Pure BLAS Beyn: cleanup commented out GSL code
This commit is contained in:
Marek Nečada
parent
2be3521333
commit
f19c590d6e
74
qpms/beyn.c
74
qpms/beyn.c
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@ -269,29 +269,18 @@ BeynSolver *BeynSolver_create(int M, int 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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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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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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@ -359,14 +348,9 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_functio
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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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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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m, // V0_full->size1 /* m, number of rows */,
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@ -385,8 +369,8 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_functio
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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 < 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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if (verbose) printf("Beyn: SV(%d)=%e\n",k, Sigma[k] );
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if (k < rank_sel_min || 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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@ -397,41 +381,26 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_functio
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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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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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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 < l; ++j)
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MAT(W0T, K, l, k, j) = MAT(W0T_full, l, 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 *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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// 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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@ -440,30 +409,20 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_functio
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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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// 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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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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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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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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//for(int m=0; m<K; m++) // B <- B * Sigma^{-1}
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// Beyn step 6.
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// Eigenvalue decomposition B -> S*Lambda*S'
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/* According to Beyn's paper (Algorithm 1), one should check conditioning
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@ -475,14 +434,10 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_functio
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*/
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if(verbose) printf(" Eigensolving (%i,%i)\n",K,K);
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//gsl_vector_complex *Lambda = gsl_vector_complex_alloc(K); // eigenvalues
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//gsl_matrix_complex *S = gsl_matrix_complex_alloc(K,K); // eigenvectors
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complex double *Lambda /* eigenvalues */ , *S /* eigenvector */;
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QPMS_CRASHING_MALLOC(Lambda, K * sizeof(complex double));
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QPMS_CRASHING_MALLOC(S, K * K * 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(Lambda->stride == 1, "Lambda vector stride must be 1 for LAPACKE_zgesdd, got %zd.", Sigma->stride);
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// dims: B[K,K], S[K,K], Lambda[K]
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QPMS_ENSURE_SUCCESS(LAPACKE_zgeev(
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LAPACK_ROW_MAJOR,
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@ -498,59 +453,44 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_t M_functio
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K //S->tda/* ldvr */
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));
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//gsl_matrix_complex_free(B);
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free(B);
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// V0S <- V0*S
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printf("Multiplying V0*S...\n");
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//gsl_matrix_complex *V0S = gsl_matrix_complex_alloc(m, K);
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//QPMS_ENSURE_SUCCESS(gsl_blas_zgemm(CblasNoTrans, CblasNoTrans,
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// one, V0, S, zero, V0S));
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complex double *V0S;
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QPMS_CRASHING_MALLOC(V0S, m * K * sizeof(complex double));
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// dims: V0[m,K], S[K,K], V0S[m,K]
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cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, m, K, K,
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&one, V0, K, S, K, &zero, V0S, K);
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//gsl_matrix_complex_free(V0);
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free(V0);
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// FIXME!!! make clear relation between KRetained and K in the results!
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// (If they differ, there are possibly some spurious eigenvalues.)
