Mercurial > octave-nkf
view liboctave/dSparse.cc @ 5261:90a9058de7e8
[project @ 2005-03-31 02:48:38 by jwe]
| author | jwe |
|---|---|
| date | Thu, 31 Mar 2005 02:48:39 +0000 |
| parents | dbeafbc0ff64 |
| children | 23b37da9fd5b |
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/* Copyright (C) 2004 David Bateman Copyright (C) 1998-2004 Andy Adler 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 2, 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 this program; see the file COPYING. If not, write to the Free Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ #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 "CSparse.h" #include "boolSparse.h" #include "dSparse.h" #include "oct-spparms.h" #include "SparsedbleLU.h" #include "SparseType.h" #ifdef HAVE_UMFPACK // External UMFPACK functions in C extern "C" { #include <umfpack/umfpack.h> } #endif // Fortran functions we call. extern "C" { F77_RET_T F77_FUNC (dgbtrf, DGBTRF) (const int&, const int&, const int&, const int&, double*, const int&, int*, int&); F77_RET_T F77_FUNC (dgbtrs, DGBTRS) (F77_CONST_CHAR_ARG_DECL, const int&, const int&, const int&, const int&, const double*, const int&, const int*, double*, const int&, int& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dgbcon, DGBCON) (F77_CONST_CHAR_ARG_DECL, const int&, const int&, const int&, double*, const int&, const int*, const double&, double&, double*, int*, int& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dpbtrf, DPBTRF) (F77_CONST_CHAR_ARG_DECL, const int&, const int&, double*, const int&, int& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dpbtrs, DPBTRS) (F77_CONST_CHAR_ARG_DECL, const int&, const int&, const int&, double*, const int&, double*, const int&, int& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dpbcon, DPBCON) (F77_CONST_CHAR_ARG_DECL, const int&, const int&, double*, const int&, const double&, double&, double*, int*, int& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dptsv, DPTSV) (const int&, const int&, double*, double*, double*, const int&, int&); F77_RET_T F77_FUNC (dgtsv, DGTSV) (const int&, const int&, double*, double*, double*, double*, const int&, int&); F77_RET_T F77_FUNC (dgttrf, DGTTRF) (const int&, double*, double*, double*, double*, int*, int&); F77_RET_T F77_FUNC (dgttrs, DGTTRS) (F77_CONST_CHAR_ARG_DECL, const int&, const int&, const double*, const double*, const double*, const double*, const int*, double *, const int&, int& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zptsv, ZPTSV) (const int&, const int&, Complex*, Complex*, Complex*, const int&, int&); F77_RET_T F77_FUNC (zgtsv, ZGTSV) (const int&, const int&, Complex*, Complex*, Complex*, Complex*, const int&, int&); } SparseMatrix::SparseMatrix (const SparseBoolMatrix &a) : MSparse<double> (a.rows (), a.cols (), a.nnz ()) { int nc = cols (); int nz = nnz (); for (int i = 0; i < nc + 1; i++) cidx (i) = a.cidx (i); for (int i = 0; i < nz; i++) { data (i) = a.data (i); ridx (i) = a.ridx (i); } } bool SparseMatrix::operator == (const SparseMatrix& a) const { int nr = rows (); int nc = cols (); int nz = nnz (); int nr_a = a.rows (); int nc_a = a.cols (); int nz_a = a.nnz (); if (nr != nr_a || nc != nc_a || nz != nz_a) return false; for (int i = 0; i < nc + 1; i++) if (cidx(i) != a.cidx(i)) return false; for (int 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 { if (is_square () && rows () > 0) { for (int i = 0; i < rows (); i++) for (int j = i+1; j < cols (); j++) if (elem (i, j) != elem (j, i)) return false; return true; } return false; } SparseMatrix& SparseMatrix::insert (const SparseMatrix& a, int r, int c) { MSparse<double>::insert (a, r, c); return *this; } SparseMatrix SparseMatrix::max (int dim) const { Array2<int> dummy_idx; return max (dummy_idx, dim); } SparseMatrix SparseMatrix::max (Array2<int>& idx_arg, int dim) const { SparseMatrix result; dim_vector dv = dims (); if (dv.numel () == 0 || dim > dv.length () || dim < 0) return result; int nr = dv(0); int nc = dv(1); if (dim == 0) { idx_arg.resize (1, nc); int nel = 0; for (int j = 0; j < nc; j++) { double tmp_max = octave_NaN; int idx_j = 0; for (int 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 (int i = cidx(j); i < cidx(j+1); i++) { double tmp = data (i); if (octave_is_NaN_or_NA (tmp)) continue; else if (octave_is_NaN_or_NA (tmp_max) || tmp > tmp_max) { idx_j = ridx (i); tmp_max = tmp; } } idx_arg.elem (j) = octave_is_NaN_or_NA (tmp_max) ? 0 : idx_j; if (tmp_max != 0.) nel++; } result = SparseMatrix (1, nc, nel); int ii = 0; result.xcidx (0) = 0; for (int 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 (int i = cidx(0); i < cidx(1); i++) idx_arg.elem(ridx(i)) = -1; for (int j = 0; j < nc; j++) for (int i = 0; i < nr; i++) { if (idx_arg.elem(i) != -1) continue; bool found = false; for (int k = cidx(j); k < cidx(j+1); k++) if (ridx(k) == i) { found = true; break; } if (!found) idx_arg.elem(i) = j; } for (int j = 0; j < nc; j++) { for (int i = cidx(j); i < cidx(j+1); i++) { int ir = ridx (i); int ix = idx_arg.elem (ir); double tmp = data (i); if (octave_is_NaN_or_NA (tmp)) continue; else if (ix == -1 || tmp > elem (ir, ix)) idx_arg.elem (ir) = j; } } int nel = 0; for (int j = 0; j < nr; j++) if (idx_arg.elem(j) == -1 || elem (j, idx_arg.elem (j)) != 0.) nel++; result = SparseMatrix (nr, 1, nel); int ii = 0; result.xcidx (0) = 0; result.xcidx (1) = nel; for (int 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<int> dummy_idx; return min (dummy_idx, dim); } SparseMatrix SparseMatrix::min (Array2<int>& idx_arg, int dim) const { SparseMatrix result; dim_vector dv = dims (); if (dv.numel () == 0 || dim > dv.length () || dim < 0) return result; int nr = dv(0); int nc = dv(1); if (dim == 0) { idx_arg.resize (1, nc); int nel = 0; for (int j = 0; j < nc; j++) { double tmp_min = octave_NaN; int idx_j = 0; for (int 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 (int i = cidx(j); i < cidx(j+1); i++) { double tmp = data (i); if (octave_is_NaN_or_NA (tmp)) continue; else if (octave_is_NaN_or_NA (tmp_min) || tmp < tmp_min) { idx_j = ridx (i); tmp_min = tmp; } } idx_arg.elem (j) = octave_is_NaN_or_NA (tmp_min) ? 0 : idx_j; if (tmp_min != 0.) nel++; } result = SparseMatrix (1, nc, nel); int ii = 0; result.xcidx (0) = 0; for (int 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 (int i = cidx(0); i < cidx(1); i++) idx_arg.elem(ridx(i)) = -1; for (int j = 0; j < nc; j++) for (int i = 0; i < nr; i++) { if (idx_arg.elem(i) != -1) continue; bool found = false; for (int k = cidx(j); k < cidx(j+1); k++) if (ridx(k) == i) { found = true; break; } if (!found) idx_arg.elem(i) = j; } for (int j = 0; j < nc; j++) { for (int i = cidx(j); i < cidx(j+1); i++) { int ir = ridx (i); int ix = idx_arg.elem (ir); double tmp = data (i); if (octave_is_NaN_or_NA (tmp)) continue; else if (ix == -1 || tmp < elem (ir, ix)) idx_arg.elem (ir) = j; } } int nel = 0; for (int j = 0; j < nr; j++) if (idx_arg.elem(j) == -1 || elem (j, idx_arg.elem (j)) != 0.) nel++; result = SparseMatrix (nr, 1, nel); int ii = 0; result.xcidx (0) = 0; result.xcidx (1) = nel; for (int 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::concat (const SparseMatrix& rb, const Array<int>& 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<int>& 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) { int nr = a.rows (); int nc = a.cols (); int nz = a.nnz (); SparseMatrix r (nr, nc, nz); for (int i = 0; i < nc +1; i++) r.cidx(i) = a.cidx(i); for (int 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) { int nr = a.rows (); int nc = a.cols (); int nz = a.nnz (); SparseMatrix r (nr, nc, nz); for (int i = 0; i < nc +1; i++) r.cidx(i) = a.cidx(i); for (int 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) { int nr = y.rows (); int 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 (int j = 0; j < nc; j++) for (int 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) { int nr = x.rows (); int nc = x.cols (); int nz = x.nnz (); SparseMatrix retval (nr, nc, nz); int ii = 0; retval.xcidx(0) = 0; for (int i = 0; i < nc; i++) { for (int 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 (int i = 0; i < nc+1; i++) retval2.xcidx (i) = retval.cidx (i); for (int 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())) { int x_nr = x.rows (); int x_nc = x.cols (); int y_nr = y.rows (); int 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 ())); int jx = 0; r.cidx (0) = 0; for (int i = 0 ; i < x_nc ; i++) { int ja = x.cidx(i); int ja_max = x.cidx(i+1); bool ja_lt_max= ja < ja_max; int jb = y.cidx(i); int 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 { int info; double rcond; return inverse (info, rcond, 0, 0); } SparseMatrix SparseMatrix::inverse (int& info) const { double rcond; return inverse (info, rcond, 0, 0); } SparseMatrix SparseMatrix::inverse (int& info, double& rcond, int force, int calc_cond) const { info = -1; (*current_liboctave_error_handler) ("SparseMatrix::inverse not implemented yet"); return SparseMatrix (); } DET SparseMatrix::determinant (void) const { int info; double rcond; return determinant (info, rcond, 0); } DET SparseMatrix::determinant (int& info) const { double rcond; return determinant (info, rcond, 0); } DET SparseMatrix::determinant (int& err, double& rcond, int) const { DET retval; #ifdef HAVE_UMFPACK int nr = rows (); int nc = cols (); if (nr == 0 || nc == 0 || nr != nc) { double d[2]; d[0] = 1.0; d[1] = 0.0; retval = DET (d); } else { err = 0; // Setup the control parameters Matrix Control (UMFPACK_CONTROL, 1); double *control = Control.fortran_vec (); umfpack_di_defaults (control); double tmp = Voctave_sparse_controls.get_key ("spumoni"); if (!xisnan (tmp)) Control (UMFPACK_PRL) = tmp; tmp = Voctave_sparse_controls.