```      SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          UPLO
INTEGER            INCX, N
COMPLEX*16         ALPHA
*     ..
*     .. Array Arguments ..
COMPLEX*16         AP( * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  ZSPR    performs the symmetric rank 1 operation
*
*     A := alpha*x*conjg( x' ) + A,
*
*  where alpha is a complex scalar, x is an n element vector and A is an
*  n by n symmetric matrix, supplied in packed form.
*
*  Arguments
*  ==========
*
*  UPLO     (input) 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        (input) INTEGER
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA    (input) COMPLEX*16
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  X        (input) COMPLEX*16 array, 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     (input) INTEGER
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  AP       (input/output) COMPLEX*16 array, 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.
*           Note that the imaginary parts of the diagonal elements need
*           not be set, they are assumed to be zero, and on exit they
*           are set to zero.
*
* =====================================================================
*
*     .. Parameters ..
COMPLEX*16         ZERO
PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Local Scalars ..
INTEGER            I, INFO, IX, J, JX, K, KK, KX
COMPLEX*16         TEMP
*     ..
*     .. 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( 'ZSPR  ', 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 - 1
AP( K ) = AP( K ) + X( I )*TEMP
K = K + 1
10             CONTINUE
AP( KK+J-1 ) = AP( KK+J-1 ) + X( J )*TEMP
ELSE
AP( KK+J-1 ) = AP( KK+J-1 )
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 - 2
AP( K ) = AP( K ) + X( IX )*TEMP
IX = IX + INCX
30             CONTINUE
AP( KK+J-1 ) = AP( KK+J-1 ) + X( JX )*TEMP
ELSE
AP( KK+J-1 ) = AP( KK+J-1 )
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 )
AP( KK ) = AP( KK ) + TEMP*X( J )
K = KK + 1
DO 50 I = J + 1, N
AP( K ) = AP( K ) + X( I )*TEMP
K = K + 1
50             CONTINUE
ELSE
AP( KK ) = AP( KK )
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 )
AP( KK ) = AP( KK ) + TEMP*X( JX )
IX = JX
DO 70 K = KK + 1, KK + N - J
IX = IX + INCX
AP( K ) = AP( K ) + X( IX )*TEMP
70             CONTINUE
ELSE
AP( KK ) = AP( KK )
END IF
JX = JX + INCX
KK = KK + N - J + 1
80       CONTINUE
END IF
END IF
*
RETURN
*
*     End of ZSPR
*
END

```