INNER_PRODUCT

Description

Computes the scalar product of two dense vectors represented by arrays, or two sparse vectors represented by maps. For sparse vectors, each map key identifies a dimension and its value is the coordinate. Only dimensions present in both maps contribute to the result.

Syntax

INNER_PRODUCT(<array1>, <array2>)
INNER_PRODUCT(<map1>, <map2>)

Parameters

Parameter	Description
<array1>	The first dense vector. Supported element types are TINYINT, SMALLINT, INT, BIGINT, LARGEINT, FLOAT, and DOUBLE. The number of elements must equal that of <array2>.
<array2>	The second dense vector. Supported element types are TINYINT, SMALLINT, INT, BIGINT, LARGEINT, FLOAT, and DOUBLE. The number of elements must equal that of <array1>.
<map1>	The first sparse vector. Its type must be MAP<K, FLOAT>, where K is an integer type (TINYINT, SMALLINT, INT, BIGINT, or LARGEINT) or a string type (CHAR, VARCHAR, or STRING). Its key type must be from the same type family as that of <map2>.
<map2>	The second sparse vector. It has the same type constraints as <map1>. The two maps can contain different numbers of entries.

Return Value

Returns the scalar product as a FLOAT.

For array inputs, corresponding elements are multiplied and summed. If either array is NULL, contains a NULL element, or the arrays have different lengths, the function returns an error.

For map inputs, values with the same key are multiplied and summed. A key that occurs in only one map has no effect, which is equivalent to treating the missing coordinate as zero. NULL keys match other NULL keys. If a key occurs more than once, its last value is used. If either map is NULL, or the value retained for any key is NULL, the function returns an error.

Example

SELECT INNER_PRODUCT([1, 2], [2, 3]),INNER_PRODUCT([3, 6], [4, 7]);

+-------------------------------+-------------------------------+
| inner_product([1, 2], [2, 3]) | inner_product([3, 6], [4, 7]) |
+-------------------------------+-------------------------------+
|                             8 |                            54 |
+-------------------------------+-------------------------------+

The following example computes the inner product of two sparse vectors. Only keys a and b occur in both maps, so the result is 2 * 5 + 3 * 4 = 22:

SELECT INNER_PRODUCT(
    MAP('a', CAST(2 AS FLOAT), 'b', CAST(3 AS FLOAT)),
    MAP('b', CAST(4 AS FLOAT), 'c', CAST(100 AS FLOAT), 'a', CAST(5 AS FLOAT))
) AS result;

+--------+
| result |
+--------+
|     22 |
+--------+

If an input array is NULL, the function returns an error:

SELECT INNER_PRODUCT(NULL, [1, 2]);

ERROR 1105 (HY000): errCode = 2, detailMessage = (127.0.0.1)[INVALID_ARGUMENT]First argument for function inner_product cannot be null

If an input array contains a NULL element, the function returns an error:

SELECT INNER_PRODUCT([1, NULL], [1, 2]);

ERROR 1105 (HY000): errCode = 2, detailMessage = (127.0.0.1)[INVALID_ARGUMENT]First argument for function inner_product cannot have null

If a map value is NULL, the function returns an error:

SELECT INNER_PRODUCT(
    MAP(1, CAST(NULL AS FLOAT)),
    MAP(1, CAST(2 AS FLOAT))
);

ERROR 1105 (HY000): errCode = 2, detailMessage = (127.0.0.1)[INVALID_ARGUMENT]First argument for function inner_product cannot have null