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- *DECK COSQF
- SUBROUTINE COSQF (N, X, WSAVE)
- C***BEGIN PROLOGUE COSQF
- C***PURPOSE Compute the forward cosine transform with odd wave numbers.
- C***LIBRARY SLATEC (FFTPACK)
- C***CATEGORY J1A3
- C***TYPE SINGLE PRECISION (COSQF-S)
- C***KEYWORDS COSINE FOURIER TRANSFORM, FFTPACK
- C***AUTHOR Swarztrauber, P. N., (NCAR)
- C***DESCRIPTION
- C
- C Subroutine COSQF computes the fast Fourier transform of quarter
- C wave data. That is, COSQF computes the coefficients in a cosine
- C series representation with only odd wave numbers. The transform
- C is defined below at Output Parameter X
- C
- C COSQF is the unnormalized inverse of COSQB since a call of COSQF
- C followed by a call of COSQB will multiply the input sequence X
- C by 4*N.
- C
- C The array WSAVE which is used by subroutine COSQF must be
- C initialized by calling subroutine COSQI(N,WSAVE).
- C
- C
- C Input Parameters
- C
- C N the length of the array X to be transformed. The method
- C is most efficient when N is a product of small primes.
- C
- C X an array which contains the sequence to be transformed
- C
- C WSAVE a work array which must be dimensioned at least 3*N+15
- C in the program that calls COSQF. The WSAVE array must be
- C initialized by calling subroutine COSQI(N,WSAVE), and a
- C different WSAVE array must be used for each different
- C value of N. This initialization does not have to be
- C repeated so long as N remains unchanged. Thus subsequent
- C transforms can be obtained faster than the first.
- C
- C Output Parameters
- C
- C X For I=1,...,N
- C
- C X(I) = X(1) plus the sum from K=2 to K=N of
- C
- C 2*X(K)*COS((2*I-1)*(K-1)*PI/(2*N))
- C
- C A call of COSQF followed by a call of
- C COSQB will multiply the sequence X by 4*N.
- C Therefore COSQB is the unnormalized inverse
- C of COSQF.
- C
- C WSAVE contains initialization calculations which must not
- C be destroyed between calls of COSQF or COSQB.
- C
- C***REFERENCES P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
- C Computations (G. Rodrigue, ed.), Academic Press,
- C 1982, pp. 51-83.
- C***ROUTINES CALLED COSQF1
- C***REVISION HISTORY (YYMMDD)
- C 790601 DATE WRITTEN
- C 830401 Modified to use SLATEC library source file format.
- C 860115 Modified by Ron Boisvert to adhere to Fortran 77 by
- C (a) changing dummy array size declarations (1) to (*),
- C (b) changing definition of variable SQRT2 by using
- C FORTRAN intrinsic function SQRT instead of a DATA
- C statement.
- C 861211 REVISION DATE from Version 3.2
- C 881128 Modified by Dick Valent to meet prologue standards.
- C 891214 Prologue converted to Version 4.0 format. (BAB)
- C 920501 Reformatted the REFERENCES section. (WRB)
- C***END PROLOGUE COSQF
- DIMENSION X(*), WSAVE(*)
- C***FIRST EXECUTABLE STATEMENT COSQF
- SQRT2 = SQRT(2.)
- IF (N-2) 102,101,103
- 101 TSQX = SQRT2*X(2)
- X(2) = X(1)-TSQX
- X(1) = X(1)+TSQX
- 102 RETURN
- 103 CALL COSQF1 (N,X,WSAVE,WSAVE(N+1))
- RETURN
- END
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