/*! \brief
*
* <pre>
* Purpose
* =======
*
* pzgssvx_ABglobal 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, and its dimensions ldb and nrhs
* - 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 several 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
*
* - A, the input matrix
*
* as well as the following options, which are described in more
* detail below:
*
* - 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)
*
* - options->RowPerm, to specify how to permute the rows of A
* (typically to control numerical stability)
*
* - options->ColPerm, to specify how to permute the columns of A
* (typically to control fill-in and enhance
* parallelism during factorization)
*
* - options->ReplaceTinyPivot, to specify how to deal with tiny
* pivots encountered during factorization
* (to control numerical stability)
*
* The outputs returned include
*
* - 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).
*
* - 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
*
* - 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:
*
* - options->Equil
* - options->RowPerm
* - 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
*
* - A, the input matrix
* - ScalePermstruct->perm_c, the column permutation
* - LUstruct->etree, the elimination tree
*
* The outputs returned include
*
* - A, the input matrix A overwritten by the scaled and permuted matrix
* as described above
* - ScalePermstruct, modified to describe how the input matrix A was
* equilibrated and row permuted
* - 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:
*
* - options->Equil
* - 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
*
* - A, the input matrix
* - ScalePermstruct->DiagScale, how the previous matrix was row and/or
* column scaled
* - ScalePermstruct->R, the row scalings of the previous matrix, if any
* - ScalePermstruct->C, the columns scalings of the previous matrix,
* if any
* - ScalePermstruct->perm_r, the row permutation of the previous matrix
* - ScalePermstruct->perm_c, the column permutation of the previous
* matrix
* - 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
*
* - A, the input matrix A overwritten by the scaled and permuted matrix
* as described above
* - ScalePermstruct, modified to describe how the input matrix A was
* equilibrated
* (thus ScalePermstruct->DiagScale, R and C may be modified)
* - 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
*
* - 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)
* - all of ScalePermstruct
* - 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*
* 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.
* = 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.
* = SLU_DOUBLE: accumulate residual in double precision.
* = SLU_EXTRA: accumulate residual in extra precision.
*
* NOTE: all options must be indentical on all processes when
* calling this routine.
*
* A (input/output) SuperMatrix*
* 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_NC; Dtype = SLU_Z; Mtype = SLU_GE. That is, A is stored in
* compressed column format (also known as Harwell-Boeing format).
* See supermatrix.h for the definition of 'SuperMatrix'.
* This routine only handles square A, however, the LU factorization
* routine pzgstrf can factorize rectangular matrices.
* On exit, A may be overwritten by Pc*Pr*diag(R)*A*diag(C),
* depending on ScalePermstruct->DiagScale, options->RowPerm and
* options->colpem:
* 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.
*
* NOTE: Currently, A must reside in all processes when calling
* this routine.
*
* ScalePermstruct (input/output) ScalePermstruct_t*
* 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) doublecomplex*
* On entry, the right-hand side matrix of dimension (A->nrow, nrhs).
* On exit, the solution matrix if info = 0;
*
* NOTE: Currently, B must reside in all processes when calling
* this routine.
*
* ldb (input) int (global)
* 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*
* 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_zdefs.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)
* Elimination tree of Pc*(A'+A)*Pc' or Pc*A'*A*Pc', dimension A->ncol.
* 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 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*)
* The distributed data structures to store L and U factors.
* See superlu_ddefs.h for the definition of 'LocalLU_t'.
*
* berr (output) double*, dimension (nrhs)
* 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_zdefs.h for the definitions of various data types.
* </pre>
*/
void
pzgssvx_ABglobal(superlu_options_t *options, SuperMatrix *A,
ScalePermstruct_t *ScalePermstruct,
doublecomplex B[], int ldb, int nrhs, gridinfo_t *grid,
LUstruct_t *LUstruct, double *berr,
SuperLUStat_t *stat, int *info)
{
SuperMatrix AC;
NCformat *Astore;
NCPformat *ACstore;
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 DDISTRIBUTE
routine. They will be freed after DDISTRIBUTE routine.
