Mercurial > octave-nkf
view src/DLD-FUNCTIONS/hess.cc @ 8828:8463d1a2e544
Doc fixes.
* 2]$$. => 2].$$
* @var{extrapval} => @var{extrapval}.
* call helloworld.oct => called @file{helloworld.oct}
* @itemize => @table @code
* shows. => shows:
* save => @code{save}
* @ref{Breakpoints} => @pxref{Breakpoints}
* add @noindent following example
* which is computed => and compute it
* clarify wording
* remove comma
* good => well
* set => number
* by writing => with the command
* has the option of directly calling => can call
* [-like-] {+of the right size,+}
* solvers => routines
* handle => test for
* add introductory section
* add following
* {+the+} [0..bitmax] => [0,bitmax]
* of the => with
* number => value
* add usual
* Besides when doing comparisons, logical => Logical {+also+}
* array comparison => array, comparisons
* param => parameter
* works very similar => is similar
* strings, => strings
* most simple => simplest
* easier => more easily
* like => as
* called => called,
* clarify wording
* you should simply type => use
* clarify wording
* means => way
* equally => also
* [-way much-] {+way+}
* add with mean value parameter given by the first argument, @var{l}
* add Functions described as @dfn{mapping functions} apply the given
operation to each element when given a matrix argument.
* in this brief introduction => here
* It is worth noticing => Note
* add following
* means => ways
author | Brian Gough <bjg@network-theory.co.uk> |
---|---|
date | Fri, 20 Feb 2009 11:17:01 -0500 |
parents | 81d6ab3ac93c |
children | eb63fbe60fab |
line wrap: on
line source
/* Copyright (C) 1996, 1997, 1999, 2000, 2004, 2005, 2006, 2007 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-dld.h" #include "error.h" #include "gripes.h" #include "oct-obj.h" #include "utils.h" DEFUN_DLD (hess, args, nargout, "-*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{h} =} hess (@var{a})\n\ @deftypefnx {Loadable Function} {[@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 usually used as the first step in an\n\ eigenvalue computation, but has other applications as well (see Golub,\n\ Nash, and Van Loan, IEEE Transactions on Automatic Control, 1979). The\n\ Hessenberg decomposition is\n\ @iftex\n\ @tex\n\ $$\n\ A = PHP^T\n\ $$\n\ where $P$ is a square unitary matrix ($P^HP = I$), and $H$\n\ is upper Hessenberg ($H_{i,j} = 0, \\forall i \\ge j+1$).\n\ @end tex\n\ @end iftex\n\ @ifnottex\n\ @code{p * h * p' = a} where @code{p} is a square unitary matrix\n\ (@code{p' * p = I}, using complex-conjugate transposition) and @code{h}\n\ is upper Hessenberg (@code{i >= j+1 => h (i, j) = 0}).\n\ @end ifnottex\n\ @end deftypefn") { octave_value_list retval; int nargin = args.length (); if (nargin != 1 || nargout > 2) { print_usage (); return retval; } 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 retval; else if (arg_is_empty > 0) return octave_value_list (2, Matrix ()); if (nr != nc) { gripe_square_matrix_required ("hess"); return retval; } if (arg.is_single_type ()) { if (arg.is_real_type ()) { FloatMatrix tmp = arg.float_matrix_value (); if (! error_state) { FloatHESS result (tmp); retval(1) = result.hess_matrix (); retval(0) = result.unitary_hess_matrix (); } } else if (arg.is_complex_type ()) { FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); if (! error_state) { FloatComplexHESS result (ctmp); retval(1) = result.hess_matrix (); retval(0) = result.unitary_hess_matrix (); } } } else { if (arg.is_real_type ()) { Matrix tmp = arg.matrix_value (); if (! error_state) { HESS result (tmp); retval(1) = result.hess_matrix (); retval(0) = result.unitary_hess_matrix (); } } else if (arg.is_complex_type ()) { ComplexMatrix ctmp = arg.complex_matrix_value (); if (! error_state) { ComplexHESS result (ctmp); retval(1) = result.hess_matrix (); retval(0) = result.unitary_hess_matrix (); } } else { gripe_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 <Invalid call to hess.*> hess (); %!error <Invalid call to hess.*> hess ([1, 2; 3, 4], 2); %!error hess ([1, 2; 3, 4; 5, 6]); */ /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */