/*! \brief Solves one of the systems of equations A*x = b, or A'*x = b
*
* <pre>
* Purpose
* =======
*
* sp_ztrsv() solves one of the systems of equations
* A*x = b, or A'*x = b,
* where b and x are n element vectors and A is a sparse unit , or
* non-unit, upper or lower triangular matrix.
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* Parameters
* ==========
*
* uplo - (input) char*
* On entry, uplo specifies whether the matrix is an upper or
* lower triangular matrix as follows:
* uplo = 'U' or 'u' A is an upper triangular matrix.
* uplo = 'L' or 'l' A is a lower triangular matrix.
*
* trans - (input) char*
* On entry, trans specifies the equations to be solved as
* follows:
* trans = 'N' or 'n' A*x = b.
* trans = 'T' or 't' A'*x = b.
* trans = 'C' or 'c' A^H*x = b.
*
* diag - (input) char*
* On entry, diag specifies whether or not A is unit
* triangular as follows:
* diag = 'U' or 'u' A is assumed to be unit triangular.
* diag = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* L - (input) SuperMatrix*
* The factor L from the factorization Pr*A*Pc=L*U. Use
* compressed row subscripts storage for supernodes,
* i.e., L has types: Stype = SC, Dtype = SLU_Z, Mtype = TRLU.
*
* U - (input) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U.
* U has types: Stype = NC, Dtype = SLU_Z, Mtype = TRU.
*
* x - (input/output) doublecomplex*
* Before entry, the incremented array X must contain the n
* element right-hand side vector b. On exit, X is overwritten
* with the solution vector x.
*
* info - (output) int*
* If *info = -i, the i-th argument had an illegal value.
* </pre>
*/
int
sp_ztrsv(char *uplo, char *trans, char *diag, SuperMatrix *L,
SuperMatrix *U, doublecomplex *x, SuperLUStat_t *stat, int *info)
{
#ifdef _CRAY
_fcd ftcs1 = _cptofcd("L", strlen("L")),
ftcs2 = _cptofcd("N", strlen("N")),
ftcs3 = _cptofcd("U", strlen("U"));
#endif
SCformat *Lstore;
NCformat *Ustore;
doublecomplex *Lval, *Uval;
int incx = 1, incy = 1;
doublecomplex temp;
doublecomplex alpha = {1.0, 0.0}, beta = {1.0, 0.0};
doublecomplex comp_zero = {0.0, 0.0};
int nrow;
int fsupc, nsupr, nsupc, luptr, istart, irow;
int i, k, iptr, jcol;
doublecomplex *work;
flops_t solve_ops;
/* Test the input parameters */
*info = 0;
if ( strncmp(uplo,"L", 1)!=0 && strncmp(uplo, "U", 1)!=0 ) *info = -1;
else if ( strncmp(trans, "N", 1)!=0 && strncmp(trans, "T", 1)!=0 &&
strncmp(trans, "C", 1)!=0) *info = -2;
else if ( strncmp(diag, "U", 1)!=0 && strncmp(diag, "N", 1)!=0 )
*info = -3;
else if ( L->nrow != L->ncol || L->nrow < 0 ) *info = -4;
else if ( U->nrow != U->ncol || U->nrow < 0 ) *info = -5;
if ( *info ) {
i = -(*info);
input_error("sp_ztrsv", &i);
return 0;
}
Lstore = L->Store;
Lval = Lstore->nzval;
Ustore = U->Store;
Uval = Ustore->nzval;
solve_ops = 0;
if ( !(work = doublecomplexCalloc(L->nrow)) )
ABORT("Malloc fails for work in sp_ztrsv().");
if ( strncmp(trans, "N", 1)==0 ) { /* Form x := inv(A)*x. */
if ( strncmp(uplo, "L", 1)==0 ) {
/* Form x := inv(L)*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
nrow = nsupr - nsupc;
/* 1 z_div costs 10 flops */
solve_ops += 4 * nsupc * (nsupc - 1) + 10 * nsupc;
solve_ops += 8 * nrow * nsupc;
if ( nsupc == 1 ) {
for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); ++iptr) {
irow = L_SUB(iptr);
++luptr;
zz_mult(&comp_zero, &x[fsupc], &Lval[luptr]);
z_sub(&x[irow], &x[irow], &comp_zero);
}
} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
CGEMV(ftcs2, &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#else
ztrsv_("L", "N", "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
zgemv_("N", &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#endif
#else
zlsolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc]);
zmatvec ( nsupr, nsupr-nsupc, nsupc, &Lval[luptr+nsupc],
&x[fsupc], &work[0] );
#endif
iptr = istart + nsupc;
for (i = 0; i < nrow; ++i, ++iptr) {
irow = L_SUB(iptr);
z_sub(&x[irow], &x[irow], &work[i]); /* Scatter */
work[i] = comp_zero;
}
}
} /* for k ... */
} else {
/* Form x := inv(U)*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; k--) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
/* 1 z_div costs 10 flops */
solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
if ( nsupc == 1 ) {
z_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
for (i = U_NZ_START(fsupc); i < U_NZ_START(fsupc+1); ++i) {
irow = U_SUB(i);
zz_mult(&comp_zero, &x[fsupc], &Uval[i]);
z_sub(&x[irow], &x[irow], &comp_zero);
}
} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV(ftcs3, ftcs2, ftcs2, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ztrsv_("U", "N", "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
#else
zusolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc] );
#endif
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1);
i++) {
irow = U_SUB(i);
zz_mult(&comp_zero, &x[jcol], &Uval[i]);
z_sub(&x[irow], &x[irow], &comp_zero);
}
}
}
} /* for k ... */
}
} else if ( strncmp(trans, "T", 1)==0 ) { /* Form x := inv(A')*x */
if ( strncmp(uplo, "L", 1)==0 ) {
/* Form x := inv(L')*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; --k) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
solve_ops += 8 * (nsupr - nsupc) * nsupc;
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
iptr = istart + nsupc;
for (i = L_NZ_START(jcol) + nsupc;
i < L_NZ_START(jcol+1); i++) {
irow = L_SUB(iptr);
zz_mult(&comp_zero, &x[irow], &Lval[i]);
z_sub(&x[jcol], &x[jcol], &comp_zero);
iptr++;
}
}
if ( nsupc > 1 ) {
solve_ops += 4 * nsupc * (nsupc - 1);
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("T", strlen("T"));
ftcs3 = _cptofcd("U", strlen("U"));
CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ztrsv_("L", "T", "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
}
} else {
/* Form x := inv(U')*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
irow = U_SUB(i);
zz_mult(&comp_zero, &x[irow], &Uval[i]);
z_sub(&x[jcol], &x[jcol], &comp_zero);
}
}
/* 1 z_div costs 10 flops */
solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
if ( nsupc == 1 ) {
z_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
} else {
#ifdef _CRAY
ftcs1 = _cptofcd("U", strlen("U"));
ftcs2 = _cptofcd("T", strlen("T"));
ftcs3 = _cptofcd("N", strlen("N"));
CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ztrsv_("U", "T", "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
} /* for k ... */
}
} else { /* Form x := conj(inv(A'))*x */
if ( strncmp(uplo, "L", 1)==0 ) {
/* Form x := conj(inv(L'))*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; --k) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
solve_ops += 8 * (nsupr - nsupc) * nsupc;
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
iptr = istart + nsupc;
for (i = L_NZ_START(jcol) + nsupc;
i < L_NZ_START(jcol+1); i++) {
irow = L_SUB(iptr);
zz_conj(&temp, &Lval[i]);
zz_mult(&comp_zero, &x[irow], &temp);
z_sub(&x[jcol], &x[jcol], &comp_zero);
iptr++;
}
}
if ( nsupc > 1 ) {
solve_ops += 4 * nsupc * (nsupc - 1);
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd(trans, strlen("T"));
ftcs3 = _cptofcd("U", strlen("U"));
ZTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ztrsv_("L", trans, "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
}
} else {
/* Form x := conj(inv(U'))*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
irow = U_SUB(i);
zz_conj(&temp, &Uval[i]);
zz_mult(&comp_zero, &x[irow], &temp);
z_sub(&x[jcol], &x[jcol], &comp_zero);
}
}
/* 1 z_div costs 10 flops */
solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
if ( nsupc == 1 ) {
zz_conj(&temp, &Lval[luptr]);
z_div(&x[fsupc], &x[fsupc], &temp);
} else {
#ifdef _CRAY
ftcs1 = _cptofcd("U", strlen("U"));
ftcs2 = _cptofcd(trans, strlen("T"));
ftcs3 = _cptofcd("N", strlen("N"));
ZTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ztrsv_("U", trans, "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
} /* for k ... */
}
}
stat->ops[SOLVE] += solve_ops;
SUPERLU_FREE(work);
return 0;
}
float
sPivotGrowth(int ncols, SuperMatrix *A, int *perm_c,
SuperMatrix *L, SuperMatrix *U)
{
/*
* -- SuperLU MT routine (version 2.0) --
* Lawrence Berkeley National Lab, Univ. of California Berkeley,
* and Xerox Palo Alto Research Center.
* September 10, 2007
*
*
* Purpose
* =======
*
* Compute the reciprocal pivot growth factor of the leading ncols columns
* of the matrix, using the formula:
* min_j ( max_i(abs(A_ij)) / max_i(abs(U_ij)) )
*
* Arguments
* =========
*
* ncols (input) int
* The number of columns of matrices A, L and U.
*
* A (input) SuperMatrix*
* Original matrix A, permuted by columns, of dimension
* (A->nrow, A->ncol). The type of A can be:
* Stype = NC; Dtype = _D; Mtype = GE.
*
* L (output) SuperMatrix*
* The factor L from the factorization Pr*A=L*U; use compressed row
* subscripts storage for supernodes, i.e., L has type:
* Stype = SC; Dtype = _D; Mtype = TRLU.
*
* U (output) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U. Use column-wise
* storage scheme, i.e., U has types: Stype = NC;
* Dtype = _D; Mtype = TRU.
*
*/
NCformat *Astore;
SCPformat *Lstore;
NCPformat *Ustore;
float *Aval, *Lval, *Uval;
int fsupc, nsupr, luptr, nz_in_U;
int i, j, k, oldcol;
int *inv_perm_c;
float rpg, maxaj, maxuj;
extern double slamch_(char *);
float smlnum;
float *luval;
/* Get machine constants. */
smlnum = slamch_("S");
rpg = 1. / smlnum;
Astore = A->Store;
Lstore = L->Store;
Ustore = U->Store;
Aval = Astore->nzval;
Lval = Lstore->nzval;
Uval = Ustore->nzval;
inv_perm_c = (int *) SUPERLU_MALLOC( (size_t) A->ncol*sizeof(int) );
for (j = 0; j < A->ncol; ++j) inv_perm_c[perm_c[j]] = j;
for (k = 0; k <= Lstore->nsuper; ++k) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_END(fsupc) - L_SUB_START(fsupc);
luptr = L_NZ_START(fsupc);
luval = &Lval[luptr];
nz_in_U = 1;
for (j = fsupc; j < L_LAST_SUPC(k) && j < ncols; ++j) {
maxaj = 0.;
oldcol = inv_perm_c[j];
for (i = Astore->colptr[oldcol]; i < Astore->colptr[oldcol+1]; i++)
maxaj = SUPERLU_MAX( maxaj, fabs(Aval[i]) );
maxuj = 0.;
for (i = Ustore->colbeg[j]; i < Ustore->colend[j]; i++)
maxuj = SUPERLU_MAX( maxuj, fabs(Uval[i]) );
/* Supernode */
for (i = 0; i < nz_in_U; ++i)
maxuj = SUPERLU_MAX( maxuj, fabs(luval[i]) );
++nz_in_U;
luval += nsupr;
if ( maxuj == 0. )
rpg = SUPERLU_MIN( rpg, 1.);
else
rpg = SUPERLU_MIN( rpg, maxaj / maxuj );
}
if ( j >= ncols ) break;
}
SUPERLU_FREE(inv_perm_c);
return (rpg);
}
/*! \brief
*
* <pre>
* Create the distributed modified sparse row (MSR) matrix: bindx/val.
* For a submatrix of size m-by-n, the MSR arrays are as follows:
* bindx[0] = m + 1
* bindx[0..m] = pointer to start of each row
* bindx[ks..ke] = column indices of the off-diagonal nonzeros in row k,
* where, ks = bindx[k], ke = bindx[k+1]-1
* val[k] = A(k,k), k < m, diagonal elements
* val[m] = not used
* val[ki] = A(k, bindx[ki]), where ks <= ki <= ke
* Both arrays are of length nnz + 1.
* </pre>
*/
static void dcreate_msr_matrix
(
SuperMatrix *A, /* Matrix A permuted by columns (input).
The type of A can be:
Stype = SLU_NCP; Dtype = SLU_D; Mtype = SLU_GE. */
int_t update[], /* input (local) */
int_t N_update, /* input (local) */
double **val, /* output */
int_t **bindx /* output */
)
{
int hi, i, irow, j, k, lo, n, nnz_local, nnz_diag;
NCPformat *Astore;
double *nzval;
int_t *rowcnt;
double zero = 0.0;
if ( !N_update ) return;
n = A->ncol;
Astore = A->Store;
nzval = Astore->nzval;
/* One pass of original matrix A to count nonzeros of each row. */
if ( !(rowcnt = (int_t *) intCalloc_dist(N_update)) )
ABORT("Malloc fails for rowcnt[]");
lo = update[0];
hi = update[N_update-1];
nnz_local = 0;
nnz_diag = 0;
for (j = 0; j < n; ++j) {
for (i = Astore->colbeg[j]; i < Astore->colend[j]; ++i) {
irow = Astore->rowind[i];
if ( irow >= lo && irow <= hi ) {
if ( irow != j ) /* Exclude diagonal */
++rowcnt[irow - lo];
else ++nnz_diag; /* Count nonzero diagonal entries */
++nnz_local;
}
}
}
/* Add room for the logical diagonal zeros which are not counted
in nnz_local. */
nnz_local += (N_update - nnz_diag);
/* Allocate storage for bindx[] and val[]. */
if ( !(*val = (double *) doubleMalloc_dist(nnz_local+1)) )
ABORT("Malloc fails for val[]");
for (i = 0; i < N_update; ++i) (*val)[i] = zero; /* Initialize diagonal */
if ( !(*bindx = (int_t *) SUPERLU_MALLOC((nnz_local+1) * sizeof(int_t))) )
ABORT("Malloc fails for bindx[]");
/* Set up row pointers. */
(*bindx)[0] = N_update + 1;
for (j = 1; j <= N_update; ++j) {
(*bindx)[j] = (*bindx)[j-1] + rowcnt[j-1];
rowcnt[j-1] = (*bindx)[j-1];
}
/* One pass of original matrix A to fill in matrix entries. */
for (j = 0; j < n; ++j) {
for (i = Astore->colbeg[j]; i < Astore->colend[j]; ++i) {
irow = Astore->rowind[i];
if ( irow >= lo && irow <= hi ) {
if ( irow == j ) /* Diagonal */
(*val)[irow - lo] = nzval[i];
else {
irow -= lo;
k = rowcnt[irow];
(*bindx)[k] = j;
(*val)[k] = nzval[i];
++rowcnt[irow];
}
}
}
}
SUPERLU_FREE(rowcnt);
}
void f_destroy_SuperLUStat_handle(fptr *handle)
{
SUPERLU_FREE((void *)*handle);
}
void f_destroy_options_handle(fptr *handle)
{
SUPERLU_FREE((void *)*handle);
}
int main(int argc, char *argv[])
{
superlu_options_t options;
SuperLUStat_t stat;
SuperMatrix A;
ScalePermstruct_t ScalePermstruct;
LUstruct_t LUstruct;
gridinfo_t grid;
double *berr;
doublecomplex *a, *b, *b1, *xtrue;
int_t *asub, *xa;
int_t i, j, m, n, nnz;
int_t nprow, npcol;
int iam, info, ldb, ldx, nrhs;
char trans[1];
char **cpp, c;
FILE *fp, *fopen();
extern int cpp_defs();
nprow = 1; /* Default process rows. */
npcol = 1; /* Default process columns. */
nrhs = 1; /* Number of right-hand side. */
/* ------------------------------------------------------------
INITIALIZE MPI ENVIRONMENT.
------------------------------------------------------------*/
MPI_Init( &argc, &argv );
/* Parse command line argv[]. */
for (cpp = argv+1; *cpp; ++cpp) {
if ( **cpp == '-' ) {
c = *(*cpp+1);
++cpp;
switch (c) {
case 'h':
printf("Options:\n");
printf("\t-r <int>: process rows (default %d)\n", nprow);
printf("\t-c <int>: process columns (default %d)\n", npcol);
exit(0);
break;
case 'r': nprow = atoi(*cpp);
break;
case 'c': npcol = atoi(*cpp);
break;
}
} else { /* Last arg is considered a filename */
if ( !(fp = fopen(*cpp, "r")) ) {
ABORT("File does not exist");
}
break;
}
}
/* ------------------------------------------------------------
INITIALIZE THE SUPERLU PROCESS GRID.
------------------------------------------------------------*/
superlu_gridinit(MPI_COMM_WORLD, nprow, npcol, &grid);
/* Bail out if I do not belong in the grid. */
iam = grid.iam;
if ( iam >= nprow * npcol )
goto out;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter main()");
#endif
/* ------------------------------------------------------------
PROCESS 0 READS THE MATRIX A, AND THEN BROADCASTS IT TO ALL
THE OTHER PROCESSES.
------------------------------------------------------------*/
if ( !iam ) {
/* Print the CPP definitions. */
cpp_defs();
/* Read the matrix stored on disk in Harwell-Boeing format. */
zreadhb_dist(iam, fp, &m, &n, &nnz, &a, &asub, &xa);
printf("Input matrix file: %s\n", *cpp);
printf("\tDimension\t%dx%d\t # nonzeros %d\n", m, n, nnz);
printf("\tProcess grid\t%d X %d\n", grid.nprow, grid.npcol);
/* Broadcast matrix A to the other PEs. */
MPI_Bcast( &m, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( &n, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( &nnz, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( a, nnz, SuperLU_MPI_DOUBLE_COMPLEX, 0, grid.comm );
MPI_Bcast( asub, nnz, mpi_int_t, 0, grid.comm );
MPI_Bcast( xa, n+1, mpi_int_t, 0, grid.comm );
} else {
/* Receive matrix A from PE 0. */
MPI_Bcast( &m, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( &n, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( &nnz, 1, mpi_int_t, 0, grid.comm );
/* Allocate storage for compressed column representation. */
zallocateA_dist(n, nnz, &a, &asub, &xa);
MPI_Bcast( a, nnz, SuperLU_MPI_DOUBLE_COMPLEX, 0, grid.comm );
MPI_Bcast( asub, nnz, mpi_int_t, 0, grid.comm );
MPI_Bcast( xa, n+1, mpi_int_t, 0, grid.comm );
}
/* Create compressed column matrix for A. */
zCreate_CompCol_Matrix_dist(&A, m, n, nnz, a, asub, xa,
SLU_NC, SLU_Z, SLU_GE);
/* Generate the exact solution and compute the right-hand side. */
if ( !(b = doublecomplexMalloc_dist(m * nrhs)) ) ABORT("Malloc fails for b[]");
if ( !(b1 = doublecomplexMalloc_dist(m * nrhs)) ) ABORT("Malloc fails for b1[]");
if ( !(xtrue = doublecomplexMalloc_dist(n*nrhs)) ) ABORT("Malloc fails for xtrue[]");
*trans = 'N';
ldx = n;
ldb = m;
zGenXtrue_dist(n, nrhs, xtrue, ldx);
zFillRHS_dist(trans, nrhs, xtrue, ldx, &A, b, ldb);
for (j = 0; j < nrhs; ++j)
for (i = 0; i < m; ++i) b1[i+j*ldb] = b[i+j*ldb];
if ( !(berr = doubleMalloc_dist(nrhs)) )
ABORT("Malloc fails for berr[].");
/* ------------------------------------------------------------
WE SOLVE THE LINEAR SYSTEM FOR THE FIRST TIME.
------------------------------------------------------------*/
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = METIS_AT_PLUS_A;
options.RowPerm = LargeDiag;
options.ReplaceTinyPivot = YES;
options.Trans = NOTRANS;
options.IterRefine = DOUBLE;
options.SolveInitialized = NO;
options.RefineInitialized = NO;
options.PrintStat = YES;
*/
set_default_options_dist(&options);
if (!iam) {
print_sp_ienv_dist(&options);
print_options_dist(&options);
}
/* Initialize ScalePermstruct and LUstruct. */
ScalePermstructInit(m, n, &ScalePermstruct);
LUstructInit(n, &LUstruct);
/* Initialize the statistics variables. */
PStatInit(&stat);
/* Call the linear equation solver: factorize and solve. */
pzgssvx_ABglobal(&options, &A, &ScalePermstruct, b, ldb, nrhs, &grid,
&LUstruct, berr, &stat, &info);
/* Check the accuracy of the solution. */
if ( !iam ) {
zinf_norm_error_dist(n, nrhs, b, ldb, xtrue, ldx, &grid);
}
PStatPrint(&options, &stat, &grid); /* Print the statistics. */
PStatFree(&stat);
/* ------------------------------------------------------------
NOW WE SOLVE ANOTHER SYSTEM WITH THE SAME A BUT DIFFERENT
RIGHT-HAND SIDE, WE WILL USE THE EXISTING L AND U FACTORS IN
LUSTRUCT OBTAINED FROM A PREVIOUS FATORIZATION.
------------------------------------------------------------*/
options.Fact = FACTORED; /* Indicate the factored form of A is supplied. */
PStatInit(&stat); /* Initialize the statistics variables. */
pzgssvx_ABglobal(&options, &A, &ScalePermstruct, b1, ldb, nrhs, &grid,
&LUstruct, berr, &stat, &info);
/* Check the accuracy of the solution. */
if ( !iam ) {
printf("Solve the system with a different B.\n");
zinf_norm_error_dist(n, nrhs, b1, ldb, xtrue, ldx, &grid);
}
/* Print the statistics. */
PStatPrint(&options, &stat, &grid);
/* ------------------------------------------------------------
DEALLOCATE STORAGE.
------------------------------------------------------------*/
PStatFree(&stat);
Destroy_CompCol_Matrix_dist(&A);
Destroy_LU(n, &grid, &LUstruct);
ScalePermstructFree(&ScalePermstruct);
LUstructFree(&LUstruct);
SUPERLU_FREE(b);
SUPERLU_FREE(b1);
SUPERLU_FREE(xtrue);
SUPERLU_FREE(berr);
/* ------------------------------------------------------------
RELEASE THE SUPERLU PROCESS GRID.
------------------------------------------------------------*/
out:
superlu_gridexit(&grid);
/* ------------------------------------------------------------
TERMINATES THE MPI EXECUTION ENVIRONMENT.
