Mercurial > octave
view libinterp/corefcn/mgorth.cc @ 31197:8d4c87e88d0e
maint: Merge stable to default.
author | Markus Mützel <markus.muetzel@gmx.de> |
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date | Tue, 23 Aug 2022 19:45:19 +0200 |
parents | 796f54d4ddbf |
children | e88a07dec498 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 2009-2022 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 "oct-norm.h" #include "defun.h" #include "error.h" #include "errwarn.h" OCTAVE_NAMESPACE_BEGIN template <typename ColumnVector, typename Matrix, typename RowVector> static void do_mgorth (ColumnVector& x, const Matrix& V, RowVector& h) { octave_idx_type Vc = V.columns (); h = RowVector (Vc + 1); for (octave_idx_type j = 0; j < Vc; j++) { ColumnVector Vcj = V.column (j); RowVector Vcjh = Vcj.hermitian (); h(j) = Vcjh * x; x -= h(j) * Vcj; } h(Vc) = xnorm (x); if (std::real (h(Vc)) > 0) x /= h(Vc); } DEFUN (mgorth, args, , doc: /* -*- texinfo -*- @deftypefn {} {[@var{y}, @var{h}] =} mgorth (@var{x}, @var{v}) Orthogonalize a given column vector @var{x} with respect to a set of orthonormal vectors comprising the columns of @var{v} using the modified Gram-Schmidt method. On exit, @var{y} is a unit vector such that: @example @group norm (@var{y}) = 1 @var{v}' * @var{y} = 0 @var{x} = [@var{v}, @var{y}]*@var{h}' @end group @end example @end deftypefn */) { if (args.length () != 2) print_usage (); octave_value arg_x = args(0); octave_value arg_v = args(1); if (arg_v.ndims () != 2 || arg_x.ndims () != 2 || arg_x.columns () != 1 || arg_v.rows () != arg_x.rows ()) error ("mgorth: V should be a matrix, and X a column vector with" " the same number of rows as V."); if (! arg_x.isnumeric () && ! arg_v.isnumeric ()) error ("mgorth: X and V must be numeric"); octave_value_list retval; bool iscomplex = (arg_x.iscomplex () || arg_v.iscomplex ()); if (arg_x.is_single_type () || arg_v.is_single_type ()) { if (iscomplex) { FloatComplexColumnVector x = arg_x.float_complex_column_vector_value (); FloatComplexMatrix V = arg_v.float_complex_matrix_value (); FloatComplexRowVector h; do_mgorth (x, V, h); retval = ovl (x, h); } else { FloatColumnVector x = arg_x.float_column_vector_value (); FloatMatrix V = arg_v.float_matrix_value (); FloatRowVector h; do_mgorth (x, V, h); retval = ovl (x, h); } } else { if (iscomplex) { ComplexColumnVector x = arg_x.complex_column_vector_value (); ComplexMatrix V = arg_v.complex_matrix_value (); ComplexRowVector h; do_mgorth (x, V, h); retval = ovl (x, h); } else { ColumnVector x = arg_x.column_vector_value (); Matrix V = arg_v.matrix_value (); RowVector h; do_mgorth (x, V, h); retval = ovl (x, h); } } return retval; } /* %!test %! for ii=1:100 %! assert (abs (mgorth (randn (5, 1), eye (5, 4))), [0 0 0 0 1]', eps); %! endfor %!test %! a = hilb (5); %! a(:, 1) /= norm (a(:, 1)); %! for ii = 1:5 %! a(:, ii) = mgorth (a(:, ii), a(:, 1:ii-1)); %! endfor %! assert (a' * a, eye (5), 1e10); */ OCTAVE_NAMESPACE_END