SuccessCode NewtonLoop(Vec<ComplexType> & next_space,
System const& S,
Vec<ComplexType> const& current_space, // pass by value to get a copy of it
ComplexType const& current_time,
RealType const& tracking_tolerance,
unsigned min_num_newton_iterations,
unsigned max_num_newton_iterations)
{
#ifndef BERTINI_DISABLE_ASSERTS
assert(max_num_newton_iterations >= min_num_newton_iterations && "max number newton iterations must be at least the min.");
#endif
next_space = current_space;
for (unsigned ii = 0; ii < max_num_newton_iterations; ++ii)
{
auto f = S.Eval(next_space, current_time);
auto J = S.Jacobian(next_space, current_time);
auto LU = J.lu();
if (LUPartialPivotDecompositionSuccessful(LU.matrixLU())!=MatrixSuccessCode::Success)
return SuccessCode::MatrixSolveFailure;
auto delta_z = LU.solve(-f);
next_space += delta_z;
if ( (delta_z.norm() < tracking_tolerance) && (ii >= (min_num_newton_iterations-1)) )
return SuccessCode::Success;
}
return SuccessCode::FailedToConverge;
}
SuccessCode NewtonLoop(Vec<ComplexType> & next_space,
RealType & norm_delta_z,
RealType & norm_J,
RealType & norm_J_inverse,
RealType & condition_number_estimate,
System const& S,
Vec<ComplexType> const& current_space, // pass by value to get a copy of it
ComplexType const& current_time,
RealType const& tracking_tolerance,
unsigned min_num_newton_iterations,
unsigned max_num_newton_iterations,
config::AdaptiveMultiplePrecisionConfig const& AMP_config)
{
#ifndef BERTINI_DISABLE_ASSERTS
assert(max_num_newton_iterations >= min_num_newton_iterations && "max number newton iterations must be at least the min.");
#endif
next_space = current_space;
for (unsigned ii = 0; ii < max_num_newton_iterations; ++ii)
{
//TODO: wrap these into a single line.
auto f = S.Eval(next_space, current_time);
auto J = S.Jacobian(next_space, current_time);
auto LU = J.lu();
if (LUPartialPivotDecompositionSuccessful(LU.matrixLU())!=MatrixSuccessCode::Success)
return SuccessCode::MatrixSolveFailure;
auto delta_z = LU.solve(-f);
next_space += delta_z;
norm_delta_z = delta_z.norm();
norm_J = J.norm();
norm_J_inverse = LU.solve(RandomOfUnits<ComplexType>(S.NumVariables())).norm();
condition_number_estimate = norm_J*norm_J_inverse;
if ( (norm_delta_z < tracking_tolerance) && (ii >= (min_num_newton_iterations-1)) )
return SuccessCode::Success;
if (!amp::CriterionB(norm_J, norm_J_inverse, max_num_newton_iterations - ii, tracking_tolerance, norm_delta_z, AMP_config))
return SuccessCode::HigherPrecisionNecessary;
if (!amp::CriterionC(norm_J_inverse, next_space, tracking_tolerance, AMP_config))
return SuccessCode::HigherPrecisionNecessary;
}
return SuccessCode::FailedToConverge;
}
