octave: scripts/sparse/ichol.m annotate

annotate scripts/sparse/ichol.m @ 19053:168c0aa9bb05

Added all the files related with ilu.m and ichol.m functions. * ichol0.cc: New file added to libinterp/dldfcn * icholt.cc: New file added to libinterp/dldfcn * ilu0.cc: New file added to libinterp/dldfcn * iluc.cc: New file added to libinterp/dldfcn * ilutp.cc: New file added to libinterp/dldfcn * ichol.m: New file added to libinterp/dldfcn. Wrapper for ichol0 and icholt. * ilu.m: New file added to libinterp/dldfcn. Wrapper for ilu0, iluc and ilutp. * module-files: Added the above files to allow their compilation.

author	Eduardo Ramos (edu159) <eduradical951@gmail.com>
date	Tue, 12 Aug 2014 15:58:18 +0100
parents
children	df64071e538c

rev	line source
19053 168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	1 ## Copyright (C) 2013 Kai T. Ohlhus <k.ohlhus@gmail.com>
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	2 ## Copyright (C) 2014 Eduardo Ramos Fernández <eduradical951@gmail.com>
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	3 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	4 ## This file is part of Octave.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	5 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	6 ## Octave is free software; you can redistribute it and/or modify it under the
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	7 ## terms of the GNU General Public License as published by the Free Software
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	8 ## Foundation; either version 3 of the License, or (at your option) any later
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	9 ## version.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	10 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	11 ## Octave is distributed in the hope that it will be useful, but WITHOUT ANY
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	12 ## WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	13 ## FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	14 ## details.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	15 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	16 ## You should have received a copy of the GNU General Public License along with
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	17 ## Octave; see the file COPYING. If not, see <http://www.gnu.org/licenses/>.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	18
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	19 ## -- texinfo --
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	20 ## @deftypefn {Function File} ichol (@var{A}, @var{opts})
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	21 ## @deftypefnx {Function File} {@var{L} =} ichol (@var{A}, @var{opts})
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	22 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	23 ## @code{@var{L} = ichol (@var{A})} performs the incomplete Cholesky
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	24 ## factorization of A with zero-fill.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	25 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	26 ## @code{@var{L} = ichol (@var{A}, @var{opts})} performs the incomplete Cholesky
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	27 ## factorization of A with options specified by opts.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	28 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	29 ## By default, ichol references the lower triangle of A and produces lower
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	30 ## triangular factors.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	31 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	32 ## The factor given by this routine may be useful as a preconditioner for a
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	33 ## system of linear equations being solved by iterative methods such as
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	34 ## PCG (Preconditioned conjugate gradient).
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	35 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	36 ## ichol works only for sparse square matrices.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	37 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	38 ## The fields of @var{opts} must be named exactly as shown below. You can
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	39 ## include any number of these fields in the structure and define them in any
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	40 ## order. Any additional fields are ignored. Names and specifiers are case
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	41 ## sensitive.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	42 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	43 ## @table @asis
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	44 ## @item type
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	45 ## Type of factorization.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	46 ## String indicating which flavor of incomplete Cholesky to perform. Valid
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	47 ## values of this field are @samp{nofill} and @samp{ict}. The
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	48 ## @samp{nofill} variant performs incomplete Cholesky with zero-fill [IC(0)].
