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annotate libinterp/corefcn/hess.cc @ 17787:175b392e91fe

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Use GNU style coding conventions for code in libinterp/ * libinterp/corefcn/Cell.h, libinterp/corefcn/__contourc__.cc, libinterp/corefcn/__dispatch__.cc, libinterp/corefcn/__lin_interpn__.cc, libinterp/corefcn/__pchip_deriv__.cc, libinterp/corefcn/__qp__.cc, libinterp/corefcn/balance.cc, libinterp/corefcn/besselj.cc, libinterp/corefcn/betainc.cc, libinterp/corefcn/bitfcns.cc, libinterp/corefcn/bsxfun.cc, libinterp/corefcn/c-file-ptr-stream.cc, libinterp/corefcn/c-file-ptr-stream.h, libinterp/corefcn/cellfun.cc, libinterp/corefcn/colloc.cc, libinterp/corefcn/comment-list.h, libinterp/corefcn/conv2.cc, libinterp/corefcn/daspk.cc, libinterp/corefcn/dasrt.cc, libinterp/corefcn/dassl.cc, libinterp/corefcn/data.cc, libinterp/corefcn/debug.cc, libinterp/corefcn/defaults.cc, libinterp/corefcn/defaults.in.h, libinterp/corefcn/defun-int.h, libinterp/corefcn/defun.cc, libinterp/corefcn/det.cc, libinterp/corefcn/dirfns.cc, libinterp/corefcn/display.cc, libinterp/corefcn/dlmread.cc, libinterp/corefcn/dot.cc, libinterp/corefcn/dynamic-ld.cc, libinterp/corefcn/dynamic-ld.h, libinterp/corefcn/eig.cc, libinterp/corefcn/ellipj.cc, libinterp/corefcn/error.cc, libinterp/corefcn/error.h, libinterp/corefcn/event-queue.h, libinterp/corefcn/fft.cc, libinterp/corefcn/fft2.cc, libinterp/corefcn/fftn.cc, libinterp/corefcn/file-io.cc, libinterp/corefcn/filter.cc, libinterp/corefcn/find.cc, libinterp/corefcn/gammainc.cc, libinterp/corefcn/gcd.cc, libinterp/corefcn/getgrent.cc, libinterp/corefcn/getpwent.cc, libinterp/corefcn/getrusage.cc, libinterp/corefcn/givens.cc, libinterp/corefcn/gl-render.cc, libinterp/corefcn/gl2ps-renderer.cc, libinterp/corefcn/gl2ps-renderer.h, libinterp/corefcn/graphics.cc, libinterp/corefcn/graphics.in.h, libinterp/corefcn/gripes.cc, libinterp/corefcn/gripes.h, libinterp/corefcn/help.cc, libinterp/corefcn/hess.cc, libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc, libinterp/corefcn/input.h, libinterp/corefcn/inv.cc, libinterp/corefcn/jit-ir.h, libinterp/corefcn/jit-typeinfo.cc, libinterp/corefcn/jit-typeinfo.h, libinterp/corefcn/jit-util.h, libinterp/corefcn/kron.cc, libinterp/corefcn/load-path.cc, libinterp/corefcn/load-path.h, libinterp/corefcn/load-save.cc, libinterp/corefcn/load-save.h, libinterp/corefcn/lookup.cc, libinterp/corefcn/ls-ascii-helper.cc, libinterp/corefcn/ls-hdf5.cc, libinterp/corefcn/ls-hdf5.h, libinterp/corefcn/ls-mat-ascii.cc, libinterp/corefcn/ls-mat-ascii.h, libinterp/corefcn/ls-mat4.cc, libinterp/corefcn/ls-mat5.cc, libinterp/corefcn/ls-mat5.h, libinterp/corefcn/ls-oct-ascii.cc, libinterp/corefcn/lsode.cc, libinterp/corefcn/lu.cc, libinterp/corefcn/luinc.cc, libinterp/corefcn/mappers.cc, libinterp/corefcn/matrix_type.cc, libinterp/corefcn/max.cc, libinterp/corefcn/md5sum.cc, libinterp/corefcn/mex.cc, libinterp/corefcn/mexproto.h, libinterp/corefcn/mgorth.cc, libinterp/corefcn/mxarray.in.h, libinterp/corefcn/nproc.cc, libinterp/corefcn/oct-hist.cc, libinterp/corefcn/oct-lvalue.h, libinterp/corefcn/oct-map.cc, libinterp/corefcn/oct-map.h, libinterp/corefcn/oct-obj.h, libinterp/corefcn/oct-prcstrm.h, libinterp/corefcn/oct-stdstrm.h, libinterp/corefcn/oct-stream.cc, libinterp/corefcn/oct-stream.h, libinterp/corefcn/octave-link.cc, libinterp/corefcn/octave-link.h, libinterp/corefcn/pager.cc, libinterp/corefcn/pinv.cc, libinterp/corefcn/pr-output.cc, libinterp/corefcn/procstream.h, libinterp/corefcn/profiler.cc, libinterp/corefcn/pt-jit.cc, libinterp/corefcn/pt-jit.h, libinterp/corefcn/quad.cc, libinterp/corefcn/quadcc.cc, libinterp/corefcn/qz.cc, libinterp/corefcn/rand.cc, libinterp/corefcn/rcond.cc, libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc, libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sighandlers.h, libinterp/corefcn/sparse-xdiv.cc, libinterp/corefcn/sparse-xdiv.h, libinterp/corefcn/sparse-xpow.cc, libinterp/corefcn/sparse.cc, libinterp/corefcn/spparms.cc, libinterp/corefcn/sqrtm.cc, libinterp/corefcn/str2double.cc, libinterp/corefcn/strfind.cc, libinterp/corefcn/strfns.cc, libinterp/corefcn/sub2ind.cc, libinterp/corefcn/svd.cc, libinterp/corefcn/syl.cc, libinterp/corefcn/symtab.cc, libinterp/corefcn/symtab.h, libinterp/corefcn/syscalls.cc, libinterp/corefcn/sysdep.cc, libinterp/corefcn/sysdep.h, libinterp/corefcn/time.cc, libinterp/corefcn/toplev.cc, libinterp/corefcn/toplev.h, libinterp/corefcn/tril.cc, libinterp/corefcn/txt-eng-ft.cc, libinterp/corefcn/txt-eng-ft.h, libinterp/corefcn/txt-eng.h, libinterp/corefcn/typecast.cc, libinterp/corefcn/urlwrite.cc, libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc, libinterp/corefcn/variables.h, libinterp/corefcn/xdiv.cc, libinterp/corefcn/xdiv.h, libinterp/corefcn/xnorm.h, libinterp/corefcn/xpow.cc, libinterp/corefcn/xpow.h, libinterp/corefcn/zfstream.cc, libinterp/corefcn/zfstream.h, libinterp/dldfcn/__delaunayn__.cc, libinterp/dldfcn/__dsearchn__.cc, libinterp/dldfcn/__eigs__.cc, libinterp/dldfcn/__fltk_uigetfile__.cc, libinterp/dldfcn/__glpk__.cc, libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/__init_gnuplot__.cc, libinterp/dldfcn/__magick_read__.cc, libinterp/dldfcn/__voronoi__.cc, libinterp/dldfcn/amd.cc, libinterp/dldfcn/ccolamd.cc, libinterp/dldfcn/chol.cc, libinterp/dldfcn/colamd.cc, libinterp/dldfcn/convhulln.cc, libinterp/dldfcn/dmperm.