Calculate critical curves using JAX#207
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CKrawczyk merged 1 commit intofeature/jax_wrapperfrom Nov 4, 2024
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This overhauls the current critical curve method from a grid search to an application of Newton's method for zero finding. The steps are as follows: 1) Create a set of `n_points` initial points in a circle of radius `init_r` and centred on `init_centre` 2) Apply `n_steps` of Newton's method to these points in the "radial" direction only (i.e. keeping angle fixed). Jax's auto differentiation is used to find the radial derivatives of the eigen value function for this step. 3) Filter the results and only keep point that have their eigen value `threshold` of 0. This step is needed because Newton's method will fail when the radial derivative is equal to zero (i.e. near a max or min of the eigen value). No underlying grid is needed for this method, but the quality of the results are dependent on the initial circle of points. For best results the circle should be drawn around *each* max/min of the eigen value function. This is typically the centre of each mass in the profile.
Jammy2211
approved these changes
Nov 4, 2024
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This overhauls the current critical curve method from a grid search to an application of Newton's method for zero finding.
The steps are as follows:
Create a set of
n_pointsinitial points in a circle of radiusinit_rand centred oninit_centreApply
n_stepsof Newton's method to these points in the "radial" direction only (i.e. keeping the angle fixed). Jax's auto differentiation is used to find the radial derivatives of the eigenvalue function for this step.Filter the results and only keep points that have their eigenvalue
thresholdof 0. This step is needed because Newton's method will fail when the radial derivative is equal to zero (i.e. near a max or min of the eigenvalue).No underlying grid is needed for this method, but the quality of the results are dependent on the initial circle of points. For best results, the circle should be drawn around each max/min of the eigenvalue function. This is typically the centre of each mass in the profile.