Mercurial > octave
view liboctave/array/dSparse.cc @ 31130:0c637fa9529a
build: Search for python executable with multiple names (bug #62372)
* m4/acinclude.m4 (OCTAVE_PROG_PYTHON): Switch to AC_CHECK_PROGS and search for
a range of possible names for python executable.
author | Rik <rik@octave.org> |
---|---|
date | Sat, 09 Jul 2022 09:58:02 -0700 |
parents | 796f54d4ddbf |
children | 597f3ee61a48 |
line wrap: on
line source
//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1998-2022 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 <istream> #include <ostream> #include "quit.h" #include "lo-ieee.h" #include "lo-lapack-proto.h" #include "lo-mappers.h" #include "dRowVector.h" #include "oct-locbuf.h" #include "dDiagMatrix.h" #include "CSparse.h" #include "boolSparse.h" #include "dSparse.h" #include "oct-spparms.h" #include "sparse-lu.h" #include "MatrixType.h" #include "oct-sparse.h" #include "sparse-util.h" #include "sparse-chol.h" #include "sparse-qr.h" #include "Sparse-op-defs.h" #include "Sparse-diag-op-defs.h" #include "Sparse-perm-op-defs.h" // Define whether to use a basic QR solver or one that uses a Dulmange // Mendelsohn factorization to separate the problem into under-determined, // well-determined and over-determined parts and solves them separately #if ! defined (USE_QRSOLVE) # include "sparse-dmsolve.h" #endif SparseMatrix::SparseMatrix (const SparseBoolMatrix& a) : MSparse<double> (a.rows (), a.cols (), a.nnz ()) { octave_idx_type nc = cols (); octave_idx_type nz = a.nnz (); for (octave_idx_type i = 0; i < nc + 1; i++) cidx (i) = a.cidx (i); for (octave_idx_type i = 0; i < nz; i++) { data (i) = a.data (i); ridx (i) = a.ridx (i); } } SparseMatrix::SparseMatrix (const DiagMatrix& a) : MSparse<double> (a.rows (), a.cols (), a.length ()) { octave_idx_type j = 0; octave_idx_type l = a.length (); for (octave_idx_type i = 0; i < l; i++) { cidx (i) = j; if (a(i, i) != 0.0) { data (j) = a(i, i); ridx (j) = i; j++; } } for (octave_idx_type i = l; i <= a.cols (); i++) cidx (i) = j; } bool SparseMatrix::operator == (const SparseMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nz = nnz (); octave_idx_type nr_a = a.rows (); octave_idx_type nc_a = a.cols (); octave_idx_type nz_a = a.nnz (); if (nr != nr_a || nc != nc_a || nz != nz_a) return false; for (octave_idx_type i = 0; i < nc + 1; i++) if (cidx (i) != a.cidx (i)) return false; for (octave_idx_type i = 0; i < nz; i++) if (data (i) != a.data (i) || ridx (i) != a.ridx (i)) return false; return true; } bool SparseMatrix::operator != (const SparseMatrix& a) const { return !(*this == a); } bool SparseMatrix::issymmetric (void) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr == nc && nr > 0) { for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { octave_idx_type ri = ridx (i); if (ri != j) { bool found = false; for (octave_idx_type k = cidx (ri); k < cidx (ri+1); k++) { if (ridx (k) == j) { if (data (i) == data (k)) found = true; break; } } if (! found) return false; } } } return true; } return false; } SparseMatrix& SparseMatrix::insert (const SparseMatrix& a, octave_idx_type r, octave_idx_type c) { MSparse<double>::insert (a, r, c); return *this; } SparseMatrix& SparseMatrix::insert (const SparseMatrix& a, const Array<octave_idx_type>& indx) { MSparse<double>::insert (a, indx); return *this; } SparseMatrix SparseMatrix::max (int dim) const { Array<octave_idx_type> dummy_idx; return max (dummy_idx, dim); } SparseMatrix SparseMatrix::max (Array<octave_idx_type>& idx_arg, int dim) const { SparseMatrix result; dim_vector dv = dims (); octave_idx_type nr = dv(0); octave_idx_type nc = dv(1); if (dim >= dv.ndims ()) { idx_arg.resize (dim_vector (nr, nc), 0); return *this; } if (dim < 0) dim = dv.first_non_singleton (); if (dim == 0) { idx_arg.resize (dim_vector (nr == 0 ? 0 : 1, nc), 0); if (nr == 0 || nc == 0 || dim >= dv.ndims ()) return SparseMatrix (nr == 0 ? 0 : 1, nc); octave_idx_type nel = 0; for (octave_idx_type j = 0; j < nc; j++) { double tmp_max = octave::numeric_limits<double>::NaN (); octave_idx_type idx_j = 0; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { if (ridx (i) != idx_j) break; else idx_j++; } if (idx_j != nr) tmp_max = 0.; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { double tmp = data (i); if (octave::math::isnan (tmp)) continue; else if (octave::math::isnan (tmp_max) || tmp > tmp_max) { idx_j = ridx (i); tmp_max = tmp; } } idx_arg.elem (j) = (octave::math::isnan (tmp_max) ? 0 : idx_j); if (tmp_max != 0.) nel++; } result = SparseMatrix (1, nc, nel); octave_idx_type ii = 0; result.xcidx (0) = 0; for (octave_idx_type j = 0; j < nc; j++) { double tmp = elem (idx_arg(j), j); if (tmp != 0.) { result.xdata (ii) = tmp; result.xridx (ii++) = 0; } result.xcidx (j+1) = ii; } } else { idx_arg.resize (dim_vector (nr, nc == 0 ? 0 : 1), 0); if (nr == 0 || nc == 0 || dim >= dv.ndims ()) return SparseMatrix (nr, nc == 0 ? 0 : 1); OCTAVE_LOCAL_BUFFER (octave_idx_type, found, nr); for (octave_idx_type i = 0; i < nr; i++) found[i] = 0; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) if (found[ridx (i)] == -j) found[ridx (i)] = -j - 1; for (octave_idx_type i = 0; i < nr; i++) if (found[i] > -nc && found[i] < 0) idx_arg.elem (i) = -found[i]; for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { octave_idx_type ir = ridx (i); octave_idx_type ix = idx_arg.elem (ir); double tmp = data (i); if (octave::math::isnan (tmp)) continue; else if (ix == -1 || tmp > elem (ir, ix)) idx_arg.elem (ir) = j; } } octave_idx_type nel = 0; for (octave_idx_type j = 0; j < nr; j++) if (idx_arg.elem (j) == -1 || elem (j, idx_arg.elem (j)) != 0.) nel++; result = SparseMatrix (nr, 1, nel); octave_idx_type ii = 0; result.xcidx (0) = 0; result.xcidx (1) = nel; for (octave_idx_type j = 0; j < nr; j++) { if (idx_arg(j) == -1) { idx_arg(j) = 0; result.xdata (ii) = octave::numeric_limits<double>::NaN (); result.xridx (ii++) = j; } else { double tmp = elem (j, idx_arg(j)); if (tmp != 0.) { result.xdata (ii) = tmp; result.xridx (ii++) = j; } } } } return result; } SparseMatrix SparseMatrix::min (int dim) const { Array<octave_idx_type> dummy_idx; return min (dummy_idx, dim); } SparseMatrix SparseMatrix::min (Array<octave_idx_type>& idx_arg, int dim) const { SparseMatrix result; dim_vector dv = dims (); octave_idx_type nr = dv(0); octave_idx_type nc = dv(1); if (dim >= dv.ndims ()) { idx_arg.resize (dim_vector (nr, nc), 0); return *this; } if (dim < 0) dim = dv.first_non_singleton (); if (dim == 0) { idx_arg.resize (dim_vector (nr == 0 ? 0 : 1, nc), 0); if (nr == 0 || nc == 0 || dim >= dv.ndims ()) return SparseMatrix (nr == 0 ? 0 : 1, nc); octave_idx_type nel = 0; for (octave_idx_type j = 0; j < nc; j++) { double tmp_min = octave::numeric_limits<double>::NaN (); octave_idx_type idx_j = 0; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { if (ridx (i) != idx_j) break; else idx_j++; } if (idx_j != nr) tmp_min = 0.; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { double tmp = data (i); if (octave::math::isnan (tmp)) continue; else if (octave::math::isnan (tmp_min) || tmp < tmp_min) { idx_j = ridx (i); tmp_min = tmp; } } idx_arg.elem (j) = (octave::math::isnan (tmp_min) ? 0 : idx_j); if (tmp_min != 0.) nel++; } result = SparseMatrix (1, nc, nel); octave_idx_type ii = 0; result.xcidx (0) = 0; for (octave_idx_type j = 0; j < nc; j++) { double tmp = elem (idx_arg(j), j); if (tmp != 0.) { result.xdata (ii) = tmp; result.xridx (ii++) = 0; } result.xcidx (j+1) = ii; } } else { idx_arg.resize (dim_vector (nr, nc == 0 ? 0 : 1), 0); if (nr == 0 || nc == 0 || dim >= dv.ndims ()) return SparseMatrix (nr, nc == 0 ? 0 : 1); OCTAVE_LOCAL_BUFFER (octave_idx_type, found, nr); for (octave_idx_type i = 0; i < nr; i++) found[i] = 0; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) if (found[ridx (i)] == -j) found[ridx (i)] = -j - 1; for (octave_idx_type i = 0; i < nr; i++) if (found[i] > -nc && found[i] < 0) idx_arg.elem (i) = -found[i]; for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { octave_idx_type ir = ridx (i); octave_idx_type ix = idx_arg.elem (ir); double tmp = data (i); if (octave::math::isnan (tmp)) continue; else if (ix == -1 || tmp < elem (ir, ix)) idx_arg.elem (ir) = j; } } octave_idx_type nel = 0; for (octave_idx_type j = 0; j < nr; j++) if (idx_arg.elem (j) == -1 || elem (j, idx_arg.elem (j)) != 0.) nel++; result = SparseMatrix (nr, 1, nel); octave_idx_type ii = 0; result.xcidx (0) = 0; result.xcidx (1) = nel; for (octave_idx_type j = 0; j < nr; j++) { if (idx_arg(j) == -1) { idx_arg(j) = 0; result.xdata (ii) = octave::numeric_limits<double>::NaN (); result.xridx (ii++) = j; } else { double tmp = elem (j, idx_arg(j)); if (tmp != 0.) { result.xdata (ii) = tmp; result.xridx (ii++) = j; } } } } return result; } /* %!assert (max (max (speye (65536))), sparse (1)) %!assert (min (min (speye (65536))), sparse (0)) %!assert (size (max (sparse (8, 0), [], 1)), [1, 0]) %!assert (size (max (sparse (8, 0), [], 2)), [8, 0]) %!assert (size (max (sparse (0, 8), [], 1)), [0, 8]) %!assert (size (max (sparse (0, 8), [], 2)), [0, 1]) %!assert (size (min (sparse (8, 0), [], 1)), [1, 0]) %!assert (size (min (sparse (8, 0), [], 2)), [8, 0]) %!assert (size (min (sparse (0, 8), [], 1)), [0, 8]) %!assert (size (min (sparse (0, 8), [], 2)), [0, 1]) */ RowVector SparseMatrix::row (octave_idx_type i) const { octave_idx_type nc = columns (); RowVector retval (nc, 0); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type k = cidx (j); k < cidx (j+1); k++) { if (ridx (k) == i) { retval(j) = data (k); break; } } return retval; } ColumnVector SparseMatrix::column (octave_idx_type i) const { octave_idx_type nr = rows (); ColumnVector retval (nr, 0); for (octave_idx_type k = cidx (i); k < cidx (i+1); k++) retval(ridx (k)) = data (k); return retval; } SparseMatrix SparseMatrix::concat (const SparseMatrix& rb, const Array<octave_idx_type>& ra_idx) { // Don't use numel to avoid all possibility of an overflow if (rb.rows () > 0 && rb.cols () > 0) insert (rb, ra_idx(0), ra_idx(1)); return *this; } SparseComplexMatrix SparseMatrix::concat (const SparseComplexMatrix& rb, const Array<octave_idx_type>& ra_idx) { SparseComplexMatrix retval (*this); if (rb.rows () > 0 && rb.cols () > 0) retval.insert (rb, ra_idx(0), ra_idx(1)); return retval; } SparseMatrix real (const SparseComplexMatrix& a) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); octave_idx_type nz = a.nnz (); SparseMatrix r (nr, nc, nz); for (octave_idx_type i = 0; i < nc +1; i++) r.cidx (i) = a.cidx (i); for (octave_idx_type i = 0; i < nz; i++) { r.data (i) = std::real (a.data (i)); r.ridx (i) = a.ridx (i); } r.maybe_compress (true); return r; } SparseMatrix imag (const SparseComplexMatrix& a) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); octave_idx_type nz = a.nnz (); SparseMatrix r (nr, nc, nz); for (octave_idx_type i = 0; i < nc +1; i++) r.cidx (i) = a.cidx (i); for (octave_idx_type i = 0; i < nz; i++) { r.data (i) = std::imag (a.data (i)); r.ridx (i) = a.ridx (i); } r.maybe_compress (true); return r; } /* %!assert (nnz (real (sparse ([1i,1]))), 1) %!assert (nnz (real (sparse ([1i,1]))), 1) */ SparseMatrix SparseMatrix::inverse (void) const { octave_idx_type info; double rcond; MatrixType mattype (*this); return inverse (mattype, info, rcond, 0, 0); } SparseMatrix SparseMatrix::inverse (MatrixType& mattype) const { octave_idx_type info; double rcond; return inverse (mattype, info, rcond, 0, 0); } SparseMatrix SparseMatrix::inverse (MatrixType& mattype, octave_idx_type& info) const { double rcond; return inverse (mattype, info, rcond, 0, 0); } SparseMatrix SparseMatrix::dinverse (MatrixType& mattype, octave_idx_type& info, double& rcond, const bool, const bool calccond) const { SparseMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); info = 0; if (nr == 0 || nc == 0 || nr != nc) (*current_liboctave_error_handler) ("inverse requires square matrix"); // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Diagonal && typ != MatrixType::Permuted_Diagonal) (*current_liboctave_error_handler) ("incorrect matrix type"); if (typ == MatrixType::Permuted_Diagonal) retval = transpose (); else retval = *this; // Force make_unique to be called double *v = retval.data (); if (calccond) { double dmax = 0.; double dmin = octave::numeric_limits<double>::Inf (); for (octave_idx_type i = 0; i < nr; i++) { double tmp = fabs (v[i]); if (tmp > dmax) dmax = tmp; if (tmp < dmin) dmin = tmp; } rcond = dmin / dmax; } for (octave_idx_type i = 0; i < nr; i++) v[i] = 1.0 / v[i]; return retval; } SparseMatrix SparseMatrix::tinverse (MatrixType& mattype, octave_idx_type& info, double& rcond, const bool, const bool calccond) const { SparseMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); info = 0; if (nr == 0 || nc == 0 || nr != nc) (*current_liboctave_error_handler) ("inverse requires square matrix"); // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Upper && typ != MatrixType::Permuted_Upper && typ != MatrixType::Lower && typ != MatrixType::Permuted_Lower) (*current_liboctave_error_handler) ("incorrect matrix type"); double anorm = 0.; double ainvnorm = 0.; if (calccond) { // Calculate the 1-norm of matrix for rcond calculation for (octave_idx_type j = 0; j < nr; j++) { double atmp = 0.; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } if (typ == MatrixType::Upper || typ == MatrixType::Lower) { octave_idx_type nz = nnz (); octave_idx_type cx = 0; octave_idx_type nz2 = nz; retval = SparseMatrix (nr, nc, nz2); for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); // place the 1 in the identity position octave_idx_type cx_colstart = cx; if (cx == nz2) { nz2 *= 2; retval.change_capacity (nz2); } retval.xcidx (i) = cx; retval.xridx (cx) = i; retval.xdata (cx) = 1.0; cx++; // iterate across columns of input matrix for (octave_idx_type j = i+1; j < nr; j++) { double v = 0.; // iterate to calculate sum octave_idx_type colXp = retval.xcidx (i); octave_idx_type colUp = cidx (j); octave_idx_type rpX, rpU; if (cidx (j) == cidx (j+1)) (*current_liboctave_error_handler) ("division by zero"); do { octave_quit (); rpX = retval.xridx (colXp); rpU = ridx (colUp); if (rpX < rpU) colXp++; else if (rpX > rpU) colUp++; else { v -= retval.xdata (colXp) * data (colUp); colXp++; colUp++; } } while (rpX < j && rpU < j && colXp < cx && colUp < nz); // get A(m,m) if (typ == MatrixType::Upper) colUp = cidx (j+1) - 1; else colUp = cidx (j); double pivot = data (colUp); if (pivot == 0. || ridx (colUp) != j) (*current_liboctave_error_handler) ("division by zero"); if (v != 0.) { if (cx == nz2) { nz2 *= 2; retval.change_capacity (nz2); } retval.xridx (cx) = j; retval.xdata (cx) = v / pivot; cx++; } } // get A(m,m) octave_idx_type colUp; if (typ == MatrixType::Upper) colUp = cidx (i+1) - 1; else colUp = cidx (i); double pivot = data (colUp); if (pivot == 0. || ridx (colUp) != i) (*current_liboctave_error_handler) ("division by zero"); if (pivot != 1.0) for (octave_idx_type j = cx_colstart; j < cx; j++) retval.xdata (j) /= pivot; } retval.xcidx (nr) = cx; retval.maybe_compress (); } else { octave_idx_type nz = nnz (); octave_idx_type cx = 0; octave_idx_type nz2 = nz; retval = SparseMatrix (nr, nc, nz2); OCTAVE_LOCAL_BUFFER (double, work, nr); OCTAVE_LOCAL_BUFFER (octave_idx_type, rperm, nr); octave_idx_type *perm = mattype.triangular_perm (); if (typ == MatrixType::Permuted_Upper) { for (octave_idx_type i = 0; i < nr; i++) rperm[perm[i]] = i; } else { for (octave_idx_type i = 0; i < nr; i++) rperm[i] = perm[i]; for (octave_idx_type i = 0; i < nr; i++) perm[rperm[i]] = i; } for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); octave_idx_type iidx = rperm[i]; for (octave_idx_type j = 0; j < nr; j++) work[j] = 0.; // place the 1 in the identity position work[iidx] = 1.0; // iterate across columns of input matrix for (octave_idx_type j = iidx+1; j < nr; j++) { double v = 0.; octave_idx_type jidx = perm[j]; // iterate to calculate sum for (octave_idx_type k = cidx (jidx); k < cidx (jidx+1); k++) { octave_quit (); v -= work[ridx (k)] * data (k); } // get A(m,m) double pivot; if (typ == MatrixType::Permuted_Upper) pivot = data (cidx (jidx+1) - 1); else pivot = data (cidx (jidx)); if (pivot == 0.) (*current_liboctave_error_handler) ("division by zero"); work[j] = v / pivot; } // get A(m,m) octave_idx_type colUp; if (typ == MatrixType::Permuted_Upper) colUp = cidx (perm[iidx]+1) - 1; else colUp = cidx (perm[iidx]); double pivot = data (colUp); if (pivot == 0.) (*current_liboctave_error_handler) ("division by zero"); octave_idx_type