symv(3F)

NAME
     SSYMV, DSYMV - Multiplies a real or complex vector by a real or
     complex symmetric matrix

SYNOPSIS
     Real

        CALL SSYMV (uplo, n, alpha, a, lda, x, incx, beta, y, incy)

     Double precision

        CALL DSYMV (uplo, n, alpha, a, lda, x, incx, beta, y, incy)

DESCRIPTION
     SSYMV and DSYMV multiplies a real vector by a real symmetric matrix.

     These routines perform the following matrix-vector operation:

          y <- alpha Ax + beta y

     where alpha and beta are scalars, x and y are n-element vectors, and A
     is an n-by-n symmetric matrix.

     These routines have the following arguments:

     uplo      Character*1.  (input)
               Specifies whether the upper or lower triangular part of
               matrix A is being supplied, as follows:

               uplo= 'U' or 'u':  only the upper triangular part of A is
               being supplied.
               uplo= 'L' or 'l':  only the lower triangular part of A is
               being supplied.

     n         Integer.  (input)
               Specifies the order of matrix A.  n >= 0.

     alpha     Scalar alpha.  (input)
               SSYMV: Real.
               DSYMV: Double precision.

     a         Array of dimension (lda,n).  (input)
               SSYMV: Real array.
               DSYMV: Double precision array.

               Before entry with uplo = 'U' or 'u', the leading n-by-n
               upper triangular part of array a must contain the upper
               triangular part of the symmetric matrix.  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 array a must contain the lower
               triangular part of the symmetric matrix.  The strictly upper
               triangular part of a is not referenced.

     lda       Integer.  (input)
               Specifies the first dimension of a as declared in the
               calling program.  lda >= MAX(1,n).

     x         Array of dimension 1+(n-1) * |incx|.  (input)
               SSYMV: Real array.
               DSYMV: Double precision array.
               Contains the vector x.

     incx      Integer.  (input)
               Specifies the increment for the elements of x.  incx must
               not be 0.

     beta      Scalar beta.  (input)
               If beta is supplied as 0, y need not be set on input.
               SSYMV: Real.
               DSYMV: Double precision.

     y         Array of dimension 1+(n-1) * |incy|.  (input and output)
               SSYMV: Real array.
               DSYMV: Double precision array.
               Contains the vector y.  On exit, the updated vector
               overwrites array y.

     incy      Integer.  (input)
               Specifies the increment for the elements of y.  incy must
               not be 0.

NOTES
     SSYMV/DSYMV is a Level 2 Basic Linear Algebra Subprogram (Level 2
     BLAS).

     When working backward (incx < 0 or incy < 0), each routine starts at
     the end of the vector and moves backward, as follows:

          x(1-incx * (n-1)), x(1-incx * (n-2)) , ..., x(1)

          y(1-incy * (n-1)), y(1-incy * (n-2)) , ..., y(1)

SEE ALSO
     HEMV(3F)