double ChLcpIterativePCG::Solve(
ChLcpSystemDescriptor& sysd ///< system description with constraints and variables
)
{
std::vector<ChLcpConstraint*>& mconstraints = sysd.GetConstraintsList();
std::vector<ChLcpVariables*>& mvariables = sysd.GetVariablesList();
tot_iterations = 0;
double maxviolation = 0.;
// Update auxiliary data in all constraints before starting,
// that is: g_i=[Cq_i]*[invM_i]*[Cq_i]' and [Eq_i]=[invM_i]*[Cq_i]'
for (unsigned int ic = 0; ic< mconstraints.size(); ic++)
mconstraints[ic]->Update_auxiliary();
// Allocate auxiliary vectors;
int nc = sysd.CountActiveConstraints();
if (verbose) GetLog() <<"\n-----Projected CG, solving nc=" << nc << "unknowns \n";
ChMatrixDynamic<> ml(nc,1);
ChMatrixDynamic<> mb(nc,1);
ChMatrixDynamic<> mu(nc,1);
ChMatrixDynamic<> mp(nc,1);
ChMatrixDynamic<> mw(nc,1);
ChMatrixDynamic<> mz(nc,1);
ChMatrixDynamic<> mNp(nc,1);
ChMatrixDynamic<> mtmp(nc,1);
double graddiff= 0.00001; // explorative search step for gradient
// ***TO DO*** move the following thirty lines in a short function ChLcpSystemDescriptor::ShurBvectorCompute() ?
// Compute the b_shur vector in the Shur complement equation N*l = b_shur
// with
// N_shur = D'* (M^-1) * D
// b_shur = - c + D'*(M^-1)*k = b_i + D'*(M^-1)*k
// but flipping the sign of lambdas, b_shur = - b_i - D'*(M^-1)*k
// Do this in three steps:
// Put (M^-1)*k in q sparse vector of each variable..
for (unsigned int iv = 0; iv< mvariables.size(); iv++)
if (mvariables[iv]->IsActive())
mvariables[iv]->Compute_invMb_v(mvariables[iv]->Get_qb(), mvariables[iv]->Get_fb()); // q = [M]'*fb
// ...and now do b_shur = - D' * q ..
int s_i = 0;
for (unsigned int ic = 0; ic< mconstraints.size(); ic++)
if (mconstraints[ic]->IsActive())
{
mb(s_i, 0) = - mconstraints[ic]->Compute_Cq_q();
++s_i;
}
// ..and finally do b_shur = b_shur - c
sysd.BuildBiVector(mtmp); // b_i = -c = phi/h
mb.MatrDec(mtmp);
// Optimization: backup the q sparse data computed above,
// because (M^-1)*k will be needed at the end when computing primals.
ChMatrixDynamic<> mq;
sysd.FromVariablesToVector(mq, true);
// Initialize lambdas
if (warm_start)
sysd.FromConstraintsToVector(ml);
else
ml.FillElem(0);
// Initial projection of ml ***TO DO***?
// ...
std::vector<bool> en_l(nc);
// Initially all constraints are enabled
for (int ie= 0; ie < nc; ie++)
en_l[ie] = true;
// u = -N*l+b
sysd.ShurComplementProduct(mu, &ml, &en_l); // 1) u = N*l ... #### MATR.MULTIPLICATION!!!###
mu.MatrNeg(); // 2) u =-N*l
mu.MatrInc(mb); // 3) u =-N*l+b
mp = mu;
//
// THE LOOP
//
std::vector<double> f_hist;
for (int iter = 0; iter < max_iterations; iter++)
{
// alpha = u'*p / p'*N*p
sysd.ShurComplementProduct(mNp, &mp, &en_l);// 1) Np = N*p ... #### MATR.MULTIPLICATION!!!###
double pNp = mp.MatrDot(&mp,&mNp); // 2) pNp = p'*N*p
double up = mu.MatrDot(&mu,&mp); // 3) up = u'*p
double alpha = up/pNp; // 4) alpha = u'*p / p'*N*p
if (fabs(pNp)<10e-10) GetLog() << "Rayleygh quotient pNp breakdown \n";
// l = l + alpha * p;
mtmp.CopyFromMatrix(mp);
mtmp.MatrScale(alpha);
ml.MatrInc(mtmp);
double maxdeltalambda = mtmp.NormInf();
// l = Proj(l)
sysd.ConstraintsProject(ml); // 5) l = P(l)
// u = -N*l+b
sysd.ShurComplementProduct(mu, &ml, 0); // 6) u = N*l ... #### MATR.MULTIPLICATION!!!###
mu.MatrNeg(); // 7) u =-N*l
mu.MatrInc(mb); // 8) u =-N*l+b
// w = (Proj(l+lambda*u) -l) /lambda;
mw.CopyFromMatrix(mu);
mw.MatrScale(graddiff);
mw.MatrInc(ml);
sysd.ConstraintsProject(mw); // 9) w = P(l+lambda*u) ...
