norm

→Tensor

norm(x: Tensor, ord: int | float | str | None = None, dim: int | list[int] | None = None, keepdim: bool = False)

source

Compute a vector or matrix norm.

Generic norm dispatcher that delegates to vector_norm or matrix_norm based on the input rank and reduction axes. The default behaviour computes the Frobenius norm of a matrix input and the Euclidean ( $\ell_2$ ) norm of a vector input:

\|x\|_2 \,=\, \Big(\sum_i |x_i|^2\Big)^{1/2}, \qquad \|A\|_F \,=\, \Big(\sum_{i,j} |A_{ij}|^2\Big)^{1/2}.

Parameters

xTensor

Input tensor. May be a vector (n,), a matrix (m, n), or higher-rank with explicit dim.

ord(int, float, str or None)= None

Order of the norm. Vector orders: 0, 1, 2 (default when None), inf, -inf, or any positive real. Matrix orders: "fro", "nuc", 1, -1, 2, -2, inf, -inf.

dimint, list of int or None= None

Reduction axis (or pair of axes for matrix norms). None reduces over all elements.

keepdimbool= False

If True, retains reduced dimensions with size 1.

Returns

Tensor

Norm value(s); shape depends on dim / keepdim.

Notes

Many norm orders (spectral, nuclear) require an SVD and therefore cost $O(\min(m,n) \cdot mn)$ ; entry-wise norms reduce in a single pass.

Examples

>>> import lucid
>>> from lucid.linalg import norm
>>> norm(lucid.tensor([3.0, 4.0]))
Tensor(5.0)