new_cx = cx; for (octave_idx_type j = iidx; j < nr; j++) if (work[j] != 0.0) { new_cx++; if (pivot != 1.0) work[j] /= pivot; } if (cx < new_cx) { nz2 = (2*nz2 < new_cx ? new_cx : 2*nz2); retval.change_capacity (nz2); } retval.xcidx (i) = cx; for (octave_idx_type j = iidx; j < nr; j++) if (work[j] != 0.) { retval.xridx (cx) = j; retval.xdata (cx++) = work[j]; } } retval.xcidx (nr) = cx; retval.maybe_compress (); } if (calccond) { // Calculate the 1-norm of inverse matrix for rcond calculation for (octave_idx_type j = 0; j < nr; j++) { double atmp = 0.; for (octave_idx_type i = retval.cidx (j); i < retval.cidx (j+1); i++) atmp += fabs (retval.data (i)); if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } return retval; } SparseMatrix SparseMatrix::inverse (MatrixType& mattype, octave_idx_type& info, double& rcond, bool, bool calc_cond) const { if (nnz () == 0) { (*current_liboctave_error_handler) ("inverse of the null matrix not defined"); } int typ = mattype.type (false); SparseMatrix ret; if (typ == MatrixType::Unknown) typ = mattype.type (*this); if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal) ret = dinverse (mattype, info, rcond, true, calc_cond); else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) ret = tinverse (mattype, info, rcond, true, calc_cond).transpose (); else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) { MatrixType newtype = mattype.transpose (); ret = transpose ().tinverse (newtype, info, rcond, true, calc_cond); } else { if (mattype.ishermitian ()) { MatrixType tmp_typ (MatrixType::Upper); octave::math::sparse_chol<SparseMatrix> fact (*this, info, false); rcond = fact.rcond (); if (info == 0) { double rcond2; SparseMatrix Q = fact.Q (); SparseMatrix InvL = fact.L ().transpose ().tinverse (tmp_typ, info, rcond2, true, false); ret = Q * InvL.transpose () * InvL * Q.transpose (); } else { // Matrix is either singular or not positive definite mattype.mark_as_unsymmetric (); } } if (! mattype.ishermitian ()) { octave_idx_type n = rows (); ColumnVector Qinit(n); for (octave_idx_type i = 0; i < n; i++) Qinit(i) = i; MatrixType tmp_typ (MatrixType::Upper); octave::math::sparse_lu<SparseMatrix> fact (*this, Qinit, Matrix (), false, false); rcond = fact.rcond (); if (rcond == 0.0) { // Return all Inf matrix with sparsity pattern of input. octave_idx_type nz = nnz (); ret = SparseMatrix (rows (), cols (), nz); std::fill (ret.xdata (), ret.xdata () + nz, octave::numeric_limits<double>::Inf ()); std::copy_n (ridx (), nz, ret.xridx ()); std::copy_n (cidx (), cols () + 1, ret.xcidx ()); return ret; } double rcond2; SparseMatrix InvL = fact.L ().transpose ().tinverse (tmp_typ, info, rcond2, true, false); SparseMatrix InvU = fact.U ().tinverse (tmp_typ, info, rcond2, true, false).transpose (); ret = fact.Pc ().transpose () * InvU * InvL * fact.Pr (); } } return ret; } DET SparseMatrix::determinant (void) const { octave_idx_type info; double rcond; return determinant (info, rcond, 0); } DET SparseMatrix::determinant (octave_idx_type& info) const { double rcond; return determinant (info, rcond, 0); } DET SparseMatrix::determinant (octave_idx_type& err, double& rcond, bool) const { DET retval; #if defined (HAVE_UMFPACK) octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr == 0 || nc == 0 || nr != nc) { retval = DET (1.0); } else { err = 0; // Setup the control parameters Matrix Control (UMFPACK_CONTROL, 1); double *control = Control.fortran_vec (); UMFPACK_DNAME (defaults) (control); double tmp = octave::sparse_params::get_key ("spumoni"); if (! octave::math::isnan (tmp)) Control (UMFPACK_PRL) = tmp; tmp = octave::sparse_params::get_key ("piv_tol"); if (! octave::math::isnan (tmp)) { Control (UMFPACK_SYM_PIVOT_TOLERANCE) = tmp; Control (UMFPACK_PIVOT_TOLERANCE) = tmp; } // Set whether we are allowed to modify Q or not tmp = octave::sparse_params::get_key ("autoamd"); if (! octave::math::isnan (tmp)) Control (UMFPACK_FIXQ) = tmp; // Turn-off UMFPACK scaling for LU Control (UMFPACK_SCALE) = UMFPACK_SCALE_NONE; UMFPACK_DNAME (report_control) (control); const octave_idx_type *Ap = cidx (); const octave_idx_type *Ai = ridx (); const double *Ax = data (); UMFPACK_DNAME (report_matrix) (nr, nc, octave::to_suitesparse_intptr (Ap), octave::to_suitesparse_intptr (Ai), Ax, 1, control); void *Symbolic; Matrix Info (1, UMFPACK_INFO); double *info = Info.fortran_vec (); int status = UMFPACK_DNAME (qsymbolic) (nr, nc, octave::to_suitesparse_intptr (Ap), octave::to_suitesparse_intptr (Ai), Ax, nullptr, &Symbolic, control, info); if (status < 0) { UMFPACK_DNAME (report_status) (control, status); UMFPACK_DNAME (report_info) (control, info); UMFPACK_DNAME (free_symbolic) (&Symbolic); (*current_liboctave_error_handler) ("SparseMatrix::determinant symbolic factorization failed"); } else { UMFPACK_DNAME (report_symbolic) (Symbolic, control); void *Numeric; status = UMFPACK_DNAME (numeric) (octave::to_suitesparse_intptr (Ap), octave::to_suitesparse_intptr (Ai), Ax, Symbolic, &Numeric, control, info); UMFPACK_DNAME (free_symbolic) (&Symbolic); rcond = Info (UMFPACK_RCOND); if (status < 0) { UMFPACK_DNAME (report_status) (control, status); UMFPACK_DNAME (report_info) (control, info); UMFPACK_DNAME (free_numeric) (&Numeric); (*current_liboctave_error_handler) ("SparseMatrix::determinant numeric factorization failed"); } else { UMFPACK_DNAME (report_numeric) (Numeric, control); double c10, e10; status = UMFPACK_DNAME (get_determinant) (&c10, &e10, Numeric, info); if (status < 0) { UMFPACK_DNAME (report_status) (control, status); UMFPACK_DNAME (report_info) (control, info); (*current_liboctave_error_handler) ("SparseMatrix::determinant error calculating determinant"); } else retval = DET (c10, e10, 10); UMFPACK_DNAME (free_numeric) (&Numeric); } } } #else octave_unused_parameter (err); octave_unused_parameter (rcond); (*current_liboctave_error_handler) ("support for UMFPACK was unavailable or disabled " "when liboctave was built"); #endif return retval; } Matrix SparseMatrix::dsolve (MatrixType& mattype, const Matrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler, bool calc_cond) const { Matrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nm = (nc < nr ? nc : nr); err = 0; if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = Matrix (nc, b.cols (), 0.0); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Diagonal && typ != MatrixType::Permuted_Diagonal) (*current_liboctave_error_handler) ("incorrect matrix type"); retval.resize (nc, b.cols (), 0.); if (typ == MatrixType::Diagonal) for (octave_idx_type j = 0; j < b.cols (); j++) for (octave_idx_type i = 0; i < nm; i++) retval(i, j) = b(i, j) / data (i); else for (octave_idx_type j = 0; j < b.cols (); j++) for (octave_idx_type k = 0; k < nc; k++) for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) retval(k, j) = b(ridx (i), j) / data (i); if (calc_cond) { double dmax = 0.; double dmin = octave::numeric_limits<double>::Inf (); for (octave_idx_type i = 0; i < nm; i++) { double tmp = fabs (data (i)); if (tmp > dmax) dmax = tmp; if (tmp < dmin) dmin = tmp; } rcond = dmin / dmax; } else rcond = 1.; } return retval; } SparseMatrix SparseMatrix::dsolve (MatrixType& mattype, const SparseMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler, bool calc_cond) const { SparseMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nm = (nc < nr ? nc : nr); err = 0; if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = SparseMatrix (nc, b.cols ()); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Diagonal && typ != MatrixType::Permuted_Diagonal) (*current_liboctave_error_handler) ("incorrect matrix type"); octave_idx_type b_nc = b.cols (); octave_idx_type b_nz = b.nnz (); retval = SparseMatrix (nc, b_nc, b_nz); retval.xcidx (0) = 0; octave_idx_type ii = 0; if (typ == MatrixType::Diagonal) for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) { if (b.ridx (i) >= nm) break; retval.xridx (ii) = b.ridx (i); retval.xdata (ii++) = b.data (i) / data (b.ridx (i)); } retval.xcidx (j+1) = ii; } else for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type l = 0; l < nc; l++) for (octave_idx_type i = cidx (l); i < cidx (l+1); i++) { bool found = false; octave_idx_type k; for (k = b.cidx (j); k < b.cidx (j+1); k++) if (ridx (i) == b.ridx (k)) { found = true; break; } if (found) { retval.xridx (ii) = l; retval.xdata (ii++) = b.data (k) / data (i); } } retval.xcidx (j+1) = ii; } if (calc_cond) { double dmax = 0.; double dmin = octave::numeric_limits<double>::Inf (); for (octave_idx_type i = 0; i < nm; i++) { double tmp = fabs (data (i)); if (tmp > dmax) dmax = tmp; if (tmp < dmin) dmin = tmp; } rcond = dmin / dmax; } else rcond = 1.; } return retval; } ComplexMatrix SparseMatrix::dsolve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler, bool calc_cond) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nm = (nc < nr ? nc : nr); err = 0; if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Diagonal && typ != MatrixType::Permuted_Diagonal) (*current_liboctave_error_handler) ("incorrect matrix type"); retval.resize (nc, b.cols (), 0); if (typ == MatrixType::Diagonal) for (octave_idx_type j = 0; j < b.cols (); j++) for (octave_idx_type i = 0; i < nm; i++) retval(i, j) = b(i, j) / data (i); else for (octave_idx_type j = 0; j < b.cols (); j++) for (octave_idx_type k = 0; k < nc; k++) for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) retval(k, j) = b(ridx (i), j) / data (i); if (calc_cond) { double dmax = 0.; double dmin = octave::numeric_limits<double>::Inf (); for (octave_idx_type i = 0; i < nm; i++) { double tmp = fabs (data (i)); if (tmp > dmax) dmax = tmp; if (tmp < dmin) dmin = tmp; } rcond = dmin / dmax; } else rcond = 1.; } return retval; } SparseComplexMatrix SparseMatrix::dsolve (MatrixType& mattype, const SparseComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler, bool calc_cond) const { SparseComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nm = (nc < nr ? nc : nr); err = 0; if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = SparseComplexMatrix (nc, b.cols ()); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Diagonal && typ != MatrixType::Permuted_Diagonal) (*current_liboctave_error_handler) ("incorrect matrix type"); octave_idx_type b_nc = b.cols (); octave_idx_type b_nz = b.nnz (); retval = SparseComplexMatrix (nc, b_nc, b_nz); retval.xcidx (0) = 0; octave_idx_type ii = 0; if (typ == MatrixType::Diagonal) for (octave_idx_type j = 0; j < b.cols (); j++) { for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) { if (b.ridx (i) >= nm) break; retval.xridx (ii) = b.ridx (i); retval.xdata (ii++) = b.data (i) / data (b.ridx (i)); } retval.xcidx (j+1) = ii; } else for (octave_idx_type j = 0; j < b.cols (); j++) { for (octave_idx_type l = 0; l < nc; l++) for (octave_idx_type i = cidx (l); i < cidx (l+1); i++) { bool found = false; octave_idx_type k; for (k = b.cidx (j); k < b.cidx (j+1); k++) if (ridx (i) == b.ridx (k)) { found = true; break; } if (found) { retval.xridx (ii) = l; retval.xdata (ii++) = b.data (k) / data (i); } } retval.xcidx (j+1) = ii; } if (calc_cond) { double dmax = 0.; double dmin = octave::numeric_limits<double>::Inf (); for (octave_idx_type i = 0; i < nm; i++) { double tmp = fabs (data (i)); if (tmp > dmax) dmax = tmp; if (tmp < dmin) dmin = tmp; } rcond = dmin / dmax; } else rcond = 1.; } return retval; } Matrix SparseMatrix::utsolve (MatrixType& mattype, const Matrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { Matrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nm = (nc > nr ? nc : nr); err = 0; if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = Matrix (nc, b.cols (), 0.0); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Permuted_Upper && typ != MatrixType::Upper) (*current_liboctave_error_handler) ("incorrect matrix type"); double anorm = 0.; double ainvnorm = 0.; octave_idx_type b_nc = b.cols (); rcond = 1.; if (calc_cond) { // Calculate the 1-norm of matrix for rcond calculation for (octave_idx_type j = 0; j < nc; j++) { double atmp = 0.; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } if (typ == MatrixType::Permuted_Upper) { retval.resize (nc, b_nc); octave_idx_type *perm = mattype.triangular_perm (); OCTAVE_LOCAL_BUFFER (double, work, nm); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nr; i++) work[i] = b(i, j); for (octave_idx_type i = nr; i < nc; i++) work[i] = 0.; for (octave_idx_type k = nc-1; k >= 0; k--) { octave_idx_type kidx = perm[k]; if (work[k] != 0.) { if (ridx (cidx (kidx+1)-1) != k || data (cidx (kidx+1)-1) == 0.) { err = -2; goto triangular_error; } double tmp = work[k] / data (cidx (kidx+1)-1); work[k] = tmp; for (octave_idx_type i = cidx (kidx); i < cidx (kidx+1)-1; i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } for (octave_idx_type i = 0; i < nc; i++) retval.xelem (perm[i], j) = work[i]; } if (calc_cond) { // Calculation of 1-norm of inv(*this) for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = j; k >= 0; k--) { octave_idx_type iidx = perm[k]; if (work[k] != 0.) { double tmp = work[k] / data (cidx (iidx+1)-1); work[k] = tmp; for (octave_idx_type i = cidx (iidx); i < cidx (iidx+1)-1; i++) { octave_idx_type idx2 = ridx (i); work[idx2] = work[idx2] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = 0; i < j+1; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } else { OCTAVE_LOCAL_BUFFER (double, work, nm); retval.resize (nc, b_nc); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nr; i++) work[i] = b(i, j); for (octave_idx_type i = nr; i < nc; i++) work[i] = 0.; for (octave_idx_type k = nc-1; k >= 0; k--) { if (work[k] != 0.) { if (ridx (cidx (k+1)-1) != k || data (cidx (k+1)-1) == 0.) { err = -2; goto triangular_error; } double tmp = work[k] / data (cidx (k+1)-1); work[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } for (octave_idx_type i = 0; i < nc; i++) retval.xelem (i, j) = work[i]; } if (calc_cond) { // Calculation of 1-norm of inv(*this) for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = j; k >= 0; k--) { if (work[k] != 0.) { double tmp = work[k] / data (cidx (k+1)-1); work[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = 0; i < j+1; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } triangular_error: if (err != 0) { if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } return retval; } SparseMatrix SparseMatrix::utsolve (MatrixType& mattype, const SparseMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { SparseMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nm = (nc > nr ? nc : nr); err = 0; if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = SparseMatrix (nc, b.cols ()); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Permuted_Upper && typ != MatrixType::Upper) (*current_liboctave_error_handler) ("incorrect matrix type"); double anorm = 0.; double ainvnorm = 0.; rcond = 1.; if (calc_cond) { // Calculate the 1-norm of matrix for rcond calculation for (octave_idx_type j = 0; j < nc; j++) { double atmp = 0.; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } octave_idx_type b_nc = b.cols (); octave_idx_type b_nz = b.nnz (); retval = SparseMatrix (nc, b_nc, b_nz); retval.xcidx (0) = 0; octave_idx_type ii = 0; octave_idx_type x_nz = b_nz; if (typ == MatrixType::Permuted_Upper) { octave_idx_type *perm = mattype.triangular_perm (); OCTAVE_LOCAL_BUFFER (double, work, nm); OCTAVE_LOCAL_BUFFER (octave_idx_type, rperm, nc); for (octave_idx_type i = 0; i < nc; i++) rperm[perm[i]] = i; for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) work[b.ridx (i)] = b.data (i); for (octave_idx_type k = nc-1; k >= 0; k--) { octave_idx_type kidx = perm[k]; if (work[k] != 0.) { if (ridx (cidx (kidx+1)-1) != k || data (cidx (kidx+1)-1) == 0.) { err = -2; goto triangular_error; } double tmp = work[k] / data (cidx (kidx+1)-1); work[k] = tmp; for (octave_idx_type i = cidx (kidx); i < cidx (kidx+1)-1; i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } // Count nonzeros in work vector and adjust space in // retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nc; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nc; i++) if (work[rperm[i]] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = work[rperm[i]]; } retval.xcidx (j+1) = ii; } retval.maybe_compress (); if (calc_cond) { // Calculation of 1-norm of inv(*this) for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = j; k >= 0; k--) { octave_idx_type iidx = perm[k]; if (work[k] != 0.) { double tmp = work[k] / data (cidx (iidx+1)-1); work[k] = tmp; for (octave_idx_type i = cidx (iidx); i < cidx (iidx+1)-1; i++) { octave_idx_type idx2 = ridx (i); work[idx2] = work[idx2] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = 0; i < j+1; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } else { OCTAVE_LOCAL_BUFFER (double, work, nm); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) work[b.ridx (i)] = b.data (i); for (octave_idx_type k = nc-1; k >= 0; k--) { if (work[k] != 0.) { if (ridx (cidx (k+1)-1) != k || data (cidx (k+1)-1) == 0.) { err = -2; goto triangular_error; } double tmp = work[k] / data (cidx (k+1)-1); work[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } // Count nonzeros in work vector and adjust space in // retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nc; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nc; i++) if (work[i] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = work[i]; } retval.xcidx (j+1) = ii; } retval.maybe_compress (); if (calc_cond) { // Calculation of 1-norm of inv(*this) for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = j; k >= 0; k--) { if (work[k] != 0.) { double tmp = work[k] / data (cidx (k+1)-1); work[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = 0; i < j+1; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } triangular_error: if (err != 0) { if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } return retval; } ComplexMatrix SparseMatrix::utsolve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nm = (nc > nr ? nc : nr); err = 0; if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Permuted_Upper && typ != MatrixType::Upper) (*current_liboctave_error_handler) ("incorrect matrix type"); double anorm = 0.; double ainvnorm = 0.; octave_idx_type b_nc = b.cols (); rcond = 1.; if (calc_cond) { // Calculate the 1-norm of matrix for rcond calculation for (octave_idx_type j = 0; j < nc; j++) { double atmp = 0.; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } if (typ == MatrixType::Permuted_Upper) { retval.resize (nc, b_nc); octave_idx_type *perm = mattype.triangular_perm (); OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nr; i++) cwork[i] = b(i, j); for (octave_idx_type i = nr; i < nc; i++) cwork[i] = 0.; for (octave_idx_type k = nc-1; k >= 0; k--) { octave_idx_type kidx = perm[k]; if (cwork[k] != 0.) { if (ridx (cidx (kidx+1)-1) != k || data (cidx (kidx+1)-1) == 0.) { err = -2; goto triangular_error; } Complex tmp = cwork[k] / data (cidx (kidx+1)-1); cwork[k] = tmp; for (octave_idx_type i = cidx (kidx); i < cidx (kidx+1)-1; i++) { octave_idx_type iidx = ridx (i); cwork[iidx] = cwork[iidx] - tmp * data (i); } } } for (octave_idx_type i = 0; i < nc; i++) retval.xelem (perm[i], j) = cwork[i]; } if (calc_cond) { // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work, nm); for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = j; k >= 0; k--) { octave_idx_type iidx = perm[k]; if (work[k] != 0.) { double tmp = work[k] / data (cidx (iidx+1)-1); work[k] = tmp; for (octave_idx_type i = cidx (iidx); i < cidx (iidx+1)-1; i++) { octave_idx_type idx2 = ridx (i); work[idx2] = work[idx2] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = 0; i < j+1; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } else { OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); retval.resize (nc, b_nc); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nr; i++) cwork[i] = b(i, j); for (octave_idx_type i = nr; i < nc; i++) cwork[i] = 0.; for (octave_idx_type k = nc-1; k >= 0; k--) { if (cwork[k] != 0.) { if (ridx (cidx (k+1)-1) != k || data (cidx (k+1)-1) == 0.) { err = -2; goto triangular_error; } Complex tmp = cwork[k] / data (cidx (k+1)-1); cwork[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++) { octave_idx_type iidx = ridx (i); cwork[iidx] = cwork[iidx] - tmp * data (i); } } } for (octave_idx_type i = 0; i < nc; i++) retval.xelem (i, j) = cwork[i]; } if (calc_cond) { // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work, nm); for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = j; k >= 0; k--) { if (work[k] != 0.) { double tmp = work[k] / data (cidx (k+1)-1); work[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = 0; i < j+1; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } triangular_error: if (err != 0) { if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } return retval; } SparseComplexMatrix SparseMatrix::utsolve (MatrixType& mattype, const SparseComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { SparseComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nm = (nc > nr ? nc : nr); err = 0; if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = SparseComplexMatrix (nc, b.cols ()); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Permuted_Upper && typ != MatrixType::Upper) (*current_liboctave_error_handler) ("incorrect matrix type"); double anorm = 0.; double ainvnorm = 0.; rcond = 1.; if (calc_cond) { // Calculate the 1-norm of matrix for rcond calculation for (octave_idx_type j = 0; j < nc; j++) { double atmp = 0.; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } octave_idx_type b_nc = b.cols (); octave_idx_type b_nz = b.nnz (); retval = SparseComplexMatrix (nc, b_nc, b_nz); retval.xcidx (0) = 0; octave_idx_type ii = 0; octave_idx_type x_nz = b_nz; if (typ == MatrixType::Permuted_Upper) { octave_idx_type *perm = mattype.triangular_perm (); OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); OCTAVE_LOCAL_BUFFER (octave_idx_type, rperm, nc); for (octave_idx_type i = 0; i < nc; i++) rperm[perm[i]] = i; for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nm; i++) cwork[i] = 0.; for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) cwork[b.ridx (i)] = b.data (i); for (octave_idx_type k = nc-1; k >= 0; k--) { octave_idx_type kidx = perm[k]; if (cwork[k] != 0.) { if (ridx (cidx (kidx+1)-1) != k || data (cidx (kidx+1)-1) == 0.) { err = -2; goto triangular_error; } Complex tmp = cwork[k] / data (cidx (kidx+1)-1); cwork[k] = tmp; for (octave_idx_type i = cidx (kidx); i < cidx (kidx+1)-1; i++) { octave_idx_type iidx = ridx (i); cwork[iidx] = cwork[iidx] - tmp * data (i); } } } // Count nonzeros in work vector and adjust space in // retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nc; i++) if (cwork[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nc; i++) if (cwork[rperm[i]] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = cwork[rperm[i]]; } retval.xcidx (j+1) = ii; } retval.maybe_compress (); if (calc_cond) { // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work, nm); for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = j; k >= 0; k--) { octave_idx_type iidx = perm[k]; if (work[k] != 0.) { double tmp = work[k] / data (cidx (iidx+1)-1); work[k] = tmp; for (octave_idx_type i = cidx (iidx); i < cidx (iidx+1)-1; i++) { octave_idx_type idx2 = ridx (i); work[idx2] = work[idx2] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = 0; i < j+1; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } else { OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nm; i++) cwork[i] = 0.; for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) cwork[b.ridx (i)] = b.data (i); for (octave_idx_type k = nc-1; k >= 0; k--) { if (cwork[k] != 0.) { if (ridx (cidx (k+1)-1) != k || data (cidx (k+1)-1) == 0.) { err = -2; goto triangular_error; } Complex tmp = cwork[k] / data (cidx (k+1)-1); cwork[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++) { octave_idx_type iidx = ridx (i); cwork[iidx] = cwork[iidx] - tmp * data (i); } } } // Count nonzeros in work vector and adjust space in // retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nc; i++) if (cwork[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nc; i++) if (cwork[i] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = cwork[i]; } retval.xcidx (j+1) = ii; } retval.maybe_compress (); if (calc_cond) { // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work, nm); for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = j; k >= 0; k--) { if (work[k] != 0.) { double tmp = work[k] / data (cidx (k+1)-1); work[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = 0; i < j+1; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } triangular_error: if (err != 0) { if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } return retval; } Matrix SparseMatrix::ltsolve (MatrixType& mattype, const Matrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { Matrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nm = (nc > nr ? nc : nr); err = 0; if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = Matrix (nc, b.cols (), 0.0); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Permuted_Lower && typ != MatrixType::Lower) (*current_liboctave_error_handler) ("incorrect matrix type"); double anorm = 0.; double ainvnorm = 0.; octave_idx_type b_nc = b.cols (); rcond = 1.; if (calc_cond) { // Calculate the 1-norm of matrix for rcond calculation for (octave_idx_type j = 0; j < nc; j++) { double atmp = 0.; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } if (typ == MatrixType::Permuted_Lower) { retval.resize (nc, b_nc); OCTAVE_LOCAL_BUFFER (double, work, nm); octave_idx_type *perm = mattype.triangular_perm (); for (octave_idx_type j = 0; j < b_nc; j++) { if (nc > nr) for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type i = 0; i < nr; i++) work[perm[i]] = b(i, j); for (octave_idx_type k = 0; k < nc; k++) { if (work[k] != 0.) { octave_idx_type minr = nr; octave_idx_type mini = 0; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) if (perm[ridx (i)] < minr) { minr = perm[ridx (i)]; mini = i; } if (minr != k || data (mini) == 0) { err = -2; goto triangular_error; } double tmp = work[k] / data (mini); work[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) { if (i == mini) continue; octave_idx_type iidx = perm[ridx (i)]; work[iidx] = work[iidx] - tmp * data (i); } } } for (octave_idx_type i = 0; i < nc; i++) retval(i, j) = work[i]; } if (calc_cond) { // Calculation of 1-norm of inv(*this) for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = 0; k < nc; k++) { if (work[k] != 0.) { octave_idx_type minr = nr; octave_idx_type mini = 0; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) if (perm[ridx (i)] < minr) { minr = perm[ridx (i)]; mini = i; } double tmp = work[k] / data (mini); work[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) { if (i == mini) continue; octave_idx_type iidx = perm[ridx (i)]; work[iidx] = work[iidx] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = j; i < nc; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } else { OCTAVE_LOCAL_BUFFER (double, work, nm); retval.resize (nc, b_nc, 0.); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nr; i++) work[i] = b(i, j); for (octave_idx_type i = nr; i < nc; i++) work[i] = 0.; for (octave_idx_type k = 0; k < nc; k++) { if (work[k] != 0.) { if (ridx (cidx (k)) != k || data (cidx (k)) == 0.) { err = -2; goto triangular_error; } double tmp = work[k] / data (cidx (k)); work[k] = tmp; for (octave_idx_type i = cidx (k)+1; i < cidx (k+1); i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } for (octave_idx_type i = 0; i < nc; i++) retval.xelem (i, j) = work[i]; } if (calc_cond) { // Calculation of 1-norm of inv(*this) for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = j; k < nc; k++) { if (work[k] != 0.) { double tmp = work[k] / data (cidx (k)); work[k] = tmp; for (octave_idx_type i = cidx (k)+1; i < cidx (k+1); i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = j; i < nc; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } triangular_error: if (err != 0) { if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } return retval; } SparseMatrix SparseMatrix::ltsolve (MatrixType& mattype, const SparseMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { SparseMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nm = (nc > nr ? nc : nr); err = 0; if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = SparseMatrix (nc, b.cols ()); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Permuted_Lower && typ != MatrixType::Lower) (*current_liboctave_error_handler) ("incorrect matrix type"); double anorm = 0.; double ainvnorm = 0.; rcond = 1.; if (calc_cond) { // Calculate the 1-norm of matrix for rcond calculation for (octave_idx_type j = 0; j < nc; j++) { double atmp = 0.; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } octave_idx_type b_nc = b.cols (); octave_idx_type b_nz = b.nnz (); retval = SparseMatrix (nc, b_nc, b_nz); retval.xcidx (0) = 0; octave_idx_type ii = 0; octave_idx_type x_nz = b_nz; if (typ == MatrixType::Permuted_Lower) { OCTAVE_LOCAL_BUFFER (double, work, nm); octave_idx_type *perm = mattype.triangular_perm (); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) work[perm[b.ridx (i)]] = b.data (i); for (octave_idx_type k = 0; k < nc; k++) { if (work[k] != 0.) { octave_idx_type minr = nr; octave_idx_type mini = 0; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) if (perm[ridx (i)] < minr) { minr = perm[ridx (i)]; mini = i; } if (minr != k || data (mini) == 0) { err = -2; goto triangular_error; } double tmp = work[k] / data (mini); work[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) { if (i == mini) continue; octave_idx_type iidx = perm[ridx (i)]; work[iidx] = work[iidx] - tmp * data (i); } } } // Count nonzeros in work vector and adjust space in // retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nc; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nc; i++) if (work[i] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = work[i]; } retval.xcidx (j+1) = ii; } retval.maybe_compress (); if (calc_cond) { // Calculation of 1-norm of inv(*this) for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = 0; k < nc; k++) { if (work[k] != 0.) { octave_idx_type minr = nr; octave_idx_type mini = 0; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) if (perm[ridx (i)] < minr) { minr = perm[ridx (i)]; mini = i; } double tmp = work[k] / data (mini); work[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) { if (i == mini) continue; octave_idx_type iidx = perm[ridx (i)]; work[iidx] = work[iidx] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = j; i < nr; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } else { OCTAVE_LOCAL_BUFFER (double, work, nm); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) work[b.ridx (i)] = b.data (i); for (octave_idx_type k = 0; k < nc; k++) { if (work[k] != 0.) { if (ridx (cidx (k)) != k || data (cidx (k)) == 0.) { err = -2; goto triangular_error; } double tmp = work[k] / data (cidx (k)); work[k] = tmp; for (octave_idx_type i = cidx (k)+1; i < cidx (k+1); i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } // Count nonzeros in work vector and adjust space in // retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nc; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nc; i++) if (work[i] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = work[i]; } retval.xcidx (j+1) = ii; } retval.maybe_compress (); if (calc_cond) { // Calculation of 1-norm of inv(*this) for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = j; k < nc; k++) { if (work[k] != 0.) { double tmp = work[k] / data (cidx (k)); work[k] = tmp; for (octave_idx_type i = cidx (k)+1; i < cidx (k+1); i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = j; i < nc; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } triangular_error: if (err != 0) { if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } return retval; } ComplexMatrix SparseMatrix::ltsolve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nm = (nc > nr ? nc : nr); err = 0; if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Permuted_Lower && typ != MatrixType::Lower) (*current_liboctave_error_handler) ("incorrect matrix type"); double anorm = 0.; double ainvnorm = 0.; octave_idx_type b_nc = b.cols (); rcond = 1.; if (calc_cond) { // Calculate the 1-norm of matrix for rcond calculation for (octave_idx_type j = 0; j < nc; j++) { double atmp = 0.; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } if (typ == MatrixType::Permuted_Lower) { retval.resize (nc, b_nc); OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); octave_idx_type *perm = mattype.triangular_perm (); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nm; i++) cwork[i] = 0.; for (octave_idx_type i = 0; i < nr; i++) cwork[perm[i]] = b(i, j); for (octave_idx_type k = 0; k < nc; k++) { if (cwork[k] != 0.) { octave_idx_type minr = nr; octave_idx_type mini = 0; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) if (perm[ridx (i)] < minr) { minr = perm[ridx (i)]; mini = i; } if (minr != k || data (mini) == 0) { err = -2; goto triangular_error; } Complex tmp = cwork[k] / data (mini); cwork[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) { if (i == mini) continue; octave_idx_type iidx = perm[ridx (i)]; cwork[iidx] = cwork[iidx] - tmp * data (i); } } } for (octave_idx_type i = 0; i < nc; i++) retval(i, j) = cwork[i]; } if (calc_cond) { // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work, nm); for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = 0; k < nc; k++) { if (work[k] != 0.) { octave_idx_type minr = nr; octave_idx_type mini = 0; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) if (perm[ridx (i)] < minr) { minr = perm[ridx (i)]; mini = i; } double tmp = work[k] / data (mini); work[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) { if (i == mini) continue; octave_idx_type iidx = perm[ridx (i)]; work[iidx] = work[iidx] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = j; i < nc; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } else { OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); retval.resize (nc, b_nc, 0.); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nr; i++) cwork[i] = b(i, j); for (octave_idx_type i = nr; i < nc; i++) cwork[i] = 0.; for (octave_idx_type k = 0; k < nc; k++) { if (cwork[k] != 0.) { if (ridx (cidx (k)) != k || data (cidx (k)) == 0.) { err = -2; goto triangular_error; } Complex tmp = cwork[k] / data (cidx (k)); cwork[k] = tmp; for (octave_idx_type i = cidx (k)+1; i < cidx (k+1); i++) { octave_idx_type iidx = ridx (i); cwork[iidx] = cwork[iidx] - tmp * data (i); } } } for (octave_idx_type i = 0; i < nc; i++) retval.xelem (i, j) = cwork[i]; } if (calc_cond) { // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work, nm); for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = j; k < nc; k++) { if (work[k] != 0.) { double tmp = work[k] / data (cidx (k)); work[k] = tmp; for (octave_idx_type i = cidx (k)+1; i < cidx (k+1); i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = j; i < nc; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } triangular_error: if (err != 0) { if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } return retval; } SparseComplexMatrix SparseMatrix::ltsolve (MatrixType& mattype, const SparseComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { SparseComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nm = (nc > nr ? nc : nr); err = 0; if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = SparseComplexMatrix (nc, b.cols ()); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ != MatrixType::Permuted_Lower && typ != MatrixType::Lower) (*current_liboctave_error_handler) ("incorrect matrix type"); double anorm = 0.; double ainvnorm = 0.; rcond = 1.; if (calc_cond) { // Calculate the 1-norm of matrix for rcond calculation for (octave_idx_type j = 0; j < nc; j++) { double atmp = 0.; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } octave_idx_type b_nc = b.cols (); octave_idx_type b_nz = b.nnz (); retval = SparseComplexMatrix (nc, b_nc, b_nz); retval.xcidx (0) = 0; octave_idx_type ii = 0; octave_idx_type x_nz = b_nz; if (typ == MatrixType::Permuted_Lower) { OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); octave_idx_type *perm = mattype.triangular_perm (); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nm; i++) cwork[i] = 0.; for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) cwork[perm[b.ridx (i)]] = b.data (i); for (octave_idx_type k = 0; k < nc; k++) { if (cwork[k] != 0.) { octave_idx_type minr = nr; octave_idx_type mini = 0; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) if (perm[ridx (i)] < minr) { minr = perm[ridx (i)]; mini = i; } if (minr != k || data (mini) == 0) { err = -2; goto triangular_error; } Complex tmp = cwork[k] / data (mini); cwork[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) { if (i == mini) continue; octave_idx_type iidx = perm[ridx (i)]; cwork[iidx] = cwork[iidx] - tmp * data (i); } } } // Count nonzeros in work vector and adjust space in // retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nc; i++) if (cwork[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nc; i++) if (cwork[i] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = cwork[i]; } retval.xcidx (j+1) = ii; } retval.maybe_compress (); if (calc_cond) { // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work, nm); for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = 0; k < nc; k++) { if (work[k] != 0.) { octave_idx_type minr = nr; octave_idx_type mini = 0; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) if (perm[ridx (i)] < minr) { minr = perm[ridx (i)]; mini = i; } double tmp = work[k] / data (mini); work[k] = tmp; for (octave_idx_type i = cidx (k); i < cidx (k+1); i++) { if (i == mini) continue; octave_idx_type iidx = perm[ridx (i)]; work[iidx] = work[iidx] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = j; i < nc; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } else { OCTAVE_LOCAL_BUFFER (Complex, cwork, nm); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nm; i++) cwork[i] = 0.; for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) cwork[b.ridx (i)] = b.data (i); for (octave_idx_type k = 0; k < nc; k++) { if (cwork[k] != 0.) { if (ridx (cidx (k)) != k || data (cidx (k)) == 0.) { err = -2; goto triangular_error; } Complex tmp = cwork[k] / data (cidx (k)); cwork[k] = tmp; for (octave_idx_type i = cidx (k)+1; i < cidx (k+1); i++) { octave_idx_type iidx = ridx (i); cwork[iidx] = cwork[iidx] - tmp * data (i); } } } // Count nonzeros in work vector and adjust space in // retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nc; i++) if (cwork[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nc; i++) if (cwork[i] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = cwork[i]; } retval.xcidx (j+1) = ii; } retval.maybe_compress (); if (calc_cond) { // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work, nm); for (octave_idx_type i = 0; i < nm; i++) work[i] = 0.; for (octave_idx_type j = 0; j < nr; j++) { work[j] = 1.; for (octave_idx_type k = j; k < nc; k++) { if (work[k] != 0.) { double tmp = work[k] / data (cidx (k)); work[k] = tmp; for (octave_idx_type i = cidx (k)+1; i < cidx (k+1); i++) { octave_idx_type iidx = ridx (i); work[iidx] = work[iidx] - tmp * data (i); } } } double atmp = 0; for (octave_idx_type i = j; i < nc; i++) { atmp += fabs (work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } rcond = 1. / ainvnorm / anorm; } } triangular_error: if (err != 0) { if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } return retval; } Matrix SparseMatrix::trisolve (MatrixType& mattype, const Matrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { Matrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); err = 0; if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = Matrix (nc, b.cols (), 0.0); else if (calc_cond) (*current_liboctave_error_handler) ("calculation of condition number not implemented"); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == MatrixType::Tridiagonal_Hermitian) { OCTAVE_LOCAL_BUFFER (double, D, nr); OCTAVE_LOCAL_BUFFER (double, DL, nr - 1); if (mattype.is_dense ()) { octave_idx_type ii = 0; for (octave_idx_type j = 0; j < nc-1; j++) { D[j] = data (ii++); DL[j] = data (ii); ii += 2; } D[nc-1] = data (ii); } else { D[0] = 0.; for (octave_idx_type i = 0; i < nr - 1; i++) { D[i+1] = 0.; DL[i] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { if (ridx (i) == j) D[j] = data (i); else if (ridx (i) == j + 1) DL[j] = data (i); } } F77_INT tmp_nr = octave::to_f77_int (nr); F77_INT b_nr = octave::to_f77_int (b.rows ()); F77_INT b_nc = octave::to_f77_int (b.cols ()); retval = b; double *result = retval.fortran_vec (); F77_INT tmp_err = 0; F77_XFCN (dptsv, DPTSV, (tmp_nr, b_nc, D, DL, result, b_nr, tmp_err)); err = tmp_err; if (err != 0) { err = 0; mattype.mark_as_unsymmetric (); typ = MatrixType::Tridiagonal; } else rcond = 1.; } if (typ == MatrixType::Tridiagonal) { OCTAVE_LOCAL_BUFFER (double, DU, nr - 1); OCTAVE_LOCAL_BUFFER (double, D, nr); OCTAVE_LOCAL_BUFFER (double, DL, nr - 1); if (mattype.is_dense ()) { octave_idx_type ii = 0; for (octave_idx_type j = 0; j < nc-1; j++) { D[j] = data (ii++); DL[j] = data (ii++); DU[j] = data (ii++); } D[nc-1] = data (ii); } else { D[0] = 0.; for (octave_idx_type i = 0; i < nr - 1; i++) { D[i+1] = 0.; DL[i] = 0.; DU[i] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { if (ridx (i) == j) D[j] = data (i); else if (ridx (i) == j + 1) DL[j] = data (i); else if (ridx (i) == j - 1) DU[j-1] = data (i); } } F77_INT tmp_nr = octave::to_f77_int (nr); F77_INT b_nr = octave::to_f77_int (b.rows ()); F77_INT b_nc = octave::to_f77_int (b.cols ()); retval = b; double *result = retval.fortran_vec (); F77_INT tmp_err = 0; F77_XFCN (dgtsv, DGTSV, (tmp_nr, b_nc, DL, D, DU, result, b_nr, tmp_err)); err = tmp_err; if (err != 0) { rcond = 0.; err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (); } else rcond = 1.; } else if (typ != MatrixType::Tridiagonal_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseMatrix SparseMatrix::trisolve (MatrixType& mattype, const SparseMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { SparseMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); err = 0; if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = SparseMatrix (nc, b.cols ()); else if (calc_cond) (*current_liboctave_error_handler) ("calculation of condition number not implemented"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); // Note can't treat symmetric case as there is no dpttrf function if (typ == MatrixType::Tridiagonal || typ == MatrixType::Tridiagonal_Hermitian) { OCTAVE_LOCAL_BUFFER (double, DU2, nr - 2); OCTAVE_LOCAL_BUFFER (double, DU, nr - 1); OCTAVE_LOCAL_BUFFER (double, D, nr); OCTAVE_LOCAL_BUFFER (double, DL, nr - 1); Array<F77_INT> ipvt (dim_vector (nr, 1)); F77_INT *pipvt = ipvt.fortran_vec (); if (mattype.is_dense ()) { octave_idx_type ii = 0; for (octave_idx_type j = 0; j < nc-1; j++) { D[j] = data (ii++); DL[j] = data (ii++); DU[j] = data (ii++); } D[nc-1] = data (ii); } else { D[0] = 0.; for (octave_idx_type i = 0; i < nr - 1; i++) { D[i+1] = 0.; DL[i] = 0.; DU[i] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { if (ridx (i) == j) D[j] = data (i); else if (ridx (i) == j + 1) DL[j] = data (i); else if (ridx (i) == j - 1) DU[j-1] = data (i); } } F77_INT tmp_nr = octave::to_f77_int (nr); F77_INT tmp_err = 0; F77_XFCN (dgttrf, DGTTRF, (tmp_nr, DL, D, DU, DU2, pipvt, tmp_err)); if (err != 0) { rcond = 0.0; err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (); } else { rcond = 1.0; char job = 'N'; volatile octave_idx_type x_nz = b.nnz (); octave_idx_type b_nc = b.cols (); retval = SparseMatrix (nr, b_nc, x_nz); retval.xcidx (0) = 0; volatile octave_idx_type ii = 0; OCTAVE_LOCAL_BUFFER (double, work, nr); for (volatile octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nr; i++) work[i] = 0.; for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) work[b.ridx (i)] = b.data (i); F77_INT b_nr = octave::to_f77_int (b.rows ()); F77_XFCN (dgttrs, DGTTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, 1, DL, D, DU, DU2, pipvt, work, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; // Count nonzeros in work vector and adjust // space in retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nr; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nr; i++) if (work[i] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = work[i]; } retval.xcidx (j+1) = ii; } retval.maybe_compress (); } } else if (typ != MatrixType::Tridiagonal_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } ComplexMatrix SparseMatrix::trisolve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); err = 0; if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); else if (calc_cond) (*current_liboctave_error_handler) ("calculation of condition number not implemented"); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == MatrixType::Tridiagonal_Hermitian) { OCTAVE_LOCAL_BUFFER (double, D, nr); OCTAVE_LOCAL_BUFFER (Complex, DL, nr - 1); if (mattype.is_dense ()) { octave_idx_type ii = 0; for (octave_idx_type j = 0; j < nc-1; j++) { D[j] = data (ii++); DL[j] = data (ii); ii += 2; } D[nc-1] = data (ii); } else { D[0] = 0.; for (octave_idx_type i = 0; i < nr - 1; i++) { D[i+1] = 0.; DL[i] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { if (ridx (i) == j) D[j] = data (i); else if (ridx (i) == j + 1) DL[j] = data (i); } } F77_INT tmp_nr = octave::to_f77_int (nr); F77_INT b_nr = octave::to_f77_int (b.rows ()); F77_INT b_nc = octave::to_f77_int (b.cols ()); rcond = 1.; retval = b; Complex *result = retval.fortran_vec (); F77_INT tmp_err = 0; F77_XFCN (zptsv, ZPTSV, (tmp_nr, b_nc, D, F77_DBLE_CMPLX_ARG (DL), F77_DBLE_CMPLX_ARG (result), b_nr, tmp_err)); err = tmp_err; if (err != 0) { err = 0; mattype.mark_as_unsymmetric (); typ = MatrixType::Tridiagonal; } } if (typ == MatrixType::Tridiagonal) { OCTAVE_LOCAL_BUFFER (Complex, DU, nr - 1); OCTAVE_LOCAL_BUFFER (Complex, D, nr); OCTAVE_LOCAL_BUFFER (Complex, DL, nr - 1); if (mattype.is_dense ()) { octave_idx_type ii = 0; for (octave_idx_type j = 0; j < nc-1; j++) { D[j] = data (ii++); DL[j] = data (ii++); DU[j] = data (ii++); } D[nc-1] = data (ii); } else { D[0] = 0.; for (octave_idx_type i = 0; i < nr - 1; i++) { D[i+1] = 0.; DL[i] = 0.; DU[i] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { if (ridx (i) == j) D[j] = data (i); else if (ridx (i) == j + 1) DL[j] = data (i); else if (ridx (i) == j - 1) DU[j-1] = data (i); } } F77_INT tmp_nr = octave::to_f77_int (nr); F77_INT b_nr = octave::to_f77_int (b.rows ()); F77_INT b_nc = octave::to_f77_int (b.cols ()); rcond = 1.; retval = b; Complex *result = retval.fortran_vec (); F77_INT tmp_err = 0; F77_XFCN (zgtsv, ZGTSV, (tmp_nr, b_nc, F77_DBLE_CMPLX_ARG (DL), F77_DBLE_CMPLX_ARG (D), F77_DBLE_CMPLX_ARG (DU), F77_DBLE_CMPLX_ARG (result), b_nr, tmp_err)); err = tmp_err; if (err != 0) { rcond = 0.; err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (); } } else if (typ != MatrixType::Tridiagonal_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseComplexMatrix SparseMatrix::trisolve (MatrixType& mattype, const SparseComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { SparseComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); err = 0; if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = SparseComplexMatrix (nc, b.cols ()); else if (calc_cond) (*current_liboctave_error_handler) ("calculation of condition number not implemented"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); // Note can't treat symmetric case as there is no dpttrf function if (typ == MatrixType::Tridiagonal || typ == MatrixType::Tridiagonal_Hermitian) { OCTAVE_LOCAL_BUFFER (double, DU2, nr - 2); OCTAVE_LOCAL_BUFFER (double, DU, nr - 1); OCTAVE_LOCAL_BUFFER (double, D, nr); OCTAVE_LOCAL_BUFFER (double, DL, nr - 1); Array<F77_INT> ipvt (dim_vector (nr, 1)); F77_INT *pipvt = ipvt.fortran_vec (); if (mattype.is_dense ()) { octave_idx_type ii = 0; for (octave_idx_type j = 0; j < nc-1; j++) { D[j] = data (ii++); DL[j] = data (ii++); DU[j] = data (ii++); } D[nc-1] = data (ii); } else { D[0] = 0.; for (octave_idx_type i = 0; i < nr - 1; i++) { D[i+1] = 0.; DL[i] = 0.; DU[i] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { if (ridx (i) == j) D[j] = data (i); else if (ridx (i) == j + 1) DL[j] = data (i); else if (ridx (i) == j - 1) DU[j-1] = data (i); } } F77_INT tmp_nr = octave::to_f77_int (nr); F77_INT tmp_err = 0; F77_XFCN (dgttrf, DGTTRF, (tmp_nr, DL, D, DU, DU2, pipvt, tmp_err)); err = tmp_err; if (err != 0) { rcond = 0.0; err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (); } else { rcond = 1.; char job = 'N'; F77_INT b_nr = octave::to_f77_int (b.rows ()); octave_idx_type b_nc = b.cols (); OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); OCTAVE_LOCAL_BUFFER (double, Bz, b_nr); // Take a first guess that the number of nonzero terms // will be as many as in b volatile octave_idx_type x_nz = b.nnz (); volatile octave_idx_type ii = 0; retval = SparseComplexMatrix (b_nr, b_nc, x_nz); retval.xcidx (0) = 0; for (volatile octave_idx_type j = 0; j < b_nc; j++) { for (F77_INT i = 0; i < b_nr; i++) { Complex c = b(i, j); Bx[i] = c.real (); Bz[i] = c.imag (); } F77_XFCN (dgttrs, DGTTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, 1, DL, D, DU, DU2, pipvt, Bx, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) { // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } F77_XFCN (dgttrs, DGTTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, 1, DL, D, DU, DU2, pipvt, Bz, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) { // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } // Count nonzeros in work vector and adjust // space in retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nr; i++) if (Bx[i] != 0. || Bz[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nr; i++) if (Bx[i] != 0. || Bz[i] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = Complex (Bx[i], Bz[i]); } retval.xcidx (j+1) = ii; } retval.maybe_compress (); } } else if (typ != MatrixType::Tridiagonal_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } Matrix SparseMatrix::bsolve (MatrixType& mattype, const Matrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { Matrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); err = 0; if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = Matrix (nc, b.cols (), 0.0); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == MatrixType::Banded_Hermitian) { F77_INT n_lower = octave::to_f77_int (mattype.nlower ()); F77_INT ldm = n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { octave_idx_type ii = 0; for (octave_idx_type j = 0; j < ldm; j++) for (octave_idx_type i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { octave_idx_type ri = ridx (i); if (ri >= j) m_band(ri - j, j) = data (i); } // Calculate the norm of the matrix, for later use. double anorm; if (calc_cond) anorm = m_band.abs ().sum ().row (0).max (); F77_INT tmp_nr = octave::to_f77_int (nr); F77_INT tmp_err = 0; char job = 'L'; F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, tmp_data, ldm, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) { // Matrix is not positive definite!! Fall through to // unsymmetric banded solver. mattype.mark_as_unsymmetric (); typ = MatrixType::Banded; rcond = 0.0; err = 0; } else { if (calc_cond) { Array<double> z (dim_vector (3 * nr, 1)); double *pz = z.fortran_vec (); Array<F77_INT> iz (dim_vector (nr, 1)); F77_INT *piz = iz.fortran_vec (); F77_XFCN (dpbcon, DPBCON, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, tmp_data, ldm, anorm, rcond, pz, piz, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } else rcond = 1.; if (err == 0) { retval = b; double *result = retval.fortran_vec (); F77_INT b_nr = octave::to_f77_int (b.rows ()); F77_INT b_nc = octave::to_f77_int (b.cols ()); F77_XFCN (dpbtrs, DPBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, b_nc, tmp_data, ldm, result, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) { // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; } } } } if (typ == MatrixType::Banded) { // Create the storage for the banded form of the sparse matrix F77_INT n_upper = octave::to_f77_int (mattype.nupper ()); F77_INT n_lower = octave::to_f77_int (mattype.nlower ()); F77_INT ldm = n_upper + 2 * n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { octave_idx_type ii = 0; for (F77_INT j = 0; j < ldm; j++) for (octave_idx_type i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) m_band(ridx (i) - j + n_lower + n_upper, j) = data (i); // Calculate the norm of the matrix, for later use. double anorm = 0.0; if (calc_cond) { for (octave_idx_type j = 0; j < nr; j++) { double atmp = 0.; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } F77_INT tmp_nr = octave::to_f77_int (nr); Array<F77_INT> ipvt (dim_vector (nr, 1)); F77_INT *pipvt = ipvt.fortran_vec (); F77_INT tmp_err = 0; F77_XFCN (dgbtrf, DGBTRF, (tmp_nr, tmp_nr, n_lower, n_upper, tmp_data, ldm, pipvt, tmp_err)); err = tmp_err; // Throw away extra info LAPACK gives so as to not // change output. if (err != 0) { err = -2; rcond = 0.0; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (); } else { if (calc_cond) { char job = '1'; Array<double> z (dim_vector (3 * nr, 1)); double *pz = z.fortran_vec (); Array<F77_INT> iz (dim_vector (nr, 1)); F77_INT *piz = iz.fortran_vec (); F77_INT tmp_nc = octave::to_f77_int (nc); F77_XFCN (dgbcon, DGBCON, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nc, n_lower, n_upper, tmp_data, ldm, pipvt, anorm, rcond, pz, piz, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } else rcond = 1.; if (err == 0) { retval = b; double *result = retval.fortran_vec (); F77_INT b_nr = octave::to_f77_int (b.rows ()); F77_INT b_nc = octave::to_f77_int (b.cols ()); char job = 'N'; F77_XFCN (dgbtrs, DGBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, n_upper, b_nc, tmp_data, ldm, pipvt, result, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; } } } else if (typ != MatrixType::Banded_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseMatrix SparseMatrix::bsolve (MatrixType& mattype, const SparseMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { SparseMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); err = 0; if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = SparseMatrix (nc, b.cols ()); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == MatrixType::Banded_Hermitian) { F77_INT n_lower = octave::to_f77_int (mattype.nlower ()); F77_INT ldm = octave::to_f77_int (n_lower + 1); Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { octave_idx_type ii = 0; for (F77_INT j = 0; j < ldm; j++) for (octave_idx_type i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { octave_idx_type ri = ridx (i); if (ri >= j) m_band(ri - j, j) = data (i); } // Calculate the norm of the matrix, for later use. double anorm; if (calc_cond) anorm = m_band.abs ().sum ().row (0).max (); F77_INT tmp_nr = octave::to_f77_int (nr); F77_INT tmp_err = 0; char job = 'L'; F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, tmp_data, ldm, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) { mattype.mark_as_unsymmetric (); typ = MatrixType::Banded; rcond = 0.0; err = 0; } else { if (calc_cond) { Array<double> z (dim_vector (3 * nr, 1)); double *pz = z.fortran_vec (); Array<F77_INT> iz (dim_vector (nr, 1)); F77_INT *piz = iz.fortran_vec (); F77_XFCN (dpbcon, DPBCON, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, tmp_data, ldm, anorm, rcond, pz, piz, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } else rcond = 1.; if (err == 0) { F77_INT b_nr = octave::to_f77_int (b.rows ()); octave_idx_type b_nc = b.cols (); OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); // Take a first guess that the number of nonzero terms // will be as many as in b volatile octave_idx_type x_nz = b.nnz (); volatile octave_idx_type ii = 0; retval = SparseMatrix (b_nr, b_nc, x_nz); retval.xcidx (0) = 0; for (volatile octave_idx_type j = 0; j < b_nc; j++) { for (F77_INT i = 0; i < b_nr; i++) Bx[i] = b.elem (i, j); F77_XFCN (dpbtrs, DPBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, 1, tmp_data, ldm, Bx, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) { // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } for (F77_INT i = 0; i < b_nr; i++) { double tmp = Bx[i]; if (tmp != 0.0) { if (ii == x_nz) { // Resize the sparse matrix octave_idx_type sz; sz = (static_cast<double> (b_nc) - j) / b_nc * x_nz; sz = x_nz + (sz > 100 ? sz : 100); retval.change_capacity (sz); x_nz = sz; } retval.xdata (ii) = tmp; retval.xridx (ii++) = i; } } retval.xcidx (j+1) = ii; } retval.maybe_compress (); } } } if (typ == MatrixType::Banded) { // Create the storage for the banded form of the sparse matrix F77_INT n_upper = octave::to_f77_int (mattype.nupper ()); F77_INT n_lower = octave::to_f77_int (mattype.nlower ()); F77_INT ldm = octave::to_f77_int (n_upper + 2 * n_lower + 1); Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { octave_idx_type ii = 0; for (octave_idx_type j = 0; j < ldm; j++) for (octave_idx_type i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) m_band(ridx (i) - j + n_lower + n_upper, j) = data (i); // Calculate the norm of the matrix, for later use. double anorm; if (calc_cond) { anorm = 0.0; for (octave_idx_type j = 0; j < nr; j++) { double atmp = 0.0; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } F77_INT tmp_nr = octave::to_f77_int (nr); Array<F77_INT> ipvt (dim_vector (nr, 1)); F77_INT *pipvt = ipvt.fortran_vec (); F77_INT tmp_err = 0; F77_XFCN (dgbtrf, DGBTRF, (tmp_nr, tmp_nr, n_lower, n_upper, tmp_data, ldm, pipvt, tmp_err)); err = tmp_err; if (err != 0) { err = -2; rcond = 0.0; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (); } else { if (calc_cond) { char job = '1'; Array<double> z (dim_vector (3 * nr, 1)); double *pz = z.fortran_vec (); Array<F77_INT> iz (dim_vector (nr, 1)); F77_INT *piz = iz.fortran_vec (); F77_INT tmp_nc = octave::to_f77_int (nc); F77_XFCN (dgbcon, DGBCON, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nc, n_lower, n_upper, tmp_data, ldm, pipvt, anorm, rcond, pz, piz, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } else rcond = 1.; if (err == 0) { char job = 'N'; volatile octave_idx_type x_nz = b.nnz (); octave_idx_type b_nc = b.cols (); retval = SparseMatrix (nr, b_nc, x_nz); retval.xcidx (0) = 0; volatile octave_idx_type ii = 0; OCTAVE_LOCAL_BUFFER (double, work, nr); for (volatile octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nr; i++) work[i] = 0.; for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) work[b.ridx (i)] = b.data (i); F77_INT b_nr = octave::to_f77_int (b.rows ()); F77_XFCN (dgbtrs, DGBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, n_upper, 1, tmp_data, ldm, pipvt, work, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; // Count nonzeros in work vector and adjust // space in retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nr; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nr; i++) if (work[i] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = work[i]; } retval.xcidx (j+1) = ii; } retval.maybe_compress (); } } } else if (typ != MatrixType::Banded_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } ComplexMatrix SparseMatrix::bsolve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); err = 0; if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == MatrixType::Banded_Hermitian) { F77_INT n_lower = octave::to_f77_int (mattype.nlower ()); F77_INT ldm = n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { octave_idx_type ii = 0; for (F77_INT j = 0; j < ldm; j++) for (octave_idx_type i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { octave_idx_type ri = ridx (i); if (ri >= j) m_band(ri - j, j) = data (i); } // Calculate the norm of the matrix, for later use. double anorm; if (calc_cond) anorm = m_band.abs ().sum ().row (0).max (); F77_INT tmp_nr = octave::to_f77_int (nr); F77_INT tmp_err = 0; char job = 'L'; F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, tmp_data, ldm, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) { // Matrix is not positive definite!! Fall through to // unsymmetric banded solver. mattype.mark_as_unsymmetric (); typ = MatrixType::Banded; rcond = 0.0; err = 0; } else { if (calc_cond) { Array<double> z (dim_vector (3 * nr, 1)); double *pz = z.fortran_vec (); Array<F77_INT> iz (dim_vector (nr, 1)); F77_INT *piz = iz.fortran_vec (); F77_XFCN (dpbcon, DPBCON, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, tmp_data, ldm, anorm, rcond, pz, piz, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } else rcond = 1.; if (err == 0) { F77_INT b_nr = octave::to_f77_int (b.rows ()); octave_idx_type b_nc = b.cols (); OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); OCTAVE_LOCAL_BUFFER (double, Bz, b_nr); retval.resize (b_nr, b_nc); for (volatile octave_idx_type j = 0; j < b_nc; j++) { for (F77_INT i = 0; i < b_nr; i++) { Complex c = b(i, j); Bx[i] = c.real (); Bz[i] = c.imag (); } F77_XFCN (dpbtrs, DPBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, 1, tmp_data, ldm, Bx, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) { // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } F77_XFCN (dpbtrs, DPBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, 1, tmp_data, ldm, Bz, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) { // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } for (octave_idx_type i = 0; i < b_nr; i++) retval(i, j) = Complex (Bx[i], Bz[i]); } } } } if (typ == MatrixType::Banded) { // Create the storage for the banded form of the sparse matrix F77_INT n_upper = octave::to_f77_int (mattype.nupper ()); F77_INT n_lower = octave::to_f77_int (mattype.nlower ()); F77_INT ldm = n_upper + 2 * n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { octave_idx_type ii = 0; for (F77_INT j = 0; j < ldm; j++) for (octave_idx_type i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) m_band(ridx (i) - j + n_lower + n_upper, j) = data (i); // Calculate the norm of the matrix, for later use. double anorm; if (calc_cond) { anorm = 0.0; for (octave_idx_type j = 0; j < nr; j++) { double atmp = 0.0; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } F77_INT tmp_nr = octave::to_f77_int (nr); Array<F77_INT> ipvt (dim_vector (nr, 1)); F77_INT *pipvt = ipvt.fortran_vec (); F77_INT tmp_err = 0; F77_XFCN (dgbtrf, DGBTRF, (tmp_nr, tmp_nr, n_lower, n_upper, tmp_data, ldm, pipvt, tmp_err)); err = tmp_err; if (err != 0) { err = -2; rcond = 0.0; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (); } else { if (calc_cond) { char job = '1'; Array<double> z (dim_vector (3 * nr, 1)); double *pz = z.fortran_vec (); Array<F77_INT> iz (dim_vector (nr, 1)); F77_INT *piz = iz.fortran_vec (); F77_INT tmp_nc = octave::to_f77_int (nc); F77_XFCN (dgbcon, DGBCON, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nc, n_lower, n_upper, tmp_data, ldm, pipvt, anorm, rcond, pz, piz, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } else rcond = 1.; if (err == 0) { char job = 'N'; F77_INT b_nr = octave::to_f77_int (b.rows ()); octave_idx_type b_nc = b.cols (); retval.resize (nr, b_nc); OCTAVE_LOCAL_BUFFER (double, Bz, nr); OCTAVE_LOCAL_BUFFER (double, Bx, nr); for (volatile octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nr; i++) { Complex c = b(i, j); Bx[i] = c.real (); Bz[i] = c.imag (); } F77_XFCN (dgbtrs, DGBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, n_upper, 1, tmp_data, ldm, pipvt, Bx, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; F77_XFCN (dgbtrs, DGBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, n_upper, 1, tmp_data, ldm, pipvt, Bz, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; for (octave_idx_type i = 0; i < nr; i++) retval(i, j) = Complex (Bx[i], Bz[i]); } } } } else if (typ != MatrixType::Banded_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseComplexMatrix SparseMatrix::bsolve (MatrixType& mattype, const SparseComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { SparseComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); err = 0; if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = SparseComplexMatrix (nc, b.cols ()); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == MatrixType::Banded_Hermitian) { F77_INT n_lower = octave::to_f77_int (mattype.nlower ()); F77_INT ldm = n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { octave_idx_type ii = 0; for (F77_INT j = 0; j < ldm; j++) for (octave_idx_type i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) { octave_idx_type ri = ridx (i); if (ri >= j) m_band(ri - j, j) = data (i); } // Calculate the norm of the matrix, for later use. double anorm; if (calc_cond) anorm = m_band.abs ().sum ().row (0).max (); F77_INT tmp_nr = octave::to_f77_int (nr); F77_INT tmp_err = 0; char job = 'L'; F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, tmp_data, ldm, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) { // Matrix is not positive definite!! Fall through to // unsymmetric banded solver. mattype.mark_as_unsymmetric (); typ = MatrixType::Banded; rcond = 0.0; err = 0; } else { if (calc_cond) { Array<double> z (dim_vector (3 * nr, 1)); double *pz = z.fortran_vec (); Array<F77_INT> iz (dim_vector (nr, 1)); F77_INT *piz = iz.fortran_vec (); F77_XFCN (dpbcon, DPBCON, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, tmp_data, ldm, anorm, rcond, pz, piz, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } else rcond = 1.; if (err == 0) { F77_INT b_nr = octave::to_f77_int (b.rows ()); octave_idx_type b_nc = b.cols (); OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); OCTAVE_LOCAL_BUFFER (double, Bz, b_nr); // Take a first guess that the number of nonzero terms // will be as many as in b volatile octave_idx_type x_nz = b.nnz (); volatile octave_idx_type ii = 0; retval = SparseComplexMatrix (b_nr, b_nc, x_nz); retval.xcidx (0) = 0; for (volatile octave_idx_type j = 0; j < b_nc; j++) { for (F77_INT i = 0; i < b_nr; i++) { Complex c = b(i, j); Bx[i] = c.real (); Bz[i] = c.imag (); } F77_XFCN (dpbtrs, DPBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, 1, tmp_data, ldm, Bx, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) { // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } F77_XFCN (dpbtrs, DPBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, 1, tmp_data, ldm, Bz, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) { // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } // Count nonzeros in work vector and adjust // space in retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nr; i++) if (Bx[i] != 0. || Bz[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nr; i++) if (Bx[i] != 0. || Bz[i] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = Complex (Bx[i], Bz[i]); } retval.xcidx (j+1) = ii; } retval.maybe_compress (); } } } if (typ == MatrixType::Banded) { // Create the storage for the banded form of the sparse matrix F77_INT n_upper = octave::to_f77_int (mattype.nupper ()); F77_INT n_lower = octave::to_f77_int (mattype.nlower ()); F77_INT ldm = n_upper + 2 * n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { octave_idx_type ii = 0; for (F77_INT j = 0; j < ldm; j++) for (octave_idx_type i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) m_band(ridx (i) - j + n_lower + n_upper, j) = data (i); // Calculate the norm of the matrix, for later use. double anorm; if (calc_cond) { anorm = 0.0; for (octave_idx_type j = 0; j < nr; j++) { double atmp = 0.0; for (octave_idx_type i = cidx (j); i < cidx (j+1); i++) atmp += fabs (data (i)); if (atmp > anorm) anorm = atmp; } } F77_INT tmp_nr = octave::to_f77_int (nr); Array<F77_INT> ipvt (dim_vector (nr, 1)); F77_INT *pipvt = ipvt.fortran_vec (); F77_INT tmp_err = 0; F77_XFCN (dgbtrf, DGBTRF, (tmp_nr, tmp_nr, n_lower, n_upper, tmp_data, ldm, pipvt, tmp_err)); err = tmp_err; if (err != 0) { err = -2; rcond = 0.0; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (); } else { if (calc_cond) { char job = '1'; Array<double> z (dim_vector (3 * nr, 1)); double *pz = z.fortran_vec (); Array<F77_INT> iz (dim_vector (nr, 1)); F77_INT *piz = iz.fortran_vec (); F77_INT tmp_nc = octave::to_f77_int (nc); F77_XFCN (dgbcon, DGBCON, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nc, n_lower, n_upper, tmp_data, ldm, pipvt, anorm, rcond, pz, piz, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); } } else rcond = 1.; if (err == 0) { char job = 'N'; volatile octave_idx_type x_nz = b.nnz (); F77_INT b_nr = octave::to_f77_int (b.rows ()); octave_idx_type b_nc = b.cols (); retval = SparseComplexMatrix (nr, b_nc, x_nz); retval.xcidx (0) = 0; volatile octave_idx_type ii = 0; OCTAVE_LOCAL_BUFFER (double, Bx, nr); OCTAVE_LOCAL_BUFFER (double, Bz, nr); for (volatile octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < nr; i++) { Bx[i] = 0.; Bz[i] = 0.; } for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++) { Complex c = b.data (i); Bx[b.ridx (i)] = c.real (); Bz[b.ridx (i)] = c.imag (); } F77_XFCN (dgbtrs, DGBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, n_upper, 1, tmp_data, ldm, pipvt, Bx, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; F77_XFCN (dgbtrs, DGBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), tmp_nr, n_lower, n_upper, 1, tmp_data, ldm, pipvt, Bz, b_nr, tmp_err F77_CHAR_ARG_LEN (1))); err = tmp_err; // Count nonzeros in work vector and adjust // space in retval if needed octave_idx_type new_nnz = 0; for (octave_idx_type i = 0; i < nr; i++) if (Bx[i] != 0. || Bz[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix octave_idx_type sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (octave_idx_type i = 0; i < nr; i++) if (Bx[i] != 0. || Bz[i] != 0.) { retval.xridx (ii) = i; retval.xdata (ii++) = Complex (Bx[i], Bz[i]); } retval.xcidx (j+1) = ii; } retval.maybe_compress (); } } } else if (typ != MatrixType::Banded_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } void * SparseMatrix::factorize (octave_idx_type& err, double& rcond, Matrix& Control, Matrix& Info, solve_singularity_handler sing_handler, bool calc_cond) const { // The return values void *Numeric = nullptr; err = 0; #if defined (HAVE_UMFPACK) // Setup the control parameters Control = Matrix (UMFPACK_CONTROL, 1); double *control = Control.fortran_vec (); UMFPACK_DNAME (defaults) (control); double tmp = octave::sparse_params::get_key ("spumoni"); if (! octave::math::isnan (tmp)) Control (UMFPACK_PRL) = tmp; tmp = octave::sparse_params::get_key ("piv_tol"); if (! octave::math::isnan (tmp)) { Control (UMFPACK_SYM_PIVOT_TOLERANCE) = tmp; Control (UMFPACK_PIVOT_TOLERANCE) = tmp; } // Set whether we are allowed to modify Q or not tmp = octave::sparse_params::get_key ("autoamd"); if (! octave::math::isnan (tmp)) Control (UMFPACK_FIXQ) = tmp; UMFPACK_DNAME (report_control) (control); const octave_idx_type *Ap = cidx (); const octave_idx_type *Ai = ridx (); const double *Ax = data (); octave_idx_type nr = rows (); octave_idx_type nc = cols (); UMFPACK_DNAME (report_matrix) (nr, nc, octave::to_suitesparse_intptr (Ap), octave::to_suitesparse_intptr (Ai), Ax, 1, control); void *Symbolic; Info = Matrix (1, UMFPACK_INFO); double *info = Info.fortran_vec (); int status = UMFPACK_DNAME (qsymbolic) (nr, nc, octave::to_suitesparse_intptr (Ap), octave::to_suitesparse_intptr (Ai), Ax, nullptr, &Symbolic, control, info); if (status < 0) { UMFPACK_DNAME (report_status) (control, status); UMFPACK_DNAME (report_info) (control, info); UMFPACK_DNAME (free_symbolic) (&Symbolic); // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve symbolic factorization failed"); err = -1; } else { UMFPACK_DNAME (report_symbolic) (Symbolic, control); status = UMFPACK_DNAME (numeric) (octave::to_suitesparse_intptr (Ap), octave::to_suitesparse_intptr (Ai), Ax, Symbolic, &Numeric, control, info); UMFPACK_DNAME (free_symbolic) (&Symbolic); if (calc_cond) rcond = Info (UMFPACK_RCOND); else rcond = 1.; volatile double rcond_plus_one = rcond + 1.0; if (status == UMFPACK_WARNING_singular_matrix || rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { UMFPACK_DNAME (report_numeric) (Numeric, control); err = -2; if (sing_handler) sing_handler (rcond); else octave::warn_singular_matrix (rcond); } else if (status < 0) { UMFPACK_DNAME (report_status) (control, status); UMFPACK_DNAME (report_info) (control, info); // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve numeric factorization failed"); err = -1; } else { UMFPACK_DNAME (report_numeric) (Numeric, control); } } if (err != 0) UMFPACK_DNAME (free_numeric) (&Numeric); #else octave_unused_parameter (rcond); octave_unused_parameter (Control); octave_unused_parameter (Info); octave_unused_parameter (sing_handler); octave_unused_parameter (calc_cond); (*current_liboctave_error_handler) ("support for UMFPACK was unavailable or disabled " "when liboctave was built"); #endif return Numeric; } Matrix SparseMatrix::fsolve (MatrixType& mattype, const Matrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { Matrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); err = 0; if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = Matrix (nc, b.cols (), 0.0); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == MatrixType::Hermitian) { #if defined (HAVE_CHOLMOD) cholmod_common Common; cholmod_common *cm = &Common; // Setup initial parameters CHOLMOD_NAME(start) (cm); cm->prefer_zomplex = false; double spu = octave::sparse_params::get_key ("spumoni"); if (spu == 0.) { cm->print = -1; SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, nullptr); } else { cm->print = static_cast<int> (spu) + 2; SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, &SparseCholPrint); } cm->error_handler = &SparseCholError; SUITESPARSE_ASSIGN_FPTR2 (divcomplex_func, cm->complex_divide, divcomplex); SUITESPARSE_ASSIGN_FPTR2 (hypot_func, cm->hypotenuse, hypot); cm->final_ll = true; cholmod_sparse Astore; cholmod_sparse *A = &Astore; A->nrow = nr; A->ncol = nc; A->p = cidx (); A->i = ridx (); A->nzmax = nnz (); A->packed = true; A->sorted = true; A->nz = nullptr; #if defined (OCTAVE_ENABLE_64) A->itype = CHOLMOD_LONG; #else A->itype = CHOLMOD_INT; #endif A->dtype = CHOLMOD_DOUBLE; A->stype = 1; A->xtype = CHOLMOD_REAL; A->x = data (); cholmod_dense Bstore; cholmod_dense *B = &Bstore; B->nrow = b.rows (); B->ncol = b.cols (); B->d = B->nrow; B->nzmax = B->nrow * B->ncol; B->dtype = CHOLMOD_DOUBLE; B->xtype = CHOLMOD_REAL; B->x = const_cast<double *> (b.data ()); cholmod_factor *L = CHOLMOD_NAME(analyze) (A, cm); CHOLMOD_NAME(factorize) (A, L, cm); if (calc_cond) rcond = CHOLMOD_NAME(rcond)(L, cm); else rcond = 1.0; if (rcond == 0.0) { // Either its indefinite or singular. Try UMFPACK mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); return retval; } cholmod_dense *X = CHOLMOD_NAME(solve) (CHOLMOD_A, L, B, cm); retval.resize (b.rows (), b.cols ()); for (octave_idx_type j = 0; j < b.cols (); j++) { octave_idx_type jr = j * b.rows (); for (octave_idx_type i = 0; i < b.rows (); i++) retval.xelem (i, j) = static_cast<double *>(X->x)[jr + i]; } CHOLMOD_NAME(free_dense) (&X, cm); CHOLMOD_NAME(free_factor) (&L, cm); CHOLMOD_NAME(finish) (cm); static char blank_name[] = " "; CHOLMOD_NAME(print_common) (blank_name, cm); } #else (*current_liboctave_warning_with_id_handler) ("Octave:missing-dependency", "support for CHOLMOD was unavailable or disabled " "when liboctave was built"); mattype.mark_as_unsymmetric (); typ = MatrixType::Full; #endif } if (typ == MatrixType::Full) { #if defined (HAVE_UMFPACK) Matrix Control, Info; void *Numeric = factorize (err, rcond, Control, Info, sing_handler, calc_cond); if (err == 0) { // one iterative refinement instead of the default two in UMFPACK Control (UMFPACK_IRSTEP) = 1; const double *Bx = b.data (); retval.resize (b.rows (), b.cols ()); double *result = retval.fortran_vec (); octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); int status = 0; double *control = Control.fortran_vec (); double *info = Info.fortran_vec (); const octave_idx_type *Ap = cidx (); const octave_idx_type *Ai = ridx (); const double *Ax = data (); for (octave_idx_type j = 0, iidx = 0; j < b_nc; j++, iidx += b_nr) { status = UMFPACK_DNAME (solve) (UMFPACK_A, octave::to_suitesparse_intptr (Ap), octave::to_suitesparse_intptr (Ai), Ax, &result[iidx], &Bx[iidx], Numeric, control, info); if (status < 0) { UMFPACK_DNAME (report_status) (control, status); // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } } UMFPACK_DNAME (report_info) (control, info); UMFPACK_DNAME (free_numeric) (&Numeric); } else mattype.mark_as_rectangular (); #else octave_unused_parameter (rcond); octave_unused_parameter (sing_handler); octave_unused_parameter (calc_cond); (*current_liboctave_error_handler) ("support for UMFPACK was unavailable or disabled " "when liboctave was built"); #endif } else if (typ != MatrixType::Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseMatrix SparseMatrix::fsolve (MatrixType& mattype, const SparseMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { SparseMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); err = 0; if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = SparseMatrix (nc, b.cols ()); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == MatrixType::Hermitian) { #if defined (HAVE_CHOLMOD) cholmod_common Common; cholmod_common *cm = &Common; // Setup initial parameters CHOLMOD_NAME(start) (cm); cm->prefer_zomplex = false; double spu = octave::sparse_params::get_key ("spumoni"); if (spu == 0.) { cm->print = -1; SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, nullptr); } else { cm->print = static_cast<int> (spu) + 2; SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, &SparseCholPrint); } cm->error_handler = &SparseCholError; SUITESPARSE_ASSIGN_FPTR2 (divcomplex_func, cm->complex_divide, divcomplex); SUITESPARSE_ASSIGN_FPTR2 (hypot_func, cm->hypotenuse, hypot); cm->final_ll = true; cholmod_sparse Astore; cholmod_sparse *A = &Astore; A->nrow = nr; A->ncol = nc; A->p = cidx (); A->i = ridx (); A->nzmax = nnz (); A->packed = true; A->sorted = true; A->nz = nullptr; #if defined (OCTAVE_ENABLE_64) A->itype = CHOLMOD_LONG; #else A->itype = CHOLMOD_INT; #endif A->dtype = CHOLMOD_DOUBLE; A->stype = 1; A->xtype = CHOLMOD_REAL; A->x = data (); cholmod_sparse Bstore; cholmod_sparse *B = &Bstore; B->nrow = b.rows (); B->ncol = b.cols (); B->p = b.cidx (); B->i = b.ridx (); B->nzmax = b.nnz (); B->packed = true; B->sorted = true; B->nz = nullptr; #if defined (OCTAVE_ENABLE_64) B->itype = CHOLMOD_LONG; #else B->itype = CHOLMOD_INT; #endif B->dtype = CHOLMOD_DOUBLE; B->stype = 0; B->xtype = CHOLMOD_REAL; B->x = b.data (); cholmod_factor *L = CHOLMOD_NAME(analyze) (A, cm); CHOLMOD_NAME(factorize) (A, L, cm); if (calc_cond) rcond = CHOLMOD_NAME(rcond)(L, cm); else rcond = 1.; if (rcond == 0.0) { // Either its indefinite or singular. Try UMFPACK mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); return retval; } cholmod_sparse *X = CHOLMOD_NAME(spsolve) (CHOLMOD_A, L, B, cm); retval = SparseMatrix (static_cast<octave_idx_type> (X->nrow), static_cast<octave_idx_type> (X->ncol), static_cast<octave_idx_type> (X->nzmax)); for (octave_idx_type j = 0; j <= static_cast<octave_idx_type> (X->ncol); j++) retval.xcidx (j) = static_cast<octave_idx_type *>(X->p)[j]; for (octave_idx_type j = 0; j < static_cast<octave_idx_type> (X->nzmax); j++) { retval.xridx (j) = static_cast<octave_idx_type *>(X->i)[j]; retval.xdata (j) = static_cast<double *>(X->x)[j]; } CHOLMOD_NAME(free_sparse) (&X, cm); CHOLMOD_NAME(free_factor) (&L, cm); CHOLMOD_NAME(finish) (cm); static char blank_name[] = " "; CHOLMOD_NAME(print_common) (blank_name, cm); } #else (*current_liboctave_warning_with_id_handler) ("Octave:missing-dependency", "support for CHOLMOD was unavailable or disabled " "when liboctave was built"); mattype.mark_as_unsymmetric (); typ = MatrixType::Full; #endif } if (typ == MatrixType::Full) { #if defined (HAVE_UMFPACK) Matrix Control, Info; void *Numeric = factorize (err, rcond, Control, Info, sing_handler, calc_cond); if (err == 0) { // one iterative refinement instead of the default two in UMFPACK Control (UMFPACK_IRSTEP) = 1; octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); int status = 0; double *control = Control.fortran_vec (); double *info = Info.fortran_vec (); const octave_idx_type *Ap = cidx (); const octave_idx_type *Ai = ridx (); const double *Ax = data (); OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); OCTAVE_LOCAL_BUFFER (double, Xx, b_nr); // Take a first guess that the number of nonzero terms // will be as many as in b octave_idx_type x_nz = b.nnz (); octave_idx_type ii = 0; retval = SparseMatrix (b_nr, b_nc, x_nz); retval.xcidx (0) = 0; for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < b_nr; i++) Bx[i] = b.elem (i, j); status = UMFPACK_DNAME (solve) (UMFPACK_A, octave::to_suitesparse_intptr (Ap), octave::to_suitesparse_intptr (Ai), Ax, Xx, Bx, Numeric, control, info); if (status < 0) { UMFPACK_DNAME (report_status) (control, status); // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } for (octave_idx_type i = 0; i < b_nr; i++) { double tmp = Xx[i]; if (tmp != 0.0) { if (ii == x_nz) { // Resize the sparse matrix octave_idx_type sz; sz = (static_cast<double> (b_nc) - j) / b_nc * x_nz; sz = x_nz + (sz > 100 ? sz : 100); retval.change_capacity (sz); x_nz = sz; } retval.xdata (ii) = tmp; retval.xridx (ii++) = i; } } retval.xcidx (j+1) = ii; } retval.maybe_compress (); UMFPACK_DNAME (report_info) (control, info); UMFPACK_DNAME (free_numeric) (&Numeric); } else mattype.mark_as_rectangular (); #else octave_unused_parameter (rcond); octave_unused_parameter (sing_handler); octave_unused_parameter (calc_cond); (*current_liboctave_error_handler) ("support for UMFPACK was unavailable or disabled " "when liboctave was built"); #endif } else if (typ != MatrixType::Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } ComplexMatrix SparseMatrix::fsolve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); err = 0; if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == MatrixType::Hermitian) { #if defined (HAVE_CHOLMOD) cholmod_common Common; cholmod_common *cm = &Common; // Setup initial parameters CHOLMOD_NAME(start) (cm); cm->prefer_zomplex = false; double spu = octave::sparse_params::get_key ("spumoni"); if (spu == 0.) { cm->print = -1; SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, nullptr); } else { cm->print = static_cast<int> (spu) + 2; SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, &SparseCholPrint); } cm->error_handler = &SparseCholError; SUITESPARSE_ASSIGN_FPTR2 (divcomplex_func, cm->complex_divide, divcomplex); SUITESPARSE_ASSIGN_FPTR2 (hypot_func, cm->hypotenuse, hypot); cm->final_ll = true; cholmod_sparse Astore; cholmod_sparse *A = &Astore; A->nrow = nr; A->ncol = nc; A->p = cidx (); A->i = ridx (); A->nzmax = nnz (); A->packed = true; A->sorted = true; A->nz = nullptr; #if defined (OCTAVE_ENABLE_64) A->itype = CHOLMOD_LONG; #else A->itype = CHOLMOD_INT; #endif A->dtype = CHOLMOD_DOUBLE; A->stype = 1; A->xtype = CHOLMOD_REAL; A->x = data (); cholmod_dense Bstore; cholmod_dense *B = &Bstore; B->nrow = b.rows (); B->ncol = b.cols (); B->d = B->nrow; B->nzmax = B->nrow * B->ncol; B->dtype = CHOLMOD_DOUBLE; B->xtype = CHOLMOD_COMPLEX; B->x = const_cast<Complex *> (b.data ()); cholmod_factor *L = CHOLMOD_NAME(analyze) (A, cm); CHOLMOD_NAME(factorize) (A, L, cm); if (calc_cond) rcond = CHOLMOD_NAME(rcond)(L, cm); else rcond = 1.0; if (rcond == 0.0) { // Either its indefinite or singular. Try UMFPACK mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); return retval; } cholmod_dense *X = CHOLMOD_NAME(solve) (CHOLMOD_A, L, B, cm); retval.resize (b.rows (), b.cols ()); for (octave_idx_type j = 0; j < b.cols (); j++) { octave_idx_type jr = j * b.rows (); for (octave_idx_type i = 0; i < b.rows (); i++) retval.xelem (i, j) = static_cast<Complex *>(X->x)[jr + i]; } CHOLMOD_NAME(free_dense) (&X, cm); CHOLMOD_NAME(free_factor) (&L, cm); CHOLMOD_NAME(finish) (cm); static char blank_name[] = " "; CHOLMOD_NAME(print_common) (blank_name, cm); } #else (*current_liboctave_warning_with_id_handler) ("Octave:missing-dependency", "support for CHOLMOD was unavailable or disabled " "when liboctave was built"); mattype.mark_as_unsymmetric (); typ = MatrixType::Full; #endif } if (typ == MatrixType::Full) { #if defined (HAVE_UMFPACK) Matrix Control, Info; void *Numeric = factorize (err, rcond, Control, Info, sing_handler, calc_cond); if (err == 0) { // one iterative refinement instead of the default two in UMFPACK Control (UMFPACK_IRSTEP) = 1; octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); int status = 0; double *control = Control.fortran_vec (); double *info = Info.fortran_vec (); const octave_idx_type *Ap = cidx (); const octave_idx_type *Ai = ridx (); const double *Ax = data (); OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); OCTAVE_LOCAL_BUFFER (double, Bz, b_nr); retval.resize (b_nr, b_nc); OCTAVE_LOCAL_BUFFER (double, Xx, b_nr); OCTAVE_LOCAL_BUFFER (double, Xz, b_nr); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < b_nr; i++) { Complex c = b(i, j); Bx[i] = c.real (); Bz[i] = c.imag (); } status = UMFPACK_DNAME (solve) (UMFPACK_A, octave::to_suitesparse_intptr (Ap), octave::to_suitesparse_intptr (Ai), Ax, Xx, Bx, Numeric, control, info); int status2 = UMFPACK_DNAME (solve) (UMFPACK_A, octave::to_suitesparse_intptr (Ap), octave::to_suitesparse_intptr (Ai), Ax, Xz, Bz, Numeric, control, info); if (status < 0 || status2 < 0) { UMFPACK_DNAME (report_status) (control, status); // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } for (octave_idx_type i = 0; i < b_nr; i++) retval(i, j) = Complex (Xx[i], Xz[i]); } UMFPACK_DNAME (report_info) (control, info); UMFPACK_DNAME (free_numeric) (&Numeric); } else mattype.mark_as_rectangular (); #else octave_unused_parameter (rcond); octave_unused_parameter (sing_handler); octave_unused_parameter (calc_cond); (*current_liboctave_error_handler) ("support for UMFPACK was unavailable or disabled " "when liboctave was built"); #endif } else if (typ != MatrixType::Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseComplexMatrix SparseMatrix::fsolve (MatrixType& mattype, const SparseComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { SparseComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); err = 0; if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = SparseComplexMatrix (nc, b.cols ()); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == MatrixType::Hermitian) { #if defined (HAVE_CHOLMOD) cholmod_common Common; cholmod_common *cm = &Common; // Setup initial parameters CHOLMOD_NAME(start) (cm); cm->prefer_zomplex = false; double spu = octave::sparse_params::get_key ("spumoni"); if (spu == 0.) { cm->print = -1; SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, nullptr); } else { cm->print = static_cast<int> (spu) + 2; SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, &SparseCholPrint); } cm->error_handler = &SparseCholError; SUITESPARSE_ASSIGN_FPTR2 (divcomplex_func, cm->complex_divide, divcomplex); SUITESPARSE_ASSIGN_FPTR2 (hypot_func, cm->hypotenuse, hypot); cm->final_ll = true; cholmod_sparse Astore; cholmod_sparse *A = &Astore; A->nrow = nr; A->ncol = nc; A->p = cidx (); A->i = ridx (); A->nzmax = nnz (); A->packed = true; A->sorted = true; A->nz = nullptr; #if defined (OCTAVE_ENABLE_64) A->itype = CHOLMOD_LONG; #else A->itype = CHOLMOD_INT; #endif A->dtype = CHOLMOD_DOUBLE; A->stype = 1; A->xtype = CHOLMOD_REAL; A->x = data (); cholmod_sparse Bstore; cholmod_sparse *B = &Bstore; B->nrow = b.rows (); B->ncol = b.cols (); B->p = b.cidx (); B->i = b.ridx (); B->nzmax = b.nnz (); B->packed = true; B->sorted = true; B->nz = nullptr; #if defined (OCTAVE_ENABLE_64) B->itype = CHOLMOD_LONG; #else B->itype = CHOLMOD_INT; #endif B->dtype = CHOLMOD_DOUBLE; B->stype = 0; B->xtype = CHOLMOD_COMPLEX; B->x = b.data (); cholmod_factor *L = CHOLMOD_NAME(analyze) (A, cm); CHOLMOD_NAME(factorize) (A, L, cm); if (calc_cond) rcond = CHOLMOD_NAME(rcond)(L, cm); else rcond = 1.0; if (rcond == 0.0) { // Either its indefinite or singular. Try UMFPACK mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else octave::warn_singular_matrix (rcond); return retval; } cholmod_sparse *X = CHOLMOD_NAME(spsolve) (CHOLMOD_A, L, B, cm); retval = SparseComplexMatrix (static_cast<octave_idx_type> (X->nrow), static_cast<octave_idx_type> (X->ncol), static_cast<octave_idx_type> (X->nzmax)); for (octave_idx_type j = 0; j <= static_cast<octave_idx_type> (X->ncol); j++) retval.xcidx (j) = static_cast<octave_idx_type *>(X->p)[j]; for (octave_idx_type j = 0; j < static_cast<octave_idx_type> (X->nzmax); j++) { retval.xridx (j) = static_cast<octave_idx_type *>(X->i)[j]; retval.xdata (j) = static_cast<Complex *>(X->x)[j]; } CHOLMOD_NAME(free_sparse) (&X, cm); CHOLMOD_NAME(free_factor) (&L, cm); CHOLMOD_NAME(finish) (cm); static char blank_name[] = " "; CHOLMOD_NAME(print_common) (blank_name, cm); } #else (*current_liboctave_warning_with_id_handler) ("Octave:missing-dependency", "support for CHOLMOD was unavailable or disabled " "when liboctave was built"); mattype.mark_as_unsymmetric (); typ = MatrixType::Full; #endif } if (typ == MatrixType::Full) { #if defined (HAVE_UMFPACK) Matrix Control, Info; void *Numeric = factorize (err, rcond, Control, Info, sing_handler, calc_cond); if (err == 0) { // one iterative refinement instead of the default two in UMFPACK Control (UMFPACK_IRSTEP) = 1; octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); int status = 0; double *control = Control.fortran_vec (); double *info = Info.fortran_vec (); const octave_idx_type *Ap = cidx (); const octave_idx_type *Ai = ridx (); const double *Ax = data (); OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); OCTAVE_LOCAL_BUFFER (double, Bz, b_nr); // Take a first guess that the number of nonzero terms // will be as many as in b octave_idx_type x_nz = b.nnz (); octave_idx_type ii = 0; retval = SparseComplexMatrix (b_nr, b_nc, x_nz); OCTAVE_LOCAL_BUFFER (double, Xx, b_nr); OCTAVE_LOCAL_BUFFER (double, Xz, b_nr); retval.xcidx (0) = 0; for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < b_nr; i++) { Complex c = b(i, j); Bx[i] = c.real (); Bz[i] = c.imag (); } status = UMFPACK_DNAME (solve) (UMFPACK_A, octave::to_suitesparse_intptr (Ap), octave::to_suitesparse_intptr (Ai), Ax, Xx, Bx, Numeric, control, info); int status2 = UMFPACK_DNAME (solve) (UMFPACK_A, octave::to_suitesparse_intptr (Ap), octave::to_suitesparse_intptr (Ai), Ax, Xz, Bz, Numeric, control, info); if (status < 0 || status2 < 0) { UMFPACK_DNAME (report_status) (control, status); // FIXME: Should this be a warning? (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } for (octave_idx_type i = 0; i < b_nr; i++) { Complex tmp = Complex (Xx[i], Xz[i]); if (tmp != 0.0) { if (ii == x_nz) { // Resize the sparse matrix octave_idx_type sz; sz = (static_cast<double> (b_nc) - j) / b_nc * x_nz; sz = x_nz + (sz > 100 ? sz : 100); retval.change_capacity (sz); x_nz = sz; } retval.xdata (ii) = tmp; retval.xridx (ii++) = i; } } retval.xcidx (j+1) = ii; } retval.maybe_compress (); UMFPACK_DNAME (report_info) (control, info); UMFPACK_DNAME (free_numeric) (&Numeric); } else mattype.mark_as_rectangular (); #else octave_unused_parameter (rcond); octave_unused_parameter (sing_handler); octave_unused_parameter (calc_cond); (*current_liboctave_error_handler) ("support for UMFPACK was unavailable or disabled " "when liboctave was built"); #endif } else if (typ != MatrixType::Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } Matrix SparseMatrix::solve (MatrixType& mattype, const Matrix& b) const { octave_idx_type info; double rcond; return solve (mattype, b, info, rcond, nullptr); } Matrix SparseMatrix::solve (MatrixType& mattype, const Matrix& b, octave_idx_type& info) const { double rcond; return solve (mattype, b, info, rcond, nullptr); } Matrix SparseMatrix::solve (MatrixType& mattype, const Matrix& b, octave_idx_type& info, double& rcond) const { return solve (mattype, b, info, rcond, nullptr); } Matrix SparseMatrix::solve (MatrixType& mattype, const Matrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool singular_fallback) const { Matrix retval; int typ = mattype.type (false); if (typ == MatrixType::Unknown) typ = mattype.type (*this); // Only calculate the condition number for CHOLMOD/UMFPACK if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal) retval = dsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) retval = utsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) retval = ltsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Banded || typ == MatrixType::Banded_Hermitian) retval = bsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Tridiagonal || typ == MatrixType::Tridiagonal_Hermitian) retval = trisolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) retval = fsolve (mattype, b, err, rcond, sing_handler, true); else if (typ != MatrixType::Rectangular) (*current_liboctave_error_handler) ("unknown matrix type"); // Rectangular or one of the above solvers flags a singular matrix if (singular_fallback && mattype.type (false) == MatrixType::Rectangular) { rcond = 1.; #if defined (USE_QRSOLVE) retval = qrsolve (*this, b, err); #else retval = dmsolve<Matrix, SparseMatrix, Matrix> (*this, b, err); #endif } return retval; } SparseMatrix SparseMatrix::solve (MatrixType& mattype, const SparseMatrix& b) const { octave_idx_type info; double rcond; return solve (mattype, b, info, rcond, nullptr); } SparseMatrix SparseMatrix::solve (MatrixType& mattype, const SparseMatrix& b, octave_idx_type& info) const { double rcond; return solve (mattype, b, info, rcond, nullptr); } SparseMatrix SparseMatrix::solve (MatrixType& mattype, const SparseMatrix& b, octave_idx_type& info, double& rcond) const { return solve (mattype, b, info, rcond, nullptr); } SparseMatrix SparseMatrix::solve (MatrixType& mattype, const SparseMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool singular_fallback) const { SparseMatrix retval; int typ = mattype.type (false); if (typ == MatrixType::Unknown) typ = mattype.type (*this); if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal) retval = dsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) retval = utsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) retval = ltsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Banded || typ == MatrixType::Banded_Hermitian) retval = bsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Tridiagonal || typ == MatrixType::Tridiagonal_Hermitian) retval = trisolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) retval = fsolve (mattype, b, err, rcond, sing_handler, true); else if (typ != MatrixType::Rectangular) (*current_liboctave_error_handler) ("unknown matrix type"); if (singular_fallback && mattype.type (false) == MatrixType::Rectangular) { rcond = 1.; #if defined (USE_QRSOLVE) retval = qrsolve (*this, b, err); #else retval = dmsolve<SparseMatrix, SparseMatrix, SparseMatrix> (*this, b, err); #endif } return retval; } ComplexMatrix SparseMatrix::solve (MatrixType& mattype, const ComplexMatrix& b) const { octave_idx_type info; double rcond; return solve (mattype, b, info, rcond, nullptr); } ComplexMatrix SparseMatrix::solve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& info) const { double rcond; return solve (mattype, b, info, rcond, nullptr); } ComplexMatrix SparseMatrix::solve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& info, double& rcond) const { return solve (mattype, b, info, rcond, nullptr); } ComplexMatrix SparseMatrix::solve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool singular_fallback) const { ComplexMatrix retval; int typ = mattype.type (false); if (typ == MatrixType::Unknown) typ = mattype.type (*this); if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal) retval = dsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) retval = utsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) retval = ltsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Banded || typ == MatrixType::Banded_Hermitian) retval = bsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Tridiagonal || typ == MatrixType::Tridiagonal_Hermitian) retval = trisolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) retval = fsolve (mattype, b, err, rcond, sing_handler, true); else if (typ != MatrixType::Rectangular) (*current_liboctave_error_handler) ("unknown matrix type"); if (singular_fallback && mattype.type (false) == MatrixType::Rectangular) { rcond = 1.; #if defined (USE_QRSOLVE) retval = qrsolve (*this, b, err); #else retval = dmsolve<ComplexMatrix, SparseMatrix, ComplexMatrix> (*this, b, err); #endif } return retval; } SparseComplexMatrix SparseMatrix::solve (MatrixType& mattype, const SparseComplexMatrix& b) const { octave_idx_type info; double rcond; return solve (mattype, b, info, rcond, nullptr); } SparseComplexMatrix SparseMatrix::solve (MatrixType& mattype, const SparseComplexMatrix& b, octave_idx_type& info) const { double rcond; return solve (mattype, b, info, rcond, nullptr); } SparseComplexMatrix SparseMatrix::solve (MatrixType& mattype, const SparseComplexMatrix& b, octave_idx_type& info, double& rcond) const { return solve (mattype, b, info, rcond, nullptr); } SparseComplexMatrix SparseMatrix::solve (MatrixType& mattype, const SparseComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler, bool singular_fallback) const { SparseComplexMatrix retval; int typ = mattype.type (false); if (typ == MatrixType::Unknown) typ = mattype.type (*this); if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal) retval = dsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) retval = utsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) retval = ltsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Banded || typ == MatrixType::Banded_Hermitian) retval = bsolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Tridiagonal || typ == MatrixType::Tridiagonal_Hermitian) retval = trisolve (mattype, b, err, rcond, sing_handler, false); else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) retval = fsolve (mattype, b, err, rcond, sing_handler, true); else if (typ != MatrixType::Rectangular) (*current_liboctave_error_handler) ("unknown matrix type"); if (singular_fallback && mattype.type (false) == MatrixType::Rectangular) { rcond = 1.; #if defined (USE_QRSOLVE) retval = qrsolve (*this, b, err); #else retval = dmsolve<SparseComplexMatrix, SparseMatrix, SparseComplexMatrix> (*this, b, err); #endif } return retval; } ColumnVector SparseMatrix::solve (MatrixType& mattype, const ColumnVector& b) const { octave_idx_type info; double rcond; return solve (mattype, b, info, rcond); } ColumnVector SparseMatrix::solve (MatrixType& mattype, const ColumnVector& b, octave_idx_type& info) const { double rcond; return solve (mattype, b, info, rcond); } ColumnVector SparseMatrix::solve (MatrixType& mattype, const ColumnVector& b, octave_idx_type& info, double& rcond) const { return solve (mattype, b, info, rcond, nullptr); } ColumnVector