Supported operations¶

Arithmetics¶

Python scalars
numpy ndarray with dimensionality <2
broadcasting
mathematical operators (+, -, …)
numpy elementwise mathematical functions (sin, exp, …)

Indexing¶

sparsegrad has full support for indexing for reading arrays:

indexing by scalars, for example x[0] and x[-1]
indexing by slice, for example x[::-1]
indexing by arrays, for example x[np.arange(10)]

Setting individual elements in arrays should be replaced with summing sparse vectors.

dtype promotion¶

sparsegrad does not assume a specific dtype. It follows numpy dtype coercion rules.

Branching and control flow¶

Since sparsegrad does not reuse data between evaluations, arbitrary branching of execution is allowed through Python control flow statements such as if. sparsegrad objects implements all the comparison operators.

Branching at vector element level is supported through functions where and branch.

where is an equivalent of the standard numpy function, but it supports correctly sparsegrad objects. As the standard version, it has a disadvantage that both possible values must be evaluated for each element. In the case of expensive calculations, this is avoided by using branch function, which only evaluates used values.

Sparse vectors¶

sparsegrad provides functions for summing sparse vectors with derivative information.

Irregular memory access¶

Collecting values from non-sequential locations in memory, with optional summing, is supported through multiplication by sparse matrix (dot).

Writing values to non-sequential locations in memory, with optional summing, is supported through summing sparse vectors (sparsesum).

Calculation of sparsity pattern¶

Sparsity pattern is calculating using seed_sparsity.

Other functions¶

sparsegrad provides variants of standard functions that work for both numpy and sparsegrad values:

dot(A,x) : matrix - vector multiplication, where matrix A is constant
sum(x) : sum of elements of a vector x
hstack(vecs), stack(*vecs) : concatenation of vectors vecs