1
/* ========================================================================== */
2
/* === ldllsimple.c: a simple LDL main program (long integer version) ====== */
3
/* ========================================================================== */
5
/* LDLSIMPLE: this is a very simple main program that illustrates the basic
6
* usage of the LDL routines. The output of this program is in ldlsimple.out.
7
* This program factorizes the matrix
10
* 1.7 0 0 0 0 0 0 0 .13 0
11
* 0 1. 0 0 .02 0 0 0 0 .01
12
* 0 0 1.5 0 0 0 0 0 0 0
13
* 0 0 0 1.1 0 0 0 0 0 0
14
* 0 .02 0 0 2.6 0 .16 .09 .52 .53
15
* 0 0 0 0 0 1.2 0 0 0 0
16
* 0 0 0 0 .16 0 1.3 0 0 .56
17
* 0 0 0 0 .09 0 0 1.6 .11 0
18
* .13 0 0 0 .52 0 0 .11 1.4 0
19
* 0 .01 0 0 .53 0 .56 0 0 3.1 ] ;
21
* and then solves a system Ax=b whose true solution is
22
* x = [.1 .2 .3 .4 .5 .6 .7 .8 .9 1]' ;
24
* Note that Li and Lx are statically allocated, with length 13. This is just
25
* enough to hold the factor L, but normally this size is not known until after
26
* ldl_symbolic has analyzed the matrix. The size of Li and Lx must be greater
27
* than or equal to lnz = Lp [N], which is 13 for this matrix L.
29
* LDL Version 1.3, Copyright (c) 2006 by Timothy A Davis,
30
* University of Florida. All Rights Reserved. See README for the License.
39
#define N 10 /* A is 10-by-10 */
40
#define ANZ 19 /* # of nonzeros on diagonal and upper triangular part of A */
41
#define LNZ 13 /* # of nonzeros below the diagonal of L */
45
/* only the upper triangular part of A is required */
46
UF_long Ap[N+1] = {0, 1, 2, 3, 4, 6, 7, 9, 11, 15, ANZ},
47
Ai [ANZ] = {0, 1, 2, 3, 1,4, 5, 4,6, 4,7, 0,4,7,8, 1,4,6,9 } ;
48
double Ax [ANZ] = {1.7, 1., 1.5, 1.1, .02,2.6, 1.2, .16,1.3, .09,1.6,
49
.13,.52,.11,1.4, .01,.53,.56,3.1},
50
b [N] = {.287, .22, .45, .44, 2.486, .72, 1.55, 1.424, 1.621, 3.759};
51
double Lx [LNZ], D [N], Y [N] ;
52
UF_long Li [LNZ], Lp [N+1], Parent [N], Lnz [N], Flag [N], Pattern [N], d, i ;
54
/* factorize A into LDL' (P and Pinv not used) */
55
ldl_l_symbolic (N, Ap, Ai, Lp, Parent, Lnz, Flag, NULL, NULL) ;
56
printf ("Nonzeros in L, excluding diagonal: %d\n", Lp [N]) ;
57
d = ldl_l_numeric (N, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D, Y, Pattern,
62
/* solve Ax=b, overwriting b with the solution x */
63
ldl_l_lsolve (N, b, Lp, Li, Lx) ;
64
ldl_l_dsolve (N, b, D) ;
65
ldl_l_ltsolve (N, b, Lp, Li, Lx) ;
66
for (i = 0 ; i < N ; i++) printf ("x [%d] = %g\n", i, b [i]) ;
70
printf ("ldl_l_numeric failed, D (%d,%d) is zero\n", d, d) ;