**Purpose**

To perform the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are vectors of length n and A is an n-by-n skew-symmetric matrix. This is a modified version of the vanilla implemented BLAS routine DSYMV written by Jack Dongarra, Jeremy Du Croz, Sven Hammarling, and Richard Hanson.

SUBROUTINE MB01MD( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, $ INCY ) C .. Scalar Arguments .. DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, LDA, N CHARACTER UPLO C .. Array Arguments .. DOUBLE PRECISION A(LDA,*), X(*), Y(*)

**Mode Parameters**

UPLO CHARACTER*1 Specifies whether the upper or lower triangular part of the array A is to be referenced as follows: = 'U': only the strictly upper triangular part of A is to be referenced; = 'L': only the strictly lower triangular part of A is to be referenced.

N (input) INTEGER The order of the matrix A. N >= 0. ALPHA (input) DOUBLE PRECISION The scalar alpha. If alpha is zero the array A is not referenced. A (input) DOUBLE PRECISION array, dimension (LDA,N) On entry with UPLO = 'U', the leading N-by-N part of this array must contain the strictly upper triangular part of the matrix A. The lower triangular part of this array is not referenced. On entry with UPLO = 'L', the leading N-by-N part of this array must contain the strictly lower triangular part of the matrix A. The upper triangular part of this array is not referenced. LDA INTEGER The leading dimension of the array A. LDA >= MAX(1,N) X (input) DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ). On entry, elements 1, INCX+1, .., ( N - 1 )*INCX + 1 of this array must contain the elements of the vector X. INCX (input) INTEGER The increment for the elements of X. IF INCX < 0 then the elements of X are accessed in reversed order. INCX <> 0. BETA (input) DOUBLE PRECISION The scalar beta. If beta is zero then Y need not be set on input. Y (input/output) DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ). On entry, elements 1, INCY+1, .., ( N - 1 )*INCY + 1 of this array must contain the elements of the vector Y. On exit, elements 1, INCY+1, .., ( N - 1 )*INCY + 1 of this array contain the updated elements of the vector Y. INCY (input) INTEGER The increment for the elements of Y. IF INCY < 0 then the elements of Y are accessed in reversed order. INCY <> 0.

Though being almost identical with the vanilla implementation of the BLAS routine DSYMV the performance of this routine could be significantly lower in the case of vendor supplied, highly optimized BLAS.

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**Program Text**

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