/*! \file
Copyright (c) 2003, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required 
approvals from U.S. Dept. of Energy) 

All rights reserved. 

The source code is distributed under BSD license, see the file License.txt
at the top-level directory.
*/

/*
 * -- SuperLU routine (version 3.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * October 15, 2003
 *
 */
/*
 * File name:		zsp_blas2.c
 * Purpose:		Sparse BLAS 2, using some dense BLAS 2 operations.
 */

#include "slu_mt_zdefs.h"


/* 
 * Function prototypes 
 */
extern void zusolve(int_t, int_t, doublecomplex*, doublecomplex*);
extern void zlsolve(int_t, int_t, doublecomplex*, doublecomplex*);
extern void zmatvec(int_t, int_t, int_t, doublecomplex*, doublecomplex*, doublecomplex*);


int_t
sp_ztrsv(char *uplo, char *trans, char *diag, SuperMatrix *L, 
         SuperMatrix *U, doublecomplex *x, int_t *info)
{
/*
 *   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 = _Z, Mtype = TRLU.
 *
 *   U       - (input) SuperMatrix*
 *	        The factor U from the factorization Pr*A*Pc=L*U.
 *	        U has types: Stype = NCP, Dtype = _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_t*
 *             If *info = -i, the i-th argument had an illegal value.
 *
 */
#if ( MACH==CRAY_PVP )
    _fcd ftcs1, ftcs2, ftcs3;
#endif
    SCPformat *Lstore;
    NCPformat *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};
    register int_t fsupc, luptr, istart, irow, k, iptr, jcol, nsuper;
    int          nsupr, nsupc, nrow, i;
    doublecomplex *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") ) *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_ztrsv", &i);
	return 0;
    }

    Lstore = (SCPformat*) L->Store;
    Lval = (doublecomplex*) Lstore->nzval;
    Ustore = (NCPformat*) U->Store;
    Uval = (doublecomplex*) Ustore->nzval;
    nsuper = Lstore->nsuper;
    solve_ops = 0;

    if ( !(work = doublecomplexCalloc(L->nrow)) )
	SUPERLU_ABORT("Malloc fails for work in sp_ztrsv().");
    
    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 <= nsuper; k++) {
		fsupc = L_FST_SUPC(k);
		istart = L_SUB_START(fsupc);
                nsupr = L_SUB_END(fsupc) - istart;
                nsupc = L_LAST_SUPC(k) - 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_END(fsupc); ++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
#if ( MACH==CRAY_PVP )
                    ftcs1 = _cptofcd("L", strlen("L"));
                    ftcs2 = _cptofcd("N", strlen("N"));
                    ftcs3 = _cptofcd("U", strlen("U"));

		    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 = nsuper; k >= 0; k--) {
	    	fsupc = L_FST_SUPC(k);
                nsupr = L_SUB_END(fsupc) - L_SUB_START(fsupc);
                nsupc = L_LAST_SUPC(k) - 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_END(fsupc); ++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
#if ( MACH==CRAY_PVP )
                    ftcs1 = _cptofcd("U", strlen("U"));
                    ftcs2 = _cptofcd("N", strlen("N"));
                    ftcs3 = _cptofcd("N", strlen("N"));

		    CTRSV(ftcs1, ftcs2, ftcs3, &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 < fsupc + nsupc; jcol++) {
		        solve_ops += 8*(U_NZ_END(jcol) - U_NZ_START(jcol));
		    	for (i = U_NZ_START(jcol); i < U_NZ_END(jcol); 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 ( lsame_(trans, "T") ) { /* 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_END(fsupc) - istart;
                nsupc = L_LAST_SUPC(k) - fsupc;
	    	luptr = L_NZ_START(fsupc);

		solve_ops += 8 * (nsupr - nsupc) * nsupc;

		for (jcol = fsupc; jcol < L_LAST_SUPC(k); jcol++) {
		    iptr = istart + nsupc;
		    for (i = L_NZ_START(jcol) + nsupc; 
				i < L_NZ_END(jcol); 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 <= nsuper; k++) {
	    	fsupc = L_FST_SUPC(k);
                nsupr = L_SUB_END(fsupc) - L_SUB_START(fsupc);
                nsupc = L_LAST_SUPC(k) - fsupc;
	    	luptr = L_NZ_START(fsupc);

                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_END(jcol); 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 ( lsame_(uplo, "L") ) {
	    /* 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_END(fsupc) - istart;
	    	nsupc = L_LAST_SUPC(k) - 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 ... */
  	}
    }

    SUPERLU_FREE(work);
    return 0;
}



int_t
sp_zgemv(char *trans, doublecomplex alpha, SuperMatrix *A, doublecomplex *x, 
	 int_t incx, doublecomplex beta, doublecomplex *y, int_t incy)
{
/*  Purpose   
    =======   

    sp_zgemv()  performs one of the matrix-vector operations   
       y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,   
    where alpha and beta are scalars, x and y are vectors and A is a
    sparse A->nrow by A->ncol matrix.   

