Mercurial > octave
view libinterp/corefcn/schur.cc @ 21966:112b20240c87
move docstrings in C++ files out of C strings and into comments
* __contourc__.cc, __dispatch__.cc, __dsearchn__.cc, __ichol__.cc,
__ilu__.cc, __lin_interpn__.cc, __luinc__.cc, __magick_read__.cc,
__pchip_deriv__.cc, __qp__.cc, balance.cc, besselj.cc, betainc.cc,
bitfcns.cc, bsxfun.cc, cellfun.cc, colloc.cc, conv2.cc, daspk.cc,
dasrt.cc, dassl.cc, data.cc, debug.cc, defaults.cc, det.cc, dirfns.cc,
dlmread.cc, dot.cc, eig.cc, ellipj.cc, error.cc, fft.cc, fft2.cc,
fftn.cc, file-io.cc, filter.cc, find.cc, gammainc.cc, gcd.cc,
getgrent.cc, getpwent.cc, getrusage.cc, givens.cc, graphics.cc,
hash.cc, help.cc, hess.cc, hex2num.cc, input.cc, inv.cc, kron.cc,
load-path.cc, load-save.cc, lookup.cc, ls-oct-text.cc, lsode.cc,
lu.cc, mappers.cc, matrix_type.cc, max.cc, mgorth.cc, nproc.cc,
oct-hist.cc, octave-link.cc, ordschur.cc, pager.cc, pinv.cc,
pr-output.cc, profiler.cc, psi.cc, pt-jit.cc, quad.cc, quadcc.cc,
qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, sighandlers.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,
time.cc, toplev.cc, tril.cc, tsearch.cc, typecast.cc, urlwrite.cc,
utils.cc, variables.cc, __delaunayn__.cc, __eigs__.cc,
__fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.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,
ov-base.cc, ov-bool-mat.cc, ov-cell.cc, ov-class.cc, ov-classdef.cc,
ov-fcn-handle.cc, ov-fcn-inline.cc, ov-flt-re-mat.cc, ov-int16.cc,
ov-int32.cc, ov-int64.cc, ov-int8.cc, ov-java.cc, ov-null-mat.cc,
ov-oncleanup.cc, ov-range.cc, ov-re-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, octave.cc, pt-arg-list.cc, pt-binop.cc,
pt-eval.cc, pt-mat.cc, lex.ll, oct-parse.in.yy:
Docstrings are now comments instead of C strings.
* build-aux/mk-opts.pl: Emit docstrings as comments instead of C
strings.
* DASPK-opts.in, LSODE-opts.in: Don't quote " in docstring fragments.
* builtins.h: Include builtin-defun-decls.h unconditionally.
* defun.h (DEFUN, DEFUNX, DEFCONSTFUN): Simply emit declaration.
(DEFALIAS): Always expand to nothing.
* defun-dld.h: No special macro expansions for MAKE_BUILTINS.
(DEFUN_DLD): Use FORWARD_DECLARE_FUN.
(DEFUNX_DLD): Use FORWARD_DECLARE_FUNX.
* defun-int.h: No special macro expansions for MAKE_BUILTINS.
(FORWARD_DECLARE_FUN, FORWARD_DECLARE_FUNX): New macros.
(DEFINE_FUN_INSTALLER_FUN): If compiling an Octave source file, pass
"external-doc" to DEFINE_FUNX_INSTALLER_FUN.
(DEFUN_INTERNAL, DEFCONSTFUN_INTERNAL, DEFUNX_INTERNAL,
DEFALIAS_INTERNAL): Delete.
* common.mk (move_if_change_rule): New macro.
(simple_move_if_change_rule): Define using move_if_change_rule.
* find-defun-files.sh (DEFUN_PATTERN): Update. Don't transform file
name extension to ".df".
* libinterp/mk-pkg-add, gendoc.pl: Operate directly on source files.
* mkbuiltins: New argument, SRCDIR. Operate directly on source files.
* mkdefs: Delete.
* libinterp/module.mk (BUILT_SOURCES): Update list to contain only
files included in other source files.
(GENERATED_MAKE_BUILTINS_INCS, DEF_FILES): Delete.
(LIBINTERP_BUILT_DISTFILES): Include $(OPT_HANDLERS) here.
(LIBINTERP_BUILT_NODISTFILES): Not here. Remove $(ALL_DEF_FILES from
the list.
(libinterp_EXTRA_DIST): Remove mkdefs from the list.
(FOUND_DEFUN_FILES): Rename from SRC_DEF_FILES.
(DLDFCN_DEFUN_FILES): Rename from DLDFCN_DEF_FILES.
(SRC_DEFUN_FILES): Rename from SRC_DEF_FILES.
(ALL_DEFUN_FILES): Rename from ALL_DEF_FILES.
(%.df: %.cc): Delete pattern rule.
