In this article, we will discuss torch.linalg.solve() method in PyTorch.
Example:
Let's consider the linear equations : 6x + 3y = 1 3x - 4y = 2 Then M values can be - [[6,3],[3,-4]] and t is [1,2]
torch.linalg.solve() Function
The torch.linalg.solve() method is used to solve a square system of linear equations with a unique solution. It will take two parameters, in which the first parameter is a matrix that is a tensor and the second parameter is also a tensor with one dimension.
Syntax: torch.linalg.solve(M, t)
Parameters:
- M is an tensor matrix
- t is a tensor vector.
Return: It will return a tensor.
Example1:
In this example, we will Solve the linear equation – 6x + 3y = 1, 3x – 4y = 2 and check the solution is true or not. Here M is [[6,3],[3,-4]] and t [1,2]. After that we will apply torch.linalg.solve() method to return unique tensor solution. Finally we will use torch.allclose() method to check the equation is true or not.
Python3
# import torch import torch ''' Let's consider the linear equations : 6x + 3y = 1 3x - 4y = 2 Then M values can be - [[6,3],[3,-4]] and t is [1,2] ''' # consider M which is an 2 D tensor that # has 2 elements each M = torch.tensor([[6., 3.], [3., -4.]]) # consider t which is 1D that has two elements t = torch.tensor([1., 2.]) # Solve the equation using linalg.solve(M,t) solved = torch.linalg.solve(M, t) # display the solved solution print(solved) # check the solution is true or not using # allclose() method print(torch.allclose(M @ solved, t)) |
Output:
tensor([ 0.3030, -0.2727]) True
Example 2:
In this example, we will Solve the linear equation – 6x + 3y = 1,3x – 4y = 2 and check the solution is true or not. Here the elements of M is [[6,3],[3,-4]] and t is [0,2]. After that, we will apply torch.linalg.solve() method which will return a unique tensor solution. Finally, we will use a torch.allclose() method to check whether the equation is true or not.
Python3
# import torch import torch ''' Let's consider the linear equations : 5x - 3y = 0 3x - 4y = 2 Then M values can be - [[5,-3],[3,-4]] and t is [0,2] ''' # consider M which is an 2 D tensor that # has 2 elements each M = torch.tensor([[5., -3.], [3., -4.]]) # consider t which is an 1 D tensor that # has 2 elements t = torch.tensor([0., 2.]) # Solve the equation using linalg.solve(M,t) # method solved = torch.linalg.solve(M, t) # display the solved solution print(solved) # check the solution is true or not using # allclose() method print(torch.allclose(M @ solved, t)) |
Output:
tensor([-0.5455, -0.9091]) True
Example 3:
In this example, we will Solve the linear equation – 9x – y = 0, 3x – 4y = 0 and check the solution is true or not. Here the elements of M is [[9,-1],[3,-4]] and t [0,0]. After that, we will apply the torch.linalg.solve() method which will return a unique tensor solution, and last we will use a torch.allclose() method to check whether the equation is true or not.
Python3
# import torch import torch ''' Solve the linear equation - 9x - y = 0, 3x - 4y = 0 and check the solution is true or not Here the elements of M is - [[9,-1],[3,-4]] and t - [0,0]. ''' # consider M which is an 2 D tensor that # has 2 elements each M = torch.tensor([[9., -1.], [3., -4.]]) # consider t which is an 1 D tensor that # has 2 elements t = torch.tensor([0., 0.]) # Solve t using linalg.solve(M,t) method solved = torch.linalg.solve(M, t) # display the solved solution print(solved) # check the solution is true or not using # allclose() method print(torch.allclose(M @ solved, t)) |
Output:
tensor([0., -0.]) True
