```      SUBROUTINE CSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          UPLO
INTEGER            INCX, INCY, N
COMPLEX            ALPHA, BETA
*     ..
*     .. Array Arguments ..
COMPLEX            AP( * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  CSPMV  performs the matrix-vector operation
*
*     y := alpha*A*x + beta*y,
*
*  where alpha and beta are scalars, x and y are n element vectors 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
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  AP       (input) COMPLEX 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.
*           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.
*           Unchanged on exit.
*
*  X        (input) COMPLEX 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.
*
*  BETA     (input) COMPLEX
*           On entry, BETA specifies the scalar beta. When BETA is
*           supplied as zero then Y need not be set on input.
*           Unchanged on exit.
*
*  Y        (input/output) COMPLEX array, dimension at least
*           ( 1 + ( N - 1 )*abs( INCY ) ).
*           Before entry, the incremented array Y must contain the n
*           element vector y. On exit, Y is overwritten by the updated
*           vector y.
*
*  INCY     (input) INTEGER
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
* =====================================================================
*
*     .. Parameters ..
COMPLEX            ONE
PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )
COMPLEX            ZERO
PARAMETER          ( ZERO = ( 0.0E+0, 0.0E+0 ) )
*     ..
*     .. Local Scalars ..
INTEGER            I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY
COMPLEX            TEMP1, TEMP2
*     ..
*     .. 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 = 6
ELSE IF( INCY.EQ.0 ) THEN
INFO = 9
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CSPMV ', INFO )
RETURN
END IF
*
*     Quick return if possible.
*
IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) )
\$   RETURN
*
*     Set up the start points in  X  and  Y.
*
IF( INCX.GT.0 ) THEN
KX = 1
ELSE
KX = 1 - ( N-1 )*INCX
END IF
IF( INCY.GT.0 ) THEN
KY = 1
ELSE
KY = 1 - ( N-1 )*INCY
END IF
*
*     Start the operations. In this version the elements of the array AP
*     are accessed sequentially with one pass through AP.
*
*     First form  y := beta*y.
*
IF( BETA.NE.ONE ) THEN
IF( INCY.EQ.1 ) THEN
IF( BETA.EQ.ZERO ) THEN
DO 10 I = 1, N
Y( I ) = ZERO
10          CONTINUE
ELSE
DO 20 I = 1, N
Y( I ) = BETA*Y( I )
20          CONTINUE
END IF
ELSE
IY = KY
IF( BETA.EQ.ZERO ) THEN
DO 30 I = 1, N
Y( IY ) = ZERO
IY = IY + INCY
30          CONTINUE
ELSE
DO 40 I = 1, N
Y( IY ) = BETA*Y( IY )
IY = IY + INCY
40          CONTINUE
END IF
END IF
END IF
IF( ALPHA.EQ.ZERO )
\$   RETURN
KK = 1
IF( LSAME( UPLO, 'U' ) ) THEN
*
*        Form  y  when AP contains the upper triangle.
*
IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
DO 60 J = 1, N
TEMP1 = ALPHA*X( J )
TEMP2 = ZERO
K = KK
DO 50 I = 1, J - 1
Y( I ) = Y( I ) + TEMP1*AP( K )
TEMP2 = TEMP2 + AP( K )*X( I )
K = K + 1
50          CONTINUE
Y( J ) = Y( J ) + TEMP1*AP( KK+J-1 ) + ALPHA*TEMP2
KK = KK + J
60       CONTINUE
ELSE
JX = KX
JY = KY
DO 80 J = 1, N
TEMP1 = ALPHA*X( JX )
TEMP2 = ZERO
IX = KX
IY = KY
DO 70 K = KK, KK + J - 2
Y( IY ) = Y( IY ) + TEMP1*AP( K )
TEMP2 = TEMP2 + AP( K )*X( IX )
IX = IX + INCX
IY = IY + INCY
70          CONTINUE
Y( JY ) = Y( JY ) + TEMP1*AP( KK+J-1 ) + ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
KK = KK + J
80       CONTINUE
END IF
ELSE
*
*        Form  y  when AP contains the lower triangle.
*
IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
DO 100 J = 1, N
TEMP1 = ALPHA*X( J )
TEMP2 = ZERO
Y( J ) = Y( J ) + TEMP1*AP( KK )
K = KK + 1
DO 90 I = J + 1, N
Y( I ) = Y( I ) + TEMP1*AP( K )
TEMP2 = TEMP2 + AP( K )*X( I )
K = K + 1
90          CONTINUE
Y( J ) = Y( J ) + ALPHA*TEMP2
KK = KK + ( N-J+1 )
100       CONTINUE
ELSE
JX = KX
JY = KY
DO 120 J = 1, N
TEMP1 = ALPHA*X( JX )
TEMP2 = ZERO
Y( JY ) = Y( JY ) + TEMP1*AP( KK )
IX = JX
IY = JY
DO 110 K = KK + 1, KK + N - J
IX = IX + INCX
IY = IY + INCY
Y( IY ) = Y( IY ) + TEMP1*AP( K )
TEMP2 = TEMP2 + AP( K )*X( IX )
110          CONTINUE
Y( JY ) = Y( JY ) + ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
KK = KK + ( N-J+1 )
120       CONTINUE
END IF
END IF
*
RETURN
*
*     End of CSPMV
*
END

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