Mercurial > octave
view libinterp/corefcn/inv.cc @ 29359:7854d5752dd2
maint: merge stable to default.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 10 Feb 2021 10:10:40 -0500 |
parents | 06c8e0877864 0a5b15007766 |
children | 32c3a5805893 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1996-2021 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // This file is part of Octave. // // Octave is free software: you can redistribute it and/or modify it // under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // Octave is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with Octave; see the file COPYING. If not, see // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include "defun.h" #include "error.h" #include "errwarn.h" #include "ovl.h" #include "ops.h" #include "ov-re-diag.h" #include "ov-cx-diag.h" #include "ov-flt-re-diag.h" #include "ov-flt-cx-diag.h" #include "ov-perm.h" DEFUN (inv, args, nargout, doc: /* -*- texinfo -*- @deftypefn {} {@var{x} =} inv (@var{A}) @deftypefnx {} {[@var{x}, @var{rcond}] =} inv (@var{A}) @deftypefnx {} {[@dots{}] =} inverse (@dots{}) Compute the inverse of the square matrix @var{A}. Return an estimate of the reciprocal condition number if requested, otherwise warn of an ill-conditioned matrix if the reciprocal condition number is small. In general it is best to avoid calculating the inverse of a matrix directly. For example, it is both faster and more accurate to solve systems of equations (@var{A}*@math{x} = @math{b}) with @code{@var{y} = @var{A} \ @math{b}}, rather than @code{@var{y} = inv (@var{A}) * @math{b}}. If called with a sparse matrix, then in general @var{x} will be a full matrix requiring significantly more storage. Avoid forming the inverse of a sparse matrix if possible. @code{inverse} is an alias and may be used identically in place of @code{inv}. @seealso{ldivide, rdivide, pinv} @end deftypefn */) { if (args.length () != 1) print_usage (); octave_value arg = args(0); if (arg.isempty ()) return ovl (Matrix ()); if (arg.rows () != arg.columns ()) err_square_matrix_required ("inverse", "A"); octave_value result; octave_idx_type info; double rcond = 0.0; float frcond = 0.0; bool isfloat = arg.is_single_type (); if (arg.is_diag_matrix ()) { rcond = 1.0; frcond = 1.0f; if (arg.iscomplex ()) { if (isfloat) { result = arg.float_complex_diag_matrix_value ().inverse (info); if (info == -1) frcond = 0.0f; else if (nargout > 1) frcond = arg.float_complex_diag_matrix_value ().rcond (); } else { result = arg.complex_diag_matrix_value ().inverse (info); if (info == -1) rcond = 0.0; else if (nargout > 1) rcond = arg.complex_diag_matrix_value ().rcond (); } } else { if (isfloat) { result = arg.float_diag_matrix_value ().inverse (info); if (info == -1) frcond = 0.0f; else if (nargout > 1) frcond = arg.float_diag_matrix_value ().rcond (); } else { result = arg.diag_matrix_value ().inverse (info); if (info == -1) rcond = 0.0; else if (nargout > 1) rcond = arg.diag_matrix_value ().rcond (); } } } else if (arg.is_perm_matrix ()) { rcond = 1.0; info = 0; result = arg.perm_matrix_value ().inverse (); } else if (isfloat) { if (arg.isreal ()) { FloatMatrix m = arg.float_matrix_value (); MatrixType mattyp = args(0).matrix_type (); result = m.inverse (mattyp, info, frcond, 1); args(0).matrix_type (mattyp); } else if (arg.iscomplex ()) { FloatComplexMatrix m = arg.float_complex_matrix_value (); MatrixType mattyp = args(0).matrix_type (); result = m.inverse (mattyp, info, frcond, 1); args(0).matrix_type (mattyp); } } else { if (arg.isreal ()) { if (arg.issparse ()) { SparseMatrix m = arg.sparse_matrix_value (); MatrixType mattyp = args(0).matrix_type (); result = m.inverse (mattyp, info, rcond, 1); args(0).matrix_type (mattyp); } else { Matrix m = arg.matrix_value (); MatrixType mattyp = args(0).matrix_type (); result = m.inverse (mattyp, info, rcond, 1); args(0).matrix_type (mattyp); } } else if (arg.iscomplex ()) { if (arg.issparse ()) { SparseComplexMatrix m = arg.sparse_complex_matrix_value (); MatrixType mattyp = args(0).matrix_type (); result = m.inverse (mattyp, info, rcond, 1); args(0).matrix_type (mattyp); } else { ComplexMatrix m = arg.complex_matrix_value (); MatrixType mattyp = args(0).matrix_type (); result = m.inverse (mattyp, info, rcond, 1); args(0).matrix_type (mattyp); } } else err_wrong_type_arg ("inv", arg); } octave_value_list retval (nargout > 1 ? 2 : 1); retval(0) = result; if (nargout > 1) retval(1) = (isfloat ? octave_value (frcond) : octave_value (rcond)); bool rcond_plus_one_eq_one = false; if (isfloat) { volatile float xrcond = frcond; rcond_plus_one_eq_one = xrcond + 1.0f == 1.0f; } else { volatile double xrcond = rcond; rcond_plus_one_eq_one = xrcond + 1.0 == 1.0; } if (nargout < 2 && (info == -1 || rcond_plus_one_eq_one)) octave::warn_singular_matrix (isfloat ? frcond : rcond); return retval; } /* %!assert (inv ([1, 2; 3, 4]), [-2, 1; 1.5, -0.5], sqrt (eps)) %!assert (inv (single ([1, 2; 3, 4])), single ([-2, 1; 1.5, -0.5]), sqrt (eps ("single"))) ## Test special inputs %!assert (inv (zeros (2,0)), []) %!warning <matrix singular> assert (inv (Inf), 0) %!warning <matrix singular> assert (inv (-Inf), -0) %!warning <matrix singular> assert (inv (single (Inf)), single (0)) %!warning <matrix singular> assert (inv (complex (1, Inf)), 0) %!warning <matrix singular> assert (inv (single (complex (1,Inf))), single (0)) %!test %! [xinv, rcond] = inv (single ([1,2;3,4])); %! assert (isa (xinv, "single")); %! assert (isa (rcond, "single")); %!test %! [xinv, rcond] = inv ([1,2;3,4]); %! assert (isa (xinv, "double")); %! assert (isa (rcond, "double")); %!testif HAVE_UMFPACK <*56232> %! fail ("A = inv (sparse ([1, 2;0 ,0]))", "warning", "matrix singular"); %! assert (A, sparse ([Inf, Inf; 0, 0])); %!testif HAVE_UMFPACK <*56232> %! fail ("A = inv (sparse ([1i, 2;0 ,0]))", "warning", "matrix singular"); %! assert (A, sparse ([Inf, Inf; 0, 0])); %!test %! fail ("A = inv (diag ([1, 0, 1]))", "warning", "matrix singular"); %! assert (A, diag ([Inf, Inf, Inf])); %!error <inverse of the null matrix not defined> inv (diag ([0, 0])) %!error <inverse of the null matrix not defined> inv (diag (complex ([0, 0]))) %!testif HAVE_UMFPACK <*56232> %! fail ("A = inv (sparse ([1, 0, 0; 0, 0, 0; 0, 0, 1]))", "warning", "matrix singular"); %! assert (A, sparse ([Inf, 0, 0; 0, 0, 0; 0, 0, Inf])); %!error inv () %!error inv ([1, 2; 3, 4], 2) %!error <must be a square matrix> inv ([1, 2; 3, 4; 5, 6]) %!error <inverse of the null matrix not defined> inv (sparse (2, 2, 0)) */ DEFALIAS (inverse, inv);