dsyr2.F90 Source File


Source Code

#include "ESMF_LapackBlas.inc"
!> \brief \b DSYR2
!
!  =========== DOCUMENTATION ===========
!
! Online html documentation available at
!            http://www.netlib.org/lapack/explore-html/
!
!  Definition:
!  ===========
!
!       SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
!
!       .. Scalar Arguments ..
!       DOUBLE PRECISION ALPHA
!       INTEGER INCX,INCY,LDA,N
!       CHARACTER UPLO
!       ..
!       .. Array Arguments ..
!       DOUBLE PRECISION A(LDA,*),X(*),Y(*)
!       ..
!
!
!> \par Purpose:
!  =============
!>
!> \verbatim
!>
!> DSYR2  performs the symmetric rank 2 operation
!>
!>    A := alpha*x*y**T + alpha*y*x**T + A,
!>
!> where alpha is a scalar, x and y are n element vectors 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] Y
!> \verbatim
!>          Y is DOUBLE PRECISION array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCY ) ).
!>           Before entry, the incremented array Y must contain the n
!>           element vector y.
!> \endverbatim
!>
!> \param[in] INCY
!> \verbatim
!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y. INCY 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.
!
!> \date December 2016
!
!> \ingroup double_blas_level2
!
!> \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 DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
!
!  -- Reference BLAS level2 routine (version 3.7.0) --
!  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
!  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
!     December 2016
!
!     .. Scalar Arguments ..
      DOUBLE PRECISION ALPHA
      INTEGER INCX,INCY,LDA,N
      CHARACTER UPLO
!     ..
!     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*),X(*),Y(*)
!     ..
!
!  =====================================================================
!
!     .. Parameters ..
      DOUBLE PRECISION ZERO
      PARAMETER (ZERO=0.0D+0)
!     ..
!     .. Local Scalars ..
      DOUBLE PRECISION TEMP1,TEMP2
      INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
!     ..
!     .. 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 (INCY.EQ.0) THEN
          INFO = 7
      ELSE IF (LDA.LT.MAX(1,N)) THEN
          INFO = 9
      END IF
      IF (INFO.NE.0) THEN
          CALL XERBLA('DSYR2 ',INFO)
          RETURN
      END IF
!
!     Quick return if possible.
!
      IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
!
!     Set up the start points in X and Y if the increments are not both
!     unity.
!
      IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
          IF (INCX.GT.0) THEN
              KX = 1
          ELSE
              KX = 1 - (N-1)*INCX
          END IF
          IF (INCY.GT.0) THEN
              KY = 1
          ELSE
              KY = 1 - (N-1)*INCY
          END IF
          JX = KX
          JY = KY
      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 the upper triangle.
!
          IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
              DO 20 J = 1,N
                  IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
                      TEMP1 = ALPHA*Y(J)
                      TEMP2 = ALPHA*X(J)
                      DO 10 I = 1,J
                          A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
   10                 CONTINUE
                  END IF
   20         CONTINUE
          ELSE
              DO 40 J = 1,N
                  IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
                      TEMP1 = ALPHA*Y(JY)
                      TEMP2 = ALPHA*X(JX)
                      IX = KX
                      IY = KY
                      DO 30 I = 1,J
                          A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
                          IX = IX + INCX
                          IY = IY + INCY
   30                 CONTINUE
                  END IF
                  JX = JX + INCX
                  JY = JY + INCY
   40         CONTINUE
          END IF
      ELSE
!
!        Form  A  when A is stored in the lower triangle.
!
          IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
              DO 60 J = 1,N
                  IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
                      TEMP1 = ALPHA*Y(J)
                      TEMP2 = ALPHA*X(J)
                      DO 50 I = J,N
                          A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
   50                 CONTINUE
                  END IF
   60         CONTINUE
          ELSE
              DO 80 J = 1,N
                  IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
                      TEMP1 = ALPHA*Y(JY)
                      TEMP2 = ALPHA*X(JX)
                      IX = JX
                      IY = JY
                      DO 70 I = J,N
                          A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
                          IX = IX + INCX
                          IY = IY + INCY
   70                 CONTINUE
                  END IF
                  JX = JX + INCX
                  JY = JY + INCY
   80         CONTINUE
          END IF
      END IF
!
      RETURN
!
!     End of DSYR2 .
!
      END