/*
* Sets up all data structures needed.
* Replace by codegen
*/
pwork* ECOS_setup(idxint n, idxint m, idxint p, idxint l, idxint ncones, idxint* q,
pfloat* Gpr, idxint* Gjc, idxint* Gir,
pfloat* Apr, idxint* Ajc, idxint* Air,
pfloat* c, pfloat* h, pfloat* b)
{
idxint i, j, k, cidx, conesize, lnz, amd_result, nK, *Ljc, *Lir, *P, *Pinv, *Sign;
pwork* mywork;
double Control [AMD_CONTROL], Info [AMD_INFO];
pfloat rx, ry, rz, *Lpr;
spmat *At, *Gt, *KU;
#if PROFILING > 0
timer tsetup;
#endif
#if PROFILING > 1
timer tcreatekkt;
timer tmattranspose;
timer tordering;
#endif
#if PROFILING > 0
tic(&tsetup);
#endif
#if PRINTLEVEL > 2
PRINTTEXT("\n");
PRINTTEXT(" *******************************************************************************\n");
PRINTTEXT(" * ECOS: Embedded Conic Solver - Sparse Interior Point method for SOCPs *\n");
PRINTTEXT(" * *\n");
PRINTTEXT(" * NOTE: The solver is based on L. Vandenberghe's 'The CVXOPT linear and quad- *\n");
PRINTTEXT(" * ratic cone program solvers', March 20, 2010. Available online: *\n");
PRINTTEXT(" * [http://abel.ee.ucla.edu/cvxopt/documentation/coneprog.pdf] *\n");
PRINTTEXT(" * *\n");
PRINTTEXT(" * This code uses T.A. Davis' sparse LDL package and AMD code. *\n");
PRINTTEXT(" * [http://www.cise.ufl.edu/research/sparse] *\n");
PRINTTEXT(" * *\n");
PRINTTEXT(" * Written during a summer visit at Stanford University with S. Boyd. *\n");
PRINTTEXT(" * *\n");
PRINTTEXT(" * (C) Alexander Domahidi, Automatic Control Laboratory, ETH Zurich, 2012-13. *\n");
PRINTTEXT(" * Email: [email protected] *\n");
PRINTTEXT(" *******************************************************************************\n");
PRINTTEXT("\n\n");
PRINTTEXT("PROBLEM SUMMARY:\n");
PRINTTEXT(" Primal variables (n): %d\n", (int)n);
PRINTTEXT("Equality constraints (p): %d\n", (int)p);
PRINTTEXT(" Conic variables (m): %d\n", (int)m);
PRINTTEXT("- - - - - - - - - - - - - - -\n");
PRINTTEXT(" Size of LP cone: %d\n", (int)l);
PRINTTEXT(" Number of SOCs: %d\n", (int)ncones);
for( i=0; i<ncones; i++ ){
PRINTTEXT(" Size of SOC #%02d: %d\n", (int)(i+1), (int)q[i]);
}
#endif
/* get work data structure */
mywork = (pwork *)MALLOC(sizeof(pwork));
#if PRINTLEVEL > 2
PRINTTEXT("Memory allocated for WORK struct\n");
#endif
/* dimensions */
mywork->n = n;
mywork->m = m;
mywork->p = p;
mywork->D = l + ncones;
#if PRINTLEVEL > 2
PRINTTEXT("Set dimensions\n");
#endif
/* variables */
mywork->x = (pfloat *)MALLOC(n*sizeof(pfloat));
mywork->y = (pfloat *)MALLOC(p*sizeof(pfloat));
mywork->z = (pfloat *)MALLOC(m*sizeof(pfloat));
mywork->s = (pfloat *)MALLOC(m*sizeof(pfloat));
mywork->lambda = (pfloat *)MALLOC(m*sizeof(pfloat));
mywork->dsaff_by_W = (pfloat *)MALLOC(m*sizeof(pfloat));
mywork->dsaff = (pfloat *)MALLOC(m*sizeof(pfloat));
mywork->dzaff = (pfloat *)MALLOC(m*sizeof(pfloat));
mywork->saff = (pfloat *)MALLOC(m*sizeof(pfloat));
mywork->zaff = (pfloat *)MALLOC(m*sizeof(pfloat));
mywork->W_times_dzaff = (pfloat *)MALLOC(m*sizeof(pfloat));
#if PRINTLEVEL > 2
PRINTTEXT("Memory allocated for variables\n");
#endif
/* best iterates so far */
mywork->best_x = (pfloat *)MALLOC(n*sizeof(pfloat));
mywork->best_y = (pfloat *)MALLOC(p*sizeof(pfloat));
mywork->best_z = (pfloat *)MALLOC(m*sizeof(pfloat));
mywork->best_s = (pfloat *)MALLOC(m*sizeof(pfloat));
mywork->best_info = (stats *)MALLOC(sizeof(stats));
/* cones */
mywork->C = (cone *)MALLOC(sizeof(cone));
#if PRINTLEVEL > 2
PRINTTEXT("Memory allocated for cone struct\n");
#endif
/* LP cone */
mywork->C->lpc = (lpcone *)MALLOC(sizeof(lpcone));
mywork->C->lpc->p = l;
if( l > 0 ){