mw.MatrDec(ml);
mw.MatrScale(1.0/graddiff); //10) w = (P(l+lambda*u)-l)/lambda ...
// z = (Proj(l+lambda*p) -l) /lambda;
mz.CopyFromMatrix(mp);
mz.MatrScale(graddiff);
mz.MatrInc(ml);
sysd.ConstraintsProject(mz); //11) z = P(l+lambda*u) ...
mz.MatrDec(ml);
mz.MatrScale(1.0/graddiff); //12) z = (P(l+lambda*u)-l)/lambda ...
// beta = w'*Np / pNp;
double wNp = mw.MatrDot(&mw, &mNp);
double beta = wNp / pNp;
// p = w + beta * z;
mp.CopyFromMatrix(mz);
mp.MatrScale(beta);
mp.MatrInc(mw);
// METRICS - convergence, plots, etc
double maxd = mu.NormInf(); // ***TO DO*** should be max violation, but just for test...
// For recording into correction/residuals/violation history, if debugging
if (this->record_violation_history)
AtIterationEnd(maxd, maxdeltalambda, iter);
tot_iterations++;
}
// Resulting DUAL variables:
// store ml temporary vector into ChLcpConstraint 'l_i' multipliers
sysd.FromVectorToConstraints(ml);
// Resulting PRIMAL variables:
// compute the primal variables as v = (M^-1)(k + D*l)
// v = (M^-1)*k ... (by rewinding to the backup vector computed ad the beginning)
sysd.FromVectorToVariables(mq);
// ... + (M^-1)*D*l (this increment and also stores 'qb' in the ChLcpVariable items)
for (unsigned int ic = 0; ic < mconstraints.size(); ic++)
{
if (mconstraints[ic]->IsActive())
mconstraints[ic]->Increment_q( mconstraints[ic]->Get_l_i() );
}
if (verbose) GetLog() <<"-----\n";
return maxviolation;
}
double ChLcpIterativeAPGD::Solve(
ChLcpSystemDescriptor& sysd ///< system description with constraints and variables
)
{
std::vector<ChLcpConstraint*>& mconstraints = sysd.GetConstraintsList();
std::vector<ChLcpVariables*>& mvariables = sysd.GetVariablesList();
double gdiff= 0.000001;
double maxviolation = 0.;
int i_friction_comp = 0;
double theta_k=1.0;
double theta_k1=theta_k;
double beta_k1=0.0;
double L_k=0.0;
double t_k=0.0;
tot_iterations = 0;
// Allocate auxiliary vectors;
int nc = sysd.CountActiveConstraints();
if (verbose) GetLog() <<"\n-----Accelerated Projected Gradient Descent, solving nc=" << nc << "unknowns \n";
//ChMatrixDynamic<> ml(nc,1); //I made this into a class variable so I could print it easier -Hammad
ml.Resize(nc,1);
ChMatrixDynamic<> mx(nc,1);
ChMatrixDynamic<> ms(nc,1);
ChMatrixDynamic<> my(nc,1);
ChMatrixDynamic<> ml_candidate(nc,1);
ChMatrixDynamic<> mg(nc,1);
ChMatrixDynamic<> mg_tmp(nc,1);
ChMatrixDynamic<> mg_tmp1(nc,1);
ChMatrixDynamic<> mg_tmp2(nc,1);
//ChMatrixDynamic<> mb(nc,1); //I made this into a class variable so I could print it easier -Hammad
mb.Resize(nc,1);
ChMatrixDynamic<> mb_tmp(nc,1);
// Update auxiliary data in all constraints before starting,
// that is: g_i=[Cq_i]*[invM_i]*[Cq_i]' and [Eq_i]=[invM_i]*[Cq_i]'
for (unsigned int ic = 0; ic< mconstraints.size(); ic++)
mconstraints[ic]->Update_auxiliary();
// Average all g_i for the triplet of contact constraints n,u,v.
