574 lines
17 KiB
C
574 lines
17 KiB
C
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/*! @file zsp_blas2.c
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* \brief Sparse BLAS 2, using some dense BLAS 2 operations
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*
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* <pre>
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* -- SuperLU routine (version 3.0) --
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* Univ. of California Berkeley, Xerox Palo Alto Research Center,
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* and Lawrence Berkeley National Lab.
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* October 15, 2003
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* </pre>
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*/
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/*
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* File name: zsp_blas2.c
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* Purpose: Sparse BLAS 2, using some dense BLAS 2 operations.
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*/
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#include "slu_zdefs.h"
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/*
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* Function prototypes
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*/
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void zusolve(int, int, doublecomplex*, doublecomplex*);
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void zlsolve(int, int, doublecomplex*, doublecomplex*);
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void zmatvec(int, int, int, doublecomplex*, doublecomplex*, doublecomplex*);
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/*! \brief Solves one of the systems of equations A*x = b, or A'*x = b
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*
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* <pre>
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* Purpose
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* =======
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*
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* sp_ztrsv() solves one of the systems of equations
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* A*x = b, or A'*x = b,
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* where b and x are n element vectors and A is a sparse unit , or
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* non-unit, upper or lower triangular matrix.
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* No test for singularity or near-singularity is included in this
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* routine. Such tests must be performed before calling this routine.
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*
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* Parameters
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* ==========
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*
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* uplo - (input) char*
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* On entry, uplo specifies whether the matrix is an upper or
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* lower triangular matrix as follows:
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* uplo = 'U' or 'u' A is an upper triangular matrix.
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* uplo = 'L' or 'l' A is a lower triangular matrix.
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*
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* trans - (input) char*
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* On entry, trans specifies the equations to be solved as
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* follows:
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* trans = 'N' or 'n' A*x = b.
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* trans = 'T' or 't' A'*x = b.
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* trans = 'C' or 'c' A^H*x = b.
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*
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* diag - (input) char*
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* On entry, diag specifies whether or not A is unit
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* triangular as follows:
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* diag = 'U' or 'u' A is assumed to be unit triangular.
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* diag = 'N' or 'n' A is not assumed to be unit
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* triangular.
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*
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* L - (input) SuperMatrix*
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* The factor L from the factorization Pr*A*Pc=L*U. Use
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* compressed row subscripts storage for supernodes,
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* i.e., L has types: Stype = SC, Dtype = SLU_Z, Mtype = TRLU.
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*
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* U - (input) SuperMatrix*
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* The factor U from the factorization Pr*A*Pc=L*U.
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* U has types: Stype = NC, Dtype = SLU_Z, Mtype = TRU.
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*
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* x - (input/output) doublecomplex*
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* Before entry, the incremented array X must contain the n
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* element right-hand side vector b. On exit, X is overwritten
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* with the solution vector x.
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*
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* info - (output) int*
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* If *info = -i, the i-th argument had an illegal value.
