Implement fast, accurate integrator for power-law type functions about gammapy HOT 6 CLOSED

One option to implement this is trapz_loglog in gammafit.
We could also try UnivariateSpline in loglog space.

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Update: we now have gammapy.spectrum.integrate_spectrum.

• move to a method on the gammapy.spectrum.models.SpectralModel class.
• find good settings to get results with reasonable accuracy and speed for most models.

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Note: http://docs.gammapy.org/en/latest/api/gammapy.spectrum.models.SpectralModel.html#gammapy.spectrum.models.SpectralModel.integral

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@joleroi - I know. I'll close these spectrum integral issues in the next days. I just want to do some more testing and clean-up of old code, and keep them as a reminder.

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Is there anything left to be done for this issue? Compare against gammalib?

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This is a key piece of spectral analysis, and probably there will still be a lot of work on getting the precision / speed trade off right in Gammapy, and https://github.com/joleroi/wstat/issues/12 might be related, i.e. things can improve a lot by changing to integrating over bins use power-law approximation over bins by default instead of a simple diff flux times bin width method (cc @joleroi).

But the main thing suggested above was implemented by you a few months ago, and there is no concrete action item here, so I'm closing this issue. We can re-open or file new issues in the future when we encounter precision or speed problems from Gammapy spectral analyses.

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