--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/liboctave/UMFPACK/UMFPACK/MATLAB/umfpack_details.m	Fri Feb 25 19:55:28 2005 +0000
@@ -0,0 +1,164 @@
+function [out1, out2, out3, out4, out5] = umfpack (in1, in2, in3, in4, in5)
+% UMFPACK v4.4:  details on each usage.
+%
+% Factor or solve a sparse linear system, returning either the solution x to
+% Ax=b or A'x'=b', the factorization LU=PAQ, or LU=P(R\A)Q.  A must be sparse.
+% For the solve, A must be square and b must be a dense n-by-1 vector.  For LU
+% factorization, A can be rectangular.  In both cases, A and/or b can be real
+% or complex.
+%
+% UMFPACK analyzes the matrix and selects one of three strategies to factorize
+% the matrix.  It first finds a set of k initial pivot entries of zero Markowitz
+% cost.  This forms the first k rows and columns of L and U.  The remaining
+% submatrix S is then analyzed, based on the symmetry of the nonzero pattern of
+% the submatrix and the values on the diagaonal.  The strategies include:
+%
+%	(1) unsymmetric:  use a COLAMD pre-ordering, a column elimination tree
+%	    post-ordering, refine the column ordering during factorization,
+%	    and make no effort at selecting pivots on the diagonal.
+%	(2) 2-by-2:  like the symmetric strategy (see below), except that local
+%	    row permutations are first made to attempt to place large entries
+%	    on the diagonal.
+%	(3) symmetric:  use an AMD pre-ordering on the matrix S+S', an
+%	    elimination tree post-ordering, do not refine the column ordering
+%	    during factorization, and attempt to select pivots on the diagonal.
+%
+% Each of the following uses of umfpack (except for "Control = umfpack") is
+% stand-alone.  That is, no call to umfpack is required for any subsequent
+% call.  In each usage, the Info output argument is optional.
+%
+% Usage:
+%
+% [x, Info] = umfpack (A, '\', b) ;
+% [x, Info] = umfpack (A, '\', b, Control) ;
+% [x, Info] = umfpack (A, Qinit, '\', b, Control) ;
+% [x, Info] = umfpack (A, Qinit, '\', b) ;
+%
+%       Solves Ax=b (similar to x = A\b in MATLAB).
+%
+% [x, Info] = umfpack (b, '/', A) ;
+% [x, Info] = umfpack (b, '/', A, Control) ;
+% [x, Info] = umfpack (b, '/', A, Qinit) ;
+% [x, Info] = umfpack (b, '/', A, Qinit, Control) ;
+%
+%       Solves A'x'=b' (similar to x = b/A in MATLAB).
+%
+% [L, U, P, Q, R, Info] = umfpack (A) ;
+% [L, U, P, Q, R, Info] = umfpack (A, Control) ;
+% [L, U, P, Q, R, Info] = umfpack (A, Qinit) ;
+% [L, U, P, Q, R, Info] = umfpack (A, Qinit, Control) ;
+%
+%       Returns the LU factorization of A.  P and Q are returned as permutation
+%       matrices.  R is a diagonal sparse matrix of scale factors for the rows
+%	of A, L is lower triangular, and U is upper triangular.  The
+%	factorization is L*U = P*(R\A)*Q.  You can turn off scaling by setting
+%	Control (17) to zero (in which case R = speye (m)), or by using the
+%	following syntaxes (in which case Control (17) is ignored):
+%
+% [L, U, P, Q] = umfpack (A) ;
+% [L, U, P, Q] = umfpack (A, Control) ;
+% [L, U, P, Q] = umfpack (A, Qinit) ;
+% [L, U, P, Q] = umfpack (A, Qinit, Control) ;
+%
+%       Same as above, except that no row scaling is performed.  The Info array
+%	is not returned, either.
+%
+% [P1, Q1, Fr, Ch, Info] = umfpack (A, 'symbolic') ;
+% [P1, Q1, Fr, Ch, Info] = umfpack (A, 'symbolic', Control) ;
+% [P1, Q1, Fr, Ch, Info] = umfpack (A, Qinit, 'symbolic') ;
+% [P1, Q1, Fr, Ch, Info] = umfpack (A, Qinit, 'symbolic', Control);
+%
+%       Performs only the fill-reducing column pre-ordering (including the
+%       elimination tree post-ordering) and symbolic factorization.  Q1 is the
+%	initial column permutation (either from colamd, amd, or the input
+%	ordering Qinit), possibly followed by a column elimination tree post-
+%	ordering or a symmetric elimination tree post-ordering, depending on
+%	the strategy used.
