Operations on COO arrays


COO objects support a number of operations. They interact with scalars, Numpy arrays, other COO objects, and scipy.sparse.spmatrix objects, all following standard Python and Numpy conventions.

For example, the following Numpy expression produces equivalent results for both Numpy arrays, COO arrays, or a mix of the two:

np.log(X.dot(beta.T) + 1)

However some operations are not supported, like inplace operations, operations that implicitly cause dense structures, or numpy functions that are not yet implemented for sparse arrays

x += y     # inplace operations not supported
x + 1      # operations that produce dense results not supported
np.svd(x)  # sparse svd not implemented

This page describes those valid operations, and their limitations.


This function allows you to apply any arbitrary broadcasting function to any number of arguments where the arguments can be SparseArray objects or scipy.sparse.spmatrix objects. For example, the following will add two arrays:

sparse.elemwise(np.add, x, y)


Previously, elemwise was a method of the COO class. Now, it has been moved to the sparse module.


Operations that would result in dense matrices, such as binary operations with Numpy arrays objects or certain operations with scalars are not allowed and will raise a ValueError. For example, all of the following will raise a ValueError. Here, x and y are COO objects.

x == y
x + 5
x == 0
x != 5
x / y

However, all of the following are valid operations.

x + 0
x != y
x + y
x == 5
5 * x
x / 7.3
x != 0

If densification is needed, it must be explicit. In other words, you must call COO.todense on the COO object. If both operands are COO, both must be densified.


Previously, operations with Numpy arrays were sometimes supported. Now, it is necessary to convert Numpy arrays to COO objects.

Operations with scipy.sparse.spmatrix

Certain operations with scipy.sparse.spmatrix are also supported. For example, the following are all allowed if y is a scipy.sparse.spmatrix:

x + y
x - y
x * y
x > y
x < y

In general, if operating on a scipy.sparse.spmatrix is the same as operating on COO, as long as it is to the right of the operator.


Results are not guaranteed if x is a scipy.sparse.spmatrix. For this reason, we recommend that all Scipy sparse matrices should be explicitly converted to COO before any operations.


All binary operators support broadcasting. This means that (under certain conditions) you can perform binary operations on arrays with unequal shape. Namely, when the shape is missing a dimension, or when a dimension is 1. For example, performing a binary operation on two COO arrays with shapes (4,) and (5, 1) yields an object of shape (5, 4). The same happens with arrays of shape (1, 4) and (5, 1). However, (4, 1) and (5, 1) will raise a ValueError.

Full List of Operators

Here, x and y can be COO arrays, numpy.ndarray objects or scalars, keeping in mind auto densification rules. In addition, y can also be a scipy.sparse.spmatrix The following operators are supported:


In-place operators are not supported at this time.

Element-wise Operations

COO arrays support a variety of element-wise operations. However, as with operators, operations that map zero to a nonzero value are not supported.

To illustrate, the following are all possible, and will produce another COO array:


However, the following are all unsupported and will raise a ValueError:


Notice that you can apply any unary or binary numpy.ufunc to COO arrays, and numpy.ndarray objects and scalars and it will work so long as the result is not dense. When applying to numpy.ndarray objects, we check that operating on the array with zero would always produce a zero.


COO objects support a number of reductions. However, not all important reductions are currently implemented (help welcome!) All of the following currently work:

np.min(x, axis=(0, 2))


If you are performing multiple reductions along the same axes, it may be beneficial to call COO.enable_caching.


This method can take an arbitrary numpy.ufunc and performs a reduction using that method. For example, the following will perform a sum:

x.reduce(np.add, axis=1)


This library currently performs reductions by grouping together all coordinates along the supplied axes and reducing those. Then, if the number in a group is deficient, it reduces an extra time with zero. As a result, if reductions can change by adding multiple zeros to it, this method won’t be accurate. However, it works in most cases.

Partial List of Supported Reductions

Although any binary numpy.ufunc should work for reductions, when calling in the form x.reduction(), the following reductions are supported:


COO arrays can be indexed just like regular numpy.ndarray objects. They support integer, slice and boolean indexing. However, currently, numpy advanced indexing is not properly supported. This means that all of the following work like in Numpy, except that they will produce COO arrays rather than numpy.ndarray objects, and will produce scalars where expected. Assume that z.shape is (5, 6, 7)

z[1, 3]
z[1, 4, 3]
z[:3, :2, 3]
z[::-1, 1, 3]
z[[True, False, True, False, True], 3, 4]

All of the following will raise an IndexError, like in Numpy 1.13 and later.

z[3, 6]
z[1, 4, 8]
z[[True, True, False, True], 3, 4]


Numpy advanced indexing is currently not supported.

Other Operations

COO arrays support a number of other common operations. Among them are dot, tensordot, concatenate and stack, transpose and reshape. You can view the full list on the API reference page.