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chebyshev_uniform for Generator1D #213

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samuelperezdi
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As a result of my excellent learning experience in the Harvard ComputeFest 2024: Physics-Informed Neural Networks, I wanted to contribute to neurodiffeq. The perfect opportunity presented by initiative of @shuheng-liu. I open this pull request to create the chebyshev_uniform method for Generator1D. This should:

  • Sample randomly from an uniform distribution between 0 and π
  • Generate the Chebyshev nodes of the first kind from this sample
  • Map output from (-1, 1) to (tmin, tmax)

I have also updated the documentation and added a test, accordingly.

Thank you!

@@ -4,21 +4,25 @@
import numpy as np
from typing import List

def _chebyshev_uniform(a, b, n):
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I am not sure that this makes sense. Chebyshev nodes are deterministic sequence of numbers. Its not a function which is valid for a random number.
I think Its better to define "chebyshev_noisy" which adds noise to the chebyshev sequence rather than doing this.

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Thank you for your comments, Sathvik! I pushed a new commit with an attempt of chebyshev_noisy.

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