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komm.ProductLabeling

Cartesian product of labelings.

Parameters:

  • *labelings (Labeling) –

    The labelings to be combined. At least one labeling is required.

  • repeat (int) –

    Number of times to repeat the full sequence of labelings. Must be a positive integer. Has the same semantics as itertools.product. The default value is 1.

Examples:

>>> labeling1 = komm.Labeling([[0, 0], [1, 1], [1, 0], [0, 1]])
>>> labeling2 = komm.Labeling([[1], [0]])
>>> labeling = komm.ProductLabeling(labeling1, labeling2)
>>> labeling.matrix
array([[0, 0, 1],
       [0, 0, 0],
       [1, 1, 1],
       [1, 1, 0],
       [1, 0, 1],
       [1, 0, 0],
       [0, 1, 1],
       [0, 1, 0]])

>>> labeling = komm.ProductLabeling(
...    komm.Labeling([[1, 0], [1, 1], [0, 1], [0, 0]]),
...    repeat=2,
... )
>>> labeling.matrix
array([[1, 0, 1, 0],
       [1, 0, 1, 1],
       [1, 0, 0, 1],
       [1, 0, 0, 0],
       [1, 1, 1, 0],
       [1, 1, 1, 1],
       [1, 1, 0, 1],
       [1, 1, 0, 0],
       [0, 1, 1, 0],
       [0, 1, 1, 1],
       [0, 1, 0, 1],
       [0, 1, 0, 0],
       [0, 0, 1, 0],
       [0, 0, 1, 1],
       [0, 0, 0, 1],
       [0, 0, 0, 0]])

from_matrices() classmethod

Constructs a product labeling from labeling matrices.

Parameters:

  • *matrices (ArrayLike) –

    The labeling matrices. At least one matrix is required. See labeling documentation.

  • repeat (int) –

    Number of times to repeat the full sequence of matrices. Must be a positive integer. Has the same semantics as itertools.product. The default value is 1.

Examples:

>>> labeling = komm.ProductLabeling.from_matrices(
...     [[0, 0], [1, 1], [1, 0], [0, 1]],
...     [[1], [0]],
... )
>>> labeling.matrix
array([[0, 0, 1],
       [0, 0, 0],
       [1, 1, 1],
       [1, 1, 0],
       [1, 0, 1],
       [1, 0, 0],
       [0, 1, 1],
       [0, 1, 0]])

>>> labeling = komm.ProductLabeling.from_matrices(
...     [[1, 0], [1, 1], [0, 1], [0, 0]],
...     repeat=2,
... )
>>> labeling.matrix
array([[1, 0, 1, 0],
       [1, 0, 1, 1],
       [1, 0, 0, 1],
       [1, 0, 0, 0],
       [1, 1, 1, 0],
       [1, 1, 1, 1],
       [1, 1, 0, 1],
       [1, 1, 0, 0],
       [0, 1, 1, 0],
       [0, 1, 1, 1],
       [0, 1, 0, 1],
       [0, 1, 0, 0],
       [0, 0, 1, 0],
       [0, 0, 1, 1],
       [0, 0, 0, 1],
       [0, 0, 0, 0]])

matrix NDArray[integer] cached property

The labeling matrix $\mathbf{Q}$.

num_bits int property

The number $m$ of bits per index of the labeling.

Examples:

>>> labeling = komm.ProductLabeling.from_matrices(
...     [[0, 0], [1, 1], [1, 0], [0, 1]],
...     [[1], [0]],
... )
>>> labeling.num_bits
3

cardinality int property

The cardinality $2^m$ of the labeling.

Examples:

>>> labeling = komm.ProductLabeling.from_matrices(
...     [[0, 0], [1, 1], [1, 0], [0, 1]],
...     [[1], [0]],
... )
>>> labeling.cardinality
8

inverse_mapping dict[tuple[int, ...], int] cached property

The inverse mapping of the labeling. It is a dictionary that maps each binary tuple to the corresponding index.

Examples:

>>> labeling = komm.ProductLabeling.from_matrices(
...     [[0, 0], [1, 1], [1, 0], [0, 1]],
...     [[1], [0]],
... )
>>> labeling.inverse_mapping
{(0, 0, 1): 0,
 (0, 0, 0): 1,
 (1, 1, 1): 2,
 (1, 1, 0): 3,
 (1, 0, 1): 4,
 (1, 0, 0): 5,
 (0, 1, 1): 6,
 (0, 1, 0): 7}

indices_to_bits()

Returns the binary representation of the given indices.

Parameters:

  • indices (ArrayLike) –

    The indices to be converted to bits. Must be an array of integers in $[0:2^m)$.

Returns:

  • bits (NDArray[integer]) –

    The binary representations of the given indices. Has the same shape as indices, but with the last dimension expanded by a factor of $m$.

Examples:

>>> labeling = komm.ProductLabeling.from_matrices(
...     [[0, 0], [1, 1], [1, 0], [0, 1]],
...     [[1], [0]],
... )
>>> labeling.indices_to_bits([2, 0])
array([1, 1, 1, 0, 0, 1])

bits_to_indices()

Returns the indices corresponding to a given sequence of bits.

Parameters:

  • bits (ArrayLike) –

    The bits to be converted to indices. Must be an array with elements in $\mathbb{B}$ whose last dimension is a multiple $m$.

Returns:

  • indices (NDArray[integer]) –

    The indices corresponding to the given bits. Has the same shape as bits, but with the last dimension contracted by a factor of $m$.

Examples:

>>> labeling = komm.ProductLabeling.from_matrices(
...     [[0, 0], [1, 1], [1, 0], [0, 1]],
...     [[1], [0]],
... )
>>> labeling.bits_to_indices([1, 1, 1, 0, 0, 1])
array([2, 0])

marginalize()

Marginalize metrics over the bits of the labeling. The metrics may represent likelihoods or probabilities, for example. The marginalization is done by computing the L-values of the bits, which are defined as $$ L(\mathtt{b}_i) = \log \frac{\Pr[\mathtt{b}_i = 0]}{\Pr[\mathtt{b}_i = 1]}. $$

Parameters:

  • metrics (ArrayLike) –

    The metrics for each index of the labeling. Must be an array whose last dimension is a multiple of $2^m$.

Returns:

  • lvalues (NDArray[floating]) –

    The marginalized metrics over the bits of the labeling. Has the same shape as metrics, but with the last dimension changed by a factor of $m / 2^m$.