253,39 +248,51 @@ beyn_contour_t *beyn_contour_kidney(complex double centre, double rRe,
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return c;
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}
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void beyn_result_gsl_free(beyn_result_gsl_t *r) {
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void beyn_result_free(beyn_result_t *r) {
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if(r) {
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gsl_vector_complex_free(r->eigval);
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gsl_vector_complex_free(r->eigval_err);
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gsl_vector_free(r->residuals);
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gsl_matrix_complex_free(r->eigvec);
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gsl_vector_free(r->ranktest_SV);
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free(r->eigval);
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free(r->eigval_err);
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free(r->residuals);
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free(r->eigvec);
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free(r->ranktest_SV);
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free(r);
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}
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}
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BeynSolver *BeynSolver_create(int M, int L)
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{
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BeynSolver *solver= (BeynSolver *)malloc(sizeof(*solver));
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BeynSolver *solver;
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QPMS_CRASHING_CALLOC(solver, 1, sizeof(*solver));
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solver->M = M;
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solver->L = L;
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QPMS_ENSURE(L <= M, "We expect L <= M, but we got L = %d, M = %d ", L, M);
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// storage for eigenvalues and eigenvectors
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solver->eigenvalues = gsl_vector_complex_calloc(L);
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solver->eigenvalue_errors = gsl_vector_complex_calloc(L);
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solver->residuals = gsl_vector_calloc(L);
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solver->eigenvectors = gsl_matrix_complex_calloc(L, M);
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//solver->eigenvalues = gsl_vector_complex_calloc(L);
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QPMS_CRASHING_CALLOC(solver->eigenvalues, L, sizeof(complex double));
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//solver->eigenvalue_errors = gsl_vector_complex_calloc(L);
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QPMS_CRASHING_CALLOC(solver->eigenvalue_errors, L, sizeof(complex double));
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//solver->residuals = gsl_vector_calloc(L);
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QPMS_CRASHING_CALLOC(solver->residuals, L, sizeof(double));
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//solver->eigenvectors = gsl_matrix_complex_calloc(L, M);
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QPMS_CRASHING_CALLOC(solver->eigenvectors, L * M, sizeof(complex double));
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// storage for singular values, random VHat matrix, etc. used in algorithm
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solver->A0 = gsl_matrix_complex_calloc(M,L);
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solver->A1 = gsl_matrix_complex_calloc(M,L);
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solver->A0_coarse = gsl_matrix_complex_calloc(M,L);
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solver->A1_coarse = gsl_matrix_complex_calloc(M,L);
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solver->MInvVHat = gsl_matrix_complex_calloc(M,L);
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solver->VHat = gsl_matrix_complex_calloc(M,L);
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solver->Sigma = gsl_vector_calloc(L);
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//solver->A0 = gsl_matrix_complex_calloc(M,L);
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QPMS_CRASHING_CALLOC(solver->A0, M * L, sizeof(complex double));
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//solver->A1 = gsl_matrix_complex_calloc(M,L);
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QPMS_CRASHING_CALLOC(solver->A1, M * L, sizeof(complex double));
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//solver->A0_coarse = gsl_matrix_complex_calloc(M,L);
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QPMS_CRASHING_CALLOC(solver->A0_coarse, M * L, sizeof(complex double));
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//solver->A1_coarse = gsl_matrix_complex_calloc(M,L);
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QPMS_CRASHING_CALLOC(solver->A1_coarse, M * L, sizeof(complex double));
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//solver->MInvVHat = gsl_matrix_complex_calloc(M,L);
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QPMS_CRASHING_CALLOC(solver->MInvVHat, M * L, sizeof(complex double));
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//solver->VHat = gsl_matrix_complex_calloc(M,L);
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QPMS_CRASHING_CALLOC(solver->VHat, M * L, sizeof(complex double));
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//solver->Sigma = gsl_vector_calloc(L);
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QPMS_CRASHING_CALLOC(solver->Sigma, L, sizeof(double));
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// Beyn Step 1: Generate random matrix VHat
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BeynSolver_srandom(solver,(unsigned)time(NULL));
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@ -295,30 +302,30 @@ BeynSolver *BeynSolver_create(int M, int L)
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void BeynSolver_free(BeynSolver *solver)
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{
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gsl_vector_complex_free(solver->eigenvalues);
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gsl_vector_complex_free(solver->eigenvalue_errors);
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gsl_matrix_complex_free(solver->eigenvectors);
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free(solver->eigenvalues);
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free(solver->eigenvalue_errors);
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free(solver->eigenvectors);
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gsl_matrix_complex_free(solver->A0);
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gsl_matrix_complex_free(solver->A1);
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gsl_matrix_complex_free(solver->A0_coarse);
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gsl_matrix_complex_free(solver->A1_coarse);
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gsl_matrix_complex_free(solver->MInvVHat);
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gsl_vector_free(solver->Sigma);
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gsl_vector_free(solver->residuals);
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gsl_matrix_complex_free(solver->VHat);
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free(solver->A0);
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free(solver->A1);
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free(solver->A0_coarse);
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free(solver->A1_coarse);
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free(solver->MInvVHat);
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free(solver->Sigma);
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free(solver->residuals);
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free(solver->VHat);
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free(solver);
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}
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void BeynSolver_free_partial(BeynSolver *solver)
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{
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gsl_matrix_complex_free(solver->A0);
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gsl_matrix_complex_free(solver->A1);
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gsl_matrix_complex_free(solver->A0_coarse);
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gsl_matrix_complex_free(solver->A1_coarse);
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gsl_matrix_complex_free(solver->MInvVHat);
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gsl_matrix_complex_free(solver->VHat);
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free(solver->A0);
