octave: libinterp/corefcn/schur.cc annotate

annotate libinterp/corefcn/schur.cc @ 31605:e88a07dec498 stable

maint: Use macros to begin/end C++ namespaces. * oct-conf-post-public.in.h: Define two macros (OCTAVE_BEGIN_NAMESPACE, OCTAVE_END_NAMESPACE) that can be used to start/end a namespace. * mk-opts.pl, build-env.h, build-env.in.cc, __betainc__.cc, __contourc__.cc, __dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc, __ichol__.cc, __ilu__.cc, __isprimelarge__.cc, __lin_interpn__.cc, __magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, auto-shlib.cc, auto-shlib.h, balance.cc, base-text-renderer.cc, base-text-renderer.h, besselj.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h, call-stack.cc, call-stack.h, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc, colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc, defaults.cc, defaults.h, defun-int.h, defun.cc, det.cc, dirfns.cc, display.cc, display.h, dlmread.cc, dmperm.cc, dot.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc, ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.h, event-manager.cc, event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc, fcn-info.h, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc, ft-text-renderer.cc, ft-text-renderer.h, gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc, gl-render.cc, gl-render.h, gl2ps-print.cc, gl2ps-print.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc, graphics.in.h, gsvd.cc, gtk-manager.cc, gtk-manager.h, hash.cc, help.cc, help.h, hess.cc, hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h, interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h, inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, latex-text-renderer.cc, latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h, lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-oct-text.cc, ls-utils.cc, ls-utils.h, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex-private.h, mex.cc, mgorth.cc, nproc.cc, oct-fstrm.cc, oct-fstrm.h, oct-hdf5-types.cc, oct-hdf5-types.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h, oct-opengl.h, oct-prcstrm.cc, oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h, oct-process.cc, oct-process.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h, oct-strstrm.cc, oct-strstrm.h, oct-tex-lexer.in.ll, oct-tex-parser.yy, ordqz.cc, ordschur.cc, pager.cc, pager.h, pinv.cc, pow2.cc, pr-flt-fmt.cc, pr-output.cc, procstream.cc, procstream.h, psi.cc, qr.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, settings.h, sighandlers.cc, sighandlers.h, sparse-xdiv.cc, sparse-xdiv.h, sparse-xpow.cc, sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc, stack-frame.cc, stack-frame.h, stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc, symbfact.cc, syminfo.cc, syminfo.h, symrcm.cc, symrec.cc, symrec.h, symscope.cc, symscope.h, symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h, text-engine.cc, text-engine.h, text-renderer.cc, text-renderer.h, time.cc, toplev.cc, tril.cc, tsearch.cc, typecast.cc, url-handle-manager.cc, url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc, variables.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc, xpow.h, __delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc, __init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc, audioread.cc, convhulln.cc, fftw.cc, gzip.cc, mk-build-env-features.sh, mk-builtins.pl, cdef-class.cc, cdef-class.h, cdef-fwd.h, cdef-manager.cc, cdef-manager.h, cdef-method.cc, cdef-method.h, cdef-object.cc, cdef-object.h, cdef-package.cc, cdef-package.h, cdef-property.cc, cdef-property.h, cdef-utils.cc, cdef-utils.h, ov-base.cc, ov-base.h, ov-bool-mat.cc, ov-builtin.h, ov-cell.cc, ov-class.cc, ov-class.h, ov-classdef.cc, ov-classdef.h, ov-complex.cc, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.h, ov-java.cc, ov-java.h, ov-mex-fcn.h, ov-null-mat.cc, ov-oncleanup.cc, ov-struct.cc, