.. 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

    99 463.81201171875
    199 312.108154296875
    299 211.08497619628906
    399 143.78140258789062
    499 98.92195129394531
    599 69.00719451904297
    699 49.04833984375
    799 35.724693298339844
    899 26.82526397705078
    999 20.877582550048828
    1099 16.900102615356445
    1199 14.238385200500488
    1299 12.455989837646484
    1399 11.26158618927002
    1499 10.46059799194336
    1599 9.923055648803711
    1699 9.561992645263672
    1799 9.319270133972168
    1899 9.15597152709961
    1999 9.045997619628906
    Result: y = 0.009059899486601353 + 0.8446162343025208 x + -0.0015629848930984735 x^2 + -0.0916057676076889 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  0.327 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>`_