.. 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：张量(Tensors)
------------

一个三次多项式，通过最小化欧几里得距离的平方来训练预测从 :math:`-\pi` 到 :math:`\pi` 的 :math:`y=\sin(x)`。

该实现使用 PyTorch 张量手动计算前向传递、损失和反向传递。

PyTorch 张量基本上与 numpy 数组相同：它不了解深度学习、计算图或梯度，只是用于任意数值计算的通用n维数组。

numpy 数组和 PyTorch 张量之间最大的区别是， PyTorch 张量可以在 CPU 或 GPU 上运行。要在 GPU 上运行操作，只需将张量转换为 cuda 数据类型。

.. GENERATED FROM PYTHON SOURCE LINES 14-58

.. 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 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

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