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free(solver->A1);
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free(solver->A0_coarse);
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free(solver->A1_coarse);
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free(solver->MInvVHat);
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free(solver->VHat);
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free(solver);
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}
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@ -328,11 +335,8 @@ void BeynSolver_srandom(BeynSolver *solver, unsigned int RandSeed)
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if (RandSeed==0)
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RandSeed=time(0);
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srandom(RandSeed);
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gsl_matrix_complex *VHat=solver->VHat;
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for(int nr=0; nr<VHat->size1; nr++)
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for(int nc=0; nc<VHat->size2; nc++)
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gsl_matrix_complex_set(VHat,nr,nc,cs2g(zrandN(1, 0)));
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for(size_t i = 0; i < solver->M * solver->L; ++i)
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solver->VHat[i] = zrandN(1, 0);
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}
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@ -342,44 +346,47 @@ void BeynSolver_srandom(BeynSolver *solver, unsigned int RandSeed)
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* and eigenvectors
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*/
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static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_gsl_t M_function,
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static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_function,
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void *Params,
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gsl_matrix_complex *A0, gsl_matrix_complex *A1, double complex z0,
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gsl_vector_complex *eigenvalues, gsl_matrix_complex *eigenvectors, const double rank_tol, size_t rank_sel_min, const double res_tol)
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complex double *A0, complex double *A1, double complex z0,
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complex double *eigenvalues, complex double *eigenvectors, const double rank_tol, size_t rank_sel_min, const double res_tol)
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{
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const size_t m = solver->M;
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const size_t l = solver->L;
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gsl_vector *Sigma = solver->Sigma;
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double *Sigma = solver->Sigma;
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int verbose = 1; // TODO
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// Beyn Step 3: Compute SVD: A0 = V0_full * Sigma * W0T_full
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if(verbose) printf(" Beyn: computing SVD...\n");
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gsl_matrix_complex* V0_full = gsl_matrix_complex_alloc(m,l);
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gsl_matrix_complex_memcpy(V0_full,A0);
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gsl_matrix_complex* W0T_full = gsl_matrix_complex_alloc(l,l);
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QPMS_ENSURE(Sigma->stride == 1, "Sigma vector stride must be 1 for LAPACKE_zgesdd, got %zd.", Sigma->stride);
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QPMS_ENSURE(V0_full->size1 >= V0_full->size2, "m = %zd, l = %zd, what the hell?");
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//gsl_matrix_complex* V0_full = gsl_matrix_complex_alloc(m,l);
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//gsl_matrix_complex_memcpy(V0_full,A0);
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complex double *V0_full;
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QPMS_CRASHING_MALLOCPY(V0_full, A0, m * l * sizeof(complex double));
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//gsl_matrix_complex* W0T_full = gsl_matrix_complex_alloc(l,l);
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complex double *W0T_full; QPMS_CRASHING_MALLOC(W0T_full, l * l * sizeof(complex double));
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//QPMS_ENSURE(Sigma->stride == 1, "Sigma vector stride must be 1 for LAPACKE_zgesdd, got %zd.", Sigma->stride);
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//QPMS_ENSURE(V0_full->size1 >= V0_full->size2, "m = %zd, l = %zd, what the hell?");
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QPMS_ENSURE_SUCCESS(LAPACKE_zgesdd(LAPACK_ROW_MAJOR, // A = U*Σ*conjg(V')
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'O' /*jobz, 'O' overwrites a with U and saves conjg(V') in vt if m >= n, i.e. if M >= L, which holds*/,
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V0_full->size1 /* m, number of rows */,
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V0_full->size2 /* n, number of columns */,
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(lapack_complex_double *)(V0_full->data) /*a*/,
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V0_full->tda /*lda*/,
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Sigma->data /*s*/,
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m, // V0_full->size1 /* m, number of rows */,
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l, // V0_full->size2 /* n, number of columns */,
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V0_full, //(lapack_complex_double *)(V0_full->data) /*a*/,
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l, //V0_full->tda /*lda*/,
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Sigma, //Sigma->data /*s*/,
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NULL /*u; not used*/,
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m /*ldu; should not be really used but lapacke requires it for some obscure reason*/,
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(lapack_complex_double *)W0T_full->data /*vt*/,
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W0T_full->tda /*ldvt*/
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W0T_full, //(lapack_complex_double *)W0T_full->data /*vt*/,
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l //W0T_full->tda /*ldvt*/
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));
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// Beyn Step 4: Rank test for Sigma
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// compute effective rank K (number of eigenvalue candidates)
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int K=0;
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for (int k=0; k<Sigma->size /* this is l, actually */; k++) {
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if (verbose) printf("Beyn: SV(%d)=%e\n",k,gsl_vector_get(Sigma, k));
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if (k < rank_sel_min || gsl_vector_get(Sigma, k) > rank_tol)
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for (int k=0; k < l/* k<Sigma->size*/ /* this is l, actually */; k++) {
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if (verbose) printf("Beyn: SV(%d)=%e\n",k, Sigma[k] /*gsl_vector_get(Sigma, k)*/);
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if (k < rank_sel_min || Sigma[k] /*gsl_vector_get(Sigma, k)*/ > rank_tol)
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K++;
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}
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if (verbose)printf(" Beyn: %d/%zd relevant singular values\n",K,l);
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@ -390,46 +397,70 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_gsl_t M_fun
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// Beyn step 5: B = V0' * A1 * W0 * Sigma^-1
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// set V0, W0T = matrices of first K right, left singular vectors
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gsl_matrix_complex *V0 = gsl_matrix_complex_alloc(m,K);
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gsl_matrix_complex *W0T= gsl_matrix_complex_alloc(K,l);
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//gsl_matrix_complex *V0 = gsl_matrix_complex_alloc(m,K);
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//gsl_matrix_complex *W0T= gsl_matrix_complex_alloc(K,l);
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complex double *V0, *W0T;
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QPMS_CRASHING_MALLOC(V0, m * K * sizeof(complex double));
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QPMS_CRASHING_MALLOC(W0T, K * l * sizeof(complex double));
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// TODO this is stupid, some parts could be handled simply by realloc.