------------------------------------------------------------*/
MPI_Finalize();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit main()");
#endif
}
void f_destroy_SOLVEstruct_handle(fptr *handle)
{
SUPERLU_FREE((void *)*handle);
}
void
zgstrf (superlu_options_t *options, SuperMatrix *A, double drop_tol,
int relax, int panel_size, int *etree, void *work, int lwork,
int *perm_c, int *perm_r, SuperMatrix *L, SuperMatrix *U,
SuperLUStat_t *stat, int *info)
{
/* Local working arrays */
NCPformat *Astore;
int *iperm_r = NULL; /* inverse of perm_r; used when
options->Fact == SamePattern_SameRowPerm */
int *iperm_c; /* inverse of perm_c */
int *iwork;
doublecomplex *zwork;
int *segrep, *repfnz, *parent, *xplore;
int *panel_lsub; /* dense[]/panel_lsub[] pair forms a w-wide SPA */
int *xprune;
int *marker;
doublecomplex *dense, *tempv;
int *relax_end;
doublecomplex *a;
int *asub;
int *xa_begin, *xa_end;
int *xsup, *supno;
int *xlsub, *xlusup, *xusub;
int nzlumax;
static GlobalLU_t Glu; /* persistent to facilitate multiple factors. */
/* Local scalars */
fact_t fact = options->Fact;
double diag_pivot_thresh = options->DiagPivotThresh;
int pivrow; /* pivotal row number in the original matrix A */
int nseg1; /* no of segments in U-column above panel row jcol */
int nseg; /* no of segments in each U-column */
register int jcol;
register int kcol; /* end column of a relaxed snode */
register int icol;
register int i, k, jj, new_next, iinfo;
int m, n, min_mn, jsupno, fsupc, nextlu, nextu;
int w_def; /* upper bound on panel width */
int usepr, iperm_r_allocated = 0;
int nnzL, nnzU;
int *panel_histo = stat->panel_histo;
flops_t *ops = stat->ops;
iinfo = 0;
m = A->nrow;
n = A->ncol;
min_mn = SUPERLU_MIN(m, n);
Astore = A->Store;
a = Astore->nzval;
asub = Astore->rowind;
xa_begin = Astore->colbeg;
xa_end = Astore->colend;
/* Allocate storage common to the factor routines */
*info = zLUMemInit(fact, work, lwork, m, n, Astore->nnz,
panel_size, L, U, &Glu, &iwork, &zwork);
if ( *info ) return;
xsup = Glu.xsup;
supno = Glu.supno;
xlsub = Glu.xlsub;
xlusup = Glu.xlusup;
xusub = Glu.xusub;
SetIWork(m, n, panel_size, iwork, &segrep, &parent, &xplore,
&repfnz, &panel_lsub, &xprune, &marker);
zSetRWork(m, panel_size, zwork, &dense, &tempv);
usepr = (fact == SamePattern_SameRowPerm);
if ( usepr ) {
/* Compute the inverse of perm_r */
iperm_r = (int *) intMalloc(m);
for (k = 0; k < m; ++k) iperm_r[perm_r[k]] = k;
iperm_r_allocated = 1;
}
iperm_c = (int *) intMalloc(n);
for (k = 0; k < n; ++k) iperm_c[perm_c[k]] = k;
/* Identify relaxed snodes */
relax_end = (int *) intMalloc(n);
if ( options->SymmetricMode == YES ) {
heap_relax_snode(n, etree, relax, marker, relax_end);
} else {
relax_snode(n, etree, relax, marker, relax_end);
}
ifill (perm_r, m, EMPTY);
ifill (marker, m * NO_MARKER, EMPTY);
supno[0] = -1;
xsup[0] = xlsub[0] = xusub[0] = xlusup[0] = 0;
w_def = panel_size;
/*
* Work on one "panel" at a time. A panel is one of the following:
* (a) a relaxed supernode at the bottom of the etree, or
* (b) panel_size contiguous columns, defined by the user
*/
for (jcol = 0; jcol < min_mn; ) {
if ( relax_end[jcol] != EMPTY ) { /* start of a relaxed snode */
kcol = relax_end[jcol]; /* end of the relaxed snode */
panel_histo[kcol-jcol+1]++;
/* --------------------------------------
* Factorize the relaxed supernode(jcol:kcol)
* -------------------------------------- */
/* Determine the union of the row structure of the snode */
if ( (*info = zsnode_dfs(jcol, kcol, asub, xa_begin, xa_end,
xprune, marker, &Glu)) != 0 )
return;
nextu = xusub[jcol];
nextlu = xlusup[jcol];
jsupno = supno[jcol];
fsupc = xsup[jsupno];
new_next = nextlu + (xlsub[fsupc+1]-xlsub[fsupc])*(kcol-jcol+1);
nzlumax = Glu.nzlumax;
while ( new_next > nzlumax ) {
*info = zLUMemXpand(jcol, nextlu, LUSUP, &nzlumax, &Glu);
if ( (*info) )
return;
}
for (icol = jcol; icol<= kcol; icol++) {
xusub[icol+1] = nextu;
/* Scatter into SPA dense[*] */
for (k = xa_begin[icol]; k < xa_end[icol]; k++)
dense[asub[k]] = a[k];
/* Numeric update within the snode */
zsnode_bmod(icol, jsupno, fsupc, dense, tempv, &Glu, stat);
*info = zpivotL(icol, diag_pivot_thresh, &usepr, perm_r,iperm_r, iperm_c, &pivrow, &Glu, stat);
if ( (*info) )
if ( iinfo == 0 ) iinfo = *info;
#ifdef DEBUG
zprint_lu_col("[1]: ", icol, pivrow, xprune, &Glu);
#endif
}
jcol = icol;
} else { /* Work on one panel of panel_size columns */
/* Adjust panel_size so that a panel won't overlap with the next
* relaxed snode.
*/
panel_size = w_def;
for (k = jcol + 1; k < SUPERLU_MIN(jcol+panel_size, min_mn); k++)
if ( relax_end[k] != EMPTY ) {
panel_size = k - jcol;
break;
}
if ( k == min_mn ) panel_size = min_mn - jcol;
panel_histo[panel_size]++;
/* symbolic factor on a panel of columns */
zpanel_dfs(m, panel_size, jcol, A, perm_r, &nseg1,
dense, panel_lsub, segrep, repfnz, xprune,
marker, parent, xplore, &Glu);
/* numeric sup-panel updates in topological order */
zpanel_bmod(m, panel_size, jcol, nseg1, dense,
tempv, segrep, repfnz, &Glu, stat);
/* Sparse LU within the panel, and below panel diagonal */
for ( jj = jcol; jj < jcol + panel_size; jj++) {
k = (jj - jcol) * m; /* column index for w-wide arrays */
nseg = nseg1; /* Begin after all the panel segments */
if ((*info = zcolumn_dfs(m, jj, perm_r, &nseg, &panel_lsub[k],
segrep, &repfnz[k], xprune, marker,
parent, xplore, &Glu)) != 0) return;
/* Numeric updates */
if ((*info = zcolumn_bmod(jj, (nseg - nseg1), &dense[k],
tempv, &segrep[nseg1], &repfnz[k],
jcol, &Glu, stat)) != 0) return;
/* Copy the U-segments to ucol[*] */
if ((*info = zcopy_to_ucol(jj, nseg, segrep, &repfnz[k],
perm_r, &dense[k], &Glu)) != 0)
return;
*info = zpivotL(jj, diag_pivot_thresh, &usepr, perm_r,iperm_r, iperm_c, &pivrow, &Glu, stat);
if ( (*info) )
if ( iinfo == 0 ) iinfo = *info;
/* Prune columns (0:jj-1) using column jj */
zpruneL(jj, perm_r, pivrow, nseg, segrep,
&repfnz[k], xprune, &Glu);
/* Reset repfnz[] for this column */
resetrep_col (nseg, segrep, &repfnz[k]);
#ifdef DEBUG
zprint_lu_col("[2]: ", jj, pivrow, xprune, &Glu);
#endif
}
jcol += panel_size; /* Move to the next panel */
} /* else */
} /* for */
*info = iinfo;
if ( m > n ) {
k = 0;
for (i = 0; i < m; ++i)
if ( perm_r[i] == EMPTY ) {
perm_r[i] = n + k;
++k;
}
}
countnz(min_mn, xprune, &nnzL, &nnzU, &Glu);
fixupL(min_mn, perm_r, &Glu);
zLUWorkFree(iwork, zwork, &Glu); /* Free work space and compress storage */
if ( fact == SamePattern_SameRowPerm ) {
/* L and U structures may have changed due to possibly different
pivoting, even though the storage is available.
There could also be memory expansions, so the array locations
may have changed, */
((SCformat *)L->Store)->nnz = nnzL;
((SCformat *)L->Store)->nsuper = Glu.supno[n];
((SCformat *)L->Store)->nzval = Glu.lusup;
((SCformat *)L->Store)->nzval_colptr = Glu.xlusup;
((SCformat *)L->Store)->rowind = Glu.lsub;
((SCformat *)L->Store)->rowind_colptr = Glu.xlsub;
((NCformat *)U->Store)->nnz = nnzU;
((NCformat *)U->Store)->nzval = Glu.ucol;
((NCformat *)U->Store)->rowind = Glu.usub;
((NCformat *)U->Store)->colptr = Glu.xusub;
} else {
zCreate_SuperNode_Matrix(L, A->nrow, min_mn, nnzL, Glu.lusup,
Glu.xlusup, Glu.lsub, Glu.xlsub, Glu.supno,
Glu.xsup, SLU_SC, SLU_Z, SLU_TRLU);
zCreate_CompCol_Matrix(U, min_mn, min_mn, nnzU, Glu.ucol,
Glu.usub, Glu.xusub, SLU_NC, SLU_Z, SLU_TRU);
}
ops[FACT] += ops[TRSV] + ops[GEMV];
if ( iperm_r_allocated ) SUPERLU_FREE (iperm_r);
SUPERLU_FREE (iperm_c);
SUPERLU_FREE (relax_end);
}
void
cgscon(char *norm, SuperMatrix *L, SuperMatrix *U,
float anorm, float *rcond, SuperLUStat_t *stat, int *info)
{
/* Local variables */
int kase, kase1, onenrm, i;
float ainvnm;
complex *work;
int isave[3];
extern int crscl_(int *, complex *, complex *, int *);
extern int clacon2_(int *, complex *, complex *, float *, int *, int []);
/* Test the input parameters. */
*info = 0;
onenrm = *(unsigned char *)norm == '1' || strncmp(norm, "O", 1)==0;
if (! onenrm && ! strncmp(norm, "I", 1)==0) *info = -1;
else if (L->nrow < 0 || L->nrow != L->ncol ||
L->Stype != SLU_SC || L->Dtype != SLU_C || L->Mtype != SLU_TRLU)
*info = -2;
else if (U->nrow < 0 || U->nrow != U->ncol ||
U->Stype != SLU_NC || U->Dtype != SLU_C || U->Mtype != SLU_TRU)
*info = -3;
if (*info != 0) {
i = -(*info);
input_error("cgscon", &i);
return;
}
/* Quick return if possible */
*rcond = 0.;
if ( L->nrow == 0 || U->nrow == 0) {
*rcond = 1.;
return;
}
work = complexCalloc( 3*L->nrow );
if ( !work )
ABORT("Malloc fails for work arrays in cgscon.");
/* Estimate the norm of inv(A). */
ainvnm = 0.;
if ( onenrm ) kase1 = 1;
else kase1 = 2;
kase = 0;
do {
clacon2_(&L->nrow, &work[L->nrow], &work[0], &ainvnm, &kase, isave);
if (kase == 0) break;
if (kase == kase1) {
/* Multiply by inv(L). */
sp_ctrsv("L", "No trans", "Unit", L, U, &work[0], stat, info);
/* Multiply by inv(U). */
sp_ctrsv("U", "No trans", "Non-unit", L, U, &work[0], stat, info);
} else {
/* Multiply by inv(U'). */
sp_ctrsv("U", "Transpose", "Non-unit", L, U, &work[0], stat, info);
/* Multiply by inv(L'). */
sp_ctrsv("L", "Transpose", "Unit", L, U, &work[0], stat, info);
}
} while ( kase != 0 );
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.) *rcond = (1. / ainvnm) / anorm;
SUPERLU_FREE (work);
return;
} /* cgscon */
/*! \brief
*
* <pre>
* Purpose
* =======
*
* SGSRFS improves the computed solution to a system of linear
* equations and provides error bounds and backward error estimates for
* the solution.
*
* If equilibration was performed, the system becomes:
* (diag(R)*A_original*diag(C)) * X = diag(R)*B_original.
*
* See supermatrix.h for the definition of 'SuperMatrix' structure.
*
* Arguments
* =========
*
* trans (input) trans_t
* Specifies the form of the system of equations:
* = NOTRANS: A * X = B (No transpose)
* = TRANS: A'* X = B (Transpose)
* = CONJ: A**H * X = B (Conjugate transpose)
*
* A (input) SuperMatrix*
* The original matrix A in the system, or the scaled A if
* equilibration was done. The type of A can be:
* Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_GE.
*
* L (input) SuperMatrix*
* The factor L from the factorization Pr*A*Pc=L*U. Use
* compressed row subscripts storage for supernodes,
* i.e., L has types: Stype = SLU_SC, Dtype = SLU_S, Mtype = SLU_TRLU.
*
* U (input) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U as computed by
* sgstrf(). Use column-wise storage scheme,
* i.e., U has types: Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_TRU.
*
* perm_c (input) int*, dimension (A->ncol)
* Column permutation vector, which defines the
* permutation matrix Pc; perm_c[i] = j means column i of A is
* in position j in A*Pc.
*
* perm_r (input) int*, dimension (A->nrow)
* Row permutation vector, which defines the permutation matrix Pr;
* perm_r[i] = j means row i of A is in position j in Pr*A.
*
* equed (input) Specifies the form of equilibration that was done.
* = 'N': No equilibration.
* = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
* = 'C': Column equilibration, i.e., A was postmultiplied by
* diag(C).
* = 'B': Both row and column equilibration, i.e., A was replaced
* by diag(R)*A*diag(C).
*
* R (input) float*, dimension (A->nrow)
* The row scale factors for A.
* If equed = 'R' or 'B', A is premultiplied by diag(R).
* If equed = 'N' or 'C', R is not accessed.
*
* C (input) float*, dimension (A->ncol)
* The column scale factors for A.
* If equed = 'C' or 'B', A is postmultiplied by diag(C).
* If equed = 'N' or 'R', C is not accessed.
*
* B (input) SuperMatrix*
* B has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
* The right hand side matrix B.
* if equed = 'R' or 'B', B is premultiplied by diag(R).
*
* X (input/output) SuperMatrix*
* X has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
* On entry, the solution matrix X, as computed by sgstrs().
* On exit, the improved solution matrix X.
* if *equed = 'C' or 'B', X should be premultiplied by diag(C)
* in order to obtain the solution to the original system.
*
* FERR (output) float*, dimension (B->ncol)
* The estimated forward error bound for each solution vector
* X(j) (the j-th column of the solution matrix X).
* If XTRUE is the true solution corresponding to X(j), FERR(j)
* is an estimated upper bound for the magnitude of the largest
* element in (X(j) - XTRUE) divided by the magnitude of the
* largest element in X(j). The estimate is as reliable as
* the estimate for RCOND, and is almost always a slight
* overestimate of the true error.
*
* BERR (output) float*, dimension (B->ncol)
* The componentwise relative backward error of each solution
* vector X(j) (i.e., the smallest relative change in
* any element of A or B that makes X(j) an exact solution).
*
* stat (output) SuperLUStat_t*
* Record the statistics on runtime and floating-point operation count.
* See util.h for the definition of 'SuperLUStat_t'.
*
* info (output) int*
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* Internal Parameters
* ===================
*
* ITMAX is the maximum number of steps of iterative refinement.
*
* </pre>
*/
void
sgsrfs(trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix *U,
int *perm_c, int *perm_r, char *equed, float *R, float *C,
SuperMatrix *B, SuperMatrix *X, float *ferr, float *berr,
SuperLUStat_t *stat, int *info)
{
#define ITMAX 5
/* Table of constant values */
int ione = 1;
float ndone = -1.;
float done = 1.;
/* Local variables */
NCformat *Astore;
float *Aval;
SuperMatrix Bjcol;
DNformat *Bstore, *Xstore, *Bjcol_store;
float *Bmat, *Xmat, *Bptr, *Xptr;
int kase;
float safe1, safe2;
int i, j, k, irow, nz, count, notran, rowequ, colequ;
int ldb, ldx, nrhs;
float s, xk, lstres, eps, safmin;
char transc[1];
trans_t transt;
float *work;
float *rwork;
int *iwork;
extern int slacon_(int *, float *, float *, int *, float *, int *);
#ifdef _CRAY
extern int SCOPY(int *, float *, int *, float *, int *);
extern int SSAXPY(int *, float *, float *, int *, float *, int *);
#else
extern int scopy_(int *, float *, int *, float *, int *);
extern int saxpy_(int *, float *, float *, int *, float *, int *);
#endif
Astore = A->Store;
Aval = Astore->nzval;
Bstore = B->Store;
Xstore = X->Store;
Bmat = Bstore->nzval;
Xmat = Xstore->nzval;
ldb = Bstore->lda;
ldx = Xstore->lda;
nrhs = B->ncol;
/* Test the input parameters */
*info = 0;
notran = (trans == NOTRANS);
if ( !notran && trans != TRANS && trans != CONJ ) *info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
A->Stype != SLU_NC || A->Dtype != SLU_S || A->Mtype != SLU_GE )
*info = -2;
else if ( L->nrow != L->ncol || L->nrow < 0 ||
L->Stype != SLU_SC || L->Dtype != SLU_S || L->Mtype != SLU_TRLU )
*info = -3;
else if ( U->nrow != U->ncol || U->nrow < 0 ||
U->Stype != SLU_NC || U->Dtype != SLU_S || U->Mtype != SLU_TRU )
*info = -4;
else if ( ldb < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_S || B->Mtype != SLU_GE )
*info = -10;
else if ( ldx < SUPERLU_MAX(0, A->nrow) ||
X->Stype != SLU_DN || X->Dtype != SLU_S || X->Mtype != SLU_GE )
*info = -11;
if (*info != 0) {
i = -(*info);
xerbla_("sgsrfs", &i);
return;
}
/* Quick return if possible */
if ( A->nrow == 0 || nrhs == 0) {
for (j = 0; j < nrhs; ++j) {
ferr[j] = 0.;
berr[j] = 0.;
}
return;
}
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
/* Allocate working space */
work = floatMalloc(2*A->nrow);
rwork = (float *) SUPERLU_MALLOC( A->nrow * sizeof(float) );
iwork = intMalloc(2*A->nrow);
if ( !work || !rwork || !iwork )
ABORT("Malloc fails for work/rwork/iwork.");
if ( notran ) {
*(unsigned char *)transc = 'N';
transt = TRANS;
} else {
*(unsigned char *)transc = 'T';
transt = NOTRANS;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = A->ncol + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
/* Set SAFE1 essentially to be the underflow threshold times the
number of additions in each row. */
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Compute the number of nonzeros in each row (or column) of A */
for (i = 0; i < A->nrow; ++i) iwork[i] = 0;
if ( notran ) {
for (k = 0; k < A->ncol; ++k)
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
++iwork[Astore->rowind[i]];
} else {
for (k = 0; k < A->ncol; ++k)
iwork[k] = Astore->colptr[k+1] - Astore->colptr[k];
}
/* Copy one column of RHS B into Bjcol. */
Bjcol.Stype = B->Stype;
Bjcol.Dtype = B->Dtype;
Bjcol.Mtype = B->Mtype;
Bjcol.nrow = B->nrow;
Bjcol.ncol = 1;
Bjcol.Store = (void *) SUPERLU_MALLOC( sizeof(DNformat) );
if ( !Bjcol.Store ) ABORT("SUPERLU_MALLOC fails for Bjcol.Store");
Bjcol_store = Bjcol.Store;
Bjcol_store->lda = ldb;
Bjcol_store->nzval = work; /* address aliasing */
/* Do for each right hand side ... */
for (j = 0; j < nrhs; ++j) {
count = 0;
lstres = 3.;
Bptr = &Bmat[j*ldb];
Xptr = &Xmat[j*ldx];
while (1) { /* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - op(A) * X,
where op(A) = A, A**T, or A**H, depending on TRANS. */
#ifdef _CRAY
SCOPY(&A->nrow, Bptr, &ione, work, &ione);
#else
scopy_(&A->nrow, Bptr, &ione, work, &ione);
#endif
sp_sgemv(transc, ndone, A, Xptr, ione, done, work, ione);
/* Compute componentwise relative backward error from formula
max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) )
where abs(Z) is the componentwise absolute value of the matrix
or vector Z. If the i-th component of the denominator is less
than SAFE2, then SAFE1 is added to the i-th component of the
numerator before dividing. */
for (i = 0; i < A->nrow; ++i) rwork[i] = fabs( Bptr[i] );
/* Compute abs(op(A))*abs(X) + abs(B). */
if (notran) {
for (k = 0; k < A->ncol; ++k) {
xk = fabs( Xptr[k] );
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
rwork[Astore->rowind[i]] += fabs(Aval[i]) * xk;
}
} else {
for (k = 0; k < A->ncol; ++k) {
s = 0.;
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
irow = Astore->rowind[i];
s += fabs(Aval[i]) * fabs(Xptr[irow]);
}
rwork[k] += s;
}
}
s = 0.;
for (i = 0; i < A->nrow; ++i) {
if (rwork[i] > safe2) {
s = SUPERLU_MAX( s, fabs(work[i]) / rwork[i] );
} else if ( rwork[i] != 0.0 ) {
/* Adding SAFE1 to the numerator guards against
spuriously zero residuals (underflow). */
s = SUPERLU_MAX( s, (safe1 + fabs(work[i])) / rwork[i] );
}
/* If rwork[i] is exactly 0.0, then we know the true
residual also must be exactly 0.0. */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if
1) The residual BERR(J) is larger than machine epsilon, and
2) BERR(J) decreased by at least a factor of 2 during the
last iteration, and
3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2. <= lstres && count < ITMAX) {
/* Update solution and try again. */
sgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
#ifdef _CRAY
SAXPY(&A->nrow, &done, work, &ione,
&Xmat[j*ldx], &ione);
#else
saxpy_(&A->nrow, &done, work, &ione,
&Xmat[j*ldx], &ione);
#endif
lstres = berr[j];
++count;
} else {
break;
}
} /* end while */
stat->RefineSteps = count;
/* Bound error from formula:
norm(X - XTRUE) / norm(X) .le. FERR = norm( abs(inv(op(A)))*
( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X)
where
norm(Z) is the magnitude of the largest component of Z
inv(op(A)) is the inverse of op(A)
abs(Z) is the componentwise absolute value of the matrix or
vector Z
NZ is the maximum number of nonzeros in any row of A, plus 1
EPS is machine epsilon
The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B))
is incremented by SAFE1 if the i-th component of
abs(op(A))*abs(X) + abs(B) is less than SAFE2.
Use SLACON to estimate the infinity-norm of the matrix
inv(op(A)) * diag(W),
where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
for (i = 0; i < A->nrow; ++i) rwork[i] = fabs( Bptr[i] );
/* Compute abs(op(A))*abs(X) + abs(B). */
if ( notran ) {
for (k = 0; k < A->ncol; ++k) {
xk = fabs( Xptr[k] );
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
rwork[Astore->rowind[i]] += fabs(Aval[i]) * xk;
}
} else {
for (k = 0; k < A->ncol; ++k) {
s = 0.;
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
irow = Astore->rowind[i];
xk = fabs( Xptr[irow] );
s += fabs(Aval[i]) * xk;
}
rwork[k] += s;
}
}
for (i = 0; i < A->nrow; ++i)
if (rwork[i] > safe2)
rwork[i] = fabs(work[i]) + (iwork[i]+1)*eps*rwork[i];
else
rwork[i] = fabs(work[i])+(iwork[i]+1)*eps*rwork[i]+safe1;
kase = 0;
do {
slacon_(&A->nrow, &work[A->nrow], work,
&iwork[A->nrow], &ferr[j], &kase);
if (kase == 0) break;
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**T)*(diag(C) or diag(R)). */
if ( notran && colequ )
for (i = 0; i < A->ncol; ++i) work[i] *= C[i];
else if ( !notran && rowequ )
for (i = 0; i < A->nrow; ++i) work[i] *= R[i];
sgstrs (transt, L, U, perm_c, perm_r, &Bjcol, stat, info);
for (i = 0; i < A->nrow; ++i) work[i] *= rwork[i];
} else {
/* Multiply by (diag(C) or diag(R))*inv(op(A))*diag(W). */
for (i = 0; i < A->nrow; ++i) work[i] *= rwork[i];
sgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
if ( notran && colequ )
for (i = 0; i < A->ncol; ++i) work[i] *= C[i];
else if ( !notran && rowequ )
for (i = 0; i < A->ncol; ++i) work[i] *= R[i];
}
} while ( kase != 0 );
/* Normalize error. */
lstres = 0.;
if ( notran && colequ ) {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, C[i] * fabs( Xptr[i]) );
} else if ( !notran && rowequ ) {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, R[i] * fabs( Xptr[i]) );
} else {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, fabs( Xptr[i]) );
}
if ( lstres != 0. )
ferr[j] /= lstres;
} /* for each RHS j ... */
SUPERLU_FREE(work);
SUPERLU_FREE(rwork);
SUPERLU_FREE(iwork);
SUPERLU_FREE(Bjcol.Store);
return;
} /* sgsrfs */
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 = NOTRANS;
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);
}
}
void
cgsrfs(trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix *U,
int *perm_c, int *perm_r, char *equed, float *R, float *C,
SuperMatrix *B, SuperMatrix *X, float *ferr, float *berr,
SuperLUStat_t *stat, int *info)
{
/*
* Purpose
* =======
*
* CGSRFS improves the computed solution to a system of linear
* equations and provides error bounds and backward error estimates for
* the solution.
*
* If equilibration was performed, the system becomes:
* (diag(R)*A_original*diag(C)) * X = diag(R)*B_original.
*
* See supermatrix.h for the definition of 'SuperMatrix' structure.
*
* Arguments
* =========
*
* trans (input) trans_t
* Specifies the form of the system of equations:
* = NOTRANS: A * X = B (No transpose)
* = TRANS: A'* X = B (Transpose)
* = CONJ: A**H * X = B (Conjugate transpose)
*
* A (input) SuperMatrix*
* The original matrix A in the system, or the scaled A if
* equilibration was done. The type of A can be:
* Stype = SLU_NC, Dtype = SLU_C, Mtype = SLU_GE.
*
* L (input) SuperMatrix*
* The factor L from the factorization Pr*A*Pc=L*U. Use
* compressed row subscripts storage for supernodes,
* i.e., L has types: Stype = SLU_SC, Dtype = SLU_C, Mtype = SLU_TRLU.
*
* U (input) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U as computed by
* cgstrf(). Use column-wise storage scheme,
* i.e., U has types: Stype = SLU_NC, Dtype = SLU_C, Mtype = SLU_TRU.
*
* perm_c (input) int*, dimension (A->ncol)
* Column permutation vector, which defines the
* permutation matrix Pc; perm_c[i] = j means column i of A is
* in position j in A*Pc.
*
* perm_r (input) int*, dimension (A->nrow)
* Row permutation vector, which defines the permutation matrix Pr;
* perm_r[i] = j means row i of A is in position j in Pr*A.
