void CholeskyDecompositionComplex(long int run)
{
int k, i, j;
unsigned int dimension;
double sum, temp;
double complex sum2;
#if DEBUG
int l;
double complex temp_val;
#endif
dimension = circuit_simulation.number_of_nodes + circuit_simulation.group2_elements;
if (circuit_simulation.matrix_sparsity == SPARSE)
{
if(run == 0) {
printf( "\n\nCholesky Decomposition...\n\n" );
}
Scomplex = cs_ci_schol( 1, G2complex );
Ncomplex = cs_ci_chol( G2complex, Scomplex );
cs_ci_spfree( G2complex );
if (Ncomplex == NULL)
{
printf( "Error, the matrix must be hermitian & positive definite.\n\n" );
printf( "Terminating.\n" );
exit( -1 );
}
}
else
{
if(run == 0) {
printf( "\n\nCholesky Decomposition...\n\n" );
}
for (k = 0; k < dimension; k++)
{
for (sum = 0, j = 0; j < k; j++)
{
if (matrix_Gcomplex[k * dimension + j] != conj(matrix_Gcomplex[j * dimension + k]))
{
printf( "Error, the matrix must be hermitian & positive definite.\n\n" );
printf( "Terminating.\n" );
exit( -1 );
}
sum += creal(conj(matrix_Gcomplex[k * dimension + j]) * matrix_Gcomplex[k * dimension + j]);
}
if(cimag(matrix_Gcomplex[k * dimension + k]) != 0) {
printf( "Error, the matrix must be hermitian & positive definite.\n\n" );
printf( "Terminating.\n" );
exit( -1 );
}
if ((temp = creal(matrix_Gcomplex[k * dimension + k]) - sum) < 0)
{
printf( "Error, the matrix must be hermitian & positive definite.\n\n" );
printf( "Terminating.\n" );
exit( -1 );
}
matrix_Gcomplex[k * dimension + k] = sqrt( temp );
for (i = k + 1; i < dimension; i++)
{
for (sum2 = 0, j = 0; j < k; j++)
{
sum2 += conj(matrix_Gcomplex[i * dimension + j]) * matrix_Gcomplex[k * dimension + j];
}
matrix_Gcomplex[k * dimension + i] = matrix_Gcomplex[i * dimension + k] = (matrix_Gcomplex[k * dimension + i] - sum2) / matrix_Gcomplex[k * dimension + k];
}
}
}
#if DEBUG
printf("\nCholesky Decomposition\n~~~~~~~~~~~~~~~~~~~~~~~\n\n");
printf("\nDecomposed Matrix:\n\n");
for(k = 0; k < dimension; k++)
{
for(l = 0; l < dimension; l++)
{
if(l == k)
{
printf(" \\\\");
}
if (circuit_simulation.matrix_sparsity == SPARSE)
{
if(l <= k)
{
temp_val = getElementAtComplex(Ncomplex -> L, k, l);
printf("(%7.3lf %7.3lfi) ", creal(temp_val), cimag(temp_val));
}
else
{
temp_val = getElementAtComplex(Ncomplex -> L, l, k);
printf("(%7.3lf %7.3lfi) ", creal(temp_val), cimag(temp_val));
}
}
else {
printf("(%7.3lf %7.3lfi) ", creal(matrix_Gcomplex[k * dimension + l]), cimag(matrix_Gcomplex[k * dimension + l]));
}
if(l == k)
{
printf(" \\\\");
}
}
printf("\n\n");
}
printf("\n\n");
#endif
}
/* Cholesky update/downdate */
int demo3 (problem *Prob)
{
cs_ci *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ;
int n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ;
cs_complex_t *b, *x, *resid, *y = NULL, *Lx, *Wx, s ;
double t, t1 ;
cs_cis *S = NULL ;
cs_cin *N = NULL ;
if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ;
A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
n = A->n ;
