// Given column compressed form of matrix A
// perform LU decomposition and store the result in Numeric
// n is the dimension of matrix A
void Algebra::LU_decomposition(int n, UF_long * Ap, UF_long * Ai, double * Ax,
void ** p_Numeric){
int status;
double Control [UMFPACK_CONTROL];
umfpack_dl_defaults (Control) ;
double *null = (double *) NULL;
void * Symbolic;
// perform ordering
status = umfpack_dl_symbolic(n, n, Ap, Ai, Ax,
&Symbolic, Control, null);
if( status < 0 ){
umfpack_dl_report_status (Control, status) ;
report_exit("umfpack_dl_symbolic failed\n") ;
}
// LU decomposition
status = umfpack_dl_numeric(Ap, Ai, Ax, Symbolic,
p_Numeric, Control, null) ;
if( status < 0 ){
umfpack_dl_report_status (Control, status) ;
report_exit("umfpack_dl_numeric failed\n") ;
}
umfpack_dl_free_symbolic (&Symbolic) ;
}
int main (int argc, char **argv)
{
double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], *Ax, *Cx, *Lx, *Ux,
*W, t [2], *Dx, rnorm, *Rb, *y, *Rs ;
UF_long *Ap, *Ai, *Cp, *Ci, row, col, p, lnz, unz, nr, nc, *Lp, *Li, *Ui, *Up,
*P, *Q, *Lj, i, j, k, anz, nfr, nchains, *Qinit, fnpiv, lnz1, unz1, nz1,
status, *Front_npivcol, *Front_parent, *Chain_start, *Wi, *Pinit, n1,
*Chain_maxrows, *Chain_maxcols, *Front_1strow, *Front_leftmostdesc,
nzud, do_recip ;
void *Symbolic, *Numeric ;
/* ---------------------------------------------------------------------- */
/* initializations */
/* ---------------------------------------------------------------------- */
umfpack_tic (t) ;
printf ("\nUMFPACK V%d.%d (%s) demo: _dl_ version\n",
UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_DATE) ;
/* get the default control parameters */
umfpack_dl_defaults (Control) ;
/* change the default print level for this demo */
/* (otherwise, nothing will print) */
Control [UMFPACK_PRL] = 6 ;
/* print the license agreement */
umfpack_dl_report_status (Control, UMFPACK_OK) ;
Control [UMFPACK_PRL] = 5 ;
/* print the control parameters */
umfpack_dl_report_control (Control) ;
/* ---------------------------------------------------------------------- */
/* print A and b, and convert A to column-form */
/* ---------------------------------------------------------------------- */
/* print the right-hand-side */
printf ("\nb: ") ;
(void) umfpack_dl_report_vector (n, b, Control) ;
/* print the triplet form of the matrix */
printf ("\nA: ") ;
(void) umfpack_dl_report_triplet (n, n, nz, Arow, Acol, Aval,
Control) ;
/* convert to column form */
nz1 = MAX (nz,1) ; /* ensure arrays are not of size zero. */
Ap = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
Ai = (UF_long *) malloc (nz1 * sizeof (UF_long)) ;
Ax = (double *) malloc (nz1 * sizeof (double)) ;
if (!Ap || !Ai || !Ax)
{
error ("out of memory") ;
}
status = umfpack_dl_triplet_to_col (n, n, nz, Arow, Acol, Aval,
Ap, Ai, Ax, (UF_long *) NULL) ;
if (status < 0)
{
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_triplet_to_col failed") ;
}
/* print the column-form of A */
printf ("\nA: ") ;
(void) umfpack_dl_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ;
/* ---------------------------------------------------------------------- */
/* symbolic factorization */
/* ---------------------------------------------------------------------- */
status = umfpack_dl_symbolic (n, n, Ap, Ai, Ax, &Symbolic,
Control, Info) ;
if (status < 0)
{
umfpack_dl_report_info (Control, Info) ;
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_symbolic failed") ;
}
/* print the symbolic factorization */
printf ("\nSymbolic factorization of A: ") ;
(void) umfpack_dl_report_symbolic (Symbolic, Control) ;
/* ---------------------------------------------------------------------- */
/* numeric factorization */
/* ---------------------------------------------------------------------- */
status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric,
Control, Info) ;
if (status < 0)
{
umfpack_dl_report_info (Control, Info) ;
