Mercurial > octave
view libinterp/corefcn/hess.cc @ 21199:dd6605e1eaea
make gl2ps_renderer implementation private
* gl2ps-print.h: Rename from gl2ps-renderer.h.
* gl2ps-print.cc: Rename from gl2ps-renderer.cc.
* libinterp/corefcn/module.mk: Update.
* Canvas.cc, __init_fltk__.cc, __osmesa_print__.cc: Update.
author | John W. Eaton <jwe@octave.org> |
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date | Thu, 04 Feb 2016 18:07:46 -0500 |
parents | 228b65504557 |
children | fcac5dbbf9ed |
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/* Copyright (C) 1996-2015 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/>. */ #ifdef HAVE_CONFIG_H #include <config.h> #endif #include "CmplxHESS.h" #include "dbleHESS.h" #include "fCmplxHESS.h" #include "floatHESS.h" #include "defun.h" #include "error.h" #include "errwarn.h" #include "ovl.h" #include "utils.h" DEFUN (hess, args, nargout, "-*- texinfo -*-\n\ @deftypefn {} {@var{H} =} hess (@var{A})\n\ @deftypefnx {} {[@var{P}, @var{H}] =} hess (@var{A})\n\ @cindex Hessenberg decomposition\n\ Compute the Hessenberg decomposition of the matrix @var{A}.\n\ \n\ The Hessenberg decomposition is\n\ @tex\n\ $$\n\ A = PHP^T\n\ $$\n\ where $P$ is a square unitary matrix ($P^TP = I$), and $H$\n\ is upper Hessenberg ($H_{i,j} = 0, \\forall i > j+1$).\n\ @end tex\n\ @ifnottex\n\ @code{@var{P} * @var{H} * @var{P}' = @var{A}} where @var{P} is a square\n\ unitary matrix (@code{@var{P}' * @var{P} = I}, using complex-conjugate\n\ transposition) and @var{H} is upper Hessenberg\n\ (@code{@var{H}(i, j) = 0 forall i > j+1)}.\n\ @end ifnottex\n\ \n\ The Hessenberg decomposition is usually used as the first step in an\n\ eigenvalue computation, but has other applications as well\n\ (see @nospell{Golub, Nash, and Van Loan},\n\ IEEE Transactions on Automatic Control, 1979).\n\ @seealso{eig, chol, lu, qr, qz, schur, svd}\n\ @end deftypefn") { if (args.length () != 1) print_usage (); octave_value arg = args(0); octave_idx_type nr = arg.rows (); octave_idx_type nc = arg.columns (); int arg_is_empty = empty_arg ("hess", nr, nc); if (arg_is_empty < 0) return ovl (); else if (arg_is_empty > 0) return octave_value_list (2, Matrix ()); if (nr != nc) err_square_matrix_required ("hess", "A"); octave_value_list retval; if (arg.is_single_type ()) { if (arg.is_real_type ()) { FloatMatrix tmp = arg.float_matrix_value (); FloatHESS result (tmp); if (nargout <= 1) retval = ovl (result.hess_matrix ()); else retval = ovl (result.unitary_hess_matrix (), result.hess_matrix ()); } else if (arg.is_complex_type ()) { FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); FloatComplexHESS result (ctmp); if (nargout <= 1) retval = ovl (result.hess_matrix ()); else retval = ovl (result.unitary_hess_matrix (), result.hess_matrix ()); } } else { if (arg.is_real_type ()) { Matrix tmp = arg.matrix_value (); HESS result (tmp); if (nargout <= 1) retval = ovl (result.hess_matrix ()); else retval = ovl (result.unitary_hess_matrix (), result.hess_matrix ()); } else if (arg.is_complex_type ()) { ComplexMatrix ctmp = arg.complex_matrix_value (); ComplexHESS result (ctmp); if (nargout <= 1) retval = ovl (result.hess_matrix ()); else retval = ovl (result.unitary_hess_matrix (), result.hess_matrix ()); } else err_wrong_type_arg ("hess", arg); } return retval; } /* %!test %! a = [1, 2, 3; 5, 4, 6; 8, 7, 9]; %! [p, h] = hess (a); %! assert (p * h * p', a, sqrt (eps)); %!test %! a = single ([1, 2, 3; 5, 4, 6; 8, 7, 9]); %! [p, h] = hess (a); %! assert (p * h * p', a, sqrt (eps ("single"))); %!error hess () %!error hess ([1, 2; 3, 4], 2) %!error <must be a square matrix> hess ([1, 2; 3, 4; 5, 6]) */