cost1f

NAME

SYNOPSIS

 SUBROUTINE COST1F (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 COST1F computes the one-dimensional Fourier 
 transform of an even sequence within a real array.  This 
 transform 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 COST1F followed
 by a call to COST1B (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-1 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 COST1I before the 
         first call to routine COST1F or COST1B for a given transform
         length N.  WSAVE's contents may be re-used for subsequent 
         calls to COST1F and COST1B with the same N.


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


 WORK    Real work array of dimension at least LENWRK.
 
 LENWRK  Integer dimension of WORK array.  LENWRK must be at 
         least N-1.


 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).
 
         The output values of R are written over the input values.

          R(0) = 

              0.5*X(0)/(N-1)
 
              N-2
            + SUM  R(N1*INC)/(N-1)
              N1=1

            + 0.5*X((N-1)*INC)/(N-1)
 
         For J=1,...,N-2
          R(J*INC) = 

              R(0)/(N-1)
 
              N-2
            + SUM  2.0*(X(N1*INC)*COS(J*N1*PI/(N-1)))/(N-1)
              N1=1

            + ((-1)**J)*X((N-1)*INC)/(N-1)
 
          R((N-1)*INC) = 

              0.5*X(0)/(N-1)
 
              N-2
            + SUM  R(N1*INC)*((-1)**N1)/(N-1)
              N1=1

            + 0.5*((-1)**(N-1))*X((N-1)*INC)/(N-1)
 
 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
         = 20 input error returned by lower level routine