Mercurial > octave
view libinterp/corefcn/inv.cc @ 23083:e9a0469dedd9 stable
maint: strip extra trailing newlines from files.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Fri, 20 Jan 2017 12:19:08 -0500 |
parents | 34ce5be04942 |
children | ef4d915df748 3ac9f9ecfae5 |
line wrap: on
line source
/* Copyright (C) 1996-2016 John W. Eaton This file is part of Octave. Octave is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. Octave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with Octave; see the file COPYING. If not, see <http://www.gnu.org/licenses/>. */ #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}) 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. @seealso{ldivide, rdivide} @end deftypefn */) { if (args.length () != 1) print_usage (); octave_value arg = args(0); if (arg.is_empty ()) 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.is_complex_type ()) { if (isfloat) { result = arg.float_complex_diag_matrix_value ().inverse (info); if (nargout > 1) frcond = arg.float_complex_diag_matrix_value ().rcond (); } else { result = arg.complex_diag_matrix_value ().inverse (info); if (nargout > 1) rcond = arg.complex_diag_matrix_value ().rcond (); } } else { if (isfloat) { result = arg.float_diag_matrix_value ().inverse (info); if (nargout > 1) frcond = arg.float_diag_matrix_value ().rcond (); } else { result = arg.diag_matrix_value ().inverse (info); 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.is_real_type ()) { 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.is_complex_type ()) { 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.is_real_type ()) { if (arg.is_sparse_type ()) { 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.is_complex_type ()) { if (arg.is_sparse_type ()) { 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"))) %!error inv () %!error inv ([1, 2; 3, 4], 2) %!error <must be a square matrix> inv ([1, 2; 3, 4; 5, 6]) %!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')); */ // FIXME: this should really be done with an alias, but // alias_builtin() won't do the right thing if we are actually using // dynamic linking. DEFUN (inverse, args, nargout, doc: /* -*- texinfo -*- @deftypefn {} {@var{x} =} inverse (@var{A}) @deftypefnx {} {[@var{x}, @var{rcond}] =} inverse (@var{A}) Compute the inverse of the square matrix @var{A}. This is an alias for @code{inv}. @seealso{inv} @end deftypefn */) { return Finv (args, nargout); }