void
MultiGrid::solve (MultiFab& _sol,
const MultiFab& _rhs,
Real _eps_rel,
Real _eps_abs,
LinOp::BC_Mode bc_mode)
{
//
// Prepare memory for new level, and solve the general boundary
// value problem to within relative error _eps_rel. Customized
// to solve at level=0.
//
const int level = 0;
prepareForLevel(level);
//
// Copy the initial guess, which may contain inhomogeneous boundray conditions,
// into both "initialsolution" (to be added back later) and into "cor[0]" which
// we will only use here to compute the residual, then will set back to 0 below
//
initialsolution->copy(_sol);
cor[level]->copy(_sol);
//
// Put the problem in residual-correction form: we will now use "rhs[level
// the initial residual (rhs[0]) rather than the initial RHS (_rhs)
// to begin the solve.
//
Lp.residual(*rhs[level],_rhs,*cor[level],level,bc_mode);
//
// Now initialize correction to zero at this level (auto-filled at levels below)
//
(*cor[level]).setVal(0.0); //
//
// Elide a reduction by doing these together.
//
Real tmp[2] = { norm_inf(_rhs,true), norm_inf(*rhs[level],true) };
ParallelDescriptor::ReduceRealMax(tmp,2);
if ( ParallelDescriptor::IOProcessor() && verbose > 0)
{
Spacer(std::cout, level);
std::cout << "MultiGrid: Initial rhs = " << tmp[0] << '\n';
std::cout << "MultiGrid: Initial residual = " << tmp[1] << '\n';
}
if (tmp[1] == 0.0)
return;
//
// We can now use homogeneous bc's because we have put the problem into residual-correction form.
//
if ( !solve_(_sol, _eps_rel, _eps_abs, LinOp::Homogeneous_BC, tmp[0], tmp[1]) )
BoxLib::Error("MultiGrid:: failed to converge!");
}
int
MultiGrid::solve_ (MultiFab& _sol,
Real eps_rel,
Real eps_abs,
LinOp::BC_Mode bc_mode,
Real bnorm,
Real resnorm0)
{
BL_PROFILE("MultiGrid::solve_()");
//
// If do_fixed_number_of_iters = 1, then do maxiter iterations without checking for convergence
//
// If do_fixed_number_of_iters = 0, then relax system maxiter times,
// and stop if relative error <= _eps_rel or if absolute err <= _abs_eps
//
const Real strt_time = ParallelDescriptor::second();
const int level = 0;
//
// We take the max of the norms of the initial RHS and the initial residual in order to capture both cases
//
Real norm_to_test_against;
bool using_bnorm;
if (bnorm >= resnorm0)
{
norm_to_test_against = bnorm;
using_bnorm = true;
} else {
norm_to_test_against = resnorm0;
using_bnorm = false;
}
int returnVal = 0;
Real error = resnorm0;
//
// Note: if eps_rel, eps_abs < 0 then that test is effectively bypassed
//
if ( ParallelDescriptor::IOProcessor() && eps_rel < 1.0e-16 && eps_rel > 0 )
{
std::cout << "MultiGrid: Tolerance "
<< eps_rel
<< " < 1e-16 is probably set too low" << '\n';
}
//
// We initially define norm_cor based on the initial solution only so we can use it in the very first iteration
// to decide whether the problem is already solved (this is relevant if the previous solve used was only solved
// according to the Anorm test and not the bnorm test).
//
Real norm_cor = norm_inf(*initialsolution,true);
ParallelDescriptor::ReduceRealMax(norm_cor);
int nit = 1;
const Real norm_Lp = Lp.norm(0, level);
Real cg_time = 0;
if ( use_Anorm_for_convergence == 1 )
{
//
// Don't need to go any further -- no iterations are required
//
if (error <= eps_abs || error < eps_rel*(norm_Lp*norm_cor+norm_to_test_against))
{
if ( ParallelDescriptor::IOProcessor() && (verbose > 0) )
{
std::cout << " Problem is already converged -- no iterations required\n";
}
return 1;
}
for ( ;
( (error > eps_abs &&
error > eps_rel*(norm_Lp*norm_cor+norm_to_test_against)) ||
(do_fixed_number_of_iters == 1) )
&& nit <= maxiter;
++nit)
{
relax(*cor[level], *rhs[level], level, eps_rel, eps_abs, bc_mode, cg_time);
Real tmp[2] = { norm_inf(*cor[level],true), errorEstimate(level,bc_mode,true) };
ParallelDescriptor::ReduceRealMax(tmp,2);
norm_cor = tmp[0];
error = tmp[1];
if ( ParallelDescriptor::IOProcessor() && verbose > 1 )
{
const Real rel_error = error / norm_to_test_against;
Spacer(std::cout, level);
if (using_bnorm)
{
std::cout << "MultiGrid: Iteration "
<< nit
<< " resid/bnorm = "
<< rel_error << '\n';
} else {
std::cout << "MultiGrid: Iteration "
<< nit
<< " resid/resid0 = "
<< rel_error << '\n';
}
}
}
}
else
{
//
// Don't need to go any further -- no iterations are required
//
if (error <= eps_abs || error < eps_rel*norm_to_test_against)
{
if ( ParallelDescriptor::IOProcessor() && (verbose > 0) )
{
std::cout << " Problem is already converged -- no iterations required\n";
}
return 1;
}
for ( ;
( (error > eps_abs &&
error > eps_rel*norm_to_test_against) ||
(do_fixed_number_of_iters == 1) )
&& nit <= maxiter;
++nit)
{
relax(*cor[level], *rhs[level], level, eps_rel, eps_abs, bc_mode, cg_time);
error = errorEstimate(level, bc_mode);
if ( ParallelDescriptor::IOProcessor() && verbose > 1 )
{
const Real rel_error = error / norm_to_test_against;
Spacer(std::cout, level);
if (using_bnorm)
{
std::cout << "MultiGrid: Iteration "
<< nit
<< " resid/bnorm = "
<< rel_error << '\n';
} else {
std::cout << "MultiGrid: Iteration "
<< nit
<< " resid/resid0 = "
<< rel_error << '\n';
}
}
}
}
Real run_time = (ParallelDescriptor::second() - strt_time);
if ( verbose > 0 )
{
if ( ParallelDescriptor::IOProcessor() )
{
const Real rel_error = error / norm_to_test_against;
Spacer(std::cout, level);
if (using_bnorm)
{
std::cout << "MultiGrid: Iteration "
<< nit-1
<< " resid/bnorm = "
<< rel_error << '\n';
} else {
std::cout << "MultiGrid: Iteration "
<< nit-1
<< " resid/resid0 = "
<< rel_error << '\n';
}
}
if ( verbose > 1 )
{
Real tmp[2] = { run_time, cg_time };
ParallelDescriptor::ReduceRealMax(tmp,2,ParallelDescriptor::IOProcessorNumber());
if ( ParallelDescriptor::IOProcessor() )
std::cout << ", Solve time: " << tmp[0] << ", CG time: " << tmp[1];
}
if ( ParallelDescriptor::IOProcessor() ) std::cout << '\n';
}
if ( ParallelDescriptor::IOProcessor() && (verbose > 0) )
{
if ( do_fixed_number_of_iters == 1)
{
std::cout << " Did fixed number of iterations: " << maxiter << std::endl;
}
else if ( error < eps_rel*norm_to_test_against )
{
std::cout << " Converged res < eps_rel*max(bnorm,res_norm)\n";
}
else if ( (use_Anorm_for_convergence == 1) && (error < eps_rel*norm_Lp*norm_cor) )
{
std::cout << " Converged res < eps_rel*Anorm*sol\n";
}
else if ( error < eps_abs )
{
std::cout << " Converged res < eps_abs\n";
}
}
//
// Omit ghost update since maybe not initialized in calling routine.
