## MB01MD

### Matrix-vector operation alpha*A*x + beta*y, with A a skew-symmetric matrix

[Specification] [Arguments] [Method] [References] [Comments] [Example]

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.

```
Specification
```      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(*)

```
Arguments

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.

```
Input/Output Parameters
```  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.

```
Numerical Aspects
```  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.

```
```  None
```
Example

Program Text

```  None
```
Program Data
```  None
```
Program Results
```  None
```