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* </pre>
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*/
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int
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sp_ztrsv(char *uplo, char *trans, char *diag, SuperMatrix *L,
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SuperMatrix *U, doublecomplex *x, SuperLUStat_t *stat, int *info)
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{
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#ifdef _CRAY
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_fcd ftcs1 = _cptofcd("L", strlen("L")),
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ftcs2 = _cptofcd("N", strlen("N")),
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ftcs3 = _cptofcd("U", strlen("U"));
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#endif
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SCformat *Lstore;
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NCformat *Ustore;
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doublecomplex *Lval, *Uval;
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int incx = 1, incy = 1;
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doublecomplex temp;
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doublecomplex alpha = {1.0, 0.0}, beta = {1.0, 0.0};
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doublecomplex comp_zero = {0.0, 0.0};
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int nrow;
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int fsupc, nsupr, nsupc, luptr, istart, irow;
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int i, k, iptr, jcol;
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doublecomplex *work;
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flops_t solve_ops;
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/* Test the input parameters */
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*info = 0;
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if ( !lsame_(uplo,"L") && !lsame_(uplo, "U") ) *info = -1;
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else if ( !lsame_(trans, "N") && !lsame_(trans, "T") &&
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!lsame_(trans, "C")) *info = -2;
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else if ( !lsame_(diag, "U") && !lsame_(diag, "N") ) *info = -3;
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else if ( L->nrow != L->ncol || L->nrow < 0 ) *info = -4;
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else if ( U->nrow != U->ncol || U->nrow < 0 ) *info = -5;
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if ( *info ) {
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i = -(*info);
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xerbla_("sp_ztrsv", &i);
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return 0;
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}
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Lstore = L->Store;
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Lval = Lstore->nzval;
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Ustore = U->Store;
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Uval = Ustore->nzval;
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solve_ops = 0;
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if ( !(work = doublecomplexCalloc(L->nrow)) )
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ABORT("Malloc fails for work in sp_ztrsv().");
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if ( lsame_(trans, "N") ) { /* Form x := inv(A)*x. */
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if ( lsame_(uplo, "L") ) {
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/* Form x := inv(L)*x */
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if ( L->nrow == 0 ) return 0; /* Quick return */
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for (k = 0; k <= Lstore->nsuper; k++) {
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fsupc = L_FST_SUPC(k);
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istart = L_SUB_START(fsupc);
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nsupr = L_SUB_START(fsupc+1) - istart;
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nsupc = L_FST_SUPC(k+1) - fsupc;
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luptr = L_NZ_START(fsupc);
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nrow = nsupr - nsupc;
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/* 1 z_div costs 10 flops */
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solve_ops += 4 * nsupc * (nsupc - 1) + 10 * nsupc;
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solve_ops += 8 * nrow * nsupc;
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if ( nsupc == 1 ) {
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for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); ++iptr) {
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irow = L_SUB(iptr);
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++luptr;
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zz_mult(&comp_zero, &x[fsupc], &Lval[luptr]);
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z_sub(&x[irow], &x[irow], &comp_zero);
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}
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} else {
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#ifdef USE_VENDOR_BLAS
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#ifdef _CRAY
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CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
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&x[fsupc], &incx);
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CGEMV(ftcs2, &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
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&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
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#else
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ztrsv_("L", "N", "U", &nsupc, &Lval[luptr], &nsupr,
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&x[fsupc], &incx);
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zgemv_("N", &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
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&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
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#endif
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#else
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zlsolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc]);
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zmatvec ( nsupr, nsupr-nsupc, nsupc, &Lval[luptr+nsupc],
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&x[fsupc], &work[0] );
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#endif
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iptr = istart + nsupc;
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for (i = 0; i < nrow; ++i, ++iptr) {
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irow = L_SUB(iptr);
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z_sub(&x[irow], &x[irow], &work[i]); /* Scatter */
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work[i] = comp_zero;
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}
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}
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} /* for k ... */