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_numeric failed") ;
}
/* print the numeric factorization */
printf ("\nNumeric factorization of A: ") ;
(void) umfpack_dl_report_numeric (Numeric, Control) ;
/* ---------------------------------------------------------------------- */
/* solve Ax=b */
/* ---------------------------------------------------------------------- */
status = umfpack_dl_solve (UMFPACK_A, Ap, Ai, Ax, x, b,
Numeric, Control, Info) ;
umfpack_dl_report_info (Control, Info) ;
umfpack_dl_report_status (Control, status) ;
if (status < 0)
{
error ("umfpack_dl_solve failed") ;
}
printf ("\nx (solution of Ax=b): ") ;
(void) umfpack_dl_report_vector (n, x, Control) ;
rnorm = resid (FALSE, Ap, Ai, Ax) ;
printf ("maxnorm of residual: %g\n\n", rnorm) ;
/* ---------------------------------------------------------------------- */
/* compute the determinant */
/* ---------------------------------------------------------------------- */
status = umfpack_dl_get_determinant (x, r, Numeric, Info) ;
umfpack_dl_report_status (Control, status) ;
if (status < 0)
{
error ("umfpack_dl_get_determinant failed") ;
}
printf ("determinant: (%g", x [0]) ;
printf (") * 10^(%g)\n", r [0]) ;
/* ---------------------------------------------------------------------- */
/* solve Ax=b, broken down into steps */
/* ---------------------------------------------------------------------- */
/* Rb = R*b */
Rb = (double *) malloc (n * sizeof (double)) ;
y = (double *) malloc (n * sizeof (double)) ;
if (!Rb || !y) error ("out of memory") ;
status = umfpack_dl_scale (Rb, b, Numeric) ;
if (status < 0) error ("umfpack_dl_scale failed") ;
/* solve Ly = P*(Rb) */
status = umfpack_dl_solve (UMFPACK_Pt_L, Ap, Ai, Ax, y, Rb,
Numeric, Control, Info) ;
if (status < 0) error ("umfpack_dl_solve failed") ;
/* solve UQ'x=y */
status = umfpack_dl_solve (UMFPACK_U_Qt, Ap, Ai, Ax, x, y,
Numeric, Control, Info) ;
if (status < 0) error ("umfpack_dl_solve failed") ;
printf ("\nx (solution of Ax=b, solve is split into 3 steps): ") ;
(void) umfpack_dl_report_vector (n, x, Control) ;
rnorm = resid (FALSE, Ap, Ai, Ax) ;
printf ("maxnorm of residual: %g\n\n", rnorm) ;
free (Rb) ;
free (y) ;
/* ---------------------------------------------------------------------- */
/* solve A'x=b */
/* ---------------------------------------------------------------------- */
status = umfpack_dl_solve (UMFPACK_At, Ap, Ai, Ax, x, b,
Numeric, Control, Info) ;
umfpack_dl_report_info (Control, Info) ;
if (status < 0)
{
error ("umfpack_dl_solve failed") ;
}
printf ("\nx (solution of A'x=b): ") ;
(void) umfpack_dl_report_vector (n, x, Control) ;
rnorm = resid (TRUE, Ap, Ai, Ax) ;
printf ("maxnorm of residual: %g\n\n", rnorm) ;
/* ---------------------------------------------------------------------- */
/* modify one numerical value in the column-form of A */
/* ---------------------------------------------------------------------- */
/* change A (1,4), look for row index 1 in column 4. */
row = 1 ;
col = 4 ;
for (p = Ap [col] ; p < Ap [col+1] ; p++)
{
if (row == Ai [p])
{
printf ("\nchanging A (%ld,%ld) to zero\n", row, col) ;
Ax [p] = 0.0 ;
break ;
}
}
printf ("\nmodified A: ") ;
(void) umfpack_dl_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ;
/* ---------------------------------------------------------------------- */
/* redo the numeric factorization */
/* ---------------------------------------------------------------------- */
/* The pattern (Ap and Ai) hasn't changed, so the symbolic factorization */
/* doesn't have to be redone, no matter how much we change Ax. */
/* We don't need the Numeric object any more, so free it. */
umfpack_dl_free_numeric (&Numeric) ;
/* Note that a memory leak would have occurred if the old Numeric */
/* had not been free'd with umfpack_dl_free_numeric above. */
status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric,
Control, Info) ;
if (status < 0)
{