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h, ov.cc, ov.h, octave.cc, octave.h, mk-ops.sh, op-b-b.cc, op-b-bm.cc, op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc, op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc, op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc, op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc, op-dm-template.cc, op-dms-template.cc, op-fcdm-fcdm.cc, op-fcm-fcm.cc, op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc, op-fcs-fcm.cc, op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fdm.cc, op-fm-fcm.cc, op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc, op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc, op-i8-i8.cc, op-int-concat.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc, op-m-scm.cc, op-m-sm.cc, op-mi.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc, op-pm-template.cc, op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc, op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc, op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc, op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc, op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc, op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, ops.h, anon-fcn-validator.cc, anon-fcn-validator.h, bp-table.cc, bp-table.h, comment-list.cc, comment-list.h, filepos.h, lex.h, lex.ll, oct-lvalue.cc, oct-lvalue.h, oct-parse.yy, parse.h, profiler.cc, profiler.h, pt-anon-scopes.cc, pt-anon-scopes.h, pt-arg-list.cc, pt-arg-list.h, pt-args-block.cc, pt-args-block.h, pt-array-list.cc, pt-array-list.h, pt-assign.cc, pt-assign.h, pt-binop.cc, pt-binop.h, pt-bp.cc, pt-bp.h, pt-cbinop.cc, pt-cbinop.h, pt-cell.cc, pt-cell.h, pt-check.cc, pt-check.h, pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc, pt-const.h, pt-decl.cc, pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc, pt-except.h, pt-exp.cc, pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-id.cc, pt-id.h, pt-idx.cc, pt-idx.h, pt-jump.h, pt-loop.cc, pt-loop.h, pt-mat.cc, pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc, pt-pr-code.h, pt-select.cc, pt-select.h, pt-spmd.cc, pt-spmd.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc, pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-vm-eval.cc, pt-walk.cc, pt-walk.h, pt.cc, pt.h, token.cc, token.h, Range.cc, Range.h, idx-vector.cc, idx-vector.h, range-fwd.h, CollocWt.cc, CollocWt.h, aepbalance.cc, aepbalance.h, chol.cc, chol.h, gepbalance.cc, gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h, lo-mappers.cc, lo-mappers.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h, oct-convn.cc, oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h, oct-rand.cc, oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc, qrp.h, randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc, randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h, sparse-lu.cc, sparse-lu.h, sparse-qr.cc, sparse-qr.h, svd.cc, svd.h, child-list.cc, child-list.h, dir-ops.cc, dir-ops.h, file-ops.cc, file-ops.h, file-stat.cc, file-stat.h, lo-sysdep.cc, lo-sysdep.h, lo-sysinfo.cc, lo-sysinfo.h, mach-info.cc, mach-info.h, oct-env.cc, oct-env.h, oct-group.cc, oct-group.h, oct-password.cc, oct-password.h, oct-syscalls.cc, oct-syscalls.h, oct-time.cc, oct-time.h, oct-uname.cc, oct-uname.h, action-container.cc, action-container.h, base-list.h, cmd-edit.cc, cmd-edit.h, cmd-hist.cc, cmd-hist.h, f77-fcn.h, file-info.cc, file-info.h, lo-array-errwarn.cc, lo-array-errwarn.h, lo-hash.cc, lo-hash.h, lo-ieee.h, lo-regexp.cc, lo-regexp.h, lo-utils.cc, lo-utils.h, oct-base64.cc, oct-base64.h, oct-glob.cc, oct-glob.h, oct-inttypes.h, oct-mutex.cc, oct-mutex.h, oct-refcount.h, oct-shlib.cc, oct-shlib.h, oct-sparse.cc, oct-sparse.h, oct-string.h, octave-preserve-stream-state.h, pathsearch.cc, pathsearch.h, quit.cc, quit.h, unwind-prot.cc, unwind-prot.h, url-transfer.cc, url-transfer.h : Use new macros to begin/end C++ namespaces.

