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| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Sat, 07 Mar 2009 10:41:27 -0500 |
| parents | 6e9f26506804 |
| children | 5bce1357edd6 |
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/* Copyright (C) 2004, 2005, 2006, 2007, 2008, 2009 David Bateman Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004 Andy Adler 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 <http://www.gnu.org/licenses/>. */ #ifdef HAVE_CONFIG_H #include <config.h> #endif #include <cfloat> #include <iostream> #include <vector> #include "quit.h" #include "lo-ieee.h" #include "lo-mappers.h" #include "f77-fcn.h" #include "dRowVector.h" #include "oct-locbuf.h" #include "CSparse.h" #include "boolSparse.h" #include "dSparse.h" #include "functor.h" #include "oct-spparms.h" #include "SparsedbleLU.h" #include "MatrixType.h" #include "oct-sparse.h" #include "sparse-util.h" #include "SparsedbleCHOL.h" #include "SparseQR.h" // Define whether to use a basic QR solver or one that uses a Dulmange // Mendelsohn factorization to seperate the problem into under-determined, // well-determined and over-determined parts and solves them seperately #ifndef USE_QRSOLVE #include "sparse-dmsolve.cc" #endif // Fortran functions we call. extern "C" { F77_RET_T F77_FUNC (dgbtrf, DGBTRF) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type*, octave_idx_type&); F77_RET_T F77_FUNC (dgbtrs, DGBTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const double*, const octave_idx_type&, const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dgbcon, DGBCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, const double&, double&, double*, octave_idx_type*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dpbtrf, DPBTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dpbtrs, DPBTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dpbcon, DPBCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, const double&, double&, double*, octave_idx_type*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dptsv, DPTSV) (const octave_idx_type&, const octave_idx_type&, double*, double*, double*, const octave_idx_type&, octave_idx_type&); F77_RET_T F77_FUNC (dgtsv, DGTSV) (const octave_idx_type&, const octave_idx_type&, double*, double*, double*, double*, const octave_idx_type&, octave_idx_type&); F77_RET_T F77_FUNC (dgttrf, DGTTRF) (const octave_idx_type&, double*, double*, double*, double*, octave_idx_type*, octave_idx_type&); F77_RET_T F77_FUNC (dgttrs, DGTTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const double*, const double*, const double*, const double*, const octave_idx_type*, double *, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zptsv, ZPTSV) (const octave_idx_type&, const octave_idx_type&, double*, Complex*, Complex*, const octave_idx_type&, octave_idx_type&); F77_RET_T F77_FUNC (zgtsv, ZGTSV) (const octave_idx_type&, const octave_idx_type&, Complex*, Complex*, Complex*, Complex*, const octave_idx_type&, octave_idx_type&); } 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, 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; } SparseMatrix::SparseMatrix (const PermMatrix& a) : MSparse<double> (a.rows (), a.cols (), a.rows ()) { octave_idx_type n = a.rows (); for (octave_idx_type i = 0; i <= n; i++) cidx (i) = i; const Array<octave_idx_type> pv = a.pvec (); if (a.is_row_perm ()) { for (octave_idx_type i = 0; i < n; i++) ridx (i) = pv (i); } else { for (octave_idx_type i = 0; i < n; i++) ridx (pv (i)) = i; } } 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::is_symmetric (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 { Array2<octave_idx_type> dummy_idx; return max (dummy_idx, dim); } SparseMatrix SparseMatrix::max (Array2<octave_idx_type>& idx_arg, int dim) const { SparseMatrix result; dim_vector dv = dims (); if (dv.numel () == 0 || dim > dv.length () || dim < 0) return result; octave_idx_type nr = dv(0); octave_idx_type nc = dv(1); if (dim == 0) { idx_arg.resize (1, nc); octave_idx_type nel = 0; for (octave_idx_type j = 0; j < nc; j++) { double tmp_max = octave_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 (xisnan (tmp)) continue; else if (xisnan (tmp_max) || tmp > tmp_max) { idx_j = ridx (i); tmp_max = tmp; } } idx_arg.elem (j) = xisnan (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 (nr, 1, 0); for (octave_idx_type i = cidx(0); i < cidx(1); i++) idx_arg.elem(ridx(i)) = -1; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { if (idx_arg.elem(i) != -1) continue; bool found = false; for (octave_idx_type k = cidx(j); k < cidx(j+1); k++) if (ridx(k) == i) { found = true; break; } if (!found) idx_arg.elem(i) = j; } 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 (xisnan (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_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 { Array2<octave_idx_type> dummy_idx; return min (dummy_idx, dim); } SparseMatrix SparseMatrix::min (Array2<octave_idx_type>& idx_arg, int dim) const { SparseMatrix result; dim_vector dv = dims (); if (dv.numel () == 0 || dim > dv.length () || dim < 0) return result; octave_idx_type nr = dv(0); octave_idx_type nc = dv(1); if (dim == 0) { idx_arg.resize (1, nc); octave_idx_type nel = 0; for (octave_idx_type j = 0; j < nc; j++) { double tmp_min = octave_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 (xisnan (tmp)) continue; else if (xisnan (tmp_min) || tmp < tmp_min) { idx_j = ridx (i); tmp_min = tmp; } } idx_arg.elem (j) = xisnan (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 (nr, 1, 0); for (octave_idx_type i = cidx(0); i < cidx(1); i++) idx_arg.elem(ridx(i)) = -1; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { if (idx_arg.elem(i) != -1) continue; bool found = false; for (octave_idx_type k = cidx(j); k < cidx(j+1); k++) if (ridx(k) == i) { found = true; break; } if (!found) idx_arg.elem(i) = j; } 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 (xisnan (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_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; } 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); 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 possiblity 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); } 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); } return r; } SparseMatrix atan2 (const double& x, const SparseMatrix& y) { octave_idx_type nr = y.rows (); octave_idx_type nc = y.cols (); if (x == 0.) return SparseMatrix (nr, nc); else { // Its going to be basically full, so this is probably the // best way to handle it. Matrix tmp (nr, nc, atan2 (x, 0.)); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = y.cidx (j); i < y.cidx (j+1); i++) tmp.elem (y.ridx(i), j) = atan2 (x, y.data(i)); return SparseMatrix (tmp); } } SparseMatrix atan2 (const SparseMatrix& x, const double& y) { octave_idx_type nr = x.rows (); octave_idx_type nc = x.cols (); octave_idx_type nz = x.nnz (); SparseMatrix retval (nr, nc, nz); octave_idx_type ii = 0; retval.xcidx(0) = 0; for (octave_idx_type i = 0; i < nc; i++) { for (octave_idx_type j = x.cidx(i); j < x.cidx(i+1); j++) { double tmp = atan2 (x.data(j), y); if (tmp != 0.) { retval.xdata (ii) = tmp; retval.xridx (ii++) = x.ridx (j); } } retval.xcidx (i+1) = ii; } if (ii != nz) { SparseMatrix retval2 (nr, nc, ii); for (octave_idx_type i = 0; i < nc+1; i++) retval2.xcidx (i) = retval.cidx (i); for (octave_idx_type i = 0; i < ii; i++) { retval2.xdata (i) = retval.data (i); retval2.xridx (i) = retval.ridx (i); } return retval2; } else return retval; } SparseMatrix atan2 (const SparseMatrix& x, const SparseMatrix& y) { SparseMatrix r; if ((x.rows() == y.rows()) && (x.cols() == y.cols())) { octave_idx_type x_nr = x.rows (); octave_idx_type x_nc = x.cols (); octave_idx_type y_nr = y.rows (); octave_idx_type y_nc = y.cols (); if (x_nr != y_nr || x_nc != y_nc) gripe_nonconformant ("atan2", x_nr, x_nc, y_nr, y_nc); else { r = SparseMatrix (x_nr, x_nc, (x.nnz () + y.nnz ())); octave_idx_type jx = 0; r.cidx (0) = 0; for (octave_idx_type i = 0 ; i < x_nc ; i++) { octave_idx_type ja = x.cidx(i); octave_idx_type ja_max = x.cidx(i+1); bool ja_lt_max= ja < ja_max; octave_idx_type jb = y.cidx(i); octave_idx_type jb_max = y.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 && (x.ridx(ja) < y.ridx(jb)))) { r.ridx(jx) = x.ridx(ja); r.data(jx) = atan2 (x.data(ja), 0.); jx++; ja++; ja_lt_max= ja < ja_max; } else if (( !ja_lt_max ) || (jb_lt_max && (y.ridx(jb) < x.ridx(ja)) ) ) { jb++; jb_lt_max= jb < jb_max; } else { double tmp = atan2 (x.data(ja), y.data(jb)); if (tmp != 0.) { r.data(jx) = tmp; r.ridx(jx) = x.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 (*current_liboctave_error_handler) ("matrix size mismatch"); return r; } 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 &mattyp, 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"); else { // Print spparms("spumoni") info if requested int typ = mattyp.type (); mattyp.info (); if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal) { 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., dmin = octave_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]; } else (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseMatrix SparseMatrix::tinverse (MatrixType &mattyp, 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"); else { // Print spparms("spumoni") info if requested int typ = mattyp.type (); mattyp.info (); if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper || typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) { 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 accross 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"); goto inverse_singular; } 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"); goto inverse_singular; } 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"); goto inverse_singular; } 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 = mattyp.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 accross 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"); goto inverse_singular; } 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"); goto inverse_singular; } 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; } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; inverse_singular: return SparseMatrix(); } SparseMatrix SparseMatrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcond, int, int calc_cond) const { 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.is_hermitian()) { MatrixType tmp_typ (MatrixType::Upper); SparseCHOL 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 (); typ = MatrixType::Full; } } if (!mattype.is_hermitian()) { 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); SparseLU fact (*this, Qinit, Matrix(), false, false); rcond = fact.rcond(); 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, int) const { DET retval; #ifdef 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 (!xisnan (tmp)) Control (UMFPACK_PRL) = tmp; tmp = octave_sparse_params::get_key ("piv_tol"); if (!xisnan (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 (!xisnan (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, Ap, Ai, Ax, 1, control); void *Symbolic; Matrix Info (1, UMFPACK_INFO); double *info = Info.fortran_vec (); int status = UMFPACK_DNAME (qsymbolic) (nr, nc, Ap, Ai, Ax, 0, &Symbolic, control, info); if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::determinant symbolic factorization failed"); UMFPACK_DNAME (report_status) (control, status); UMFPACK_DNAME (report_info) (control, info); UMFPACK_DNAME (free_symbolic) (&Symbolic) ; } else { UMFPACK_DNAME (report_symbolic) (Symbolic, control); void *Numeric; status = UMFPACK_DNAME (numeric) (Ap, Ai, Ax, Symbolic, &Numeric, control, info) ; UMFPACK_DNAME (free_symbolic) (&Symbolic) ; rcond = Info (UMFPACK_RCOND); if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::determinant numeric factorization failed"); UMFPACK_DNAME (report_status) (control, status); UMFPACK_DNAME (report_info) (control, info); UMFPACK_DNAME (free_numeric) (&Numeric); } else { UMFPACK_DNAME (report_numeric) (Numeric, control); double c10, e10; status = UMFPACK_DNAME (get_determinant) (&c10, &e10, Numeric, info); if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::determinant error calculating determinant"); UMFPACK_DNAME (report_status) (control, status); UMFPACK_DNAME (report_info) (control, info); } else retval = DET (c10, e10, 10); UMFPACK_DNAME (free_numeric) (&Numeric); } } } #else (*current_liboctave_error_handler) ("UMFPACK not installed"); #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"); else 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) { 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., dmin = octave_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.; } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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"); else 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) { 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., dmin = octave_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.; } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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"); else 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) { 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., dmin = octave_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.; } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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"); else 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) { 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., dmin = octave_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.; } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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"); else 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) { 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 (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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"); else 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) { 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 non-zeros 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 non-zeros 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 (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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"); else 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) { 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 (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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"); else 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) { 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 non-zeros 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 non-zeros 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 (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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"); else 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) { 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 (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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"); else 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) { 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 non-zeros 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 non-zeros 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 (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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"); else 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) { 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 (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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"); else 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) { 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 non-zeros 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 non-zeros 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 (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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"); else 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); } } octave_idx_type b_nc = b.cols(); retval = b; double *result = retval.fortran_vec (); F77_XFCN (dptsv, DPTSV, (nr, b_nc, D, DL, result, b.rows(), 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); } } octave_idx_type b_nc = b.cols(); retval = b; double *result = retval.fortran_vec (); F77_XFCN (dgtsv, DGTSV, (nr, b_nc, DL, D, DU, result, b.rows(), err)); if (err != 0) { rcond = 0.; err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } 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"); else 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<octave_idx_type> ipvt (nr); octave_idx_type *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_XFCN (dgttrf, DGTTRF, (nr, DL, D, DU, DU2, pipvt, err)); if (err != 0) { rcond = 0.0; err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } 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_XFCN (dgttrs, DGTTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, 1, DL, D, DU, DU2, pipvt, work, b.rows (), err F77_CHAR_ARG_LEN (1))); // Count non-zeros 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"); else 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); } } octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols(); rcond = 1.; retval = b; Complex *result = retval.fortran_vec (); F77_XFCN (zptsv, ZPTSV, (nr, b_nc, D, DL, result, b_nr, 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); } } octave_idx_type b_nr = b.rows(); octave_idx_type b_nc = b.cols(); rcond = 1.; retval = b; Complex *result = retval.fortran_vec (); F77_XFCN (zgtsv, ZGTSV, (nr, b_nc, DL, D, DU, result, b_nr, err)); if (err != 0) { rcond = 0.; err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } } 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"); else 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<octave_idx_type> ipvt (nr); octave_idx_type *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_XFCN (dgttrf, DGTTRF, (nr, DL, D, DU, DU2, pipvt, err)); if (err != 0) { rcond = 0.0; err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } else { rcond = 1.; char job = 'N'; octave_idx_type b_nr = 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 non-zero 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 (octave_idx_type i = 0; i < b_nr; i++) { Complex c = b (i,j); Bx[i] = std::real (c); Bz[i] = std::imag (c); } F77_XFCN (dgttrs, DGTTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, 1, DL, D, DU, DU2, pipvt, Bx, b_nr, err F77_CHAR_ARG_LEN (1))); if (err != 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } F77_XFCN (dgttrs, DGTTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, 1, DL, D, DU, DU2, pipvt, Bz, b_nr, err F77_CHAR_ARG_LEN (1))); if (err != 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } // Count non-zeros 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"); else 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) { octave_idx_type n_lower = mattype.nlower (); octave_idx_type 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(); char