Mercurial > octave-nkf
view src/DLD-FUNCTIONS/eig.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 | 18c4ded8612a |
children | eb63fbe60fab |
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/* Copyright (C) 1996, 1997, 1999, 2000, 2003, 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 "EIG.h" #include "fEIG.h" #include "defun-dld.h" #include "error.h" #include "gripes.h" #include "oct-obj.h" #include "utils.h" DEFUN_DLD (eig, args, nargout, "-*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{lambda} =} eig (@var{a})\n\ @deftypefnx {Loadable Function} {@var{lambda} =} eig (@var{a}, @var{b})\n\ @deftypefnx {Loadable Function} {[@var{v}, @var{lambda}] =} eig (@var{a})\n\ @deftypefnx {Loadable Function} {[@var{v}, @var{lambda}] =} eig (@var{a}, @var{b})\n\ The eigenvalues (and eigenvectors) of a matrix are computed in a several\n\ step process which begins with a Hessenberg decomposition, followed by a\n\ Schur decomposition, from which the eigenvalues are apparent. The\n\ eigenvectors, when desired, are computed by further manipulations of the\n\ Schur decomposition.\n\ \n\ The eigenvalues returned by @code{eig} are not ordered.\n\ @end deftypefn") { octave_value_list retval; int nargin = args.length (); if (nargin > 2 || nargin == 0 || nargout > 2) { print_usage (); return retval; } octave_value arg_a, arg_b; octave_idx_type nr_a = 0, nr_b = 0; octave_idx_type nc_a = 0, nc_b = 0; arg_a = args(0); nr_a = arg_a.rows (); nc_a = arg_a.columns (); int arg_is_empty = empty_arg ("eig", nr_a, nc_a); if (arg_is_empty < 0) return retval; else if (arg_is_empty > 0) return octave_value_list (2, Matrix ()); if (!(arg_a.is_single_type () || arg_a.is_double_type ())) { gripe_wrong_type_arg ("eig", arg_a); return retval; } if (nargin == 2) { arg_b = args(1); nr_b = arg_b.rows (); nc_b = arg_b.columns (); arg_is_empty = empty_arg ("eig", nr_b, nc_b); if (arg_is_empty < 0) return retval; else if (arg_is_empty > 0) return octave_value_list (2, Matrix ()); if (!(arg_b.is_single_type() || arg_b.is_double_type ())) { gripe_wrong_type_arg ("eig", arg_b); return retval; } } if (nr_a != nc_a) { gripe_square_matrix_required ("eig"); return retval; } if (nargin == 2 && nr_b != nc_b) { gripe_square_matrix_required ("eig"); return retval; } Matrix tmp_a, tmp_b; ComplexMatrix ctmp_a, ctmp_b; FloatMatrix ftmp_a, ftmp_b; FloatComplexMatrix fctmp_a, fctmp_b; if (arg_a.is_single_type ()) { FloatEIG result; if (nargin == 1) { if (arg_a.is_real_type ()) { ftmp_a = arg_a.float_matrix_value (); if (error_state) return retval; else result = FloatEIG (ftmp_a, nargout > 1); } else { fctmp_a = arg_a.float_complex_matrix_value (); if (error_state) return retval; else result = FloatEIG (fctmp_a, nargout > 1); } } else if (nargin == 2) { if (arg_a.is_real_type () && arg_b.is_real_type ()) { ftmp_a = arg_a.float_matrix_value (); ftmp_b = arg_b.float_matrix_value (); if (error_state) return retval; else result = FloatEIG (ftmp_a, ftmp_b, nargout > 1); } else { fctmp_a = arg_a.float_complex_matrix_value (); fctmp_b = arg_b.float_complex_matrix_value (); if (error_state) return retval; else result = FloatEIG (fctmp_a, fctmp_b, nargout > 1); } } if (! error_state) { if (nargout == 0 || nargout == 1) { retval(0) = result.eigenvalues (); } else { // Blame it on Matlab. FloatComplexDiagMatrix d (result.eigenvalues ()); retval(1) = d; retval(0) = result.eigenvectors (); } } } else { EIG result; if (nargin == 1) { if (arg_a.is_real_type ()) { tmp_a = arg_a.matrix_value (); if (error_state) return retval; else result = EIG (tmp_a, nargout > 1); } else { ctmp_a = arg_a.complex_matrix_value (); if (error_state) return retval; else result = EIG (ctmp_a, nargout > 1); } } else if (nargin == 2) { if (arg_a.is_real_type () && arg_b.is_real_type ()) { tmp_a = arg_a.matrix_value (); tmp_b = arg_b.matrix_value (); if (error_state) return retval; else result = EIG (tmp_a, tmp_b, nargout > 1); } else { ctmp_a = arg_a.complex_matrix_value (); ctmp_b = arg_b.complex_matrix_value (); if (error_state) return retval; else result = EIG (ctmp_a, ctmp_b, nargout > 1); } } if (! error_state) { if (nargout == 0 || nargout == 1) { retval(0) = result.eigenvalues (); } else { // Blame it on Matlab. ComplexDiagMatrix d (result.eigenvalues ()); retval(1) = d; retval(0) = result.eigenvectors (); } } } return retval; } /* %!assert(eig ([1, 2; 2, 1]), [-1; 3], sqrt (eps)); %!test %! [v, d] = eig ([1, 2; 2, 1]); %! x = 1 / sqrt (2); %! assert(d, [-1, 0; 0, 3], sqrt (eps)); %! assert(v, [-x, x; x, x], sqrt (eps)); %!assert(eig (single ([1, 2; 2, 1])), single([-1; 3]), sqrt (eps('single'))); %!test %! [v, d] = eig (single([1, 2; 2, 1])); %! x = single(1 / sqrt (2)); %! assert(d, single([-1, 0; 0, 3]), sqrt (eps('single'))); %! assert(v, [-x, x; x, x], sqrt (eps('single'))); %!test %! A = [1, 2; -1, 1]; B = [3, 3; 1, 2]; %! [v, d] = eig (A, B); %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); %!test %! A = single([1, 2; -1, 1]); B = single([3, 3; 1, 2]); %! [v, d] = eig (A, B); %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps('single'))); %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps('single'))); %!test %! A = [1, 2; 2, 1]; B = [3, -2; -2, 3]; %! [v, d] = eig (A, B); %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); %!test %! A = single([1, 2; 2, 1]); B = single([3, -2; -2, 3]); %! [v, d] = eig (A, B); %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps('single'))); %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps('single'))); %!test %! A = [1+3i, 2+i; 2-i, 1+3i]; B = [5+9i, 2+i; 2-i, 5+9i]; %! [v, d] = eig (A, B); %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); %!test %! A = single([1+3i, 2+i; 2-i, 1+3i]); B = single([5+9i, 2+i; 2-i, 5+9i]); %! [v, d] = eig (A, B); %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps('single'))); %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps('single'))); %!test %! A = [1+3i, 2+3i; 3-8i, 8+3i]; B = [8+i, 3+i; 4-9i, 3+i]; %! [v, d] = eig (A, B); %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); %!test %! A = single([1+3i, 2+3i; 3-8i, 8+3i]); B = single([8+i, 3+i; 4-9i, 3+i]); %! [v, d] = eig (A, B); %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps('single'))); %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps('single'))); %!test %! A = [1, 2; 3, 8]; B = [8, 3; 4, 3]; %! [v, d] = eig (A, B); %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); %!error <Invalid call to eig.*> eig (); %!error <Invalid call to eig.*> eig ([1, 2; 3, 4], [4, 3; 2, 1], 1); %!error eig ([1, 2; 3, 4], 2); %!error eig ([1, 2; 3, 4; 5, 6]); %!error eig ("abcd"); %!error eig ([1 2 ; 2 3], "abcd"); %!error eig (false, [1 2 ; 2 3]); */ /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */