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 operations that implicitly cause dense structures, or numpy functions that are not yet implemented for sparse arrays.
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
For example, the following will add two arrays:
sparse.elemwise(np.add, x, y)
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
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
Previously, operations with Numpy arrays were sometimes supported. Now,
it is necessary to convert Numpy arrays to
x + y x - y x * y x > y x < y
In general, if operating on a
scipy.sparse.spmatrix is the same as operating
COO, as long as it is to the right of the operator.
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
COO arrays with shapes
(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
will raise a
Full List of Operators¶
Basic algebraic operations
While in-place operations are supported for compatibility with Numpy, they are not truly in-place, and will effectively calculate the result separately.
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
np.abs(x) np.sin(x) np.sqrt(x) np.conj(x) np.expm1(x) np.log1p(x)
However, the following are all unsupported and will raise a
np.exp(x) np.cos(x) np.log(x)
Notice that you can apply any unary or binary numpy.ufunc to
numpy.ndarray objects and scalars and it will work so
long as the result is not dense. When applying to
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
x.sum(axis=1) np.max(x) np.min(x, axis=(0, 2)) x.prod()
If you are performing multiple reductions along the same axes, it may
be beneficial to call
This method can take an arbitrary numpy.ufunc and performs a reduction using that method. For example, the following will perform a sum:
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.
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
(5, 6, 7)
z z[1, 3] z[1, 4, 3] z[:3, :2, 3] z[::-1, 1, 3] z[-1] z[[True, False, True, False, True], 3, 4]
All of the following will raise an
IndexError, like in Numpy 1.13 and later.
z z[3, 6] z[1, 4, 8] z[-6] z[[True, True, False, True], 3, 4]
Numpy advanced indexing is currently not supported.