/*! @file zgstrs.c

 * \brief Solves a system using LU factorization

 *

 * 

 * -- SuperLU routine (version 3.0) --

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

 * and Lawrence Berkeley National Lab.

 * October 15, 2003

 *

 * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.

 *

 * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY

 * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.

 *

 * Permission is hereby granted to use or copy this program for any

 * purpose, provided the above notices are retained on all copies.

 * Permission to modify the code and to distribute modified code is

 * granted, provided the above notices are retained, and a notice that

 * the code was modified is included with the above copyright notice.

 * 

 */

#include "slu_zdefs.h"

/* 

 * Function prototypes 

 */

void zusolve(int, int, doublecomplex*, doublecomplex*);

void zlsolve(int, int, doublecomplex*, doublecomplex*);

void zmatvec(int, int, int, doublecomplex*, doublecomplex*, doublecomplex*);

/*! \brief

 *

 * 

 * Purpose

 * =======

 *

 * ZGSTRS solves a system of linear equations A*X=B or A'*X=B

 * with A sparse and B dense, using the LU factorization computed by

 * ZGSTRF.

 *

 * 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)

 *

 * L       (input) SuperMatrix*

 *         The factor L from the factorization Pr*A*Pc=L*U as computed by

 *         zgstrf(). Use compressed row subscripts storage for supernodes,

 *         i.e., L has types: Stype = SLU_SC, Dtype = SLU_Z, Mtype = SLU_TRLU.

 *

 * U       (input) SuperMatrix*

 *         The factor U from the factorization Pr*A*Pc=L*U as computed by

 *         zgstrf(). Use column-wise storage scheme, i.e., U has types:

 *         Stype = SLU_NC, Dtype = SLU_Z, Mtype = SLU_TRU.

 *

 * perm_c  (input) int*, dimension (L->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 (L->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.

 *

 * 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, the solution matrix if info = 0;

 *

 * 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

 * 

 */

void

zgstrs (trans_t trans, SuperMatrix *L, SuperMatrix *U,

        int *perm_c, int *perm_r, SuperMatrix *B,

        SuperLUStat_t *stat, int *info)

{

#ifdef _CRAY

    _fcd ftcs1, ftcs2, ftcs3, ftcs4;

#endif

    int      incx = 1, incy = 1;

#ifdef USE_VENDOR_BLAS

    doublecomplex   alpha = {1.0, 0.0}, beta = {1.0, 0.0};

    doublecomplex   *work_col;

#endif

    doublecomplex   temp_comp;

    DNformat *Bstore;

    doublecomplex   *Bmat;

    SCformat *Lstore;

    NCformat *Ustore;

    doublecomplex   *Lval, *Uval;

    int      fsupc, nrow, nsupr, nsupc, luptr, istart, irow;

    int      i, j, k, iptr, jcol, n, ldb, nrhs;

    doublecomplex   *work, *rhs_work, *soln;

    flops_t  solve_ops;

    void zprint_soln();

    /* Test input parameters ... */

    *info = 0;

    Bstore = B->Store;

    ldb = Bstore->lda;

    nrhs = B->ncol;

    if ( trans != NOTRANS && trans != TRANS && trans != CONJ ) *info = -1;

    else if ( L->nrow != L->ncol || L->nrow < 0 ||

	      L->Stype != SLU_SC || L->Dtype != SLU_Z || L->Mtype != SLU_TRLU )

	*info = -2;

    else if ( U->nrow != U->ncol || U->nrow < 0 ||

	      U->Stype != SLU_NC || U->Dtype != SLU_Z || U->Mtype != SLU_TRU )

	*info = -3;

    else if ( ldb < SUPERLU_MAX(0, L->nrow) ||

	      B->Stype != SLU_DN || B->Dtype != SLU_Z || B->Mtype != SLU_GE )

	*info = -6;

    if ( *info ) {

	i = -(*info);

	xerbla_("zgstrs", &i);

	return;

