/*! @file cgssvx.c

 * \brief Solves the system of linear equations A*X=B or A'*X=B

 *

 * 

 * -- SuperLU routine (version 3.0) --

 * Univ. of California Berkeley, Xerox Palo Alto Research Center,

 * and Lawrence Berkeley National Lab.

 * October 15, 2003

 * 

 */

#include "slu_cdefs.h"

/*! \brief

 *

 * 

 * Purpose

 * =======

 *

 * CGSSVX solves the system of linear equations A*X=B or A'*X=B, using

 * the LU factorization from cgstrf(). 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 options->Equil = YES, scaling factors are computed to

 *           equilibrate the system:

 *           options->Trans = NOTRANS:

 *               diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B

 *           options->Trans = TRANS:

 *               (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B

 *           options->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 options->Trans=NOTRANS) or diag(C)*B (if options->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_preorder.c.

 *

 *      1.3. If options->Fact != FACTORED, the LU decomposition is used to

 *           factor the matrix A (after equilibration if options->Equil = YES)

 *           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. If options->IterRefine != NOREFINE, 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 options->Trans = NOTRANS) or diag(R)

 *           (if options->Trans = TRANS or CONJ) 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 options->Equil = YES, scaling factors are computed to

 *           equilibrate the system:

 *           options->Trans = NOTRANS:

 *               diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B

 *           options->Trans = TRANS:

 *               (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B

 *           options->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='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 options->Fact != FACTORED, the LU decomposition is used to

 *           factor the transpose(A) (after equilibration if 

 *           options->Fact = YES) 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. If options->IterRefine != NOREFINE, 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 options->Trans = NOTRANS) or diag(R) 

 *           (if options->Trans = TRANS or CONJ) so that it solves the

 *           original system before equilibration.

 *

 *   See supermatrix.h for the definition of 'SuperMatrix' structure.

 *

 * Arguments

 * =========

 *

 * options (input) superlu_options_t*

 *         The structure defines the input parameters to control

 *         how the LU decomposition will be performed and how the

 *         system will be solved.

 *

 * 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_D, Mtype = SLU_GE.

 *         In the future, more general A may be handled.

 *

 *         On entry, If options->Fact = FACTORED and equed is not 'N', 

 *         then A must have been equilibrated by the scaling factors in

 *         R and/or C.  

 *         On exit, A is not modified if options->Equil = NO, or if 

 *         options->Equil = YES but equed = 'N' on exit.

 *         Otherwise, if options->Equil = YES 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).

 *

 * 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 options->Fact = SamePattern_SameRowPerm, 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.

 *         Otherwise, perm_r is output argument.

 * 

 * etree   (input/output) int*,  dimension (A->ncol)

 *         Elimination tree of Pc'*A'*A*Pc.

 *         If options->Fact != FACTORED and options->Fact != DOFACT,

 *         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 options->Fact = FACTORED, equed is an input argument,

 *         otherwise it is an output argument.

 *

 * R       (input/output) float*, 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 options->Fact = FACTORED, R is an input argument,

 *             otherwise, R is output.

 *         If options->zFact = FACTORED and equed = 'R' or 'B', each element

 *             of R must be positive.

 * 

 * C       (input/output) float*, 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 options->Fact = FACTORED, C is an input argument,

 *             otherwise, C is output.

 *         If options->Fact = FACTORED 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 = SLU_SC, Dtype = SLU_C, Mtype = SLU_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_C, Mtype = SLU_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_C, Mtype = SLU_GE.

 *         On entry, the right hand side matrix.

 *         If B->ncol = 0, only LU decomposition is performed, the triangular

 *                         solve is skipped.

 *         On exit,

 *            if equed = 'N', B is not modified; otherwise

 *            if A->Stype = SLU_NC:

 *               if options->Trans = NOTRANS and equed = 'R' or 'B',

 *                  B is overwritten by diag(R)*B;

 *               if options->Trans = TRANS or CONJ and equed = 'C' of 'B',

 *                  B is overwritten by diag(C)*B;

 *            if A->Stype = SLU_NR:

 *               if options->Trans = NOTRANS and equed = 'C' or 'B',

 *                  B is overwritten by diag(C)*B;

 *               if options->Trans = TRANS or CONJ and equed = 'R' of 'B',

 *                  B is overwritten by diag(R)*B.

 *

 * X       (output) SuperMatrix*

 *         X has types: Stype = SLU_DN, Dtype = SLU_C, 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 options->Trans = NOTRANS and

 *         equed = 'C' or 'B', or inv(diag(R))*X if options->Trans = 'T' or 'C'

 *         and equed = 'R' or 'B'.

 *

 * recip_pivot_growth (output) float*

 *         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) float*

 *         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) 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.

 *         If options->IterRefine = NOREFINE, ferr = 1.0.

 *

 * 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).

 *         If options->IterRefine = NOREFINE, berr = 1.0.

 *

 * 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.

 *

 * stat   (output) SuperLUStat_t*

 *        Record the statistics on runtime and floating-point operation count.

 *        See slu_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   

 *         > 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.

 * 

 */

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 (!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_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 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||

		      B->Stype != SLU_DN || B->Dtype != SLU_C || 

		      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_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 ( 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]);

	        }

        }

    }

    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 ) {

        /* 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);

    }

}