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for (int k = 0; k < K; ++k) {
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gsl_vector_complex_view tmp;
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tmp = gsl_matrix_complex_column(V0_full, k);
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gsl_matrix_complex_set_col(V0, k, &(tmp.vector));
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tmp = gsl_matrix_complex_row(W0T_full, k);
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gsl_matrix_complex_set_row(W0T, k, &(tmp.vector));
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//gsl_vector_complex_view tmp;
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//tmp = gsl_matrix_complex_column(V0_full, k);
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//gsl_matrix_complex_set_col(V0, k, &(tmp.vector));
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for(int i = 0; i < m; ++i)
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MAT(V0, m, K, i, k) = MAT(V0_full, m, l, i, k);
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//tmp = gsl_matrix_complex_row(W0T_full, k);
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//gsl_matrix_complex_set_row(W0T, k, &(tmp.vector));
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for(int j = 0; j < K; ++j)
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MAT(W0T, K, l, k, j) = MAT(W0T_full, m, l, k, j);
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}
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//gsl_matrix_complex_free(V0_full);
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free(V0_full);
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//gsl_matrix_complex_free(W0T_full);
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free(W0T_full);
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gsl_matrix_complex_free(V0_full);
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gsl_matrix_complex_free(W0T_full);
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gsl_matrix_complex *TM2 = gsl_matrix_complex_calloc(K,l);
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gsl_matrix_complex *B = gsl_matrix_complex_calloc(K,K);
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//gsl_matrix_complex *TM2 = gsl_matrix_complex_calloc(K,l);
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//gsl_matrix_complex *B = gsl_matrix_complex_calloc(K,K);
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complex double *TM2, *B;
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QPMS_CRASHING_CALLOC(TM2, K * l, sizeof(complex double));
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QPMS_CRASHING_CALLOC(B, K * K, sizeof(complex double));
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if(verbose) printf(" Multiplying V0*A1->TM...\n");
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const gsl_complex one = gsl_complex_rect(1,0);
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const gsl_complex zero = gsl_complex_rect(0,0);
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gsl_blas_zgemm(CblasConjTrans, CblasNoTrans, one,
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V0, A1, zero, TM2);
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//const gsl_complex one = gsl_complex_rect(1,0);
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//const gsl_complex zero = gsl_complex_rect(0,0);
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//gsl_blas_zgemm(CblasConjTrans, CblasNoTrans, one,
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// V0, A1, zero, TM2);
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// dims: V0[m,K], A1[m,l], TM2[K,l]
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const complex double one = 1, zero = 0;
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cblas_zgemm(CblasRowMajor, CblasConjTrans, CblasNoTrans, K, l, m,
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&one, V0, K, A1, l, &zero, TM2, l);
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if(verbose) printf(" Multiplying TM*W0T->B...\n");
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gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, one,
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TM2, W0T, zero, B);
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//gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, one,
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// TM2, W0T, zero, B);
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// DIMS: TM2[K,l], W0T[K,l], B[K,K]
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cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasConjTrans, K, K, l,
