Vector API

Utilities for manipulating vector data. Vectors can either be represented as dense (using array<numeric>) or sparse (using map<any_type, numeric>)

`mismo.vector.norm(vec: T, *, metric: Literal['l1', 'l2'] = 'l2') -> ir.FloatingValue`

Compute the norm (length) of a vector.

The vector can either be a dense vector, represented as array, or a sparse vector, represented as map.

PARAMETER	DESCRIPTION
`vec`	The vector to compute the norm of. TYPE: `T`
`metric`	The metric to use. "l1" for Manhattan distance, "l2" for Euclidean distance. TYPE: `('l1', 'l2')` DEFAULT: `"l1"`

RETURNS	DESCRIPTION
`The norm of the vector.`

Examples:

>>> import ibis
>>> from mismo.vector import norm
>>> v = ibis.array([-3, 4])
>>> norm(v).execute()
np.float64(5.0)
>>> m = ibis.map({"a": -3, "b": 4})
>>> norm(m, metric="l1").execute()
np.float64(7.0)

`mismo.vector.normalize(vec: T, *, metric: Literal['l1', 'l2'] = 'l2') -> T`

Normalize a vector to have unit length.

The vector can either be a dense vector, represented as array, or a sparse vector, represented as map. The returned vector will have the same type as the input vector.

PARAMETER	DESCRIPTION
`vec`	The vector to normalize. TYPE: `T`
`metric`	The metric to use. "l1" for Manhattan distance, "l2" for Euclidean distance. TYPE: `('l1', 'l2')` DEFAULT: `"l1"`

RETURNS	DESCRIPTION
`ArrayValue`	The normalized vector.

Examples:

>>> import ibis
>>> ibis.options.interactive = True
>>> from mismo.vector import normalize
>>> normalize(ibis.array([1, 2])).execute()
[0.4472135954999579, 0.8944271909999159]
>>> normalize(ibis.array([1, 2]), metric="l1").execute()
[0.3333333333333333, 0.6666666666666666]
>>> normalize(ibis.map({"a": 1, "b": 2})).execute()
{'a': 0.4472135954999579, 'b': 0.8944271909999159}

`mismo.vector.dot(a: T, b: T) -> ir.FloatingValue`

Compute the dot product of two vectors

The vectors can either be dense vectors, represented as array, or sparse vectors, represented as map. Both vectors must be of the same type though.

PARAMETER	DESCRIPTION
`a`	The first vector. TYPE: `T`
`b`	The second vector. TYPE: `T`

RETURNS	DESCRIPTION
`FloatingValue`	The dot product of the two vectors.

Examples:

>>> import ibis
>>> from mismo.vector import dot
>>> v1 = ibis.array([1, 2])
>>> v2 = ibis.array([4, 5])
>>> dot(v1, v2).execute()  # 1*4 + 2*5
np.float64(14.0)
>>> m1 = ibis.map({"a": 1, "b": 2})
>>> m2 = ibis.map({"b": 3, "c": 4})
>>> dot(m1, m2).execute() # 2*3
np.float64(6.0)

`mismo.vector.cosine_similarity(a: T, b: T) -> ir.FloatingValue`

Compute the cosine similarity of two vectors

The vectors can either be dense vectors, represented as array, or sparse vectors, represented as map. Both vectors must be of the same type though.

PARAMETER	DESCRIPTION
`a`	The first vector. TYPE: `T`
`b`	The second vector. TYPE: `T`

RETURNS	DESCRIPTION
`FloatingValue`	The cosine similarity of the two vectors.

Examples:

>>> import ibis
>>> from mismo.vector import cosine_similarity

Opposite directions:

>>> cosine_similarity(ibis.array([1, 1]), ibis.array([-2, -2])).execute()
-1.0

Orthogonal vectors:

>>> cosine_similarity(ibis.array([1, 0]), ibis.array([0, 1])).execute()
np.float64(0.0)

`mismo.vector.mul(a: T, b: T) -> T`

Element-wise multiplication of two vectors