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 3.6 or above is supported.
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 https://csaps.readthedocs.io.
Testing
pytest, tox and Travis CI are used for testing. Please see tests.
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.