job = 'L'; F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, tmp_data, ldm, err F77_CHAR_ARG_LEN (1))); 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 (3 * nr); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nr); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dpbcon, DPBCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, tmp_data, ldm, anorm, rcond, pz, piz, err F77_CHAR_ARG_LEN (1))); if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else rcond = 1.; if (err == 0) { retval = b; double *result = retval.fortran_vec (); octave_idx_type b_nc = b.cols (); F77_XFCN (dpbtrs, DPBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, b_nc, tmp_data, ldm, result, b.rows(), err F77_CHAR_ARG_LEN (1))); if (err != 0) { (*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 octave_idx_type n_upper = mattype.nupper (); octave_idx_type n_lower = mattype.nlower (); octave_idx_type 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 (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) { 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; } } Array<octave_idx_type> ipvt (nr); octave_idx_type *pipvt = ipvt.fortran_vec (); F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, ldm, pipvt, 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 (*current_liboctave_error_handler) ("matrix singular to machine precision"); } else { if (calc_cond) { char job = '1'; Array<double> z (3 * nr); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nr); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dgbcon, DGBCON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, n_lower, n_upper, tmp_data, ldm, pipvt, anorm, rcond, pz, piz, err F77_CHAR_ARG_LEN (1))); if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else rcond = 1.; if (err == 0) { retval = b; double *result = retval.fortran_vec (); octave_idx_type b_nc = b.cols (); char job = 'N'; F77_XFCN (dgbtrs, DGBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, n_upper, b_nc, tmp_data, ldm, pipvt, result, b.rows(), err F77_CHAR_ARG_LEN (1))); } } } 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"); else 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) { octave_idx_type n_lower = mattype.nlower (); octave_idx_type 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(); char job = 'L'; F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, tmp_data, ldm, err F77_CHAR_ARG_LEN (1))); if (err != 0) { mattype.mark_as_unsymmetric (); typ = MatrixType::Banded; rcond = 0.0; err = 0; } else { if (calc_cond) { Array<double> z (3 * nr); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nr); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dpbcon, DPBCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, tmp_data, ldm, anorm, rcond, pz, piz, err F77_CHAR_ARG_LEN (1))); if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else rcond = 1.; if (err == 0) { octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); OCTAVE_LOCAL_BUFFER (double, Bx, b_nr); // Take a first guess that the number of non-zero 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 (octave_idx_type i = 0; i < b_nr; i++) Bx[i] = b.elem (i, j); F77_XFCN (dpbtrs, DPBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, 1, tmp_data, ldm, Bx, b_nr, err F77_CHAR_ARG_LEN (1))); if (err != 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } for (octave_idx_type 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 = x_nz * (b_nc - j) / b_nc; sz = (sz > 10 ? sz : 10) + x_nz; 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 octave_idx_type n_upper = mattype.nupper (); octave_idx_type n_lower = mattype.nlower (); octave_idx_type 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 (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) { 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; } } Array<octave_idx_type> ipvt (nr); octave_idx_type *pipvt = ipvt.fortran_vec (); F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, ldm, pipvt, err)); if (err != 0) { err = -2; rcond = 0.0; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } else { if (calc_cond) { char job = '1'; Array<double> z (3 * nr); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nr); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dgbcon, DGBCON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, n_lower, n_upper, tmp_data, ldm, pipvt, anorm, rcond, pz, piz, err F77_CHAR_ARG_LEN (1))); if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", 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_XFCN (dgbtrs, DGBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, n_upper, 1, tmp_data, ldm, pipvt, work, b.rows (), err F77_CHAR_ARG_LEN (1))); // Count non-zeros 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"); else 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) { octave_idx_type n_lower = mattype.nlower (); octave_idx_type 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(); char job = 'L'; F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, tmp_data, ldm, err F77_CHAR_ARG_LEN (1))); 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 (3 * nr); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nr); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dpbcon, DPBCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, tmp_data, ldm, anorm, rcond, pz, piz, err F77_CHAR_ARG_LEN (1))); if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else rcond = 1.; if (err == 0) { octave_idx_type b_nr = 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 (octave_idx_type i = 0; i < b_nr; i++) { Complex c = b (i,j); Bx[i] = std::real (c); Bz[i] = std::imag (c); } F77_XFCN (dpbtrs, DPBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, 1, tmp_data, ldm, Bx, b_nr, err F77_CHAR_ARG_LEN (1))); if (err != 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } F77_XFCN (dpbtrs, DPBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, 1, tmp_data, ldm, Bz, b.rows(), err F77_CHAR_ARG_LEN (1))); if (err != 0) { (*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 octave_idx_type n_upper = mattype.nupper (); octave_idx_type n_lower = mattype.nlower (); octave_idx_type 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 (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) { 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; } } Array<octave_idx_type> ipvt (nr); octave_idx_type *pipvt = ipvt.fortran_vec (); F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, ldm, pipvt, err)); if (err != 0) { err = -2; rcond = 0.0; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } else { if (calc_cond) { char job = '1'; Array<double> z (3 * nr); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nr); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dpbcon, DPBCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, tmp_data, ldm, anorm, rcond, pz, piz, err F77_CHAR_ARG_LEN (1))); if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else rcond = 1.; if (err == 0) { char job = 'N'; 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] = std::real (c); Bz[i] = std::imag (c); } F77_XFCN (dgbtrs, DGBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, n_upper, 1, tmp_data, ldm, pipvt, Bx, b.rows (), err F77_CHAR_ARG_LEN (1))); F77_XFCN (dgbtrs, DGBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, n_upper, 1, tmp_data, ldm, pipvt, Bz, b.rows (), err F77_CHAR_ARG_LEN (1))); 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"); else 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) { octave_idx_type n_lower = mattype.nlower (); octave_idx_type 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(); char job = 'L'; F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, tmp_data, ldm, err F77_CHAR_ARG_LEN (1))); 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 (3 * nr); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nr); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dpbcon, DPBCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, tmp_data, ldm, anorm, rcond, pz, piz, err F77_CHAR_ARG_LEN (1))); if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } else rcond = 1.; if (err == 0) { octave_idx_type b_nr = 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 non-zero 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 (octave_idx_type i = 0; i < b_nr; i++) { Complex c = b (i,j); Bx[i] = std::real (c); Bz[i] = std::imag (c); } F77_XFCN (dpbtrs, DPBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, 1, tmp_data, ldm, Bx, b_nr, err F77_CHAR_ARG_LEN (1))); if (err != 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } F77_XFCN (dpbtrs, DPBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, 1, tmp_data, ldm, Bz, b_nr, err F77_CHAR_ARG_LEN (1))); if (err != 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } // Count non-zeros 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 octave_idx_type n_upper = mattype.nupper (); octave_idx_type n_lower = mattype.nlower (); octave_idx_type 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 (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) { 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; } } Array<octave_idx_type> ipvt (nr); octave_idx_type *pipvt = ipvt.fortran_vec (); F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, ldm, pipvt, err)); if (err != 0) { err = -2; rcond = 0.0; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } else { if (calc_cond) { char job = '1'; Array<double> z (3 * nr); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nr); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dgbcon, DGBCON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, n_lower, n_upper, tmp_data, ldm, pipvt, anorm, rcond, pz, piz, err F77_CHAR_ARG_LEN (1))); if (err != 0) err = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", 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 = 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)] = std::real (c); Bz[b.ridx(i)] = std::imag (c); } F77_XFCN (dgbtrs, DGBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, n_upper, 1, tmp_data, ldm, pipvt, Bx, b.rows (), err F77_CHAR_ARG_LEN (1))); F77_XFCN (dgbtrs, DGBTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, n_lower, n_upper, 1, tmp_data, ldm, pipvt, Bz, b.rows (), err F77_CHAR_ARG_LEN (1))); // Count non-zeros 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 = 0; err = 0; #ifdef 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 (!xisnan (tmp)) Control (UMFPACK_PRL) = tmp; tmp = octave_sparse_params::get_key ("piv_tol"); if (!xisnan (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 (!xisnan (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, Ap, Ai, Ax, 1, control); void *Symbolic; Info = Matrix (1, UMFPACK_INFO); double *info = Info.fortran_vec (); int status = UMFPACK_DNAME (qsymbolic) (nr, nc, Ap, Ai, Ax, 0, &Symbolic, control, info); if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve symbolic factorization failed"); err = -1; UMFPACK_DNAME (report_status) (control, status); UMFPACK_DNAME (report_info) (control, info); UMFPACK_DNAME (free_symbolic) (&Symbolic) ; } else { UMFPACK_DNAME (report_symbolic) (Symbolic, control); status = UMFPACK_DNAME (numeric) (Ap, 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 || xisnan (rcond)) { UMFPACK_DNAME (report_numeric) (Numeric, control); err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } else if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve numeric factorization failed"); UMFPACK_DNAME (report_status) (control, status); UMFPACK_DNAME (report_info) (control, info); err = -1; } else { UMFPACK_DNAME (report_numeric) (Numeric, control); } } if (err != 0) UMFPACK_DNAME (free_numeric) (&Numeric); #else (*current_liboctave_error_handler) ("UMFPACK not installed"); #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"); else 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) { #ifdef 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; cm->print_function = 0; } else { cm->print = static_cast<int> (spu) + 2; cm->print_function =&SparseCholPrint; } cm->error_handler = &SparseCholError; cm->complex_divide = CHOLMOD_NAME(divcomplex); cm->hypotenuse = CHOLMOD_NAME(hypot); cm->final_ll = true; cholmod_sparse Astore; cholmod_sparse *A = &Astore; double dummy; A->nrow = nr; A->ncol = nc; A->p = cidx(); A->i = ridx(); A->nzmax = nnz(); A->packed = true; A->sorted = true; A->nz = 0; #ifdef IDX_TYPE_LONG A->itype = CHOLMOD_LONG; #else A->itype = CHOLMOD_INT; #endif A->dtype = CHOLMOD_DOUBLE; A->stype = 1; A->xtype = CHOLMOD_REAL; if (nr < 1) A->x = &dummy; else 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; if (nc < 1 || b.cols() < 1) B->x = &dummy; else // We won't alter it, honest :-) B->x = const_cast<double *>(b.fortran_vec()); cholmod_factor *L; BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; 