//' @title Model Score
//' @description Calculates the modeling score of a GMWM
//' @param A A \code{mat} that contains the first derivatives of the processes
//' @param At_j A \code{mat} that contains the second derivative of each process
//' @param omega A \code{mat} that contains the omega used when calculating the GMWM
//' @param v_hat A \code{mat} that contains the covariance matrix
//' @param diff A \code{vec} that is the difference of the WV empirical and WV theoretical
//' @return A \code{vec}
//' @keywords internal
//' @backref src/model_selection.cpp
//' @backref src/model_selection.h
//' @details
//' The equation is slightly different than that stated in the paper due to the bootstrap already incorporating in
//' N.
// [[Rcpp::export]]
arma::vec model_score(arma::mat A, arma::mat D, arma::mat omega, arma::mat v_hat, double obj_value){
arma::mat At = arma::trans(A);
arma::mat B = B_matrix(A, At*omega);
arma::mat d_b = D-B;
arma::mat db_t = arma::trans(d_b);
arma::mat dTheta = -1*arma::pinv(db_t * d_b)*db_t*At*omega;
arma::vec score_info(2);
double optimism = 2.0*arma::as_scalar(arma::trace(A * dTheta * omega * v_hat));
score_info(0) = obj_value + optimism;
score_info(1) = optimism;
// Return the score
return score_info;
}
//with matrixtype, constant coefficient
void NoNewtonianMonolithicPFEM22D::AddViscousTerm(MatrixType& OutputMatrix,
const boost::numeric::ublas::bounded_matrix<double, 3, 2 >& rShapeDeriv,
double Viscosity, const double Area)
{
const double theta = 0.35;
const double Cohesion = 0.0;
double base_viscosity = Viscosity;
boost::numeric::ublas::bounded_matrix<double, 6, 3 > B_matrix = ZeroMatrix(6,3);
for (unsigned int i=0; i!=3; i++) //i node
{
B_matrix(i*2,0)=rShapeDeriv(i,0);
B_matrix(i*2+1,1)=rShapeDeriv(i,1);
B_matrix(i*2,2)=rShapeDeriv(i,1);
B_matrix(i*2+1,2)=rShapeDeriv(i,0);
}
boost::numeric::ublas::bounded_matrix<double, 3, 3 > C_matrix = ZeroMatrix(3,3);
C_matrix(0,0)=2.0;
C_matrix(1,1)=2.0;
C_matrix(2,2)=1.0;
double pressure = 0.0;
double negative_nodes=0.0;
double has_fixed_vel=false; //if some nodes are fixed, then we are on a boundary and then we can set different material properties (for example to simulate a lower basal friction angle)
for (unsigned int i=0; i!=3; i++) //i node
{
if (this->GetGeometry()[i].FastGetSolutionStepValue(DISTANCE)<0.0)
{
pressure += this->GetGeometry()[i].FastGetSolutionStepValue(PRESSURE);
negative_nodes +=1.0;
}
if (this->GetGeometry()[i].IsFixed(VELOCITY_X)==true)
has_fixed_vel = true;
}
pressure /=negative_nodes;
if (pressure<0.0)
pressure=0.0;
double YieldStress = Cohesion + tan(theta) * pressure;
//if (theta>basal_theta && has_fixed_vel)
// YieldStress = tan(basal_theta) * pressure;
if (negative_nodes>0.5)
{
Viscosity = this->EffectiveViscosity(base_viscosity,YieldStress,rShapeDeriv);
}
C_matrix *= Viscosity*Area;
boost::numeric::ublas::bounded_matrix<double, 3, 6 > temp_matrix = prod(C_matrix,trans(B_matrix));
boost::numeric::ublas::bounded_matrix<double, 6, 6 > viscosity_matrix = prod(B_matrix, temp_matrix );
for (unsigned int i=0; i!=3; i++) //i node
{
for (unsigned int j=0; j!=3; j++) //j neighbour
{
//OutputMatrix(i*4+0,j*4+0)+=viscosity_matrix(i*2+0,j*2+0); //0,0
//OutputMatrix(i*4+0,j*4+1)+=viscosity_matrix(i*2+0,j*2+1); //0,1
//OutputMatrix(i*4+1,j*4+0)+=viscosity_matrix(i*2+1,j*2+0); //1,0
//OutputMatrix(i*4+1,j*4+1)+=viscosity_matrix(i*2+1,j*2+1); //1,1
OutputMatrix(i*3+0,j*3+0)+=viscosity_matrix(i*2+0,j*2+0); //0,0
OutputMatrix(i*3+0,j*3+1)+=viscosity_matrix(i*2+0,j*2+1); //0,1
OutputMatrix(i*3+1,j*3+0)+=viscosity_matrix(i*2+1,j*2+0); //1,0
OutputMatrix(i*3+1,j*3+1)+=viscosity_matrix(i*2+1,j*2+1); //1,1
}
}
//OutputMatrix += viscosity_matrix;
}