// Can be used for the fixed point phase and/or by preconditioner.
int j_friction_comp = 0;
double gi_values[3];
for (unsigned int ic = 0; ic< mconstraints.size(); ic++)
{
if (mconstraints[ic]->GetMode() == CONSTRAINT_FRIC)
{
gi_values[j_friction_comp] = mconstraints[ic]->Get_g_i();
j_friction_comp++;
if (j_friction_comp==3)
{
double average_g_i = (gi_values[0]+gi_values[1]+gi_values[2])/3.0;
mconstraints[ic-2]->Set_g_i(average_g_i);
mconstraints[ic-1]->Set_g_i(average_g_i);
mconstraints[ic-0]->Set_g_i(average_g_i);
j_friction_comp=0;
}
}
}
// ***TO DO*** move the following thirty lines in a short function ChLcpSystemDescriptor::ShurBvectorCompute() ?
// Compute the b_shur vector in the Shur complement equation N*l = b_shur
// with
// N_shur = D'* (M^-1) * D
// b_shur = - c + D'*(M^-1)*k = b_i + D'*(M^-1)*k
// but flipping the sign of lambdas, b_shur = - b_i - D'*(M^-1)*k
// Do this in three steps:
// Put (M^-1)*k in q sparse vector of each variable..
for (unsigned int iv = 0; iv< mvariables.size(); iv++)
if (mvariables[iv]->IsActive())
mvariables[iv]->Compute_invMb_v(mvariables[iv]->Get_qb(), mvariables[iv]->Get_fb()); // q = [M]'*fb
// ...and now do b_shur = - D'*q = - D'*(M^-1)*k ..
int s_i = 0;
for (unsigned int ic = 0; ic< mconstraints.size(); ic++)
if (mconstraints[ic]->IsActive())
{
mb(s_i, 0) = - mconstraints[ic]->Compute_Cq_q();
++s_i;
}
// ..and finally do b_shur = b_shur - c
sysd.BuildBiVector(mb_tmp); // b_i = -c = phi/h
mb.MatrDec(mb_tmp);
// Optimization: backup the q sparse data computed above,
// because (M^-1)*k will be needed at the end when computing primals.
ChMatrixDynamic<> mq;
sysd.FromVariablesToVector(mq, true);
// Initialize lambdas
if (warm_start)
sysd.FromConstraintsToVector(ml);
else
ml.FillElem(0);
// Initial projection of ml ***TO DO***?
sysd.ConstraintsProject(ml);
// Fallback solution
double lastgoodres = 10e30;
double lastgoodfval = 10e30;
ml_candidate.CopyFromMatrix(ml);
// g = gradient of 0.5*l'*N*l-l'*b
// g = N*l-b
sysd.ShurComplementProduct(mg, &ml, 0); // 1) g = N*l ... #### MATR.MULTIPLICATION!!!###
mg.MatrDec(mb); // 2) g = N*l - b_shur ...
//
// THE LOOP
//
double mf_p =0;
mb_tmp.FillElem(-1.0);
mb_tmp.MatrInc(ml);
sysd.ShurComplementProduct(mg_tmp,&mb_tmp,0); // 1) g = N*l ... #### MATR.MULTIPLICATION!!!###
if(mb_tmp.NormTwo()==0){
L_k=1;
}else{
L_k=mg_tmp.NormTwo()/mb_tmp.NormTwo();
}
t_k=1/L_k;
double obj1=0;
double obj2=0;
my.CopyFromMatrix(ml);
mx.CopyFromMatrix(ml);
for (int iter = 0; iter < max_iterations; iter++)
{
sysd.ShurComplementProduct(mg_tmp1, &my, 0); // 1) g_tmp1 = N*yk ... #### MATR.MULTIPLICATION!!!###
mg.MatrSub(mg_tmp1,mb); // 2) g = N*yk - b_shur ...
