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doc: Update NEWS.10.md file.
* NEWS.10.md: Indent NEWS.10.md for clarity.
Add note about changes to colormap() functionality.
author | Rik <rik@octave.org> |
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date | Thu, 09 May 2024 18:23:33 -0700 |
parents | f53ac65ffba6 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 2016-2024 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.rwdata ()), n, F77_DBLE_CMPLX_ARG (U.rwdata ()), n, F77_DBLE_CMPLX_ARG (w.rwdata ()), m, cond1, cond2, F77_DBLE_CMPLX_ARG (work.rwdata ()), 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.rwdata (), n, U.rwdata (), n, w.rwdata (), wi.rwdata (), m, cond1, cond2, work.rwdata (), n, iwork.rwdata (), 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.rwdata ()), n, F77_CMPLX_ARG (U.rwdata ()), n, F77_CMPLX_ARG (w.rwdata ()), m, cond1, cond2, F77_CMPLX_ARG (work.rwdata ()), 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.rwdata (), n, U.rwdata (), n, w.rwdata (), wi.rwdata (), m, cond1, cond2, work.rwdata (), n, iwork.rwdata (), 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)