(libinterp/build-env-features.cc, libinterp/builtins.cc,
libinterp/dldfcn/PKG_ADD): Use mv instead of move-if-change.
(libinterp/builtins.cc, libinterp/builtin-defun-decls.h):
Update mkbuiltins command.
($(srcdir)/libinterp/DOCSTRINGS): Update gendoc.pl command.
* liboctave/module.mk (BUILT_SOURCES): Don't include
liboctave-build-info.cc in the list.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 21 Jun 2016 16:07:51 -0400 |
parents | aba2e6293dd8 |
children | 6ca3acf5fad8 |
line wrap: on
line source
/* Copyright (C) 1996-2015 John W. Eaton 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 <http://www.gnu.org/licenses/>. */ #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <string> #include "schur.h" #include "defun.h" #include "error.h" #include "errwarn.h" #include "ovl.h" #include "utils.h" template <typename Matrix> static octave_value mark_upper_triangular (const Matrix& a) { octave_value retval = a; octave_idx_type n = a.rows (); assert (a.columns () == n); const typename Matrix::element_type zero = typename Matrix::element_type (); for (octave_idx_type i = 0; i < n; i++) if (a(i,i) == zero) return retval; retval.matrix_type (MatrixType::Upper); return retval; } DEFUN (schur, args, nargout, doc: /* -*- texinfo -*- @deftypefn {} {@var{S} =} schur (@var{A}) @deftypefnx {} {@var{S} =} schur (@var{A}, "real") @deftypefnx {} {@var{S} =} schur (@var{A}, "complex") @deftypefnx {} {@var{S} =} schur (@var{A}, @var{opt}) @deftypefnx {} {[@var{U}, @var{S}] =} schur (@dots{}) @cindex Schur decomposition Compute the Schur@tie{}decomposition of @var{A}. The Schur@tie{}decomposition is defined as @tex $$ S = U^T A U $$ @end tex @ifnottex @example @code{@var{S} = @var{U}' * @var{A} * @var{U}} @end example @end ifnottex where @var{U} is a unitary matrix @tex ($U^T U$ is identity) @end tex @ifnottex (@code{@var{U}'* @var{U}} is identity) @end ifnottex and @var{S} is upper triangular. The eigenvalues of @var{A} (and @var{S}) are the diagonal elements of @var{S}. If the matrix @var{A} is real, then the real Schur@tie{}decomposition is computed, in which the matrix @var{U} is orthogonal and @var{S} is block upper triangular with blocks of size at most @tex $2 \times 2$ @end tex @ifnottex @code{2 x 2} @end ifnottex along the diagonal. The diagonal elements of @var{S} (or the eigenvalues of the @tex $2 \times 2$ @end tex @ifnottex @code{2 x 2} @end ifnottex blocks, when appropriate) are the eigenvalues of @var{A} and @var{S}. The default for real matrices is a real Schur@tie{}decomposition. A complex decomposition may be forced by passing the flag @qcode{"complex"}. The eigenvalues are optionally ordered along the diagonal according to the value of @var{opt}. @code{@var{opt} = "a"} indicates that all eigenvalues with negative real parts should be moved to the leading block of @var{S} (used in @code{are}), @code{@var{opt} = "d"} indicates that all eigenvalues with magnitude less than one should be moved to the leading block of @var{S} (used in @code{dare}), and @code{@var{opt} = "u"}, the default, indicates that no ordering of eigenvalues should occur. The leading @var{k} columns of @var{U} always span the @var{A}-invariant subspace corresponding to the @var{k} leading eigenvalues of @var{S}. The Schur@tie{}decomposition is used to compute eigenvalues of a square matrix, and has applications in the solution of algebraic Riccati equations in control (see @code{are} and @code{dare}). @seealso{rsf2csf, ordschur, lu, chol, hess, qr, qz, svd} @end deftypefn */) { int nargin = args.length (); if (nargin < 1 || nargin > 2 || nargout > 2) print_usage (); octave_value arg = args(0); std::string ord; if (nargin == 2) ord = args(1).xstring_value ("schur: second argument must be a string"); bool force_complex = false; if (ord == "real") { ord = ""; } else if (ord == "complex") { force_complex = true; ord = ""; } else { char ord_char = ord.empty () ? 