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; END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; 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 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); return retval; } cholmod_dense *X; BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; X = CHOLMOD_NAME(solve) (CHOLMOD_A, L, B, cm); END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; 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]; } BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; CHOLMOD_NAME(free_dense) (&X, cm); CHOLMOD_NAME(free_factor) (&L, cm); CHOLMOD_NAME(finish) (cm); static char tmp[] = " "; CHOLMOD_NAME(print_common) (tmp, cm); END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; } #else (*current_liboctave_warning_handler) ("CHOLMOD not installed"); mattype.mark_as_unsymmetric (); typ = MatrixType::Full; #endif } if (typ == MatrixType::Full) { #ifdef HAVE_UMFPACK Matrix Control, Info; void *Numeric = factorize (err, rcond, Control, Info, sing_handler, calc_cond); if (err == 0) { const double *Bx = b.fortran_vec (); 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, Ap, Ai, Ax, &result[iidx], &Bx[iidx], Numeric, control, info); if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); UMFPACK_DNAME (report_status) (control, status); err = -1; break; } } UMFPACK_DNAME (report_info) (control, info); UMFPACK_DNAME (free_numeric) (&Numeric); } else mattype.mark_as_rectangular (); #else (*current_liboctave_error_handler) ("UMFPACK not installed"); #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"); else 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) { #ifdef 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; cm->print_function = 0; } else { cm->print = static_cast<int> (spu) + 2; cm->print_function =&SparseCholPrint; } cm->error_handler = &SparseCholError; cm->complex_divide = CHOLMOD_NAME(divcomplex); cm->hypotenuse = CHOLMOD_NAME(hypot); cm->final_ll = true; cholmod_sparse Astore; cholmod_sparse *A = &Astore; double dummy; A->nrow = nr; A->ncol = nc; A->p = cidx(); A->i = ridx(); A->nzmax = nnz(); A->packed = true; A->sorted = true; A->nz = 0; #ifdef IDX_TYPE_LONG A->itype = CHOLMOD_LONG; #else A->itype = CHOLMOD_INT; #endif A->dtype = CHOLMOD_DOUBLE; A->stype = 1; A->xtype = CHOLMOD_REAL; if (nr < 1) A->x = &dummy; else 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 = 0; #ifdef IDX_TYPE_LONG B->itype = CHOLMOD_LONG; #else B->itype = CHOLMOD_INT; #endif B->dtype = CHOLMOD_DOUBLE; B->stype = 0; B->xtype = CHOLMOD_REAL; if (b.rows() < 1 || b.cols() < 1) B->x = &dummy; else B->x = b.data(); cholmod_factor *L; BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; L = CHOLMOD_NAME(analyze) (A, cm); CHOLMOD_NAME(factorize) (A, L, cm); if (calc_cond) rcond = CHOLMOD_NAME(rcond)(L, cm); else rcond = 1.; END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; 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 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); return retval; } cholmod_sparse *X; BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; X = CHOLMOD_NAME(spsolve) (CHOLMOD_A, L, B, cm); END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; 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]; } BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; CHOLMOD_NAME(free_sparse) (&X, cm); CHOLMOD_NAME(free_factor) (&L, cm); CHOLMOD_NAME(finish) (cm); static char tmp[] = " "; CHOLMOD_NAME(print_common) (tmp, cm); END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; } #else (*current_liboctave_warning_handler) ("CHOLMOD not installed"); mattype.mark_as_unsymmetric (); typ = MatrixType::Full; #endif } if (typ == MatrixType::Full) { #ifdef HAVE_UMFPACK Matrix Control, Info; void *Numeric = factorize (err, rcond, Control, Info, sing_handler, calc_cond); if (err == 0) { 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 non-zero 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, Ap, Ai, Ax, Xx, Bx, Numeric, control, info); if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); UMFPACK_DNAME (report_status) (control, status); 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 = x_nz * (b_nc - j) / b_nc; sz = (sz > 10 ? sz : 10) + x_nz; 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 (*current_liboctave_error_handler) ("UMFPACK not installed"); #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"); else 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) { #ifdef 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; cm->print_function = 0; } else { cm->print = static_cast<int> (spu) + 2; cm->print_function =&SparseCholPrint; } cm->error_handler = &SparseCholError; cm->complex_divide = CHOLMOD_NAME(divcomplex); cm->hypotenuse = CHOLMOD_NAME(hypot); cm->final_ll = true; cholmod_sparse Astore; cholmod_sparse *A = &Astore; double dummy; A->nrow = nr; A->ncol = nc; A->p = cidx(); A->i = ridx(); A->nzmax = nnz(); A->packed = true; A->sorted = true; A->nz = 0; #ifdef IDX_TYPE_LONG A->itype = CHOLMOD_LONG; #else A->itype = CHOLMOD_INT; #endif A->dtype = CHOLMOD_DOUBLE; A->stype = 1; A->xtype = CHOLMOD_REAL; if (nr < 1) A->x = &dummy; else 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; if (nc < 1 || b.cols() < 1) B->x = &dummy; else // We won't alter it, honest :-) B->x = const_cast<Complex *>(b.fortran_vec()); cholmod_factor *L; BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; 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; END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; 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 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); return retval; } cholmod_dense *X; BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; X = CHOLMOD_NAME(solve) (CHOLMOD_A, L, B, cm); END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; 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]; } BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; CHOLMOD_NAME(free_dense) (&X, cm); CHOLMOD_NAME(free_factor) (&L, cm); CHOLMOD_NAME(finish) (cm); static char tmp[] = " "; CHOLMOD_NAME(print_common) (tmp, cm); END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; } #else (*current_liboctave_warning_handler) ("CHOLMOD not installed"); mattype.mark_as_unsymmetric (); typ = MatrixType::Full; #endif } if (typ == MatrixType::Full) { #ifdef HAVE_UMFPACK Matrix