tensorplay.linalg.matrix_rank

tensorplay.linalg.matrix_rank(A, *, atol=None, rtol=None, hermitian=False)[source]

Computes the numerical rank of each matrix in A.

A singular value counts towards the rank when it exceeds the sum of an absolute tolerance and a relative tolerance scaled by the largest singular value of its matrix.

Parameters:

• A (Tensor) – tensor of shape (..., m, n) holding the matrices.

• atol (float, Tensor, optional) – absolute threshold applied to the singular values. Defaults to 0.

• rtol (float, Tensor, optional) – relative threshold applied to the largest singular value. Defaults to max(m, n) times the machine epsilon of A’s dtype.

• hermitian (bool) – when True, A is treated as Hermitian and its rank is derived from eigenvalues instead of singular values.

Returns:

integer tensor with the rank of each matrix, with the batch dimensions of A.

Return type:

Tensor