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85 lines
3.1 KiB
Fortran
85 lines
3.1 KiB
Fortran
*DECK COSQB
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SUBROUTINE COSQB (N, X, WSAVE)
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C***BEGIN PROLOGUE COSQB
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C***PURPOSE Compute the unnormalized inverse cosine transform.
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C***LIBRARY SLATEC (FFTPACK)
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C***CATEGORY J1A3
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C***TYPE SINGLE PRECISION (COSQB-S)
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C***KEYWORDS FFTPACK, INVERSE COSINE 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 COSQB computes the fast Fourier transform of quarter
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C wave data. That is, COSQB computes a sequence from its
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C representation in terms of a cosine 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 COSQB is the unnormalized inverse of COSQF since a call of COSQB
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C followed by a call of COSQF 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 COSQB must be
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C initialized by calling subroutine COSQI(N,WSAVE).
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C
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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 COSQB. The WSAVE array must be
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C initialized by calling subroutine COSQI(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 2*X(K)*COS((2*K-1)*(I-1)*PI/(2*N))
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C
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C A call of COSQB followed by a call of
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C COSQF will multiply the sequence X by 4*N.
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C Therefore COSQF is the unnormalized inverse
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C of COSQB.
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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 COSQB or COSQF.
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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 COSQB1
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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 definition of variable TSQRT2 by using
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C FORTRAN intrinsic function SQRT instead of a DATA
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C statement.
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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 COSQB
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DIMENSION X(*), WSAVE(*)
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C***FIRST EXECUTABLE STATEMENT COSQB
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TSQRT2 = 2.*SQRT(2.)
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IF (N-2) 101,102,103
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101 X(1) = 4.*X(1)
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RETURN
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102 X1 = 4.*(X(1)+X(2))
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X(2) = TSQRT2*(X(1)-X(2))
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X(1) = X1
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RETURN
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103 CALL COSQB1 (N,X,WSAVE,WSAVE(N+1))
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RETURN
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END
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