.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/linear_model/plot_omp.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_linear_model_plot_omp.py>`
        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_linear_model_plot_omp.py:


===========================
Orthogonal Matching Pursuit
===========================

Using orthogonal matching pursuit for recovering a sparse signal from a noisy
measurement encoded with a dictionary

.. GENERATED FROM PYTHON SOURCE LINES 10-78



.. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_omp_001.png
   :alt: Sparse signal recovery with Orthogonal Matching Pursuit, Sparse signal, Recovered signal from noise-free measurements, Recovered signal from noisy measurements, Recovered signal from noisy measurements with CV
   :srcset: /auto_examples/linear_model/images/sphx_glr_plot_omp_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.datasets import make_sparse_coded_signal
    from sklearn.linear_model import OrthogonalMatchingPursuit, OrthogonalMatchingPursuitCV

    n_components, n_features = 512, 100
    n_nonzero_coefs = 17

    # generate the data

    # y = Xw
    # |x|_0 = n_nonzero_coefs

    y, X, w = make_sparse_coded_signal(
        n_samples=1,
        n_components=n_components,
        n_features=n_features,
        n_nonzero_coefs=n_nonzero_coefs,
        random_state=0,
    )
    X = X.T

    (idx,) = w.nonzero()

    # distort the clean signal
    y_noisy = y + 0.05 * np.random.randn(len(y))

    # plot the sparse signal
    plt.figure(figsize=(7, 7))
    plt.subplot(4, 1, 1)
    plt.xlim(0, 512)
    plt.title("Sparse signal")
    plt.stem(idx, w[idx])

    # plot the noise-free reconstruction
    omp = OrthogonalMatchingPursuit(n_nonzero_coefs=n_nonzero_coefs)
    omp.fit(X, y)
    coef = omp.coef_
    (idx_r,) = coef.nonzero()
    plt.subplot(4, 1, 2)
    plt.xlim(0, 512)
    plt.title("Recovered signal from noise-free measurements")
    plt.stem(idx_r, coef[idx_r])

    # plot the noisy reconstruction
    omp.fit(X, y_noisy)
    coef = omp.coef_
    (idx_r,) = coef.nonzero()
    plt.subplot(4, 1, 3)
    plt.xlim(0, 512)
    plt.title("Recovered signal from noisy measurements")
    plt.stem(idx_r, coef[idx_r])

    # plot the noisy reconstruction with number of non-zeros set by CV
    omp_cv = OrthogonalMatchingPursuitCV()
    omp_cv.fit(X, y_noisy)
    coef = omp_cv.coef_
    (idx_r,) = coef.nonzero()
    plt.subplot(4, 1, 4)
    plt.xlim(0, 512)
    plt.title("Recovered signal from noisy measurements with CV")
    plt.stem(idx_r, coef[idx_r])

    plt.subplots_adjust(0.06, 0.04, 0.94, 0.90, 0.20, 0.38)
    plt.suptitle("Sparse signal recovery with Orthogonal Matching Pursuit", fontsize=16)
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.182 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_omp.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/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/linear_model/plot_omp.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/?path=auto_examples/linear_model/plot_omp.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_omp.ipynb <plot_omp.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_omp.py <plot_omp.py>`


.. include:: plot_omp.recommendations


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_