kusano 2b45e8
      SUBROUTINE DSBMVF( UPLO, N, K, ALPHA, A, LDA, X, INCX,
kusano 2b45e8
     $                   BETA, Y, INCY )
kusano 2b45e8
*     .. Scalar Arguments ..
kusano 2b45e8
      DOUBLE PRECISION   ALPHA, BETA
kusano 2b45e8
      INTEGER            INCX, INCY, K, LDA, N
kusano 2b45e8
      CHARACTER*1        UPLO
kusano 2b45e8
*     .. Array Arguments ..
kusano 2b45e8
      DOUBLE PRECISION   A( LDA, * ), X( * ), Y( * )
kusano 2b45e8
*     ..
kusano 2b45e8
*
kusano 2b45e8
*  Purpose
kusano 2b45e8
*  =======
kusano 2b45e8
*
kusano 2b45e8
*  DSBMV  performs the matrix-vector  operation
kusano 2b45e8
*
kusano 2b45e8
*     y := alpha*A*x + beta*y,
kusano 2b45e8
*
kusano 2b45e8
*  where alpha and beta are scalars, x and y are n element vectors and
kusano 2b45e8
*  A is an n by n symmetric band matrix, with k super-diagonals.
kusano 2b45e8
*
kusano 2b45e8
*  Parameters
kusano 2b45e8
*  ==========
kusano 2b45e8
*
kusano 2b45e8
*  UPLO   - CHARACTER*1.
kusano 2b45e8
*           On entry, UPLO specifies whether the upper or lower
kusano 2b45e8
*           triangular part of the band matrix A is being supplied as
kusano 2b45e8
*           follows:
kusano 2b45e8
*
kusano 2b45e8
*              UPLO = 'U' or 'u'   The upper triangular part of A is
kusano 2b45e8
*                                  being supplied.
kusano 2b45e8
*
kusano 2b45e8
*              UPLO = 'L' or 'l'   The lower triangular part of A is
kusano 2b45e8
*                                  being supplied.
kusano 2b45e8
*
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  N      - INTEGER.
kusano 2b45e8
*           On entry, N specifies the order of the matrix A.
kusano 2b45e8
*           N must be at least zero.
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  K      - INTEGER.
kusano 2b45e8
*           On entry, K specifies the number of super-diagonals of the
kusano 2b45e8
*           matrix A. K must satisfy  0 .le. K.
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  ALPHA  - DOUBLE PRECISION.
kusano 2b45e8
*           On entry, ALPHA specifies the scalar alpha.
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
kusano 2b45e8
*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
kusano 2b45e8
*           by n part of the array A must contain the upper triangular
kusano 2b45e8
*           band part of the symmetric matrix, supplied column by
kusano 2b45e8
*           column, with the leading diagonal of the matrix in row
kusano 2b45e8
*           ( k + 1 ) of the array, the first super-diagonal starting at
kusano 2b45e8
*           position 2 in row k, and so on. The top left k by k triangle
kusano 2b45e8
*           of the array A is not referenced.
kusano 2b45e8
*           The following program segment will transfer the upper
kusano 2b45e8
*           triangular part of a symmetric band matrix from conventional
kusano 2b45e8
*           full matrix storage to band storage:
kusano 2b45e8
*
kusano 2b45e8
*                 DO 20, J = 1, N
kusano 2b45e8
*                    M = K + 1 - J
kusano 2b45e8
*                    DO 10, I = MAX( 1, J - K ), J
kusano 2b45e8
*                       A( M + I, J ) = matrix( I, J )
kusano 2b45e8
*              10    CONTINUE
kusano 2b45e8
*              20 CONTINUE
kusano 2b45e8
*
kusano 2b45e8
*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
kusano 2b45e8
*           by n part of the array A must contain the lower triangular
kusano 2b45e8
*           band part of the symmetric matrix, supplied column by
kusano 2b45e8
*           column, with the leading diagonal of the matrix in row 1 of
kusano 2b45e8
*           the array, the first sub-diagonal starting at position 1 in
kusano 2b45e8
*           row 2, and so on. The bottom right k by k triangle of the
kusano 2b45e8
*           array A is not referenced.
