zsyr()

subroutine zsyr	(	character	uplo,
		integer	n,
		complex*16	alpha,
		complex*16, dimension( * )	x,
		integer	incx,
		complex*16, dimension( lda, * )	a,
		integer	lda
	)

ZSYR performs the symmetric rank-1 update of a complex symmetric matrix.

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Purpose:

 ZSYR   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.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced. 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]	A	A is COMPLEX*16 array, dimension ( LDA, N ) Before entry, with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. Before entry, with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix.
[in]	LDA	LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, N ). Unchanged on exit.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 134 of file zsyr.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, LDA, N
      COMPLEX*16         ALPHA
*     ..
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * )
*     ..
*
* =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      parameter( zero = ( 0.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            I, INFO, IX, J, JX, KX
      COMPLEX*16         TEMP
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. 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
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = 7
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZSYR  ', 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 A are
*     accessed sequentially with one pass through the triangular part
*     of A.
*
      IF( lsame( uplo, 'U' ) ) THEN
*
*        Form  A  when A is stored in upper triangle.
*
         IF( incx.EQ.1 ) THEN
            DO 20 j = 1, n
               IF( x( j ).NE.zero ) THEN
                  temp = alpha*x( j )
                  DO 10 i = 1, j
                     a( i, j ) = a( i, j ) + x( i )*temp
   10             CONTINUE
               END IF
   20       CONTINUE
         ELSE
            jx = kx
            DO 40 j = 1, n
               IF( x( jx ).NE.zero ) THEN
                  temp = alpha*x( jx )
                  ix = kx
                  DO 30 i = 1, j
                     a( i, j ) = a( i, j ) + x( ix )*temp
                     ix = ix + incx
   30             CONTINUE
               END IF
               jx = jx + incx
   40       CONTINUE
         END IF
      ELSE
*
*        Form  A  when A is stored in lower triangle.
*
         IF( incx.EQ.1 ) THEN
            DO 60 j = 1, n
               IF( x( j ).NE.zero ) THEN
                  temp = alpha*x( j )
                  DO 50 i = j, n
                     a( i, j ) = a( i, j ) + x( i )*temp
   50             CONTINUE
               END IF
   60       CONTINUE
         ELSE
            jx = kx
            DO 80 j = 1, n
               IF( x( jx ).NE.zero ) THEN
                  temp = alpha*x( jx )
                  ix = jx
                  DO 70 i = j, n
                     a( i, j ) = a( i, j ) + x( ix )*temp
                     ix = ix + incx
   70             CONTINUE
               END IF
               jx = jx + incx
   80       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZSYR
*

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