Mercurial > octave
annotate libinterp/corefcn/schur.cc @ 21301:40de9f8f23a6
Use '#include "config.h"' rather than <config.h>.
* mk-octave-config-h.sh, mk-opts.pl, Backend.cc, BaseControl.cc,
ButtonControl.cc, Canvas.cc, CheckBoxControl.cc, Container.cc, ContextMenu.cc,
EditControl.cc, Figure.cc, FigureWindow.cc, GLCanvas.cc, KeyMap.cc,
ListBoxControl.cc, Logger.cc, Menu.cc, MouseModeActionGroup.cc, Object.cc,
ObjectFactory.cc, ObjectProxy.cc, Panel.cc, PopupMenuControl.cc,
PushButtonControl.cc, PushTool.cc, QtHandlesUtils.cc, RadioButtonControl.cc,
SliderControl.cc, TextControl.cc, TextEdit.cc, ToggleButtonControl.cc,
ToggleTool.cc, ToolBar.cc, ToolBarButton.cc, __init_qt__.cc,
annotation-dialog.cc, gl-select.cc, module.mk, kpty.cpp, color-picker.cc,
dialog.cc, documentation-dock-widget.cc, files-dock-widget.cc,
find-files-dialog.cc, find-files-model.cc, history-dock-widget.cc,
file-editor-tab.cc, file-editor-tab.h, file-editor.cc, find-dialog.cc,
marker.cc, octave-qscintilla.cc, octave-txt-lexer.cc, main-window.cc,
octave-cmd.cc, octave-dock-widget.cc, octave-gui.cc, octave-interpreter.cc,
octave-qt-link.cc, parser.cc, webinfo.cc, resource-manager.cc,
settings-dialog.cc, shortcut-manager.cc, terminal-dock-widget.cc,
thread-manager.cc, welcome-wizard.cc, workspace-model.cc, workspace-view.cc,
build-env-features.sh, build-env.in.cc, Cell.cc, __contourc__.cc,
__dispatch__.cc, __dsearchn__.cc, __ichol__.cc, __ilu__.cc, __lin_interpn__.cc,
__pchip_deriv__.cc, __qp__.cc, balance.cc, besselj.cc, betainc.cc, bitfcns.cc,
bsxfun.cc, c-file-ptr-stream.cc, cdisplay.c, cellfun.cc, coct-hdf5-types.c,
colloc.cc, comment-list.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc,
debug.cc, defaults.cc, defun.cc, det.cc, dirfns.cc, display.cc, dlmread.cc,
dot.cc, dynamic-ld.cc, eig.cc, ellipj.cc, error.cc, errwarn.cc, event-queue.cc,
fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc, ft-text-renderer.cc,
gammainc.cc, gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc,
gl-render.cc, gl2ps-print.cc, graphics.cc, gripes.cc, hash.cc, help.cc,
hess.cc, hex2num.cc, hook-fcn.cc, input.cc, inv.cc, jit-ir.cc, jit-typeinfo.cc,
jit-util.cc, kron.cc, load-path.cc, load-save.cc, lookup.cc,
ls-ascii-helper.cc, ls-hdf5.cc, ls-mat-ascii.cc, ls-mat4.cc, ls-mat5.cc,
ls-oct-binary.cc, ls-oct-text.cc, ls-utils.cc, lsode.cc, lu.cc, luinc.cc,
mappers.cc, matrix_type.cc, max.cc, mex.cc, mgorth.cc, nproc.cc,
oct-errno.in.cc, oct-fstrm.cc, oct-hdf5-types.cc, oct-hist.cc, oct-iostrm.cc,
oct-lvalue.cc, oct-map.cc, oct-prcstrm.cc, oct-procbuf.cc, oct-stream.cc,
oct-strstrm.cc, oct-tex-lexer.in.ll, oct-tex-parser.in.yy, octave-link.cc,
ordschur.cc, pager.cc, pinv.cc, pr-output.cc, procstream.cc, profiler.cc,
psi.cc, pt-jit.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc, regexp.cc,
schur.cc, sighandlers.cc, siglist.c, sparse-xdiv.cc, sparse-xpow.cc, sparse.cc,
spparms.cc, sqrtm.cc, str2double.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc,
sylvester.cc, symtab.cc, syscalls.cc, sysdep.cc, text-renderer.cc, time.cc,
toplev.cc, tril.cc, tsearch.cc, txt-eng.cc, typecast.cc, urlwrite.cc, utils.cc,
variables.cc, xdiv.cc, xgl2ps.c, xnorm.cc, xpow.cc, zfstream.cc,
__delaunayn__.cc, __eigs__.cc, __fltk_uigetfile__.cc, __glpk__.cc,
__init_fltk__.cc, __init_gnuplot__.cc, __magick_read__.cc, __osmesa_print__.cc,
__voronoi__.cc, amd.cc, audiodevinfo.cc, audioread.cc, ccolamd.cc, chol.cc,
colamd.cc, convhulln.cc, dmperm.cc, fftw.cc, qr.cc, symbfact.cc, symrcm.cc,
mkbuiltins, mkops, ov-base-diag.cc, ov-base-int.cc, ov-base-mat.cc,
ov-base-scalar.cc, ov-base-sparse.cc, ov-base.cc, ov-bool-mat.cc,
ov-bool-sparse.cc, ov-bool.cc, ov-builtin.cc, ov-cell.cc, ov-ch-mat.cc,
ov-class.cc, ov-classdef.cc, ov-colon.cc, ov-complex.cc, ov-cs-list.cc,
ov-cx-diag.cc, ov-cx-mat.cc, ov-cx-sparse.cc, ov-dld-fcn.cc, ov-fcn-handle.cc,
ov-fcn-inline.cc, ov-fcn.cc, ov-float.cc, ov-flt-complex.cc, ov-flt-cx-diag.cc,
ov-flt-cx-mat.cc, ov-flt-re-diag.cc, ov-flt-re-mat.cc, ov-int16.cc,
ov-int32.cc, ov-int64.cc, ov-int8.cc, ov-java.cc, ov-lazy-idx.cc,
ov-mex-fcn.cc, ov-null-mat.cc, ov-oncleanup.cc, ov-perm.cc, ov-range.cc,
ov-re-diag.cc, ov-re-mat.cc, ov-re-sparse.cc, ov-scalar.cc, ov-str-mat.cc,
ov-struct.cc, ov-typeinfo.cc, ov-uint16.cc, ov-uint32.cc, ov-uint64.cc,
ov-uint8.cc, ov-usr-fcn.cc, ov.cc, ovl.cc, octave.cc, 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-double-conv.cc, op-fcdm-fcdm.cc,
op-fcdm-fdm.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-float-conv.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-int-conv.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-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, lex.ll, oct-parse.in.yy,
pt-arg-list.cc, pt-array-list.cc, pt-assign.cc, pt-binop.cc, pt-bp.cc,
pt-cbinop.cc, pt-cell.cc, pt-check.cc, pt-classdef.cc, pt-cmd.cc, pt-colon.cc,
pt-const.cc, pt-decl.cc, pt-eval.cc, pt-except.cc, pt-exp.cc, pt-fcn-handle.cc,
pt-funcall.cc, pt-id.cc, pt-idx.cc, pt-jump.cc, pt-loop.cc, pt-mat.cc,
pt-misc.cc, pt-pr-code.cc, pt-select.cc, pt-stmt.cc, pt-unop.cc, pt.cc,
