#include "ESMF_LapackBlas.inc" !> \brief \b DSYMV ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! ! Definition: ! =========== ! ! SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) ! ! .. Scalar Arguments .. ! DOUBLE PRECISION ALPHA,BETA ! INTEGER INCX,INCY,LDA,N ! CHARACTER UPLO ! .. ! .. Array Arguments .. ! DOUBLE PRECISION A(LDA,*),X(*),Y(*) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DSYMV performs the matrix-vector operation !> !> y := alpha*A*x + beta*y, !> !> where alpha and beta are scalars, 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] 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. !> 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. !> \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 !> !> \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] BETA !> \verbatim !> BETA is DOUBLE PRECISION. !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then Y need not be set on input. !> \endverbatim !> !> \param[in,out] 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. On exit, Y is overwritten by the updated !> 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 ! ! 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. !> The vector and matrix arguments are not referenced when N = 0, or M = 0 !> !> -- 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 DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) ! ! -- 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,BETA INTEGER INCX,INCY,LDA,N CHARACTER UPLO ! .. ! .. Array Arguments .. DOUBLE PRECISION A(LDA,*),X(*),Y(*) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,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 (LDA.LT.MAX(1,N)) THEN INFO = 5 ELSE IF (INCX.EQ.0) THEN INFO = 7 ELSE IF (INCY.EQ.0) THEN INFO = 10 END IF IF (INFO.NE.0) THEN CALL XERBLA('DSYMV ',INFO) RETURN END IF ! ! Quick return if possible. ! IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN ! ! Set up the start points in X and Y. ! 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 ! ! Start the operations. In this version the elements of A are ! accessed sequentially with one pass through the triangular part ! of A. ! ! First form y := beta*y. ! IF (BETA.NE.ONE) THEN IF (INCY.EQ.1) THEN IF (BETA.EQ.ZERO) THEN DO 10 I = 1,N Y(I) = ZERO 10 CONTINUE ELSE DO 20 I = 1,N Y(I) = BETA*Y(I) 20 CONTINUE END IF ELSE IY = KY IF (BETA.EQ.ZERO) THEN DO 30 I = 1,N Y(IY) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40 I = 1,N Y(IY) = BETA*Y(IY) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF (ALPHA.EQ.ZERO) RETURN IF (LSAME(UPLO,'U')) THEN ! ! Form y when A is stored in upper triangle. ! IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 60 J = 1,N TEMP1 = ALPHA*X(J) TEMP2 = ZERO DO 50 I = 1,J - 1 Y(I) = Y(I) + TEMP1*A(I,J) TEMP2 = TEMP2 + A(I,J)*X(I) 50 CONTINUE Y(J) = Y(J) + TEMP1*A(J,J) + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80 J = 1,N TEMP1 = ALPHA*X(JX) TEMP2 = ZERO IX = KX IY = KY DO 70 I = 1,J - 1 Y(IY) = Y(IY) + TEMP1*A(I,J) TEMP2 = TEMP2 + A(I,J)*X(IX) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y(JY) = Y(JY) + TEMP1*A(J,J) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF ELSE ! ! Form y when A is stored in lower triangle. ! IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 100 J = 1,N TEMP1 = ALPHA*X(J) TEMP2 = ZERO Y(J) = Y(J) + TEMP1*A(J,J) DO 90 I = J + 1,N Y(I) = Y(I) + TEMP1*A(I,J) TEMP2 = TEMP2 + A(I,J)*X(I) 90 CONTINUE Y(J) = Y(J) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120 J = 1,N TEMP1 = ALPHA*X(JX) TEMP2 = ZERO Y(JY) = Y(JY) + TEMP1*A(J,J) IX = JX IY = JY DO 110 I = J + 1,N IX = IX + INCX IY = IY + INCY Y(IY) = Y(IY) + TEMP1*A(I,J) TEMP2 = TEMP2 + A(I,J)*X(IX) 110 CONTINUE Y(JY) = Y(JY) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF ! RETURN ! ! End of DSYMV . ! END