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} else {
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/* Form x := inv(U)*x */
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if ( U->nrow == 0 ) return 0; /* Quick return */
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for (k = Lstore->nsuper; k >= 0; k--) {
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fsupc = L_FST_SUPC(k);
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nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
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nsupc = L_FST_SUPC(k+1) - fsupc;
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luptr = L_NZ_START(fsupc);
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/* 1 z_div costs 10 flops */
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solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
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if ( nsupc == 1 ) {
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z_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
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for (i = U_NZ_START(fsupc); i < U_NZ_START(fsupc+1); ++i) {
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irow = U_SUB(i);
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zz_mult(&comp_zero, &x[fsupc], &Uval[i]);
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z_sub(&x[irow], &x[irow], &comp_zero);
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}
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} else {
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#ifdef USE_VENDOR_BLAS
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#ifdef _CRAY
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CTRSV(ftcs3, ftcs2, ftcs2, &nsupc, &Lval[luptr], &nsupr,
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&x[fsupc], &incx);
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#else
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ztrsv_("U", "N", "N", &nsupc, &Lval[luptr], &nsupr,
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&x[fsupc], &incx);
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#endif
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#else
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zusolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc] );
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#endif
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for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
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solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
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for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1);
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i++) {
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irow = U_SUB(i);
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zz_mult(&comp_zero, &x[jcol], &Uval[i]);
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z_sub(&x[irow], &x[irow], &comp_zero);
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}
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}
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}
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} /* for k ... */
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}
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} else if ( lsame_(trans, "T") ) { /* Form x := inv(A')*x */
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if ( lsame_(uplo, "L") ) {
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/* Form x := inv(L')*x */
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if ( L->nrow == 0 ) return 0; /* Quick return */
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for (k = Lstore->nsuper; k >= 0; --k) {
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fsupc = L_FST_SUPC(k);
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istart = L_SUB_START(fsupc);
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nsupr = L_SUB_START(fsupc+1) - istart;
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nsupc = L_FST_SUPC(k+1) - fsupc;
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luptr = L_NZ_START(fsupc);
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solve_ops += 8 * (nsupr - nsupc) * nsupc;
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for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
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iptr = istart + nsupc;
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for (i = L_NZ_START(jcol) + nsupc;
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i < L_NZ_START(jcol+1); i++) {
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irow = L_SUB(iptr);
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zz_mult(&comp_zero, &x[irow], &Lval[i]);
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z_sub(&x[jcol], &x[jcol], &comp_zero);
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iptr++;
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}
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}
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if ( nsupc > 1 ) {
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solve_ops += 4 * nsupc * (nsupc - 1);
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#ifdef _CRAY
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ftcs1 = _cptofcd("L", strlen("L"));
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ftcs2 = _cptofcd("T", strlen("T"));
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ftcs3 = _cptofcd("U", strlen("U"));
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CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
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&x[fsupc], &incx);
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#else
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ztrsv_("L", "T", "U", &nsupc, &Lval[luptr], &nsupr,
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&x[fsupc], &incx);
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#endif
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}
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}
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} else {
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/* Form x := inv(U')*x */
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if ( U->nrow == 0 ) return 0; /* Quick return */
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for (k = 0; k <= Lstore->nsuper; k++) {
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fsupc = L_FST_SUPC(k);
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nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
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nsupc = L_FST_SUPC(k+1) - fsupc;
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luptr = L_NZ_START(fsupc);
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for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
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solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
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for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
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irow = U_SUB(i);
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zz_mult(&comp_zero, &x[irow], &Uval[i]);
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z_sub(&x[jcol], &x[jcol], &comp_zero);
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}
