.. 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

        :ref:`Go to the end <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 2729.919677734375
    199 1924.0516357421875
    299 1357.2864990234375
    399 958.5342407226562
    499 677.8916625976562
    599 480.30877685546875
    699 341.15966796875
    799 243.13400268554688
    899 174.05943298339844
    999 125.37262725830078
    1099 91.04769134521484
    1199 66.8423080444336
    1299 49.769351959228516
    1399 37.724700927734375
    1499 29.225833892822266
    1599 23.227773666381836
    1699 18.99394989013672
    1799 16.004974365234375
    1899 13.894484519958496
    1999 12.404093742370605
    Result: y = 0.06262663006782532 + 0.8657717704772949 x + -0.010804136283695698 x^2 + -0.09461496025323868 x^3






|

.. code-block:: Python


    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 0.214 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-jupyter

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

    .. 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-zip

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


.. only:: html

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

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