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc, libinterp/dldfcn/symbfact.cc, libinterp/dldfcn/symrcm.cc, libinterp/dldfcn/tsearch.cc, libinterp/octave-value/ov-base-diag.cc, libinterp/octave-value/ov-base-diag.h, libinterp/octave-value/ov-base-int.cc, libinterp/octave-value/ov-base-int.h, libinterp/octave-value/ov-base-mat.h, libinterp/octave-value/ov-base-scalar.cc, libinterp/octave-value/ov-base-scalar.h, libinterp/octave-value/ov-base-sparse.cc, libinterp/octave-value/ov-base-sparse.h, libinterp/octave-value/ov-base.cc, libinterp/octave-value/ov-base.h, libinterp/octave-value/ov-bool-mat.cc, libinterp/octave-value/ov-bool-mat.h, libinterp/octave-value/ov-bool-sparse.cc, libinterp/octave-value/ov-bool-sparse.h, libinterp/octave-value/ov-bool.cc, libinterp/octave-value/ov-bool.h, libinterp/octave-value/ov-builtin.cc, libinterp/octave-value/ov-builtin.h, libinterp/octave-value/ov-cell.cc, libinterp/octave-value/ov-cell.h, libinterp/octave-value/ov-ch-mat.cc, libinterp/octave-value/ov-ch-mat.h, libinterp/octave-value/ov-class.cc, libinterp/octave-value/ov-class.h, libinterp/octave-value/ov-colon.h, libinterp/octave-value/ov-complex.cc, libinterp/octave-value/ov-complex.h, libinterp/octave-value/ov-cx-diag.cc, libinterp/octave-value/ov-cx-diag.h, libinterp/octave-value/ov-cx-mat.cc, libinterp/octave-value/ov-cx-mat.h, libinterp/octave-value/ov-cx-sparse.cc, libinterp/octave-value/ov-cx-sparse.h, libinterp/octave-value/ov-dld-fcn.h, libinterp/octave-value/ov-fcn-handle.cc, libinterp/octave-value/ov-fcn-handle.h, libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-fcn-inline.h, libinterp/octave-value/ov-fcn.h, libinterp/octave-value/ov-float.cc, libinterp/octave-value/ov-float.h, libinterp/octave-value/ov-flt-complex.cc, libinterp/octave-value/ov-flt-complex.h, libinterp/octave-value/ov-flt-cx-diag.cc, libinterp/octave-value/ov-flt-cx-diag.h, libinterp/octave-value/ov-flt-cx-mat.cc, libinterp/octave-value/ov-flt-cx-mat.h, libinterp/octave-value/ov-flt-re-diag.cc, libinterp/octave-value/ov-flt-re-diag.h, libinterp/octave-value/ov-flt-re-mat.cc, libinterp/octave-value/ov-flt-re-mat.h, libinterp/octave-value/ov-int16.cc, libinterp/octave-value/ov-int32.cc, libinterp/octave-value/ov-int64.cc, libinterp/octave-value/ov-int8.cc, libinterp/octave-value/ov-intx.h, libinterp/octave-value/ov-java.cc, libinterp/octave-value/ov-lazy-idx.h, libinterp/octave-value/ov-mex-fcn.cc, libinterp/octave-value/ov-mex-fcn.h, libinterp/octave-value/ov-null-mat.cc, libinterp/octave-value/ov-null-mat.h, libinterp/octave-value/ov-oncleanup.cc, libinterp/octave-value/ov-perm.cc, libinterp/octave-value/ov-perm.h, libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-range.h, libinterp/octave-value/ov-re-diag.cc, libinterp/octave-value/ov-re-diag.h, libinterp/octave-value/ov-re-mat.cc, libinterp/octave-value/ov-re-mat.h, libinterp/octave-value/ov-re-sparse.cc, libinterp/octave-value/ov-re-sparse.h, libinterp/octave-value/ov-scalar.cc, libinterp/octave-value/ov-scalar.h, libinterp/octave-value/ov-str-mat.cc, libinterp/octave-value/ov-str-mat.h, libinterp/octave-value/ov-struct.cc, libinterp/octave-value/ov-struct.h, libinterp/octave-value/ov-type-conv.h, libinterp/octave-value/ov-typeinfo.cc, libinterp/octave-value/ov-typeinfo.h, libinterp/octave-value/ov-uint16.cc, libinterp/octave-value/ov-uint32.cc, libinterp/octave-value/ov-uint64.cc, libinterp/octave-value/ov-uint8.cc, libinterp/octave-value/ov-usr-fcn.cc, libinterp/octave-value/ov-usr-fcn.h, libinterp/octave-value/ov.cc, libinterp/octave-value/ov.h, libinterp/octave.cc, libinterp/operators/op-b-bm.cc, libinterp/operators/op-b-sbm.cc, libinterp/operators/op-bm-b.cc, libinterp/operators/op-bm-bm.cc, libinterp/operators/op-cdm-cdm.cc, libinterp/operators/op-chm.cc, libinterp/operators/op-class.cc, libinterp/operators/op-cm-cm.cc, libinterp/operators/op-cm-cs.cc, libinterp/operators/op-cm-s.cc, libinterp/operators/op-cm-scm.cc, libinterp/operators/op-cm-sm.cc, libinterp/operators/op-cs-cm.cc, libinterp/operators/op-cs-cs.cc, libinterp/operators/op-cs-scm.cc, libinterp/operators/op-cs-sm.cc, libinterp/operators/op-dm-dm.cc, libinterp/operators/op-dm-scm.cc, libinterp/operators/op-double-conv.cc, libinterp/operators/op-fcdm-fcdm.cc, libinterp/operators/op-fcm-fcm.cc, libinterp/operators/op-fcm-fcs.cc, libinterp/operators/op-fcm-fm.cc, libinterp/operators/op-fcm-fs.cc, libinterp/operators/op-fcs-fcm.cc, libinterp/operators/op-fcs-fcs.cc, libinterp/operators/op-fcs-fm.cc, libinterp/operators/op-fcs-fs.cc, libinterp/operators/op-fdm-fdm.cc, libinterp/operators/op-float-conv.cc, libinterp/operators/op-fm-fcm.cc, libinterp/operators/op-fm-fcs.cc, libinterp/operators/op-fm-fm.cc, libinterp/operators/op-fm-fs.cc, libinterp/operators/op-fs-fcm.cc, libinterp/operators/op-fs-fcs.cc, libinterp/operators/op-fs-fm.cc, libinterp/operators/op-fs-fs.cc, libinterp/operators/op-m-cm.cc, libinterp/operators/op-m-cs.cc, libinterp/operators/op-m-m.cc, libinterp/operators/op-m-s.cc, libinterp/operators/op-m-scm.cc, libinterp/operators/op-m-sm.cc, libinterp/operators/op-pm-scm.cc, libinterp/operators/op-range.cc, libinterp/operators/op-s-cm.cc, libinterp/operators/op-s-cs.cc, libinterp/operators/op-s-scm.cc, libinterp/operators/op-sbm-b.cc, libinterp/operators/op-sbm-bm.cc, libinterp/operators/op-sbm-sbm.cc, libinterp/operators/op-scm-cm.cc, libinterp/operators/op-scm-cs.cc, libinterp/operators/op-scm-m.cc, libinterp/operators/op-scm-s.cc, libinterp/operators/op-scm-scm.cc, libinterp/operators/op-scm-sm.cc, libinterp/operators/op-sm-cm.cc, libinterp/operators/op-sm-m.cc, libinterp/operators/op-sm-s.cc, libinterp/operators/op-sm-scm.cc, libinterp/operators/op-sm-sm.cc, libinterp/operators/op-str-m.cc, libinterp/operators/op-str-s.cc, libinterp/operators/op-str-str.cc, libinterp/operators/ops.h, libinterp/parse-tree/lex.h, libinterp/parse-tree/parse.h, libinterp/parse-tree/pt-arg-list.cc, libinterp/parse-tree/pt-arg-list.h, libinterp/parse-tree/pt-assign.cc, libinterp/parse-tree/pt-assign.h, libinterp/parse-tree/pt-binop.cc, libinterp/parse-tree/pt-binop.h, libinterp/parse-tree/pt-bp.h, libinterp/parse-tree/pt-cbinop.cc, libinterp/parse-tree/pt-check.cc, libinterp/parse-tree/pt-colon.cc, libinterp/parse-tree/pt-colon.h, libinterp/parse-tree/pt-const.cc, libinterp/parse-tree/pt-decl.cc, libinterp/parse-tree/pt-decl.h, libinterp/parse-tree/pt-eval.cc, libinterp/parse-tree/pt-except.h, libinterp/parse-tree/pt-exp.h, libinterp/parse-tree/pt-fcn-handle.cc, libinterp/parse-tree/pt-id.cc, libinterp/parse-tree/pt-id.h, libinterp/parse-tree/pt-idx.cc, libinterp/parse-tree/pt-idx.h, libinterp/parse-tree/pt-loop.h, libinterp/parse-tree/pt-mat.cc, libinterp/parse-tree/pt-misc.cc, libinterp/parse-tree/pt-misc.h, libinterp/parse-tree/pt-pr-code.cc, libinterp/parse-tree/pt-select.h, libinterp/parse-tree/pt-stmt.h, libinterp/parse-tree/token.h, libinterp/version.cc: Use GNU style coding conventions for code in libinterp/
author Rik <rik@octave.org>
date Mon, 28 Oct 2013 19:51:46 -0700
parents d63878346099
children 0850b5212619
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1 /*
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2
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3 Copyright (C) 1996-2013 John W. Eaton
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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23 #ifdef HAVE_CONFIG_H
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24 #include <config.h>
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25 #endif
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27 #include "CmplxHESS.h"
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28 #include "dbleHESS.h"
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29 #include "fCmplxHESS.h"
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30 #include "floatHESS.h"
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31
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32 #include "defun.h"
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33 #include "error.h"
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34 #include "gripes.h"
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35 #include "oct-obj.h"
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36 #include "utils.h"
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37
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38 DEFUN (hess, args, nargout,
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39 "-*- texinfo -*-\n\
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40 @deftypefn {Built-in Function} {@var{H} =} hess (@var{A})\n\
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41 @deftypefnx {Built-in Function} {[@var{P}, @var{H}] =} hess (@var{A})\n\
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42 @cindex Hessenberg decomposition\n\
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43 Compute the Hessenberg decomposition of the matrix @var{A}.\n\
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44 \n\
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45 The Hessenberg decomposition is\n\
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46 @tex\n\
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47 $$\n\
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48 A = PHP^T\n\
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49 $$\n\
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50 where $P$ is a square unitary matrix ($P^TP = I$), and $H$\n\
3372
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51 is upper Hessenberg ($H_{i,j} = 0, \\forall i \\ge j+1$).\n\
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52 @end tex\n\
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53 @ifnottex\n\
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54 @code{@var{P} * @var{H} * @var{P}' = @var{A}} where @var{P} is a square\n\
