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