RKWidget::~RKWidget()
{
if ( N_ != 0 ) {
SUPERLU_FREE (rhsb);
SUPERLU_FREE (rhsx);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
/// ???
if(aexist) {
/// ??? Destroy_CompCol_Matrix(&A);
delete[] a;
delete[] xa;
delete[] asub;
}
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
if ( lwork == 0 && !dirty) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&Up);
} else if ( lwork > 0 ) {
SUPERLU_FREE(work);
}
}
}
PetscErrorCode MatDestroy_SuperLU(Mat A)
{
PetscErrorCode ierr;
Mat_SuperLU *lu=(Mat_SuperLU*)A->spptr;
PetscFunctionBegin;
if (lu && lu->CleanUpSuperLU) { /* Free the SuperLU datastructures */
Destroy_SuperMatrix_Store(&lu->A);
Destroy_SuperMatrix_Store(&lu->B);
Destroy_SuperMatrix_Store(&lu->X);
StatFree(&lu->stat);
if (lu->lwork >= 0) {
Destroy_SuperNode_Matrix(&lu->L);
Destroy_CompCol_Matrix(&lu->U);
}
}
if (lu) {
ierr = PetscFree(lu->etree);CHKERRQ(ierr);
ierr = PetscFree(lu->perm_r);CHKERRQ(ierr);
ierr = PetscFree(lu->perm_c);CHKERRQ(ierr);
ierr = PetscFree(lu->R);CHKERRQ(ierr);
ierr = PetscFree(lu->C);CHKERRQ(ierr);
ierr = PetscFree(lu->rhs_dup);CHKERRQ(ierr);
ierr = MatDestroy(&lu->A_dup);CHKERRQ(ierr);
}
ierr = PetscFree(A->spptr);CHKERRQ(ierr);
/* clear composed functions */
ierr = PetscObjectComposeFunctionDynamic((PetscObject)A,"MatFactorGetSolverPackage_C","",PETSC_NULL);CHKERRQ(ierr);
ierr = PetscObjectComposeFunctionDynamic((PetscObject)A,"MatSuperluSetILUDropTol_C","",PETSC_NULL);CHKERRQ(ierr);
ierr = MatDestroy_SeqAIJ(A);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
void tlin::solve(SuperMatrix *A, SuperMatrix *BX, superlu_options_t *opt)
{
assert(A->nrow == A->ncol);
int n = A->nrow;
if (!opt)
opt = &defaultOpt;
SuperMatrix L, U;
int *perm_c, *perm_r;
perm_c = intMalloc(n);
perm_r = intMalloc(n);
SuperLUStat_t stat;
StatInit(&stat);
int result;
dgssv(opt, A, perm_c, perm_r, &L, &U, BX, &stat, &result);
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
SUPERLU_FREE(perm_r);
SUPERLU_FREE(perm_c);
StatFree(&stat);
}
void XDestroy_SuperNode_Matrix(SuperMatrix *A)
{
if (A->Store) {
Destroy_SuperNode_Matrix(A);
}
A->Store = NULL;
}
void RKWidget::setSize ( const size_t value )
{
int add = value%nblock;
size_t newval = value + add;
if ( newval == N_ ) return;
dirty = true;
if ( N_ != 0 ) {
if(nStage != 0) delete[] b_k;
SUPERLU_FREE (rhsb);
SUPERLU_FREE (rhsx);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
if(aexist) {
// ??? Destroy_CompCol_Matrix(&A);
//delete[] a;
//delete[] xa;
//delete[] asub;
}
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
if ( lwork == 0 && !dirty) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&Up);
} else if ( lwork > 0 ) {
SUPERLU_FREE(work);
}
aexist= false;
dirty = true;
}
if(nStage != 0) b_k = new double[value*nStage];
if ( !(rhsb = doubleMalloc(value)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsx = doubleMalloc(value)) ) ABORT("Malloc fails for rhsx[].");
dCreate_Dense_Matrix(&B, value, 1, rhsb, value, SLU_DN, SLU_D, SLU_GE);
dCreate_Dense_Matrix(&X, value, 1, rhsx, value, SLU_DN, SLU_D, SLU_GE);
if ( !(etree = intMalloc(value)) ) ABORT("Malloc fails for etree[].");
if ( !(perm_r = intMalloc(value)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(value)) ) ABORT("Malloc fails for perm_c[].");
if ( !(R = (double *) SUPERLU_MALLOC(value * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (double *) SUPERLU_MALLOC(value * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for C[].");
if ( !(ferr = (double *) SUPERLU_MALLOC( sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for ferr[].");
if ( !(berr = (double *) SUPERLU_MALLOC( sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for berr[].");
resize(value);
}
void nlClear_SUPERLU() {
superlu_context* context = (superlu_context*)(nlCurrentContext->direct_solver_context) ;
if(context != NULL) {
Destroy_SuperNode_Matrix(&(context->L)) ;
Destroy_CompCol_Matrix(&(context->U)) ;
NL_DELETE_ARRAY(context->perm_c) ;
NL_DELETE_ARRAY(context->perm_r) ;
}
}
void tlin::freeF(SuperFactors *F) {
if (!F) return;
Destroy_SuperNode_Matrix(F->L);
Destroy_CompCol_Matrix(F->U);
SUPERLU_FREE(F->L);
SUPERLU_FREE(F->U);
SUPERLU_FREE(F->perm_r);
SUPERLU_FREE(F->perm_c);
SUPERLU_FREE(F);
}
static void __nlFree_SUPERLU(__NLContext *context) {
Destroy_SuperNode_Matrix(&(context->slu.L));
Destroy_CompCol_Matrix(&(context->slu.U));
StatFree(&(context->slu.stat));
__NL_DELETE_ARRAY(context->slu.perm_r);
__NL_DELETE_ARRAY(context->slu.perm_c);
context->slu.alloc_slu = NL_FALSE;
}
static void
SparseFactor_dealloc(SparseFactor* self)
{
free(self->perm_c);
free(self->perm_r);
free(self->etree);
if (self->AC.Store != NULL)
Destroy_CompCol_Permuted(&self->AC);
if (self->L.Store != NULL)
Destroy_SuperNode_Matrix(&self->L);
if (self->U.Store != NULL)
Destroy_CompCol_Matrix(&self->U);
StatFree(&self->stat);
self->ob_type->tp_free((PyObject*)self);
}
//! \brief The destructor frees the dynamically allocated data members.
~SuperLUdata()
{
Destroy_SuperMatrix_Store(&A);
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
if (R) delete[] R;
if (C) delete[] C;
if (perm_r) delete[] perm_r;
if (perm_c) delete[] perm_c;
if (etree) delete[] etree;
#ifdef HAS_SUPERLU_MT
delete[] opts->etree;
delete[] opts->colcnt_h;
delete[] opts->part_super_h;
#endif
if (opts) delete opts;
}
~SolveSuperLU () {
if (verbosity > 3) {
cout << "~SolveSuperLU S:" << endl;
}
// if (etree) delete[] etree;
// if (perm_r) delete[] perm_r;
// if (perm_c) delete[] perm_c;
if (RR) {delete [] RR;}
if (CC) {delete [] CC;}
if (A.Store) {Destroy_SuperMatrix_Store(&A);}
if (L.Store) {Destroy_SuperNode_Matrix(&L);}
if (U.Store) {Destroy_CompCol_Matrix(&U);}
}
static void slm_dtor(void* context)
{
slm_t* mat = context;
if (mat->cperm != NULL)
{
SUPERLU_FREE(mat->cperm);
SUPERLU_FREE(mat->rperm);
Destroy_SuperNode_Matrix(&mat->L);
Destroy_CompCol_Matrix(&mat->U);
}
supermatrix_free(mat->A);
Destroy_SuperMatrix_Store(&mat->rhs);
polymec_free(mat->rhs_data);
Destroy_SuperMatrix_Store(&mat->X);
polymec_free(mat->X_data);
polymec_free(mat->R);
polymec_free(mat->C);
StatFree(&mat->stat);
if (mat->etree != NULL)
polymec_free(mat->etree);
mat->ilu_params = NULL;
adj_graph_free(mat->sparsity);
polymec_free(mat);
}
void
c_fortran_zgssv_(int *iopt, int *n, int *nnz, int *nrhs,
doublecomplex *values, int *rowind, int *colptr,
doublecomplex *b, int *ldb,
fptr *f_factors, /* a handle containing the address
pointing to the factored matrices */
int *info)
{
/*
* This routine can be called from Fortran.
*
* iopt (input) int
* Specifies the operation:
* = 1, performs LU decomposition for the first time
* = 2, performs triangular solve
* = 3, free all the storage in the end
*
* f_factors (input/output) fptr*
* If iopt == 1, it is an output and contains the pointer pointing to
* the structure of the factored matrices.
* Otherwise, it it an input.
*
*/
SuperMatrix A, AC, B;
SuperMatrix *L, *U;
int *perm_r; /* row permutations from partial pivoting */
int *perm_c; /* column permutation vector */
int *etree; /* column elimination tree */
SCformat *Lstore;
NCformat *Ustore;
int i, panel_size, permc_spec, relax;
trans_t trans;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
factors_t *LUfactors;
trans = TRANS;
if ( *iopt == 1 ) { /* LU decomposition */
/* Set the default input options. */
set_default_options(&options);
/* Initialize the statistics variables. */
StatInit(&stat);
/* Adjust to 0-based indexing */
for (i = 0; i < *nnz; ++i) --rowind[i];
for (i = 0; i <= *n; ++i) --colptr[i];
zCreate_CompCol_Matrix(&A, *n, *n, *nnz, values, rowind, colptr,
SLU_NC, SLU_Z, SLU_GE);
L = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
U = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
if ( !(perm_r = intMalloc(*n)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(*n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(etree = intMalloc(*n)) ) ABORT("Malloc fails for etree[].");
/*
* Get column permutation vector perm_c[], according to permc_spec:
* permc_spec = 0: natural ordering
* permc_spec = 1: minimum degree on structure of A'*A
* permc_spec = 2: minimum degree on structure of A'+A
* permc_spec = 3: approximate minimum degree for unsymmetric matrices
*/
permc_spec = options.ColPerm;
get_perm_c(permc_spec, &A, perm_c);
sp_preorder(&options, &A, perm_c, etree, &AC);
panel_size = sp_ienv(1);
relax = sp_ienv(2);
zgstrf(&options, &AC, relax, panel_size, etree,
NULL, 0, perm_c, perm_r, L, U, &stat, info);
if ( *info == 0 ) {
Lstore = (SCformat *) L->Store;
Ustore = (NCformat *) U->Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz);
zQuerySpace(L, U, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
} else {
printf("zgstrf() error returns INFO= %d\n", *info);
if ( *info <= *n ) { /* factorization completes */
zQuerySpace(L, U, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
}
}
/* Restore to 1-based indexing */
for (i = 0; i < *nnz; ++i) ++rowind[i];
for (i = 0; i <= *n; ++i) ++colptr[i];
/* Save the LU factors in the factors handle */
LUfactors = (factors_t*) SUPERLU_MALLOC(sizeof(factors_t));
LUfactors->L = L;
LUfactors->U = U;
LUfactors->perm_c = perm_c;
LUfactors->perm_r = perm_r;
*f_factors = (fptr) LUfactors;
/* Free un-wanted storage */
SUPERLU_FREE(etree);
Destroy_SuperMatrix_Store(&A);
Destroy_CompCol_Permuted(&AC);
StatFree(&stat);
} else if ( *iopt == 2 ) { /* Triangular solve */
/* Initialize the statistics variables. */
StatInit(&stat);
/* Extract the LU factors in the factors handle */
LUfactors = (factors_t*) *f_factors;
L = LUfactors->L;
U = LUfactors->U;
perm_c = LUfactors->perm_c;
perm_r = LUfactors->perm_r;
zCreate_Dense_Matrix(&B, *n, *nrhs, b, *ldb, SLU_DN, SLU_Z, SLU_GE);
/* Solve the system A*X=B, overwriting B with X. */
zgstrs (trans, L, U, perm_c, perm_r, &B, &stat, info);
Destroy_SuperMatrix_Store(&B);
StatFree(&stat);
} else if ( *iopt == 3 ) { /* Free storage */
/* Free the LU factors in the factors handle */
LUfactors = (factors_t*) *f_factors;
SUPERLU_FREE (LUfactors->perm_r);
SUPERLU_FREE (LUfactors->perm_c);
Destroy_SuperNode_Matrix(LUfactors->L);
Destroy_CompCol_Matrix(LUfactors->U);
SUPERLU_FREE (LUfactors->L);
SUPERLU_FREE (LUfactors->U);
SUPERLU_FREE (LUfactors);
} else {
fprintf(stderr,"Invalid iopt=%d passed to c_fortran_zgssv()\n",*iopt);
exit(-1);
}
}
bool SparseMatrix::solveSLU (Vector& B)
{
int ierr = ncol+1;
if (!factored) this->optimiseSLU();
#ifdef HAS_SUPERLU_MT
if (!slu) {
// Create a new SuperLU matrix
slu = new SuperLUdata;
slu->perm_c = new int[ncol];
slu->perm_r = new int[nrow];
dCreate_CompCol_Matrix(&slu->A, nrow, ncol, this->size(),
&A.front(), &JA.front(), &IA.front(),
SLU_NC, SLU_D, SLU_GE);
}
else {
Destroy_SuperMatrix_Store(&slu->A);
Destroy_SuperNode_Matrix(&slu->L);
Destroy_CompCol_Matrix(&slu->U);
dCreate_CompCol_Matrix(&slu->A, nrow, ncol, this->size(),
&A.front(), &JA.front(), &IA.front(),
SLU_NC, SLU_D, SLU_GE);
}
// Get column permutation vector perm_c[], according to permc_spec:
// permc_spec = 0: natural ordering
// permc_spec = 1: minimum degree ordering on structure of A'*A
// permc_spec = 2: minimum degree ordering on structure of A'+A
// permc_spec = 3: approximate minimum degree for unsymmetric matrices
int permc_spec = 1;
get_perm_c(permc_spec, &slu->A, slu->perm_c);
// Create right-hand-side/solution vector(s)
size_t nrhs = B.size() / nrow;
SuperMatrix Bmat;
dCreate_Dense_Matrix(&Bmat, nrow, nrhs, B.ptr(), nrow,
SLU_DN, SLU_D, SLU_GE);
// Invoke the simple driver
pdgssv(numThreads, &slu->A, slu->perm_c, slu->perm_r,
&slu->L, &slu->U, &Bmat, &ierr);
if (ierr > 0)
std::cerr <<"SuperLU_MT Failure "<< ierr << std::endl;
Destroy_SuperMatrix_Store(&Bmat);
#elif defined(HAS_SUPERLU)
if (!slu) {
// Create a new SuperLU matrix
slu = new SuperLUdata(1);
slu->perm_c = new int[ncol];
slu->perm_r = new int[nrow];
dCreate_CompCol_Matrix(&slu->A, nrow, ncol, this->size(),
&A.front(), &JA.front(), &IA.front(),
SLU_NC, SLU_D, SLU_GE);
}
else if (factored)
slu->opts->Fact = FACTORED; // Re-use previous factorization
else {
Destroy_SuperMatrix_Store(&slu->A);
Destroy_SuperNode_Matrix(&slu->L);
Destroy_CompCol_Matrix(&slu->U);
dCreate_CompCol_Matrix(&slu->A, nrow, ncol, this->size(),
&A.front(), &JA.front(), &IA.front(),
SLU_NC, SLU_D, SLU_GE);
}
// Create right-hand-side/solution vector(s)
size_t nrhs = B.size() / nrow;
SuperMatrix Bmat;
dCreate_Dense_Matrix(&Bmat, nrow, nrhs, B.ptr(), nrow,
SLU_DN, SLU_D, SLU_GE);
SuperLUStat_t stat;
StatInit(&stat);
// Invoke the simple driver
dgssv(slu->opts, &slu->A, slu->perm_c, slu->perm_r,
&slu->L, &slu->U, &Bmat, &stat, &ierr);
if (ierr > 0)
std::cerr <<"SuperLU Failure "<< ierr << std::endl;
else
factored = true;
if (printSLUstat)
StatPrint(&stat);
StatFree(&stat);
Destroy_SuperMatrix_Store(&Bmat);
#else
std::cerr <<"SparseMatrix::solve: SuperLU solver not available"<< std::endl;
#endif
return ierr == 0;
}
int main(int argc, char *argv[])
{
/*
* Purpose
* =======
*
* The driver program CLINSOLX2.
*
* This example illustrates how to use CGSSVX to solve systems repeatedly
* with the same sparsity pattern of matrix A.
* In this case, the column permutation vector perm_c is computed once.
* The following data structures will be reused in the subsequent call to
* CGSSVX: perm_c, etree
*
*/
char equed[1];
yes_no_t equil;
trans_t trans;
SuperMatrix A, A1, L, U;
SuperMatrix B, B1, X;
NCformat *Astore;
NCformat *Ustore;
SCformat *Lstore;
complex *a, *a1;
int *asub, *xa, *asub1, *xa1;
int *perm_r; /* row permutations from partial pivoting */
int *perm_c; /* column permutation vector */
int *etree;
void *work;
int info, lwork, nrhs, ldx;
int i, j, m, n, nnz;
complex *rhsb, *rhsb1, *rhsx, *xact;
float *R, *C;
float *ferr, *berr;
float u, rpg, rcond;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
extern void parse_command_line();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Defaults */
lwork = 0;
nrhs = 1;
equil = YES;
u = 1.0;
trans = NOTRANS;
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options(&options);
/* Can use command line input to modify the defaults. */
parse_command_line(argc, argv, &lwork, &u, &equil, &trans);
options.Equil = equil;
options.DiagPivotThresh = u;
options.Trans = trans;
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) {
ABORT("DLINSOLX: cannot allocate work[]");
}
}
/* Read matrix A from a file in Harwell-Boeing format.*/
creadhb(&m, &n, &nnz, &a, &asub, &xa);
if ( !(a1 = complexMalloc(nnz)) ) ABORT("Malloc fails for a1[].");
if ( !(asub1 = intMalloc(nnz)) ) ABORT("Malloc fails for asub1[].");
if ( !(xa1 = intMalloc(n+1)) ) ABORT("Malloc fails for xa1[].");
for (i = 0; i < nnz; ++i) {
a1[i] = a[i];
asub1[i] = asub[i];
}
for (i = 0; i < n+1; ++i) xa1[i] = xa[i];
cCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_C, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
if ( !(rhsb = complexMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsb1 = complexMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb1[].");
if ( !(rhsx = complexMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
cCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_C, SLU_GE);
cCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_C, SLU_GE);
xact = complexMalloc(n * nrhs);
ldx = n;
cGenXtrue(n, nrhs, xact, ldx);
cFillRHS(trans, nrhs, xact, ldx, &A, &B);
for (j = 0; j < nrhs; ++j)
for (i = 0; i < m; ++i) rhsb1[i+j*m] = rhsb[i+j*m];
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for C[].");
if ( !(ferr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for ferr[].");
if ( !(berr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for berr[].");
/* Initialize the statistics variables. */
StatInit(&stat);
/* ------------------------------------------------------------
WE SOLVE THE LINEAR SYSTEM FOR THE FIRST TIME: AX = B
------------------------------------------------------------*/
cgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info);
printf("First system: cgssvx() returns info %d\n", info);
if ( info == 0 || info == n+1 ) {
/* This is how you could access the solution matrix. */
complex *sol = (complex*) ((DNformat*) X.Store)->nzval;
if ( options.PivotGrowth ) printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber )
printf("Recip. condition number = %e\n", rcond);
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
if ( options.IterRefine ) {
printf("Iterative Refinement:\n");
printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
for (i = 0; i < nrhs; ++i)
printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
}
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
Destroy_CompCol_Matrix(&A);
Destroy_Dense_Matrix(&B);
if ( lwork >= 0 ) { /* Deallocate storage associated with L and U. */
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
/* ------------------------------------------------------------
NOW WE SOLVE ANOTHER LINEAR SYSTEM: A1*X = B1
ONLY THE SPARSITY PATTERN OF A1 IS THE SAME AS THAT OF A.
