void TRBDF2SolverNewtonFunction::evalF(RealVector& Z, RealVector& F){
Bool refining = (ref.all() == false);
if(refining == false){
Integer n = Z.size();
RealVector Y(n);
Y.fill(0.0);
F.fill(0.0);
Y = ya + d * Z;
RealVector f = fun->evalF(tnp,Y);
F = Z - dt * f;
}
else{
Integer n = ref.cast<Real>().size();
RealVector Y(n);
Y.fill(0.0);
F.fill(0.0);
RealVector Z_long = VectorUtility::vectorProlong(Z,ref);
Y = ya + d * Z_long;
RealVector f = fun->evalF(tnp,Y,ref);
F = Z - dt * f;
}
}
void TRBDF2SolverNewtonFunction::evalFJ(RealVector& Z, RealVector& F, RealMatrixSparse& J){
Bool refining = (ref.all() == false);
if(refining == false){
Integer n = Z.size();
RealVector Y(n);
Y.fill(0.0);
F.fill(0.0);
RealMatrixSparse DZ_DZ(n,n); //Identity matrix
DZ_DZ.setIdentity();
Y = ya + d * Z;
RealVector f = fun->evalF(tnp,Y);
RealMatrixSparse Df_DY = fun->evaldFdY(tnp,Y);
F = Z - dt * f;
J = DZ_DZ - dt * d * Df_DY; //J = DF_DZ
}
else{
Real d = (2 - sqrt(2))/2;
Integer n = ref.cast<Real>().size();
RealVector Y(n);
Y.fill(0);
F.fill(0);
Integer elem_ref = ref.sum();
RealMatrixSparse DZ_DZ;
DZ_DZ.resize(elem_ref,elem_ref);
DZ_DZ.setIdentity();
RealVector Z_long = VectorUtility::vectorProlong(Z,ref);
Y = ya + d * Z_long;
RealVector f = fun->evalF(tnp,Y,ref);
RealMatrixSparse Df_DY = fun->evaldFdY(tnp,Y,ref);
F = Z - dt * f;
J = DZ_DZ - dt * d * Df_DY; //J = DF_DZ
}
}
///////////////////////////////////////////////////////////////////////////////
//
/// Changes the variable of a polynomial represented in P and stores the
/// result in Q so that \f$P(x) = Q(x')\f$ where
///
/// \f$x = \alpha x' + (1 - \alpha)\f$
//
///////////////////////////////////////////////////////////////////////////////
void AntisymmetricExpFit::change_variable(RealVector &P, const Real &alpha, RealVector &Q) {
const int M = P.size(); // degree of P + 1
const int SMAX = 96; // maximum degree of Q
int m; // index into P
int r; // index into Q
Real beta = 1.0-alpha; // offset
Real lgb; // log of alpha^r beta^(m-r) (m choose r)
Q.resize(SMAX);
Q.fill(0.0);
for(r = 0; r<SMAX; ++r) {
lgb = r*log(alpha);
for(m = r; m<M; ++m) {
Q(r) += exp(lgb)*P(m);
lgb += log(beta) + log((m+1.0)/(m+1.0-r));
}
}
}