rfft2b

NAME

SYNOPSIS

 SUBROUTINE RFFT2B (LDIM, L, M, R, WSAVE, LENSAV, WORK, LENWRK, IER)
 INTEGER    LDIM, L, M, LENSAV, LENWRK, IER
 REAL       R(LDIM,M), WSAVE(LENSAV), WORK(LENWRK)
 

DESCRIPTION

 FFTPACK 5.0 routine RFFT2B computes the two-dimensional discrete
 Fourier transform of the complex Fourier coefficients a real 
 periodic array.  This transform is known as the backward transform 
 or Fourier synthesis, transforming from spectral to physical space.
 
 Routine RFFT2B is normalized: a call to RFFT2B followed by a
 call to RFFT2F (or vice-versa) reproduces the original array
 within roundoff error.
 
 Input Arguments
 
 LDIM    Integer first dimension of the two-dimensional real
         array R, which must be at least 2*(L/2+1).
 
 L       Integer number of elements to be transformed in the first 
         dimension of the two-dimensional real array R.  The value 
         of L must be less than or equal to that of LDIM.  The 
         transform is most efficient when L is a product of small 
         primes.
 
 M       Integer number of elements to be transformed in the second 
         dimension of the two-dimensional real array R.  The 
         transform is most efficient when M is a product of small 
         primes.


 R       Real array of two dimensions containing the L/2+1-by-M 
         complex subarray of spectral coefficients to be transformed.  
         R's first dimension is LDIM and its second dimension must be at 
         least as large as M.
 

 WSAVE   Real work array of length LENSAV.  WSAVE's contents must 
         be initialized with a call to subroutine RFFT2I before the 
         first call to routine RFFT2F or RFFT2B with lengths L and M.
         WSAVE's contents may be re-used for subsequent calls 
         to RFFT2F and RFFT2B with the same transform lengths L and M.


 LENSAV  Integer number of elements in the WSAVE array.  LENSAV must
         be at least L + M + INT(LOG(REAL(L))) + INT(LOG(REAL(M))) +8.


 WORK    Real array of dimension LENWRK, where LENWRK is defined 
         below. WORK provides workspace, and its contents need not 
         be saved between calls to routines RFFT2B and RFFT2F.
 
 LENWRK  Integer number of elements in the WORK array.  LENWRK must
         be at least LDIM*M.

 Output Arguments
 
 R       Real output array R of size LDIM-by-M, where LDIM is at 
         least L.   For purposes of exposition, assume the index 
         ranges of array R are defined by R(0:L-1,0:M-1), and the
         complex Fouier coefficient array by C(0:L/2,0:M-2). 

                   L/2  M-1
          R(I,J) = SUM  SUM  C(L1,M1)
                   L1=0 M1=0

               *EXP(SQRT(-1)*2*PI*(I*L1/L+J*M1/M))

            L-1  M-1
          + SUM  SUM  CONJ(C(L1,M1))
       L1=L/2+1  M1=0

               *EXP(SQRT(-1)*2*PI*(I*(L-L1)/L+J*M1/M))


 IER     Integer error return
         =  0 successful exit
         =  2 input parameter LENSAV not big enough
         =  3 input parameter LENWRK not big enough
         =  6 input parameter LDIM < 2*(L/2+1)
         = 20 input error returned by lower level routine