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 representing vector or matrix.

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 operations such as dot products, norms, and vector addition.
• BLAS 2 : All algorithms have general complexity in quadratic time. These algorithms contain matrix-vector operations such as matrix-vector multiplications and a solver of the triangular linear system.
• BLAS 3 : All algorithms have general complexity in cubic time. These algorithms contain matrix-matrix operations such as matrix-matrix multiplications and a solver of the multiple triangular linear systems.

Notes

Example

#include <cassert>
#include <cstddef>
#include <execution>
#include <linalg>
#include <mdspan>
#include <numeric>
#include <vector>
 
int main()
{
    constexpr std::size_t N = 40;
    std::vector<double> x_vec(N);
    std::ranges::iota(x_vec, 0);
 
    std::mdspan x(x_vec.data(), N);
 
    // 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 != N; ++i)
        assert(x[i] == 6.0 * static_cast<double>(i));
}