.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_gallery/4-computation-tips/plot_sparse_inputs.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_gallery_4-computation-tips_plot_sparse_inputs.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_gallery_4-computation-tips_plot_sparse_inputs.py:


Sparse Inputs
=============
We sometimes meet with problems where the :math:`N × p` input matrix :math:`X` is extremely sparse, i.e.,
many entries in :math:`X` have zero values. A notable example comes from document classification: aiming to assign classes to a document,
making it easier to manage for publishers and news sites. The input variables for characterizing documents are generated from a so called "bag-of-words" model.
In this model, each variable is scored for the presence of each of the words in the entire dictionary under consideration.
Since most words are absent, the input variables for each document is mostly zero, and so the entire matrix is mostly zero.

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Example
^^^^^^^
We create a sparse matrix as our example:


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.. code-block:: Python

    from time import time
    from abess import LinearRegression
    from scipy.sparse import coo_matrix
    import numpy as np
    import matplotlib.pyplot as plt

    row = np.array([0, 1, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9])
    col = np.array([0, 3, 1, 2, 4, 3, 5, 2, 3, 1, 5, 2])
    data = np.array([4, 5, 7, 9, 1, 23, 4, 5, 6, 8, 77, 100])
    x = coo_matrix((data, (row, col)))








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And visualize the sparsity pattern via:

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.. code-block:: Python

    plt.spy(x)
    plt.show()




.. image-sg:: /auto_gallery/4-computation-tips/images/sphx_glr_plot_sparse_inputs_001.png
   :alt: plot sparse inputs
   :srcset: /auto_gallery/4-computation-tips/images/sphx_glr_plot_sparse_inputs_001.png
   :class: sphx-glr-single-img





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Usage: sparse matrix
^^^^^^^^^^^^^^^^^^^^
The sparse matrix can be directly used in ``abess`` pacakages. We just
need to set argument ``sparse_matrix = True``. Note that if the input
matrix is not sparse matrix, the program would automatically transfer it
into the sparse one, so this argument can also make some improvement.

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.. code-block:: Python



    coef = np.array([1, 1, 1, 0, 0, 0])
    y = x.dot(coef)
    model = LinearRegression()
    model.fit(x, y, sparse_matrix=True)

    print("real coef: \n", coef)
    print("pred coef: \n", model.coef_)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    real coef: 
     [1 1 1 0 0 0]
    pred coef: 
     [1. 1. 1. 0. 0. 0.]




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Sparse v.s. Dense: runtime comparsion
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
We compare the runtime under a larger sparse data:


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.. code-block:: Python

    from scipy.sparse import rand
    from numpy.random import default_rng

    rng = default_rng(12345)
    x = rand(1000, 200, density=0.01, format='coo', random_state=rng)
    coef = np.repeat([1, 0], 100)
    y = x.dot(coef)

    t = time()
    model.fit(x.toarray(), y)
    print("dense matrix:  ", time() - t)

    t = time()
    model.fit(x, y, sparse_matrix=True)
    print("sparse matrix:  ", time() - t)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    dense matrix:   0.263674259185791
    sparse matrix:   0.12428140640258789




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From the comparison, we see that the time required by sparse matrix is smaller,
and this sould be more visible when the sparse imput matrix is large.
Hence, we suggest to assign a sparse matrix to ``abess`` when the input matrix have a lot of zero entries.

The ``abess`` R package also supports sparse matrix. For R tutorial,
please view
https://abess-team.github.io/abess/articles/v09-fasterSetting.html


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

   **Total running time of the script:** (0 minutes 0.525 seconds)


.. _sphx_glr_download_auto_gallery_4-computation-tips_plot_sparse_inputs.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

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

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

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


.. only:: html

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

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