Mercurial > octave
view liboctave/numeric/eigs-base.cc @ 31231:a026fb2be108
sparse-xpow.cc: Return empty matrix for empty input (bug #63080)
author | Arun Giridhar <arungiridhar@gmail.com> |
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date | Mon, 19 Sep 2022 07:05:31 -0400 |
parents | 51a3d3a69193 |
children | 597f3ee61a48 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 2005-2022 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // This file is part of Octave. // // Octave is free software: you can redistribute it and/or modify it // under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // Octave is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with Octave; see the file COPYING. If not, see // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <cmath> #include <ostream> #include "Array.h" #include "CSparse.h" #include "MatrixType.h" #include "PermMatrix.h" #include "chol.h" #include "dSparse.h" #include "eigs-base.h" #include "lo-arpack-proto.h" #include "lo-blas-proto.h" #include "lo-error.h" #include "lo-ieee.h" #include "lu.h" #include "mx-ops.h" #include "oct-locbuf.h" #include "oct-rand.h" #include "sparse-chol.h" #include "sparse-lu.h" #if defined (HAVE_ARPACK) static void warn_convergence (void) { (*current_liboctave_warning_with_id_handler) ("Octave:convergence", "eigs: 'A - sigma*B' is singular, indicating sigma is exactly " "an eigenvalue so convergence is not guaranteed"); } // Conversion from error number to strings std::string arpack_errno2str (const octave_idx_type& errnum, const std::string& fcn_name) { std::string msg; std::string bug_msg = "\nThis should not happen. Please, see https://www.gnu.org/software/octave/bugs.html, and file a bug report"; switch (errnum) { case -1: msg = "N must be positive"; break; case -2: msg = "NEV must be positive"; break; case -3: msg = "NCV-NEV >= 2 and less than or equal to N"; break; case -4: msg = "The maximum number of Arnoldi update iterations allowed must be greater than zero"; break; case -5: msg = "WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI'"; break; case -6: msg = "BMAT must be one of 'I' or 'G'"; break; case -7: msg = "Length of private work WORKL array is insufficient"; break; case -8: msg = "Error return from LAPACK eigenvalue calculation"; break; case -9: if (fcn_name.compare ("zneupd") == 0) msg = "Error return from calculation of eigenvectors. Informational error from LAPACK routine ztrevc"; else if (fcn_name.compare ("dneupd") == 0) msg = "Error return from calculation of eigenvectors. Informational error from LAPACK routine dtrevc"; else msg = "Starting vector is zero"; break; case -10: if (fcn_name.compare ("dneupd") == 0 || fcn_name.compare ("dnaupd") == 0) msg = "IPARAM(7) must be 1,2,3,4"; else if (fcn_name.compare ("zneupd") == 0 || fcn_name.compare ("znaupd") == 0) msg = "IPARAM(7) must be 1,2,3"; else msg = "IPARAM(7) must be 1,2,3,4,5"; break; case -11: msg = "IPARAM(7) = 1 and BMAT = 'G' are incompatible"; break; case -12: if (fcn_name.compare ("dnaupd") == 0 || fcn_name.compare ("znaupd") == 0 || fcn_name.compare ("dsaupd") == 0) msg = std::string ("IPARAM(1) must be equal to 0 or 1"); else if (fcn_name.compare ("dneupd") == 0 || fcn_name.compare ("zneupd") == 0) msg = "HOWMNY = 'S' not yet implemented"; else msg = "NEV and WHICH = 'BE' are incompatible"; break; case -13: if (fcn_name.compare ("dneupd") == 0 || fcn_name.compare ("zneupd") == 0) msg = "HOWMNY must be one of 'A' or 'P' if RVEC = .true."; else if (fcn_name.compare ("dsaupd") == 0) msg = "NEV and WHICH = 'BE' are incompatible"; break; case -14: if (fcn_name.compare ("dneupd") == 0) msg = "DNAUPD did not find any eigenvalues to sufficient accuracy."; else if (fcn_name.compare ("zneupd") == 0) msg = "ZNAUPD did not find any eigenvalues to sufficient accuracy."; else if (fcn_name.compare ("dseupd") == 0) msg = "DSAUPD did not find any eigenvalues to sufficient accuracy."; msg += " Consider changing tolerance (TOL), maximum iterations (MAXIT), number of Lanzcos basis vectors (P), or starting vector (V0) in OPTS structure."; break; case -15: if (fcn_name.compare ("dseupd") == 0) msg = "HOWMNY must be one of 'A' or 'S' if RVEC = .true."; break; case -16: if (fcn_name.compare ("dseupd") == 0) msg = "HOWMNY = 'S' not yet implemented"; break; case -9999: if (fcn_name.compare ("dnaupd") == 0) msg = "Could not build an Arnoldi factorization. IPARAM(5) returns the size of the current Arnoldi factorization"; break; case 1: if (fcn_name.compare ("dneupd") == 0) msg = "The Schur form computed by LAPACK routine dlahqr could not be reordered by LAPACK routine dtrsen. Re-enter subroutine DNEUPD with IPARAM(5)=NCV and increase the size of the arrays DR and DI to have dimension at least dimension NCV and allocate at least NCV columns for Z. NOTE: Not necessary if Z and V share the same space. Please notify the authors if this error occurs."; else if (fcn_name.compare ("dnaupd") == 0 || fcn_name.compare ("znaupd") == 0 || fcn_name.compare ("dsaupd") == 0) msg = "Maximum number of iterations taken. All possible eigenvalues of OP has been found. IPARAM(5) returns the number of wanted converged Ritz values"; else if (fcn_name.compare ("znaupd") == 0) msg = "The Schur form computed by LAPACK routine csheqr could not be reordered by LAPACK routine ztrsen. Re-enter subroutine ZNEUPD with IPARAM(5)=NCV and increase the size of the array D to have dimension at least dimension NCV and allocate at least NCV columns for Z. NOTE: Not necessary if Z and V share the same space. Please notify the authors if this error occurs."; break; case 2: if (fcn_name.compare ("dnaupd") == 0 || fcn_name.compare ("znaupd") == 0 || fcn_name.compare ("dsaupd") == 0) msg = "No longer an informational error. Deprecated starting with release 2 of ARPACK."; break; case 3: if (fcn_name.compare ("dnaupd") == 0 || fcn_name.compare ("znaupd") == 0 || fcn_name.compare ("dsaupd") == 0) msg = "No shifts could be applied during a cycle of the implicitly restarted Arnoldi iteration. One possibility is to increase the size of NCV relative to NEV."; break; } if ((errnum != -9) && (errnum != -14) && (errnum != -9999)) msg.append (bug_msg); // This is a bug in Octave interface to ARPACK return msg; } template <typename M, typename SM> static octave_idx_type lusolve (const SM& L, const SM& U, M& m) { octave_idx_type err = 0; double rcond; MatrixType utyp (MatrixType::Upper); // Sparse L is lower triangular, Dense L is permuted lower triangular!!! MatrixType ltyp (MatrixType::Lower); m = L.solve (ltyp, m, err, rcond, nullptr); if (err) return err; m = U.solve (utyp, m, err, rcond, nullptr); return err; } template <typename SM, typename M> static M ltsolve (const SM& L, const ColumnVector& Q, const M& m) { // Solve (Q_mat * L) * x = m, that is L * x = Q_mat' * m = m(Q) octave_idx_type n = L.cols (); octave_idx_type b_nc = m.cols (); octave_idx_type err = 0; double rcond; MatrixType ltyp (MatrixType::Lower); M retval (n, b_nc); const double *qv = Q.data (); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < n; i++) retval.elem (i, j) = m.elem (static_cast<octave_idx_type> (qv[i]), j); } return L.solve (ltyp, retval, err, rcond, nullptr); } template <typename SM, typename M> static M utsolve (const SM& U, const ColumnVector& Q, const M& m) { // Solve (U * Q_mat') * x = m by U * tmp = m, x(Q) = tmp (Q_mat * tmp = x) octave_idx_type n = U.cols (); octave_idx_type b_nc = m.cols (); octave_idx_type err = 0; double rcond; MatrixType utyp (MatrixType::Upper); M tmp = U.solve (utyp, m, err, rcond, nullptr); M retval; const double *qv = Q.data (); if (! err) { retval.resize (n, b_nc); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < n; i++) retval.elem (static_cast<octave_idx_type> (qv[i]), j) = tmp.elem (i, j); } } return retval; } static bool vector_product (const SparseMatrix& m, const double *x, double *y) { octave_idx_type nc = m.cols (); for (octave_idx_type j = 0; j < nc; j++) y[j] = 0.; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++) y[m.ridx (i)] += m.data (i) * x[j]; return true; } static bool vector_product (const Matrix& m, const double *x, double *y) { F77_INT nr = octave::to_f77_int (m.rows ()); F77_INT nc = octave::to_f77_int (m.cols ()); F77_XFCN (dgemv, DGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), nr, nc, 1.0, m.data (), nr, x, 1, 0.0, y, 1 F77_CHAR_ARG_LEN (1))); return true; } static bool vector_product (const SparseComplexMatrix& m, const Complex *x, Complex *y) { octave_idx_type nc = m.cols (); for (octave_idx_type j = 0; j < nc; j++) y[j] = 0.; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++) y[m.ridx (i)] += m.data (i) * x[j]; return true; } static bool vector_product (const ComplexMatrix& m, const Complex *x, Complex *y) { F77_INT nr = octave::to_f77_int (m.rows ()); F77_INT nc = octave::to_f77_int (m.cols ()); F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), nr, nc, 1.0, F77_CONST_DBLE_CMPLX_ARG (m.data ()), nr, F77_CONST_DBLE_CMPLX_ARG (x), 1, 0.0, F77_DBLE_CMPLX_ARG (y), 1 F77_CHAR_ARG_LEN (1))); return true; } static bool make_cholb (Matrix& b, Matrix& bt, ColumnVector& permB) { octave_idx_type info; octave::math::chol<Matrix> fact (b, info); octave_idx_type n = b.cols (); if (info != 0) return false; else { bt = fact.chol_matrix (); // upper triangular b = bt.transpose (); permB = ColumnVector (n); for (octave_idx_type i = 0; i < n; i++) permB(i) = i; return true; } } static bool make_cholb (SparseMatrix& b, SparseMatrix& bt, ColumnVector& permB) { octave_idx_type info; octave::math::sparse_chol<SparseMatrix> fact (b, info, false); if (info != 0) return false; else { b = fact.L (); // lower triangular bt = b.transpose (); permB = fact.perm () - 1.0; return true; } } static bool make_cholb (ComplexMatrix& b, ComplexMatrix& bt, ColumnVector& permB) { octave_idx_type info; octave::math::chol<ComplexMatrix> fact (b, info); octave_idx_type