Mercurial > octave
view libinterp/corefcn/sqrtm.cc @ 20232:a9574e3c6e9e
Deprecate Array::length() and Sparse::length() in favour of ::numel().
* liboctave/array/Array.h (Array::length): deprecate for ::numel.
* liboctave/array/Sparse.h (Sparse::length): deprecate for ::numel.
* libgui/graphics/QtHandlesUtils.cc, libgui/src/octave-qt-link.cc,
libinterp/corefcn/Cell.cc, libinterp/corefcn/__contourc__.cc,
libinterp/corefcn/__pchip_deriv__.cc, libinterp/corefcn/__qp__.cc,
libinterp/corefcn/cellfun.cc, libinterp/corefcn/daspk.cc,
libinterp/corefcn/dasrt.cc, libinterp/corefcn/dassl.cc,
libinterp/corefcn/data.cc, libinterp/corefcn/filter.cc,
libinterp/corefcn/find.cc, libinterp/corefcn/gl-render.cc,
libinterp/corefcn/gl-render.h, libinterp/corefcn/graphics.cc,
libinterp/corefcn/graphics.in.h, libinterp/corefcn/help.cc,
libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc,
libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc,
libinterp/corefcn/ls-oct-ascii.h, libinterp/corefcn/lsode.cc,
libinterp/corefcn/matrix_type.cc, libinterp/corefcn/oct-hist.cc,
libinterp/corefcn/oct-map.cc, libinterp/corefcn/oct-map.h,
libinterp/corefcn/oct-obj.h, libinterp/corefcn/oct-stream.cc,
libinterp/corefcn/oct-stream.h, libinterp/corefcn/pr-output.cc,
libinterp/corefcn/quadcc.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/strfns.cc,
libinterp/corefcn/sub2ind.cc, libinterp/corefcn/symtab.h,
libinterp/corefcn/syscalls.cc, libinterp/corefcn/tsearch.cc,
libinterp/corefcn/urlwrite.cc, libinterp/corefcn/utils.cc,
libinterp/corefcn/variables.cc, libinterp/corefcn/xdiv.cc,
libinterp/corefcn/xpow.cc, libinterp/dldfcn/__glpk__.cc,
libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/__magick_read__.cc,
libinterp/dldfcn/audiodevinfo.cc, libinterp/dldfcn/ccolamd.cc,
libinterp/dldfcn/colamd.cc, libinterp/octave-value/ov-cell.cc,
libinterp/octave-value/ov-class.cc, libinterp/octave-value/ov-class.h,
libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc,
libinterp/octave-value/ov-perm.cc, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-typeinfo.cc, libinterp/octave-value/ov.cc,
libinterp/operators/op-int.h, libinterp/parse-tree/pt-pr-code.cc,
liboctave/array/Array-util.cc, liboctave/array/Array.cc,
liboctave/array/CColVector.cc, liboctave/array/CDiagMatrix.cc,
liboctave/array/CMatrix.cc, liboctave/array/CRowVector.cc,
liboctave/array/DiagArray2.cc, liboctave/array/DiagArray2.h,
liboctave/array/MArray.cc, liboctave/array/PermMatrix.cc,
liboctave/array/PermMatrix.h, liboctave/array/Sparse.cc,
liboctave/array/boolMatrix.cc, liboctave/array/chMatrix.cc,
liboctave/array/chNDArray.cc, liboctave/array/dColVector.cc,
liboctave/array/dDiagMatrix.cc, liboctave/array/dMatrix.cc,
liboctave/array/dRowVector.cc, liboctave/array/fCColVector.cc,
liboctave/array/fCDiagMatrix.cc, liboctave/array/fCMatrix.cc,
liboctave/array/fCRowVector.cc, liboctave/array/fColVector.cc,
liboctave/array/fDiagMatrix.cc, liboctave/array/fMatrix.cc,
liboctave/array/fRowVector.cc, liboctave/array/idx-vector.cc,
liboctave/array/intNDArray.cc, liboctave/numeric/CmplxCHOL.cc,
liboctave/numeric/CmplxLU.cc, liboctave/numeric/CmplxQR.cc,
liboctave/numeric/DASPK.cc, liboctave/numeric/DASRT.cc,
liboctave/numeric/DASSL.cc, liboctave/numeric/LSODE.cc,
liboctave/numeric/ODES.cc, liboctave/numeric/ODES.h,
liboctave/numeric/base-dae.h, liboctave/numeric/base-lu.cc,
liboctave/numeric/dbleCHOL.cc, liboctave/numeric/dbleLU.cc,
liboctave/numeric/dbleQR.cc, liboctave/numeric/eigs-base.cc,
liboctave/numeric/fCmplxCHOL.cc, liboctave/numeric/fCmplxLU.cc,
liboctave/numeric/fCmplxQR.cc, liboctave/numeric/floatCHOL.cc,
liboctave/numeric/floatLU.cc, liboctave/numeric/floatQR.cc,
liboctave/numeric/lo-specfun.cc, liboctave/numeric/oct-rand.cc,
liboctave/numeric/oct-spparms.cc, liboctave/numeric/sparse-base-chol.cc,
liboctave/operators/mx-inlines.cc, liboctave/system/file-ops.cc,
liboctave/util/glob-match.h, liboctave/util/kpse.cc,
liboctave/util/lo-regexp.cc, liboctave/util/oct-glob.cc,
liboctave/util/pathsearch.cc, liboctave/util/str-vec.cc,
liboctave/util/str-vec.h, liboctave/util/url-transfer.cc: replace all usage
of Array::length() and Sparse::length() with ::numel().
author | Carnë Draug <carandraug@octave.org> |
---|---|
date | Sat, 30 May 2015 03:14:07 +0100 |
parents | 4197fc428c7d |
children | f90c8372b7ba |
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/* Copyright (C) 2001-2015 Ross Lippert and Paul Kienzle Copyright (C) 2010 VZLU Prague 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/>. */ #ifdef HAVE_CONFIG_H #include <config.h> #endif #include <float.h> #include "CmplxSCHUR.h" #include "fCmplxSCHUR.h" #include "lo-ieee.h" #include "lo-mappers.h" #include "oct-norm.h" #include "defun.h" #include "error.h" #include "gripes.h" #include "utils.h" #include "xnorm.h" template <class Matrix> static void sqrtm_utri_inplace (Matrix& T) { typedef typename Matrix::element_type element_type; const element_type zero = element_type (); bool singular = false; // The following code is equivalent to this triple loop: // // n = rows (T); // for j = 1:n // T(j,j) = sqrt (T(j,j)); // for i = j-1:-1:1 // T(i,j) /= (T(i,i) + T(j,j)); // k = 1:i-1; // T(k,j) -= T(k,i) * T(i,j); // endfor // endfor // // this is an in-place, cache-aligned variant of the code // given in Higham's paper. const octave_idx_type n = T.rows (); element_type *Tp = T.fortran_vec (); for (octave_idx_type j = 0; j < n; j++) { element_type *colj = Tp + n*j; if (colj[j] != zero) colj[j] = sqrt (colj[j]); else singular = true; for (octave_idx_type i = j-1; i >= 0; i--) { const element_type *coli = Tp + n*i; const element_type colji = colj[i] /= (coli[i] + colj[j]); for (octave_idx_type k = 0; k < i; k++) colj[k] -= coli[k] * colji; } } if (singular) warning_with_id ("Octave:sqrtm:SingularMatrix", "sqrtm: matrix is singular, may not have a square root"); } template <class Matrix, class ComplexMatrix, class ComplexSCHUR> static octave_value do_sqrtm (const octave_value& arg) { octave_value retval; MatrixType mt = arg.matrix_type (); bool iscomplex = arg.is_complex_type (); typedef typename Matrix::element_type real_type; real_type cutoff = 0; real_type one = 1; real_type eps = std::numeric_limits<real_type>::epsilon (); if (! iscomplex) { Matrix x = octave_value_extract<Matrix> (arg); if (mt.is_unknown ()) // if type is not known, compute it now. arg.matrix_type (mt = MatrixType (x)); switch (mt.type ()) { case MatrixType::Upper: case MatrixType::Diagonal: if (! x.diag ().any_element_is_negative ()) { // Do it in real arithmetic. sqrtm_utri_inplace (x); retval = x; retval.matrix_type (mt); } else iscomplex = true; break; case MatrixType::Lower: if (! x.diag ().any_element_is_negative ()) { x = x.transpose (); sqrtm_utri_inplace (x); retval = x.transpose (); retval.matrix_type (mt); } else iscomplex = true; break; default: iscomplex = true; break; } if (iscomplex) cutoff = 10 * x.rows () * eps * xnorm (x, one); } if (iscomplex) { ComplexMatrix x = octave_value_extract<ComplexMatrix> (arg); if (mt.is_unknown ()) // if type is not known, compute it now. arg.matrix_type (mt = MatrixType (x)); switch (mt.type ()) { case MatrixType::Upper: case MatrixType::Diagonal: sqrtm_utri_inplace (x); retval = x; retval.matrix_type (mt); break; case MatrixType::Lower: x = x.transpose (); sqrtm_utri_inplace (x); retval = x.transpose (); retval.matrix_type (mt); break; default: { ComplexMatrix u; do { ComplexSCHUR schur (x, std::string (), true); x = schur.schur_matrix (); u = schur.unitary_matrix (); } while (0); // schur no longer needed. sqrtm_utri_inplace (x); x = u * x; // original x no longer needed. ComplexMatrix res = xgemm (x, u, blas_no_trans, blas_conj_trans); if (cutoff > 0 && xnorm (imag (res), one) <= cutoff) retval = real (res); else retval = res; } break; } } return retval; } DEFUN (sqrtm, args, nargout, "-*- texinfo -*-\n\ @deftypefn {Built-in Function} {@var{s} =} sqrtm (@var{A})\n\ @deftypefnx {Built-in Function} {[@var{s}, @var{error_estimate}] =} sqrtm (@var{A})\n\ Compute the matrix square root of the square matrix @var{A}.\n\ \n\ Ref: @nospell{N.J. Higham}. @cite{A New sqrtm for @sc{matlab}}. Numerical\n\ Analysis Report No. 336, Manchester @nospell{Centre} for Computational\n\ Mathematics, Manchester, England, January 1999.\n\ @seealso{expm, logm}\n\ @end deftypefn") { octave_value_list retval; int nargin = args.length (); if (nargin != 1) { print_usage (); return retval; } octave_value arg = args(0); octave_idx_type n = arg.rows (); octave_idx_type nc = arg.columns (); if (n != nc || arg.ndims () > 2) { gripe_square_matrix_required ("sqrtm"); return retval; } if (nargout > 1) { retval.resize (1, 2); retval(2) = -1.0; } if (arg.is_diag_matrix ()) // sqrtm of a diagonal matrix is just sqrt. retval(0) = arg.sqrt (); else if (arg.is_single_type ()) retval(0) = do_sqrtm<FloatMatrix, FloatComplexMatrix, FloatComplexSCHUR> (arg); else if (arg.is_numeric_type ()) retval(0) = do_sqrtm<Matrix, ComplexMatrix, ComplexSCHUR> (arg); if (nargout > 1 && ! error_state) { // This corresponds to generic code // // norm (s*s - x, "fro") / norm (x, "fro"); octave_value s = retval(0); retval(1) = xfrobnorm (s*s - arg) / xfrobnorm (arg); } return retval; } /* %!assert (sqrtm (2*ones (2)), ones (2), 3*eps) ## The following two tests are from the reference in the docstring above. %!test %! x = [0 1; 0 0]; %! assert (any (isnan (sqrtm (x))(:))); %!test %! x = eye (4); x(2,2) = x(3,3) = 2^-26; x(1,4) = 1; %! z = eye (4); z(2,2) = z(3,3) = 2^-13; z(1,4) = 0.5; %! [y, err] = sqrtm (x); %! assert (y, z); %! assert (err, 0); # Yes, this one has to hold exactly */