# HG changeset patch
# User David Bateman <dbateman@free.fr>
# Date 1204829176 18000
# Node ID 6b07c15eb8e1e74b5d5cdcf00e91e8e13d81e950
# Parent  b3acdf1c41a52562b0f878e9c25339c95f4aaebc
Document positive definite behavior of matrix_type

diff -r b3acdf1c41a5 -r 6b07c15eb8e1 src/ChangeLog
--- a/src/ChangeLog	Thu Mar 06 13:42:08 2008 -0500
+++ b/src/ChangeLog	Thu Mar 06 13:46:16 2008 -0500
@@ -1,3 +1,10 @@
+2008-03-06  David Bateman  <dbateman@free.fr>
+
+	* DLD-FUNCTIONS/matrix_type.cc (Fmatrix_type): Document that
+	the initial interpretation of a positive definite return from
+	matrix_type is that the matrix is "probably" positive definite and
+	not certainly so.
+
 2008-03-06  John W. Eaton  <jwe@octave.org>
 
 	* parse.y: Move tests here from test/test_eval.m.
diff -r b3acdf1c41a5 -r 6b07c15eb8e1 src/DLD-FUNCTIONS/matrix_type.cc
--- a/src/DLD-FUNCTIONS/matrix_type.cc	Thu Mar 06 13:42:08 2008 -0500
+++ b/src/DLD-FUNCTIONS/matrix_type.cc	Thu Mar 06 13:46:16 2008 -0500
@@ -59,7 +59,7 @@
 Mark the matrix as full.\n\
 \n\
 @item 'positive definite'\n\
-Full positive definite matrix.\n\
+Probable full positive definite matrix.\n\
 \n\
 @item 'diagonal'\n\
 Diagonal Matrix. (Sparse matrices only)\n\
@@ -83,8 +83,8 @@
 @itemx 'banded positive definite'\n\
 Banded matrix with the band size of @var{nl} below the diagonal and @var{nu} above\n\
 it. If @var{nl} and @var{nu} are 1, then the matrix is tridiagonal and treated\n\
-with specialized code. In addition the matrix can be marked as positive definite\n\
-(Sparse matrices only)\n\
+with specialized code. In addition the matrix can be marked as probably a\n\
+positive definite (Sparse matrices only)\n\
 \n\
 @item 'singular'\n\
 The matrix is assumed to be singular and will be treated with a minimum norm solution\n\
@@ -97,6 +97,14 @@
 matrix type will result in incorrect results from solutions of linear equations,\n\
 and so it is entirely the responsibility of the user to correctly identify the\n\
 matrix type.\n\
+\n\
+Also the test for positive definiteness is a low cost test for a hermitian\n\
+matrix with a real positive diagonal. This does not guarentee that the matrix\n\
+is positive definite, but only that it is a probable candidate. When such a\n\
+matrix is factorized, a Cholesky factorization is first attempted, and if\n\
+that fails the matrix is then treated with an LU factorization. Once the\n\
+matrix has been factorized, @code{matrix_type} will return the correct\n\
+classification of the matrix.\n\
 @end deftypefn")
 {
   int nargin = args.length ();