First try at implementing evaluation of legendrePolynomial #136
Conversation
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This doesn't seem like it would be very efficient or numerically robust approach. I would suggest looking in the literature on how these are used and evaluated. |
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Thank you for your opinion. I tried again with a different approach using recursion. I took ispiration from here: http://people.sc.fsu.edu/~jburkardt/py_src/legendre_polynomial/legendre_polynomial.html Happy holidays! Ludovico |
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If you want pointwise evaluation of associated Legendre polynomials, you will definitely want to use Clenshaw-Smith recurrence. See here: https://github.com/MikaelSlevinsky/FastTransforms.jl/blob/master/src/SphericalHarmonics/sphfunctions.jl |
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What about using tabulated coefficients? The coefficients are defined by that series |
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Definitely not. The coefficients of Legendre polynomials in the monomial basis grow geometrically, so any numerics based on this approach would be ill-conditioned. The three-term recurrence relation is preferred. See also ApproxFun.jl for numerical computing with orthogonal polynomials. |
4 participants
Hello everyone!
As I wrote in issue #124, I tried to implement an evaluation of Legendre Polynomials.
As there are derivatives, I used a closed form, as found here:
https://en.wikipedia.org/wiki/Legendre_polynomials
I am sure I should write some tests for this function, as well as some kind of documentation. However I wanted to put this out here so people can comment and give their opinions on things I should improve.
Let me know what you think!
Ludovico