------------------------------------------------------------*/
options.Fact = SamePattern;
StatInit(&stat); /* Initialize the statistics variables. */
cCreate_CompCol_Matrix(&A1, m, n, nnz, a1, asub1, xa1,
SLU_NC, SLU_C, SLU_GE);
cCreate_Dense_Matrix(&B1, m, nrhs, rhsb1, m, SLU_DN, SLU_C, SLU_GE);
cgssvx(&options, &A1, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B1, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info);
printf("\nSecond system: cgssvx() returns info %d\n", info);
if ( info == 0 || info == n+1 ) {
/* This is how you could access the solution matrix. */
complex *sol = (complex*) ((DNformat*) X.Store)->nzval;
if ( options.PivotGrowth ) printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber )
printf("Recip. condition number = %e\n", rcond);
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
if ( options.IterRefine ) {
printf("Iterative Refinement:\n");
printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
for (i = 0; i < nrhs; ++i)
printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
}
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
Destroy_CompCol_Matrix(&A1);
Destroy_Dense_Matrix(&B1);
Destroy_Dense_Matrix(&X);
if ( lwork == 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
} else if ( lwork > 0 ) {
SUPERLU_FREE(work);
}
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
}
main(int argc, char *argv[])
{
SuperMatrix A;
NCformat *Astore;
double *a;
int *asub, *xa;
int *perm_c; /* column permutation vector */
int *perm_r; /* row permutations from partial pivoting */
SuperMatrix L; /* factor L */
SCformat *Lstore;
SuperMatrix U; /* factor U */
NCformat *Ustore;
SuperMatrix B;
int nrhs, ldx, info, m, n, nnz;
double *xact, *rhs;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options(&options);
/* Now we modify the default options to use the symmetric mode. */
options.SymmetricMode = YES;
options.ColPerm = MMD_AT_PLUS_A;
options.DiagPivotThresh = 0.001;
#if 1
/* Read matrix A from a file in Harwell-Boeing format.*/
if (argc < 2)
{
printf("Usage:\n%s [OPTION] < [INPUT] > [OUTPUT]\nOPTION:\n"
"-h -hb:\n\t[INPUT] is a Harwell-Boeing format matrix.\n"
"-r -rb:\n\t[INPUT] is a Rutherford-Boeing format matrix.\n"
"-t -triplet:\n\t[INPUT] is a triplet format matrix.\n",
argv[0]);
return 0;
}
else
{
switch (argv[1][1])
{
case 'H':
case 'h':
printf("Input a Harwell-Boeing format matrix:\n");
dreadhb(&m, &n, &nnz, &a, &asub, &xa);
break;
case 'R':
case 'r':
printf("Input a Rutherford-Boeing format matrix:\n");
dreadrb(&m, &n, &nnz, &a, &asub, &xa);
break;
case 'T':
case 't':
printf("Input a triplet format matrix:\n");
dreadtriple(&m, &n, &nnz, &a, &asub, &xa);
break;
default:
printf("Unrecognized format.\n");
return 0;
}
}
#else
/* Read the matrix in Harwell-Boeing format. */
dreadhb(&m, &n, &nnz, &a, &asub, &xa);
#endif
dCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_D, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
nrhs = 1;
if ( !(rhs = doubleMalloc(m * nrhs)) ) ABORT("Malloc fails for rhs[].");
dCreate_Dense_Matrix(&B, m, nrhs, rhs, m, SLU_DN, SLU_D, SLU_GE);
xact = doubleMalloc(n * nrhs);
ldx = n;
dGenXtrue(n, nrhs, xact, ldx);
dFillRHS(options.Trans, nrhs, xact, ldx, &A, &B);
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
/* Initialize the statistics variables. */
StatInit(&stat);
dgssv(&options, &A, perm_c, perm_r, &L, &U, &B, &stat, &info);
if ( info == 0 ) {
/* This is how you could access the solution matrix. */
double *sol = (double*) ((DNformat*) B.Store)->nzval;
/* Compute the infinity norm of the error. */
dinf_norm_error(nrhs, &B, xact);
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);
dQuerySpace(&L, &U, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
} else {
printf("dgssv() error returns INFO= %d\n", info);
if ( info <= n ) { /* factorization completes */
dQuerySpace(&L, &U, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
}
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (rhs);
SUPERLU_FREE (xact);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
}
static PyObject *
Py_gssv(PyObject *self, PyObject *args, PyObject *kwdict)
{
PyObject *Py_B=NULL, *Py_X=NULL;
PyArrayObject *nzvals=NULL;
PyArrayObject *colind=NULL, *rowptr=NULL;
int N, nnz;
int info;
int csc=0;
int *perm_r=NULL, *perm_c=NULL;
SuperMatrix A, B, L, U;
superlu_options_t options;
SuperLUStat_t stat;
PyObject *option_dict = NULL;
int type;
int ssv_finished = 0;
static char *kwlist[] = {"N","nnz","nzvals","colind","rowptr","B", "csc",
"options",NULL};
/* Get input arguments */
if (!PyArg_ParseTupleAndKeywords(args, kwdict, "iiO!O!O!O|iO", kwlist,
&N, &nnz, &PyArray_Type, &nzvals,
&PyArray_Type, &colind, &PyArray_Type,
&rowptr, &Py_B, &csc, &option_dict)) {
return NULL;
}
if (!_CHECK_INTEGER(colind) || !_CHECK_INTEGER(rowptr)) {
PyErr_SetString(PyExc_TypeError,
"colind and rowptr must be of type cint");
return NULL;
}
type = PyArray_TYPE(nzvals);
if (!CHECK_SLU_TYPE(type)) {
PyErr_SetString(PyExc_TypeError,
"nzvals is not of a type supported by SuperLU");
return NULL;
}
if (!set_superlu_options_from_dict(&options, 0, option_dict, NULL, NULL)) {
return NULL;
}
/* Create Space for output */
Py_X = PyArray_CopyFromObject(Py_B, type, 1, 2);
if (Py_X == NULL) return NULL;
if (csc) {
if (NCFormat_from_spMatrix(&A, N, N, nnz, nzvals, colind, rowptr,
type)) {
Py_DECREF(Py_X);
return NULL;
}
}
else {
if (NRFormat_from_spMatrix(&A, N, N, nnz, nzvals, colind, rowptr,
type)) {
Py_DECREF(Py_X);
return NULL;
}
}
if (DenseSuper_from_Numeric(&B, Py_X)) {
Destroy_SuperMatrix_Store(&A);
Py_DECREF(Py_X);
return NULL;
}
/* B and Py_X share same data now but Py_X "owns" it */
/* Setup options */
if (setjmp(_superlu_py_jmpbuf)) {
goto fail;
}
else {
perm_c = intMalloc(N);
perm_r = intMalloc(N);
StatInit(&stat);
/* Compute direct inverse of sparse Matrix */
gssv(type, &options, &A, perm_c, perm_r, &L, &U, &B, &stat, &info);
}
ssv_finished = 1;
SUPERLU_FREE(perm_r);
SUPERLU_FREE(perm_c);
Destroy_SuperMatrix_Store(&A); /* holds just a pointer to the data */
Destroy_SuperMatrix_Store(&B);
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
StatFree(&stat);
return Py_BuildValue("Ni", Py_X, info);
fail:
SUPERLU_FREE(perm_r);
SUPERLU_FREE(perm_c);
Destroy_SuperMatrix_Store(&A); /* holds just a pointer to the data */
Destroy_SuperMatrix_Store(&B);
if (ssv_finished) {
/* Avoid trying to free partially initialized matrices;
might leak some memory, but avoids a crash */
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
StatFree(&stat);
Py_XDECREF(Py_X);
return NULL;
}
static PyObject* superluWrappersSparseFactorPrepare(PyObject* self,
PyObject* args)
{
int i,n,relax=1,panel_size=10,lwork=0,info=0,permc_spec=3;
double drop_tol=-1.0;/* not used by superlu */
void *work=NULL;
PyObject *mat,*sparseFactor;
if(!PyArg_ParseTuple(args,"OO",
&mat,
&sparseFactor))
return NULL;
SFP(sparseFactor)->storeA.nnz = ((SparseMatrix*)mat)->A.nnz;
SFP(sparseFactor)->storeA.nzval = ((SparseMatrix*)mat)->A.nzval;
SFP(sparseFactor)->storeA.colptr = ((SparseMatrix*)mat)->A.rowptr;
SFP(sparseFactor)->storeA.rowind = ((SparseMatrix*)mat)->A.colind;
/* calc column permutation */
if ( SFP(sparseFactor)->use_same_perm_c == 0)
{
get_perm_c(permc_spec,
&SFP(sparseFactor)->A,
SFP(sparseFactor)->perm_c);
SFP(sparseFactor)->use_same_perm_c = 1;
}
if ( SFP(sparseFactor)->use_same_sparsity == 0)
{
if (SFP(sparseFactor)->AC.Store != NULL)
{
Destroy_CompCol_Permuted(&SFP(sparseFactor)->AC);
Destroy_SuperNode_Matrix(&SFP(sparseFactor)->L);
Destroy_CompCol_Matrix(&SFP(sparseFactor)->U);
}
/* apply column permutation and build AC and etree*/
sp_preorder(&SFP(sparseFactor)->options,
&SFP(sparseFactor)->A,
SFP(sparseFactor)->perm_c,
SFP(sparseFactor)->etree,
&SFP(sparseFactor)->AC);
SFP(sparseFactor)->use_same_sparsity = 1;
}
else
{
/* apply column permutation */
SFP(sparseFactor)->options.Fact = SamePattern_SameRowPerm;
n = SFP(sparseFactor)->A.ncol;
for (i = 0; i < n; i++)
{
((NCPformat*)SFP(sparseFactor)->AC.Store)->colbeg[SFP(sparseFactor)->perm_c[i]] = ((NCformat*)SFP(sparseFactor)->A.Store)->colptr[i];
((NCPformat*)SFP(sparseFactor)->AC.Store)->colend[SFP(sparseFactor)->perm_c[i]] = ((NCformat*)SFP(sparseFactor)->A.Store)->colptr[i+1];
}
}
dgstrf(&SFP(sparseFactor)->options,
&SFP(sparseFactor)->AC,
relax,
panel_size,
SFP(sparseFactor)->etree,
work,
lwork,
SFP(sparseFactor)->perm_c,
SFP(sparseFactor)->perm_r,
&SFP(sparseFactor)->L,
&SFP(sparseFactor)->U,
&SFP(sparseFactor)->Glu,
&SFP(sparseFactor)->stat,
&info);
Py_INCREF(Py_None);
return Py_None;
}
main(int argc, char *argv[])
{
/*
* Purpose
* =======
*
* The driver program ZLINSOLX1.
*
* This example illustrates how to use ZGSSVX to solve systems with the same
* A but different right-hand side.
* In this case, we factorize A only once in the first call to DGSSVX,
* and reuse the following data structures in the subsequent call to ZGSSVX:
* perm_c, perm_r, R, C, L, U.
*
*/
char equed[1];
yes_no_t equil;
trans_t trans;
SuperMatrix A, L, U;
SuperMatrix B, X;
NCformat *Astore;
NCformat *Ustore;
SCformat *Lstore;
doublecomplex *a;
int *asub, *xa;
int *perm_c; /* column permutation vector */
int *perm_r; /* row permutations from partial pivoting */
int *etree;
void *work;
int info, lwork, nrhs, ldx;
int i, m, n, nnz;
doublecomplex *rhsb, *rhsx, *xact;
double *R, *C;
double *ferr, *berr;
double u, rpg, rcond;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
extern void parse_command_line();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Defaults */
lwork = 0;
nrhs = 1;
equil = YES;
u = 1.0;
trans = NOTRANS;
/* Set the default values for options argument:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options(&options);
/* Can use command line input to modify the defaults. */
parse_command_line(argc, argv, &lwork, &u, &equil, &trans);
options.Equil = equil;
options.DiagPivotThresh = u;
options.Trans = trans;
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) {
ABORT("ZLINSOLX: cannot allocate work[]");
}
}
/* Read matrix A from a file in Harwell-Boeing format.*/
zreadhb(&m, &n, &nnz, &a, &asub, &xa);
zCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_Z, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
if ( !(rhsb = doublecomplexMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsx = doublecomplexMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
zCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_Z, SLU_GE);
zCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_Z, SLU_GE);
xact = doublecomplexMalloc(n * nrhs);
ldx = n;
zGenXtrue(n, nrhs, xact, ldx);
zFillRHS(trans, nrhs, xact, ldx, &A, &B);
if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(R = (double *) SUPERLU_MALLOC(A.nrow * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (double *) SUPERLU_MALLOC(A.ncol * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for C[].");
if ( !(ferr = (double *) SUPERLU_MALLOC(nrhs * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for ferr[].");
if ( !(berr = (double *) SUPERLU_MALLOC(nrhs * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for berr[].");
/* Initialize the statistics variables. */
StatInit(&stat);
/* ONLY PERFORM THE LU DECOMPOSITION */
B.ncol = 0; /* Indicate not to solve the system */
zgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info);
printf("LU factorization: zgssvx() returns info %d\n", info);
if ( info == 0 || info == n+1 ) {
if ( options.PivotGrowth ) printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber )
printf("Recip. condition number = %e\n", rcond);
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
/* ------------------------------------------------------------
NOW WE SOLVE THE LINEAR SYSTEM USING THE FACTORED FORM OF A.