n = b.cols (); if (info != 0) return false; else { bt = fact.chol_matrix (); // upper triangular b = bt.hermitian (); permB = ColumnVector (n); for (octave_idx_type i = 0; i < n; i++) permB(i) = i; return true; } } static bool make_cholb (SparseComplexMatrix& b, SparseComplexMatrix& bt, ColumnVector& permB) { octave_idx_type info; octave::math::sparse_chol<SparseComplexMatrix> fact (b, info, false); if (info != 0) return false; else { b = fact.L (); // lower triangular bt = b.hermitian (); permB = fact.perm () - 1.0; return true; } } static bool LuAminusSigmaB (const SparseMatrix& m, const SparseMatrix& b, bool cholB, const ColumnVector& permB, double sigma, SparseMatrix& L, SparseMatrix& U, octave_idx_type *P, octave_idx_type *Q, ColumnVector& r) { bool have_b = ! b.isempty (); octave_idx_type n = m.rows (); // Calculate LU decomposition of 'M = A - sigma * B' // P * (R \ M) * Q = L * U SparseMatrix AminusSigmaB (m); if (sigma != 0.0) { if (have_b) { if (cholB) { if (permB.numel ()) { SparseMatrix tmp (n, n, n); for (octave_idx_type i = 0; i < n; i++) { tmp.xcidx (i) = i; tmp.xridx (i) = static_cast<octave_idx_type> (permB(i)); tmp.xdata (i) = 1; } tmp.xcidx (n) = n; AminusSigmaB -= sigma * tmp * b.transpose () * b * tmp.transpose (); } else AminusSigmaB -= sigma * b.transpose () * b; } else AminusSigmaB -= sigma * b; } else { SparseMatrix sigmat (n, n, n); // Create sigma * speye (n,n) sigmat.xcidx (0) = 0; for (octave_idx_type i = 0; i < n; i++) { sigmat.xdata (i) = sigma; sigmat.xridx (i) = i; sigmat.xcidx (i+1) = i + 1; } AminusSigmaB -= sigmat; } } octave::math::sparse_lu<SparseMatrix> fact (AminusSigmaB, Matrix (), true); L = fact.L (); U = fact.U (); SparseMatrix R = fact.R (); for (octave_idx_type i = 0; i < n; i++) r(i) = R.xdata(i); const octave_idx_type *P2 = fact.row_perm (); const octave_idx_type *Q2 = fact.col_perm (); for (octave_idx_type j = 0; j < n; j++) { P[j] = P2[j]; Q[j] = Q2[j]; } // Test condition number of LU decomposition double minU = octave::numeric_limits<double>::NaN (); double maxU = octave::numeric_limits<double>::NaN (); for (octave_idx_type j = 0; j < n; j++) { double d = 0.; if (U.xcidx (j+1) > U.xcidx (j) && U.xridx (U.xcidx (j+1)-1) == j) d = std::abs (U.xdata (U.xcidx (j+1)-1)); if (octave::math::isnan (minU) || d < minU) minU = d; if (octave::math::isnan (maxU) || d > maxU) maxU = d; } double rcond = (minU / maxU); volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) warn_convergence (); return true; } static bool LuAminusSigmaB (const Matrix& m, const Matrix& b, bool cholB, const ColumnVector& permB, double sigma, Matrix& L, Matrix& U, octave_idx_type *P, octave_idx_type *Q, ColumnVector& r) { bool have_b = ! b.isempty (); octave_idx_type n = m.cols (); // Calculate LU decomposition of 'M = A - sigma * B' // P * M = L * U Matrix AminusSigmaB (m); if (sigma != 0.0) { if (have_b) { if (cholB) { Matrix tmp = sigma * b.transpose () * b; const double *pB = permB.data (); double *p = AminusSigmaB.fortran_vec (); if (permB.numel ()) { for (octave_idx_type j = 0; j < b.cols (); j++) for (octave_idx_type i = 0; i < b.rows (); i++) *p++ -= tmp.xelem (static_cast<octave_idx_type> (pB[i]), static_cast<octave_idx_type> (pB[j])); } else AminusSigmaB -= tmp; } else AminusSigmaB -= sigma * b; } else { double *p = AminusSigmaB.fortran_vec (); for (octave_idx_type i = 0; i < n; i++) p[i*(n+1)] -= sigma; } } octave::math::lu<Matrix> fact (AminusSigmaB); L = fact.L (); U = fact.U (); ColumnVector P2 = fact.P_vec(); for (octave_idx_type j = 0; j < n; j++) { Q[j] = j; P[j] = P2(j) - 1; r(j) = 1.; } // Test condition number of LU decomposition double minU = octave::numeric_limits<double>::NaN (); double maxU = octave::numeric_limits<double>::NaN (); for (octave_idx_type j = 0; j < n; j++) { double d = std::abs (U.xelem (j, j)); if (octave::math::isnan (minU) || d < minU) minU = d; if (octave::math::isnan (maxU) || d > maxU) maxU = d; } double rcond = (minU / maxU); volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) warn_convergence (); return true; } static bool LuAminusSigmaB (const SparseComplexMatrix& m, const SparseComplexMatrix& b, bool cholB, const ColumnVector& permB, Complex sigma, SparseComplexMatrix& L, SparseComplexMatrix& U, octave_idx_type *P, octave_idx_type *Q, ColumnVector& r) { bool have_b = ! b.isempty (); octave_idx_type n = m.rows (); // Calculate LU decomposition of 'M = A - sigma * B' // P * (R \ M) * Q = L * U SparseComplexMatrix AminusSigmaB (m); if (std::real (sigma) != 0.0 || std::imag (sigma) != 0.0) { if (have_b) { if (cholB) { if (permB.numel ()) { SparseMatrix tmp (n, n, n); for (octave_idx_type i = 0; i < n; i++) { tmp.xcidx (i) = i; tmp.xridx (i) = static_cast<octave_idx_type> (permB(i)); tmp.xdata (i) = 1; } tmp.xcidx (n) = n; AminusSigmaB -= tmp * b.hermitian () * b * tmp.transpose () * sigma; } else AminusSigmaB -= sigma * b.hermitian () * b; } else AminusSigmaB -= sigma * b; } else { SparseComplexMatrix sigmat (n, n, n); // Create sigma * speye (n,n) sigmat.xcidx (0) = 0; for (octave_idx_type i = 0; i < n; i++) { sigmat.xdata (i) = sigma; sigmat.xridx (i) = i; sigmat.xcidx (i+1) = i + 1; } AminusSigmaB -= sigmat; } } octave::math::sparse_lu<SparseComplexMatrix> fact (AminusSigmaB, Matrix(), true); L = fact.L (); U = fact.U (); SparseMatrix R = fact.R (); for (octave_idx_type i = 0; i < n; i++) r(i) = R.xdata(i); const octave_idx_type *P2 = fact.row_perm (); const octave_idx_type *Q2 = fact.col_perm (); for (octave_idx_type j = 0; j < n; j++) { P[j] = P2[j]; Q[j] = Q2[j]; } // Test condition number of LU decomposition double minU = octave::numeric_limits<double>::NaN (); double maxU = octave::numeric_limits<double>::NaN (); for (octave_idx_type j = 0; j < n; j++) { double d = 0.; if (U.xcidx (j+1) > U.xcidx (j) && U.xridx (U.xcidx (j+1)-1) == j) d = std::abs (U.xdata (U.xcidx (j+1)-1)); if (octave::math::isnan (minU) || d < minU) minU = d; if (octave::math::isnan (maxU) || d > maxU) maxU = d; } double rcond = (minU / maxU); volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) warn_convergence (); return true; } static bool LuAminusSigmaB (const ComplexMatrix& m, const ComplexMatrix& b, bool cholB, const ColumnVector& permB, Complex sigma, ComplexMatrix& L, ComplexMatrix& U, octave_idx_type *P, octave_idx_type *Q, ColumnVector& r) { bool have_b = ! b.isempty (); octave_idx_type n = m.cols (); // Calculate LU decomposition of 'M = A - sigma * B' // P * M = L * U ComplexMatrix AminusSigmaB (m); if (std::real (sigma) != 0.0 || std::imag (sigma) != 0.0) { if (have_b) { if (cholB) { ComplexMatrix tmp = sigma * b.hermitian () * b; const double *pB = permB.data (); Complex *p = AminusSigmaB.fortran_vec (); if (permB.numel ()) { for (octave_idx_type j = 0; j < b.cols (); j++) for (octave_idx_type i = 0; i < b.rows (); i++) *p++ -= tmp.xelem (static_cast<octave_idx_type> (pB[i]), static_cast<octave_idx_type> (pB[j])); } else AminusSigmaB -= tmp; } else AminusSigmaB -= sigma * b; } else { Complex *p = AminusSigmaB.fortran_vec (); for (octave_idx_type i = 0; i < n; i++) p[i*(n+1)] -= sigma; } } octave::math::lu<ComplexMatrix> fact (AminusSigmaB); L = fact.L (); U = fact.U (); ColumnVector P2 = fact.P_vec (); for (octave_idx_type j = 0; j < n; j++) { Q[j] = j; P[j] = P2(j) - 1; r(j) = 1.; } // Test condition number of LU decomposition double minU = octave::numeric_limits<double>::NaN (); double maxU = octave::numeric_limits<double>::NaN (); for (octave_idx_type j = 0; j < n; j++) { double d = std::abs (U.xelem (j, j)); if (octave::math::isnan (minU) || d < minU) minU = d; if (octave::math::isnan (maxU) || d > maxU) maxU = d; } double rcond = (minU / maxU); volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) warn_convergence (); return true; } template <typename M> octave_idx_type EigsRealSymmetricMatrix (const M& m, const std::string typ, octave_idx_type k_arg, octave_idx_type p_arg, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const M& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { F77_INT k = octave::to_f77_int (k_arg); F77_INT p = octave::to_f77_int (p_arg); M b(_b); F77_INT n = octave::to_f77_int (m.cols ()); F77_INT mode = 1; bool have_b = ! b.isempty (); bool note3 = false; char bmat = 'I'; double sigma = 0.; M bt; if (m.rows () != m.cols ()) (*current_liboctave_error_handler) ("eigs: A must be square"); if (have_b && (m.rows () != b.rows () || m.rows () != b.cols ())) (*current_liboctave_error_handler) ("eigs: B must be square and the same size as A"); if (resid.isempty ()) { std::string rand_dist = octave::rand::distribution (); octave::rand::distribution ("uniform"); resid = ColumnVector (octave::rand::vector (n)); octave::rand::distribution (rand_dist); } else if (m.cols () != resid.numel ()) (*current_liboctave_error_handler) ("eigs: opts.v0 must be n-by-1"); if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2; if (p < 20) p = 20; if (p > n) p = n; } if (k < 1 || k > n - 2) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract" " (must be 0 < k < n-1-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p > n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than or equal to n"); if (have_b && cholB && ! permB.isempty ()) { // Check the we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (F77_INT i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || octave::math::x_nint (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } if (typ != "LM" && typ != "SM" && typ != "LA" && typ != "SA" && typ != "BE" && typ != "LR" && typ != "SR" && typ != "LI" && typ != "SI") (*current_liboctave_error_handler) ("eigs: unrecognized sigma value"); if (typ == "LI" || typ == "SI" || typ == "LR" || typ == "SR") (*current_liboctave_error_handler) ("eigs: invalid sigma value for real symmetric problem"); if (have_b) { // See Note 3 dsaupd note3 = true; if (cholB) { bt = b; b = b.transpose (); if (permB.isempty ()) { permB = ColumnVector (n); for (F77_INT i = 0; i < n; i++) permB(i) = i; } } else { if (! make_cholb (b, bt, permB)) (*current_liboctave_error_handler) ("eigs: The matrix B is not positive definite"); } } Array<F77_INT> ip (dim_vector (11, 1)); F77_INT *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<F77_INT> iptr (dim_vector (14, 1)); F77_INT *ipntr = iptr.fortran_vec (); F77_INT ido = 0; int iter = 0; F77_INT lwork = p * (p + 8); OCTAVE_LOCAL_BUFFER (double, v, n * p); OCTAVE_LOCAL_BUFFER (double, workl, lwork); OCTAVE_LOCAL_BUFFER (double, workd, 3 * n); double *presid = resid.fortran_vec (); do { F77_INT tmp_info = octave::to_f77_int (info); F77_FUNC (dsaupd, DSAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, tmp_info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); info = tmp_info; if (disp > 0 && ! octave::math::isnan (workl[iptr (5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; if (ido == 99) // convergence { for (F77_INT i = 0; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } else { // the wanted Ritz estimates are at the end for (F77_INT i = p - k; i < p; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave::numeric_limits<double>::NaN (); } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { Matrix mtmp (n, 1); for (F77_INT i = 0; i < n; i++) mtmp(i, 0) = workd[i + iptr(0) - 1]; mtmp = ltsolve (b, permB, m * utsolve (bt, permB, mtmp)); for (F77_INT i = 0; i < n; i++) workd[i+iptr(1)-1] = mtmp(i, 0); } else if (! vector_product (m, workd + iptr(0) - 1, workd + iptr(1) - 1)) break; } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error in dsaupd: %s", arpack_errno2str (info, "dsaupd").c_str ()); break; } } while (1); F77_INT info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<F77_INT> s (dim_vector (p, 1)); F77_INT *sel = s.fortran_vec (); eig_vec.resize (n, k); double *z = eig_vec.fortran_vec (); eig_val.resize (k); double *d = eig_val.fortran_vec (); F77_FUNC (dseupd, DSEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, d, z, n, sigma, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (info2 == 0) { for (F77_INT i = ip(4); i < k; i++) d[i] = octave::numeric_limits<double>::NaN (); F77_INT k2 = ip(4) / 2; if (typ != "SM" && typ != "BE" && ! (typ == "SA" && rvec)) { for (F77_INT i = 0; i < k2; i++) { double dtmp = d[i]; d[i] = d[ip(4) - i - 1]; d[ip(4) - i - 1] = dtmp; } } if (rvec) { for (F77_INT i = ip(4); i < k; i++) { F77_INT off1 = i * n; for (F77_INT j = 0; j < n; j++) z[off1 + j] = octave::numeric_limits<double>::NaN (); } if (typ != "SM" && typ != "BE" && typ != "SA") { OCTAVE_LOCAL_BUFFER (double, dtmp, n); for (F77_INT i = 0; i < k2; i++) { F77_INT off1 = i * n; F77_INT off2 = (ip(4) - i - 1) * n; if (off1 == off2) continue; for (F77_INT j = 0; j < n; j++) dtmp[j] = z[off1 + j]; for (F77_INT j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (F77_INT j = 0; j < n; j++) z[off2 + j] = dtmp[j]; } } if (note3) eig_vec = utsolve (bt, permB, eig_vec); } } else (*current_liboctave_error_handler) ("eigs: error in dseupd: %s", arpack_errno2str (info2, "dseupd").c_str ()); return ip(4); } template <typename M> octave_idx_type EigsRealSymmetricMatrixShift (const M& m, double sigma, octave_idx_type k_arg, octave_idx_type p_arg, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const M& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { F77_INT k = octave::to_f77_int (k_arg); F77_INT p = octave::to_f77_int (p_arg); M b(_b); F77_INT n = octave::to_f77_int (m.cols ()); F77_INT mode = 3; bool have_b = ! b.isempty (); std::string typ = "LM"; if (m.rows () != m.cols ()) (*current_liboctave_error_handler) ("eigs: A must be square"); if (have_b && (m.rows () != b.rows () || m.rows () != b.cols ())) (*current_liboctave_error_handler) ("eigs: B must be square and the same size as A"); // FIXME: The "SM" type for mode 1 seems unstable though faster!! //if (! std::abs (sigma)) // return EigsRealSymmetricMatrix (m, "SM", k, p, info, eig_vec, eig_val, // _b, permB, resid, os, tol, rvec, cholB, // disp, maxit); if (resid.isempty ()) { std::string rand_dist = octave::rand::distribution (); octave::rand::distribution ("uniform"); resid = ColumnVector (octave::rand::vector (n)); octave::rand::distribution (rand_dist); } else if (m.cols () != resid.numel ()) (*current_liboctave_error_handler) ("eigs: opts.v0 must be n-by-1"); if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract" " (must be 0 < k < n-1-1).\n" " Use 'eig (full (A))' instead"); if (p < 0) { p = k * 2; if (p < 20) p = 20; if (p > n) p = n; } if (p <= k || p > n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than or equal to n"); if (have_b && cholB && ! permB.isempty ()) { // Check the we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (F77_INT i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || octave::math::x_nint (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } char bmat = 'I'; if (have_b) bmat = 'G'; Array<F77_INT> ip (dim_vector (11, 1)); F77_INT *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<F77_INT> iptr (dim_vector (14, 1)); F77_INT *ipntr = iptr.fortran_vec (); F77_INT ido = 0; int iter = 0; M L, U; ColumnVector r(n); OCTAVE_LOCAL_BUFFER (octave_idx_type, P, (have_b ? b.rows () : m.rows ())); OCTAVE_LOCAL_BUFFER (octave_idx_type, Q, (have_b ? b.cols () : m.cols ())); if (! LuAminusSigmaB (m, b, cholB, permB, sigma, L, U, P, Q, r)) return -1; F77_INT lwork = p * (p + 8); OCTAVE_LOCAL_BUFFER (double, v, n * p); OCTAVE_LOCAL_BUFFER (double, workl, lwork); OCTAVE_LOCAL_BUFFER (double, workd, 3 * n); double *presid = resid.fortran_vec (); do { F77_INT tmp_info = octave::to_f77_int (info); F77_FUNC (dsaupd, DSAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, tmp_info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); info = tmp_info; if (disp > 0 && ! octave::math::isnan (workl[iptr (5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; if (ido == 99) // convergence { for (F77_INT i = 0; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } else { // the wanted Ritz estimates are at the end for (F77_INT i = p - k; i < p; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave::numeric_limits<double>::NaN (); } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { if (ido == -1) { OCTAVE_LOCAL_BUFFER (double, dtmp, n); vector_product (b, workd+iptr(0)-1, dtmp); Matrix tmp (n, 1); for (F77_INT i = 0; i < n; i++) tmp(i, 0) = dtmp[P[i]] / r(P[i]); lusolve (L, U, tmp); double *ip2 = workd+iptr(1)-1; for (F77_INT i = 0; i < n; i++) ip2[Q[i]] = tmp(i, 0); } else if (ido == 2) vector_product (b, workd+iptr(0)-1, workd+iptr(1)-1); else { double *ip2 = workd+iptr(2)-1; Matrix tmp (n, 1); for (F77_INT i = 0; i < n; i++) tmp(i, 0) = ip2[P[i]] / r(P[i]); lusolve (L, U, tmp); ip2 = workd+iptr(1)-1; for (F77_INT i = 0; i < n; i++) ip2[Q[i]] = tmp(i, 0); } } else { // ido cannot be 2 for non-generalized problems (see dsaupd2). double *ip2 = workd+iptr(0)-1; Matrix tmp (n, 1); for (F77_INT i = 0; i < n; i++) tmp(i, 0) = ip2[P[i]] / r(P[i]); lusolve (L, U, tmp); ip2 = workd+iptr(1)-1; for (F77_INT i = 0; i < n; i++) ip2[Q[i]] = tmp(i, 0); } } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error in dsaupd: %s", arpack_errno2str (info, "dsaupd").c_str ()); break; } } while (1); F77_INT info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<F77_INT> s (dim_vector (p, 1)); F77_INT *sel = s.fortran_vec (); eig_vec.resize (n, k); double *z = eig_vec.fortran_vec (); eig_val.resize (k); double *d = eig_val.fortran_vec (); F77_FUNC (dseupd, DSEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, d, z, n, sigma, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (info2 == 0) { for (F77_INT i = ip(4); i < k; i++) d[i] = octave::numeric_limits<double>::NaN (); F77_INT k2 = ip(4) / 2; for (F77_INT i = 0; i < k2; i++) { double dtmp = d[i]; d[i] = d[ip(4) - i - 1]; d[ip(4) - i - 1] = dtmp; } if (rvec) { OCTAVE_LOCAL_BUFFER (double, dtmp, n); for (F77_INT i = ip(4); i < k; i++) { F77_INT off1 = i * n; for (F77_INT j = 0; j < n; j++) z[off1 + j] = octave::numeric_limits<double>::NaN (); } for (F77_INT i = 0; i < k2; i++) { F77_INT off1 = i * n; F77_INT off2 = (ip(4) - i - 1) * n; if (off1 == off2) continue; for (F77_INT j = 0; j < n; j++) dtmp[j] = z[off1 + j]; for (F77_INT j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (F77_INT j = 0; j < n; j++) z[off2 + j] = dtmp[j]; } } } else (*current_liboctave_error_handler) ("eigs: error in dseupd: %s", arpack_errno2str (info2, "dseupd").c_str ()); return ip(4); } template <typename M> octave_idx_type EigsRealSymmetricFunc (EigsFunc fcn, octave_idx_type n_arg, const std::string& _typ, double sigma, octave_idx_type k_arg, octave_idx_type p_arg, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const M& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { F77_INT n = octave::to_f77_int (n_arg); F77_INT k = octave::to_f77_int (k_arg); F77_INT p = octave::to_f77_int (p_arg); M b(_b); std::string typ (_typ); bool have_sigma = (sigma ? true : false); bool have_b = ! b.isempty (); bool note3 = false; char bmat = 'I'; F77_INT mode = 1; int err = 0; M bt; if (resid.isempty ()) { std::string rand_dist = octave::rand::distribution (); octave::rand::distribution ("uniform"); resid = ColumnVector (octave::rand::vector (n)); octave::rand::distribution (rand_dist); } else if (n != resid.numel ()) (*current_liboctave_error_handler) ("eigs: opts.v0 must be n-by-1"); if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2; if (p < 20) p = 20; if (p > n) p = n; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract" " (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p > n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than or equal to n"); if (have_b && cholB && ! permB.isempty ()) { // Check the we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (F77_INT i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || octave::math::x_nint (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } if (! have_sigma) { if (typ != "LM" && typ != "SM" && typ != "LA" && typ != "SA" && typ != "BE" && typ != "LR" && typ != "SR" && typ != "LI" && typ != "SI") (*current_liboctave_error_handler) ("eigs: unrecognized sigma value"); if (typ == "LI" || typ == "SI" || typ == "LR" || typ == "SR") (*current_liboctave_error_handler) ("eigs: invalid sigma value for real symmetric problem"); if (typ != "SM" && have_b) note3 = true; if (typ == "SM") { typ = "LM"; sigma = 0.; mode = 3; if (have_b) bmat = 'G'; } } else if (! std::abs (sigma)) { typ = "SM"; if (have_b) bmat = 'G'; } else { typ = "LM"; mode = 3; if (have_b) bmat = 'G'; } if (mode == 1 && have_b) { // See Note 3 dsaupd note3 = true; if (cholB) { bt = b; b = b.transpose (); if (permB.isempty ()) { permB = ColumnVector (n); for (F77_INT i = 0; i < n; i++) permB(i) = i; } } else { if (! make_cholb (b, bt, permB)) (*current_liboctave_error_handler) ("eigs: The matrix B is not positive definite"); } } Array<F77_INT> ip (dim_vector (11, 1)); F77_INT *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<F77_INT> iptr (dim_vector (14, 1)); F77_INT *ipntr = iptr.fortran_vec (); F77_INT ido = 0; int iter = 0; F77_INT lwork = p * (p + 8); OCTAVE_LOCAL_BUFFER (double, v, n * p); OCTAVE_LOCAL_BUFFER (double, workl, lwork); OCTAVE_LOCAL_BUFFER (double, workd, 3 * n); double *presid = resid.fortran_vec (); do { F77_INT tmp_info = octave::to_f77_int (info); F77_FUNC (dsaupd, DSAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, tmp_info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); info = tmp_info; if (disp > 0 && ! octave::math::isnan (workl[iptr (5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; if (ido == 99) // convergence { for (F77_INT i = 0; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } else { // the wanted Ritz estimates are at the end for (F77_INT i = p - k; i < p; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave::numeric_limits<double>::NaN (); } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { if (mode == 1) // regular mode with factorized B { Matrix mtmp (n, 1); for (F77_INT i = 0; i < n; i++) mtmp(i, 0) = workd[i + iptr(0) - 1]; mtmp = utsolve (bt, permB, mtmp); ColumnVector y = fcn (mtmp, err); if (err) return false; mtmp = ltsolve (b, permB, y); for (F77_INT i = 0; i < n; i++) workd[i+iptr(1)-1] = mtmp(i, 0); } else // shift-invert mode { if (ido == -1) { OCTAVE_LOCAL_BUFFER (double, dtmp, n); vector_product (b, workd+iptr(0)-1, dtmp); ColumnVector x(n); for (F77_INT i = 0; i < n; i++) x(i) = dtmp[i]; ColumnVector y = fcn (x, err); if (err) return false; double *ip2 = workd + iptr(1) - 1; for (F77_INT i = 0; i < n; i++) ip2[i] = y(i); } else if (ido == 2) vector_product (b, workd+iptr(0)-1, workd+iptr(1)-1); else { double *ip2 = workd+iptr(2)-1; ColumnVector x(n); for (F77_INT i = 0; i < n; i++) x(i) = *ip2++; ColumnVector y = fcn (x, err); if (err) return false; ip2 = workd + iptr(1) - 1; for (F77_INT i = 0; i < n; i++) *ip2++ = y(i); } } } else { double *ip2 = workd + iptr(0) - 1; ColumnVector x(n); for (F77_INT i = 0; i < n; i++) x(i) = *ip2++; ColumnVector y = fcn (x, err); if (err) return false; ip2 = workd + iptr(1) - 1; for (F77_INT i = 0; i < n; i++) *ip2++ = y(i); } } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error in dsaupd: %s", arpack_errno2str (info, "dsaupd").c_str ()); break; } } while (1); F77_INT info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<F77_INT> s (dim_vector (p, 1)); F77_INT *sel = s.fortran_vec (); eig_vec.resize (n, k); double *z = eig_vec.fortran_vec (); eig_val.resize (k); double *d = eig_val.fortran_vec (); F77_FUNC (dseupd, DSEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, d, z, n, sigma, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (info2 == 0) { for (F77_INT i = ip(4); i < k; i++) d[i] = octave::numeric_limits<double>::NaN (); F77_INT k2 = ip(4) / 2; if (mode == 3 || (mode == 1 && typ != "SM" && typ != "BE")) { for (F77_INT i = 0; i < k2; i++) { double dtmp = d[i]; d[i] = d[ip(4) - i - 1]; d[ip(4) - i - 1] = dtmp; } } if (rvec) { for (F77_INT i = ip(4); i < k; i++) { F77_INT off1 = i * n; for (F77_INT j = 0; j < n; j++) z[off1 + j] = octave::numeric_limits<double>::NaN (); } if (mode == 3 || (mode == 1 && typ != "SM" && typ != "BE")) { OCTAVE_LOCAL_BUFFER (double, dtmp, n); for (F77_INT i = 0; i < k2; i++) { F77_INT off1 = i * n; F77_INT off2 = (ip(4) - i - 1) * n; if (off1 == off2) continue; for (F77_INT j = 0; j < n; j++) dtmp[j] = z[off1 + j]; for (F77_INT j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (F77_INT j = 0; j < n; j++) z[off2 + j] = dtmp[j]; } } if (note3) eig_vec = utsolve (bt, permB, eig_vec); } } else (*current_liboctave_error_handler) ("eigs: error in dseupd: %s", arpack_errno2str (info2, "dseupd").c_str ()); return ip(4); } template <typename M> octave_idx_type EigsRealNonSymmetricMatrix (const M& m, const std::string typ, octave_idx_type k_arg, octave_idx_type p_arg, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const M& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { F77_INT k = octave::to_f77_int (k_arg); F77_INT p = octave::to_f77_int (p_arg); M b(_b); F77_INT n = octave::to_f77_int (m.cols ()); F77_INT mode = 1; bool have_b = ! b.isempty (); bool note3 = false; char bmat = 'I'; double sigmar = 0.; double sigmai = 0.; M bt; if (m.rows () != m.cols ()) (*current_liboctave_error_handler) ("eigs: A must be square"); if (have_b && (m.rows () != b.rows () || m.rows () != b.cols ())) (*current_liboctave_error_handler) ("eigs: B must be square and the same size as A"); if (resid.isempty ()) { std::string rand_dist = octave::rand::distribution (); octave::rand::distribution ("uniform"); resid = ColumnVector (octave::rand::vector (n)); octave::rand::distribution (rand_dist); } else if (m.cols () != resid.numel ()) (*current_liboctave_error_handler) ("eigs: opts.v0 must be n-by-1"); if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2 + 1; if (p < 20) p = 20; if (p > n) p = n; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract" " (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p > n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than or equal to n"); if (have_b && cholB && ! permB.isempty ()) { // Check the we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (F77_INT i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || octave::math::x_nint (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } if (typ != "LM" && typ != "SM" && typ != "LA" && typ != "SA" && typ != "BE" && typ != "LR" && typ != "SR" && typ != "LI" && typ != "SI") (*current_liboctave_error_handler) ("eigs: unrecognized sigma value"); if (typ == "LA" || typ == "SA" || typ == "BE") (*current_liboctave_error_handler) ("eigs: invalid sigma value for unsymmetric problem"); if (have_b) { // See Note 3 dsaupd note3 = true; if (cholB) { bt = b; b = b.transpose (); if (permB.isempty ()) { permB = ColumnVector (n); for (F77_INT i = 0; i < n; i++) permB(i) = i; } } else { if (! make_cholb (b, bt, permB)) (*current_liboctave_error_handler) ("eigs: The matrix B is not positive definite"); } } Array<F77_INT> ip (dim_vector (11, 1)); F77_INT *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<F77_INT> iptr (dim_vector (14, 1)); F77_INT *ipntr = iptr.fortran_vec (); F77_INT ido = 0; int iter = 0; F77_INT lwork = 3 * p * (p + 2); OCTAVE_LOCAL_BUFFER (double, v, n * (p + 1)); OCTAVE_LOCAL_BUFFER (double, workl, lwork + 1); OCTAVE_LOCAL_BUFFER (double, workd, 3 * n + 1); double *presid = resid.fortran_vec (); do { F77_INT tmp_info = octave::to_f77_int (info); // On exit, ip(4) <= k + 1 is the number of converged eigenvalues. // See dnaupd2. F77_FUNC (dnaupd, DNAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, tmp_info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); // k is not changed info = tmp_info; if (disp > 0 && ! octave::math::isnan(workl[iptr(5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; if (ido == 99) // convergence { os << " " << workl[iptr(5)+k] << "\n"; for (F77_INT i = 0; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } else { // the wanted Ritz estimates are at the end for (F77_INT i = p - k - 1; i < p; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave::numeric_limits<double>::NaN (); } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { Matrix mtmp (n, 1); for (F77_INT i = 0; i < n; i++) mtmp(i, 0) = workd[i + iptr(0) - 1]; mtmp = ltsolve (b, permB, m * utsolve (bt, permB, mtmp)); for (F77_INT i = 0; i < n; i++) workd[i+iptr(1)-1] = mtmp(i, 0); } else if (! vector_product (m, workd + iptr(0) - 1, workd + iptr(1) - 1)) break; } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error in dnaupd: %s", arpack_errno2str (info, "dnaupd").c_str ()); break; } } while (1); F77_INT info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<F77_INT> s (dim_vector (p, 1)); F77_INT *sel = s.fortran_vec (); // FIXME: initialize eig_vec2 to zero; apparently dneupd can skip // the assignment to elements of Z that represent imaginary parts. // Found with valgrind and // // A = [1,0,0,-1;0,1,0,0;0,0,1,0;0,0,2,1]; // [vecs, vals, f] = eigs (A, 1) Matrix eig_vec2 (n, k + 1, 0.0); double *z = eig_vec2.fortran_vec (); OCTAVE_LOCAL_BUFFER (double, dr, k + 1); OCTAVE_LOCAL_BUFFER (double, di, k + 1); OCTAVE_LOCAL_BUFFER (double, workev, 3 * p); for (F77_INT i = 0; i < k+1; i++) dr[i] = di[i] = 0.; F77_INT k0 = k; // original number of eigenvalues required F77_FUNC (dneupd, DNEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, dr, di, z, n, sigmar, sigmai, workev, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); // on exit, if (and only if) rvec == true, k may have been increased by one // and be equal to ip(4), see dngets. if (! rvec && ip(4) > k) k = ip(4); eig_val.resize (k); Complex *d = eig_val.fortran_vec (); if (info2 == 0) { bool have_cplx_eig = false; for (F77_INT i = 0; i < ip(4); i++) { if (di[i] == 0) d[i] = Complex (dr[i], 0.); else { have_cplx_eig = true; d[i] = Complex (dr[i], di[i]); } } if (have_cplx_eig) { for (F77_INT i = ip(4); i < k; i++) d[i] = Complex (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); } else { for (F77_INT i = ip(4); i < k; i++) d[i] = Complex (octave::numeric_limits<double>::NaN (), 0.); } if (! rvec) { // ARPACK seems to give the eigenvalues in reversed order F77_INT k2 = ip(4) / 2; for (F77_INT i = 0; i < k2; i++) { Complex dtmp = d[i]; d[i] = d[ip(4) - i - 1]; d[ip(4) - i - 1] = dtmp; } } else { // When eigenvectors required, ARPACK seems to give the right order eig_vec.resize (n, k); F77_INT i = 0; while (i < ip(4)) { F77_INT off1 = i * n; F77_INT off2 = (i+1) * n; if (std::imag (eig_val(i)) == 0) { for (F77_INT j = 0; j < n; j++) eig_vec(j, i) = Complex (z[j+off1], 0.); i++; } else { for (F77_INT j = 0; j < n; j++) { eig_vec(j, i) = Complex (z[j+off1], z[j+off2]); if (i < ip(4) - 1) eig_vec(j, i+1) = Complex (z[j+off1], -z[j+off2]); } i+=2; } } if (have_cplx_eig) { for (F77_INT ii = ip(4); ii < k; ii++) for (F77_INT jj = 0; jj < n; jj++) eig_vec(jj, ii) = Complex (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); } else { for (F77_INT ii = ip(4); ii < k; ii++) for (F77_INT jj = 0; jj < n; jj++) eig_vec(jj, ii) = Complex (octave::numeric_limits<double>::NaN (), 0.); } if (note3) eig_vec = utsolve (bt, permB, eig_vec); } if (k0 < k) { eig_val.resize (k0); eig_vec.resize (n, k0); } } else (*current_liboctave_error_handler) ("eigs: error in dneupd: %s", arpack_errno2str (info2, "dneupd").c_str ()); return ip(4); } template <typename M> octave_idx_type EigsRealNonSymmetricMatrixShift (const M& m, double sigmar, octave_idx_type k_arg, octave_idx_type p_arg, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const M& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { F77_INT k = octave::to_f77_int (k_arg); F77_INT p = octave::to_f77_int (p_arg); M b(_b); F77_INT n = octave::to_f77_int (m.cols ()); F77_INT mode = 3; bool have_b = ! b.isempty (); std::string typ = "LM"; double sigmai = 0.; if (m.rows () != m.cols ()) (*current_liboctave_error_handler) ("eigs: A must be square"); if (have_b && (m.rows () != b.rows () || m.rows () != b.cols ())) (*current_liboctave_error_handler) ("eigs: B must be square and the same size as A"); // FIXME: The "SM" type for mode 1 seems unstable though faster!! //if (! std::abs (sigmar)) // return EigsRealNonSymmetricMatrix (m, "SM", k, p, info, eig_vec, eig_val, // _b, permB, resid, os, tol, rvec, cholB, // disp, maxit); if (resid.isempty ()) { std::string rand_dist = octave::rand::distribution (); octave::rand::distribution ("uniform"); resid = ColumnVector (octave::rand::vector (n)); octave::rand::distribution (rand_dist); } else if (m.cols () != resid.numel ()) (*current_liboctave_error_handler) ("eigs: opts.v0 must be n-by-1"); if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2 + 1; if (p < 20) p = 20; if (p > n) p = n; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract" " (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p > n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than or equal to n"); if (have_b && cholB && ! permB.isempty ()) { // Check that we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (F77_INT i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || octave::math::x_nint (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } char bmat = 'I'; if (have_b) bmat = 'G'; Array<F77_INT> ip (dim_vector (11, 1)); F77_INT *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<F77_INT> iptr (dim_vector (14, 1)); F77_INT *ipntr = iptr.fortran_vec (); F77_INT ido = 0; int iter = 0; M L, U; ColumnVector r(n); OCTAVE_LOCAL_BUFFER (octave_idx_type, P, (have_b ? b.rows () : m.rows ())); OCTAVE_LOCAL_BUFFER (octave_idx_type, Q, (have_b ? b.cols () : m.cols ())); if (! LuAminusSigmaB (m, b, cholB, permB, sigmar, L, U, P, Q, r)) return -1; F77_INT lwork = 3 * p * (p + 2); OCTAVE_LOCAL_BUFFER (double, v, n * (p + 1)); OCTAVE_LOCAL_BUFFER (double, workl, lwork + 1); OCTAVE_LOCAL_BUFFER (double, workd, 3 * n + 1); double *presid = resid.fortran_vec (); do { F77_INT tmp_info = octave::to_f77_int (info); // On exit, ip(4) <= k + 1 is the number of converged eigenvalues. // See dnaupd2. F77_FUNC (dnaupd, DNAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, tmp_info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); // k is not changed info = tmp_info; if (disp > 0 && ! octave::math::isnan (workl[iptr (5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; if (ido == 99) // convergence { os << " " << workl[iptr(5)+k] << "\n"; for (F77_INT i = 0; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } else { // the wanted Ritz estimates are at the end for (F77_INT i = p - k - 1; i < p; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave::numeric_limits<double>::NaN (); } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { if (ido == -1) { OCTAVE_LOCAL_BUFFER (double, dtmp, n); vector_product (b, workd+iptr(0)-1, dtmp); Matrix tmp (n, 1); for (F77_INT i = 0; i < n; i++) tmp(i, 0) = dtmp[P[i]] / r(P[i]); lusolve (L, U, tmp); double *ip2 = workd+iptr(1)-1; for (F77_INT i = 0; i < n; i++) ip2[Q[i]] = tmp(i, 0); } else if (ido == 2) vector_product (b, workd+iptr(0)-1, workd+iptr(1)-1); else { double *ip2 = workd+iptr(2)-1; Matrix tmp (n, 1); for (F77_INT i = 0; i < n; i++) tmp(i, 0) = ip2[P[i]] / r(P[i]); lusolve (L, U, tmp); ip2 = workd+iptr(1)-1; for (F77_INT i = 0; i < n; i++) ip2[Q[i]] = tmp(i, 0); } } else { // ido cannot be 2 for non-generalized problems (see dnaupd2). double *ip2 = workd+iptr(0)-1; Matrix tmp (n, 1); for (F77_INT i = 0; i < n; i++) tmp(i, 0) = ip2[P[i]] / r(P[i]); lusolve (L, U, tmp); ip2 = workd+iptr(1)-1; for (F77_INT i = 0; i < n; i++) ip2[Q[i]] = tmp(i, 0); } } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error in dnaupd: %s", arpack_errno2str (info, "dnaupd").c_str ()); break; } } while (1); F77_INT info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<F77_INT> s (dim_vector (p, 1)); F77_INT *sel = s.fortran_vec (); // FIXME: initialize eig_vec2 to zero; apparently dneupd can skip // the assignment to elements of Z that represent imaginary parts. // Found with valgrind and // // A = [1,0,0,-1;0,1,0,0;0,0,1,0;0,0,2,1]; // [vecs, vals, f] = eigs (A, 1) Matrix eig_vec2 (n, k + 1, 0.0); double *z = eig_vec2.fortran_vec (); OCTAVE_LOCAL_BUFFER (double, dr, k + 1); OCTAVE_LOCAL_BUFFER (double, di, k + 1); OCTAVE_LOCAL_BUFFER (double, workev, 3 * p); for (F77_INT i = 0; i < k+1; i++) dr[i] = di[i] = 0.; F77_INT k0 = k; // original number of eigenvalues required F77_FUNC (dneupd, DNEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, dr, di, z, n, sigmar, sigmai, workev, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); // On exit, if (and only if) rvec == true, k may have been increased by one // and be equal to ip(4), see dngets. if (! rvec && ip(4) > k) k = ip(4); eig_val.resize (k); Complex *d = eig_val.fortran_vec (); if (info2 == 0) { bool have_cplx_eig = false; for (F77_INT i = 0; i < ip(4); i++) { if (di[i] == 0.) d[i] = Complex (dr[i], 0.); else { have_cplx_eig = true; d[i] = Complex (dr[i], di[i]); } } if (have_cplx_eig) { for (F77_INT i = ip(4); i < k; i++) d[i] = Complex (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); } else { for (F77_INT i = ip(4); i < k; i++) d[i] = Complex (octave::numeric_limits<double>::NaN (), 0.); } if (! rvec) { // ARPACK seems to give the eigenvalues in reversed order F77_INT k2 = ip(4) / 2; for (F77_INT i = 0; i < k2; i++) { Complex dtmp = d[i]; d[i] = d[ip(4) - i - 1]; d[ip(4) - i - 1] = dtmp; } } else { // When eigenvectors required, ARPACK seems to give the right order eig_vec.resize (n, k); F77_INT i = 0; while (i < ip(4)) { F77_INT off1 = i * n; F77_INT off2 = (i+1) * n; if (std::imag (eig_val(i)) == 0) { for (F77_INT j = 0; j < n; j++) eig_vec(j, i) = Complex (z[j+off1], 0.); i++; } else { for (F77_INT j = 0; j < n; j++) { eig_vec(j, i) = Complex (z[j+off1], z[j+off2]); if (i < ip(4) - 1) eig_vec(j, i+1) = Complex (z[j+off1], -z[j+off2]); } i+=2; } } if (have_cplx_eig) { for (F77_INT ii = ip(4); ii < k; ii++) for (F77_INT jj = 0; jj < n; jj++) eig_vec(jj, ii) = Complex (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); } else { for (F77_INT ii = ip(4); ii < k; ii++) for (F77_INT jj = 0; jj < n; jj++) eig_vec(jj, ii) = Complex (octave::numeric_limits<double>::NaN (), 0.); } } if (k0 < k) { eig_val.resize (k0); eig_vec.resize (n, k0); } } else (*current_liboctave_error_handler) ("eigs: error in dneupd: %s", arpack_errno2str (info2, "dneupd").c_str ()); return ip(4); } template <typename M> octave_idx_type EigsRealNonSymmetricFunc (EigsFunc fcn, octave_idx_type n_arg, const std::string& _typ, double sigmar, octave_idx_type k_arg, octave_idx_type p_arg, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const M& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { F77_INT n = octave::to_f77_int (n_arg); F77_INT k = octave::to_f77_int (k_arg); F77_INT p = octave::to_f77_int (p_arg); M b(_b); std::string typ (_typ); bool have_sigma = (sigmar ? true : false); double sigmai = 0.; F77_INT mode = 1; bool have_b = ! b.isempty (); bool note3 = false; char bmat = 'I'; int err = 0; M bt; if (resid.isempty ()) { std::string rand_dist = octave::rand::distribution (); octave::rand::distribution ("uniform"); resid = ColumnVector (octave::rand::vector (n)); octave::rand::distribution (rand_dist); } else if (n != resid.numel ()) (*current_liboctave_error_handler) ("eigs: opts.v0 must be n-by-1"); if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2 + 1; if (p < 20) p = 20; if (p > n) p = n; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract" " (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p > n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than