# COO¶

class sparse.COO(coords, data=None, shape=None, has_duplicates=True, sorted=False, cache=False)[source]

A sparse multidimensional array.

This is stored in COO format. It depends on NumPy and Scipy.sparse for computation, but supports arrays of arbitrary dimension.

Parameters: coords (numpy.ndarray (COO.ndim, COO.nnz)) – An array holding the index locations of every value Should have shape (number of dimensions, number of non-zeros) data (numpy.ndarray (COO.nnz,)) – An array of Values shape (tuple[int] (COO.ndim,)) – The shape of the array. has_duplicates (bool, optional) – A value indicating whether the supplied value for coords has duplicates. Note that setting this to False when coords does have duplicates may result in undefined behaviour. See COO.sum_duplicates sorted (bool, optional) – A value indicating whether the values in coords are sorted. Note that setting this to False when coords isn’t sorted may result in undefined behaviour. See COO.sort_indices. cache (bool, optional) – Whether to enable cacheing for various operations. See COO.enable_caching
coords

numpy.ndarray (ndim, nnz) – An array holding the coordinates of every nonzero element.

data

numpy.ndarray (nnz,) – An array holding the values corresponding to COO.coords.

shape

tuple[int] (ndim,) – The dimensions of this array.

See also

DOK
A mostly write-only sparse array.

Examples

You can create COO objects from Numpy arrays.

>>> x = np.eye(4, dtype=np.uint8)
>>> x[2, 3] = 5
>>> s = COO.from_numpy(x)
>>> s
<COO: shape=(4, 4), dtype=uint8, nnz=5, sorted=True, duplicates=False>
>>> s.data
array([1, 1, 1, 5, 1], dtype=uint8)
>>> s.coords
array([[0, 1, 2, 2, 3],
[0, 1, 2, 3, 3]], dtype=uint8)


COO objects support basic arithmetic and binary operations.

>>> x2 = np.eye(4, dtype=np.uint8)
>>> x2[3, 2] = 5
>>> s2 = COO.from_numpy(x2)
>>> (s + s2).todense()
array([[2, 0, 0, 0],
[0, 2, 0, 0],
[0, 0, 2, 5],
[0, 0, 5, 2]], dtype=uint8)
>>> (s * s2).todense()
array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]], dtype=uint8)


Binary operations support broadcasting.

>>> x3 = np.zeros((4, 1), dtype=np.uint8)
>>> x3[2, 0] = 1
>>> s3 = COO.from_numpy(x3)
>>> (s * s3).todense()
array([[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 1, 5],
[0, 0, 0, 0]], dtype=uint8)


COO objects also support dot products and reductions.

>>> s.dot(s.T).sum(axis=0).todense()
array([ 1,  1, 31,  6], dtype=uint64)


You can use Numpy ufunc operations on COO arrays as well.

>>> np.sum(s, axis=1).todense()
array([1, 1, 6, 1], dtype=uint64)
>>> np.round(np.sqrt(s, dtype=np.float64), decimals=1).todense()
array([[ 1. ,  0. ,  0. ,  0. ],
[ 0. ,  1. ,  0. ,  0. ],
[ 0. ,  0. ,  1. ,  2.2],
[ 0. ,  0. ,  0. ,  1. ]])


Operations that will result in a dense array will raise a ValueError, such as the following.

>>> np.exp(s)
Traceback (most recent call last):
...
ValueError: Performing this operation would produce a dense result: <ufunc 'exp'>


You can also create COO arrays from coordinates and data.

