Basic linear algebra algorithms (since C++26)

Basic linear algebra algorithms are based on the dense Basic Linear Algebra Subroutines (BLAS) which corresponds to a subset of the BLAS Standard. These algorithms that access the elements of arrays view those elements through std::mdspan

The BLAS algorithms are categorized into three sets of operations called levels, which generally correspond to the degree of the polynomial in the complexities of algorithms:

• BLAS 1: All algorithms with std::mdspan parameters perform a count of std::mdspan array accesses and arithmetic operations that are linear in the maximum product of extents of any std::mdspan parameter. These algorithms contain vector
• BLAS 2: All algorithms have general complexity in quadratic time. These algorithms contain matrix-vector
• BLAS 3: All algorithms have general complexity in cubic time. These algorithms contain matrix-matrix

Notes

Example

#include <cassert>
#include <cstddef>
#include <execution>
#include <linalg>
#include <mdspan>
#include <numeric>
#include <vector>
 
int main()
{
    std::vector<double> x_vec(42);
    std::ranges::iota(x_vec, 0.0);
 
    std::mdspan x(x_vec.data(), x_vec.size());
 
    // x[i] *= 2.0, executed sequentially
    std::linalg::scale(2.0, x);
 
    // x[i] *= 3.0, executed in parallel
    std::linalg::scale(std::execution::par_unseq, 3.0, x);
 
    for (std::size_t i{}; i != x.size(); ++i)
        assert(x[i] == 6.0 * static_cast<double>(i));
}

External links