SparseMatrix::solve (MatrixType& mattype, const ColumnVector& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler) const { Matrix tmp (b); return solve (mattype, tmp, info, rcond, sing_handler).column (static_cast<octave_idx_type> (0)); } ComplexColumnVector SparseMatrix::solve (MatrixType& mattype, const ComplexColumnVector& b) const { octave_idx_type info; double rcond; return solve (mattype, b, info, rcond, nullptr); } ComplexColumnVector SparseMatrix::solve (MatrixType& mattype, const ComplexColumnVector& b, octave_idx_type& info) const { double rcond; return solve (mattype, b, info, rcond, nullptr); } ComplexColumnVector SparseMatrix::solve (MatrixType& mattype, const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const { return solve (mattype, b, info, rcond, nullptr); } ComplexColumnVector SparseMatrix::solve (MatrixType& mattype, const ComplexColumnVector& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler) const { ComplexMatrix tmp (b); return solve (mattype, tmp, info, rcond, sing_handler).column (static_cast<octave_idx_type> (0)); } Matrix SparseMatrix::solve (const Matrix& b) const { octave_idx_type info; double rcond; return solve (b, info, rcond, nullptr); } Matrix SparseMatrix::solve (const Matrix& b, octave_idx_type& info) const { double rcond; return solve (b, info, rcond, nullptr); } Matrix SparseMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, nullptr); } Matrix SparseMatrix::solve (const Matrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler) const { MatrixType mattype (*this); return solve (mattype, b, err, rcond, sing_handler); } SparseMatrix SparseMatrix::solve (const SparseMatrix& b) const { octave_idx_type info; double rcond; return solve (b, info, rcond, nullptr); } SparseMatrix SparseMatrix::solve (const SparseMatrix& b, octave_idx_type& info) const { double rcond; return solve (b, info, rcond, nullptr); } SparseMatrix SparseMatrix::solve (const SparseMatrix& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, nullptr); } SparseMatrix SparseMatrix::solve (const SparseMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler) const { MatrixType mattype (*this); return solve (mattype, b, err, rcond, sing_handler); } ComplexMatrix SparseMatrix::solve (const ComplexMatrix& b, octave_idx_type& info) const { double rcond; return solve (b, info, rcond, nullptr); } ComplexMatrix SparseMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, nullptr); } ComplexMatrix SparseMatrix::solve (const ComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler) const { MatrixType mattype (*this); return solve (mattype, b, err, rcond, sing_handler); } SparseComplexMatrix SparseMatrix::solve (const SparseComplexMatrix& b) const { octave_idx_type info; double rcond; return solve (b, info, rcond, nullptr); } SparseComplexMatrix SparseMatrix::solve (const SparseComplexMatrix& b, octave_idx_type& info) const { double rcond; return solve (b, info, rcond, nullptr); } SparseComplexMatrix SparseMatrix::solve (const SparseComplexMatrix& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, nullptr); } SparseComplexMatrix SparseMatrix::solve (const SparseComplexMatrix& b, octave_idx_type& err, double& rcond, solve_singularity_handler sing_handler) const { MatrixType mattype (*this); return solve (mattype, b, err, rcond, sing_handler); } ColumnVector SparseMatrix::solve (const ColumnVector& b) const { octave_idx_type info; double rcond; return solve (b, info, rcond); } ColumnVector SparseMatrix::solve (const ColumnVector& b, octave_idx_type& info) const { double rcond; return solve (b, info, rcond); } ColumnVector SparseMatrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, nullptr); } ColumnVector SparseMatrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler) const { Matrix tmp (b); return solve (tmp, info, rcond, sing_handler).column (static_cast<octave_idx_type> (0)); } ComplexColumnVector SparseMatrix::solve (const ComplexColumnVector& b) const { octave_idx_type info; double rcond; return solve (b, info, rcond, nullptr); } ComplexColumnVector SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const { double rcond; return solve (b, info, rcond, nullptr); } ComplexColumnVector SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, nullptr); } ComplexColumnVector SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler) const { ComplexMatrix tmp (b); return solve (tmp, info, rcond, sing_handler).column (static_cast<octave_idx_type> (0)); } // other operations. bool SparseMatrix::any_element_is_negative (bool neg_zero) const { octave_idx_type nel = nnz (); if (neg_zero) { for (octave_idx_type i = 0; i < nel; i++) if (lo_ieee_signbit (data (i))) return true; } else { for (octave_idx_type i = 0; i < nel; i++) if (data (i) < 0) return true; } return false; } bool SparseMatrix::any_element_is_nan (void) const { octave_idx_type nel = nnz (); for (octave_idx_type i = 0; i < nel; i++) { double val = data (i); if (octave::math::isnan (val)) return true; } return false; } bool SparseMatrix::any_element_is_inf_or_nan (void) const { octave_idx_type nel = nnz (); for (octave_idx_type i = 0; i < nel; i++) { double val = data (i); if (octave::math::isinf (val) || octave::math::isnan (val)) return true; } return false; } bool SparseMatrix::any_element_not_one_or_zero (void) const { octave_idx_type nel = nnz (); for (octave_idx_type i = 0; i < nel; i++) { double val = data (i); if (val != 0.0 && val != 1.0) return true; } return false; } bool SparseMatrix::all_elements_are_zero (void) const { octave_idx_type nel = nnz (); for (octave_idx_type i = 0; i < nel; i++) if (data (i) != 0) return false; return true; } bool SparseMatrix::all_elements_are_int_or_inf_or_nan (void) const { octave_idx_type nel = nnz (); for (octave_idx_type i = 0; i < nel; i++) { double val = data (i); if (octave::math::isnan (val) || octave::math::x_nint (val) == val) continue; else return false; } return true; } // Return nonzero if any element of M is not an integer. Also extract // the largest and smallest values and return them in MAX_VAL and MIN_VAL. bool SparseMatrix::all_integers (double& max_val, double& min_val) const { octave_idx_type nel = nnz (); if (nel == 0) return false; max_val = data (0); min_val = data (0); for (octave_idx_type i = 0; i < nel; i++) { double val = data (i); if (val > max_val) max_val = val; if (val < min_val) min_val = val; if (octave::math::x_nint (val) != val) return false; } return true; } bool SparseMatrix::too_large_for_float (void) const { return test_any (octave::too_large_for_float); } SparseBoolMatrix SparseMatrix::operator ! (void) const { if (any_element_is_nan ()) octave::err_nan_to_logical_conversion (); octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type nz1 = nnz (); octave_idx_type nz2 = nr*nc - nz1; SparseBoolMatrix r (nr, nc, nz2); octave_idx_type ii = 0; octave_idx_type jj = 0; r.cidx (0) = 0; for (octave_idx_type i = 0; i < nc; i++) { for (octave_idx_type j = 0; j < nr; j++) { if (jj < cidx (i+1) && ridx (jj) == j) jj++; else { r.data (ii) = true; r.ridx (ii++) = j; } } r.cidx (i+1) = ii; } return r; } // FIXME: Do these really belong here? Maybe they should be in a base class? SparseBoolMatrix SparseMatrix::all (int dim) const { SPARSE_ALL_OP (dim); } SparseBoolMatrix SparseMatrix::any (int dim) const { SPARSE_ANY_OP (dim); } SparseMatrix SparseMatrix::cumprod (int dim) const { SPARSE_CUMPROD (SparseMatrix, double, cumprod); } SparseMatrix SparseMatrix::cumsum (int dim) const { SPARSE_CUMSUM (SparseMatrix, double, cumsum); } SparseMatrix SparseMatrix::prod (int dim) const { if ((rows () == 1 && dim == -1) || dim == 1) return transpose ().prod (0).transpose (); else { SPARSE_REDUCTION_OP (SparseMatrix, double, *=, (cidx (j+1) - cidx (j) < nr ? 0.0 : 1.0), 1.0); } } SparseMatrix SparseMatrix::sum (int dim) const { SPARSE_REDUCTION_OP (SparseMatrix, double, +=, 0.0, 0.0); } SparseMatrix SparseMatrix::sumsq (int dim) const { #define ROW_EXPR \ double d = data (i); \ tmp[ridx (i)] += d * d #define COL_EXPR \ double d = data (i); \ tmp[j] += d * d SPARSE_BASE_REDUCTION_OP (SparseMatrix, double, ROW_EXPR, COL_EXPR, 0.0, 0.0); #undef ROW_EXPR #undef COL_EXPR } SparseMatrix SparseMatrix::abs (void) const { octave_idx_type nz = nnz (); SparseMatrix retval (*this); for (octave_idx_type i = 0; i < nz; i++) retval.data (i) = fabs (retval.data (i)); return retval; } SparseMatrix SparseMatrix::diag (octave_idx_type k) const { return MSparse<double>::diag (k); } Matrix SparseMatrix::matrix_value (void) const { return Sparse<double>::array_value (); } std::ostream& operator << (std::ostream& os, const SparseMatrix& a) { octave_idx_type nc = a.cols (); // add one to the printed indices to go from // zero-based to one-based arrays for (octave_idx_type j = 0; j < nc; j++) { octave_quit (); for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { os << a.ridx (i) + 1 << ' ' << j + 1 << ' '; octave::write_value<double> (os, a.data (i)); os << "\n"; } } return os; } std::istream& operator >> (std::istream& is, SparseMatrix& a) { typedef SparseMatrix::element_type elt_type; return read_sparse_matrix<elt_type> (is, a, octave::read_value<double>); } SparseMatrix SparseMatrix::squeeze (void) const { return MSparse<double>::squeeze (); } SparseMatrix SparseMatrix::reshape (const dim_vector& new_dims) const { return MSparse<double>::reshape (new_dims); } SparseMatrix SparseMatrix::permute (const Array<octave_idx_type>& vec, bool inv) const { return MSparse<double>::permute (vec, inv); } SparseMatrix SparseMatrix::ipermute (const Array<octave_idx_type>& vec) const { return MSparse<double>::ipermute (vec); } // matrix by matrix -> matrix operations SparseMatrix operator * (const SparseMatrix& m, const SparseMatrix& a) { SPARSE_SPARSE_MUL (SparseMatrix, double, double); } Matrix operator * (const Matrix& m, const SparseMatrix& a) { FULL_SPARSE_MUL (Matrix, double); } Matrix mul_trans (const Matrix& m, const SparseMatrix& a) { FULL_SPARSE_MUL_TRANS (Matrix, double, ); } Matrix operator * (const SparseMatrix& m, const Matrix& a) { SPARSE_FULL_MUL (Matrix, double); } Matrix trans_mul (const SparseMatrix& m, const Matrix& a) { SPARSE_FULL_TRANS_MUL (Matrix, double, ); } // diag * sparse and sparse * diag SparseMatrix operator * (const DiagMatrix& d, const SparseMatrix& a) { return do_mul_dm_sm<SparseMatrix> (d, a); } SparseMatrix operator * (const SparseMatrix& a, const DiagMatrix& d) { return do_mul_sm_dm<SparseMatrix> (a, d); } SparseMatrix operator + (const DiagMatrix& d, const SparseMatrix& a) { return do_add_dm_sm<SparseMatrix> (d, a); } SparseMatrix operator - (const DiagMatrix& d, const SparseMatrix& a) { return do_sub_dm_sm<SparseMatrix> (d, a); } SparseMatrix operator + (const SparseMatrix& a, const DiagMatrix& d) { return do_add_sm_dm<SparseMatrix> (a, d); } SparseMatrix operator - (const SparseMatrix& a, const DiagMatrix& d) { return do_sub_sm_dm<SparseMatrix> (a, d); } // perm * sparse and sparse * perm SparseMatrix operator * (const PermMatrix& p, const SparseMatrix& a) { return octinternal_do_mul_pm_sm (p, a); } SparseMatrix operator * (const SparseMatrix& a, const PermMatrix& p) { return octinternal_do_mul_sm_pm (a, p); } // FIXME: it would be nice to share code among the min/max functions below. #define EMPTY_RETURN_CHECK(T) \ if (nr == 0 || nc == 0) \ return T (nr, nc); SparseMatrix min (double d, const SparseMatrix& m) { SparseMatrix result; octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (SparseMatrix); // Count the number of nonzero elements if (d < 0.) { result = SparseMatrix (nr, nc, d); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++) { double tmp = octave::math::min (d, m.data (i)); if (tmp != 0.) { octave_idx_type idx = m.ridx (i) + j * nr; result.xdata (idx) = tmp; result.xridx (idx) = m.ridx (i); } } } else { octave_idx_type nel = 0; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++) if (octave::math::min (d, m.data (i)) != 0.) nel++; result = SparseMatrix (nr, nc, nel); octave_idx_type ii = 0; result.xcidx (0) = 0; for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++) { double tmp = octave::math::min (d, m.data (i)); if (tmp != 0.) { result.xdata (ii) = tmp; result.xridx (ii++) = m.ridx (i); } } result.xcidx (j+1) = ii; } } return result; } SparseMatrix min (const SparseMatrix& m, double d) { return min (d, m); } SparseMatrix min (const SparseMatrix& a, const SparseMatrix& b) { SparseMatrix r; octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); if (a_nr == b_nr && a_nc == b_nc) { r = SparseMatrix (a_nr, a_nc, (a.nnz () + b.nnz ())); octave_idx_type jx = 0; r.cidx (0) = 0; for (octave_idx_type i = 0 ; i < a_nc ; i++) { octave_idx_type ja = a.cidx (i); octave_idx_type ja_max = a.cidx (i+1); bool ja_lt_max = ja < ja_max; octave_idx_type jb = b.cidx (i); octave_idx_type jb_max = b.cidx (i+1); bool jb_lt_max = jb < jb_max; while (ja_lt_max || jb_lt_max) { octave_quit (); if ((! jb_lt_max) || (ja_lt_max && (a.ridx (ja) < b.ridx (jb)))) { double tmp = octave::math::min (a.data (ja), 0.); if (tmp != 0.) { r.ridx (jx) = a.ridx (ja); r.data (jx) = tmp; jx++; } ja++; ja_lt_max= ja < ja_max; } else if ((! ja_lt_max) || (jb_lt_max && (b.ridx (jb) < a.ridx (ja)))) { double tmp = octave::math::min (0., b.data (jb)); if (tmp != 0.) { r.ridx (jx) = b.ridx (jb); r.data (jx) = tmp; jx++; } jb++; jb_lt_max= jb < jb_max; } else { double tmp = octave::math::min (a.data (ja), b.data (jb)); if (tmp != 0.) { r.data (jx) = tmp; r.ridx (jx) = a.ridx (ja); jx++; } ja++; ja_lt_max= ja < ja_max; jb++; jb_lt_max= jb < jb_max; } } r.cidx (i+1) = jx; } r.maybe_compress (); } else { if (a_nr == 0 || a_nc == 0) r.resize (a_nr, a_nc); else if (b_nr == 0 || b_nc == 0) r.resize (b_nr, b_nc); else octave::err_nonconformant ("min", a_nr, a_nc, b_nr, b_nc); } return r; } SparseMatrix max (double d, const SparseMatrix& m) { SparseMatrix result; octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (SparseMatrix); // Count the number of nonzero elements if (d > 0.) { result = SparseMatrix (nr, nc, d); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++) { double tmp = octave::math::max (d, m.data (i)); if (tmp != 0.) { octave_idx_type idx = m.ridx (i) + j * nr; result.xdata (idx) = tmp; result.xridx (idx) = m.ridx (i); } } } else { octave_idx_type nel = 0; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++) if (octave::math::max (d, m.data (i)) != 0.) nel++; result = SparseMatrix (nr, nc, nel); octave_idx_type ii = 0; result.xcidx (0) = 0; for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++) { double tmp = octave::math::max (d, m.data (i)); if (tmp != 0.) { result.xdata (ii) = tmp; result.xridx (ii++) = m.ridx (i); } } result.xcidx (j+1) = ii; } } return result; } SparseMatrix max (const SparseMatrix& m, double d) { return max (d, m); } SparseMatrix max (const SparseMatrix& a, const SparseMatrix& b) { SparseMatrix r; octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); if (a_nr == b_nr && a_nc == b_nc) { r = SparseMatrix (a_nr, a_nc, (a.nnz () + b.nnz ())); octave_idx_type jx = 0; r.cidx (0) = 0; for (octave_idx_type i = 0 ; i < a_nc ; i++) { octave_idx_type ja = a.cidx (i); octave_idx_type ja_max = a.cidx (i+1); bool ja_lt_max = ja < ja_max; octave_idx_type jb = b.cidx (i); octave_idx_type jb_max = b.cidx (i+1); bool jb_lt_max = jb < jb_max; while (ja_lt_max || jb_lt_max) { octave_quit (); if ((! jb_lt_max) || (ja_lt_max && (a.ridx (ja) < b.ridx (jb)))) { double tmp = octave::math::max (a.data (ja), 0.); if (tmp != 0.) { r.ridx (jx) = a.ridx (ja); r.data (jx) = tmp; jx++; } ja++; ja_lt_max= ja < ja_max; } else if ((! ja_lt_max) || (jb_lt_max && (b.ridx (jb) < a.ridx (ja)))) { double tmp = octave::math::max (0., b.data (jb)); if (tmp != 0.) { r.ridx (jx) = b.ridx (jb); r.data (jx) = tmp; jx++; } jb++; jb_lt_max= jb < jb_max; } else { double tmp = octave::math::max (a.data (ja), b.data (jb)); if (tmp != 0.) { r.data (jx) = tmp; r.ridx (jx) = a.ridx (ja); jx++; } ja++; ja_lt_max= ja < ja_max; jb++; jb_lt_max= jb < jb_max; } } r.cidx (i+1) = jx; } r.maybe_compress (); } else { if (a_nr == 0 || a_nc == 0) r.resize (a_nr, a_nc); else if (b_nr == 0 || b_nc == 0) r.resize (b_nr, b_nc); else octave::err_nonconformant ("max", a_nr, a_nc, b_nr, b_nc); } return r; } SPARSE_SMS_CMP_OPS (SparseMatrix, double) SPARSE_SMS_BOOL_OPS (SparseMatrix, double) SPARSE_SSM_CMP_OPS (double, SparseMatrix) SPARSE_SSM_BOOL_OPS (double, SparseMatrix) SPARSE_SMSM_CMP_OPS (SparseMatrix, SparseMatrix) SPARSE_SMSM_BOOL_OPS (SparseMatrix, SparseMatrix)