Real GeneralStatistics::mean() const {
Size N = samples();
QL_REQUIRE(N != 0, "empty sample set");
// eat our own dog food
return expectationValue(identity<Real>(),
everywhere()).first;
}
InputParameters validParams<ElementIndicator>()
{
InputParameters params = validParams<Indicator>();
params.addRequiredParam<VariableName>("variable", "The name of the variable that this Indicator operates on");
std::vector<SubdomainName> everywhere(1, "ANY_BLOCK_ID");
params.addParam<std::vector<SubdomainName> >("block", everywhere, "block ID or name where the object works");
params += validParams<TransientInterface>();
return params;
}
Real GeneralStatistics::variance() const {
Size N = samples();
QL_REQUIRE(N > 1,
"sample number <=1, unsufficient");
// Subtract the mean and square. Repeat on the whole range.
// Hopefully, the whole thing will be inlined in a single loop.
Real s2 = expectationValue(compose(square<Real>(),
subtract<Real>(mean())),
everywhere()).first;
return s2*N/(N-1.0);
}
Real GeneralStatistics::skewness() const {
Size N = samples();
QL_REQUIRE(N > 2,
"sample number <=2, unsufficient");
Real x = expectationValue(compose(cube<Real>(),
subtract<Real>(mean())),
everywhere()).first;
Real sigma = standardDeviation();
return (x/(sigma*sigma*sigma))*(N/(N-1.0))*(N/(N-2.0));
}
InputParameters validParams<AddNodalNormalsAction>()
{
InputParameters params = validParams<Action>();
// Initialize the 'boundary' input option to default to any boundary
std::vector<BoundaryName> everywhere(1, "ANY_BOUNDARY_ID");
params.addParam<std::vector<BoundaryName> >("boundary", everywhere, "The boundary ID or name where the normals will be computed");
params.addParam<BoundaryName>("corner_boundary", "boundary ID or name with nodes at 'corners'");
MooseEnum orders("FIRST, SECOND", "FIRST");
params.addParam<MooseEnum>("order", orders, "Specifies the order of variables that hold the nodal normals. Needs to match the order of the mesh");
return params;
}
Real GeneralStatistics::kurtosis() const {
Size N = samples();
QL_REQUIRE(N > 3,
"sample number <=3, unsufficient");
Real x = expectationValue(compose(fourth_power<Real>(),
subtract<Real>(mean())),
everywhere()).first;
Real sigma2 = variance();
Real c1 = (N/(N-1.0)) * (N/(N-2.0)) * ((N+1.0)/(N-3.0));
Real c2 = 3.0 * ((N-1.0)/(N-2.0)) * ((N-1.0)/(N-3.0));
return c1*(x/(sigma2*sigma2))-c2;
}