author	Rik <rik@octave.org>
date	Thu, 01 Dec 2022 14:23:45 -0800
parents	cad5406329be
children	597f3ee61a48

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ////////////////////////////////////////////////////////////////////////
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 //
30564 796f54d4ddbf update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 30390 diff changeset	3 // Copyright (C) 1996-2022 The Octave Project Developers
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	4 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 // See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 // distribution or <https://octave.org/copyright/>.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	7 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	8 // This file is part of Octave.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	9 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	10 // Octave is free software: you can redistribute it and/or modify it
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	11 // under the terms of the GNU General Public License as published by
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	12 // the Free Software Foundation, either version 3 of the License, or
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	13 // (at your option) any later version.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	14 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	15 // Octave is distributed in the hope that it will be useful, but
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	16 // WITHOUT ANY WARRANTY; without even the implied warranty of
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	18 // GNU General Public License for more details.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	19 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	20 // You should have received a copy of the GNU General Public License
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	21 // along with Octave; see the file COPYING. If not, see
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	22 // <https://www.gnu.org/licenses/>.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ////////////////////////////////////////////////////////////////////////
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	25
21724 aba2e6293dd8 use "#if ..." consistently instead of "#ifdef" and "#ifndef" John W. Eaton <jwe@octave.org> parents: 21547 diff changeset	26 #if defined (HAVE_CONFIG_H)
21301 40de9f8f23a6 Use '#include "config.h"' rather than <config.h>. Rik <rik@octave.org> parents: 21266 diff changeset	27 # include "config.h"
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	28 #endif
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	29
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	30 #include <string>
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	31
21266 e69eaee28737 make better use of templates for Schur decomposition John W. Eaton <jwe@octave.org> parents: 21200 diff changeset	32 #include "schur.h"
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	33
15039 e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory Rik <rik@octave.org> parents: 14854 diff changeset	34 #include "defun.h"
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	35 #include "error.h"
21100 e39e05d90788 Switch gripe_XXX to either err_XXX or warn_XXX naming scheme. Rik <rik@octave.org> parents: 21055 diff changeset	36 #include "errwarn.h"
20940 48b2ad5ee801 maint: Rename oct-obj.[cc\|h] to ovl.[cc\|h] for clarity. Rik <rik@octave.org> parents: 20939 diff changeset	37 #include "ovl.h"
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	38 #include "utils.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	39
31605 e88a07dec498 maint: Use macros to begin/end C++ namespaces. Rik <rik@octave.org> parents: 31382 diff changeset	40 OCTAVE_BEGIN_NAMESPACE(octave)
29958 32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	41
21139 538b57866b90 consistently use "typename" intead of "class" in template declarations John W. Eaton <jwe@octave.org> parents: 21120 diff changeset	42 template <typename Matrix>
10617 9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	43 static octave_value
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	44 mark_upper_triangular (const Matrix& a)
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	45 {
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	46 octave_value retval = a;
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	47
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	48 octave_idx_type n = a.rows ();
30723 08b08b7f05b2 Replace direct calls to C library assert() with Octave specialty functions in libinterp/ (bug #61753) Arun Giridhar <arungiridhar@gmail.com> and Rik <rik@octave.org> parents: 30564 diff changeset	49 error_unless (a.columns () == n);
10617 9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	50
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	51 const typename Matrix::element_type zero = typename Matrix::element_type ();
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	52
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	53 for (octave_idx_type i = 0; i < n; i++)
30390 a61e1a0f6024 maint: style check C++ files in libinterp/ ahead of 7.1 release. Rik <rik@octave.org> parents: 30073 diff changeset	54 if (a(i, i) == zero)
10617 9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	55 return retval;
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	56
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	57 retval.matrix_type (MatrixType::Upper);
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	58
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	59 return retval;
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	60 }
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	61
15039 e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory Rik <rik@octave.org> parents: 14854 diff changeset	62 DEFUN (schur, args, nargout,
21966 112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	63 doc: /* -- texinfo --
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	64 @deftypefn {} {@var{S} =} schur (@var{A})
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	65 @deftypefnx {} {@var{S} =} schur (@var{A}, "real")
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	66 @deftypefnx {} {@var{S} =} schur (@var{A}, "complex")
