csaps

csaps is a Python package for univariate, multivariate and n-dimensional grid data approximation using cubic smoothing splines. The package can be useful in practical engineering tasks for data approximation and smoothing.

Installing

Use pip for installing:

pip install -U csaps

The module depends only on NumPy and SciPy. Python 3.9 or above is supported.

Simple Examples

Here is 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 https://csaps.readthedocs.io.

Testing

We use pytest for testing.

cd /path/to/csaps/project/directory
pip install -e .[tests]
pytest

Algorithm and Implementation

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

Also the algothithm implementation in other languages:

• csaps-rs Rust ndarray/sprs based implementation
• csaps-cpp C++11 Eigen based implementation (incomplete)

References

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

License

MIT