Construct Sparse Arrays

From coordinates and data

You can construct COO arrays from coordinates and value data.

The coords parameter contains the indices where the data is nonzero, and the data parameter contains the data corresponding to those indices. For example, the following code will generate a \(5 \times 5\) diagonal matrix:

>>> import sparse

>>> coords = [[0, 1, 2, 3, 4],
...           [0, 1, 2, 3, 4]]
>>> data = [10, 20, 30, 40, 50]
>>> s = sparse.COO(coords, data, shape=(5, 5))

>>> s.todense()
array([[10,  0,  0,  0,  0],
       [ 0, 20,  0,  0,  0],
       [ 0,  0, 30,  0,  0],
       [ 0,  0,  0, 40,  0],
       [ 0,  0,  0,  0, 50]])

In general coords should be a (ndim, nnz) shaped array. Each row of coords contains one dimension of the desired sparse array, and each column contains the index corresponding to that nonzero element. data contains the nonzero elements of the array corresponding to the indices in coords. Its shape should be (nnz,).

If data is the same across all the coordinates, it can be passed in as a scalar. For example, the following produces the \(4 \times 4\) identity matrix:

>>> import sparse

>>> coords = [[0, 1, 2, 3],
...           [0, 1, 2, 3]]
>>> data = 1
>>> s = sparse.COO(coords, data, shape=(4, 4))

You can, and should, pass in numpy.ndarray objects for coords and data.

In this case, the shape of the resulting array was determined from the maximum index in each dimension. If the array extends beyond the maximum index in coords, you should supply a shape explicitly. For example, if we did the following without the shape keyword argument, it would result in a \(4 \times 5\) matrix, but maybe we wanted one that was actually \(5 \times 5\).

coords = [[0, 3, 2, 1], [4, 1, 2, 0]]
data = [1, 4, 2, 1]
s = COO(coords, data, shape=(5, 5))

COO arrays support arbitrary fill values. Fill values are the “default” value, or value to not store. This can be given a value other than zero. For example, the following builds a (bad) representation of a \(2 \times 2\) identity matrix. Note that not all operations are supported for operations with nonzero fill values.

coords = [[0, 1], [1, 0]]
data = [0, 0]
s = COO(coords, data, fill_value=1)

From Scipy sparse matrices

To construct COO array from spmatrix objects, you can use the COO.from_scipy_sparse method. As an example, if x is a scipy.sparse.spmatrix, you can do the following to get an equivalent COO array:

s = COO.from_scipy_sparse(x)

From Numpy arrays

To construct COO arrays from numpy.ndarray objects, you can use the COO.from_numpy method. As an example, if x is a numpy.ndarray, you can do the following to get an equivalent COO array:

s = COO.from_numpy(x)

Generating random COO objects

The sparse.random method can be used to create random COO arrays. For example, the following will generate a \(10 \times 10\) matrix with \(10\) nonzero entries, each in the interval \([0, 1)\).

s = sparse.random((10, 10), density=0.1)

Building COO Arrays from DOK Arrays

It’s possible to build COO arrays from DOK arrays, if it is not easy to construct the coords and data in a simple way. DOK arrays provide a simple builder interface to build COO arrays, but at this time, they can do little else.

You can get started by defining the shape (and optionally, datatype) of the DOK array. If you do not specify a dtype, it is inferred from the value dictionary or is set to dtype('float64') if that is not present.

s = DOK((6, 5, 2))
s2 = DOK((2, 3, 4), dtype=np.uint8)

After this, you can build the array by assigning arrays or scalars to elements or slices of the original array. Broadcasting rules are followed.

s[1:3, 3:1:-1] = [[6, 5]]

DOK arrays also support fancy indexing assignment if and only if all dimensions are indexed.

s[[0, 2], [2, 1], [0, 1]] = 5
s[[0, 3], [0, 4], [0, 1]] = [1, 5]

Alongside indexing assignment and retrieval, DOK arrays support any arbitrary broadcasting function to any number of arguments where the arguments can be SparseArray objects, scipy.sparse.spmatrix objects, or numpy.ndarrays.

x = sparse.random((10, 10), 0.5, format="dok")
y = sparse.random((10, 10), 0.5, format="dok")
sparse.elemwise(np.add, x, y)

DOK arrays also support standard ufuncs and operators, including comparison operators, in combination with other objects implementing the numpy ndarray.__array_ufunc__ method. For example, the following code will perform elementwise equality comparison on the two arrays and return a new boolean DOK array.

x = sparse.random((10, 10), 0.5, format="dok")
y = np.random.random((10, 10))
x == y

DOK arrays are returned from elemwise functions and standard ufuncs if and only if all SparseArray objects are obj:DOK arrays. Otherwise, a COO array or dense array are returned.

At the end, you can convert the DOK array to a COO arrays.

s3 = COO(s)

In addition, it is possible to access single elements and slices of the DOK array using normal Numpy indexing, as well as fancy indexing if and only if all dimensions are indexed. Slicing and fancy indexing will always return a new DOK array.

s[1, 2, 1]  # 5
s[5, 1, 1]  # 0
s[[0, 3], [0, 4], [0, 1]] # <DOK: shape=(2,), dtype=float64, nnz=2, fill_value=0.0>

Converting COO objects to other Formats

COO arrays can be converted to Numpy arrays, or to some spmatrix subclasses via the following methods: