.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/mlearning/dimension_reduction/plot_pca_burgers.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_mlearning_dimension_reduction_plot_pca_burgers.py: PCA on Burgers equation ======================= Example using PCA on solutions of the Burgers equation. .. GENERATED FROM PYTHON SOURCE LINES 27-36 .. code-block:: default import matplotlib.pyplot as plt from gemseo.api import configure_logger from gemseo.mlearning.transform.dimension_reduction.pca import PCA from gemseo.problems.dataset.burgers import BurgersDataset from numpy import eye configure_logger() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 37-39 Load dataset ~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 39-46 .. code-block:: default dataset = BurgersDataset(n_samples=20) print(dataset) t = dataset.get_data_by_group(dataset.INPUT_GROUP)[:, 0] u_t = dataset.get_data_by_group(dataset.OUTPUT_GROUP) t_split = 0.87 .. rst-class:: sphx-glr-script-out Out: .. code-block:: none Burgers Number of samples: 20 Number of variables: 2 Variables names and sizes by group: inputs: t (1) outputs: u_t (501) Number of dimensions (total = 502) by group: inputs: 1 outputs: 501 .. GENERATED FROM PYTHON SOURCE LINES 47-49 Plot dataset ~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 49-73 .. code-block:: default def lines_gen(): """Linestyle generator.""" yield "-" for i in range(1, dataset.n_samples): yield 0, (i, 1, 1, 1) color = "red" lines = lines_gen() for i in range(dataset.n_samples): # Switch mode if discontinuity is gone if color == "red" and t[i] > t_split: color = "blue" lines = lines_gen() # reset linestyle generator plt.plot(u_t[i], color=color, linestyle=next(lines), label=f"t={t[i]:.2f}") plt.legend() plt.title("Solutions to Burgers equation") plt.show() .. image-sg:: /examples/mlearning/dimension_reduction/images/sphx_glr_plot_pca_burgers_001.png :alt: Solutions to Burgers equation :srcset: /examples/mlearning/dimension_reduction/images/sphx_glr_plot_pca_burgers_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 74-76 Create PCA ~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 76-86 .. code-block:: default n_components = 7 pca = PCA(n_components=n_components) pca.fit(u_t) means = u_t.mean(axis=1) # u_t = u_t - means[:, None] u_t_reduced = pca.transform(u_t) u_t_restored = pca.inverse_transform(u_t_reduced) .. GENERATED FROM PYTHON SOURCE LINES 87-89 Plot restored data ~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 89-107 .. code-block:: default color = "red" lines = lines_gen() for i in range(dataset.n_samples): # Switch mode if discontinuity is gone if color == "red" and t[i] > t_split: color = "blue" lines = lines_gen() # reset linestyle generator plt.plot( u_t_restored[i], color=color, # linestyle=next(lines), label=f"t={t[i]:.2f}", ) plt.legend() plt.title("Reconstructed solution after PCA reduction.") plt.show() .. image-sg:: /examples/mlearning/dimension_reduction/images/sphx_glr_plot_pca_burgers_002.png :alt: Reconstructed solution after PCA reduction. :srcset: /examples/mlearning/dimension_reduction/images/sphx_glr_plot_pca_burgers_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 108-110 Plot principal components ~~~~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 110-116 .. code-block:: default red_component = eye(n_components) components = pca.inverse_transform(red_component) for i in range(n_components): plt.plot(components[i]) plt.title("Principal components") plt.show() .. image-sg:: /examples/mlearning/dimension_reduction/images/sphx_glr_plot_pca_burgers_003.png :alt: Principal components :srcset: /examples/mlearning/dimension_reduction/images/sphx_glr_plot_pca_burgers_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.607 seconds) .. _sphx_glr_download_examples_mlearning_dimension_reduction_plot_pca_burgers.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_pca_burgers.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_pca_burgers.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_