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96 lines
3.8 KiB
Fortran
96 lines
3.8 KiB
Fortran
*DECK RFFTB
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SUBROUTINE RFFTB (N, R, WSAVE)
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C***BEGIN PROLOGUE RFFTB
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C***SUBSIDIARY
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C***PURPOSE Compute the backward fast Fourier transform of a real
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C coefficient array.
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C***LIBRARY SLATEC (FFTPACK)
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C***CATEGORY J1A1
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C***TYPE SINGLE PRECISION (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 RFFTB1. *
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C * *
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C ********************************************************************
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C
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C Subroutine RFFTB computes the real periodic sequence from its
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C Fourier coefficients (Fourier synthesis). The transform is defined
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C below at output parameter R.
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C
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C Input Arguments
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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 a product of small primes.
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C N may change so long as different work arrays are provided.
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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.
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C
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C WSAVE a work array which must be dimensioned at least 2*N+15
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C in the program that calls RFFTB. The WSAVE array must be
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C initialized by calling subroutine RFFTI, and a different
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C WSAVE array must be used for each different value of N.
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C This initialization does not have to be repeated so long as
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C remains unchanged. Thus subsequent transforms can be
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C obtained faster than the first. Moreover, the same WSAVE
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C array can be used by RFFTF and RFFTB as long as N remains
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C unchanged.
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C
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C Output Argument
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C
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C R For N even and for I = 1,...,N
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C
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C R(I) = R(1)+(-1)**(I-1)*R(N)
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C
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C plus the sum from K=2 to K=N/2 of
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C
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C 2.*R(2*K-2)*COS((K-1)*(I-1)*2*PI/N)
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C
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C -2.*R(2*K-1)*SIN((K-1)*(I-1)*2*PI/N)
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C
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C For N odd and for I = 1,...,N
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C
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C R(I) = R(1) plus the sum from K=2 to K=(N+1)/2 of
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C
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C 2.*R(2*K-2)*COS((K-1)*(I-1)*2*PI/N)
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C
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C -2.*R(2*K-1)*SIN((K-1)*(I-1)*2*PI/N)
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C
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C Note: This transform is unnormalized since a call of RFFTF
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C followed by a call of RFFTB will multiply the input
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C sequence by N.
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C
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C WSAVE contains results which must not be destroyed between
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C calls of RFFTB or RFFTF.
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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 RFFTB1
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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 RFFTB
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DIMENSION R(*), WSAVE(*)
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C***FIRST EXECUTABLE STATEMENT RFFTB
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IF (N .EQ. 1) RETURN
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CALL RFFTB1 (N,R,WSAVE,WSAVE(N+1),WSAVE(2*N+1))
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RETURN
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END
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