if (!Prob->sym || n == 0) return (1) ;
rhs (x, b, n) ; /* compute right-hand side */
printf ("\nchol then update/downdate ") ;
print_order (1) ;
y = cs_ci_malloc (n, sizeof (cs_complex_t)) ;
t = tic () ;
S = cs_ci_schol (1, C) ; /* symbolic Chol, amd(A+A') */
printf ("\nsymbolic chol time %8.2f\n", toc (t)) ;
t = tic () ;
N = cs_ci_chol (C, S) ; /* numeric Cholesky */
printf ("numeric chol time %8.2f\n", toc (t)) ;
if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ;
t = tic () ;
cs_ci_ipvec (S->pinv, b, y, n) ; /* y = P*b */
cs_ci_lsolve (N->L, y) ; /* y = L\y */
cs_ci_ltsolve (N->L, y) ; /* y = L'\y */
cs_ci_pvec (S->pinv, y, x, n) ; /* x = P'*y */
printf ("solve chol time %8.2f\n", toc (t)) ;
printf ("original: ") ;
print_resid (1, C, x, b, resid) ; /* print residual */
k = n/2 ; /* construct W */
W = cs_ci_spalloc (n, 1, n, 1, 0) ;
if (!W) return (done3 (0, S, N, y, W, E, p)) ;
Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ;
Wp = W->p ; Wi = W->i ; Wx = W->x ;
Wp [0] = 0 ;
p1 = Lp [k] ;
Wp [1] = Lp [k+1] - p1 ;
s = Lx [p1] ;
srand (1) ;
for ( ; p1 < Lp [k+1] ; p1++)
{
p2 = p1 - Lp [k] ;
Wi [p2] = Li [p1] ;
Wx [p2] = s * rand () / ((double) RAND_MAX) ;
}
t = tic () ;
ok = cs_ci_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */
t1 = toc (t) ;
printf ("update: time: %8.2f\n", t1) ;
if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
t = tic () ;
cs_ci_ipvec (S->pinv, b, y, n) ; /* y = P*b */
cs_ci_lsolve (N->L, y) ; /* y = L\y */
cs_ci_ltsolve (N->L, y) ; /* y = L'\y */
cs_ci_pvec (S->pinv, y, x, n) ; /* x = P'*y */
t = toc (t) ;
p = cs_ci_pinv (S->pinv, n) ;
W2 = cs_ci_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */
WT = cs_ci_transpose (W2,1) ;
WW = cs_ci_multiply (W2, WT) ;
cs_ci_spfree (WT) ;
cs_ci_spfree (W2) ;
E = cs_ci_add (C, WW, 1, 1) ;
cs_ci_spfree (WW) ;
if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ;
printf ("update: time: %8.2f (incl solve) ", t1+t) ;
print_resid (1, E, x, b, resid) ; /* print residual */
cs_ci_nfree (N) ; /* clear N */
t = tic () ;
N = cs_ci_chol (E, S) ; /* numeric Cholesky */
if (!N) return (done3 (0, S, N, y, W, E, p)) ;
cs_ci_ipvec (S->pinv, b, y, n) ; /* y = P*b */
cs_ci_lsolve (N->L, y) ; /* y = L\y */
cs_ci_ltsolve (N->L, y) ; /* y = L'\y */
cs_ci_pvec (S->pinv, y, x, n) ; /* x = P'*y */
t = toc (t) ;
printf ("rechol: time: %8.2f (incl solve) ", t) ;
print_resid (1, E, x, b, resid) ; /* print residual */
t = tic () ;
ok = cs_ci_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */
t1 = toc (t) ;
if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
printf ("downdate: time: %8.2f\n", t1) ;
t = tic () ;
cs_ci_ipvec (S->pinv, b, y, n) ; /* y = P*b */
cs_ci_lsolve (N->L, y) ; /* y = L\y */
cs_ci_ltsolve (N->L, y) ; /* y = L'\y */
cs_ci_pvec (S->pinv, y, x, n) ; /* x = P'*y */
t = toc (t) ;
printf ("downdate: time: %8.2f (incl solve) ", t1+t) ;
print_resid (1, C, x, b, resid) ; /* print residual */
return (done3 (1, S, N, y, W, E, p)) ;
}