If options->Fact == SamePattern_SameRowPerm, these
structures are not used. */
fact_t Fact;
doublecomplex *a;
int_t *perm_r; /* row permutations from partial pivoting */
int_t *perm_c; /* column permutation vector */
int_t *etree; /* elimination tree */
int_t *colptr, *rowind;
int_t colequ, Equil, factored, job, notran, rowequ;
int_t i, iinfo, j, irow, m, n, nnz, permc_spec, dist_mem_use;
int iam;
int ldx; /* LDA for matrix X (global). */
char equed[1], norm[1];
double *C, *R, *C1, *R1, amax, anorm, colcnd, rowcnd;
doublecomplex *X, *b_col, *b_work, *x_col;
double t;
static mem_usage_t num_mem_usage, symb_mem_usage;
#if ( PRNTlevel>= 2 )
double dmin, dsum, dprod;
#endif
/* Test 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 > SLU_EXTRA )
*info = -1;
else if ( options->IterRefine == SLU_EXTRA ) {
*info = -1;
fprintf(stderr, "Extra precise iterative refinement yet to support.");
} else if ( A->nrow != A->ncol || A->nrow < 0 ||
A->Stype != SLU_NC || A->Dtype != SLU_Z || A->Mtype != SLU_GE )
*info = -2;
else if ( ldb < A->nrow )
*info = -5;
else if ( nrhs < 0 )
*info = -6;
if ( *info ) {
i = -(*info);
pxerbla("pzgssvx_ABglobal", grid, -*info);
return;
}
/* Initialization */
factored = (Fact == FACTORED);
Equil = (!factored && options->Equil == YES);
notran = (options->Trans == NOTRANS);
iam = grid->iam;
job = 5;
m = A->nrow;
n = A->ncol;
Astore = A->Store;
nnz = Astore->nnz;
a = Astore->nzval;
colptr = Astore->colptr;
rowind = Astore->rowind;
if ( factored || (Fact == SamePattern_SameRowPerm && Equil) ) {
rowequ = (ScalePermstruct->DiagScale == ROW) ||
(ScalePermstruct->DiagScale == BOTH);
colequ = (ScalePermstruct->DiagScale == COL) ||
(ScalePermstruct->DiagScale == BOTH);
} else rowequ = colequ = FALSE;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pzgssvx_ABglobal()");
#endif
perm_r = ScalePermstruct->perm_r;
perm_c = ScalePermstruct->perm_c;
etree = LUstruct->etree;
R = ScalePermstruct->R;
C = ScalePermstruct->C;
if ( Equil && Fact != SamePattern_SameRowPerm ) {
/* 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:
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i) {
irow = rowind[i];
zd_mult(&a[i], &a[i], R[i]); /* Scale rows. */
}
}
break;
case COL:
for (j = 0; j < n; ++j)
for (i = colptr[j]; i < colptr[j+1]; ++i)
zd_mult(&a[i], &a[i], C[j]); /* Scale columns. */
break;
case BOTH:
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i) {
irow = rowind[i];
zd_mult(&a[i], &a[i], R[irow]); /* Scale rows. */
zd_mult(&a[i], &a[i], C[j]); /* Scale columns. */
}
}
break;
}
} else {
if ( !iam ) {
/* Compute row and column scalings to equilibrate matrix A. */
zgsequ_dist(A, R, C, &rowcnd, &colcnd, &amax, &iinfo);
MPI_Bcast( &iinfo, 1, mpi_int_t, 0, grid->comm );
if ( iinfo == 0 ) {
MPI_Bcast( R, m, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( C, n, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( &rowcnd, 1, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( &colcnd, 1, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( &amax, 1, MPI_DOUBLE, 0, grid->comm );
} else {
if ( iinfo > 0 ) {
if ( iinfo <= m )
fprintf(stderr, "The %d-th row of A is exactly zero\n",
iinfo);
else fprintf(stderr, "The %d-th column of A is exactly zero\n",
iinfo-n);
exit(-1);
}
}
} else {
MPI_Bcast( &iinfo, 1, mpi_int_t, 0, grid->comm );
if ( iinfo == 0 ) {
MPI_Bcast( R, m, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( C, n, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( &rowcnd, 1, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( &colcnd, 1, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( &amax, 1, MPI_DOUBLE, 0, grid->comm );
} else {
ABORT("ZGSEQU failed\n");
}
}
/* Equilibrate matrix A. */
zlaqgs_dist(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
} /* end if Equil ... */
/* ------------------------------------------------------------
Permute rows of A.
