*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