*DECK POLCOF
SUBROUTINE POLCOF (XX, N, X, C, D, WORK)
C***BEGIN PROLOGUE POLCOF
C***PURPOSE Compute the coefficients of the polynomial fit (including
C Hermite polynomial fits) produced by a previous call to
C POLINT.
C***LIBRARY SLATEC
C***CATEGORY E1B
C***TYPE SINGLE PRECISION (POLCOF-S, DPOLCF-D)
C***KEYWORDS COEFFICIENTS, POLYNOMIAL
C***AUTHOR Huddleston, R. E., (SNLL)
C***DESCRIPTION
C
C Written by Robert E. Huddleston, Sandia Laboratories, Livermore
C
C Abstract
C Subroutine POLCOF computes the coefficients of the polynomial
C fit (including Hermite polynomial fits ) produced by a previous
C call to POLINT. The coefficients of the polynomial, expanded about
C XX, are stored in the array D. The expansion is of the form
C P(Z) = D(1) + D(2)*(Z-XX) +D(3)*((Z-XX)**2) + ... +
C D(N)*((Z-XX)**(N-1)).
C Between the call to POLINT and the call to POLCOF the variable N
C and the arrays X and C must not be altered.
C
C ***** INPUT PARAMETERS
C
C XX - The point about which the Taylor expansion is to be made.
C
C N - ****
C * N, X, and C must remain unchanged between the
C X - * call to POLINT or the call to POLCOF.
C C - ****
C
C ***** OUTPUT PARAMETER
C
C D - The array of coefficients for the Taylor expansion as
C explained in the abstract
C
C ***** STORAGE PARAMETER
C
C WORK - This is an array to provide internal working storage. It
C must be dimensioned by at least 2*N in the calling program.
C
C
C **** Note - There are two methods for evaluating the fit produced
C by POLINT. You may call POLYVL to perform the task, or you may
C call POLCOF to obtain the coefficients of the Taylor expansion and
C then write your own evaluation scheme. Due to the inherent errors
C in the computations of the Taylor expansion from the Newton
C coefficients produced by POLINT, much more accuracy may be
C expected by calling POLYVL as opposed to writing your own scheme.
C
C***REFERENCES (NONE)
C***ROUTINES CALLED (NONE)
C***REVISION HISTORY (YYMMDD)
C 890213 DATE WRITTEN
C 891024 Corrected KEYWORD section. (WRB)
C 891024 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C***END PROLOGUE POLCOF
C
DIMENSION X(*), C(*), D(*), WORK(*)
C***FIRST EXECUTABLE STATEMENT POLCOF
DO 10010 K=1,N
D(K)=C(K)
10010 CONTINUE
IF (N.EQ.1) RETURN
WORK(1)=1.0
PONE=C(1)
NM1=N-1
DO 10020 K=2,N
KM1=K-1
NPKM1=N+K-1
WORK(NPKM1)=XX-X(KM1)
WORK(K)=WORK(NPKM1)*WORK(KM1)
PTWO=PONE+WORK(K)*C(K)
PONE=PTWO
10020 CONTINUE
D(1)=PTWO
IF (N.EQ.2) RETURN
DO 10030 K=2,NM1
KM1=K-1
KM2N=K-2+N
NMKP1=N-K+1
DO 10030 I=2,NMKP1
KM2NPI=KM2N+I
IM1=I-1
KM1PI=KM1+I
WORK(I)=WORK(KM2NPI)*WORK(IM1)+WORK(I)
D(K)=D(K)+WORK(I)*D(KM1PI)
10030 CONTINUE
RETURN
END