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	67 @deftypefnx {} {@var{S} =} schur (@var{A}, @var{opt})
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	68 @deftypefnx {} {[@var{U}, @var{S}] =} schur (@dots{})
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	69 @cindex Schur decomposition
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	70 Compute the Schur@tie{}decomposition of @var{A}.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	71
31381 b1ee095baa5b doc: Fix terminology in da3ac42a143d Arun Giridhar <arungiridhar@gmail.com> parents: 31373 diff changeset	72 The Schur@tie{}decomposition of a square matrix @var{A} is defined as
21966 112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	73 @tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	74 $$
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	75 S = U^T A U
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	76 $$
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	77 @end tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	78 @ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	79
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	80 @example
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	81 @code{@var{S} = @var{U}' * @var{A} * @var{U}}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	82 @end example
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	83
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	84 @end ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	85 where @var{U} is a unitary matrix
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	86 @tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	87 ($U^T U$ is identity)
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	88 @end tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	89 @ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	90 (@code{@var{U}'* @var{U}} is identity)
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	91 @end ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	92 and @var{S} is upper triangular. The eigenvalues of @var{A} (and @var{S})
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	93 are the diagonal elements of @var{S}. If the matrix @var{A} is real, then
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	94 the real Schur@tie{}decomposition is computed, in which the matrix @var{U}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	95 is orthogonal and @var{S} is block upper triangular with blocks of size at
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	96 most
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	97 @tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	98 $2 \times 2$
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	99 @end tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	100 @ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	101 @code{2 x 2}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	102 @end ifnottex
31373 da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	103 along the diagonal.
21966 112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	104
31373 da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	105 The default for real matrices is a real Schur@tie{}decomposition. A complex
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	106 decomposition may be forced by passing the flag @qcode{"complex"}.
21966 112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	107
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	108 The eigenvalues are optionally ordered along the diagonal according to the
31373 da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	109 value of @var{opt}:
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	110
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	111 @table @asis
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	112 @item @qcode{@var{opt} = "a"}
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	113 Move eigenvalues with negative real parts to the leading block of @var{S}.
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	114 Mnemonic: @qcode{"a"} for Algebraic @nospell{Riccati} Equations, where this
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	115 ordering is useful.
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	116
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	117 @item @qcode{@var{opt} = "d"}
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	118 Move eigenvalues with magnitude less than one to the leading block of @var{S}.
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	119 Mnemonic: @qcode{"d"} for Discrete Algebraic @nospell{Riccati} Equations,
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	120 where this ordering is useful.
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	121
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	122 @item @qcode{@var{opt} = "u"}
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	123 Unordered. No particular ordering of eigenvalues (default).
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	124 @end table
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	125
da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	126 The leading @var{k} columns of @var{U} always span the @var{A}-invariant
21966 112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	127 subspace corresponding to the @var{k} leading eigenvalues of @var{S}.
31373 da3ac42a143d doc: Update doc for schur.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	128 @seealso{rsf2csf, ordschur, ordeig, lu, chol, hess, qr, qz, svd, eig}
21966 112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	129 @end deftypefn */)
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	130 {
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	131 int nargin = args.length ();
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	132
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	133 if (nargin < 1 \|\| nargin > 2 \|\| nargout > 2)
20802 8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	134 print_usage ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	135
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	136 octave_value arg = args(0);
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	137
3523 b80bbb43a1a9 [project @ 2000-02-02 10:25:52 by jwe] jwe parents: 3372 diff changeset	138 std::string ord;
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	139 if (nargin == 2)
