vector_norm

→Tensor

vector_norm(x: Tensor, ord: int | float = 2, dim: int | list[int] | None = None, keepdim: bool = False, dtype: object = None)

source

Compute a vector $p$ -norm along an axis.

Reduces along dim (or all elements if dim is None) using

\|x\|_p \,=\, \Big(\sum_i |x_i|^{\,p}\Big)^{1/p}

for any positive real $p$ . Special-cased values:

$p = 0$ — count of non-zero entries (not a true norm).
$p = 1$ — $\sum_i |x_i|$ .
$p = 2$ — Euclidean norm.
$p = +\infty$ — $\max_i |x_i|$ .
$p = -\infty$ — $\min_i |x_i|$ .

Parameters

xTensor

Input tensor.

ordint or float= 2

Order of the norm. Default 2.

dimint, list of int or None= None

Axis or axes to reduce. None flattens first.

keepdimbool= False

If True, reduced dimensions are retained with size 1.

dtypeoptional= None

Currently unused; reserved for future accumulation-dtype control.

Returns

Tensor

Norm along the specified axes.

Notes

All operations are routed through autograd-aware engine kernels, so gradients flow naturally even for non-integer $p$ (via $p$ -power and root).

Examples

>>> import lucid
>>> from lucid.linalg import vector_norm
>>> vector_norm(lucid.tensor([3.0, 4.0]))
Tensor(5.0)
>>> vector_norm(lucid.tensor([1.0, -2.0, 3.0]), ord=1)
Tensor(6.0)