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86 lines
3 KiB
Fortran
86 lines
3 KiB
Fortran
*DECK SINQB
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SUBROUTINE SINQB (N, X, WSAVE)
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C***BEGIN PROLOGUE SINQB
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C***PURPOSE Compute the unnormalized inverse of SINQF.
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C***LIBRARY SLATEC (FFTPACK)
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C***CATEGORY J1A3
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C***TYPE SINGLE PRECISION (SINQB-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 SINQB computes the fast Fourier transform of quarter
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C wave data. That is, SINQB computes a sequence from its
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C representation in terms of a sine series with odd wave numbers.
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C the transform is defined below at output parameter X.
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C
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C SINQF is the unnormalized inverse of SINQB since a call of SINQB
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C followed by a call of SINQF will multiply the input sequence X
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C by 4*N.
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C
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C The array WSAVE which is used by subroutine SINQB must be
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C initialized by calling subroutine SINQI(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 array X 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
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C X an array which contains the sequence to be transformed
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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 SINQB. The WSAVE array must be
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C initialized by calling subroutine SINQI(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
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C Output Parameters
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C
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C X For I=1,...,N
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C
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C X(I)= the sum from K=1 to K=N of
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C
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C 4*X(K)*SIN((2*K-1)*I*PI/(2*N))
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C
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C a call of SINQB followed by a call of
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C SINQF will multiply the sequence X by 4*N.
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C Therefore SINQF is the unnormalized inverse
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C of SINQB.
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C
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C WSAVE contains initialization calculations which must not
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C be destroyed between calls of SINQB or SINQF.
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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 COSQB
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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 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE SINQB
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DIMENSION X(*), WSAVE(*)
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C***FIRST EXECUTABLE STATEMENT SINQB
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IF (N .GT. 1) GO TO 101
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X(1) = 4.*X(1)
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RETURN
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101 NS2 = N/2
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DO 102 K=2,N,2
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X(K) = -X(K)
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102 CONTINUE
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CALL COSQB (N,X,WSAVE)
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DO 103 K=1,NS2
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KC = N-K
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XHOLD = X(K)
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X(K) = X(KC+1)
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X(KC+1) = XHOLD
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103 CONTINUE
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RETURN
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END
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