*
* equed (input) Specifies the form of equilibration that was done.
* = 'N': No equilibration.
* = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
* = 'C': Column equilibration, i.e., A was postmultiplied by
* diag(C).
* = 'B': Both row and column equilibration, i.e., A was replaced
* by diag(R)*A*diag(C).
*
* R (input) float*, dimension (A->nrow)
* The row scale factors for A.
* If equed = 'R' or 'B', A is premultiplied by diag(R).
* If equed = 'N' or 'C', R is not accessed.
*
* C (input) float*, dimension (A->ncol)
* The column scale factors for A.
* If equed = 'C' or 'B', A is postmultiplied by diag(C).
* If equed = 'N' or 'R', C is not accessed.
*
* B (input) SuperMatrix*
* B has types: Stype = SLU_DN, Dtype = SLU_C, Mtype = SLU_GE.
* The right hand side matrix B.
* if equed = 'R' or 'B', B is premultiplied by diag(R).
*
* X (input/output) SuperMatrix*
* X has types: Stype = SLU_DN, Dtype = SLU_C, Mtype = SLU_GE.
* On entry, the solution matrix X, as computed by cgstrs().
* On exit, the improved solution matrix X.
* if *equed = 'C' or 'B', X should be premultiplied by diag(C)
* in order to obtain the solution to the original system.
*
* FERR (output) float*, dimension (B->ncol)
* The estimated forward error bound for each solution vector
* X(j) (the j-th column of the solution matrix X).
* If XTRUE is the true solution corresponding to X(j), FERR(j)
* is an estimated upper bound for the magnitude of the largest
* element in (X(j) - XTRUE) divided by the magnitude of the
* largest element in X(j). The estimate is as reliable as
* the estimate for RCOND, and is almost always a slight
* overestimate of the true error.
*
* BERR (output) float*, dimension (B->ncol)
* The componentwise relative backward error of each solution
* vector X(j) (i.e., the smallest relative change in
* any element of A or B that makes X(j) an exact solution).
*
* stat (output) SuperLUStat_t*
* Record the statistics on runtime and floating-point operation count.
* See util.h for the definition of 'SuperLUStat_t'.
*
* info (output) int*
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* Internal Parameters
* ===================
*
* ITMAX is the maximum number of steps of iterative refinement.
*
*/
#define ITMAX 5
/* Table of constant values */
int ione = 1;
complex ndone = {-1., 0.};
complex done = {1., 0.};
/* Local variables */
NCformat *Astore;
complex *Aval;
SuperMatrix Bjcol;
DNformat *Bstore, *Xstore, *Bjcol_store;
complex *Bmat, *Xmat, *Bptr, *Xptr;
int kase;
float safe1, safe2;
int i, j, k, irow, nz, count, notran, rowequ, colequ;
int ldb, ldx, nrhs;
float s, xk, lstres, eps, safmin;
char transc[1];
trans_t transt;
complex *work;
float *rwork;
int *iwork;
extern double slamch_(char *);
extern int clacon_(int *, complex *, complex *, float *, int *);
#ifdef _CRAY
extern int CCOPY(int *, complex *, int *, complex *, int *);
extern int CSAXPY(int *, complex *, complex *, int *, complex *, int *);
#else
extern int ccopy_(int *, complex *, int *, complex *, int *);
extern int caxpy_(int *, complex *, complex *, int *, complex *, int *);
#endif
Astore = A->Store;
Aval = Astore->nzval;
Bstore = B->Store;
Xstore = X->Store;
Bmat = Bstore->nzval;
Xmat = Xstore->nzval;
ldb = Bstore->lda;
ldx = Xstore->lda;
nrhs = B->ncol;
/* Test the input parameters */
*info = 0;
notran = (trans == NOTRANS);
if ( !notran && trans != TRANS && trans != CONJ ) *info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
A->Stype != SLU_NC || A->Dtype != SLU_C || A->Mtype != SLU_GE )
*info = -2;
else if ( L->nrow != L->ncol || L->nrow < 0 ||
L->Stype != SLU_SC || L->Dtype != SLU_C || L->Mtype != SLU_TRLU )
*info = -3;
else if ( U->nrow != U->ncol || U->nrow < 0 ||
U->Stype != SLU_NC || U->Dtype != SLU_C || U->Mtype != SLU_TRU )
*info = -4;
else if ( ldb < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_C || B->Mtype != SLU_GE )
*info = -10;
else if ( ldx < SUPERLU_MAX(0, A->nrow) ||
X->Stype != SLU_DN || X->Dtype != SLU_C || X->Mtype != SLU_GE )
*info = -11;
if (*info != 0) {
i = -(*info);
xerbla_("cgsrfs", &i);
return;
}
/* Quick return if possible */
if ( A->nrow == 0 || nrhs == 0) {
for (j = 0; j < nrhs; ++j) {
ferr[j] = 0.;
berr[j] = 0.;
}
return;
}
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
/* Allocate working space */
work = complexMalloc(2*A->nrow);
rwork = (float *) SUPERLU_MALLOC( A->nrow * sizeof(float) );
iwork = intMalloc(A->nrow);
if ( !work || !rwork || !iwork )
ABORT("Malloc fails for work/rwork/iwork.");
if ( notran ) {
*(unsigned char *)transc = 'N';
transt = TRANS;
} else {
*(unsigned char *)transc = 'T';
transt = NOTRANS;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = A->ncol + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Compute the number of nonzeros in each row (or column) of A */
for (i = 0; i < A->nrow; ++i) iwork[i] = 0;
if ( notran ) {
for (k = 0; k < A->ncol; ++k)
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
++iwork[Astore->rowind[i]];
} else {
for (k = 0; k < A->ncol; ++k)
iwork[k] = Astore->colptr[k+1] - Astore->colptr[k];
}
/* Copy one column of RHS B into Bjcol. */
Bjcol.Stype = B->Stype;
Bjcol.Dtype = B->Dtype;
Bjcol.Mtype = B->Mtype;
Bjcol.nrow = B->nrow;
Bjcol.ncol = 1;
Bjcol.Store = (void *) SUPERLU_MALLOC( sizeof(DNformat) );
if ( !Bjcol.Store ) ABORT("SUPERLU_MALLOC fails for Bjcol.Store");
Bjcol_store = Bjcol.Store;
Bjcol_store->lda = ldb;
Bjcol_store->nzval = work; /* address aliasing */
/* Do for each right hand side ... */
for (j = 0; j < nrhs; ++j) {
count = 0;
lstres = 3.;
Bptr = &Bmat[j*ldb];
Xptr = &Xmat[j*ldx];
while (1) { /* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - op(A) * X,
where op(A) = A, A**T, or A**H, depending on TRANS. */
#ifdef _CRAY
CCOPY(&A->nrow, Bptr, &ione, work, &ione);
#else
ccopy_(&A->nrow, Bptr, &ione, work, &ione);
#endif
sp_cgemv(transc, ndone, A, Xptr, ione, done, work, ione);
/* Compute componentwise relative backward error from formula
max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) )
where abs(Z) is the componentwise absolute value of the matrix
or vector Z. If the i-th component of the denominator is less
than SAFE2, then SAFE1 is added to the i-th component of the
numerator and denominator before dividing. */
for (i = 0; i < A->nrow; ++i) rwork[i] = slu_c_abs1( &Bptr[i] );
/* Compute abs(op(A))*abs(X) + abs(B). */
if (notran) {
for (k = 0; k < A->ncol; ++k) {
xk = slu_c_abs1( &Xptr[k] );
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
rwork[Astore->rowind[i]] += slu_c_abs1(&Aval[i]) * xk;
}
} else {
for (k = 0; k < A->ncol; ++k) {
s = 0.;
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
irow = Astore->rowind[i];
s += slu_c_abs1(&Aval[i]) * slu_c_abs1(&Xptr[irow]);
}
rwork[k] += s;
}
}
s = 0.;
for (i = 0; i < A->nrow; ++i) {
if (rwork[i] > safe2)
s = SUPERLU_MAX( s, slu_c_abs1(&work[i]) / rwork[i] );
else
s = SUPERLU_MAX( s, (slu_c_abs1(&work[i]) + safe1) /
(rwork[i] + safe1) );
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if
1) The residual BERR(J) is larger than machine epsilon, and
2) BERR(J) decreased by at least a factor of 2 during the
last iteration, and
3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2. <= lstres && count < ITMAX) {
/* Update solution and try again. */
cgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
#ifdef _CRAY
CAXPY(&A->nrow, &done, work, &ione,
&Xmat[j*ldx], &ione);
#else
caxpy_(&A->nrow, &done, work, &ione,
&Xmat[j*ldx], &ione);
#endif
lstres = berr[j];
++count;
} else {
break;
}
} /* end while */
stat->RefineSteps = count;
/* Bound error from formula:
norm(X - XTRUE) / norm(X) .le. FERR = norm( abs(inv(op(A)))*
( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X)
where
norm(Z) is the magnitude of the largest component of Z
inv(op(A)) is the inverse of op(A)
abs(Z) is the componentwise absolute value of the matrix or
vector Z
NZ is the maximum number of nonzeros in any row of A, plus 1
EPS is machine epsilon
The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B))
is incremented by SAFE1 if the i-th component of
abs(op(A))*abs(X) + abs(B) is less than SAFE2.
Use CLACON to estimate the infinity-norm of the matrix
inv(op(A)) * diag(W),
where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
for (i = 0; i < A->nrow; ++i) rwork[i] = slu_c_abs1( &Bptr[i] );
/* Compute abs(op(A))*abs(X) + abs(B). */
if ( notran ) {
for (k = 0; k < A->ncol; ++k) {
xk = slu_c_abs1( &Xptr[k] );
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
rwork[Astore->rowind[i]] += slu_c_abs1(&Aval[i]) * xk;
}
} else {
for (k = 0; k < A->ncol; ++k) {
s = 0.;
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
irow = Astore->rowind[i];
xk = slu_c_abs1( &Xptr[irow] );
s += slu_c_abs1(&Aval[i]) * xk;
}
rwork[k] += s;
}
}
for (i = 0; i < A->nrow; ++i)
if (rwork[i] > safe2)
rwork[i] = slu_c_abs(&work[i]) + (iwork[i]+1)*eps*rwork[i];
else
rwork[i] = slu_c_abs(&work[i])+(iwork[i]+1)*eps*rwork[i]+safe1;
kase = 0;
do {
clacon_(&A->nrow, &work[A->nrow], work,
&ferr[j], &kase);
if (kase == 0) break;
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**T)*(diag(C) or diag(R)). */
if ( notran && colequ )
for (i = 0; i < A->ncol; ++i) {
cs_mult(&work[i], &work[i], C[i]);
}
else if ( !notran && rowequ )
for (i = 0; i < A->nrow; ++i) {
cs_mult(&work[i], &work[i], R[i]);
}
cgstrs (transt, L, U, perm_c, perm_r, &Bjcol, stat, info);
for (i = 0; i < A->nrow; ++i) {
cs_mult(&work[i], &work[i], rwork[i]);
}
} else {
/* Multiply by (diag(C) or diag(R))*inv(op(A))*diag(W). */
for (i = 0; i < A->nrow; ++i) {
cs_mult(&work[i], &work[i], rwork[i]);
}
cgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
if ( notran && colequ )
for (i = 0; i < A->ncol; ++i) {
cs_mult(&work[i], &work[i], C[i]);
}
else if ( !notran && rowequ )
for (i = 0; i < A->ncol; ++i) {
cs_mult(&work[i], &work[i], R[i]);
}
}
} while ( kase != 0 );
/* Normalize error. */
lstres = 0.;
if ( notran && colequ ) {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, C[i] * slu_c_abs1( &Xptr[i]) );
} else if ( !notran && rowequ ) {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, R[i] * slu_c_abs1( &Xptr[i]) );
} else {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, slu_c_abs1( &Xptr[i]) );
}
if ( lstres != 0. )
ferr[j] /= lstres;
} /* for each RHS j ... */
SUPERLU_FREE(work);
SUPERLU_FREE(rwork);
SUPERLU_FREE(iwork);
SUPERLU_FREE(Bjcol.Store);
return;
} /* cgsrfs */
/*! \brief Solves one of the systems of equations A*x = b, or A'*x = b
*
* <pre>
* Purpose
* =======
*
* sp_strsv() solves one of the systems of equations
* A*x = b, or A'*x = b,
* where b and x are n element vectors and A is a sparse unit , or
* non-unit, upper or lower triangular matrix.
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* Parameters
* ==========
*
* uplo - (input) char*
* On entry, uplo specifies whether the matrix is an upper or
* lower triangular matrix as follows:
* uplo = 'U' or 'u' A is an upper triangular matrix.
* uplo = 'L' or 'l' A is a lower triangular matrix.
*
* trans - (input) char*
* On entry, trans specifies the equations to be solved as
* follows:
* trans = 'N' or 'n' A*x = b.
* trans = 'T' or 't' A'*x = b.
* trans = 'C' or 'c' A'*x = b.
*
* diag - (input) char*
* On entry, diag specifies whether or not A is unit
* triangular as follows:
* diag = 'U' or 'u' A is assumed to be unit triangular.
* diag = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* L - (input) SuperMatrix*
* The factor L from the factorization Pr*A*Pc=L*U. Use
* compressed row subscripts storage for supernodes,
* i.e., L has types: Stype = SC, Dtype = SLU_S, Mtype = TRLU.
*
* U - (input) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U.
* U has types: Stype = NC, Dtype = SLU_S, Mtype = TRU.
*
* x - (input/output) float*
* Before entry, the incremented array X must contain the n
* element right-hand side vector b. On exit, X is overwritten
* with the solution vector x.
*
* info - (output) int*
* If *info = -i, the i-th argument had an illegal value.
* </pre>
*/
int
sp_strsv(char *uplo, char *trans, char *diag, SuperMatrix *L,
SuperMatrix *U, float *x, SuperLUStat_t *stat, int *info)
{
#ifdef _CRAY
_fcd ftcs1 = _cptofcd("L", strlen("L")),
ftcs2 = _cptofcd("N", strlen("N")),
ftcs3 = _cptofcd("U", strlen("U"));
#endif
SCformat *Lstore;
NCformat *Ustore;
float *Lval, *Uval;
int incx = 1, incy = 1;
float alpha = 1.0, beta = 1.0;
int nrow;
int fsupc, nsupr, nsupc, luptr, istart, irow;
int i, k, iptr, jcol;
float *work;
flops_t solve_ops;
/* Test the input parameters */
*info = 0;
if ( !lsame_(uplo,"L") && !lsame_(uplo, "U") ) *info = -1;
else if ( !lsame_(trans, "N") && !lsame_(trans, "T") &&
!lsame_(trans, "C")) *info = -2;
else if ( !lsame_(diag, "U") && !lsame_(diag, "N") ) *info = -3;
else if ( L->nrow != L->ncol || L->nrow < 0 ) *info = -4;
else if ( U->nrow != U->ncol || U->nrow < 0 ) *info = -5;
if ( *info ) {
i = -(*info);
xerbla_("sp_strsv", &i);
return 0;
}
Lstore = L->Store;
Lval = Lstore->nzval;
Ustore = U->Store;
Uval = Ustore->nzval;
solve_ops = 0;
if ( !(work = floatCalloc(L->nrow)) )
ABORT("Malloc fails for work in sp_strsv().");
if ( lsame_(trans, "N") ) { /* Form x := inv(A)*x. */
if ( lsame_(uplo, "L") ) {
/* Form x := inv(L)*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
nrow = nsupr - nsupc;
solve_ops += nsupc * (nsupc - 1);
solve_ops += 2 * nrow * nsupc;
if ( nsupc == 1 ) {
for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); ++iptr) {
irow = L_SUB(iptr);
++luptr;
x[irow] -= x[fsupc] * Lval[luptr];
}
} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
STRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
SGEMV(ftcs2, &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#else
strsv_("L", "N", "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
sgemv_("N", &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#endif
#else
slsolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc]);
smatvec ( nsupr, nsupr-nsupc, nsupc, &Lval[luptr+nsupc],
&x[fsupc], &work[0] );
#endif
iptr = istart + nsupc;
for (i = 0; i < nrow; ++i, ++iptr) {
irow = L_SUB(iptr);
x[irow] -= work[i]; /* Scatter */
work[i] = 0.0;
}
}
} /* for k ... */
} else {
/* Form x := inv(U)*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; k--) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
solve_ops += nsupc * (nsupc + 1);
if ( nsupc == 1 ) {
x[fsupc] /= Lval[luptr];
for (i = U_NZ_START(fsupc); i < U_NZ_START(fsupc+1); ++i) {
irow = U_SUB(i);
x[irow] -= x[fsupc] * Uval[i];
}
} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
STRSV(ftcs3, ftcs2, ftcs2, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
strsv_("U", "N", "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
#else
susolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc] );
#endif
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 2*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1);
i++) {
irow = U_SUB(i);
x[irow] -= x[jcol] * Uval[i];
}
}
}
} /* for k ... */
}
} else { /* Form x := inv(A')*x */
if ( lsame_(uplo, "L") ) {
/* Form x := inv(L')*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; --k) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
solve_ops += 2 * (nsupr - nsupc) * nsupc;
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
iptr = istart + nsupc;
for (i = L_NZ_START(jcol) + nsupc;
i < L_NZ_START(jcol+1); i++) {
irow = L_SUB(iptr);
x[jcol] -= x[irow] * Lval[i];
iptr++;
}
}
if ( nsupc > 1 ) {
solve_ops += nsupc * (nsupc - 1);
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("T", strlen("T"));
ftcs3 = _cptofcd("U", strlen("U"));
STRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
strsv_("L", "T", "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
}
} else {
/* Form x := inv(U')*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 2*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
irow = U_SUB(i);
x[jcol] -= x[irow] * Uval[i];
}
}
solve_ops += nsupc * (nsupc + 1);
if ( nsupc == 1 ) {
x[fsupc] /= Lval[luptr];
} else {
#ifdef _CRAY
ftcs1 = _cptofcd("U", strlen("U"));
ftcs2 = _cptofcd("T", strlen("T"));
ftcs3 = _cptofcd("N", strlen("N"));
STRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
strsv_("U", "T", "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
} /* for k ... */
}
}
stat->ops[SOLVE] += solve_ops;
SUPERLU_FREE(work);
return 0;
}
void
pzgsrfs_ABXglobal(int_t n, SuperMatrix *A, double anorm, LUstruct_t *LUstruct,
gridinfo_t *grid, doublecomplex *B, int_t ldb, doublecomplex *X, int_t ldx,
int nrhs, double *berr, SuperLUStat_t *stat, int *info)
{
#define ITMAX 20
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
LocalLU_t *Llu = LUstruct->Llu;
/*
* Data structures used by matrix-vector multiply routine.
*/
int_t N_update; /* Number of variables updated on this process */
int_t *update; /* vector elements (global index) updated
on this processor. */
int_t *bindx;
doublecomplex *val;
int_t *mv_sup_to_proc; /* Supernode to process mapping in
matrix-vector multiply. */
/*-- end data structures for matrix-vector multiply --*/
doublecomplex *b, *ax, *R, *B_col, *temp, *work, *X_col,
*x_trs, *dx_trs;
double *rwork;
int_t notran;
int_t count, ii, j, jj, k, knsupc, lk, lwork,
nprow, nsupers, nz, p;
int i, iam, pkk;
int_t *ilsum, *xsup;
double eps, lstres;
double s, safmin, safe1, safe2;
/* NEW STUFF */
int_t num_diag_procs, *diag_procs; /* Record diagonal process numbers. */
int_t *diag_len; /* Length of the X vector on diagonal processes. */
/*-- Function prototypes --*/
extern void pzgstrs1(int_t, LUstruct_t *, gridinfo_t *,
doublecomplex *, int, SuperLUStat_t *, int *);
/*extern double dlamch_(char *);*/
/* Test the input parameters. */
*info = 0;
if ( n < 0 ) *info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
A->Stype != SLU_NCP || A->Dtype != SLU_Z || A->Mtype != SLU_GE )
*info = -2;
else if ( ldb < SUPERLU_MAX(0, n) ) *info = -10;
else if ( ldx < SUPERLU_MAX(0, n) ) *info = -12;
else if ( nrhs < 0 ) *info = -13;
if (*info != 0) {
i = -(*info);
xerbla_("pzgsrfs_ABXglobal", &i);
return;
}
/* Quick return if possible. */
if ( n == 0 || nrhs == 0 ) {
return;
}
/* Initialization. */
iam = grid->iam;
nprow = grid->nprow;
nsupers = Glu_persist->supno[n-1] + 1;
xsup = Glu_persist->xsup;
ilsum = Llu->ilsum;
notran = 1;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pzgsrfs_ABXglobal()");
#endif
get_diag_procs(n, Glu_persist, grid, &num_diag_procs,
&diag_procs, &diag_len);
#if ( PRNTlevel>=1 )
if ( !iam ) {
printf(".. number of diag processes = %d\n", num_diag_procs);
PrintInt10("diag_procs", num_diag_procs, diag_procs);
PrintInt10("diag_len", num_diag_procs, diag_len);
}
#endif
if ( !(mv_sup_to_proc = intCalloc_dist(nsupers)) )
ABORT("Calloc fails for mv_sup_to_proc[]");
pzgsmv_AXglobal_setup(A, Glu_persist, grid, &N_update, &update,
&val, &bindx, mv_sup_to_proc);
i = CEILING( nsupers, nprow ); /* Number of local block rows */
ii = Llu->ldalsum + i * XK_H;
k = SUPERLU_MAX(N_update, sp_ienv_dist(3));
jj = diag_len[0];
for (j = 1; j < num_diag_procs; ++j) jj = SUPERLU_MAX( jj, diag_len[j] );
jj = SUPERLU_MAX( jj, N_update );
lwork = N_update /* For ax and R */
+ ii /* For dx_trs */
+ ii /* For x_trs */
+ k /* For b */
+ jj; /* for temp */
if ( !(work = doublecomplexMalloc_dist(lwork)) )
ABORT("Malloc fails for work[]");
ax = R = work;
dx_trs = work + N_update;
x_trs = dx_trs + ii;
b = x_trs + ii;
temp = b + k;
if ( !(rwork = SUPERLU_MALLOC(N_update * sizeof(double))) )
ABORT("Malloc fails for rwork[]");
#if ( DEBUGlevel>=2 )
{
doublecomplex *dwork = doublecomplexMalloc_dist(n);
for (i = 0; i < n; ++i) {
if ( i & 1 ) dwork[i].r = 1.;
else dwork[i].r = 2.;
dwork[i].i = 0.;
}
/* Check correctness of matrix-vector multiply. */
pzgsmv_AXglobal(N_update, update, val, bindx, dwork, ax);
PrintDouble5("Mult A*x", N_update, ax);
SUPERLU_FREE(dwork);
}
#endif
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = A->ncol + 1;
eps = dlamch_("Epsilon");
safmin = dlamch_("Safe minimum");
/* Set SAFE1 essentially to be the underflow threshold times the
number of additions in each row. */
safe1 = nz * safmin;
safe2 = safe1 / eps;
#if ( DEBUGlevel>=1 )
if ( !iam ) printf(".. eps = %e\tanorm = %e\tsafe1 = %e\tsafe2 = %e\n",
eps, anorm, safe1, safe2);
#endif
/* Do for each right-hand side ... */
for (j = 0; j < nrhs; ++j) {
count = 0;
lstres = 3.;
/* Copy X into x on the diagonal processes. */
B_col = &B[j*ldb];
X_col = &X[j*ldx];
for (p = 0; p < num_diag_procs; ++p) {
pkk = diag_procs[p];
if ( iam == pkk ) {
for (k = p; k < nsupers; k += num_diag_procs) {
knsupc = SuperSize( k );
lk = LBi( k, grid );
ii = ilsum[lk] + (lk+1)*XK_H;
jj = FstBlockC( k );
for (i = 0; i < knsupc; ++i) x_trs[i+ii] = X_col[i+jj];
dx_trs[ii-XK_H].r = k;/* Block number prepended in header. */
}
}
}
/* Copy B into b distributed the same way as matrix-vector product. */
if ( N_update ) ii = update[0];
for (i = 0; i < N_update; ++i) b[i] = B_col[i + ii];
while (1) { /* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - op(A) * X,
where op(A) = A, A**T, or A**H, depending on TRANS. */
/* Matrix-vector multiply. */
pzgsmv_AXglobal(N_update, update, val, bindx, X_col, ax);
/* Compute residual. */
for (i = 0; i < N_update; ++i) z_sub(&R[i], &b[i], &ax[i]);
/* Compute abs(op(A))*abs(X) + abs(B). */
pzgsmv_AXglobal_abs(N_update, update, val, bindx, X_col, rwork);
for (i = 0; i < N_update; ++i) rwork[i] += slud_z_abs1(&b[i]);
s = 0.0;
for (i = 0; i < N_update; ++i) {
if ( rwork[i] > safe2 ) {
s = SUPERLU_MAX(s, slud_z_abs1(&R[i]) / rwork[i]);
} else if ( rwork[i] != 0.0 ) {
s = SUPERLU_MAX(s, (safe1 + slud_z_abs1(&R[i])) / rwork[i]);
}
/* If temp[i] is exactly 0.0 (computed by PxGSMV), then
we know the true residual also must be exactly 0.0. */
}
MPI_Allreduce( &s, &berr[j], 1, MPI_DOUBLE, MPI_MAX, grid->comm );
#if ( PRNTlevel>= 1 )
if ( !iam )
printf("(%2d) .. Step %2d: berr[j] = %e\n", iam, count, berr[j]);
#endif
if ( berr[j] > eps && berr[j] * 2 <= lstres && count < ITMAX ) {
/* Compute new dx. */
redist_all_to_diag(n, R, Glu_persist, Llu, grid,
mv_sup_to_proc, dx_trs);
pzgstrs1(n, LUstruct, grid, dx_trs, 1, stat, info);
/* Update solution. */
for (p = 0; p < num_diag_procs; ++p)
if ( iam == diag_procs[p] )
for (k = p; k < nsupers; k += num_diag_procs) {
lk = LBi( k, grid );
ii = ilsum[lk] + (lk+1)*XK_H;
knsupc = SuperSize( k );
for (i = 0; i < knsupc; ++i)
z_add(&x_trs[i + ii], &x_trs[i + ii],
&dx_trs[i + ii]);
}
lstres = berr[j];
++count;
/* Transfer x_trs (on diagonal processes) into X
(on all processes). */
gather_1rhs_diag_to_all(n, x_trs, Glu_persist, Llu, grid,
num_diag_procs, diag_procs, diag_len,
X_col, temp);
} else {
break;
}
} /* end while */
stat->RefineSteps = count;
} /* for j ... */
/* Deallocate storage used by matrix-vector multiplication. */
SUPERLU_FREE(diag_procs);
SUPERLU_FREE(diag_len);
if ( N_update ) {
SUPERLU_FREE(update);
SUPERLU_FREE(bindx);
SUPERLU_FREE(val);
}
SUPERLU_FREE(mv_sup_to_proc);
SUPERLU_FREE(work);
SUPERLU_FREE(rwork);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit pzgsrfs_ABXglobal()");
#endif
} /* PZGSRFS_ABXGLOBAL */
void tlin::freeS(SuperMatrix *m) {
if (!m) return;
Destroy_CompCol_Matrix(m);
SUPERLU_FREE(m);
}
void
pdgssvx(int nprocs, pdgstrf_options_t *pdgstrf_options, SuperMatrix *A,
int *perm_c, int *perm_r, equed_t *equed, double *R, double *C,
SuperMatrix *L, SuperMatrix *U,
SuperMatrix *B, SuperMatrix *X, double *recip_pivot_growth,
double *rcond, double *ferr, double *berr,
superlu_memusage_t *superlu_memusage, int *info)
{
/*
* -- SuperLU MT routine (version 1.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* August 15, 1997
*
* Purpose
* =======
*
* pdgssvx() solves the system of linear equations A*X=B or A'*X=B, using
* the LU factorization from dgstrf(). Error bounds on the solution and
* a condition estimate are also provided. It performs the following steps:
*
* 1. If A is stored column-wise (A->Stype = NC):
*
* 1.1. If fact = EQUILIBRATE, scaling factors are computed to equilibrate
* the system:
* trans = NOTRANS: diag(R)*A*diag(C)*inv(diag(C))*X = diag(R)*B
* trans = TRANS: (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
* trans = CONJ: (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
* Whether or not the system will be equilibrated depends on the
* scaling of the matrix A, but if equilibration is used, A is
* overwritten by diag(R)*A*diag(C) and B by diag(R)*B
* (if trans = NOTRANS) or diag(C)*B (if trans = TRANS or CONJ).