token.cc, Array-jit.cc, Array-os.cc, Array-sym.cc, Array-tc.cc, version.cc,
Array-C.cc, Array-b.cc, Array-ch.cc, Array-d.cc, Array-f.cc, Array-fC.cc,
Array-i.cc, Array-idx-vec.cc, Array-s.cc, Array-str.cc, Array-util.cc,
Array-voidp.cc, Array.cc, CColVector.cc, CDiagMatrix.cc, CMatrix.cc,
CNDArray.cc, CRowVector.cc, CSparse.cc, DiagArray2.cc, MArray-C.cc,
MArray-d.cc, MArray-f.cc, MArray-fC.cc, MArray-i.cc, MArray-s.cc, MArray.cc,
MDiagArray2.cc, MSparse-C.cc, MSparse-d.cc, MatrixType.cc, PermMatrix.cc,
Range.cc, Sparse-C.cc, Sparse-b.cc, Sparse-d.cc, Sparse.cc, boolMatrix.cc,
boolNDArray.cc, boolSparse.cc, chMatrix.cc, chNDArray.cc, dColVector.cc,
dDiagMatrix.cc, dMatrix.cc, dNDArray.cc, dRowVector.cc, dSparse.cc,
dim-vector.cc, fCColVector.cc, fCDiagMatrix.cc, fCMatrix.cc, fCNDArray.cc,
fCRowVector.cc, fColVector.cc, fDiagMatrix.cc, fMatrix.cc, fNDArray.cc,
fRowVector.cc, idx-vector.cc, int16NDArray.cc, int32NDArray.cc,
int64NDArray.cc, int8NDArray.cc, intNDArray.cc, uint16NDArray.cc,
uint32NDArray.cc, uint64NDArray.cc, uint8NDArray.cc, blaswrap.c, cquit.c,
f77-extern.cc, f77-fcn.c, lo-error.c, quit.cc, CollocWt.cc, DASPK.cc, DASRT.cc,
DASSL.cc, EIG.cc, LSODE.cc, ODES.cc, Quad.cc, aepbalance.cc, chol.cc,
eigs-base.cc, fEIG.cc, gepbalance.cc, hess.cc, lo-mappers.cc, lo-specfun.cc,
lu.cc, oct-convn.cc, oct-fftw.cc, oct-norm.cc, oct-rand.cc, oct-spparms.cc,
qr.cc, qrp.cc, randgamma.c, randmtzig.c, randpoisson.c, schur.cc,
sparse-chol.cc, sparse-dmsolve.cc, sparse-lu.cc, sparse-qr.cc, svd.cc,
mk-ops.awk, dir-ops.cc, file-ops.cc, file-stat.cc, lo-sysdep.cc, mach-info.cc,
oct-env.cc, oct-group.cc, oct-passwd.cc, oct-syscalls.cc, oct-time.cc,
oct-uname.cc, cmd-edit.cc, cmd-hist.cc, data-conv.cc, f2c-main.c,
glob-match.cc, kpse.cc, lo-array-errwarn.cc, lo-array-gripes.cc, lo-cutils.c,
lo-ieee.cc, lo-regexp.cc, lo-utils.cc, oct-base64.cc, oct-glob.cc,
oct-inttypes.cc, oct-locbuf.cc, oct-mutex.cc, oct-rl-edit.c, oct-rl-hist.c,
oct-shlib.cc, oct-sort.cc, pathsearch.cc, singleton-cleanup.cc, sparse-sort.cc,
sparse-util.cc, str-vec.cc, unwind-prot.cc, url-transfer.cc,
display-available.c, main-cli.cc, main-gui.cc, main.in.cc, mkoctfile.in.cc,
octave-config.in.cc:
Use '#include "config.h"' rather than <config.h>.
| author | Rik <rik@octave.org> |
|---|---|
| date | Thu, 18 Feb 2016 13:34:50 -0800 |
| parents | e69eaee28737 |
| children | ad0599a0acc6 |
| rev | line source |
|---|---|
| 2928 | 1 /* |
| 2 | |
|
19697
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3 Copyright (C) 1996-2015 John W. Eaton |
| 2928 | 4 |
| 5 This file is part of Octave. | |
| 6 | |
| 7 Octave is free software; you can redistribute it and/or modify it | |
| 8 under the terms of the GNU General Public License as published by the | |
| 7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
| 10 option) any later version. | |
| 2928 | 11 |
| 12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 15 for more details. | |
| 16 | |
| 17 You should have received a copy of the GNU General Public License | |
| 7016 | 18 along with Octave; see the file COPYING. If not, see |
| 19 <http://www.gnu.org/licenses/>. | |
| 2928 | 20 |
| 21 */ | |
| 22 | |
| 23 #ifdef HAVE_CONFIG_H | |
|
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24 # include "config.h" |
| 2928 | 25 #endif |
| 26 | |
| 27 #include <string> | |
| 28 | |
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29 #include "schur.h" |
| 2928 | 30 |
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31 #include "defun.h" |
| 2928 | 32 #include "error.h" |
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33 #include "errwarn.h" |
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34 #include "ovl.h" |
| 2928 | 35 #include "utils.h" |
| 36 | |
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37 template <typename Matrix> |
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38 static octave_value |
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39 mark_upper_triangular (const Matrix& a) |
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40 { |
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41 octave_value retval = a; |
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42 |
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43 octave_idx_type n = a.rows (); |
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44 assert (a.columns () == n); |
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45 |
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46 const typename Matrix::element_type zero = typename Matrix::element_type (); |
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47 |
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48 for (octave_idx_type i = 0; i < n; i++) |
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49 if (a(i,i) == zero) |
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50 return retval; |
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51 |
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52 retval.matrix_type (MatrixType::Upper); |
