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dgbmv examples
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Man Page Details
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 NAME
      DGBMV - perform one of the matrix-vector operations   y :=
      alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,

 SYNOPSIS
      SUBROUTINE DGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X,
                       INCX, BETA, Y, INCY )

          DOUBLE       PRECISION ALPHA, BETA

          INTEGER      INCX, INCY, KL, KU, LDA, M, N

          CHARACTER*1  TRANS

          DOUBLE       PRECISION A( LDA, * ), X( * ), Y( * )

 PURPOSE
      DGBMV  performs one of the matrix-vector operations

      where alpha and beta are scalars, x and y are vectors and A
      is an m by n band matrix, with kl sub-diagonals and ku
      super-diagonals.

 PARAMETERS
      TRANS  - CHARACTER*1.
             On entry, TRANS specifies the operation to be per-
             formed as follows:

             TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.

             TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.

             TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.

             Unchanged on exit.

      M      - INTEGER.
             On entry, M specifies the number of rows of the
             matrix A.  M must be at least zero.  Unchanged on
             exit.

      N      - INTEGER.
             On entry, N specifies the number of columns of the
             matrix A.  N must be at least zero.  Unchanged on
             exit.

      KL     - INTEGER.
             On entry, KL specifies the number of sub-diagonals of
             the matrix A. KL must satisfy  0 .le. KL.  Unchanged
             on exit.

      KU     - INTEGER.
             On entry, KU specifies the number of super-diagonals
             of the matrix A. KU must satisfy  0 .le. KU.
             Unchanged on exit.

      ALPHA  - DOUBLE PRECISION.
             On entry, ALPHA specifies the scalar alpha.
             Unchanged on exit.

      A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
             Before entry, the leading ( kl + ku + 1 ) by n part
             of the array A must contain the matrix of coeffi-
             cients, supplied column by column, with the leading
             diagonal of the matrix in row ( ku + 1 ) of the
             array, the first super-diagonal starting at position
             2 in row ku, the first sub-diagonal starting at posi-
             tion 1 in row ( ku + 2 ), and so on.  Elements in the
             array A that do not correspond to elements in the
             band matrix (such as the top left ku by ku triangle)
             are not referenced.  The following program segment
             will transfer a band matrix from conventional full
             matrix storage to band storage:

             DO 20, J = 1, N K = KU + 1 - J DO 10, I = MAX( 1, J -
             KU ), MIN( M, J + KL ) A( K + 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 ( kl + ku + 1 ).  Unchanged on exit.

      X      - DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
             and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
             Before entry, the incremented array X must contain
             the vector x.  Unchanged on exit.

      INCX   - INTEGER.
             On entry, INCX specifies the increment for the ele-
             ments of X. INCX must not be zero.  Unchanged on
             exit.

      BETA   - DOUBLE PRECISION.
             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      - DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'

             and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
             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 ele-
             ments of Y. INCY must not be zero.  Unchanged on
             exit.

