# dtrmv.f

          SUBROUTINE DTRMV (UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
    C***BEGIN PROLOGUE  DTRMV
    C***PURPOSE  Perform one of the matrix-vector operations.
    C***LIBRARY   SLATEC (BLAS)
    C***CATEGORY  D1B4
    C***TYPE      DOUBLE PRECISION (STRMV-S, DTRMV-D, CTRMV-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  DTRMV  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 matrix.
    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  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n).
    C           Before entry with  UPLO = 'U' or 'u', the leading n by n
    C           upper triangular part of the array A must contain the upper
    C           triangular matrix and the strictly lower triangular part of
    C           A is not referenced.
    C           Before entry with UPLO = 'L' or 'l', the leading n by n
    C           lower triangular part of the array A must contain the lower
    C           triangular matrix and the strictly upper triangular part of
    C           A is not referenced.
    C           Note that when  DIAG = 'U' or 'u', the diagonal elements of
    C           A are not referenced either, 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           max( 1, n ).
    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  DTRMV