[role="xpack"]
[[vector-functions]]
===== Functions for vector fields

NOTE: During vector functions' calculation, all matched documents are
linearly scanned. Thus, expect the query time grow linearly
with the number of matched documents. For this reason, we recommend
to limit the number of matched documents with a `query` parameter.

This is the list of available vector functions and vector access methods:

1. <<vector-functions-cosine,`cosineSimilarity`>> – calculates cosine similarity
2. <<vector-functions-dot-product,`dotProduct`>> – calculates dot product
3. <<vector-functions-l1,`l1norm`>> – calculates L^1^ distance
4. <<vector-functions-l2,`l2norm`>> - calculates L^2^ distance
5. <<vector-functions-accessing-vectors,`doc[<field>].vectorValue`>> – returns a vector's value as an array of floats
6. <<vector-functions-accessing-vectors,`doc[<field>].magnitude`>> – returns a vector's magnitude

NOTE: The recommended way to access dense vectors is through the
`cosineSimilarity`, `dotProduct`, `l1norm` or `l2norm` functions. Please note
however, that you should call these functions only once per script. For example,
don’t use these functions in a loop to calculate the similarity between a
document vector and multiple other vectors. If you need that functionality,
reimplement these functions yourself by
<<vector-functions-accessing-vectors,accessing vector values directly>>.

Let's create an index with a `dense_vector` mapping and index a couple
of documents into it.

[source,console]
--------------------------------------------------
PUT my-index-000001
{
  "mappings": {
    "properties": {
      "my_dense_vector": {
        "type": "dense_vector",
        "dims": 3
      },
      "status" : {
        "type" : "keyword"
      }
    }
  }
}

PUT my-index-000001/_doc/1
{
  "my_dense_vector": [0.5, 10, 6],
  "status" : "published"
}

PUT my-index-000001/_doc/2
{
  "my_dense_vector": [-0.5, 10, 10],
  "status" : "published"
}

POST my-index-000001/_refresh

--------------------------------------------------
// TESTSETUP

[[vector-functions-cosine]]
====== Cosine similarity

The `cosineSimilarity` function calculates the measure of
cosine similarity between a given query vector and document vectors.

[source,console]
--------------------------------------------------
GET my-index-000001/_search
{
  "query": {
    "script_score": {
      "query" : {
        "bool" : {
          "filter" : {
            "term" : {
              "status" : "published" <1>
            }
          }
        }
      },
      "script": {
        "source": "cosineSimilarity(params.query_vector, 'my_dense_vector') + 1.0", <2>
        "params": {
          "query_vector": [4, 3.4, -0.2]  <3>
        }
      }
    }
  }
}
--------------------------------------------------

<1> To restrict the number of documents on which script score calculation is applied, provide a filter.
<2> The script adds 1.0 to the cosine similarity to prevent the score from being negative.
<3> To take advantage of the script optimizations, provide a query vector as a script parameter.

NOTE: If a document's dense vector field has a number of dimensions
different from the query's vector, an error will be thrown.

[[vector-functions-dot-product]]
====== Dot product

The `dotProduct` function calculates the measure of
dot product between a given query vector and document vectors.

[source,console]
--------------------------------------------------
GET my-index-000001/_search
{
  "query": {
    "script_score": {
      "query" : {
        "bool" : {
          "filter" : {
            "term" : {
              "status" : "published"
            }
          }
        }
      },
      "script": {
        "source": """
          double value = dotProduct(params.query_vector, 'my_dense_vector');
          return sigmoid(1, Math.E, -value); <1>
        """,
        "params": {
          "query_vector": [4, 3.4, -0.2]
        }
      }
    }
  }
}
--------------------------------------------------

<1> Using the standard sigmoid function prevents scores from being negative.

[[vector-functions-l1]]
====== L^1^ distance (Manhattan distance)

The `l1norm` function calculates L^1^ distance
(Manhattan distance) between a given query vector and
document vectors.

[source,console]
--------------------------------------------------
GET my-index-000001/_search
{
  "query": {
    "script_score": {
      "query" : {
        "bool" : {
          "filter" : {
            "term" : {
              "status" : "published"
            }
          }
        }
      },
      "script": {
        "source": "1 / (1 + l1norm(params.queryVector, 'my_dense_vector'))", <1>
        "params": {
          "queryVector": [4, 3.4, -0.2]
        }
      }
    }
  }
}
--------------------------------------------------

<1> Unlike `cosineSimilarity` that represent similarity, `l1norm` and
`l2norm` shown below represent distances or differences. This means, that
the more similar the vectors are, the lower the scores will be that are
produced by the `l1norm` and `l2norm` functions.
Thus, as we need more similar vectors to score higher,
we reversed the output from `l1norm` and `l2norm`. Also, to avoid
division by 0 when a document vector matches the query exactly,
we added `1` in the denominator.

[[vector-functions-l2]]
====== L^2^ distance (Euclidean distance)

The `l2norm` function calculates L^2^ distance
(Euclidean distance) between a given query vector and
document vectors.

[source,console]
--------------------------------------------------
GET my-index-000001/_search
{
  "query": {
    "script_score": {
      "query" : {
        "bool" : {
          "filter" : {
            "term" : {
              "status" : "published"
            }
          }
        }
      },
      "script": {
        "source": "1 / (1 + l2norm(params.queryVector, 'my_dense_vector'))",
        "params": {
          "queryVector": [4, 3.4, -0.2]
        }
      }
    }
  }
}
--------------------------------------------------

[[vector-functions-missing-values]]
====== Checking for missing values

If a document doesn't have a value for a vector field on which a vector function
is executed, an error will be thrown.

You can check if a document has a value for the field `my_vector` with
`doc['my_vector'].size() == 0`. Your overall script can look like this:

[source,js]
--------------------------------------------------
"source": "doc['my_vector'].size() == 0 ? 0 : cosineSimilarity(params.queryVector, 'my_vector')"
--------------------------------------------------
// NOTCONSOLE

[[vector-functions-accessing-vectors]]
====== Accessing vectors directly

You can access vector values directly through the following functions:

- `doc[<field>].vectorValue` – returns a vector's value as an array of floats

- `doc[<field>].magnitude` – returns a vector's magnitude as a float
(for vectors created prior to version 7.5 the magnitude is not stored.
So this function calculates it anew every time it is called).

For example, the script below implements a cosine similarity using these
two functions:

[source,console]
--------------------------------------------------
GET my-index-000001/_search
{
  "query": {
    "script_score": {
      "query" : {
        "bool" : {
          "filter" : {
            "term" : {
              "status" : "published"
            }
          }
        }
      },
      "script": {
        "source": """
          float[] v = doc['my_dense_vector'].vectorValue;
          float vm = doc['my_dense_vector'].magnitude;
          float dotProduct = 0;
          for (int i = 0; i < v.length; i++) {
            dotProduct += v[i] * params.queryVector[i];
          }
          return dotProduct / (vm * (float) params.queryVectorMag);
        """,
        "params": {
          "queryVector": [4, 3.4, -0.2],
          "queryVectorMag": 5.25357
        }
      }
    }
  }
}
--------------------------------------------------