Extrapolation when kmax not high enough is not really linear

[joezuntz]

CMBdata.get_matter_power_interpolator shows slightly odd behaviour when extrapolating matter power to higher k, depending on the kmax value, in a way that doesn't match previous camb versions. This usually shows up in the NL power.

Because the extrapolation is cubic and the function only adds a single extrapolated point onto the end of the k array, you can end up with strange behaviour like up-ticks at high k.

See the code and figure below.

One solution would be to add a bunch more log-linearly extrapolated points to the array instead of just one.

Cheers,
Joe

import numpy as np
import matplotlib.pyplot as plt
import camb

# Example invocation from docs
cp = camb.set_params(ns=1, H0=67, ombh2=0.022, omch2=0.1, w=-0.95, Alens=1.2, lmax=2000, 
                     WantTransfer=True, dark_energy_model='DarkEnergyPPF', kmax=1.0)

r = camb.get_results(cp)

P, z, k = r.get_matter_power_interpolator(nonlinear=True, return_z_k=True, extrap_kmax=500.)

k_plot = np.logspace(-4, np.log10(500), 300)
P_plot = P.P(0.0, k_plot)


plt.loglog(k_plot, P_plot)

# Maximum actual calculated value
plt.axvline(k.max(), color='r')

plt.show()

[cmbant]

Good point, that would certainly be a simple fix. Which CAMB version are you comparing to, it didn't change recently I think? (it looks OK with kmax=10, which I think is what I usually use)

[joezuntz]

This was a comparison to the fortran equivalent, so very very old!

[cmbant]

Ah, I think the currently MatterPowerData_k still does the same as before: it does direct log-linear extrapolation outside the compute range.

(With kmax=1 the extrapolation seems to be orders of magnitude off anyway)

[cmbant]

For this Python issue I think there was actually an indexing bug, as well as the issue with bicubic interpolation. In fc024fe I've changed it so that the gradient it pinned near the end point. The new extrapolation accuracy looks like this:

For linear it's much more accurate (should think about smarter extrapolation, c.f. #53).

[joezuntz]

Thanks so much for fixing! Will close this now.