mywork->C->lpc->w = (pfloat *)MALLOC(l*sizeof(pfloat));
mywork->C->lpc->v = (pfloat *)MALLOC(l*sizeof(pfloat));
mywork->C->lpc->kkt_idx = (idxint *)MALLOC(l*sizeof(idxint));
#if PRINTLEVEL > 2
PRINTTEXT("Memory allocated for LP cone\n");
#endif
} else {
mywork->C->lpc->w = NULL;
mywork->C->lpc->v = NULL;
mywork->C->lpc->kkt_idx = NULL;
#if PRINTLEVEL > 2
PRINTTEXT("No LP cone present, pointers filled with NULL\n");
#endif
}
/* Second-order cones */
mywork->C->soc = (socone *)MALLOC(ncones*sizeof(socone));
mywork->C->nsoc = ncones;
cidx = 0;
for( i=0; i<ncones; i++ ){
conesize = (idxint)q[i];
mywork->C->soc[i].p = conesize;
mywork->C->soc[i].a = 0;
mywork->C->soc[i].eta = 0;
mywork->C->soc[i].q = (pfloat *)MALLOC((conesize-1)*sizeof(pfloat));
mywork->C->soc[i].skbar = (pfloat *)MALLOC((conesize)*sizeof(pfloat));
mywork->C->soc[i].zkbar = (pfloat *)MALLOC((conesize)*sizeof(pfloat));
#if CONEMODE == 0
mywork->C->soc[i].Didx = (idxint *)MALLOC((conesize)*sizeof(idxint));
#endif
#if CONEMODE > 0
mywork->C->soc[i].colstart = (idxint *)MALLOC((conesize)*sizeof(idxint));
#endif
cidx += conesize;
}
#if PRINTLEVEL > 2
PRINTTEXT("Memory allocated for second-order cones\n");
#endif
/* info struct */
mywork->info = (stats *)MALLOC(sizeof(stats));
#if PROFILING > 1
mywork->info->tfactor = 0;
mywork->info->tkktsolve = 0;
mywork->info->tfactor_t1 = 0;
mywork->info->tfactor_t2 = 0;
#endif
#if PRINTLEVEL > 2
PRINTTEXT("Memory allocated for info struct\n");
#endif
#if defined EQUILIBRATE && EQUILIBRATE > 0
/* equilibration vector */
mywork->xequil = (pfloat *)MALLOC(n*sizeof(pfloat));
mywork->Aequil = (pfloat *)MALLOC(p*sizeof(pfloat));
mywork->Gequil = (pfloat *)MALLOC(m*sizeof(pfloat));
#if PRINTLEVEL > 2
PRINTTEXT("Memory allocated for equilibration vectors\n");
#endif
#endif
/* settings */
mywork->stgs = (settings *)MALLOC(sizeof(settings));
mywork->stgs->maxit = MAXIT;
mywork->stgs->gamma = GAMMA;
mywork->stgs->delta = DELTA;
mywork->stgs->eps = EPS;
mywork->stgs->nitref = NITREF;
mywork->stgs->abstol = ABSTOL;
mywork->stgs->feastol = FEASTOL;
mywork->stgs->reltol = RELTOL;
mywork->stgs->abstol_inacc = ATOL_INACC;
mywork->stgs->feastol_inacc = FTOL_INACC;
mywork->stgs->reltol_inacc = RTOL_INACC;
mywork->stgs->verbose = VERBOSE;
#if PRINTLEVEL > 2
PRINTTEXT("Written settings\n");
#endif
mywork->c = c;
mywork->h = h;
mywork->b = b;
#if PRINTLEVEL > 2
PRINTTEXT("Hung pointers for c, h and b into WORK struct\n");
#endif
/* Store problem data */
if(Apr && Ajc && Air) {
mywork->A = createSparseMatrix(p, n, Ajc[n], Ajc, Air, Apr);
} else {
mywork->A = NULL;
}
if (Gpr && Gjc && Gir) {
mywork->G = createSparseMatrix(m, n, Gjc[n], Gjc, Gir, Gpr);
} else {
/* create an empty sparse matrix */
mywork->G = createSparseMatrix(m, n, 0, Gjc, Gir, Gpr);
}
#if defined EQUILIBRATE && EQUILIBRATE > 0
set_equilibration(mywork);
#if PRINTLEVEL > 2
PRINTTEXT("Done equilibrating\n");
#endif
#endif
#if PROFILING > 1
mywork->info->ttranspose = 0;
tic(&tmattranspose);
#endif
if(mywork->A)
At = transposeSparseMatrix(mywork->A);
else
At = NULL;
#if PROFILING > 1
mywork->info->ttranspose += toc(&tmattranspose);
#endif
#if PRINTLEVEL > 2
PRINTTEXT("Transposed A\n");
#endif
#if PROFILING > 1
tic(&tmattranspose);
#endif
Gt = transposeSparseMatrix(mywork->G);
#if PROFILING > 1
mywork->info->ttranspose += toc(&tmattranspose);
#endif
#if PRINTLEVEL > 2
PRINTTEXT("Transposed G\n");
#endif
/* set up KKT system */
#if PROFILING > 1
tic(&tcreatekkt);
#endif
createKKT_U(Gt, At, mywork->C, &Sign, &KU);
#if PROFILING > 1
mywork->info->tkktcreate = toc(&tcreatekkt);
#endif
#if PRINTLEVEL > 2