>>> coords = [[0, 0, 0, 1, 1],
...           [0, 1, 2, 0, 3],
...           [0, 3, 2, 0, 1]]
>>> data = [1, 2, 3, 4, 5]
>>> s4 = COO(coords, data, shape=(3, 4, 5))
>>> s4
<COO: shape=(3, 4, 5), dtype=int64, nnz=5, sorted=False, duplicates=True>


Following scipy.sparse conventions you can also pass these as a tuple with rows and columns

>>> rows = [0, 1, 2, 3, 4]
>>> cols = [0, 0, 0, 1, 1]
>>> data = [10, 20, 30, 40, 50]
>>> z = COO((data, (rows, cols)))
>>> z.todense()
array([[10,  0],
[20,  0],
[30,  0],
[ 0, 40],
[ 0, 50]])


You can also pass a dictionary or iterable of index/value pairs. Repeated indices imply summation:

>>> d = {(0, 0, 0): 1, (1, 2, 3): 2, (1, 1, 0): 3}
>>> COO(d)
<COO: shape=(2, 3, 4), dtype=int64, nnz=3, sorted=False, duplicates=False>
>>> L = [((0, 0), 1),
...      ((1, 1), 2),
...      ((0, 0), 3)]
>>> COO(L).todense()
array([[4, 0],
[0, 2]])


You can convert DOK arrays to COO arrays.

>>> from sparse import DOK
>>> s5 = DOK((5, 5), dtype=np.int64)
>>> s5[1:3, 1:3] = [[4, 5], [6, 7]]
>>> s5
<DOK: shape=(5, 5), dtype=int64, nnz=4>
>>> s6 = COO(s5)
>>> s6
<COO: shape=(5, 5), dtype=int64, nnz=4, sorted=False, duplicates=False>
>>> s6.todense()
array([[0, 0, 0, 0, 0],
[0, 4, 5, 0, 0],
[0, 6, 7, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]])


Note

COO objects also support operators and indexing

Attributes

 COO.T Returns a new array which has the order of the axes reversed. COO.dtype The datatype of this array. COO.nbytes The number of bytes taken up by this object. COO.ndim The number of dimensions of this array. COO.nnz The number of nonzero elements in this array. COO.size The number of all elements (including zeros) in this array. COO.density The ratio of nonzero to all elements in this array.

Constructing COO objects

 COO.from_numpy(x) Convert the given numpy.ndarray to a COO object. COO.from_scipy_sparse(x) Construct a COO array from a scipy.sparse.spmatrix

Element-wise operations

 COO.astype(dtype[, out]) Copy of the array, cast to a specified type. COO.round([decimals, out]) Evenly round to the given number of decimals.

Reductions

 COO.reduce(method[, axis, keepdims]) Performs a reduction operation on this array. COO.sum([axis, keepdims, dtype, out]) Performs a sum operation along the given axes. COO.max([axis, keepdims, out]) Maximize along the given axes. COO.min([axis, keepdims, out]) Minimize along the given axes. COO.prod([axis, keepdims, dtype, out]) Performs a product operation along the given axes. COO.nanreduce(method[, identity, axis, keepdims]) Performs an NaN skipping reduction on this array.

Converting to other formats

 COO.todense() Convert this COO array to a dense numpy.ndarray. COO.maybe_densify([max_size, min_density]) Converts this COO array to a numpy.ndarray if not too costly. COO.to_scipy_sparse() Converts this COO object into a scipy.sparse.coo_matrix. COO.tocsc() Converts this array to a scipy.sparse.csc_matrix. COO.tocsr() Converts this array to a scipy.sparse.csr_matrix.

Other operations

 COO.dot(other) Performs the equivalent of x.dot(y) for COO. COO.reshape(shape) Returns a new COO array that is a reshaped version of this array. COO.transpose([axes]) Returns a new array which has the order of the axes switched.

Utility functions

 COO.broadcast_to(shape) Performs the equivalent of numpy.broadcast_to for COO. COO.enable_caching() Enable caching of reshape, transpose, and tocsr/csc operations COO.linear_loc([signed]) The nonzero coordinates of a flattened version of this array. COO.sort_indices() Sorts the COO.coords attribute. COO.sum_duplicates() Sums data corresponding to duplicates in COO.coords.