dsyr.f.html

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      SUBROUTINE <a name="DSYR.1"></a><a href="dsyr.f.html#DSYR.1">DSYR</a>(UPLO,N,ALPHA,X,INCX,A,LDA)
<span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      DOUBLE PRECISION ALPHA
      INTEGER INCX,LDA,N
      CHARACTER UPLO
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION 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="DSYR.14"></a><a href="dsyr.f.html#DSYR.1">DSYR</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 real 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   - 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      - 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  - DOUBLE PRECISION.
</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      - DOUBLE PRECISION array of 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   - 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      - DOUBLE PRECISION array of 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    - 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">  Level 2 Blas routine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- Written on 22-October-1986.
</span><span class="comment">*</span><span class="comment">     Jack Dongarra, Argonne National Lab.
</span><span class="comment">*</span><span class="comment">     Jeremy Du Croz, Nag Central Office.
</span><span class="comment">*</span><span class="comment">     Sven Hammarling, Nag Central Office.
</span><span class="comment">*</span><span class="comment">     Richard Hanson, Sandia National Labs.
</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>      DOUBLE PRECISION ZERO
      PARAMETER (ZERO=0.0D+0)
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      DOUBLE PRECISION TEMP
      INTEGER I,INFO,IX,J,JX,KX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL <a name="LSAME.96"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL <a name="LSAME.97"></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.100"></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">
</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.109"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(UPLO,<span class="string">'U'</span>) .AND. .NOT.<a name="LSAME.109"></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.119"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>(<span class="string">'<a name="DSYR.119"></a><a href="dsyr.f.html#DSYR.1">DSYR</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.139"></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="DSYR.197"></a><a href="dsyr.f.html#DSYR.1">DSYR</a>  .
</span><span class="comment">*</span><span class="comment">
</span>      END

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