CSAPS: Cubic spline approximation (smoothing)

csaps is a package for univariate, multivariate and nd-gridded data approximation using cubic smoothing splines.

Installation

Python 3.6 or above is supported.

pip install -U csaps

The module depends only on NumPy and SciPy.

Simple Examples

Here are a couple of examples of smoothing data.

An univariate data smoothing:

import numpy as np
import matplotlib.pyplot as plt

from csaps import csaps

np.random.seed(1234)

x = np.linspace(-5., 5., 25)
y = np.exp(-(x/2.5)**2) + (np.random.rand(25) - 0.2) * 0.3
xs = np.linspace(x[0], x[-1], 150)

ys = csaps(x, y, xs, smooth=0.85)

plt.plot(x, y, 'o', xs, ys, '-')
plt.show()

A surface data smoothing:

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

from csaps import csaps

np.random.seed(1234)
xdata = [np.linspace(-3, 3, 41), np.linspace(-3.5, 3.5, 31)]
i, j = np.meshgrid(*xdata, indexing='ij')
ydata = (3 * (1 - j)**2. * np.exp(-(j**2) - (i + 1)**2)
         - 10 * (j / 5 - j**3 - i**5) * np.exp(-j**2 - i**2)
         - 1 / 3 * np.exp(-(j + 1)**2 - i**2))
ydata = ydata + (np.random.randn(*ydata.shape) * 0.75)

ydata_s = csaps(xdata, ydata, xdata, smooth=0.988)

fig = plt.figure(figsize=(7, 4.5))
ax = fig.add_subplot(111, projection='3d')
ax.set_facecolor('none')
c = [s['color'] for s in plt.rcParams['axes.prop_cycle']]
ax.plot_wireframe(j, i, ydata, linewidths=0.5, color=c[0], alpha=0.5)
ax.scatter(j, i, ydata, s=10, c=c[0], alpha=0.5)
ax.plot_surface(j, i, ydata_s, color=c[1], linewidth=0, alpha=1.0)
ax.view_init(elev=9., azim=290)

plt.show()

Documentation

More examples of usage and the full documentation can be found at ReadTheDocs.

https://csaps.readthedocs.io

Testing

pytest, tox and Travis CI are used for testing. Please see tests.

Algorithms and implementations

csaps package is a Python modified port of MATLAB CSAPS function that is an implementation of Fortran routine SMOOTH from PGS (originally written by Carl de Boor).

csaps-cpp C++11 Eigen based implementation of the algorithm.

References

C. de Boor, A Practical Guide to Splines, Springer-Verlag, 1978.

License

MIT

Changelog

v0.9.0

• Drop support of Python 3.5
• weights, smooth and axis arguments in csaps function are keyword-only now
• UnivariateCubicSmoothingSpline and MultivariateCubicSmoothingSpline classes are deprecated and will be removed in 1.0.0 version. Use CubicSmoothingSpline instead.

v0.8.0

• Add csaps function that can be used as the main API
• Refactor the internal structure of the package
• Add the documentation

Attention

This is the last version that supports Python 3.5. The next versions will support Python 3.6 or above.

v0.7.0

• Add Generic-based type-hints and mypy-compatibility

v0.6.1

• A slight refactoring and extra data copies removing

v0.6.0

• Add "axis" parameter for univariate/multivariate cases

v0.5.0

• Reorganize the project to package-based structure
• Add the interface class for all smoothing spline classes

v0.4.2

• FIX: "smooth" value is 0.0 was not used

v0.4.1

• First PyPI release