spr(3F)

NAME
     SSPR, DSPR - Performs symmetric rank 1 update of a real or complex
     symmetric packed matrix

SYNOPSIS
     Real

        CALL SSPR (uplo, n, alpha, x, incx, ap)

     Double precision

        CALL DSPR (uplo, n, alpha, x, incx, ap)

IMPLEMENTATION
     IRIX systems

DESCRIPTION
     These routines perform the following symmetric rank 1 operation:
                       T
          A <- alpha xx  + A
            T
     where x   is the transpose of x, alpha is a real or complex scalar, x
     is an n-element vector, 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)
               SSPR: Real.
               DSPR: Double precision.

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

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

     ap        Array of dimension (n(n+1))/2 .  (input and output)
               SSPR: Real array.
               DSPR: 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
     SSPR/DSPR is a Level 2 Basic Linear Algebra Subprogram (Level 2 BLAS).

     When working backward (incx < 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)

SEE ALSO
     HPR(3F)

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