doublereal LiquidTransport::getElectricConduct()
{
vector_fp gradT(m_nDim,0.0);
vector_fp gradX(m_nDim * m_nsp);
vector_fp gradV(m_nDim);
for (size_t i = 0; i < m_nDim; i++) {
for (size_t k = 0; k < m_nsp; k++) {
gradX[ i*m_nDim + k] = 0.0;
}
gradV[i] = 1.0;
}
set_Grad_T(&gradT[0]);
set_Grad_X(&gradX[0]);
set_Grad_V(&gradV[0]);
vector_fp fluxes(m_nsp * m_nDim);
doublereal current;
getSpeciesFluxesExt(m_nDim, &fluxes[0]);
//sum over species charges, fluxes, Faraday to get current
// Since we want the scalar conductivity, we need only consider one-dim
for (size_t i = 0; i < 1; i++) {
current = 0.0;
for (size_t k = 0; k < m_nsp; k++) {
current += m_chargeSpecies[k] * Faraday * fluxes[k] / m_mw[k];
}
//divide by unit potential gradient
current /= - gradV[i];
}
return current;
}
void softAbsMetric::fPrepareSpatialGradients()
{
// Compute the discrete Jacobian of the SoftAbs transform
double delta = 0;
double lambda = 0;
double alphaLambda = 0;
double sdx = 0;
for(int i = 0; i < mDim; ++i)
{
for(int j = 0; j <= i; ++j)
{
delta = mEigenDeco.eigenvalues()(i) - mEigenDeco.eigenvalues()(j);
if(fabs(delta) < 1e-10)
{
lambda = mEigenDeco.eigenvalues()(i);
alphaLambda = mSoftAbsAlpha * lambda;
if(fabs(alphaLambda) < 1e-4)
{
mPseudoJ(i, j) = (2.0 / 3.0) * alphaLambda * (1.0 - (2.0 / 15.0) * alphaLambda * alphaLambda);
}
else if(fabs(alphaLambda) > 18)
{
mPseudoJ(i, j) = lambda > 0 ? 1 : -1;
}
else
{
sdx = sinh(mSoftAbsAlpha * lambda) / lambda;
mPseudoJ(i, j) = (mSoftAbsLambda(i) - mSoftAbsAlpha / (sdx * sdx) ) / lambda;
}
}
else
{
mPseudoJ(i, j) = ( mSoftAbsLambda(i) - mSoftAbsLambda(j) ) / delta;
}
}
}
// And make sure the gradient has been calculated
gradV();
// Along with the third-derivative tensor
for(int i = 0; i < mDim; ++i) fComputeGradH(i);
}
void constMetric::fEvolveP(const double epsilon)
{
mP -= epsilon * gradV();
}
void FilterAeroForces::v_Update(
const Array<OneD, const MultiRegions::ExpListSharedPtr> &pFields,
const NekDouble &time)
{
// Only output every m_outputFrequency.
if ((m_index++) % m_outputFrequency)
{
return;
}
int n, cnt, elmtid, nq, offset, nt, boundary;
nt = pFields[0]->GetNpoints();
int dim = pFields.num_elements()-1;
StdRegions::StdExpansionSharedPtr elmt;
Array<OneD, int> BoundarytoElmtID;
Array<OneD, int> BoundarytoTraceID;
Array<OneD, MultiRegions::ExpListSharedPtr> BndExp;
Array<OneD, const NekDouble> P(nt);
Array<OneD, const NekDouble> U(nt);
Array<OneD, const NekDouble> V(nt);
Array<OneD, const NekDouble> W(nt);
Array<OneD, Array<OneD, NekDouble> > gradU(dim);
Array<OneD, Array<OneD, NekDouble> > gradV(dim);
Array<OneD, Array<OneD, NekDouble> > gradW(dim);
Array<OneD, Array<OneD, NekDouble> > fgradU(dim);
Array<OneD, Array<OneD, NekDouble> > fgradV(dim);
Array<OneD, Array<OneD, NekDouble> > fgradW(dim);
Array<OneD, NekDouble> values;
LibUtilities::CommSharedPtr vComm = pFields[0]->GetComm();
NekDouble Fx,Fy,Fz,Fxp,Fxv,Fyp,Fyv,Fzp,Fzv;
Fxp = 0.0; // x-component of the force due to pressure difference
Fxv = 0.0; // x-component of the force due to viscous stress
Fx = 0.0; // x-component of the force (total) Fx = Fxp + Fxv (Drag)
Fyp = 0.0; // y-component of the force due to pressure difference
Fyv = 0.0; // y-component of the force due to viscous stress
Fy = 0.0; // y-component of the force (total) Fy = Fyp + Fyv (Lift)
Fzp = 0.0; // z-component of the force due to pressure difference
Fzv = 0.0; // z-component of the force due to viscous stress
Fz = 0.0; // z-component of the force (total) Fz = Fzp + Fzv (Side)
NekDouble rho = (m_session->DefinesParameter("rho"))
? (m_session->GetParameter("rho"))
: 1;
NekDouble mu = rho*m_session->GetParameter("Kinvis");
for(int i = 0; i < pFields.num_elements(); ++i)
{
pFields[i]->SetWaveSpace(false);
pFields[i]->BwdTrans(pFields[i]->GetCoeffs(),
pFields[i]->UpdatePhys());
pFields[i]->SetPhysState(true);
}
// Homogeneous 1D case Compute forces on all WALL boundaries
// This only has to be done on the zero (mean) Fourier mode.
