cspr()

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

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

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Purpose:

 CSPR    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 On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
[in]	X	X is COMPLEX 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 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 131 of file cspr.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            ALPHA
*     ..
*     .. Array Arguments ..
      COMPLEX            AP( * ), X( * )
*     ..
*
* =====================================================================
*
*     .. Parameters ..
      COMPLEX            ZERO
      parameter( zero = ( 0.0e+0, 0.0e+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            I, INFO, IX, J, JX, K, KK, KX
      COMPLEX            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( 'CSPR  ', 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 CSPR
*

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