```      SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
*     .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER INCX,N
CHARACTER UPLO
*     ..
*     .. Array Arguments ..
DOUBLE PRECISION AP(*),X(*)
*     ..
*
*  Purpose
*  =======
*
*  DSPR    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.
*
*  Arguments
*  ==========
*
*  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  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  X      - DOUBLE PRECISION 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     - DOUBLE PRECISION 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 ..
DOUBLE PRECISION ZERO
PARAMETER (ZERO=0.0D+0)
*     ..
*     .. Local Scalars ..
DOUBLE PRECISION TEMP
INTEGER I,INFO,IX,J,JX,K,KK,KX
*     ..
*     .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
EXTERNAL XERBLA
*     ..
*
*     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('DSPR  ',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 DSPR  .
*
END

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