zspmv()

subroutine zspmv	(	character	uplo,
		integer	n,
		complex*16	alpha,
		complex*16, dimension( * )	ap,
		complex*16, dimension( * )	x,
		integer	incx,
		complex*16	beta,
		complex*16, dimension( * )	y,
		integer	incy
	)

ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix

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Purpose:

 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.

Parameters

[in]	UPLO	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.
[in]	N	N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.
[in]	ALPHA	ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
[in]	AP	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.
[in]	X	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.
[in]	INCX	INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
[in]	BETA	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.
[in,out]	Y	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.
[in]	INCY	INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 150 of file zspmv.f.

*
*  -- 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
*

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