zsyr.f.html

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      SUBROUTINE <a name="ZSYR.1"></a><a href="zsyr.f.html#ZSYR.1">ZSYR</a>( UPLO, N, ALPHA, X, INCX, A, LDA )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          UPLO
      INTEGER            INCX, LDA, N
      COMPLEX*16         ALPHA
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      COMPLEX*16         A( LDA, * ), X( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="ZSYR.19"></a><a href="zsyr.f.html#ZSYR.1">ZSYR</a>   performs the symmetric rank 1 operation
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     A := alpha*x*( x' ) + A,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where alpha is a complex scalar, x is an n element vector and A is an
</span><span class="comment">*</span><span class="comment">  n by n symmetric matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  ==========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO     (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">           On entry, UPLO specifies whether the upper or lower
</span><span class="comment">*</span><span class="comment">           triangular part of the array A is to be referenced as
</span><span class="comment">*</span><span class="comment">           follows:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              UPLO = 'U' or 'u'   Only the upper triangular part of A
</span><span class="comment">*</span><span class="comment">                                  is to be referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              UPLO = 'L' or 'l'   Only the lower triangular part of A
</span><span class="comment">*</span><span class="comment">                                  is to be referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N        (input) INTEGER
</span><span class="comment">*</span><span class="comment">           On entry, N specifies the order of the matrix A.
</span><span class="comment">*</span><span class="comment">           N must be at least zero.
</span><span class="comment">*</span><span class="comment">           Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ALPHA    (input) COMPLEX*16
</span><span class="comment">*</span><span class="comment">           On entry, ALPHA specifies the scalar alpha.
</span><span class="comment">*</span><span class="comment">           Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  X        (input) COMPLEX*16 array, dimension at least
</span><span class="comment">*</span><span class="comment">           ( 1 + ( N - 1 )*abs( INCX ) ).
</span><span class="comment">*</span><span class="comment">           Before entry, the incremented array X must contain the N-
</span><span class="comment">*</span><span class="comment">           element vector x.
</span><span class="comment">*</span><span class="comment">           Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INCX     (input) INTEGER
</span><span class="comment">*</span><span class="comment">           On entry, INCX specifies the increment for the elements of
</span><span class="comment">*</span><span class="comment">           X. INCX must not be zero.
</span><span class="comment">*</span><span class="comment">           Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A        (input/output) COMPLEX*16 array, dimension ( LDA, N )
</span><span class="comment">*</span><span class="comment">           Before entry, with  UPLO = 'U' or 'u', the leading n by n
</span><span class="comment">*</span><span class="comment">           upper triangular part of the array A must contain the upper
</span><span class="comment">*</span><span class="comment">           triangular part of the symmetric matrix and the strictly
</span><span class="comment">*</span><span class="comment">           lower triangular part of A is not referenced. On exit, the
</span><span class="comment">*</span><span class="comment">           upper triangular part of the array A is overwritten by the
</span><span class="comment">*</span><span class="comment">           upper triangular part of the updated matrix.
</span><span class="comment">*</span><span class="comment">           Before entry, with UPLO = 'L' or 'l', the leading n by n
</span><span class="comment">*</span><span class="comment">           lower triangular part of the array A must contain the lower
</span><span class="comment">*</span><span class="comment">           triangular part of the symmetric matrix and the strictly
</span><span class="comment">*</span><span class="comment">           upper triangular part of A is not referenced. On exit, the
</span><span class="comment">*</span><span class="comment">           lower triangular part of the array A is overwritten by the
</span><span class="comment">*</span><span class="comment">           lower triangular part of the updated matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA      (input) INTEGER
</span><span class="comment">*</span><span class="comment">           On entry, LDA specifies the first dimension of A as declared
</span><span class="comment">*</span><span class="comment">           in the calling (sub) program. LDA must be at least
</span><span class="comment">*</span><span class="comment">           max( 1, N ).
</span><span class="comment">*</span><span class="comment">           Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      COMPLEX*16         ZERO
      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, INFO, IX, J, JX, KX
      COMPLEX*16         TEMP
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.93"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.94"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="XERBLA.97"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( .NOT.<a name="LSAME.107"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) .AND. .NOT.<a name="LSAME.107"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) 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 <a name="XERBLA.117"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="ZSYR.117"></a><a href="zsyr.f.html#ZSYR.1">ZSYR</a>  '</span>, INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible.
</span><span class="comment">*</span><span class="comment">
</span>      IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Set the start point in X if the increment is not unity.
</span><span class="comment">*</span><span class="comment">
</span>      IF( INCX.LE.0 ) THEN
         KX = 1 - ( N-1 )*INCX
      ELSE IF( INCX.NE.1 ) THEN
         KX = 1
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Start the operations. In this version the elements of A are
</span><span class="comment">*</span><span class="comment">     accessed sequentially with one pass through the triangular part
</span><span class="comment">*</span><span class="comment">     of A.
</span><span class="comment">*</span><span class="comment">
</span>      IF( <a name="LSAME.138"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Form  A  when A is stored in upper triangle.
</span><span class="comment">*</span><span class="comment">
</span>         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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Form  A  when A is stored in lower triangle.
</span><span class="comment">*</span><span class="comment">
</span>         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
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="ZSYR.196"></a><a href="zsyr.f.html#ZSYR.1">ZSYR</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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