What is the best way to create a sparse array in C++?

What is the best way to create a sparse array in C++?

"I am working on a project that requires the manipulation of enormous matrices, specifically pyramidal summation for a copula calculation.

In short, I need to keep track of a relatively small number of values (usually a value of 1, and in rare cases more than 1) in a sea of zeros in the matrix (multidimensional array).

A sparse array allows the user to store a small number of values, and assume all undefined records to be a preset value. Since it is not physically possibly to store all values in memory, I need to store only the few non-zero elements. This could be several million entries.

Speed is a huge priority, and I would also like to dynamically choose the number of variables in the class at runtime.

I currently work on a system that uses a binary search tree (b-tree) to store entries. Does anyone know of a better system?"

class triple { public: int x; int y; int z; bool operator<(const triple &other) const { if (x < other.x) return true; if (other.x < x) return false; if (y < other.y) return true; if (other.y < y) return false; return z < other.z; } };

int main(int, char**) { std::map<triple,int> data; triple point; int i;

for (i = 0; i < 10000000; ++i) { point.x = rand(); point.y = rand(); point.z = rand(); //printf(""%d %d %d %d\n"", i, point.x, point.y, point.z); data[point] = i; } return 0; }

Now to dynamically choose the number of variables, the easiest solution is to represent index as a string, and then use string as a key for the map. For instance, an item located at [23][55] can be represented via ""23,55"" string. We can also extend this solution for higher dimensions; such as for three dimensions an arbitrary index will look like ""34,45,56"". A simple implementation of this technique is as follows:

std::map data<string,int> data; char ix[100];

sprintf(ix, ""%d,%d"", x, y); // 2 vars data[ix] = i;

sprintf(ix, ""%d,%d,%d"", x, y, z); // 3 vars data[ix] = i;"

"The accepted answer recommends using strings to represent multi-dimensional indices.

However, constructing strings is needlessly wasteful for this. If the size isn’t known at compile time (and thus std::tuple doesn’t work), std::vector works well as an index, both with hash maps and ordered trees. For std::map, this is almost trivial:

#include <vector> #include <map>

using index_type = std::vector<int>;

template <typename T> using sparse_array = std::map<index_type, T>;

For std::unordered_map (or similar hash table-based dictionaries) it’s slightly more work, since std::vector does not specialise std::hash:

Eigen is a C++ linear algebra library that has an implementation of a sparse matrix. It even supports matrix operations and solvers (LU factorization etc) that are optimized for sparse matrices.