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PyTorch – torch.linalg.solve() Method
To solve a square system of linear equations with unique solution, we could apply the torch.linalg.solve() method. This method takes two parameters −
first, the coefficient matrix A, and
second, the right-hand tensor b.
Where A is a square matrix and b is a vector. The solution is unique if A invertible. We can solve a number of systems of linear equations. In this case, A is a batch of square matrices and b is a batch of vectors.
Syntax
torch.linalg.solve(A, b)
Parameters
A – Square matrix or batch of square matrices. It is the coefficient matrix of system of linear equations.
b – Vector or a batch of vectors. It's the right-hand tensor of the linear system.
It returns a tensor of the solution of the system of linear equations.
Note − This method assumes that the coefficient matrix A is invertible. If it is not invertible, a Runtime Error will be raised.
Steps
We could use the following steps to solve a square system of linear equations.
Import the required library. In all the following examples, the required Python library is torch. Make sure you have already installed it.
import torch
Define a Coefficient matrix and the right-hand side tensor for the given square system of linear equations.
A = torch.tensor([[2., 3.],[1., -2.]]) b = torch.tensor([3., 0.])
Compute the unique solution using torch.linalg.solve(A,b). Coefficient matrix A must be invertible.
X = torch.linalg.solve(A, b)
Display the solution.
print("Solution:
", X)Check if the calculated solution is correct or not.
print(torch.allclose(A @ X, b)) # True for correct solution
Example 1
Take a look at the following example −
# import required library
import torch
'''
Let's suppose our square system of linear equations is:
2x + 3y = 3
x - 2y = 0
'''
print("Linear equation:")
print("2x + 3y = 3")
print("x - 2y = 0")
# define the coefficient matrix A
A = torch.tensor([[2., 3.],[1., -2.]])
# define right hand side tensor b
b = torch.tensor([3., 0.])
# Solve the linear equation
X = torch.linalg.solve(A, b)
# print the solution of above linear equation
print("Solution:
", X)
# check above solution to be true
print(torch.allclose(A @ X, b))Output
It will produce the following output −
Linear equation: 2x + 3y = 3 x - 2y = 0 Solution: tensor([0.8571, 0.4286]) True
Example 2
Let's take another example −
# import required library
import torch
# define the coefficient matrix A for a 3x3
# square system of linear equations
A = torch.randn(3,3)
# define right hand side tensor b
b = torch.randn(3)
# Solve the linear equation
X = torch.linalg.solve(A, b)
# print the solution of above linear equation
print("Solution:
", X)
# check above solution to be true
print(torch.allclose(A @ X, b))Output
It will produce the following output −
Solution: tensor([-0.2867, -0.9850, 0.9938]) True
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