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