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}
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/* 1 z_div costs 10 flops */
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solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
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if ( nsupc == 1 ) {
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z_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
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} else {
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#ifdef _CRAY
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ftcs1 = _cptofcd("U", strlen("U"));
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ftcs2 = _cptofcd("T", strlen("T"));
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ftcs3 = _cptofcd("N", strlen("N"));
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CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
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&x[fsupc], &incx);
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#else
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ztrsv_("U", "T", "N", &nsupc, &Lval[luptr], &nsupr,
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&x[fsupc], &incx);
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#endif
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}
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} /* for k ... */
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}
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} else { /* Form x := conj(inv(A'))*x */
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if ( lsame_(uplo, "L") ) {
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/* Form x := conj(inv(L'))*x */
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if ( L->nrow == 0 ) return 0; /* Quick return */
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for (k = Lstore->nsuper; k >= 0; --k) {
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fsupc = L_FST_SUPC(k);
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istart = L_SUB_START(fsupc);
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nsupr = L_SUB_START(fsupc+1) - istart;
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nsupc = L_FST_SUPC(k+1) - fsupc;
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luptr = L_NZ_START(fsupc);
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solve_ops += 8 * (nsupr - nsupc) * nsupc;
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for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
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iptr = istart + nsupc;
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for (i = L_NZ_START(jcol) + nsupc;
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i < L_NZ_START(jcol+1); i++) {
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irow = L_SUB(iptr);
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zz_conj(&temp, &Lval[i]);
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zz_mult(&comp_zero, &x[irow], &temp);
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z_sub(&x[jcol], &x[jcol], &comp_zero);
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iptr++;
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}
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}
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if ( nsupc > 1 ) {
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solve_ops += 4 * nsupc * (nsupc - 1);
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#ifdef _CRAY
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ftcs1 = _cptofcd("L", strlen("L"));
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ftcs2 = _cptofcd(trans, strlen("T"));
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ftcs3 = _cptofcd("U", strlen("U"));
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ZTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
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&x[fsupc], &incx);
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#else
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ztrsv_("L", trans, "U", &nsupc, &Lval[luptr], &nsupr,
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&x[fsupc], &incx);
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#endif
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}
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}
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} else {
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/* Form x := conj(inv(U'))*x */
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if ( U->nrow == 0 ) return 0; /* Quick return */
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for (k = 0; k <= Lstore->nsuper; k++) {
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fsupc = L_FST_SUPC(k);
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nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
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nsupc = L_FST_SUPC(k+1) - fsupc;
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luptr = L_NZ_START(fsupc);
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for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
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solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
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for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
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irow = U_SUB(i);
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zz_conj(&temp, &Uval[i]);
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zz_mult(&comp_zero, &x[irow], &temp);
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z_sub(&x[jcol], &x[jcol], &comp_zero);
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}
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}
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/* 1 z_div costs 10 flops */
|
||
|
solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
|
||
|
|
||
|
if ( nsupc == 1 ) {
|
||
|
zz_conj(&temp, &Lval[luptr]);
|
||
|
z_div(&x[fsupc], &x[fsupc], &temp);
|
||
|
} else {
|
||
|
#ifdef _CRAY
|
||
|
ftcs1 = _cptofcd("U", strlen("U"));
|
||
|
ftcs2 = _cptofcd(trans, strlen("T"));
|
||
|
ftcs3 = _cptofcd("N", strlen("N"));
|
||
|
ZTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
|
||
|
&x[fsupc], &incx);
|
||
|
#else
|
||
|
ztrsv_("U", trans, "N", &nsupc, &Lval[luptr], &nsupr,
|
||
|
&x[fsupc], &incx);
|
||
|
#endif
|
||
|
}
|
||
|
} /* for k ... */
|
||
|
}
|
||
|
}
|
||
|
|
||
|
stat->ops[SOLVE] += solve_ops;
|
||
|
SUPERLU_FREE(work);
|
||
|
return 0;
|
||
|
}
|
||
|
|
||
|
|
||
|
|
||
|
/*! \brief Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y
|
||
|
*
|
||
|
* <pre>
|
||
|
* 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.
|
||
|
* </pre>
|
||
|
*/
|
||
|
int
|
||
|
sp_zgemv(char *trans, doublecomplex alpha, SuperMatrix *A, doublecomplex *x,
|
||
|
int incx, doublecomplex beta, doublecomplex *y, int incy)
|
||
|
{
|
||
|
|
||
|
/* Local variables */
|
||
|
NCformat *Astore;
|
||
|
doublecomplex *Aval;
|
||
|
int info;
|
||
|
doublecomplex temp, temp1;
|
||
|
int lenx, leny, i, j, irow;
|
||
|
int iy, jx, jy, kx, ky;
|
||
|
int 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 {
|
||
|
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 {
|
||
|
ABORT("Not implemented.");
|
||
|
}
|
||
|
}
|
||
|
return 0;
|
||
|
} /* sp_zgemv */
|
||
|
|