// Add to boundary values stored in initialsolution.
//
_sol.copy(*cor[level]);
_sol.plus(*initialsolution,0,_sol.nComp(),0);
if ( use_Anorm_for_convergence == 1 )
{
if ( do_fixed_number_of_iters == 1 ||
error <= eps_rel*(norm_Lp*norm_cor+norm_to_test_against) ||
error <= eps_abs )
returnVal = 1;
}
else
{
if ( do_fixed_number_of_iters == 1 ||
error <= eps_rel*(norm_to_test_against) ||
error <= eps_abs )
returnVal = 1;
}
//
// Otherwise, failed to solve satisfactorily
//
return returnVal;
}
void runGui(OrbGui &gui)
{
// GUI state
vec2i wndSize = gui.input->getWindowSize();
// set up the default projection & modelview matrices
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glOrtho(0.0, (double)wndSize.x, (double)wndSize.y, 0.0, 10.0, -10.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
ColumnLayout lyt(FixedLayout(10, 10, 200, wndSize.y), 10, 10, 10, 10, 3);
Label("Ikarus").run(gui, lyt);
Spacer(vec2i(0, 10)).run(gui, lyt);
Label("Skeleton:").run(gui, lyt);
ComboBox skelSel("skeleton-sel", WidgetID(curSkel));
for (int i = 0; i < (int)skeletons.size(); ++i)
skelSel.add(WidgetID(i), skeletons[i].name);
curSkel = skelSel.run(gui, lyt).getIndex();
if (Button("reload-btn", "Reload").run(gui, lyt))
skeletons.reset_at(curSkel, new SkeletonItem(skeletons[curSkel].fname, skeletons[curSkel].name));
SkeletonItem &skel = skeletons[curSkel];
Spacer(vec2i(0, 10)).run(gui, lyt);
if (Button("reset-btn", "Reset Pose").run(gui, lyt))
{
skel.solver->resetPose();
skel.targetPos = skel.solver->getEffectorPos();
targetSpeed = 0.0;
}
if (Button("reset-all-btn", "Reset All").run(gui, lyt))
{
skel.solver->resetAll();
skel.targetPos = skel.solver->getEffectorPos();
targetSpeed = 0.0;
}
// the grid is always shown
// (no point turning it off really)
//showGrid = CheckBox("show-grid-chk", "Show grid", showGrid).run(gui, lyt);
showJointBasis = CheckBox("show-joint-basis-chk", "Show joint basis vectors", showJointBasis).run(gui, lyt);
showConstraints = CheckBox("show-constraints-chk", "Show joint constraints", showConstraints).run(gui, lyt);
ikMode = CheckBox("ik-mode-chk", "IK Mode", ikMode).run(gui, lyt);
ikEnabled = CheckBox("ik-enabled-chk", "IK Enabled", ikEnabled, ikMode).run(gui, lyt);
bool constraintsOn = CheckBox("ik-constrained-chk", "Enable Constraints", skel.solver->areConstraintsEnabled(), ikMode).run(gui, lyt);
skel.solver->enableConstraints(constraintsOn);
if (Button("solve-btn", "Solve", ikMode && !ikEnabled).run(gui, lyt))
skel.solver->solveIk(30);
if (Button("step-btn", "Step IK", ikMode && !ikEnabled).run(gui, lyt))
skel.solver->iterateIk();
if (Button("constraint-btn", "Apply Constraints", ikMode).run(gui, lyt))
{
skel.solver->applyAllConstraints();
skel.targetPos = skel.solver->getEffectorPos();
targetSpeed = 0.0;
}
Label("Root bone:").run(gui, lyt);
ComboBox rootSel("root-sel", WidgetID(&skel.solver->getRootBone()));
for (int i = 0; i < skel.skeleton.numBones(); ++i)
{
const Bone &b = skel.skeleton[i];
if (! b.isEffector())
rootSel.add(WidgetID(&b), b.name);
}
const Bone *newRootBone = rootSel.run(gui, lyt).getData<const Bone>();
skel.solver->setRootBone(*newRootBone);
Label("Effector:").run(gui, lyt);
ComboBox effectorSel("effector-sel", WidgetID(&skel.solver->getEffector()));
for (int i = 0; i < skel.skeleton.numBones(); ++i)
{
const Bone &b = skel.skeleton[i];
if (b.isEffector())
effectorSel.add(WidgetID(&b), b.name);
}
const Bone *newEffector = effectorSel.run(gui, lyt).getData<const Bone>();
if (newEffector != &skel.solver->getEffector())
{
skel.solver->setEffector(*newEffector);
skel.solver->setTargetPos(skel.solver->getEffectorPos());
skel.targetPos = skel.solver->getEffectorPos();
}
int leftRightSplit = 250;
int topBottomSplit = wndSize.y - 200;
int a = leftRightSplit + (wndSize.x - leftRightSplit) / 3;
int b = leftRightSplit + ((wndSize.x - leftRightSplit)*2) / 3;
FixedLayout mainViewLyt(leftRightSplit, 0, wndSize.x - leftRightSplit, topBottomSplit);
FixedLayout ortho0Lyt(leftRightSplit, topBottomSplit, a - leftRightSplit, wndSize.y - topBottomSplit);
FixedLayout ortho1Lyt(a, topBottomSplit, b - a, wndSize.y - topBottomSplit);
FixedLayout ortho2Lyt(b, topBottomSplit, wndSize.x - b, wndSize.y - topBottomSplit);
