zsyr.f

Go to the documentation of this file.

*> \brief \b ZSYR performs the symmetric rank-1 update of a complex symmetric matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZSYR + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsyr.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsyr.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsyr.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INCX, LDA, N
*       COMPLEX*16         ALPHA
*       ..
*       .. Array Arguments ..
*       COMPLEX*16         A( LDA, * ), X( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          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.
*> \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] 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,out] A
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          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.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup her
*
*  =====================================================================
      SUBROUTINE zsyr( UPLO, N, ALPHA, X, INCX, A, LDA )
*
*  -- 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
*
      END