PRINTTEXT("Created upper part of KKT matrix K\n");
#endif
/*
* Set up KKT system related data
* (L comes later after symbolic factorization)
*/
nK = KU->n;
#if DEBUG > 0
dumpSparseMatrix(KU, "KU0.txt");
#endif
#if PRINTLEVEL > 2
PRINTTEXT("Dimension of KKT matrix: %d\n", (int)nK);
PRINTTEXT("Non-zeros in KKT matrix: %d\n", (int)KU->nnz);
#endif
/* allocate memory in KKT system */
mywork->KKT = (kkt *)MALLOC(sizeof(kkt));
mywork->KKT->D = (pfloat *)MALLOC(nK*sizeof(pfloat));
mywork->KKT->Parent = (idxint *)MALLOC(nK*sizeof(idxint));
mywork->KKT->Pinv = (idxint *)MALLOC(nK*sizeof(idxint));
mywork->KKT->work1 = (pfloat *)MALLOC(nK*sizeof(pfloat));
mywork->KKT->work2 = (pfloat *)MALLOC(nK*sizeof(pfloat));
mywork->KKT->work3 = (pfloat *)MALLOC(nK*sizeof(pfloat));
mywork->KKT->work4 = (pfloat *)MALLOC(nK*sizeof(pfloat));
mywork->KKT->work5 = (pfloat *)MALLOC(nK*sizeof(pfloat));
mywork->KKT->work6 = (pfloat *)MALLOC(nK*sizeof(pfloat));
mywork->KKT->Flag = (idxint *)MALLOC(nK*sizeof(idxint));
mywork->KKT->Pattern = (idxint *)MALLOC(nK*sizeof(idxint));
mywork->KKT->Lnz = (idxint *)MALLOC(nK*sizeof(idxint));
mywork->KKT->RHS1 = (pfloat *)MALLOC(nK*sizeof(pfloat));
mywork->KKT->RHS2 = (pfloat *)MALLOC(nK*sizeof(pfloat));
mywork->KKT->dx1 = (pfloat *)MALLOC(mywork->n*sizeof(pfloat));
mywork->KKT->dx2 = (pfloat *)MALLOC(mywork->n*sizeof(pfloat));
mywork->KKT->dy1 = (pfloat *)MALLOC(mywork->p*sizeof(pfloat));
mywork->KKT->dy2 = (pfloat *)MALLOC(mywork->p*sizeof(pfloat));
mywork->KKT->dz1 = (pfloat *)MALLOC(mywork->m*sizeof(pfloat));
mywork->KKT->dz2 = (pfloat *)MALLOC(mywork->m*sizeof(pfloat));
mywork->KKT->Sign = (idxint *)MALLOC(nK*sizeof(idxint));
mywork->KKT->PKPt = newSparseMatrix(nK, nK, KU->nnz);
mywork->KKT->PK = (idxint *)MALLOC(KU->nnz*sizeof(idxint));
#if PRINTLEVEL > 2
PRINTTEXT("Created memory for KKT-related data\n");
#endif
/* calculate ordering of KKT matrix using AMD */
P = (idxint *)MALLOC(nK*sizeof(idxint));
#if PROFILING > 1
tic(&tordering);
#endif
AMD_defaults(Control);
amd_result = AMD_order(nK, KU->jc, KU->ir, P, Control, Info);
#if PROFILING > 1
mywork->info->torder = toc(&tordering);
#endif
if( amd_result == AMD_OK ){
#if PRINTLEVEL > 2
PRINTTEXT("AMD ordering successfully computed.\n");
AMD_info(Info);
#endif
} else {
#if PRINTLEVEL > 2
PRINTTEXT("Problem in AMD ordering, exiting.\n");
AMD_info(Info);
#endif
return NULL;
}
/* calculate inverse permutation and permutation mapping of KKT matrix */
pinv(nK, P, mywork->KKT->Pinv);
Pinv = mywork->KKT->Pinv;
#if DEBUG > 0
dumpDenseMatrix_i(P, nK, 1, "P.txt");
dumpDenseMatrix_i(mywork->KKT->Pinv, nK, 1, "PINV.txt");
#endif
permuteSparseSymmetricMatrix(KU, mywork->KKT->Pinv, mywork->KKT->PKPt, mywork->KKT->PK);
/* permute sign vector */
for( i=0; i<nK; i++ ){ mywork->KKT->Sign[Pinv[i]] = Sign[i]; }
#if PRINTLEVEL > 3
PRINTTEXT("P = [");
for( i=0; i<nK; i++ ){ PRINTTEXT("%d ", (int)P[i]); }
PRINTTEXT("];\n");
PRINTTEXT("Pinv = [");
for( i=0; i<nK; i++ ){ PRINTTEXT("%d ", (int)Pinv[i]); }
PRINTTEXT("];\n");
PRINTTEXT("Sign = [");
for( i=0; i<nK; i++ ){ PRINTTEXT("%+d ", (int)Sign[i]); }
PRINTTEXT("];\n");
PRINTTEXT("SignP = [");
for( i=0; i<nK; i++ ){ PRINTTEXT("%+d ", (int)mywork->KKT->Sign[i]); }
PRINTTEXT("];\n");
#endif
/* symbolic factorization */
Ljc = (idxint *)MALLOC((nK+1)*sizeof(idxint));
#if PRINTLEVEL > 2
PRINTTEXT("Allocated memory for cholesky factor L\n");
#endif
LDL_symbolic2(
mywork->KKT->PKPt->n, /* A and L are n-by-n, where n >= 0 */
mywork->KKT->PKPt->jc, /* input of size n+1, not modified */
mywork->KKT->PKPt->ir, /* input of size nz=Ap[n], not modified */
