Mercurial > octave-dspies
view scripts/linear-algebra/linsolve.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 | 0a8c35ae5ce1 |
children |
line wrap: on
line source
## Copyright (C) 2013 Nir Krakauer ## ## 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; If not, see <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{x} =} linsolve (@var{A}, @var{b}) ## @deftypefnx {Function File} {@var{x} =} linsolve (@var{A}, @var{b}, @var{opts}) ## @deftypefnx {Function File} {[@var{x}, @var{R}] =} linsolve (@dots{}) ## Solve the linear system @code{A*x = b}. ## ## With no options, this function is equivalent to the left division operator ## @w{(@code{x = A \ b})} or the matrix-left-divide function ## @w{(@code{x = mldivide (A, b)})}. ## ## Octave ordinarily examines the properties of the matrix @var{A} and chooses ## a solver that best matches the matrix. By passing a structure @var{opts} ## to @code{linsolve} you can inform Octave directly about the matrix @var{A}. ## In this case Octave will skip the matrix examination and proceed directly ## to solving the linear system. ## ## @strong{Warning:} If the matrix @var{A} does not have the properties ## listed in the @var{opts} structure then the result will not be accurate ## AND no warning will be given. When in doubt, let Octave examine the matrix ## and choose the appropriate solver as this step takes little time and the ## result is cached so that it is only done once per linear system. ## ## Possible @var{opts} fields (set value to true/false): ## ## @table @asis ## @item LT ## @var{A} is lower triangular ## ## @item UT ## @var{A} is upper triangular ## ## @item UHESS ## @var{A} is upper Hessenberg (currently makes no difference) ## ## @item SYM ## @var{A} is symmetric or complex Hermitian (currently makes no difference) ## ## @item POSDEF ## @var{A} is positive definite ## ## @item RECT ## @var{A} is general rectangular (currently makes no difference) ## ## @item TRANSA ## Solve @code{A'*x = b} by @code{transpose (A) \ b} ## @end table ## ## The optional second output @var{R} is the inverse condition number of ## @var{A} (zero if matrix is singular). ## @seealso{mldivide, matrix_type, rcond} ## @end deftypefn ## Author: Nir Krakauer <nkrakauer@ccny.cuny.edu> function [x, R] = linsolve (A, b, opts) if (nargin < 2 || nargin > 3) print_usage (); endif if (! (isnumeric (A) && isnumeric (b))) error ("linsolve: A and B must be numeric"); endif ## Process any opts if (nargin > 2) if (! isstruct (opts)) error ("linsolve: OPTS must be a structure"); endif trans_A = false; if (isfield (opts, "TRANSA") && opts.TRANSA) trans_A = true; A = A'; endif if (isfield (opts, "POSDEF") && opts.POSDEF) A = matrix_type (A, "positive definite"); endif if (isfield (opts, "LT") && opts.LT) if (trans_A) A = matrix_type (A, "upper"); else A = matrix_type (A, "lower"); endif endif if (isfield (opts, "UT") && opts.UT) if (trans_A) A = matrix_type (A, "lower"); else A = matrix_type (A, "upper"); endif endif endif x = A \ b; if (nargout > 1) if (issquare (A)) R = rcond (A); else R = 0; endif endif endfunction %!test %! n = 4; %! A = triu (rand (n)); %! x = rand (n, 1); %! b = A' * x; %! opts.UT = true; %! opts.TRANSA = true; %! assert (linsolve (A, b, opts), A' \ b); %!error linsolve () %!error linsolve (1) %!error linsolve (1,2,3) %!error <A and B must be numeric> linsolve ({1},2) %!error <A and B must be numeric> linsolve (1,{2}) %!error <OPTS must be a structure> linsolve (1,2,3)