kusano 2b45e8
*           The following program segment will transfer the lower
kusano 2b45e8
*           triangular part of a symmetric band matrix from conventional
kusano 2b45e8
*           full matrix storage to band storage:
kusano 2b45e8
*
kusano 2b45e8
*                 DO 20, J = 1, N
kusano 2b45e8
*                    M = 1 - J
kusano 2b45e8
*                    DO 10, I = J, MIN( N, J + K )
kusano 2b45e8
*                       A( M + I, J ) = matrix( I, J )
kusano 2b45e8
*              10    CONTINUE
kusano 2b45e8
*              20 CONTINUE
kusano 2b45e8
*
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  LDA    - INTEGER.
kusano 2b45e8
*           On entry, LDA specifies the first dimension of A as declared
kusano 2b45e8
*           in the calling (sub) program. LDA must be at least
kusano 2b45e8
*           ( k + 1 ).
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  X      - DOUBLE PRECISION array of DIMENSION at least
kusano 2b45e8
*           ( 1 + ( n - 1 )*abs( INCX ) ).
kusano 2b45e8
*           Before entry, the incremented array X must contain the
kusano 2b45e8
*           vector x.
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  INCX   - INTEGER.
kusano 2b45e8
*           On entry, INCX specifies the increment for the elements of
kusano 2b45e8
*           X. INCX must not be zero.
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  BETA   - DOUBLE PRECISION.
kusano 2b45e8
*           On entry, BETA specifies the scalar beta.
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  Y      - DOUBLE PRECISION array of DIMENSION at least
kusano 2b45e8
*           ( 1 + ( n - 1 )*abs( INCY ) ).
kusano 2b45e8
*           Before entry, the incremented array Y must contain the
kusano 2b45e8
*           vector y. On exit, Y is overwritten by the updated vector y.
kusano 2b45e8
*
kusano 2b45e8
*  INCY   - INTEGER.
kusano 2b45e8
*           On entry, INCY specifies the increment for the elements of
kusano 2b45e8
*           Y. INCY must not be zero.
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*
kusano 2b45e8
*  Level 2 Blas routine.
kusano 2b45e8
*
kusano 2b45e8
*  -- Written on 22-October-1986.
kusano 2b45e8
*     Jack Dongarra, Argonne National Lab.
kusano 2b45e8
*     Jeremy Du Croz, Nag Central Office.
kusano 2b45e8
*     Sven Hammarling, Nag Central Office.
kusano 2b45e8
*     Richard Hanson, Sandia National Labs.
kusano 2b45e8
*
kusano 2b45e8
*
kusano 2b45e8
*     .. Parameters ..
kusano 2b45e8
      DOUBLE PRECISION   ONE         , ZERO
kusano 2b45e8
      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )
kusano 2b45e8
*     .. Local Scalars ..
kusano 2b45e8
      DOUBLE PRECISION   TEMP1, TEMP2
kusano 2b45e8
      INTEGER            I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L
kusano 2b45e8
*     .. External Functions ..
kusano 2b45e8
      LOGICAL            LSAME
kusano 2b45e8
      EXTERNAL           LSAME
kusano 2b45e8
*     .. External Subroutines ..
kusano 2b45e8
      EXTERNAL           XERBLA
kusano 2b45e8
*     .. Intrinsic Functions ..
kusano 2b45e8
      INTRINSIC          MAX, MIN
kusano 2b45e8
*     ..
kusano 2b45e8
*     .. Executable Statements ..
kusano 2b45e8
*
kusano 2b45e8
*     Test the input parameters.
kusano 2b45e8
*
kusano 2b45e8
      INFO = 0
kusano 2b45e8
      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.