------------------------------------------------------------*/
if ( options->RowPerm != NO ) {
t = SuperLU_timer_();
if ( Fact == SamePattern_SameRowPerm /* Reuse perm_r. */
|| options->RowPerm == MY_PERMR ) { /* Use my perm_r. */
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i) {
irow = rowind[i];
rowind[i] = perm_r[irow];
}
}
} else if ( !factored ) {
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. */
zldperm(job, m, nnz, colptr, rowind, a, 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]);
}
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i) {
irow = rowind[i];
zd_mult(&a[i], &a[i], R1[irow]); /* Scale rows. */
zd_mult(&a[i], &a[i], C1[j]); /* Scale columns. */
rowind[i] = perm_r[irow];
#if ( PRNTlevel>=2 )
if ( rowind[i] == j ) /* New diagonal */
dprod *= slud_z_abs1(&a[i]);
#endif
}
}
/* 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. */
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++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, slud_z_abs1(&a[i]));
else if ( job == 4 )
dsum += slud_z_abs1(&a[i]);
else if ( job == 5 )
dprod *= slud_z_abs1(&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;
} else { /* options->RowPerm == NOROWPERM */
for (i = 0; i < m; ++i) perm_r[i] = i;
}
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 = zlangs_dist(norm, A);
}
/* ------------------------------------------------------------
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 = MY_PERMC: the ordering already supplied in perm_c[]
*/
permc_spec = options->ColPerm;
if ( permc_spec != MY_PERMC && Fact == DOFACT )
/* Use an ordering provided by SuperLU */
get_perm_c_dist(iam, permc_spec, A, 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, A, perm_c, etree, &AC);
/* Form Pc*A*Pc' to preserve the diagonal of the matrix Pr*A. */
ACstore = AC.Store;
for (j = 0; j < n; ++j)
for (i = ACstore->colbeg[j]; i < ACstore->colend[j]; ++i) {
irow = ACstore->rowind[i];
ACstore->rowind[i] = perm_c[irow];
}
stat->utime[COLPERM] = SuperLU_timer_() - t;
/* Perform a symbolic factorization on matrix A 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.");
iinfo = symbfact(options, iam, &AC, perm_c, etree,
Glu_persist, Glu_freeable);
stat->utime[SYMBFAC] = SuperLU_timer_() - t;
if ( iinfo < 0 ) {
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);
}
}
}
/* Distribute the L and U factors onto the process grid. */
t = SuperLU_timer_();
dist_mem_use = zdistribute(Fact, n, &AC, Glu_freeable, LUstruct, grid);
stat->utime[DIST] = SuperLU_timer_() - t;
/* Deallocate storage used in symbolic factor. */
if ( Fact != SamePattern_SameRowPerm ) {
iinfo = symbfact_SubFree(Glu_freeable);
SUPERLU_FREE(Glu_freeable);
}
/* Perform numerical factorization in parallel. */
t = SuperLU_timer_();
pzgstrf(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;
zQuerySpace_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
#if ( PRNTlevel>=2 )
if ( !iam ) printf(".. pzgstrf INFO = %d\n", *info);
#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.
*/
sp_colorder(options, A, perm_c, NULL, &AC);
} /* if !factored ... */
/* ------------------------------------------------------------
Compute the solution matrix X.
------------------------------------------------------------*/
if ( nrhs ) {
if ( !(b_work = doublecomplexMalloc_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) {
for (i = 0; i < m; ++i) zd_mult(&b_col[i], &b_col[i], R[i]);
b_col += ldb;
}
}
} else if ( colequ ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < m; ++i) zd_mult(&b_col[i], &b_col[i], C[i]);
b_col += ldb;
}
}
/* ------------------------------------------------------------
Permute the right-hand side to form Pr*B.
------------------------------------------------------------*/
if ( options->RowPerm != NO ) {
if ( notran ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < m; ++i) b_work[perm_r[i]] = b_col[i];
for (i = 0; i < m; ++i) b_col[i] = b_work[i];
b_col += ldb;
}
}
}
/* ------------------------------------------------------------
Permute the right-hand side to form Pc*B.
------------------------------------------------------------*/
if ( notran ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < m; ++i) b_work[perm_c[i]] = b_col[i];
for (i = 0; i < m; ++i) b_col[i] = b_work[i];
b_col += ldb;
}
}
/* Save a copy of the right-hand side. */
ldx = ldb;
if ( !(X = doublecomplexMalloc_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 < ldb; ++i) x_col[i] = b_col[i];
x_col += ldx; b_col += ldb;
}
/* ------------------------------------------------------------
Solve the linear system.
