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
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).
For the contact, the values seem more precise with c0 = -5.24e-17 +- 1.21e-15 in [fm**(-2)].
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 thesphericalzeta witha1gprojector atunitarity. The solver precision are at1.0e-16and1.0e-15. The distributions are generated for all values ofn1d,nstep,epsilonandnlevel(see the notebook for more details).x-distribution
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-eigsmultiplier), 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).For the contact, the values seem more precise with
c0 = -5.24e-17 +- 1.21e-15in [fm**(-2)].