.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "beginner/examples_tensor/polynomial_tensor.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_tensor.py>`
        to download the full example code

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

.. _sphx_glr_beginner_examples_tensor_polynomial_tensor.py:


PyTorch: Tensors
----------------

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 PyTorch tensors to manually compute the forward pass,
loss, and backward pass.

A PyTorch Tensor is basically the same as a numpy array: it does not know
anything about deep learning or computational graphs or gradients, and is just
a generic n-dimensional array to be used for arbitrary numeric computation.

The biggest difference between a numpy array and a PyTorch Tensor is that
a PyTorch Tensor can run on either CPU or GPU. To run operations on the GPU,
just cast the Tensor to a cuda datatype.

.. GENERATED FROM PYTHON SOURCE LINES 20-64




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

 .. code-block:: none

    99 1384.2685546875
    199 934.1965942382812
    299 631.9491577148438
    399 428.8066711425781
    499 292.1564025878906
    599 200.1529998779297
    699 138.15284729003906
    799 96.3322982788086
    899 68.09615325927734
    999 49.01300811767578
    1099 36.102542877197266
    1199 27.359159469604492
    1299 21.43155860900879
    1399 17.408597946166992
    1499 14.675280570983887
    1599 12.816092491149902
    1699 11.550116539001465
    1799 10.687067031860352
    1899 10.09803581237793
    1999 9.695555686950684
    Result: y = 0.02316771261394024 + 0.8373154997825623 x + -0.003996816463768482 x^2 + -0.09056729823350906 x^3






|

.. code-block:: default


    import torch
    import math


    dtype = torch.float
    device = torch.device("cpu")
    # device = torch.device("cuda:0") # Uncomment this to run on GPU

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

    # Randomly initialize weights
    a = torch.randn((), device=device, dtype=dtype)
    b = torch.randn((), device=device, dtype=dtype)
    c = torch.randn((), device=device, dtype=dtype)
    d = torch.randn((), device=device, dtype=dtype)

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

        # Compute and print loss
        loss = (y_pred - y).pow(2).sum().item()
        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 using gradient descent
        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.item()} + {b.item()} x + {c.item()} x^2 + {d.item()} x^3')


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

   **Total running time of the script:** ( 0 minutes  0.218 seconds)


.. _sphx_glr_download_beginner_examples_tensor_polynomial_tensor.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_tensor.py <polynomial_tensor.py>`

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

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


.. only:: html

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

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