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	49 ## The @samp{ict} variant performs incomplete Cholesky with threshold dropping
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	50 ## [ICT]. The default value is @samp{nofill}.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	51 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	52 ## @item droptol
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	53 ## Drop tolerance when type is @samp{ict}.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	54 ## Nonnegative scalar used as a drop tolerance when performing ICT. Elements
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	55 ## which are smaller in magnitude than a local drop tolerance are dropped from
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	56 ## the resulting factor except for the diagonal element which is never dropped.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	57 ## The local drop tolerance at step j of the factorization is
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	58 ## @code{norm (@var{A}(j:end, j), 1) * droptol}. @samp{droptol} is ignored if
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	59 ## @samp{type} is @samp{nofill}. The default value is 0.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	60 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	61 ## @item michol
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	62 ## Indicates whether to perform modified incomplete Cholesky.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	63 ## Indicates whether or not modified incomplete Cholesky [MIC] is performed.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	64 ## The field may be @samp{on} or @samp{off}. When performing MIC, the diagonal
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	65 ## is compensated for dropped elements to enforce the relationship
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	66 ## @code{@var{A} * @var{e} = @var{L} * @var{L}' * @var{e}} where
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	67 ## @code{@var{e} = ones (size (@var{A}, 2), 1))}. The default value is
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	68 ## @samp{off}.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	69 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	70 ## @item diagcomp
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	71 ## Perform compensated incomplete Cholesky with the specified coefficient.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	72 ## Real nonnegative scalar used as a global diagonal shift @code{@var{alpha}}
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	73 ## in forming the incomplete Cholesky factor. That is, instead of performing
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	74 ## incomplete Cholesky on @code{@var{A}}, the factorization of
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	75 ## @code{@var{A} + @var{alpha} * diag (diag (@var{A}))} is formed. The default
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	76 ## value is 0.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	77 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	78 ## @item shape
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	79 ## Determines which triangle is referenced and returned.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	80 ## Valid values are @samp{upper} and @samp{lower}. If @samp{upper} is specified,
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	81 ## only the upper triangle of @code{@var{A}} is referenced and @code{@var{R}}
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	82 ## is constructed such that @code{@var{A}} is approximated by
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	83 ## @code{@var{R}' * @var{R}}. If @samp{lower} is specified, only the lower
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	84 ## triangle of @code{@var{A}} is referenced and @code{@var{L}} is constructed
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	85 ## such that @code{@var{A}} is approximated by @code{@var{L} * @var{L}'}. The
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	86 ## default value is @samp{lower}.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	87 ## @end table
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	88 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	89 ## EXAMPLES
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	90 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	91 ## The following problem demonstrates how to factorize a sample symmetric
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	92 ## positive definite matrix with the full Cholesky decomposition and with the
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	93 ## incomplete one.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	94 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	95 ## @example
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	96 ## A = [ 0.37, -0.05, -0.05, -0.07;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	97 ## -0.05, 0.116, 0.0, -0.05;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	98 ## -0.05, 0.0, 0.116, -0.05;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	99 ## -0.07, -0.05, -0.05, 0.202];
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	100 ## A = sparse(A);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	101 ## nnz(tril (A))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	102 ## ans = 9
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	103 ## L = chol(A, "lower");
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	104 ## nnz (L)
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	105 ## ans = 10
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	106 ## norm (A - L * L', 'fro') / norm (A, 'fro')
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	107 ## ans = 1.1993e-16
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	108 ## opts.type = 'nofill';
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	109 ## L = ichol(A,opts);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	110 ## nnz (L)
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	111 ## ans = 9
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	112 ## norm (A - L * L', 'fro') / norm (A, 'fro')
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	113 ## ans = 0.019736
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	114 ## @end example
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	115 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	116 ## Another example for decomposition is finite difference matrix to solve a
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	117 ## boundary value problem on the unit square.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	118 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	119 ## @example
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	120 ## nx = 400; ny = 200;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	121 ## hx = 1 / (nx + 1); hy = 1 / (ny + 1);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	122 ## Dxx = spdiags ([ones(nx, 1), -2 * ones(nx, 1), ones(nx, 1)], [-1 0 1 ], nx, nx) / (hx ^ 2);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	123 ## Dyy = spdiags ([ones(ny, 1), -2 * ones(ny, 1), ones(ny, 1)], [-1 0 1 ], ny, ny) / (hy ^ 2);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	124 ## A = -kron (Dxx, speye (ny)) - kron (speye (nx), Dyy);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	125 ## nnz (tril (A))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	126 ## ans = 239400
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	127 ## opts.type = 'nofill';
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	128 ## L = ichol (A, opts);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	129 ## nnz (tril (A))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	130 ## ans = 239400
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	131 ## norm (A - L * L', 'fro') / norm (A, 'fro')
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	132 ## ans = 0.062327
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	133 ## @end example
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	134 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	135 ## References for the implemented algorithms:
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	136 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	137 ## [1] Saad, Yousef. "Preconditioning Techniques." Iterative Methods for Sparse Linear
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	138 ## Systems. PWS Publishing Company, 1996.
