linear-operator

import torch from linear_operator.operators import LowRankRootLinearOperator, DiagLinearOperator # Example: Represent a 10000 x 10000 matrix A = C C^T + D # A is never explicitly instantiated as a dense matrix, saving memory C = torch.randn(10000, 20) # A "skinny" matrix (e.g., 10000x20) d = torch.randn(10000).abs() + 1e-6 # Diagonal elements (ensure positive) b = torch.randn(10000) A = LowRankRootLinearOperator(C) + DiagLinearOperator(d) # Perform a linear solve efficiently without instantiating the full dense matrix # This uses structure-exploiting algorithms like Woodbury formula under the hood x = torch.linalg.solve(A, b) print(f"Shape of A: {A.shape}") print(f"Shape of b: {b.shape}") print(f"Shape of x (solution): {x.shape}")