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55 unitary matrix (@code{@var{P}' * @var{P} = I}, using complex-conjugate\n\
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56 transposition) and @var{H} is upper Hessenberg\n\
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57 (@code{@var{H}(i, j) = 0 forall i >= j+1)}.\n\
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58 @end ifnottex\n\
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59 \n\
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60 The Hessenberg decomposition is usually used as the first step in an\n\
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61 eigenvalue computation, but has other applications as well (see Golub,\n\
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62 Nash, and Van Loan, IEEE Transactions on Automatic Control, 1979).\n\
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63 @seealso{eig, chol, lu, qr, qz, schur, svd}\n\
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64 @end deftypefn")
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65 {
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66 octave_value_list retval;
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67
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68 int nargin = args.length ();
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69
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70 if (nargin != 1 || nargout > 2)
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71 {
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72 print_usage ();
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73 return retval;
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74 }
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75
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76 octave_value arg = args(0);
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77
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78 octave_idx_type nr = arg.rows ();
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79 octave_idx_type nc = arg.columns ();
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80
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81 int arg_is_empty = empty_arg ("hess", nr, nc);
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82
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83 if (arg_is_empty < 0)
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84 return retval;
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85 else if (arg_is_empty > 0)
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86 return octave_value_list (2, Matrix ());
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87
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88 if (nr != nc)
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89 {
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90 gripe_square_matrix_required ("hess");
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91 return retval;
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92 }
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93
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94 if (arg.is_single_type ())
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95 {
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96 if (arg.is_real_type ())
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97 {
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98 FloatMatrix tmp = arg.float_matrix_value ();
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99
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100 if (! error_state)
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101 {
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102 FloatHESS result (tmp);
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103
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104 if (nargout <= 1)
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105 retval(0) = result.hess_matrix ();
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106 else
8db807a0eb78 Return correct Hessenberg matrix when called with 0 or 1 output arguments
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107 {
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108 retval(1) = result.hess_matrix ();
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109 retval(0) = result.unitary_hess_matrix ();
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110 }
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111 }
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112 }
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113 else if (arg.is_complex_type ())
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114 {
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115 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
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116
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117 if (! error_state)
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118 {
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119 FloatComplexHESS result (ctmp);
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120
