jax.lax.linalg.qdwh#

jax.lax.linalg.qdwh(x,*,is_hermitian=False,max_iterations=None,eps=None,dynamic_shape=None)[source]#

QR-based dynamically weighted Halley iteration for polar decomposition.

Parameters:

• x – A full-rank matrix, with shapeM x N. The matrix may be padded up tothat size from a smaller true shape (dynamic_shape).

• is_hermitian (bool) – True ifx is Hermitian. Default toFalse. This parameteris currently unused, but exists for backward compatibility.

• eps (float |None) – The final result will satisfy|x_k-x_k-1|<|x_k|*(4*eps)**(1/3) wherex_k is the iterate.

• max_iterations (int |None) – Iterations will terminate after this many steps even if theabove is unsatisfied.

• dynamic_shape (tuple[int,int]|None) – the unpadded shape as an(m,n) tuple; optional.

Returns:

A four-tuple of (u, h, num_iters, is_converged) containing thepolar decomposition ofx = u * h, the number of iterations to computeu,andis_converged, whose value isTrue when the convergence is achievedwithin the maximum number of iterations.