Boolean and equality

Kulczynski 1

kulczynski1_distances

all-pairspairedcondensedsingledistanceVectors

d=\frac{a}{b+c}

A legacy ratio rather than a conventional distance; equal nonempty supports may give infinity. For Boolean formulas a=c11, b=c10, c=c01, d=c00 and t=a+b+c+d. Optional w replaces counts by weight sums.

Shapes and Modes

Input	Layout
One sample	`[D]`
Collection X	`[...,N,D]`
Collection Y	`[...,M,D]`

Mode	Selector	Output
all-pairs	`compare(X,Y,metric=...)`	`[...,N,M]`
paired	`compare(X,Y,metric=...,mode="paired")`	`[...,N]`; equal sample counts
condensed	`compare(X,metric=...,mode="condensed")`	`[...,N*(N-1)//2]`; strict upper triangle
single	`compare(x,y,metric=...,mode="single")`	`[...]`; leading batches only

Leading batch dimensions broadcast. See mode and shape conventions.

Entry Points

Named Python entry	Function
All-pairs	`kulczynski1_distances`

The Python and C++ compare selectors cover every mode shown above. cdist / pairwise_distances and paired_distances select this comparison; pdist / condensed_distances select its condensed mode. single_comparison is shorthand for single mode.

Catalog aliases: kulczynski1.

Accepted metric options: w. Omitted options keep the metric defaults; unused options are rejected.

Example

Choose Python or C++ in the top bar; the setting applies across this guide.

Python

import torch
import torchpairwise as tp

X = torch.tensor([[True, False], [True, True]])  # [2,2]
Y = torch.tensor([[True, True], [False, True], [True, False]])

metric = "kulczynski1_distances"
all_pairs = tp.compare(X, Y, metric=metric)  # [2,3]
paired_Y = Y[:2]
paired = tp.compare(X, paired_Y, metric=metric, mode="paired")  # [2]
condensed = tp.compare(X, metric=metric, mode="condensed")      # [1]
x, y = X[0], Y[0]
single = tp.compare(x, y, metric=metric, mode="single")  # scalar

C++ / LibTorch

#include <torchpairwise.h>

namespace tp = torchpairwise::ops;
auto X = at::tensor({true, false, true, true}, at::kBool).reshape({2, 2});
auto Y = at::tensor({true, true, false, true, true, false}, at::kBool).reshape({3, 2});

const std::string metric = "kulczynski1_distances";
tp::ComparisonOptions options;
auto all_pairs = tp::compare(X, Y, metric, "all_pairs", options);  // [2,3]
auto paired_Y = Y.narrow(0, 0, 2);
auto paired = tp::compare(X, paired_Y, metric, "paired", options);  // [2]
// [1]
auto condensed = tp::compare(X, c10::nullopt, metric, "condensed", options);
auto x = X[0], y = Y[0];
auto single = tp::compare(x, y, metric, "single", options);  // scalar

Streamed Evaluation

tp.lazy(x, y, name) binds this distance for reductions, selection and products without retaining its full generated comparison matrix. Native source factories depend on the sample family; see streamed operators and C++ use.

Numerical Contract

Boolean/equality inputs do not have derivatives; feature weights may have derivatives for finite weighted formulas. See the detailed conventions and precision and deployment.

SciPy kulczynski1.

Related APIs can differ in reduction, normalization, units or boundary behavior; match these before comparing values.

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