.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/05_regress/05_01_regress_module.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. or to run this example in your browser via JupyterLite or Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_05_regress_05_01_regress_module.py: Regress Module ============== We use the regress module to perform linear regression on a set of 1D points. .. GENERATED FROM PYTHON SOURCE LINES 13-15 Imports ------- .. GENERATED FROM PYTHON SOURCE LINES 15-22 .. code-block:: Python import numpy as np from matplotlib import pyplot as plt from splineops.regress.denoising import denoise_y from splineops.regress.sparsification import sparsest_interpolant, linear_spline .. GENERATED FROM PYTHON SOURCE LINES 23-27 Data Preparation ---------------- Create a dataset as (x,y) coordinates. .. GENERATED FROM PYTHON SOURCE LINES 27-84 .. code-block:: Python # Directly embedded data data = np.array([ [0.0107766212868331, 0.260227935166001], [0.0310564395737153, 0.124128829346261], [0.0568406178471921, -0.0319625924377939], [0.0624834663023982, -0.305487158118621], [0.0855836735802228, 0.0198584921896104], [0.111715185429166, 0.132374842819488], [0.139391914966393, 0.0346881909310438], [0.151220604385114, 0.225044726396834], [0.160372945787459, -0.0839333693634482], [0.196012653453612, 0.100524891786437], [0.20465948547682, 0.286553206119747], [0.236142103912376, -0.0969023194982265], [0.247757212881283, 0.344416030734225], [0.277270837091189, 0.322338105021903], [0.294942432854744, 0.628493233708394], [0.311124804679808, 0.238685146788896], [0.322729104513214, 0.0314182350548619], [0.341198353790244, 0.554001442697049], [0.362426869114815, 0.658491185386012], [0.380891037570895, 0.622866466731061], [0.402149882582122, 0.832680133314763], [0.424514186772157, 0.282871329344068], [0.454259779607654, 0.418961645149398], [0.471194339641083, 0.765569673816136], [0.480251119603182, 0.936269519087734], [0.50143948559379, 1.21690697362292], [0.539345526600005, 0.856785149480669], [0.551362009238399, 0.918563536364133], [0.56406586469322, 1.04369945227154], [0.585046514891406, 0.891659244596406], [0.614876517081502, 1.01020862285029], [0.623908589622186, 1.05646068606692], [0.651627178545465, 1.13455056187785], [0.679400399781766, 1.56682321923577], [0.696936576029801, 1.47238622944877], [0.704796955182952, 1.20492985044235], [0.729875394285375, 1.45329058102288], [0.752399114367628, 1.26394538858847], [0.776579617991004, 1.4052754431186], [0.783135827892922, 1.2534612824523], [0.800371524043548, 1.58782975330571], [0.821400442874384, 1.3740621261335], [0.849726902218741, 2.27247168443063], [0.872126589233067, 1.98304748773148], [0.89137702874173, 1.59274379691406], [0.906347248186443, 1.82991582958117], [0.939772323088249, 1.9344157693364], [0.951594904384916, 1.71570985938051], [0.967602823452471, 2.32573940626424], [0.991018964382358, 2.11540602201059] ]) x, y = data[:, 0], data[:, 1] .. GENERATED FROM PYTHON SOURCE LINES 85-89 Denoising --------- The function `denoise_y` applies a regularized least-squares method to smooth the noisy data. .. GENERATED FROM PYTHON SOURCE LINES 89-96 .. code-block:: Python # Regularization parameter lamb = 1e-2 # Compute denoised y y_denoised = denoise_y(x, y, lamb, rho=lamb) .. GENERATED FROM PYTHON SOURCE LINES 97-102 Sparsest Linear Regression -------------------------- The `sparsest_interpolant` function computes the sparsest set of knots that fit the denoised data. .. GENERATED FROM PYTHON SOURCE LINES 102-106 .. code-block:: Python # Compute sparsest linear spline that connects denoised data points knots, amplitudes, polynomial = sparsest_interpolant(x, y_denoised) .. GENERATED FROM PYTHON SOURCE LINES 107-111 Visualization ------------- The original, denoised, and sparsest spline solutions are plotted for comparison. .. GENERATED FROM PYTHON SOURCE LINES 111-125 .. code-block:: Python # Plot result margin = (x[-1]-x[0]) / 10 t_grid = np.concatenate(([x[0]-margin], knots, [x[-1]+margin])) fig = plt.figure() ax = plt.gca() ax.plot(x, y, 'x', label='Original data', markersize=10) if lamb > 0: ax.plot(x, y_denoised, 'x', label='Denoised data', markersize=10) ax.plot(t_grid, linear_spline(t_grid, knots, amplitudes, polynomial), label='Sparsest solution') if len(knots) > 0: ax.plot(knots, linear_spline(knots, knots, amplitudes, polynomial), 'o', label='Knots') ax.legend() plt.show() .. image-sg:: /auto_examples/05_regress/images/sphx_glr_05_01_regress_module_001.png :alt: 05 01 regress module :srcset: /auto_examples/05_regress/images/sphx_glr_05_01_regress_module_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.107 seconds) .. _sphx_glr_download_auto_examples_05_regress_05_01_regress_module.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/splineops/splineops.github.io/main?urlpath=lab/tree/notebooks_binder/auto_examples/05_regress/05_01_regress_module.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../../lite/lab/index.html?path=auto_examples/05_regress/05_01_regress_module.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: 05_01_regress_module.ipynb <05_01_regress_module.ipynb>` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: 05_01_regress_module.py <05_01_regress_module.py>` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: 05_01_regress_module.zip <05_01_regress_module.zip>` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_