---
layout: default
title: k-NN Painless extensions
nav_order: 4
parent: k-NN
has_children: false
has_math: true
---

# k-NN Painless Scripting extensions

With the k-NN plugin's Painless Scripting extensions, you can use k-NN distance functions directly in your Painless scripts to perform operations on `knn_vector` fields. Painless has a strict list of allowed functions and classes per context to ensure its scripts are secure. The k-NN plugin adds Painless Scripting extensions to a few of the distance functions used in [k-NN score script]({{site.url}}{{site.baseurl}}/search-plugins/knn/knn-score-script), so you can use them to customize your k-NN workload.

## Get started with k-NN's Painless Scripting functions

To use k-NN's Painless Scripting functions, first create an index with `knn_vector` fields like in [k-NN score script]({{site.url}}{{site.baseurl}}/search-plugins/knn/knn-score-script#getting-started-with-the-score-script-for-vectors). Once the index is created and you ingest some data, you can use the painless extensions:

```json
GET my-knn-index-2/_search
{
  "size": 2,
  "query": {
    "script_score": {
      "query": {
        "bool": {
          "filter": {
            "term": {
              "color": "BLUE"
            }
          }
        }
      },
      "script": {
        "source": "1.0 + cosineSimilarity(params.query_value, doc[params.field])",
        "params": {
          "field": "my_vector",
          "query_value": [9.9, 9.9]
        }
      }
    }
  }
}
```

`field` needs to map to a `knn_vector` field, and `query_value` needs to be a floating point array with the same dimension as `field`.

## Function types
The following table describes the available painless functions the k-NN plugin provides:

Function name | Function signature | Description
:--- | :---
l2Squared | `float l2Squared (float[] queryVector, doc['vector field'])` | This function calculates the square of the L2 distance (Euclidean distance) between a given query vector and document vectors. The shorter the distance, the more relevant the document is, so this example inverts the return value of the l2Squared function. If the document vector matches the query vector, the result is 0, so this example also adds 1 to the distance to avoid divide by zero errors.
l1Norm | `float l1Norm (float[] queryVector, doc['vector field'])` | This function calculates the square of the L2 distance (Euclidean distance) between a given query vector and document vectors. The shorter the distance, the more relevant the document is, so this example inverts the return value of the l2Squared function. If the document vector matches the query vector, the result is 0, so this example also adds 1 to the distance to avoid divide by zero errors.
cosineSimilarity | `float cosineSimilarity (float[] queryVector, doc['vector field'])` | Cosine similarity is an inner product of the query vector and document vector normalized to both have a length of 1. If the magnitude of the query vector doesn't change throughout the query, you can pass the magnitude of the query vector to improve performance, instead of calculating the magnitude every time for every filtered document:<br /> `float cosineSimilarity (float[] queryVector, doc['vector field'], float normQueryVector)` <br />In general, the range of cosine similarity is [-1, 1]. However, in the case of information retrieval, the cosine similarity of two documents ranges from 0 to 1 because the tf-idf statistic can't be negative. Therefore, the k-NN plugin adds 1.0 in order to always yield a positive cosine similarity score.

## Constraints

1. If a document’s `knn_vector` field has different dimensions than the query, the function throws an `IllegalArgumentException`.

2. If a vector field doesn't have a value, the function throws an <code>IllegalStateException</code>.

   You can avoid this situation by first checking if a document has a value in its field:

   ```
   "source": "doc[params.field].size() == 0 ? 0 : 1 / (1 + l2Squared(params.query_value, doc[params.field]))",
   ```

   Because scores can only be positive, this script ranks documents with vector fields higher than those without.
