.. 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.


.. 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  0.000 seconds)


.. _sphx_glr_download_beginner_examples_tensor_polynomial_tensor.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

     :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.readthedocs.io>`_