if (ikMode)
{
IkSolverDisplay("displayP", &camPerspective, skel.solver.get(), showJointBasis, showConstraints, showGrid ? gridList : 0).run(gui, mainViewLyt);
IkSolverDisplay("displayX", &camX, skel.solver.get(), showJointBasis, showConstraints).run(gui, ortho0Lyt);
IkSolverDisplay("displayY", &camY, skel.solver.get(), showJointBasis, showConstraints).run(gui, ortho1Lyt);
IkSolverDisplay("displayZ", &camZ, skel.solver.get(), showJointBasis, showConstraints).run(gui, ortho2Lyt);
}
else
{
SkeletonDisplay("displayP", &camPerspective, &skel.skeleton, showJointBasis, showConstraints, showGrid ? gridList : 0).run(gui, mainViewLyt);
SkeletonDisplay("displayX", &camX, &skel.skeleton, showJointBasis, showConstraints).run(gui, ortho0Lyt);
SkeletonDisplay("displayY", &camY, &skel.skeleton, showJointBasis, showConstraints).run(gui, ortho1Lyt);
SkeletonDisplay("displayZ", &camZ, &skel.skeleton, showJointBasis, showConstraints).run(gui, ortho2Lyt);
}
}
int
CGSolver::solve_bicgstab (MultiFab& sol,
const MultiFab& rhs,
Real eps_rel,
Real eps_abs,
LinOp::BC_Mode bc_mode)
{
BL_PROFILE("CGSolver::solve_bicgstab()");
const int nghost = sol.nGrow(), ncomp = 1;
const BoxArray& ba = sol.boxArray();
const DistributionMapping& dm = sol.DistributionMap();
BL_ASSERT(sol.nComp() == ncomp);
BL_ASSERT(sol.boxArray() == Lp.boxArray(lev));
BL_ASSERT(rhs.boxArray() == Lp.boxArray(lev));
MultiFab ph(ba, ncomp, nghost, dm);
MultiFab sh(ba, ncomp, nghost, dm);
MultiFab sorig(ba, ncomp, 0, dm);
MultiFab p (ba, ncomp, 0, dm);
MultiFab r (ba, ncomp, 0, dm);
MultiFab s (ba, ncomp, 0, dm);
MultiFab rh (ba, ncomp, 0, dm);
MultiFab v (ba, ncomp, 0, dm);
MultiFab t (ba, ncomp, 0, dm);
Lp.residual(r, rhs, sol, lev, bc_mode);
MultiFab::Copy(sorig,sol,0,0,1,0);
MultiFab::Copy(rh, r, 0,0,1,0);
sol.setVal(0);
const LinOp::BC_Mode temp_bc_mode = LinOp::Homogeneous_BC;
#ifdef CG_USE_OLD_CONVERGENCE_CRITERIA
Real rnorm = norm_inf(r);
#else
//
// Calculate the local values of these norms & reduce their values together.
//
Real vals[2] = { norm_inf(r, true), Lp.norm(0, lev, true) };
ParallelDescriptor::ReduceRealMax(vals,2,color());
Real rnorm = vals[0];
const Real Lp_norm = vals[1];
Real sol_norm = 0;
#endif
const Real rnorm0 = rnorm;
if ( verbose > 0 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << "CGSolver_BiCGStab: Initial error (error0) = " << rnorm0 << '\n';
}
int ret = 0, nit = 1;
Real rho_1 = 0, alpha = 0, omega = 0;
if ( rnorm0 == 0 || rnorm0 < eps_abs )
{
if ( verbose > 0 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << "CGSolver_BiCGStab: niter = 0,"
<< ", rnorm = " << rnorm
<< ", eps_abs = " << eps_abs << std::endl;
}
return ret;
}
for (; nit <= maxiter; ++nit)
{
const Real rho = dotxy(rh,r);
if ( rho == 0 )
{
ret = 1; break;
}
if ( nit == 1 )
{
MultiFab::Copy(p,r,0,0,1,0);
}
else
{
const Real beta = (rho/rho_1)*(alpha/omega);
sxay(p, p, -omega, v);
sxay(p, r, beta, p);
}
if ( use_mg_precond )
{
ph.setVal(0);
mg_precond->solve(ph, p, eps_rel, eps_abs, temp_bc_mode);
}
else if ( use_jacobi_precond )
{
ph.setVal(0);
Lp.jacobi_smooth(ph, p, lev, temp_bc_mode);
}
else
{
MultiFab::Copy(ph,p,0,0,1,0);
}
Lp.apply(v, ph, lev, temp_bc_mode);
if ( Real rhTv = dotxy(rh,v) )
{
alpha = rho/rhTv;
}
else
{
ret = 2; break;
}
sxay(sol, sol, alpha, ph);
sxay(s, r, -alpha, v);
rnorm = norm_inf(s);
if ( verbose > 2 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << "CGSolver_BiCGStab: Half Iter "
<< std::setw(11) << nit
<< " rel. err. "
<< rnorm/(rnorm0) << '\n';
}
#ifdef CG_USE_OLD_CONVERGENCE_CRITERIA
if ( rnorm < eps_rel*rnorm0 || rnorm < eps_abs ) break;
#else
sol_norm = norm_inf(sol);
if ( rnorm < eps_rel*(Lp_norm*sol_norm + rnorm0 ) || rnorm < eps_abs ) break;
#endif
if ( use_mg_precond )
{
sh.setVal(0);
mg_precond->solve(sh, s, eps_rel, eps_abs, temp_bc_mode);
}
else if ( use_jacobi_precond )
{
sh.setVal(0);
Lp.jacobi_smooth(sh, s, lev, temp_bc_mode);
}
else
{
MultiFab::Copy(sh,s,0,0,1,0);
}
Lp.apply(t, sh, lev, temp_bc_mode);
//
// This is a little funky. I want to elide one of the reductions
// in the following two dotxy()s. We do that by calculating the "local"
// values and then reducing the two local values at the same time.
