# HG changeset patch
# User dbateman
# Date 1113518448 0
# Node ID bb224e6c26a73dfbd820720eb05aa1b97434293a
# Parent  5bdc3f24cd5f9371698aa129e178d6b95a69a67e
[project @ 2005-04-14 22:40:48 by dbateman]

diff -r 5bdc3f24cd5f -r bb224e6c26a7 src/DLD-FUNCTIONS/luinc.cc
--- a/src/DLD-FUNCTIONS/luinc.cc	Thu Apr 14 22:17:27 2005 +0000
+++ b/src/DLD-FUNCTIONS/luinc.cc	Thu Apr 14 22:40:48 2005 +0000
@@ -265,100 +265,3 @@
 ;;; mode: C++ ***
 ;;; End: ***
 */
-
-/* 
- LUINC  Sparse Incomplete LU factorization.
-    LUINC produces two different kinds of incomplete LU factorizations -- the
-    drop tolerance and the 0 level of fill-in factorizations.  These factors
-    may be useful as preconditioners for a system of linear equations being
-    solved by an iterative method such as BICG (BiConjugate Gradients).
- 
-    LUINC(X,DROPTOL) performs the incomplete LU factorization of
-    X with drop tolerance DROPTOL.
- 
-    LUINC(X,OPTS) allows additional options to the incomplete LU
-    factorization.  OPTS is a structure with up to four fields:
-        droptol --- the drop tolerance of incomplete LU
-        milu    --- modified incomplete LU
-        udiag   --- replace zeros on the diagonal of U
-        thresh  --- the pivot threshold (see also LU)
- 
-    Only the fields of interest need to be set.
- 
-    droptol is a non-negative scalar used as the drop
-    tolerance for the incomplete LU factorization.  This factorization
-    is computed in the same (column-oriented) manner as the
-    LU factorization except after each column of L and U has
-    been calculated, all entries in that column which are smaller
-    in magnitude than the local drop tolerance, which is 
-    droptol * NORM of the column of X, are "dropped" from L or U.
-    The only exception to this dropping rule is the diagonal of the
-    upper triangular factor U which remains even if it is too small.
-    Note that entries of the lower triangular factor L are tested
-    before being scaled by the pivot.  Setting droptol = 0
-    produces the complete LU factorization, which is the default.
- 
-    milu stands for modified incomplete LU factorization.  Its
-    value is either 0 (unmodified, the default) or 1 (modified).
-    Instead of discarding those entries from the newly-formed
-    column of the factors, they are subtracted from the diagonal
-    of the upper triangular factor, U.
- 
-    udiag is either 0 or 1.  If it is 1, any zero diagonal entries
-    of the upper triangular factor U are replaced by the local drop
-    tolerance in an attempt to avoid a singular factor.  The default
-    is 0.
- 
-    thresh is a pivot threshold in [0,1].  Pivoting occurs
-    when the diagonal entry in a column has magnitude less
-    than thresh times the magnitude of any sub-diagonal entry in
-    that column.  thresh = 0 forces diagonal pivoting.  thresh = 1 is
-    the default.
- 
-    Example:
- 
-       load west0479
-       A = west0479;
-       nnz(A)
-       nnz(lu(A))
-       nnz(luinc(A,1e-6))
- 
-       This shows that A has 1887 nonzeros, its complete LU factorization
-       has 16777 nonzeros, and its incomplete LU factorization with a
-       drop tolerance of 1e-6 has 10311 nonzeros.
- 
- 
-    [L,U,P] = LUINC(X,'0') produces the incomplete LU factors of a sparse
-    matrix with 0 level of fill-in (i.e. no fill-in).  L is unit lower
-    trianglar, U is upper triangular and P is a permutation matrix.  U has the
-    same sparsity pattern as triu(P*X).  L has the same sparsity pattern as
-    tril(P*X), except for 1's on the diagonal of L where P*X may be zero.  Both
-    L and U may have a zero because of cancellation where P*X is nonzero.  L*U
-    differs from P*X only outside of the sparsity pattern of P*X.
- 
-    [L,U] = LUINC(X,'0') produces upper triangular U and L is a permutation of
-    unit lower triangular matrix.  Thus no comparison can be made between the
-    sparsity patterns of L,U and X, although nnz(L) + nnz(U) = nnz(X) + n.  L*U
-    differs from X only outside of its sparsity pattern.
- 
-    LU = LUINC(X,'0') returns "L+U-I", where L is unit lower triangular, U is
-    upper triangular and the permutation information is lost.
- 
-    Example:
- 
-       load west0479
-       A = west0479;
-       [L,U,P] = luinc(A,'0');
-       isequal(spones(U),spones(triu(P*A)))
-       spones(L) ~= spones(tril(P*A))
-       D = (L*U) .* spones(P*A) - P*A
- 
-       spones(L) differs from spones(tril(P*A)) at some positions on the
-       diagonal and at one position in L where cancellation zeroed out a
-       nonzero element of P*A.  The entries of D are of the order of eps.
- 
-    LUINC works only for sparse matrices.
- 
-    See also LU, CHOLINC, BICG.
-
-*/