if(m_isHomogeneous1D)
{
if(vComm->GetColumnComm()->GetRank() == 0)
{
pFields[0]->GetPlane(0)->GetBoundaryToElmtMap(
BoundarytoElmtID,BoundarytoTraceID);
BndExp = pFields[0]->GetPlane(0)->GetBndCondExpansions();
StdRegions::StdExpansion1DSharedPtr bc;
// loop over the types of boundary conditions
for(cnt = n = 0; n < BndExp.num_elements(); ++n)
{
if(m_boundaryRegionIsInList[n] == 1)
{
for(int i = 0; i < BndExp[n]->GetExpSize();
++i, cnt++)
{
// find element of this expansion.
elmtid = BoundarytoElmtID[cnt];
elmt = pFields[0]->GetPlane(0)->GetExp(elmtid);
nq = elmt->GetTotPoints();
offset = pFields[0]->GetPlane(0)->GetPhys_Offset(elmtid);
// Initialise local arrays for the velocity
// gradients size of total number of quadrature
// points for each element (hence local).
for(int j = 0; j < dim; ++j)
{
gradU[j] = Array<OneD, NekDouble>(nq,0.0);
gradV[j] = Array<OneD, NekDouble>(nq,0.0);
gradW[j] = Array<OneD, NekDouble>(nq,0.0);
}
// identify boundary of element
boundary = BoundarytoTraceID[cnt];
// Extract fields
U = pFields[0]->GetPlane(0)->GetPhys() + offset;
V = pFields[1]->GetPlane(0)->GetPhys() + offset;
P = pFields[3]->GetPlane(0)->GetPhys() + offset;
// compute the gradients
elmt->PhysDeriv(U,gradU[0],gradU[1]);
elmt->PhysDeriv(V,gradV[0],gradV[1]);
// Get face 1D expansion from element expansion
bc = boost::dynamic_pointer_cast<LocalRegions
::Expansion1D> (BndExp[n]->GetExp(i));
// number of points on the boundary
int nbc = bc->GetTotPoints();
// several vectors for computing the forces
Array<OneD, NekDouble> Pb(nbc,0.0);
for(int j = 0; j < dim; ++j)
{
fgradU[j] = Array<OneD, NekDouble>(nbc,0.0);
fgradV[j] = Array<OneD, NekDouble>(nbc,0.0);
}
Array<OneD, NekDouble> drag_t(nbc,0.0);
Array<OneD, NekDouble> lift_t(nbc,0.0);
Array<OneD, NekDouble> drag_p(nbc,0.0);
Array<OneD, NekDouble> lift_p(nbc,0.0);
Array<OneD, NekDouble> temp(nbc,0.0);
Array<OneD, NekDouble> temp2(nbc,0.0);
// identify boundary of element .
boundary = BoundarytoTraceID[cnt];
// extraction of the pressure and wss on the
// boundary of the element
elmt->GetEdgePhysVals(boundary,bc,P,Pb);
for(int j = 0; j < dim; ++j)
{
elmt->GetEdgePhysVals(boundary,bc,gradU[j],
fgradU[j]);
elmt->GetEdgePhysVals(boundary,bc,gradV[j],
fgradV[j]);
}
//normals of the element
const Array<OneD, Array<OneD, NekDouble> > &normals
= elmt->GetEdgeNormal(boundary);
//
// Compute viscous tractive forces on wall from
//
// t_i = - T_ij * n_j (minus sign for force
// exerted BY fluid ON wall),
//
// where
//
// T_ij = viscous stress tensor (here in Cartesian
// coords)
// dU_i dU_j
// = RHO * KINVIS * ( ---- + ---- ) .
