rfft1f

NAME

SYNOPSIS

 SUBROUTINE RFFT1F (N, INC, R, LENR, WSAVE, LENSAV, WORK, LENWRK, IER)

 INTEGER    N, INC, LENR, LENSAV, LENWRK, IER
 REAL       R(LENR), WSAVE(LENSAV), WORK(LENWRK)

DESCRIPTION

 FFTPACK 5.0 routine RFFT1F computes the one-dimensional Fourier 
 transform of a periodic sequence within a real array.  This  
 is referred to as the forward transform or Fourier analysis, 
 transforming the sequence from physical to spectral space.

 
 This transform is normalized since a call to RFFT1F followed
 by a call to RFFT1B (or vice-versa) reproduces the original
 array  within roundoff error.
 
 Input Arguments
 
 N       Integer length of the sequence to be transformed.  The 
         transform is most efficient when N is a product of 
         small primes.
 
 INC     Integer increment between the locations, in array R,
         of two consecutive elements within the sequence.
 
 R       Real array of length LENR containing the sequence to be 
         transformed.
 
 LENR    Integer dimension of R array.  LENR must be at least 
         INC*(N-1) + 1.

 WSAVE   Real work array of length LENSAV.  WSAVE's contents must 
         be initialized with a call to subroutine RFFT1I before the 
         first call to routine RFFT1F or RFFT1B for a given transform
         length N. 


 LENSAV  Integer dimension of WSAVE array.  LENSAV must be at least 
         N + INT(LOG (REAL(N))) +4.


 WORK    Real work array of dimension LENWRK.
 
 LENWRK  Integer dimension of WORK array.  LENWRK must be at N.


 Output Arguments
 
  R      Real output array R.  For purposes of exposition, 
         assume R's range of indices is given by 
         R(0:(N-1)*INC).
 
         Then
 
                        N-1
         R(0) =         SUM  R(N1*INC)/N
                        N1=0
 
         If N is even, set NH=N/2-1; if N is odd set NH=(N-1)/2;
         then for J=1,...,NH
 
           R((2*J-1)*INC) = 
 
                     N-1
                  2.*SUM  (R(N1*INC)*COS(J*N1*2*PI/N)/N
                    N1=0
 
          and
 
            R(2*J*INC) = 
 
                     N-1
                  2.*SUM  (R(N1*INC)*SIN(J*N1*2*PI/N)/N
                    N1=0
 
          Also if N is even then
 
            R((N-1)*INC) = 
 
                     N-1
                     SUM  (-1)**N1*R(N1*INC)/N
                     N1=0
 
 
 IER     Integer error return
         =  0 successful exit
         =  1 input parameter LENR   not big enough
         =  2 input parameter LENSAV not big enough
         =  3 input parameter LENWRK not big enough