1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
|
*DECK DCSEVL
DOUBLE PRECISION FUNCTION DCSEVL (X, CS, N)
C***BEGIN PROLOGUE DCSEVL
C***PURPOSE Evaluate a Chebyshev series.
C***LIBRARY SLATEC (FNLIB)
C***CATEGORY C3A2
C***TYPE DOUBLE PRECISION (CSEVL-S, DCSEVL-D)
C***KEYWORDS CHEBYSHEV SERIES, FNLIB, SPECIAL FUNCTIONS
C***AUTHOR Fullerton, W., (LANL)
C***DESCRIPTION
C
C Evaluate the N-term Chebyshev series CS at X. Adapted from
C a method presented in the paper by Broucke referenced below.
C
C Input Arguments --
C X value at which the series is to be evaluated.
C CS array of N terms of a Chebyshev series. In evaluating
C CS, only half the first coefficient is summed.
C N number of terms in array CS.
C
C***REFERENCES R. Broucke, Ten subroutines for the manipulation of
C Chebyshev series, Algorithm 446, Communications of
C the A.C.M. 16, (1973) pp. 254-256.
C L. Fox and I. B. Parker, Chebyshev Polynomials in
C Numerical Analysis, Oxford University Press, 1968,
C page 56.
C***ROUTINES CALLED D1MACH, XERMSG
C***REVISION HISTORY (YYMMDD)
C 770401 DATE WRITTEN
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
C 900329 Prologued revised extensively and code rewritten to allow
C X to be slightly outside interval (-1,+1). (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE DCSEVL
DOUBLE PRECISION B0, B1, B2, CS(*), ONEPL, TWOX, X, D1MACH
LOGICAL FIRST
SAVE FIRST, ONEPL
DATA FIRST /.TRUE./
C***FIRST EXECUTABLE STATEMENT DCSEVL
IF (FIRST) ONEPL = 1.0D0 + D1MACH(4)
FIRST = .FALSE.
IF (N .LT. 1) CALL XERMSG ('SLATEC', 'DCSEVL',
+ 'NUMBER OF TERMS .LE. 0', 2, 2)
IF (N .GT. 1000) CALL XERMSG ('SLATEC', 'DCSEVL',
+ 'NUMBER OF TERMS .GT. 1000', 3, 2)
IF (ABS(X) .GT. ONEPL) CALL XERMSG ('SLATEC', 'DCSEVL',
+ 'X OUTSIDE THE INTERVAL (-1,+1)', 1, 1)
C
B1 = 0.0D0
B0 = 0.0D0
TWOX = 2.0D0*X
DO 10 I = 1,N
B2 = B1
B1 = B0
NI = N + 1 - I
B0 = TWOX*B1 - B2 + CS(NI)
10 CONTINUE
C
DCSEVL = 0.5D0*(B0-B2)
C
RETURN
END
|
