DPCOEF(3)

SYNOPSIS
SUBROUTINE DPCOEF (L, C, TC, A)

NAME
dpcoef - Convert the DPOLFT coefficients to Taylor series form.

LIBRARY
SLATEC

CATEGORY
K1A1A2

TYPE
DOUBLE PRECISION (PCOEF-S, DPCOEF-D)

KEYWORDS
CURVE FITTING, DATA FITTING, LEAST SQUARES, POLYNOMIAL FIT

AUTHOR
Shampine, L. F., (SNLA) Davenport, S. M., (SNLA)

DESCRIPTION
Abstract DPOLFT computes the least squares polynomial fit of degree L as a sum of orthogonal polynomials. DPCOEF changes this fit to its Taylor expansion about any point C , i.e. writes the polynomial as a sum of powers of (X-C). Taking C=0. gives the polynomial in powers of X, but a suitable non-zero C often leads to polynomials which are better scaled and more accurately evaluated. The parameters for DPCOEF are INPUT -- All TYPE REAL variables are DOUBLE PRECISION L - Indicates the degree of polynomial to be changed to its Taylor expansion. To obtain the Taylor coefficients in reverse order, input L as the negative of the degree desired. The absolute value of L must be less than or equal to NDEG, the highest degree polynomial fitted by DPOLFT . C - The point about which the Taylor expansion is to be made. A - Work and output array containing values from last call to DPOLFT . OUTPUT -- All TYPE REAL variables are DOUBLE PRECISION TC - Vector containing the first LL+1 Taylor coefficients where LL=ABS(L). If L.GT.0 , the coefficients are in the usual Taylor series order, i.e. P(X) = TC(1) + TC(2)*(X-C) + ... + TC(N+1)*(X-C)**N If L .LT. 0, the coefficients are in reverse order, i.e. P(X) = TC(1)*(X-C)**N + ... + TC(N)*(X-C) + TC(N+1)

REFERENCES
L. F. Shampine, S. M. Davenport and R. E. Huddleston, Curve fitting by polynomials in one variable, Report SLA-74-0270, Sandia Laboratories, June 1974.

ROUTINES CALLED
DP1VLU

REVISION HISTORY (YYMMDD)
740601 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
891006 Cosmetic changes to prologue. (WRB)
891006 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
920501 Reformatted the REFERENCES section. (WRB)