zspmv.f

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*> \brief \b ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE ZSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INCX, INCY, N
*       COMPLEX*16         ALPHA, BETA
*       ..
*       .. Array Arguments ..
*       COMPLEX*16         AP( * ), X( * ), Y( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZSPMV  performs the matrix-vector operation
*>
*>    y := alpha*A*x + beta*y,
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric matrix, supplied in packed form.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>           On entry, UPLO specifies whether the upper or lower
*>           triangular part of the matrix A is supplied in the packed
*>           array AP as follows:
*>
*>              UPLO = 'U' or 'u'   The upper triangular part of A is
*>                                  supplied in AP.
*>
*>              UPLO = 'L' or 'l'   The lower triangular part of A is
*>                                  supplied in AP.
*>
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>           On entry, N specifies the order of the matrix A.
*>           N must be at least zero.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*>          ALPHA is COMPLEX*16
*>           On entry, ALPHA specifies the scalar alpha.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*>          AP is COMPLEX*16 array, dimension at least
*>           ( ( N*( N + 1 ) )/2 ).
*>           Before entry, with UPLO = 'U' or 'u', the array AP must
*>           contain the upper triangular part of the symmetric matrix
*>           packed sequentially, column by column, so that AP( 1 )
*>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
*>           and a( 2, 2 ) respectively, and so on.
*>           Before entry, with UPLO = 'L' or 'l', the array AP must
*>           contain the lower triangular part of the symmetric matrix
*>           packed sequentially, column by column, so that AP( 1 )
*>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
*>           and a( 3, 1 ) respectively, and so on.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is COMPLEX*16 array, dimension at least
*>           ( 1 + ( N - 1 )*abs( INCX ) ).
*>           Before entry, the incremented array X must contain the N-
*>           element vector x.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*>          INCX is INTEGER
*>           On entry, INCX specifies the increment for the elements of
*>           X. INCX must not be zero.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*>          BETA is COMPLEX*16
*>           On entry, BETA specifies the scalar beta. When BETA is
*>           supplied as zero then Y need not be set on input.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*>          Y is COMPLEX*16 array, dimension at least
*>           ( 1 + ( N - 1 )*abs( INCY ) ).
*>           Before entry, the incremented array Y must contain the n
*>           element vector y. On exit, Y is overwritten by the updated
*>           vector y.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*>          INCY is INTEGER
*>           On entry, INCY specifies the increment for the elements of
*>           Y. INCY must not be zero.
*>           Unchanged on exit.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hpmv
*
*  =====================================================================
      SUBROUTINE zspmv( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
*
*  -- LAPACK auxiliary routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INCX, INCY, N
      COMPLEX*16         ALPHA, BETA
*     ..
*     .. Array Arguments ..
      COMPLEX*16         AP( * ), X( * ), Y( * )
*     ..
*
* =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ONE
      parameter( one = ( 1.0d+0, 0.0d+0 ) )
      COMPLEX*16         ZERO
      parameter( zero = ( 0.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY
      COMPLEX*16         TEMP1, TEMP2
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
         info = 1
      ELSE IF( n.LT.0 ) THEN
         info = 2
      ELSE IF( incx.EQ.0 ) THEN
         info = 6
      ELSE IF( incy.EQ.0 ) THEN
         info = 9
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZSPMV ', info )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( n.EQ.0 ) .OR. ( ( alpha.EQ.zero ) .AND. ( beta.EQ.one ) ) )
     $   RETURN
*
*     Set up the start points in  X  and  Y.
*
      IF( incx.GT.0 ) THEN
         kx = 1
      ELSE
         kx = 1 - ( n-1 )*incx
      END IF
      IF( incy.GT.0 ) THEN
         ky = 1
      ELSE
         ky = 1 - ( n-1 )*incy
      END IF
*
*     Start the operations. In this version the elements of the array AP
*     are accessed sequentially with one pass through AP.
*
*     First form  y := beta*y.
*
      IF( beta.NE.one ) THEN
         IF( incy.EQ.1 ) THEN
            IF( beta.EQ.zero ) THEN
               DO 10 i = 1, n
                  y( i ) = zero
   10          CONTINUE
            ELSE
               DO 20 i = 1, n
                  y( i ) = beta*y( i )
   20          CONTINUE
            END IF
         ELSE
            iy = ky
            IF( beta.EQ.zero ) THEN
               DO 30 i = 1, n
                  y( iy ) = zero
                  iy = iy + incy
   30          CONTINUE
            ELSE
               DO 40 i = 1, n
                  y( iy ) = beta*y( iy )
                  iy = iy + incy
   40          CONTINUE
            END IF
         END IF
      END IF
      IF( alpha.EQ.zero )
     $   RETURN
      kk = 1
      IF( lsame( uplo, 'U' ) ) THEN
*
*        Form  y  when AP contains the upper triangle.
*
         IF( ( incx.EQ.1 ) .AND. ( incy.EQ.1 ) ) THEN
            DO 60 j = 1, n
               temp1 = alpha*x( j )
               temp2 = zero
               k = kk
               DO 50 i = 1, j - 1
                  y( i ) = y( i ) + temp1*ap( k )
                  temp2 = temp2 + ap( k )*x( i )
                  k = k + 1
   50          CONTINUE
               y( j ) = y( j ) + temp1*ap( kk+j-1 ) + alpha*temp2
               kk = kk + j
   60       CONTINUE
         ELSE
            jx = kx
            jy = ky
            DO 80 j = 1, n
               temp1 = alpha*x( jx )
               temp2 = zero
               ix = kx
               iy = ky
               DO 70 k = kk, kk + j - 2
                  y( iy ) = y( iy ) + temp1*ap( k )
                  temp2 = temp2 + ap( k )*x( ix )
                  ix = ix + incx
                  iy = iy + incy
   70          CONTINUE
               y( jy ) = y( jy ) + temp1*ap( kk+j-1 ) + alpha*temp2
               jx = jx + incx
               jy = jy + incy
               kk = kk + j
   80       CONTINUE
         END IF
      ELSE
*
*        Form  y  when AP contains the lower triangle.
*
         IF( ( incx.EQ.1 ) .AND. ( incy.EQ.1 ) ) THEN
            DO 100 j = 1, n
               temp1 = alpha*x( j )
               temp2 = zero
               y( j ) = y( j ) + temp1*ap( kk )
               k = kk + 1
               DO 90 i = j + 1, n
                  y( i ) = y( i ) + temp1*ap( k )
                  temp2 = temp2 + ap( k )*x( i )
                  k = k + 1
   90          CONTINUE
               y( j ) = y( j ) + alpha*temp2
               kk = kk + ( n-j+1 )
  100       CONTINUE
         ELSE
            jx = kx
            jy = ky
            DO 120 j = 1, n
               temp1 = alpha*x( jx )
               temp2 = zero
               y( jy ) = y( jy ) + temp1*ap( kk )
               ix = jx
               iy = jy
               DO 110 k = kk + 1, kk + n - j
                  ix = ix + incx
                  iy = iy + incy
                  y( iy ) = y( iy ) + temp1*ap( k )
                  temp2 = temp2 + ap( k )*x( ix )
  110          CONTINUE
               y( jy ) = y( jy ) + alpha*temp2
               jx = jx + incx
               jy = jy + incy
               kk = kk + ( n-j+1 )
  120       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZSPMV
*
      END