mx.CopyFromMatrix(mg); // 1) xk1=g
mx.MatrScale(-t_k); // 2) xk1=-tk*g
mx.MatrInc(my); // 3) xk1=y-tk*g
sysd.ConstraintsProject(mx); // 4) xk1=P(y-tk*g)
//Now do backtracking for the steplength
sysd.ShurComplementProduct(mg_tmp, &mx, 0); // 1) g_tmp = N*xk1 ... #### MATR.MULTIPLICATION!!!###
mg_tmp2.MatrSub(mg_tmp,mb); // 2) g_tmp2 = N*xk1 - b_shur ...
mg_tmp.MatrScale(0.5); // 3) g_tmp=0.5*N*xk1
mg_tmp.MatrDec(mb); // 4) g_tmp=0.5*N*xk1-b_shur
obj1 = mx.MatrDot(&mx,&mg_tmp); // 5) obj1=xk1'*(0.5*N*x_k1-b_shur)
mg_tmp1.MatrScale(0.5); // 1) g_tmp1 = 0.5*N*yk
mg_tmp1.MatrDec(mb); // 2) g_tmp1 = 0.5*N*yk-b_shur
obj2 = my.MatrDot(&my,&mg_tmp1); // 3) obj2 = yk'*(0.5*N*yk-b_shur)
ms.MatrSub(mx,my); // 1) s=xk1-yk
while(obj1>obj2+mg.MatrDot(&mg,&ms)+0.5*L_k*pow(ms.NormTwo(),2.0))
{
L_k=2*L_k;
t_k=1/L_k;
mx.CopyFromMatrix(mg); // 1) xk1=g
mx.MatrScale(-t_k); // 2) xk1=-tk*g
mx.MatrInc(my); // 3) xk1=yk-tk*g
sysd.ConstraintsProject(mx); // 4) xk1=P(yk-tk*g)
sysd.ShurComplementProduct(mg_tmp, &mx, 0); // 1) g_tmp = N*xk1 ... #### MATR.MULTIPLICATION!!!###
mg_tmp2.MatrSub(mg_tmp,mb); // 2) g_tmp2 = N*xk1 - b_shur ...
mg_tmp.MatrScale(0.5); // 3) g_tmp=0.5*N*xk1
mg_tmp.MatrDec(mb); // 4) g_tmp=0.5*N*xk1-b_shur
obj1 = mx.MatrDot(&mx,&mg_tmp); // 5) obj1=xk1'*(0.5*N*x_k1-b_shur)
ms.MatrSub(mx,my); // 1) s=xk1-yk
if (verbose) GetLog() << "APGD halving stepsize at it " << iter << "\n";
}
theta_k1=(-pow(theta_k,2)+theta_k*sqrt(pow(theta_k,2)+4))/2.0;
beta_k1=theta_k*(1.0-theta_k)/(pow(theta_k,2)+theta_k1);
my.CopyFromMatrix(mx); // 1) y=xk1;
my.MatrDec(ml); // 2) y=xk1-xk;
my.MatrScale(beta_k1); // 3) y=beta_k1*(xk1-xk);
my.MatrInc(mx); // 4) y=xk1+beta_k1*(xk1-xk);
ms.MatrSub(mx,ml); // 0) s = xk1 - xk;
// Restarting logic if momentum is not appropriate
if (mg.MatrDot(&mg,&ms)>0)
{
my.CopyFromMatrix(mx); // 1) y=xk1
theta_k1=1.0; // 2) theta_k=1
if (verbose) GetLog() << "Restarting APGD at it " << iter << "\n";
}
//Allow the step to grow...
L_k=0.9*L_k;
t_k=1/L_k;
ml.CopyFromMatrix(mx); // 1) xk=xk1;
theta_k=theta_k1; // 2) theta_k=theta_k1;
//****METHOD 1 for residual, same as ChLcpIterativeBB
// Project the gradient (for rollback strategy)
// g_proj = (l-project_orthogonal(l - gdiff*g, fric))/gdiff;
mb_tmp.CopyFromMatrix(mg_tmp2);
mb_tmp.MatrScale(-gdiff);
mb_tmp.MatrInc(ml);
sysd.ConstraintsProject(mb_tmp);
mb_tmp.MatrDec(ml);
mb_tmp.MatrDivScale(-gdiff);
double g_proj_norm = mb_tmp.NormTwo(); // NormInf() is faster..
