#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