umfpack_dl_report_info (Control, Info) ;
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_numeric failed") ;
}
printf ("\nNumeric factorization of modified A: ") ;
(void) umfpack_dl_report_numeric (Numeric, Control) ;
/* ---------------------------------------------------------------------- */
/* solve Ax=b, with the modified A */
/* ---------------------------------------------------------------------- */
status = umfpack_dl_solve (UMFPACK_A, Ap, Ai, Ax, x, b,
Numeric, Control, Info) ;
umfpack_dl_report_info (Control, Info) ;
if (status < 0)
{
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_solve failed") ;
}
printf ("\nx (with modified A): ") ;
(void) umfpack_dl_report_vector (n, x, Control) ;
rnorm = resid (FALSE, Ap, Ai, Ax) ;
printf ("maxnorm of residual: %g\n\n", rnorm) ;
/* ---------------------------------------------------------------------- */
/* modify all of the numerical values of A, but not the pattern */
/* ---------------------------------------------------------------------- */
for (col = 0 ; col < n ; col++)
{
for (p = Ap [col] ; p < Ap [col+1] ; p++)
{
row = Ai [p] ;
printf ("changing ") ;
printf ("A (%ld,%ld) from %g", row, col, Ax [p]) ;
Ax [p] = Ax [p] + col*10 - row ;
printf (" to %g\n", Ax [p]) ;
}
}
printf ("\ncompletely modified A (same pattern): ") ;
(void) umfpack_dl_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ;
/* ---------------------------------------------------------------------- */
/* save the Symbolic object to file, free it, and load it back in */
/* ---------------------------------------------------------------------- */
/* use the default filename, "symbolic.umf" */
printf ("\nSaving symbolic object:\n") ;
status = umfpack_dl_save_symbolic (Symbolic, (char *) NULL) ;
if (status < 0)
{
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_save_symbolic failed") ;
}
printf ("\nFreeing symbolic object:\n") ;
umfpack_dl_free_symbolic (&Symbolic) ;
printf ("\nLoading symbolic object:\n") ;
status = umfpack_dl_load_symbolic (&Symbolic, (char *) NULL) ;
if (status < 0)
{
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_load_symbolic failed") ;
}
printf ("\nDone loading symbolic object\n") ;
/* ---------------------------------------------------------------------- */
/* redo the numeric factorization */
/* ---------------------------------------------------------------------- */
umfpack_dl_free_numeric (&Numeric) ;
status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric,
Control, Info) ;
if (status < 0)
{
umfpack_dl_report_info (Control, Info) ;
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_numeric failed") ;
}
printf ("\nNumeric factorization of completely modified A: ") ;
(void) umfpack_dl_report_numeric (Numeric, Control) ;
/* ---------------------------------------------------------------------- */
/* solve Ax=b, with the modified A */
/* ---------------------------------------------------------------------- */
status = umfpack_dl_solve (UMFPACK_A, Ap, Ai, Ax, x, b,
Numeric, Control, Info) ;
umfpack_dl_report_info (Control, Info) ;
if (status < 0)
{
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_solve failed") ;
}
printf ("\nx (with completely modified A): ") ;
(void) umfpack_dl_report_vector (n, x, Control) ;
rnorm = resid (FALSE, Ap, Ai, Ax) ;
printf ("maxnorm of residual: %g\n\n", rnorm) ;
/* ---------------------------------------------------------------------- */
/* free the symbolic and numeric factorization */
/* ---------------------------------------------------------------------- */
umfpack_dl_free_symbolic (&Symbolic) ;
umfpack_dl_free_numeric (&Numeric) ;
/* ---------------------------------------------------------------------- */
/* C = transpose of A */
/* ---------------------------------------------------------------------- */
Cp = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
Ci = (UF_long *) malloc (nz1 * sizeof (UF_long)) ;
