# cosqf.f

          SUBROUTINE COSQF (N, X, WSAVE)
    C***BEGIN PROLOGUE  COSQF
    C***PURPOSE  Compute the forward cosine transform with odd wave numbers.
    C***LIBRARY   SLATEC (FFTPACK)
    C***CATEGORY  J1A3
    C***TYPE      SINGLE PRECISION (COSQF-S)
    C***KEYWORDS  COSINE FOURIER TRANSFORM, FFTPACK
    C***AUTHOR  Swarztrauber, P. N., (NCAR)
    C***DESCRIPTION
    C
    C  Subroutine COSQF computes the fast Fourier transform of quarter
    C  wave data. That is, COSQF computes the coefficients in a cosine
    C  series representation with only odd wave numbers.  The transform
    C  is defined below at Output Parameter X
    C
    C  COSQF is the unnormalized inverse of COSQB since a call of COSQF
    C  followed by a call of COSQB will multiply the input sequence X
    C  by 4*N.
    C
    C  The array WSAVE which is used by subroutine COSQF 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 COSQF.  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) = X(1) plus the sum from K=2 to K=N of
    C
    C                  2*X(K)*COS((2*I-1)*(K-1)*PI/(2*N))
    C
    C               A call of COSQF followed by a call of
    C               COSQB will multiply the sequence X by 4*N.
    C               Therefore COSQB is the unnormalized inverse
    C               of COSQF.
    C
    C  WSAVE   contains initialization calculations which must not
    C          be destroyed between calls of COSQF or COSQB.
    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  COSQF1
    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 SQRT2 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  COSQF