From f19c590d6ee3974be3497b56c89f82ecaa67c7e5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= Date: Fri, 11 Jun 2021 10:38:49 +0300 Subject: [PATCH] Pure BLAS Beyn: cleanup commented out GSL code --- qpms/beyn.c | 74 ++--------------------------------------------------- 1 file changed, 2 insertions(+), 72 deletions(-) diff --git a/qpms/beyn.c b/qpms/beyn.c index 6d59d1c..492bc32 100644 --- a/qpms/beyn.c +++ b/qpms/beyn.c @@ -269,29 +269,18 @@ BeynSolver *BeynSolver_create(int M, int L) QPMS_ENSURE(L <= M, "We expect L <= M, but we got L = %d, M = %d ", L, M); // storage for eigenvalues and eigenvectors - //solver->eigenvalues = gsl_vector_complex_calloc(L); QPMS_CRASHING_CALLOC(solver->eigenvalues, L, sizeof(complex double)); - //solver->eigenvalue_errors = gsl_vector_complex_calloc(L); QPMS_CRASHING_CALLOC(solver->eigenvalue_errors, L, sizeof(complex double)); - //solver->residuals = gsl_vector_calloc(L); QPMS_CRASHING_CALLOC(solver->residuals, L, sizeof(double)); - //solver->eigenvectors = gsl_matrix_complex_calloc(L, M); QPMS_CRASHING_CALLOC(solver->eigenvectors, L * M, sizeof(complex double)); // storage for singular values, random VHat matrix, etc. used in algorithm - //solver->A0 = gsl_matrix_complex_calloc(M,L); QPMS_CRASHING_CALLOC(solver->A0, M * L, sizeof(complex double)); - //solver->A1 = gsl_matrix_complex_calloc(M,L); QPMS_CRASHING_CALLOC(solver->A1, M * L, sizeof(complex double)); - //solver->A0_coarse = gsl_matrix_complex_calloc(M,L); QPMS_CRASHING_CALLOC(solver->A0_coarse, M * L, sizeof(complex double)); - //solver->A1_coarse = gsl_matrix_complex_calloc(M,L); QPMS_CRASHING_CALLOC(solver->A1_coarse, M * L, sizeof(complex double)); - //solver->MInvVHat = gsl_matrix_complex_calloc(M,L); QPMS_CRASHING_CALLOC(solver->MInvVHat, M * L, sizeof(complex double)); - //solver->VHat = gsl_matrix_complex_calloc(M,L); QPMS_CRASHING_CALLOC(solver->VHat, M * L, sizeof(complex double)); - //solver->Sigma = gsl_vector_calloc(L); QPMS_CRASHING_CALLOC(solver->Sigma, L, sizeof(double)); // Beyn Step 1: Generate random matrix VHat BeynSolver_srandom(solver,(unsigned)time(NULL)); @@ -359,14 +348,9 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_functio // Beyn Step 3: Compute SVD: A0 = V0_full * Sigma * W0T_full if(verbose) printf(" Beyn: computing SVD...\n"); - //gsl_matrix_complex* V0_full = gsl_matrix_complex_alloc(m,l); - //gsl_matrix_complex_memcpy(V0_full,A0); complex double *V0_full; QPMS_CRASHING_MALLOCPY(V0_full, A0, m * l * sizeof(complex double)); - //gsl_matrix_complex* W0T_full = gsl_matrix_complex_alloc(l,l); complex double *W0T_full; QPMS_CRASHING_MALLOC(W0T_full, l * l * sizeof(complex double)); - //QPMS_ENSURE(Sigma->stride == 1, "Sigma vector stride must be 1 for LAPACKE_zgesdd, got %zd.", Sigma->stride); - //QPMS_ENSURE(V0_full->size1 >= V0_full->size2, "m = %zd, l = %zd, what the hell?"); 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*/, m, // V0_full->size1 /* m, number of rows */, @@ -385,8 +369,8 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_functio // compute effective rank K (number of eigenvalue candidates) int K=0; for (int k=0; k < l/* ksize*/ /* this is l, actually */; k++) { - if (verbose) printf("Beyn: SV(%d)=%e\n",k, Sigma[k] /*gsl_vector_get(Sigma, k)*/); - if (k < rank_sel_min || Sigma[k] /*gsl_vector_get(Sigma, k)*/ > rank_tol) + if (verbose) printf("Beyn: SV(%d)=%e\n",k, Sigma[k] ); + if (k < rank_sel_min || Sigma[k] > rank_tol) K++; } if (verbose)printf(" Beyn: %d/%zd relevant singular values\n",K,l); @@ -397,41 +381,26 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_functio // Beyn step 5: B = V0' * A1 * W0 * Sigma^-1 // set V0, W0T = matrices of first K right, left singular vectors - //gsl_matrix_complex *V0 = gsl_matrix_complex_alloc(m,K); - //gsl_matrix_complex *W0T= gsl_matrix_complex_alloc(K,l); complex double *V0, *W0T; QPMS_CRASHING_MALLOC(V0, m * K * sizeof(complex double)); QPMS_CRASHING_MALLOC(W0T, K * l * sizeof(complex double)); // TODO this is stupid, some parts could be handled simply by realloc. for (int k = 0; k < K; ++k) { - //gsl_vector_complex_view tmp; - //tmp = gsl_matrix_complex_column(V0_full, k); - //gsl_matrix_complex_set_col(V0, k, &(tmp.vector)); for(int i = 0; i < m; ++i) MAT(V0, m, K, i, k) = MAT(V0_full, m, l, i, k); - //tmp = gsl_matrix_complex_row(W0T_full, k); - //gsl_matrix_complex_set_row(W0T, k, &(tmp.vector)); for(int j = 0; j < l; ++j) MAT(W0T, K, l, k, j) = MAT(W0T_full, l, l, k, j); } - //gsl_matrix_complex_free(V0_full); free(V0_full); - //gsl_matrix_complex_free(W0T_full); free(W0T_full); - //gsl_matrix_complex *TM2 = gsl_matrix_complex_calloc(K,l); - //gsl_matrix_complex *B = gsl_matrix_complex_calloc(K,K); complex double *TM2, *B; QPMS_CRASHING_CALLOC(TM2, K * l, sizeof(complex double)); QPMS_CRASHING_CALLOC(B, K * K, sizeof(complex double)); if(verbose) printf(" Multiplying V0*A1->TM...\n"); - //const gsl_complex one = gsl_complex_rect(1,0); - //const gsl_complex zero = gsl_complex_rect(0,0); - //gsl_blas_zgemm(CblasConjTrans, CblasNoTrans, one, - // V0, A1, zero, TM2); // dims: V0[m,K], A1[m,l], TM2[K,l] const complex double one = 1, zero = 0; cblas_zgemm(CblasRowMajor, CblasConjTrans, CblasNoTrans, K, l, m, @@ -440,30 +409,20 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_functio if(verbose) printf(" Multiplying TM*W0T->B...\n"); - //gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, one, // TM2, W0T, zero, B); // DIMS: TM2[K,l], W0T[K,l], B[K,K] cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasConjTrans, K, K, l, &one, TM2, l, W0T, l, &zero, B, K); - //gsl_matrix_complex_free(W0T); - //gsl_matrix_complex_free(TM2); free(W0T); free(TM2); if(verbose) printf(" Scaling B <- B*Sigma^{-1}\n"); - //gsl_vector_complex *tmp = gsl_vector_complex_calloc(K); for(int i = 0; i < K; i++) { - //gsl_matrix_complex_get_col(tmp, B, i); - //gsl_vector_complex_scale(tmp, gsl_complex_rect(1.0/gsl_vector_get(Sigma,i), 0)); - //gsl_matrix_complex_set_col(B,i,tmp); for(int j = 0; j < K; j++) MAT(B, K, K, j, i) /= Sigma[i]; } - //gsl_vector_complex_free(tmp); - //for(int m=0; m S*Lambda*S' /* According to Beyn's paper (Algorithm 1), one should check conditioning @@ -475,14 +434,10 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_functio */ 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 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); // dims: B[K,K], S[K,K], Lambda[K] QPMS_ENSURE_SUCCESS(LAPACKE_zgeev( LAPACK_ROW_MAJOR, @@ -498,59 +453,44 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_functio K //S->tda/* ldvr */ )); - //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)); 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); 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); 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); 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, 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), K /* 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); eigenvalues[KRetained] = z; if(eigenvectors) { - //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; @@ -607,7 +547,6 @@ beyn_result_t *beyn_solve(const size_t m, const size_t l, 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); complex double *Mmat; QPMS_CRASHING_MALLOC(Mmat, m * m * sizeof(complex double)); QPMS_ENSURE_SUCCESS(M_function(Mmat, m, z, params)); @@ -630,30 +569,22 @@ beyn_result_t *beyn_solve(const size_t m, const size_t l, free(Mmat); } - // 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); for(size_t i = 0; i < m * l; ++i) A0_coarse[i] += 2 * MInvVHat[i]; } // 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) { 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]; } } @@ -669,7 +600,6 @@ beyn_result_t *beyn_solve(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); 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);