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kron

Kronecker product of 2 sparse arrays.

Parameters:

Name Type Description Default
a SparseArray, scipy.sparse.spmatrix, or np.ndarray

The arrays over which to compute the Kronecker product.

 required
b SparseArray, scipy.sparse.spmatrix, or np.ndarray

The arrays over which to compute the Kronecker product.

 required

Returns:

Name Type Description
res COO

The kronecker product

Raises:

Type Description
ValueError

If all arguments are dense or arguments have nonzero fill-values.

Examples:

>>> from sparse import eye
>>> a = eye(3, dtype="i8")
>>> b = np.array([1, 2, 3], dtype="i8")
>>> res = kron(a, b)
>>> res.todense()
array([[1, 2, 3, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 1, 2, 3, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 1, 2, 3]], dtype=int64)
Source code in sparse/numba_backend/_coo/common.py 
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def kron(a, b):
    """Kronecker product of 2 sparse arrays.

    Parameters
    ----------
    a, b : SparseArray, scipy.sparse.spmatrix, or np.ndarray
        The arrays over which to compute the Kronecker product.

    Returns
    -------
    res : COO
        The kronecker product

    Raises
    ------
    ValueError
        If all arguments are dense or arguments have nonzero fill-values.

    Examples
    --------
    >>> from sparse import eye
    >>> a = eye(3, dtype="i8")
    >>> b = np.array([1, 2, 3], dtype="i8")
    >>> res = kron(a, b)
    >>> res.todense()  # doctest: +SKIP
    array([[1, 2, 3, 0, 0, 0, 0, 0, 0],
           [0, 0, 0, 1, 2, 3, 0, 0, 0],
           [0, 0, 0, 0, 0, 0, 1, 2, 3]], dtype=int64)
    """
    from .._common import _is_sparse
    from .._umath import _cartesian_product
    from .core import COO

    check_zero_fill_value(a, b)

    a_sparse = _is_sparse(a)
    b_sparse = _is_sparse(b)
    a_ndim = np.ndim(a)
    b_ndim = np.ndim(b)

    if not (a_sparse or b_sparse):
        raise ValueError("Performing this operation would produce a dense result: kron")

    if a_ndim == 0 or b_ndim == 0:
        return a * b

    a = asCOO(a, check=False)
    b = asCOO(b, check=False)

    # Match dimensions
    max_dim = max(a.ndim, b.ndim)
    a = a.reshape((1,) * (max_dim - a.ndim) + a.shape)
    b = b.reshape((1,) * (max_dim - b.ndim) + b.shape)

    a_idx, b_idx = _cartesian_product(np.arange(a.nnz), np.arange(b.nnz))

    a_expanded_coords = a.coords[:, a_idx]
    b_expanded_coords = b.coords[:, b_idx]
    o_coords = a_expanded_coords * np.asarray(b.shape)[:, None] + b_expanded_coords
    o_data = a.data[a_idx] * b.data[b_idx]
    o_shape = tuple(i * j for i, j in zip(a.shape, b.shape, strict=True))

    return COO(o_coords, o_data, shape=o_shape, has_duplicates=False)