------------------------------------------------------------*/
options.Fact = FACTORED; /* Indicate the factored form of A is supplied. */
B.ncol = nrhs; /* Set the number of right-hand side */
/* Initialize the statistics variables. */
StatInit(&stat);
zgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info);
printf("Triangular solve: zgssvx() returns info %d\n", info);
if ( info == 0 || info == n+1 ) {
/* This is how you could access the solution matrix. */
doublecomplex *sol = (doublecomplex*) ((DNformat*) X.Store)->nzval;
if ( options.IterRefine ) {
printf("Iterative Refinement:\n");
printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
for (i = 0; i < nrhs; ++i)
printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
}
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (rhsb);
SUPERLU_FREE (rhsx);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
if ( lwork == 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
} else if ( lwork > 0 ) {
SUPERLU_FREE(work);
}
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
}
main(int argc, char *argv[])
{
SuperMatrix A;
NCformat *Astore;
doublecomplex *a;
int *asub, *xa;
int *perm_c; /* column permutation vector */
int *perm_r; /* row permutations from partial pivoting */
SuperMatrix L; /* factor L */
SCformat *Lstore;
SuperMatrix U; /* factor U */
NCformat *Ustore;
SuperMatrix B;
int nrhs, ldx, info, m, n, nnz;
doublecomplex *xact, *rhs;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options(&options);
/* Now we modify the default options to use the symmetric mode. */
options.SymmetricMode = YES;
options.ColPerm = MMD_AT_PLUS_A;
options.DiagPivotThresh = 0.001;
/* Read the matrix in Harwell-Boeing format. */
zreadhb(&m, &n, &nnz, &a, &asub, &xa);
zCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_Z, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
nrhs = 1;
if ( !(rhs = doublecomplexMalloc(m * nrhs)) ) ABORT("Malloc fails for rhs[].");
zCreate_Dense_Matrix(&B, m, nrhs, rhs, m, SLU_DN, SLU_Z, SLU_GE);
xact = doublecomplexMalloc(n * nrhs);
ldx = n;
zGenXtrue(n, nrhs, xact, ldx);
zFillRHS(options.Trans, nrhs, xact, ldx, &A, &B);
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
/* Initialize the statistics variables. */
StatInit(&stat);
zgssv(&options, &A, perm_c, perm_r, &L, &U, &B, &stat, &info);
if ( info == 0 ) {
/* This is how you could access the solution matrix. */
doublecomplex *sol = (doublecomplex*) ((DNformat*) B.Store)->nzval;
/* Compute the infinity norm of the error. */
zinf_norm_error(nrhs, &B, xact);
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
zQuerySpace(&L, &U, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
mem_usage.expansions);
} else {
printf("zgssv() error returns INFO= %d\n", info);
if ( info <= n ) { /* factorization completes */
zQuerySpace(&L, &U, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
mem_usage.expansions);
}
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (rhs);
SUPERLU_FREE (xact);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
}
PetscErrorCode MatLUFactorNumeric_SuperLU(Mat F,Mat A,const MatFactorInfo *info)
{
Mat_SuperLU *lu = (Mat_SuperLU*)F->spptr;
Mat_SeqAIJ *aa;
PetscErrorCode ierr;
PetscInt sinfo;
PetscReal ferr, berr;
NCformat *Ustore;
SCformat *Lstore;
PetscFunctionBegin;
if (lu->flg == SAME_NONZERO_PATTERN){ /* successing numerical factorization */
lu->options.Fact = SamePattern;
/* Ref: ~SuperLU_3.0/EXAMPLE/dlinsolx2.c */
Destroy_SuperMatrix_Store(&lu->A);
if (lu->options.Equil){
ierr = MatCopy_SeqAIJ(A,lu->A_dup,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
}
if ( lu->lwork >= 0 ) {
Destroy_SuperNode_Matrix(&lu->L);
Destroy_CompCol_Matrix(&lu->U);
lu->options.Fact = SamePattern;
}
}
/* Create the SuperMatrix for lu->A=A^T:
Since SuperLU likes column-oriented matrices,we pass it the transpose,
and then solve A^T X = B in MatSolve(). */
if (lu->options.Equil){
aa = (Mat_SeqAIJ*)(lu->A_dup)->data;
} else {
aa = (Mat_SeqAIJ*)(A)->data;
}
#if defined(PETSC_USE_COMPLEX)
zCreate_CompCol_Matrix(&lu->A,A->cmap->n,A->rmap->n,aa->nz,(doublecomplex*)aa->a,aa->j,aa->i,
SLU_NC,SLU_Z,SLU_GE);
#else
dCreate_CompCol_Matrix(&lu->A,A->cmap->n,A->rmap->n,aa->nz,aa->a,aa->j,aa->i,
SLU_NC,SLU_D,SLU_GE);
#endif
/* Numerical factorization */
lu->B.ncol = 0; /* Indicate not to solve the system */
if (F->factortype == MAT_FACTOR_LU){
#if defined(PETSC_USE_COMPLEX)
zgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
&lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
&lu->mem_usage, &lu->stat, &sinfo);
#else
dgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
&lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
&lu->mem_usage, &lu->stat, &sinfo);
#endif
} else if (F->factortype == MAT_FACTOR_ILU){
/* Compute the incomplete factorization, condition number and pivot growth */
#if defined(PETSC_USE_COMPLEX)
zgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r,lu->etree, lu->equed, lu->R, lu->C,
&lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
&lu->mem_usage, &lu->stat, &sinfo);
#else
dgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
&lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
&lu->mem_usage, &lu->stat, &sinfo);
#endif
} else {
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");
}
if ( !sinfo || sinfo == lu->A.ncol+1 ) {
if ( lu->options.PivotGrowth )
ierr = PetscPrintf(PETSC_COMM_SELF," Recip. pivot growth = %e\n", lu->rpg);
if ( lu->options.ConditionNumber )
ierr = PetscPrintf(PETSC_COMM_SELF," Recip. condition number = %e\n", lu->rcond);
} else if ( sinfo > 0 ){
if ( lu->lwork == -1 ) {
ierr = PetscPrintf(PETSC_COMM_SELF," ** Estimated memory: %D bytes\n", sinfo - lu->A.ncol);
} else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot in row %D",sinfo);
} else { /* sinfo < 0 */
SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB, "info = %D, the %D-th argument in gssvx() had an illegal value", sinfo,-sinfo);
}
if ( lu->options.PrintStat ) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatLUFactorNumeric_SuperLU():\n");
StatPrint(&lu->stat);
Lstore = (SCformat *) lu->L.Store;
Ustore = (NCformat *) lu->U.Store;
ierr = PetscPrintf(PETSC_COMM_SELF," No of nonzeros in factor L = %D\n", Lstore->nnz);
ierr = PetscPrintf(PETSC_COMM_SELF," No of nonzeros in factor U = %D\n", Ustore->nnz);
ierr = PetscPrintf(PETSC_COMM_SELF," No of nonzeros in L+U = %D\n", Lstore->nnz + Ustore->nnz - lu->A.ncol);
ierr = PetscPrintf(PETSC_COMM_SELF," L\\U MB %.3f\ttotal MB needed %.3f\n",
lu->mem_usage.for_lu/1e6, lu->mem_usage.total_needed/1e6);
}
lu->flg = SAME_NONZERO_PATTERN;
F->ops->solve = MatSolve_SuperLU;
F->ops->solvetranspose = MatSolveTranspose_SuperLU;
F->ops->matsolve = MatMatSolve_SuperLU;
PetscFunctionReturn(0);
}
int main ( int argc, char *argv[] )
/**********************************************************************/
/*
Purpose:
SUPER_LU_S3 solves a sparse system read from a file using SGSSVX.
Discussion:
The sparse matrix is stored in a file using the Harwell-Boeing
sparse matrix format. The file should be assigned to the standard
input of this program. For instance, if the matrix is stored
in the file "g10_rua.txt", the execution command might be:
super_lu_s3 < g10_rua.txt
Modified:
25 April 2004
Reference:
James Demmel, John Gilbert, Xiaoye Li,
SuperLU Users's Guide,
Sections 1 and 2.
Local parameters:
SuperMatrix L, the computed L factor.
int *perm_c, the column permutation vector.
int *perm_r, the row permutations from partial pivoting.
SuperMatrix U, the computed U factor.
*/
{
SuperMatrix A;
NCformat *Astore;
float *a;
int *asub;
SuperMatrix B;
float *berr;
float *C;
char equed[1];
yes_no_t equil;
int *etree;
float *ferr;
int i;
int info;
SuperMatrix L;
int ldx;
SCformat *Lstore;
int lwork;
int m;
mem_usage_t mem_usage;
int n;
int nnz;
int nrhs;
superlu_options_t options;
int *perm_c;
int *perm_r;
float *R;
float rcond;
float *rhsb;
float *rhsx;
float rpg;
float *sol;
SuperLUStat_t stat;
trans_t trans;
SuperMatrix U;
float u;
NCformat *Ustore;
void *work;
SuperMatrix X;
int *xa;
float *xact;
/*
Say hello.
*/
printf ( "\n" );
printf ( "SUPER_LU_S3:\n" );
printf ( " Read a sparse matrix A from standard input,\n");
printf ( " stored in Harwell-Boeing Sparse Matrix format.\n" );
printf ( "\n" );
printf ( " Solve a linear system A * X = B using SGSSVX.\n" );
/*
Defaults
*/
lwork = 0;
nrhs = 1;
equil = YES;
u = 1.0;
trans = NOTRANS;
/*
Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options ( &options );
/*
Can use command line input to modify the defaults.
*/
parse_command_line ( argc, argv, &lwork, &u, &equil, &trans );
options.Equil = equil;
options.DiagPivotThresh = u;
options.Trans = trans;
printf ( "\n" );
printf ( " Length of work array LWORK = %d\n", lwork );
printf ( " Equilibration option EQUIL = %d\n", equil );
printf ( " Diagonal pivot threshhold value U = %f\n", u );
printf ( " Tranpose option TRANS = %d\n", trans );
/*
Add more functionalities that the defaults.
Compute reciprocal pivot growth
*/
options.PivotGrowth = YES;
/*
Compute reciprocal condition number
*/
options.ConditionNumber = YES;
/*
Perform single-precision refinement
*/
options.IterRefine = SINGLE;
if ( 0 < lwork )
{
work = SUPERLU_MALLOC(lwork);
if ( !work )
{
ABORT ( "SUPERLU_MALLOC cannot allocate work[]" );
}
}
/*
Read matrix A from a file in Harwell-Boeing format.
*/
sreadhb ( &m, &n, &nnz, &a, &asub, &xa );
/*
Create storage for a compressed column matrix.
*/
sCreate_CompCol_Matrix ( &A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE );
Astore = A.Store;
printf ( "\n" );
printf ( " Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz );
rhsb = floatMalloc ( m * nrhs );
if ( !rhsb )
{
ABORT ( "Malloc fails for rhsb[]." );
}
rhsx = floatMalloc ( m * nrhs );
if ( !rhsx )
{
ABORT ( "Malloc fails for rhsx[]." );
}
sCreate_Dense_Matrix ( &B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE );
sCreate_Dense_Matrix ( &X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE );
xact = floatMalloc ( n * nrhs );
if ( !xact )
{
ABORT ( "SUPERLU_MALLOC cannot allocate xact[]" );
}
ldx = n;
sGenXtrue ( n, nrhs, xact, ldx );
sFillRHS ( trans, nrhs, xact, ldx, &A, &B );
etree = intMalloc ( n );
if ( !etree )
{
ABORT ( "Malloc fails for etree[]." );
}
perm_c = intMalloc ( n );
if ( !perm_c )
{
ABORT ( "Malloc fails for perm_c[]." );
}
perm_r = intMalloc ( m );
if ( !perm_r )
{
ABORT ( "Malloc fails for perm_r[]." );
}
R = (float *) SUPERLU_MALLOC ( A.nrow * sizeof(float) );
if ( !R )
{
ABORT ( "SUPERLU_MALLOC fails for R[]." );
}
C = (float *) SUPERLU_MALLOC ( A.ncol * sizeof(float) );
if ( !C )
{
ABORT ( "SUPERLU_MALLOC fails for C[]." );
}
ferr = (float *) SUPERLU_MALLOC ( nrhs * sizeof(float) );
if ( !ferr )
{
ABORT ( "SUPERLU_MALLOC fails for ferr[]." );
}
berr = (float *) SUPERLU_MALLOC ( nrhs * sizeof(float) );
if ( !berr )
{
ABORT ( "SUPERLU_MALLOC fails for berr[]." );
}
/*
Initialize the statistics variables.