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 = Voctave_sparse_controls.get_key ("autoamd"); if (!xisnan (tmp)) Control (UMFPACK_FIXQ) = tmp; // Turn-off UMFPACK scaling for LU Control (UMFPACK_SCALE) = UMFPACK_SCALE_NONE; umfpack_di_report_control (control); const int *Ap = cidx (); const int *Ai = ridx (); const double *Ax = data (); umfpack_di_report_matrix (nr, nc, Ap, Ai, Ax, 1, control); void *Symbolic; Matrix Info (1, UMFPACK_INFO); double *info = Info.fortran_vec (); int status = umfpack_di_qsymbolic (nr, nc, Ap, Ai, Ax, NULL, &Symbolic, control, info); if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::determinant symbolic factorization failed"); umfpack_di_report_status (control, status); umfpack_di_report_info (control, info); umfpack_di_free_symbolic (&Symbolic) ; } else { umfpack_di_report_symbolic (Symbolic, control); void *Numeric; status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, control, info) ; umfpack_di_free_symbolic (&Symbolic) ; rcond = Info (UMFPACK_RCOND); if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::determinant numeric factorization failed"); umfpack_di_report_status (control, status); umfpack_di_report_info (control, info); umfpack_di_free_numeric (&Numeric); } else { umfpack_di_report_numeric (Numeric, control); double d[2]; status = umfpack_di_get_determinant (&d[0], &d[1], Numeric, info); if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::determinant error calculating determinant"); umfpack_di_report_status (control, status); umfpack_di_report_info (control, info); umfpack_di_free_numeric (&Numeric); } else retval = DET (d); } } } #else (*current_liboctave_error_handler) ("UMFPACK not installed"); #endif return retval; } Matrix SparseMatrix::dsolve (SparseType &mattype, const Matrix& b, int& err, double& rcond, solve_singularity_handler) const { Matrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Diagonal || typ == SparseType::Permuted_Diagonal) { retval.resize (b.rows (), b.cols()); if (typ == SparseType::Diagonal) for (int j = 0; j < b.cols(); j++) for (int i = 0; i < nr; i++) retval(i,j) = b(i,j) / data (i); else for (int j = 0; j < b.cols(); j++) for (int i = 0; i < nr; i++) retval(i,j) = b(ridx(i),j) / data (i); double dmax = 0., dmin = octave_Inf; for (int i = 0; i < nr; i++) { double tmp = fabs(data(i)); if (tmp > dmax) dmax = tmp; if (tmp < dmin) dmin = tmp; } rcond = dmin / dmax; } else (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseMatrix SparseMatrix::dsolve (SparseType &mattype, const SparseMatrix& b, int& err, double& rcond, solve_singularity_handler) const { SparseMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Diagonal || typ == SparseType::Permuted_Diagonal) { int b_nr = b.rows (); int b_nc = b.cols (); int b_nz = b.nnz (); retval = SparseMatrix (b_nr, b_nc, b_nz); retval.xcidx(0) = 0; int ii = 0; if (typ == SparseType::Diagonal) for (int j = 0; j < b.cols(); j++) { for (int i = b.cidx(j); i < b.cidx(j+1); i++) { retval.xridx (ii) = b.ridx(i); retval.xdata (ii++) = b.data(i) / data (b.ridx (i)); } retval.xcidx(j+1) = ii; } else for (int j = 0; j < b.cols(); j++) { for (int i = 0; i < nr; i++) { bool found = false; int 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) = i; retval.xdata (ii++) = b.data(k) / data (i); } } retval.xcidx(j+1) = ii; } double dmax = 0., dmin = octave_Inf; for (int i = 0; i < nr; i++) { double tmp = fabs(data(i)); if (tmp > dmax) dmax = tmp; if (tmp < dmin) dmin = tmp; } rcond = dmin / dmax; } else (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } ComplexMatrix SparseMatrix::dsolve (SparseType &mattype, const ComplexMatrix& b, int& err, double& rcond, solve_singularity_handler) const { ComplexMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Diagonal || typ == SparseType::Permuted_Diagonal) { retval.resize (b.rows (), b.cols()); if (typ == SparseType::Diagonal) for (int j = 0; j < b.cols(); j++) for (int i = 0; i < nr; i++) retval(i,j) = b(i,j) / data (i); else for (int j = 0; j < b.cols(); j++) for (int i = 0; i < nr; i++) retval(i,j) = b(ridx(i),j) / data (i); double dmax = 0., dmin = octave_Inf; for (int i = 0; i < nr; i++) { double tmp = fabs(data(i)); if (tmp > dmax) dmax = tmp; if (tmp < dmin) dmin = tmp; } rcond = dmin / dmax; } else (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseComplexMatrix SparseMatrix::dsolve (SparseType &mattype, const SparseComplexMatrix& b, int& err, double& rcond, solve_singularity_handler) const { SparseComplexMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Diagonal || typ == SparseType::Permuted_Diagonal) { int b_nr = b.rows (); int b_nc = b.cols (); int b_nz = b.nnz (); retval = SparseComplexMatrix (b_nr, b_nc, b_nz); retval.xcidx(0) = 0; int ii = 0; if (typ == SparseType::Diagonal) for (int j = 0; j < b.cols(); j++) { for (int i = b.cidx(j); i < b.cidx(j+1); i++) { retval.xridx (ii) = b.ridx(i); retval.xdata (ii++) = b.data(i) / data (b.ridx (i)); } retval.xcidx(j+1) = ii; } else for (int j = 0; j < b.cols(); j++) { for (int i = 0; i < nr; i++) { bool found = false; int 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) = i; retval.xdata (ii++) = b.data(k) / data (i); } } retval.xcidx(j+1) = ii; } double dmax = 0., dmin = octave_Inf; for (int i = 0; i < nr; i++) { double tmp = fabs(data(i)); if (tmp > dmax) dmax = tmp; if (tmp < dmin) dmin = tmp; } rcond = dmin / dmax; } else (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } Matrix SparseMatrix::utsolve (SparseType &mattype, const Matrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { Matrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Permuted_Upper || typ == SparseType::Upper) { double anorm = 0.; double ainvnorm = 0.; int b_cols = b.cols (); rcond = 0.; // Calculate the 1-norm of matrix for rcond calculation for (int j = 0; j < nr; j++) { double atmp = 0.; for (int i = cidx(j); i < cidx(j+1); i++) atmp += fabs(data(i)); if (atmp > anorm) anorm = atmp; } if (typ == SparseType::Permuted_Upper) { retval.resize (b.rows (), b.cols ()); OCTAVE_LOCAL_BUFFER (double, work, nr); int *p_perm = mattype.triangular_row_perm (); int *q_perm = mattype.triangular_col_perm (); (*current_liboctave_warning_handler) ("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested"); for (int j = 0; j < b_cols; j++) { for (int i = 0; i < nr; i++) work[i] = b(i,j); for (int k = nr-1; k >= 0; k--) { int iidx = q_perm[k]; if (work[iidx] != 0.) { if (ridx(cidx(iidx+1)-1) != iidx) { err = -2; goto triangular_error; } double tmp = work[iidx] / data(cidx(iidx+1)-1); work[iidx] = tmp; for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++) { int idx2 = q_perm[ridx(i)]; work[idx2] = work[idx2] - tmp * data(i); } } } for (int i = 0; i < nr; i++) retval (i, j) = work[p_perm[i]]; } // Calculation of 1-norm of inv(*this) for (int i = 0; i < nr; i++) work[i] = 0.; for (int j = 0; j < nr; j++) { work[q_perm[j]] = 1.; for (int k = j; k >= 0; k--) { int iidx = q_perm[k]; if (work[iidx] != 0.) { double tmp = work[iidx] / data(cidx(iidx+1)-1); work[iidx] = tmp; for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++) { int idx2 = q_perm[ridx(i)]; work[idx2] = work[idx2] - tmp * data(i); } } } double atmp = 0; for (int i = 0; i < j+1; i++) { atmp += fabs(work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } } else { retval = b; double *x_vec = retval.fortran_vec (); for (int j = 0; j < b_cols; j++) { int offset = j * nr; for (int k = nr-1; k >= 0; k--) { if (x_vec[k+offset] != 0.) { if (ridx(cidx(k+1)-1) != k) { err = -2; goto triangular_error; } double tmp = x_vec[k+offset] / data(cidx(k+1)-1); x_vec[k+offset] = tmp; for (int i = cidx(k); i < cidx(k+1)-1; i++) { int iidx = ridx(i); x_vec[iidx+offset] = x_vec[iidx+offset] - tmp * data(i); } } } } // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work, nr); for (int i = 0; i < nr; i++) work[i] = 0.; for (int j = 0; j < nr; j++) { work[j] = 1.; for (int k = j; k >= 0; k--) { if (work[k] != 0.) { double tmp = work[k] / data(cidx(k+1)-1); work[k] = tmp; for (int i = cidx(k); i < cidx(k+1)-1; i++) { int iidx = ridx(i); work[iidx] = work[iidx] - tmp * data(i); } } } double atmp = 0; for (int 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); 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); 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 (SparseType &mattype, const SparseMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Permuted_Upper || typ == SparseType::Upper) { double anorm = 0.; double ainvnorm = 0.; rcond = 0.; // Calculate the 1-norm of matrix for rcond calculation for (int j = 0; j < nr; j++) { double atmp = 0.; for (int i = cidx(j); i < cidx(j+1); i++) atmp += fabs(data(i)); if (atmp > anorm) anorm = atmp; } int b_nr = b.rows (); int b_nc = b.cols (); int b_nz = b.nnz (); retval = SparseMatrix (b_nr, b_nc, b_nz); retval.xcidx(0) = 0; int ii = 0; int x_nz = b_nz; if (typ == SparseType::Permuted_Upper) { OCTAVE_LOCAL_BUFFER (double, work, nr); int *p_perm = mattype.triangular_row_perm (); int *q_perm = mattype.triangular_col_perm (); (*current_liboctave_warning_handler) ("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested"); for (int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) work[i] = 0.; for (int i = b.cidx(j); i < b.cidx(j+1); i++) work[b.ridx(i)] = b.data(i); for (int k = nr-1; k >= 0; k--) { int iidx = q_perm[k]; if (work[iidx] != 0.) { if (ridx(cidx(iidx+1)-1) != iidx) { err = -2; goto triangular_error; } double tmp = work[iidx] / data(cidx(iidx+1)-1); work[iidx] = tmp; for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++) { int idx2 = q_perm[ridx(i)]; work[idx2] = work[idx2] - tmp * data(i); } } } // Count non-zeros in work vector and adjust space in // retval if needed int new_nnz = 0; for (int i = 0; i < nr; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int i = 0; i < nr; i++) if (work[p_perm[i]] != 0.) { retval.xridx(ii) = i; retval.xdata(ii++) = work[p_perm[i]]; } retval.xcidx(j+1) = ii; } retval.maybe_compress (); // Calculation of 1-norm of inv(*this) for (int i = 0; i < nr; i++) work[i] = 0.; for (int j = 0; j < nr; j++) { work[q_perm[j]] = 1.; for (int k = j; k >= 0; k--) { int iidx = q_perm[k]; if (work[iidx] != 0.) { double tmp = work[iidx] / data(cidx(iidx+1)-1); work[iidx] = tmp; for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++) { int idx2 = q_perm[ridx(i)]; work[idx2] = work[idx2] - tmp * data(i); } } } double atmp = 0; for (int i = 0; i < j+1; i++) { atmp += fabs(work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } } else { OCTAVE_LOCAL_BUFFER (double, work, nr); for (int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) work[i] = 0.; for (int i = b.cidx(j); i < b.cidx(j+1); i++) work[b.ridx(i)] = b.data(i); for (int k = nr-1; k >= 0; k--) { if (work[k] != 0.) { if (ridx(cidx(k+1)-1) != k) { err = -2; goto triangular_error; } double tmp = work[k] / data(cidx(k+1)-1); work[k] = tmp; for (int i = cidx(k); i < cidx(k+1)-1; i++) { int iidx = ridx(i); work[iidx] = work[iidx] - tmp * data(i); } } } // Count non-zeros in work vector and adjust space in // retval if needed int new_nnz = 0; for (int i = 0; i < nr; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int 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 (); // Calculation of 1-norm of inv(*this) for (int i = 0; i < nr; i++) work[i] = 0.; for (int j = 0; j < nr; j++) { work[j] = 1.; for (int k = j; k >= 0; k--) { if (work[k] != 0.) { double tmp = work[k] / data(cidx(k+1)-1); work[k] = tmp; for (int i = cidx(k); i < cidx(k+1)-1; i++) { int iidx = ridx(i); work[iidx] = work[iidx] - tmp * data(i); } } } double atmp = 0; for (int 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); 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); 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 (SparseType &mattype, const ComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { ComplexMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Permuted_Upper || typ == SparseType::Upper) { double anorm = 0.; double ainvnorm = 0.; int b_nc = b.cols (); rcond = 0.; // Calculate the 1-norm of matrix for rcond calculation for (int j = 0; j < nr; j++) { double atmp = 0.; for (int i = cidx(j); i < cidx(j+1); i++) atmp += fabs(data(i)); if (atmp > anorm) anorm = atmp; } if (typ == SparseType::Permuted_Upper) { retval.resize (b.rows (), b.cols ()); OCTAVE_LOCAL_BUFFER (Complex, work, nr); int *p_perm = mattype.triangular_row_perm (); int *q_perm = mattype.triangular_col_perm (); (*current_liboctave_warning_handler) ("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested"); for (int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) work[i] = b(i,j); for (int k = nr-1; k >= 0; k--) { int iidx = q_perm[k]; if (work[iidx] != 0.) { if (ridx(cidx(iidx+1)-1) != iidx) { err = -2; goto triangular_error; } Complex tmp = work[iidx] / data(cidx(iidx+1)-1); work[iidx] = tmp; for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++) { int idx2 = q_perm[ridx(i)]; work[idx2] = work[idx2] - tmp * data(i); } } } for (int i = 0; i < nr; i++) retval (i, j) = work[p_perm[i]]; } // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work2, nr); for (int i = 0; i < nr; i++) work2[i] = 0.; for (int j = 0; j < nr; j++) { work2[q_perm[j]] = 1.; for (int k = j; k >= 0; k--) { int iidx = q_perm[k]; if (work2[iidx] != 0.) { double tmp = work2[iidx] / data(cidx(iidx+1)-1); work2[iidx] = tmp; for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++) { int idx2 = q_perm[ridx(i)]; work2[idx2] = work2[idx2] - tmp * data(i); } } } double atmp = 0; for (int i = 0; i < j+1; i++) { atmp += fabs(work2[i]); work2[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } } else { retval = b; Complex *x_vec = retval.fortran_vec (); for (int j = 0; j < b_nc; j++) { int offset = j * nr; for (int k = nr-1; k >= 0; k--) { if (x_vec[k+offset] != 0.) { if (ridx(cidx(k+1)-1) != k) { err = -2; goto triangular_error; } Complex tmp = x_vec[k+offset] / data(cidx(k+1)-1); x_vec[k+offset] = tmp; for (int i = cidx(k); i < cidx(k+1)-1; i++) { int iidx = ridx(i); x_vec[iidx+offset] = x_vec[iidx+offset] - tmp * data(i); } } } } // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work, nr); for (int i = 0; i < nr; i++) work[i] = 0.; for (int j = 0; j < nr; j++) { work[j] = 1.; for (int k = j; k >= 0; k--) { if (work[k] != 0.) { double tmp = work[k] / data(cidx(k+1)-1); work[k] = tmp; for (int i = cidx(k); i < cidx(k+1)-1; i++) { int iidx = ridx(i); work[iidx] = work[iidx] - tmp * data(i); } } } double atmp = 0; for (int 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); 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); 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 (SparseType &mattype, const SparseComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseComplexMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Permuted_Upper || typ == SparseType::Upper) { double anorm = 0.; double ainvnorm = 0.; rcond = 0.; // Calculate the 1-norm of matrix for rcond calculation for (int j = 0; j < nr; j++) { double atmp = 0.; for (int i = cidx(j); i < cidx(j+1); i++) atmp += fabs(data(i)); if (atmp > anorm) anorm = atmp; } int b_nr = b.rows (); int b_nc = b.cols (); int b_nz = b.nnz (); retval = SparseComplexMatrix (b_nr, b_nc, b_nz); retval.xcidx(0) = 0; int ii = 0; int x_nz = b_nz; if (typ == SparseType::Permuted_Upper) { OCTAVE_LOCAL_BUFFER (Complex, work, nr); int *p_perm = mattype.triangular_row_perm (); int *q_perm = mattype.triangular_col_perm (); (*current_liboctave_warning_handler) ("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested"); for (int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) work[i] = 0.; for (int i = b.cidx(j); i < b.cidx(j+1); i++) work[b.ridx(i)] = b.data(i); for (int k = nr-1; k >= 0; k--) { int iidx = q_perm[k]; if (work[iidx] != 0.) { if (ridx(cidx(iidx+1)-1) != iidx) { err = -2; goto triangular_error; } Complex tmp = work[iidx] / data(cidx(iidx+1)-1); work[iidx] = tmp; for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++) { int idx2 = q_perm[ridx(i)]; work[idx2] = work[idx2] - tmp * data(i); } } } // Count non-zeros in work vector and adjust space in // retval if needed int new_nnz = 0; for (int i = 0; i < nr; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int i = 0; i < nr; i++) if (work[p_perm[i]] != 0.) { retval.xridx(ii) = i; retval.xdata(ii++) = work[p_perm[i]]; } retval.xcidx(j+1) = ii; } retval.maybe_compress (); OCTAVE_LOCAL_BUFFER (double, work2, nr); // Calculation of 1-norm of inv(*this) for (int i = 0; i < nr; i++) work2[i] = 0.; for (int j = 0; j < nr; j++) { work2[q_perm[j]] = 1.; for (int k = j; k >= 0; k--) { int iidx = q_perm[k]; if (work2[iidx] != 0.) { double tmp = work2[iidx] / data(cidx(iidx+1)-1); work2[iidx] = tmp; for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++) { int idx2 = q_perm[ridx(i)]; work2[idx2] = work2[idx2] - tmp * data(i); } } } double atmp = 0; for (int i = 0; i < j+1; i++) { atmp += fabs(work2[i]); work2[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } } else { OCTAVE_LOCAL_BUFFER (Complex, work, nr); for (int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) work[i] = 0.; for (int i = b.cidx(j); i < b.cidx(j+1); i++) work[b.ridx(i)] = b.data(i); for (int k = nr-1; k >= 0; k--) { if (work[k] != 0.) { if (ridx(cidx(k+1)-1) != k) { err = -2; goto triangular_error; } Complex tmp = work[k] / data(cidx(k+1)-1); work[k] = tmp; for (int i = cidx(k); i < cidx(k+1)-1; i++) { int iidx = ridx(i); work[iidx] = work[iidx] - tmp * data(i); } } } // Count non-zeros in work vector and adjust space in // retval if needed int new_nnz = 0; for (int i = 0; i < nr; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int 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 (); // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work2, nr); for (int i = 0; i < nr; i++) work2[i] = 0.; for (int j = 0; j < nr; j++) { work2[j] = 1.; for (int k = j; k >= 0; k--) { if (work2[k] != 0.) { double tmp = work2[k] / data(cidx(k+1)-1); work2[k] = tmp; for (int i = cidx(k); i < cidx(k+1)-1; i++) { int iidx = ridx(i); work2[iidx] = work2[iidx] - tmp * data(i); } } } double atmp = 0; for (int i = 0; i < j+1; i++) { atmp += fabs(work2[i]); work2[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } } rcond = 1. / ainvnorm / anorm; triangular_error: if (err != 0) { if (sing_handler) sing_handler (rcond); 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); 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 (SparseType &mattype, const Matrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { Matrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Permuted_Lower || typ == SparseType::Lower) { double anorm = 0.; double ainvnorm = 0.; int b_cols = b.cols (); rcond = 0.; // Calculate the 1-norm of matrix for rcond calculation for (int j = 0; j < nr; j++) { double atmp = 0.; for (int i = cidx(j); i < cidx(j+1); i++) atmp += fabs(data(i)); if (atmp > anorm) anorm = atmp; } if (typ == SparseType::Permuted_Lower) { retval.resize (b.rows (), b.cols ()); OCTAVE_LOCAL_BUFFER (double, work, nr); int *p_perm = mattype.triangular_row_perm (); int *q_perm = mattype.triangular_col_perm (); (*current_liboctave_warning_handler) ("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested"); for (int j = 0; j < b_cols; j++) { for (int i = 0; i < nr; i++) work[i] = b(i,j); for (int k = 0; k < nr; k++) { int iidx = q_perm[k]; if (work[iidx] != 0.) { if (ridx(cidx(iidx)) != iidx) { err = -2; goto triangular_error; } double tmp = work[iidx] / data(cidx(iidx+1)-1); work[iidx] = tmp; for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++) { int idx2 = q_perm[ridx(i)]; work[idx2] = work[idx2] - tmp * data(i); } } } for (int i = 0; i < nr; i++) retval (i, j) = work[p_perm[i]]; } // Calculation of 1-norm of inv(*this) for (int i = 0; i < nr; i++) work[i] = 0.; for (int j = 0; j < nr; j++) { work[q_perm[j]] = 1.; for (int k = 0; k < nr; k++) { int iidx = q_perm[k]; if (work[iidx] != 0.) { double tmp = work[iidx] / data(cidx(iidx+1)-1); work[iidx] = tmp; for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++) { int idx2 = q_perm[ridx(i)]; work[idx2] = work[idx2] - tmp * data(i); } } } double atmp = 0; for (int i = 0; i < j+1; i++) { atmp += fabs(work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } } else { retval = b; double *x_vec = retval.fortran_vec (); for (int j = 0; j < b_cols; j++) { int offset = j * nr; for (int k = 0; k < nr; k++) { if (x_vec[k+offset] != 0.) { if (ridx(cidx(k)) != k) { err = -2; goto triangular_error; } double tmp = x_vec[k+offset] / data(cidx(k)); x_vec[k+offset] = tmp; for (int i = cidx(k)+1; i < cidx(k+1); i++) { int iidx = ridx(i); x_vec[iidx+offset] = x_vec[iidx+offset] - tmp * data(i); } } } } // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work, nr); for (int i = 0; i < nr; i++) work[i] = 0.; for (int j = 0; j < nr; j++) { work[j] = 1.; for (int k = j; k < nr; k++) { if (work[k] != 0.) { double tmp = work[k] / data(cidx(k)); work[k] = tmp; for (int i = cidx(k)+1; i < cidx(k+1); i++) { int iidx = ridx(i); work[iidx] = work[iidx] - tmp * data(i); } } } double atmp = 0; for (int i = j; i < nr; 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); 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); 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 (SparseType &mattype, const SparseMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Permuted_Lower || typ == SparseType::Lower) { double anorm = 0.; double ainvnorm = 0.; rcond = 0.; // Calculate the 1-norm of matrix for rcond calculation for (int j = 0; j < nr; j++) { double atmp = 0.; for (int i = cidx(j); i < cidx(j+1); i++) atmp += fabs(data(i)); if (atmp > anorm) anorm = atmp; } int b_nr = b.rows (); int b_nc = b.cols (); int b_nz = b.nnz (); retval = SparseMatrix (b_nr, b_nc, b_nz); retval.xcidx(0) = 0; int ii = 0; int x_nz = b_nz; if (typ == SparseType::Permuted_Lower) { OCTAVE_LOCAL_BUFFER (double, work, nr); int *p_perm = mattype.triangular_row_perm (); int *q_perm = mattype.triangular_col_perm (); (*current_liboctave_warning_handler) ("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested"); for (int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) work[i] = 0.; for (int i = b.cidx(j); i < b.cidx(j+1); i++) work[b.ridx(i)] = b.data(i); for (int k = 0; k < nr; k++) { int iidx = q_perm[k]; if (work[iidx] != 0.) { if (ridx(cidx(iidx)) != iidx) { err = -2; goto triangular_error; } double tmp = work[iidx] / data(cidx(iidx+1)-1); work[iidx] = tmp; for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++) { int idx2 = q_perm[ridx(i)]; work[idx2] = work[idx2] - tmp * data(i); } } } // Count non-zeros in work vector and adjust space in // retval if needed int new_nnz = 0; for (int i = 0; i < nr; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int i = 0; i < nr; i++) if (work[p_perm[i]] != 0.) { retval.xridx(ii) = i; retval.xdata(ii++) = work[p_perm[i]]; } retval.xcidx(j+1) = ii; } retval.maybe_compress (); // Calculation of 1-norm of inv(*this) for (int i = 0; i < nr; i++) work[i] = 0.; for (int j = 0; j < nr; j++) { work[q_perm[j]] = 1.; for (int k = 0; k < nr; k++) { int iidx = q_perm[k]; if (work[iidx] != 0.) { double tmp = work[iidx] / data(cidx(iidx+1)-1); work[iidx] = tmp; for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++) { int idx2 = q_perm[ridx(i)]; work[idx2] = work[idx2] - tmp * data(i); } } } double atmp = 0; for (int i = 0; i < j+1; i++) { atmp += fabs(work[i]); work[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } } else { OCTAVE_LOCAL_BUFFER (double, work, nr); for (int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) work[i] = 0.; for (int i = b.cidx(j); i < b.cidx(j+1); i++) work[b.ridx(i)] = b.data(i); for (int k = 0; k < nr; k++) { if (work[k] != 0.) { if (ridx(cidx(k)) != k) { err = -2; goto triangular_error; } double tmp = work[k] / data(cidx(k)); work[k] = tmp; for (int i = cidx(k)+1; i < cidx(k+1); i++) { int iidx = ridx(i); work[iidx] = work[iidx] - tmp * data(i); } } } // Count non-zeros in work vector and adjust space in // retval if needed int new_nnz = 0; for (int i = 0; i < nr; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int 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 (); // Calculation of 1-norm of inv(*this) for (int i = 0; i < nr; i++) work[i] = 0.; for (int j = 0; j < nr; j++) { work[j] = 1.; for (int k = j; k < nr; k++) { if (work[k] != 0.) { double tmp = work[k] / data(cidx(k)); work[k] = tmp; for (int i = cidx(k)+1; i < cidx(k+1); i++) { int iidx = ridx(i); work[iidx] = work[iidx] - tmp * data(i); } } } double atmp = 0; for (int i = j; i < nr; 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); 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); 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 (SparseType &mattype, const ComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { ComplexMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Permuted_Lower || typ == SparseType::Lower) { double anorm = 0.; double ainvnorm = 0.; int b_nc = b.cols (); rcond = 0.; // Calculate the 1-norm of matrix for rcond calculation for (int j = 0; j < nr; j++) { double atmp = 0.; for (int i = cidx(j); i < cidx(j+1); i++) atmp += fabs(data(i)); if (atmp > anorm) anorm = atmp; } if (typ == SparseType::Permuted_Lower) { retval.resize (b.rows (), b.cols ()); OCTAVE_LOCAL_BUFFER (Complex, work, nr); int *p_perm = mattype.triangular_row_perm (); int *q_perm = mattype.triangular_col_perm (); (*current_liboctave_warning_handler) ("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested"); for (int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) work[i] = b(i,j); for (int k = 0; k < nr; k++) { int iidx = q_perm[k]; if (work[iidx] != 0.) { if (ridx(cidx(iidx)) != iidx) { err = -2; goto triangular_error; } Complex tmp = work[iidx] / data(cidx(iidx+1)-1); work[iidx] = tmp; for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++) { int idx2 = q_perm[ridx(i)]; work[idx2] = work[idx2] - tmp * data(i); } } } for (int i = 0; i < nr; i++) retval (i, j) = work[p_perm[i]]; } // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work2, nr); for (int i = 0; i < nr; i++) work2[i] = 0.; for (int j = 0; j < nr; j++) { work2[q_perm[j]] = 1.; for (int k = 0; k < nr; k++) { int iidx = q_perm[k]; if (work2[iidx] != 0.) { double tmp = work2[iidx] / data(cidx(iidx+1)-1); work2[iidx] = tmp; for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++) { int idx2 = q_perm[ridx(i)]; work2[idx2] = work2[idx2] - tmp * data(i); } } } double atmp = 0; for (int i = 0; i < j+1; i++) { atmp += fabs(work2[i]); work2[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } } else { retval = b; Complex *x_vec = retval.fortran_vec (); for (int j = 0; j < b_nc; j++) { int offset = j * nr; for (int k = 0; k < nr; k++) { if (x_vec[k+offset] != 0.) { if (ridx(cidx(k)) != k) { err = -2; goto triangular_error; } Complex tmp = x_vec[k+offset] / data(cidx(k)); x_vec[k+offset] = tmp; for (int i = cidx(k)+1; i < cidx(k+1); i++) { int iidx = ridx(i); x_vec[iidx+offset] = x_vec[iidx+offset] - tmp * data(i); } } } } // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work, nr); for (int i = 0; i < nr; i++) work[i] = 0.; for (int j = 0; j < nr; j++) { work[j] = 1.; for (int k = j; k < nr; k++) { if (work[k] != 0.) { double tmp = work[k] / data(cidx(k)); work[k] = tmp; for (int i = cidx(k)+1; i < cidx(k+1); i++) { int iidx = ridx(i); work[iidx] = work[iidx] - tmp * data(i); } } } double atmp = 0; for (int i = j; i < nr; 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); 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); 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 (SparseType &mattype, const SparseComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseComplexMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Permuted_Lower || typ == SparseType::Lower) { double anorm = 0.; double ainvnorm = 0.; rcond = 0.; // Calculate the 1-norm of matrix for rcond calculation for (int j = 0; j < nr; j++) { double atmp = 0.; for (int i = cidx(j); i < cidx(j+1); i++) atmp += fabs(data(i)); if (atmp > anorm) anorm = atmp; } int b_nr = b.rows (); int b_nc = b.cols (); int b_nz = b.nnz (); retval = SparseComplexMatrix (b_nr, b_nc, b_nz); retval.xcidx(0) = 0; int ii = 0; int x_nz = b_nz; if (typ == SparseType::Permuted_Lower) { OCTAVE_LOCAL_BUFFER (Complex, work, nr); int *p_perm = mattype.triangular_row_perm (); int *q_perm = mattype.triangular_col_perm (); (*current_liboctave_warning_handler) ("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested"); for (int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) work[i] = 0.; for (int i = b.cidx(j); i < b.cidx(j+1); i++) work[b.ridx(i)] = b.data(i); for (int k = 0; k < nr; k++) { int iidx = q_perm[k]; if (work[iidx] != 0.) { if (ridx(cidx(iidx)) != iidx) { err = -2; goto triangular_error; } Complex tmp = work[iidx] / data(cidx(iidx+1)-1); work[iidx] = tmp; for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++) { int idx2 = q_perm[ridx(i)]; work[idx2] = work[idx2] - tmp * data(i); } } } // Count non-zeros in work vector and adjust space in // retval if needed int new_nnz = 0; for (int i = 0; i < nr; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int i = 0; i < nr; i++) if (work[p_perm[i]] != 0.) { retval.xridx(ii) = i; retval.xdata(ii++) = work[p_perm[i]]; } retval.xcidx(j+1) = ii; } retval.maybe_compress (); // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work2, nr); for (int i = 0; i < nr; i++) work2[i] = 0.; for (int j = 0; j < nr; j++) { work2[q_perm[j]] = 1.; for (int k = 0; k < nr; k++) { int iidx = q_perm[k]; if (work2[iidx] != 0.) { double tmp = work2[iidx] / data(cidx(iidx+1)-1); work2[iidx] = tmp; for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++) { int idx2 = q_perm[ridx(i)]; work2[idx2] = work2[idx2] - tmp * data(i); } } } double atmp = 0; for (int i = 0; i < j+1; i++) { atmp += fabs(work2[i]); work2[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } } else { OCTAVE_LOCAL_BUFFER (Complex, work, nr); for (int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) work[i] = 0.; for (int i = b.cidx(j); i < b.cidx(j+1); i++) work[b.ridx(i)] = b.data(i); for (int k = 0; k < nr; k++) { if (work[k] != 0.) { if (ridx(cidx(k)) != k) { err = -2; goto triangular_error; } Complex tmp = work[k] / data(cidx(k)); work[k] = tmp; for (int i = cidx(k)+1; i < cidx(k+1); i++) { int iidx = ridx(i); work[iidx] = work[iidx] - tmp * data(i); } } } // Count non-zeros in work vector and adjust space in // retval if needed int new_nnz = 0; for (int i = 0; i < nr; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int 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 (); // Calculation of 1-norm of inv(*this) OCTAVE_LOCAL_BUFFER (double, work2, nr); for (int i = 0; i < nr; i++) work2[i] = 0.; for (int j = 0; j < nr; j++) { work2[j] = 1.; for (int k = j; k < nr; k++) { if (work2[k] != 0.) { double tmp = work2[k] / data(cidx(k)); work2[k] = tmp; for (int i = cidx(k)+1; i < cidx(k+1); i++) { int iidx = ridx(i); work2[iidx] = work2[iidx] - tmp * data(i); } } } double atmp = 0; for (int i = j; i < nr; i++) { atmp += fabs(work2[i]); work2[i] = 0.; } if (atmp > ainvnorm) ainvnorm = atmp; } } rcond = 1. / ainvnorm / anorm; triangular_error: if (err != 0) { if (sing_handler) sing_handler (rcond); 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); 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 (SparseType &mattype, const Matrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { Matrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == SparseType::Tridiagonal_Hermitian) { OCTAVE_LOCAL_BUFFER (double, D, nr); OCTAVE_LOCAL_BUFFER (double, DL, nr - 1); if (mattype.is_dense ()) { int ii = 0; for (int 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 (int i = 0; i < nr - 1; i++) { D[i+1] = 0.; DL[i] = 0.; } for (int j = 0; j < nc; j++) for (int 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); } } int 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 (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dptsv"); else if (err != 0) { err = 0; mattype.mark_as_unsymmetric (); typ = SparseType::Tridiagonal; } else rcond = 1.; } if (typ == SparseType::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 ()) { int ii = 0; for (int 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 (int i = 0; i < nr - 1; i++) { D[i+1] = 0.; DL[i] = 0.; DU[i] = 0.; } for (int j = 0; j < nc; j++) for (int 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] = data(i); } } int 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 (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgtsv"); else if (err != 0) { rcond = 0.; err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } else rcond = 1.; } else if (typ != SparseType::Tridiagonal_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseMatrix SparseMatrix::trisolve (SparseType &mattype, const SparseMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); 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 == SparseType::Tridiagonal || typ == SparseType::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<int> ipvt (nr); int *pipvt = ipvt.fortran_vec (); if (mattype.is_dense ()) { int ii = 0; for (int 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 (int i = 0; i < nr - 1; i++) { D[i+1] = 0.; DL[i] = 0.; DU[i] = 0.; } for (int j = 0; j < nc; j++) for (int 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] = data(i); } } F77_XFCN (dgttrf, DGTTRF, (nr, DL, D, DU, DU2, pipvt, err)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgttrf"); else { rcond = 0.0; if (err != 0) { err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } else { char job = 'N'; volatile int x_nz = b.nnz (); int b_nc = b.cols (); retval = SparseMatrix (nr, b_nc, x_nz); retval.xcidx(0) = 0; volatile int ii = 0; OCTAVE_LOCAL_BUFFER (double, work, nr); for (volatile int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) work[i] = 0.; for (int 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))); if (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dgttrs"); break; } // Count non-zeros in work vector and adjust // space in retval if needed int new_nnz = 0; for (int i = 0; i < nr; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int 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 != SparseType::Tridiagonal_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } ComplexMatrix SparseMatrix::trisolve (SparseType &mattype, const ComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { ComplexMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); // Note can't treat symmetric case as there is no dpttrf function if (typ == SparseType::Tridiagonal_Hermitian) { OCTAVE_LOCAL_BUFFER (Complex, D, nr); OCTAVE_LOCAL_BUFFER (Complex, DL, nr - 1); if (mattype.is_dense ()) { int ii = 0; for (int 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 (int i = 0; i < nr - 1; i++) { D[i+1] = 0.; DL[i] = 0.; } for (int j = 0; j < nc; j++) for (int 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); } } int b_nr = b.rows (); int 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 (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in zptsv"); err = -1; } else if (err != 0) { err = 0; mattype.mark_as_unsymmetric (); typ = SparseType::Tridiagonal; } } if (typ == SparseType::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 ()) { int ii = 0; for (int 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 (int i = 0; i < nr - 1; i++) { D[i+1] = 0.; DL[i] = 0.; DU[i] = 0.; } for (int j = 0; j < nc; j++) for (int 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] = data(i); } } int b_nr = b.rows(); int 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 (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in