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53 |
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54 return retval; |
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55 } |
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56 |
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57 DEFUN (schur, args, nargout, |
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58 "-*- texinfo -*-\n\ |
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59 @deftypefn {} {@var{S} =} schur (@var{A})\n\ |
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60 @deftypefnx {} {@var{S} =} schur (@var{A}, \"real\")\n\ |
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61 @deftypefnx {} {@var{S} =} schur (@var{A}, \"complex\")\n\ |
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62 @deftypefnx {} {@var{S} =} schur (@var{A}, @var{opt})\n\ |
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63 @deftypefnx {} {[@var{U}, @var{S}] =} schur (@dots{})\n\ |
| 3372 | 64 @cindex Schur decomposition\n\ |
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65 Compute the Schur@tie{}decomposition of @var{A}.\n\ |
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66 \n\ |
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67 The Schur@tie{}decomposition is defined as\n\ |
| 3372 | 68 @tex\n\ |
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69 $$\n\ |
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70 S = U^T A U\n\ |
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71 $$\n\ |
| 3372 | 72 @end tex\n\ |
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73 @ifnottex\n\ |
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74 \n\ |
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75 @example\n\ |
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76 @code{@var{S} = @var{U}' * @var{A} * @var{U}}\n\ |
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77 @end example\n\ |
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78 \n\ |
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79 @end ifnottex\n\ |
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80 where @var{U} is a unitary matrix\n\ |
| 3372 | 81 @tex\n\ |
| 82 ($U^T U$ is identity)\n\ | |
| 83 @end tex\n\ | |
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84 @ifnottex\n\ |
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85 (@code{@var{U}'* @var{U}} is identity)\n\ |
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86 @end ifnottex\n\ |
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87 and @var{S} is upper triangular. The eigenvalues of @var{A} (and @var{S})\n\ |
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88 are the diagonal elements of @var{S}. If the matrix @var{A} is real, then\n\ |
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89 the real Schur@tie{}decomposition is computed, in which the matrix @var{U}\n\ |
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90 is orthogonal and @var{S} is block upper triangular with blocks of size at\n\ |
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91 most\n\ |
| 3372 | 92 @tex\n\ |
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93 $2 \\times 2$\n\ |
| 3372 | 94 @end tex\n\ |
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95 @ifnottex\n\ |
| 3372 | 96 @code{2 x 2}\n\ |
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97 @end ifnottex\n\ |
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98 along the diagonal. The diagonal elements of @var{S}\n\ |
| 3372 | 99 (or the eigenvalues of the\n\ |
| 100 @tex\n\ | |
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101 $2 \\times 2$\n\ |
| 3372 | 102 @end tex\n\ |
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103 @ifnottex\n\ |
| 3372 | 104 @code{2 x 2}\n\ |
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105 @end ifnottex\n\ |
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106 blocks, when appropriate) are the eigenvalues of @var{A} and @var{S}.\n\ |
| 2928 | 107 \n\ |
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108 The default for real matrices is a real Schur@tie{}decomposition.\n\ |
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109 A complex decomposition may be forced by passing the flag\n\ |
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110 @qcode{\"complex\"}.\n\ |
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111 \n\ |
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112 The eigenvalues are optionally ordered along the diagonal according to the\n\ |
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113 value of @var{opt}. @code{@var{opt} = \"a\"} indicates that all eigenvalues\n\ |
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114 with negative real parts should be moved to the leading block of @var{S}\n\ |
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115 (used in @code{are}), @code{@var{opt} = \"d\"} indicates that all\n\ |
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116 eigenvalues with magnitude less than one should be moved to the leading\n\ |
