00001 *DECK CSEVL 00002 FUNCTION CSEVL (X, CS, N) 00003 C***BEGIN PROLOGUE CSEVL 00004 C***PURPOSE Evaluate a Chebyshev series. 00005 C***LIBRARY SLATEC (FNLIB) 00006 C***CATEGORY C3A2 00007 C***TYPE SINGLE PRECISION (CSEVL-S, DCSEVL-D) 00008 C***KEYWORDS CHEBYSHEV SERIES, FNLIB, SPECIAL FUNCTIONS 00009 C***AUTHOR Fullerton, W., (LANL) 00010 C***DESCRIPTION 00011 C 00012 C Evaluate the N-term Chebyshev series CS at X. Adapted from 00013 C a method presented in the paper by Broucke referenced below. 00014 C 00015 C Input Arguments -- 00016 C X value at which the series is to be evaluated. 00017 C CS array of N terms of a Chebyshev series. In evaluating 00018 C CS, only half the first coefficient is summed. 00019 C N number of terms in array CS. 00020 C 00021 C***REFERENCES R. Broucke, Ten subroutines for the manipulation of 00022 C Chebyshev series, Algorithm 446, Communications of 00023 C the A.C.M. 16, (1973) pp. 254-256. 00024 C L. Fox and I. B. Parker, Chebyshev Polynomials in 00025 C Numerical Analysis, Oxford University Press, 1968, 00026 C page 56. 00027 C***ROUTINES CALLED R1MACH, XERMSG 00028 C***REVISION HISTORY (YYMMDD) 00029 C 770401 DATE WRITTEN 00030 C 890831 Modified array declarations. (WRB) 00031 C 890831 REVISION DATE from Version 3.2 00032 C 891214 Prologue converted to Version 4.0 format. (BAB) 00033 C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ) 00034 C 900329 Prologued revised extensively and code rewritten to allow 00035 C X to be slightly outside interval (-1,+1). (WRB) 00036 C 920501 Reformatted the REFERENCES section. (WRB) 00037 C***END PROLOGUE CSEVL 00038 REAL B0, B1, B2, CS(*), ONEPL, TWOX, X 00039 LOGICAL FIRST 00040 SAVE FIRST, ONEPL 00041 DATA FIRST /.TRUE./ 00042 C***FIRST EXECUTABLE STATEMENT CSEVL 00043 IF (FIRST) ONEPL = 1.0E0 + R1MACH(4) 00044 FIRST = .FALSE. 00045 IF (N .LT. 1) CALL XERMSG ('SLATEC', 'CSEVL', 00046 + 'NUMBER OF TERMS .LE. 0', 2, 2) 00047 IF (N .GT. 1000) CALL XERMSG ('SLATEC', 'CSEVL', 00048 + 'NUMBER OF TERMS .GT. 1000', 3, 2) 00049 IF (ABS(X) .GT. ONEPL) CALL XERMSG ('SLATEC', 'CSEVL', 00050 + 'X OUTSIDE THE INTERVAL (-1,+1)', 1, 1) 00051 C 00052 B1 = 0.0E0 00053 B0 = 0.0E0 00054 TWOX = 2.0*X 00055 DO 10 I = 1,N 00056 B2 = B1 00057 B1 = B0 00058 NI = N + 1 - I 00059 B0 = TWOX*B1 - B2 + CS(NI) 00060 10 CONTINUE 00061 C 00062 CSEVL = 0.5E0*(B0-B2) 00063 C 00064 RETURN 00065 END
1.7.1
