Factor pi missing in compute_cheby_coeff

[kieranricardo]

It looks like a factor of pi is missing in the numerical integration in

pygsp/pygsp/filters/approximations.py

Line 52 in d780954

c[o] = 2. / N * np.dot(f._kernels[i](a1 * num + a2),

compared Eq 8 https://arxiv.org/pdf/1105.1891.pdf throwing off the Chebyshev coefficients by a factor of pi.

[nperraud]

Hi thanks for reporting that.
@mdeff , do you know if this is intentional or a mistake. I have the feeling we knew about that... If it is intentional, we should document it.

[mdeff]

Indeed, we use 2/n as a factor instead of 2/pi. As for #74, the definition of the coefficients came from the matlab implementation. I believe that is intentional and correct, as the integration over pi is approximated by a summation over n evaluation points. Do you agree @nperraud?

In my overhaul of the Chebyshev approximation (in the polynomial-approximations branch), I used 2/n and documented the definition. I could add that the summation is an approximation of the integral.