diagonalize

Diagonalize a COO array. The new dimension is appended at the end.

Warning

sparse.diagonalize is not numpy compatible as there is no direct numpy equivalent. The API may change in the future.

Parameters:

Name	Type	Description	Default
a	Union[COO, ndarray, spmatrix]	The array to diagonalize.	required
axis	int	The axis to diagonalize. Defaults to first axis (0).	0

Examples:

>>> import sparse
>>> x = sparse.as_coo(np.arange(1, 4))
>>> sparse.diagonalize(x).todense()
array([[1, 0, 0],
       [0, 2, 0],
       [0, 0, 3]])

>>> x = sparse.as_coo(np.arange(24).reshape((2, 3, 4)))
>>> x_diag = sparse.diagonalize(x, axis=1)
>>> x_diag.shape
(2, 3, 4, 3)

sparse.diagonalize is the inverse of sparse.diagonal

>>> a = sparse.random((3, 3, 3, 3, 3), density=0.3)
>>> a_diag = sparse.diagonalize(a, axis=2)
>>> (sparse.diagonal(a_diag, axis1=2, axis2=5) == a.transpose([0, 1, 3, 4, 2])).all()
np.True_

Returns:

Name	Type	Description
out	COO	The result of the operation.

See Also

numpy.diag : NumPy equivalent for 1D array

Source code in sparse/numba_backend/_coo/common.py

def diagonalize(a, axis=0):
    """
    Diagonalize a COO array. The new dimension is appended at the end.

    !!! warning

        [`sparse.diagonalize`][] is not [numpy][] compatible as there is no direct [numpy][] equivalent. The
        API may change in the future.

    Parameters
    ----------
    a : Union[COO, np.ndarray, scipy.sparse.spmatrix]
        The array to diagonalize.
    axis : int, optional
        The axis to diagonalize. Defaults to first axis (0).

    Examples
    --------
    >>> import sparse
    >>> x = sparse.as_coo(np.arange(1, 4))
    >>> sparse.diagonalize(x).todense()
    array([[1, 0, 0],
           [0, 2, 0],
           [0, 0, 3]])

    >>> x = sparse.as_coo(np.arange(24).reshape((2, 3, 4)))
    >>> x_diag = sparse.diagonalize(x, axis=1)
    >>> x_diag.shape
    (2, 3, 4, 3)

    [`sparse.diagonalize`][] is the inverse of [`sparse.diagonal`][]

    >>> a = sparse.random((3, 3, 3, 3, 3), density=0.3)
    >>> a_diag = sparse.diagonalize(a, axis=2)
    >>> (sparse.diagonal(a_diag, axis1=2, axis2=5) == a.transpose([0, 1, 3, 4, 2])).all()
    np.True_

    Returns
    -------
    out: COO
        The result of the operation.

    See Also
    --------
    [`numpy.diag`][] : NumPy equivalent for 1D array
    """
    from .core import COO, as_coo

    a = as_coo(a)

    diag_shape = a.shape + (a.shape[axis],)
    diag_coords = np.vstack([a.coords, a.coords[axis]])

    return COO(diag_coords, a.data, diag_shape)