mgplvm.fast_utils.linear_cg module

This file taken from GPytorch https://github.com/cornellius-gp/gpytorch/blob/c74b8ed8d590fcb1d79808d9ee7cde168588ef99/gpytorch/utils/linear_cg.py

With this License: MIT License

Copyright (c) 2017 Jake Gardner

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mgplvm.fast_utils.linear_cg.linear_cg(matmul_closure, rhs, n_tridiag=0, tolerance=0.01, eps=1e-10, stop_updating_after=1e-10, max_iter=1000, max_tridiag_iter=20, initial_guess=None, preconditioner=None, verbose=False)[source]

Implements the linear conjugate gradients method for (approximately) solving systems of the form

lhs result = rhs

for positive definite and symmetric matrices.

Args:

  • matmul_closure - a function which performs a left matrix multiplication with lhs_mat

  • rhs - the right-hand side of the equation

  • n_tridiag - returns a tridiagonalization of the first n_tridiag columns of rhs

  • tolerance - stop the solve when the max residual is less than this

  • eps - noise to add to prevent division by zero

  • stop_updating_after - will stop updating a vector after this residual norm is reached

  • max_iter - the maximum number of CG iterations

  • max_tridiag_iter - the maximum size of the tridiagonalization matrix

  • initial_guess - an initial guess at the solution result

  • precondition_closure - a functions which left-preconditions a supplied vector

Returns:

result - a solution to the system (if n_tridiag is 0) result, tridiags - a solution to the system, and corresponding tridiagonal matrices (if n_tridiag > 0)