**Purpose**

To perform the skew-symmetric rank 2 operation A := alpha*x*y' - alpha*y*x' + A, where alpha is a scalar, 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 DSYR2 written by Jack Dongarra, Jeremy Du Croz, Sven Hammarling, and Richard Hanson.

SUBROUTINE MB01ND( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA ) C .. Scalar Arguments .. DOUBLE PRECISION ALPHA 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 X and Y are not referenced. 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. Y (input) 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. 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. A (input/output) 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. On exit with UPLO = 'U', the leading N-by-N part of this array contains the strictly upper triangular part of the updated matrix A. On exit with UPLO = 'L', the leading N-by-N part of this array contains the strictly lower triangular part of the updated matrix A. LDA INTEGER The leading dimension of the array A. LDA >= MAX(1,N)

Though being almost identical with the vanilla implementation of the BLAS routine DSYR2 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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