zsyr.f

          SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          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 symmetric matrix.
    *
    *  Arguments
    *  ==========
    *
    *  UPLO     (input) 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.
    *
    *  N        (input) INTEGER
    *           On entry, N specifies the order of the matrix A.
    *           N must be at least zero.
    *           Unchanged on exit.
    *
    *  ALPHA    (input) COMPLEX*16
    *           On entry, ALPHA specifies the scalar alpha.
    *           Unchanged on exit.
    *
    *  X        (input) 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.
    *
    *  INCX     (input) INTEGER
    *           On entry, INCX specifies the increment for the elements of
    *           X. INCX must not be zero.
    *           Unchanged on exit.
    *
    *  A        (input/output) 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.
    *
    *  LDA      (input) 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.
    *
    * =====================================================================
    *
    *     .. 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