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117 block of @var{S} (used in @code{dare}), and @code{@var{opt} = \"u\"}, the\n\ |
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118 default, indicates that no ordering of eigenvalues should occur. The\n\ |
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119 leading @var{k} columns of @var{U} always span the @var{A}-invariant\n\ |
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120 subspace corresponding to the @var{k} leading eigenvalues of @var{S}.\n\ |
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121 \n\ |
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122 The Schur@tie{}decomposition is used to compute eigenvalues of a square\n\ |
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123 matrix, and has applications in the solution of algebraic Riccati equations\n\ |
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124 in control (see @code{are} and @code{dare}).\n\ |
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125 @seealso{rsf2csf, ordschur, lu, chol, hess, qr, qz, svd}\n\ |
| 3372 | 126 @end deftypefn") |
| 2928 | 127 { |
| 128 int nargin = args.length (); | |
| 129 | |
| 130 if (nargin < 1 || nargin > 2 || nargout > 2) | |
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131 print_usage (); |
| 2928 | 132 |
| 133 octave_value arg = args(0); | |
| 134 | |
| 3523 | 135 std::string ord; |
| 2928 | 136 if (nargin == 2) |
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137 ord = args(1).xstring_value ("schur: second argument must be a string"); |
| 2928 | 138 |
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139 bool force_complex = false; |
| 2928 | 140 |
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141 if (ord == "real") |
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142 { |
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143 ord = ""; |
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144 } |
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145 else if (ord == "complex") |
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146 { |
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147 force_complex = true; |
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148 ord = ""; |
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149 } |
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150 else |
| 2928 | 151 { |
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152 char ord_char = ord.empty () ? 'U' : ord[0]; |
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153 |
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154 if (ord_char != 'U' && ord_char != 'A' && ord_char != 'D' |
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155 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd') |
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156 { |
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157 warning ("schur: incorrect ordered schur argument '%s'", |
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158 ord.c_str ()); |
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159 return ovl (); |
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160 } |
| 2928 | 161 } |
| 162 | |
| 5275 | 163 octave_idx_type nr = arg.rows (); |
| 164 octave_idx_type nc = arg.columns (); | |
| 2928 | 165 |
| 166 if (nr != nc) | |
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167 err_square_matrix_required ("schur", "A"); |
| 2928 | 168 |
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169 if (! arg.is_numeric_type ()) |
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170 err_wrong_type_arg ("schur", arg); |
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171 |
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172 octave_value_list retval; |
| 20892 | 173 |
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174 if (arg.is_single_type ()) |
| 2928 | 175 { |
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176 if (! force_complex && arg.is_real_type ()) |
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177 { |
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178 FloatMatrix tmp = arg.float_matrix_value (); |
| 2928 | 179 |
| 20892 | 180 if (nargout <= 1) |
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181 { |
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182 schur<FloatMatrix> result (tmp, ord, false); |
| 20892 | 183 retval = ovl (result.schur_matrix ()); |
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184 } |
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185 else |
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186 { |
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187 schur<FloatMatrix> result (tmp, ord, true); |
| 20892 | 188 retval = ovl (result.unitary_matrix (), |
| 189 result.schur_matrix ()); | |
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190 } |
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191 } |
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192 else |
