This is a Python package for multivariate B-splines with performant NumPy and C (via Cython) implementations. For a mathematical overview of tensor product B-splines, see the Splines page of the documentation.
The primary goal of this package is to provide a unified API for tensor product splines of arbitrary input and output dimension. For a list of related packages see the Comparisons page.
Install ndsplines with pip:
$ pip install ndsplines
or from source:
$ git clone https://github.com/kb-press/ndsplines $ cd ndsplines $ pip install .
Note: If installing from source, to use the C implementation, install with the
build_ext feature (i.e.,
$ pip install .[build_ext]) or install Cython
$ pip install cython) before installing
ndsplines. The system
must have a C compiler configured before installing.
The easiest way to use
ndsplines is to use one of the
make_lsq_spline, which return an
NDSpline object which can be used to
evaluate the spline. For example, suppose we have data over a two-dimensional
import ndsplines import numpy as np # generate grid of independent variables x = np.array([-1, -7/8, -3/4, -1/2, -1/4, -1/8, 0, 1/8, 1/4, 1/2, 3/4, 7/8, 1])*np.pi y = np.array([-1, -1/2, 0, 1/2, 1]) meshx, meshy = np.meshgrid(x, y, indexing='ij') gridxy = np.stack((meshx, meshy), axis=-1) # evaluate a function to interpolate over input grid meshf = np.sin(meshx) * (meshy-3/8)**2 + 2
We can then use
make_interp_spline to create an interpolating spline and
evaluate it over a denser mesh.
# create the interpolating splane interp = ndsplines.make_interp_spline(gridxy, meshf) # generate denser grid of independent variables to interpolate sparse_dense = 2**7 xx = np.concatenate([np.linspace(x[i], x[i+1], sparse_dense) for i in range(x.size-1)]) yy = np.concatenate([np.linspace(y[i], y[i+1], sparse_dense) for i in range(y.size-1)]) gridxxyy = np.stack(np.meshgrid(xx, yy, indexing='ij'), axis=-1) # evaluate spline over denser grid meshff = interp(gridxxyy)
Generally, we construct data so that the first
ndim axes index the
independent variables and the remaining axes index output. This is
a generalization of using rows to index time and columns to index output
variables for time-series data.
We can also create an interpolating spline from a tidy data format:
tidy_data = np.dstack((gridxy, meshf)).reshape((-1,3)) tidy_interp = ndsplines.make_interp_spline_from_tidy( tidy_data, [0,1], # columns to use as independent variable data  # columns to use as dependent variable data ) print("\nCoefficients all same?", np.all(tidy_interp.coefficients == interp.coefficients)) print("Knots all same?", np.all([np.all(k0 == k1) for k0, k1 in zip(tidy_interp.knots, interp.knots)]))
Note however, that the tidy dataset must be over a structured rectangular grid equivalent to the N-dimensional tensor product representation. Also note that Pandas dataframes can be used, in which case lists of column names can be used instead of lists of column indices.
Derivatives of constructed splines can be evaluated in two ways: (1) by using
nus parameter while calling the interpolator or (2) by creating a new spline
derivative method. In this codeblock, we show both ways of
evaluating derivatives in each direction.
# two ways to evaluate derivatives x-direction: create a derivative spline or call with nus: deriv_interp = interp.derivative(0) deriv1 = deriv_interp(gridxxy) deriv2 = interp(gridxy, nus=np.array([1,0])) # two ways to evaluate derivative - y direction deriv_interp = interp.derivative(1) deriv1 = deriv_interp(gridxy) deriv2 = interp(gridxxyy, nus=np.array([0,1]))
NDSpline class also has an
antiderivative method for creating a
spline representative of the anti-derivative in the specified direction.
# Calculus demonstration interp1 = deriv_interp.antiderivative(0) coeff_diff = interp1.coefficients - interp.coefficients print("\nAntiderivative of derivative:\n","Coefficients differ by constant?", np.allclose(interp1.coefficients+2.0, interp.coefficients)) print("Knots all same?", np.all([np.all(k0 == k1) for k0, k1 in zip(interp1.knots, interp.knots)])) antideriv_interp = interp.antiderivative(0) interp2 = antideriv_interp.derivative(0) print("\nDerivative of antiderivative:\n","Coefficients the same?", np.allclose(interp2.coefficients, interp.coefficients)) print("Knots all same?", np.all([np.all(k0 == k1) for k0, k1 in zip(interp2.knots, interp.knots)]))
Please feel free to share any thoughts or opinions about the design and implementation of this software by opening an issue on GitHub. Constructive feedback is welcomed and appreciated.
Bug fix pull requests are always welcome. For feature additions, breaking changes, etc. check if there is an open issue discussing the change and reference it in the pull request. If there isn't one, it is recommended to open one with your rationale for the change before spending significant time preparing the pull request.
Ideally, new/changed functionality should come with tests and documentation. If you are new to contributing, it is perfectly fine to open a work-in-progress pull request and have it iteratively reviewed.
To test, install the developer requirements and use
$ pip install -r requirements-dev.txt $ pip install -e . $ pytest
To build the docs, install the
docs feature requirements (a subset of
the developer requirements above):
$ pip install -e .[docs] $ cd docs $ make html