SparseMatrix Basis::evalBasisJacobian(DenseVector &x) const
{
// Jacobian basis matrix
SparseMatrix J(numBasisFunctions(), numVariables);
//J.setZero(numBasisFunctions(), numInputs);
// Calculate partial derivatives
for (unsigned int i = 0; i < numVariables; i++)
{
// One column in basis jacobian
SparseMatrix Ji(1,1);
Ji.insert(0,0) = 1;
for (unsigned int j = 0; j < numVariables; j++)
{
SparseMatrix temp = Ji;
SparseMatrix xi;
if (j == i)
{
// Differentiated basis
xi = bases.at(j).evaluateDerivative(x(j),1);
}
else
{
// Normal basis
xi = bases.at(j).evaluate(x(j));
}
Ji = kroneckerProduct(temp, xi);
//myKroneckerProduct(temp,xi,Ji);
//Ji = kroneckerProduct(Ji, xi).eval();
}
// Fill out column
for (int k = 0; k < Ji.outerSize(); ++k)
for (SparseMatrix::InnerIterator it(Ji,k); it; ++it)
{
if (it.value() != 0)
J.insert(it.row(),i) = it.value();
}
//J.block(0,i,Ji.rows(),1) = bi.block(0,0,Ji.rows(),1);
}
J.makeCompressed();
return J;
}
void system::compute_fluid_grad(const bool do_ngb)
{
#if 0
const int nimport = Uimport.size();
assert(nimport == (int)site_import.size());
Wextra_import.resize(nimport);
const int nactive_site = site_active_list.size();
const int nactive_site_with_ngb = nactive_site + (do_ngb ? site_with_ngb_active_list.size() : 0);
for (int isite = 0; isite < nactive_site_with_ngb; isite++)
{
const int i = isite < nactive_site ?
site_active_list[isite] : site_with_ngb_active_list[isite - nactive_site];
const Cell &ci = cell_list[i];
const Fluid_st &Wst_i = W_st [i];
const Fluid &Wi = Wst_i.w;
const vec3 &ipos = Wst_i.pos;
vec3 Ji(0.0); // current, J = Del x B
const vec3 Bi(Wi[Fluid::BX], Wi[Fluid::BY], Wi[Fluid::BZ]);
const int nface = ci.faces().size();
for (int iface = 0; iface < nface; iface++)
{
const Face &face = face_list[ci.faces()[iface]];
vec3 dri = face.centroid - ipos;
if (dri.x > 0.5*global_domain_size.x) dri.x -= global_domain_size.x;
else if (dri.x < -0.5*global_domain_size.x) dri.x += global_domain_size.x;
if (dri.y > 0.5*global_domain_size.y) dri.y -= global_domain_size.y;
else if (dri.y < -0.5*global_domain_size.y) dri.y += global_domain_size.y;
if (dri.z > 0.5*global_domain_size.z) dri.z -= global_domain_size.z;
else if (dri.z < -0.5*global_domain_size.z) dri.z += global_domain_size.z;
assert(std::abs(dri.x) < 0.5*global_domain_size.x);
assert(std::abs(dri.y) < 0.5*global_domain_size.y);
assert(std::abs(dri.z) < 0.5*global_domain_size.z);
const vec3 centroid = dri;
const real area = face.area();
const vec3 normal = face.n * ((centroid * face.n < 0.0) ? (-1.0/area) : (1.0/area));
const real dsh = centroid * normal;
assert(dsh > 0.0);
const real ids = (dsh != 0.0) ? 0.5/dsh : 0.0;
const real idsA = area * ids;
const vec3 drh = normal * (dsh * idsA);
const vec3 fij = (centroid - drh) * idsA;
const int j = site_map(face.ngb<false>(i));
assert(j >= 0);
const Fluid &Wj = W_st[j].w;
const vec3 Bj(Wj[Fluid::BX], Wj[Fluid::BY], Wj[Fluid::BZ]);
Ji += drh.cross(Bj+Bi) + fij.cross(Bj-Bi);
}
const real invV = 1.0/cell_list[i].Volume;
Ji *= ptcl_import[i].etaOhm * invV;
if (do_ngb) W_st[i].J = Ji;
else
{
const real dt = t_global - std::abs(W_st[i].tlast);
// assert(dt > 0.0);
// W_rec[i].J = (Ji - W_st[i].J) * (1.0/dt);
}
}
#endif
}
