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adimensional_system.cpp
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			/*-------------------------------------------------------------------------------

			Copyright (c) 2014,2015 F. Georget <fabieng@princeton.edu>, Princeton University
			All rights reserved.

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			ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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			#include <cmath>
			#include "adimensional_system.hpp"
			#include "../../utils/log.hpp"

			#include "../../physics/constants.hpp"
			#include "../../physics/laws.hpp"

			#include "adimensional_system_solution.hpp"

			#include <random>
			#include <iostream>

			// uncomment to activate the finite difference jacobian
			// #define SPECMICP_DEBUG_EQUATION_FD_JACOBIAN

			namespace specmicp {

			constexpr scalar_t log10 = std::log(10.0);

			// Constructor
			// ===========

			// No previous solution
			// --------------------

			AdimensionalSystem::AdimensionalSystem(
			RawDatabasePtr& ptrdata,
			const AdimensionalSystemConstraints& constraints,
			const AdimensionalSystemOptions& options,
			const units::UnitsSet& units_set
			):
			AdimemsionalSystemNumbering(ptrdata),
			OptionsHandler<AdimensionalSystemOptions>(options),
			units::UnitBaseClass(units_set),
			m_inert_volume_fraction(constraints.inert_volume_fraction),
			m_second(ptrdata),
			m_equations(total_dofs(), ptrdata)
			{
			specmicp_assert(ptrdata->is_valid());
			m_fixed_values.setZero(ptrdata->nb_component()+1);
			number_eq(constraints);
			}

			// Previous solution
			// -----------------

			AdimensionalSystem::AdimensionalSystem(
			RawDatabasePtr& ptrdata,
			const AdimensionalSystemConstraints& constraints,
			const AdimensionalSystemSolution& previous_solution,
			const AdimensionalSystemOptions& options,
			const units::UnitsSet& units_set
			):
			AdimemsionalSystemNumbering(ptrdata),
			OptionsHandler<AdimensionalSystemOptions>(options),
			units::UnitBaseClass(units_set),
			m_inert_volume_fraction(constraints.inert_volume_fraction),
			m_second(previous_solution),
			m_equations(total_dofs(), ptrdata)
			{
			specmicp_assert(ptrdata->is_valid());
			m_fixed_values.setZero(ptrdata->nb_component()+1);
			number_eq(constraints);
			}

			// Secondary variables constructor
			// ===============================

			// No previous solution
			// --------------------

			AdimensionalSystem::SecondaryVariables::SecondaryVariables(
			const RawDatabasePtr& data
			):
			secondary_molalities(Vector::Zero(data->nb_aqueous())),
			loggamma(Vector::Zero(data->nb_component()+data->nb_aqueous())),
			gas_fugacity(Vector::Zero(data->nb_gas())),
			gas_concentration(Vector::Zero(data->nb_gas())),
			sorbed_concentrations(Vector::Zero(data->nb_sorbed()))
			{}

			// Previous solution
			// -----------------

			AdimensionalSystem::SecondaryVariables::SecondaryVariables(
			const AdimensionalSystemSolution& previous_solution
			):
			secondary_molalities(previous_solution.secondary_molalities),
			loggamma(previous_solution.log_gamma),
			gas_fugacity(previous_solution.gas_fugacities),
			gas_concentration(Vector::Zero(previous_solution.gas_fugacities.rows())),
			sorbed_concentrations(previous_solution.sorbed_molalities)
			{}

			// IdEquations constructor
			// =======================

			AdimensionalSystem::IdEquations::IdEquations(
			index_t nb_dofs,
			const RawDatabasePtr& data
			):
			ideq(nb_dofs, no_equation),
			component_equation_type(data->nb_component()+1, no_equation),
			fixed_activity_species(data->nb_component()+1, no_species),
			active_aqueous(data->nb_aqueous(), false),
			active_gas(data->nb_gas(), false),
			active_sorbed(data->nb_sorbed())
			{}

			// Equation numbering
			// ==================

			void AdimensionalSystem::number_eq(
			const AdimensionalSystemConstraints& constraints
			)
			{
			index_t neq = 0;

			// Water
			// =====
			if (constraints.water_equation != WaterEquationType::NoEquation)
			{
			m_equations.type_equation(dof_water()) = static_cast<index_t>(constraints.water_equation);
			if (constraints.water_equation == WaterEquationType::MassConservation)
			{
			m_fixed_values(dof_water()) = constraints.total_concentrations(dof_water());
			}
			m_equations.add_equation(dof_water(), &neq);
			}
			// Aqueous components
			// ==================
			number_eq_aqueous_component(constraints, neq);

