*DECK COSQB SUBROUTINE COSQB (N, X, WSAVE) C***BEGIN PROLOGUE COSQB C***PURPOSE Compute the unnormalized inverse cosine transform. C***LIBRARY SLATEC (FFTPACK) C***CATEGORY J1A3 C***TYPE SINGLE PRECISION (COSQB-S) C***KEYWORDS FFTPACK, INVERSE COSINE FOURIER TRANSFORM C***AUTHOR Swarztrauber, P. N., (NCAR) C***DESCRIPTION C C Subroutine COSQB computes the fast Fourier transform of quarter C wave data. That is, COSQB computes a sequence from its C representation in terms of a cosine series with odd wave numbers. C The transform is defined below at output parameter X. C C COSQB is the unnormalized inverse of COSQF since a call of COSQB C followed by a call of COSQF will multiply the input sequence X C by 4*N. C C The array WSAVE which is used by subroutine COSQB 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 COSQB. 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)= the sum from K=1 to K=N of C C 2*X(K)*COS((2*K-1)*(I-1)*PI/(2*N)) C C A call of COSQB followed by a call of C COSQF will multiply the sequence X by 4*N. C Therefore COSQF is the unnormalized inverse C of COSQB. C C WSAVE contains initialization calculations which must not C be destroyed between calls of COSQB or COSQF. 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 COSQB1 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 TSQRT2 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 COSQB DIMENSION X(*), WSAVE(*) C***FIRST EXECUTABLE STATEMENT COSQB TSQRT2 = 2.*SQRT(2.) IF (N-2) 101,102,103 101 X(1) = 4.*X(1) RETURN 102 X1 = 4.*(X(1)+X(2)) X(2) = TSQRT2*(X(1)-X(2)) X(1) = X1 RETURN 103 CALL COSQB1 (N,X,WSAVE,WSAVE(N+1)) RETURN END