// dx_j dx_i
//a) DRAG TERMS
//-rho*kinvis*(2*du/dx*nx+(du/dy+dv/dx)*ny
Vmath::Vadd(nbc,fgradU[1],1,fgradV[0],1,drag_t,1);
Vmath::Vmul(nbc,drag_t,1,normals[1],1,drag_t,1);
Vmath::Smul(nbc,2.0,fgradU[0],1,fgradU[0],1);
Vmath::Vmul(nbc,fgradU[0],1,normals[0],1,temp2,1);
Vmath::Smul(nbc,0.5,fgradU[0],1,fgradU[0],1);
Vmath::Vadd(nbc,temp2,1,drag_t,1,drag_t,1);
Vmath::Smul(nbc,-mu,drag_t,1,drag_t,1);
//zero temporary storage vector
Vmath::Zero(nbc,temp,0);
Vmath::Zero(nbc,temp2,0);
//b) LIFT TERMS
//-rho*kinvis*(2*dv/dy*nx+(du/dy+dv/dx)*nx
Vmath::Vadd(nbc,fgradU[1],1,fgradV[0],1,lift_t,1);
Vmath::Vmul(nbc,lift_t,1,normals[0],1,lift_t,1);
Vmath::Smul(nbc,2.0,fgradV[1],1,fgradV[1],1);
Vmath::Vmul(nbc,fgradV[1],1,normals[1],1,temp2,1);
Vmath::Smul(nbc,-0.5,fgradV[1],1,fgradV[1],1);
Vmath::Vadd(nbc,temp2,1,lift_t,1,lift_t,1);
Vmath::Smul(nbc,-mu,lift_t,1,lift_t,1);
// Compute normal tractive forces on all WALL
// boundaries
Vmath::Vvtvp(nbc,Pb,1,normals[0],1,
drag_p,1,drag_p, 1);
Vmath::Vvtvp(nbc,Pb,1,normals[1],1,
lift_p,1,lift_p,1);
//integration over the boundary
Fxv += bc->Integral(drag_t);
Fyv += bc->Integral(lift_t);
Fxp += bc->Integral(drag_p);
Fyp += bc->Integral(lift_p);
}
}
else
{
cnt += BndExp[n]->GetExpSize();
}
}
}
for(int i = 0; i < pFields.num_elements(); ++i)
{
pFields[i]->SetWaveSpace(true);
pFields[i]->BwdTrans(pFields[i]->GetCoeffs(),
pFields[i]->UpdatePhys());
pFields[i]->SetPhysState(false);
}
}
//3D WALL case
else if(dim==3 && !m_isHomogeneous1D)
{
pFields[0]->GetBoundaryToElmtMap(BoundarytoElmtID,
BoundarytoTraceID);
BndExp = pFields[0]->GetBndCondExpansions();
LocalRegions::Expansion2DSharedPtr bc;
// loop over the types of boundary conditions
for(cnt = n = 0; n < BndExp.num_elements(); ++n)
{
if(m_boundaryRegionIsInList[n] == 1)
{
for(int i = 0; i < BndExp[n]->GetExpSize(); ++i, cnt++)
{
// find element of this expansion.
elmtid = BoundarytoElmtID[cnt];
elmt = pFields[0]->GetExp(elmtid);
nq = elmt->GetTotPoints();
offset = pFields[0]->GetPhys_Offset(elmtid);
// Initialise local arrays for the velocity
// gradients size of total number of quadrature
// points for each element (hence local).
for(int j = 0; j < dim; ++j)
{
gradU[j] = Array<OneD, NekDouble>(nq,0.0);
gradV[j] = Array<OneD, NekDouble>(nq,0.0);
gradW[j] = Array<OneD, NekDouble>(nq,0.0);
}
//identify boundary of element
boundary = BoundarytoTraceID[cnt];
//Extract fields
U = pFields[0]->GetPhys() + offset;
V = pFields[1]->GetPhys() + offset;
W = pFields[2]->GetPhys() + offset;
P = pFields[3]->GetPhys() + offset;
//compute the gradients
elmt->PhysDeriv(U,gradU[0],gradU[1],gradU[2]);
elmt->PhysDeriv(V,gradV[0],gradV[1],gradV[2]);
elmt->PhysDeriv(W,gradW[0],gradW[1],gradW[2]);
// Get face 2D expansion from element expansion
bc = boost::dynamic_pointer_cast<LocalRegions
::Expansion2D> (BndExp[n]->GetExp(i));
//number of points on the boundary
int nbc = bc->GetTotPoints();
//several vectors for computing the forces
Array<OneD, NekDouble> Pb(nbc,0.0);
for(int j = 0; j < dim; ++j)
{
fgradU[j] = Array<OneD, NekDouble>(nbc,0.0);
fgradV[j] = Array<OneD, NekDouble>(nbc,0.0);
fgradW[j] = Array<OneD, NekDouble>(nbc,0.0);
}
Array<OneD, NekDouble> drag_t(nbc,0.0);
Array<OneD, NekDouble> lift_t(nbc,0.0);
Array<OneD, NekDouble> side_t(nbc,0.0);
Array<OneD, NekDouble> drag_p(nbc,0.0);
Array<OneD, NekDouble> lift_p(nbc,0.0);
Array<OneD, NekDouble> side_p(nbc,0.0);
Array<OneD, NekDouble> temp(nbc,0.0);
Array<OneD, NekDouble> temp2(nbc,0.0);
// identify boundary of element .