//
Real vals[2] = { dotxy(t,t,true), dotxy(t,s,true) };
ParallelDescriptor::ReduceRealSum(vals,2,color());
if ( vals[0] )
{
omega = vals[1]/vals[0];
}
else
{
ret = 3; break;
}
sxay(sol, sol, omega, sh);
sxay(r, s, -omega, t);
rnorm = norm_inf(r);
if ( verbose > 2 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << "CGSolver_BiCGStab: Iteration "
<< std::setw(11) << nit
<< " rel. err. "
<< rnorm/(rnorm0) << '\n';
}
#ifdef CG_USE_OLD_CONVERGENCE_CRITERIA
if ( rnorm < eps_rel*rnorm0 || rnorm < eps_abs ) break;
#else
sol_norm = norm_inf(sol);
if ( rnorm < eps_rel*(Lp_norm*sol_norm + rnorm0 ) || rnorm < eps_abs ) break;
#endif
if ( omega == 0 )
{
ret = 4; break;
}
rho_1 = rho;
}
if ( verbose > 0 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << "CGSolver_BiCGStab: Final: Iteration "
<< std::setw(4) << nit
<< " rel. err. "
<< rnorm/(rnorm0) << '\n';
}
#ifdef CG_USE_OLD_CONVERGENCE_CRITERIA
if ( ret == 0 && rnorm > eps_rel*rnorm0 && rnorm > eps_abs)
#else
if ( ret == 0 && rnorm > eps_rel*(Lp_norm*sol_norm + rnorm0 ) && rnorm > eps_abs )
#endif
{
if ( ParallelDescriptor::IOProcessor(color()) )
BoxLib::Warning("CGSolver_BiCGStab:: failed to converge!");
ret = 8;
}
if ( ( ret == 0 || ret == 8 ) && (rnorm < rnorm0) )
{
sol.plus(sorig, 0, 1, 0);
}
else
{
sol.setVal(0);
sol.plus(sorig, 0, 1, 0);
}
return ret;
}
int
CGSolver::solve_cabicgstab (MultiFab& sol,
const MultiFab& rhs,
Real eps_rel,
Real eps_abs,
LinOp::BC_Mode bc_mode)
{
BL_PROFILE("CGSolver::solve_cabicgstab()");
BL_ASSERT(sol.nComp() == 1);
BL_ASSERT(sol.boxArray() == Lp.boxArray(lev));
BL_ASSERT(rhs.boxArray() == Lp.boxArray(lev));
Real temp1[4*SSS_MAX+1];
Real temp2[4*SSS_MAX+1];
Real temp3[4*SSS_MAX+1];
Real Tp[4*SSS_MAX+1][4*SSS_MAX+1];
Real Tpp[4*SSS_MAX+1][4*SSS_MAX+1];
Real aj[4*SSS_MAX+1];
Real cj[4*SSS_MAX+1];
Real ej[4*SSS_MAX+1];
Real Tpaj[4*SSS_MAX+1];
Real Tpcj[4*SSS_MAX+1];
Real Tppaj[4*SSS_MAX+1];
Real G[4*SSS_MAX+1][4*SSS_MAX+1]; // Extracted from first 4*SSS+1 columns of Gg[][]. indexed as [row][col]
Real g[4*SSS_MAX+1]; // Extracted from last [4*SSS+1] column of Gg[][].
Real Gg[(4*SSS_MAX+1)*(4*SSS_MAX+2)]; // Buffer to hold the Gram-like matrix produced by matmul(). indexed as [row*(4*SSS+2) + col]
//
// If variable_SSS we "telescope" SSS.
// We start with 1 and increase it up to SSS_MAX on the outer iterations.
//
if (variable_SSS) SSS = 1;
zero( aj, 4*SSS_MAX+1);
zero( cj, 4*SSS_MAX+1);
zero( ej, 4*SSS_MAX+1);
zero( Tpaj, 4*SSS_MAX+1);
zero( Tpcj, 4*SSS_MAX+1);
zero(Tppaj, 4*SSS_MAX+1);
zero(temp1, 4*SSS_MAX+1);
zero(temp2, 4*SSS_MAX+1);
zero(temp3, 4*SSS_MAX+1);
SetMonomialBasis(Tp,Tpp,SSS);
const int ncomp = 1, nghost = sol.nGrow();
//
// Contains the matrix powers of p[] and r[].
//
// First 2*SSS+1 components are powers of p[].
// Next 2*SSS components are powers of r[].
