zsyr.f

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      SUBROUTINE zsyr( UPLO, N, ALPHA, X, INCX, A, LDA )
*
*  -- PBLAS auxiliary routine (version 2.0) --
*     University of Tennessee, Knoxville, Oak Ridge National Laboratory,
*     and University of California, Berkeley.
*     April 1, 1998
*
*     .. Scalar Arguments ..
      CHARACTER*1        UPLO
      INTEGER            INCX, LDA, N
      COMPLEX*16         ALPHA
*     ..
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  ZSYR  performs the symmetric rank 1 operation
*
*     A := alpha*x*x' + A,
*
*  where alpha is a complex scalar, x is an n element vector and A is an
*  n by n SY matrix.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          On entry, UPLO  specifies which part of the matrix A is to be
*          referenced as follows:
*
*             UPLO = 'L' or 'l' the lower trapezoid of A is referenced,
*
*             UPLO = 'U' or 'u' the upper trapezoid of A is referenced,
*
*             otherwise         all of the matrix A is referenced.
*
*  N       (input) INTEGER
*          On entry, N specifies the order of the matrix A. N must be at
*          least zero.
*
*  ALPHA   (input) COMPLEX*16
*          On entry, ALPHA specifies the scalar alpha.
*
*  X       (input) COMPLEX*16 array of dimension at least
*          ( 1 + ( n - 1 )*abs( INCX ) ).  Before entry, the incremented
*          array X must contain the vector x.
*
*  INCX    (input) INTEGER
*          On entry, INCX specifies the increment for the elements of X.
*          INCX must not be zero.
*
*  A       (input/output) COMPLEX*16 array
*          On entry,  A  is an array of dimension (LDA,N).  Before entry
*          with UPLO = 'U' or 'u', the leading n by n part of the  array
*          A must contain the upper triangular part of the symmetric ma-
*          trix and the strictly lower triangular part of A is not refe-
*          renced. On exit, the upper triangular part of the array A  is
*          overwritten  by  the upper triangular part of the updated ma-
*          trix. When UPLO = 'L' or 'l', the leading n by n part of  the
*          the array  A  must  contain  the lower triangular part of the
*          symmetric matrix and the strictly upper trapezoidal 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.
*
*  LDA     (input) INTEGER
*          On entry, LDA specifies the leading dimension of the array A.
*          LDA must be at least max( 1, N ).
*
*  =====================================================================
*
*     .. 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.
*
    kx = 1
      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