Ljc, /* output of size n+1, not defined on input */
mywork->KKT->Parent, /* output of size n, not defined on input */
mywork->KKT->Lnz, /* output of size n, not defined on input */
mywork->KKT->Flag /* workspace of size n, not defn. on input or output */
);
/* assign memory for L */
lnz = Ljc[nK];
#if PRINTLEVEL > 2
PRINTTEXT("Nonzeros in L, excluding diagonal: %d\n", (int)lnz) ;
#endif
Lir = (idxint *)MALLOC(lnz*sizeof(idxint));
Lpr = (pfloat *)MALLOC(lnz*sizeof(pfloat));
mywork->KKT->L = createSparseMatrix(nK, nK, lnz, Ljc, Lir, Lpr);
#if PRINTLEVEL > 2
PRINTTEXT("Created Cholesky factor of K in KKT struct\n");
#endif
/* permute KKT matrix - we work on this one from now on */
permuteSparseSymmetricMatrix(KU, mywork->KKT->Pinv, mywork->KKT->PKPt, NULL);
#if DEBUG > 0
dumpSparseMatrix(mywork->KKT->PKPt, "PKPt.txt");
#endif
#if CONEMODE > 0
/* zero any off-diagonal elements in (permuted) scalings in KKT matrix */
for (i=0; i<mywork->C->nsoc; i++) {
for (j=1; j<mywork->C->soc[i].p; j++) {
for (k=0; k<j; k++) {
mywork->KKT->PKPt->pr[mywork->KKT->PK[mywork->C->soc[i].colstart[j]+k]] = 0;
}
}
}
#endif
#if DEBUG > 0
dumpSparseMatrix(mywork->KKT->PKPt, "PKPt0.txt");
#endif
/* set up RHSp for initialization */
k = 0; j = 0;
for( i=0; i<n; i++ ){ mywork->KKT->RHS1[Pinv[k++]] = 0; }
for( i=0; i<p; i++ ){ mywork->KKT->RHS1[Pinv[k++]] = b[i]; }
for( i=0; i<l; i++ ){ mywork->KKT->RHS1[Pinv[k++]] = h[i]; j++; }
for( l=0; l<ncones; l++ ){
for( i=0; i < mywork->C->soc[l].p; i++ ){ mywork->KKT->RHS1[Pinv[k++]] = h[j++]; }
#if CONEMODE == 0
mywork->KKT->RHS1[Pinv[k++]] = 0;
mywork->KKT->RHS1[Pinv[k++]] = 0;
#endif
}
#if PRINTLEVEL > 2
PRINTTEXT("Written %d entries of RHS1\n", (int)k);
#endif
/* set up RHSd for initialization */
for( i=0; i<n; i++ ){ mywork->KKT->RHS2[Pinv[i]] = -c[i]; }
for( i=n; i<nK; i++ ){ mywork->KKT->RHS2[Pinv[i]] = 0; }
/* get scalings of problem data */
rx = norm2(c, n); mywork->resx0 = MAX(1, rx);
ry = norm2(b, p); mywork->resy0 = MAX(1, ry);
rz = norm2(h, m); mywork->resz0 = MAX(1, rz);
/* get memory for residuals */
mywork->rx = (pfloat *)MALLOC(n*sizeof(pfloat));
mywork->ry = (pfloat *)MALLOC(p*sizeof(pfloat));
mywork->rz = (pfloat *)MALLOC(m*sizeof(pfloat));
/* clean up */
mywork->KKT->P = P;
FREE(Sign);
if(At) freeSparseMatrix(At);
freeSparseMatrix(Gt);
freeSparseMatrix(KU);
#if PROFILING > 0
mywork->info->tsetup = toc(&tsetup);
#endif
return mywork;
}
void amdtest (cholmod_sparse *A)
{
double Control [AMD_CONTROL], Info [AMD_INFO], alpha ;
Int *P, *Cp, *Ci, *Sp, *Si, *Bp, *Bi, *Ep, *Ei, *Fp, *Fi,
*Len, *Nv, *Next, *Head, *Elen, *Deg, *Wi, *W, *Flag ;
cholmod_sparse *C, *B, *S, *E, *F ;
Int i, j, n, nrow, ncol, ok, cnz, bnz, p, trial, sorted ;
/* ---------------------------------------------------------------------- */
/* get inputs */
/* ---------------------------------------------------------------------- */
printf ("\nAMD test\n") ;
if (A == NULL)
{
return ;
}
if (A->stype)
{
B = CHOLMOD(copy) (A, 0, 0, cm) ;
}
else
{
B = CHOLMOD(aat) (A, NULL, 0, 0, cm) ;
}
if (A->nrow != A->ncol)
{
F = CHOLMOD(copy_sparse) (B, cm) ;
OK (F->nrow == F->ncol) ;
CHOLMOD(sort) (F, cm) ;
}
else
{
/* A is square and unsymmetric, and may have entries in A+A' that
* are not in A */
F = CHOLMOD(copy_sparse) (A, cm) ;
CHOLMOD(sort) (F, cm) ;
}
C = CHOLMOD(copy_sparse) (B, cm) ;
nrow = C->nrow ;
ncol = C->ncol ;
n = nrow ;
OK (nrow == ncol) ;
Cp = C->p ;
Ci = C->i ;
Bp = B->p ;
Bi = B->i ;
/* ---------------------------------------------------------------------- */
/* S = sorted form of B, using AMD_preprocess */