20700 68e3a747ca02 rename octave_value value extractors that accept error message args John W. Eaton <jwe@octave.org> parents: 20582 diff changeset	140 ord = args(1).xstring_value ("schur: second argument must be a string");
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	141
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	142 bool force_complex = false;
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	143
13224 0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	144 if (ord == "real")
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	145 {
21017 93748bcaec17 maint: Replace emtpy 'std::string ()' calls with "". Rik <rik@octave.org> parents: 20941 diff changeset	146 ord = "";
13224 0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	147 }
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	148 else if (ord == "complex")
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	149 {
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	150 force_complex = true;
21017 93748bcaec17 maint: Replace emtpy 'std::string ()' calls with "". Rik <rik@octave.org> parents: 20941 diff changeset	151 ord = "";
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	152 }
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	153 else
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	154 {
23450 855122b993da maint: Wrap tertiary operator in parentheses "(COND ? x : y)". Rik <rik@octave.org> parents: 23220 diff changeset	155 char ord_char = (ord.empty () ? 'U' : ord[0]);
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	156
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	157 if (ord_char != 'U' && ord_char != 'A' && ord_char != 'D'
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	158 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd')
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	159 {
19016 b155fad47055 Fix error messages and %!fail tests for schur(). Rik <rik@octave.org> parents: 17787 diff changeset	160 warning ("schur: incorrect ordered schur argument '%s'",
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	161 ord.c_str ());
20941 a4f5da7c5463 maint: Replace "octave_value_list ()" with "ovl ()". Rik <rik@octave.org> parents: 20940 diff changeset	162 return ovl ();
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	163 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	164 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	165
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5008 diff changeset	166 octave_idx_type nr = arg.rows ();
23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5008 diff changeset	167 octave_idx_type nc = arg.columns ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	168
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	169 if (nr != nc)
21110 3d0d84305600 Use err_square_matrix_required more widely. Rik <rik@octave.org> parents: 21100 diff changeset	170 err_square_matrix_required ("schur", "A");
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	171
23586 f6c5db0a02e7 maint: Deprecate is_numeric_type and replace with isnumeric. Rik <rik@octave.org> parents: 23582 diff changeset	172 if (! arg.isnumeric ())
21120 499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	173 err_wrong_type_arg ("schur", arg);
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	174
20939 b17fda023ca6 maint: Use new C++ archetype in more files. Rik <rik@octave.org> parents: 20898 diff changeset	175 octave_value_list retval;
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	176
21120 499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	177 if (arg.is_single_type ())
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	178 {
23582 0cc2011d800e maint: Deprecate is_real_type and replace with isreal. Rik <rik@octave.org> parents: 23581 diff changeset	179 if (! force_complex && arg.isreal ())
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	180 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	181 FloatMatrix tmp = arg.float_matrix_value ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	182
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	183 if (nargout <= 1)
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	184 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	185 math::schur<FloatMatrix> result (tmp, ord, false);
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	186 retval = ovl (result.schur_matrix ());
20555 f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	187 }
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	188 else
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	189 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	190 math::schur<FloatMatrix> result (tmp, ord, true);
30073 1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix" Rik <rik@octave.org> parents: 29961 diff changeset	191 retval = ovl (result.unitary_schur_matrix (),
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	192 result.schur_matrix ());
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	193 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	194 }
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	195 else
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	196 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	197 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7017 diff changeset	198
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	199 if (nargout <= 1)
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	200 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	201 math::schur<FloatComplexMatrix> result (ctmp, ord, false);
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	202 retval = ovl (mark_upper_triangular (result.schur_matrix ()));
20555 f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	203 }
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	204 else
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	205 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	206 math::schur<FloatComplexMatrix> result (ctmp, ord, true);
30073 1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix" Rik <rik@octave.org> parents: 29961 diff changeset	207 retval = ovl (result.unitary_schur_matrix (),
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	208 mark_upper_triangular (result.schur_matrix ()));
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	209 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	210 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	211 }
