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78 lines
3.1 KiB
Fortran
78 lines
3.1 KiB
Fortran
*DECK DPCOEF
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SUBROUTINE DPCOEF (L, C, TC, A)
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C***BEGIN PROLOGUE DPCOEF
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C***PURPOSE Convert the DPOLFT coefficients to Taylor series form.
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C***LIBRARY SLATEC
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C***CATEGORY K1A1A2
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C***TYPE DOUBLE PRECISION (PCOEF-S, DPCOEF-D)
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C***KEYWORDS CURVE FITTING, DATA FITTING, LEAST SQUARES, POLYNOMIAL FIT
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C***AUTHOR Shampine, L. F., (SNLA)
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C Davenport, S. M., (SNLA)
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C***DESCRIPTION
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C
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C Abstract
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C
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C DPOLFT computes the least squares polynomial fit of degree L as
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C a sum of orthogonal polynomials. DPCOEF changes this fit to its
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C Taylor expansion about any point C , i.e. writes the polynomial
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C as a sum of powers of (X-C). Taking C=0. gives the polynomial
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C in powers of X, but a suitable non-zero C often leads to
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C polynomials which are better scaled and more accurately evaluated.
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C
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C The parameters for DPCOEF are
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C
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C INPUT -- All TYPE REAL variables are DOUBLE PRECISION
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C L - Indicates the degree of polynomial to be changed to
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C its Taylor expansion. To obtain the Taylor
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C coefficients in reverse order, input L as the
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C negative of the degree desired. The absolute value
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C of L must be less than or equal to NDEG, the highest
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C degree polynomial fitted by DPOLFT .
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C C - The point about which the Taylor expansion is to be
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C made.
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C A - Work and output array containing values from last
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C call to DPOLFT .
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C
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C OUTPUT -- All TYPE REAL variables are DOUBLE PRECISION
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C TC - Vector containing the first LL+1 Taylor coefficients
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C where LL=ABS(L). If L.GT.0 , the coefficients are
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C in the usual Taylor series order, i.e.
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C P(X) = TC(1) + TC(2)*(X-C) + ... + TC(N+1)*(X-C)**N
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C If L .LT. 0, the coefficients are in reverse order,
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C i.e.
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C P(X) = TC(1)*(X-C)**N + ... + TC(N)*(X-C) + TC(N+1)
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C
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C***REFERENCES L. F. Shampine, S. M. Davenport and R. E. Huddleston,
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C Curve fitting by polynomials in one variable, Report
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C SLA-74-0270, Sandia Laboratories, June 1974.
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C***ROUTINES CALLED DP1VLU
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C***REVISION HISTORY (YYMMDD)
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C 740601 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 891006 Cosmetic changes to prologue. (WRB)
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C 891006 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 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE DPCOEF
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C
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INTEGER I,L,LL,LLP1,LLP2,NEW,NR
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DOUBLE PRECISION A(*),C,FAC,SAVE,TC(*)
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C***FIRST EXECUTABLE STATEMENT DPCOEF
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LL = ABS(L)
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LLP1 = LL + 1
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CALL DP1VLU (LL,LL,C,TC(1),TC(2),A)
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IF (LL .LT. 2) GO TO 2
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FAC = 1.0D0
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DO 1 I = 3,LLP1
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FAC = FAC*(I-1)
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1 TC(I) = TC(I)/FAC
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2 IF (L .GE. 0) GO TO 4
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NR = LLP1/2
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LLP2 = LL + 2
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DO 3 I = 1,NR
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SAVE = TC(I)
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NEW = LLP2 - I
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TC(I) = TC(NEW)
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3 TC(NEW) = SAVE
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4 RETURN
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END
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