boundary = BoundarytoTraceID[cnt];
// extraction of the pressure and wss on the
// boundary of the element
elmt->GetFacePhysVals(boundary,bc,P,Pb);
for(int j = 0; j < dim; ++j)
{
elmt->GetFacePhysVals(boundary,bc,gradU[j],
fgradU[j]);
elmt->GetFacePhysVals(boundary,bc,gradV[j],
fgradV[j]);
elmt->GetFacePhysVals(boundary,bc,gradW[j],
fgradW[j]);
}
// normals of the element
const Array<OneD, Array<OneD, NekDouble> > &normals
= elmt->GetFaceNormal(boundary);
//
// Compute viscous tractive forces on wall from
//
// t_i = - T_ij * n_j (minus sign for force
// exerted BY fluid ON wall),
//
// where
//
// T_ij = viscous stress tensor (here in Cartesian
// coords)
// dU_i dU_j
// = RHO * KINVIS * ( ---- + ---- ) .
// dx_j dx_i
//a) DRAG TERMS
//-rho*kinvis*
// (2*du/dx*nx+(du/dy+dv/dx)*ny+(du/dz+dw/dx)*nz)
Vmath::Vadd(nbc,fgradU[2],1,fgradW[0],1,temp,1);
Vmath::Neg(nbc,temp,1);
Vmath::Vmul(nbc,temp,1,normals[2],1,temp,1);
Vmath::Vadd(nbc,fgradU[1],1,fgradV[0],1,drag_t,1);
Vmath::Neg(nbc,drag_t,1);
Vmath::Vmul(nbc,drag_t,1,normals[1],1,drag_t,1);
Vmath::Smul(nbc,-2.0,fgradU[0],1,fgradU[0],1);
Vmath::Vmul(nbc,fgradU[0],1,normals[0],1,temp2,1);
Vmath::Smul(nbc,-0.5,fgradU[0],1,fgradU[0],1);
Vmath::Vadd(nbc,temp,1,temp2,1,temp,1);
Vmath::Vadd(nbc,temp,1,drag_t,1,drag_t,1);
Vmath::Smul(nbc,mu,drag_t,1,drag_t,1);
//zero temporary storage vector
Vmath::Zero(nbc,temp,0);
Vmath::Zero(nbc,temp2,0);
//b) LIFT TERMS
//-rho*kinvis*
// (2*dv/dy*nx+(du/dy+dv/dx)*nx+(dv/dz+dw/dy)*nz)
Vmath::Vadd(nbc,fgradV[2],1,fgradW[1],1,temp,1);
Vmath::Neg(nbc,temp,1);
Vmath::Vmul(nbc,temp,1,normals[2],1,temp,1);
Vmath::Vadd(nbc,fgradU[1],1,fgradV[0],1,lift_t,1);
Vmath::Neg(nbc,lift_t,1);
Vmath::Vmul(nbc,lift_t,1,normals[0],1,lift_t,1);
Vmath::Smul(nbc,-2.0,fgradV[1],1,fgradV[1],1);
Vmath::Vmul(nbc,fgradV[1],1,normals[1],1,temp2,1);
Vmath::Smul(nbc,-0.5,fgradV[1],1,fgradV[1],1);
Vmath::Vadd(nbc,temp,1,temp2,1,temp,1);
Vmath::Vadd(nbc,temp,1,lift_t,1,lift_t,1);
Vmath::Smul(nbc,mu,lift_t,1,lift_t,1);
//zero temporary storage vector
Vmath::Zero(nbc,temp,0);
Vmath::Zero(nbc,temp2,0);
//b) SIDE TERMS
//-rho*kinvis*
// (2*dv/dy*nx+(du/dy+dv/dx)*nx+(dv/dz+dw/dy)*nz)
Vmath::Vadd(nbc,fgradV[2],1,fgradW[1],1,temp,1);
Vmath::Neg(nbc,temp,1);
Vmath::Vmul(nbc,temp,1,normals[1],1,temp,1);
Vmath::Vadd(nbc,fgradU[2],1,fgradW[0],1,side_t,1);
Vmath::Neg(nbc,side_t,1);
Vmath::Vmul(nbc,side_t,1,normals[0],1,side_t,1);
Vmath::Smul(nbc,-2.0,fgradW[2],1,fgradW[2],1);
Vmath::Vmul(nbc,fgradW[2],1,normals[2],1,temp2,1);
Vmath::Smul(nbc,-0.5,fgradW[2],1,fgradW[2],1);
Vmath::Vadd(nbc,temp,1,temp2,1,temp,1);
Vmath::Vadd(nbc,temp,1,side_t,1,side_t,1);
Vmath::Smul(nbc,mu,side_t,1,side_t,1);
// Compute normal tractive forces on all WALL
// boundaries
Vmath::Vvtvp(nbc,Pb,1,normals[0],1,
drag_p,1,drag_p,1);
Vmath::Vvtvp(nbc,Pb,1,normals[1],1,
lift_p,1,lift_p,1);
Vmath::Vvtvp(nbc,Pb,1,normals[2],1,
side_p,1,side_p,1);
//integration over the boundary
Fxv += bc->Expansion::Integral(drag_t);
Fyv += bc->Expansion::Integral(lift_t);
Fzv += bc->Expansion::Integral(side_t);
Fxp += bc->Expansion::Integral(drag_p);
Fyp += bc->Expansion::Integral(lift_p);
Fzp += bc->Expansion::Integral(side_p);
}
}
else
{
cnt += BndExp[n]->GetExpSize();
}
}
}
//2D WALL Condition
else
{
pFields[0]->GetBoundaryToElmtMap(BoundarytoElmtID,
