Lagrange polynomials

[dlouk]

Hi there!

I was trying to use the lagrange_polynomial function which is in chaospy/orthogonal.py. I assume that those are the Lagrange basis polynomials. I have encountered the following issues:

1. Calling chaospy.orthogonal.lagrange_polynomial([0,1]) (or with any number combination, as long as there is a zero in there) results in the error "raise numpy.linalg.LinAlgError("invertable matrix") LinAlgError: invertable matrix".

2. Calling chaospy.orthogonal.lagrange_polynomial([1, 2]) results in the polynomials [-q0^2+2.0q0, 0.5q0^2-0.5q0]. However, using the definition of Lagrange polynomials, e.g. https://en.wikipedia.org/wiki/Lagrange_polynomial, one should get [-q0+2.0, q0-1.0].

Therefore, I would like to ask what exactly am I missing in how chaospy constructs Lagrange polynomials?

Best regards,
Dimitris

[jonathf]

The Lagrange polynomials have been experimental so far, but should work fine. What you have found is a bug.

I've made a quickfix and I it seems to solve the problem. Please let me know if it works as it should now.

[dlouk]

Hi again and sorry for the late reply,

I have run the following tests:

1. lagrange_polynomial[1.] or any other test with just one point in the array fails. Error message "Arrays cannot be empty".
2. Same to my first comment, given any array with a zero in it, the lagrange_polynomial function produces the error message "LinAlgError: invertible matrix"
3. Again as before, when the function works, the polynomial order is always one higher than the one I expect, according to theory (e.g. given as input the array [1.0, 2.0]).

Best,
Dimitris

[jonathf]

Are you getting the following output?

[1]: print chaospy.orthogonal.lagrange_polynomial([0, 1])
[-q0+1.0, q0]

[2]: print chaospy.orthogonal.lagrange_polynomial([1, 2])
[-q0+2.0, q0-1.0]

[3]: print chaospy.orthogonal.lagrange_polynomial([-1, 0, 1])
[0.5q0^2-0.5q0, -q0^2+1.0, 0.5q0^2+0.5q0]

If not are you sure you have updated your verision of the repo. If not:

• Download/update the repo
• (re)install with python setup.py install
• then try to run it again.

[jonathf]

Sorry about that. I pushed it directly to master, which I really shouldn't.

I merged the changes to the development branch now.
Do git pull and you should see the updates.

[dlouk]

Hi again,

one small thing that I noticed: if one gives as input an array with just one point, then the result is not the expected one, e.g.:
print cp.orthogonal.lagrange_polynomial([1]) --> q0-1.0
print cp.orthogonal.lagrange_polynomial([0]) --> q0

I would have expected a constant, e.g. 1.0.

Thanks for your time and effort and best regards,
Dimitris

[jonathf]

Thank you. I made the fix for the single point as well now, and added it to development.

I consider the issue as close. If that is not the case, feel free to reopen.