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annotate libcruft/slatec-fn/csevl.f @ 12747:901d466ee55a stable release-3-4-1

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Version 3.4.1 released. * configure.ac (AC_INIT): Version is now 3.4.1. (OCTAVE_API_VERSION_NUMBER): Now 45. (OCTAVE_RELEASE_DATE): Now 2011-06-15.
author John W. Eaton <jwe@octave.org>
date Wed, 15 Jun 2011 10:35:37 -0400
parents 82be108cc558
children
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1 *DECK CSEVL
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2 FUNCTION CSEVL (X, CS, N)
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3 C***BEGIN PROLOGUE CSEVL
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4 C***PURPOSE Evaluate a Chebyshev series.
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5 C***LIBRARY SLATEC (FNLIB)
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6 C***CATEGORY C3A2
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7 C***TYPE SINGLE PRECISION (CSEVL-S, DCSEVL-D)
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8 C***KEYWORDS CHEBYSHEV SERIES, FNLIB, SPECIAL FUNCTIONS
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9 C***AUTHOR Fullerton, W., (LANL)
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10 C***DESCRIPTION
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11 C
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12 C Evaluate the N-term Chebyshev series CS at X. Adapted from
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13 C a method presented in the paper by Broucke referenced below.
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14 C
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15 C Input Arguments --
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16 C X value at which the series is to be evaluated.
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17 C CS array of N terms of a Chebyshev series. In evaluating
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18 C CS, only half the first coefficient is summed.
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19 C N number of terms in array CS.
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20 C
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21 C***REFERENCES R. Broucke, Ten subroutines for the manipulation of
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22 C Chebyshev series, Algorithm 446, Communications of
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23 C the A.C.M. 16, (1973) pp. 254-256.
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24 C L. Fox and I. B. Parker, Chebyshev Polynomials in
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25 C Numerical Analysis, Oxford University Press, 1968,
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26 C page 56.
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27 C***ROUTINES CALLED R1MACH, XERMSG
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28 C***REVISION HISTORY (YYMMDD)
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29 C 770401 DATE WRITTEN
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30 C 890831 Modified array declarations. (WRB)
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31 C 890831 REVISION DATE from Version 3.2
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32 C 891214 Prologue converted to Version 4.0 format. (BAB)
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33 C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
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34 C 900329 Prologued revised extensively and code rewritten to allow
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35 C X to be slightly outside interval (-1,+1). (WRB)
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36 C 920501 Reformatted the REFERENCES section. (WRB)
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37 C***END PROLOGUE CSEVL
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38 REAL B0, B1, B2, CS(*), ONEPL, TWOX, X
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39 LOGICAL FIRST
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40 SAVE FIRST, ONEPL
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41 DATA FIRST /.TRUE./
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42 C***FIRST EXECUTABLE STATEMENT CSEVL
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43 IF (FIRST) ONEPL = 1.0E0 + R1MACH(4)
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44 FIRST = .FALSE.
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45 IF (N .LT. 1) CALL XERMSG ('SLATEC', 'CSEVL',
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46 + 'NUMBER OF TERMS .LE. 0', 2, 2)
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47 IF (N .GT. 1000) CALL XERMSG ('SLATEC', 'CSEVL',
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48 + 'NUMBER OF TERMS .GT. 1000', 3, 2)
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49 IF (ABS(X) .GT. ONEPL) CALL XERMSG ('SLATEC', 'CSEVL',
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50 + 'X OUTSIDE THE INTERVAL (-1,+1)', 1, 1)
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51 C
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52 B1 = 0.0E0
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53 B0 = 0.0E0
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54 TWOX = 2.0*X
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55 DO 10 I = 1,N
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56 B2 = B1
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57 B1 = B0
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58 NI = N + 1 - I
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59 B0 = TWOX*B1 - B2 + CS(NI)
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60 10 CONTINUE
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61 C
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62 CSEVL = 0.5E0*(B0-B2)
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63 C
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64 RETURN
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65 END