Visual Examples

This page provides interactive visualizations of PyDelt’s differentiation capabilities across various scenarios.

1D Method Comparison

This visualization compares different PyDelt interpolation methods on a simple 1D function (sine wave with noise). Each method balances smoothness and accuracy differently, with GLLA providing the best overall performance.

Noise Robustness Comparison

This visualization demonstrates how different PyDelt methods perform with increasing levels of noise. LOWESS and LOESS show superior noise robustness, while GLLA maintains better accuracy at peaks.

Multivariate Derivatives

This visualization shows PyDelt’s capabilities for computing derivatives of multivariate functions. The example demonstrates gradient computation for a 2D scalar function, showing the original function, gradient magnitude, and partial derivatives.

Higher-Order Derivatives

This visualization demonstrates PyDelt’s ability to compute higher-order derivatives (up to 2nd order) with minimal error propagation. GLLA is particularly effective for higher-order derivatives.

Stochastic Process Differentiation

This visualization shows PyDelt’s application to stochastic processes, demonstrating drift estimation in an Ornstein-Uhlenbeck process. This capability is particularly useful for SDE parameter inference.

Generating Your Own Visualizations

The visualizations on this page were generated using the generate_visualizations.py script in the docs/_static directory. You can modify this script to create your own visualizations for your specific data.

# Example: Generate 1D method comparison visualization
from docs._static.generate_visualizations import generate_1d_comparison

# Generate and save the visualization
fig = generate_1d_comparison()

# Display the figure in a Jupyter notebook
from IPython.display import IFrame
IFrame('_static/images/method_comparison_1d.html', width=1000, height=800)