The sparse Matrices
A sparse matrix has the property that only nonzero elements are stored in the underlying data structure.
Sparse storage can be used to construct a Matrix, Vector, Array, or table. This page focuses on sparse rtables. For information on and examples of sparse tables, see indexfcn/sparse.
Ignoring semi-sparse rtable data structures like triangular[upper], and band, there are two sparse formats used by rtables.
The first is identical to the table format (indexfcn/sparse), and is only used when the datatype is a non-hardware type.
The second format is always used when the datatype is a hardware numeric type, and matches the format used by the NAG numerical algorithms. The NAG sparse format has N index vectors and one data vector for a N-dimensional Matrix. Thus, a 2-D sparse rtable with datatype=float will have two integer index vectors, v1, and v2, plus a vector of 64-bit hardware float data. If v1 = 1, and v2 = 2, then the index [1,2] will retrieve the element stored at the first position of the data vector.
M≔0000000000…0000000000…0000000000…0000000000…0000000000…0000000000…0000000000…0000000000…0000000000…0000000000…⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮1073741824 × 1073741824 Matrix
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