Mercurial > octave
view libinterp/corefcn/hess.cc @ 23581:c3075ae020e1
maint: Deprecate is_complex_type and replace with iscomplex.
* ov.h (is_complex_type): Use OCTAVE_DEPRECATED macro around function.
* ov.h (iscomplex): New function.
* __ichol__.cc, __ilu__.cc, balance.cc, bsxfun.cc, cellfun.cc, conv2.cc,
daspk.cc, dasrt.cc, dassl.cc, data.cc, det.cc, dot.cc, fft.cc, fft2.cc,
fftn.cc, filter.cc, find.cc, givens.cc, graphics.cc, gsvd.cc, hess.cc,
hex2num.cc, inv.cc, kron.cc, lookup.cc, ls-mat-ascii.cc, ls-mat4.cc,
ls-mat5.cc, lsode.cc, lu.cc, matrix_type.cc, mex.cc, mgorth.cc, ordschur.cc,
pinv.cc, psi.cc, quad.cc, qz.cc, rcond.cc, schur.cc, sparse-xpow.cc, sparse.cc,
sqrtm.cc, svd.cc, sylvester.cc, symtab.cc, typecast.cc, variables.cc, xnorm.cc,
__eigs__.cc, amd.cc, ccolamd.cc, chol.cc, colamd.cc, qr.cc, symbfact.cc,
ov-base.h, ov-complex.h, ov-cx-diag.h, ov-cx-mat.h, ov-cx-sparse.h,
ov-flt-complex.h, ov-flt-cx-diag.h, ov-flt-cx-mat.h, jit-typeinfo.cc,
pt-tm-const.cc: Replace instances of is_complex_type with iscomplex.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 12 Jun 2017 21:18:23 -0700 |
parents | 80c42f4cca13 |
children | 0cc2011d800e |
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/* Copyright (C) 1996-2017 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 "hess.h" #include "defun.h" #include "error.h" #include "errwarn.h" #include "ovl.h" DEFUN (hess, args, nargout, doc: /* -*- texinfo -*- @deftypefn {} {@var{H} =} hess (@var{A}) @deftypefnx {} {[@var{P}, @var{H}] =} hess (@var{A}) @cindex Hessenberg decomposition Compute the Hessenberg decomposition of the matrix @var{A}. The Hessenberg decomposition is @tex $$ A = PHP^T $$ where $P$ is a square unitary matrix ($P^TP = I$), and $H$ is upper Hessenberg ($H_{i,j} = 0, \forall i > j+1$). @end tex @ifnottex @code{@var{P} * @var{H} * @var{P}' = @var{A}} where @var{P} is a square unitary matrix (@code{@var{P}' * @var{P} = I}, using complex-conjugate transposition) and @var{H} is upper Hessenberg (@code{@var{H}(i, j) = 0 forall i > j+1)}. @end ifnottex The Hessenberg decomposition is usually used as the first step in an eigenvalue computation, but has other applications as well (see @nospell{Golub, Nash, and Van Loan}, IEEE Transactions on Automatic Control, 1979). @seealso{eig, chol, lu, qr, qz, schur, svd} @end deftypefn */) { if (args.length () != 1) print_usage (); octave_value arg = args(0); if (arg.isempty ()) return octave_value_list (2, Matrix ()); if (arg.rows () != arg.columns ()) 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 (); octave::math::hess<FloatMatrix> result (tmp); if (nargout <= 1) retval = ovl (result.hess_matrix ()); else retval = ovl (result.unitary_hess_matrix (), result.hess_matrix ()); } else if (arg.iscomplex ()) { FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); octave::math::hess<FloatComplexMatrix> 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 (); octave::math::hess<Matrix> result (tmp); if (nargout <= 1) retval = ovl (result.hess_matrix ()); else retval = ovl (result.unitary_hess_matrix (), result.hess_matrix ()); } else if (arg.iscomplex ()) { ComplexMatrix ctmp = arg.complex_matrix_value (); octave::math::hess<ComplexMatrix> 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]) */