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int KRetained = 0;
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//gsl_matrix_complex *Mmat = gsl_matrix_complex_alloc(m, m);
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//gsl_vector_complex *MVk = gsl_vector_complex_alloc(m);
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complex double *Mmat, *MVk;
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QPMS_CRASHING_MALLOC(Mmat, m * m * sizeof(complex double));
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QPMS_CRASHING_MALLOC(MVk, m * sizeof(complex double));
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for (int k = 0; k < K; ++k) {
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//const gsl_complex zgsl = gsl_complex_add(gsl_complex_rect(creal(z0), cimag(z0)), gsl_vector_complex_get(Lambda, k));
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//const complex double z = GSL_REAL(zgsl) + I*GSL_IMAG(zgsl);
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const complex double z = z0 + Lambda[k];
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//gsl_vector_complex_const_view Vk = gsl_matrix_complex_const_column(V0S, k);
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double residual = 0;
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if(res_tol > 0) {
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QPMS_ENSURE_SUCCESS(M_function(Mmat, m, z, Params));
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//QPMS_ENSURE_SUCCESS(gsl_blas_zgemv(CblasNoTrans, one, Mmat, &(Vk.vector), zero, MVk));
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// Vk[i] == V0S[i, k]; dims: Mmat[m,m], Vk[m] (V0S[m, K]), MVk[m]
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cblas_zgemv(CblasRowMajor, CblasNoTrans, m, m,
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&one, Mmat, m, &MAT(V0S, m, K, 0, k), K /* stride of Vk in V0S */,
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&zero, MVk, 1);
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//residual = gsl_blas_dznrm2(MVk);
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residual = cblas_dznrm2(m, MVk, 1);
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if (verbose) printf("Beyn: Residual(%i)=%e\n",k,residual);
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}
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if (res_tol > 0 && residual > res_tol) continue;
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//gsl_vector_complex_set(eigenvalues, KRetained, zgsl);
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eigenvalues[KRetained] = z;
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if(eigenvectors) {
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//gsl_matrix_complex_set_row(eigenvectors, KRetained, &(Vk.vector));
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for(int j = 0; j < m; ++j)
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MAT(eigenvectors, l, m, KRetained, j) = MAT(V0S, m, K, j, k);
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//gsl_vector_set(solver->residuals, KRetained, residual);
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}
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++KRetained;
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@ -607,7 +547,6 @@ beyn_result_t *beyn_solve(const size_t m, const size_t l,
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QPMS_ENSURE_SUCCESS(M_inv_Vhat_function(MInvVHat, m, l, VHat, z, params));
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} else {
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lapack_int *pivot;
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//gsl_matrix_complex *Mmat = gsl_matrix_complex_alloc(m,m);
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complex double *Mmat;
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QPMS_CRASHING_MALLOC(Mmat, m * m * sizeof(complex double));
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QPMS_ENSURE_SUCCESS(M_function(Mmat, m, z, params));
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@ -630,30 +569,22 @@ beyn_result_t *beyn_solve(const size_t m, const size_t l,
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free(Mmat);
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}
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// gsl_matrix_complex_scale(MInvVHat, cs2g(dz));
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for(size_t i = 0; i < m * l; ++i)
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MInvVHat[i] *= dz;
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//gsl_matrix_complex_add(A0, MInvVHat);
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for(size_t i = 0; i < m * l; ++i)
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A0[i] += MInvVHat[i];
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if((n%2)==0) {
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//gsl_matrix_complex_add(A0_coarse, MInvVHat);
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//gsl_matrix_complex_add(A0_coarse, MInvVHat);
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for(size_t i = 0; i < m * l; ++i)
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A0_coarse[i] += 2 * MInvVHat[i];
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}
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// A_1 scaling as in Beyn's Remark 3.2(b) for numerical stability.
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//gsl_matrix_complex_scale(MInvVHat, cs2g(z - z0));
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for(size_t i = 0; i < m * l; ++i)
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MInvVHat[i] *= (z - z0);
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//gsl_matrix_complex_add(A1, MInvVHat);
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for(size_t i = 0; i < m * l; ++i)
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A1[i] += MInvVHat[i];
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if((n%2)==0) {
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for(size_t i = 0; i < m * l; ++i)
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//gsl_matrix_complex_add(A1_coarse, MInvVHat);
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//gsl_matrix_complex_add(A1_coarse, MInvVHat);
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A1_coarse[i] += 2 * MInvVHat[i];
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}
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}
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@ -669,7 +600,6 @@ beyn_result_t *beyn_solve(const size_t m, const size_t l,
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// Beyn Steps 3–6
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int K = beyn_process_matrices(solver, M_function, params, A0, A1, z0, eigenvalues, eigenvectors, rank_tol, rank_sel_min, res_tol);
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//gsl_blas_zaxpy(gsl_complex_rect(-1,0), eigenvalues, eigenvalue_errors);
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const complex double minusone = -1.;
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//TODO maybe change the sizes to correspend to retained eigval count K, not l
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cblas_zaxpy(l, &minusone, eigenvalues, 1, eigenvalue_errors, 1);
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