/* ---------------------------------------------------------------------- */
cnz = CHOLMOD(nnz) (C, cm) ;
S = CHOLMOD(allocate_sparse) (n, n, cnz, TRUE, TRUE, 0, CHOLMOD_PATTERN,
cm);
Sp = S->p ;
Si = S->i ;
W = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
Flag = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
AMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ;
/* ---------------------------------------------------------------------- */
/* allocate workspace for amd */
/* ---------------------------------------------------------------------- */
P = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ;
Len = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
Nv = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
Next = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
Head = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ;
Elen = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
Deg = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
Wi = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
/* ---------------------------------------------------------------------- */
for (sorted = 0 ; sorted <= 1 ; sorted++)
{
if (sorted) CHOLMOD(sort) (C, cm) ;
Cp = C->p ;
Ci = C->i ;
/* ------------------------------------------------------------------ */
/* order C with AMD_order */
/* ------------------------------------------------------------------ */
AMD_defaults (Control) ;
AMD_defaults (NULL) ;
AMD_control (Control) ;
AMD_control (NULL) ;
AMD_info (NULL) ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
printf ("amd return value: "ID"\n", ok) ;
AMD_info (Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation", cm)) ;
/* no dense rows/cols */
alpha = Control [AMD_DENSE] ;
Control [AMD_DENSE] = -1 ;
AMD_control (Control) ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
printf ("amd return value: "ID"\n", ok) ;
AMD_info (Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation (alpha=-1)", cm)) ;
/* many dense rows/cols */
Control [AMD_DENSE] = 0 ;
AMD_control (Control) ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
printf ("amd return value: "ID"\n", ok) ;
AMD_info (Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation (alpha=0)", cm)) ;
Control [AMD_DENSE] = alpha ;
/* no aggressive absorption */
Control [AMD_AGGRESSIVE] = FALSE ;
AMD_control (Control) ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
printf ("amd return value: "ID"\n", ok) ;
AMD_info (Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation (no agg) ", cm)) ;
Control [AMD_AGGRESSIVE] = TRUE ;
/* ------------------------------------------------------------------ */
/* order F with AMD_order */
/* ------------------------------------------------------------------ */
Fp = F->p ;
Fi = F->i ;
ok = AMD_order (n, Fp, Fi, P, Control, Info) ;
printf ("amd return value: "ID"\n", ok) ;
AMD_info (Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
OK (CHOLMOD(print_perm) (P, n, n, "F: AMD permutation", cm)) ;
/* ------------------------------------------------------------------ */
/* order S with AMD_order */
/* ------------------------------------------------------------------ */
ok = AMD_order (n, Sp, Si, P, Control, Info) ;
printf ("amd return value: "ID"\n", ok) ;
AMD_info (Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation", cm)) ;
/* ------------------------------------------------------------------ */
/* order E with AMD_2, which destroys its contents */
/* ------------------------------------------------------------------ */
E = CHOLMOD(copy) (B, 0, -1, cm) ; /* remove diagonal entries */
