svdvals

→Tensor

svdvals(x: Tensor)

source

Compute only the singular values of a matrix.

Returns the singular values $\sigma_1 \ge \cdots \ge \sigma_k \ge 0$ (with $k = \min(m, n)$ ) of an input matrix $A$ without forming $U$ or $V^\top$ . Equivalent to svd(A)[1] but avoids the work of constructing the singular vectors.

Parameters

xTensor

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

Returns

Tensor

Singular values in descending order, shape (*, k).

Notes

When gradients are required this routes through the full svd so backward still works. Without requires_grad, the engine kernel skips assembly of the singular vectors and is roughly $2\times$ faster. Useful for computing matrix_rank, cond, or the nuclear / spectral norms.

Examples

>>> import lucid
>>> from lucid.linalg import svdvals
>>> svdvals(lucid.tensor([[3.0, 0.0], [0.0, 4.0]]))
Tensor([4.0000, 3.0000])