zgtsv"); err = -1; } else if (err != 0) { rcond = 0.; err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } } else if (typ != SparseType::Tridiagonal_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseComplexMatrix SparseMatrix::trisolve (SparseType &mattype, const SparseComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseComplexMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); 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 == SparseType::Tridiagonal || typ == SparseType::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<int> ipvt (nr); int *pipvt = ipvt.fortran_vec (); if (mattype.is_dense ()) { int ii = 0; for (int 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 (int i = 0; i < nr - 1; i++) { D[i+1] = 0.; DL[i] = 0.; DU[i] = 0.; } for (int j = 0; j < nc; j++) for (int 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] = data(i); } } F77_XFCN (dgttrf, DGTTRF, (nr, DL, D, DU, DU2, pipvt, err)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgttrf"); else { rcond = 0.0; if (err != 0) { err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } else { rcond = 1.; char job = 'N'; int b_nr = b.rows (); int 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 int x_nz = b.nnz (); volatile int ii = 0; retval = SparseComplexMatrix (b_nr, b_nc, x_nz); retval.xcidx(0) = 0; for (volatile int j = 0; j < b_nc; j++) { for (int 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 (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dgttrs"); break; } 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 (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dgttrs"); break; } 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 int new_nnz = 0; for (int i = 0; i < nr; i++) if (Bx[i] != 0. || Bz[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int 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 != SparseType::Tridiagonal_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } Matrix SparseMatrix::bsolve (SparseType &mattype, const Matrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { Matrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == SparseType::Banded_Hermitian) { int n_lower = mattype.nlower (); int ldm = n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { int ii = 0; for (int j = 0; j < ldm; j++) for (int i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (int j = 0; j < nc; j++) for (int i = cidx(j); i < cidx(j+1); i++) { int ri = ridx (i); if (ri >= j) m_band(ri - j, j) = data(i); } // Calculate the norm of the matrix, for later use. // double 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 (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dpbtrf"); else { rcond = 0.0; if (err != 0) { // Matrix is not positive definite!! Fall through to // unsymmetric banded solver. mattype.mark_as_unsymmetric (); typ = SparseType::Banded; err = 0; } else { // Unfortunately, the time to calculate the condition // number is dominant for narrow banded matrices and // so we rely on the "err" flag from xPBTRF to flag // singularity. The commented code below is left here // for reference //Array<double> z (3 * nr); //double *pz = z.fortran_vec (); //Array<int> iz (nr); //int *piz = iz.fortran_vec (); // //F77_XFCN (dpbcon, DGBCON, // (F77_CONST_CHAR_ARG2 (&job, 1), // nr, n_lower, tmp_data, ldm, // anorm, rcond, pz, piz, err // F77_CHAR_ARG_LEN (1))); // // //if (f77_exception_encountered) // (*current_liboctave_error_handler) // ("unrecoverable error in dpbcon"); // //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); // else // (*current_liboctave_error_handler) // ("matrix singular to machine precision, rcond = %g", // rcond); // } //else // REST OF CODE, EXCEPT rcond=1 rcond = 1.; retval = b; double *result = retval.fortran_vec (); int 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 (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dpbtrs"); if (err != 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; } } } } if (typ == SparseType::Banded) { // Create the storage for the banded form of the sparse matrix int n_upper = mattype.nupper (); int n_lower = mattype.nlower (); int ldm = n_upper + 2 * n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { int ii = 0; for (int j = 0; j < ldm; j++) for (int i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (int j = 0; j < nc; j++) for (int i = cidx(j); i < cidx(j+1); i++) m_band(ridx(i) - j + n_lower + n_upper, j) = data(i); Array<int> ipvt (nr); int *pipvt = ipvt.fortran_vec (); F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, ldm, pipvt, err)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgbtrf"); else { // Throw-away extra info LAPACK gives so as to not // change output. rcond = 0.0; if (err != 0) { err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } else { char job = '1'; // Unfortunately, the time to calculate the condition // number is dominant for narrow banded matrices and // so we rely on the "err" flag from xPBTRF to flag // singularity. The commented code below is left here // for reference //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 (f77_exception_encountered) // (*current_liboctave_error_handler) // ("unrecoverable error in dgbcon"); // // 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); // else // (*current_liboctave_error_handler) // ("matrix singular to machine precision, rcond = %g", // rcond); // } //else // REST OF CODE, EXCEPT rcond=1 rcond = 1.; retval = b; double *result = retval.fortran_vec (); int b_nc = b.cols (); 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))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgbtrs"); } } } else if (typ != SparseType::Banded_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseMatrix SparseMatrix::bsolve (SparseType &mattype, const SparseMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == SparseType::Banded_Hermitian) { int n_lower = mattype.nlower (); int ldm = n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { int ii = 0; for (int j = 0; j < ldm; j++) for (int i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (int j = 0; j < nc; j++) for (int i = cidx(j); i < cidx(j+1); i++) { int ri = ridx (i); if (ri >= j) m_band(ri - j, j) = data(i); } 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 (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dpbtrf"); else { rcond = 0.0; if (err != 0) { mattype.mark_as_unsymmetric (); typ = SparseType::Banded; err = 0; } else { rcond = 1.; int b_nr = b.rows (); int 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 int x_nz = b.nnz (); volatile int ii = 0; retval = SparseMatrix (b_nr, b_nc, x_nz); retval.xcidx(0) = 0; for (volatile int j = 0; j < b_nc; j++) { for (int 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 (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dpbtrs"); err = -1; break; } if (err != 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } for (int i = 0; i < b_nr; i++) { double tmp = Bx[i]; if (tmp != 0.0) { if (ii == x_nz) { // Resize the sparse matrix int 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 == SparseType::Banded) { // Create the storage for the banded form of the sparse matrix int n_upper = mattype.nupper (); int n_lower = mattype.nlower (); int ldm = n_upper + 2 * n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { int ii = 0; for (int j = 0; j < ldm; j++) for (int i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (int j = 0; j < nc; j++) for (int i = cidx(j); i < cidx(j+1); i++) m_band(ridx(i) - j + n_lower + n_upper, j) = data(i); Array<int> ipvt (nr); int *pipvt = ipvt.fortran_vec (); F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, ldm, pipvt, err)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgbtrf"); else { rcond = 0.0; if (err != 0) { err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } else { char job = 'N'; volatile int x_nz = b.nnz (); int b_nc = b.cols (); retval = SparseMatrix (nr, b_nc, x_nz); retval.xcidx(0) = 0; volatile int ii = 0; OCTAVE_LOCAL_BUFFER (double, work, nr); for (volatile int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) work[i] = 0.; for (int 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))); if (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dgbtrs"); break; } // Count non-zeros in work vector and adjust // space in retval if needed int new_nnz = 0; for (int i = 0; i < nr; i++) if (work[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int 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 != SparseType::Banded_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } ComplexMatrix SparseMatrix::bsolve (SparseType &mattype, const ComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { ComplexMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == SparseType::Banded_Hermitian) { int n_lower = mattype.nlower (); int ldm = n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { int ii = 0; for (int j = 0; j < ldm; j++) for (int i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (int j = 0; j < nc; j++) for (int i = cidx(j); i < cidx(j+1); i++) { int ri = ridx (i); if (ri >= j) m_band(ri - j, j) = data(i); } 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 (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dpbtrf"); else { rcond = 0.0; if (err != 0) { // Matrix is not positive definite!! Fall through to // unsymmetric banded solver. mattype.mark_as_unsymmetric (); typ = SparseType::Banded; err = 0; } else { rcond = 1.; int b_nr = b.rows (); int 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 int j = 0; j < b_nc; j++) { for (int 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 (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dpbtrs"); err = -1; break; } 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 (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dpbtrs"); err = -1; break; } if (err != 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); err = -1; break; } for (int i = 0; i < b_nr; i++) retval (i, j) = Complex (Bx[i], Bz[i]); } } } } if (typ == SparseType::Banded) { // Create the storage for the banded form of the sparse matrix int n_upper = mattype.nupper (); int n_lower = mattype.nlower (); int ldm = n_upper + 2 * n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { int ii = 0; for (int j = 0; j < ldm; j++) for (int i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (int j = 0; j < nc; j++) for (int i = cidx(j); i < cidx(j+1); i++) m_band(ridx(i) - j + n_lower + n_upper, j) = data(i); Array<int> ipvt (nr); int *pipvt = ipvt.fortran_vec (); F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, ldm, pipvt, err)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgbtrf"); else { rcond = 0.0; if (err != 0) { err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } else { char job = 'N'; int b_nc = b.cols (); retval.resize (nr,b_nc); OCTAVE_LOCAL_BUFFER (double, Bz, nr); OCTAVE_LOCAL_BUFFER (double, Bx, nr); for (volatile int j = 0; j < b_nc; j++) { for (int 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))); if (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dgbtrs"); break; } 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))); if (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dgbtrs"); break; } for (int i = 0; i < nr; i++) retval (i, j) = Complex (Bx[i], Bz[i]); } } } } else if (typ != SparseType::Banded_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseComplexMatrix SparseMatrix::bsolve (SparseType &mattype, const SparseComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseComplexMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested volatile int typ = mattype.type (); mattype.info (); if (typ == SparseType::Banded_Hermitian) { int n_lower = mattype.nlower (); int ldm = n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { int ii = 0; for (int j = 0; j < ldm; j++) for (int i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (int j = 0; j < nc; j++) for (int i = cidx(j); i < cidx(j+1); i++) { int ri = ridx (i); if (ri >= j) m_band(ri - j, j) = data(i); } 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 (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dpbtrf"); else { rcond = 0.0; if (err != 0) { // Matrix is not positive definite!! Fall through to // unsymmetric banded solver. mattype.mark_as_unsymmetric (); typ = SparseType::Banded; err = 0; } else { rcond = 1.; int b_nr = b.rows (); int 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 int x_nz = b.nnz (); volatile int ii = 0; retval = SparseComplexMatrix (b_nr, b_nc, x_nz); retval.xcidx(0) = 0; for (volatile int j = 0; j < b_nc; j++) { for (int 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 (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dpbtrs"); err = -1; break; } 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 (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dpbtrs"); err = -1; break; } 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 int new_nnz = 0; for (int i = 0; i < nr; i++) if (Bx[i] != 0. || Bz[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int 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 == SparseType::Banded) { // Create the storage for the banded form of the sparse matrix int n_upper = mattype.nupper (); int n_lower = mattype.nlower (); int ldm = n_upper + 2 * n_lower + 1; Matrix m_band (ldm, nc); double *tmp_data = m_band.fortran_vec (); if (! mattype.is_dense ()) { int ii = 0; for (int j = 0; j < ldm; j++) for (int i = 0; i < nc; i++) tmp_data[ii++] = 0.; } for (int j = 0; j < nc; j++) for (int i = cidx(j); i < cidx(j+1); i++) m_band(ridx(i) - j + n_lower + n_upper, j) = data(i); Array<int> ipvt (nr); int *pipvt = ipvt.fortran_vec (); F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, ldm, pipvt, err)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgbtrf"); else { rcond = 0.0; if (err != 0) { err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("matrix singular to machine precision"); } else { char job = 'N'; volatile int x_nz = b.nnz (); int b_nc = b.cols (); retval = SparseComplexMatrix (nr, b_nc, x_nz); retval.xcidx(0) = 0; volatile int ii = 0; OCTAVE_LOCAL_BUFFER (double, Bx, nr); OCTAVE_LOCAL_BUFFER (double, Bz, nr); for (volatile int j = 0; j < b_nc; j++) { for (int i = 0; i < nr; i++) { Bx[i] = 0.; Bz[i] = 0.; } for (int 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))); if (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dgbtrs"); break; } 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))); if (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dgbtrs"); break; } // Count non-zeros in work vector and adjust // space in retval if needed int new_nnz = 0; for (int i = 0; i < nr; i++) if (Bx[i] != 0. || Bz[i] != 0.) new_nnz++; if (ii + new_nnz > x_nz) { // Resize the sparse matrix int sz = new_nnz * (b_nc - j) + x_nz; retval.change_capacity (sz); x_nz = sz; } for (int 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 != SparseType::Banded_Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } void * SparseMatrix::factorize (int& err, double &rcond, Matrix &Control, Matrix &Info, solve_singularity_handler sing_handler) const { // The return values void *Numeric; err = 0; #ifdef HAVE_UMFPACK // Setup the control parameters Control = Matrix (UMFPACK_CONTROL, 1); double *control = Control.fortran_vec (); umfpack_di_defaults (control); double tmp = Voctave_sparse_controls.get_key ("spumoni"); if (!xisnan (tmp)) Control (UMFPACK_PRL) = tmp; tmp = Voctave_sparse_controls.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 = Voctave_sparse_controls.get_key ("autoamd"); if (!xisnan (tmp)) Control (UMFPACK_FIXQ) = tmp; umfpack_di_report_control (control); const int *Ap = cidx (); const int *Ai = ridx (); const double *Ax = data (); int nr = rows (); int nc = cols (); umfpack_di_report_matrix (nr, nc, Ap, Ai, Ax, 1, control); void *Symbolic; Info = Matrix (1, UMFPACK_INFO); double *info = Info.fortran_vec (); int status = umfpack_di_qsymbolic (nr, nc, Ap, Ai, Ax, NULL, &Symbolic, control, info); if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve symbolic factorization failed"); err = -1; umfpack_di_report_status (control, status); umfpack_di_report_info (control, info); umfpack_di_free_symbolic (&Symbolic) ; } else { umfpack_di_report_symbolic (Symbolic, control); status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, control, info) ; umfpack_di_free_symbolic (&Symbolic) ; #ifdef HAVE_LSSOLVE rcond = Info (UMFPACK_RCOND); volatile double rcond_plus_one = rcond + 1.0; if (status == UMFPACK_WARNING_singular_matrix || rcond_plus_one == 1.0 || xisnan (rcond)) { umfpack_di_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 #endif if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve numeric factorization failed"); umfpack_di_report_status (control, status); umfpack_di_report_info (control, info); err = -1; } else { umfpack_di_report_numeric (Numeric, control); } } if (err != 0) umfpack_di_free_numeric (&Numeric); #else (*current_liboctave_error_handler) ("UMFPACK not installed"); #endif return Numeric; } Matrix SparseMatrix::fsolve (SparseType &mattype, const Matrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { Matrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Hermitian) { // XXX FIXME XXX Write the cholesky solver and only fall // through if cholesky factorization fails (*current_liboctave_warning_handler) ("SparseMatrix::solve XXX FIXME XXX Cholesky code not done"); mattype.mark_as_unsymmetric (); typ = SparseType::Full; } if (typ == SparseType::Full) { #ifdef HAVE_UMFPACK Matrix Control, Info; void *Numeric = factorize (err, rcond, Control, Info, sing_handler); if (err == 0) { const double *Bx = b.fortran_vec (); retval.resize (b.rows (), b.cols()); double *result = retval.fortran_vec (); int b_nr = b.rows (); int b_nc = b.cols (); int status = 0; double *control = Control.fortran_vec (); double *info = Info.fortran_vec (); const int *Ap = cidx (); const int *Ai = ridx (); const double *Ax = data (); for (int j = 0, iidx = 0; j < b_nc; j++, iidx += b_nr) { status = umfpack_di_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_di_report_status (control, status); err = -1; break; } } #ifndef HAVE_LSSOLVE rcond = Info (UMFPACK_RCOND); volatile double rcond_plus_one = rcond + 1.0; if (status == UMFPACK_WARNING_singular_matrix || rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } #endif umfpack_di_report_info (control, info); umfpack_di_free_numeric (&Numeric); } #else (*current_liboctave_error_handler) ("UMFPACK not installed"); #endif } else if (typ != SparseType::Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseMatrix SparseMatrix::fsolve (SparseType &mattype, const SparseMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Hermitian) { // XXX FIXME XXX Write the cholesky solver and only fall // through if cholesky factorization fails (*current_liboctave_warning_handler) ("SparseMatrix::solve XXX FIXME XXX Cholesky code not done"); mattype.mark_as_unsymmetric (); typ = SparseType::Full; } if (typ == SparseType::Full) { #ifdef HAVE_UMFPACK Matrix Control, Info; void *Numeric = factorize (err, rcond, Control, Info, sing_handler); if (err == 0) { int b_nr = b.rows (); int b_nc = b.cols (); int status = 0; double *control = Control.fortran_vec (); double *info = Info.fortran_vec (); const int *Ap = cidx (); const int *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 int x_nz = b.nnz (); int ii = 0; retval = SparseMatrix (b_nr, b_nc, x_nz); retval.xcidx(0) = 0; for (int j = 0; j < b_nc; j++) { for (int i = 0; i < b_nr; i++) Bx[i] = b.elem (i, j); status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, Xx, Bx, Numeric, control, info); if (status < 0) { (*current_liboctave_error_handler) ("SparseMatrix::solve solve failed"); umfpack_di_report_status (control, status); err = -1; break; } for (int i = 0; i < b_nr; i++) { double tmp = Xx[i]; if (tmp != 0.0) { if (ii == x_nz) { // Resize the sparse matrix int 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 (); #ifndef HAVE_LSSOLVE rcond = Info (UMFPACK_RCOND); volatile double rcond_plus_one = rcond + 1.0; if (status == UMFPACK_WARNING_singular_matrix || rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } #endif umfpack_di_report_info (control, info); umfpack_di_free_numeric (&Numeric); } #else (*current_liboctave_error_handler) ("UMFPACK not installed"); #endif } else if (typ != SparseType::Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } ComplexMatrix SparseMatrix::fsolve (SparseType &mattype, const ComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { ComplexMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Hermitian) { // XXX FIXME XXX Write the cholesky solver and only fall // through if cholesky factorization fails (*current_liboctave_warning_handler) ("SparseMatrix::solve XXX FIXME XXX Cholesky code not done"); mattype.mark_as_unsymmetric (); typ = SparseType::Full; } if (typ == SparseType::Full) { #ifdef HAVE_UMFPACK Matrix Control, Info; void *Numeric = factorize (err, rcond, Control, Info, sing_handler); if (err == 0) { int b_nr = b.rows (); int b_nc = b.cols (); int status = 0; double *control = Control.fortran_vec (); double *info = Info.fortran_vec (); const int *Ap = cidx (); const int *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 (int j = 0; j < b_nc; j++) { for (int i = 0; i < b_nr; i++) { Complex c = b (i,j); Bx[i] = std::real (c); Bz[i] = std::imag (c); } status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, Xx, Bx, Numeric, control, info); int status2 = umfpack_di_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_di_report_status (control, status); err = -1; break; } for (int i = 0; i < b_nr; i++) retval (i, j) = Complex (Xx[i], Xz[i]); } #ifndef HAVE_LSSOLVE rcond = Info (UMFPACK_RCOND); volatile double rcond_plus_one = rcond + 1.0; if (status == UMFPACK_WARNING_singular_matrix || rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } #endif umfpack_di_report_info (control, info); umfpack_di_free_numeric (&Numeric); } #else (*current_liboctave_error_handler) ("UMFPACK not installed"); #endif } else if (typ != SparseType::Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } SparseComplexMatrix SparseMatrix::fsolve (SparseType &mattype, const SparseComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseComplexMatrix retval; int nr = rows (); int nc = cols (); err = 0; if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else { // Print spparms("spumoni") info if requested int typ = mattype.type (); mattype.info (); if (typ == SparseType::Hermitian) { // XXX FIXME XXX Write the cholesky solver and only fall // through if cholesky factorization fails (*current_liboctave_warning_handler) ("SparseMatrix::solve XXX FIXME XXX Cholesky code not