public void ItemGradientAtStart(TestFunctions.TestCase test_case)
{
for (var item_index = 0; item_index < test_case.Function.ItemDimension; ++item_index)
{
var a_grad = test_case.Function.ItemGradient(test_case.InitialGuess, item_index);
var h = 1e-4;
var fd_grad = Vector <double> .Build.Dense(test_case.Function.ParameterDimension, 0.0);
for (int ii = 0; ii < test_case.Function.ParameterDimension; ++ii)
{
var bump_up = test_case.InitialGuess.Clone();
bump_up[ii] += h;
var bump_down = test_case.InitialGuess.Clone();
bump_down[ii] -= h;
var up_val = test_case.Function.ItemValue(bump_up, item_index);
var down_val = test_case.Function.ItemValue(bump_down, item_index);
fd_grad[ii] = 0.5 * (up_val - down_val) / h;
}
for (int ii = 0; ii < test_case.Function.ParameterDimension; ++ii)
{
Assert.That(Math.Abs(fd_grad[ii] - a_grad[ii]) < 1e-3, $"Failed for parameter {ii}");
}
}
}
public void GradientAtStart(TestFunctions.TestCase test_case)
{
var a_grad = test_case.Function.SsqGradient(test_case.InitialGuess);
var fd_grad = Vector <double> .Build.Dense(test_case.Function.ParameterDimension, 0.0);
for (int ii = 0; ii < test_case.Function.ParameterDimension; ++ii)
{
var h = 1e-6;
var bump_up = test_case.InitialGuess.Clone();
bump_up[ii] += h;
var bump_down = test_case.InitialGuess.Clone();
bump_down[ii] -= h;
var up_val = test_case.Function.SsqValue(bump_up);
var down_val = test_case.Function.SsqValue(bump_down);
fd_grad[ii] = 0.5 * (up_val - down_val) / h;
}
for (int ii = 0; ii < test_case.Function.ParameterDimension; ++ii)
{
var val1 = a_grad[ii];
var val2 = fd_grad[ii];
var min_abs_val = Math.Min(Math.Abs(val1), Math.Abs(val2));
if (min_abs_val <= 1)
{
Assert.That(Math.Abs(val1 - val2) < 1e-3, $"Problem with gradient value at start point.");
}
else
{
Assert.That(Math.Abs(val1 - val2) / min_abs_val < 1e-3, $"Problem with gradient value at start point.");
}
}
}
public void ItemHessianAtStart(TestFunctions.TestCase test_case)
{
for (var item_index = 0; item_index < test_case.Function.ItemDimension; ++item_index)
{
var a_hess = test_case.Function.ItemHessian(test_case.InitialGuess, item_index);
var h = 1e-4;
var fd_hess = Matrix <double> .Build.Dense(test_case.Function.ParameterDimension, test_case.Function.ParameterDimension);
for (int ii = 0; ii < test_case.Function.ParameterDimension; ++ii)
{
for (int jj = 0; jj < test_case.Function.ParameterDimension; ++jj)
{
var bump_uu = test_case.InitialGuess.Clone();
bump_uu[ii] += h;
bump_uu[jj] += h;
var bump_dd = test_case.InitialGuess.Clone();
bump_dd[ii] -= h;
bump_dd[jj] -= h;
var bump_ud = test_case.InitialGuess.Clone();
bump_ud[ii] += h;
bump_ud[jj] -= h;
var bump_du = test_case.InitialGuess.Clone();
bump_du[ii] -= h;
bump_du[jj] += h;
var val_uu = test_case.Function.ItemValue(bump_uu, item_index);
var val_dd = test_case.Function.ItemValue(bump_dd, item_index);
var val_ud = test_case.Function.ItemValue(bump_ud, item_index);
var val_du = test_case.Function.ItemValue(bump_du, item_index);
fd_hess[ii, jj] = (val_uu - val_ud + val_dd - val_du) / (4 * h * h);
}
}
for (int ii = 0; ii < test_case.Function.ParameterDimension; ++ii)
{
for (int jj = 0; jj < test_case.Function.ParameterDimension; ++jj)
{
var val1 = fd_hess[ii, jj];
var val2 = a_hess[ii, jj];
var abs_min = Math.Min(Math.Abs(val1), Math.Abs(val2));
if (abs_min <= 1)
{
Assert.That(Math.Abs(val1 - val2) < 1e-3, $"Problem with hessian at start point.");
}
else
{
Assert.That(Math.Abs(val1 - val2) / abs_min < 0.05, $"Problem with hessian at start point.");
}
}
}
}
}