or equal to n"); if (have_b && cholB && ! permB.isempty ()) { // Check the we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (F77_INT i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || octave::math::x_nint (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } if (! have_sigma) { if (typ != "LM" && typ != "SM" && typ != "LA" && typ != "SA" && typ != "BE" && typ != "LR" && typ != "SR" && typ != "LI" && typ != "SI") (*current_liboctave_error_handler) ("eigs: unrecognized sigma value"); if (typ == "LA" || typ == "SA" || typ == "BE") (*current_liboctave_error_handler) ("eigs: invalid sigma value for unsymmetric problem"); if (typ != "SM" && have_b) note3 = true; if (typ == "SM") { typ = "LM"; sigmar = 0.; mode = 3; if (have_b) bmat = 'G'; } } else if (! std::abs (sigmar)) { typ = "SM"; if (have_b) bmat = 'G'; } else { typ = "LM"; mode = 3; if (have_b) bmat = 'G'; } if (mode == 1 && have_b) { // See Note 3 dsaupd note3 = true; if (cholB) { bt = b; b = b.transpose (); if (permB.isempty ()) { permB = ColumnVector (n); for (F77_INT i = 0; i < n; i++) permB(i) = i; } } else { if (! make_cholb (b, bt, permB)) (*current_liboctave_error_handler) ("eigs: The matrix B is not positive definite"); } } Array<F77_INT> ip (dim_vector (11, 1)); F77_INT *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<F77_INT> iptr (dim_vector (14, 1)); F77_INT *ipntr = iptr.fortran_vec (); F77_INT ido = 0; int iter = 0; F77_INT lwork = 3 * p * (p + 2); OCTAVE_LOCAL_BUFFER (double, v, n * (p + 1)); OCTAVE_LOCAL_BUFFER (double, workl, lwork + 1); OCTAVE_LOCAL_BUFFER (double, workd, 3 * n + 1); double *presid = resid.fortran_vec (); do { F77_INT tmp_info = octave::to_f77_int (info); // On exit, ip(4) <= k + 1 is the number of converged eigenvalues // see dnaupd2. F77_FUNC (dnaupd, DNAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, tmp_info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); // k is not changed info = tmp_info; if (disp > 0 && ! octave::math::isnan(workl[iptr(5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; if (ido == 99) // convergence { os << " " << workl[iptr(5)+k] << "\n"; for (F77_INT i = 0; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } else { // the wanted Ritz estimates are at the end for (F77_INT i = p - k - 1; i < p; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave::numeric_limits<double>::NaN (); } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { if (mode == 1) // regular mode with factorized B { Matrix mtmp (n, 1); for (F77_INT i = 0; i < n; i++) mtmp(i, 0) = workd[i + iptr(0) - 1]; mtmp = utsolve (bt, permB, mtmp); ColumnVector y = fcn (mtmp, err); if (err) return false; mtmp = ltsolve (b, permB, y); for (F77_INT i = 0; i < n; i++) workd[i+iptr(1)-1] = mtmp(i, 0); } else // shift-invert mode { if (ido == -1) { OCTAVE_LOCAL_BUFFER (double, dtmp, n); vector_product (b, workd+iptr(0)-1, dtmp); ColumnVector x(n); for (F77_INT i = 0; i < n; i++) x(i) = dtmp[i]; ColumnVector y = fcn (x, err); if (err) return false; double *ip2 = workd + iptr(1) - 1; for (F77_INT i = 0; i < n; i++) ip2[i] = y(i); } else if (ido == 2) vector_product (b, workd+iptr(0)-1, workd+iptr(1)-1); else { double *ip2 = workd+iptr(2)-1; ColumnVector x(n); for (F77_INT i = 0; i < n; i++) x(i) = *ip2++; ColumnVector y = fcn (x, err); if (err) return false; ip2 = workd + iptr(1) - 1; for (F77_INT i = 0; i < n; i++) *ip2++ = y(i); } } } else { double *ip2 = workd + iptr(0) - 1; ColumnVector x(n); for (F77_INT i = 0; i < n; i++) x(i) = *ip2++; ColumnVector y = fcn (x, err); if (err) return false; ip2 = workd + iptr(1) - 1; for (F77_INT i = 0; i < n; i++) *ip2++ = y(i); } } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error in dnaupd: %s", arpack_errno2str (info, "dnaupd").c_str ()); break; } } while (1); F77_INT info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<F77_INT> s (dim_vector (p, 1)); F77_INT *sel = s.fortran_vec (); // FIXME: initialize eig_vec2 to zero; apparently dneupd can skip // the assignment to elements of Z that represent imaginary parts. // Found with valgrind and // // A = [1,0,0,-1;0,1,0,0;0,0,1,0;0,0,2,1]; // [vecs, vals, f] = eigs (A, 1) Matrix eig_vec2 (n, k + 1, 0.0); double *z = eig_vec2.fortran_vec (); OCTAVE_LOCAL_BUFFER (double, dr, k + 1); OCTAVE_LOCAL_BUFFER (double, di, k + 1); OCTAVE_LOCAL_BUFFER (double, workev, 3 * p); for (F77_INT i = 0; i < k+1; i++) dr[i] = di[i] = 0.; F77_INT k0 = k; // original number of eigenvalues required F77_FUNC (dneupd, DNEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, dr, di, z, n, sigmar, sigmai, workev, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); // On exit, if (and only if) rvec == true, k may have been increased by one // and be equal to ip(4), see dngets. if (! rvec && ip(4) > k) k = ip(4); eig_val.resize (k); Complex *d = eig_val.fortran_vec (); if (info2 == 0) { bool have_cplx_eig = false; for (F77_INT i = 0; i < ip(4); i++) { if (di[i] == 0.) d[i] = Complex (dr[i], 0.); else { have_cplx_eig = true; d[i] = Complex (dr[i], di[i]); } } if (have_cplx_eig) { for (F77_INT i = ip(4); i < k; i++) d[i] = Complex (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); } else { for (F77_INT i = ip(4); i < k; i++) d[i] = Complex (octave::numeric_limits<double>::NaN (), 0.); } if (! rvec) { // ARPACK seems to give the eigenvalues in reversed order octave_idx_type k2 = ip(4) / 2; for (F77_INT i = 0; i < k2; i++) { Complex dtmp = d[i]; d[i] = d[ip(4) - i - 1]; d[ip(4) - i - 1] = dtmp; } } else { // ARPACK seems to give the eigenvalues in reversed order eig_vec.resize (n, k); F77_INT i = 0; while (i < ip(4)) { F77_INT off1 = i * n; F77_INT off2 = (i+1) * n; if (std::imag (eig_val(i)) == 0) { for (F77_INT j = 0; j < n; j++) eig_vec(j, i) = Complex (z[j+off1], 0.); i++; } else { for (F77_INT j = 0; j < n; j++) { eig_vec(j, i) = Complex (z[j+off1], z[j+off2]); if (i < ip(4) - 1) eig_vec(j, i+1) = Complex (z[j+off1], -z[j+off2]); } i+=2; } } if (have_cplx_eig) { for (F77_INT ii = ip(4); ii < k; ii++) for (F77_INT jj = 0; jj < n; jj++) eig_vec(jj, ii) = Complex (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); } else { for (F77_INT ii = ip(4); ii < k; ii++) for (F77_INT jj = 0; jj < n; jj++) eig_vec(jj, ii) = Complex (octave::numeric_limits<double>::NaN (), 0.); } if (note3) eig_vec = utsolve (bt, permB, eig_vec); } if (k0 < k) { eig_val.resize (k0); eig_vec.resize (n, k0); } } else (*current_liboctave_error_handler) ("eigs: error in dneupd: %s", arpack_errno2str (info2, "dneupd").c_str ()); return ip(4); } template <typename M> octave_idx_type EigsComplexNonSymmetricMatrix (const M& m, const std::string typ, octave_idx_type k_arg, octave_idx_type p_arg, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const M& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { F77_INT k = octave::to_f77_int (k_arg); F77_INT p = octave::to_f77_int (p_arg); M b(_b); F77_INT n = octave::to_f77_int (m.cols ()); F77_INT mode = 1; bool have_b = ! b.isempty (); bool note3 = false; char bmat = 'I'; Complex sigma = 0.; M bt; if (m.rows () != m.cols ()) (*current_liboctave_error_handler) ("eigs: A must be square"); if (have_b && (m.rows () != b.rows () || m.rows () != b.cols ())) (*current_liboctave_error_handler) ("eigs: B must be square and the same size as A"); if (cresid.isempty ()) { std::string rand_dist = octave::rand::distribution (); octave::rand::distribution ("uniform"); Array<double> rr (octave::rand::vector (n)); Array<double> ri (octave::rand::vector (n)); cresid = ComplexColumnVector (n); for (F77_INT i = 0; i < n; i++) cresid(i) = Complex (rr(i), ri(i)); octave::rand::distribution (rand_dist); } else if (m.cols () != cresid.numel ()) (*current_liboctave_error_handler) ("eigs: opts.v0 must be n-by-1"); if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2 + 1; if (p < 20) p = 20; if (p > n) p = n; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract" " (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p > n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than or equal to n"); if (have_b && cholB && ! permB.isempty ()) { // Check the we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (F77_INT i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || octave::math::x_nint (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } if (typ != "LM" && typ != "SM" && typ != "LA" && typ != "SA" && typ != "BE" && typ != "LR" && typ != "SR" && typ != "LI" && typ != "SI") (*current_liboctave_error_handler) ("eigs: unrecognized sigma value"); if (typ == "LA" || typ == "SA" || typ == "BE") (*current_liboctave_error_handler) ("eigs: invalid sigma value for complex problem"); if (have_b) { // See Note 3 dsaupd note3 = true; if (cholB) { bt = b; b = b.hermitian (); if (permB.isempty ()) { permB = ColumnVector (n); for (F77_INT i = 0; i < n; i++) permB(i) = i; } } else { if (! make_cholb (b, bt, permB)) (*current_liboctave_error_handler) ("eigs: The matrix B is not positive definite"); } } Array<F77_INT> ip (dim_vector (11, 1)); F77_INT *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<F77_INT> iptr (dim_vector (14, 1)); F77_INT *ipntr = iptr.fortran_vec (); F77_INT ido = 0; int iter = 0; F77_INT lwork = p * (3 * p + 5); OCTAVE_LOCAL_BUFFER (Complex, v, n * p); OCTAVE_LOCAL_BUFFER (Complex, workl, lwork); OCTAVE_LOCAL_BUFFER (Complex, workd, 3 * n); OCTAVE_LOCAL_BUFFER (double, rwork, p); Complex *presid = cresid.fortran_vec (); do { F77_INT tmp_info = octave::to_f77_int (info); F77_FUNC (znaupd, ZNAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 (typ.c_str (), 2), k, tol, F77_DBLE_CMPLX_ARG (presid), p, F77_DBLE_CMPLX_ARG (v), n, iparam, ipntr, F77_DBLE_CMPLX_ARG (workd), F77_DBLE_CMPLX_ARG (workl), lwork, rwork, tmp_info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); info = tmp_info; if (disp > 0 && ! octave::math::isnan (workl[iptr (5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; if (ido == 99) // convergence { for (F77_INT i = 0; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } else { // the wanted Ritz estimates are at the end for (F77_INT i = p - k; i < p; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave::numeric_limits<double>::NaN (); } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { ComplexMatrix mtmp (n, 1); for (F77_INT i = 0; i < n; i++) mtmp(i, 0) = workd[i + iptr(0) - 1]; mtmp = ltsolve (b, permB, m * utsolve (bt, permB, mtmp)); for (F77_INT i = 0; i < n; i++) workd[i+iptr(1)-1] = mtmp(i, 0); } else if (! vector_product (m, workd + iptr(0) - 1, workd + iptr(1) - 1)) break; } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error in znaupd: %s", arpack_errno2str (info, "znaupd").c_str ()); break; } } while (1); F77_INT info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<F77_INT> s (dim_vector (p, 1)); F77_INT *sel = s.fortran_vec (); eig_vec.resize (n, k); Complex *z = eig_vec.fortran_vec (); eig_val.resize (k+1); Complex *d = eig_val.fortran_vec (); OCTAVE_LOCAL_BUFFER (Complex, workev, 2 * p); F77_FUNC (zneupd, ZNEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, F77_DBLE_CMPLX_ARG (d), F77_DBLE_CMPLX_ARG (z), n, F77_CONST_DBLE_CMPLX_ARG (&sigma), F77_DBLE_CMPLX_ARG (workev), F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, F77_DBLE_CMPLX_ARG (presid), p, F77_DBLE_CMPLX_ARG (v), n, iparam, ipntr, F77_DBLE_CMPLX_ARG (workd), F77_DBLE_CMPLX_ARG (workl), lwork, rwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (info2 == 0) { for (F77_INT i = ip(4); i < k; i++) d[i] = Complex (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); F77_INT k2 = ip(4) / 2; for (F77_INT i = 0; i < k2; i++) { Complex ctmp = d[i]; d[i] = d[ip(4) - i - 1]; d[ip(4) - i - 1] = ctmp; } eig_val.resize (k); if (rvec) { OCTAVE_LOCAL_BUFFER (Complex, ctmp, n); for (F77_INT i = ip(4); i < k; i++) { F77_INT off1 = i * n; for (F77_INT j = 0; j < n; j++) z[off1 + j] = Complex (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); } for (F77_INT i = 0; i < k2; i++) { F77_INT off1 = i * n; F77_INT off2 = (ip(4) - i - 1) * n; if (off1 == off2) continue; for (F77_INT j = 0; j < n; j++) ctmp[j] = z[off1 + j]; for (F77_INT j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (F77_INT j = 0; j < n; j++) z[off2 + j] = ctmp[j]; } if (note3) eig_vec = utsolve (bt, permB, eig_vec); } } else (*current_liboctave_error_handler) ("eigs: error in zneupd: %s", arpack_errno2str (info2, "zneupd").c_str ()); return ip(4); } template <typename M> octave_idx_type EigsComplexNonSymmetricMatrixShift (const M& m, Complex sigma, octave_idx_type k_arg, octave_idx_type p_arg, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const M& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { F77_INT k = octave::to_f77_int (k_arg); F77_INT p = octave::to_f77_int (p_arg); M b(_b); F77_INT n = octave::to_f77_int (m.cols ()); F77_INT mode = 3; bool have_b = ! b.isempty (); std::string typ = "LM"; if (m.rows () != m.cols ()) (*current_liboctave_error_handler) ("eigs: A must be square"); if (have_b && (m.rows () != b.rows () || m.rows () != b.cols ())) (*current_liboctave_error_handler) ("eigs: B must be square and the same size as A"); // FIXME: The "SM" type for mode 1 seems unstable though faster!! //if (! std::abs (sigma)) // return EigsComplexNonSymmetricMatrix (m, "SM", k, p, info, eig_vec, // eig_val, _b, permB, cresid, os, tol, // rvec, cholB, disp, maxit); if (cresid.isempty ()) { std::string rand_dist = octave::rand::distribution (); octave::rand::distribution ("uniform"); Array<double> rr (octave::rand::vector (n)); Array<double> ri (octave::rand::vector (n)); cresid = ComplexColumnVector (n); for (F77_INT i = 0; i < n; i++) cresid(i) = Complex (rr(i), ri(i)); octave::rand::distribution (rand_dist); } else if (m.cols () != cresid.numel ()) (*current_liboctave_error_handler) ("eigs: opts.v0 must be n-by-1"); if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2 + 1; if (p < 20) p = 20; if (p > n) p = n; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract" " (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p > n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than or equal to n"); if (have_b && cholB && ! permB.isempty ()) { // Check that we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (F77_INT i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || octave::math::x_nint (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } char bmat = 'I'; if (have_b) bmat = 'G'; Array<F77_INT> ip (dim_vector (11, 1)); F77_INT *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<F77_INT> iptr (dim_vector (14, 1)); F77_INT *ipntr = iptr.fortran_vec (); F77_INT ido = 0; int iter = 0; M L, U; ColumnVector r(n); OCTAVE_LOCAL_BUFFER (octave_idx_type, P, (have_b ? b.rows () : m.rows ())); OCTAVE_LOCAL_BUFFER (octave_idx_type, Q, (have_b ? b.cols () : m.cols ())); if (! LuAminusSigmaB (m, b, cholB, permB, sigma, L, U, P, Q, r)) return -1; F77_INT lwork = p * (3 * p + 5); OCTAVE_LOCAL_BUFFER (Complex, v, n * p); OCTAVE_LOCAL_BUFFER (Complex, workl, lwork); OCTAVE_LOCAL_BUFFER (Complex, workd, 3 * n); OCTAVE_LOCAL_BUFFER (double, rwork, p); Complex *presid = cresid.fortran_vec (); do { F77_INT tmp_info = octave::to_f77_int (info); F77_FUNC (znaupd, ZNAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, F77_DBLE_CMPLX_ARG (presid), p, F77_DBLE_CMPLX_ARG (v), n, iparam, ipntr, F77_DBLE_CMPLX_ARG (workd), F77_DBLE_CMPLX_ARG (workl), lwork, rwork, tmp_info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); info = tmp_info; if (disp > 0 && ! octave::math::isnan(workl[iptr(5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; if (ido == 99) // convergence { for (F77_INT i = 0; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } else { // the wanted Ritz estimates are at the end for (F77_INT i = p - k; i < p; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave::numeric_limits<double>::NaN (); } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { if (ido == -1) { OCTAVE_LOCAL_BUFFER (Complex, ctmp, n); vector_product (b, workd+iptr(0)-1, ctmp); ComplexMatrix tmp (n, 1); for (F77_INT i = 0; i < n; i++) tmp(i, 0) = ctmp[P[i]] / r(P[i]); lusolve (L, U, tmp); Complex *ip2 = workd+iptr(1)-1; for (F77_INT i = 0; i < n; i++) ip2[Q[i]] = tmp(i, 0); } else if (ido == 2) vector_product (b, workd + iptr(0) - 1, workd + iptr(1) - 1); else { Complex *ip2 = workd+iptr(2)-1; ComplexMatrix tmp (n, 1); for (F77_INT i = 0; i < n; i++) tmp(i, 0) = ip2[P[i]] / r(P[i]); lusolve (L, U, tmp); ip2 = workd+iptr(1)-1; for (F77_INT i = 0; i < n; i++) ip2[Q[i]] = tmp(i, 0); } } else { // ido cannot be 2 for non-generalized problems (see znaup2). Complex *ip2 = workd+iptr(0)-1; ComplexMatrix tmp (n, 1); for (F77_INT i = 0; i < n; i++) tmp(i, 0) = ip2[P[i]] / r(P[i]); lusolve (L, U, tmp); ip2 = workd+iptr(1)-1; for (F77_INT i = 0; i < n; i++) ip2[Q[i]] = tmp(i, 0); } } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error in znaupd: %s", arpack_errno2str (info, "znaupd").c_str ()); break; } } while (1); F77_INT info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<F77_INT> s (dim_vector (p, 1)); F77_INT *sel = s.fortran_vec (); eig_vec.resize (n, k); Complex *z = eig_vec.fortran_vec (); eig_val.resize (k+1); Complex *d = eig_val.fortran_vec (); OCTAVE_LOCAL_BUFFER (Complex, workev, 2 * p); F77_FUNC (zneupd, ZNEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, F77_DBLE_CMPLX_ARG (d), F77_DBLE_CMPLX_ARG (z), n, F77_CONST_DBLE_CMPLX_ARG (&sigma), F77_DBLE_CMPLX_ARG (workev), F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, F77_DBLE_CMPLX_ARG (presid), p, F77_DBLE_CMPLX_ARG (v), n, iparam, ipntr, F77_DBLE_CMPLX_ARG (workd), F77_DBLE_CMPLX_ARG (workl), lwork, rwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (info2 == 0) { for (F77_INT i = ip(4); i < k; i++) d[i] = Complex (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); F77_INT k2 = ip(4) / 2; for (F77_INT i = 0; i < k2; i++) { Complex ctmp = d[i]; d[i] = d[ip(4) - i - 1]; d[ip(4) - i - 1] = ctmp; } eig_val.resize (k); if (rvec) { OCTAVE_LOCAL_BUFFER (Complex, ctmp, n); for (F77_INT i = ip(4); i < k; i++) { F77_INT off1 = i * n; for (F77_INT j = 0; j < n; j++) z[off1 + j] = Complex (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); } for (F77_INT i = 0; i < k2; i++) { F77_INT off1 = i * n; F77_INT off2 = (ip(4) - i - 1) * n; if (off1 == off2) continue; for (F77_INT j = 0; j < n; j++) ctmp[j] = z[off1 + j]; for (F77_INT j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (F77_INT j = 0; j < n; j++) z[off2 + j] = ctmp[j]; } } } else (*current_liboctave_error_handler) ("eigs: error in zneupd: %s", arpack_errno2str (info2, "zneupd").c_str ()); return ip(4); } template <typename M> octave_idx_type EigsComplexNonSymmetricFunc (EigsComplexFunc fcn, octave_idx_type n_arg, const std::string& _typ, Complex sigma, octave_idx_type k_arg, octave_idx_type p_arg, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const M& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { F77_INT n = octave::to_f77_int (n_arg); F77_INT k = octave::to_f77_int (k_arg); F77_INT p = octave::to_f77_int (p_arg); M b(_b); std::string typ (_typ); bool have_sigma = (std::abs (sigma) ? true : false); F77_INT mode = 1; bool have_b = ! b.isempty (); bool note3 = false; char bmat = 'I'; int err = 0; M bt; if (cresid.isempty ()) { std::string rand_dist = octave::rand::distribution (); octave::rand::distribution ("uniform"); Array<double> rr (octave::rand::vector (n)); Array<double> ri (octave::rand::vector (n)); cresid = ComplexColumnVector (n); for (F77_INT i = 0; i < n; i++) cresid(i) = Complex (rr(i), ri(i)); octave::rand::distribution (rand_dist); } else if (n != cresid.numel ()) (*current_liboctave_error_handler) ("eigs: opts.v0 must be n-by-1"); if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2 + 1; if (p < 20) p = 20; if (p > n) p = n; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract" " (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p > n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than or equal to n"); if (have_b && cholB && ! permB.isempty ()) { // Check the we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (F77_INT i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || octave::math::x_nint (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } if (! have_sigma) { if (typ != "LM" && typ != "SM" && typ != "LA" && typ != "SA" && typ != "BE" && typ != "LR" && typ != "SR" && typ != "LI" && typ != "SI") (*current_liboctave_error_handler) ("eigs: unrecognized sigma value"); if (typ == "LA" || typ == "SA" || typ == "BE") (*current_liboctave_error_handler) ("eigs: invalid sigma value for complex problem"); if (typ != "SM" && have_b) note3 = true; if (typ == "SM") { typ = "LM"; sigma = 0.; mode = 3; if (have_b) bmat ='G'; } } else if (! std::abs (sigma)) { typ = "SM"; if (have_b) bmat = 'G'; } else { typ = "LM"; mode = 3; if (have_b) bmat = 'G'; } if (mode == 1 && have_b) { // See Note 3 dsaupd note3 = true; if (cholB) { bt = b; b = b.hermitian (); if (permB.isempty ()) { permB = ColumnVector (n); for (F77_INT i = 0; i < n; i++) permB(i) = i; } } else { if (! make_cholb (b, bt, permB)) (*current_liboctave_error_handler) ("eigs: The matrix B is not positive definite"); } } Array<F77_INT> ip (dim_vector (11, 1)); F77_INT *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<F77_INT> iptr (dim_vector (14, 1)); F77_INT *ipntr = iptr.fortran_vec (); F77_INT ido = 0; int iter = 0; F77_INT lwork = p * (3 * p + 5); OCTAVE_LOCAL_BUFFER (Complex, v, n * p); OCTAVE_LOCAL_BUFFER (Complex, workl, lwork); OCTAVE_LOCAL_BUFFER (Complex, workd, 3 * n); OCTAVE_LOCAL_BUFFER (double, rwork, p); Complex *presid = cresid.fortran_vec (); do { F77_INT tmp_info = octave::to_f77_int (info); F77_FUNC (znaupd, ZNAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, F77_DBLE_CMPLX_ARG (presid), p, F77_DBLE_CMPLX_ARG (v), n, iparam, ipntr, F77_DBLE_CMPLX_ARG (workd), F77_DBLE_CMPLX_ARG (workl), lwork, rwork, tmp_info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); info = tmp_info; if (disp > 0 && ! octave::math::isnan(workl[iptr(5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; if (ido == 99) // convergence { for (F77_INT i = 0; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } else { // the wanted Ritz estimates are at the end for (F77_INT i = p - k; i < p; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave::numeric_limits<double>::NaN (); } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { if (mode == 1) // regular mode with factorized B { ComplexMatrix mtmp (n, 1); for (F77_INT i = 0; i < n; i++) mtmp(i, 0) = workd[i + iptr(0) - 1]; mtmp = utsolve (bt, permB, mtmp); ComplexColumnVector y = fcn (mtmp, err); if (err) return false; mtmp = ltsolve (b, permB, y); for (F77_INT i = 0; i < n; i++) workd[i+iptr(1)-1] = mtmp(i, 0); } else // shift-invert mode { if (ido == -1) { OCTAVE_LOCAL_BUFFER (Complex, ctmp, n); vector_product (b, workd+iptr(0)-1, ctmp); ComplexColumnVector x(n); for (F77_INT i = 0; i < n; i++) x(i) = ctmp[i]; ComplexColumnVector y = fcn (x, err); if (err) return false; Complex *ip2 = workd+iptr(1)-1; for (F77_INT i = 0; i < n; i++) ip2[i] = y(i); } else if (ido == 2) vector_product (b, workd+iptr(0)-1, workd+iptr(1)-1); else { Complex *ip2 = workd+iptr(2)-1; ComplexColumnVector x(n); for (F77_INT i = 0; i < n; i++) x(i) = *ip2++; ComplexColumnVector y = fcn (x, err); if (err) return false; ip2 = workd + iptr(1) - 1; for (F77_INT i = 0; i < n; i++) *ip2++ = y(i); } } } else { Complex *ip2 = workd + iptr(0) - 1; ComplexColumnVector x(n); for (F77_INT i = 0; i < n; i++) x(i) = *ip2++; ComplexColumnVector y = fcn (x, err); if (err) return false; ip2 = workd + iptr(1) - 1; for (F77_INT i = 0; i < n; i++) *ip2++ = y(i); } } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error in znaupd: %s", arpack_errno2str (info, "znaupd").c_str ()); break; } } while (1); F77_INT info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<F77_INT> s (dim_vector (p, 1)); F77_INT *sel = s.fortran_vec (); eig_vec.resize (n, k); Complex *z = eig_vec.fortran_vec (); eig_val.resize (k+1); Complex *d = eig_val.fortran_vec (); OCTAVE_LOCAL_BUFFER (Complex, workev, 2 * p); F77_FUNC (zneupd, ZNEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, F77_DBLE_CMPLX_ARG (d), F77_DBLE_CMPLX_ARG (z), n, F77_DBLE_CMPLX_ARG (&sigma), F77_DBLE_CMPLX_ARG (workev), F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, F77_DBLE_CMPLX_ARG (presid), p, F77_DBLE_CMPLX_ARG (v), n, iparam, ipntr, F77_DBLE_CMPLX_ARG (workd), F77_DBLE_CMPLX_ARG (workl), lwork, rwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (info2 == 0) { for (F77_INT i = ip(4); i < k; i++) d[i] = Complex (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); F77_INT k2 = ip(4) / 2; for (F77_INT i = 0; i < k2; i++) { Complex ctmp = d[i]; d[i] = d[ip(4) - i - 1]; d[ip(4) - i - 1] = ctmp; } eig_val.resize (k); if (rvec) { OCTAVE_LOCAL_BUFFER (Complex, ctmp, n); for (F77_INT i = ip(4); i < k; i++) { F77_INT off1 = i * n; for (F77_INT j = 0; j < n; j++) z[off1 + j] = Complex (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); } for (F77_INT i = 0; i < k2; i++) { F77_INT off1 = i * n; F77_INT off2 = (ip(4) - i - 1) * n; if (off1 == off2) continue; for (F77_INT j = 0; j < n; j++) ctmp[j] = z[off1 + j]; for (F77_INT j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (F77_INT j = 0; j < n; j++) z[off2 + j] = ctmp[j]; } if (note3) eig_vec = utsolve (bt, permB, eig_vec); } } else (*current_liboctave_error_handler) ("eigs: error in zneupd: %s", arpack_errno2str (info2, "zneupd").c_str ()); return ip(4); } // Instantiations for the types we need. // Matrix template OCTAVE_API octave_idx_type EigsRealSymmetricMatrix<Matrix> (const Matrix& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const Matrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsRealSymmetricMatrixShift<Matrix> (const Matrix& m, double sigma, octave_idx_type k, octave_idx_type p, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const Matrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsRealSymmetricFunc<Matrix> (EigsFunc fcn, octave_idx_type n, const std::string& _typ, double sigma, octave_idx_type k, octave_idx_type p, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const Matrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsRealNonSymmetricMatrix<Matrix> (const Matrix& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const Matrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsRealNonSymmetricMatrixShift<Matrix> (const Matrix& m, double sigmar, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const Matrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsRealNonSymmetricFunc<Matrix> (EigsFunc fcn, octave_idx_type n, const std::string& _typ, double sigmar, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const Matrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); // SparseMatrix template OCTAVE_API octave_idx_type EigsRealSymmetricMatrix<SparseMatrix> (const SparseMatrix& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const SparseMatrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsRealSymmetricMatrixShift<SparseMatrix> (const SparseMatrix& m, double sigma, octave_idx_type k, octave_idx_type p, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const SparseMatrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsRealSymmetricFunc<SparseMatrix> (EigsFunc fcn, octave_idx_type n, const std::string& _typ, double sigma, octave_idx_type k, octave_idx_type p, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const SparseMatrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsRealNonSymmetricMatrix<SparseMatrix> (const SparseMatrix& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const SparseMatrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsRealNonSymmetricMatrixShift<SparseMatrix> (const SparseMatrix& m, double sigmar, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const SparseMatrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsRealNonSymmetricFunc<SparseMatrix> (EigsFunc fcn, octave_idx_type n, const std::string& _typ, double sigmar, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const SparseMatrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); // ComplexMatrix template OCTAVE_API octave_idx_type EigsComplexNonSymmetricMatrix<ComplexMatrix> (const ComplexMatrix& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const ComplexMatrix& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsComplexNonSymmetricMatrixShift<ComplexMatrix> (const ComplexMatrix& m, Complex sigma, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const ComplexMatrix& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsComplexNonSymmetricFunc<ComplexMatrix> (EigsComplexFunc fcn, octave_idx_type n, const std::string& _typ, Complex sigma, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const ComplexMatrix& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); // SparseComplexMatrix template OCTAVE_API octave_idx_type EigsComplexNonSymmetricMatrix<SparseComplexMatrix> (const SparseComplexMatrix& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const SparseComplexMatrix& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsComplexNonSymmetricMatrixShift<SparseComplexMatrix> (const SparseComplexMatrix& m, Complex sigma, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const SparseComplexMatrix& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template OCTAVE_API octave_idx_type EigsComplexNonSymmetricFunc<SparseComplexMatrix> (EigsComplexFunc fcn, octave_idx_type n, const std::string& _typ, Complex sigma, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const SparseComplexMatrix& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); #endif