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