SUBROUTINEDSPRF(UPLO,N,ALPHA,X,INCX,AP)
*..ScalarArguments..
DOUBLE PRECISIONALPHA
INTEGERINCX,N
CHARACTER*1UPLO
*..ArrayArguments..
DOUBLE PRECISIONAP(*),X(*)
*..
*
*Purpose
*=======
*
*DSPRperformsthesymmetricrank1operation
*
*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 - 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
* ..
* .. 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( '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