ValueError: The cumulative sum of the true energy probability is not monotonically increasing! Values of the cumsum are [0. 0.04514964 0.23739487 0.51615731 0.73989165 0.85946367

[mskarl]

Simulating a source at the direction of TXS with gamma = 5, I get the following error:

File ~/ice-cube/skyllh/skyllh/analyses/i3/publicdata_ps/signal_generator.py:91, in PDDatasetSignalGenerator._generate_inv_cdf_spline(self, flux_model, log_e_min, log_e_max) 89 cum_per_bin = np.concatenate(([0], cum_per_bin)) 90 if np.any(np.diff(cum_per_bin) == 0): ---> 91 raise ValueError( 92 'The cumulative sum of the true energy probability is not ' 93 'monotonically increasing! Values of the cumsum are ' 94 f'{cum_per_bin}.') 96 bin_centers = np.concatenate(([low_bin_edges[0]], bin_centers)) 98 # Build a spline for the inverse CDF.

ValueError: The cumulative sum of the true energy probability is not monotonically increasing! Values of the cumsum are [0. 0.04514964 0.23739487 0.51615731 0.73989165 0.85946367 0.93071848 0.96670947 0.98463529 0.99343831 0.99720162 0.99888929 0.99960012 0.99986353 0.99995501 0.99998571 0.99999572 0.99999871 0.99999963 0.9999999 0.99999997 0.99999999 1. 1.

1. 1. 1. 1. 1. 1.
2. 1. 1. 1. 1. 1. ].

[chiarabellenghi]

This is a numerical issue. It happens because the neutrino energy probability per bin has very small values for high energies when the spectral index is extremely soft:

[7.91065093e-02 2.67555284e-01 3.08171310e-01 1.96467446e-01
 8.34041164e-02 3.94795480e-02 1.58398740e-02 6.26667326e-03
 2.44449702e-03 8.30095346e-04 2.95695299e-04 9.89295692e-05
 2.91193705e-05 8.03339192e-06 2.14109336e-06 5.54931404e-07
 1.31573344e-07 3.20391743e-08 7.66283566e-09 1.58228759e-09
 3.29396317e-10 6.53738558e-11 1.32045069e-11 2.64000713e-12
 5.01224077e-13 9.91672101e-14 1.81044808e-14 2.97017111e-15
 5.47836854e-16 8.85532170e-17 1.45610807e-17 2.36148615e-18
 3.09097602e-19 4.49721198e-20 6.23703166e-21]

On the other hand, we need the cumsum_per_bin to be monotonically increasing to build the spline for the inverse sampling.

To fix this behaviour we cut the prob_per_bin array so that all its items are >1e-15. This should be safe enough since the probability to sample those energies is so low.