lsqr

deepinv.optim.utils.lsqr(A, AT, b, eta=0.0, x0=None, tol=1e-6, conlim=1e8, max_iter=100, parallel_dim=0, verbose=False, **kwargs)

LSQR algorithm for solving linear systems.

Code adapted from SciPy’s implementation of LSQR: scipy/scipy

The function solves the linear system \(\min_x \|Ax-b\|^2 + \eta \|x-x_0\|^2\) in the least squares sense using the LSQR algorithm from

Paige, C. C. and M. A. Saunders, “LSQR: An Algorithm for Sparse Linear Equations And Sparse Least Squares,” ACM Trans. Math. Soft., Vol.8, 1982, pp. 43-71.

Parameters:

• A (Callable) – Linear operator as a callable function.

• AT (Callable) – Adjoint operator as a callable function.

• b (torch.Tensor) – input tensor of shape (B, …)

• eta (float) – damping parameter \(eta \geq 0\).

• x0 (None, torch.Tensor) – Optional \(x_0\), which is also used as the initial guess.

• tol (float) – relative tolerance for stopping the LSQR algorithm.

• conlim (float) – maximum value of the condition number of the system.

• max_iter (int) – maximum number of LSQR iterations.

• parallel_dim (None, int, List[int]) – dimensions to be considered as batch dimensions. If None, all dimensions are considered as batch dimensions.

• verbose (bool) – Output progress information in the console.

Retrun:

(torch.Tensor) \(x\) of shape (B, …), (torch.Tensor) condition number of the system.