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&one, TM2, l, W0T, l, &zero, B, K);
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gsl_matrix_complex_free(W0T);
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gsl_matrix_complex_free(TM2);
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//gsl_matrix_complex_free(W0T);
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//gsl_matrix_complex_free(TM2);
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free(W0T);
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free(TM2);
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if(verbose) printf(" Scaling B <- B*Sigma^{-1}\n");
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gsl_vector_complex *tmp = gsl_vector_complex_calloc(K);
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//gsl_vector_complex *tmp = gsl_vector_complex_calloc(K);
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for(int i = 0; i < K; i++) {
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gsl_matrix_complex_get_col(tmp, B, i);
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gsl_vector_complex_scale(tmp, gsl_complex_rect(1.0/gsl_vector_get(Sigma,i), 0));
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gsl_matrix_complex_set_col(B,i,tmp);
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//gsl_matrix_complex_get_col(tmp, B, i);
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//gsl_vector_complex_scale(tmp, gsl_complex_rect(1.0/gsl_vector_get(Sigma,i), 0));
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//gsl_matrix_complex_set_col(B,i,tmp);
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for(int j = 0; j < K; j++)
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MAT(B, K, K, j, i) /= Sigma[i];
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}
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gsl_vector_complex_free(tmp);
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//gsl_vector_complex_free(tmp);
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//for(int m=0; m<K; m++) // B <- B * Sigma^{-1}
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@ -444,95 +475,121 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_gsl_t M_fun
|
|||
*/
|
||||
if(verbose) printf(" Eigensolving (%i,%i)\n",K,K);
|
||||
|
||||
gsl_vector_complex *Lambda = gsl_vector_complex_alloc(K); // eigenvalues
|
||||
gsl_matrix_complex *S = gsl_matrix_complex_alloc(K,K); // eigenvectors
|
||||
//gsl_vector_complex *Lambda = gsl_vector_complex_alloc(K); // eigenvalues
|
||||
//gsl_matrix_complex *S = gsl_matrix_complex_alloc(K,K); // eigenvectors
|
||||
complex double *Lambda /* eigenvalues */ , *S /* eigenvector */;
|
||||
QPMS_CRASHING_MALLOC(Lambda, K * sizeof(complex double));
|
||||
QPMS_CRASHING_MALLOC(S, K * K * sizeof(complex double));
|
||||
|
||||
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(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);
|
||||
// dims: B[K,K], S[K,K], Lambda[K]
|
||||
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 *)(B->data) /* a */,
|
||||
B->tda /* lda */,
|
||||
(lapack_complex_double *) Lambda->data /* w */,
|
||||
B, //(lapack_complex_double *)(B->data) /* a */,
|
||||
K, //B->tda /* lda */,
|
||||
Lambda, //(lapack_complex_double *) Lambda->data /* w */,
|
||||
NULL /* vl */,
|
||||
m /* ldvl, not used by for some reason needed */,
|
||||
(lapack_complex_double *)(S->data)/* vr */,
|
||||
S->tda/* ldvr */
|
||||
m /* ldvl, not used but for some reason needed */,
|
||||
S, //(lapack_complex_double *)(S->data)/* vr */,
|
||||
K //S->tda/* ldvr */
|
||||
));
|
||||
|
||||
gsl_matrix_complex_free(B);
|
||||
//gsl_matrix_complex_free(B);
|
||||
free(B);
|
||||
|
||||
// V0S <- V0*S
|
||||
printf("Multiplying V0*S...\n");
|
||||
gsl_matrix_complex *V0S = gsl_matrix_complex_alloc(m, K);
|
||||
QPMS_ENSURE_SUCCESS(gsl_blas_zgemm(CblasNoTrans, CblasNoTrans,
|
||||
one, V0, S, zero, V0S));
|
||||
//gsl_matrix_complex *V0S = gsl_matrix_complex_alloc(m, K);
|
||||
//QPMS_ENSURE_SUCCESS(gsl_blas_zgemm(CblasNoTrans, CblasNoTrans,
|
||||
// one, V0, S, zero, V0S));
|
||||
complex double *V0S;
|
||||
QPMS_CRASHING_MALLOC(V0S, m * K * sizeof(complex double));
|
||||
// dims: V0[m,K], S[K,K], V0S[m,K]
|
||||
cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, m, K, K,
|
||||
&one, V0, K, S, K, &zero, V0S, K);
|
||||
|
||||
gsl_matrix_complex_free(V0);
|
||||
//gsl_matrix_complex_free(V0);
|
||||
free(V0);
|
||||
|
||||
// FIXME!!! make clear relation between KRetained and K in the results!
|
||||
// (If they differ, there are possibly some spurious eigenvalues.)
