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# PyTorch torch.lu_solve Function * * PyTorch torch Reference Manual](#) `torch.lu_solve` is a PyTorch function that uses LU decomposition to solve systems of linear equations. It leverages precomputed LU decomposition to efficiently solve AX = B. ### Function Definition torch.lu_solve(B, LU, pivots, out=None) **Parameters**: * `B` (Tensor): Right-hand side matrix or vector. * `LU` (Tensor): Matrix obtained from LU decomposition. * `pivots` (Tensor): Pivot indices from LU decomposition. * `out` (Tensor, optional): Output tensor. **Returns**: * `torch.Tensor`: Returns the solution to the system of linear equations. * * * ## Usage Example ## Example import torch # Create matrix and right-hand side vector A = torch.tensor([[1.0,2.0,3.0], [4.0,5.0,6.0], [7.0,8.0,9.0]], dtype=torch.float64) B = torch.tensor([14.0,32.0,50.0], dtype=torch.float64) # LU decomposition LU, pivots = torch.lu(A) # Use LU decomposition to solve X = torch.lu_solve(B, LU, pivots) print("Matrix A:") print(A) print("nRight-hand side vector B:") print(B) print("nSolution X:") print(X) print("nVerification: A @ X =") print(A @ X) Output: Matrix A: tensor([[1., 2., 3.], [4., 5., 6.], [7., 8., 9.]], dtype=torch.float64)Right-hand side vector B: tensor([14., 32., 50.], dtype=torch.float64)Solution X: tensor([1., 2., 3.], dtype=torch.float64)Verification: A @ X = tensor([14., 32., 50.], dtype=torch.float64) * * PyTorch torch Reference Manual](#)