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

    Click :ref:`here <sphx_glr_download_auto_examples_plot_jax_copt.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_plot_jax_copt.py:


Combining COPT with JAX
=======================

This example shows how `JAX <https://github.com/google/jax>`_
can be used within COPT to compute the gradients of the
objective function. 



.. image:: /auto_examples/images/sphx_glr_plot_jax_copt_001.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)





|


.. code-block:: default

    import jax
    from jax import numpy as np
    import numpy as onp
    import matplotlib.pyplot as plt
    from sklearn import datasets
    import copt as cp

    # .. construct (random) dataset ..
    import copt.penalty

    X, y = datasets.make_regression()
    n_samples, n_features = X.shape


    def loss(w):
        """Squared error loss."""
        z = np.dot(X, w) - y
        return np.sum(z * z) / n_samples


    # .. use JAX to compute the gradient of loss value_and_grad ..
    # .. returns both the gradient and the objective, which is ..
    # .. the format that COPT accepts ..
    f_grad = jax.value_and_grad(loss)

    w0 = onp.zeros(n_features)

    l1_ball = copt.penalty.L1Norm(0.1)
    cb = cp.utils.Trace(lambda x: loss(x) + l1_ball(x))
    sol = cp.minimize_proximal_gradient(
        f_grad, w0, prox=l1_ball.prox, callback=cb, jac=True
    )
    plt.plot(cb.trace_fx, lw=3)
    plt.yscale("log")
    plt.xlabel("# Iterations")
    plt.ylabel("Objective value")
    plt.grid()
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  9.940 seconds)

**Estimated memory usage:**  78 MB


.. _sphx_glr_download_auto_examples_plot_jax_copt.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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