Mercurial > octave
view libinterp/corefcn/pinv.cc @ 27800:5a6a19a4e3da
doc: Use Texinfo non-sentence ending periods in citations.
* geometry.txi, quadcc.cc, rand.cc, sqrtm.cc, symrcm.cc, integral2.m,
integral3.m, quad2d.m, quadgk.m, quadl.m, cubehelix.m, commutation_matrix.m,
condest.m, duplication_matrix.m, normest1.m, qmr.m, cosint.m, gammainc.m,
gammaincinv.m, invhilb.m:
Use Texinfo non-sentence ending periods in citations.
author | Rik <rik@octave.org> |
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date | Tue, 10 Dec 2019 15:17:01 -0800 |
parents | 00f796120a6d |
children | b442ec6dda5c |
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/* Copyright (C) 1996-2019 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 <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 (pinv, args, , doc: /* -*- texinfo -*- @deftypefn {} {} pinv (@var{x}) @deftypefnx {} {} pinv (@var{x}, @var{tol}) Return the @nospell{Moore-Penrose} pseudoinverse of @var{x}. Singular values less than @var{tol} are ignored. If the second argument is omitted, it is taken to be @example tol = max ([rows(@var{x}), columns(@var{x})]) * norm (@var{x}) * eps @end example @seealso{inv, ldivide} @end deftypefn */) { int nargin = args.length (); if (nargin < 1 || nargin > 2) print_usage (); octave_value arg = args(0); if (arg.isempty ()) return ovl (Matrix ()); octave_value retval; bool isfloat = arg.is_single_type (); if (arg.is_diag_matrix ()) { if (isfloat) { float tol = 0.0; if (nargin == 2) tol = args(1).float_value (); if (tol < 0.0) error ("pinv: TOL must be greater than zero"); if (arg.isreal ()) retval = arg.float_diag_matrix_value ().pseudo_inverse (tol); else retval = arg.float_complex_diag_matrix_value ().pseudo_inverse (tol); } else { double tol = 0.0; if (nargin == 2) tol = args(1).double_value (); if (tol < 0.0) error ("pinv: TOL must be greater than zero"); if (arg.isreal ()) retval = arg.diag_matrix_value ().pseudo_inverse (tol); else retval = arg.complex_diag_matrix_value ().pseudo_inverse (tol); } } else if (arg.is_perm_matrix ()) { retval = arg.perm_matrix_value ().inverse (); } else if (isfloat) { float tol = 0.0; if (nargin == 2) tol = args(1).float_value (); if (tol < 0.0) error ("pinv: TOL must be greater than zero"); if (arg.isreal ()) { FloatMatrix m = arg.float_matrix_value (); retval = m.pseudo_inverse (tol); } else if (arg.iscomplex ()) { FloatComplexMatrix m = arg.float_complex_matrix_value (); retval = m.pseudo_inverse (tol); } else err_wrong_type_arg ("pinv", arg); } else { double tol = 0.0; if (nargin == 2) tol = args(1).double_value (); if (tol < 0.0) error ("pinv: TOL must be greater than zero"); if (arg.isreal ()) { Matrix m = arg.matrix_value (); retval = m.pseudo_inverse (tol); } else if (arg.iscomplex ()) { ComplexMatrix m = arg.complex_matrix_value (); retval = m.pseudo_inverse (tol); } else err_wrong_type_arg ("pinv", arg); } return retval; } /* %!shared a, b, tol, hitol, d, u, x, y %! old_state = rand ("state"); %! restore_state = onCleanup (@() rand ("state", old_state)); %! rand ("state", 42); # initialize generator to make behavior reproducible %! a = reshape (rand*[1:16], 4, 4); # Rank 2 matrix %! b = pinv (a); %! tol = 4e-14; %! hitol = 40*sqrt (eps); %! d = diag ([rand, rand, hitol, hitol]); %! u = rand (4); # Could be singular by freak accident %! x = inv (u)*d*u; %! y = pinv (x, sqrt (eps)); ## Verify Penrose conditions for pseudoinverse %!assert (a*b*a, a, tol) %!assert (b*a*b, b, tol) %!assert ((b*a)', b*a, tol) %!assert ((a*b)', a*b, tol) %!assert (x*y*x, x, -hitol) %!assert (y*x*y, y, -hitol) %!assert ((x*y)', x*y, hitol) %!assert ((y*x)', y*x, hitol) ## Clear shared variables %!shared ## Test pinv for Diagonal matrices %!test %! x = diag ([3 2 1 0 -0.5]); %! y = pinv (x); %! assert (typeinfo (y)(1:8), "diagonal"); %! assert (isa (y, "double")); %! assert (diag (y), [1/3, 1/2, 1, 0 1/-0.5]'); %! y = pinv (x, 1); %! assert (diag (y), [1/3 1/2 1 0 0]'); %! y = pinv (x, 2); %! assert (diag (y), [1/3 1/2 0 0 0]'); ## Test special case of 0 scalars and vectors %!assert (pinv (0), 0) %!assert (pinv ([0, 0, 0]), [0; 0; 0]) %!assert (pinv (single (0)), single (0)) %!assert (pinv (single ([0, 0, 0])), single ([0; 0; 0])) %!assert (pinv (complex (0,0)), 0) %!assert (pinv (complex ([0,0,0], [0,0,0])), [0; 0; 0]) %!assert (pinv (complex (single (0),0)), single (0)) %!assert (pinv (complex (single ([0,0,0]), [0,0,0])), single ([0; 0; 0])) */