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121 if (nargout <= 1)
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122 retval(0) = result.hess_matrix ();
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123 else
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124 {
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125 retval(1) = result.hess_matrix ();
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126 retval(0) = result.unitary_hess_matrix ();
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127 }
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128 }
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129 }
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130 }
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131 else
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132 {
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133 if (arg.is_real_type ())
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134 {
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135 Matrix tmp = arg.matrix_value ();
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136
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137 if (! error_state)
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138 {
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139 HESS result (tmp);
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140
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141 if (nargout <= 1)
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142 retval(0) = result.hess_matrix ();
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143 else
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144 {
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145 retval(1) = result.hess_matrix ();
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146 retval(0) = result.unitary_hess_matrix ();
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147 }
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148 }
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149 }
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150 else if (arg.is_complex_type ())
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151 {
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152 ComplexMatrix ctmp = arg.complex_matrix_value ();
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153
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154 if (! error_state)
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155 {
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156 ComplexHESS result (ctmp);
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157
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158 if (nargout <= 1)
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159 retval(0) = result.hess_matrix ();
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160 else
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161 {
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162 retval(1) = result.hess_matrix ();
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163 retval(0) = result.unitary_hess_matrix ();
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164 }
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165 }
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166 }
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167 else
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168 {
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169 gripe_wrong_type_arg ("hess", arg);
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170 }
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171 }
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172
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173 return retval;
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174 }
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175
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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176 /*
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177 %!test
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178 %! a = [1, 2, 3; 5, 4, 6; 8, 7, 9];
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179 %! [p, h] = hess (a);
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180 %! assert (p * h * p', a, sqrt (eps));
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181
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182 %!test
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183 %! a = single ([1, 2, 3; 5, 4, 6; 8, 7, 9]);
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184 %! [p, h] = hess (a);
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185 %! assert (p * h * p', a, sqrt (eps ("single")));
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186
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187 %!error hess ()
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188 %!error hess ([1, 2; 3, 4], 2)
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189 %!error <argument must be a square matrix> hess ([1, 2; 3, 4; 5, 6])
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190 */