GCXS objects support a number of operations. They interact with scalars,
Numpy arrays, other
scipy.sparse.spmatrix objects, all following standard Python and Numpy
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.
np.linalg.cholesky(x) # sparse cholesky 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)
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 x == 0 ~x x + 5
We also support operations with a nonzero fill value. These are operations
that map zero values to nonzero values, such as
x + 1 or
In these cases, they will produce an output with a fill value of
assuming the original array has a fill value of
Operations with NumPy arrays
In certain situations, operations with NumPy arrays are also supported. For example,
the following will work if
y is a NumPy array:
x * y
The following conditions must be met when performing element-wise operations with NumPy arrays:
The operation must produce a consistent fill-values. In other words, the resulting array must also be sparse.
Operating on the NumPy arrays must not increase the size when broadcasting the arrays.
x + y x - y x * y x > y x < y
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
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) np.exp(x) np.cos(x) np.log(x)
As above, in the last three cases, an array with a nonzero fill value will be produced.
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.
x.sum(axis=1) np.max(x) np.min(x, axis=(0, 2)) x.prod()
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.
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:
GCXS 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
SparseArray 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]
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]
Advanced indexing (indexing arrays with other arrays) is supported, but only for indexing
with a single array. Indexing a single array with multiple arrays is not supported at
this time. As above, if
(5, 6, 7), all of the following will
work like NumPy:
z[[0, 1, 2]] z[1, ] z[1, 4, [3, 6]] z[:3, :2, [1, 5]]
By default, when performing something like
np.array(COO), we allow the array
to be converted into a dense one. To prevent this and raise a
instead, set the environment variable
If it is desired to raise a warning if creating a sparse array that takes no less
memory than an equivalent desne array, set the environment variable