Performance regression since 0.12.11

[burnpanck]

I have some code that performs a parallel line integral using quadpy.line_segment.integrate_adaptive. The integral is of oscillatory type. Previously, I got reasonable looking result in relatively little time. Since the upgrade to 0.14.11, that integration consumes huge amounts of RAM (50 GB+ for 1k line integrals) and never finishes (running out of patience after 10 min +). Downgrading to 0.13.6 did not help, but to 0.12.11 did.
I assume something in the algorithm must have changed such that the stop condition is not reached anymore. It's well possible that previously, the result was inaccurate (but good enough for my use case).

[nschloe]

Without an MWE, I can't do anything about it.

[burnpanck]

I was hoping that you could point out a change in the implementation of the adaptive integration (e.g. a bug fix), which may have changed the interpretation of the convergence criteria (e.g. the recent introduction of eps_abs and eps_rel) and that the runtime might be an inherent case of my integrand. In that case, it would have been difficult to provide an MVP, since the integrand function is distributed over a larger code-base (a physical model that involves among others a linear interpolation of a sampled spectrum).

However, the MVE that I just provided for #316 seems to trigger the same behaviour. So there it is, just use that MVE for this issue aswell.

[nschloe]

The MWE in the other bug is too complex. Please provide a shorter one and also post it here.

[burnpanck]

It seems that this is fixed in 0.16. The following shortened example would subdivide until memory exhaustion in 0.15:

import numpy as np
import quadpy

# parameters
lo = -2
hi = 2
A = np.array(1)[...,None]
eps = 1e-7

# integrand
def func(x):
    n_times_p, = x.shape
    print(x.shape)
    return A*np.sign(x)

# perform integration
domain = np.array([lo,hi])
val,error = quadpy.c1.integrate_adaptive(
    func,
    domain,
    kronrod_degree=5,
    eps_abs=eps,
    eps_rel=eps,
)

In 0.12 (when adjusting for the API change of #316), the code runs fine too. Given that the true integral is zero and somewhere between 0.12 and 0.15 eps has been split into eps_rel and eps_abs, it likely had to do with eps_abs not being taken into account correctly.

[nschloe]

Good to hear! The default concatenation methods for stopping tests were all, meaning for example that both relative and absolute tolerances had to be fulfilled. It's now any, such that one of the two will suffice.