//
const BoxArray& ba = sol.boxArray();
const DistributionMapping& dm = sol.DistributionMap();
MultiFab PR(ba, 4*SSS_MAX+1, 0, dm);
MultiFab p(ba, ncomp, 0, dm);
MultiFab r(ba, ncomp, 0, dm);
MultiFab rt(ba, ncomp, 0, dm);
MultiFab tmp(ba, 4, nghost, dm);
Lp.residual(r, rhs, sol, lev, bc_mode);
BL_ASSERT(!r.contains_nan());
MultiFab::Copy(rt,r,0,0,1,0);
MultiFab::Copy( p,r,0,0,1,0);
const Real rnorm0 = norm_inf(r);
Real delta = dotxy(r,rt);
const Real L2_norm_of_rt = sqrt(delta);
const LinOp::BC_Mode temp_bc_mode = LinOp::Homogeneous_BC;
if ( verbose > 0 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << "CGSolver_CABiCGStab: Initial error (error0) = " << rnorm0 << '\n';
}
if ( rnorm0 == 0 || delta == 0 || rnorm0 < eps_abs )
{
if ( verbose > 0 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << "CGSolver_CABiCGStab: niter = 0,"
<< ", rnorm = " << rnorm0
<< ", delta = " << delta
<< ", eps_abs = " << eps_abs << '\n';
}
return 0;
}
int niters = 0, ret = 0;
Real L2_norm_of_resid = 0, atime = 0, gtime = 0;
bool BiCGStabFailed = false, BiCGStabConverged = false;
for (int m = 0; m < maxiter && !BiCGStabFailed && !BiCGStabConverged; )
{
const Real time1 = ParallelDescriptor::second();
//
// Compute the matrix powers on p[] & r[] (monomial basis).
// The 2*SSS+1 powers of p[] followed by the 2*SSS powers of r[].
//
MultiFab::Copy(PR,p,0,0,1,0);
MultiFab::Copy(PR,r,0,2*SSS+1,1,0);
BL_ASSERT(!PR.contains_nan(0, 1));
BL_ASSERT(!PR.contains_nan(2*SSS+1,1));
//
// We use "tmp" to minimize the number of Lp.apply()s.
// We do this by doing p & r together in a single call.
//
MultiFab::Copy(tmp,p,0,0,1,0);
MultiFab::Copy(tmp,r,0,1,1,0);
for (int n = 1; n < 2*SSS; n++)
{
Lp.apply(tmp, tmp, lev, temp_bc_mode, false, 0, 2, 2);
MultiFab::Copy(tmp,tmp,2,0,2,0);
MultiFab::Copy(PR,tmp,0, n,1,0);
MultiFab::Copy(PR,tmp,1,2*SSS+n+1,1,0);
BL_ASSERT(!PR.contains_nan(n, 1));
BL_ASSERT(!PR.contains_nan(2*SSS+n+1,1));
}
MultiFab::Copy(tmp,PR,2*SSS-1,0,1,0);
Lp.apply(tmp, tmp, lev, temp_bc_mode, false, 0, 1, 1);
MultiFab::Copy(PR,tmp,1,2*SSS,1,0);
BL_ASSERT(!PR.contains_nan(2*SSS-1,1));
BL_ASSERT(!PR.contains_nan(2*SSS, 1));
Real time2 = ParallelDescriptor::second();
atime += (time2-time1);
BuildGramMatrix(Gg, PR, rt, SSS);
const Real time3 = ParallelDescriptor::second();
gtime += (time3-time2);
//
// Form G[][] and g[] from Gg.
//
for (int i = 0, k = 0; i < 4*SSS+1; i++)
{
for (int j = 0; j < 4*SSS+1; j++)
//
// First 4*SSS+1 elements in each row go to G[][].
//
G[i][j] = Gg[k++];
//
// Last element in row goes to g[].
//
g[i] = Gg[k++];
}
zero(aj, 4*SSS+1); aj[0] = 1;
zero(cj, 4*SSS+1); cj[2*SSS+1] = 1;
zero(ej, 4*SSS+1);
for (int nit = 0; nit < SSS; nit++)
{
gemv( Tpaj, Tp, aj, 4*SSS+1, 4*SSS+1);
gemv( Tpcj, Tp, cj, 4*SSS+1, 4*SSS+1);
gemv(Tppaj, Tpp, aj, 4*SSS+1, 4*SSS+1);
const Real g_dot_Tpaj = dot(g, Tpaj, 4*SSS+1);
if ( g_dot_Tpaj == 0 )
{
if ( verbose > 1 && ParallelDescriptor::IOProcessor(color()) )
std::cout << "CGSolver_CABiCGStab: g_dot_Tpaj == 0, nit = " << nit << '\n';
BiCGStabFailed = true; ret = 1; break;
}
const Real alpha = delta / g_dot_Tpaj;
if ( std::isinf(alpha) )
{
if ( verbose > 1 && ParallelDescriptor::IOProcessor(color()) )
std::cout << "CGSolver_CABiCGStab: alpha == inf, nit = " << nit << '\n';
BiCGStabFailed = true; ret = 2; break;
}
axpy(temp1, Tpcj, -alpha, Tppaj, 4*SSS+1);
gemv(temp2, G, temp1, 4*SSS+1, 4*SSS+1);
axpy(temp3, cj, -alpha, Tpaj, 4*SSS+1);
const Real omega_numerator = dot(temp3, temp2, 4*SSS+1);
const Real omega_denominator = dot(temp1, temp2, 4*SSS+1);
//
// NOTE: omega_numerator/omega_denominator can be 0/x or 0/0, but should never be x/0.
//
// If omega_numerator==0, and ||s||==0, then convergence, x=x+alpha*aj.
// If omega_numerator==0, and ||s||!=0, then stabilization breakdown.
//
// Partial update of ej must happen before the check on omega to ensure forward progress !!!
//
axpy(ej, ej, alpha, aj, 4*SSS+1);
//
// ej has been updated so consider that we've done an iteration since
// even if we break out of the loop we'll be able to update both sol.
//
niters++;
//
// Calculate the norm of Saad's vector 's' to check intra s-step convergence.