|
||||
int KRetained = 0;
|
||||
gsl_matrix_complex *Mmat = gsl_matrix_complex_alloc(m, m);
|
||||
gsl_vector_complex *MVk = gsl_vector_complex_alloc(m);
|
||||
//gsl_matrix_complex *Mmat = gsl_matrix_complex_alloc(m, m);
|
||||
//gsl_vector_complex *MVk = gsl_vector_complex_alloc(m);
|
||||
complex double *Mmat, *MVk;
|
||||
QPMS_CRASHING_MALLOC(Mmat, m * m * sizeof(complex double));
|
||||
QPMS_CRASHING_MALLOC(MVk, m * sizeof(complex double));
|
||||
for (int k = 0; k < K; ++k) {
|
||||
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_const_view Vk = gsl_matrix_complex_const_column(V0S, k);
|
||||
//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);
|
||||
const complex double z = z0 + Lambda[k];
|
||||
//gsl_vector_complex_const_view Vk = gsl_matrix_complex_const_column(V0S, k);
|
||||
|
||||
double residual = 0;
|
||||
if(res_tol > 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);
|
||||
QPMS_ENSURE_SUCCESS(M_function(Mmat, m, z, Params));
|
||||
//QPMS_ENSURE_SUCCESS(gsl_blas_zgemv(CblasNoTrans, one, Mmat, &(Vk.vector), zero, MVk));
|
||||
// Vk[i] == V0S[i, k]; dims: Mmat[m,m], Vk[m] (V0S[m, K]), MVk[m]
|
||||
cblas_zgemv(CblasRowMajor, CblasNoTrans, m, m,
|
||||
&one, Mmat, m, &MAT(V0S, m, K, 0, k), m /* stride of Vk in V0S */,
|
||||
&zero, MVk, 1);
|
||||
|
||||
//residual = gsl_blas_dznrm2(MVk);
|
||||
residual = cblas_dznrm2(m, MVk, 1);
|
||||
if (verbose) printf("Beyn: Residual(%i)=%e\n",k,residual);
|
||||
}
|
||||
if (res_tol > 0 && residual > res_tol) continue;
|
||||
|
||||
gsl_vector_complex_set(eigenvalues, KRetained, zgsl);
|
||||
//gsl_vector_complex_set(eigenvalues, KRetained, zgsl);
|
||||
eigenvalues[KRetained] = z;
|
||||
if(eigenvectors) {
|
||||
gsl_matrix_complex_set_row(eigenvectors, KRetained, &(Vk.vector));
|
||||
gsl_vector_set(solver->residuals, KRetained, residual);
|
||||
//gsl_matrix_complex_set_row(eigenvectors, KRetained, &(Vk.vector));
|
||||
for(int j = 0; j < m; ++j)
|
||||
MAT(eigenvectors, l, m, KRetained, j) = MAT(V0S, m, K, j, k);
|
||||
//gsl_vector_set(solver->residuals, KRetained, residual);
|
||||
|
||||
}
|
||||
++KRetained;
|
||||
}
|
||||
|
||||
gsl_matrix_complex_free(V0S);
|
||||
gsl_matrix_complex_free(Mmat);
|
||||
gsl_vector_complex_free(MVk);
|
||||
gsl_matrix_complex_free(S);
|
||||
gsl_vector_complex_free(Lambda);
|
||||
free(V0S);
|
||||
free(Mmat);
|
||||
free(MVk);
|
||||
free(S);
|
||||
free(Lambda);
|
||||
|
||||
return KRetained;
|
||||
}
|
||||
|
||||
|
||||
beyn_result_gsl_t *beyn_solve_gsl(const size_t m, const size_t l,
|
||||
beyn_function_M_gsl_t M_function, beyn_function_M_inv_Vhat_gsl_t M_inv_Vhat_function,
|
||||
beyn_result_t *beyn_solve(const size_t m, const size_t l,
|
||||
beyn_function_M_t M_function, beyn_function_M_inv_Vhat_t M_inv_Vhat_function,
|
||||
void *params, const beyn_contour_t *contour,
|
||||
double rank_tol, size_t rank_sel_min, double res_tol)
|
||||
{
|
||||
BeynSolver *solver = BeynSolver_create(m, l);
|
||||
|
||||
gsl_matrix_complex *A0 = solver->A0;
|
||||
gsl_matrix_complex *A1 = solver->A1;
|
||||
gsl_matrix_complex *A0_coarse = solver->A0_coarse;
|
||||
gsl_matrix_complex *A1_coarse = solver->A1_coarse;
|
||||
gsl_matrix_complex *MInvVHat = solver->MInvVHat;
|
||||
gsl_matrix_complex *VHat = solver->VHat;
|
||||
complex double *A0 = solver->A0;
|
||||
complex double *A1 = solver->A1;
|
||||
complex double *A0_coarse = solver->A0_coarse;
|
||||
complex double *A1_coarse = solver->A1_coarse;
|
||||
complex double *MInvVHat = solver->MInvVHat;
|
||||
complex double *VHat = solver->VHat;
|
||||
|
||||
/***************************************************************/
|
||||
/* evaluate contour integrals by numerical quadrature to get */
|
||||
/* A0 and A1 matrices */
|
||||
/***************************************************************/
|
||||
|
||||
gsl_matrix_complex_set_zero(A0);
|
||||
gsl_matrix_complex_set_zero(A1);
|
||||
gsl_matrix_complex_set_zero(A0_coarse);
|
||||
gsl_matrix_complex_set_zero(A1_coarse);
|
||||
// TODO zeroing probably redundant (Used calloc...)
