# ott.geometry.geometry.Geometry.to_LRCGeometry#

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

Factorize the cost matrix 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
• rank (int) – Target rank of the cost_matrix.

• tol (float) – Tolerance of the error. The total number of sampled points is $$min(n, m,\frac{rank}{tol})$$.

• seed (int) – Random seed.

Return type

LRCGeometry

Returns

Low-rank geometry.