kusano 2b45e8
     $         .NOT.LSAME( UPLO, 'L' )      )THEN
kusano 2b45e8
         INFO = 1
kusano 2b45e8
      ELSE IF( N.LT.0 )THEN
kusano 2b45e8
         INFO = 2
kusano 2b45e8
      ELSE IF( K.LT.0 )THEN
kusano 2b45e8
         INFO = 3
kusano 2b45e8
      ELSE IF( LDA.LT.( K + 1 ) )THEN
kusano 2b45e8
         INFO = 6
kusano 2b45e8
      ELSE IF( INCX.EQ.0 )THEN
kusano 2b45e8
         INFO = 8
kusano 2b45e8
      ELSE IF( INCY.EQ.0 )THEN
kusano 2b45e8
         INFO = 11
kusano 2b45e8
      END IF
kusano 2b45e8
      IF( INFO.NE.0 )THEN
kusano 2b45e8
         CALL XERBLA( 'DSBMV ', INFO )
kusano 2b45e8
         RETURN
kusano 2b45e8
      END IF
kusano 2b45e8
*
kusano 2b45e8
*     Quick return if possible.
kusano 2b45e8
*
kusano 2b45e8
      IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
kusano 2b45e8
     $   RETURN
kusano 2b45e8
*
kusano 2b45e8
*     Set up the start points in  X  and  Y.
kusano 2b45e8
*
kusano 2b45e8
      IF( INCX.GT.0 )THEN
kusano 2b45e8
         KX = 1
kusano 2b45e8
      ELSE
kusano 2b45e8
         KX = 1 - ( N - 1 )*INCX
kusano 2b45e8
      END IF
kusano 2b45e8
      IF( INCY.GT.0 )THEN
kusano 2b45e8
         KY = 1
kusano 2b45e8
      ELSE
kusano 2b45e8
         KY = 1 - ( N - 1 )*INCY
kusano 2b45e8
      END IF
kusano 2b45e8
*
kusano 2b45e8
*     Start the operations. In this version the elements of the array A
kusano 2b45e8
*     are accessed sequentially with one pass through A.
kusano 2b45e8
*
kusano 2b45e8
*     First form  y := beta*y.
kusano 2b45e8
*
kusano 2b45e8
      IF( BETA.NE.ONE )THEN
kusano 2b45e8
         IF( INCY.EQ.1 )THEN
kusano 2b45e8
            IF( BETA.EQ.ZERO )THEN
kusano 2b45e8
               DO 10, I = 1, N
kusano 2b45e8
                  Y( I ) = ZERO
kusano 2b45e8
   10          CONTINUE
kusano 2b45e8
            ELSE
kusano 2b45e8
               DO 20, I = 1, N
kusano 2b45e8
                  Y( I ) = BETA*Y( I )
kusano 2b45e8
   20          CONTINUE
kusano 2b45e8
            END IF
kusano 2b45e8
         ELSE
kusano 2b45e8
            IY = KY
kusano 2b45e8
            IF( BETA.EQ.ZERO )THEN
kusano 2b45e8
               DO 30, I = 1, N
kusano 2b45e8
                  Y( IY ) = ZERO
kusano 2b45e8
                  IY      = IY   + INCY
kusano 2b45e8
   30          CONTINUE
kusano 2b45e8
            ELSE
kusano 2b45e8
               DO 40, I = 1, N
kusano 2b45e8
                  Y( IY ) = BETA*Y( IY )
kusano 2b45e8
                  IY      = IY           + INCY
kusano 2b45e8
   40          CONTINUE
kusano 2b45e8
            END IF
kusano 2b45e8
         END IF
kusano 2b45e8
      END IF
kusano 2b45e8
      IF( ALPHA.EQ.ZERO )
kusano 2b45e8
     $   RETURN
kusano 2b45e8
      IF( LSAME( UPLO, 'U' ) )THEN
kusano 2b45e8
*
kusano 2b45e8
*        Form  y  when upper triangle of A is stored.