|
||||
memset(A0, 0, m * l * sizeof(complex double));
|
||||
memset(A1, 0, m * l * sizeof(complex double));
|
||||
memset(A0_coarse, 0, m * l * sizeof(complex double));
|
||||
memset(A1_coarse, 0, m * l * sizeof(complex double));
|
||||
const size_t N = contour->n;
|
||||
if(N & 1) QPMS_WARN("Contour discretisation point number is odd (%zd),"
|
||||
" the error estimates might be a bit off.", N);
|
||||
|
|
@ -544,44 +601,66 @@ beyn_result_gsl_t *beyn_solve_gsl(const size_t m, const size_t l,
|
|||
const complex double z = contour->z_dz[n][0];
|
||||
const complex double dz = contour->z_dz[n][1];
|
||||
|
||||
gsl_matrix_complex_memcpy(MInvVHat, VHat);
|
||||
memcpy(MInvVHat, VHat, m * l * sizeof(complex double));
|
||||
|
||||
if(M_inv_Vhat_function) {
|
||||
QPMS_ENSURE_SUCCESS(M_inv_Vhat_function(MInvVHat, VHat, z, params));
|
||||
QPMS_ENSURE_SUCCESS(M_inv_Vhat_function(MInvVHat, m, l, VHat, z, params));
|
||||
} else {
|
||||
lapack_int *pivot;
|
||||
gsl_matrix_complex *Mmat = gsl_matrix_complex_alloc(m,m);
|
||||
QPMS_ENSURE_SUCCESS(M_function(Mmat, z, params));
|
||||
//gsl_matrix_complex *Mmat = gsl_matrix_complex_alloc(m,m);
|
||||
complex double *Mmat;
|
||||
QPMS_CRASHING_MALLOC(Mmat, m * m * sizeof(complex double));
|
||||
QPMS_ENSURE_SUCCESS(M_function(Mmat, m, z, params));
|
||||
QPMS_CRASHING_MALLOC(pivot, sizeof(lapack_int) * m);
|
||||
#if 0
|
||||
QPMS_ENSURE_SUCCESS(LAPACKE_zgetrf(LAPACK_ROW_MAJOR,
|
||||
m /*m*/, m /*n*/,(lapack_complex_double *) Mmat->data /*a*/, Mmat->tda /*lda*/, pivot /*ipiv*/));
|
||||
QPMS_ENSURE(MInvVHat->tda == l, "wut?");
|
||||
QPMS_ENSURE_SUCCESS(LAPACKE_zgetrs(LAPACK_ROW_MAJOR, 'N' /*trans*/,
|
||||
m /*n*/, l/*nrhs*/, (lapack_complex_double *)(Mmat->data) /*a*/, Mmat->tda /*lda*/, pivot/*ipiv*/,
|
||||
(lapack_complex_double *)(MInvVHat->data) /*b*/, MInvVHat->tda/*ldb*/));
|
||||
#endif
|
||||
QPMS_ENSURE_SUCCESS(LAPACKE_zgetrf(LAPACK_ROW_MAJOR,
|
||||
m /*m*/, m /*n*/, Mmat /*a*/, m /*lda*/, pivot /*ipiv*/));
|
||||
QPMS_ENSURE_SUCCESS(LAPACKE_zgetrs(LAPACK_ROW_MAJOR, 'N' /*trans*/,
|
||||
m /*n*/, l/*nrhs*/, Mmat /*a*/, m /*lda*/, pivot/*ipiv*/,
|
||||
MInvVHat /*b*/, l /*ldb*/));
|
||||
|
||||
free(pivot);
|
||||
gsl_matrix_complex_free(Mmat);
|
||||
free(Mmat);
|
||||
}
|
||||
|
||||
gsl_matrix_complex_scale(MInvVHat, cs2g(dz));
|
||||
gsl_matrix_complex_add(A0, MInvVHat);
|
||||
// gsl_matrix_complex_scale(MInvVHat, cs2g(dz));
|
||||
for(size_t i = 0; i < m * l; ++i)
|
||||
MInvVHat[i] *= dz;
|
||||
//gsl_matrix_complex_add(A0, MInvVHat);
|
||||
for(size_t i = 0; i < m * l; ++i)
|
||||
A0[i] += MInvVHat[i];
|
||||
if((n%2)==0) {
|
||||
gsl_matrix_complex_add(A0_coarse, MInvVHat);
|
||||
gsl_matrix_complex_add(A0_coarse, MInvVHat);
|
||||
//gsl_matrix_complex_add(A0_coarse, MInvVHat);
|
||||
//gsl_matrix_complex_add(A0_coarse, MInvVHat);
|
||||
for(size_t i = 0; i < m * l; ++i)
|
||||
A0_coarse[i] += 2 * MInvVHat[i];
|
||||
}
|
||||
|
||||
gsl_matrix_complex_scale(MInvVHat, cs2g(z - z0)); // A_1 scaling as in Beyn's Remark 3.2(b) for numerical stability.
|
||||
gsl_matrix_complex_add(A1, MInvVHat);
|
||||
// A_1 scaling as in Beyn's Remark 3.2(b) for numerical stability.
|
||||
//gsl_matrix_complex_scale(MInvVHat, cs2g(z - z0));
|
||||
for(size_t i = 0; i < m * l; ++i)
|
||||
MInvVHat[i] *= (z - z0);
|
||||
//gsl_matrix_complex_add(A1, MInvVHat);
|
||||
for(size_t i = 0; i < m * l; ++i)
|
||||
A1[i] += MInvVHat[i];
|
||||
if((n%2)==0) {
|
||||
gsl_matrix_complex_add(A1_coarse, MInvVHat);
|
||||
gsl_matrix_complex_add(A1_coarse, MInvVHat);
|
||||
for(size_t i = 0; i < m * l; ++i)
|
||||
//gsl_matrix_complex_add(A1_coarse, MInvVHat);
|
||||
//gsl_matrix_complex_add(A1_coarse, MInvVHat);
|
||||
A1_coarse[i] += 2 * MInvVHat[i];
|
||||
}
|
||||
}
|
||||
|
||||
gsl_vector_complex *eigenvalues = solver->eigenvalues;
|
||||
gsl_vector_complex *eigenvalue_errors = solver->eigenvalue_errors;
|
||||
gsl_matrix_complex *eigenvectors = solver->eigenvectors;
|
||||
complex double *eigenvalues = solver->eigenvalues;
|
||||
complex double *eigenvalue_errors = solver->eigenvalue_errors;
|
||||
complex double *eigenvectors = solver->eigenvectors;
|
||||
|
||||
// Repeat Steps 3–6 with rougher contour approximation to get an error estimate.