    Parameters   
    ==========   

    TRANS  - (input) char*
             On entry, TRANS specifies the operation to be performed as   
             follows:   
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.   
                TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.   
                TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.   

    ALPHA  - (input) doublecomplex
             On entry, ALPHA specifies the scalar alpha.   

    A      - (input) SuperMatrix*
             Before entry, the leading m by n part of the array A must   
             contain the matrix of coefficients.   

    X      - (input) doublecomplex*, array of DIMENSION at least   
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'   
             and at least   
             ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.   
             Before entry, the incremented array X must contain the   
             vector x.   

    INCX   - (input) int
             On entry, INCX specifies the increment for the elements of   
             X. INCX must not be zero.   

    BETA   - (input) doublecomplex
             On entry, BETA specifies the scalar beta. When BETA is   
             supplied as zero then Y need not be set on input.   

    Y      - (output) doublecomplex*,  array of DIMENSION at least   
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'   
             and at least   
             ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.   
             Before entry with BETA non-zero, the incremented array Y   
             must contain the vector y. On exit, Y is overwritten by the 
             updated vector y.
	     
    INCY   - (input) int
             On entry, INCY specifies the increment for the elements of   
             Y. INCY must not be zero.   

    ==== Sparse Level 2 Blas routine.   
*/

    /* Local variables */
    NCformat *Astore;
    doublecomplex   *Aval;
    int info;
    doublecomplex temp, temp1;
    int_t lenx, leny, i, j, irow;
    int_t iy, jx, jy, kx, ky;
    int_t notran;
    doublecomplex comp_zero = {0.0, 0.0};
    doublecomplex comp_one = {1.0, 0.0};

    notran = lsame_(trans, "N");
    Astore = A->Store;
    Aval = Astore->nzval;
    
    /* Test the input parameters */
    info = 0;
    if ( !notran && !lsame_(trans, "T") && !lsame_(trans, "C")) info = 1;
    else if ( A->nrow < 0 || A->ncol < 0 ) info = 3;
    else if (incx == 0) info = 5;
    else if (incy == 0)	info = 8;
    if (info != 0) {
	xerbla_("sp_zgemv ", &info);
	return 0;
    }

    /* Quick return if possible. */
    if (A->nrow == 0 || A->ncol == 0 || 
	z_eq(&alpha, &comp_zero) && 
	z_eq(&beta, &comp_one))
	return 0;


    /* Set  LENX  and  LENY, the lengths of the vectors x and y, and set 
       up the start points in  X  and  Y. */
    if (lsame_(trans, "N")) {
	lenx = A->ncol;
	leny = A->nrow;
    } else {
	lenx = A->nrow;
	leny = A->ncol;
    }
    if (incx > 0) kx = 0;
    else kx =  - (lenx - 1) * incx;
    if (incy > 0) ky = 0;
    else ky =  - (leny - 1) * incy;

    /* Start the operations. In this version the elements of A are   
       accessed sequentially with one pass through A. */
    /* First form  y := beta*y. */
    if ( !z_eq(&beta, &comp_one) ) {
	if (incy == 1) {
	    if ( z_eq(&beta, &comp_zero) )
		for (i = 0; i < leny; ++i) y[i] = comp_zero;
	    else
		for (i = 0; i < leny; ++i) 
		  zz_mult(&y[i], &beta, &y[i]);
	} else {
	    iy = ky;
	    if ( z_eq(&beta, &comp_zero) )
		for (i = 0; i < leny; ++i) {
		    y[iy] = comp_zero;
		    iy += incy;
		}
	    else
		for (i = 0; i < leny; ++i) {
		    zz_mult(&y[iy], &beta, &y[iy]);
		    iy += incy;
		}
	}
    }
    
    if ( z_eq(&alpha, &comp_zero) ) return 0;

    if ( notran ) {
	/* Form  y := alpha*A*x + y. */
	jx = kx;
	if (incy == 1) {
	    for (j = 0; j < A->ncol; ++j) {
		if ( !z_eq(&x[jx], &comp_zero) ) {
		    zz_mult(&temp, &alpha, &x[jx]);
		    for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
			irow = Astore->rowind[i];
			zz_mult(&temp1, &temp,  &Aval[i]);
			z_add(&y[irow], &y[irow], &temp1);
		    }
		}
		jx += incx;
	    }
	} else {
	    SUPERLU_ABORT("Not implemented.");
	}
    } else {
	/* Form  y := alpha*A'*x + y. */
	jy = ky;
	if (incx == 1) {
	    for (j = 0; j < A->ncol; ++j) {
		temp = comp_zero;
		for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
		    irow = Astore->rowind[i];
		    zz_mult(&temp1, &Aval[i], &x[irow]);
		    z_add(&temp, &temp, &temp1);
		}
		zz_mult(&temp1, &alpha, &temp);
		z_add(&y[jy], &y[jy], &temp1);
		jy += incy;
	    }
	} else {
	    SUPERLU_ABORT("Not implemented.");
	}
    }
    return 0;    
} /* sp_zgemv */