bool NOX::Direction::QuasiNewton::compute(NOX::Abstract::Vector& dir,
NOX::Abstract::Group& soln,
const Solver::Generic& solver)
{
NOX::Abstract::Group::ReturnType status;
// Compute F at current solution
status = soln.computeF();
if (status != NOX::Abstract::Group::Ok)
throwError("compute", "Unable to compute F");
// Compute Jacobian at current solution.
status = soln.computeJacobian();
if (status != NOX::Abstract::Group::Ok)
throwError("compute", "Unable to compute Jacobian");
// Compute the gradient at the current solution
status = soln.computeGradient();
if (status != NOX::Abstract::Group::Ok)
throwError("compute", "Unable to compute gradient");
// Push the old information onto the memory, but only after at least one previous iteration
if (solver.getNumIterations() > 0)
{
const NOX::Abstract::Group& oldSoln = solver.getPreviousSolutionGroup();
if (oldSoln.isGradient())
memory.add(soln.getX(), oldSoln.getX(), soln.getGradient(), oldSoln.getGradient());
}
// *** Calculate the QN direction ***
// d = -g
dir = soln.getGradient();
dir.scale(-1.0);
if (!memory.empty())
{
int m = memory.size();
vector<double> alpha(m);
double beta;
for (int i = m-1; i >= 0; i --)
{
alpha[i] = memory[i].rho() * dir.innerProduct( memory[i].s() );
dir.update(-1.0 * alpha[i], memory[i].y(), 1.0);
}
dir.scale( memory[m-1].sdoty() / memory[m-1].ydoty() );
for (int i = 0; i < m; i ++)
{
beta = memory[i].rho() * dir.innerProduct( memory[i].y() );
dir.update(alpha[i] - beta, memory[i].s(), 1.0);
}
}
return true;
}
StatusType NormUpdate::checkStatus(const Solver::Generic& problem,
NOX::StatusTest::CheckType checkType)
{
if (checkType == None)
{
status = Unevaluated;
normUpdate = -1.0;
return status;
}
// On the first iteration, the old and current solution are the same so
// we should return the test as unconverged until there is a valid
// old solution (i.e. the number of iterations is greater than zero).
int niters = problem.getNumIterations();
if (niters == 0)
{
status = Unconverged;
normUpdate = -1.0;
return status;
}
// Check that F exists!
if (!problem.getSolutionGroup().isF())
{
status = Unconverged;
normUpdate = -1.0;
return status;
}
const Abstract::Vector& oldSoln = problem.getPreviousSolutionGroup().getX();
const Abstract::Vector& curSoln = problem.getSolutionGroup().getX();
if (Teuchos::is_null(updateVectorPtr))
updateVectorPtr = curSoln.clone();
updateVectorPtr->update(1.0, curSoln, -1.0, oldSoln, 0.0);
int n = (scaleType == Scaled) ? updateVectorPtr->length() : 0;
switch (normType) {
case NOX::Abstract::Vector::TwoNorm:
normUpdate = updateVectorPtr->norm();
if (scaleType == Scaled)
normUpdate /= sqrt(1.0 * n);
break;
default:
normUpdate = updateVectorPtr->norm(normType);
if (scaleType == Scaled)
normUpdate /= n;
break;
}
status = (normUpdate < tolerance) ? Converged : Unconverged;
return status;
}
NOX::StatusTest::StatusType
NOX::StatusTest::Stagnation::
checkStatus(const Solver::Generic& problem,
NOX::StatusTest::CheckType checkType)
{
status = Unconverged;
// This test should ignore the checkType! This test must be run
// each iteration because it triggers after a set number of
// iterations.
// First time through we don't do anything
int niters = problem.getNumIterations();
if (niters == 0) {
lastIteration = 0;
numSteps = 0;
return Unconverged;
}
// Make sure we have not already counted the last nonlinear iteration.
// This protects against multiple calls to checkStatus() in between
// nonlinear iterations.
