Mercurial > octave
view libinterp/corefcn/hess.cc @ 29654:d13d090cb03a stable
use std::size_t and std::ptrdiff_t in C++ code (bug #60471)
Files affected: make_int.cc, file-editor-tab.cc, octave-qscintilla.cc,
Cell.cc, Cell.h, call-stack.cc, call-stack.h, cellfun.cc, data.cc,
debug.cc, dlmread.cc, error.cc, event-queue.h, fcn-info.cc,
fcn-info.h, file-io.cc, ft-text-renderer.cc, gl2ps-print.cc,
graphics.cc, graphics.in.h, help.cc, hex2num.cc, input.cc,
latex-text-renderer.cc, load-path.cc, load-save.cc, load-save.h,
ls-hdf5.cc, ls-mat-ascii.cc, ls-mat5.cc, ls-oct-text.cc, mex.cc,
mexproto.h, mxarray.h, oct-map.cc, oct-stream.cc, oct-stream.h,
pager.cc, pager.h, pr-output.cc, regexp.cc, settings.h,
stack-frame.cc, stack-frame.h, strfns.cc, syminfo.cc, symrec.h,
symscope.cc, symscope.h, symtab.cc, sysdep.cc, toplev.cc, utils.cc,
utils.h, variables.cc, __fltk_uigetfile__.cc, __init_fltk__.cc,
audioread.cc, gzip.cc, cdef-class.cc, cdef-manager.cc, cdef-method.cc,
cdef-object.cc, cdef-object.h, ov-base-diag.cc, ov-base-diag.h,
ov-base-mat.cc, ov-base-mat.h, ov-base-scalar.cc, ov-base-scalar.h,
ov-base-sparse.h, ov-base.cc, ov-base.h, ov-cell.cc, ov-cell.h,
ov-ch-mat.cc, ov-class.cc, ov-class.h, ov-classdef.cc,
ov-fcn-handle.cc, ov-java.cc, ov-lazy-idx.h, ov-perm.cc, ov-perm.h,
ov-range.h, ov-str-mat.cc, ov-struct.cc, ov-struct.h, ov-usr-fcn.cc,
ov-usr-fcn.h, ov.cc, ov.h, ovl.cc, octave.cc, bp-table.cc, jit-ir.cc,
jit-ir.h, jit-typeinfo.cc, jit-typeinfo.h, jit-util.h, lex.h, lex.ll,
oct-lvalue.cc, oct-parse.yy, parse.h, profiler.h, pt-eval.cc,
pt-eval.h, pt-jit.cc, pt-jit.h, pt-pr-code.cc, pt-tm-const.cc,
pt-tm-const.h, Array.h, CMatrix.cc, DiagArray2.h, PermMatrix.h,
Sparse.h, dMatrix.cc, fCMatrix.cc, fMatrix.cc, bsxfun-defs.cc,
oct-fftw.cc, oct-fftw.h, randpoisson.cc, sparse-chol.cc,
mx-inlines.cc, file-ops.cc, lo-sysdep.cc, oct-env.cc, oct-time.cc,
action-container.cc, action-container.h, base-list.h, caseless-str.h,
cmd-edit.cc, cmd-hist.cc, data-conv.cc, data-conv.h, f77-fcn.h,
file-info.cc, file-info.h, kpse.cc, kpse.h, lo-cutils.h, lo-hash.h,
lo-regexp.cc, oct-base64.cc, oct-base64.h, oct-binmap.h, oct-glob.cc,
oct-shlib.cc, oct-shlib.h, oct-sort.cc, oct-sparse.h, oct-string.cc,
quit.cc, unwind-prot.h, url-transfer.cc, main.in.cc, mkoctfile.in.cc,
and shared-fcns.h.
(grafted from aef11bb4e6d1f303ad9de5688fcb7244ef48867e)
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Wed, 28 Apr 2021 22:57:42 -0400 |
parents | 0a5b15007766 |
children | 7854d5752dd2 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1996-2021 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // 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 "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.isreal ()) { 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.isreal ()) { 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]) */