# sinqb.f

          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