Control, Info; void *Numeric = factorize (err, rcond, Control, Info, sing_handler, calc_cond); if (err == 0) { 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] = std::real (c); Bz[i] = std::imag (c); } status = UMFPACK_DNAME (solve) (UMFPACK_A, Ap, Ai, Ax, Xx, Bx, Numeric, control, info); int status2 = UMFPACK_DNAME (solve) (UMFPACK_A, Ap, Ai, Ax, Xz, Bz, Numeric, control, info) ; if (status < 0 || status2 < 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); UMFPACK_DNAME (report_status) (control, status); 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 (*current_liboctave_error_handler) ("UMFPACK not installed"); #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"); else 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) { #ifdef 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; cm->print_function = 0; } else { cm->print = static_cast<int> (spu) + 2; cm->print_function =&SparseCholPrint; } cm->error_handler = &SparseCholError; cm->complex_divide = CHOLMOD_NAME(divcomplex); cm->hypotenuse = CHOLMOD_NAME(hypot); cm->final_ll = true; cholmod_sparse Astore; cholmod_sparse *A = &Astore; double dummy; A->nrow = nr; A->ncol = nc; A->p = cidx(); A->i = ridx(); A->nzmax = nnz(); A->packed = true; A->sorted = true; A->nz = 0; #ifdef IDX_TYPE_LONG A->itype = CHOLMOD_LONG; #else A->itype = CHOLMOD_INT; #endif A->dtype = CHOLMOD_DOUBLE; A->stype = 1; A->xtype = CHOLMOD_REAL; if (nr < 1) A->x = &dummy; else 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 = 0; #ifdef IDX_TYPE_LONG B->itype = CHOLMOD_LONG; #else B->itype = CHOLMOD_INT; #endif B->dtype = CHOLMOD_DOUBLE; B->stype = 0; B->xtype = CHOLMOD_COMPLEX; if (b.rows() < 1 || b.cols() < 1) B->x = &dummy; else B->x = b.data(); cholmod_factor *L; BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; 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; END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; 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 || xisnan (rcond)) { err = -2; if (sing_handler) { sing_handler (rcond); mattype.mark_as_rectangular (); } else (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); return retval; } cholmod_sparse *X; BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; X = CHOLMOD_NAME(spsolve) (CHOLMOD_A, L, B, cm); END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; 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]; } BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; CHOLMOD_NAME(free_sparse) (&X, cm); CHOLMOD_NAME(free_factor) (&L, cm); CHOLMOD_NAME(finish) (cm); static char tmp[] = " "; CHOLMOD_NAME(print_common) (tmp, cm); END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; } #else (*current_liboctave_warning_handler) ("CHOLMOD not installed"); mattype.mark_as_unsymmetric (); typ = MatrixType::Full; #endif } if (typ == MatrixType::Full) { #ifdef HAVE_UMFPACK Matrix Control, Info; void *Numeric = factorize (err, rcond, Control, Info, sing_handler, calc_cond); if (err == 0) { 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 non-zero 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] = std::real (c); Bz[i] = std::imag (c); } status = UMFPACK_DNAME (solve) (UMFPACK_A, Ap, Ai, Ax, Xx, Bx, Numeric, control, info); int status2 = UMFPACK_DNAME (solve) (UMFPACK_A, Ap, Ai, Ax, Xz, Bz, Numeric, control, info) ; if (status < 0 || status2 < 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); UMFPACK_DNAME (report_status) (control, status); 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 = x_nz * (b_nc - j) / b_nc; sz = (sz > 10 ? sz : 10) + x_nz; 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 (*current_liboctave_error_handler) ("UMFPACK not installed"); #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, 0); } Matrix SparseMatrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info) const { double rcond; return solve (mattype, b, info, rcond, 0); } Matrix SparseMatrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, double& rcond) const { return solve (mattype, b, info, rcond, 0); } 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"); return Matrix (); } // Rectangular or one of the above solvers flags a singular matrix if (singular_fallback && mattype.type (false) == MatrixType::Rectangular) { rcond = 1.; #ifdef 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, 0); } SparseMatrix SparseMatrix::solve (MatrixType &mattype, const SparseMatrix& b, octave_idx_type& info) const { double rcond; return solve (mattype, b, info, rcond, 0); } SparseMatrix SparseMatrix::solve (MatrixType &mattype, const SparseMatrix& b, octave_idx_type& info, double& rcond) const { return solve (mattype, b, info, rcond, 0); } 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"); return SparseMatrix (); } if (singular_fallback && mattype.type (false) == MatrixType::Rectangular) { rcond = 1.; #ifdef 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, 0); } ComplexMatrix SparseMatrix::solve (MatrixType &mattype, const ComplexMatrix& b, octave_idx_type& info) const { double rcond; return solve (mattype, b, info, rcond, 0); } ComplexMatrix SparseMatrix::solve (MatrixType &mattype, const ComplexMatrix& b, octave_idx_type& info, double& rcond) const { return solve (mattype, b, info, rcond, 0); } 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"); return ComplexMatrix (); } if (singular_fallback && mattype.type(false) == MatrixType::Rectangular) { rcond = 1.; #ifdef 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, 0); } SparseComplexMatrix SparseMatrix::solve (MatrixType &mattype, const SparseComplexMatrix& b, octave_idx_type& info) const { double rcond; return solve (mattype, b, info, rcond, 0); } SparseComplexMatrix SparseMatrix::solve (MatrixType &mattype, const SparseComplexMatrix& b, octave_idx_type& info, double& rcond) const { return solve (mattype, b, info, rcond, 0); } 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"); return SparseComplexMatrix (); } if (singular_fallback && mattype.type(false) == MatrixType::Rectangular) { rcond = 1.; #ifdef 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, 0); } 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, 0); } ComplexColumnVector SparseMatrix::solve (MatrixType &mattype, const ComplexColumnVector& b, octave_idx_type& info) const { double rcond; return solve (mattype, b, info, rcond, 0); } ComplexColumnVector SparseMatrix::solve (MatrixType &mattype, const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const { return solve (mattype, b, info, rcond, 0); } 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, 0); } Matrix SparseMatrix::solve (const Matrix& b, octave_idx_type& info) const { double rcond; return solve (b, info, rcond, 0); } Matrix SparseMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, 0); } 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, 0); } SparseMatrix SparseMatrix::solve (const SparseMatrix& b, octave_idx_type& info) const { double rcond; return solve (b, info, rcond, 0); } SparseMatrix SparseMatrix::solve (const SparseMatrix& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, 0); } 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, 0); } ComplexMatrix SparseMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, 0); } 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, 0); } SparseComplexMatrix SparseMatrix::solve (const SparseComplexMatrix& b, octave_idx_type& info) const { double rcond; return solve (b, info, rcond, 0); } SparseComplexMatrix SparseMatrix::solve (const SparseComplexMatrix& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, 0); } 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, 0); } 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, 0); } ComplexColumnVector SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const { double rcond; return solve (b, info, rcond, 0); } ComplexColumnVector SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, 0); } 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 (xisnan (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 (xisinf (val) || xisnan (val)) 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 (xisnan (val) || D_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 (D_NINT (val) != val) return false; } return true; } bool SparseMatrix::too_large_for_float (void) const { octave_idx_type nel = nnz (); for (octave_idx_type i = 0; i < nel; i++) { double val = data (i); if (val > FLT_MAX || val < FLT_MIN) return true; } return false; } SparseBoolMatrix SparseMatrix::operator ! (void) const { 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) < nc ? 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 { octave_idx_type nr = rows (); octave_idx_type nc = cols (); Matrix retval (nr, nc, 0.0); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = cidx(j); i < cidx(j+1); i++) retval.elem (ridx(i), j) = data (i); return retval; } SparseMatrix SparseMatrix::map (dmapper fcn) const { return MSparse<double>::map<double> (func_ptr (fcn)); } SparseComplexMatrix SparseMatrix::map (cmapper fcn) const { return MSparse<double>::map<Complex> (func_ptr (fcn)); } SparseBoolMatrix SparseMatrix::map (bmapper fcn) const { return MSparse<double>::map<bool> (func_ptr (fcn)); } 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_double (os, a.data(i)); os << "\n"; } } return os; } std::istream& operator >> (std::istream& is, SparseMatrix& a) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); octave_idx_type nz = a.nzmax (); if (nr < 1 || nc < 1) is.clear (std::ios::badbit); else { octave_idx_type itmp, jtmp, jold = 0; double tmp; octave_idx_type ii = 0; a.cidx (0) = 0; for (octave_idx_type i = 0; i < nz; i++) { is >> itmp; itmp--; is >> jtmp; jtmp--; tmp = octave_read_double (is); if (is) { if (jold != jtmp) { for (octave_idx_type j = jold; j < jtmp; j++) a.cidx(j+1) = ii; jold = jtmp; } a.data (ii) = tmp; a.ridx (ii++) = itmp; } else goto done; } for (octave_idx_type j = jold; j < nc; j++) a.cidx(j+1) = ii; } done: return is; } SparseMatrix SparseMatrix::squeeze (void) const { return MSparse<double>::squeeze (); } SparseMatrix SparseMatrix::index (idx_vector& i, int resize_ok) const { return MSparse<double>::index (i, resize_ok); } SparseMatrix SparseMatrix::index (idx_vector& i, idx_vector& j, int resize_ok) const { return MSparse<double>::index (i, j, resize_ok); } SparseMatrix SparseMatrix::index (Array<idx_vector>& ra_idx, int resize_ok) const { return MSparse<double>::index (ra_idx, resize_ok); } 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, 0.); } Matrix mul_trans (const Matrix& m, const SparseMatrix& a) { FULL_SPARSE_MUL_TRANS (Matrix, double, 0., ); } Matrix operator * (const SparseMatrix& m, const Matrix& a) { SPARSE_FULL_MUL (Matrix, double, 0.); } Matrix trans_mul (const SparseMatrix& m, const Matrix& a) { SPARSE_FULL_TRANS_MUL (Matrix, double, 0., ); } // 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 non-zero 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 = xmin (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 (xmin (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 = xmin (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; if ((a.rows() == b.rows()) && (a.cols() == b.cols())) { 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) gripe_nonconformant ("min", a_nr, a_nc, b_nr, b_nc); else { 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 = xmin (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 = xmin (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 = xmin (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 (*current_liboctave_error_handler) ("matrix size mismatch"); 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 non-zero 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 = xmax (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 (xmax (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 = xmax (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; if ((a.rows() == b.rows()) && (a.cols() == b.cols())) { 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) gripe_nonconformant ("min", a_nr, a_nc, b_nr, b_nc); else { 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 = xmax (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 = xmax (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 = xmax (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 (*current_liboctave_error_handler) ("matrix size mismatch"); return r; } SPARSE_SMS_CMP_OPS (SparseMatrix, 0.0, , double, 0.0, ) SPARSE_SMS_BOOL_OPS (SparseMatrix, double, 0.0) SPARSE_SSM_CMP_OPS (double, 0.0, , SparseMatrix, 0.0, ) SPARSE_SSM_BOOL_OPS (double, SparseMatrix, 0.0) SPARSE_SMSM_CMP_OPS (SparseMatrix, 0.0, , SparseMatrix, 0.0, ) SPARSE_SMSM_BOOL_OPS (SparseMatrix, SparseMatrix, 0.0) /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */