Mercurial > octave-dspies
view scripts/linear-algebra/isdefinite.m @ 19010:3fb030666878 draft default tip dspies
Added special-case logical-indexing function
* logical-index.h (New file) : Logical-indexing function. May be called on
octave_value types via call_bool_index
* nz-iterators.h : Add base-class nz_iterator for iterator types. Array has
template bool for whether to internally store row-col or compute on the fly
Add skip_ahead method which skips forward to the next nonzero after its
argument
Add flat_index for computing octave_idx_type index of current position (with
assertion failure in the case of overflow)
Move is_zero to separate file
* ov-base-diag.cc, ov-base-mat.cc, ov-base-sparse.cc, ov-perm.cc
(do_index_op): Add call to call_bool_index in logical-index.h
* Array.h : Move forward-declaration for array_iterator to separate header file
* dim-vector.cc (dim_max): Refers to idx-bounds.h (max_idx)
* array-iter-decl.h (New file): Header file for forward declaration of
array-iterator
* direction.h : Add constants fdirc and bdirc to avoid having to reconstruct
them
* dv-utils.h, dv-utils.cc (New files) :
Utility functions for querying and constructing dim-vectors
* idx-bounds.h (New file) :
Utility constants and functions for determining whether things will overflow
the maximum allowed bounds
* interp-idx.h (New function : to_flat_idx) : Converts row-col pair to linear
index of octave_idx_type
* is-zero.h (New file) : Function for determining whether an element is zero
* logical-index.tst : Add tests for correct return-value dimensions and large
sparse matrix behavior
author | David Spies <dnspies@gmail.com> |
---|---|
date | Fri, 25 Jul 2014 13:39:31 -0600 |
parents | d0d0858cfab1 |
children |
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## Copyright (C) 2003-2013 Gabriele Pannocchia ## ## 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/>. ## -*- texinfo -*- ## @deftypefn {Function File} {} isdefinite (@var{A}) ## @deftypefnx {Function File} {} isdefinite (@var{A}, @var{tol}) ## Return 1 if @var{A} is symmetric positive definite within the ## tolerance specified by @var{tol} or 0 if @var{A} is symmetric ## positive semidefinite. Otherwise, return -1. If @var{tol} ## is omitted, use a tolerance of ## @code{100 * eps * norm (@var{A}, "fro")} ## @seealso{issymmetric, ishermitian} ## @end deftypefn ## Author: Gabriele Pannocchia <g.pannocchia@ing.unipi.it> ## Created: November 2003 ## Adapted-By: jwe function retval = isdefinite (A, tol) if (nargin < 1 || nargin > 2) print_usage (); endif if (! isfloat (A)) A = double (A); endif if (nargin == 1) tol = 100 * eps (class (A)) * norm (A, "fro"); endif if (! ishermitian (A, tol)) error ("isdefinite: A must be a Hermitian matrix"); endif e = tol * eye (rows (A)); [r, p] = chol (A - e); if (p == 0) retval = 1; else [r, p] = chol (A + e); if (p == 0) retval = 0; else retval = -1; endif endif endfunction %!test %! A = [-1 0; 0 -1]; %! assert (isdefinite (A), -1); %!test %! A = [1 0; 0 1]; %! assert (isdefinite (A), 1); %!test %! A = [2 -1 0; -1 2 -1; 0 -1 2]; %! assert (isdefinite (A), 1); %!test %! A = [1 0; 0 0]; %! assert (isdefinite (A), 0); %!error isdefinite () %!error isdefinite (1,2,3) %!error <A must be a Hermitian matrix> isdefinite ([1 2; 3 4])