*
* 1.2. Permute columns of A, forming A*Pc, where Pc is a permutation matrix
* that usually preserves sparsity.
* For more details of this step, see sp_colorder.c.
*
* 1.3. If fact = DOFACT or EQUILIBRATE, the LU decomposition is used to
* factor the matrix A (after equilibration if fact = EQUILIBRATE) as
* Pr*A*Pc = L*U, with Pr determined by partial pivoting.
*
* 1.4. Compute the reciprocal pivot growth factor.
*
* 1.5. If some U(i,i) = 0, so that U is exactly singular, then the routine
* returns with info = i. Otherwise, the factored form of A is used to
* estimate the condition number of the matrix A. If the reciprocal of
* the condition number is less than machine precision,
* info = A->ncol+1 is returned as a warning, but the routine still
* goes on to solve for X and computes error bounds as described below.
*
* 1.6. The system of equations is solved for X using the factored form
* of A.
*
* 1.7. Iterative refinement is applied to improve the computed solution
* matrix and calculate error bounds and backward error estimates
* for it.
*
* 1.8. If equilibration was used, the matrix X is premultiplied by
* diag(C) (if trans = NOTRANS) or diag(R) (if trans = TRANS or CONJ)
* so that it solves the original system before equilibration.
*
* 2. If A is stored row-wise (A->Stype = NR), apply the above algorithm
* to the tranpose of A:
*
* 2.1. If fact = EQUILIBRATE, scaling factors are computed to equilibrate
* the system:
* trans = NOTRANS:diag(R)*A'*diag(C)*inv(diag(C))*X = diag(R)*B
* trans = TRANS: (diag(R)*A'*diag(C))**T *inv(diag(R))*X = diag(C)*B
* trans = CONJ: (diag(R)*A'*diag(C))**H *inv(diag(R))*X = diag(C)*B
* Whether or not the system will be equilibrated depends on the
* scaling of the matrix A, but if equilibration is used, A' is
* overwritten by diag(R)*A'*diag(C) and B by diag(R)*B
* (if trans = NOTRANS) or diag(C)*B (if trans = TRANS or CONJ).
*
* 2.2. Permute columns of transpose(A) (rows of A),
* forming transpose(A)*Pc, where Pc is a permutation matrix that
* usually preserves sparsity.
* For more details of this step, see sp_colorder.c.
*
* 2.3. If fact = DOFACT or EQUILIBRATE, the LU decomposition is used to
* factor the matrix A (after equilibration if fact = EQUILIBRATE) as
* Pr*transpose(A)*Pc = L*U, with the permutation Pr determined by
* partial pivoting.
*
* 2.4. Compute the reciprocal pivot growth factor.
*
* 2.5. If some U(i,i) = 0, so that U is exactly singular, then the routine
* returns with info = i. Otherwise, the factored form of transpose(A)
* is used to estimate the condition number of the matrix A.
* If the reciprocal of the condition number is less than machine
* precision, info = A->nrow+1 is returned as a warning, but the
* routine still goes on to solve for X and computes error bounds
* as described below.
*
* 2.6. The system of equations is solved for X using the factored form
* of transpose(A).
*
* 2.7. Iterative refinement is applied to improve the computed solution
* matrix and calculate error bounds and backward error estimates
* for it.
*
* 2.8. If equilibration was used, the matrix X is premultiplied by
* diag(C) (if trans = NOTRANS) or diag(R) (if trans = TRANS or CONJ)
* so that it solves the original system before equilibration.
*
* See supermatrix.h for the definition of 'SuperMatrix' structure.
*
* Arguments
* =========
*
* nprocs (input) int
* Number of processes (or threads) to be spawned and used to perform
* the LU factorization by pdgstrf(). There is a single thread of
* control to call pdgstrf(), and all threads spawned by pdgstrf()
* are terminated before returning from pdgstrf().
*
* pdgstrf_options (input) pdgstrf_options_t*
* The structure defines the input parameters and data structure
* to control how the LU factorization will be performed.
* The following fields should be defined for this structure:
*
* o fact (fact_t)
* Specifies whether or not the factored form of the matrix
* A is supplied on entry, and if not, whether the matrix A should
* be equilibrated before it is factored.
* = FACTORED: On entry, L, U, perm_r and perm_c contain the
* factored form of A. If equed is not NOEQUIL, the matrix A has
* been equilibrated with scaling factors R and C.
* A, L, U, perm_r are not modified.
* = DOFACT: The matrix A will be factored, and the factors will be
* stored in L and U.
* = EQUILIBRATE: The matrix A will be equilibrated if necessary,
* then factored into L and U.
*
* o trans (trans_t)
* Specifies the form of the system of equations:
* = NOTRANS: A * X = B (No transpose)
* = TRANS: A**T * X = B (Transpose)
* = CONJ: A**H * X = B (Transpose)
*
* o refact (yes_no_t)
* Specifies whether this is first time or subsequent factorization.
* = NO: this factorization is treated as the first one;
* = YES: it means that a factorization was performed prior to this
* one. Therefore, this factorization will re-use some
* existing data structures, such as L and U storage, column
* elimination tree, and the symbolic information of the
* Householder matrix.
*
* o panel_size (int)
* A panel consists of at most panel_size consecutive columns.
*
* o relax (int)
* To control degree of relaxing supernodes. If the number
* of nodes (columns) in a subtree of the elimination tree is less
* than relax, this subtree is considered as one supernode,
* regardless of the row structures of those columns.
*
* o diag_pivot_thresh (double)
* Diagonal pivoting threshold. At step j of the Gaussian
* elimination, if
* abs(A_jj) >= diag_pivot_thresh * (max_(i>=j) abs(A_ij)),
* use A_jj as pivot, else use A_ij with maximum magnitude.
* 0 <= diag_pivot_thresh <= 1. The default value is 1,
* corresponding to partial pivoting.
*
* o usepr (yes_no_t)
* Whether the pivoting will use perm_r specified by the user.
* = YES: use perm_r; perm_r is input, unchanged on exit.
* = NO: perm_r is determined by partial pivoting, and is output.
*
* o drop_tol (double) (NOT IMPLEMENTED)
* Drop tolerance parameter. At step j of the Gaussian elimination,
* if abs(A_ij)/(max_i abs(A_ij)) < drop_tol, drop entry A_ij.
* 0 <= drop_tol <= 1. The default value of drop_tol is 0,
* corresponding to not dropping any entry.
*
* o work (void*) of size lwork
* User-supplied work space and space for the output data structures.
* Not referenced if lwork = 0;
*
* o lwork (int)
* Specifies the length of work array.
* = 0: allocate space internally by system malloc;
* > 0: use user-supplied work array of length lwork in bytes,
* returns error if space runs out.
* = -1: the routine guesses the amount of space needed without
* performing the factorization, and returns it in
* superlu_memusage->total_needed; no other side effects.
*
* A (input/output) SuperMatrix*
* Matrix A in A*X=B, of dimension (A->nrow, A->ncol), where
* A->nrow = A->ncol. Currently, the type of A can be:
* Stype = NC or NR, Dtype = _D, Mtype = GE. In the future,
* more general A will be handled.
*
* On entry, If pdgstrf_options->fact = FACTORED and equed is not
* NOEQUIL, then A must have been equilibrated by the scaling factors
* in R and/or C. On exit, A is not modified
* if pdgstrf_options->fact = FACTORED or DOFACT, or
* if pdgstrf_options->fact = EQUILIBRATE and equed = NOEQUIL.
*
* On exit, if pdgstrf_options->fact = EQUILIBRATE and equed is not
* NOEQUIL, A is scaled as follows:
* If A->Stype = NC:
* equed = ROW: A := diag(R) * A
* equed = COL: A := A * diag(C)
* equed = BOTH: A := diag(R) * A * diag(C).
* If A->Stype = NR:
* equed = ROW: transpose(A) := diag(R) * transpose(A)
* equed = COL: transpose(A) := transpose(A) * diag(C)
* equed = BOTH: transpose(A) := diag(R) * transpose(A) * diag(C).
*
* perm_c (input/output) int*
* If A->Stype = NC, Column permutation vector of size A->ncol,
* which defines the permutation matrix Pc; perm_c[i] = j means
* column i of A is in position j in A*Pc.
* On exit, perm_c may be overwritten by the product of the input
* perm_c and a permutation that postorders the elimination tree
* of Pc'*A'*A*Pc; perm_c is not changed if the elimination tree
* is already in postorder.
*
* If A->Stype = NR, column permutation vector of size A->nrow,
* which describes permutation of columns of tranpose(A)
* (rows of A) as described above.
*
* perm_r (input/output) int*
* If A->Stype = NC, row permutation vector of size A->nrow,
* which defines the permutation matrix Pr, and is determined
* by partial pivoting. perm_r[i] = j means row i of A is in
* position j in Pr*A.
*
* If A->Stype = NR, permutation vector of size A->ncol, which
* determines permutation of rows of transpose(A)
* (columns of A) as described above.
*
* If pdgstrf_options->usepr = NO, perm_r is output argument;
* If pdgstrf_options->usepr = YES, the pivoting routine will try
* to use the input perm_r, unless a certain threshold criterion
* is violated. In that case, perm_r is overwritten by a new
* permutation determined by partial pivoting or diagonal
* threshold pivoting.
*
* equed (input/output) equed_t*
* Specifies the form of equilibration that was done.
* = NOEQUIL: No equilibration.
* = ROW: Row equilibration, i.e., A was premultiplied by diag(R).
* = COL: Column equilibration, i.e., A was postmultiplied by diag(C).
* = BOTH: Both row and column equilibration, i.e., A was replaced
* by diag(R)*A*diag(C).
* If pdgstrf_options->fact = FACTORED, equed is an input argument,
* otherwise it is an output argument.
*
* R (input/output) double*, dimension (A->nrow)
* The row scale factors for A or transpose(A).
* If equed = ROW or BOTH, A (if A->Stype = NC) or transpose(A)
* (if A->Stype = NR) is multiplied on the left by diag(R).
* If equed = NOEQUIL or COL, R is not accessed.
* If fact = FACTORED, R is an input argument; otherwise, R is output.
* If fact = FACTORED and equed = ROW or BOTH, each element of R must
* be positive.
*
* C (input/output) double*, dimension (A->ncol)
* The column scale factors for A or transpose(A).
* If equed = COL or BOTH, A (if A->Stype = NC) or trnspose(A)
* (if A->Stype = NR) is multiplied on the right by diag(C).
* If equed = NOEQUIL or ROW, C is not accessed.
* If fact = FACTORED, C is an input argument; otherwise, C is output.
* If fact = FACTORED and equed = COL or BOTH, each element of C must
* be positive.
*
* L (output) SuperMatrix*
* The factor L from the factorization
* Pr*A*Pc=L*U (if A->Stype = NC) or
* Pr*transpose(A)*Pc=L*U (if A->Stype = NR).
* Uses compressed row subscripts storage for supernodes, i.e.,
* L has types: Stype = SCP, Dtype = _D, Mtype = TRLU.
*
* U (output) SuperMatrix*
* The factor U from the factorization
* Pr*A*Pc=L*U (if A->Stype = NC) or
* Pr*transpose(A)*Pc=L*U (if A->Stype = NR).
* Uses column-wise storage scheme, i.e., U has types:
* Stype = NCP, Dtype = _D, Mtype = TRU.
*
* B (input/output) SuperMatrix*
* B has types: Stype = DN, Dtype = _D, Mtype = GE.
* On entry, the right hand side matrix.
* On exit,
* if equed = NOEQUIL, B is not modified; otherwise
* if A->Stype = NC:
* if trans = NOTRANS and equed = ROW or BOTH, B is overwritten
* by diag(R)*B;
* if trans = TRANS or CONJ and equed = COL of BOTH, B is
* overwritten by diag(C)*B;
* if A->Stype = NR:
* if trans = NOTRANS and equed = COL or BOTH, B is overwritten
* by diag(C)*B;
* if trans = TRANS or CONJ and equed = ROW of BOTH, B is
* overwritten by diag(R)*B.
*
* X (output) SuperMatrix*
* X has types: Stype = DN, Dtype = _D, Mtype = GE.
* If info = 0 or info = A->ncol+1, X contains the solution matrix
* to the original system of equations. Note that A and B are modified
* on exit if equed is not NOEQUIL, and the solution to the
* equilibrated system is inv(diag(C))*X if trans = NOTRANS and
* equed = COL or BOTH, or inv(diag(R))*X if trans = TRANS or CONJ
* and equed = ROW or BOTH.
*
* recip_pivot_growth (output) double*
* The reciprocal pivot growth factor computed as
* max_j ( max_i(abs(A_ij)) / max_i(abs(U_ij)) ).
* If recip_pivot_growth is much less than 1, the stability of the
* LU factorization could be poor.
*
* rcond (output) double*
* The estimate of the reciprocal condition number of the matrix A
* after equilibration (if done). If rcond is less than the machine
* precision (in particular, if rcond = 0), the matrix is singular
* to working precision. This condition is indicated by a return
* code of info > 0.
*
* ferr (output) double*, dimension (B->ncol)
* The estimated forward error bound for each solution vector
* X(j) (the j-th column of the solution matrix X).
* If XTRUE is the true solution corresponding to X(j), FERR(j)
* is an estimated upper bound for the magnitude of the largest
* element in (X(j) - XTRUE) divided by the magnitude of the
* largest element in X(j). The estimate is as reliable as
* the estimate for RCOND, and is almost always a slight
* overestimate of the true error.
*
* berr (output) double*, dimension (B->ncol)
* The componentwise relative backward error of each solution
* vector X(j) (i.e., the smallest relative change in
* any element of A or B that makes X(j) an exact solution).
*
* superlu_memusage (output) superlu_memusage_t*
* Record the memory usage statistics, consisting of following fields:
* - for_lu (float)
* The amount of space used in bytes for L\U data structures.
* - total_needed (float)
* The amount of space needed in bytes to perform factorization.
* - expansions (int)
* The number of memory expansions during the LU factorization.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
* > 0: if info = i, and i is
* <= A->ncol: U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly
* singular, so the solution and error bounds
* could not be computed.
* = A->ncol+1: U is nonsingular, but RCOND is less than machine
* precision, meaning that the matrix is singular to
* working precision. Nevertheless, the solution and
* error bounds are computed because there are a number
* of situations where the computed solution can be more
* accurate than the value of RCOND would suggest.
* > A->ncol+1: number of bytes allocated when memory allocation
* failure occurred, plus A->ncol.
*
*/
NCformat *Astore;
DNformat *Bstore, *Xstore;
double *Bmat, *Xmat;
int ldb, ldx, nrhs;
SuperMatrix *AA; /* A in NC format used by the factorization routine.*/
SuperMatrix AC; /* Matrix postmultiplied by Pc */
int colequ, equil, dofact, notran, rowequ;
char norm[1];
trans_t trant;
int i, j, info1;
double amax, anorm, bignum, smlnum, colcnd, rowcnd, rcmax, rcmin;
int n, relax, panel_size;
Gstat_t Gstat;
double t0; /* temporary time */
double *utime;
flops_t *ops, flopcnt;
/* External functions */
extern double dlangs(char *, SuperMatrix *);
extern double dlamch_(char *);
Astore = A->Store;
Bstore = B->Store;
Xstore = X->Store;
Bmat = Bstore->nzval;
Xmat = Xstore->nzval;
n = A->ncol;
ldb = Bstore->lda;
ldx = Xstore->lda;
nrhs = B->ncol;
pdgstrf_options->perm_c = perm_c;
pdgstrf_options->perm_r = perm_r;
*info = 0;
dofact = (pdgstrf_options->fact == DOFACT);
equil = (pdgstrf_options->fact == EQUILIBRATE);
notran = (pdgstrf_options->trans == NOTRANS);
if (dofact || equil) {
*equed = NOEQUIL;
rowequ = FALSE;
colequ = FALSE;
} else {
rowequ = (*equed == ROW) || (*equed == BOTH);
colequ = (*equed == COL) || (*equed == BOTH);
smlnum = dlamch_("Safe minimum");
bignum = 1. / smlnum;
}
/* ------------------------------------------------------------
Test the input parameters.
------------------------------------------------------------*/
if ( nprocs <= 0 ) *info = -1;
else if ( (!dofact && !equil && (pdgstrf_options->fact != FACTORED))
|| (!notran && (pdgstrf_options->trans != TRANS) &&
(pdgstrf_options->trans != CONJ))
|| (pdgstrf_options->refact != YES &&
pdgstrf_options->refact != NO)
|| (pdgstrf_options->usepr != YES &&
pdgstrf_options->usepr != NO)
|| pdgstrf_options->lwork < -1 )
*info = -2;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
(A->Stype != SLU_NC && A->Stype != SLU_NR) ||
A->Dtype != SLU_D || A->Mtype != SLU_GE )
*info = -3;
else if ((pdgstrf_options->fact == FACTORED) &&
!(rowequ || colequ || (*equed == NOEQUIL))) *info = -6;
else {
if (rowequ) {
rcmin = bignum;
rcmax = 0.;
for (j = 0; j < A->nrow; ++j) {
rcmin = MIN(rcmin, R[j]);
rcmax = MAX(rcmax, R[j]);
}
if (rcmin <= 0.) *info = -7;
else if ( A->nrow > 0)
rowcnd = MAX(rcmin,smlnum) / MIN(rcmax,bignum);
else rowcnd = 1.;
}
if (colequ && *info == 0) {
rcmin = bignum;
rcmax = 0.;
for (j = 0; j < A->nrow; ++j) {
rcmin = MIN(rcmin, C[j]);
rcmax = MAX(rcmax, C[j]);
}
if (rcmin <= 0.) *info = -8;
else if (A->nrow > 0)
colcnd = MAX(rcmin,smlnum) / MIN(rcmax,bignum);
else colcnd = 1.;
}
if (*info == 0) {
if ( B->ncol < 0 || Bstore->lda < MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_D ||
B->Mtype != SLU_GE )
*info = -11;
else if ( X->ncol < 0 || Xstore->lda < MAX(0, A->nrow) ||
B->ncol != X->ncol || X->Stype != SLU_DN ||
X->Dtype != SLU_D || X->Mtype != SLU_GE )
*info = -12;
}
}
if (*info != 0) {
i = -(*info);
xerbla_("dgssvx", &i);
return;
}
/* ------------------------------------------------------------
Allocate storage and initialize statistics variables.
------------------------------------------------------------*/
panel_size = pdgstrf_options->panel_size;
relax = pdgstrf_options->relax;
StatAlloc(n, nprocs, panel_size, relax, &Gstat);
StatInit(n, nprocs, &Gstat);
utime = Gstat.utime;
ops = Gstat.ops;
/* ------------------------------------------------------------
Convert A to NC format when necessary.
------------------------------------------------------------*/
if ( A->Stype == SLU_NR ) {
NRformat *Astore = A->Store;
AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
dCreate_CompCol_Matrix(AA, A->ncol, A->nrow, Astore->nnz,
Astore->nzval, Astore->colind, Astore->rowptr,
SLU_NC, A->Dtype, A->Mtype);
if ( notran ) { /* Reverse the transpose argument. */
trant = TRANS;
notran = 0;
} else {
trant = NOTRANS;
notran = 1;
}
} else { /* A->Stype == NC */
trant = pdgstrf_options->trans;
AA = A;
}
/* ------------------------------------------------------------
Diagonal scaling to equilibrate the matrix.
------------------------------------------------------------*/
if ( equil ) {
t0 = SuperLU_timer_();
/* Compute row and column scalings to equilibrate the matrix A. */
dgsequ(AA, R, C, &rowcnd, &colcnd, &amax, &info1);
if ( info1 == 0 ) {
/* Equilibrate matrix A. */
dlaqgs(AA, R, C, rowcnd, colcnd, amax, equed);
rowequ = (*equed == ROW) || (*equed == BOTH);
colequ = (*equed == COL) || (*equed == BOTH);
}
utime[EQUIL] = SuperLU_timer_() - t0;
}
/* ------------------------------------------------------------
Scale the right hand side.
------------------------------------------------------------*/
if ( notran ) {
if ( rowequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
Bmat[i + j*ldb] *= R[i];
}
}
} else if ( colequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
Bmat[i + j*ldb] *= C[i];
}
}
/* ------------------------------------------------------------
Perform the LU factorization.
------------------------------------------------------------*/
if ( dofact || equil ) {
/* Obtain column etree, the column count (colcnt_h) and supernode
partition (part_super_h) for the Householder matrix. */
t0 = SuperLU_timer_();
sp_colorder(AA, perm_c, pdgstrf_options, &AC);
utime[ETREE] = SuperLU_timer_() - t0;
#if ( PRNTlevel >= 2 )
printf("Factor PA = LU ... relax %d\tw %d\tmaxsuper %d\trowblk %d\n",
relax, panel_size, sp_ienv(3), sp_ienv(4));
fflush(stdout);
#endif
/* Compute the LU factorization of A*Pc. */
t0 = SuperLU_timer_();
pdgstrf(pdgstrf_options, &AC, perm_r, L, U, &Gstat, info);
utime[FACT] = SuperLU_timer_() - t0;
flopcnt = 0;
for (i = 0; i < nprocs; ++i) flopcnt += Gstat.procstat[i].fcops;
ops[FACT] = flopcnt;
if ( pdgstrf_options->lwork == -1 ) {
superlu_memusage->total_needed = *info - A->ncol;
return;
}
}
if ( *info > 0 ) {
if ( *info <= A->ncol ) {
/* Compute the reciprocal pivot growth factor of the leading
rank-deficient *info columns of A. */
*recip_pivot_growth = dPivotGrowth(*info, AA, perm_c, L, U);
}
} else {
/* ------------------------------------------------------------
Compute the reciprocal pivot growth factor *recip_pivot_growth.