|
||||
int K_coarse = beyn_process_matrices(solver, M_function, params, A0_coarse, A1_coarse, z0, eigenvalue_errors, /*eigenvectors_coarse*/ NULL, rank_tol, rank_sel_min, res_tol);
|
||||
|
|
@ -589,10 +668,14 @@ beyn_result_gsl_t *beyn_solve_gsl(const size_t m, const size_t l,
|
|||
|
||||
// Beyn Steps 3–6
|
||||
int K = beyn_process_matrices(solver, M_function, params, A0, A1, z0, eigenvalues, eigenvectors, rank_tol, rank_sel_min, res_tol);
|
||||
gsl_blas_zaxpy(gsl_complex_rect(-1,0), eigenvalues, eigenvalue_errors);
|
||||
|
||||
beyn_result_gsl_t *result;
|
||||
QPMS_CRASHING_MALLOC(result, sizeof(beyn_result_gsl_t));
|
||||
//gsl_blas_zaxpy(gsl_complex_rect(-1,0), eigenvalues, eigenvalue_errors);
|
||||
const complex double minusone = -1.;
|
||||
//TODO maybe change the sizes to correspend to retained eigval count K, not l
|
||||
cblas_zaxpy(l, &minusone, eigenvalues, 1, eigenvalue_errors, 1);
|
||||
|
||||
beyn_result_t *result;
|
||||
QPMS_CRASHING_MALLOC(result, sizeof(*result));
|
||||
result->eigval = solver->eigenvalues;
|
||||
result->eigval_err = solver->eigenvalue_errors;
|
||||
result->residuals = solver->residuals;
|
||||
|
|
@ -605,6 +688,7 @@ beyn_result_gsl_t *beyn_solve_gsl(const size_t m, const size_t l,
|
|||
return result;
|
||||
}
|
||||
|
||||
#if 0
|
||||
// Wrapper of pure C array M-matrix function to GSL.
|
||||
|
||||
struct beyn_function_M_carr2gsl_param {
|
||||
|
|
@ -664,4 +748,5 @@ void beyn_result_free(beyn_result_t *result) {
|
|||
beyn_result_gsl_free(result->gsl);
|
||||
free(result);
|
||||
}
|
||||
#endif
|
||||
|
||||
|
|
|
|||
51
qpms/beyn.h
51
qpms/beyn.h
|
|
@ -4,20 +4,10 @@
|
|||
#ifndef BEYN_H
|
||||
#define BEYN_H
|
||||
|
||||
#include <stddef.h>
|
||||
#include <complex.h>
|
||||
#include <gsl/gsl_matrix.h>
|
||||
#include <gsl/gsl_complex_math.h>
|
||||
|
||||
/// User-supplied function that provides the operator M(z) whose "roots" are to be found.
|
||||
/** GSL matrix version */
|
||||
typedef int (*beyn_function_M_gsl_t)(gsl_matrix_complex *target_M, complex double z, void *params);
|
||||
|
||||
/// (optional) User-supplied function that, given \f$ \hat V \f$, calculates \f$ M(z)^{-1} \hat V \f$.
|
||||
/** GSL matrix version */
|
||||
typedef int (*beyn_function_M_inv_Vhat_gsl_t)(gsl_matrix_complex *target_M_inv_Vhat,
|
||||
const gsl_matrix_complex *Vhat, complex double z, void *params);
|
||||
|
||||
/// User-supplied function that provides the operator M(z) whose "roots" are to be found.
|
||||
/// User-supplied function that provides the (row-major) m × m matrix M(z) whose "roots" are to be found.
|
||||
/** Pure C array version */
|
||||
typedef int (*beyn_function_M_t)(complex double *target_M, size_t m, complex double z, void *params);
|
||||
|
||||
|
|
@ -66,18 +56,6 @@ beyn_contour_t *beyn_contour_kidney(complex double centre, double halfax_re, dou
|
|||
size_t n, beyn_contour_halfellipse_orientation or);
|
||||
|
||||
|
||||
/// Beyn algorithm result structure (GSL matrix/vector version).
|
||||
typedef struct beyn_result_gsl_t {
|
||||
size_t neig; ///< Number of eigenvalues found (a bit redundant?).
|
||||
gsl_vector_complex *eigval;
|
||||
gsl_vector_complex *eigval_err;
|
||||
gsl_vector *residuals;
|
||||
gsl_matrix_complex *eigvec; // Rows are the eigenvectors
|
||||
gsl_vector *ranktest_SV;
|
||||
} beyn_result_gsl_t;
|
||||
|
||||
void beyn_result_gsl_free(beyn_result_gsl_t *result);
|
||||
|
||||
/// Beyn algorithm result structure (pure C array version).
