cfft1b

NAME

SYNOPSIS

 SUBROUTINE CFFT1B (N, INC, C, LENC, WSAVE, LENSAV,
1                  WORK, LENWRK, IER)

 INTEGER    N, INC, LENC, LENSAV, LENWRK, IER
 COMPLEX    C(LENC)
 REAL       WSAVE(LENSAV), WORK(LENWRK)

DESCRIPTION

 FFTPACK 5.0 routine CFFT1B computes the one-dimensional Fourier 
 transform of a single periodic sequence within a complex array.  
 This transform is referred to as the backward transform or Fourier 
 synthesis, transforming the sequence from spectral to physical 
 space.
 
 This transform is normalized since a call to CFFT1B followed
 by a call to CFFT1F (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 C, of two 
         consecutive elements within the sequence to be transformed.
 
 C       Complex array of length LENC containing the sequence to be 
         transformed.
 
 LENC    Integer dimension of C array.  LENC must be at least 
         INC*(N-1) + 1.


 WSAVE   Real work array with dimension LENSAV.  WSAVE's contents 
         must be initialized with a call to subroutine CFFT1I before 
         the first call to routine CFFT1F or CFFT1B for a given 
         transform length N.  WSAVE's contents may be re-used for 
         subsequent calls to CFFT1F and CFFT1B 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 LENWRK.
 
 LENWRK  Integer dimension of WORK array.  LENWRK must be at
         least 2*N.


 Output Arguments
 
 C       For index J*INC+1 where J=0,...,N-1,
 
            C(J*INC+1) = 
 
            N-1
            SUM C(K*INC+1)*EXP(I*J*K*2*PI/N)
            K=0

         where I=SQRT(-1).
 
         At other indices, the output value of C does not differ
         from input.
 
 IER     =  0 successful exit
         =  1 input parameter LENC   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