1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
|
function [count, h, parent, post, L] = symbfact2 (A, mode, Lmode) %#ok
%SYMBFACT2 symbolic factorization
%
% Analyzes the Cholesky factorization of A, A'*A, or A*A'.
%
% Example:
% count = symbfact2 (A) returns row counts of R=chol(A)
% count = symbfact2 (A,'col') returns row counts of R=chol(A'*A)
% count = symbfact2 (A,'sym') same as symbfact2(A)
% count = symbfact2 (A,'lo') same as symbfact2(A'), uses tril(A)
% count = symbfact2 (A,'row') returns row counts of R=chol(A*A')
%
% The flop count for a subsequent LL' factorization is sum(count.^2)
%
% [count, h, parent, post, R] = symbfact2 (...) returns:
%
% h: height of the elimination tree
% parent: the elimination tree itself
% post: postordering of the elimination tree
% R: a 0-1 matrix whose structure is that of chol(A) for the
% symmetric case, chol(A'*A) for the 'col' case, or chol(A*A')
% for the 'row' case.
%
% symbfact2(A) and symbfact2(A,'sym') uses the upper triangular part of A
% (triu(A)) and assumes the lower triangular part is the transpose of the
% upper triangular part. symbfact2(A,'lo') uses tril(A) instead.
%
% With one to four output arguments, symbfact2 takes time almost
% proportional to nnz(A)+n where n is the dimension of R, and memory
% proportional to nnz(A). Computing the 5th argument takes more time and
% memory, both O(nnz(L)). Internally, the pattern of L is computed and
% R=L' is returned.
%
% The following forms return L = R' instead of R. They are faster and
% take less memory than the forms above. They return the same count, h,
% parent, and post outputs.
%
% [count, h, parent, post, L] = symbfact2 (A,'col','L')
% [count, h, parent, post, L] = symbfact2 (A,'sym','L')
% [count, h, parent, post, L] = symbfact2 (A,'lo', 'L')
% [count, h, parent, post, L] = symbfact2 (A,'row','L')
%
% See also chol, etree, treelayout, symbfact.
% Copyright 2006-2023, Timothy A. Davis, All Rights Reserved.
% SPDX-License-Identifier: GPL-2.0+
error ('symbfact2 mexFunction not found!') ;
|