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193 { |
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194 FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); |
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195 |
| 20892 | 196 if (nargout <= 1) |
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197 { |
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198 schur<FloatComplexMatrix> result (ctmp, ord, false); |
| 20892 | 199 retval = ovl (mark_upper_triangular (result.schur_matrix ())); |
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200 } |
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201 else |
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202 { |
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203 schur<FloatComplexMatrix> result (ctmp, ord, true); |
| 20892 | 204 retval = ovl (result.unitary_matrix (), |
| 205 mark_upper_triangular (result.schur_matrix ())); | |
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206 } |
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207 } |
| 2928 | 208 } |
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209 else |
| 2928 | 210 { |
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211 if (! force_complex && arg.is_real_type ()) |
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212 { |
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213 Matrix tmp = arg.matrix_value (); |
| 2928 | 214 |
| 20892 | 215 if (nargout <= 1) |
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216 { |
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217 schur<Matrix> result (tmp, ord, false); |
| 20892 | 218 retval = ovl (result.schur_matrix ()); |
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219 } |
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220 else |
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221 { |
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222 schur<Matrix> result (tmp, ord, true); |
| 20892 | 223 retval = ovl (result.unitary_matrix (), |
| 224 result.schur_matrix ()); | |
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225 } |
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226 } |
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227 else |
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228 { |
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229 ComplexMatrix ctmp = arg.complex_matrix_value (); |
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230 |
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232 { |
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233 schur<ComplexMatrix> result (ctmp, ord, false); |
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235 } |
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236 else |
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237 { |
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238 schur<ComplexMatrix> result (ctmp, ord, true); |
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| 240 mark_upper_triangular (result.schur_matrix ())); | |
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241 } |
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242 } |
| 2928 | 243 } |
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244 |
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245 return retval; |
| 2928 | 246 } |
| 247 | |
| 248 /* | |
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249 %!test |
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250 %! a = [1, 2, 3; 4, 5, 9; 7, 8, 6]; |
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251 %! [u, s] = schur (a); |
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252 %! assert (u' * a * u, s, sqrt (eps)); |
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253 |
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254 %!test |
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255 %! a = single ([1, 2, 3; 4, 5, 9; 7, 8, 6]); |
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256 %! [u, s] = schur (a); |
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257 %! assert (u' * a * u, s, sqrt (eps ("single"))); |
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258 |
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259 %!error schur () |
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260 %!error schur (1,2,3) |
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261 %!error [a,b,c] = schur (1) |
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262 %!error <must be a square matrix> schur ([1, 2, 3; 4, 5, 6]) |
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263 %!error <wrong type argument 'cell'> schur ({1}) |
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264 %!warning <incorrect ordered schur argument> schur ([1, 2; 3, 4], "bad_opt"); |
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265 |
| 2928 | 266 */ |
| 10822 | 267 |
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268 DEFUN (rsf2csf, args, nargout, |
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269 "-*- texinfo -*-\n\ |
