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Update circular domain notebook to use simplified API
Replace wrap_angle() calls with inline arithmetic, update circular_vars/circular_units params to circular=True/False, remove degrees section, and simplify multidim demo to differentiate circular and non-circular dimensions separately. Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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‎notebooks/7_circular_domain.ipynb‎

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "8b85da6f",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import pynumdiff\n",
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"\n",
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"from pynumdiff.utils import simulate, evaluate\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7a77ab05",
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"metadata": {},
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"source": [
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"# Generate testing data\n",
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"\n",
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"Here we amplify the usual signal to get outside the -pi to pi bound."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "e351d4d1",
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"metadata": {},
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"outputs": [],
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"source": [
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"noise_type = 'normal' # noise is generated using np.random, e.g. 'normal', 'uniform', 'poisson'\n",
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"noise_parameters = [0, 0.5] # compatible with np.random functions \n",
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"random_seed = 1\n",
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"\n",
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"dt = 0.01 # step size and series length in terms of independent variable\n",
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"duration = 4\n",
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"\n",
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"x, x_truth, dxdt_truth = simulate.lorenz_x(duration=duration, dt=dt, outliers=False,\n",
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" noise_type=noise_type, noise_parameters=noise_parameters)\n",
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"\n",
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"# amplify signal\n",
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"gain = 4\n",
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"x_truth *= gain\n",
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"dxdt_truth *= gain\n",
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"\n",
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"# add noise\n",
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"x = simulate._add_noise(x_truth, random_seed, noise_type, noise_parameters)\n",
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"\n",
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"# wrap to [-pi, pi]\n",
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"x = (x + np.pi) % (2*np.pi) - np.pi\n",
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"x_truth = (x_truth + np.pi) % (2*np.pi) - np.pi\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a4ae1732",
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"metadata": {},
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"source": [
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"# Naive numerical differentiation (without considering wrapping)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "cfd04e33",
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"metadata": {},
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"outputs": [],
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"source": [
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"x_hat, dxdt_hat = pynumdiff.kalman_smooth.rtsdiff(x, dt, 1, 5, True, axis=0, circular=False)\n",
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"x_hat_wrapped = (x_hat + np.pi) % (2*np.pi) - np.pi\n",
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"\n",
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"evaluate.plot(x, dt, x_hat_wrapped, dxdt_hat, x_truth, dxdt_truth)\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e9a43fff",
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"metadata": {},
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"source": [
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"# Now with circular=True\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "17083a61",
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"metadata": {},
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"outputs": [],
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"source": [
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"x_hat, dxdt_hat = pynumdiff.kalman_smooth.rtsdiff(x, dt, 1, 3, True, axis=0, circular=True)\n",
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"x_hat_wrapped = (x_hat + np.pi) % (2*np.pi) - np.pi\n",
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"\n",
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"evaluate.plot(x, dt, x_hat_wrapped, dxdt_hat, x_truth, dxdt_truth)\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a49062c2",
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"metadata": {},
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"source": [
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"# Test multidimensional"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "baf0a4a0",
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"metadata": {},
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"outputs": [],
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"source": [
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"v, v_truth, dvdt_truth = simulate.triangle(duration=duration, dt=dt, outliers=False,\n",
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" noise_type=noise_type, noise_parameters=noise_parameters)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "9dc4418f",
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"metadata": {},
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"outputs": [],
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"source": [
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"X = np.vstack((x, v)).T\n",
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"print('Shape:', X.shape)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "67ffcb8c",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Differentiate circular and non-circular dimensions separately\n",
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"x_hat_col, dxdt_hat_col = pynumdiff.kalman_smooth.rtsdiff(X[:,0], dt, 1, 3, True, circular=True)\n",
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"v_hat_col, dvdt_hat_col = pynumdiff.kalman_smooth.rtsdiff(X[:,1], dt, 1, 3, True)\n",
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"\n",
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"x_hat_wrapped = (x_hat_col + np.pi) % (2*np.pi) - np.pi\n",
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"evaluate.plot(x, dt, x_hat_wrapped, dxdt_hat_col, x_truth, dxdt_truth)\n"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.13.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎notebooks/7_circular_variables.ipynb‎

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‎notebooks/README.md‎

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| [Automatic Method Suggestion](https://github.com/florisvb/PyNumDiff/blob/master/notebooks/3_automatic_method_suggestion.ipynb) | A short demo of how to allow `pynumdiff` to choose a differentiation method for your data. |
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| [Performance Analysis](https://github.com/florisvb/PyNumDiff/blob/master/notebooks/4_performance_analysis.ipynb) | Experiments to compare methods' accuracy and bias across simulations. |
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| [Robustness to Outliers Demo](https://github.com/florisvb/PyNumDiff/blob/master/notebooks/5_robust_outliers_demo.ipynb) | This notebook shows a head-to-head of `RTSDiff`'s and `RobustDiff`'s minimum-RMSE performances on simulations with outliers, to illustrate the value of using a Huber loss in the Kalman MAP problem. |
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| [Multidimensionality Demo](https://github.com/florisvb/PyNumDiff/blob/master/notebooks/6_multidimensionality_demo.ipynb) | Demonstration of differentating multidimensional data along particular axes. |
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| [Multidimensionality Demo](https://github.com/florisvb/PyNumDiff/blob/master/notebooks/6_multidimensionality_demo.ipynb) | Demonstration of differentating multidimensional data along particular axes. |
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| [Circular Domain](https://github.com/florisvb/PyNumDiff/blob/master/notebooks/7_circular_domain.ipynb) | Shows how using |

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