syr(3F)

NAME
     SSYR, DSYR - Performs symmetric rank 1 update of a real or complex
     symmetric matrix

SYNOPSIS
     Real

        CALL SSYR (uplo, n, alpha, x, incx, a, lda)

     Double precision

        CALL DSYR (uplo, n, alpha, x, incx, a, lda)

DESCRIPTION
     These routines perform the following symmetric rank 1 operation:

          A <- alpha xxT + A

     where xT 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 matrix.

     These routines have the following arguments:

     uplo      Character*1.  (input)
               Specifies whether the upper or lower triangular part of
               array a is referenced, as follows:

               uplo= 'U' or 'u':  only the upper triangular part of a is
               referenced.
               uplo= 'L' or 'l':  only the lower triangular part of a is
               referenced.

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

     alpha     Scalar alpha.  (input)
               SSYR: Real.
               DSYR: Double precision.

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

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

     a         Array of dimension (lda,n).  (input and output)
               SSYR: Real array.
               DSYR: 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.  On exit, the upper
               triangular part of the updated matrix overwrites the upper
               triangular part of array a.

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

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

NOTES
     SSYR/DSYR 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
     HER(3F)