+%
+%	For the unsymmetric strategy, P1 is the row ordering induced by Q1
+%	(row-merge order). For the 2-by-2 strategy, P1 is the row ordering that
+%	places large entries on the diagonal of P1*A*Q1.  For the symmetric
+%	strategy, P1 = Q1.
+%
+%       Fr is a (nfr+1)-by-4 array containing information about each frontal
+%       matrix, where nfr <= n is the number of frontal matrices.  Fr (:,1) is
+%       the number of pivot columns in each front, and Fr (:,2) is the parent
+%       of each front in the supercolumn elimination tree.  Fr (k,2) is zero if
+%       k is a root.  The first Fr (1,1) columns of P1*A*Q1 are the pivot
+%       columns for the first front, the next Fr (2,1) columns of P1*A*Q1
+%       are the pivot columns for the second front, and so on.
+%
+%	For the unsymmetric strategy, Fr (:,3) is the row index of the first
+%	row in P1*A*Q1 whose leftmost nonzero entry is in a pivot column for
+%	the kth front.  Fr (:,4) is the leftmost descendent of the kth front.
+%	Rows in the range Fr (Fr (k,4),3) to Fr (k+1,3)-1 form the entire set
+%	of candidate pivot rows for the kth front (some of these will typically
+%	have been selected as pivot rows of fronts Fr (k,3) to k-1, before the
+%	factorization reaches the kth front.  If front k is a leaf node, then
+%	Fr (k,4) is k.
+%
+%       Ch is a (nchains+1)-by-3 array containing information about each "chain"
+%       (unifrontal sequence) of frontal matrices, and where nchains <= nfr
+%       is the number of chains.  The ith chain consists of frontal matrices.
+%       Chain (i,1) to Chain (i+1,1)-1, and the largest front in chain i is
+%       Chain (i,2)-by-Chain (i,3).
+%
+%       This use of umfpack is not required to factor or solve a linear system
+%       in MATLAB.  It analyzes the matrix A and provides information only.
+%       The MATLAB statement "treeplot (Fr (:,2)')" plots the column elimination
+%       tree.
+%
+% Control = umfpack ;
+%
+%       Returns a 20-by-1 vector of default parameter settings for umfpack.
+%
+% umfpack_report (Control, Info) ;
+%
+%       Prints the current Control settings, and Info
+%
+% det = umfpack (A, 'det') ;
+% [det dexp] = umfpack (A, 'det') ;
+%
+%	Computes the determinant of A.  The 2nd form returns the determinant
+%	in the form det*10^dexp, where det is in the range +/- 1 to 10,
+%	which helps to avoid overflow/underflow when dexp is out of range of
+%	normal floating-point numbers.
+%
+% If present, Qinit is a user-supplied 1-by-n permutation vector.  It is an
+% initial fill-reducing column pre-ordering for A; if not present, then colamd
+% or amd are used instead.  If present, Control is a user-supplied 20-by-1
+% array.   Control and Info are optional; if Control is not present, defaults
+% are used.  If a Control entry is NaN, then the default is used for that entry.
+%
+%
+% UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis.
+% All Rights Reserved.  Type umfpack_details for License.
+%
+% UMFPACK License:
+%
+%     Your use or distribution of UMFPACK or any modified version of
+%     UMFPACK implies that you agree to this License.
+%
+%     THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+%     EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.
+%
+%     Permission is hereby granted to use or copy this program, provided
+%     that the Copyright, this License, and the Availability of the original
+%     version is retained on all copies.  User documentation of any code that
+%     uses UMFPACK or any modified version of UMFPACK code must cite the
+%     Copyright, this License, the Availability note, and "Used by permission."
+%     Permission to modify the code and to distribute modified code is granted,
+%     provided the Copyright, this License, and the Availability note are
+%     retained, and a notice that the code was modified is included.  This
+%     software was developed with support from the National Science Foundation,
+%     and is provided to you free of charge.
+%
+% Availability: http://www.cise.ufl.edu/research/sparse/umfpack
+%
+% See also umfpack, umfpack_make, umfpack_report,
+%    umfpack_demo, and umfpack_simple.
+
+more on
+help umfpack_details
+more off
+