*/
StatInit(&stat);
/*
Solve the system and compute the condition number and error bounds using SGSSVX.
*/
sgssvx ( &options, &A, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info );
printf ( "\n" );
printf ( " SGSSVX returns INFO = %d\n", info );
if ( info == 0 || info == n+1 )
{
sol = (float*) ((DNformat*) X.Store)->nzval;
if ( options.PivotGrowth == YES )
{
printf ( "\n" );
printf ( " Reciprocal pivot growth = %e\n", rpg);
}
if ( options.ConditionNumber == YES )
{
printf ( "\n" );
printf ( " Reciprocal condition number = %e\n", rcond);
}
if ( options.IterRefine != NOREFINE )
{
printf ( "\n" );
printf ( " Iterative Refinement:\n");
printf ( "%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
for ( i = 0; i < nrhs; i++ )
{
printf ( "%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
}
}
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf ( "\n" );
printf ( " Number of nonzeros in factor L = %d\n", Lstore->nnz );
printf ( " Number of nonzeros in factor U = %d\n", Ustore->nnz );
printf ( " Number of nonzeros in L+U = %d\n",
Lstore->nnz + Ustore->nnz - n );
printf ( "\n" );
printf ( " L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
mem_usage.expansions );
fflush ( stdout );
}
else if ( info > 0 && lwork == -1 )
{
printf ( "\n" );
printf ( " Estimated memory: %d bytes\n", info - n );
}
if ( options.PrintStat )
{
StatPrint ( &stat );
}
StatFree ( &stat );
SUPERLU_FREE ( rhsb );
SUPERLU_FREE ( rhsx );
SUPERLU_FREE ( xact );
SUPERLU_FREE ( etree );
SUPERLU_FREE ( perm_r );
SUPERLU_FREE ( perm_c );
SUPERLU_FREE ( R );
SUPERLU_FREE ( C );
SUPERLU_FREE ( ferr );
SUPERLU_FREE ( berr );
Destroy_CompCol_Matrix ( &A );
Destroy_SuperMatrix_Store ( &B );
Destroy_SuperMatrix_Store ( &X );
if ( 0 <= lwork )
{
Destroy_SuperNode_Matrix ( &L );
Destroy_CompCol_Matrix ( &U );
}
/*
Say goodbye.
*/
printf ( "\n" );
printf ( "SUPER_LU_S3:\n" );
printf ( " Normal end of execution.\n");
return 0;
}
main(int argc, char *argv[])
{
SuperMatrix A;
NCformat *Astore;
doublecomplex *a;
int *asub, *xa;
int *perm_r; /* row permutations from partial pivoting */
int *perm_c; /* column permutation vector */
SuperMatrix L; /* factor L */
SCformat *Lstore;
SuperMatrix U; /* factor U */
NCformat *Ustore;
SuperMatrix B;
int nrhs, ldx, info, panel_size, m, n, nnz, permc_spec;
char trans[1];
doublecomplex *xact, *rhs;
mem_usage_t mem_usage;
nrhs = 1;
*trans = 'N';
zreadhb(&m, &n, &nnz, &a, &asub, &xa);
zCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_Z, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
if ( !(rhs = doublecomplexMalloc(m * nrhs)) ) ABORT("Malloc fails for rhs[].");
zCreate_Dense_Matrix(&B, m, nrhs, rhs, m, SLU_DN, SLU_Z, SLU_GE);
xact = doublecomplexMalloc(n * nrhs);
ldx = n;
zGenXtrue(n, nrhs, xact, ldx);
zFillRHS(trans, nrhs, xact, ldx, &A, &B);
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
/*
* Get column permutation vector perm_c[], according to permc_spec:
* permc_spec = 0: natural ordering
* permc_spec = 1: minimum degree on structure of A'*A
* permc_spec = 2: minimum degree on structure of A'+A
* permc_spec = 3: approximate minimum degree for unsymmetric matrices
*/
permc_spec = 1;
get_perm_c(permc_spec, &A, perm_c);
panel_size = sp_ienv(1);
zgssv(&A, perm_c, perm_r, &L, &U, &B, &info);
if ( info == 0 ) {
zinf_norm_error(nrhs, &B, xact); /* Inf. norm of the error */
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
zQuerySpace(&L, &U, panel_size, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
mem_usage.expansions);
} else {
printf("zgssv() error returns INFO= %d\n", info);
if ( info <= n ) { /* factorization completes */
zQuerySpace(&L, &U, panel_size, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
mem_usage.expansions);
}
}
SUPERLU_FREE (rhs);
SUPERLU_FREE (xact);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
int main(int argc, char *argv[])
{
char equed[1];
yes_no_t equil;
trans_t trans;
SuperMatrix A, L, U;
SuperMatrix B, X;
NCformat *Astore;
NCformat *Ustore;
SCformat *Lstore;
float *a;
int *asub, *xa;
int *perm_r; /* row permutations from partial pivoting */
int *perm_c; /* column permutation vector */
int *etree;
void *work;
int info, lwork, nrhs, ldx;
int i, m, n, nnz;
float *rhsb, *rhsx, *xact;
float *R, *C;
float *ferr, *berr;
float u, rpg, rcond;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
extern void parse_command_line();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Defaults */
lwork = 0;
nrhs = 1;
equil = YES;
u = 1.0;
trans = NOTRANS;
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options(&options);
/* Can use command line input to modify the defaults. */
parse_command_line(argc, argv, &lwork, &u, &equil, &trans);
options.Equil = equil;
options.DiagPivotThresh = u;
options.Trans = trans;
/* Add more functionalities that the defaults. */
options.PivotGrowth = YES; /* Compute reciprocal pivot growth */
options.ConditionNumber = YES;/* Compute reciprocal condition number */
options.IterRefine = SLU_SINGLE; /* Perform single-precision refinement */
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) {
ABORT("SLINSOLX: cannot allocate work[]");
}
}
/* Read matrix A from a file in Harwell-Boeing format.*/
sreadhb(&m, &n, &nnz, &a, &asub, &xa);
sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
if ( !(rhsb = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsx = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
sCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE);
sCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE);
xact = floatMalloc(n * nrhs);
ldx = n;
sGenXtrue(n, nrhs, xact, ldx);
sFillRHS(trans, nrhs, xact, ldx, &A, &B);
if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for C[].");
if ( !(ferr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for ferr[].");
if ( !(berr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for berr[].");
/* Initialize the statistics variables. */
StatInit(&stat);
/* Solve the system and compute the condition number
and error bounds using dgssvx. */
sgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info);
printf("sgssvx(): info %d\n", info);
if ( info == 0 || info == n+1 ) {
/* This is how you could access the solution matrix. */
float *sol = (float*) ((DNformat*) X.Store)->nzval;
if ( options.PivotGrowth == YES )
printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber == YES )
printf("Recip. condition number = %e\n", rcond);
if ( options.IterRefine != NOREFINE ) {
printf("Iterative Refinement:\n");
printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
for (i = 0; i < nrhs; ++i)
printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
}
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (rhsb);
SUPERLU_FREE (rhsx);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
if ( lwork == 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
} else if ( lwork > 0 ) {
SUPERLU_FREE(work);
}
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
}
main(int argc, char *argv[])
{
/*
* Purpose
* =======
*
* SDRIVE is the main test program for the FLOAT linear
* equation driver routines SGSSV and SGSSVX.
*
* The program is invoked by a shell script file -- stest.csh.
* The output from the tests are written into a file -- stest.out.
