Note: this is a BLAS routine and is not in libslatec.a
*DECK DTBMV
SUBROUTINE DTBMV (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
C***BEGIN PROLOGUE DTBMV
C***PURPOSE Perform one of the matrix-vector operations.
C***LIBRARY SLATEC (BLAS)
C***CATEGORY D1B4
C***TYPE DOUBLE PRECISION (STBMV-S, DTBMV-D, CTBMV-C)
C***KEYWORDS LEVEL 2 BLAS, LINEAR ALGEBRA
C***AUTHOR Dongarra, J. J., (ANL)
C Du Croz, J., (NAG)
C Hammarling, S., (NAG)
C Hanson, R. J., (SNLA)
C***DESCRIPTION
C
C DTBMV performs one of the matrix-vector operations
C
C x := A*x, or x := A'*x,
C
C where x is an n element vector and A is an n by n unit, or non-unit,
C upper or lower triangular band matrix, with ( k + 1) diagonals.
C
C Parameters
C ==========
C
C UPLO - CHARACTER*1.
C On entry, UPLO specifies whether the matrix is an upper or
C lower triangular matrix as follows:
C
C UPLO = 'U' or 'u' A is an upper triangular matrix.
C
C UPLO = 'L' or 'l' A is a lower triangular matrix.
C
C Unchanged on exit.
C
C TRANS - CHARACTER*1.
C On entry, TRANS specifies the operation to be performed as
C follows:
C
C TRANS = 'N' or 'n' x := A*x.
C
C TRANS = 'T' or 't' x := A'*x.
C
C TRANS = 'C' or 'c' x := A'*x.
C
C Unchanged on exit.
C
C DIAG - CHARACTER*1.
C On entry, DIAG specifies whether or not A is unit
C triangular as follows:
C
C DIAG = 'U' or 'u' A is assumed to be unit triangular.
C
C DIAG = 'N' or 'n' A is not assumed to be unit
C triangular.
C
C Unchanged on exit.
C
C N - INTEGER.
C On entry, N specifies the order of the matrix A.
C N must be at least zero.
C Unchanged on exit.
C
C K - INTEGER.
C On entry with UPLO = 'U' or 'u', K specifies the number of
C super-diagonals of the matrix A.
C On entry with UPLO = 'L' or 'l', K specifies the number of
C sub-diagonals of the matrix A.
C K must satisfy 0 .le. K.
C Unchanged on exit.
C
C A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
C Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
C by n part of the array A must contain the upper triangular
C band part of the matrix of coefficients, supplied column by
C column, with the leading diagonal of the matrix in row
C ( k + 1 ) of the array, the first super-diagonal starting at
C position 2 in row k, and so on. The top left k by k triangle
C of the array A is not referenced.
C The following program segment will transfer an upper
C triangular band matrix from conventional full matrix storage
C to band storage:
C
C DO 20, J = 1, N
C M = K + 1 - J
C DO 10, I = MAX( 1, J - K ), J
C A( M + I, J ) = matrix( I, J )
C 10 CONTINUE
C 20 CONTINUE
C
C Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
C by n part of the array A must contain the lower triangular
C band part of the matrix of coefficients, supplied column by
C column, with the leading diagonal of the matrix in row 1 of
C the array, the first sub-diagonal starting at position 1 in
C row 2, and so on. The bottom right k by k triangle of the
C array A is not referenced.
C The following program segment will transfer a lower
C triangular band matrix from conventional full matrix storage
C to band storage:
C
C DO 20, J = 1, N
C M = 1 - J
C DO 10, I = J, MIN( N, J + K )
C A( M + I, J ) = matrix( I, J )
C 10 CONTINUE
C 20 CONTINUE
C
C Note that when DIAG = 'U' or 'u' the elements of the array A
C corresponding to the diagonal elements of the matrix are not
C referenced, but are assumed to be unity.
C Unchanged on exit.
C
C LDA - INTEGER.
C On entry, LDA specifies the first dimension of A as declared
C in the calling (sub) program. LDA must be at least
C ( k + 1 ).
C Unchanged on exit.
C
C X - DOUBLE PRECISION array of dimension at least
C ( 1 + ( n - 1 )*abs( INCX ) ).
C Before entry, the incremented array X must contain the n
C element vector x. On exit, X is overwritten with the
C transformed vector x.
C
C INCX - INTEGER.
C On entry, INCX specifies the increment for the elements of
C X. INCX must not be zero.
C Unchanged on exit.
C
C***REFERENCES Dongarra, J. J., Du Croz, J., Hammarling, S., and
C Hanson, R. J. An extended set of Fortran basic linear
C algebra subprograms. ACM TOMS, Vol. 14, No. 1,
C pp. 1-17, March 1988.
C***ROUTINES CALLED LSAME, XERBLA
C***REVISION HISTORY (YYMMDD)
C 861022 DATE WRITTEN
C 910605 Modified to meet SLATEC prologue standards. Only comment
C lines were modified. (BKS)
C***END PROLOGUE DTBMV