bnz = CHOLMOD(nnz) (E, cm) ;
/* add the bare minimum extra space to E */
ok = CHOLMOD(reallocate_sparse) (bnz + n, E, cm) ;
OK (ok) ;
Ep = E->p ;
Ei = E->i ;
for (j = 0 ; j < n ; j++)
{
Len [j] = Ep [j+1] - Ep [j] ;
}
printf ("calling AMD_2:\n") ;
if (n > 0)
{
AMD_2 (n, Ep, Ei, Len, E->nzmax, Ep [n], Nv, Next, P, Head, Elen,
Deg, Wi, Control, Info) ;
AMD_info (Info) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD2 permutation", cm)) ;
}
/* ------------------------------------------------------------------ */
/* error tests */
/* ------------------------------------------------------------------ */
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
ok = AMD_order (-1, Cp, Ci, P, Control, Info) ;
OK (ok == AMD_INVALID);
ok = AMD_order (0, Cp, Ci, P, Control, Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
ok = AMD_order (n, NULL, Ci, P, Control, Info) ;
OK (ok == AMD_INVALID);
ok = AMD_order (n, Cp, NULL, P, Control, Info) ;
OK (ok == AMD_INVALID);
ok = AMD_order (n, Cp, Ci, NULL, Control, Info) ;
OK (ok == AMD_INVALID);
if (n > 0)
{
printf ("AMD error tests:\n") ;
p = Cp [n] ;
Cp [n] = -1 ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
OK (ok == AMD_INVALID) ;
if (Size_max/2 == Int_max)
{
Cp [n] = Int_max ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
printf ("AMD status is "ID"\n", ok) ;
OK (ok == AMD_OUT_OF_MEMORY) ;
}
Cp [n] = p ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
if (Cp [n] > 0)
{
printf ("Mangle column zero:\n") ;
i = Ci [0] ;
Ci [0] = -1 ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
AMD_info (Info) ;
OK (ok == AMD_INVALID) ;
Ci [0] = i ;
}
}
ok = AMD_valid (n, n, Sp, Si) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
ok = AMD_valid (-1, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
ok = AMD_valid (n, -1, Sp, Si) ; OK (ok == AMD_INVALID) ;
ok = AMD_valid (n, n, NULL, Si) ; OK (ok == AMD_INVALID) ;
ok = AMD_valid (n, n, Sp, NULL) ; OK (ok == AMD_INVALID) ;
if (n > 0 && Sp [n] > 0)
{
p = Sp [n] ;
Sp [n] = -1 ;
ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
Sp [n] = p ;
p = Sp [0] ;
Sp [0] = -1 ;
ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
Sp [0] = p ;
p = Sp [1] ;
Sp [1] = -1 ;
ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
Sp [1] = p ;
i = Si [0] ;
Si [0] = -1 ;
ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
Si [0] = i ;
}
ok = AMD_valid (n, n, Sp, Si) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
AMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ;
ok = AMD_valid (n, n, Sp, Si) ;
OK (ok == AMD_OK) ;
if (n > 0 && Bp [n] > 0)
{
p = Bp [n] ;
Bp [n] = -1 ;
ok = AMD_valid (n, n, Bp, Bi) ; OK (ok == AMD_INVALID) ;
Bp [n] = p ;
p = Bp [1] ;
Bp [1] = -1 ;
ok = AMD_valid (n, n, Bp, Bi) ; OK (ok == AMD_INVALID) ;
Bp [1] = p ;
i = Bi [0] ;
Bi [0] = -1 ;
ok = AMD_valid (n, n, Bp, Bi) ; OK (ok == AMD_INVALID) ;
Bi [0] = i ;
}
AMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ;
Info [AMD_STATUS] = 777 ;
AMD_info (Info) ;
/* ------------------------------------------------------------------ */
/* memory tests */
/* ------------------------------------------------------------------ */
if (n > 0)
{
amd_malloc = cm->malloc_memory ;
amd_free = cm->free_memory ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
test_memory_handler ( ) ;
amd_malloc = cm->malloc_memory ;
amd_free = cm->free_memory ;
for (trial = 0 ; trial < 6 ; trial++)
{
my_tries = trial ;
printf ("AMD memory trial "ID"\n", trial) ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
AMD_info (Info) ;
OK (ok == AMD_OUT_OF_MEMORY
