protected override bool HeightDirectionIsSuitable(
LinearSayeSpace <Cube> arg,
LinearPSI <Cube> psi, NodeSet
x_center,
int heightDirection,
MultidimensionalArray agradient, int cell)
{
//throw new NotImplementedException();
//Determine bounds
//-----------------------------------------------------------------------------------------------------------------
NodeSet nodeOnPsi = psi.ProjectOnto(x_center);
MultidimensionalArray jacobian = grid.Jacobian.GetValue_Cell(nodeOnPsi, cell, 1);
jacobian = jacobian.ExtractSubArrayShallow(new int[] { 0, 0, -1, -1 });
LevelSet levelSet = lsData.LevelSet as LevelSet;
MultidimensionalArray hessian = MultidimensionalArray.Create(1, 1, 3, 3);
levelSet.EvaluateHessian(cell, 1, nodeOnPsi, hessian);
hessian = hessian.ExtractSubArrayShallow(new int[] { 0, 0, -1, -1 }).CloneAs();
//hessian = jacobian * hessian;
hessian.ApplyAll(x => Math.Abs(x));
MultidimensionalArray gradient = lsData.GetLevelSetGradients(nodeOnPsi, cell, 1);
gradient = gradient.ExtractSubArrayShallow(0, 0, -1).CloneAs();
//abs(Hessian) * 0,5 * diameters.^2 = delta ,( square each entry of diameters) ,
//this bounds the second error term from taylor series
//+ + + +
double[] arr = arg.Diameters.CloneAs();
psi.SetInactiveDimsToZero(arr);
MultidimensionalArray diameters = MultidimensionalArray.CreateWrapper(arr, 3, 1);
diameters = jacobian * diameters;
diameters.ApplyAll(x => 0.5 * x * x);
MultidimensionalArray delta = hessian * diameters;
delta = delta.ExtractSubArrayShallow(-1, 0);
//Check if suitable
//-----------------------------------------------------------------------------------------------------------------
//|gk| > δk
//Gradient should be able to turn arround
psi.SetInactiveDimsToZero(gradient.Storage);
if (Math.Abs(gradient[heightDirection]) > delta[heightDirection])
{
bool suitable = true;
// ||Grad + maxChange|| should be smaller than 20 *
// Sum_j( g_j + delta_j)^2 / (g_k - delta_k)^2 < 20
double sum = 0;
for (int j = 0; j < delta.Length; ++j)
{
sum += Math.Pow(Math.Abs(gradient[j]) + delta[j], 2);
}
sum /= Math.Pow(Math.Abs(gradient[heightDirection]) - delta[heightDirection], 2);
suitable &= sum < 20;
return(suitable);
}
return(false);
}