BoundarytoTraceID);
BndExp = pFields[0]->GetBndCondExpansions();
StdRegions::StdExpansion1DSharedPtr bc;
// loop over the types of boundary conditions
for(cnt = n = 0; n < BndExp.num_elements(); ++n)
{
if(m_boundaryRegionIsInList[n] == 1)
{
for(int i = 0; i < BndExp[n]->GetExpSize(); ++i, cnt++)
{
elmtid = BoundarytoElmtID[cnt];
elmt = pFields[0]->GetExp(elmtid);
nq = elmt->GetTotPoints();
offset = pFields[0]->GetPhys_Offset(elmtid);
for(int j = 0; j < dim; ++j)
{
gradU[j] = Array<OneD, NekDouble>(nq,0.0);
gradV[j] = Array<OneD, NekDouble>(nq,0.0);
}
boundary = BoundarytoTraceID[cnt];
U = pFields[0]->GetPhys() + offset;
V = pFields[1]->GetPhys() + offset;
P = pFields[2]->GetPhys() + offset;
elmt->PhysDeriv(U,gradU[0],gradU[1]);
elmt->PhysDeriv(V,gradV[0],gradV[1]);
bc = boost::dynamic_pointer_cast<LocalRegions
::Expansion1D> (BndExp[n]->GetExp(i));
int nbc = bc->GetTotPoints();
Array<OneD, NekDouble> Pb(nbc,0.0);
Array<OneD, NekDouble> drag_t(nbc,0.0);
Array<OneD, NekDouble> lift_t(nbc,0.0);
Array<OneD, NekDouble> drag_p(nbc,0.0);
Array<OneD, NekDouble> lift_p(nbc,0.0);
Array<OneD, NekDouble> temp(nbc,0.0);
boundary = BoundarytoTraceID[cnt];
elmt->GetEdgePhysVals(boundary,bc,P,Pb);
for(int j = 0; j < dim; ++j)
{
fgradU[j] = Array<OneD, NekDouble>(nbc,0.0);
fgradV[j] = Array<OneD, NekDouble>(nbc,0.0);
}
for(int j = 0; j < dim; ++j)
{
elmt->GetEdgePhysVals(boundary,bc,gradU[j],
fgradU[j]);
elmt->GetEdgePhysVals(boundary,bc,gradV[j],
fgradV[j]);
}
const Array<OneD, Array<OneD, NekDouble> > &normals
= elmt->GetEdgeNormal(boundary);
Vmath::Vadd(nbc,fgradU[1],1,fgradV[0],1,drag_t,1);
Vmath::Neg(nbc,drag_t,1);
Vmath::Vmul(nbc,drag_t,1,normals[1],1,drag_t,1);
Vmath::Smul(nbc,-2.0,fgradU[0],1,fgradU[0],1);
Vmath::Vmul(nbc,fgradU[0],1,normals[0],1,temp,1);
Vmath::Vadd(nbc,temp,1,drag_t,1,drag_t,1);
Vmath::Smul(nbc,mu,drag_t,1,drag_t,1);
Vmath::Vadd(nbc,fgradU[1],1,fgradV[0],1,lift_t,1);
Vmath::Neg(nbc,lift_t,1);
Vmath::Vmul(nbc,lift_t,1,normals[0],1,lift_t,1);
Vmath::Smul(nbc,-2.0,fgradV[1],1,fgradV[1],1);
Vmath::Vmul(nbc,fgradV[1],1,normals[1],1,temp,1);
Vmath::Vadd(nbc,temp,1,lift_t,1,lift_t,1);
Vmath::Smul(nbc,mu,lift_t,1,lift_t,1);
Vmath::Vvtvp(nbc,Pb,1,normals[0],1,
drag_p,1,drag_p,1);
Vmath::Vvtvp(nbc,Pb,1,normals[1],1,
lift_p,1,lift_p,1);
Fxp += bc->Integral(drag_p);
Fyp += bc->Integral(lift_p);
Fxv += bc->Integral(drag_t);
Fyp += bc->Integral(lift_t);
}
}
else
{
cnt += BndExp[n]->GetExpSize();
}
}
}
vComm->AllReduce(Fxp, LibUtilities::ReduceSum);
vComm->AllReduce(Fxv, LibUtilities::ReduceSum);
Fx = Fxp + Fxv;
vComm->AllReduce(Fyp, LibUtilities::ReduceSum);
vComm->AllReduce(Fyv, LibUtilities::ReduceSum);
Fy = Fyp + Fyv;
vComm->AllReduce(Fzp, LibUtilities::ReduceSum);
vComm->AllReduce(Fzv, LibUtilities::ReduceSum);
Fz = Fzp + Fzv;
if (vComm->GetRank() == 0)
{
m_outputStream.width(8);
m_outputStream << setprecision(6) << time;
m_outputStream.width(25);
m_outputStream << setprecision(8) << Fxp;
m_outputStream.width(25);
m_outputStream << setprecision(8) << Fxv;
m_outputStream.width(25);
m_outputStream << setprecision(8) << Fx;
m_outputStream.width(25);
m_outputStream << setprecision(8) << Fyp;
m_outputStream.width(25);
m_outputStream << setprecision(8) << Fyv;
m_outputStream.width(25);
m_outputStream << setprecision(8) << Fy;
m_outputStream.width(25);
m_outputStream << setprecision(8) << Fzp;
m_outputStream.width(25);
m_outputStream << setprecision(8) << Fzv;
m_outputStream.width(25);
m_outputStream << setprecision(8) << Fz;
m_outputStream << endl;
}
}
void denseFisherMetric::checkEvolution(const double epsilon)
{
baseHamiltonian::checkEvolution(epsilon);
// Metric
std::cout.precision(6);
int width = 12;
int nColumn = 6;
std::cout << "Gradient of the Fisher-Rao metric (dG^{jk}/dq^{i}):" << std::endl;
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
std::cout << " "
<< std::setw(width) << std::left << "Component"
<< std::setw(width) << std::left << "Row"
<< std::setw(width) << std::left << "Column"
<< std::setw(width) << std::left << "Analytic"
<< std::setw(width) << std::left << "Finite"
<< std::setw(width) << std::left << "Delta /"
<< std::endl;
std::cout << " "
<< std::setw(width) << std::left << "(i)"
<< std::setw(width) << std::left << "(j)"
<< std::setw(width) << std::left << "(k)"
<< std::setw(width) << std::left << "Derivative"
<< std::setw(width) << std::left << "Difference"
<< std::setw(width) << std::left << "Stepsize^{2}"
<< std::endl;
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
for(int k = 0; k < mDim; ++k)
{
fComputeG();
fComputeGradG(k);
MatrixXd temp = MatrixXd::Zero(mDim, mDim);
mQ(k) += epsilon;
fComputeG();
temp += mG;
mQ(k) -= 2.0 * epsilon;
fComputeG();
temp -= mG;
mQ(k ) += epsilon;
temp /= 2.0 * epsilon;
for(int i = 0; i < mDim; ++i)
{
for(int j = 0; j < mDim; ++j)
{
std::cout << " "
<< std::setw(width) << std::left << k
<< std::setw(width) << std::left << i
<< std::setw(width) << std::left << j
<< std::setw(width) << std::left << mGradG(i, j)
<< std::setw(width) << std::left << temp(i, j)
<< std::setw(width) << std::left << (mGradG(i, j) - temp(i, j)) / (epsilon * epsilon)
<< std::endl;
}
}
}
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
std::cout << std::endl;
// Hamiltonian
fComputeCholeskyG();
mC = mGL.solve(mP);
gradV();
std::cout << "pDot (-dH/dq^{i}):" << std::endl;
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
std::cout << " "
<< std::setw(width) << std::left << "Component"
<< std::setw(width) << std::left << "Analytic"
<< std::setw(width) << std::left << "Finite"
<< std::setw(width) << std::left << "Delta /"
<< std::endl;
std::cout << " "
<< std::setw(width) << std::left << "(i)"
<< std::setw(width) << std::left << "Derivative"
<< std::setw(width) << std::left << "Difference"
<< std::setw(width) << std::left << "Stepsize^{2}"
<< std::endl;
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
for(int i = 0; i < mDim; ++i)
{
// Finite Differences
double temp = 0.0;
mQ(i) += epsilon;
temp -= H();
mQ(i) -= 2.0 * epsilon;
temp += H();
mQ(i) += epsilon;
temp /= 2.0 * epsilon;
// Exact
fComputeGradG(i);
double minusGradH = -0.5 * mGL.solve(mGradG).trace();
mAuxVector = mGradG * mC;
minusGradH += 0.5 * mC.dot(mAuxVector);
minusGradH -= mGradV(i);
std::cout << " "
<< std::setw(width) << std::left << i
<< std::setw(width) << std::left << minusGradH
<< std::setw(width) << std::left << temp
<< std::setw(width) << std::left << (minusGradH - temp) / (epsilon * epsilon)
<< std::endl;
}
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
std::cout << std::endl;
}
void softAbsMetric::checkEvolution(const double epsilon)
{
baseHamiltonian::checkEvolution(epsilon);
