```      SUBROUTINE SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*     .. Scalar Arguments ..
REAL ALPHA,BETA
INTEGER INCX,INCY,K,LDA,N
CHARACTER UPLO
*     ..
*     .. Array Arguments ..
REAL A(LDA,*),X(*),Y(*)
*     ..
*
*  Purpose
*  =======
*
*  SSBMV  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  - REAL            .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - REAL             array of 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      - REAL             array of 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   - REAL            .
*           On entry, BETA specifies the scalar beta.
*           Unchanged on exit.
*
*  Y      - REAL             array of 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.
*
*
*  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 ..
REAL ONE,ZERO
PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
*     ..
*     .. Local Scalars ..
REAL TEMP1,TEMP2
INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
*     ..
*     .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
EXTERNAL XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC MAX,MIN
*     ..
*
*     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('SSBMV ',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 SSBMV .
*
END

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