    }

    n = L->nrow;

    work = doublecomplexCalloc(n * nrhs);

    if ( !work ) ABORT("Malloc fails for local work[].");

    soln = doublecomplexMalloc(n);

    if ( !soln ) ABORT("Malloc fails for local soln[].");

    Bmat = Bstore->nzval;

    Lstore = L->Store;

    Lval = Lstore->nzval;

    Ustore = U->Store;

    Uval = Ustore->nzval;

    solve_ops = 0;

    if ( trans == NOTRANS ) {

	/* Permute right hand sides to form Pr*B */

	for (i = 0; i < nrhs; i++) {

	    rhs_work = &Bmat[i*ldb];

	    for (k = 0; k < n; k++) soln[perm_r[k]] = rhs_work[k];

	    for (k = 0; k < n; k++) rhs_work[k] = soln[k];

	}

	/* Forward solve PLy=Pb. */

	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;

	    nrow = nsupr - nsupc;

	    solve_ops += 4 * nsupc * (nsupc - 1) * nrhs;

	    solve_ops += 8 * nrow * nsupc * nrhs;

	    if ( nsupc == 1 ) {

		for (j = 0; j < nrhs; j++) {

		    rhs_work = &Bmat[j*ldb];

	    	    luptr = L_NZ_START(fsupc);

		    for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); iptr++){

			irow = L_SUB(iptr);

			++luptr;

			zz_mult(&temp_comp, &rhs_work[fsupc], &Lval[luptr]);

			z_sub(&rhs_work[irow], &rhs_work[irow], &temp_comp);

		    }

		}

	    } else {

	    	luptr = L_NZ_START(fsupc);

#ifdef USE_VENDOR_BLAS

#ifdef _CRAY

		ftcs1 = _cptofcd("L", strlen("L"));

		ftcs2 = _cptofcd("N", strlen("N"));

		ftcs3 = _cptofcd("U", strlen("U"));

		CTRSM( ftcs1, ftcs1, ftcs2, ftcs3, &nsupc, &nrhs, &alpha,

		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);

		CGEMM( ftcs2, ftcs2, &nrow, &nrhs, &nsupc, &alpha, 

			&Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb, 

			&beta, &work[0], &n );

#else

		ztrsm_("L", "L", "N", "U", &nsupc, &nrhs, &alpha,

		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);

		zgemm_( "N", "N", &nrow, &nrhs, &nsupc, &alpha, 

			&Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb, 

			&beta, &work[0], &n );

#endif

		for (j = 0; j < nrhs; j++) {

		    rhs_work = &Bmat[j*ldb];

		    work_col = &work[j*n];

		    iptr = istart + nsupc;

		    for (i = 0; i < nrow; i++) {

			irow = L_SUB(iptr);

			z_sub(&rhs_work[irow], &rhs_work[irow], &work_col[i]);

			work_col[i].r = 0.0;

	                work_col[i].i = 0.0;

			iptr++;

		    }

		}

#else		

		for (j = 0; j < nrhs; j++) {

		    rhs_work = &Bmat[j*ldb];

		    zlsolve (nsupr, nsupc, &Lval[luptr], &rhs_work[fsupc]);

		    zmatvec (nsupr, nrow, nsupc, &Lval[luptr+nsupc],

			    &rhs_work[fsupc], &work[0] );

		    iptr = istart + nsupc;

		    for (i = 0; i < nrow; i++) {

			irow = L_SUB(iptr);

			z_sub(&rhs_work[irow], &rhs_work[irow], &work[i]);

			work[i].r = 0.;

	                work[i].i = 0.;

			iptr++;

		    }

		}

#endif		    

	    } /* else ... */

	} /* for L-solve */

#ifdef DEBUG

  	printf("After L-solve: y=\n");

	zprint_soln(n, nrhs, Bmat);

#endif

	/*

	 * Back solve Ux=y.

