# ott.geometry.geometry.Geometry.to_LRCGeometry#

Geometry.to_LRCGeometry(rank=0, tol=0.01, seed=0, scale=1.0)[source]#

Factorize the cost matrix using either SVD (full) or .

When rank=min(n,m) or 0 (by default), use jax.numpy.linalg.svd().

For other values, use the routine in sublinear time . Uses the implementation of , algorithm 4.

It holds that with probability 0.99, $$||A - UV||_F^2 \leq || A - A_k ||_F^2 + tol \cdot ||A||_F^2$$, where $$A$$ is n x m cost matrix, $$UV$$ the factorization computed in sublinear time and $$A_k$$ the best rank-k approximation.

Parameters
Return type

LRCGeometry

Returns

Low-rank geometry.