SUBROUTINE ZSBMVF(UPLO, N, K, ALPHA, A, LDA, 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, K, LDA, N

      COMPLEX*16         ALPHA, BETA

*     ..

*     .. Array Arguments ..

      COMPLEX*16         A( LDA, * ), X( * ), Y( * )

*     ..

*

*  Purpose

*  =======

*

*  ZSBMV  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 band matrix, with k super-diagonals.

*

*  Arguments

*  ==========

*

*  UPLO   - CHARACTER*1

*           On entry, UPLO specifies whether the upper or lower

*           triangular part of the band matrix A is being supplied as

*           follows:

*

*              UPLO = 'U' or 'u'   The upper triangular part of A is

*                                  being supplied.

*

*              UPLO = 'L' or 'l'   The lower triangular part of A is

*                                  being supplied.

*

*           Unchanged on exit.

*

*  N      - INTEGER

*           On entry, N specifies the order of the matrix A.

*           N must be at least zero.

*           Unchanged on exit.

*

*  K      - INTEGER

*           On entry, K specifies the number of super-diagonals of the

*           matrix A. K must satisfy  0 .le. K.

*           Unchanged on exit.

*

*  ALPHA  - COMPLEX*16

*           On entry, ALPHA specifies the scalar alpha.

*           Unchanged on exit.

*

*  A      - COMPLEX*16 array, dimension( LDA, N )

*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )

*           by n part of the array A must contain the upper triangular

*           band part of the symmetric matrix, supplied column by

*           column, with the leading diagonal of the matrix in row

*           ( k + 1 ) of the array, the first super-diagonal starting at

*           position 2 in row k, and so on. The top left k by k triangle

*           of the array A is not referenced.

*           The following program segment will transfer the upper

*           triangular part of a symmetric band matrix from conventional

*           full matrix storage to band storage:

*

*                 DO 20, J = 1, N

*                    M = K + 1 - J

*                    DO 10, I = MAX( 1, J - K ), J

*                       A( M + I, J ) = matrix( I, J )

*              10    CONTINUE

*              20 CONTINUE

*

*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )

*           by n part of the array A must contain the lower triangular

*           band part of the symmetric matrix, supplied column by

*           column, with the leading diagonal of the matrix in row 1 of

*           the array, the first sub-diagonal starting at position 1 in

*           row 2, and so on. The bottom right k by k triangle of the

*           array A is not referenced.

*           The following program segment will transfer the lower

*           triangular part of a symmetric band matrix from conventional

*           full matrix storage to band storage:

*

*                 DO 20, J = 1, N

*                    M = 1 - J

*                    DO 10, I = J, MIN( N, J + K )

*                       A( M + I, J ) = matrix( I, J )

*              10    CONTINUE

*              20 CONTINUE

*

*           Unchanged on exit.

*

*  LDA    - INTEGER

*           On entry, LDA specifies the first dimension of A as declared

*           in the calling (sub) program. LDA must be at least

*           ( k + 1 ).

*           Unchanged on exit.

*

*  X      - COMPLEX*16 array, dimension at least

*           ( 1 + ( N - 1 )*abs( INCX ) ).

*           Before entry, the incremented array X must contain the

*           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.

*

*  BETA   - COMPLEX*16

*           On entry, BETA specifies the scalar beta.

*           Unchanged on exit.

*

*  Y      - COMPLEX*16 array, dimension at least

*           ( 1 + ( N - 1 )*abs( INCY ) ).

*           Before entry, the incremented array Y must contain the

*           vector y. On exit, Y is overwritten by the updated vector y.

*

*  INCY   - INTEGER

*           On entry, INCY specifies the increment for the elements of

*           Y. INCY must not be zero.

*           Unchanged on exit.

*

*  =====================================================================

*

*     .. Parameters ..

      COMPLEX*16         ONE

      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )

      COMPLEX*16         ZERO

      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )

*     ..

*     .. Local Scalars ..

      INTEGER            I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L

      COMPLEX*16         TEMP1, TEMP2

*     ..

*     .. External Functions ..

      LOGICAL            LSAME

      EXTERNAL           LSAME

*     ..

*     .. External Subroutines ..

      EXTERNAL           XERBLA

*     ..

*     .. Intrinsic Functions ..

      INTRINSIC          MAX, MIN

*     ..

*     .. 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( K.LT.0 ) THEN

         INFO = 3

      ELSE IF( LDA.LT.( K+1 ) ) THEN

         INFO = 6

      ELSE IF( INCX.EQ.0 ) THEN

         INFO = 8

      ELSE IF( INCY.EQ.0 ) THEN

         INFO = 11

      END IF

      IF( INFO.NE.0 ) THEN

         CALL XERBLA( 'ZSBMV ', 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 A

*     are accessed sequentially with one pass through A.

*

*     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

      IF( LSAME( UPLO, 'U' ) ) THEN

*

*        Form  y  when upper triangle of A is stored.

*

         KPLUS1 = K + 1

         IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN

            DO 60 J = 1, N

               TEMP1 = ALPHA*X( J )

               TEMP2 = ZERO

               L = KPLUS1 - J

               DO 50 I = MAX( 1, J-K ), J - 1

                  Y( I ) = Y( I ) + TEMP1*A( L+I, J )

                  TEMP2 = TEMP2 + A( L+I, J )*X( I )

   50          CONTINUE

               Y( J ) = Y( J ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2

   60       CONTINUE

         ELSE

            JX = KX

            JY = KY

            DO 80 J = 1, N

               TEMP1 = ALPHA*X( JX )

               TEMP2 = ZERO

               IX = KX

               IY = KY

               L = KPLUS1 - J

               DO 70 I = MAX( 1, J-K ), J - 1

                  Y( IY ) = Y( IY ) + TEMP1*A( L+I, J )

                  TEMP2 = TEMP2 + A( L+I, J )*X( IX )

                  IX = IX + INCX

                  IY = IY + INCY

   70          CONTINUE

               Y( JY ) = Y( JY ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2

               JX = JX + INCX

               JY = JY + INCY

               IF( J.GT.K ) THEN

                  KX = KX + INCX

                  KY = KY + INCY

               END IF

   80       CONTINUE

         END IF

      ELSE

*

*        Form  y  when lower triangle of A is stored.

*

         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*A( 1, J )

               L = 1 - J

               DO 90 I = J + 1, MIN( N, J+K )

                  Y( I ) = Y( I ) + TEMP1*A( L+I, J )

                  TEMP2 = TEMP2 + A( L+I, J )*X( I )

   90          CONTINUE

               Y( J ) = Y( J ) + ALPHA*TEMP2

  100       CONTINUE

         ELSE

            JX = KX

            JY = KY

            DO 120 J = 1, N

               TEMP1 = ALPHA*X( JX )

               TEMP2 = ZERO

               Y( JY ) = Y( JY ) + TEMP1*A( 1, J )

               L = 1 - J

               IX = JX

               IY = JY

               DO 110 I = J + 1, MIN( N, J+K )

                  IX = IX + INCX

                  IY = IY + INCY

                  Y( IY ) = Y( IY ) + TEMP1*A( L+I, J )

                  TEMP2 = TEMP2 + A( L+I, J )*X( IX )

  110          CONTINUE

               Y( JY ) = Y( JY ) + ALPHA*TEMP2

               JX = JX + INCX

               JY = JY + INCY

  120       CONTINUE

         END IF

      END IF

*

      RETURN

*

*     End of ZSBMV

*

      END