matrix_rank

→Tensor

matrix_rank(A: Tensor, tol: float | Tensor | None = None, hermitian: bool = False, atol: float | Tensor | None = None, rtol: float | Tensor | None = None)

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Compute the numerical rank of a matrix or a batch of matrices.

Counts singular values (or eigenvalue magnitudes when hermitian=True) above $\tau = \max(\text{atol},\, \sigma_{\max} \cdot \text{rtol})$ :

\mathrm{rank}(A) \,=\, |\{\,i : \sigma_i > \tau\,\}|.

Parameters

ATensor

Input matrix of shape (*, m, n).

tol(float, Tensor or None)= None

Alias for atol with rtol=0; mutually exclusive with atol/rtol.

hermitianbool= False

If True, use eigvalsh of the lower triangle instead of svdvals.

atol(float, Tensor or None, keyword - only)= None

Absolute tolerance (treated as 0.0 when None).

rtol(float, Tensor or None, keyword - only)= None

Relative tolerance; defaults to

\max(m, n) \cdot \varepsilon

unless atol > 0, in which case 0.0.

Returns

Tensor

int64 tensor of numerical ranks per matrix.

Examples

>>> import lucid
>>> from lucid.linalg import matrix_rank
>>> matrix_rank(lucid.tensor([[1.0, 2.0], [2.0, 4.0]]))
tensor(1, dtype=lucid.int64)