done"); mattype.mark_as_unsymmetric (); typ = SparseType::Full; } if (typ == SparseType::Full) { #ifdef HAVE_UMFPACK Matrix Control, Info; void *Numeric = factorize (err, rcond, Control, Info, sing_handler); if (err == 0) { int b_nr = b.rows (); int b_nc = b.cols (); int status = 0; double *control = Control.fortran_vec (); double *info = Info.fortran_vec (); const int *Ap = cidx (); const int *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 int x_nz = b.nnz (); int 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 (int j = 0; j < b_nc; j++) { for (int i = 0; i < b_nr; i++) { Complex c = b (i,j); Bx[i] = std::real (c); Bz[i] = std::imag (c); } status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, Xx, Bx, Numeric, control, info); int status2 = umfpack_di_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_di_report_status (control, status); err = -1; break; } for (int 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 int 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 (); #ifndef HAVE_LSSOLVE rcond = Info (UMFPACK_RCOND); volatile double rcond_plus_one = rcond + 1.0; if (status == UMFPACK_WARNING_singular_matrix || rcond_plus_one == 1.0 || xisnan (rcond)) { err = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("SparseMatrix::solve matrix singular to machine precision, rcond = %g", rcond); } #endif umfpack_di_report_info (control, info); umfpack_di_free_numeric (&Numeric); } #else (*current_liboctave_error_handler) ("UMFPACK not installed"); #endif } else if (typ != SparseType::Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } Matrix SparseMatrix::solve (SparseType &mattype, const Matrix& b) const { int info; double rcond; return solve (mattype, b, info, rcond, 0); } Matrix SparseMatrix::solve (SparseType &mattype, const Matrix& b, int& info) const { double rcond; return solve (mattype, b, info, rcond, 0); } Matrix SparseMatrix::solve (SparseType &mattype, const Matrix& b, int& info, double& rcond) const { return solve (mattype, b, info, rcond, 0); } Matrix SparseMatrix::solve (SparseType &mattype, const Matrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { int typ = mattype.type (); if (typ == SparseType::Unknown) typ = mattype.type (*this); if (typ == SparseType::Diagonal || typ == SparseType::Permuted_Diagonal) return dsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Upper || typ == SparseType::Permuted_Upper) return utsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Lower || typ == SparseType::Permuted_Lower) return ltsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Banded || typ == SparseType::Banded_Hermitian) return bsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Tridiagonal || typ == SparseType::Tridiagonal_Hermitian) return trisolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Full || typ == SparseType::Hermitian) return fsolve (mattype, b, err, rcond, sing_handler); else { (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); return Matrix (); } } SparseMatrix SparseMatrix::solve (SparseType &mattype, const SparseMatrix& b) const { int info; double rcond; return solve (mattype, b, info, rcond, 0); } SparseMatrix SparseMatrix::solve (SparseType &mattype, const SparseMatrix& b, int& info) const { double rcond; return solve (mattype, b, info, rcond, 0); } SparseMatrix SparseMatrix::solve (SparseType &mattype, const SparseMatrix& b, int& info, double& rcond) const { return solve (mattype, b, info, rcond, 0); } SparseMatrix SparseMatrix::solve (SparseType &mattype, const SparseMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { int typ = mattype.type (); if (typ == SparseType::Unknown) typ = mattype.type (*this); if (typ == SparseType::Diagonal || typ == SparseType::Permuted_Diagonal) return dsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Upper || typ == SparseType::Permuted_Upper) return utsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Lower || typ == SparseType::Permuted_Lower) return ltsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Banded || typ == SparseType::Banded_Hermitian) return bsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Tridiagonal || typ == SparseType::Tridiagonal_Hermitian) return trisolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Full || typ == SparseType::Hermitian) return fsolve (mattype, b, err, rcond, sing_handler); else { (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); return SparseMatrix (); } } ComplexMatrix SparseMatrix::solve (SparseType &mattype, const ComplexMatrix& b) const { int info; double rcond; return solve (mattype, b, info, rcond, 0); } ComplexMatrix SparseMatrix::solve (SparseType &mattype, const ComplexMatrix& b, int& info) const { double rcond; return solve (mattype, b, info, rcond, 0); } ComplexMatrix SparseMatrix::solve (SparseType &mattype, const ComplexMatrix& b, int& info, double& rcond) const { return solve (mattype, b, info, rcond, 0); } ComplexMatrix SparseMatrix::solve (SparseType &mattype, const ComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { int typ = mattype.type (); if (typ == SparseType::Unknown) typ = mattype.type (*this); if (typ == SparseType::Diagonal || typ == SparseType::Permuted_Diagonal) return dsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Upper || typ == SparseType::Permuted_Upper) return utsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Lower || typ == SparseType::Permuted_Lower) return ltsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Banded || typ == SparseType::Banded_Hermitian) return bsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Tridiagonal || typ == SparseType::Tridiagonal_Hermitian) return trisolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Full || typ == SparseType::Hermitian) return fsolve (mattype, b, err, rcond, sing_handler); else { (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); return ComplexMatrix (); } } SparseComplexMatrix SparseMatrix::solve (SparseType &mattype, const SparseComplexMatrix& b) const { int info; double rcond; return solve (mattype, b, info, rcond, 0); } SparseComplexMatrix SparseMatrix::solve (SparseType &mattype, const SparseComplexMatrix& b, int& info) const { double rcond; return solve (mattype, b, info, rcond, 0); } SparseComplexMatrix SparseMatrix::solve (SparseType &mattype, const SparseComplexMatrix& b, int& info, double& rcond) const { return solve (mattype, b, info, rcond, 0); } SparseComplexMatrix SparseMatrix::solve (SparseType &mattype, const SparseComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { int typ = mattype.type (); if (typ == SparseType::Unknown) typ = mattype.type (*this); if (typ == SparseType::Diagonal || typ == SparseType::Permuted_Diagonal) return dsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Upper || typ == SparseType::Permuted_Upper) return utsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Lower || typ == SparseType::Permuted_Lower) return ltsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Banded || typ == SparseType::Banded_Hermitian) return bsolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Tridiagonal || typ == SparseType::Tridiagonal_Hermitian) return trisolve (mattype, b, err, rcond, sing_handler); else if (typ == SparseType::Full || typ == SparseType::Hermitian) return fsolve (mattype, b, err, rcond, sing_handler); else { (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); return SparseComplexMatrix (); } } ColumnVector SparseMatrix::solve (SparseType &mattype, const ColumnVector& b) const { int info; double rcond; return solve (mattype, b, info, rcond); } ColumnVector SparseMatrix::solve (SparseType &mattype, const ColumnVector& b, int& info) const { double rcond; return solve (mattype, b, info, rcond); } ColumnVector SparseMatrix::solve (SparseType &mattype, const ColumnVector& b, int& info, double& rcond) const { return solve (mattype, b, info, rcond, 0); } ColumnVector SparseMatrix::solve (SparseType &mattype, const ColumnVector& b, int& info, double& rcond, solve_singularity_handler sing_handler) const { Matrix tmp (b); return solve (mattype, tmp, info, rcond, sing_handler).column (0); } ComplexColumnVector SparseMatrix::solve (SparseType &mattype, const ComplexColumnVector& b) const { int info; double rcond; return solve (mattype, b, info, rcond, 0); } ComplexColumnVector SparseMatrix::solve (SparseType &mattype, const ComplexColumnVector& b, int& info) const { double rcond; return solve (mattype, b, info, rcond, 0); } ComplexColumnVector SparseMatrix::solve (SparseType &mattype, const ComplexColumnVector& b, int& info, double& rcond) const { return solve (mattype, b, info, rcond, 0); } ComplexColumnVector SparseMatrix::solve (SparseType &mattype, const ComplexColumnVector& b, int& info, double& rcond, solve_singularity_handler sing_handler) const { ComplexMatrix tmp (b); return solve (mattype, tmp, info, rcond, sing_handler).column (0); } Matrix SparseMatrix::solve (const Matrix& b) const { int info; double rcond; return solve (b, info, rcond, 0); } Matrix SparseMatrix::solve (const Matrix& b, int& info) const { double rcond; return solve (b, info, rcond, 0); } Matrix SparseMatrix::solve (const Matrix& b, int& info, double& rcond) const { return solve (b, info, rcond, 0); } Matrix SparseMatrix::solve (const Matrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseType mattype (*this); return solve (mattype, b, err, rcond, sing_handler); } SparseMatrix SparseMatrix::solve (const SparseMatrix& b) const { int info; double rcond; return solve (b, info, rcond, 0); } SparseMatrix SparseMatrix::solve (const SparseMatrix& b, int& info) const { double rcond; return solve (b, info, rcond, 0); } SparseMatrix SparseMatrix::solve (const SparseMatrix& b, int& info, double& rcond) const { return solve (b, info, rcond, 0); } SparseMatrix SparseMatrix::solve (const SparseMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseType mattype (*this); return solve (mattype, b, err, rcond, sing_handler); } ComplexMatrix SparseMatrix::solve (const ComplexMatrix& b, int& info) const { double rcond; return solve (b, info, rcond, 0); } ComplexMatrix SparseMatrix::solve (const ComplexMatrix& b, int& info, double& rcond) const { return solve (b, info, rcond, 0); } ComplexMatrix SparseMatrix::solve (const ComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseType mattype (*this); return solve (mattype, b, err, rcond, sing_handler); } SparseComplexMatrix SparseMatrix::solve (const SparseComplexMatrix& b) const { int info; double rcond; return solve (b, info, rcond, 0); } SparseComplexMatrix SparseMatrix::solve (const SparseComplexMatrix& b, int& info) const { double rcond; return solve (b, info, rcond, 0); } SparseComplexMatrix SparseMatrix::solve (const SparseComplexMatrix& b, int& info, double& rcond) const { return solve (b, info, rcond, 0); } SparseComplexMatrix SparseMatrix::solve (const SparseComplexMatrix& b, int& err, double& rcond, solve_singularity_handler sing_handler) const { SparseType mattype (*this); return solve (mattype, b, err, rcond, sing_handler); } ColumnVector SparseMatrix::solve (const ColumnVector& b) const { int info; double rcond; return solve (b, info, rcond); } ColumnVector SparseMatrix::solve (const ColumnVector& b, int& info) const { double rcond; return solve (b, info, rcond); } ColumnVector SparseMatrix::solve (const ColumnVector& b, int& info, double& rcond) const { return