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4.3.3 Real-data DFTs

     fftw_plan fftw_plan_dft_r2c_1d(int n0,
                                    double *in, fftw_complex *out,
                                    unsigned flags);
     fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1,
                                    double *in, fftw_complex *out,
                                    unsigned flags);
     fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2,
                                    double *in, fftw_complex *out,
                                    unsigned flags);
     fftw_plan fftw_plan_dft_r2c(int rank, const int *n,
                                 double *in, fftw_complex *out,
                                 unsigned flags);

Plan a real-input/complex-output discrete Fourier transform (DFT) in zero or more dimensions, returning an fftw_plan (see Using Plans).

Once you have created a plan for a certain transform type and parameters, then creating another plan of the same type and parameters, but for different arrays, is fast and shares constant data with the first plan (if it still exists).

The planner returns NULL if the plan cannot be created. A non-NULL plan is always returned by the basic interface unless you are using a customized FFTW configuration supporting a restricted set of transforms, or if you use the FFTW_PRESERVE_INPUT flag with a multi-dimensional out-of-place c2r transform (see below).

Arguments

The inverse transforms, taking complex input (storing the non-redundant half of a logically Hermitian array) to real output, are given by:

     fftw_plan fftw_plan_dft_c2r_1d(int n0,
                                    fftw_complex *in, double *out,
                                    unsigned flags);
     fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1,
                                    fftw_complex *in, double *out,
                                    unsigned flags);
     fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2,
                                    fftw_complex *in, double *out,
                                    unsigned flags);
     fftw_plan fftw_plan_dft_c2r(int rank, const int *n,
                                 fftw_complex *in, double *out,
                                 unsigned flags);

The arguments are the same as for the r2c transforms, except that the input and output data formats are reversed.

FFTW computes an unnormalized transform: computing an r2c followed by a c2r transform (or vice versa) will result in the original data multiplied by the size of the transform (the product of the logical dimensions). An r2c transform produces the same output as a FFTW_FORWARD complex DFT of the same input, and a c2r transform is correspondingly equivalent to FFTW_BACKWARD. For more information, see What FFTW Really Computes.