Cx = (double *) malloc (nz1 * sizeof (double)) ;
if (!Cp || !Ci || !Cx)
{
error ("out of memory") ;
}
status = umfpack_dl_transpose (n, n, Ap, Ai, Ax,
(UF_long *) NULL, (UF_long *) NULL, Cp, Ci, Cx) ;
if (status < 0)
{
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_transpose failed: ") ;
}
printf ("\nC (transpose of A): ") ;
(void) umfpack_dl_report_matrix (n, n, Cp, Ci, Cx, 1, Control) ;
/* ---------------------------------------------------------------------- */
/* symbolic factorization of C */
/* ---------------------------------------------------------------------- */
status = umfpack_dl_symbolic (n, n, Cp, Ci, Cx, &Symbolic,
Control, Info) ;
if (status < 0)
{
umfpack_dl_report_info (Control, Info) ;
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_symbolic failed") ;
}
printf ("\nSymbolic factorization of C: ") ;
(void) umfpack_dl_report_symbolic (Symbolic, Control) ;
/* ---------------------------------------------------------------------- */
/* copy the contents of Symbolic into user arrays print them */
/* ---------------------------------------------------------------------- */
printf ("\nGet the contents of the Symbolic object for C:\n") ;
printf ("(compare with umfpack_dl_report_symbolic output, above)\n") ;
Pinit = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
Qinit = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
Front_npivcol = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
Front_1strow = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
Front_leftmostdesc = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
Front_parent = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
Chain_start = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
Chain_maxrows = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
Chain_maxcols = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
if (!Pinit || !Qinit || !Front_npivcol || !Front_parent || !Chain_start ||
!Chain_maxrows || !Chain_maxcols || !Front_1strow ||
!Front_leftmostdesc)
{
error ("out of memory") ;
}
status = umfpack_dl_get_symbolic (&nr, &nc, &n1, &anz, &nfr, &nchains,
Pinit, Qinit, Front_npivcol, Front_parent, Front_1strow,
Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
Symbolic) ;
if (status < 0)
{
error ("symbolic factorization invalid") ;
}
printf ("From the Symbolic object, C is of dimension %ld-by-%ld\n", nr, nc);
printf (" with nz = %ld, number of fronts = %ld,\n", nz, nfr) ;
printf (" number of frontal matrix chains = %ld\n", nchains) ;
printf ("\nPivot columns in each front, and parent of each front:\n") ;
k = 0 ;
for (i = 0 ; i < nfr ; i++)
{
fnpiv = Front_npivcol [i] ;
printf (" Front %ld: parent front: %ld number of pivot cols: %ld\n",
i, Front_parent [i], fnpiv) ;
for (j = 0 ; j < fnpiv ; j++)
{
col = Qinit [k] ;
printf (
" %ld-th pivot column is column %ld in original matrix\n",
k, col) ;
k++ ;
}
}
printf ("\nNote that the column ordering, above, will be refined\n") ;
printf ("in the numeric factorization below. The assignment of pivot\n") ;
printf ("columns to frontal matrices will always remain unchanged.\n") ;
printf ("\nTotal number of pivot columns in frontal matrices: %ld\n", k) ;
printf ("\nFrontal matrix chains:\n") ;
for (j = 0 ; j < nchains ; j++)
{
printf (" Frontal matrices %ld to %ld are factorized in a single\n",
Chain_start [j], Chain_start [j+1] - 1) ;
printf (" working array of size %ld-by-%ld\n",
Chain_maxrows [j], Chain_maxcols [j]) ;
}
/* ---------------------------------------------------------------------- */
/* numeric factorization of C */
/* ---------------------------------------------------------------------- */
status = umfpack_dl_numeric (Cp, Ci, Cx, Symbolic, &Numeric,
Control, Info) ;
if (status < 0)
{
error ("umfpack_dl_numeric failed") ;
}
printf ("\nNumeric factorization of C: ") ;
(void) umfpack_dl_report_numeric (Numeric, Control) ;
/* ---------------------------------------------------------------------- */
