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DTBMV(l)				   BLAS routine 				 DTBMV(l)

NAME
       DTBMV - perform one of the matrix-vector operations   x := A*x, or x := A'*x,

SYNOPSIS
       SUBROUTINE DTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )

	   INTEGER	INCX, K, LDA, N

	   CHARACTER*1	DIAG, TRANS, UPLO

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

PURPOSE
       DTBMV  performs one of the matrix-vector operations

       where  x is an n element vector and  A is an n by n unit, or non-unit, upper or lower tri-
       angular band matrix, with ( k + 1 ) diagonals.

PARAMETERS
       UPLO   - CHARACTER*1.
	      On entry, UPLO specifies whether the matrix is an upper or lower triangular  matrix
	      as follows:

	      UPLO = 'U' or 'u'   A is an upper triangular matrix.

	      UPLO = 'L' or 'l'   A is a lower triangular matrix.

	      Unchanged on exit.

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

	      TRANS = 'N' or 'n'   x := A*x.

	      TRANS = 'T' or 't'   x := A'*x.

	      TRANS = 'C' or 'c'   x := A'*x.

	      Unchanged on exit.

       DIAG   - CHARACTER*1.
	      On entry, DIAG specifies whether or not A is unit triangular as follows:

	      DIAG = 'U' or 'u'   A is assumed to be unit triangular.

	      DIAG = 'N' or 'n'   A is not assumed to be unit triangular.

	      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 with UPLO = 'U' or 'u', K specifies the number of super-diagonals  of  the
	      matrix A.  On entry with UPLO = 'L' or 'l', K specifies the number of sub-diagonals
	      of the matrix A.	K must satisfy	0 .le. K.  Unchanged on exit.

       A      - DOUBLE PRECISION 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 matrix of coefficients, 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  seg-
	      ment  will  transfer  an upper triangular 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 matrix of coefficients, 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 a lower triangular 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

	      Note that when DIAG = 'U' or 'u' the elements of the array A corresponding  to  the
	      diagonal	elements  of  the matrix are not referenced, but are assumed to be unity.
	      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      - DOUBLE PRECISION array of dimension at least
	      (  1 + ( n - 1 )*abs( INCX ) ).  Before entry, the incremented array X must contain
	      the n element vector x. On exit, X is overwritten with the tranformed vector x.

       INCX   - INTEGER.
	      On entry, INCX specifies the increment for the elements of  X.  INCX  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.

BLAS routine				 16 October 1992				 DTBMV(l)
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