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270 @deftypefn {} {[@var{U}, @var{T}] =} rsf2csf (@var{UR}, @var{TR})\n\ |
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271 Convert a real, upper quasi-triangular Schur@tie{}form @var{TR} to a complex,\n\ |
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272 upper triangular Schur@tie{}form @var{T}.\n\ |
| 10822 | 273 \n\ |
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274 Note that the following relations hold:\n\ |
| 10822 | 275 \n\ |
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276 @tex\n\ |
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277 $UR \\cdot TR \\cdot {UR}^T = U T U^{\\dagger}$ and\n\ |
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278 $U^{\\dagger} U$ is the identity matrix I.\n\ |
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279 @end tex\n\ |
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280 @ifnottex\n\ |
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281 @tcode{@var{UR} * @var{TR} * @var{UR}' = @var{U} * @var{T} * @var{U}'} and\n\ |
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282 @code{@var{U}' * @var{U}} is the identity matrix I.\n\ |
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283 @end ifnottex\n\ |
| 10822 | 284 \n\ |
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285 Note also that @var{U} and @var{T} are not unique.\n\ |
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286 @seealso{schur}\n\ |
| 10822 | 287 @end deftypefn") |
| 288 { | |
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289 if (args.length () != 2 || nargout > 2) |
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290 print_usage (); |
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291 |
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292 if (! args(0).is_numeric_type ()) |
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293 err_wrong_type_arg ("rsf2csf", args(0)); |
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294 if (! args(1).is_numeric_type ()) |
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295 err_wrong_type_arg ("rsf2csf", args(1)); |
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296 if (args(0).is_complex_type () || args(1).is_complex_type ()) |
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297 error ("rsf2csf: UR and TR must be real matrices"); |
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298 |
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299 if (args(0).is_single_type () || args(1).is_single_type ()) |
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300 { |
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301 FloatMatrix u = args(0).float_matrix_value (); |
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302 FloatMatrix t = args(1).float_matrix_value (); |
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303 |
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304 schur<FloatComplexMatrix> cs |
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305 = rsf2csf<FloatComplexMatrix, FloatMatrix> (t, u); |
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306 |
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307 return ovl (cs.unitary_matrix (), cs.schur_matrix ()); |
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308 } |
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309 else |
| 10822 | 310 { |
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311 Matrix u = args(0).matrix_value (); |
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312 Matrix t = args(1).matrix_value (); |
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313 |
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314 schur<ComplexMatrix> cs = rsf2csf<ComplexMatrix, Matrix> (t, u); |
| 10822 | 315 |
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316 return ovl (cs.unitary_matrix (), cs.schur_matrix ()); |
| 10822 | 317 } |
| 318 } | |
| 319 | |
| 320 /* | |
| 321 %!test | |
| 322 %! A = [1, 1, 1, 2; 1, 2, 1, 1; 1, 1, 3, 1; -2, 1, 1, 1]; | |
| 323 %! [u, t] = schur (A); | |
| 324 %! [U, T] = rsf2csf (u, t); | |
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325 %! assert (norm (u * t * u' - U * T * U'), 0, 1e-12); |
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326 %! assert (norm (A - U * T * U'), 0, 1e-12); |
| 10822 | 327 |
| 328 %!test | |
| 329 %! A = rand (10); | |
| 330 %! [u, t] = schur (A); | |
| 331 %! [U, T] = rsf2csf (u, t); | |
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332 %! assert (norm (tril (T, -1)), 0); |
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333 %! assert (norm (U * U'), 1, 1e-14); |
| 10822 | 334 |
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335 %!test |
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336 %! A = [0, 1;-1, 0]; |
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337 %! [u, t] = schur (A); |
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338 %! [U, T] = rsf2csf (u,t); |
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339 %! assert (U * T * U', A, 1e-14); |
| 10822 | 340 */ |