------------------------------------------------------------*/
pzgstrs_Bglobal(n, LUstruct, grid, X, ldb, nrhs, stat, info);
/* ------------------------------------------------------------
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_();
pzgsrfs_ABXglobal(n, &AC, anorm, LUstruct, grid, B, ldb,
X, ldx, nrhs, berr, stat, info);
stat->utime[REFINE] = SuperLU_timer_() - t;
}
/* Permute the solution matrix X <= Pc'*X. */
for (j = 0; j < nrhs; j++) {
b_col = &B[j*ldb];
x_col = &X[j*ldx];
for (i = 0; i < n; ++i) b_col[i] = x_col[perm_c[i]];
}
/* 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) {
for (i = 0; i < n; ++i) zd_mult(&b_col[i], &b_col[i], C[i]);
b_col += ldb;
}
}
} else if ( rowequ ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < n; ++i) zd_mult(&b_col[i], &b_col[i], R[i]);
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 R and/or C if it is not used. */
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(&AC);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit pzgssvx_ABglobal()");
#endif
}
void
zgsisx(superlu_options_t *options, SuperMatrix *A, 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,
mem_usage_t *mem_usage, SuperLUStat_t *stat, int *info)
{
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, permc_spec, mc64;
trans_t trant;
char norm[1];
int i, j, info1;
double amax, anorm, bignum, smlnum, colcnd, rowcnd, rcmax, rcmin;
int relax, panel_size;
double diag_pivot_thresh;
double t0; /* temporary time */
double *utime;
int *perm = NULL;
/* External functions */
extern double zlangs(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);
mc64 = (options->RowPerm == LargeDiag);
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 = dlamch_("Safe minimum");
bignum = 1. / smlnum;
}
/* Test the input parameters */
if (!nofact && options->Fact != DOFACT && options->Fact != SamePattern &&
options->Fact != SamePattern_SameRowPerm &&
!notran && options->Trans != TRANS && options->Trans != CONJ &&
!equil && options->Equil != NO)
*info = -1;
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 = -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 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_Z ||
B->Mtype != SLU_GE )
*info = -13;
else if ( X->ncol < 0 || Xstore->lda < SUPERLU_MAX(0, A->nrow) ||
(B->ncol != 0 && B->ncol != X->ncol) ||
X->Stype != SLU_DN ||
X->Dtype != SLU_Z || X->Mtype != SLU_GE )
*info = -14;
}
}
if (*info != 0) {
i = -(*info);
xerbla_("zgsisx", &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) );
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 = TRANS;
notran = 0;
} else {
trant = NOTRANS;
notran = 1;
}
} else { /* A->Stype == SLU_NC */
trant = options->Trans;
AA = A;
}
if ( nofact ) {
register int i, j;
NCformat *Astore = AA->Store;
int nnz = Astore->nnz;
int *colptr = Astore->colptr;
int *rowind = Astore->rowind;
doublecomplex *nzval = (doublecomplex *)Astore->nzval;
int n = AA->nrow;
if ( mc64 ) {
*equed = 'B';
rowequ = colequ = 1;
t0 = SuperLU_timer_();
if ((perm = intMalloc(n)) == NULL)
ABORT("SUPERLU_MALLOC fails for perm[]");
info1 = zldperm(5, n, nnz, colptr, rowind, nzval, perm, R, C);
if (info1 > 0) { /* MC64 fails, call zgsequ() later */
mc64 = 0;
SUPERLU_FREE(perm);
perm = NULL;
} else {
for (i = 0; i < n; i++) {
R[i] = exp(R[i]);
C[i] = exp(C[i]);
}
/* permute and scale the matrix */
for (j = 0; j < n; j++) {
for (i = colptr[j]; i < colptr[j + 1]; i++) {
zd_mult(&nzval[i], &nzval[i], R[rowind[i]] * C[j]);
rowind[i] = perm[rowind[i]];
}
}
}
utime[EQUIL] = SuperLU_timer_() - t0;
}
if ( !mc64 & 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;
}
}
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) {
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 ) {
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;
/* Compute the LU factorization of A*Pc. */
t0 = SuperLU_timer_();
zgsitrf(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 ) return;
/* Compute the reciprocal pivot growth factor *recip_pivot_growth. */
*recip_pivot_growth = zPivotGrowth(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 = zlangs(norm, AA);
zgscon(norm, L, U, anorm, rcond, stat, &info1);
utime[RCOND] = SuperLU_timer_() - t0;
}
if ( nrhs > 0 ) {
/* 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_c, perm_r, X, stat, &info1);
utime[SOLVE] = 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 ) {
if (perm) {
doublecomplex *tmp;
int n = A->nrow;
if ((tmp = doublecomplexMalloc(n)) == NULL)
ABORT("SUPERLU_MALLOC fails for tmp[]");
for (j = 0; j < nrhs; j++) {
for (i = 0; i < n; i++)
tmp[i] = Xmat[i + j * ldx]; /*dcopy*/
for (i = 0; i < n; i++)
zd_mult(&Xmat[i+j*ldx], &tmp[perm[i]], R[i]);
}
SUPERLU_FREE(tmp);
} else {
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]);
}
}
}
}
} /* end if nrhs > 0 */
if ( options->ConditionNumber ) {
/* Set INFO = A->ncol+1 if the matrix is singular to working precision. */
if ( *rcond < dlamch_("E") && *info == 0) *info = A->ncol + 1;
}
if (perm) SUPERLU_FREE(perm);
if ( nofact ) {
ilu_zQuerySpace(L, U, mem_usage);
Destroy_CompCol_Permuted(&AC);
}
if ( A->Stype == SLU_NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
}