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Cubic spline approximation (smoothing)

csaps.readthedocs.io

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MIT license

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.pre-commit-config.yaml		.pre-commit-config.yaml
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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

or Poetry:

poetry add csaps

The module depends only on NumPy and SciPy. Python 3.10 or above is supported.

Simple Examples

Here is a couple of examples of smoothing data.

An univariate data smoothing:

importnumpyasnpimportmatplotlib.pyplotaspltfromcsapsimportcsapsnp.random.seed(1234)x=np.linspace(-5.,5.,25)y=np.exp(-(x/2.5)**2)+ (np.random.rand(25)-0.2)*0.3xs=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:

importnumpyasnpimportmatplotlib.pyplotaspltfrommpl_toolkits.mplot3dimportAxes3Dfromcsapsimportcsapsnp.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']forsinplt.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 athttps://csaps.readthedocs.io.

Development

We use Poetry to manage the project:

git clone https://github.com/espdev/csaps.gitcd csapspoetry install -E docs

Also, install pre-commit hooks:

poetry run pre-commit install

Testing and Linting

We use pytest for testing and ruff/mypy for linting.Usepoethepoet to run tests and linters:

poetry run poe testpoetry run poe check

Algorithm and Implementation

csaps Python package is inspired by MATLABCSAPS function that is an implementation ofFortran routine SMOOTH fromPGS (originally written by Carl de Boor).

Also, the algothithm implementation in other languages: