PDA_CFFTF - Forward transform of a complex periodic sequence.

Origin

FFTPACK / NETLIB

Implementation Status:

A double precision version PDA_DCFFTF of the routine has been added.

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subroutine pda_cfftf(n,c,wsave)

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subroutine pda_cfftf computes the forward complex discrete fourier
transform (the fourier analysis). equivalently , pda_cfftf computes
the fourier coefficients of a complex periodic sequence.
the transform is defined below at output parameter c.

the transform is not normalized. to obtain a normalized transform
the output must be divided by n. otherwise a call of pda_cfftf
followed by a call of pda_cfftb will multiply the sequence by n.

the array wsave which is used by subroutine pda_cfftf must be
initialized by calling subroutine pda_cffti(n,wsave).

input parameters


n      the length of the complex sequence c. the method is
       more efficient when n is the product of small primes. n

c      a complex array of length n which contains the sequence

wsave   a real work array which must be dimensioned at least 4n+15
        in the program that calls pda_cfftf. the wsave array must be
        initialized by calling subroutine pda_cffti(n,wsave) and a
        different wsave array must be used for each different
        value of n. this initialization does not have to be
        repeated so long as n remains unchanged thus subsequent
        transforms can be obtained faster than the first.
        the same wsave array can be used by pda_cfftf and pda_cfftb.

output parameters

c      for j=1,...,n

           c(j)=the sum from k=1,...,n of

                 c(k)*exp(-i*(j-1)*(k-1)*2*pi/n)

                       where i=sqrt(-1)

wsave   contains initialization calculations which must not be
        destroyed between calls of subroutine pda_cfftf or pda_cfftb