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7017 diff changeset	212 else
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	213 {
23582 0cc2011d800e maint: Deprecate is_real_type and replace with isreal. Rik <rik@octave.org> parents: 23581 diff changeset	214 if (! force_complex && arg.isreal ())
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	215 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	216 Matrix tmp = arg.matrix_value ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	217
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	218 if (nargout <= 1)
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	219 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	220 math::schur<Matrix> result (tmp, ord, false);
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	221 retval = ovl (result.schur_matrix ());
20555 f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	222 }
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	223 else
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	224 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	225 math::schur<Matrix> result (tmp, ord, true);
30073 1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix" Rik <rik@octave.org> parents: 29961 diff changeset	226 retval = ovl (result.unitary_schur_matrix (),
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	227 result.schur_matrix ());
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	228 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	229 }
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	230 else
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	231 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	232 ComplexMatrix ctmp = arg.complex_matrix_value ();
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7017 diff changeset	233
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	234 if (nargout <= 1)
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	235 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	236 math::schur<ComplexMatrix> result (ctmp, ord, false);
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	237 retval = ovl (mark_upper_triangular (result.schur_matrix ()));
20555 f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	238 }
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	239 else
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	240 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	241 math::schur<ComplexMatrix> result (ctmp, ord, true);
30073 1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix" Rik <rik@octave.org> parents: 29961 diff changeset	242 retval = ovl (result.unitary_schur_matrix (),
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	243 mark_upper_triangular (result.schur_matrix ()));
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	244 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	245 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	246 }
11586 12df7854fa7c strip trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 11553 diff changeset	247
12df7854fa7c strip trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 11553 diff changeset	248 return retval;
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	249 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	250
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	251 /*
7814 87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	252 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	253 %! a = [1, 2, 3; 4, 5, 9; 7, 8, 6];
87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	254 %! [u, s] = schur (a);
14501 60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	255 %! assert (u' * a * u, s, sqrt (eps));
7814 87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	256
87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	257 %!test
14501 60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	258 %! a = single ([1, 2, 3; 4, 5, 9; 7, 8, 6]);
7814 87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	259 %! [u, s] = schur (a);
14501 60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	260 %! assert (u' * a * u, s, sqrt (eps ("single")));
7814 87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	261
14501 60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	262 %!error schur ()
19016 b155fad47055 Fix error messages and %!fail tests for schur(). Rik <rik@octave.org> parents: 17787 diff changeset	263 %!error schur (1,2,3)
b155fad47055 Fix error messages and %!fail tests for schur(). Rik <rik@octave.org> parents: 17787 diff changeset	264 %!error [a,b,c] = schur (1)
21110 3d0d84305600 Use err_square_matrix_required more widely. Rik <rik@octave.org> parents: 21100 diff changeset	265 %!error <must be a square matrix> schur ([1, 2, 3; 4, 5, 6])
19016 b155fad47055 Fix error messages and %!fail tests for schur(). Rik <rik@octave.org> parents: 17787 diff changeset	266 %!error <wrong type argument 'cell'> schur ({1})
19034 f707835af867 Rewrite schur built-in test as a %!warning to stop failure during 'make check' Rik <rik@octave.org> parents: 19016 diff changeset	267 %!warning <incorrect ordered schur argument> schur ([1, 2; 3, 4], "bad_opt");
f707835af867 Rewrite schur built-in test as a %!warning to stop failure during 'make check' Rik <rik@octave.org> parents: 19016 diff changeset	268
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	269 */
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	270
15039 e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory Rik <rik@octave.org> parents: 14854 diff changeset	271 DEFUN (rsf2csf, args, nargout,
21966 112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	272 doc: /* -- texinfo --
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	273 @deftypefn {} {[@var{U}, @var{T}] =} rsf2csf (@var{UR}, @var{TR})
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	274 Convert a real, upper quasi-triangular Schur@tie{}form @var{TR} to a
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	275 complex, upper triangular Schur@tie{}form @var{T}.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	276
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	277 Note that the following relations hold:
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	278
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	279 @tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	280 $UR \cdot TR \cdot {UR}^T = U T U^{\dagger}$ and