*
* =====================================================================
*/
float *a, *a_save;
int *asub, *asub_save;
int *xa, *xa_save;
SuperMatrix A, B, X, L, U;
SuperMatrix ASAV, AC;
GlobalLU_t Glu; /* Not needed on return. */
mem_usage_t mem_usage;
int *perm_r; /* row permutation from partial pivoting */
int *perm_c, *pc_save; /* column permutation */
int *etree;
float zero = 0.0;
float *R, *C;
float *ferr, *berr;
float *rwork;
float *wwork;
void *work;
int info, lwork, nrhs, panel_size, relax;
int m, n, nnz;
float *xact;
float *rhsb, *solx, *bsav;
int ldb, ldx;
float rpg, rcond;
int i, j, k1;
float rowcnd, colcnd, amax;
int maxsuper, rowblk, colblk;
int prefact, nofact, equil, iequed;
int nt, nrun, nfail, nerrs, imat, fimat, nimat;
int nfact, ifact, itran;
int kl, ku, mode, lda;
int zerot, izero, ioff;
double u;
float anorm, cndnum;
float *Afull;
float result[NTESTS];
superlu_options_t options;
fact_t fact;
trans_t trans;
SuperLUStat_t stat;
static char matrix_type[8];
static char equed[1], path[4], sym[1], dist[1];
FILE *fp;
/* Fixed set of parameters */
int iseed[] = {1988, 1989, 1990, 1991};
static char equeds[] = {'N', 'R', 'C', 'B'};
static fact_t facts[] = {FACTORED, DOFACT, SamePattern,
SamePattern_SameRowPerm};
static trans_t transs[] = {NOTRANS, TRANS, CONJ};
/* Some function prototypes */
extern int sgst01(int, int, SuperMatrix *, SuperMatrix *,
SuperMatrix *, int *, int *, float *);
extern int sgst02(trans_t, int, int, int, SuperMatrix *, float *,
int, float *, int, float *resid);
extern int sgst04(int, int, float *, int,
float *, int, float rcond, float *resid);
extern int sgst07(trans_t, int, int, SuperMatrix *, float *, int,
float *, int, float *, int,
float *, float *, float *);
extern int slatb4_slu(char *, int *, int *, int *, char *, int *, int *,
float *, int *, float *, char *);
extern int slatms_slu(int *, int *, char *, int *, char *, float *d,
int *, float *, float *, int *, int *,
char *, float *, int *, float *, int *);
extern int sp_sconvert(int, int, float *, int, int, int,
float *a, int *, int *, int *);
/* Executable statements */
strcpy(path, "SGE");
nrun = 0;
nfail = 0;
nerrs = 0;
/* Defaults */
lwork = 0;
n = 1;
nrhs = 1;
panel_size = sp_ienv(1);
relax = sp_ienv(2);
u = 1.0;
strcpy(matrix_type, "LA");
parse_command_line(argc, argv, matrix_type, &n,
&panel_size, &relax, &nrhs, &maxsuper,
&rowblk, &colblk, &lwork, &u, &fp);
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) {
fprintf(stderr, "expert: cannot allocate %d bytes\n", lwork);
exit (-1);
}
}
/* Set the default input options. */
set_default_options(&options);
options.DiagPivotThresh = u;
options.PrintStat = NO;
options.PivotGrowth = YES;
options.ConditionNumber = YES;
options.IterRefine = SLU_SINGLE;
if ( strcmp(matrix_type, "LA") == 0 ) {
/* Test LAPACK matrix suite. */
m = n;
lda = SUPERLU_MAX(n, 1);
nnz = n * n; /* upper bound */
fimat = 1;
nimat = NTYPES;
Afull = floatCalloc(lda * n);
sallocateA(n, nnz, &a, &asub, &xa);
} else {
/* Read a sparse matrix */
fimat = nimat = 0;
sreadhb(fp, &m, &n, &nnz, &a, &asub, &xa);
}
sallocateA(n, nnz, &a_save, &asub_save, &xa_save);
rhsb = floatMalloc(m * nrhs);
bsav = floatMalloc(m * nrhs);
solx = floatMalloc(n * nrhs);
ldb = m;
ldx = n;
sCreate_Dense_Matrix(&B, m, nrhs, rhsb, ldb, SLU_DN, SLU_S, SLU_GE);
sCreate_Dense_Matrix(&X, n, nrhs, solx, ldx, SLU_DN, SLU_S, SLU_GE);
xact = floatMalloc(n * nrhs);
etree = intMalloc(n);
perm_r = intMalloc(n);
perm_c = intMalloc(n);
pc_save = intMalloc(n);
R = (float *) SUPERLU_MALLOC(m*sizeof(float));
C = (float *) SUPERLU_MALLOC(n*sizeof(float));
ferr = (float *) SUPERLU_MALLOC(nrhs*sizeof(float));
berr = (float *) SUPERLU_MALLOC(nrhs*sizeof(float));
j = SUPERLU_MAX(m,n) * SUPERLU_MAX(4,nrhs);
rwork = (float *) SUPERLU_MALLOC(j*sizeof(float));
for (i = 0; i < j; ++i) rwork[i] = 0.;
if ( !R ) ABORT("SUPERLU_MALLOC fails for R");
if ( !C ) ABORT("SUPERLU_MALLOC fails for C");
if ( !ferr ) ABORT("SUPERLU_MALLOC fails for ferr");
if ( !berr ) ABORT("SUPERLU_MALLOC fails for berr");
if ( !rwork ) ABORT("SUPERLU_MALLOC fails for rwork");
wwork = floatCalloc( SUPERLU_MAX(m,n) * SUPERLU_MAX(4,nrhs) );
for (i = 0; i < n; ++i) perm_c[i] = pc_save[i] = i;
options.ColPerm = MY_PERMC;
for (imat = fimat; imat <= nimat; ++imat) { /* All matrix types */
if ( imat ) {
/* Skip types 5, 6, or 7 if the matrix size is too small. */
zerot = (imat >= 5 && imat <= 7);
if ( zerot && n < imat-4 )
continue;
/* Set up parameters with SLATB4 and generate a test matrix
with SLATMS. */
slatb4_slu(path, &imat, &n, &n, sym, &kl, &ku, &anorm, &mode,
&cndnum, dist);
slatms_slu(&n, &n, dist, iseed, sym, &rwork[0], &mode, &cndnum,
&anorm, &kl, &ku, "No packing", Afull, &lda,
&wwork[0], &info);
if ( info ) {
printf(FMT3, "SLATMS", info, izero, n, nrhs, imat, nfail);
continue;
}
/* For types 5-7, zero one or more columns of the matrix
to test that INFO is returned correctly. */
if ( zerot ) {
if ( imat == 5 ) izero = 1;
else if ( imat == 6 ) izero = n;
else izero = n / 2 + 1;
ioff = (izero - 1) * lda;
if ( imat < 7 ) {
for (i = 0; i < n; ++i) Afull[ioff + i] = zero;
} else {
for (j = 0; j < n - izero + 1; ++j)
for (i = 0; i < n; ++i)
Afull[ioff + i + j*lda] = zero;
}
} else {
izero = 0;
}
/* Convert to sparse representation. */
sp_sconvert(n, n, Afull, lda, kl, ku, a, asub, xa, &nnz);
} else {
izero = 0;
zerot = 0;
}
sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
/* Save a copy of matrix A in ASAV */
sCreate_CompCol_Matrix(&ASAV, m, n, nnz, a_save, asub_save, xa_save,
SLU_NC, SLU_S, SLU_GE);
sCopy_CompCol_Matrix(&A, &ASAV);
/* Form exact solution. */
sGenXtrue(n, nrhs, xact, ldx);
StatInit(&stat);
for (iequed = 0; iequed < 4; ++iequed) {
*equed = equeds[iequed];
if (iequed == 0) nfact = 4;
else nfact = 1; /* Only test factored, pre-equilibrated matrix */
for (ifact = 0; ifact < nfact; ++ifact) {
fact = facts[ifact];
options.Fact = fact;
for (equil = 0; equil < 2; ++equil) {
options.Equil = equil;
prefact = ( options.Fact == FACTORED ||
options.Fact == SamePattern_SameRowPerm );
/* Need a first factor */
nofact = (options.Fact != FACTORED); /* Not factored */
/* Restore the matrix A. */
sCopy_CompCol_Matrix(&ASAV, &A);
if ( zerot ) {
if ( prefact ) continue;
} else if ( options.Fact == FACTORED ) {
if ( equil || iequed ) {
/* Compute row and column scale factors to
equilibrate matrix A. */
sgsequ(&A, R, C, &rowcnd, &colcnd, &amax, &info);
/* Force equilibration. */
if ( !info && n > 0 ) {
if ( strncmp(equed, "R", 1)==0 ) {
rowcnd = 0.;
colcnd = 1.;
} else if ( strncmp(equed, "C", 1)==0 ) {
rowcnd = 1.;
colcnd = 0.;
} else if ( strncmp(equed, "B", 1)==0 ) {
rowcnd = 0.;
colcnd = 0.;
}
}
/* Equilibrate the matrix. */
slaqgs(&A, R, C, rowcnd, colcnd, amax, equed);
}
}
if ( prefact ) { /* Need a factor for the first time */
/* Save Fact option. */
fact = options.Fact;
options.Fact = DOFACT;
/* Preorder the matrix, obtain the column etree. */
sp_preorder(&options, &A, perm_c, etree, &AC);
/* Factor the matrix AC. */
sgstrf(&options, &AC, relax, panel_size,
etree, work, lwork, perm_c, perm_r, &L, &U,
&Glu, &stat, &info);
if ( info ) {
printf("** First factor: info %d, equed %c\n",
info, *equed);
if ( lwork == -1 ) {
printf("** Estimated memory: %d bytes\n",
info - n);
exit(0);
}
}
Destroy_CompCol_Permuted(&AC);
/* Restore Fact option. */
options.Fact = fact;
} /* if .. first time factor */
for (itran = 0; itran < NTRAN; ++itran) {
trans = transs[itran];
options.Trans = trans;
/* Restore the matrix A. */
sCopy_CompCol_Matrix(&ASAV, &A);
/* Set the right hand side. */
sFillRHS(trans, nrhs, xact, ldx, &A, &B);
sCopy_Dense_Matrix(m, nrhs, rhsb, ldb, bsav, ldb);
/*----------------
* Test sgssv
*----------------*/
if ( options.Fact == DOFACT && itran == 0) {
/* Not yet factored, and untransposed */
sCopy_Dense_Matrix(m, nrhs, rhsb, ldb, solx, ldx);
sgssv(&options, &A, perm_c, perm_r, &L, &U, &X,
&stat, &info);
if ( info && info != izero ) {
printf(FMT3, "sgssv",
info, izero, n, nrhs, imat, nfail);
} else {
/* Reconstruct matrix from factors and
compute residual. */
sgst01(m, n, &A, &L, &U, perm_c, perm_r,
&result[0]);
nt = 1;
if ( izero == 0 ) {
/* Compute residual of the computed
solution. */
sCopy_Dense_Matrix(m, nrhs, rhsb, ldb,
wwork, ldb);
sgst02(trans, m, n, nrhs, &A, solx,
ldx, wwork,ldb, &result[1]);
nt = 2;
}
/* Print information about the tests that
did not pass the threshold. */
for (i = 0; i < nt; ++i) {
if ( result[i] >= THRESH ) {
printf(FMT1, "sgssv", n, i,
result[i]);
++nfail;
}
}
nrun += nt;
} /* else .. info == 0 */
/* Restore perm_c. */
for (i = 0; i < n; ++i) perm_c[i] = pc_save[i];
if (lwork == 0) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
} /* if .. end of testing sgssv */
/*----------------
* Test sgssvx
*----------------*/
/* Equilibrate the matrix if fact = FACTORED and
equed = 'R', 'C', or 'B'. */
if ( options.Fact == FACTORED &&
(equil || iequed) && n > 0 ) {
slaqgs(&A, R, C, rowcnd, colcnd, amax, equed);
}
/* Solve the system and compute the condition number
and error bounds using sgssvx. */
sgssvx(&options, &A, perm_c, perm_r, etree,
equed, R, C, &L, &U, work, lwork, &B, &X, &rpg,
&rcond, ferr, berr, &Glu,
&mem_usage, &stat, &info);
if ( info && info != izero ) {
printf(FMT3, "sgssvx",
info, izero, n, nrhs, imat, nfail);
if ( lwork == -1 ) {
printf("** Estimated memory: %.0f bytes\n",
mem_usage.total_needed);
exit(0);
}
} else {
if ( !prefact ) {
/* Reconstruct matrix from factors and
compute residual. */
sgst01(m, n, &A, &L, &U, perm_c, perm_r,
&result[0]);
k1 = 0;
} else {
k1 = 1;
}
if ( !info ) {
/* Compute residual of the computed solution.*/
sCopy_Dense_Matrix(m, nrhs, bsav, ldb,
wwork, ldb);
sgst02(trans, m, n, nrhs, &ASAV, solx, ldx,
wwork, ldb, &result[1]);
/* Check solution from generated exact
solution. */
sgst04(n, nrhs, solx, ldx, xact, ldx, rcond,
&result[2]);
