Mercurial > octave
view libinterp/corefcn/ordschur.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 | a3d8915b9f87 |
children | aac27ad79be6 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 2016-2022 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // This file is part of Octave. // // Octave is free software: you can redistribute it and/or modify it // under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // Octave is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with Octave; see the file COPYING. If not, see // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include "defun.h" #include "error.h" #include "lo-lapack-proto.h" #include "ovl.h" OCTAVE_BEGIN_NAMESPACE(octave) DEFUN (ordschur, args, , doc: /* -*- texinfo -*- @deftypefn {} {[@var{UR}, @var{SR}] =} ordschur (@var{U}, @var{S}, @var{select}) Reorder the real Schur factorization (@var{U},@var{S}) obtained with the @code{schur} function, so that selected eigenvalues appear in the upper left diagonal blocks of the quasi triangular Schur matrix. The logical vector @var{select} specifies the selected eigenvalues as they appear along @var{S}'s diagonal. For example, given the matrix @code{@var{A} = [1, 2; 3, 4]}, and its Schur decomposition @example [@var{U}, @var{S}] = schur (@var{A}) @end example @noindent which returns @example @group @var{U} = -0.82456 -0.56577 0.56577 -0.82456 @var{S} = -0.37228 -1.00000 0.00000 5.37228 @end group @end example It is possible to reorder the decomposition so that the positive eigenvalue is in the upper left corner, by doing: @example [@var{U}, @var{S}] = ordschur (@var{U}, @var{S}, [0,1]) @end example @seealso{schur, ordeig, ordqz} @end deftypefn */) { if (args.length () != 3) print_usage (); const Array<octave_idx_type> sel_arg = args(2).xoctave_idx_type_vector_value ("ordschur: SELECT must be an array of integers"); const octave_idx_type sel_n = sel_arg.numel (); const dim_vector dimU = args(0).dims (); const dim_vector dimS = args(1).dims (); if (sel_n != dimU(0)) error ("ordschur: SELECT must have same length as the sides of U and S"); else if (sel_n != dimU(0) || sel_n != dimS(0) || sel_n != dimU(1) || sel_n != dimS(1)) error ("ordschur: U and S must be square and of equal sizes"); octave_value_list retval; const bool double_type = args(0).is_double_type () || args(1).is_double_type (); const bool complex_type = args(0).iscomplex () || args(1).iscomplex (); #define PREPARE_ARGS(TYPE, TYPE_M, TYPE_COND) \ TYPE ## Matrix U = args(0).x ## TYPE_M ## _value \ ("ordschur: U and S must be real or complex floating point matrices"); \ TYPE ## Matrix S = args(1).x ## TYPE_M ## _value \ ("ordschur: U and S must be real or complex floating point matrices"); \ TYPE ## Matrix w (dim_vector (n, 1)); \ TYPE ## Matrix work (dim_vector (n, 1)); \ F77_INT m; \ F77_INT info; \ TYPE_COND cond1, cond2; #define PREPARE_OUTPUT() \ if (info != 0) \ error ("ordschur: trsen failed"); \ \ retval = ovl (U, S); F77_INT n = to_f77_int (sel_n); Array<F77_INT> sel (dim_vector (n, 1)); for (F77_INT i = 0; i < n; i++) sel.xelem (i) = to_f77_int (sel_arg.xelem (i)); if (double_type) { if (complex_type) { PREPARE_ARGS (Complex, complex_matrix, double) F77_XFCN (ztrsen, ztrsen, (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"), sel.data (), n, F77_DBLE_CMPLX_ARG (S.fortran_vec ()), n, F77_DBLE_CMPLX_ARG (U.fortran_vec ()), n, F77_DBLE_CMPLX_ARG (w.fortran_vec ()), m, cond1, cond2, F77_DBLE_CMPLX_ARG (work.fortran_vec ()), n, info)); PREPARE_OUTPUT() } else { PREPARE_ARGS (, matrix, double) Matrix wi (dim_vector (n, 1)); Array<F77_INT> iwork (dim_vector (n, 1)); F77_XFCN (dtrsen, dtrsen, (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"), sel.data (), n, S.fortran_vec (), n, U.fortran_vec (), n, w.fortran_vec (), wi.fortran_vec (), m, cond1, cond2, work.fortran_vec (), n, iwork.fortran_vec (), n, info)); PREPARE_OUTPUT () } } else { if (complex_type) { PREPARE_ARGS (FloatComplex, float_complex_matrix, float) F77_XFCN (ctrsen, ctrsen, (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"), sel.data (), n, F77_CMPLX_ARG (S.fortran_vec ()), n, F77_CMPLX_ARG (U.fortran_vec ()), n, F77_CMPLX_ARG (w.fortran_vec ()), m, cond1, cond2, F77_CMPLX_ARG (work.fortran_vec ()), n, info)); PREPARE_OUTPUT () } else { PREPARE_ARGS (Float, float_matrix, float) FloatMatrix wi (dim_vector (n, 1)); Array<F77_INT> iwork (dim_vector (n, 1)); F77_XFCN (strsen, strsen, (F77_CONST_CHAR_ARG ("N"), F77_CONST_CHAR_ARG ("V"), sel.data (), n, S.fortran_vec (), n, U.fortran_vec (), n, w.fortran_vec (), wi.fortran_vec (), m, cond1, cond2, work.fortran_vec (), n, iwork.fortran_vec (), n, info)); PREPARE_OUTPUT () } } #undef PREPARE_ARGS #undef PREPARE_OUTPUT return retval; } /* %!test %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4 ]; %! [U, T] = schur (A); %! [US, TS] = ordschur (U, T, [ 0, 0, 1, 1 ]); %! assert (US*TS*US', A, sqrt (eps)); %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps)); %!test %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4 ]; %! [U, T] = schur (A); %! [US, TS] = ordschur (single (U), single (T), [ 0, 0, 1, 1 ]); %! assert (US*TS*US', A, sqrt (eps ("single"))); %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps ("single"))); %!test %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4+3i ]; %! [U, T] = schur (A); %! [US, TS] = ordschur (U, T, [ 0, 0, 1, 1 ]); %! assert (US*TS*US', A, sqrt (eps)); %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps)); %!test %! A = [1, 2, 3, -2; 4, 5, 6, -5 ; 7, 8, 9, -5; 10, 11, 12, 4+3i ]; %! [U, T] = schur (A); %! [US, TS] = ordschur (single (U), single (T), [ 0, 0, 1, 1 ]); %! assert (US*TS*US', A, sqrt (eps ("single"))); %! assert (diag (T)(3:4), diag (TS)(1:2), sqrt (eps ("single"))); */ OCTAVE_END_NAMESPACE(octave)