// Hessian
std::cout.precision(6);
int width = 12;
int nColumn = 5;
std::cout << "Potential Hessian (d^{2}V/dq^{i}dq^{j}):" << std::endl;
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
std::cout << " "
<< std::setw(width) << std::left << "Row"
<< std::setw(width) << std::left << "Column"
<< std::setw(width) << std::left << "Analytic"
<< std::setw(width) << std::left << "Finite"
<< std::setw(width) << std::left << "Delta / "
<< std::endl;
std::cout << " "
<< std::setw(width) << std::left << "(i)"
<< std::setw(width) << std::left << "(j)"
<< std::setw(width) << std::left << "Derivative"
<< std::setw(width) << std::left << "Difference"
<< std::setw(width) << std::left << "Stepsize^{2}"
<< std::endl;
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
fComputeH();
for(int i = 0; i < mDim; ++i)
{
VectorXd temp = VectorXd::Zero(mDim);
mQ(i) += epsilon;
temp += gradV();
mQ(i) -= 2.0 * epsilon;
temp -= gradV();
mQ(i) += epsilon;
temp /= 2.0 * epsilon;
for(int j = 0; j < mDim; ++j)
{
std::cout << " "
<< std::setw(width) << std::left << i
<< std::setw(width) << std::left << j
<< std::setw(width) << std::left << mH(i, j)
<< std::setw(width) << std::left << temp(j)
<< std::setw(width) << std::left << (mH(i, j) - temp(j)) / (epsilon * epsilon)
<< std::endl;
}
}
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
std::cout << std::endl;
// Gradient of the Hessian
std::cout.precision(6);
width = 12;
nColumn = 6;
std::cout << "Gradient of the Hessian (d^{3}V/dq^{i}dq^{j}dq^{k}):" << std::endl;
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
std::cout << " "
<< std::setw(width) << std::left << "Component"
<< std::setw(width) << std::left << "Row"
<< std::setw(width) << std::left << "Column"
<< std::setw(width) << std::left << "Analytic"
<< std::setw(width) << std::left << "Finite"
<< std::setw(width) << std::left << "Delta /"
<< std::endl;
std::cout << " "
<< std::setw(width) << std::left << "(i)"
<< std::setw(width) << std::left << "(j)"
<< std::setw(width) << std::left << "(k)"
<< std::setw(width) << std::left << "Derivative"
<< std::setw(width) << std::left << "Difference"
<< std::setw(width) << std::left << "Stepsize^{2}"
<< std::endl;
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
for(int k = 0; k < mDim; ++k)
{
mAuxMatrixOne.setZero();
mQ(k) += epsilon;
fComputeH();
mAuxMatrixOne += mH;
mQ(k) -= 2.0 * epsilon;
fComputeH();
mAuxMatrixOne -= mH;
mQ(k) += epsilon;
mAuxMatrixOne /= 2.0 * epsilon;
fComputeGradH(k);
for(int i = 0; i < mDim; ++i)
{
for(int j = 0; j < mDim; ++j)
{
std::cout << " "
<< std::setw(width) << std::left << k
<< std::setw(width) << std::left << i
<< std::setw(width) << std::left << j
<< std::setw(width) << std::left << mGradH.block(0, k * mDim, mDim, mDim)(i, j)
<< std::setw(width) << std::left << mAuxMatrixOne(i, j)
<< std::setw(width) << std::left << (mGradH.block(0, k * mDim, mDim, mDim)(i, j) - mAuxMatrixOne(i, j)) / (epsilon * epsilon)
<< std::endl;
}
}
}
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
std::cout << std::endl;
// Metric
std::cout.precision(6);
width = 12;
nColumn = 6;
std::cout << "Gradient of the metric (dLambda^{jk}/dq^{i}):" << std::endl;
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
std::cout << " "
<< std::setw(width) << std::left << "Component"
