added zero_tol parameter for check_partials method

[kikutabryan]

Summary

• Added parameter to check_partials method called zero_tol.
• If calculated magnitude of partials is below zero_tol, they are set equal to zero to avoid situations where the check magnitude is zero and the calculated magnitude has some slight error resulting in a relative error of 1.

Before:

After:

Related Issues

• Resolves Add Zero Tolerance to Check Partials for Relative Error Checks #3164

Backwards incompatibilities

None

New Dependencies

None

[coveralls]

coverage: 89.699% (-0.3%) from 89.949%
when pulling 4d615cf on kikutabryan:master
into b46639a on OpenMDAO:master.

[robfalck]

Thanks for your contribution! Would you be able to add a test for our CI that verifies that this works?

It can be as simple as capturing the text from your example above and making sure it matches the expected value.
If you dont think you have the time to do this let us know.

[robfalck]

After testing this implementation a bit, I have a few suggestions.

I think zero_tol should specify the magnitude of the calc_mag below which the relative error is not calculated.
A tol on the derivatives themselves overlaps with abs_err_tol and rel_err_tol and is a bit confusing.

Interested to hear thoughts on this.

[kikutabryan]

After testing this implementation a bit, I have a few suggestions.

I think zero_tol should specify the magnitude of the calc_mag below which the relative error is not calculated. A tol on the derivatives themselves overlaps with abs_err_tol and rel_err_tol and is a bit confusing.

Interested to hear thoughts on this.

Not entirely sure if I understood correctly, but I just updated the to code use the norm of the Jacobian and if the norm is greater than the specified threshold (renamed zero_tol to rel_err_norm_thresh), the relative error will be computed, if it is below, it will not be computed (as you suggested).

Let me know if this sounds better.