//
axpy(temp1, cj,-alpha, Tpaj, 4*SSS+1);
gemv(temp2, G, temp1, 4*SSS+1, 4*SSS+1);
const Real L2_norm_of_s = dot(temp1,temp2,4*SSS+1);
L2_norm_of_resid = (L2_norm_of_s < 0 ? 0 : sqrt(L2_norm_of_s));
if ( L2_norm_of_resid < eps_rel*L2_norm_of_rt )
{
if ( verbose > 1 && L2_norm_of_resid == 0 && ParallelDescriptor::IOProcessor(color()) )
std::cout << "CGSolver_CABiCGStab: L2 norm of s: " << L2_norm_of_s << '\n';
BiCGStabConverged = true; break;
}
if ( omega_denominator == 0 )
{
if ( verbose > 1 && ParallelDescriptor::IOProcessor(color()) )
std::cout << "CGSolver_CABiCGStab: omega_denominator == 0, nit = " << nit << '\n';
BiCGStabFailed = true; ret = 3; break;
}
const Real omega = omega_numerator / omega_denominator;
if ( verbose > 1 && ParallelDescriptor::IOProcessor(color()) )
{
if ( omega == 0 ) std::cout << "CGSolver_CABiCGStab: omega == 0, nit = " << nit << '\n';
if ( std::isinf(omega) ) std::cout << "CGSolver_CABiCGStab: omega == inf, nit = " << nit << '\n';
}
if ( omega == 0 ) { BiCGStabFailed = true; ret = 4; break; }
if ( std::isinf(omega) ) { BiCGStabFailed = true; ret = 4; break; }
//
// Complete the update of ej & cj now that omega is known to be ok.
//
axpy(ej, ej, omega, cj, 4*SSS+1);
axpy(ej, ej,-omega*alpha, Tpaj, 4*SSS+1);
axpy(cj, cj, -omega, Tpcj, 4*SSS+1);
axpy(cj, cj, -alpha, Tpaj, 4*SSS+1);
axpy(cj, cj, omega*alpha, Tppaj, 4*SSS+1);
//
// Do an early check of the residual to determine convergence.
//
gemv(temp1, G, cj, 4*SSS+1, 4*SSS+1);
//
// sqrt( (cj,Gcj) ) == L2 norm of the intermediate residual in exact arithmetic.
// However, finite precision can lead to the norm^2 being < 0 (Jim Demmel).
// If cj_dot_Gcj < 0 we flush to zero and consider ourselves converged.
//
const Real L2_norm_of_r = dot(cj, temp1, 4*SSS+1);
L2_norm_of_resid = (L2_norm_of_r > 0 ? sqrt(L2_norm_of_r) : 0);
if ( L2_norm_of_resid < eps_rel*L2_norm_of_rt )
{
if ( verbose > 1 && L2_norm_of_resid == 0 && ParallelDescriptor::IOProcessor(color()) )
std::cout << "CGSolver_CABiCGStab: L2_norm_of_r: " << L2_norm_of_r << '\n';
BiCGStabConverged = true; break;
}
const Real delta_next = dot(g, cj, 4*SSS+1);
if ( verbose > 1 && ParallelDescriptor::IOProcessor(color()) )
{
if ( delta_next == 0 ) std::cout << "CGSolver_CABiCGStab: delta == 0, nit = " << nit << '\n';
if ( std::isinf(delta_next) ) std::cout << "CGSolver_CABiCGStab: delta == inf, nit = " << nit << '\n';
}
if ( std::isinf(delta_next) ) { BiCGStabFailed = true; ret = 5; break; } // delta = inf?
if ( delta_next == 0 ) { BiCGStabFailed = true; ret = 5; break; } // Lanczos breakdown...
const Real beta = (delta_next/delta)*(alpha/omega);
if ( verbose > 1 && ParallelDescriptor::IOProcessor(color()) )
{
if ( beta == 0 ) std::cout << "CGSolver_CABiCGStab: beta == 0, nit = " << nit << '\n';
if ( std::isinf(beta) ) std::cout << "CGSolver_CABiCGStab: beta == inf, nit = " << nit << '\n';
}
if ( std::isinf(beta) ) { BiCGStabFailed = true; ret = 6; break; } // beta = inf?
if ( beta == 0 ) { BiCGStabFailed = true; ret = 6; break; } // beta = 0? can't make further progress(?)
axpy(aj, cj, beta, aj, 4*SSS+1);
axpy(aj, aj, -omega*beta, Tpaj, 4*SSS+1);
delta = delta_next;
}
//
// Update iterates.
//
for (int i = 0; i < 4*SSS+1; i++)
sxay(sol,sol,ej[i],PR,i);
MultiFab::Copy(p,PR,0,0,1,0);
p.mult(aj[0],0,1);
for (int i = 1; i < 4*SSS+1; i++)
sxay(p,p,aj[i],PR,i);
MultiFab::Copy(r,PR,0,0,1,0);
r.mult(cj[0],0,1);
for (int i = 1; i < 4*SSS+1; i++)
sxay(r,r,cj[i],PR,i);
if ( !BiCGStabFailed && !BiCGStabConverged )
{
m += SSS;
if ( variable_SSS && SSS < SSS_MAX ) { SSS++; SetMonomialBasis(Tp,Tpp,SSS); }
}
}
if ( verbose > 0 )
{
if ( ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << "CGSolver_CABiCGStab: Final: Iteration "
<< std::setw(4) << niters
<< " rel. err. "
<< L2_norm_of_resid << '\n';
}
if ( verbose > 1 )
{
Real tmp[2] = { atime, gtime };
ParallelDescriptor::ReduceRealMax(tmp,2,color());
if ( ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << "CGSolver_CABiCGStab apply time: " << tmp[0] << ", gram time: " << tmp[1] << '\n';
}
}
}
if ( niters >= maxiter && !BiCGStabFailed && !BiCGStabConverged)
{
if ( L2_norm_of_resid > L2_norm_of_rt )
{
if ( ParallelDescriptor::IOProcessor(color()) )
BoxLib::Warning("CGSolver_CABiCGStab: failed to converge!");
//
// Return code 8 tells the MultiGrid driver to zero out the solution!
//
ret = 8;
}
else
{
//
// Return codes 1-7 tells the MultiGrid driver to smooth the solution!
//
ret = 7;
}
}
return ret;
}
int
CGSolver::jbb_precond (MultiFab& sol,
const MultiFab& rhs,
int lev,
LinOp& Lp)
{
//
// This is a local routine. No parallel is allowed to happen here.
