Normalization of Fourier transform

[sijiehuang23]

Hi,

Recently, I've started using Shenfun. I'm wondering how the Fourier transform is normalized in Shenfun, especially when it comes to multidimensional cases.

Take 2D as an example. Is it divided by the number of grid points, $N_x\cdot N_y$, in the forward transform, or is this normalization done in the backward transform, as is common in most FFT packages (such as those in MATLAB, numpy, and scipy)?

I've been experimenting with the code, and it seems like Shenfun follows the ortho strategy as in scipy, in which both the forward and backward transforms are scaled by $1/\sqrt{N_x \cdot N_y}$. However, I'm not sure if this is correct.

[mikaem]

Hi
The forward transform in Shenfun in any direction is divided by N. So in 2D with two Fourier spaces it is divided by $N_x \cdot N_y$. Note that a consecutive forward and backward should return the original data. You will probably find the FFTs better described in the mpi4py_fft source code.