spmv(3F)

NAME
     SSPMV, DSPMV - Multiplies a real or complex symmetric packed matrix by
     a real or complex vector

SYNOPSIS
     Real

        CALL SSPMV (uplo, n, alpha, ap, x, incx, beta, y, incy)

     Double precision

        CALL DSPMV (uplo, n, alpha, ap, x, incx, beta, y, incy)

IMPLEMENTATION
     IRIX systems

DESCRIPTION
     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 packed matrix.

     These routines have the following arguments:

     uplo      Character*1.  (input)
               Specifies whether the upper or lower triangular part of
               matrix A is packed into the array argument ap, as follows:

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

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

     alpha     Scalar alpha.  (input)
               SSPMV: Real.
               DSPMV: Double precision.

     ap        Array of dimension (n(n+1))/2  (input)
               SSPMV: Real array.
               DSPMV: Double precision array.

               Before entry with uplo = 'U' or 'u', array ap must contain
               the upper triangular part of the symmetric matrix packed
               sequentially, column-by-column, so that ap(1) contains
               A(1,1), ap(2) contains A(1,2), ap(3) contains A(2,2), and so
               on.

               Before entry with uplo = 'L' or 'l', array ap must contain
               the lower triangular part of the symmetric matrix packed
               sequentially, column-by-column, so that ap(1) contains
               A(1,1), ap(2) contains A(2,1), ap(3) contains A(3,1), and so
               on.

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

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

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

     y         Array of dimension 1+(n-1) * |incy|.  (input and output)
               SSPMV: Real array.
               DSPMV: Double precision array.
               Contains 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
     SSPMV/DSPMV 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
     HPMV(3F)

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