.. 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

    99 788.6863403320312
    199 536.3743896484375
    299 366.064453125
    399 250.9912567138672
    499 173.16134643554688
    599 120.4664535522461
    699 84.75176239013672
    799 60.51953887939453
    899 44.06025695800781
    999 32.86817169189453
    1099 25.249109268188477
    1199 20.056617736816406
    1299 16.5137939453125
    1399 14.093791007995605
    1499 12.438772201538086
    1599 11.305717468261719
    1699 10.529045104980469
    1799 9.996089935302734
    1899 9.629949569702148
    1999 9.378131866455078
    Result: y = 0.02004171721637249 + 0.8429091572761536 x + -0.0034575294703245163 x^2 + -0.09136295318603516 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  0.144 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>`_