public void HessianAtStart(TestFunctions.TestCase test_case)
{
var a_hess = test_case.Function.SsqHessian(test_case.InitialGuess);
var fd_hess = Matrix <double> .Build.Dense(test_case.Function.ParameterDimension, test_case.Function.ParameterDimension);
for (int ii = 0; ii < test_case.Function.ParameterDimension; ++ii)
{
for (int jj = 0; jj < test_case.Function.ParameterDimension; ++jj)
{
var h1 = 1e-3 * Math.Max(1.0, Math.Abs(test_case.InitialGuess[ii]));
var h2 = 1e-3 * Math.Max(1.0, Math.Abs(test_case.InitialGuess[jj]));
var bump_uu = test_case.InitialGuess.Clone();
bump_uu[ii] += h1;
bump_uu[jj] += h2;
var bump_dd = test_case.InitialGuess.Clone();
bump_dd[ii] -= h1;
bump_dd[jj] -= h2;
var bump_ud = test_case.InitialGuess.Clone();
bump_ud[ii] += h1;
bump_ud[jj] -= h2;
var bump_du = test_case.InitialGuess.Clone();
bump_du[ii] -= h1;
bump_du[jj] += h2;
var val_uu = test_case.Function.SsqValue(bump_uu);
var val_dd = test_case.Function.SsqValue(bump_dd);
var val_ud = test_case.Function.SsqValue(bump_ud);
var val_du = test_case.Function.SsqValue(bump_du);
fd_hess[ii, jj] = (val_uu - val_ud + val_dd - val_du) / (4 * h1 * h2);
}
}
for (int ii = 0; ii < test_case.Function.ParameterDimension; ++ii)
{
for (int jj = 0; jj < test_case.Function.ParameterDimension; ++jj)
{
var val1 = fd_hess[ii, jj];
var val2 = a_hess[ii, jj];
var abs_min = Math.Min(Math.Abs(val1), Math.Abs(val2));
if (abs_min <= 1)
{
Assert.That(Math.Abs(val1 - val2) < 1e-3, $"Problem with hessian at start point.");
}
else
{
Assert.That(Math.Abs(val1 - val2) / abs_min < 0.05, $"Problem with hessian at start point.");
}
}
}
}
public void ValueAtMinimum(TestFunctions.TestCase test_case)
{
if (test_case.MinimizingPoint != null)
{
var value_at_minimum = test_case.Function.SsqValue(test_case.MinimizingPoint);
Assert.That(
Math.Abs(value_at_minimum - test_case.MinimalValue) < 1e-3,
$"Function value at minimum not as expected."
);
}
}
public void Mgh_Tests(TestFunctions.TestCase test_case)
{
var obj = new MghObjectiveFunction(test_case.Function, true, true);
var result = NewtonMinimizer.Minimum(obj, test_case.InitialGuess, 1e-8, 1000, useLineSearch: false);
if (test_case.MinimizingPoint != null)
{
Assert.That((result.MinimizingPoint - test_case.MinimizingPoint).L2Norm(), Is.LessThan(1e-3));
}
var val1 = result.FunctionInfoAtMinimum.Value;
var val2 = test_case.MinimalValue;
var abs_min = Math.Min(Math.Abs(val1), Math.Abs(val2));
var abs_err = Math.Abs(val1 - val2);
var rel_err = abs_err / abs_min;
var success = (abs_min <= 1 && abs_err < 1e-3) || (abs_min > 1 && rel_err < 1e-3);
Assert.That(success, "Minimal function value is not as expected.");
}
public void Mgh_FiniteDifference_Tests(TestFunctions.TestCase test_case)
{
var obj1 = new MghObjectiveFunction(test_case.Function, true, true);
var obj = new ForwardDifferenceGradientObjectiveFunction(obj1, test_case.LowerBound, test_case.UpperBound, 1e-10, 1e-10);
var solver = new BfgsBMinimizer(1e-8, 1e-8, 1e-8, 1000);
var result = solver.FindMinimum(obj, test_case.LowerBound, test_case.UpperBound, test_case.InitialGuess);
if (test_case.MinimizingPoint != null)
{
Assert.That((result.MinimizingPoint - test_case.MinimizingPoint).L2Norm(), Is.LessThan(1e-3));
}
var val1 = result.FunctionInfoAtMinimum.Value;
var val2 = test_case.MinimalValue;
var abs_min = Math.Min(Math.Abs(val1), Math.Abs(val2));
var abs_err = Math.Abs(val1 - val2);
var rel_err = abs_err / abs_min;
var success = (abs_min <= 1 && abs_err < 1e-3) || (abs_min > 1 && rel_err < 1e-3);
Assert.That(success, "Minimal function value is not as expected.");
}