------------------------------------------------------------*/
*recip_pivot_growth = dPivotGrowth(A->ncol, AA, perm_c, L, U);
/* ------------------------------------------------------------
Estimate the reciprocal of the condition number of A.
------------------------------------------------------------*/
t0 = SuperLU_timer_();
if ( notran ) {
*(unsigned char *)norm = '1';
} else {
*(unsigned char *)norm = 'I';
}
anorm = dlangs(norm, AA);
dgscon(norm, L, U, anorm, rcond, info);
utime[RCOND] = SuperLU_timer_() - t0;
/* ------------------------------------------------------------
Compute the solution matrix X.
------------------------------------------------------------*/
for (j = 0; j < nrhs; j++) /* Save a copy of the right hand sides */
for (i = 0; i < B->nrow; i++)
Xmat[i + j*ldx] = Bmat[i + j*ldb];
t0 = SuperLU_timer_();
dgstrs(trant, L, U, perm_r, perm_c, X, &Gstat, info);
utime[SOLVE] = SuperLU_timer_() - t0;
ops[SOLVE] = ops[TRISOLVE];
/* ------------------------------------------------------------
Use iterative refinement to improve the computed solution and
compute error bounds and backward error estimates for it.
------------------------------------------------------------*/
t0 = SuperLU_timer_();
dgsrfs(trant, AA, L, U, perm_r, perm_c, *equed,
R, C, B, X, ferr, berr, &Gstat, info);
utime[REFINE] = SuperLU_timer_() - t0;
/* ------------------------------------------------------------
Transform the solution matrix X to a solution of the original
system.
------------------------------------------------------------*/
if ( notran ) {
if ( colequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
Xmat[i + j*ldx] *= C[i];
}
}
} else if ( rowequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
Xmat[i + j*ldx] *= R[i];
}
}
/* Set INFO = A->ncol+1 if the matrix is singular to
working precision.*/
if ( *rcond < dlamch_("E") ) *info = A->ncol + 1;
}
superlu_QuerySpace(nprocs, L, U, panel_size, superlu_memusage);
/* ------------------------------------------------------------
Deallocate storage after factorization.
------------------------------------------------------------*/
if ( pdgstrf_options->refact == NO ) {
SUPERLU_FREE(pdgstrf_options->etree);
SUPERLU_FREE(pdgstrf_options->colcnt_h);
SUPERLU_FREE(pdgstrf_options->part_super_h);
}
if ( dofact || equil ) {
Destroy_CompCol_Permuted(&AC);
}
if ( A->Stype == SLU_NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
/* ------------------------------------------------------------
Print timings, then deallocate statistic variables.
------------------------------------------------------------*/
PrintStat(&Gstat);
StatFree(&Gstat);
}
void tlin::freeD(SuperMatrix *m) {
if (!m) return;
Destroy_Dense_Matrix(m);
SUPERLU_FREE(m);
}
void
cgssvx(superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r,
int *etree, char *equed, float *R, float *C,
SuperMatrix *L, SuperMatrix *U, void *work, int lwork,
SuperMatrix *B, SuperMatrix *X, float *recip_pivot_growth,
float *rcond, float *ferr, float *berr,
mem_usage_t *mem_usage, SuperLUStat_t *stat, int *info )
{
DNformat *Bstore, *Xstore;
complex *Bmat, *Xmat;
int ldb, ldx, nrhs;
SuperMatrix *AA;/* A in SLU_NC format used by the factorization routine.*/
SuperMatrix AC; /* Matrix postmultiplied by Pc */
int colequ, equil, nofact, notran, rowequ, permc_spec;
trans_t trant;
char norm[1];
int i, j, info1;
float amax, anorm, bignum, smlnum, colcnd, rowcnd, rcmax, rcmin;
int relax, panel_size;
float diag_pivot_thresh;
double t0; /* temporary time */
double *utime;
/* External functions */
extern float clangs(char *, SuperMatrix *);
Bstore = B->Store;
Xstore = X->Store;
Bmat = Bstore->nzval;
Xmat = Xstore->nzval;
ldb = Bstore->lda;
ldx = Xstore->lda;
nrhs = B->ncol;
*info = 0;
nofact = (options->Fact != FACTORED);
equil = (options->Equil == YES);
notran = (options->Trans == NOTRANS);
if ( nofact ) {
*(unsigned char *)equed = 'N';
rowequ = FALSE;
colequ = FALSE;
} else {
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
smlnum = slamch_("Safe minimum");
bignum = 1. / smlnum;
}
#if 0
printf("dgssvx: Fact=%4d, Trans=%4d, equed=%c\n",
options->Fact, options->Trans, *equed);
#endif
/* Test the input parameters */
if (options->Fact != DOFACT && options->Fact != SamePattern &&
options->Fact != SamePattern_SameRowPerm &&
options->Fact != FACTORED &&
options->Trans != NOTRANS && options->Trans != TRANS &&
options->Trans != CONJ &&
options->Equil != NO && options->Equil != YES)
*info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
(A->Stype != SLU_NC && A->Stype != SLU_NR) ||
A->Dtype != SLU_C || A->Mtype != SLU_GE )
*info = -2;
else if (options->Fact == FACTORED &&
!(rowequ || colequ || lsame_(equed, "N")))
*info = -6;
else {
if (rowequ) {
rcmin = bignum;
rcmax = 0.;
for (j = 0; j < A->nrow; ++j) {
rcmin = SUPERLU_MIN(rcmin, R[j]);
rcmax = SUPERLU_MAX(rcmax, R[j]);
}
if (rcmin <= 0.) *info = -7;
else if ( A->nrow > 0)
rowcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
else rowcnd = 1.;
}
if (colequ && *info == 0) {
rcmin = bignum;
rcmax = 0.;
for (j = 0; j < A->nrow; ++j) {
rcmin = SUPERLU_MIN(rcmin, C[j]);
rcmax = SUPERLU_MAX(rcmax, C[j]);
}
if (rcmin <= 0.) *info = -8;
else if (A->nrow > 0)
colcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
else colcnd = 1.;
}
if (*info == 0) {
if ( lwork < -1 ) *info = -12;
else if ( B->ncol < 0 ) *info = -13;
else if ( B->ncol > 0 ) { /* no checking if B->ncol=0 */
if ( Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_C ||
B->Mtype != SLU_GE )
*info = -13;
}
if ( X->ncol < 0 ) *info = -14;
else if ( X->ncol > 0 ) { /* no checking if X->ncol=0 */
if ( Xstore->lda < SUPERLU_MAX(0, A->nrow) ||
(B->ncol != 0 && B->ncol != X->ncol) ||
X->Stype != SLU_DN ||
X->Dtype != SLU_C || X->Mtype != SLU_GE )
*info = -14;
}
}
}
if (*info != 0) {
i = -(*info);
xerbla_("cgssvx", &i);
return;
}
/* Initialization for factor parameters */
panel_size = sp_ienv(1);
relax = sp_ienv(2);
diag_pivot_thresh = options->DiagPivotThresh;
utime = stat->utime;
/* Convert A to SLU_NC format when necessary. */
if ( A->Stype == SLU_NR ) {
NRformat *Astore = A->Store;
AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
cCreate_CompCol_Matrix(AA, A->ncol, A->nrow, Astore->nnz,
Astore->nzval, Astore->colind, Astore->rowptr,
SLU_NC, A->Dtype, A->Mtype);
if ( notran ) { /* Reverse the transpose argument. */
trant = TRANS;
notran = 0;
} else {
trant = NOTRANS;
notran = 1;
}
} else { /* A->Stype == SLU_NC */
trant = options->Trans;
AA = A;
}
if ( nofact && equil ) {
t0 = SuperLU_timer_();
/* Compute row and column scalings to equilibrate the matrix A. */
cgsequ(AA, R, C, &rowcnd, &colcnd, &amax, &info1);
if ( info1 == 0 ) {
/* Equilibrate matrix A. */
claqgs(AA, R, C, rowcnd, colcnd, amax, equed);
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
}
utime[EQUIL] = SuperLU_timer_() - t0;
}
if ( nofact ) {
t0 = SuperLU_timer_();
/*
* Gnet column permutation vector perm_c[], according to permc_spec:
* permc_spec = NATURAL: natural ordering
* permc_spec = MMD_AT_PLUS_A: minimum degree on structure of A'+A
* permc_spec = MMD_ATA: minimum degree on structure of A'*A
* permc_spec = COLAMD: approximate minimum degree column ordering
* permc_spec = MY_PERMC: the ordering already supplied in perm_c[]
*/
permc_spec = options->ColPerm;
if ( permc_spec != MY_PERMC && options->Fact == DOFACT )
get_perm_c(permc_spec, AA, perm_c);
utime[COLPERM] = SuperLU_timer_() - t0;
t0 = SuperLU_timer_();
sp_preorder(options, AA, perm_c, etree, &AC);
utime[ETREE] = SuperLU_timer_() - t0;
/* printf("Factor PA = LU ... relax %d\tw %d\tmaxsuper %d\trowblk %d\n",
relax, panel_size, sp_ienv(3), sp_ienv(4));
fflush(stdout); */
/* Compute the LU factorization of A*Pc. */
t0 = SuperLU_timer_();
cgstrf(options, &AC, relax, panel_size, etree,
work, lwork, perm_c, perm_r, L, U, stat, info);
utime[FACT] = SuperLU_timer_() - t0;
if ( lwork == -1 ) {
mem_usage->total_needed = *info - A->ncol;
return;
}
}
if ( options->PivotGrowth ) {
if ( *info > 0 ) {
if ( *info <= A->ncol ) {
/* Compute the reciprocal pivot growth factor of the leading
rank-deficient *info columns of A. */
*recip_pivot_growth = cPivotGrowth(*info, AA, perm_c, L, U);
}
return;
}
/* Compute the reciprocal pivot growth factor *recip_pivot_growth. */
*recip_pivot_growth = cPivotGrowth(A->ncol, AA, perm_c, L, U);
}
if ( options->ConditionNumber ) {
/* Estimate the reciprocal of the condition number of A. */
t0 = SuperLU_timer_();
if ( notran ) {
*(unsigned char *)norm = '1';
} else {
*(unsigned char *)norm = 'I';
}
anorm = clangs(norm, AA);
cgscon(norm, L, U, anorm, rcond, stat, info);
utime[RCOND] = SuperLU_timer_() - t0;
}
if ( nrhs > 0 ) {
/* Scale the right hand side if equilibration was performed. */
if ( notran ) {
if ( rowequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i)
cs_mult(&Bmat[i+j*ldb], &Bmat[i+j*ldb], R[i]);
}
} else if ( colequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i)
cs_mult(&Bmat[i+j*ldb], &Bmat[i+j*ldb], C[i]);
}
/* Compute the solution matrix X. */
for (j = 0; j < nrhs; j++) /* Save a copy of the right hand sides */
for (i = 0; i < B->nrow; i++)
Xmat[i + j*ldx] = Bmat[i + j*ldb];
t0 = SuperLU_timer_();
cgstrs (trant, L, U, perm_c, perm_r, X, stat, info);
utime[SOLVE] = SuperLU_timer_() - t0;
/* Use iterative refinement to improve the computed solution and compute
error bounds and backward error estimates for it. */
t0 = SuperLU_timer_();
if ( options->IterRefine != NOREFINE ) {
cgsrfs(trant, AA, L, U, perm_c, perm_r, equed, R, C, B,
X, ferr, berr, stat, info);
} else {
for (j = 0; j < nrhs; ++j) ferr[j] = berr[j] = 1.0;
}
utime[REFINE] = SuperLU_timer_() - t0;
/* Transform the solution matrix X to a solution of the original system. */
if ( notran ) {
if ( colequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i)
cs_mult(&Xmat[i+j*ldx], &Xmat[i+j*ldx], C[i]);
}
} else if ( rowequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i)
cs_mult(&Xmat[i+j*ldx], &Xmat[i+j*ldx], R[i]);
}
} /* end if nrhs > 0 */
if ( options->ConditionNumber ) {
/* Set INFO = A->ncol+1 if the matrix is singular to working precision. */
if ( *rcond < slamch_("E") ) *info = A->ncol + 1;
}
if ( nofact ) {
cQuerySpace(L, U, mem_usage);
Destroy_CompCol_Permuted(&AC);
}
if ( A->Stype == SLU_NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
}
main(int argc, char *argv[])
{
/*
* Purpose
* =======
*
* ZDRIVE is the main test program for the DOUBLE COMPLEX linear
* equation driver routines ZGSSV and ZGSSVX.
*
* The program is invoked by a shell script file -- ztest.csh.
* The output from the tests are written into a file -- ztest.out.
*
* =====================================================================
*/
doublecomplex *a, *a_save;
int *asub, *asub_save;
int *xa, *xa_save;
SuperMatrix A, B, X, L, U;
SuperMatrix ASAV, AC;
mem_usage_t mem_usage;
int *perm_r; /* row permutation from partial pivoting */
int *perm_c, *pc_save; /* column permutation */
int *etree;
doublecomplex zero = {0.0, 0.0};
double *R, *C;
double *ferr, *berr;
double *rwork;
doublecomplex *wwork;
void *work;
int info, lwork, nrhs, panel_size, relax;
int m, n, nnz;
doublecomplex *xact;
doublecomplex *rhsb, *solx, *bsav;
int ldb, ldx;
double rpg, rcond;
int i, j, k1;
double 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;
double anorm, cndnum;
doublecomplex *Afull;
double 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];
/* 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 zgst01(int, int, SuperMatrix *, SuperMatrix *,
SuperMatrix *, int *, int *, double *);
extern int zgst02(trans_t, int, int, int, SuperMatrix *, doublecomplex *,
int, doublecomplex *, int, double *resid);
extern int zgst04(int, int, doublecomplex *, int,
doublecomplex *, int, double rcond, double *resid);
extern int zgst07(trans_t, int, int, SuperMatrix *, doublecomplex *, int,
doublecomplex *, int, doublecomplex *, int,
double *, double *, double *);
extern int zlatb4_(char *, int *, int *, int *, char *, int *, int *,
double *, int *, double *, char *);
extern int zlatms_(int *, int *, char *, int *, char *, double *d,
int *, double *, double *, int *, int *,
char *, doublecomplex *, int *, doublecomplex *, int *);
extern int sp_zconvert(int, int, doublecomplex *, int, int, int,
doublecomplex *a, int *, int *, int *);
/* Executable statements */
strcpy(path, "ZGE");
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);
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 = DOUBLE;
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 = doublecomplexCalloc(lda * n);
zallocateA(n, nnz, &a, &asub, &xa);
} else {
/* Read a sparse matrix */
fimat = nimat = 0;
zreadhb(&m, &n, &nnz, &a, &asub, &xa);
}
zallocateA(n, nnz, &a_save, &asub_save, &xa_save);
rhsb = doublecomplexMalloc(m * nrhs);
bsav = doublecomplexMalloc(m * nrhs);
solx = doublecomplexMalloc(n * nrhs);
ldb = m;
ldx = n;
zCreate_Dense_Matrix(&B, m, nrhs, rhsb, ldb, SLU_DN, SLU_Z, SLU_GE);
zCreate_Dense_Matrix(&X, n, nrhs, solx, ldx, SLU_DN, SLU_Z, SLU_GE);
xact = doublecomplexMalloc(n * nrhs);
etree = intMalloc(n);
perm_r = intMalloc(n);
perm_c = intMalloc(n);
pc_save = intMalloc(n);
R = (double *) SUPERLU_MALLOC(m*sizeof(double));
C = (double *) SUPERLU_MALLOC(n*sizeof(double));
ferr = (double *) SUPERLU_MALLOC(nrhs*sizeof(double));
berr = (double *) SUPERLU_MALLOC(nrhs*sizeof(double));
j = SUPERLU_MAX(m,n) * SUPERLU_MAX(4,nrhs);
rwork = (double *) SUPERLU_MALLOC(j*sizeof(double));
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 = doublecomplexCalloc( 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 ZLATB4 and generate a test matrix
with ZLATMS. */
zlatb4_(path, &imat, &n, &n, sym, &kl, &ku, &anorm, &mode,
&cndnum, dist);
zlatms_(&n, &n, dist, iseed, sym, &rwork[0], &mode, &cndnum,
&anorm, &kl, &ku, "No packing", Afull, &lda,
&wwork[0], &info);
if ( info ) {
printf(FMT3, "ZLATMS", 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_zconvert(n, n, Afull, lda, kl, ku, a, asub, xa, &nnz);
} else {
izero = 0;
zerot = 0;
}
zCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_Z, SLU_GE);
/* Save a copy of matrix A in ASAV */
zCreate_CompCol_Matrix(&ASAV, m, n, nnz, a_save, asub_save, xa_save,
SLU_NC, SLU_Z, SLU_GE);
zCopy_CompCol_Matrix(&A, &ASAV);
/* Form exact solution. */
zGenXtrue(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. */
zCopy_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. */
zgsequ(&A, R, C, &rowcnd, &colcnd, &amax, &info);
/* Force equilibration. */
if ( !info && n > 0 ) {
if ( lsame_(equed, "R") ) {
rowcnd = 0.;
colcnd = 1.;
} else if ( lsame_(equed, "C") ) {
rowcnd = 1.;
colcnd = 0.;
} else if ( lsame_(equed, "B") ) {
rowcnd = 0.;
colcnd = 0.;
}
}
/* Equilibrate the matrix. */
zlaqgs(&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. */
zgstrf(&options, &AC, relax, panel_size,
etree, work, lwork, perm_c, perm_r, &L, &U,
&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. */
zCopy_CompCol_Matrix(&ASAV, &A);
/* Set the right hand side. */
zFillRHS(trans, nrhs, xact, ldx, &A, &B);
zCopy_Dense_Matrix(m, nrhs, rhsb, ldb, bsav, ldb);
/*----------------
* Test zgssv
*----------------*/
if ( options.Fact == DOFACT && itran == 0) {
/* Not yet factored, and untransposed */
zCopy_Dense_Matrix(m, nrhs, rhsb, ldb, solx, ldx);
zgssv(&options, &A, perm_c, perm_r, &L, &U, &X,
&stat, &info);
if ( info && info != izero ) {
printf(FMT3, "zgssv",
info, izero, n, nrhs, imat, nfail);
} else {
/* Reconstruct matrix from factors and
compute residual. */
zgst01(m, n, &A, &L, &U, perm_c, perm_r,
&result[0]);
nt = 1;
if ( izero == 0 ) {
/* Compute residual of the computed
solution. */
zCopy_Dense_Matrix(m, nrhs, rhsb, ldb,
wwork, ldb);
zgst02(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, "zgssv", 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 zgssv */
/*----------------
* Test zgssvx
*----------------*/
/* Equilibrate the matrix if fact = FACTORED and
equed = 'R', 'C', or 'B'. */
if ( options.Fact == FACTORED &&
(equil || iequed) && n > 0 ) {
zlaqgs(&A, R, C, rowcnd, colcnd, amax, equed);
}
/* Solve the system and compute the condition number
and error bounds using zgssvx. */
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);
if ( info && info != izero ) {
printf(FMT3, "zgssvx",
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. */
zgst01(m, n, &A, &L, &U, perm_c, perm_r,
&result[0]);
k1 = 0;
} else {
k1 = 1;
}
if ( !info ) {
/* Compute residual of the computed solution.*/
zCopy_Dense_Matrix(m, nrhs, bsav, ldb,
wwork, ldb);
zgst02(trans, m, n, nrhs, &ASAV, solx, ldx,
wwork, ldb, &result[1]);
/* Check solution from generated exact
solution. */
zgst04(n, nrhs, solx, ldx, xact, ldx, rcond,
&result[2]);
/* Check the error bounds from iterative
refinement. */
zgst07(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, "zgssvx",
options.Fact, trans, *equed,
n, imat, i, result[i]);
++nfail;
}
}
nrun += NTESTS;
} /* if .. info == 0 */
} /* else .. end of testing zgssvx */
} /* 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
} /* for imat ... */
/* Print a summary of the results. */
PrintSumm("ZGE", nfail, nrun, nerrs);
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);
Destroy_CompCol_Matrix(&A);
Destroy_CompCol_Matrix(&ASAV);
if ( lwork > 0 ) {
SUPERLU_FREE (work);
Destroy_SuperMatrix_Store(&L);
Destroy_SuperMatrix_Store(&U);
}
StatFree(&stat);
return 0;
}
void
heap_relax_snode (
const int n,
int *et, /* column elimination tree */
const int relax_columns, /* max no of columns allowed in a
relaxed snode */
int *descendants, /* no of descendants of each node
in the etree */
int *relax_end /* last column in a supernode */
)
{
register int i, j, k, l, parent;
register int snode_start; /* beginning of a snode */
int *et_save, *post, *inv_post, *iwork;
int nsuper_et = 0, nsuper_et_post = 0;
/* The etree may not be postordered, but is heap ordered. */
iwork = (int*) intMalloc(3*n+2);
if ( !iwork ) ABORT("SUPERLU_MALLOC fails for iwork[]");
inv_post = iwork + n+1;
et_save = inv_post + n+1;
/* Post order etree */
post = (int *) TreePostorder(n, et);
for (i = 0; i < n+1; ++i) inv_post[post[i]] = i;
/* Renumber etree in postorder */
for (i = 0; i < n; ++i) {
iwork[post[i]] = post[et[i]];
et_save[i] = et[i]; /* Save the original etree */
}
for (i = 0; i < n; ++i) et[i] = iwork[i];
/* Compute the number of descendants of each node in the etree */
ifill (relax_end, n, EMPTY);
for (j = 0; j < n; j++) descendants[j] = 0;
for (j = 0; j < n; j++) {
parent = et[j];
if ( parent != n ) /* not the dummy root */
descendants[parent] += descendants[j] + 1;
}
/* Identify the relaxed supernodes by postorder traversal of the etree. */
for (j = 0; j < n; ) {
parent = et[j];
snode_start = j;
while ( parent != n && descendants[parent] < relax_columns ) {
j = parent;
parent = et[j];
}
/* Found a supernode in postordered etree; j is the last column. */
++nsuper_et_post;
k = n;
for (i = snode_start; i <= j; ++i)
k = SUPERLU_MIN(k, inv_post[i]);
l = inv_post[j];
if ( (l - k) == (j - snode_start) ) {
/* It's also a supernode in the original etree */
relax_end[k] = l; /* Last column is recorded */
++nsuper_et;
} else {
for (i = snode_start; i <= j; ++i) {
l = inv_post[i];
if ( descendants[i] == 0 ) {
relax_end[l] = l;
++nsuper_et;
}
}
}
j++;
/* Search for a new leaf */
while ( descendants[j] != 0 && j < n ) j++;
}
#if ( PRNTlevel>=1 )
printf(".. heap_snode_relax:\n"
"\tNo of relaxed snodes in postordered etree:\t%d\n"
"\tNo of relaxed snodes in original etree:\t%d\n",
nsuper_et_post, nsuper_et);
#endif
/* Recover the original etree */
for (i = 0; i < n; ++i) et[i] = et_save[i];
SUPERLU_FREE(post);
SUPERLU_FREE(iwork);
}
void f_destroy_SuperMatrix_handle(fptr *handle)
{
SUPERLU_FREE((void *)*handle);
}
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);
/* Read the matrix in Harwell-Boeing format. */
dreadhb(&m, &n, &nnz, &a, &asub, &xa);
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
}
void f_destroy_gridinfo_handle(fptr *handle)
{
SUPERLU_FREE((void *)*handle);
}
void
zgssvx(char *fact, char *trans, char *refact,
SuperMatrix *A, factor_param_t *factor_params, int *perm_c,
int *perm_r, int *etree, char *equed, double *R, double *C,
SuperMatrix *L, SuperMatrix *U, void *work, int lwork,
SuperMatrix *B, SuperMatrix *X, double *recip_pivot_growth,
double *rcond, double *ferr, double *berr,
mem_usage_t *mem_usage, int *info )
{
/*
* Purpose
* =======
*
* ZGSSVX solves the system of linear equations A*X=B or A'*X=B, using
* the LU factorization from zgstrf(). Error bounds on the solution and
* a condition estimate are also provided. It performs the following steps:
*
* 1. If A is stored column-wise (A->Stype = SLU_NC):
*
* 1.1. If fact = 'E', scaling factors are computed to equilibrate the
* system:
* trans = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
* trans = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
* trans = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
* Whether or not the system will be equilibrated depends on the
* scaling of the matrix A, but if equilibration is used, A is
* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if trans='N')
* or diag(C)*B (if trans = 'T' or 'C').
*
* 1.2. Permute columns of A, forming A*Pc, where Pc is a permutation
* matrix that usually preserves sparsity.
* For more details of this step, see sp_preorder.c.
*
* 1.3. If fact = 'N' or 'E', the LU decomposition is used to factor the
* matrix A (after equilibration if fact = 'E') as Pr*A*Pc = L*U,
* with Pr determined by partial pivoting.
*
* 1.4. Compute the reciprocal pivot growth factor.
*
* 1.5. If some U(i,i) = 0, so that U is exactly singular, then the
* routine returns with info = i. Otherwise, the factored form of
* A is used to estimate the condition number of the matrix A. If
* the reciprocal of the condition number is less than machine
* precision, info = A->ncol+1 is returned as a warning, but the
* routine still goes on to solve for X and computes error bounds
* as described below.
