*DECK DPCOEF
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
C
INTEGER I,L,LL,LLP1,LLP2,NEW,NR
DOUBLE PRECISION A(*),C,FAC,SAVE,TC(*)
C***FIRST EXECUTABLE STATEMENT DPCOEF
LL = ABS(L)
LLP1 = LL + 1
CALL DP1VLU (LL,LL,C,TC(1),TC(2),A)
IF (LL .LT. 2) GO TO 2
FAC = 1.0D0
DO 1 I = 3,LLP1
FAC = FAC*(I-1)
1 TC(I) = TC(I)/FAC
2 IF (L .GE. 0) GO TO 4
NR = LLP1/2
LLP2 = LL + 2
DO 3 I = 1,NR
SAVE = TC(I)
NEW = LLP2 - I
TC(I) = TC(NEW)
3 TC(NEW) = SAVE
4 RETURN
END