How to Estimate the Gradient of a Function in One or More Dimensions in PyTorch?

How to Estimate the Gradient of a Function in One or More Dimensions in PyTorch?

PyTorch is a popular library for deep learning, but it can also be used for general-purpose automatic differentiation. If you want to estimate the gradient of a function in one or more dimensions using PyTorch, follow these steps:

  1. Import PyTorch:

    First, you need to import PyTorch:

    import torch

  2. Define Your Function:

    Define the function you wish to compute the gradient for.

    def my_function(x): return x**3 - 4*x**2 + x

  3. Create a Tensor with requires_grad=True:

    For a scalar function of a scalar variable:

    x = torch.tensor([2.0], requires_grad=True)

    For a function of multiple variables:

    x = torch.tensor([2.0, 3.0], requires_grad=True)

  4. Compute the Function and Backward Pass:

    y = my_function(x) y.backward() # Compute the gradient

  5. Access the Gradient:

    After calling .backward(), the gradient will be stored in the .grad attribute of the tensor.

    print(x.grad)

  6. Example in Multiple Dimensions:

    Let's say you have a function f(x,y)=x2y+y3. Here's how you can compute its gradient:

    def my_function_multivar(z): x, y = z return x**2 * y + y**3 z = torch.tensor([2.0, 3.0], requires_grad=True) y = my_function_multivar(z) y.backward() print(z.grad) # This will show gradient with respect to x and y

Keep in mind that y.backward() accumulates gradients in the .grad attribute. If you're computing gradients in a loop, you'll want to zero out the old values at the beginning of each loop iteration using x.grad.zero_().

Also note, y.backward() works directly like this because y is scalar. If y were to be a vector, you would need to provide an argument to backward() which is a vector of the same shape as y, specifying which scalar function of y you want the gradient of.

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