//
int lev_loc = lev;
const Real eps_rel = 1.e-2;
const Real eps_abs = 1.e-16;
const int nghost = sol.nGrow();
const int ncomp = sol.nComp();
const bool local = true;
const LinOp::BC_Mode bc_mode = LinOp::Homogeneous_BC;
BL_ASSERT(ncomp == 1 );
BL_ASSERT(sol.boxArray() == Lp.boxArray(lev_loc));
BL_ASSERT(rhs.boxArray() == Lp.boxArray(lev_loc));
const BoxArray& ba = sol.boxArray();
const DistributionMapping& dm = sol.DistributionMap();
MultiFab sorig(ba, ncomp, nghost, dm);
MultiFab r(ba, ncomp, nghost, dm);
MultiFab z(ba, ncomp, nghost, dm);
MultiFab q(ba, ncomp, nghost, dm);
MultiFab p(ba, ncomp, nghost, dm);
sorig.copy(sol);
Lp.residual(r, rhs, sorig, lev_loc, LinOp::Homogeneous_BC, local);
sol.setVal(0);
Real rnorm = norm_inf(r,local);
const Real rnorm0 = rnorm;
Real minrnorm = rnorm;
if ( verbose > 2 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev_loc);
std::cout << " jbb_precond: Initial error : " << rnorm0 << '\n';
}
const Real Lp_norm = Lp.norm(0, lev_loc, local);
Real sol_norm = 0;
int ret = 0; // will return this value if all goes well
Real rho_1 = 0;
int nit = 1;
if ( rnorm0 == 0 || rnorm0 < eps_abs )
{
if ( verbose > 2 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev_loc);
std::cout << "jbb_precond: niter = 0,"
<< ", rnorm = " << rnorm
<< ", eps_abs = " << eps_abs << std::endl;
}
return 0;
}
for (; nit <= maxiter; ++nit)
{
z.copy(r);
Real rho = dotxy(z,r,local);
if (nit == 1)
{
p.copy(z);
}
else
{
Real beta = rho/rho_1;
sxay(p, z, beta, p);
}
Lp.apply(q, p, lev_loc, bc_mode, local);
Real alpha;
if ( Real pw = dotxy(p,q,local) )
{
alpha = rho/pw;
}
else
{
ret = 1; break;
}
if ( verbose > 3 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev_loc);
std::cout << "jbb_precond:" << " nit " << nit
<< " rho " << rho << " alpha " << alpha << '\n';
}
sxay(sol, sol, alpha, p);
sxay( r, r,-alpha, q);
rnorm = norm_inf(r, local);
sol_norm = norm_inf(sol, local);
if ( verbose > 2 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev_loc);
std::cout << "jbb_precond: Iteration"
<< std::setw(4) << nit
<< " rel. err. "
<< rnorm/(rnorm0) << '\n';
}
if ( rnorm < eps_rel*(Lp_norm*sol_norm + rnorm0) || rnorm < eps_abs )
{
break;
}
if ( rnorm > def_unstable_criterion*minrnorm )
{
ret = 2; break;
}
else if ( rnorm < minrnorm )
{
minrnorm = rnorm;
}
rho_1 = rho;
}
if ( verbose > 0 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev_loc);
std::cout << "jbb_precond: Final Iteration"
<< std::setw(4) << nit
<< " rel. err. "
<< rnorm/(rnorm0) << '\n';
}
if ( ret == 0 && rnorm > eps_rel*(Lp_norm*sol_norm + rnorm0) && rnorm > eps_abs )
{
if ( ParallelDescriptor::IOProcessor(color()) )
{
BoxLib::Warning("jbb_precond:: failed to converge!");
}
ret = 8;
}
if ( ( ret == 0 || ret == 8 ) && (rnorm < rnorm0) )
{
sol.plus(sorig, 0, 1, 0);
}
else
{
sol.setVal(0);
sol.plus(sorig, 0, 1, 0);
}
return ret;
}
int
CGSolver::solve_cg (MultiFab& sol,
const MultiFab& rhs,
Real eps_rel,
Real eps_abs,
LinOp::BC_Mode bc_mode)
{
BL_PROFILE("CGSolver::solve_cg()");
const int nghost = sol.nGrow(), ncomp = 1;
const BoxArray& ba = sol.boxArray();
const DistributionMapping& dm = sol.DistributionMap();
BL_ASSERT(sol.nComp() == ncomp);
BL_ASSERT(sol.boxArray() == Lp.boxArray(lev));
BL_ASSERT(rhs.boxArray() == Lp.boxArray(lev));
MultiFab sorig(ba, ncomp, nghost, dm);
MultiFab r(ba, ncomp, nghost, dm);
MultiFab z(ba, ncomp, nghost, dm);
MultiFab q(ba, ncomp, nghost, dm);
MultiFab p(ba, ncomp, nghost, dm);
MultiFab r1(ba, ncomp, nghost, dm);
MultiFab z1(ba, ncomp, nghost, dm);
MultiFab r2(ba, ncomp, nghost, dm);
MultiFab z2(ba, ncomp, nghost, dm);
MultiFab::Copy(sorig,sol,0,0,1,0);
Lp.residual(r, rhs, sorig, lev, bc_mode);
sol.setVal(0);
const LinOp::BC_Mode temp_bc_mode=LinOp::Homogeneous_BC;
Real rnorm = norm_inf(r);
const Real rnorm0 = rnorm;
Real minrnorm = rnorm;
if ( verbose > 0 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << " CG: Initial error : " << rnorm0 << '\n';
}
const Real Lp_norm = Lp.norm(0, lev);
Real sol_norm = 0;
Real rho_1 = 0;
int ret = 0;
int nit = 1;
if ( rnorm == 0 || rnorm < eps_abs )
{
if ( verbose > 0 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << " CG: niter = 0,"
<< ", rnorm = " << rnorm
<< ", eps_rel*(Lp_norm*sol_norm + rnorm0 )" << eps_rel*(Lp_norm*sol_norm + rnorm0 )
<< ", eps_abs = " << eps_abs << std::endl;
}
return 0;
}
for (; nit <= maxiter; ++nit)
{
if (use_jbb_precond && ParallelDescriptor::NProcs(color()) > 1)