|| (sorted ? (ok == AMD_OK) : (ok >= AMD_OK))) ;
}
normal_memory_handler ( ) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD2 permutation", cm)) ;
amd_malloc = cm->malloc_memory ;
amd_free = cm->free_memory ;
}
CHOLMOD(free_sparse) (&E, cm) ;
}
/* ---------------------------------------------------------------------- */
/* free everything */
/* ---------------------------------------------------------------------- */
CHOLMOD(free) (n, sizeof (Int), Len, cm) ;
CHOLMOD(free) (n, sizeof (Int), Nv, cm) ;
CHOLMOD(free) (n, sizeof (Int), Next, cm) ;
CHOLMOD(free) (n+1, sizeof (Int), Head, cm) ;
CHOLMOD(free) (n, sizeof (Int), Elen, cm) ;
CHOLMOD(free) (n, sizeof (Int), Deg, cm) ;
CHOLMOD(free) (n, sizeof (Int), Wi, cm) ;
CHOLMOD(free) (n+1, sizeof (Int), P, cm) ;
CHOLMOD(free) (n, sizeof (Int), W, cm) ;
CHOLMOD(free) (n, sizeof (Int), Flag, cm) ;
CHOLMOD(free_sparse) (&S, cm) ;
CHOLMOD(free_sparse) (&B, cm) ;
CHOLMOD(free_sparse) (&C, cm) ;
CHOLMOD(free_sparse) (&F, cm) ;
}
static Int analyze_worker /* returns KLU_OK or < 0 if error */
(
/* inputs, not modified */
Int n, /* A is n-by-n */
Int Ap [ ], /* size n+1, column pointers */
Int Ai [ ], /* size nz, row indices */
Int nblocks, /* # of blocks */
Int Pbtf [ ], /* BTF row permutation */
Int Qbtf [ ], /* BTF col permutation */
Int R [ ], /* size n+1, but only Rbtf [0..nblocks] is used */
Int ordering, /* what ordering to use (0, 1, or 3 for this routine) */
/* output only, not defined on input */
Int P [ ], /* size n */
Int Q [ ], /* size n */
double Lnz [ ], /* size n, but only Lnz [0..nblocks-1] is used */
/* workspace, not defined on input or output */
Int Pblk [ ], /* size maxblock */
Int Cp [ ], /* size maxblock+1 */
Int Ci [ ], /* size MAX (nz+1, Cilen) */
Int Cilen, /* nz+1, or COLAMD_recommend(nz,n,n) for COLAMD */
Int Pinv [ ], /* size maxblock */
/* input/output */
KLU_symbolic *Symbolic,
KLU_common *Common
)
{
double amd_Info [AMD_INFO], lnz, lnz1, flops, flops1 ;
Int k1, k2, nk, k, block, oldcol, pend, newcol, result, pc, p, newrow,
maxnz, nzoff, cstats [COLAMD_STATS], ok, err = KLU_INVALID ;
/* ---------------------------------------------------------------------- */
/* initializations */
/* ---------------------------------------------------------------------- */
/* compute the inverse of Pbtf */
#ifndef NDEBUG
for (k = 0 ; k < n ; k++)
{
P [k] = EMPTY ;
Q [k] = EMPTY ;
Pinv [k] = EMPTY ;
}
#endif
for (k = 0 ; k < n ; k++)
{
ASSERT (Pbtf [k] >= 0 && Pbtf [k] < n) ;
Pinv [Pbtf [k]] = k ;
}
#ifndef NDEBUG
for (k = 0 ; k < n ; k++) ASSERT (Pinv [k] != EMPTY) ;
#endif
nzoff = 0 ;
lnz = 0 ;
maxnz = 0 ;
flops = 0 ;
Symbolic->symmetry = EMPTY ; /* only computed by AMD */
/* ---------------------------------------------------------------------- */
/* order each block */
/* ---------------------------------------------------------------------- */
for (block = 0 ; block < nblocks ; block++)
{
/* ------------------------------------------------------------------ */
/* the block is from rows/columns k1 to k2-1 */
/* ------------------------------------------------------------------ */
k1 = R [block] ;
k2 = R [block+1] ;
nk = k2 - k1 ;
PRINTF (("BLOCK %d, k1 %d k2-1 %d nk %d\n", block, k1, k2-1, nk)) ;
/* ------------------------------------------------------------------ */
/* construct the kth block, C */
/* ------------------------------------------------------------------ */
Lnz [block] = EMPTY ;
pc = 0 ;
for (k = k1 ; k < k2 ; k++)
{
newcol = k-k1 ;
Cp [newcol] = pc ;
oldcol = Qbtf [k] ;
pend = Ap [oldcol+1] ;
for (p = Ap [oldcol] ; p < pend ; p++)
