SUBROUTINE MB01MD( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
$ INCY )
C
C PURPOSE
C
C To perform the matrix-vector operation
C
C y := alpha*A*x + beta*y,
C
C where alpha and beta are scalars, x and y are vectors of length
C n and A is an n-by-n skew-symmetric matrix.
C
C This is a modified version of the vanilla implemented BLAS
C routine DSYMV written by Jack Dongarra, Jeremy Du Croz,
C Sven Hammarling, and Richard Hanson.
C
C ARGUMENTS
C
C Mode Parameters
C
C UPLO CHARACTER*1
C Specifies whether the upper or lower triangular part of
C the array A is to be referenced as follows:
C = 'U': only the strictly upper triangular part of A is to
C be referenced;
C = 'L': only the strictly lower triangular part of A is to
C be referenced.
C
C Input/Output Parameters
C
C N (input) INTEGER
C The order of the matrix A. N >= 0.
C
C ALPHA (input) DOUBLE PRECISION
C The scalar alpha. If alpha is zero the array A is not
C referenced.
C
C A (input) DOUBLE PRECISION array, dimension (LDA,N)
C On entry with UPLO = 'U', the leading N-by-N part of this
C array must contain the strictly upper triangular part of
C the matrix A. The lower triangular part of this array is
C not referenced.
C On entry with UPLO = 'L', the leading N-by-N part of this
C array must contain the strictly lower triangular part of
C the matrix A. The upper triangular part of this array is
C not referenced.
C
C LDA INTEGER
C The leading dimension of the array A. LDA >= MAX(1,N)
C
C X (input) DOUBLE PRECISION array, dimension
C ( 1 + ( N - 1 )*abs( INCX ) ).
C On entry, elements 1, INCX+1, .., ( N - 1 )*INCX + 1 of
C this array must contain the elements of the vector X.
C
C INCX (input) INTEGER
C The increment for the elements of X. IF INCX < 0 then the
C elements of X are accessed in reversed order. INCX <> 0.
C
C BETA (input) DOUBLE PRECISION
C The scalar beta. If beta is zero then Y need not be set on
C input.
C
C Y (input/output) DOUBLE PRECISION array, dimension
C ( 1 + ( N - 1 )*abs( INCY ) ).
C On entry, elements 1, INCY+1, .., ( N - 1 )*INCY + 1 of
C this array must contain the elements of the vector Y.
C On exit, elements 1, INCY+1, .., ( N - 1 )*INCY + 1 of
C this array contain the updated elements of the vector Y.
C
C INCY (input) INTEGER
C The increment for the elements of Y. IF INCY < 0 then the
C elements of Y are accessed in reversed order. INCY <> 0.
C
C NUMERICAL ASPECTS
C
C Though being almost identical with the vanilla implementation
C of the BLAS routine DSYMV the performance of this routine could
C be significantly lower in the case of vendor supplied, highly
C optimized BLAS.
C
C CONTRIBUTORS
C
C D. Kressner, Technical Univ. Berlin, Germany, and
C P. Benner, Technical Univ. Chemnitz, Germany, December 2003.
C
C REVISIONS
C
C V. Sima, May 2008 (SLICOT version of the HAPACK routine DSKMV).
C
C KEYWORDS
C
C Elementary matrix operations.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
C .. Scalar Arguments ..
DOUBLE PRECISION ALPHA, BETA
INTEGER INCX, INCY, LDA, N
CHARACTER UPLO
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), X(*), Y(*)
C .. Local Scalars ..
DOUBLE PRECISION TEMP1, TEMP2
INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL XERBLA
C .. Intrinsic Functions ..
INTRINSIC MAX
C
C .. Executable Statements ..
C
C Test the input parameters.
C
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( 'MB01MD', INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF ( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
$ RETURN
C
C Set up the start points in X and Y.
C
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
C
C Start the operations. In this version the elements of A are
C accessed sequentially with one pass through the triangular part
C of A.
C
C First form y := beta*y.
C
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
C
C Quick return if possible.
C
IF ( ALPHA.EQ.ZERO )
$ RETURN
IF ( LSAME( UPLO, 'U' ) )THEN
C
C Form y when A is stored in upper triangle.
C
IF ( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
DO 60 J = 2, 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) - ALPHA*TEMP2
60 CONTINUE
ELSE
JX = KX + INCX
JY = KY + INCY
DO 80 J = 2, 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) - ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
80 CONTINUE
END IF
ELSE
C
C Form y when A is stored in lower triangle.
C
IF ( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) )THEN
DO 100 J = 1, N - 1
TEMP1 = ALPHA*X(J)
TEMP2 = ZERO
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 - 1
TEMP1 = ALPHA*X(JX)
TEMP2 = ZERO
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
C *** Last line of MB01MD ***
END