# ezfftf.f

          SUBROUTINE EZFFTF (N, R, AZERO, A, B, WSAVE)
    C***BEGIN PROLOGUE  EZFFTF
    C***PURPOSE  Compute a simplified real, periodic, fast Fourier forward
    C            transform.
    C***LIBRARY   SLATEC (FFTPACK)
    C***CATEGORY  J1A1
    C***TYPE      SINGLE PRECISION (EZFFTF-S)
    C***KEYWORDS  FFTPACK, FOURIER TRANSFORM
    C***AUTHOR  Swarztrauber, P. N., (NCAR)
    C***DESCRIPTION
    C
    C  Subroutine EZFFTF computes the Fourier coefficients of a real
    C  periodic sequence (Fourier analysis).  The transform is defined
    C  below at Output Parameters AZERO, A and B.  EZFFTF is a simplified
    C  but slower version of RFFTF.
    C
    C  Input Parameters
    C
    C  N       the length of the array R to be transformed.  The method
    C          is most efficient when N is the product of small primes.
    C
    C  R       a real array of length N which contains the sequence
    C          to be transformed.  R is not destroyed.
    C
    C
    C  WSAVE   a work array which must be dimensioned at least 3*N+15
    C          in the program that calls EZFFTF.  The WSAVE array must be
    C          initialized by calling subroutine EZFFTI(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          The same WSAVE array can be used by EZFFTF and EZFFTB.
    C
    C  Output Parameters
    C
    C  AZERO   the sum from I=1 to I=N of R(I)/N
    C
    C  A,B     for N even B(N/2)=0. and A(N/2) is the sum from I=1 to
    C          I=N of (-1)**(I-1)*R(I)/N
    C
    C          for N even define KMAX=N/2-1
    C          for N odd  define KMAX=(N-1)/2
    C
    C          then for  K=1,...,KMAX
    C
    C               A(K) equals the sum from I=1 to I=N of
    C
    C                    2./N*R(I)*COS(K*(I-1)*2*PI/N)
    C
    C               B(K) equals the sum from I=1 to I=N of
    C
    C                    2./N*R(I)*SIN(K*(I-1)*2*PI/N)
    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  RFFTF
    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 references to intrinsic function FLOAT
    C               to REAL.
    C   881128  Modified by Dick Valent to meet prologue standards.
    C   890531  Changed all specific intrinsics to generic.  (WRB)
    C   890531  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  EZFFTF