*
* 1.6. The system of equations is solved for X using the factored form
* of A.
*
* 1.7. Iterative refinement is applied to improve the computed solution
* matrix and calculate error bounds and backward error estimates
* for it.
*
* 1.8. If equilibration was used, the matrix X is premultiplied by
* diag(C) (if trans = 'N') or diag(R) (if trans = 'T' or 'C') so
* that it solves the original system before equilibration.
*
* 2. If A is stored row-wise (A->Stype = SLU_NR), apply the above algorithm
* to the transpose of A:
*
* 2.1. If fact = 'E', scaling factors are computed to equilibrate the
* system:
* trans = 'N': diag(R)*A'*diag(C) *inv(diag(C))*X = diag(R)*B
* trans = 'T': (diag(R)*A'*diag(C))**T *inv(diag(R))*X = diag(C)*B
* trans = 'C': (diag(R)*A'*diag(C))**H *inv(diag(R))*X = diag(C)*B
* Whether or not the system will be equilibrated depends on the
* scaling of the matrix A, but if equilibration is used, A' is
* overwritten by diag(R)*A'*diag(C) and B by diag(R)*B
* (if trans='N') or diag(C)*B (if trans = 'T' or 'C').
*
* 2.2. Permute columns of transpose(A) (rows of A),
* forming transpose(A)*Pc, where Pc is a permutation matrix that
* usually preserves sparsity.
* For more details of this step, see sp_preorder.c.
*
* 2.3. If fact = 'N' or 'E', the LU decomposition is used to factor the
* transpose(A) (after equilibration if fact = 'E') as
* Pr*transpose(A)*Pc = L*U with the permutation Pr determined by
* partial pivoting.
*
* 2.4. Compute the reciprocal pivot growth factor.
*
* 2.5. If some U(i,i) = 0, so that U is exactly singular, then the
* routine returns with info = i. Otherwise, the factored form
* of transpose(A) is used to estimate the condition number of the
* matrix A. If the reciprocal of the condition number
* is less than machine precision, info = A->nrow+1 is returned as
* a warning, but the routine still goes on to solve for X and
* computes error bounds as described below.
*
* 2.6. The system of equations is solved for X using the factored form
* of transpose(A).
*
* 2.7. Iterative refinement is applied to improve the computed solution
* matrix and calculate error bounds and backward error estimates
* for it.
*
* 2.8. If equilibration was used, the matrix X is premultiplied by
* diag(C) (if trans = 'N') or diag(R) (if trans = 'T' or 'C') so
* that it solves the original system before equilibration.
*
* See supermatrix.h for the definition of 'SuperMatrix' structure.
*
* Arguments
* =========
*
* fact (input) char*
* Specifies whether or not the factored form of the matrix
* A is supplied on entry, and if not, whether the matrix A should
* be equilibrated before it is factored.
* = 'F': On entry, L, U, perm_r and perm_c contain the factored
* form of A. If equed is not 'N', the matrix A has been
* equilibrated with scaling factors R and C.
* A, L, U, perm_r are not modified.
* = 'N': The matrix A will be factored, and the factors will be
* stored in L and U.
* = 'E': The matrix A will be equilibrated if necessary, then
* factored into L and U.
*
* trans (input) char*
* Specifies the form of the system of equations:
* = 'N': A * X = B (No transpose)
* = 'T': A**T * X = B (Transpose)
* = 'C': A**H * X = B (Transpose)
*
* refact (input) char*
* Specifies whether we want to re-factor the matrix.
* = 'N': Factor the matrix A.
* = 'Y': Matrix A was factored before, now we want to re-factor
* matrix A with perm_r and etree as inputs. Use
* the same storage for the L\U factors previously allocated,
* expand it if necessary. User should insure to use the same
* memory model. In this case, perm_r may be modified due to
* different pivoting determined by diagonal threshold.
* If fact = 'F', then refact is not accessed.
*
* A (input/output) SuperMatrix*
* Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number
* of the linear equations is A->nrow. Currently, the type of A can be:
* Stype = SLU_NC or SLU_NR, Dtype = SLU_Z, Mtype = SLU_GE.
* In the future, more general A may be handled.
*
* On entry, If fact = 'F' and equed is not 'N', then A must have
* been equilibrated by the scaling factors in R and/or C.
* A is not modified if fact = 'F' or 'N', or if fact = 'E' and
* equed = 'N' on exit.
*
* On exit, if fact = 'E' and equed is not 'N', A is scaled as follows:
* If A->Stype = SLU_NC:
* equed = 'R': A := diag(R) * A
* equed = 'C': A := A * diag(C)
* equed = 'B': A := diag(R) * A * diag(C).
* If A->Stype = SLU_NR:
* equed = 'R': transpose(A) := diag(R) * transpose(A)
* equed = 'C': transpose(A) := transpose(A) * diag(C)
* equed = 'B': transpose(A) := diag(R) * transpose(A) * diag(C).
*
* factor_params (input) factor_param_t*
* The structure defines the input scalar parameters, consisting of
* the following fields. If factor_params = NULL, the default
* values are used for all the fields; otherwise, the values
* are given by the user.
* - panel_size (int): Panel size. A panel consists of at most
* panel_size consecutive columns. If panel_size = -1, use
* default value 8.
* - relax (int): To control degree of relaxing supernodes. If the
* number of nodes (columns) in a subtree of the elimination
* tree is less than relax, this subtree is considered as one
* supernode, regardless of the row structures of those columns.
* If relax = -1, use default value 8.
* - diag_pivot_thresh (double): Diagonal pivoting threshold.
* At step j of the Gaussian elimination, if
* abs(A_jj) >= diag_pivot_thresh * (max_(i>=j) abs(A_ij)),
* then use A_jj as pivot. 0 <= diag_pivot_thresh <= 1.
* If diag_pivot_thresh = -1, use default value 1.0,
* which corresponds to standard partial pivoting.
* - drop_tol (double): Drop tolerance threshold. (NOT IMPLEMENTED)
* At step j of the Gaussian elimination, if
* abs(A_ij)/(max_i abs(A_ij)) < drop_tol,
* then drop entry A_ij. 0 <= drop_tol <= 1.
* If drop_tol = -1, use default value 0.0, which corresponds to
* standard Gaussian elimination.
*
* perm_c (input/output) int*
* If A->Stype = SLU_NC, Column permutation vector of size A->ncol,
* which defines the permutation matrix Pc; perm_c[i] = j means
* column i of A is in position j in A*Pc.
* On exit, perm_c may be overwritten by the product of the input
* perm_c and a permutation that postorders the elimination tree
* of Pc'*A'*A*Pc; perm_c is not changed if the elimination tree
* is already in postorder.
*
* If A->Stype = SLU_NR, column permutation vector of size A->nrow,
* which describes permutation of columns of transpose(A)
* (rows of A) as described above.
*
* perm_r (input/output) int*
* If A->Stype = SLU_NC, row permutation vector of size A->nrow,
* which defines the permutation matrix Pr, and is determined
* by partial pivoting. perm_r[i] = j means row i of A is in
* position j in Pr*A.
*
* If A->Stype = SLU_NR, permutation vector of size A->ncol, which
* determines permutation of rows of transpose(A)
* (columns of A) as described above.
*
* If refact is not 'Y', perm_r is output argument;
* If refact = 'Y', the pivoting routine will try to use the input
* perm_r, unless a certain threshold criterion is violated.
* In that case, perm_r is overwritten by a new permutation
* determined by partial pivoting or diagonal threshold pivoting.
*
* etree (input/output) int*, dimension (A->ncol)
* Elimination tree of Pc'*A'*A*Pc.
* If fact is not 'F' and refact = 'Y', etree is an input argument,
* otherwise it is an output argument.
* Note: etree is a vector of parent pointers for a forest whose
* vertices are the integers 0 to A->ncol-1; etree[root]==A->ncol.
*
* equed (input/output) char*
* Specifies the form of equilibration that was done.
* = 'N': No equilibration.
* = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
* = 'C': Column equilibration, i.e., A was postmultiplied by diag(C).
* = 'B': Both row and column equilibration, i.e., A was replaced
* by diag(R)*A*diag(C).
* If fact = 'F', equed is an input argument, otherwise it is
* an output argument.
*
* R (input/output) double*, dimension (A->nrow)
* The row scale factors for A or transpose(A).
* If equed = 'R' or 'B', A (if A->Stype = SLU_NC) or transpose(A)
* (if A->Stype = SLU_NR) is multiplied on the left by diag(R).
* If equed = 'N' or 'C', R is not accessed.
* If fact = 'F', R is an input argument; otherwise, R is output.
* If fact = 'F' and equed = 'R' or 'B', each element of R must
* be positive.
*
* C (input/output) double*, dimension (A->ncol)
* The column scale factors for A or transpose(A).
* If equed = 'C' or 'B', A (if A->Stype = SLU_NC) or transpose(A)
* (if A->Stype = SLU_NR) is multiplied on the right by diag(C).
* If equed = 'N' or 'R', C is not accessed.
* If fact = 'F', C is an input argument; otherwise, C is output.
* If fact = 'F' and equed = 'C' or 'B', each element of C must
* be positive.
*
* L (output) SuperMatrix*
* The factor L from the factorization
* Pr*A*Pc=L*U (if A->Stype SLU_= NC) or
* Pr*transpose(A)*Pc=L*U (if A->Stype = SLU_NR).
* Uses compressed row subscripts storage for supernodes, i.e.,
* L has types: Stype = SC, Dtype = SLU_Z, Mtype = TRLU.
*
* U (output) SuperMatrix*
* The factor U from the factorization
* Pr*A*Pc=L*U (if A->Stype = SLU_NC) or
* Pr*transpose(A)*Pc=L*U (if A->Stype = SLU_NR).
* Uses column-wise storage scheme, i.e., U has types:
* Stype = SLU_NC, Dtype = SLU_Z, Mtype = TRU.
*
* work (workspace/output) void*, size (lwork) (in bytes)
* User supplied workspace, should be large enough
* to hold data structures for factors L and U.
* On exit, if fact is not 'F', L and U point to this array.
*
* lwork (input) int
* Specifies the size of work array in bytes.
* = 0: allocate space internally by system malloc;
* > 0: use user-supplied work array of length lwork in bytes,
* returns error if space runs out.
* = -1: the routine guesses the amount of space needed without
* performing the factorization, and returns it in
* mem_usage->total_needed; no other side effects.
*
* See argument 'mem_usage' for memory usage statistics.
*
* B (input/output) SuperMatrix*
* B has types: Stype = SLU_DN, Dtype = SLU_Z, Mtype = SLU_GE.
* On entry, the right hand side matrix.
* On exit,
* if equed = 'N', B is not modified; otherwise
* if A->Stype = SLU_NC:
* if trans = 'N' and equed = 'R' or 'B', B is overwritten by
* diag(R)*B;
* if trans = 'T' or 'C' and equed = 'C' of 'B', B is
* overwritten by diag(C)*B;
* if A->Stype = SLU_NR:
* if trans = 'N' and equed = 'C' or 'B', B is overwritten by
* diag(C)*B;
* if trans = 'T' or 'C' and equed = 'R' of 'B', B is
* overwritten by diag(R)*B.
*
* X (output) SuperMatrix*
* X has types: Stype = SLU_DN, Dtype = SLU_Z, Mtype = SLU_GE.
* If info = 0 or info = A->ncol+1, X contains the solution matrix
* to the original system of equations. Note that A and B are modified
* on exit if equed is not 'N', and the solution to the equilibrated
* system is inv(diag(C))*X if trans = 'N' and equed = 'C' or 'B',
* or inv(diag(R))*X if trans = 'T' or 'C' and equed = 'R' or 'B'.
*
* recip_pivot_growth (output) double*
* The reciprocal pivot growth factor max_j( norm(A_j)/norm(U_j) ).
* The infinity norm is used. If recip_pivot_growth is much less
* than 1, the stability of the LU factorization could be poor.
*
* rcond (output) double*
* The estimate of the reciprocal condition number of the matrix A
* after equilibration (if done). If rcond is less than the machine
* precision (in particular, if rcond = 0), the matrix is singular
* to working precision. This condition is indicated by a return
* code of info > 0.
*
* FERR (output) double*, dimension (B->ncol)
* The estimated forward error bound for each solution vector
* X(j) (the j-th column of the solution matrix X).
* If XTRUE is the true solution corresponding to X(j), FERR(j)
* is an estimated upper bound for the magnitude of the largest
* element in (X(j) - XTRUE) divided by the magnitude of the
* largest element in X(j). The estimate is as reliable as
* the estimate for RCOND, and is almost always a slight
* overestimate of the true error.
*
* BERR (output) double*, dimension (B->ncol)
* The componentwise relative backward error of each solution
* vector X(j) (i.e., the smallest relative change in
* any element of A or B that makes X(j) an exact solution).
*
* mem_usage (output) mem_usage_t*
* Record the memory usage statistics, consisting of following fields:
* - for_lu (float)
* The amount of space used in bytes for L\U data structures.
* - total_needed (float)
* The amount of space needed in bytes to perform factorization.
* - expansions (int)
* The number of memory expansions during the LU factorization.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
* > 0: if info = i, and i is
* <= A->ncol: U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly
* singular, so the solution and error bounds
* could not be computed.
* = A->ncol+1: U is nonsingular, but RCOND is less than machine
* precision, meaning that the matrix is singular to
* working precision. Nevertheless, the solution and
* error bounds are computed because there are a number
* of situations where the computed solution can be more
* accurate than the value of RCOND would suggest.
* > A->ncol+1: number of bytes allocated when memory allocation
* failure occurred, plus A->ncol.
*
*/
DNformat *Bstore, *Xstore;
doublecomplex *Bmat, *Xmat;
int ldb, ldx, nrhs;
SuperMatrix *AA;/* A in SLU_NC format used by the factorization routine.*/
SuperMatrix AC; /* Matrix postmultiplied by Pc */
int colequ, equil, nofact, notran, rowequ;
char trant[1], norm[1];
int i, j, info1;
double amax, anorm, bignum, smlnum, colcnd, rowcnd, rcmax, rcmin;
int relax, panel_size;
double diag_pivot_thresh, drop_tol;
double t0; /* temporary time */
double *utime;
extern SuperLUStat_t SuperLUStat;
/* External functions */
extern double zlangs(char *, SuperMatrix *);
extern double dlamch_(char *);
Bstore = B->Store;
Xstore = X->Store;
Bmat = Bstore->nzval;
Xmat = Xstore->nzval;
ldb = Bstore->lda;
ldx = Xstore->lda;
nrhs = B->ncol;
#if 0
printf("zgssvx: fact=%c, trans=%c, refact=%c, equed=%c\n",
*fact, *trans, *refact, *equed);
#endif
*info = 0;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
notran = lsame_(trans, "N");
if (nofact || equil) {
*(unsigned char *)equed = 'N';
rowequ = FALSE;
colequ = FALSE;
} else {
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
smlnum = dlamch_("Safe minimum");
bignum = 1. / smlnum;
}
/* Test the input parameters */
if (!nofact && !equil && !lsame_(fact, "F")) *info = -1;
else if (!notran && !lsame_(trans, "T") && !lsame_(trans, "C")) *info = -2;
else if ( !(lsame_(refact,"Y") || lsame_(refact, "N")) ) *info = -3;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
(A->Stype != SLU_NC && A->Stype != SLU_NR) ||
A->Dtype != SLU_Z || A->Mtype != SLU_GE )
*info = -4;
else if (lsame_(fact, "F") && !(rowequ || colequ || lsame_(equed, "N")))
*info = -9;
else {
if (rowequ) {
rcmin = bignum;
rcmax = 0.;
for (j = 0; j < A->nrow; ++j) {
rcmin = SUPERLU_MIN(rcmin, R[j]);
rcmax = SUPERLU_MAX(rcmax, R[j]);
}
if (rcmin <= 0.) *info = -10;
else if ( A->nrow > 0)
rowcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
else rowcnd = 1.;
}
if (colequ && *info == 0) {
rcmin = bignum;
rcmax = 0.;
for (j = 0; j < A->nrow; ++j) {
rcmin = SUPERLU_MIN(rcmin, C[j]);
rcmax = SUPERLU_MAX(rcmax, C[j]);
}
if (rcmin <= 0.) *info = -11;
else if (A->nrow > 0)
colcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
else colcnd = 1.;
}
if (*info == 0) {
if ( lwork < -1 ) *info = -15;
else if ( B->ncol < 0 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_Z ||
B->Mtype != SLU_GE )
*info = -16;
else if ( X->ncol < 0 || Xstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->ncol != X->ncol || X->Stype != SLU_DN ||
X->Dtype != SLU_Z || X->Mtype != SLU_GE )
*info = -17;
}
}
if (*info != 0) {
i = -(*info);
xerbla_("zgssvx", &i);
return;
}
/* Default values for factor_params */
panel_size = sp_ienv(1);
relax = sp_ienv(2);
diag_pivot_thresh = 1.0;
drop_tol = 0.0;
if ( factor_params != NULL ) {
if ( factor_params->panel_size != -1 )
panel_size = factor_params->panel_size;
if ( factor_params->relax != -1 ) relax = factor_params->relax;
if ( factor_params->diag_pivot_thresh != -1 )
diag_pivot_thresh = factor_params->diag_pivot_thresh;
if ( factor_params->drop_tol != -1 )
drop_tol = factor_params->drop_tol;
}
StatInit(panel_size, relax);
utime = SuperLUStat.utime;
/* Convert A to SLU_NC format when necessary. */
if ( A->Stype == SLU_NR ) {
NRformat *Astore = A->Store;
AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
zCreate_CompCol_Matrix(AA, A->ncol, A->nrow, Astore->nnz,
Astore->nzval, Astore->colind, Astore->rowptr,
SLU_NC, A->Dtype, A->Mtype);
if ( notran ) { /* Reverse the transpose argument. */
*trant = 'T';
notran = 0;
} else {
*trant = 'N';
notran = 1;
}
} else { /* A->Stype == SLU_NC */
*trant = *trans;
AA = A;
}
if ( equil ) {
t0 = SuperLU_timer_();
/* Compute row and column scalings to equilibrate the matrix A. */
zgsequ(AA, R, C, &rowcnd, &colcnd, &amax, &info1);
if ( info1 == 0 ) {
/* Equilibrate matrix A. */
zlaqgs(AA, R, C, rowcnd, colcnd, amax, equed);
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
}
utime[EQUIL] = SuperLU_timer_() - t0;
}
/* Scale the right hand side if equilibration was performed. */
if ( notran ) {
if ( rowequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
zd_mult(&Bmat[i + j*ldb], &Bmat[i + j*ldb], R[i]);
}
}
} else if ( colequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
zd_mult(&Bmat[i + j*ldb], &Bmat[i + j*ldb], C[i]);
}
}
if ( nofact || equil ) {
t0 = SuperLU_timer_();
sp_preorder(refact, AA, perm_c, etree, &AC);
utime[ETREE] = SuperLU_timer_() - t0;
/* printf("Factor PA = LU ... relax %d\tw %d\tmaxsuper %d\trowblk %d\n",
relax, panel_size, sp_ienv(3), sp_ienv(4));
fflush(stdout); */
/* Compute the LU factorization of A*Pc. */
t0 = SuperLU_timer_();
zgstrf(refact, &AC, diag_pivot_thresh, drop_tol, relax, panel_size,
etree, work, lwork, perm_r, perm_c, L, U, info);
utime[FACT] = SuperLU_timer_() - t0;
if ( lwork == -1 ) {
mem_usage->total_needed = *info - A->ncol;
return;
}
}
if ( *info > 0 ) {
if ( *info <= A->ncol ) {
/* Compute the reciprocal pivot growth factor of the leading
rank-deficient *info columns of A. */
*recip_pivot_growth = zPivotGrowth(*info, AA, perm_c, L, U);
}
return;
}
/* Compute the reciprocal pivot growth factor *recip_pivot_growth. */
*recip_pivot_growth = zPivotGrowth(A->ncol, AA, perm_c, L, U);
/* Estimate the reciprocal of the condition number of A. */
t0 = SuperLU_timer_();
if ( notran ) {
*(unsigned char *)norm = '1';
} else {
*(unsigned char *)norm = 'I';
}
anorm = zlangs(norm, AA);
zgscon(norm, L, U, anorm, rcond, info);
utime[RCOND] = SuperLU_timer_() - t0;
/* Compute the solution matrix X. */
for (j = 0; j < nrhs; j++) /* Save a copy of the right hand sides */
for (i = 0; i < B->nrow; i++)
Xmat[i + j*ldx] = Bmat[i + j*ldb];
t0 = SuperLU_timer_();
zgstrs (trant, L, U, perm_r, perm_c, X, info);
utime[SOLVE] = SuperLU_timer_() - t0;
/* Use iterative refinement to improve the computed solution and compute
error bounds and backward error estimates for it. */
t0 = SuperLU_timer_();
zgsrfs(trant, AA, L, U, perm_r, perm_c, equed, R, C, B,
X, ferr, berr, info);
utime[REFINE] = SuperLU_timer_() - t0;
/* Transform the solution matrix X to a solution of the original system. */
if ( notran ) {
if ( colequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
zd_mult(&Xmat[i + j*ldx], &Xmat[i + j*ldx], C[i]);
}
}
} else if ( rowequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
zd_mult(&Xmat[i+ j*ldx], &Xmat[i+ j*ldx], R[i]);
}
}
/* Set INFO = A->ncol+1 if the matrix is singular to working precision. */
if ( *rcond < dlamch_("E") ) *info = A->ncol + 1;
zQuerySpace(L, U, panel_size, mem_usage);
if ( nofact || equil ) Destroy_CompCol_Permuted(&AC);
if ( A->Stype == SLU_NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
PrintStat( &SuperLUStat );
StatFree();
}
void f_destroy_ScalePerm_handle(fptr *handle)
{
SUPERLU_FREE((void *)*handle);
}
void tlin::destroyS(SuperMatrix &A, bool destroyData) {
if (destroyData)
Destroy_CompCol_Matrix(&A);
else
SUPERLU_FREE(A.Store);
}
void
pdgssvx(superlu_options_t_Distributed *options, SuperMatrix *A,
ScalePermstruct_t *ScalePermstruct,
double B[], int ldb, int nrhs, gridinfo_t *grid,
LUstruct_t *LUstruct, SOLVEstruct_t *SOLVEstruct, double *berr,
SuperLUStat_t *stat, int *info)
{
/*
* -- Distributed SuperLU routine (version 2.0) --
* Lawrence Berkeley National Lab, Univ. of California Berkeley.
* March 15, 2003
*
*
* Purpose
* =======
*
* PDGSSVX solves a system of linear equations A*X=B,
* by using Gaussian elimination with "static pivoting" to
* compute the LU factorization of A.
*
* Static pivoting is a technique that combines the numerical stability
* of partial pivoting with the scalability of Cholesky (no pivoting),
* to run accurately and efficiently on large numbers of processors.
*
* See our paper at http://www.nersc.gov/~xiaoye/SuperLU/ for a detailed
* description of the parallel algorithms.
*
* Here are the options for using this code:
*
* 1. Independent of all the other options specified below, the
* user must supply
*
* - B, the matrix of right-hand sides, distributed by block rows,
* and its dimensions ldb (local) and nrhs (global)
* - grid, a structure describing the 2D processor mesh
* - options->IterRefine, which determines whether or not to
* improve the accuracy of the computed solution using
* iterative refinement
*
* On output, B is overwritten with the solution X.
*
* 2. Depending on options->Fact, the user has four options
* for solving A*X=B. The standard option is for factoring
* A "from scratch". (The other options, described below,
* are used when A is sufficiently similar to a previously
* solved problem to save time by reusing part or all of
* the previous factorization.)
*
* - options->Fact = DOFACT: A is factored "from scratch"
*
* In this case the user must also supply
*
* o A, the input matrix
*
* as well as the following options to determine what matrix to
* factorize.
*
* o options->Equil, to specify how to scale the rows and columns
* of A to "equilibrate" it (to try to reduce its
* condition number and so improve the
* accuracy of the computed solution)
*
* o options->RowPerm, to specify how to permute the rows of A
* (typically to control numerical stability)
*
* o options->ColPerm, to specify how to permute the columns of A
* (typically to control fill-in and enhance
* parallelism during factorization)
*
* o options->ReplaceTinyPivot, to specify how to deal with tiny
* pivots encountered during factorization
* (to control numerical stability)
*
* The outputs returned include
*
* o ScalePermstruct, modified to describe how the input matrix A
* was equilibrated and permuted:
* . ScalePermstruct->DiagScale, indicates whether the rows and/or
* columns of A were scaled
* . ScalePermstruct->R, array of row scale factors
* . ScalePermstruct->C, array of column scale factors
* . ScalePermstruct->perm_r, row permutation vector
* . ScalePermstruct->perm_c, column permutation vector
*
* (part of ScalePermstruct may also need to be supplied on input,
* depending on options->RowPerm and options->ColPerm as described
* later).
