# dpcoef.f

          SUBROUTINE DPCOEF (L, C, TC, A)
    C***BEGIN PROLOGUE  DPCOEF
    C***PURPOSE  Convert the DPOLFT coefficients to Taylor series form.
    C***LIBRARY   SLATEC
    C***CATEGORY  K1A1A2
    C***TYPE      DOUBLE PRECISION (PCOEF-S, DPCOEF-D)
    C***KEYWORDS  CURVE FITTING, DATA FITTING, LEAST SQUARES, POLYNOMIAL FIT
    C***AUTHOR  Shampine, L. F., (SNLA)
    C           Davenport, S. M., (SNLA)
    C***DESCRIPTION
    C
    C     Abstract
    C
    C     DPOLFT  computes the least squares polynomial fit of degree  L  as
    C     a sum of orthogonal polynomials.  DPCOEF  changes this fit to its
    C     Taylor expansion about any point  C , i.e. writes the polynomial
    C     as a sum of powers of (X-C).  Taking  C=0.  gives the polynomial
    C     in powers of X, but a suitable non-zero  C  often leads to
    C     polynomials which are better scaled and more accurately evaluated.
    C
    C     The parameters for  DPCOEF  are
    C
    C     INPUT -- All TYPE REAL variables are DOUBLE PRECISION
    C         L -      Indicates the degree of polynomial to be changed to
    C                  its Taylor expansion.  To obtain the Taylor
    C                  coefficients in reverse order, input  L  as the
    C                  negative of the degree desired.  The absolute value
    C                  of L  must be less than or equal to NDEG, the highest
    C                  degree polynomial fitted by  DPOLFT .
    C         C -      The point about which the Taylor expansion is to be
    C                  made.
    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         TC -     Vector containing the first LL+1 Taylor coefficients
    C                  where LL=ABS(L).  If  L.GT.0 , the coefficients are
    C                  in the usual Taylor series order, i.e.
    C                    P(X) = TC(1) + TC(2)*(X-C) + ... + TC(N+1)*(X-C)**N
    C                  If L .LT. 0, the coefficients are in reverse order,
    C                  i.e.
    C                    P(X) = TC(1)*(X-C)**N + ... + TC(N)*(X-C) + TC(N+1)
    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  DP1VLU
    C***REVISION HISTORY  (YYMMDD)
    C   740601  DATE WRITTEN
    C   890531  Changed all specific intrinsics to generic.  (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   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  DPCOEF