Cubic spline approximation (smoothing)
Project description
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 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
Changelog
v1.0.4 (04.05.2021)
- Bump numpy dependency version
v1.0.3 (01.01.2021)
- Bump scipy dependency version
- Bump sphinx dependency version and use m2r2 sphinx extension instead of m2r
- Add Python 3.9 to classifiers list and to Travis CI
- Set development status classifier to "5 - Production/Stable"
- Happy New Year!
v1.0.2 (19.07.2020)
- Fix using 'nu' argument when n-d grid spline evaluating #32
v1.0.1 (19.07.2020)
- Fix n-d grid spline evaluating performance regression #31
v1.0.0 (11.07.2020)
- Use
PPoly
andNdPPoly
base classes from SciPy interpolate module forSplinePPForm
andNdGridSplinePPForm
respectively. - Remove deprecated classes
UnivariateCubicSmoothingSpline
andMultivariateCubicSmoothingSpline
- Update the documentation
Notes
In this release the spline representation (the array of spline coefficients) has been changed
according to PPoly
/NdPPoly
.
See SciPy PPoly
and NdPPoly documentation for details.
v0.11.0 (28.03.2020)
- Internal re-design
SplinePPForm
andNdGridSplinePPForm
classes #17:- Remove
shape
andaxis
properties and reshaping data in these classes NdGridSplinePPForm
coefficients array for 1D grid now is 1-d instead of 2-d
- Remove
- Refactoring the code and decrease memory consumption
- Add
overload
type-hints forcsaps
function signatures
v0.10.1 (19.03.2020)
- Fix call of
numpy.pad
function for numpy <1.17 #15
v0.10.0 (18.02.2020)
- Significant performance improvements for make/evaluate splines and memory consumption optimization
- Change format for storing spline coefficients (reshape coeffs array) to improve performance
- Add shape property to
SplinePPForm
/NdGridSplinePPForm
and axis property toSplinePPForm
- Fix issues with the smoothing factor in nd-grid case: inverted ordering and unnable to use 0.0 value
- Update documentation
v0.9.0 (21.01.2020)
- Drop support of Python 3.5
weights
,smooth
andaxis
arguments incsaps
function are keyword-only nowUnivariateCubicSmoothingSpline
andMultivariateCubicSmoothingSpline
classes are deprecated and will be removed in 1.0.0 version. UseCubicSmoothingSpline
instead.
v0.8.0 (13.01.2020)
- 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 (19.09.2019)
- Add Generic-based type-hints and mypy-compatibility
v0.6.1 (13.09.2019)
- A slight refactoring and extra data copies removing
v0.6.0 (12.09.2019)
- Add "axis" parameter for univariate/multivariate cases
v0.5.0 (10.06.2019)
- Reorganize the project to package-based structure
- Add the interface class for all smoothing spline classes
v0.4.2 (07.09.2019)
- FIX: "smooth" value is 0.0 was not used
v0.4.1 (30.05.2019)
- First PyPI release
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