spr2(3F)

NAME
     SSPR2, DSPR2 - Performs symmetric rank 2 update of a real symmetric
     packed matrix

SYNOPSIS
     Real

        CALL SSPR2 (uplo, n, alpha, x, incx, y, incy, ap)

     Double precision

        CALL DSPR2 (uplo, n, alpha, x, incx, y, incy, ap)

IMPLEMENTATION
     IRIX systems

DESCRIPTION
     These routines perform the following symmetric rank 2 operation:
                       T            T
          A <- alpha xy  +  alpha yx  +  A
            T                          T
     where x   is the transpose of x, y   is the transpose of y, alpha is a
     real scalar, x and y are n-element vectors, and A is an n-by-n
     symmetric packed matrix.

     This routine has 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)
               SSPR2: Real.
               DSPR2: Double precision.

     x         Array of dimension 1+(n-1) * |incx|.  (input)
               SSPR2: Real array.
               DSPR2: Double precision array.

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

     y         Array of dimension 1+(n-1) * |incy|.  (input)
               SSPR2: Real array.
               DSPR2: Double precision array.

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

     ap        Array of dimension (n(n+1))/2 .  (input and output)
               SSPR2: Real array.
               DSPR2: 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.  On exit, the upper triangular part of the updated
               matrix overwrites array ap.

               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.  On exit, the lower triangular part of the updated
               matrix overwrites array ap.

NOTES
     SSPR2/DSPR2 is a Level 2 Basic Linear Algebra Subprogram (Level 2
     BLAS).

     When working backward (incx < 0 or incy < 0), this 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
     HPR2(3F)

     This man page is available only online.