pdist

→Tensor

pdist(x: Tensor, p: float = 2.0)

source

Pairwise $L_p$ distances between rows of a 2-D tensor.

For an input of shape (N, M), returns the $N \cdot (N - 1) / 2$ strictly-upper-triangular pairwise distances in row-major order:

\mathrm{out}[k(i, j)] = \left( \sum_{m=1}^{M} | x_{i, m} - x_{j, m} |^p \right)^{1/p} \quad \text{for } 0 \le i < j < N

where k(i, j) enumerates pairs in row-major order.

Parameters

xTensor

2-D input of shape (N, M).

pfloat= 2.0

Exponent of the

L_p

norm. Common values: 2 for Euclidean (default), 1 for Manhattan, float("inf") for Chebyshev.

Returns

Tensor

1-D tensor of length $N (N - 1) / 2$ (empty when $N < 2$ ).

Notes

Internally computed by extracting the strict upper triangle of the full lucid.cdist matrix, which keeps the implementation simple and fully differentiable but is $O(N^2)$ in both compute and intermediate memory — for very large N, prefer a blocked / streaming pairwise routine.

Examples

>>> import lucid
>>> from lucid.nn.functional import pdist
>>> x = lucid.tensor([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]])
>>> pdist(x, p=2)
Tensor([1.0000, 1.0000, 1.4142])