# dp1vlu.f

          SUBROUTINE DP1VLU (L, NDER, X, YFIT, YP, A)
    C***BEGIN PROLOGUE  DP1VLU
    C***PURPOSE  Use the coefficients generated by DPOLFT to evaluate the
    C            polynomial fit of degree L, along with the first NDER of
    C            its derivatives, at a specified point.
    C***LIBRARY   SLATEC
    C***CATEGORY  K6
    C***TYPE      DOUBLE PRECISION (PVALUE-S, DP1VLU-D)
    C***KEYWORDS  CURVE FITTING, LEAST SQUARES, POLYNOMIAL APPROXIMATION
    C***AUTHOR  Shampine, L. F., (SNLA)
    C           Davenport, S. M., (SNLA)
    C***DESCRIPTION
    C
    C     Abstract
    C
    C     The subroutine  DP1VLU  uses the coefficients generated by  DPOLFT
    C     to evaluate the polynomial fit of degree  L , along with the first
    C     NDER  of its derivatives, at a specified point.  Computationally
    C     stable recurrence relations are used to perform this task.
    C
    C     The parameters for  DP1VLU  are
    C
    C     Input -- ALL TYPE REAL variables are DOUBLE PRECISION
    C         L -      the degree of polynomial to be evaluated.  L  may be
    C                  any non-negative integer which is less than or equal
    C                  to  NDEG , the highest degree polynomial provided
    C                  by  DPOLFT .
    C         NDER -   the number of derivatives to be evaluated.  NDER
    C                  may be 0 or any positive value.  If NDER is less
    C                  than 0, it will be treated as 0.
    C         X -      the argument at which the polynomial and its
    C                  derivatives are to be evaluated.
    C         A -      work and output array containing values from last
    C                  call to  DPOLFT .
    C
    C     Output -- ALL TYPE REAL variables are DOUBLE PRECISION
    C         YFIT -   value of the fitting polynomial of degree  L  at  X
    C         YP -     array containing the first through  NDER  derivatives
    C                  of the polynomial of degree  L .  YP  must be
    C                  dimensioned at least  NDER  in the calling program.
    C
    C***REFERENCES  L. F. Shampine, S. M. Davenport and R. E. Huddleston,
    C                 Curve fitting by polynomials in one variable, Report
    C                 SLA-74-0270, Sandia Laboratories, June 1974.
    C***ROUTINES CALLED  XERMSG
    C***REVISION HISTORY  (YYMMDD)
    C   740601  DATE WRITTEN
    C   890531  Changed all specific intrinsics to generic.  (WRB)
    C   890911  Removed unnecessary intrinsics.  (WRB)
    C   891006  Cosmetic changes to prologue.  (WRB)
    C   891006  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
    C   900510  Convert XERRWV calls to XERMSG calls.  (RWC)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  DP1VLU