assignment operator of matrix views

[sarah-quinones]

the fact that the assignment operator of matrix views does a shallow copy may come as a surprise to some users who may be used to other linear algebra libraries. i took a look at pre-existing LA libraries and Eigen, Blaze, xtensor, boost::ublas and dlib all do deep assignment. so code like this

#include <cassert>
#include <linear_algebra.hpp>

auto main() -> int {
  std::math::dynamic_matrix<double> m(2, 2);
  m(0, 0) = 1;
  m.column(0) = m.column(1);
  assert(m(0, 0) == 0);
}

is typically expected to modify m, rather than just overwrite the view temporary. we could protect against this specific case by making the copy/move assignment lvalue qualified. which would lead to a compiler error instead of silently doing the wrong thing in this case. but i don't think this is good enough to solve the issue in general, as the same issue would arise in this case

template <typename U, typename V, typename T>
void multiply_by_factor(U &&out, V const &in, T factor) {
  if (factor != 1) { out = factor * in; }
  else { out = in; }
}

where this would fail only if U and V are both views of the same type, and factor is equal to 1, making this potentially difficult to debug.

on the other hand, having copy/move assignment do a deep copy would go against what other stl view types tend to do, as std::string_view and std::span do a shallow copy. and may also potentially inhibit some optimizations since the type would no longer be trivially copyable. so a vector<matrix_view> might be less efficient, but from my experience views tend to be short lived and so this shouldn't matter all that much.

another solution would be to avoid using operator= at all, since it holds a special meaning in c++ that doesn't fit with what a user would expect in all cases. maybe an assign member functions or something like operator<<= would work better, but the syntax would slightly suffer for it.