/* extract the LU factors of C and print them */
/* ---------------------------------------------------------------------- */
if (umfpack_dl_get_lunz (&lnz, &unz, &nr, &nc, &nzud, Numeric) < 0)
{
error ("umfpack_dl_get_lunz failed") ;
}
/* ensure arrays are not of zero size */
lnz1 = MAX (lnz,1) ;
unz1 = MAX (unz,1) ;
Lp = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
Lj = (UF_long *) malloc (lnz1 * sizeof (UF_long)) ;
Lx = (double *) malloc (lnz1 * sizeof (double)) ;
Up = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
Ui = (UF_long *) malloc (unz1 * sizeof (UF_long)) ;
Ux = (double *) malloc (unz1 * sizeof (double)) ;
P = (UF_long *) malloc (n * sizeof (UF_long)) ;
Q = (UF_long *) malloc (n * sizeof (UF_long)) ;
Dx = (double *) NULL ; /* D vector not requested */
Rs = (double *) malloc (n * sizeof (double)) ;
if (!Lp || !Lj || !Lx || !Up || !Ui || !Ux || !P || !Q || !Rs)
{
error ("out of memory") ;
}
status = umfpack_dl_get_numeric (Lp, Lj, Lx, Up, Ui, Ux,
P, Q, Dx, &do_recip, Rs, Numeric) ;
if (status < 0)
{
error ("umfpack_dl_get_numeric failed") ;
}
printf ("\nL (lower triangular factor of C): ") ;
(void) umfpack_dl_report_matrix (n, n, Lp, Lj, Lx, 0, Control) ;
printf ("\nU (upper triangular factor of C): ") ;
(void) umfpack_dl_report_matrix (n, n, Up, Ui, Ux, 1, Control) ;
printf ("\nP: ") ;
(void) umfpack_dl_report_perm (n, P, Control) ;
printf ("\nQ: ") ;
(void) umfpack_dl_report_perm (n, Q, Control) ;
printf ("\nScale factors: row i of A is to be ") ;
if (do_recip)
{
printf ("multiplied by the ith scale factor\n") ;
}
else
{
printf ("divided by the ith scale factor\n") ;
}
for (i = 0 ; i < n ; i++) printf ("%ld: %g\n", i, Rs [i]) ;
/* ---------------------------------------------------------------------- */
/* convert L to triplet form and print it */
/* ---------------------------------------------------------------------- */
/* Note that L is in row-form, so it is the row indices that are created */
/* by umfpack_dl_col_to_triplet. */
printf ("\nConverting L to triplet form, and printing it:\n") ;
Li = (UF_long *) malloc (lnz1 * sizeof (UF_long)) ;
if (!Li)
{
error ("out of memory") ;
}
if (umfpack_dl_col_to_triplet (n, Lp, Li) < 0)
{
error ("umfpack_dl_col_to_triplet failed") ;
}
printf ("\nL, in triplet form: ") ;
(void) umfpack_dl_report_triplet (n, n, lnz, Li, Lj, Lx, Control) ;
/* ---------------------------------------------------------------------- */
/* save the Numeric object to file, free it, and load it back in */
/* ---------------------------------------------------------------------- */
/* use the default filename, "numeric.umf" */
printf ("\nSaving numeric object:\n") ;
status = umfpack_dl_save_numeric (Numeric, (char *) NULL) ;
if (status < 0)
{
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_save_numeric failed") ;
}
printf ("\nFreeing numeric object:\n") ;
umfpack_dl_free_numeric (&Numeric) ;
printf ("\nLoading numeric object:\n") ;
status = umfpack_dl_load_numeric (&Numeric, (char *) NULL) ;
if (status < 0)
{
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_load_numeric failed") ;
}
printf ("\nDone loading numeric object\n") ;
/* ---------------------------------------------------------------------- */
/* solve C'x=b */
/* ---------------------------------------------------------------------- */
status = umfpack_dl_solve (UMFPACK_At, Cp, Ci, Cx, x, b,
Numeric, Control, Info) ;
umfpack_dl_report_info (Control, Info) ;
if (status < 0)
{
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_solve failed") ;
}
printf ("\nx (solution of C'x=b): ") ;
(void) umfpack_dl_report_vector (n, x, Control) ;
rnorm = resid (TRUE, Cp, Ci, Cx) ;
printf ("maxnorm of residual: %g\n\n", rnorm) ;
/* ---------------------------------------------------------------------- */
/* solve C'x=b again, using umfpack_dl_wsolve instead */
/* ---------------------------------------------------------------------- */