*
* o A, the input matrix A overwritten by the scaled and permuted
* matrix Pc*Pr*diag(R)*A*diag(C), where
* Pr and Pc are row and columns permutation matrices determined
* by ScalePermstruct->perm_r and ScalePermstruct->perm_c,
* respectively, and
* diag(R) and diag(C) are diagonal scaling matrices determined
* by ScalePermstruct->DiagScale, ScalePermstruct->R and
* ScalePermstruct->C
*
* o LUstruct, which contains the L and U factorization of A1 where
*
* A1 = Pc*Pr*diag(R)*A*diag(C)*Pc^T = L*U
*
* (Note that A1 = Aout * Pc^T, where Aout is the matrix stored
* in A on output.)
*
* 3. The second value of options->Fact assumes that a matrix with the same
* sparsity pattern as A has already been factored:
*
* - options->Fact = SamePattern: A is factored, assuming that it has
* the same nonzero pattern as a previously factored matrix. In
* this case the algorithm saves time by reusing the previously
* computed column permutation vector stored in
* ScalePermstruct->perm_c and the "elimination tree" of A
* stored in LUstruct->etree
*
* In this case the user must still specify the following options
* as before:
*
* o options->Equil
* o options->RowPerm
* o options->ReplaceTinyPivot
*
* but not options->ColPerm, whose value is ignored. This is because the
* previous column permutation from ScalePermstruct->perm_c is used as
* input. The user must also supply
*
* o A, the input matrix
* o ScalePermstruct->perm_c, the column permutation
* o LUstruct->etree, the elimination tree
*
* The outputs returned include
*
* o A, the input matrix A overwritten by the scaled and permuted
* matrix as described above
* o ScalePermstruct, modified to describe how the input matrix A was
* equilibrated and row permuted
* o LUstruct, modified to contain the new L and U factors
*
* 4. The third value of options->Fact assumes that a matrix B with the same
* sparsity pattern as A has already been factored, and where the
* row permutation of B can be reused for A. This is useful when A and B
* have similar numerical values, so that the same row permutation
* will make both factorizations numerically stable. This lets us reuse
* all of the previously computed structure of L and U.
*
* - options->Fact = SamePattern_SameRowPerm: A is factored,
* assuming not only the same nonzero pattern as the previously
* factored matrix B, but reusing B's row permutation.
*
* In this case the user must still specify the following options
* as before:
*
* o options->Equil
* o options->ReplaceTinyPivot
*
* but not options->RowPerm or options->ColPerm, whose values are
* ignored. This is because the permutations from ScalePermstruct->perm_r
* and ScalePermstruct->perm_c are used as input.
*
* The user must also supply
*
* o A, the input matrix
* o ScalePermstruct->DiagScale, how the previous matrix was row
* and/or column scaled
* o ScalePermstruct->R, the row scalings of the previous matrix,
* if any
* o ScalePermstruct->C, the columns scalings of the previous matrix,
* if any
* o ScalePermstruct->perm_r, the row permutation of the previous
* matrix
* o ScalePermstruct->perm_c, the column permutation of the previous
* matrix
* o all of LUstruct, the previously computed information about
* L and U (the actual numerical values of L and U
* stored in LUstruct->Llu are ignored)
*
* The outputs returned include
*
* o A, the input matrix A overwritten by the scaled and permuted
* matrix as described above
* o ScalePermstruct, modified to describe how the input matrix A was
* equilibrated (thus ScalePermstruct->DiagScale,
* R and C may be modified)
* o LUstruct, modified to contain the new L and U factors
*
* 5. The fourth and last value of options->Fact assumes that A is
* identical to a matrix that has already been factored on a previous
* call, and reuses its entire LU factorization
*
* - options->Fact = Factored: A is identical to a previously
* factorized matrix, so the entire previous factorization
* can be reused.
*
* In this case all the other options mentioned above are ignored
* (options->Equil, options->RowPerm, options->ColPerm,
* options->ReplaceTinyPivot)
*
* The user must also supply
*
* o A, the unfactored matrix, only in the case that iterative
* refinment is to be done (specifically A must be the output
* A from the previous call, so that it has been scaled and
* permuted)
* o all of ScalePermstruct
* o all of LUstruct, including the actual numerical values of
* L and U
*
* all of which are unmodified on output.
*
* Arguments
* =========
*
* options (input) superlu_options_t_Distributed* (global)
* The structure defines the input parameters to control
* how the LU decomposition will be performed.
* The following fields should be defined for this structure:
*
* o Fact (fact_t)
* Specifies whether or not the factored form of the matrix
* A is supplied on entry, and if not, how the matrix A should
* be factorized based on the previous history.
*
* = DOFACT: The matrix A will be factorized from scratch.
* Inputs: A
* options->Equil, RowPerm, ColPerm, ReplaceTinyPivot
* Outputs: modified A
* (possibly row and/or column scaled and/or
* permuted)
* all of ScalePermstruct
* all of LUstruct
*
* = SamePattern: the matrix A will be factorized assuming
* that a factorization of a matrix with the same sparsity
* pattern was performed prior to this one. Therefore, this
* factorization will reuse column permutation vector
* ScalePermstruct->perm_c and the elimination tree
* LUstruct->etree
* Inputs: A
* options->Equil, RowPerm, ReplaceTinyPivot
* ScalePermstruct->perm_c
* LUstruct->etree
* Outputs: modified A
* (possibly row and/or column scaled and/or
* permuted)
* rest of ScalePermstruct (DiagScale, R, C, perm_r)
* rest of LUstruct (GLU_persist, Llu)
*
* = SamePattern_SameRowPerm: the matrix A will be factorized
* assuming that a factorization of a matrix with the same
* sparsity pattern and similar numerical values was performed
* prior to this one. Therefore, this factorization will reuse
* both row and column scaling factors R and C, and the
* both row and column permutation vectors perm_r and perm_c,
* distributed data structure set up from the previous symbolic
* factorization.
* Inputs: A
* options->Equil, ReplaceTinyPivot
* all of ScalePermstruct
* all of LUstruct
* Outputs: modified A
* (possibly row and/or column scaled and/or
* permuted)
* modified LUstruct->Llu
* = FACTORED: the matrix A is already factored.
* Inputs: all of ScalePermstruct
* all of LUstruct
*
* o Equil (yes_no_t)
* Specifies whether to equilibrate the system.
* = NO: no equilibration.
* = YES: scaling factors are computed to equilibrate the system:
* diag(R)*A*diag(C)*inv(diag(C))*X = diag(R)*B.
* Whether or not the system will be equilibrated depends
* on the scaling of the matrix A, but if equilibration is
* used, A is overwritten by diag(R)*A*diag(C) and B by
* diag(R)*B.
*
* o RowPerm (rowperm_t)
* Specifies how to permute rows of the matrix A.
* = NATURAL: use the natural ordering.
* = LargeDiag: use the Duff/Koster algorithm to permute rows of
* the original matrix to make the diagonal large
* relative to the off-diagonal.
* = MY_PERMR: use the ordering given in ScalePermstruct->perm_r
* input by the user.
*
* o ColPerm (colperm_t)
* Specifies what type of column permutation to use to reduce fill.
* = NATURAL: natural ordering.
* = MMD_AT_PLUS_A: minimum degree ordering on structure of A'+A.
* = MMD_ATA: minimum degree ordering on structure of A'*A.
* = COLAMD: approximate minimum degree column ordering.
* = MY_PERMC: the ordering given in ScalePermstruct->perm_c.
*
* o ReplaceTinyPivot (yes_no_t)
* = NO: do not modify pivots
* = YES: replace tiny pivots by sqrt(epsilon)*norm(A) during
* LU factorization.
*
* o IterRefine (IterRefine_t)
* Specifies how to perform iterative refinement.
* = NO: no iterative refinement.
* = DOUBLE: accumulate residual in double precision.
* = EXTRA: accumulate residual in extra precision.
*
* NOTE: all options must be indentical on all processes when
* calling this routine.
*
* A (input/output) SuperMatrix* (local)
* On entry, matrix A in A*X=B, of dimension (A->nrow, A->ncol).
* The number of linear equations is A->nrow. The type of A must be:
* Stype = SLU_NR_loc; Dtype = SLU_D; Mtype = SLU_GE.
* That is, A is stored in distributed compressed row format.
* See supermatrix.h for the definition of 'SuperMatrix'.
* This routine only handles square A, however, the LU factorization
* routine PDGSTRF can factorize rectangular matrices.
* On exit, A may be overwtirren by Pc*Pr*diag(R)*A*diag(C),
* depending on ScalePermstruct->DiagScale, options->RowPerm and
* options->ColPerm:
* if ScalePermstruct->DiagScale != NOEQUIL, A is overwritten by
* diag(R)*A*diag(C).
* if options->RowPerm != NATURAL, A is further overwritten by
* Pr*diag(R)*A*diag(C).
* if options->ColPerm != NATURAL, A is further overwritten by
* Pc*Pr*diag(R)*A*diag(C).
* If all the above condition are true, the LU decomposition is
* performed on the matrix Pc*Pr*diag(R)*A*diag(C)*Pc^T.
*
* ScalePermstruct (input/output) ScalePermstruct_t* (global)
* The data structure to store the scaling and permutation vectors
* describing the transformations performed to the matrix A.
* It contains the following fields:
*
* o DiagScale (DiagScale_t)
* Specifies the form of equilibration that was done.
* = NOEQUIL: no equilibration.
* = ROW: row equilibration, i.e., A was premultiplied by
* diag(R).
* = COL: Column equilibration, i.e., A was postmultiplied
* by diag(C).
* = BOTH: both row and column equilibration, i.e., A was
* replaced by diag(R)*A*diag(C).
* If options->Fact = FACTORED or SamePattern_SameRowPerm,
* DiagScale is an input argument; otherwise it is an output
* argument.
*
* o perm_r (int*)
* Row permutation vector, which defines the permutation matrix Pr;
* perm_r[i] = j means row i of A is in position j in Pr*A.
* If options->RowPerm = MY_PERMR, or
* options->Fact = SamePattern_SameRowPerm, perm_r is an
* input argument; otherwise it is an output argument.
*
* o perm_c (int*)
* Column permutation vector, which defines the
* permutation matrix Pc; perm_c[i] = j means column i of A is
* in position j in A*Pc.
* If options->ColPerm = MY_PERMC or options->Fact = SamePattern
* or options->Fact = SamePattern_SameRowPerm, perm_c is an
* input argument; otherwise, it is an output argument.
* On exit, perm_c may be overwritten by the product of the input
* perm_c and a permutation that postorders the elimination tree
* of Pc*A'*A*Pc'; perm_c is not changed if the elimination tree
* is already in postorder.
*
* o R (double*) dimension (A->nrow)
* The row scale factors for A.
* If DiagScale = ROW or BOTH, A is multiplied on the left by
* diag(R).
* If DiagScale = NOEQUIL or COL, R is not defined.
* If options->Fact = FACTORED or SamePattern_SameRowPerm, R is
* an input argument; otherwise, R is an output argument.
*
* o C (double*) dimension (A->ncol)
* The column scale factors for A.
* If DiagScale = COL or BOTH, A is multiplied on the right by
* diag(C).
* If DiagScale = NOEQUIL or ROW, C is not defined.
* If options->Fact = FACTORED or SamePattern_SameRowPerm, C is
* an input argument; otherwise, C is an output argument.
*
* B (input/output) double* (local)
* On entry, the right-hand side matrix of dimension (m_loc, nrhs),
* where, m_loc is the number of rows stored locally on my
* process and is defined in the data structure of matrix A.
* On exit, the solution matrix if info = 0;
*
* ldb (input) int (local)
* The leading dimension of matrix B.
*
* nrhs (input) int (global)
* The number of right-hand sides.
* If nrhs = 0, only LU decomposition is performed, the forward
* and back substitutions are skipped.
*
* grid (input) gridinfo_t* (global)
* The 2D process mesh. It contains the MPI communicator, the number
* of process rows (NPROW), the number of process columns (NPCOL),
* and my process rank. It is an input argument to all the
* parallel routines.
* Grid can be initialized by subroutine SUPERLU_GRIDINIT.
* See superlu_ddefs.h for the definition of 'gridinfo_t'.
*
* LUstruct (input/output) LUstruct_t*
* The data structures to store the distributed L and U factors.
* It contains the following fields:
*
* o etree (int*) dimension (A->ncol) (global)
* Elimination tree of Pc*(A'+A)*Pc' or Pc*A'*A*Pc'.
* It is computed in sp_colorder() during the first factorization,
* and is reused in the subsequent factorizations of the matrices
* with the same nonzero pattern.
* On exit of sp_colorder(), the columns of A are permuted so that
* the etree is in a certain postorder. This postorder is reflected
* in ScalePermstruct->perm_c.
* NOTE:
* Etree is a vector of parent pointers for a forest whose vertices
* are the integers 0 to A->ncol-1; etree[root]==A->ncol.
*
* o Glu_persist (Glu_persist_t*) (global)
* Global data structure (xsup, supno) replicated on all processes,
* describing the supernode partition in the factored matrices
* L and U:
* xsup[s] is the leading column of the s-th supernode,
* supno[i] is the supernode number to which column i belongs.
*
* o Llu (LocalLU_t*) (local)
* The distributed data structures to store L and U factors.
* See superlu_ddefs.h for the definition of 'LocalLU_t'.
*
* SOLVEstruct (input/output) SOLVEstruct_t*
* The data structure to hold the communication pattern used
* in the phases of triangular solution and iterative refinement.
* This pattern should be intialized only once for repeated solutions.
* If options->SolveInitialized = YES, it is an input argument.
* If options->SolveInitialized = NO and nrhs != 0, it is an output
* argument. See superlu_ddefs.h for the definition of 'SOLVEstruct_t'.
*
* berr (output) double*, dimension (nrhs) (global)
* The componentwise relative backward error of each solution
* vector X(j) (i.e., the smallest relative change in
* any element of A or B that makes X(j) an exact solution).
*
* stat (output) SuperLUStat_t*
* Record the statistics on runtime and floating-point operation count.
* See util.h for the definition of 'SuperLUStat_t'.
*
* info (output) int*
* = 0: successful exit
* > 0: if info = i, and i is
* <= A->ncol: U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly singular,
* so the solution could not be computed.
* > A->ncol: number of bytes allocated when memory allocation
* failure occurred, plus A->ncol.
*
* See superlu_ddefs.h for the definitions of varioous data types.
*
*/
NRformat_loc *Astore;
SuperMatrix GA; /* Global A in NC format */
NCformat *GAstore;
double *a_GA;
SuperMatrix GAC; /* Global A in NCP format (add n end pointers) */
NCPformat *GACstore;
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
Glu_freeable_t *Glu_freeable;
/* The nonzero structures of L and U factors, which are
replicated on all processrs.
(lsub, xlsub) contains the compressed subscript of
supernodes in L.
(usub, xusub) contains the compressed subscript of
nonzero segments in U.
If options->Fact != SamePattern_SameRowPerm, they are
computed by SYMBFACT routine, and then used by PDDISTRIBUTE
routine. They will be freed after PDDISTRIBUTE routine.
If options->Fact == SamePattern_SameRowPerm, these
structures are not used. */
fact_t Fact;
double *a;
int_t *colptr, *rowind;
int_t *perm_r; /* row permutations from partial pivoting */
int_t *perm_c; /* column permutation vector */
int_t *etree; /* elimination tree */
int_t *rowptr, *colind; /* Local A in NR*/
int_t *rowind_loc, *colptr_loc;
int_t colequ, Equil, factored, job, notran, rowequ, need_value;
int_t i, iinfo, j, irow, m, n, nnz, permc_spec, dist_mem_use;
int_t nnz_loc, m_loc, fst_row, icol;
int iam;
int ldx; /* LDA for matrix X (local). */
char equed[1], norm[1];
double *C, *R, *C1, *R1, amax, anorm, colcnd, rowcnd;
double *X, *b_col, *b_work, *x_col;
double t;
static mem_usage_t_Distributed num_mem_usage, symb_mem_usage;
#if ( PRNTlevel>= 2 )
double dmin, dsum, dprod;
#endif
int_t procs;
/* Initialization. */
m = A->nrow;
n = A->ncol;
Astore = (NRformat_loc *) A->Store;
nnz_loc = Astore->nnz_loc;
m_loc = Astore->m_loc;
fst_row = Astore->fst_row;
a = Astore->nzval;
rowptr = Astore->rowptr;
colind = Astore->colind;
/* Test the input parameters. */
*info = 0;
Fact = options->Fact;
if ( Fact < 0 || Fact > FACTORED )
*info = -1;
else if ( options->RowPerm < 0 || options->RowPerm > MY_PERMR )
*info = -1;
else if ( options->ColPerm < 0 || options->ColPerm > MY_PERMC )
*info = -1;
else if ( options->IterRefine < 0 || options->IterRefine > EXTRA )
*info = -1;
else if ( options->IterRefine == EXTRA ) {
*info = -1;
fprintf(stderr, "Extra precise iterative refinement yet to support.");
} else if ( A->nrow != A->ncol || A->nrow < 0 || A->Stype != SLU_NR_loc
|| A->Dtype != SLU_D || A->Mtype != SLU_GE )
*info = -2;
else if ( ldb < m_loc )
*info = -5;
else if ( nrhs < 0 )
*info = -6;
if ( *info ) {
i = -(*info);
pxerbla("pdgssvx", grid, -*info);
return;
}
factored = (Fact == FACTORED);
Equil = (!factored && options->Equil == YES);
notran = (options->Trans == NOTRANS);
iam = grid->iam;
job = 5;
if ( factored || (Fact == SamePattern_SameRowPerm && Equil) ) {
rowequ = (ScalePermstruct->DiagScale == ROW) ||
(ScalePermstruct->DiagScale == BOTH);
colequ = (ScalePermstruct->DiagScale == COL) ||
(ScalePermstruct->DiagScale == BOTH);
} else rowequ = colequ = FALSE;
/* The following arrays are replicated on all processes. */
perm_r = ScalePermstruct->perm_r;
perm_c = ScalePermstruct->perm_c;
etree = LUstruct->etree;
R = ScalePermstruct->R;
C = ScalePermstruct->C;
/********/
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pdgssvx()");
#endif
if ( Equil ) {
/* Allocate storage if not done so before. */
switch ( ScalePermstruct->DiagScale ) {
case NOEQUIL:
if ( !(R = (double *) doubleMalloc_dist(m)) )
ABORT("Malloc fails for R[].");
if ( !(C = (double *) doubleMalloc_dist(n)) )
ABORT("Malloc fails for C[].");
ScalePermstruct->R = R;
ScalePermstruct->C = C;
break;
case ROW:
if ( !(C = (double *) doubleMalloc_dist(n)) )
ABORT("Malloc fails for C[].");
ScalePermstruct->C = C;
break;
case COL:
if ( !(R = (double *) doubleMalloc_dist(m)) )
ABORT("Malloc fails for R[].");
ScalePermstruct->R = R;
break;
}
}
/* ------------------------------------------------------------
Diagonal scaling to equilibrate the matrix.
------------------------------------------------------------*/
if ( Equil ) {
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter equil");
#endif
t = SuperLU_timer_();
if ( Fact == SamePattern_SameRowPerm ) {
/* Reuse R and C. */
switch ( ScalePermstruct->DiagScale ) {
case NOEQUIL:
break;
case ROW:
irow = fst_row;
for (j = 0; j < m_loc; ++j) {
for (i = rowptr[j]; i < rowptr[j+1]; ++i) {
a[i] *= R[irow]; /* Scale rows. */
}
++irow;
}
break;
case COL:
for (j = 0; j < m_loc; ++j)
for (i = rowptr[j]; i < rowptr[j+1]; ++i) {
icol = colind[i];
a[i] *= C[icol]; /* Scale columns. */
}
break;
case BOTH:
irow = fst_row;
for (j = 0; j < m_loc; ++j) {
for (i = rowptr[j]; i < rowptr[j+1]; ++i) {
icol = colind[i];
a[i] *= R[irow] * C[icol]; /* Scale rows and cols. */
}
++irow;
}
break;
}
} else {
/* Compute the row and column scalings. */
pdgsequ(A, R, C, &rowcnd, &colcnd, &amax, &iinfo, grid);
/* Equilibrate matrix A if it is badly-scaled. */
pdlaqgs(A, R, C, rowcnd, colcnd, amax, equed);
if ( lsame_(equed, "R") ) {
ScalePermstruct->DiagScale = rowequ = ROW;
} else if ( lsame_(equed, "C") ) {
ScalePermstruct->DiagScale = colequ = COL;
} else if ( lsame_(equed, "B") ) {
ScalePermstruct->DiagScale = BOTH;
rowequ = ROW;
colequ = COL;
} else ScalePermstruct->DiagScale = NOEQUIL;
#if ( PRNTlevel>=1 )
if ( !iam ) {
printf(".. equilibrated? *equed = %c\n", *equed);
/*fflush(stdout);*/
}
#endif
} /* if Fact ... */
stat->utime[EQUIL] = SuperLU_timer_() - t;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit equil");
#endif
} /* if Equil ... */
/*
* Gather A from the distributed compressed row format to
* global A in compressed column format.
* Numerical values are gathered only when a row permutation
* for large diagonal is sought after.
*/
need_value = (options->RowPerm == LargeDiag &&
Fact != SamePattern_SameRowPerm && !factored);
pdCompRow_loc_to_CompCol_global(need_value, A, grid, &GA);
GAstore = (NCformat *) GA.Store;
colptr = GAstore->colptr;
rowind = GAstore->rowind;
nnz = GAstore->nnz;
if ( need_value ) a_GA = GAstore->nzval;
else assert(GAstore->nzval == NULL);
/* ------------------------------------------------------------
Find the row permutation for A.
------------------------------------------------------------*/
if ( options->RowPerm != NO ) {
t = SuperLU_timer_();
if ( options->RowPerm == MY_PERMR ) { /* Use user's perm_r. */
/* Permute the global matrix GA for symbfact() */
for (i = 0; i < colptr[n]; ++i) {
irow = rowind[i];
rowind[i] = perm_r[irow];
}
} else if ( !factored && Fact != SamePattern_SameRowPerm ) {
/* Get a new perm_r[] */
if ( job == 5 ) {
/* Allocate storage for scaling factors. */
if ( !(R1 = (double *) SUPERLU_MALLOC(m * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for R1[]");
if ( !(C1 = (double *) SUPERLU_MALLOC(n * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for C1[]");
}
if ( !iam ) {
/* Process 0 finds a row permutation for large diagonal. */
dldperm(job, m, nnz, colptr, rowind, a_GA, perm_r, R1, C1);
MPI_Bcast( perm_r, m, mpi_int_t, 0, grid->comm );
if ( job == 5 && Equil ) {
MPI_Bcast( R1, m, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( C1, n, MPI_DOUBLE, 0, grid->comm );
}
} else {
MPI_Bcast( perm_r, m, mpi_int_t, 0, grid->comm );
if ( job == 5 && Equil ) {
MPI_Bcast( R1, m, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( C1, n, MPI_DOUBLE, 0, grid->comm );
}
}
#if ( PRNTlevel>=2 )
dmin = dlamch_("Overflow");
dsum = 0.0;
dprod = 1.0;
#endif
if ( job == 5 ) {
if ( Equil ) {
for (i = 0; i < n; ++i) {
R1[i] = exp(R1[i]);
C1[i] = exp(C1[i]);
}
/* Permute the global matrix GA for symbfact(). */
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i) {
irow = rowind[i];
rowind[i] = perm_r[irow];
#if ( PRNTlevel>=2 )
if ( rowind[i] == j ) /* New diagonal */
dprod *= fabs(a[i]);
#endif
}
}
/* Scale the distributed matrix */
irow = fst_row;
for (j = 0; j < m_loc; ++j) {
for (i = rowptr[j]; i < rowptr[j+1]; ++i) {
icol = colind[i];
a[i] *= R1[irow] * C1[icol];
}
++irow;
}
/* Multiply together the scaling factors. */
if ( rowequ ) for (i = 0; i < m; ++i) R[i] *= R1[i];
else for (i = 0; i < m; ++i) R[i] = R1[i];
if ( colequ ) for (i = 0; i < n; ++i) C[i] *= C1[i];
else for (i = 0; i < n; ++i) C[i] = C1[i];
ScalePermstruct->DiagScale = BOTH;
rowequ = colequ = 1;
} else { /* No equilibration. Only permute the global A. */
for (i = colptr[0]; i < colptr[n]; ++i) {
irow = rowind[i];
rowind[i] = perm_r[irow];
}
}
SUPERLU_FREE (R1);
SUPERLU_FREE (C1);
} else { /* job = 2,3,4 */
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i) {
irow = rowind[i];
rowind[i] = perm_r[irow];
#if ( PRNTlevel>=2 )
if ( rowind[i] == j ) { /* New diagonal */
if ( job == 2 || job == 3 )
dmin = SUPERLU_MIN(dmin, fabs(a[i]));
else if ( job == 4 )
dsum += fabs(a[i]);
else if ( job == 5 )
dprod *= fabs(a[i]);
}
#endif
}
}
}
#if ( PRNTlevel>=2 )
if ( job == 2 || job == 3 ) {
if ( !iam ) printf("\tsmallest diagonal %e\n", dmin);
} else if ( job == 4 ) {
if ( !iam ) printf("\tsum of diagonal %e\n", dsum);
} else if ( job == 5 ) {
if ( !iam ) printf("\t product of diagonal %e\n", dprod);
}
#endif
} /* else !factored */
t = SuperLU_timer_() - t;
stat->utime[ROWPERM] = t;
#if ( PRNTlevel>=1 )
if ( !iam ) printf(".. LDPERM job %d\t time: %.2f\n", job, t);
#endif
} else { /* options->RowPerm == NOROWPERM */
for (i = 0; i <m; ++i) perm_r[i] = i;
}
#if ( DEBUGlevel>=1 )
if ( !iam ) PrintInt10("perm_r", m, perm_r);
#endif
if ( !factored || options->IterRefine ) {
/* Compute norm(A), which will be used to adjust small diagonal. */
if ( notran ) *(unsigned char *)norm = '1';
else *(unsigned char *)norm = 'I';
anorm = pdlangs(norm, A, grid);
#if ( PRNTlevel>=1 )
if ( !iam ) printf(".. anorm %e\n", anorm);
#endif
}
/* ------------------------------------------------------------
Perform the LU factorization.
