minres#

deepinv.optim.utils.minres(A, b, init=None, max_iter=1e2, tol=1e-5, eps=1e-6, parallel_dim=0, verbose=False, precon=lambda x: ...)[source]#

Minimal Residual Method for solving symmetric equations.

Solves \(Ax=b\) with \(A\) symmetric using the MINRES algorithm:

Christopher C. Paige, Michael A. Saunders (1975). “Solution of sparse indefinite systems of linear equations”. SIAM Journal on Numerical Analysis. 12 (4): 617–629.

The method assumes that \(A\) is hermite. For more details see: https://en.wikipedia.org/wiki/Minimal_residual_method

Based on cornellius-gp/linear_operator Modifications and simplifications for compatibility with deepinverse

Parameters:

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

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

  • init (torch.Tensor) – Optional initial guess.

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

  • tol (float) – absolute tolerance for stopping the MINRES algorithm.

  • 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.

  • precon (Callable) – preconditioner is a callable function (not tested). Must be positive definite

Returns:

(torch.Tensor) \(x\) of shape (B, …)

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