solve (b, info, rcond, 0); } ColumnVector SparseMatrix::solve (const ColumnVector& b, int& info, double& rcond, solve_singularity_handler sing_handler) const { Matrix tmp (b); return solve (tmp, info, rcond, sing_handler).column (0); } ComplexColumnVector SparseMatrix::solve (const ComplexColumnVector& b) const { int info; double rcond; return solve (b, info, rcond, 0); } ComplexColumnVector SparseMatrix::solve (const ComplexColumnVector& b, int& info) const { double rcond; return solve (b, info, rcond, 0); } ComplexColumnVector SparseMatrix::solve (const ComplexColumnVector& b, int& info, double& rcond) const { return solve (b, info, rcond, 0); } ComplexColumnVector SparseMatrix::solve (const ComplexColumnVector& b, int& info, double& rcond, solve_singularity_handler sing_handler) const { ComplexMatrix tmp (b); return solve (tmp, info, rcond, sing_handler).column (0); } Matrix SparseMatrix::lssolve (const Matrix& b) const { int info; int rank; return lssolve (b, info, rank); } Matrix SparseMatrix::lssolve (const Matrix& b, int& info) const { int rank; return lssolve (b, info, rank); } Matrix SparseMatrix::lssolve (const Matrix& b, int& info, int& rank) const { info = -1; (*current_liboctave_error_handler) ("SparseMatrix::lssolve not implemented yet"); return Matrix (); } SparseMatrix SparseMatrix::lssolve (const SparseMatrix& b) const { int info; int rank; return lssolve (b, info, rank); } SparseMatrix SparseMatrix::lssolve (const SparseMatrix& b, int& info) const { int rank; return lssolve (b, info, rank); } SparseMatrix SparseMatrix::lssolve (const SparseMatrix& b, int& info, int& rank) const { info = -1; (*current_liboctave_error_handler) ("SparseMatrix::lssolve not implemented yet"); return SparseMatrix (); } ComplexMatrix SparseMatrix::lssolve (const ComplexMatrix& b) const { int info; int rank; return lssolve (b, info, rank); } ComplexMatrix SparseMatrix::lssolve (const ComplexMatrix& b, int& info) const { int rank; return lssolve (b, info, rank); } ComplexMatrix SparseMatrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const { info = -1; (*current_liboctave_error_handler) ("SparseMatrix::lssolve not implemented yet"); return ComplexMatrix (); } SparseComplexMatrix SparseMatrix::lssolve (const SparseComplexMatrix& b) const { int info; int rank; return lssolve (b, info, rank); } SparseComplexMatrix SparseMatrix::lssolve (const SparseComplexMatrix& b, int& info) const { int rank; return lssolve (b, info, rank); } SparseComplexMatrix SparseMatrix::lssolve (const SparseComplexMatrix& b, int& info, int& rank) const { info = -1; (*current_liboctave_error_handler) ("SparseMatrix::lssolve not implemented yet"); return SparseComplexMatrix (); } ColumnVector SparseMatrix::lssolve (const ColumnVector& b) const { int info; int rank; return lssolve (b, info, rank); } ColumnVector SparseMatrix::lssolve (const ColumnVector& b, int& info) const { int rank; return lssolve (b, info, rank); } ColumnVector SparseMatrix::lssolve (const ColumnVector& b, int& info, int& rank) const { Matrix tmp (b); return lssolve (tmp, info, rank).column (0); } ComplexColumnVector SparseMatrix::lssolve (const ComplexColumnVector& b) const { int info; int rank; return lssolve (b, info, rank); } ComplexColumnVector SparseMatrix::lssolve (const ComplexColumnVector& b, int& info) const { int rank; return lssolve (b, info, rank); } ComplexColumnVector SparseMatrix::lssolve (const ComplexColumnVector& b, int& info, int& rank) const { ComplexMatrix tmp (b); return lssolve (tmp, info, rank).column (0); } // other operations. SparseMatrix SparseMatrix::map (d_d_Mapper f) const { int nr = rows (); int nc = cols (); int nz = nnz (); bool f_zero = (f(0.0) == 0.0); // Count number of non-zero elements int nel = (f_zero ? 0 : nr*nc - nz); for (int i = 0; i < nz; i++) if (f (data(i)) != 0.0) nel++; SparseMatrix retval (nr, nc, nel); if (f_zero) { int ii = 0; for (int j = 0; j < nc; j++) { for (int i = 0; i < nr; i++) { double tmp = f (elem (i, j)); if (tmp != 0.0) { retval.data(ii) = tmp; retval.ridx(ii++) = i; } } retval.cidx(j+1) = ii; } } else { int ii = 0; for (int j = 0; j < nc; j++) { for (int i = cidx(j); i < cidx(j+1); i++) { retval.data(ii) = f (elem(i)); retval.ridx(ii++) = ridx(i); } retval.cidx(j+1) = ii; } } return retval; } SparseBoolMatrix SparseMatrix::map (b_d_Mapper f) const { int nr = rows (); int nc = cols (); int nz = nnz (); bool f_zero = f(0.0); // Count number of non-zero elements int nel = (f_zero ? 0 : nr*nc - nz); for (int i = 0; i < nz; i++) if (f (data(i)) != 0.0) nel++; SparseBoolMatrix retval (nr, nc, nel); if (f_zero) { int ii = 0; for (int j = 0; j < nc; j++) { for (int i = 0; i < nr; i++) { bool tmp = f (elem (i, j)); if (tmp) { retval.data(ii) = tmp; retval.ridx(ii++) = i; } } retval.cidx(j+1) = ii; } } else { int ii = 0; for (int j = 0; j < nc; j++) { for (int i = cidx(j); i < cidx(j+1); i++) { retval.data(ii) = f (elem(i)); retval.ridx(ii++) = ridx(i); } retval.cidx(j+1) = ii; } } return retval; } SparseMatrix& SparseMatrix::apply (d_d_Mapper f) { *this = map (f); return *this; } bool SparseMatrix::any_element_is_negative (bool neg_zero) const { int nel = nnz (); if (neg_zero) { for (int i = 0; i < nel; i++) if (lo_ieee_signbit (data (i))) return true; } else { for (int i = 0; i < nel; i++) if (data (i) < 0) return true; } return false; } bool SparseMatrix::any_element_is_inf_or_nan (void) const { int nel = nnz (); for (int i = 0; i < nel; i++) { double val = data (i); if (xisinf (val) || xisnan (val)) return true; } return false; } bool SparseMatrix::all_elements_are_int_or_inf_or_nan (void) const { int nel = nnz (); for (int 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 { int nel = nnz (); if (nel == 0) return false; max_val = data (0); min_val = data (0); for (int 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 { int nel = nnz (); for (int 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 { int nr = rows (); int nc = cols (); int nz1 = nnz (); int nz2 = nr*nc - nz1; SparseBoolMatrix r (nr, nc, nz2); int ii = 0; int jj = 0; r.cidx (0) = 0; for (int i = 0; i < nc; i++) { for (int 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; } // XXX FIXME XXX 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 { SPARSE_REDUCTION_OP (SparseMatrix, double, *=, 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 = elem (i, j); \ tmp[i] += d * d #define COL_EXPR \ double d = elem (i, j); \ 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 { int nz = nnz (); SparseMatrix retval (*this); for (int i = 0; i < nz; i++) retval.data(i) = fabs(retval.data(i)); return retval; } SparseMatrix SparseMatrix::diag (int k) const { int nnr = rows (); int nnc = cols (); if (k > 0) nnc -= k; else if (k < 0) nnr += k; SparseMatrix d; if (nnr > 0 && nnc > 0) { int ndiag = (nnr < nnc) ? nnr : nnc; // Count the number of non-zero elements int nel = 0; if (k > 0) { for (int i = 0; i < ndiag; i++) if (elem (i, i+k) != 0.) nel++; } else if ( k < 0) { for (int i = 0; i < ndiag; i++) if (elem (i-k, i) != 0.) nel++; } else { for (int i = 0; i < ndiag; i++) if (elem (i, i) != 0.) nel++; } d = SparseMatrix (ndiag, 1, nel); d.xcidx (0) = 0; d.xcidx (1) = nel; int ii = 0; if (k > 0) { for (int i = 0; i < ndiag; i++) { double tmp = elem (i, i+k); if (tmp != 0.) { d.xdata (ii) = tmp; d.xridx (ii++) = i; } } } else if ( k < 0) { for (int i = 0; i < ndiag; i++) { double tmp = elem (i-k, i); if (tmp != 0.) { d.xdata (ii) = tmp; d.xridx (ii++) = i; } } } else { for (int i = 0; i < ndiag; i++) { double tmp = elem (i, i); if (tmp != 0.) { d.xdata (ii) = tmp; d.xridx (ii++) = i; } } } } else (*current_liboctave_error_handler) ("diag: requested diagonal out of range"); return d; } Matrix SparseMatrix::matrix_value (void) const { int nr = rows (); int nc = cols (); Matrix retval (nr, nc, 0.0); for (int j = 0; j < nc; j++) for (int i = cidx(j); i < cidx(j+1); i++) retval.elem (ridx(i), j) = data (i); return retval; } std::ostream& operator << (std::ostream& os, const SparseMatrix& a) { int nc = a.cols (); // add one to the printed indices to go from // zero-based to one-based arrays for (int j = 0; j < nc; j++) { OCTAVE_QUIT; for (int 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) { int nr = a.rows (); int nc = a.cols (); int nz = a.nnz (); if (nr < 1 || nc < 1) is.clear (std::ios::badbit); else { int itmp, jtmp, jold = 0; double tmp; int ii = 0; a.cidx (0) = 0; for (int i = 0; i < nz; i++) { is >> itmp; itmp--; is >> jtmp; jtmp--; tmp = octave_read_double (is); if (is) { if (jold != jtmp) { for (int j = jold; j < jtmp; j++) a.cidx(j+1) = ii; jold = jtmp; } a.data (ii) = tmp; a.ridx (ii++) = itmp; } else goto done; } for (int 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<int>& vec, bool inv) const { return MSparse<double>::permute (vec, inv); } SparseMatrix SparseMatrix::ipermute (const Array<int>& vec) const { return MSparse<double>::ipermute (vec); } // matrix by matrix -> matrix operations SparseMatrix operator * (const SparseMatrix& m, const SparseMatrix& a) { #ifdef HAVE_SPARSE_BLAS // XXX FIXME XXX Isn't there a sparse BLAS ?? #else // Use Andy's sparse matrix multiply function SPARSE_SPARSE_MUL (SparseMatrix, double); #endif } // XXX FIXME XXX -- 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; int nr = m.rows (); int nc = m.columns (); EMPTY_RETURN_CHECK (SparseMatrix); // Count the number of non-zero elements if (d < 0.) { result = SparseMatrix (nr, nc, d); for (int j = 0; j < nc; j++) for (int i = m.cidx(j); i < m.cidx(j+1); i++) { double tmp = xmin (d, m.data (i)); if (tmp != 0.) { int idx = m.ridx(i) + j * nr; result.xdata(idx) = tmp; result.xridx(idx) = m.ridx(i); } } } else { int nel = 0; for (int j = 0; j < nc; j++) for (int i = m.cidx(j); i < m.cidx(j+1); i++) if (xmin (d, m.data (i)) != 0.) nel++; result = SparseMatrix (nr, nc, nel); int ii = 0; result.xcidx(0) = 0; for (int j = 0; j < nc; j++) { for (int 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())) { int a_nr = a.rows (); int a_nc = a.cols (); int b_nr = b.rows (); int 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 ())); int jx = 0; r.cidx (0) = 0; for (int i = 0 ; i < a_nc ; i++) { int ja = a.cidx(i); int ja_max = a.cidx(i+1); bool ja_lt_max= ja < ja_max; int jb = b.cidx(i); int 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; int nr = m.rows (); int nc = m.columns (); EMPTY_RETURN_CHECK (SparseMatrix); // Count the number of non-zero elements if (d > 0.) { result = SparseMatrix (nr, nc, d); for (int j = 0; j < nc; j++) for (int i = m.cidx(j); i < m.cidx(j+1); i++) { double tmp = xmax (d, m.data (i)); if (tmp != 0.) { int idx = m.ridx(i) + j * nr; result.xdata(idx) = tmp; result.xridx(idx) = m.ridx(i); } } } else { int nel = 0; for (int j = 0; j < nc; j++) for (int i = m.cidx(j); i < m.cidx(j+1); i++) if (xmax (d, m.data (i)) != 0.) nel++; result = SparseMatrix (nr, nc, nel); int ii = 0; result.xcidx(0) = 0; for (int j = 0; j < nc; j++) { for (int 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())) { int a_nr = a.rows (); int a_nc = a.cols (); int b_nr = b.rows (); int 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 ())); int jx = 0; r.cidx (0) = 0; for (int i = 0 ; i < a_nc ; i++) { int ja = a.cidx(i); int ja_max = a.cidx(i+1); bool ja_lt_max= ja < ja_max; int jb = b.cidx(i); int 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: *** */