*DECK SINQB SUBROUTINE SINQB (N, X, WSAVE) C***BEGIN PROLOGUE SINQB C***PURPOSE Compute the unnormalized inverse of SINQF. C***LIBRARY SLATEC (FFTPACK) C***CATEGORY J1A3 C***TYPE SINGLE PRECISION (SINQB-S) C***KEYWORDS FFTPACK, FOURIER TRANSFORM C***AUTHOR Swarztrauber, P. N., (NCAR) C***DESCRIPTION C C Subroutine SINQB computes the fast Fourier transform of quarter C wave data. That is, SINQB computes a sequence from its C representation in terms of a sine series with odd wave numbers. C the transform is defined below at output parameter X. C C SINQF is the unnormalized inverse of SINQB since a call of SINQB C followed by a call of SINQF will multiply the input sequence X C by 4*N. C C The array WSAVE which is used by subroutine SINQB must be C initialized by calling subroutine SINQI(N,WSAVE). 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 SINQB. The WSAVE array must be C initialized by calling subroutine SINQI(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 4*X(K)*SIN((2*K-1)*I*PI/(2*N)) C C a call of SINQB followed by a call of C SINQF will multiply the sequence X by 4*N. C Therefore SINQF is the unnormalized inverse C of SINQB. C C WSAVE contains initialization calculations which must not C be destroyed between calls of SINQB or SINQF. 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 COSQB 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 changing dummy array size declarations (1) to (*). 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 SINQB DIMENSION X(*), WSAVE(*) C***FIRST EXECUTABLE STATEMENT SINQB IF (N .GT. 1) GO TO 101 X(1) = 4.*X(1) RETURN 101 NS2 = N/2 DO 102 K=2,N,2 X(K) = -X(K) 102 CONTINUE CALL COSQB (N,X,WSAVE) DO 103 K=1,NS2 KC = N-K XHOLD = X(K) X(K) = X(KC+1) X(KC+1) = XHOLD 103 CONTINUE RETURN END