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function cholmod_demo
%CHOLMOD_DEMO a demo for CHOLMOD
%
% Tests CHOLMOD with various randomly-generated matrices, and the west0479
% matrix distributed with MATLAB. Random matrices are not good test cases,
% but they are easily generated. It also compares CHOLMOD and MATLAB on the
% sparse matrix problem used in the MATLAB BENCH command.
%
% See CHOLMOD/MATLAB/Test/cholmod_test.m for a lengthy test using matrices from
% the UF sparse matrix collection.
%
% Example:
% cholmod_demo
%
% See also BENCH
% Copyright 2006-2007, Timothy A. Davis, http://www.suitesparse.com
help cholmod_demo
rand ('state', 0) ;
randn ('state', 0) ;
load west0479
A = west0479 ;
n = size (A,1) ;
A = A*A'+100*speye (n) ;
try_matrix (A) ;
clear A
n = 2000 ;
A = sprandn (n, n, 0.002) ;
A = A+A'+100*speye (n) ;
try_matrix (A) ;
clear A
for n = [100 2000]
A = rand (n) ;
A = A*A' + 10 * eye (n) ;
try_matrix (A) ;
clear A
end
fprintf ('\n--------------------------------------------------------------\n') ;
fprintf ('\nWith the matrix used in the MATLAB 7.2 "bench" program.\n') ;
n = 300 ;
A = delsq (numgrid ('L', n)) ;
b = sum (A)' ;
tic ;
x = A\b ;
t1 = toc ;
e1 = norm (A*x-b) ;
tic ;
x = cholmod2 (A,b) ;
t2 = toc ;
e2 = norm (A*x-b) ;
fprintf ('MATLAB x=A\\b time: %8.4f resid: %8.0e\n', t1, e1) ;
fprintf ('CHOLMOD x=A\\b time: %8.4f resid: %8.0e\n', t2, e2) ;
fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ;
fprintf ('\ncholmod_demo finished: all tests passed\n') ;
fprintf ('\nFor more accurate timings, run this test again.\n') ;
function try_matrix (A)
% try_matrix: try a matrix with CHOLMOD
n = size (A,1) ;
S = sparse (A) ;
fprintf ('\n--------------------------------------------------------------\n') ;
if (issparse (A))
fprintf ('cholmod_demo: sparse matrix, n %d nnz %d\n', n, nnz (A)) ;
else
fprintf ('cholmod_demo: dense matrix, n %d\n', n) ;
end
X = rand (n,1) ;
C = sparse (X) ;
try
% use built-in AMD
p = amd (S) ;
catch
try
% use AMD from SuiteSparse (../../AMD)
p = amd2 (S) ;
catch
% use SYMAMD
p = symamd (S) ;
end
end
S = S (p,p) ;
lnz = symbfact2 (S) ;
fl = sum (lnz.^2) ;
tic
L = lchol (S) ; %#ok
t1 = toc ;
fprintf ('CHOLMOD lchol(sparse(A)) time: %6.2f mflop %8.1f\n', ...
t1, 1e-6 * fl / t1) ;
tic
LD = ldlchol (S) ; %#ok
t2 = toc ;
fprintf ('CHOLMOD ldlchol(sparse(A)) time: %6.2f mflop %8.1f\n', ...
t2, 1e-6 * fl / t2) ;
tic
LD2 = ldlupdate (LD,C) ;
t3 = toc ;
fprintf ('CHOLMOD ldlupdate(sparse(A),C) time: %6.2f (rank-1, C dense)\n', t3) ;
[L,D] = ldlsplit (LD2) ;
% L = full (L) ;
err = norm ((S+C*C') - L*D*L', 1) / norm (S,1) ;
fprintf ('err: %g\n', err) ;
k = max (1,fix(n/2)) ;
tic
LD3 = ldlrowmod (LD, k) ;
t4 = toc ;
fprintf ('CHOLMOD ldlrowmod(LD,k) time: %6.2f\n', t4) ;
[L,D] = ldlsplit (LD3) ;
S2 = S ;
I = speye (n) ;
S2 (k,:) = I (k,:) ;
S2 (:,k) = I (:,k) ;
err = norm (S2 - L*D*L', 1) / norm (S,1) ;
fprintf ('err: %g\n', err) ;
LD4 = ldlchol (S2) ;
[L,D] = ldlsplit (LD4) ;
% L = full (L) ;
err = norm (S2 - L*D*L', 1) / norm (S,1) ;
fprintf ('err: %g\n', err) ;
tic
R = chol (S) ; %#ok
s1 = toc ;
fprintf ('MATLAB chol(sparse(A)) time: %6.2f mflop %8.1f\n', ...
s1, 1e-6 * fl / s1) ;
E = full (A) ;
tic
R = chol (E) ;
s2 = toc ;
fprintf ('MATLAB chol(full(A)) time: %6.2f mflop %8.1f\n', ...
s2, 1e-6 * fl / s2) ;
Z = full (R) ;
tic
Z = cholupdate (Z,X) ;
s3 = toc ;
fprintf ('MATLAB cholupdate(full(A),C) time: %6.2f (rank-1)\n', s3) ;
err = norm ((E+X*X') - Z'*Z, 1) / norm (E,1) ;
fprintf ('err: %g\n', err) ;
fprintf ('CHOLMOD lchol(sparse(A)) speedup over chol(sparse(A)): %6.1f\n', ...
s1 / t1) ;
fprintf ('CHOLMOD sparse update speedup vs MATLAB DENSE update: %6.1f\n', ...
s3 / t3) ;
clear E S L R LD X C D Z
clear err s1 s2 s3 t1 t2 t3 n
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