.. 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

        Click :ref:`here <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 1546.0365145892183
    199 1095.8992907857576
    299 777.6096767345516
    399 552.5352611528602
    499 393.3692169177716
    599 280.80664270842703
    699 201.19883404382793
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    1999 10.955552494109163
    Result: y = 0.04887728059779718 + 0.854335392917212 x + -0.008432144224579809 x^2 + -0.09298823470267067 x^3






|

.. code-block:: default

    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  0.345 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-python

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

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

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


.. only:: html

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

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