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	139 ##
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	140 ## [2] Jones, Mark T. and Plassmann, Paul E.: An Improved Incomplete Cholesky
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	141 ## Factorization (1992).
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	142 ## @end deftypefn
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	143
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	144 function [L] = ichol (A, opts)
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	145
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	146 if ((nargin > 2) \|\| (nargin < 1) \|\| (nargout > 1))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	147 print_usage ();
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	148 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	149
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	150 % Check input matrix
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	151 if (isempty (A) \|\| ~issparse(A) \|\| ~issquare (A))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	152 error ("ichol: Input A must be a non-empty sparse square matrix");
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	153 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	154
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	155 % Check input structure, otherwise set default values
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	156 if (nargin == 2)
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	157 if (~isstruct (opts))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	158 error ("ichol: Input \"opts\" must be a valid structure.");
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	159 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	160 else
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	161 opts = struct ();
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	162 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	163
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	164 if (~isfield (opts, "type"))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	165 opts.type = "nofill"; % set default
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	166 else
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	167 type = tolower (getfield (opts, "type"));
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	168 if ((strcmp (type, "nofill") == 0)
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	169 && (strcmp (type, "ict") == 0))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	170 error ("ichol: Invalid field \"type\" in input structure.");
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	171 else
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	172 opts.type = type;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	173 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	174 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	175
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	176 if (~isfield (opts, "droptol"))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	177 opts.droptol = 0; % set default
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	178 else
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	179 if (~isscalar (opts.droptol) \|\| (opts.droptol < 0))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	180 error ("ichol: Invalid field \"droptol\" in input structure.");
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	181 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	182 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	183
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	184 michol = "";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	185 if (~isfield (opts, "michol"))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	186 opts.michol = "off"; % set default
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	187 else
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	188 michol = tolower (getfield (opts, "michol"));
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	189 if ((strcmp (michol, "off") == 0)
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	190 && (strcmp (michol, "on") == 0))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	191 error ("ichol: Invalid field \"michol\" in input structure.");
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	192 else
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	193 opts.michol = michol;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	194 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	195 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	196
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	197 if (~isfield (opts, "diagcomp"))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	198 opts.diagcomp = 0; % set default
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	199 else
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	200 if (~isscalar (opts.diagcomp) \|\| (opts.diagcomp < 0))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	201 error ("ichol: Invalid field \"diagcomp\" in input structure.");
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	202 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	203 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	204
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	205 if (~isfield (opts, "shape"))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	206 opts.shape = "lower"; % set default
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	207 else
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	208 shape = tolower (getfield (opts, "shape"));
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	209 if ((strcmp (shape, "lower") == 0)
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	210 && (strcmp (shape, "upper") == 0))
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	211 error ("ichol: Invalid field \"shape\" in input structure.");
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	212 else
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	213 opts.shape = shape;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	214 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	215 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	216
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	217 % Prepare input for specialized ICHOL
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	218 A_in = [];
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	219 if (opts.diagcomp > 0)
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	220 A += opts.diagcomp * diag (diag (A));
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	221 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	222 if (strcmp (opts.shape, "upper") == 1)
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	223 disp("entro");
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	224 A_in = triu (A);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	225 A_in = A_in';
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	226
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	227 else
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	228 A_in = tril (A);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	229 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	230
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	231 % Delegate to specialized ICHOL
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	232 switch (opts.type)
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	233 case "nofill"
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	234 L = ichol0 (A_in, opts.michol);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	235 case "ict"
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	236 L = icholt (A_in, opts.droptol, opts.michol);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	237 otherwise
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	238 printf ("The input structure is invalid.\n");
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	239 endswitch
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	240
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	241 if (strcmp (opts.shape, "upper") == 1)
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	242 L = L';
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	243 endif
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	244
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	245
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	246 endfunction
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	247
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	248 %!shared A1, A2
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	249 %! A1 = [ 0.37, -0.05, -0.05, -0.07;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	250 %! -0.05, 0.116, 0.0, -0.05;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	251 %! -0.05, 0.0, 0.116, -0.05;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	252 %! -0.07, -0.05, -0.05, 0.202];
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	253 %! A1 = sparse(A1);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	254 %! nx = 400; ny = 200;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	255 %! hx = 1 / (nx + 1); hy = 1 / (ny + 1);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	256 %! Dxx = spdiags ([ones(nx, 1), -2 * ones(nx, 1), ones(nx, 1)], [-1 0 1 ], nx, nx) / (hx ^ 2);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	257 %! Dyy = spdiags ([ones(ny, 1), -2 * ones(ny, 1), ones(ny, 1)], [-1 0 1 ], ny, ny) / (hy ^ 2);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	258 %! A2 = -kron (Dxx, speye (ny)) - kron (speye (nx), Dyy);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	259 %!