	 */

	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 += 4 * nsupc * (nsupc + 1) * nrhs;

	    if ( nsupc == 1 ) {

		rhs_work = &Bmat[0];

		for (j = 0; j < nrhs; j++) {

		    z_div(&rhs_work[fsupc], &rhs_work[fsupc], &Lval[luptr]);

		    rhs_work += ldb;

		}

	    } else {

#ifdef USE_VENDOR_BLAS

#ifdef _CRAY

		ftcs1 = _cptofcd("L", strlen("L"));

		ftcs2 = _cptofcd("U", strlen("U"));

		ftcs3 = _cptofcd("N", strlen("N"));

		CTRSM( ftcs1, ftcs2, ftcs3, ftcs3, &nsupc, &nrhs, &alpha,

		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);

#else

		ztrsm_("L", "U", "N", "N", &nsupc, &nrhs, &alpha,

		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);

#endif

#else		

		for (j = 0; j < nrhs; j++)

		    zusolve ( nsupr, nsupc, &Lval[luptr], &Bmat[fsupc+j*ldb] );

#endif		

	    }

	    for (j = 0; j < nrhs; ++j) {

		rhs_work = &Bmat[j*ldb];

		for (jcol = fsupc; jcol < fsupc + nsupc; 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(&temp_comp, &rhs_work[jcol], &Uval[i]);

			z_sub(&rhs_work[irow], &rhs_work[irow], &temp_comp);

		    }

		}

	    }

	} /* for U-solve */

#ifdef DEBUG

  	printf("After U-solve: x=\n");

	zprint_soln(n, nrhs, Bmat);

#endif

	/* Compute the final solution X := Pc*X. */

	for (i = 0; i < nrhs; i++) {

	    rhs_work = &Bmat[i*ldb];

	    for (k = 0; k < n; k++) soln[k] = rhs_work[perm_c[k]];

	    for (k = 0; k < n; k++) rhs_work[k] = soln[k];

	}

        stat->ops[SOLVE] = solve_ops;

    } else { /* Solve A'*X=B or CONJ(A)*X=B */

	/* Permute right hand sides to form Pc'*B. */

	for (i = 0; i < nrhs; i++) {

	    rhs_work = &Bmat[i*ldb];

	    for (k = 0; k < n; k++) soln[perm_c[k]] = rhs_work[k];

	    for (k = 0; k < n; k++) rhs_work[k] = soln[k];

	}

	stat->ops[SOLVE] = 0;

        if (trans == TRANS) {

	    for (k = 0; k < nrhs; ++k) {

	        /* Multiply by inv(U'). */

	        sp_ztrsv("U", "T", "N", L, U, &Bmat[k*ldb], stat, info);

	        /* Multiply by inv(L'). */

	        sp_ztrsv("L", "T", "U", L, U, &Bmat[k*ldb], stat, info);

	    }

         } else { /* trans == CONJ */

            for (k = 0; k < nrhs; ++k) {                

                /* Multiply by conj(inv(U')). */

                sp_ztrsv("U", "C", "N", L, U, &Bmat[k*ldb], stat, info);

                /* Multiply by conj(inv(L')). */

                sp_ztrsv("L", "C", "U", L, U, &Bmat[k*ldb], stat, info);

	    }

         }

	/* Compute the final solution X := Pr'*X (=inv(Pr)*X) */

	for (i = 0; i < nrhs; i++) {

	    rhs_work = &Bmat[i*ldb];

	    for (k = 0; k < n; k++) soln[k] = rhs_work[perm_r[k]];

	    for (k = 0; k < n; k++) rhs_work[k] = soln[k];

	}

    }

    SUPERLU_FREE(work);

    SUPERLU_FREE(soln);

}

/*

 * Diagnostic print of the solution vector 

 */

void

zprint_soln(int n, int nrhs, doublecomplex *soln)

{

    int i;

    for (i = 0; i < n; i++) 

  	printf("\t%d: %.4f\n", i, soln[i]);

}