Some comments to beyn.c
Former-commit-id: cc756b3343a9290f3b3b8c79cec75559b11a952f
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Marek Nečada
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2762ada49c
commit
9d0f910bba
33
qpms/beyn.c
33
qpms/beyn.c
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@ -104,6 +104,7 @@ BeynSolver *BeynSolver_create(int M, int 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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// Beyn Step 1: Generate random matrix VHat
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BeynSolver_srandom(solver,(unsigned)time(NULL));
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return solver;
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@ -170,14 +171,11 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_gsl_t M_fun
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int verbose = 1; // TODO
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// A0 -> V0_full * Sigma * W0T_full'
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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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//A0->SVD(Sigma, &V0_full, &W0T_full);
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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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@ -194,6 +192,7 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_gsl_t M_fun
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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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@ -207,6 +206,7 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_gsl_t M_fun
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return 0;
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}
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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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@ -222,12 +222,11 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_gsl_t M_fun
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gsl_matrix_complex_free(V0_full);
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gsl_matrix_complex_free(W0T_full);
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// B <- V0' * A1 * W0 * Sigma^-1
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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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if(verbose) printf(" Multiplying V0*A1->TM...\n");
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//V0.Multiply(A1, &TM2, "--transA C"); // TM2 <- V0' * A1
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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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@ -252,7 +251,15 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_gsl_t M_fun
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//for(int m=0; m<K; m++) // B <- B * Sigma^{-1}
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// B -> S*Lambda*S'
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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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* of the eigenvalues; if they are ill-conditioned, one should perform
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* a procedure involving Schur decomposition and reordering.
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*
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* Beyn refers to MATLAB routines eig, condeig, schur, ordschur.
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* I am not sure about the equivalents in LAPACK, TODO check zgeevx, zgeesx.
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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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@ -285,6 +292,7 @@ static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_gsl_t M_fun
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gsl_matrix_complex_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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@ -347,6 +355,8 @@ beyn_result_gsl_t *beyn_solve_gsl(const size_t m, const size_t l,
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if(N & 1) QPMS_WARN("Contour discretisation point number is odd (%zd),"
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" the error estimates might be a bit off.", N);
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// Beyn Step 2: Computa A0, A1
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const complex double z0 = contour->centre;
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for(int n=0; n<N; n++) {
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const complex double z = contour->z_dz[n][0];
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@ -354,9 +364,6 @@ beyn_result_gsl_t *beyn_solve_gsl(const size_t m, const size_t l,
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gsl_matrix_complex_memcpy(MInvVHat, VHat);
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// Tän pitäis kutsua eval_WT
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// Output ilmeisesti tallentuun neljänteen parametriin
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if(M_inv_Vhat_function) {
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QPMS_ENSURE_SUCCESS(M_inv_Vhat_function(MInvVHat, VHat, z, params));
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} else {
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@ -382,7 +389,7 @@ beyn_result_gsl_t *beyn_solve_gsl(const size_t m, const size_t l,
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gsl_matrix_complex_add(A0_coarse, MInvVHat);
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}
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gsl_matrix_complex_scale(MInvVHat, cs2g(z - z0));
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gsl_matrix_complex_scale(MInvVHat, cs2g(z - z0)); // A_1 scaling as in Beyn's Remark 3.2(b) for numerical stability.
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gsl_matrix_complex_add(A1, MInvVHat);
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if((n%2)==0) {
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gsl_matrix_complex_add(A1_coarse, MInvVHat);
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@ -394,11 +401,13 @@ beyn_result_gsl_t *beyn_solve_gsl(const size_t m, const size_t l,
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gsl_vector_complex *eigenvalue_errors = solver->eigenvalue_errors;
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gsl_matrix_complex *eigenvectors = solver->eigenvectors;
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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, res_tol);
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// Repeat Steps 3–6 with rougher contour approximation to get an error estimate.
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int K_coarse = beyn_process_matrices(solver, M_function, params, A0_coarse, A1_coarse, z0, eigenvalue_errors, eigenvectors, rank_tol, res_tol);
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gsl_blas_zaxpy(gsl_complex_rect(-1,0), eigenvalues, eigenvalue_errors);
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// TODO Original did also fabs on the complex and real parts ^^^.
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// Reid did also fabs on the complex and real parts ^^^.
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beyn_result_gsl_t *result;
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QPMS_CRASHING_MALLOC(result, sizeof(beyn_result_gsl_t));
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@ -29,7 +29,14 @@ typedef int (*beyn_function_M_inv_Vhat_t)(complex double *target_M_inv_Vhat, siz
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/// Complex plane integration contour structure.
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typedef struct beyn_contour_t {
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size_t n; ///< Number of discretisation points.
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complex double centre; ///< TODO what is the exact purpose of this?
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/// "Centre" of the contour.
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/**
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* This point is used in the rescaling of the \f$ A_1 \f$ matrix as in
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* Beyn's Remark 3.2 (b) in order to improve the numerical stability.
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* It does not have to be a centre in some strictly defined sense,
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* but it should be "somewhere around" where the contour is.
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*/
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complex double centre;
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complex double z_dz[][2]; ///< Pairs of contour points and derivatives in that points.
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} beyn_contour_t;
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