Commit 559f4eff authored by Oliver Sander's avatar Oliver Sander
Browse files

Implement a test for positive 1-homogeneity

Functionals do not have to be positive 1-homogeneous, but some important ones are.
For those it is convenient to have a test.
parent 8755dd4e
......@@ -52,6 +52,33 @@ void testConvexity(const Functional& functional,
/** \brief Test whether a functional is positive 1-homogeneous
* Being positive 1-homogeneous is not a requirement for functionals to work
* in a TNNMG algorithm. However, various important functionals are homogeneous
* in this sense, therefore it is convenient to have a test for it.
* \tparam Functional Type of the functional to be tested
* \param functional The functional to be tested
* \param testDirections Test addGradient at these points
template <class Functional>
void testHomogeneity(const Functional& functional,
const std::vector<typename Functional::VectorType>& testDirections)
for (auto&& testDirection : testDirections)
// Test convexity at a few selected points between the two test points
for (double t : {0.0, 0.25, 0.5, 0.75, 1.0, 1.5, 2.0, 5.0})
auto scaledDirection = testDirection;
scaledDirection *= t;
if (std::abs(functional(scaledDirection) - t*functional(testDirection)) > 1e-6)
DUNE_THROW(MathError, "Functional is not positive 1-homogeneous!");
/** \brief Test the addGradient method
......@@ -35,6 +35,10 @@ int main(int argc, char** argv) try
// Test whether the functional is convex
testConvexity(functional, testPoints);
// Test whether the functional positive 1-homogeneous
// We abuse the test points as test directions.
testHomogeneity(functional, testPoints);
// Test the first derivative at the given test points
testGradient(functional, testPoints);
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment