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

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In this article, we are going to see how to estimate the gradient of a function in one or more dimensions in PyTorch.

torch.gradient() function

torch.gradient() method estimates the gradient of a function in one or more dimensions using the second-order accurate central differences method, and the function can be defined on a real or complex domain. For controllers and optimizers, gradient estimations are quite valuable. Gradient descent is a prominent optimization method that requires an estimate of the output derivatives with respect to each input at a given location. Let’s have a look at the syntax of the given method first:

Syntax: torch.gradient(values)

Parameters:

values(Tensor): this parameter is represents the values of the function.

Example 1

In this example, we estimate the gradient of a function for a 1D tensor.

Python3

# Import required library 
import torch 
  
# define the tensor 
tens = torch.tensor([-2., 1., -3., 4., 5.]) 
print(" Input tensor: ", tens) 
  
# define a function 
def fun(tens): 
    return tens**2+5
  
# values of function 
values = fun(tens) 
  
# display values 
print(" Function Values: ", values) 
  
# estimate the gradients of fun 
grad = torch.gradient(values) 
  
# Display result 
print(" Estimated Gradients of fun() - ", grad) 

Output:

Example 2

In this example, we estimate the gradient of a function for a 2D tensor.

Python3

# Import required library 
import torch 
  
# define the tensor 
tens = torch.tensor([[-1., 3., -5.], 
                     [-4., 5.,  2.], 
                     [-2., 3.,  4.], ]) 
  
print("\n Input tensor: \n", tens) 
  
# define a function 
def fun(tens): 
    return tens**3
  
# values of function 
values = fun(tens) 
  
# display values 
print("\n Function Values: \n", values) 
  
# estimate the gradients of fun in dim=0 
grad_dim_0 = torch.gradient(values, dim=0) 
print("\n Estimated Gradients of fun() in dim=0 - \n", grad_dim_0) 
  
# estimate the gradients of fun in dim=1 
grad_dim_1 = torch.gradient(values, dim=1) 
print("\n Estimated Gradients of fun() in dim=1 - \n", grad_dim_1) 