Csfft1d/Zdfft1d executes the Fast Fourier Transform in place on complex data.

Usage:

    Fortran:

        call csfft1d (data_in, num_pts, isign, temp_data)
        call zdfft1d (data_in, num_pts, isign, temp_data)

    C:

        csfft1d_ (data_in, &num_pts, &isign, temp_data);
        zdfft1d_ (data_in, &num_pts, &isign, temp_data);

Description:

    Csfft1d/zdfft1d computes the inverse FFT on complex data in single
    (csfft1d) or double (zdfft1d) precision.  Num_pts must be even and
    equal to the resulting number of real data points.

Routine parameters:

    Fortran:

        csfft1d:

            real       data_in (num_pts + 2), temp_data (num_pts + 2)
            integer    num_pts, isign

        zdfft1d:

            real*8     data_in (num_pts + 2), temp_data (num_pts + 2)
            integer    num_pts, isign

    C:

        csfft1d:

            float      data_in [num_pts + 2], temp_data [num_pts + 2];
            int        num_pts, isign;

        zdfft1d:

            double     data_in [num_pts + 2], temp_data [num_pts + 2];
            int        num_pts, isign;

Parameter descriptions:

            data_in:  array of at least size num_pts + 2 which contains the
                      data points to be transformed.

            temp_data:  array of at least size num_pts + 2 which will be used
                        by the routine for temporary storage of intermediate
                        values.

            num_pts:  integer indicating the size of the transform desired

            isign:  integer value which indicates the action desired:

                    0:  decompose the problem and initialize the coefficient
                        arrays

                   -1:  perform a forward FFT on the data held in data_in

    A call to csfft1d/zdfft1d must first be made with isign = 0 to decompose
the problem and initialize the coefficient arrays.  After this, any number of
transforms of the same length may be computed.  If a transform of a different
size is desired, another call to csfft1d/zdfft1d with isign = 0 is required to
decompose the new problem and generate new coefficients.  The array temp_data
may safely be used for other work between invocations of csfft1d/zdfft1d.

    Transform sizes are restricted to values which factor completely
into the numbers 2, 3, 5, and 7 and must be even.  Each of these numbers may
appear multiple times in the factorization.  In addition, transform sizes
whose factorizations contain 11 or 13 exactly once (11 or 13, but not both)
are also allowed.  For example, a transform of size 110 (11 * 5 * 2) or 78
(13 * 3 * 2) can be computed, while a transform of size 143 (11 * 13) can not.
Work is currently underway to allow odd sizes to be processed using an N**2
algorithm.  If an unsupported transform size is attempted, the routine will
exit with an error message.

Behavior:

    isign = 0:

        any values in data_in or temp_data are unchanged

    isign != 0:

        data_in contains the results of a inverse FFT performed on the data
        points previously held in the array.  Any previous values in
        temp_data will be lost.