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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_beginner_examples_autograd_polynomial_autograd.py>`
        to download the full example code

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

.. _sphx_glr_beginner_examples_autograd_polynomial_autograd.py:


PyTorch: Tensors and autograd
-------------------------------

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

This implementation computes the forward pass using operations on PyTorch
Tensors, and uses PyTorch autograd to compute gradients.


A PyTorch Tensor represents a node in a computational graph. If ``x`` is a
Tensor that has ``x.requires_grad=True`` then ``x.grad`` is another Tensor
holding the gradient of ``x`` with respect to some scalar value.

.. GENERATED FROM PYTHON SOURCE LINES 17-73

.. code-block:: default

    import torch
    import math

    dtype = torch.float
    device = "cuda" if torch.cuda.is_available() else "cpu"
    torch.set_default_device(device)

    # Create Tensors to hold input and outputs.
    # By default, requires_grad=False, which indicates that we do not need to
    # compute gradients with respect to these Tensors during the backward pass.
    x = torch.linspace(-math.pi, math.pi, 2000, dtype=dtype)
    y = torch.sin(x)

    # Create random Tensors for weights. For a third order polynomial, we need
    # 4 weights: y = a + b x + c x^2 + d x^3
    # Setting requires_grad=True indicates that we want to compute gradients with
    # respect to these Tensors during the backward pass.
    a = torch.randn((), dtype=dtype, requires_grad=True)
    b = torch.randn((), dtype=dtype, requires_grad=True)
    c = torch.randn((), dtype=dtype, requires_grad=True)
    d = torch.randn((), dtype=dtype, requires_grad=True)

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

        # Compute and print loss using operations on Tensors.
        # Now loss is a Tensor of shape (1,)
        # loss.item() gets the scalar value held in the loss.
        loss = (y_pred - y).pow(2).sum()
        if t % 100 == 99:
            print(t, loss.item())

        # Use autograd to compute the backward pass. This call will compute the
        # gradient of loss with respect to all Tensors with requires_grad=True.
        # After this call a.grad, b.grad. c.grad and d.grad will be Tensors holding
        # the gradient of the loss with respect to a, b, c, d respectively.
        loss.backward()

        # Manually update weights using gradient descent. Wrap in torch.no_grad()
        # because weights have requires_grad=True, but we don't need to track this
        # in autograd.
        with torch.no_grad():
            a -= learning_rate * a.grad
            b -= learning_rate * b.grad
            c -= learning_rate * c.grad
            d -= learning_rate * d.grad

            # Manually zero the gradients after updating weights
            a.grad = None
            b.grad = None
            c.grad = None
            d.grad = None

    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  0.000 seconds)


.. _sphx_glr_download_beginner_examples_autograd_polynomial_autograd.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_autograd.py <polynomial_autograd.py>`

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

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


.. only:: html

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

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