printf ("\nSolving C'x=b again, using umfpack_dl_wsolve instead:\n") ;
Wi = (UF_long *) malloc (n * sizeof (UF_long)) ;
W = (double *) malloc (5*n * sizeof (double)) ;
if (!Wi || !W)
{
error ("out of memory") ;
}
status = umfpack_dl_wsolve (UMFPACK_At, Cp, Ci, Cx, x, b,
Numeric, Control, Info, Wi, W) ;
umfpack_dl_report_info (Control, Info) ;
if (status < 0)
{
umfpack_dl_report_status (Control, status) ;
error ("umfpack_dl_wsolve failed") ;
}
printf ("\nx (solution of C'x=b): ") ;
(void) umfpack_dl_report_vector (n, x, Control) ;
rnorm = resid (TRUE, Cp, Ci, Cx) ;
printf ("maxnorm of residual: %g\n\n", rnorm) ;
/* ---------------------------------------------------------------------- */
/* free everything */
/* ---------------------------------------------------------------------- */
/* This is not strictly required since the process is exiting and the */
/* system will reclaim the memory anyway. It's useful, though, just as */
/* a list of what is currently malloc'ed by this program. Plus, it's */
/* always a good habit to explicitly free whatever you malloc. */
free (Ap) ;
free (Ai) ;
free (Ax) ;
free (Cp) ;
free (Ci) ;
free (Cx) ;
free (Pinit) ;
free (Qinit) ;
free (Front_npivcol) ;
free (Front_1strow) ;
free (Front_leftmostdesc) ;
free (Front_parent) ;
free (Chain_start) ;
free (Chain_maxrows) ;
free (Chain_maxcols) ;
free (Lp) ;
free (Lj) ;
free (Lx) ;
free (Up) ;
free (Ui) ;
free (Ux) ;
free (P) ;
free (Q) ;
free (Li) ;
free (Wi) ;
free (W) ;
umfpack_dl_free_symbolic (&Symbolic) ;
umfpack_dl_free_numeric (&Numeric) ;
/* ---------------------------------------------------------------------- */
/* print the total time spent in this demo */
/* ---------------------------------------------------------------------- */
umfpack_toc (t) ;
printf ("\numfpack_dl_demo complete.\nTotal time: %5.2f seconds"
" (CPU time), %5.2f seconds (wallclock time)\n", t [1], t [0]) ;
return (0) ;
}
// solve x for linear system Ax=b
// NOTE: UF_long and size_t must have the same size!
void Algebra::solve(const Matrix & A, const Vec & b, Vec & x){
assert(x.size() == b.size());
assert(sizeof(UF_long) == sizeof(size_t));
clock_t t1,t2;
size_t n = b.size();
//Vec x(n);
double * _x = x.val;
double * _b = b.val;
size_t n_row = n;
size_t n_col = n;
size_t nz = A.size();
// NOTE: DO NOT MODIFY. size must be n_col+1, see UMFPACK manual
UF_long * Ti = new UF_long[nz];
UF_long * Tj = new UF_long[nz];
double * Tx = new double[nz];
A.to_arrays((size_t*)Ti,(size_t*)Tj,Tx);
UF_long * Ap = new UF_long[n_col+1];
UF_long * Ai = new UF_long[nz];
double *Ax = new double [nz];
int status;
double Control [UMFPACK_CONTROL];
umfpack_dl_defaults (Control) ;
status = umfpack_dl_triplet_to_col(n_row, n_col, nz, Ti, Tj, Tx,
Ap, Ai, Ax, (UF_long *) NULL);
if( status < 0 ) {
umfpack_dl_report_status (Control, status) ;
report_exit("umfpack_zi_triplet_to_col failed\n") ;
}
double *null = (double *) NULL;
void *Symbolic, *Numeric;
t1=clock();
status = umfpack_dl_symbolic(n, n, Ap, Ai, Ax,
&Symbolic, Control, null);
t2=clock();
clog<<"Symbolic time = "<<1.0*(t2-t1)/CLOCKS_PER_SEC<<endl;
if( status < 0 ){
umfpack_dl_report_status (Control, status) ;
report_exit("umfpack_dl_symbolic failed\n") ;
}
t1=clock();
status = umfpack_dl_numeric(Ap, Ai, Ax, Symbolic,
&Numeric, Control, null) ;
t2=clock();
clog<<"Numeric time = "<<1.0*(t2-t1)/CLOCKS_PER_SEC<<endl;
if( status < 0 ){
umfpack_dl_report_status (Control, status) ;
report_exit("umfpack_dl_numeric failed\n") ;
}
umfpack_dl_free_symbolic (&Symbolic) ;
t1=clock();
status = umfpack_dl_solve(UMFPACK_A, Ap, Ai, Ax, _x, _b,
Numeric, Control, null) ;
t2=clock();
clog<<"Solve time = "<<1.0*(t2-t1)/CLOCKS_PER_SEC<<endl;
if( status < 0 ){
umfpack_dl_report_status (Control, status) ;
report_exit("umfpack_dl_solve failed\n") ;
}
umfpack_dl_free_numeric (&Numeric) ;
delete [] Ti;
delete [] Tj;
delete [] Tx;
delete [] Ax;
delete [] Ai;
delete [] Ap;
//return x;
}