{
newrow = Pinv [Ai [p]] ;
if (newrow < k1)
{
nzoff++ ;
}
else
{
/* (newrow,newcol) is an entry in the block */
ASSERT (newrow < k2) ;
newrow -= k1 ;
Ci [pc++] = newrow ;
}
}
}
Cp [nk] = pc ;
maxnz = MAX (maxnz, pc) ;
ASSERT (KLU_valid (nk, Cp, Ci, NULL)) ;
/* ------------------------------------------------------------------ */
/* order the block C */
/* ------------------------------------------------------------------ */
if (nk <= 3)
{
/* -------------------------------------------------------------- */
/* use natural ordering for tiny blocks (3-by-3 or less) */
/* -------------------------------------------------------------- */
for (k = 0 ; k < nk ; k++)
{
Pblk [k] = k ;
}
lnz1 = nk * (nk + 1) / 2 ;
flops1 = nk * (nk - 1) / 2 + (nk-1)*nk*(2*nk-1) / 6 ;
ok = TRUE ;
}
else if (ordering == 0)
{
/* -------------------------------------------------------------- */
/* order the block with AMD (C+C') */
/* -------------------------------------------------------------- */
result = AMD_order (nk, Cp, Ci, Pblk, NULL, amd_Info) ;
ok = (result >= AMD_OK) ;
if (result == AMD_OUT_OF_MEMORY)
{
err = KLU_OUT_OF_MEMORY ;
}
/* account for memory usage in AMD */
Common->mempeak = MAX (Common->mempeak,
Common->memusage + amd_Info [AMD_MEMORY]) ;
/* get the ordering statistics from AMD */
lnz1 = (Int) (amd_Info [AMD_LNZ]) + nk ;
flops1 = 2 * amd_Info [AMD_NMULTSUBS_LU] + amd_Info [AMD_NDIV] ;
if (pc == maxnz)
{
/* get the symmetry of the biggest block */
Symbolic->symmetry = amd_Info [AMD_SYMMETRY] ;
}
}
else if (ordering == 1)
{
/* -------------------------------------------------------------- */
/* order the block with COLAMD (C) */
/* -------------------------------------------------------------- */
/* order (and destroy) Ci, returning column permutation in Cp.
* COLAMD "cannot" fail since the matrix has already been checked,
* and Ci allocated. */
ok = COLAMD (nk, nk, Cilen, Ci, Cp, NULL, cstats) ;
lnz1 = EMPTY ;
flops1 = EMPTY ;
/* copy the permutation from Cp to Pblk */
for (k = 0 ; k < nk ; k++)
{
Pblk [k] = Cp [k] ;
}
}
else
{
/* -------------------------------------------------------------- */
/* pass the block to the user-provided ordering function */
/* -------------------------------------------------------------- */
lnz1 = (Common->user_order) (nk, Cp, Ci, Pblk, Common) ;
flops1 = EMPTY ;
ok = (lnz1 != 0) ;
}
if (!ok)
{
return (err) ; /* ordering method failed */
}
/* ------------------------------------------------------------------ */
/* keep track of nnz(L) and flops statistics */
/* ------------------------------------------------------------------ */
Lnz [block] = lnz1 ;
lnz = (lnz == EMPTY || lnz1 == EMPTY) ? EMPTY : (lnz + lnz1) ;
flops = (flops == EMPTY || flops1 == EMPTY) ? EMPTY : (flops + flops1) ;
/* ------------------------------------------------------------------ */
/* combine the preordering with the BTF ordering */
/* ------------------------------------------------------------------ */
PRINTF (("Pblk, 1-based:\n")) ;
for (k = 0 ; k < nk ; k++)
{
ASSERT (k + k1 < n) ;
ASSERT (Pblk [k] + k1 < n) ;
Q [k + k1] = Qbtf [Pblk [k] + k1] ;
}
for (k = 0 ; k < nk ; k++)
{
ASSERT (k + k1 < n) ;
ASSERT (Pblk [k] + k1 < n) ;
P [k + k1] = Pbtf [Pblk [k] + k1] ;
}
}
PRINTF (("nzoff %d Ap[n] %d\n", nzoff, Ap [n])) ;
ASSERT (nzoff >= 0 && nzoff <= Ap [n]) ;
/* return estimates of # of nonzeros in L including diagonal */
Symbolic->lnz = lnz ; /* EMPTY if COLAMD used */
Symbolic->unz = lnz ;
Symbolic->nzoff = nzoff ;
Symbolic->est_flops = flops ; /* EMPTY if COLAMD or user-ordering used */
return (KLU_OK) ;
}