			// Surface model
			// =============
			if (constraints.surface_model.model_type == SurfaceEquationType::Equilibrium)
			{
			// add the equation
			m_equations.add_equation(dof_surface(), &neq);
			m_equations.type_equation(dof_surface()) = static_cast<index_t>(constraints.surface_model.model_type);
			// setup the total concentration
			m_fixed_values(dof_surface()) = constraints.surface_model.concentration;
			}

			// Secondary species
			// =================

			// Secondary aqueous species
			// -------------------------
			bool include_half_cell_reaction = (constraints.electron_constraint.equation_type != ElectronEquationType::NoEquation);
			bool solve_electron_equation {false};
			for (auto j: m_data->range_aqueous())
			{
			bool can_exist { true };
			if ( include_half_cell_reaction or not m_data->is_half_cell_reaction(j))
			for (const auto& k: m_equations.nonactive_component)
			{
			if (m_data->nu_aqueous(j, k) != 0.0)
			{
			can_exist = false;
			break;
			}
			}
			else
			{
			can_exist = false;
			}
			m_equations.set_aqueous_active(j, can_exist);
			if (can_exist and m_data->is_half_cell_reaction(j))
			solve_electron_equation = true;
			//std::cout << m_data->labels_aqueous[j] << "can exist ? " << can_exist << " - logk : " << m_data->logk_aqueous(j) << std::endl;
			}
			// Gas
			// ---

			for (index_t k: m_data->range_gas())
			{
			bool can_exist = true;
			for (const index_t& n: m_equations.nonactive_component)
			{
			if (m_data->nu_gas(k, n) != 0.0)
			{
			can_exist = false;
			break;
			}
			}
			m_equations.set_gas_active(k, can_exist);
			}

			// Sorbed species
			// --------------
			for (index_t s: m_data->range_sorbed())
			{
			// Check if the surface model is computed
			if (constraints.surface_model.model_type != SurfaceEquationType::Equilibrium)
			{
			m_equations.set_sorbed_active(s, false);
			continue;
			}
			// If so, check that all components of the sorbed species exist
			bool can_exist = true;
			for (const index_t& k: m_equations.nonactive_component)
			{
			if (m_data->nu_sorbed(s, k) != 0.0)
			{
			can_exist = false;
			break;
			}
			}
			m_equations.set_sorbed_active(s, can_exist);
			}

			// Electron equation
			// -----------------
			if (solve_electron_equation)
			{
			m_equations.add_equation(dof_electron(), &neq);
			m_equations.type_equation(dof_electron()) =
			static_cast<index_t>(constraints.electron_constraint.equation_type);
			if (constraints.electron_constraint.equation_type == ElectronEquationType::Equilibrium)
			{
			m_fixed_values(dof_electron()) = 0.0;
			}
			else if (constraints.electron_constraint.equation_type == ElectronEquationType::FixedpE)
			{
			m_fixed_values(dof_electron()) = constraints.electron_constraint.fixed_value;
			m_equations.related_species(dof_electron()) = constraints.electron_constraint.species;
			//assert(m_fixed_activity_species[dof_electron()] >= 0
			// and m_fixed_activity_species[dof_electron()] < m_data->nb_aqueous());
			//assert(m_data->is_half_cell_reaction(m_fixed_activity_species[dof_electron()]));
			}
			// scaling
			if (get_options().scaling_electron == 0.0)
			{
			for (index_t component : m_data->range_aqueous_component())
			{
			if (aqueous_component_equation_type(component)
			== AqueousComponentEquationType::MassConservation)
			{
			get_options().scaling_electron = total_concentration_bc(component);
			break;
			}
			}
			}
			}
			// above equations are 'free' (i.e. non constrained)
			m_equations.nb_free_variables = neq;
			// following equations are complementarity conditions

			// Minerals
			// ========
			m_scaling_molar_volume = m_data->scaling_molar_volume(get_units().length);
			for (index_t m: m_data->range_mineral())
			{
			bool can_precipitate = true;
			// just check that the molar volume exist
			auto molar_volume = m_data->molar_volume_mineral(m);
			// Remove minerals that cannot precipitate
			for (index_t& k: m_equations.nonactive_component)
			{
			if (m_data->nu_mineral(m, k) != 0.0 and molar_volume > 0.0)
			{
			can_precipitate = false;
			break; // this is not a mineral that can precipitate
			}
			}
			if (can_precipitate)
			{
			m_equations.add_equation(dof_mineral(m), &neq);
			}
			}
			m_equations.nb_tot_variables = neq;
			m_equations.nb_complementarity_variables = m_equations.nb_tot_variables - m_equations.nb_free_variables;