/* Check the error bounds from iterative
refinement. */
sgst07(trans, n, nrhs, &ASAV, bsav, ldb,
solx, ldx, xact, ldx, ferr, berr,
&result[3]);
/* Print information about the tests that did
not pass the threshold. */
for (i = k1; i < NTESTS; ++i) {
if ( result[i] >= THRESH ) {
printf(FMT2, "sgssvx",
options.Fact, trans, *equed,
n, imat, i, result[i]);
++nfail;
}
}
nrun += NTESTS;
} /* if .. info == 0 */
} /* else .. end of testing sgssvx */
} /* for itran ... */
if ( lwork == 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
} /* for equil ... */
} /* for ifact ... */
} /* for iequed ... */
#if 0
if ( !info ) {
PrintPerf(&L, &U, &mem_usage, rpg, rcond, ferr, berr, equed);
}
#endif
Destroy_SuperMatrix_Store(&A);
Destroy_SuperMatrix_Store(&ASAV);
StatFree(&stat);
} /* for imat ... */
/* Print a summary of the results. */
PrintSumm("SGE", nfail, nrun, nerrs);
if ( strcmp(matrix_type, "LA") == 0 ) SUPERLU_FREE (Afull);
SUPERLU_FREE (rhsb);
SUPERLU_FREE (bsav);
SUPERLU_FREE (solx);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (pc_save);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
SUPERLU_FREE (rwork);
SUPERLU_FREE (wwork);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
#if 0
Destroy_CompCol_Matrix(&A);
Destroy_CompCol_Matrix(&ASAV);
#else
SUPERLU_FREE(a); SUPERLU_FREE(asub); SUPERLU_FREE(xa);
SUPERLU_FREE(a_save); SUPERLU_FREE(asub_save); SUPERLU_FREE(xa_save);
#endif
if ( lwork > 0 ) {
SUPERLU_FREE (work);
Destroy_SuperMatrix_Store(&L);
Destroy_SuperMatrix_Store(&U);
}
return 0;
}
main(int argc, char *argv[])
{
char fact[1], equed[1], trans[1], refact[1];
SuperMatrix A, L, U;
SuperMatrix B, X;
NCformat *Astore;
NCformat *Ustore;
SCformat *Lstore;
complex *a;
int *asub, *xa;
int *perm_r; /* row permutations from partial pivoting */
int *perm_c; /* column permutation vector */
int *etree;
void *work;
factor_param_t iparam;
int info, lwork, nrhs, ldx, panel_size, relax;
int m, n, nnz, permc_spec;
complex *rhsb, *rhsx, *xact;
float *R, *C;
float *ferr, *berr;
float u, rpg, rcond;
int i, firstfact;
mem_usage_t mem_usage;
void parse_command_line();
/* Defaults */
lwork = 0;
*fact = 'E';
*equed = 'N';
*trans = 'N';
*refact = 'N';
nrhs = 1;
panel_size = sp_ienv(1);
relax = sp_ienv(2);
u = 1.0;
parse_command_line(argc, argv, &lwork, &panel_size, &relax, &u,
fact, trans, refact);
firstfact = lsame_(fact, "F") || lsame_(refact, "Y");
iparam.panel_size = panel_size;
iparam.relax = relax;
iparam.diag_pivot_thresh = u;
iparam.drop_tol = -1;
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) {
ABORT("CLINSOLX: cannot allocate work[]");
}
}
creadhb(&m, &n, &nnz, &a, &asub, &xa);
cCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_C, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
if ( !(rhsb = complexMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsx = complexMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
cCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_C, SLU_GE);
cCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_C, SLU_GE);
xact = complexMalloc(n * nrhs);
ldx = n;
cGenXtrue(n, nrhs, xact, ldx);
cFillRHS(trans, nrhs, xact, ldx, &A, &B);
if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
/*
* Get column permutation vector perm_c[], according to permc_spec:
* permc_spec = 0: natural ordering
* permc_spec = 1: minimum degree on structure of A'*A
* permc_spec = 2: minimum degree on structure of A'+A
* permc_spec = 3: approximate minimum degree for unsymmetric matrices
*/
permc_spec = 1;
get_perm_c(permc_spec, &A, perm_c);
if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for C[].");
if ( !(ferr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for ferr[].");
if ( !(berr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for berr[].");
/* Solve the system and compute the condition number
and error bounds using dgssvx. */
cgssvx(fact, trans, refact, &A, &iparam, perm_c, perm_r, etree,
equed, R, C, &L, &U, work, lwork, &B, &X, &rpg, &rcond,
ferr, berr, &mem_usage, &info);
printf("cgssvx(): info %d\n", info);
if ( info == 0 || info == n+1 ) {
printf("Recip. pivot growth = %e\n", rpg);
printf("Recip. condition number = %e\n", rcond);
printf("%8s%16s%16s\n", "rhs", "FERR", "BERR");
for (i = 0; i < nrhs; ++i) {
printf("%8d%16e%16e\n", i+1, ferr[i], berr[i]);
}
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
mem_usage.expansions);
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
SUPERLU_FREE (rhsb);
SUPERLU_FREE (rhsx);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
if ( lwork >= 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
}
bool SuperLUSolver::Solve(SparseMatrixType& rA, VectorType& rX, VectorType& rB)
{
//std::cout << "matrix size in solver: " << rA.size1() << std::endl;
//std::cout << "RHS size in solver SLU: " << rB.size() << std::endl;
// typedef ublas::compressed_matrix<double, ublas::row_major, 0,
// ublas::unbounded_array<int>, ublas::unbounded_array<double> > cm_t;
//make a copy of the RHS
VectorType rC = rB;
superlu_options_t options;
SuperLUStat_t stat;
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options(&options);
options.IterRefine = SLU_DOUBLE;
// options.ColPerm = MMD_AT_PLUS_A;
//Fill the SuperLU matrices
SuperMatrix Aslu, B, L, U;
//create a copy of the matrix
int *index1_vector = new (std::nothrow) int[rA.index1_data().size()];
int *index2_vector = new (std::nothrow) int[rA.index2_data().size()];
// double *values_vector = new (std::nothrow) double[rA.value_data().size()];
for( int unsigned i = 0; i < rA.index1_data().size(); i++ )
index1_vector[i] = (int)rA.index1_data()[i];
for( unsigned int i = 0; i < rA.index2_data().size(); i++ )
index2_vector[i] = (int)rA.index2_data()[i];
/* for( unsigned int i = 0; i < rA.value_data().size(); i++ )
values_vector[i] = (double)rA.value_data()[i];*/
//create a copy of the rhs vector (it will be overwritten with the solution)
/* double *b_vector = new (std::nothrow) double[rB.size()];
for( unsigned int i = 0; i < rB.size(); i++ )
b_vector[i] = rB[i];*/
/*
dCreate_CompCol_Matrix (&Aslu, rA.size1(), rA.size2(),
rA.nnz(),
values_vector,
index2_vector,
index1_vector,
SLU_NR, SLU_D, SLU_GE
);*/
//works also with dCreate_CompCol_Matrix
dCreate_CompRow_Matrix (&Aslu, rA.size1(), rA.size2(),
rA.nnz(),
rA.value_data().begin(),
index2_vector, //can not avoid a copy as ublas uses unsigned int internally
index1_vector, //can not avoid a copy as ublas uses unsigned int internally
SLU_NR, SLU_D, SLU_GE
);
dCreate_Dense_Matrix (&B, rB.size(), 1,&rB[0],rB.size(),SLU_DN, SLU_D, SLU_GE);
//allocate memory for permutation arrays
int* perm_c;
int* perm_r;
if ( !(perm_c = intMalloc(rA.size1())) ) ABORT("Malloc fails for perm_c[].");
if ( !(perm_r = intMalloc(rA.size2())) ) ABORT("Malloc fails for perm_r[].");
//initialize container for statistical data
StatInit(&stat);
//call solver routine
int info;
dgssv(&options, &Aslu, perm_c, perm_r, &L, &U, &B, &stat, &info);
//print output
if (options.PrintStat) {
StatPrint(&stat);
}
//resubstitution of results
#pragma omp parallel for
for(int i=0; i<static_cast<int>(rB.size()); i++ )
rX[i] = rB[i]; // B(i,0);
//recover the RHS
rB=rC;
//deallocate memory used
StatFree(&stat);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
Destroy_SuperMatrix_Store(&Aslu); //note that by using the "store" function we will take care of deallocation ourselves
Destroy_SuperMatrix_Store(&B);
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
delete [] index1_vector;
delete [] index2_vector;
// delete [] b_vector;
//CHECK WITH VALGRIND IF THIS IS NEEDED ...or if it is done by the lines above
//deallocate tempory storage used for the matrix
// if(b_vector!=NULL) delete [] index1_vector;
// // if(b_vector!=NULL) delete [] index2_vector;
// if(b_vector!=NULL) delete [] values_vector;
// if(b_vector!=NULL) delete [] b_vector;
return true;
}
static PyObject *Py_sgssv (PyObject *self, PyObject *args, PyObject *kwdict)
{
PyObject *Py_B=NULL, *Py_X=NULL;
PyArrayObject *nzvals=NULL;
PyArrayObject *colind=NULL, *rowptr=NULL;
int N, nnz;
int info;
int csc=0, permc_spec=2;
int *perm_r=NULL, *perm_c=NULL;
SuperMatrix A, B, L, U;
superlu_options_t options;
SuperLUStat_t stat;
static char *kwlist[] = {"N","nnz","nzvals","colind","rowptr","B", "csc", "permc_spec",NULL};
/* Get input arguments */
if (!PyArg_ParseTupleAndKeywords(args, kwdict, "iiO!O!O!O|ii", kwlist, &N, &nnz, &PyArray_Type, &nzvals, &PyArray_Type, &colind, &PyArray_Type, &rowptr, &Py_B, &csc, &permc_spec))
return NULL;
if (!_CHECK_INTEGER(colind) || !_CHECK_INTEGER(rowptr)) {
PyErr_SetString(PyExc_TypeError, "colind and rowptr must be of type cint");
return NULL;
}
/* Create Space for output */
Py_X = PyArray_CopyFromObject(Py_B,PyArray_FLOAT,1,2);
if (Py_X == NULL) return NULL;
if (csc) {
if (NCFormat_from_spMatrix(&A, N, N, nnz, nzvals, colind, rowptr, PyArray_FLOAT)) {
Py_DECREF(Py_X);
return NULL;
}
}
else {
if (NRFormat_from_spMatrix(&A, N, N, nnz, nzvals, colind, rowptr, PyArray_FLOAT)) {
Py_DECREF(Py_X);
return NULL;
}
}
if (DenseSuper_from_Numeric(&B, Py_X)) {
Destroy_SuperMatrix_Store(&A);
Py_DECREF(Py_X);
return NULL;
}
/* B and Py_X share same data now but Py_X "owns" it */
/* Setup options */
if (setjmp(_superlu_py_jmpbuf)) goto fail;
else {
perm_c = intMalloc(N);
perm_r = intMalloc(N);
set_default_options(&options);
options.ColPerm=superlu_module_getpermc(permc_spec);
StatInit(&stat);
/* Compute direct inverse of sparse Matrix */
sgssv(&options, &A, perm_c, perm_r, &L, &U, &B, &stat, &info);
}
SUPERLU_FREE(perm_r);
SUPERLU_FREE(perm_c);
Destroy_SuperMatrix_Store(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
StatFree(&stat);
return Py_BuildValue("Ni", Py_X, info);
fail:
SUPERLU_FREE(perm_r);
SUPERLU_FREE(perm_c);
Destroy_SuperMatrix_Store(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
StatFree(&stat);
Py_XDECREF(Py_X);
return NULL;
}
int main(int argc, char *argv[])
