SLATEC Routines --- DTRMV ---


    Note: this is a BLAS routine and is not in libslatec.a

*DECK DTRMV
      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