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88 lines
3.5 KiB
Fortran
88 lines
3.5 KiB
Fortran
*DECK CFFTB
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SUBROUTINE CFFTB (N, C, WSAVE)
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C***BEGIN PROLOGUE CFFTB
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C***SUBSIDIARY
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C***PURPOSE Compute the unnormalized inverse of CFFTF.
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C***LIBRARY SLATEC (FFTPACK)
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C***CATEGORY J1A2
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C***TYPE COMPLEX (RFFTB-S, CFFTB-C)
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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 ********************************************************************
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C * NOTICE NOTICE NOTICE NOTICE NOTICE NOTICE NOTICE *
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C ********************************************************************
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C * *
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C * This routine uses non-standard Fortran 77 constructs and will *
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C * be removed from the library at a future date. You are *
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C * requested to use CFFTB1. *
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C * *
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C ********************************************************************
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C
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C Subroutine CFFTB computes the backward complex discrete Fourier
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C transform (the Fourier synthesis). Equivalently, CFFTB computes
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C a complex periodic sequence from its Fourier coefficients.
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C The transform is defined below at output parameter C.
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C
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C A call of CFFTF followed by a call of CFFTB will multiply the
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C sequence by N.
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C
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C The array WSAVE which is used by subroutine CFFTB must be
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C initialized by calling subroutine CFFTI(N,WSAVE).
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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 complex sequence C. The method is
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C more efficient when N is the product of small primes.
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C
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C C a complex array of length N which contains the sequence
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C
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C WSAVE a real work array which must be dimensioned at least 4*N+15
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C in the program that calls CFFTB. The WSAVE array must be
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C initialized by calling subroutine CFFTI(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 CFFTF and CFFTB.
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C
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C Output Parameters
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C
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C C For J=1,...,N
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C
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C C(J)=the sum from K=1,...,N of
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C
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C C(K)*EXP(I*(J-1)*(K-1)*2*PI/N)
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C
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C where I=SQRT(-1)
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C
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C WSAVE contains initialization calculations which must not be
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C destroyed between calls of subroutine CFFTF or CFFTB
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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 CFFTB1
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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 changing dummy array size declarations (1) to (*).
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C 861211 REVISION DATE from Version 3.2
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C 881128 Modified by Dick Valent to meet prologue standards.
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900131 Routine changed from user-callable to subsidiary
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C because of non-standard Fortran 77 arguments in the
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C call to CFFTB1. (WRB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE CFFTB
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COMPLEX C
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DIMENSION C(*), WSAVE(*)
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C***FIRST EXECUTABLE STATEMENT CFFTB
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IF (N .EQ. 1) RETURN
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IW1 = N+N+1
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IW2 = IW1+N+N
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CALL CFFTB1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2))
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RETURN
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END
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