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: ```python 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](https://www.mathworks.com/help/curvefit/csaps.html) function that is an implementation of Fortran routine SMOOTH from [PGS](http://pages.cs.wisc.edu/~deboor/pgs/) (originally written by Carl de Boor). Also the algothithm implementation in other languages: * [csaps-rs](https://github.com/espdev/csaps-rs) Rust ndarray/sprs based implementation * [csaps-cpp](https://github.com/espdev/csaps-cpp) C++11 Eigen based implementation (incomplete) ## References C. de Boor, A Practical Guide to Splines, Springer-Verlag, 1978. ## License [MIT](https://choosealicense.com/licenses/mit/)