kusano 2b45e8
*
kusano 2b45e8
         KPLUS1 = K + 1
kusano 2b45e8
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
kusano 2b45e8
            DO 60, J = 1, N
kusano 2b45e8
               TEMP1 = ALPHA*X( J )
kusano 2b45e8
               TEMP2 = ZERO
kusano 2b45e8
               L     = KPLUS1 - J
kusano 2b45e8
               DO 50, I = MAX( 1, J - K ), J - 1
kusano 2b45e8
                  Y( I ) = Y( I ) + TEMP1*A( L + I, J )
kusano 2b45e8
                  TEMP2  = TEMP2  + A( L + I, J )*X( I )
kusano 2b45e8
   50          CONTINUE
kusano 2b45e8
               Y( J ) = Y( J ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
kusano 2b45e8
   60       CONTINUE
kusano 2b45e8
         ELSE
kusano 2b45e8
            JX = KX
kusano 2b45e8
            JY = KY
kusano 2b45e8
            DO 80, J = 1, N
kusano 2b45e8
               TEMP1 = ALPHA*X( JX )
kusano 2b45e8
               TEMP2 = ZERO
kusano 2b45e8
               IX    = KX
kusano 2b45e8
               IY    = KY
kusano 2b45e8
               L     = KPLUS1 - J
kusano 2b45e8
               DO 70, I = MAX( 1, J - K ), J - 1
kusano 2b45e8
                  Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
kusano 2b45e8
                  TEMP2   = TEMP2   + A( L + I, J )*X( IX )
kusano 2b45e8
                  IX      = IX      + INCX
kusano 2b45e8
                  IY      = IY      + INCY
kusano 2b45e8
   70          CONTINUE
kusano 2b45e8
               Y( JY ) = Y( JY ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
kusano 2b45e8
               JX      = JX      + INCX
kusano 2b45e8
               JY      = JY      + INCY
kusano 2b45e8
               IF( J.GT.K )THEN
kusano 2b45e8
                  KX = KX + INCX
kusano 2b45e8
                  KY = KY + INCY
kusano 2b45e8
               END IF
kusano 2b45e8
   80       CONTINUE
kusano 2b45e8
         END IF
kusano 2b45e8
      ELSE
kusano 2b45e8
*
kusano 2b45e8
*        Form  y  when lower triangle of A is stored.
kusano 2b45e8
*
kusano 2b45e8
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
kusano 2b45e8
            DO 100, J = 1, N
kusano 2b45e8
               TEMP1  = ALPHA*X( J )
kusano 2b45e8
               TEMP2  = ZERO
kusano 2b45e8
               Y( J ) = Y( J )       + TEMP1*A( 1, J )
kusano 2b45e8
               L      = 1            - J
kusano 2b45e8
               DO 90, I = J + 1, MIN( N, J + K )
kusano 2b45e8
                  Y( I ) = Y( I ) + TEMP1*A( L + I, J )
kusano 2b45e8
                  TEMP2  = TEMP2  + A( L + I, J )*X( I )
kusano 2b45e8
   90          CONTINUE
kusano 2b45e8
               Y( J ) = Y( J ) + ALPHA*TEMP2
kusano 2b45e8
  100       CONTINUE
kusano 2b45e8
         ELSE
kusano 2b45e8
            JX = KX
kusano 2b45e8
            JY = KY
kusano 2b45e8
            DO 120, J = 1, N
kusano 2b45e8
               TEMP1   = ALPHA*X( JX )
kusano 2b45e8
               TEMP2   = ZERO
kusano 2b45e8
               Y( JY ) = Y( JY )       + TEMP1*A( 1, J )
kusano 2b45e8
               L       = 1             - J
kusano 2b45e8
               IX      = JX
kusano 2b45e8
               IY      = JY
kusano 2b45e8
               DO 110, I = J + 1, MIN( N, J + K )
kusano 2b45e8
                  IX      = IX      + INCX
kusano 2b45e8
                  IY      = IY      + INCY
kusano 2b45e8
                  Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
kusano 2b45e8
                  TEMP2   = TEMP2   + A( L + I, J )*X( IX )
kusano 2b45e8
  110          CONTINUE
kusano 2b45e8
               Y( JY ) = Y( JY ) + ALPHA*TEMP2
kusano 2b45e8
               JX      = JX      + INCX
kusano 2b45e8
               JY      = JY      + INCY
kusano 2b45e8
  120       CONTINUE
kusano 2b45e8
         END IF
kusano 2b45e8
      END IF
kusano 2b45e8
*
kusano 2b45e8
      RETURN
kusano 2b45e8
*
kusano 2b45e8
*     End of DSBMV .
kusano 2b45e8
*
kusano 2b45e8
      END