------------------------------------------------------------*/
if ( !factored ) {
t = SuperLU_timer_();
/*
* Get column permutation vector perm_c[], according to permc_spec:
* permc_spec = NATURAL: natural ordering
* permc_spec = MMD_AT_PLUS_A: minimum degree on structure of A'+A
* permc_spec = MMD_ATA: minimum degree on structure of A'*A
* permc_spec = COLAMD: approximate minimum degree column ordering
* permc_spec = MY_PERMC: the ordering already supplied in perm_c[]
*/
permc_spec = options->ColPerm;
if ( permc_spec != MY_PERMC && Fact == DOFACT )
get_perm_c_dist(iam, permc_spec, &GA, perm_c);
/* Compute the elimination tree of Pc*(A'+A)*Pc' or Pc*A'*A*Pc'
(a.k.a. column etree), depending on the choice of ColPerm.
Adjust perm_c[] to be consistent with a postorder of etree.
Permute columns of A to form A*Pc'. */
sp_colorder(options, &GA, perm_c, etree, &GAC);
/* Form Pc*A*Pc' to preserve the diagonal of the matrix GAC. */
{
int_t *GACcolbeg, *GACcolend, *GACrowind;
GACstore = GAC.Store;
GACcolbeg = GACstore->colbeg;
GACcolend = GACstore->colend;
GACrowind = GACstore->rowind;
for (j = 0; j < n; ++j) {
for (i = GACcolbeg[j]; i < GACcolend[j]; ++i) {
irow = GACrowind[i];
GACrowind[i] = perm_c[irow];
}
}
}
stat->utime[COLPERM] = SuperLU_timer_() - t;
/* Perform a symbolic factorization on Pc*Pr*A*Pc' and set up the
nonzero data structures which are suitable for supernodal GENP. */
if ( Fact != SamePattern_SameRowPerm ) {
#if ( PRNTlevel>=1 )
if ( !iam )
printf(".. symbfact(): relax %4d, maxsuper %4d, fill %4d\n",
sp_ienv_dist(2), sp_ienv_dist(3), sp_ienv_dist(6));
#endif
t = SuperLU_timer_();
if ( !(Glu_freeable = (Glu_freeable_t *)
SUPERLU_MALLOC(sizeof(Glu_freeable_t))) )
ABORT("Malloc fails for Glu_freeable.");
/* Every process does this. */
iinfo = symbfact(iam, &GAC, perm_c, etree,
Glu_persist, Glu_freeable);
stat->utime[SYMBFAC] = SuperLU_timer_() - t;
if ( iinfo < 0 ) { /* Successful return */
QuerySpace_dist(n, -iinfo, Glu_freeable, &symb_mem_usage);
#if ( PRNTlevel>=1 )
if ( !iam ) {
printf("\tNo of supers %ld\n", Glu_persist->supno[n-1]+1);
printf("\tSize of G(L) %ld\n", Glu_freeable->xlsub[n]);
printf("\tSize of G(U) %ld\n", Glu_freeable->xusub[n]);
printf("\tint %d, short %d, float %d, double %d\n",
sizeof(int_t), sizeof(short), sizeof(float),
sizeof(double));
printf("\tSYMBfact (MB):\tL\\U %.2f\ttotal %.2f\texpansions %d\n",
symb_mem_usage.for_lu*1e-6,
symb_mem_usage.total*1e-6,
symb_mem_usage.expansions);
}
#endif
} else {
if ( !iam ) {
fprintf(stderr, "symbfact() error returns %d\n", iinfo);
exit(-1);
}
}
}
/* Apply column permutation to the original distributed A */
for (j = 0; j < nnz_loc; ++j) colind[j] = perm_c[colind[j]];
/* Distribute Pc*Pr*diag(R)*A*diag(C)*Pc' into L and U storage.
NOTE: the row permutation Pc*Pr is applied internally in the
distribution routine. */
t = SuperLU_timer_();
dist_mem_use = pddistribute(Fact, n, A, ScalePermstruct,
Glu_freeable, LUstruct, grid);
stat->utime[DIST] = SuperLU_timer_() - t;
/* Deallocate storage used in symbolic factorization. */
if ( Fact != SamePattern_SameRowPerm ) {
iinfo = symbfact_SubFree(Glu_freeable);
SUPERLU_FREE(Glu_freeable);
}
/* Perform numerical factorization in parallel. */
t = SuperLU_timer_();
pdgstrf(options, m, n, anorm, LUstruct, grid, stat, info);
stat->utime[FACT] = SuperLU_timer_() - t;
#if ( PRNTlevel>=1 )
{
int_t TinyPivots;
float for_lu, total, max, avg, temp;
dQuerySpace_dist(n, LUstruct, grid, &num_mem_usage);
MPI_Reduce( &num_mem_usage.for_lu, &for_lu,
1, MPI_FLOAT, MPI_SUM, 0, grid->comm );
MPI_Reduce( &num_mem_usage.total, &total,
1, MPI_FLOAT, MPI_SUM, 0, grid->comm );
temp = SUPERLU_MAX(symb_mem_usage.total,
symb_mem_usage.for_lu +
(float)dist_mem_use + num_mem_usage.for_lu);
temp = SUPERLU_MAX(temp, num_mem_usage.total);
MPI_Reduce( &temp, &max,
1, MPI_FLOAT, MPI_MAX, 0, grid->comm );
MPI_Reduce( &temp, &avg,
1, MPI_FLOAT, MPI_SUM, 0, grid->comm );
MPI_Allreduce( &stat->TinyPivots, &TinyPivots, 1, mpi_int_t,
MPI_SUM, grid->comm );
stat->TinyPivots = TinyPivots;
if ( !iam ) {
printf("\tNUMfact (MB) all PEs:\tL\\U\t%.2f\tall\t%.2f\n",
for_lu*1e-6, total*1e-6);
printf("\tAll space (MB):"
"\t\ttotal\t%.2f\tAvg\t%.2f\tMax\t%.2f\n",
avg*1e-6, avg/grid->nprow/grid->npcol*1e-6, max*1e-6);
printf("\tNumber of tiny pivots: %10d\n", stat->TinyPivots);
}
}
#endif
} else if ( options->IterRefine ) { /* options->Fact==FACTORED */
/* Permute columns of A to form A*Pc' using the existing perm_c.
* NOTE: rows of A were previously permuted to Pc*A.
*
* XSL: NO; this is different now.
*/
sp_colorder(options, &GA, perm_c, NULL, &GAC); /* ????? */
} /* if !factored ... */
/* Destroy GA */
Destroy_CompCol_Matrix_dist(&GA);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Before solve");
#endif
/* ------------------------------------------------------------
Compute the solution matrix X.
------------------------------------------------------------*/
if ( nrhs ) {
if ( !(b_work = doubleMalloc_dist(n)) )
ABORT("Malloc fails for b_work[]");
/* ------------------------------------------------------------
Scale the right-hand side if equilibration was performed.
------------------------------------------------------------*/
if ( notran ) {
if ( rowequ ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
irow = fst_row;
for (i = 0; i < m_loc; ++i) {
b_col[i] *= R[irow];
++irow;
}
b_col += ldb;
}
}
} else if ( colequ ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
irow = fst_row;
for (i = 0; i < m_loc; ++i) {
b_col[i] *= C[irow];
++irow;
}
b_col += ldb;
}
}
/* Save a copy of the right-hand side. */
ldx = ldb;
if ( !(X = doubleMalloc_dist(((size_t)ldx) * nrhs)) )
ABORT("Malloc fails for X[]");
x_col = X;
b_col = B;
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < m_loc; ++i) x_col[i] = b_col[i];
x_col += ldx;
b_col += ldb;
}
/* ------------------------------------------------------------
Solve the linear system.
------------------------------------------------------------*/
if ( options->SolveInitialized == NO ) {
dSolveInit(options, A, perm_r, perm_c, nrhs, LUstruct, grid,
SOLVEstruct);
}
pdgstrs(n, LUstruct, ScalePermstruct, grid, X, m_loc,
fst_row, ldb, nrhs, SOLVEstruct, stat, info);
#if ( DEBUGlevel>=2 )
printf("\n(%d) .. After pdgstrs(): x =\n", iam);
for (i = 0; i < m_loc; ++i)
printf("\t(%d)\t%4d\t%.10f\n", iam, i+fst_row, X[i]);
#endif
/* ------------------------------------------------------------
Use iterative refinement to improve the computed solution and
compute error bounds and backward error estimates for it.
------------------------------------------------------------*/
if ( options->IterRefine ) {
/* Improve the solution by iterative refinement. */
t = SuperLU_timer_();
pdgsrfs(n, A, anorm, LUstruct, ScalePermstruct, grid,
B, ldb, X, ldx, nrhs, SOLVEstruct, berr, stat, info);
stat->utime[REFINE] = SuperLU_timer_() - t;
}
/* Permute the solution matrix B <= Pc'*X. */
pdPermute_Dense_Matrix(fst_row, m_loc, SOLVEstruct->row_to_proc,
SOLVEstruct->inv_perm_c,
X, ldx, B, ldb, nrhs, grid);
#if ( DEBUGlevel>=2 )
printf("\n (%d) .. After pdPermute_Dense_Matrix(): b =\n", iam);
for (i = 0; i < m_loc; ++i)
printf("\t(%d)\t%4d\t%.10f\n", iam, i+fst_row, B[i]);
#endif
/* Transform the solution matrix X to a solution of the original
system before the equilibration. */
if ( notran ) {
if ( colequ ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
irow = fst_row;
for (i = 0; i < m_loc; ++i) {
b_col[i] *= C[irow];
++irow;
}
b_col += ldb;
}
}
} else if ( rowequ ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
irow = fst_row;
for (i = 0; i < m_loc; ++i) {
b_col[i] *= R[irow];
++irow;
}
b_col += ldb;
}
}
SUPERLU_FREE(b_work);
SUPERLU_FREE(X);
} /* end if nrhs != 0 */
#if ( PRNTlevel>=1 )
if ( !iam ) printf(".. DiagScale = %d\n", ScalePermstruct->DiagScale);
#endif
/* Deallocate storage. */
if ( Equil && Fact != SamePattern_SameRowPerm ) {
switch ( ScalePermstruct->DiagScale ) {
case NOEQUIL:
SUPERLU_FREE(R);
SUPERLU_FREE(C);
break;
case ROW:
SUPERLU_FREE(C);
break;
case COL:
SUPERLU_FREE(R);
break;
}
}
if ( !factored || (factored && options->IterRefine) )
Destroy_CompCol_Permuted_dist(&GAC);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit pdgssvx()");
#endif
}
void tlin::destroyD(SuperMatrix &A, bool destroyData) {
if (destroyData)
Destroy_Dense_Matrix(&A);
else
SUPERLU_FREE(A.Store);
}
void
cgssv(superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r,
SuperMatrix *L, SuperMatrix *U, SuperMatrix *B,
SuperLUStat_t *stat, int *info )
{
DNformat *Bstore;
SuperMatrix *AA;/* A in SLU_NC format used by the factorization routine.*/
SuperMatrix AC; /* Matrix postmultiplied by Pc */
int lwork = 0, *etree, i;
/* Set default values for some parameters */
int panel_size; /* panel size */
int relax; /* no of columns in a relaxed snodes */
int permc_spec;
trans_t trans = NOTRANS;
double *utime;
double t; /* Temporary time */
/* Test the input parameters ... */
*info = 0;
Bstore = B->Store;
if ( options->Fact != DOFACT ) *info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
(A->Stype != SLU_NC && A->Stype != SLU_NR) ||
A->Dtype != SLU_C || A->Mtype != SLU_GE )
*info = -2;
else if ( B->ncol < 0 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_C || B->Mtype != SLU_GE )
*info = -7;
if ( *info != 0 ) {
i = -(*info);
xerbla_("cgssv", &i);
return;
}
utime = stat->utime;
/* Convert A to SLU_NC format when necessary. */
if ( A->Stype == SLU_NR ) {
NRformat *Astore = A->Store;
AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
cCreate_CompCol_Matrix(AA, A->ncol, A->nrow, Astore->nnz,
Astore->nzval, Astore->colind, Astore->rowptr,
SLU_NC, A->Dtype, A->Mtype);
trans = TRANS;
} else {
if ( A->Stype == SLU_NC ) AA = A;
}
t = SuperLU_timer_();
/*
* Get column permutation vector perm_c[], according to permc_spec:
* permc_spec = NATURAL: natural ordering
* permc_spec = MMD_AT_PLUS_A: minimum degree on structure of A'+A
* permc_spec = MMD_ATA: minimum degree on structure of A'*A
* permc_spec = COLAMD: approximate minimum degree column ordering
* permc_spec = MY_PERMC: the ordering already supplied in perm_c[]
*/
permc_spec = options->ColPerm;
if ( permc_spec != MY_PERMC && options->Fact == DOFACT )
get_perm_c(permc_spec, AA, perm_c);
utime[COLPERM] = SuperLU_timer_() - t;
etree = intMalloc(A->ncol);
t = SuperLU_timer_();
sp_preorder(options, AA, perm_c, etree, &AC);
utime[ETREE] = SuperLU_timer_() - t;
panel_size = sp_ienv(1);
relax = sp_ienv(2);
/*printf("Factor PA = LU ... relax %d\tw %d\tmaxsuper %d\trowblk %d\n",
relax, panel_size, sp_ienv(3), sp_ienv(4));*/
t = SuperLU_timer_();
/* Compute the LU factorization of A. */
cgstrf(options, &AC, relax, panel_size, etree,
NULL, lwork, perm_c, perm_r, L, U, stat, info);
utime[FACT] = SuperLU_timer_() - t;
t = SuperLU_timer_();
if ( *info == 0 ) {
/* Solve the system A*X=B, overwriting B with X. */
cgstrs (trans, L, U, perm_c, perm_r, B, stat, info);
}
utime[SOLVE] = SuperLU_timer_() - t;
SUPERLU_FREE (etree);
Destroy_CompCol_Permuted(&AC);
if ( A->Stype == SLU_NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
}
int_t
dReDistribute_A(SuperMatrix *A, ScalePermstruct_t *ScalePermstruct,
Glu_freeable_t *Glu_freeable, int_t *xsup, int_t *supno,
gridinfo_t *grid, int_t *colptr[], int_t *rowind[],
double *a[])
{
/*
* -- Distributed SuperLU routine (version 2.0) --
* Lawrence Berkeley National Lab, Univ. of California Berkeley.
* March 15, 2003
*
* Purpose
* =======
* Re-distribute A on the 2D process mesh.
*
* Arguments
* =========
*
* A (input) SuperMatrix*
* The distributed input matrix A of dimension (A->nrow, A->ncol).
* A may be overwritten by diag(R)*A*diag(C)*Pc^T.
* The type of A can be: Stype = NR; Dtype = SLU_D; Mtype = GE.
*
* ScalePermstruct (input) ScalePermstruct_t*
* The data structure to store the scaling and permutation vectors
* describing the transformations performed to the original matrix A.
*
* Glu_freeable (input) *Glu_freeable_t
* The global structure describing the graph of L and U.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* colptr (output) int*
*
* rowind (output) int*
*
* a (output) double*
*
* Return value
* ============
*
*/
NRformat_loc *Astore;
int_t *perm_r; /* row permutation vector */
int_t *perm_c; /* column permutation vector */
int_t i, irow, fst_row, j, jcol, k, gbi, gbj, n, m_loc, jsize;
int_t nnz_loc; /* number of local nonzeros */
int_t nnz_remote; /* number of remote nonzeros to be sent */
int_t SendCnt; /* number of remote nonzeros to be sent */
int_t RecvCnt; /* number of remote nonzeros to be sent */
int_t *nnzToSend, *nnzToRecv, maxnnzToRecv;
int_t *ia, *ja, **ia_send, *index, *itemp;
int_t *ptr_to_send;
double *aij, **aij_send, *nzval, *dtemp;
double *nzval_a;
int iam, it, p, procs;
MPI_Request *send_req;
MPI_Status status;
/* ------------------------------------------------------------
INITIALIZATION.
------------------------------------------------------------*/
iam = grid->iam;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter dReDistribute_A()");
#endif
perm_r = ScalePermstruct->perm_r;
perm_c = ScalePermstruct->perm_c;
procs = grid->nprow * grid->npcol;
Astore = (NRformat_loc *) A->Store;
n = A->ncol;
m_loc = Astore->m_loc;
fst_row = Astore->fst_row;
nnzToRecv = intCalloc_dist(2*procs);
nnzToSend = nnzToRecv + procs;
/* ------------------------------------------------------------
COUNT THE NUMBER OF NONZEROS TO BE SENT TO EACH PROCESS,
THEN ALLOCATE SPACE.
THIS ACCOUNTS FOR THE FIRST PASS OF A.
------------------------------------------------------------*/
for (i = 0; i < m_loc; ++i) {
for (j = Astore->rowptr[i]; j < Astore->rowptr[i+1]; ++j) {
irow = perm_c[perm_r[i+fst_row]]; /* Row number in Pc*Pr*A */
jcol = Astore->colind[j];
gbi = BlockNum( irow );
gbj = BlockNum( jcol );
p = PNUM( PROW(gbi,grid), PCOL(gbj,grid), grid );
++nnzToSend[p];
}
}
/* All-to-all communication */
MPI_Alltoall( nnzToSend, 1, mpi_int_t, nnzToRecv, 1, mpi_int_t,
grid->comm);
maxnnzToRecv = 0;
nnz_loc = SendCnt = RecvCnt = 0;
for (p = 0; p < procs; ++p) {
if ( p != iam ) {
SendCnt += nnzToSend[p];
RecvCnt += nnzToRecv[p];
maxnnzToRecv = SUPERLU_MAX( nnzToRecv[p], maxnnzToRecv );
} else {
nnz_loc += nnzToRecv[p];
/*assert(nnzToSend[p] == nnzToRecv[p]);*/
}
}
k = nnz_loc + RecvCnt; /* Total nonzeros ended up in my process. */
/* Allocate space for storing the triplets after redistribution. */
if ( !(ia = intMalloc_dist(2*k)) )
ABORT("Malloc fails for ia[].");
ja = ia + k;
if ( !(aij = doubleMalloc_dist(k)) )
ABORT("Malloc fails for aij[].");
/* Allocate temporary storage for sending/receiving the A triplets. */
if ( procs > 1 ) {
if ( !(send_req = (MPI_Request *)
SUPERLU_MALLOC(2*procs *sizeof(MPI_Request))) )
ABORT("Malloc fails for send_req[].");
if ( !(ia_send = (int_t **) SUPERLU_MALLOC(procs*sizeof(int_t*))) )
ABORT("Malloc fails for ia_send[].");
if ( !(aij_send = (double **)SUPERLU_MALLOC(procs*sizeof(double*))) )
ABORT("Malloc fails for aij_send[].");
if ( !(index = intMalloc_dist(2*SendCnt)) )
ABORT("Malloc fails for index[].");
if ( !(nzval = doubleMalloc_dist(SendCnt)) )
ABORT("Malloc fails for nzval[].");
if ( !(ptr_to_send = intCalloc_dist(procs)) )
ABORT("Malloc fails for ptr_to_send[].");
if ( !(itemp = intMalloc_dist(2*maxnnzToRecv)) )
ABORT("Malloc fails for itemp[].");
if ( !(dtemp = doubleMalloc_dist(maxnnzToRecv)) )
ABORT("Malloc fails for dtemp[].");
for (i = 0, j = 0, p = 0; p < procs; ++p) {
if ( p != iam ) {
ia_send[p] = &index[i];
i += 2 * nnzToSend[p]; /* ia/ja indices alternate */
aij_send[p] = &nzval[j];
j += nnzToSend[p];
}
}
} /* if procs > 1 */
if ( !(*colptr = intCalloc_dist(n+1)) )
ABORT("Malloc fails for *colptr[].");
/* ------------------------------------------------------------
LOAD THE ENTRIES OF A INTO THE (IA,JA,AIJ) STRUCTURES TO SEND.
THIS ACCOUNTS FOR THE SECOND PASS OF A.
------------------------------------------------------------*/
nnz_loc = 0; /* Reset the local nonzero count. */
nzval_a = Astore->nzval;
for (i = 0; i < m_loc; ++i) {
for (j = Astore->rowptr[i]; j < Astore->rowptr[i+1]; ++j) {
irow = perm_c[perm_r[i+fst_row]]; /* Row number in Pc*Pr*A */
jcol = Astore->colind[j];
gbi = BlockNum( irow );
gbj = BlockNum( jcol );
p = PNUM( PROW(gbi,grid), PCOL(gbj,grid), grid );
if ( p != iam ) { /* remote */
k = ptr_to_send[p];
ia_send[p][k] = irow;
ia_send[p][k + nnzToSend[p]] = jcol;
aij_send[p][k] = nzval_a[j];
++ptr_to_send[p];
} else { /* local */
ia[nnz_loc] = irow;
ja[nnz_loc] = jcol;
aij[nnz_loc] = nzval_a[j];
++nnz_loc;
++(*colptr)[jcol]; /* Count nonzeros in each column */
}
}
}
/* ------------------------------------------------------------
PERFORM REDISTRIBUTION. THIS INVOLVES ALL-TO-ALL COMMUNICATION.
NOTE: Can possibly use MPI_Alltoallv.
------------------------------------------------------------*/
for (p = 0; p < procs; ++p) {
if ( p != iam ) {
it = 2*nnzToSend[p];
MPI_Isend( ia_send[p], it, mpi_int_t,
p, iam, grid->comm, &send_req[p] );
it = nnzToSend[p];
MPI_Isend( aij_send[p], it, MPI_DOUBLE,
p, iam+procs, grid->comm, &send_req[procs+p] );
}
}
for (p = 0; p < procs; ++p) {
if ( p != iam ) {
it = 2*nnzToRecv[p];
MPI_Recv( itemp, it, mpi_int_t, p, p, grid->comm, &status );
it = nnzToRecv[p];
MPI_Recv( dtemp, it, MPI_DOUBLE, p, p+procs,
grid->comm, &status );
for (i = 0; i < nnzToRecv[p]; ++i) {
ia[nnz_loc] = itemp[i];
jcol = itemp[i + nnzToRecv[p]];
/*assert(jcol<n);*/
ja[nnz_loc] = jcol;
aij[nnz_loc] = dtemp[i];
++nnz_loc;
++(*colptr)[jcol]; /* Count nonzeros in each column */
}
}
}
for (p = 0; p < procs; ++p) {
if ( p != iam ) {
MPI_Wait( &send_req[p], &status);
MPI_Wait( &send_req[procs+p], &status);
}
}
/* ------------------------------------------------------------
DEALLOCATE TEMPORARY STORAGE
------------------------------------------------------------*/
SUPERLU_FREE(nnzToRecv);
if ( procs > 1 ) {
SUPERLU_FREE(send_req);
SUPERLU_FREE(ia_send);
SUPERLU_FREE(aij_send);
SUPERLU_FREE(index);
SUPERLU_FREE(nzval);
SUPERLU_FREE(ptr_to_send);
SUPERLU_FREE(itemp);
SUPERLU_FREE(dtemp);
}
/* ------------------------------------------------------------
CONVERT THE TRIPLET FORMAT INTO THE CCS FORMAT.
------------------------------------------------------------*/
if ( !(*rowind = intMalloc_dist(nnz_loc)) )
ABORT("Malloc fails for *rowind[].");
if ( !(*a = doubleMalloc_dist(nnz_loc)) )
ABORT("Malloc fails for *a[].");
/* Initialize the array of column pointers */
k = 0;
jsize = (*colptr)[0];
(*colptr)[0] = 0;
for (j = 1; j < n; ++j) {
k += jsize;
jsize = (*colptr)[j];
(*colptr)[j] = k;
}
/* Copy the triplets into the column oriented storage */
for (i = 0; i < nnz_loc; ++i) {
j = ja[i];
k = (*colptr)[j];
(*rowind)[k] = ia[i];
(*a)[k] = aij[i];
++(*colptr)[j];
}
/* Reset the column pointers to the beginning of each column */
for (j = n; j > 0; --j) (*colptr)[j] = (*colptr)[j-1];
(*colptr)[0] = 0;
SUPERLU_FREE(ia);
SUPERLU_FREE(aij);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit dReDistribute_A()");
#endif
} /* dReDistribute_A */