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

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

• BLAS 1: All algorithms withstd::mdspan parameters perform a count ofstd::mdspan array accesses and arithmetic operations that arelinear in the maximum product of extents of anystd::mdspan parameter. These algorithms containvector operations such as dot products, norms, and vector addition.
• BLAS 2: All algorithms have general complexity inquadratic time. These algorithms containmatrix-vector operations such as matrix-vector multiplications and a solver of the triangular linear system.
• BLAS 3: All algorithms have general complexity incubic time. These algorithms containmatrix-matrix operations such as matrix-matrix multiplications and a solver of the multiple triangular linear systems.

[edit]Notes

[edit]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));}

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