{
z.setVal(0);
jbb_precond(z,r,lev,Lp);
}
else
{
MultiFab::Copy(z,r,0,0,1,0);
}
Real rho = dotxy(z,r);
if (nit == 1)
{
MultiFab::Copy(p,z,0,0,1,0);
}
else
{
Real beta = rho/rho_1;
sxay(p, z, beta, p);
}
Lp.apply(q, p, lev, temp_bc_mode);
Real alpha;
if ( Real pw = dotxy(p,q) )
{
alpha = rho/pw;
}
else
{
ret = 1; break;
}
if ( verbose > 2 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << "CGSolver_cg:"
<< " nit " << nit
<< " rho " << rho
<< " alpha " << alpha << '\n';
}
sxay(sol, sol, alpha, p);
sxay( r, r,-alpha, q);
rnorm = norm_inf(r);
sol_norm = norm_inf(sol);
if ( verbose > 2 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << " CG: Iteration"
<< std::setw(4) << nit
<< " rel. err. "
<< rnorm/(rnorm0) << '\n';
}
#ifdef CG_USE_OLD_CONVERGENCE_CRITERIA
if ( rnorm < eps_rel*rnorm0 || rnorm < eps_abs ) break;
#else
if ( rnorm < eps_rel*(Lp_norm*sol_norm + rnorm0) || rnorm < eps_abs ) break;
#endif
if ( rnorm > def_unstable_criterion*minrnorm )
{
ret = 2; break;
}
else if ( rnorm < minrnorm )
{
minrnorm = rnorm;
}
rho_1 = rho;
}
if ( verbose > 0 && ParallelDescriptor::IOProcessor(color()) )
{
Spacer(std::cout, lev);
std::cout << " CG: Final Iteration"
<< std::setw(4) << nit
<< " rel. err. "
<< rnorm/(rnorm0) << '\n';
}
#ifdef CG_USE_OLD_CONVERGENCE_CRITERIA
if ( ret == 0 && rnorm > eps_rel*rnorm0 && rnorm > eps_abs )
#else
if ( ret == 0 && rnorm > eps_rel*(Lp_norm*sol_norm + rnorm0) && rnorm > eps_abs )
#endif
{
if ( ParallelDescriptor::IOProcessor(color()) )
BoxLib::Warning("CGSolver_cg: failed to converge!");
ret = 8;
}
if ( ( ret == 0 || ret == 8 ) && (rnorm < rnorm0) )
{
sol.plus(sorig, 0, 1, 0);
}
else
{
sol.setVal(0);
sol.plus(sorig, 0, 1, 0);
}
return ret;
}
int
MCMultiGrid::solve_ (MultiFab& _sol,
Real eps_rel,
Real eps_abs,
MCBC_Mode bc_mode,
int level)
{
//
// Relax system maxiter times, stop if relative error <= _eps_rel or
// if absolute err <= _abs_eps
//
const Real strt_time = ParallelDescriptor::second();
//
// Elide a reduction by doing these together.
//
Real tmp[2] = { norm_inf(*rhs[level],true), errorEstimate(level,bc_mode,true) };
ParallelDescriptor::ReduceRealMax(tmp,2);
const Real norm_rhs = tmp[0];
const Real error0 = tmp[1];
int returnVal = 0;
Real error = error0;
if ( ParallelDescriptor::IOProcessor() && (verbose > 0) )
{
Spacer(std::cout, level);
std::cout << "MCMultiGrid: Initial rhs = " << norm_rhs << '\n';
std::cout << "MCMultiGrid: Initial error (error0) = " << error0 << '\n';
}
if ( ParallelDescriptor::IOProcessor() && eps_rel < 1.0e-16 && eps_rel > 0 )
{
std::cout << "MCMultiGrid: Tolerance "
<< eps_rel
<< " < 1e-16 is probably set too low" << '\n';
}
//
// Initialize correction to zero at this level (auto-filled at levels below)
//
(*cor[level]).setVal(0.0);
//
// Note: if eps_rel, eps_abs < 0 then that test is effectively bypassed.
//
int nit = 1;
const Real new_error_0 = norm_rhs;
//const Real norm_Lp = Lp.norm(0, level);
for ( ;
error > eps_abs &&
error > eps_rel*norm_rhs &&
nit <= maxiter;
++nit)
{
relax(*cor[level], *rhs[level], level, eps_rel, eps_abs, bc_mode);
error = errorEstimate(level,bc_mode);
if ( ParallelDescriptor::IOProcessor() && verbose > 1 )
{
const Real rel_error = (error0 != 0) ? error/new_error_0 : 0;
Spacer(std::cout, level);
std::cout << "MCMultiGrid: Iteration "
<< nit
<< " error/error0 = "
<< rel_error << '\n';
}
}
Real run_time = (ParallelDescriptor::second() - strt_time);
if ( verbose > 0 )
{
if ( ParallelDescriptor::IOProcessor() )
{
const Real rel_error = (error0 != 0) ? error/error0 : 0;
Spacer(std::cout, level);
std::cout << "MCMultiGrid: Final Iter. "
<< nit-1
<< " error/error0 = "
<< rel_error;
}
if ( verbose > 1 )
{
ParallelDescriptor::ReduceRealMax(run_time);
if ( ParallelDescriptor::IOProcessor() )
std::cout << ", Solve time: " << run_time << '\n';
}
}
if ( ParallelDescriptor::IOProcessor() && (verbose > 0) )
{
if ( error < eps_rel*norm_rhs )
{
std::cout << " Converged res < eps_rel*bnorm\n";
}
else if ( error < eps_abs )
{
std::cout << " Converged res < eps_abs\n";
}
}
//
// Omit ghost update since maybe not initialized in calling routine.
// Add to boundary values stored in initialsolution.
//
_sol.copy(*cor[level]);
_sol.plus(*initialsolution,0,_sol.nComp(),0);
if ( error <= eps_rel*(norm_rhs) ||
error <= eps_abs )
returnVal = 1;
//
// Otherwise, failed to solve satisfactorily
//
return returnVal;
}
