rfftmf

NAME

SYNOPSIS

 SUBROUTINE RFFTMF (LOT, JUMP, N, INC, R, LENR, WSAVE, LENSAV,
1                  WORK, LENWRK, IER)

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

DESCRIPTION

 FFTPACK 5.0 routine RFFTMF computes the one-dimensional Fourier 
 transform of multiple periodic sequences within a real array.  
 This transform is referred to as the forward transform or Fourier 
 analysis, transforming the sequences from physical to spectral
 space.
 
 This transform is normalized since a call to RFFTMF followed
 by a call to RFFTMB (or vice-versa) reproduces the original
 array  within roundoff error.
 
 Input Arguments
 
 LOT     Integer number of sequences to be transformed within
         array R.
 
 JUMP    Integer increment between the locations, in array R,
         of the first elements of two consecutive sequences
         to be transformed.
 
 N       Integer length of each 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 same sequence.
 
 R       Real array containing LOT sequences, each having length N.
         R can have any number of dimensions, but the total number 
         of locations must be at least LENR.
 
 LENR    Integer dimension of R array.  LENR must be at 
         least (LOT-1)*JUMP + INC*(N-1) + 1.


 WSAVE   Real work array o length LENSAV.  WSAVE's contents must 
         be initialized with a call to subroutine RFFTMI before the 
         first call to routine RFFTMF or RFFTMB 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
         least LOT*N.


 Output Arguments
 
  R      Real output array R.  For purposes of exposition, 
         assume R's range of indices is given by 
         R(0:(LOT-1)*JUMP+(N-1)*INC).
 
         Then for I=0,...,LOT-1
 
                        N-1
         R(I*JUMP) =    SUM  R(I*JUMP+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(I*JUMP+(2*J-1)*INC) = 
 
                     N-1
                  2.*SUM  (R(I*JUMP+N1*INC)*COS(J*N1*2*PI/N)/N
                    N1=0
 
          and
 
            R(I*JUMP+2*J*INC) = 
 
                     N-1
                  2.*SUM  (R(I*JUMP+N1*INC)*SIN(J*N1*2*PI/N)/N
                    N1=0
 
          Also if N is even then
 
            R(I*JUMP+(N-1)*INC) = 
 
                     N-1
                     SUM  (-1)**N1*R(I*JUMP+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
         =  4 input parameters INC,JUMP,N,LOT are not consistent.

              The parameters integers INC, JUMP, N and LOT are
              consistent if equality
              I1*INC + J1*JUMP = I2*INC + J2*JUMP for I1,I2 < N
              and J1,J2 < LOT implies I1=I2 and J1=J2.

              For multiple FFTs to execute correctly, input variables
              INC, JUMP, N and LOT must be consistent ... otherwise at
              least one array element mistakenly is transformed more
              than once.