<< std::setw(width) << std::left << "Row"
<< std::setw(width) << std::left << "Column"
<< std::setw(width) << std::left << "Analytic"
<< std::setw(width) << std::left << "Finite"
<< std::setw(width) << std::left << "Delta /"
<< std::endl;
std::cout << " "
<< std::setw(width) << std::left << "(i)"
<< std::setw(width) << std::left << "(j)"
<< std::setw(width) << std::left << "(k)"
<< std::setw(width) << std::left << "Derivative"
<< std::setw(width) << std::left << "Difference"
<< std::setw(width) << std::left << "Epsilon^{2}"
<< std::endl;
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
fComputeMetric();
fPrepareSpatialGradients();
for(int k = 0; k < mDim; ++k)
{
// Approximate metric gradient
MatrixXd temp = MatrixXd::Zero(mDim, mDim);
MatrixXd G = MatrixXd::Zero(mDim, mDim);
mQ(k) += epsilon;
fComputeMetric();
G.noalias() = mEigenDeco.eigenvectors() * mSoftAbsLambda.asDiagonal() * mEigenDeco.eigenvectors().transpose();
temp += G;
mQ(k) -= 2.0 * epsilon;
fComputeMetric();
G.noalias() = mEigenDeco.eigenvectors() * mSoftAbsLambda.asDiagonal() * mEigenDeco.eigenvectors().transpose();
temp -= G;
mQ(k) += epsilon;
temp /= 2.0 * epsilon;
// Exact metric gradient
fComputeMetric();
fComputeGradH(k);
mAuxMatrixOne.noalias() = mGradH.block(0, k * mDim, mDim, mDim) * mEigenDeco.eigenvectors();
mAuxMatrixTwo.noalias() = mEigenDeco.eigenvectors().transpose() * mAuxMatrixOne;
mAuxMatrixOne.noalias() = mPseudoJ.cwiseProduct(mAuxMatrixTwo);
mCacheMatrix.noalias() = mAuxMatrixOne * mEigenDeco.eigenvectors().transpose();
MatrixXd gradG = mEigenDeco.eigenvectors() * mCacheMatrix;
// Compare
for(int i = 0; i < mDim; ++i)
{
for(int j = 0; j < mDim; ++j)
{
std::cout << " "
<< std::setw(width) << std::left << k
<< std::setw(width) << std::left << i
<< std::setw(width) << std::left << j
<< std::setw(width) << std::left << gradG(i, j)
<< std::setw(width) << std::left << temp(i, j)
<< std::setw(width) << std::left << (gradG(i, j) - temp(i, j)) / (epsilon * epsilon)
<< std::endl;
}
}
}
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
std::cout << std::endl;
// Hamiltonian
VectorXd gradH = dTaudq();
gradH += dPhidq();
std::cout << "pDot (-dH/dq^{i}):" << std::endl;
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
std::cout << " "
<< std::setw(width) << std::left << "Component"
<< std::setw(width) << std::left << "Analytic"
<< std::setw(width) << std::left << "Finite"
<< std::setw(width) << std::left << "Delta /"
<< std::endl;
std::cout << " "
<< std::setw(width) << std::left << "(i)"
<< std::setw(width) << std::left << "Derivative"
<< std::setw(width) << std::left << "Difference"
<< std::setw(width) << std::left << "Epsilon^{2}"
<< std::endl;
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
for(int i = 0; i < mDim; ++i)
{
// Finite Differences
double temp = 0.0;
mQ(i) += epsilon;
temp -= H();
mQ(i) -= 2.0 * epsilon;
temp += H();
mQ(i) += epsilon;
temp /= 2.0 * epsilon;
// Exact
double minusGradH = -gradH(i);
std::cout << " "
<< std::setw(width) << std::left << i
<< std::setw(width) << std::left << minusGradH
<< std::setw(width) << std::left << temp
<< std::setw(width) << std::left << (minusGradH - temp) / (epsilon * epsilon)
<< std::endl;
}
std::cout << " " << std::setw(nColumn * width) << std::setfill('-') << "" << std::setfill(' ') << std::endl;
std::cout << std::endl;
}