|
||||
typedef struct beyn_result_t {
|
||||
size_t neig; ///< Number of eigenvalues found.
|
||||
|
|
@ -88,31 +66,11 @@ typedef struct beyn_result_t {
|
|||
complex double *eigvec; // Rows are the eigenvectors
|
||||
double *ranktest_SV;
|
||||
|
||||
/// Private, we wrap it around beyn_result_gsl_t for now.
|
||||
beyn_result_gsl_t *gsl;
|
||||
|
||||
} beyn_result_t;
|
||||
|
||||
/// Converts beyn_result_gsl_t from beyn_result_t.
|
||||
/** After calling this, use beyn_result_free() on the returned pointer;
|
||||
* do NOT run beyn_result_gsl_free() anymore.
|
||||
*/
|
||||
beyn_result_t *beyn_result_from_beyn_result_gsl(beyn_result_gsl_t *g);
|
||||
|
||||
void beyn_result_free(beyn_result_t *result);
|
||||
|
||||
beyn_result_gsl_t *beyn_solve_gsl(
|
||||
size_t m, ///< Dimension of the matrix \a M.
|
||||
size_t l, ///< Number of columns of the random matrix \f$ \hat V \f$ (larger than the expected number of solutions).
|
||||
beyn_function_M_gsl_t M, ///< Function providing the matrix \f$ M(z) \f$.
|
||||
beyn_function_M_inv_Vhat_gsl_t M_inv_Vhat, ///< Fuction providing the matrix \f$ M^{-1}(z) \hat V \f$ (optional).
|
||||
void *params, ///< Parameter pointer passed to M() and M_inv_Vhat().
|
||||
const beyn_contour_t *contour, ///< Integration contour.
|
||||
double rank_tol, ///< (default: `1e-4`) TODO DOC.
|
||||
size_t rank_min_sel, ///< Minimum number of eigenvalue candidates, even if they don't pass \a rank_tol.
|
||||
double res_tol ///< (default: `0.0`) TODO DOC.
|
||||
);
|
||||
|
||||
/// Solve a non-linear eigenproblem using Beyn's algorithm
|
||||
beyn_result_t *beyn_solve(
|
||||
size_t m, ///< Dimension of the matrix \a M.
|
||||
size_t l, ///< Number of columns of the random matrix \f$ \hat V \f$ (larger than the expected number of solutions).
|
||||
|
|
@ -125,7 +83,4 @@ beyn_result_t *beyn_solve(
|
|||
double res_tol ///< (default: `0.0`) TODO DOC.
|
||||
);
|
||||
|
||||
static inline complex double gsl_complex_tostd(gsl_complex z) { return GSL_REAL(z) + I*GSL_IMAG(z); }
|
||||
static inline gsl_complex gsl_complex_fromstd(complex double z) { return gsl_complex_rect(creal(z), cimag(z)); }
|
||||
|
||||
#endif // BEYN_H
|
||||
|
|
|
|||
|
|
@ -72,13 +72,13 @@ target_link_libraries( tbeyn3f qpms gsl lapacke ${QPMS_AMOSLIB} m )
|
|||
target_include_directories( tbeyn3f PRIVATE .. )
|
||||
target_compile_definitions( tbeyn3f PRIVATE VARIANTF )
|
||||
|
||||
add_executable( tbeyn_gsl tbeyn_gsl.c )
|
||||
target_link_libraries( tbeyn_gsl qpms gsl lapacke ${QPMS_AMOSLIB} m )
|
||||
target_include_directories( tbeyn_gsl PRIVATE .. )
|
||||
#add_executable( tbeyn_gsl tbeyn_gsl.c )
|
||||
#target_link_libraries( tbeyn_gsl qpms gsl lapacke amos m )
|
||||
#target_include_directories( tbeyn_gsl PRIVATE .. )
|
||||
|
||||
add_executable( tbeyn_gsl2 tbeyn_gsl2.c )
|
||||
target_link_libraries( tbeyn_gsl2 qpms gsl lapacke ${QPMS_AMOSLIB} m )
|
||||
target_include_directories( tbeyn_gsl2 PRIVATE .. )
|
||||
#add_executable( tbeyn_gsl2 tbeyn_gsl2.c )
|
||||
#target_link_libraries( tbeyn_gsl2 qpms gsl lapacke amos m )
|
||||
#target_include_directories( tbeyn_gsl2 PRIVATE .. )
|
||||
|
||||
add_custom_target( mytests DEPENDS test_single_translations_vs_calc test_vswf_translations test_vswf_translations_array tbeyn )
|
||||
|
||||
|
|
|
|||
|
|
@ -1,6 +1,7 @@
|
|||
#include <qpms/beyn.h>
|
||||
#include <stdio.h>
|
||||
#include <string.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
// Matrix as in Beyn, section 4.11
|
||||
int M_function(complex double *target, const size_t m, const complex double z, void *no_params) {
|
||||
|
|
|
|||
Loading…
Reference in New Issue