bool isCounted = false;
if (niters == lastIteration) {
isCounted = true;
}
else
lastIteration = niters;
// Compute the convergence rate and set counter appropriately
if (!isCounted) {
convRate = problem.getSolutionGroup().getNormF() /
problem.getPreviousSolutionGroup().getNormF();
if (convRate >= tolerance)
numSteps ++;
else
numSteps = 0;
}
if (numSteps >= maxSteps)
status = Failed;
return status;
}
NOX::StatusTest::StatusType NOX::StatusTest::MaxIters::
checkStatus(const Solver::Generic& problem,
NOX::StatusTest::CheckType checkType)
{
switch (checkType)
{
case NOX::StatusTest::Complete:
case NOX::StatusTest::Minimal:
niters = problem.getNumIterations();
status = (niters >= maxiters) ? Failed : Unconverged;
break;
case NOX::StatusTest::None:
default:
niters = -1;
status = Unevaluated;
break;
}
return status;
}
NOX::StatusTest::StatusType NOX::StatusTest::FiniteValue::
checkStatus(const Solver::Generic& problem,
NOX::StatusTest::CheckType checkType)
{
// Reset the check
normValue = -1.0;
const NOX::Abstract::Group& grp = problem.getSolutionGroup();
switch (checkType)
{
case NOX::StatusTest::Complete:
case NOX::StatusTest::Minimal:
if (vectorType == FVector)
{
if (normType == NOX::Abstract::Vector::TwoNorm)
normValue = grp.getNormF(); // More efficient than recomputing norm
else
normValue = grp.getF().norm(normType);
}
else
normValue = grp.getX().norm(normType);
result = finiteNumberTest(normValue);
status = (result == 0) ? Unconverged : Failed;
break;
case NOX::StatusTest::None:
default:
result = 1;
status = Unevaluated;
break;
}
return status;
}
bool NonlinearCG::compute(Abstract::Vector& dir, Abstract::Group& soln,
const Solver::Generic& solver)
{
Abstract::Group::ReturnType ok;
// Initialize vector memory if haven't already
if(Teuchos::is_null(oldDirPtr))
oldDirPtr = soln.getX().clone(NOX::ShapeCopy);
if(Teuchos::is_null(oldDescentDirPtr))
oldDescentDirPtr = soln.getX().clone(NOX::ShapeCopy);
// These are conditionally created
if(Teuchos::is_null(diffVecPtr) && usePRbeta)
diffVecPtr = soln.getX().clone(NOX::ShapeCopy);
if(Teuchos::is_null(tmpVecPtr) && doPrecondition)
tmpVecPtr = soln.getX().clone(NOX::ShapeCopy);
// Get a reference to the old solution group (const)
oldSolnPtr = &solver.getPreviousSolutionGroup();
const Abstract::Group& oldSoln(*oldSolnPtr);
niter = solver.getNumIterations();
// Construct Residual and precondition (if desired) as first step in
// getting new search direction
ok = soln.computeF();
if (ok != Abstract::Group::Ok)
{
if (utils->isPrintType(Utils::Warning))
utils->out() << "NOX::Direction::NonlinearCG::compute - Unable to compute F." << std::endl;
return false;
}
dir = soln.getF();
if(doPrecondition)
{
if(!soln.isJacobian())
ok = soln.computeJacobian();
if (ok != Abstract::Group::Ok)
{
if (utils->isPrintType(Utils::Warning))
utils->out() << "NOX::Direction::NonlinearCG::compute - Unable to compute Jacobian." << std::endl;
return false;
}
*tmpVecPtr = dir;
ok = soln.applyRightPreconditioning(false, paramsPtr->sublist("Nonlinear CG").sublist("Linear Solver"), *tmpVecPtr, dir);
if( ok != Abstract::Group::Ok )
{
if (utils->isPrintType(Utils::Warning))
utils->out() << "NOX::Direction::NonlinearCG::compute - Unable to apply Right Preconditioner." << std::endl;
return false;
}
}
dir.scale(-1.0);
// Orthogonalize using previous search direction
beta = 0.0;
if( niter!=0 )
{
// Two choices (for now) for orthogonalizing descent direction with previous:
if( usePRbeta )
{
// Polak-Ribiere beta
*diffVecPtr = dir;
diffVecPtr->update(-1.0, *oldDescentDirPtr, 1.0);
double denominator = oldDescentDirPtr->innerProduct(oldSoln.getF());
beta = diffVecPtr->innerProduct(soln.getF()) / denominator;
// Constrain beta >= 0
if( beta < 0.0 )
{
if (utils->isPrintType(Utils::OuterIteration))
utils->out() << "BETA < 0, (" << beta << ") --> Resetting to zero" << std::endl;
beta = 0.0;
}
}
else
{
// Fletcher-Reeves beta
double denominator = oldDescentDirPtr->innerProduct(oldSoln.getF());
beta = dir.innerProduct(soln.getF()) / denominator;
}
// Allow for restart after specified number of nonlinear iterations
if( (niter % restartFrequency) == 0 )
{
if( utils->isPrintType(Utils::OuterIteration) )
utils->out() << "Resetting beta --> 0" << std::endl;
beta = 0 ; // Restart with Steepest Descent direction
}
} // niter != 0
*oldDescentDirPtr = dir;
dir.update(beta, *oldDirPtr, 1.0);
*oldDirPtr = dir;
return (ok == Abstract::Group::Ok);
}
bool NOX::LineSearch::Polynomial::compute(Abstract::Group& newGrp,
double& step,
const Abstract::Vector& dir,
const Solver::Generic& s)
{
printOpeningRemarks();
int nNonlinearIters = s.getNumIterations();
if (useCounter)
counter.incrementNumLineSearches();
// Get the linear solve tolerance if doing ared/pred for conv criteria
std::string direction = const_cast<Teuchos::ParameterList&>(s.getList()).
sublist("Direction").get("Method", "Newton");
double eta = (suffDecrCond == AredPred) ?
const_cast<Teuchos::ParameterList&>(s.getList()).
sublist("Direction").sublist(direction).sublist("Linear Solver").