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	260 %!test
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	261 %!error ichol ([]);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	262 %!error ichol (0);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	263 %!error ichol (-0);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	264 %!error ichol (1);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	265 %!error ichol (-1);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	266 %!error ichol (i);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	267 %!error ichol (-i);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	268 %!error ichol (1 + 1i);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	269 %!error ichol (1 - 1i);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	270 %!error ichol (sparse (0));
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	271 %!error ichol (sparse (-0));
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	272 %!error ichol (sparse (-1));
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	273 %!error ichol (sparse (-1));
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	274 %!
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	275 %!test
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	276 %! opts.type = "nofill";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	277 %! opts.michol = "off";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	278 %! assert (nnz (tril (A1)), nnz (ichol (A1, opts)));
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	279 %! assert (nnz (tril (A2)), nnz (ichol (A2, opts)));
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	280 %!
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	281 %!test
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	282 %! opts.type = "nofill";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	283 %! opts.michol = "off";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	284 %! L = ichol (A1, opts);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	285 %! assert (norm (A1 - L * L', 'fro') / norm (A1, 'fro'), 0.01, 0.01);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	286 %! L = ichol (A2, opts);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	287 %! assert (norm (A2 - L * L', 'fro') / norm (A2, 'fro'), 0.06, 0.01);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	288 %!
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	289 %%!test
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	290 %%! opts.type = "nofill";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	291 %%! opts.michol = "off";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	292 %%! opts.shape = "upper";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	293 %%! U = ichol (A1, opts);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	294 %%! assert (norm (A1 - U' * U, 'fro') / norm (A1, 'fro'), 0.01, 0.01);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	295 %!
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	296 %!test
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	297 %! opts.type = "nofill";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	298 %! opts.michol = "off";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	299 %! opts.shape = "lower";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	300 %! L = ichol (A1, opts);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	301 %! assert (norm (A1 - L * L', 'fro') / norm (A1, 'fro'), 0.01, 0.01);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	302 %!
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	303 %!test
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	304 %! opts.type = "nofill";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	305 %! opts.michol = "on";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	306 %! L = ichol (A1, opts);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	307 %! assert (norm (A1 - L * L', 'fro') / norm (A1, 'fro'), 0.02, 0.01);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	308 %!
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	309 %!test
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	310 %! opts.type = "nofill";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	311 %! opts.michol = "on";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	312 %! opts.diagcomp = 3e-3;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	313 %! L = ichol (A1, opts);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	314 %! assert (norm (A1 - L * L', 'fro') / norm (A1, 'fro'), 0.02, 0.01);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	315 %!
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	316 %!test
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	317 %! opts.type = "ict";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	318 %! opts.michol = "off";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	319 %! opts.droptol = 1e-4;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	320 %! L = ichol (A1, opts);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	321 %! assert (norm (A1 - L * L', 'fro') / norm (A1, 'fro'), eps, eps);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	322 %!
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	323 %!test
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	324 %! opts.type = "ict";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	325 %! opts.michol = "off";
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	326 %! opts.droptol = 1e-4;
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	327 %! L = ichol (A2, opts);
168c0aa9bb05 Added all the files related with ilu.m and ichol.m functions. Eduardo Ramos (edu159) <eduradical951@gmail.com> parents: diff changeset	328 %! assert (norm (A2 - L * L', 'fro') / norm (A2, 'fro'), 5e-4, 5e-4);

Mercurial > octave

annotate scripts/sparse/ichol.m @ 19053:168c0aa9bb05