interpax: Interpolation and Function Approximation with JAX

interpax provides several interpolation schemes across different dimensions:

• 1D, 2D, and 3D: Nearest neighbor, linear, and several cubic interpolation schemes.
• 1D and 2D: Fourier interpolation for periodic functions.

Planned features include spline interpolation for rectilinear grids in N-dimensions, RBF interpolation for unstructured data in N-dimensions, and smoothing splines for noisy data.

The testing suite uses pytest.

Run all unit tests:

pytest -m unit

Run specific tests by name:

pytest -k <substring>

Check test coverage: Use the --cov flag to report coverage. Detailed information is saved to a .coverage file. You can generate an HTML report using:

coverage html

This creates a htmlcov/ directory which can be viewed in a browser.

pytest -m unit
pytest -k foo
pytest --cov
coverage html

You can install the interpax library using pip to enable interpolation and function approximation using JAX.

pip install interpax

To contribute code, you should install the development dependencies and linting tools.

Install linting tools: Install the pinned version of ruff from the lint extra:

pip install -e ".[lint]"

Install pre-commit hooks: To automatically run checks during commits:

pip install pre-commit
pre-commit install

Install development dependencies: To install the full suite including pytest and other dev tools:

pip install -e ".[dev]"

Follow these rules for commit messages to maintain project history quality:

• Template: Use the provided .gitmessagetemplate. You can set it as your default with: git config commit.template .gitmessagetemplate
• Structure: Separate the subject line from the body with a single blank line.
• Subject Line:
  • Limit to 50 characters or less.
  • Capitalize the first letter.
  • Use the imperative mood (e.g., "Add feature" or "Fix issue", not "Added" or "Fixed").
• Body:
  • Wrap lines at 72 characters.
  • Explain what and why the change was made, rather than how (implementation details belong in the code).
  • Reference issues and pull requests (e.g., Resolves: #123).

Before suggesting an enhancement, please:

1. Check the official documentation to see if the feature already exists.
2. Search existing GitHub issues to see if it has already been suggested. If it has, comment on the existing issue instead of opening a new one.

If you proceed with a new suggestion, include:

• A clear, descriptive title.
• A step-by-step description of the suggested enhancement.
• Specific examples using Markdown code blocks.
• A description of current behavior vs. expected behavior.
• A justification of why this enhancement is useful.
• References to relevant physics papers if applicable.

The interpolation logic supports several methods, which determine how the function is reconstructed from the grid:

• nearest: Returns the value of the nearest grid point. Derivatives for this method are either zero or computed via a neighbor-search approach.
• linear: Performs multi-linear interpolation between grid points.
• Cubic Methods: A set of methods (defined in CUBIC_METHODS) that use higher-order polynomials. These require pre-computed or approximated derivatives (fx, fy, fz, fxy, etc.) to ensure smoothness.

Use interp1d to interpolate a 1D function. It requires the query points (xq), the sample points (xp), and the function values at the sample points (fp). You can specify the interpolation scheme using the method argument (e.g., "cubic").

import jax.numpy as jnp
import numpy as np
from interpax import interp1d

# Define sample points and function values
xp = jnp.linspace(0, 2 * np.pi, 100)
f = lambda x: jnp.sin(x)
fp = f(xp)

# Define query points
xq = jnp.linspace(0, 2 * np.pi, 10000)

# Perform cubic interpolation
fq = interp1d(xq, xp, fp, method="cubic")

# Verify results
np.testing.assert_allclose(fq, f(xq), rtol=1e-6, atol=1e-5)

If you prefer a functional approach rather than instantiating class objects, use the following functions:

• interpax.interp1d
• interpax.interp2d
• interpax.interp3d