SUBROUTINE SSPRF ( UPLO, N, ALPHA, X, INCX, AP )

*     .. Scalar Arguments ..

      REAL               ALPHA

      INTEGER            INCX, N

      CHARACTER*1        UPLO

*     .. Array Arguments ..

      REAL               AP( * ), X( * )

*     ..

*

*  Purpose

*  =======

*

*  SSPR    performs the symmetric rank 1 operation

*

*     A := alpha*x*x' + A,

*

*  where alpha is a real scalar, x is an n element vector and A is an

*  n by n symmetric matrix, supplied in packed form.

*

*  Parameters

*  ==========

*

*  UPLO   - CHARACTER*1.

*           On entry, UPLO specifies whether the upper or lower

*           triangular part of the matrix A is supplied in the packed

*           array AP as follows:

*

*              UPLO = 'U' or 'u'   The upper triangular part of A is

*                                  supplied in AP.

*

*              UPLO = 'L' or 'l'   The lower triangular part of A is

*                                  supplied in AP.

*

*           Unchanged on exit.

*

*  N      - INTEGER.

*           On entry, N specifies the order of the matrix A.

*           N must be at least zero.

*           Unchanged on exit.

*

*  ALPHA  - REAL            .

*           On entry, ALPHA specifies the scalar alpha.

*           Unchanged on exit.

*

*  X      - REAL             array of dimension at least

*           ( 1 + ( n - 1 )*abs( INCX ) ).

*           Before entry, the incremented array X must contain the n

*           element vector x.

*           Unchanged on exit.

*

*  INCX   - INTEGER.

*           On entry, INCX specifies the increment for the elements of

*           X. INCX must not be zero.

*           Unchanged on exit.

*

*  AP     - REAL             array of DIMENSION at least

*           ( ( n*( n + 1 ) )/2 ).

*           Before entry with  UPLO = 'U' or 'u', the 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 ) and AP( 3 ) contain a( 1, 2 )

*           and a( 2, 2 ) respectively, and so on. On exit, the array

*           AP is overwritten by the upper triangular part of the

*           updated matrix.

*           Before entry with UPLO = 'L' or 'l', the 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 ) and AP( 3 ) contain a( 2, 1 )

*           and a( 3, 1 ) respectively, and so on. On exit, the array

*           AP is overwritten by the lower triangular part of the

*           updated matrix.

*

*

*  Level 2 Blas routine.

*

*  -- Written on 22-October-1986.

*     Jack Dongarra, Argonne National Lab.

*     Jeremy Du Croz, Nag Central Office.

*     Sven Hammarling, Nag Central Office.

*     Richard Hanson, Sandia National Labs.

*

*

*     .. Parameters ..

      REAL               ZERO

      PARAMETER        ( ZERO = 0.0E+0 )

*     .. Local Scalars ..

      REAL               TEMP

      INTEGER            I, INFO, IX, J, JX, K, KK, KX

*     .. External Functions ..

      LOGICAL            LSAME

      EXTERNAL           LSAME

*     .. External Subroutines ..

      EXTERNAL           XERBLA

*     ..

*     .. Executable Statements ..

*

*     Test the input parameters.

*

      INFO = 0

      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.

     $         .NOT.LSAME( UPLO, 'L' )      )THEN

         INFO = 1

      ELSE IF( N.LT.0 )THEN

         INFO = 2

      ELSE IF( INCX.EQ.0 )THEN

         INFO = 5

      END IF

      IF( INFO.NE.0 )THEN

         CALL XERBLA( 'SSPR  ', INFO )

         RETURN

      END IF

*

*     Quick return if possible.

*

      IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )

     $   RETURN

*

*     Set the start point in X if the increment is not unity.

*

      IF( INCX.LE.0 )THEN

         KX = 1 - ( N - 1 )*INCX

      ELSE IF( INCX.NE.1 )THEN

         KX = 1

      END IF

*

*     Start the operations. In this version the elements of the array AP

*     are accessed sequentially with one pass through AP.

*

      KK = 1

      IF( LSAME( UPLO, 'U' ) )THEN

*

*        Form  A  when upper triangle is stored in AP.

*

         IF( INCX.EQ.1 )THEN

            DO 20, J = 1, N

               IF( X( J ).NE.ZERO )THEN

                  TEMP = ALPHA*X( J )

                  K    = KK

                  DO 10, I = 1, J

                     AP( K ) = AP( K ) + X( I )*TEMP

                     K       = K       + 1

   10             CONTINUE

               END IF

               KK = KK + J

   20       CONTINUE

         ELSE

            JX = KX

            DO 40, J = 1, N

               IF( X( JX ).NE.ZERO )THEN

                  TEMP = ALPHA*X( JX )

                  IX   = KX

                  DO 30, K = KK, KK + J - 1

                     AP( K ) = AP( K ) + X( IX )*TEMP

                     IX      = IX      + INCX

   30             CONTINUE

               END IF

               JX = JX + INCX

               KK = KK + J

   40       CONTINUE

         END IF

      ELSE

*

*        Form  A  when lower triangle is stored in AP.

*

         IF( INCX.EQ.1 )THEN

            DO 60, J = 1, N

               IF( X( J ).NE.ZERO )THEN

                  TEMP = ALPHA*X( J )

                  K    = KK

                  DO 50, I = J, N

                     AP( K ) = AP( K ) + X( I )*TEMP

                     K       = K       + 1

   50             CONTINUE

               END IF

               KK = KK + N - J + 1

   60       CONTINUE

         ELSE

            JX = KX

            DO 80, J = 1, N

               IF( X( JX ).NE.ZERO )THEN

                  TEMP = ALPHA*X( JX )

                  IX   = JX

                  DO 70, K = KK, KK + N - J

                     AP( K ) = AP( K ) + X( IX )*TEMP

                     IX      = IX      + INCX

   70             CONTINUE

               END IF

               JX = JX + INCX

               KK = KK + N - J + 1

   80       CONTINUE

         END IF

      END IF

*

      RETURN

*

*     End of SSPR  .

*

      END