mirror of
https://git.planet-casio.com/Lephenixnoir/OpenLibm.git
synced 2025-01-01 06:23:39 +01:00
83 lines
3.1 KiB
Fortran
83 lines
3.1 KiB
Fortran
*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
|