//****End of METHOD 1 for residual, same as ChLcpIterativeBB
//****METHOD 2 for residual, same as ChLcpIterativeSOR
maxviolation = 0;
i_friction_comp = 0;
for (unsigned int ic = 0; ic< mconstraints.size(); ic++)
{
if (mconstraints[ic]->IsActive())
{
// true constraint violation may be different from 'mresidual' (ex:clamped if unilateral)
double candidate_violation = fabs(mconstraints[ic]->Violation(mg_tmp2.ElementN(ic)));
if (mconstraints[ic]->GetMode() == CONSTRAINT_FRIC)
{
candidate_violation = 0;
i_friction_comp++;
if (i_friction_comp==1)
candidate_violation = fabs(ChMin(0.0,mg_tmp2.ElementN(ic)));
if (i_friction_comp==3)
i_friction_comp =0;
}
else
{
}
maxviolation = ChMax(maxviolation, fabs(candidate_violation));
}
}
g_proj_norm=maxviolation;
//****End of METHOD 2 for residual, same as ChLcpIterativeSOR
// Rollback solution: the last best candidate ('l' with lowest projected gradient)
// in fact the method is not monotone and it is quite 'noisy', if we do not
// do this, a prematurely truncated iteration might give a crazy result.
if(g_proj_norm < lastgoodres)
{
lastgoodres = g_proj_norm;
ml_candidate = ml;
}
// METRICS - convergence, plots, etc
if (verbose)
{
// f_p = 0.5*l_candidate'*N*l_candidate - l_candidate'*b = l_candidate'*(0.5*Nl_candidate - b);
sysd.ShurComplementProduct(mg_tmp, &ml_candidate, 0); // 1) g_tmp = N*l_candidate ... #### MATR.MULTIPLICATION!!!###
mg_tmp.MatrScale(0.5); // 2) g_tmp = 0.5*N*l_candidate
mg_tmp.MatrDec(mb); // 3) g_tmp = 0.5*N*l_candidate-b_shur
mf_p = ml_candidate.MatrDot(&ml_candidate,&mg_tmp); // 4) mf_p = l_candidate'*(0.5*N*l_candidate-b_shur)
}
double maxdeltalambda = ms.NormInf();
double maxd = lastgoodres;
// For recording into correction/residuals/violation history, if debugging
if (this->record_violation_history)
AtIterationEnd(maxd, maxdeltalambda, iter);
if (verbose) GetLog() << " iter=" << iter << " f=" << mf_p << " |d|=" << maxd << " |s|=" << maxdeltalambda << "\n";
tot_iterations++;
// Terminate the loop if violation in constraints has been succesfully limited.
// ***TO DO*** a reliable termination creterion..
///*
if (maxd < this->tolerance)
{
if (verbose) GetLog() <<"APGD premature converged at i=" << iter << "\n";
break;
}
//*/
}
// Fallback to best found solution (might be useful because of nonmonotonicity)
ml.CopyFromMatrix(ml_candidate);
// Resulting DUAL variables:
// store ml temporary vector into ChLcpConstraint 'l_i' multipliers
sysd.FromVectorToConstraints(ml);
// Resulting PRIMAL variables:
// compute the primal variables as v = (M^-1)(k + D*l)
// v = (M^-1)*k ... (by rewinding to the backup vector computed ad the beginning)
sysd.FromVectorToVariables(mq);
// ... + (M^-1)*D*l (this increment and also stores 'qb' in the ChLcpVariable items)
for (unsigned int ic = 0; ic < mconstraints.size(); ic++)
{
if (mconstraints[ic]->IsActive())
mconstraints[ic]->Increment_q( mconstraints[ic]->Get_l_i() );
}
if (verbose) GetLog() <<"-----\n";
current_residual = lastgoodres;
return lastgoodres;
}