zspr()

subroutine zspr	(	character	uplo,
		integer	n,
		complex*16	alpha,
		complex*16, dimension( * )	x,
		integer	incx,
		complex*16, dimension( * )	ap )

ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.

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Purpose:

!>
!> ZSPR    performs the symmetric rank 1 operation
!>
!>    A := alpha*x*x**H + A,
!>
!> where alpha is a complex scalar, x is an n element vector 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]	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,out]	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. On exit, the array !> AP is overwritten by the upper triangular part of the !> updated matrix. !> 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. On exit, the array !> AP is overwritten by the lower triangular part of the !> updated matrix. !> Note that the imaginary parts of the diagonal elements need !> not be set, they are assumed to be zero, and on exit they !> are set to zero. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 129 of file zspr.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, N
      COMPLEX*16         ALPHA
*     ..
*     .. Array Arguments ..
      COMPLEX*16         AP( * ), X( * )
*     ..
*
* =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      parameter( zero = ( 0.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            I, INFO, IX, J, JX, K, KK, KX
      COMPLEX*16         TEMP
*     ..
*     .. 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 = 5
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZSPR  ', info )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( n.EQ.0 ) .OR. ( alpha.EQ.zero ) )
     $   RETURN
*
*     Set the start point in X if the increment is not unity.
*
      IF( incx.LE.0 ) THEN
         kx = 1 - ( n-1 )*incx
      ELSE IF( incx.NE.1 ) THEN
         kx = 1
      END IF
*
*     Start the operations. In this version the elements of the array AP
*     are accessed sequentially with one pass through AP.
*
      kk = 1
      IF( lsame( uplo, 'U' ) ) THEN
*
*        Form  A  when upper triangle is stored in AP.
*
         IF( incx.EQ.1 ) THEN
            DO 20 j = 1, n
               IF( x( j ).NE.zero ) THEN
                  temp = alpha*x( j )
                  k = kk
                  DO 10 i = 1, j - 1
                     ap( k ) = ap( k ) + x( i )*temp
                     k = k + 1
   10             CONTINUE
                  ap( kk+j-1 ) = ap( kk+j-1 ) + x( j )*temp
               ELSE
                  ap( kk+j-1 ) = ap( kk+j-1 )
               END IF
               kk = kk + j
   20       CONTINUE
         ELSE
            jx = kx
            DO 40 j = 1, n
               IF( x( jx ).NE.zero ) THEN
                  temp = alpha*x( jx )
                  ix = kx
                  DO 30 k = kk, kk + j - 2
                     ap( k ) = ap( k ) + x( ix )*temp
                     ix = ix + incx
   30             CONTINUE
                  ap( kk+j-1 ) = ap( kk+j-1 ) + x( jx )*temp
               ELSE
                  ap( kk+j-1 ) = ap( kk+j-1 )
               END IF
               jx = jx + incx
               kk = kk + j
   40       CONTINUE
         END IF
      ELSE
*
*        Form  A  when lower triangle is stored in AP.
*
         IF( incx.EQ.1 ) THEN
            DO 60 j = 1, n
               IF( x( j ).NE.zero ) THEN
                  temp = alpha*x( j )
                  ap( kk ) = ap( kk ) + temp*x( j )
                  k = kk + 1
                  DO 50 i = j + 1, n
                     ap( k ) = ap( k ) + x( i )*temp
                     k = k + 1
   50             CONTINUE
               ELSE
                  ap( kk ) = ap( kk )
               END IF
               kk = kk + n - j + 1
   60       CONTINUE
         ELSE
            jx = kx
            DO 80 j = 1, n
               IF( x( jx ).NE.zero ) THEN
                  temp = alpha*x( jx )
                  ap( kk ) = ap( kk ) + temp*x( jx )
                  ix = jx
                  DO 70 k = kk + 1, kk + n - j
                     ix = ix + incx
                     ap( k ) = ap( k ) + x( ix )*temp
   70             CONTINUE
               ELSE
                  ap( kk ) = ap( kk )
               END IF
               jx = jx + incx
               kk = kk + n - j + 1
   80       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZSPR
*

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