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
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
|
*DECK EZFFTF
SUBROUTINE EZFFTF (N, R, AZERO, A, B, WSAVE)
C***BEGIN PROLOGUE EZFFTF
C***PURPOSE Compute a simplified real, periodic, fast Fourier forward
C transform.
C***LIBRARY SLATEC (FFTPACK)
C***CATEGORY J1A1
C***TYPE SINGLE PRECISION (EZFFTF-S)
C***KEYWORDS FFTPACK, FOURIER TRANSFORM
C***AUTHOR Swarztrauber, P. N., (NCAR)
C***DESCRIPTION
C
C Subroutine EZFFTF computes the Fourier coefficients of a real
C periodic sequence (Fourier analysis). The transform is defined
C below at Output Parameters AZERO, A and B. EZFFTF is a simplified
C but slower version of RFFTF.
C
C Input Parameters
C
C N the length of the array R to be transformed. The method
C is most efficient when N is the product of small primes.
C
C R a real array of length N which contains the sequence
C to be transformed. R is not destroyed.
C
C
C WSAVE a work array which must be dimensioned at least 3*N+15
C in the program that calls EZFFTF. The WSAVE array must be
C initialized by calling subroutine EZFFTI(N,WSAVE), and a
C different WSAVE array must be used for each different
C value of N. This initialization does not have to be
C repeated so long as N remains unchanged. Thus subsequent
C transforms can be obtained faster than the first.
C The same WSAVE array can be used by EZFFTF and EZFFTB.
C
C Output Parameters
C
C AZERO the sum from I=1 to I=N of R(I)/N
C
C A,B for N even B(N/2)=0. and A(N/2) is the sum from I=1 to
C I=N of (-1)**(I-1)*R(I)/N
C
C for N even define KMAX=N/2-1
C for N odd define KMAX=(N-1)/2
C
C then for K=1,...,KMAX
C
C A(K) equals the sum from I=1 to I=N of
C
C 2./N*R(I)*COS(K*(I-1)*2*PI/N)
C
C B(K) equals the sum from I=1 to I=N of
C
C 2./N*R(I)*SIN(K*(I-1)*2*PI/N)
C
C***REFERENCES P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
C Computations (G. Rodrigue, ed.), Academic Press,
C 1982, pp. 51-83.
C***ROUTINES CALLED RFFTF
C***REVISION HISTORY (YYMMDD)
C 790601 DATE WRITTEN
C 830401 Modified to use SLATEC library source file format.
C 860115 Modified by Ron Boisvert to adhere to Fortran 77 by
C (a) changing dummy array size declarations (1) to (*),
C (b) changing references to intrinsic function FLOAT
C to REAL.
C 881128 Modified by Dick Valent to meet prologue standards.
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890531 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE EZFFTF
DIMENSION R(*), A(*), B(*), WSAVE(*)
C***FIRST EXECUTABLE STATEMENT EZFFTF
IF (N-2) 101,102,103
101 AZERO = R(1)
RETURN
102 AZERO = .5*(R(1)+R(2))
A(1) = .5*(R(1)-R(2))
RETURN
103 DO 104 I=1,N
WSAVE(I) = R(I)
104 CONTINUE
CALL RFFTF (N,WSAVE,WSAVE(N+1))
CF = 2./N
CFM = -CF
AZERO = .5*CF*WSAVE(1)
NS2 = (N+1)/2
NS2M = NS2-1
DO 105 I=1,NS2M
A(I) = CF*WSAVE(2*I)
B(I) = CFM*WSAVE(2*I+1)
105 CONTINUE
IF (MOD(N,2) .EQ. 0) A(NS2) = .5*CF*WSAVE(N)
RETURN
END
|
