Linear Algebra

Factorization routines

• QR factorization

#include <ten/tensor>
#include <ten/io>
#include <ten/linalg>

int main() {
   auto a = ten::range<ten::matrix<float>>({4, 4});

   auto [q, r] = ten::linalg::qr(a);

   std::cout << q << std::endl;
   std::cout << r << std::endl;

   std::cout << (q * r).eval() << std::endl;
   std::cout << a << std::endl;
}

• LU factorization

#include <ten/tensor>
#include <ten/io>
#include <ten/linalg>

int main() {
   auto a = ten::range<ten::matrix<float>>({4, 4});

   auto [p, l, u] = ten::linalg::lu(a);

   std::cout << "PA = LU" << std::endl;
   ten::matrix<float> x = p * l * u;
   std::cout << x << std::endl;
   ::ten::matrix<float> v = a - x;
   std::cout << ten::all_close(v) << std::endl;
}

• Cholesky factorization

#include <ten/tensor>
#include <ten/io>
#include <ten/linalg>

int main() {

   ten::matrix<float> a({3, 3}, {4., 12., -16., 12., 37., -43.,
      -16., -43., 98.});

   auto [l, u] = ten::linalg::cholesky(a);

   std::cout << "LU" << std::endl;
   ten::matrix<float> lu = l * u;
   std::cout << lu << std::endl;

   ::ten::matrix<float> v = (l*u).eval() - a;
   std::cout << ten::all_close(v) << std::endl;
}

• SVD decomposition

#include <ten/tensor>
#include <ten/linalg>

int main() {

   ten::matrix<float> a({3, 3}, {4., 12., -16., 12., 37., -43.,
      -16., -43., 98.});

   auto [u, s, vt] = ten::linalg::svd(a);

   std::cout << u << std::endl;
   std::cout << s << std::endl;
   std::cout << vt << std::endl;
}