Scaling

The real-to-complex and complex-to-real S3L parallel FFTs do not include scaling of the data. Consequently, for a forward 1D real-to-complex FFT of a vector of length n, followed by an inverse 1D complex-to-real FFT of the result, the original vector is multiplied by n/2.

If the data fits in a single process, a 1D real-to-complex FFT of a vector of length n, followed by a 1D complex-to-real FFT results in the original vector being scaled by n.

For a real-to-complex FFT of a 2D real array of size n x m, followed by a complex-to-real FFT, the original array is scaled by n x m.

Similarly, a real-to-complex FFT applied to a 3D real array of size n x m x k, followed by a complex-to-real FFT, results in the original array being scaled by n x m x k.