dsyr.f

Go to the documentation of this file.

*> \brief \b DSYR
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DSYR(UPLO,N,ALPHA,X,INCX,A,LDA)
*
*       .. Scalar Arguments ..
*       DOUBLE PRECISION ALPHA
*       INTEGER INCX,LDA,N
*       CHARACTER UPLO
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION A(LDA,*),X(*)
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DSYR   performs the symmetric rank 1 operation
*>
*>    A := alpha*x*x**T + A,
*>
*> where alpha is a real 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>           On entry, N specifies the order of the matrix A.
*>           N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*>          ALPHA is DOUBLE PRECISION.
*>           On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is DOUBLE PRECISION array, dimension at least
*>           ( 1 + ( n - 1 )*abs( INCX ) ).
*>           Before entry, the incremented array X must contain the n
*>           element vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*>          INCX is INTEGER
*>           On entry, INCX specifies the increment for the elements of
*>           X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is DOUBLE PRECISION 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 ).
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup her
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*>
*>  Level 2 Blas routine.
*>
*>  -- Written on 22-October-1986.
*>     Jack Dongarra, Argonne National Lab.
*>     Jeremy Du Croz, Nag Central Office.
*>     Sven Hammarling, Nag Central Office.
*>     Richard Hanson, Sandia National Labs.
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE dsyr(UPLO,N,ALPHA,X,INCX,A,LDA)
*
*  -- Reference BLAS level2 routine --
*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION ALPHA
      INTEGER INCX,LDA,N
      CHARACTER UPLO
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*),X(*)
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION ZERO
      parameter(zero=0.0d+0)
*     ..
*     .. Local Scalars ..
      DOUBLE PRECISION TEMP
      INTEGER I,INFO,IX,J,JX,KX
*     ..
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC max
*     ..
*
*     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('DSYR  ',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 DSYR
*
      END