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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_beginner_examples_tensor_polynomial_numpy.py>`
        to download the full example code.

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

.. _sphx_glr_beginner_examples_tensor_polynomial_numpy.py:


Warm-up: numpy
--------------

A third order polynomial, trained to predict :math:`y=\sin(x)` from :math:`-\pi`
to :math:`pi` by minimizing squared Euclidean distance.

This implementation uses numpy to manually compute the forward pass, loss, and
backward pass.

A numpy array is a generic n-dimensional array; it does not know anything about
deep learning or gradients or computational graphs, and is just a way to perform
generic numeric computations.

.. GENERATED FROM PYTHON SOURCE LINES 16-54




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

 .. code-block:: none

    99 1118.942019966937
    199 756.1189056001887
    299 512.3342954198914
    399 348.39422979567036
    499 238.05166677725487
    599 163.71678510307976
    699 113.59274972286524
    799 79.76174043399425
    899 56.905187892025204
    999 41.447516098143375
    1099 30.982855992640406
    1199 23.890945305608916
    1299 19.07959380115159
    1399 15.81187729239062
    1499 13.590092677613795
    1599 12.07776570441537
    1699 11.047188727662363
    1799 10.344100328414365
    1899 9.863884086068648
    1999 9.535514667832281
    Result: y = -0.02116013723669262 + 0.8393866176952383 x + 0.0036504757795329367 x^2 + -0.09086190160242484 x^3






|

.. code-block:: Python

    import numpy as np
    import math

    # Create random input and output data
    x = np.linspace(-math.pi, math.pi, 2000)
    y = np.sin(x)

    # Randomly initialize weights
    a = np.random.randn()
    b = np.random.randn()
    c = np.random.randn()
    d = np.random.randn()

    learning_rate = 1e-6
    for t in range(2000):
        # Forward pass: compute predicted y
        # y = a + b x + c x^2 + d x^3
        y_pred = a + b * x + c * x ** 2 + d * x ** 3

        # Compute and print loss
        loss = np.square(y_pred - y).sum()
        if t % 100 == 99:
            print(t, loss)

        # Backprop to compute gradients of a, b, c, d with respect to loss
        grad_y_pred = 2.0 * (y_pred - y)
        grad_a = grad_y_pred.sum()
        grad_b = (grad_y_pred * x).sum()
        grad_c = (grad_y_pred * x ** 2).sum()
        grad_d = (grad_y_pred * x ** 3).sum()

        # Update weights
        a -= learning_rate * grad_a
        b -= learning_rate * grad_b
        c -= learning_rate * grad_c
        d -= learning_rate * grad_d

    print(f'Result: y = {a} + {b} x + {c} x^2 + {d} x^3')


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

   **Total running time of the script:** (0 minutes 0.236 seconds)


.. _sphx_glr_download_beginner_examples_tensor_polynomial_numpy.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: polynomial_numpy.zip <polynomial_numpy.zip>`


.. only:: html

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

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