Python PyTorch – torch.linalg.solve() Function

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.

# 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.

# 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.

# 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