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	281 $U^{\dagger} U$ is the identity matrix I.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	282 @end tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	283 @ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	284 @tcode{@var{UR} * @var{TR} * @var{UR}' = @var{U} * @var{T} * @var{U}'} and
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	285 @code{@var{U}' * @var{U}} is the identity matrix I.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	286 @end ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	287
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	288 Note also that @var{U} and @var{T} are not unique.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	289 @seealso{schur}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	290 @end deftypefn */)
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	291 {
20802 8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	292 if (args.length () != 2 \|\| nargout > 2)
8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	293 print_usage ();
8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	294
23586 f6c5db0a02e7 maint: Deprecate is_numeric_type and replace with isnumeric. Rik <rik@octave.org> parents: 23582 diff changeset	295 if (! args(0).isnumeric ())
21100 e39e05d90788 Switch gripe_XXX to either err_XXX or warn_XXX naming scheme. Rik <rik@octave.org> parents: 21055 diff changeset	296 err_wrong_type_arg ("rsf2csf", args(0));
23586 f6c5db0a02e7 maint: Deprecate is_numeric_type and replace with isnumeric. Rik <rik@octave.org> parents: 23582 diff changeset	297 if (! args(1).isnumeric ())
21100 e39e05d90788 Switch gripe_XXX to either err_XXX or warn_XXX naming scheme. Rik <rik@octave.org> parents: 21055 diff changeset	298 err_wrong_type_arg ("rsf2csf", args(1));
23581 c3075ae020e1 maint: Deprecate is_complex_type and replace with iscomplex. Rik <rik@octave.org> parents: 23450 diff changeset	299 if (args(0).iscomplex () \|\| args(1).iscomplex ())
20802 8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	300 error ("rsf2csf: UR and TR must be real matrices");
21120 499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	301
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	302 if (args(0).is_single_type () \|\| args(1).is_single_type ())
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	303 {
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	304 FloatMatrix u = args(0).float_matrix_value ();
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	305 FloatMatrix t = args(1).float_matrix_value ();
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	306
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	307 math::schur<FloatComplexMatrix> cs
7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	308 = math::rsf2csf<FloatComplexMatrix, FloatMatrix> (t, u);
21120 499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	309
30073 1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix" Rik <rik@octave.org> parents: 29961 diff changeset	310 return ovl (cs.unitary_schur_matrix (), cs.schur_matrix ());
21120 499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	311 }
20802 8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	312 else
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	313 {
21120 499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	314 Matrix u = args(0).matrix_value ();
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	315 Matrix t = args(1).matrix_value ();
20802 8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	316
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	317 math::schur<ComplexMatrix> cs
7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	318 = math::rsf2csf<ComplexMatrix, Matrix> (t, u);
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	319
30073 1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix" Rik <rik@octave.org> parents: 29961 diff changeset	320 return ovl (cs.unitary_schur_matrix (), cs.schur_matrix ());
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	321 }
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	322 }
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	323
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	324 /*
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	325 %!test
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	326 %! A = [1, 1, 1, 2; 1, 2, 1, 1; 1, 1, 3, 1; -2, 1, 1, 1];
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	327 %! [u, t] = schur (A);
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	328 %! [U, T] = rsf2csf (u, t);
14501 60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	329 %! assert (norm (u * t * u' - U * T * U'), 0, 1e-12);
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	330 %! assert (norm (A - U * T * U'), 0, 1e-12);
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	331
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	332 %!test
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	333 %! A = rand (10);
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	334 %! [u, t] = schur (A);
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	335 %! [U, T] = rsf2csf (u, t);
14501 60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	336 %! assert (norm (tril (T, -1)), 0);
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	337 %! assert (norm (U * U'), 1, 1e-14);
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	338
14460 6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893). Marco Caliari <marco.caliari@univr.it> parents: 14138 diff changeset	339 %!test
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893). Marco Caliari <marco.caliari@univr.it> parents: 14138 diff changeset	340 %! A = [0, 1;-1, 0];
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893). Marco Caliari <marco.caliari@univr.it> parents: 14138 diff changeset	341 %! [u, t] = schur (A);
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893). Marco Caliari <marco.caliari@univr.it> parents: 14138 diff changeset	342 %! [U, T] = rsf2csf (u,t);
14501 60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	343 %! assert (U * T * U', A, 1e-14);
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	344 */
29958 32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	345
31605 e88a07dec498 maint: Use macros to begin/end C++ namespaces. Rik <rik@octave.org> parents: 31382 diff changeset	346 OCTAVE_END_NAMESPACE(octave)

Mercurial > octave

annotate libinterp/corefcn/schur.cc @ 31605:e88a07dec498 stable