get("Tolerance", -1.0) : 0.0;
// Computations with old group
const Abstract::Group& oldGrp = s.getPreviousSolutionGroup();
double oldPhi = meritFuncPtr->computef(oldGrp); // \phi(0)
double oldValue = computeValue(oldGrp, oldPhi);
double oldSlope = meritFuncPtr->computeSlope(dir, oldGrp);
// Computations with new group
step = defaultStep;
updateGrp(newGrp, oldGrp, dir, step);
double newPhi = meritFuncPtr->computef(newGrp);
double newValue = computeValue(newGrp, newPhi);
bool isConverged = false;
bool isFailed = false;
int nIters = 1;
if (oldSlope >= 0.0)
{
printBadSlopeWarning(oldSlope);
isFailed = true;
}
else
isConverged = checkConvergence(newValue, oldValue, oldSlope, step,
eta, nIters, nNonlinearIters);
// Increment the number of newton steps requiring a line search
if ((useCounter) && (!isConverged))
counter.incrementNumNonTrivialLineSearches();
double prevPhi = 0.0; // \phi(\lambda_{k-1})
double prevPrevPhi = 0.0; // \phi(\lambda_{k-2})
double prevStep = 0.0; // \lambda_{k-1}
double prevPrevStep = 0.0; // \lambda_{k-2}
while ((!isConverged) && (!isFailed))
{
print.printStep(nIters, step, oldValue, newValue,
"", (suffDecrCond != AredPred));
if (nIters > maxIters)
{
isFailed = true;
break;
}
if (interpolationType == Quadratic3)
{
/* 3-Point Quadratic Interpolation */
prevPrevPhi = prevPhi;
prevPhi = newPhi;
prevPrevStep = prevStep;
prevStep = step;
if (nIters == 1)
{
step = 0.5 * step;
}
else
{
double c1 = prevStep * prevStep * (prevPrevPhi - oldPhi) -
prevPrevStep * prevPrevStep * (prevPhi - oldPhi);
double c2 = prevPrevStep * (prevPhi - oldPhi) -
prevStep * (prevPrevPhi - oldPhi);
if (c1 < 0)
step = -0.5 * c1 / c2;
}
}
else if ((nIters == 1) || (interpolationType == Quadratic))
{
/* Quadratic Interpolation */
prevPhi = newPhi;
prevStep = step;
step = - (oldSlope * prevStep * prevStep) /
(2.0 * (prevPhi - oldPhi - prevStep * oldSlope)) ;
}
else
{
/* Cubic Interpolation */
prevPrevPhi = prevPhi;
prevPhi = newPhi;
prevPrevStep = prevStep;
prevStep = step;
double term1 = prevPhi - oldPhi - prevStep * oldSlope ;
double term2 = prevPrevPhi - oldPhi - prevPrevStep * oldSlope ;
double a = 1.0 / (prevStep - prevPrevStep) *
(term1 / (prevStep * prevStep) - term2 /
(prevPrevStep * prevPrevStep)) ;
double b = 1.0 / (prevStep - prevPrevStep) *
(-1.0 * term1 * prevPrevStep / (prevStep * prevStep) +
term2 * prevStep / (prevPrevStep * prevPrevStep)) ;
double disc = b * b - 3.0 * a * oldSlope;
if (disc < 0)
{
isFailed = true;
break;
}
if (b > 0.0) // Check to prevent round off error (H. Walker)
{
step = -oldSlope / (b + sqrt(disc));
}
else
{
if (fabs(a) < 1.e-12) // check for when a is small
{
step = -oldSlope / (2.0 * b);
}
else
{
step = (-b + sqrt(disc))/ (3.0 * a);
}
}
}
// Apply bounds
if (step < minBoundFactor * prevStep)
step = minBoundFactor * prevStep;
else if (step > maxBoundFactor * prevStep)
step = maxBoundFactor * prevStep;
// Check that step isn't too small
if (step < minStep)
{
isFailed = true;
break;
}
// Update the new group and compute new measures
updateGrp(newGrp, oldGrp, dir, step);
newPhi = meritFuncPtr->computef(newGrp);
newValue = computeValue(newGrp, newPhi);
nIters ++;
if (useCounter)
counter.incrementNumIterations();
isConverged = checkConvergence(newValue, oldValue, oldSlope, step,
eta, nIters, nNonlinearIters);
} // End while loop
if (isFailed)
{
if (useCounter)
counter.incrementNumFailedLineSearches();
if (recoveryStepType == Constant)
step = recoveryStep;
if (step == 0.0)
{
newGrp = oldGrp;
newPhi = oldPhi;
newValue = oldValue;
}
else
{
updateGrp(newGrp, oldGrp, dir, step);
newPhi = meritFuncPtr->computef(newGrp);
newValue = computeValue(newGrp, newPhi);
}
}
std::string message = (isFailed) ? "(USING RECOVERY STEP!)" : "(STEP ACCEPTED!)";
print.printStep(nIters, step, oldValue, newValue, message, (suffDecrCond != AredPred));
paramsPtr->set("Adjusted Tolerance", 1.0 - step * (1.0 - eta));
if (useCounter)
counter.setValues(*paramsPtr);
return (!isFailed);
}