SUBROUTINE ZSPRF( 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