test-gradient-sample.cc

/* Checks if the descent direction is computed correctly using the
   analytic solution; also checks if the algorithm converges
   regardless of where it starts */

#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include <cassert>

#include <dune/common/shared_ptr.hh>

#include <dune/tectonic/ellipticenergy.hh>

#include "test-gradient-method-nicefunction.hh"
#include "test-gradient-method-helper.hh"

int main() {
  int const dim = 2;
  typedef Dune::EllipticEnergy<dim> Functional;
  typedef Functional::SmallMatrix SmallMatrix;
  typedef Functional::SmallVector SmallVector;

  SmallMatrix const A = { { 3, 1.5 }, { 1.5, 4 } };
  SmallVector const b = { 1, 2 };

  auto const f = Dune::make_shared<Dune::SampleFunction<2> const>();
  auto const phi = Dune::make_shared<Functional::NonlinearityType const>(f);
  Functional const J(A, b, phi);

  /*
    j(x)
    = Ax - b + 2/|x| x
    = 17*(6, 9.5) - (1, 2) + 2/sqrt(5) (1, 2)
    = (102 - 1 + 2/sqrt(5), 161.5 - 2 + 4/sqrt(5))
  */
  SmallVector analytic_descent = { -(102 - 1 + 2 / std::sqrt(5)),
                                   -(161.5 - 2 + 4 / std::sqrt(5)) };
  SmallVector numerical_descent;
  J.descentDirection(SmallVector({ 17, 34 }), numerical_descent);
  assert(two_distance<dim>(analytic_descent, numerical_descent) < 1e-10);

  double ret1;
  {
    SmallVector start = { 17, 34 };
    ret1 = functionTester(J, start, 8);
    SmallVector minimum;
    functionTester2(J, minimum, 8);
    assert(two_distance<dim>(start, minimum) < 1e-5);
  }

  double ret2;
  {
    // Something random
    SmallVector start = { 279, -96 };
    ret2 = functionTester(J, start, 10);
    SmallVector minimum;
    functionTester2(J, minimum, 10);
    assert(two_distance<dim>(start, minimum) < 1e-5);
  }
  assert(std::abs(ret1 - ret2) < 1e-5);

  double ret3;
  {
    SmallVector start = { 0, 0 };
    ret3 = functionTester(J, start, 3);
    SmallVector minimum;
    functionTester2(J, minimum, 3);
    assert(two_distance<dim>(start, minimum) < 1e-5);
  }
  assert(std::abs(ret1 - ret3) < 1e-5);
}