ckoerber / luescher-nd

This repository supports the publication https://arxiv.org/abs/1912.04425
https://ckoerber.github.io/luescher-nd/
BSD 3-Clause "New" or "Revised" License
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Numerical uncertainty #27

Closed ckoerber closed 5 years ago

ckoerber commented 5 years ago

Here is a brief summary of how I have extracted numerical uncertainties. The key file is the numerical-errors notebook pushed with 956f982c9aeab3da1dcd0b9feaafaaa93783ec6c.

The key idea is the following: Repeat computation for all the same parameters but different numerical precisions (eigenvalue solver precision and contact fitter precision). Compute the difference of extracted quantities and hope that they follow a normal distribution.

Below you can find the distribution for errors of the energy eigenvalues (x-values) and the the fitted contact for the spherical zeta with a1g projector at unitarity. The solver precision are at 1.0e-16 and 1.0e-15. The distributions are generated for all values of n1d, nstep, epsilon and nlevel (see the notebook for more details).

x-distribution

x-numerical-error

Blue line is Kernel Density Estimate, green line is normal fit with cut-out outliers (abs(zcore) < 2). The error centers around machine precision zero with standard deviation at three orders of magnitude larger then machine precision: 1.12e-16 +- 1.25e-13.

c-distribution

Because we have less values for the contact interactions (compared just one contact value for fixed meta parameters; no n-eigs multiplier), the distribution does not look as normal as the distribution above.

Blue line is Kernel Density Estimate, green line is normal fit with cut-out outliers (abs(zcore) < 4).

c-numerical-error

For the contact, the values seem more precise with c0 = -5.24e-17 +- 1.21e-15 in [fm**(-2)].