'U' : ord[0]; if (ord_char != 'U' && ord_char != 'A' && ord_char != 'D' && ord_char != 'u' && ord_char != 'a' && ord_char != 'd') { warning ("schur: incorrect ordered schur argument '%s'", ord.c_str ()); return ovl (); } } octave_idx_type nr = arg.rows (); octave_idx_type nc = arg.columns (); if (nr != nc) err_square_matrix_required ("schur", "A"); if (! arg.is_numeric_type ()) err_wrong_type_arg ("schur", arg); octave_value_list retval; if (arg.is_single_type ()) { if (! force_complex && arg.is_real_type ()) { FloatMatrix tmp = arg.float_matrix_value (); if (nargout <= 1) { schur<FloatMatrix> result (tmp, ord, false); retval = ovl (result.schur_matrix ()); } else { schur<FloatMatrix> result (tmp, ord, true); retval = ovl (result.unitary_matrix (), result.schur_matrix ()); } } else { FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); if (nargout <= 1) { schur<FloatComplexMatrix> result (ctmp, ord, false); retval = ovl (mark_upper_triangular (result.schur_matrix ())); } else { schur<FloatComplexMatrix> result (ctmp, ord, true); retval = ovl (result.unitary_matrix (), mark_upper_triangular (result.schur_matrix ())); } } } else { if (! force_complex && arg.is_real_type ()) { Matrix tmp = arg.matrix_value (); if (nargout <= 1) { schur<Matrix> result (tmp, ord, false); retval = ovl (result.schur_matrix ()); } else { schur<Matrix> result (tmp, ord, true); retval = ovl (result.unitary_matrix (), result.schur_matrix ()); } } else { ComplexMatrix ctmp = arg.complex_matrix_value (); if (nargout <= 1) { schur<ComplexMatrix> result (ctmp, ord, false); retval = ovl (mark_upper_triangular (result.schur_matrix ())); } else { schur<ComplexMatrix> result (ctmp, ord, true); retval = ovl (result.unitary_matrix (), mark_upper_triangular (result.schur_matrix ())); } } } return retval; } /* %!test %! a = [1, 2, 3; 4, 5, 9; 7, 8, 6]; %! [u, s] = schur (a); %! assert (u' * a * u, s, sqrt (eps)); %!test %! a = single ([1, 2, 3; 4, 5, 9; 7, 8, 6]); %! [u, s] = schur (a); %! assert (u' * a * u, s, sqrt (eps ("single"))); %!error schur () %!error schur (1,2,3) %!error [a,b,c] = schur (1) %!error <must be a square matrix> schur ([1, 2, 3; 4, 5, 6]) %!error <wrong type argument 'cell'> schur ({1}) %!warning <incorrect ordered schur argument> schur ([1, 2; 3, 4], "bad_opt"); */ DEFUN (rsf2csf, args, nargout, doc: /* -*- texinfo -*- @deftypefn {} {[@var{U}, @var{T}] =} rsf2csf (@var{UR}, @var{TR}) Convert a real, upper quasi-triangular Schur@tie{}form @var{TR} to a complex, upper triangular Schur@tie{}form @var{T}. Note that the following relations hold: @tex $UR \cdot TR \cdot {UR}^T = U T U^{\dagger}$ and $U^{\dagger} U$ is the identity matrix I. @end tex @ifnottex @tcode{@var{UR} * @var{TR} * @var{UR}' = @var{U} * @var{T} * @var{U}'} and @code{@var{U}' * @var{U}} is the identity matrix I. @end ifnottex Note also that @var{U} and @var{T} are not unique. @seealso{schur} @end deftypefn */) { if (args.length () != 2 || nargout > 2) print_usage (); if (! args(0).is_numeric_type ()) err_wrong_type_arg ("rsf2csf", args(0)); if (! args(1).is_numeric_type ()) err_wrong_type_arg ("rsf2csf", args(1)); if (args(0).is_complex_type () || args(1).is_complex_type ()) error ("rsf2csf: UR and TR must be real matrices"); if (args(0).is_single_type () || args(1).is_single_type ()) { FloatMatrix u = args(0).float_matrix_value (); FloatMatrix t = args(1).float_matrix_value (); schur<FloatComplexMatrix> cs = rsf2csf<FloatComplexMatrix, FloatMatrix> (t, u); return ovl (cs.unitary_matrix (), cs.schur_matrix ()); } else { Matrix u = args(0).matrix_value (); Matrix t = args(1).matrix_value (); schur<ComplexMatrix> cs = rsf2csf<ComplexMatrix, Matrix> (t, u); return ovl (cs.unitary_matrix (), cs.schur_matrix ()); } } /* %!test %! A = [1, 1, 1, 2; 1, 2, 1, 1; 1, 1, 3, 1; -2, 1, 1, 1]; %! [u, t] = schur (A); %! [U, T] = rsf2csf (u, t); %! assert (norm (u * t * u' - U * T * U'), 0, 1e-12); %! assert (norm (A - U * T * U'), 0, 1e-12); %!test %! A = rand (10); %! [u, t] = schur (A); %! [U, T] = rsf2csf (u, t); %! assert (norm (tril (T, -1)), 0); %! assert (norm (U * U'), 1, 1e-14); %!test %! A = [0, 1;-1, 0]; %! [u, t] = schur (A); %! [U, T] = rsf2csf (u,t); %! assert (U * T * U', A, 1e-14); */