{
void smatvec_mult(float alpha, float x[], float beta, float y[]);
void spsolve(int n, float x[], float y[]);
extern int sfgmr( int n,
void (*matvec_mult)(float, float [], float, float []),
void (*psolve)(int n, float [], float[]),
float *rhs, float *sol, double tol, int restrt, int *itmax,
FILE *fits);
extern int sfill_diag(int n, NCformat *Astore);
char equed[1] = {'B'};
yes_no_t equil;
trans_t trans;
SuperMatrix A, L, U;
SuperMatrix B, X;
NCformat *Astore;
NCformat *Ustore;
SCformat *Lstore;
GlobalLU_t Glu; /* facilitate multiple factorizations with
SamePattern_SameRowPerm */
float *a;
int *asub, *xa;
int *etree;
int *perm_c; /* column permutation vector */
int *perm_r; /* row permutations from partial pivoting */
int nrhs, ldx, lwork, info, m, n, nnz;
float *rhsb, *rhsx, *xact;
float *work = NULL;
float *R, *C;
float u, rpg, rcond;
float zero = 0.0;
float one = 1.0;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
FILE *fp = stdin;
int restrt, iter, maxit, i;
double resid;
float *x, *b;
#ifdef DEBUG
extern int num_drop_L, num_drop_U;
#endif
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Defaults */
lwork = 0;
nrhs = 1;
trans = NOTRANS;
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 0.1; //different from complete LU
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
options.RowPerm = LargeDiag;
options.ILU_DropTol = 1e-4;
options.ILU_FillTol = 1e-2;
options.ILU_FillFactor = 10.0;
options.ILU_DropRule = DROP_BASIC | DROP_AREA;
options.ILU_Norm = INF_NORM;
options.ILU_MILU = SILU;
*/
ilu_set_default_options(&options);
/* Modify the defaults. */
options.PivotGrowth = YES; /* Compute reciprocal pivot growth */
options.ConditionNumber = YES;/* Compute reciprocal condition number */
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) ABORT("Malloc fails for work[].");
}
/* Read matrix A from a file in Harwell-Boeing format.*/
if (argc < 2)
{
printf("Usage:\n%s [OPTION] < [INPUT] > [OUTPUT]\nOPTION:\n"
"-h -hb:\n\t[INPUT] is a Harwell-Boeing format matrix.\n"
"-r -rb:\n\t[INPUT] is a Rutherford-Boeing format matrix.\n"
"-t -triplet:\n\t[INPUT] is a triplet format matrix.\n",
argv[0]);
return 0;
}
else
{
switch (argv[1][1])
{
case 'H':
case 'h':
printf("Input a Harwell-Boeing format matrix:\n");
sreadhb(fp, &m, &n, &nnz, &a, &asub, &xa);
break;
case 'R':
case 'r':
printf("Input a Rutherford-Boeing format matrix:\n");
sreadrb(&m, &n, &nnz, &a, &asub, &xa);
break;
case 'T':
case 't':
printf("Input a triplet format matrix:\n");
sreadtriple(&m, &n, &nnz, &a, &asub, &xa);
break;
default:
printf("Unrecognized format.\n");
return 0;
}
}
sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa,
SLU_NC, SLU_S, SLU_GE);
Astore = A.Store;
sfill_diag(n, Astore);
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
fflush(stdout);
/* Generate the right-hand side */
if ( !(rhsb = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsx = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
sCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE);
sCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE);
xact = floatMalloc(n * nrhs);
ldx = n;
sGenXtrue(n, nrhs, xact, ldx);
sFillRHS(trans, nrhs, xact, ldx, &A, &B);
if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for C[].");
info = 0;
#ifdef DEBUG
num_drop_L = 0;
num_drop_U = 0;
#endif
/* Initialize the statistics variables. */
StatInit(&stat);
/* Compute the incomplete factorization and compute the condition number
and pivot growth using dgsisx. */
B.ncol = 0; /* not to perform triangular solution */
sgsisx(&options, &A, perm_c, perm_r, etree, equed, R, C, &L, &U, work,
lwork, &B, &X, &rpg, &rcond, &Glu, &mem_usage, &stat, &info);
/* Set RHS for GMRES. */
if (!(b = floatMalloc(m))) ABORT("Malloc fails for b[].");
if (*equed == 'R' || *equed == 'B') {
for (i = 0; i < n; ++i) b[i] = rhsb[i] * R[i];
} else {
for (i = 0; i < m; i++) b[i] = rhsb[i];
}
printf("sgsisx(): info %d, equed %c\n", info, equed[0]);
if (info > 0 || rcond < 1e-8 || rpg > 1e8)
printf("WARNING: This preconditioner might be unstable.\n");
if ( info == 0 || info == n+1 ) {
if ( options.PivotGrowth == YES )
printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber == YES )
printf("Recip. condition number = %e\n", rcond);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("n(A) = %d, nnz(A) = %d\n", n, Astore->nnz);
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("Fill ratio: nnz(F)/nnz(A) = %.3f\n",
((double)(Lstore->nnz) + (double)(Ustore->nnz) - (double)n)
/ (double)Astore->nnz);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
fflush(stdout);
/* Set the global variables. */
GLOBAL_A = &A;
GLOBAL_L = &L;
GLOBAL_U = &U;
GLOBAL_STAT = &stat;
GLOBAL_PERM_C = perm_c;
GLOBAL_PERM_R = perm_r;
GLOBAL_OPTIONS = &options;
GLOBAL_R = R;
GLOBAL_C = C;
GLOBAL_MEM_USAGE = &mem_usage;
/* Set the options to do solve-only. */
options.Fact = FACTORED;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
/* Set the variables used by GMRES. */
restrt = SUPERLU_MIN(n / 3 + 1, 50);
maxit = 1000;
iter = maxit;
resid = 1e-8;
if (!(x = floatMalloc(n))) ABORT("Malloc fails for x[].");
if (info <= n + 1)
{
int i_1 = 1;
double maxferr = 0.0, nrmA, nrmB, res, t;
float temp;
extern float snrm2_(int *, float [], int *);
extern void saxpy_(int *, float *, float [], int *, float [], int *);
/* Initial guess */
for (i = 0; i < n; i++) x[i] = zero;
t = SuperLU_timer_();
/* Call GMRES */
sfgmr(n, smatvec_mult, spsolve, b, x, resid, restrt, &iter, stdout);
t = SuperLU_timer_() - t;
/* Output the result. */
nrmA = snrm2_(&(Astore->nnz), (float *)((DNformat *)A.Store)->nzval,
&i_1);
nrmB = snrm2_(&m, b, &i_1);
sp_sgemv("N", -1.0, &A, x, 1, 1.0, b, 1);
res = snrm2_(&m, b, &i_1);
resid = res / nrmB;
printf("||A||_F = %.1e, ||B||_2 = %.1e, ||B-A*X||_2 = %.1e, "
"relres = %.1e\n", nrmA, nrmB, res, resid);
if (iter >= maxit)
{
if (resid >= 1.0) iter = -180;
else if (resid > 1e-8) iter = -111;
}
printf("iteration: %d\nresidual: %.1e\nGMRES time: %.2f seconds.\n",
iter, resid, t);
/* Scale the solution back if equilibration was performed. */
if (*equed == 'C' || *equed == 'B')
for (i = 0; i < n; i++) x[i] *= C[i];
for (i = 0; i < m; i++) {
maxferr = SUPERLU_MAX(maxferr, fabs(x[i] - xact[i]));
}
printf("||X-X_true||_oo = %.1e\n", maxferr);
}
#ifdef DEBUG
printf("%d entries in L and %d entries in U dropped.\n",
num_drop_L, num_drop_U);
#endif
fflush(stdout);
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (rhsb);
SUPERLU_FREE (rhsx);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
if ( lwork >= 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
SUPERLU_FREE(b);
SUPERLU_FREE(x);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
return 0;
}
int main ( int argc, char *argv[] )
/**********************************************************************/
/*
Purpose:
SUPER_LU_D0 runs a small 5 by 5 example of the use of SUPER_LU.
Modified:
23 April 2004
Reference:
James Demmel, John Gilbert, Xiaoye Li,
SuperLU Users's Guide,
Sections 1 and 2.
*/
{
double *a;
SuperMatrix A;
int *asub;
SuperMatrix B;
int i;
int info;
SuperMatrix L;
int m;
int n;
int nnz;
int nrhs;
superlu_options_t options;
int *perm_c;
int *perm_r;
int permc_spec;
double *rhs;
double sol[5];
SuperLUStat_t stat;
SuperMatrix U;
int *xa;
/*
Say hello.
*/
printf ( "\n" );
printf ( "SUPER_LU_D0:\n" );
printf ( " Simple 5 by 5 example of SUPER_LU solver.\n" );
/*
Initialize parameters.
*/
m = 5;
n = 5;
nnz = 12;
/*
Set aside space for the arrays.
*/
a = doubleMalloc ( nnz );
if ( !a )
{
ABORT ( "Malloc fails for a[]." );
}
asub = intMalloc ( nnz );
if ( !asub )
{
ABORT ( "Malloc fails for asub[]." );
}
xa = intMalloc ( n+1 );
if ( !xa )
{
ABORT ( "Malloc fails for xa[]." );
}
/*
Initialize matrix A.
*/
a[0] = 19.0;
a[1] = 12.0;
a[2] = 12.0;
a[3] = 21.0;
a[4] = 12.0;
a[5] = 12.0;
a[6] = 21.0;
a[7] = 16.0;
a[8] = 21.0;
a[9] = 5.0;
a[10]= 21.0;
a[11]= 18.0;
asub[0] = 0;
asub[1] = 1;
asub[2] = 4;
asub[3] = 1;
asub[4] = 2;
asub[5] = 4;
asub[6] = 0;
asub[7] = 2;
asub[8] = 0;
asub[9] = 3;
asub[10]= 3;
asub[11]= 4;
xa[0] = 0;
xa[1] = 3;
xa[2] = 6;
xa[3] = 8;
xa[4] = 10;
xa[5] = 12;
sol[0] = -0.031250000;
sol[1] = 0.065476190;
sol[2] = 0.013392857;
sol[3] = 0.062500000;
sol[4] = 0.032738095;
/*
Create matrix A in the format expected by SuperLU.
*/
dCreate_CompCol_Matrix ( &A, m, n, nnz, a, asub, xa, SLU_NC, SLU_D, SLU_GE );
/*
Create the right-hand side matrix B.
*/
nrhs = 1;
rhs = doubleMalloc ( m * nrhs );
if ( !rhs )
{
ABORT("Malloc fails for rhs[].");
}
for ( i = 0; i < m; i++ )
{
rhs[i] = 1.0;
}
dCreate_Dense_Matrix ( &B, m, nrhs, rhs, m, SLU_DN, SLU_D, SLU_GE );
/*
Set up the arrays for the permutations.
*/
perm_r = intMalloc ( m );
if ( !perm_r )
{
ABORT ( "Malloc fails for perm_r[]." );
}
perm_c = intMalloc ( n );
if ( !perm_c )
{
ABORT ( "Malloc fails for perm_c[]." );
}
/*
Set the default input options, and then adjust some of them.
*/
set_default_options ( &options );
options.ColPerm = NATURAL;
/*
Initialize the statistics variables.
*/
StatInit ( &stat );
/*
Factor the matrix and solve the linear system.
*/
dgssv ( &options, &A, perm_c, perm_r, &L, &U, &B, &stat, &info );
/*
Print some of the results.
*/
dPrint_CompCol_Matrix ( "Matrix A", &A );
dPrint_SuperNode_Matrix ( "Factor L", &L );
dPrint_CompCol_Matrix ( "Factor U", &U );
dPrint_Dense_Matrix ( "Solution X", &B );
printf ( "\n" );
printf ( " The exact solution:\n" );
printf ( "\n" );
for ( i = 0; i < n; i++ )
{
printf ( "%d %f\n", i, sol[i] );
}
printf ( "\n" );
print_int_vec ( "perm_r", m, perm_r );
/*
De-allocate storage.
*/
SUPERLU_FREE ( rhs );
SUPERLU_FREE ( perm_r );
SUPERLU_FREE ( perm_c );
Destroy_CompCol_Matrix ( &A );
Destroy_SuperMatrix_Store ( &B );
Destroy_SuperNode_Matrix ( &L );
Destroy_CompCol_Matrix ( &U );
StatFree ( &stat );
printf ( "\n" );
printf ( "SUPER_LU_D0:\n" );
printf ( " Normal end of execution.\n" );
return 0;
}
