# Exact Metric and Operator Matrix

This file is generated from `docs/user_guide/metric_operator_matrix.data`.
Run `scripts/generate-metric-operator-matrix.sh` after changing the source data.

Each row identifies the exact framework-free kernel, its SQL-facing operator or helper, and its score direction. Operators apply only to like representations.
Definitions and edge-case behavior are pinned in [Metric Semantics](metric_semantics.md).

| Representation | Metric | Exact core operator | SQL operator | Order for nearest-first search | Current SQL lifecycle |
|---|---|---|---|---|---|
| dense | L2 | `DistanceMetric::L2::distance` | `<->` | ascending distance | `stable` |
| dense | Inner product | `DistanceMetric::InnerProduct::distance` | `inner_product` helper | descending raw similarity | `stable` |
| dense | Negative inner product | `DistanceMetric::NegativeInnerProduct::distance` | `<#>` | ascending distance | `stable` |
| dense | Cosine distance | `DistanceMetric::Cosine::distance` | `<=>` | ascending distance | `stable` |
| dense | L1 | `DistanceMetric::L1::distance` | `<+>` | ascending distance | `stable` |
| half | L2 | `DistanceMetric::L2::distance_half` | `<->` | ascending distance | `experimental` |
| half | Inner product | `DistanceMetric::InnerProduct::distance_half` | `halfvec_inner_product` helper | descending raw similarity | `experimental` |
| half | Negative inner product | `DistanceMetric::NegativeInnerProduct::distance_half` | `<#>` | ascending distance | `experimental` |
| half | Cosine distance | `DistanceMetric::Cosine::distance_half` | `<=>` | ascending distance | `experimental` |
| half | L1 | `DistanceMetric::L1::distance_half` | `<+>` | ascending distance | `experimental` |
| sparse | L2 | `DistanceMetric::L2::distance_sparse` | `<->` | ascending distance | `experimental` |
| sparse | Inner product | `DistanceMetric::InnerProduct::distance_sparse` | `sparsevec_inner_product` helper | descending raw similarity | `experimental` |
| sparse | Negative inner product | `DistanceMetric::NegativeInnerProduct::distance_sparse` | `<#>` | ascending distance | `experimental` |
| sparse | Cosine distance | `DistanceMetric::Cosine::distance_sparse` | `<=>` | ascending distance | `experimental` |
| sparse | L1 | `DistanceMetric::L1::distance_sparse` | `<+>` | ascending distance | `experimental` |
| bit | Hamming | `BitVector::hamming_distance` | `<~>` | ascending distance | `experimental` |
| bit | Jaccard distance | `BitVector::jaccard_distance` | `<%>` | ascending distance | `experimental` |