			}


			void AdimensionalSystem::number_eq_aqueous_component(
			const AdimensionalSystemConstraints& constraints,
			index_t& neq
			)
			{
			using EqT = AqueousComponentEquationType;
			// First set the charge keeper
			if (constraints.charge_keeper != no_species)
			{
			if (constraints.charge_keeper == 0 or constraints.charge_keeper > m_data->nb_component())
			{
			throw std::invalid_argument("The charge keeper must be an aqueous component. Invalid argument : "
			+ std::to_string(constraints.charge_keeper));
			}
			m_equations.type_equation(dof_component(constraints.charge_keeper)) = static_cast<index_t>(EqT::ChargeBalance);
			}
			// Then go over fix fugacity gas
			for (const auto& it: constraints.fixed_fugacity_cs)
			{
			if (m_equations.type_equation(dof_component(it.id_component)) != static_cast<index_t>(EqT::NoEquation))
			{
			throw std::invalid_argument("Component '" + m_data->components.get_label(it.id_component)
			+ "' is already constrained, a fixed fugacity condition can not be applied");
			}
			m_equations.type_equation(dof_component(it.id_component)) = static_cast<int>(EqT::FixedFugacity);
			m_fixed_values(it.id_component) = it.log_value;
			m_equations.related_species(it.id_component) = it.id_gas;
			}
			// Then over the fix activity species
			for (const auto& it: constraints.fixed_activity_cs)
			{
			if (m_equations.type_equation(dof_component(it.id_component)) != static_cast<index_t>(EqT::NoEquation))
			{
			throw std::invalid_argument("Component '" + m_data->components.get_label(it.id_component)
			+ "' is already constrained, a fixed activity condition can not be applied.");
			}
			m_equations.type_equation(dof_component(it.id_component)) = static_cast<index_t>(EqT::FixedActivity);
			m_fixed_values(it.id_component) = it.log_value;
			}
			// Finally number the equations
			for (index_t component: m_data->range_aqueous_component())
			{
			// If no equation is assigned yet
			if (m_equations.type_equation(dof_component(component)) == static_cast<index_t>(EqT::NoEquation))
			{
			// Mass is conserved for this component
			//###FIXME: H[+], HO[-]
			const scalar_t& total_concentration = constraints.total_concentrations(dof_component(component));
			if (std::abs(total_concentration) > get_options().cutoff_total_concentration)
			{
			m_equations.type_equation(dof_component(component)) = static_cast<index_t>(EqT::MassConservation);
			m_fixed_values(dof_component(component)) = total_concentration;
			m_equations.add_equation(component, &neq);
			}
			else // add component to the nonactive component list
			{
			m_equations.add_non_active_component(component);
			}
			}
			// If equation is already assigned
			else
			{
			m_equations.add_equation(component, &neq);
			}
			}
			if (stdlog::ReportLevel() >= logger::Debug and m_equations.nonactive_component.size() > 0)
			{
			// if in debug mode list the non active components
			DEBUG << "Non active components :";
			for (auto it: m_equations.nonactive_component)
			{
			DEBUG << " - " << it;
			}
			}
			}

			// ================ //
			// //
			// Residuals //
			// //
			// ================ //


			scalar_t AdimensionalSystem::weigthed_sum_aqueous(index_t component) const
			{
			scalar_t sum = 0.0;
			for (index_t aqueous: m_data->range_aqueous())
			{
			if (not is_aqueous_active(aqueous)) continue;
			sum += m_data->nu_aqueous(aqueous,component)*secondary_molality(aqueous);
			}
			return sum;
			}

			scalar_t AdimensionalSystem::diff_weigthed_sum_aqueous(index_t diff_component, index_t component) const
			{
			scalar_t sum = 0.0;
			for (index_t aqueous: m_data->range_aqueous())
			{
			if (not is_aqueous_active(aqueous)) continue;
			sum += log10m_data->nu_aqueous(aqueous,diff_component)m_data->nu_aqueous(aqueous,component)*secondary_molality(aqueous);
			}
			return sum;
			}

			scalar_t AdimensionalSystem::weigthed_sum_sorbed(index_t component) const
			{
			scalar_t sum = 0.0;
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			sum += m_data->nu_sorbed(s, component)*sorbed_species_concentration(s);
			}
			return sum;
			}

			scalar_t AdimensionalSystem::diff_weigthed_sum_sorbed(index_t diff_component, index_t component) const
			{
			scalar_t sum = 0.0;
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			sum += log10m_data->nu_sorbed(s, diff_component)m_data->nu_sorbed(s, component)*sorbed_species_concentration(s);
			}
			return sum;
			}

			scalar_t AdimensionalSystem::diff_surface_weigthed_sum_sorbed(index_t component) const
			{
			scalar_t sum = 0.0;
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			sum += log10m_data->nb_sorption_sites(s)m_data->nu_sorbed(s, component)*sorbed_species_concentration(s);
			}
			return sum;
			}

			scalar_t AdimensionalSystem::weigthed_sum_mineral(const Vector& x, index_t component) const
			{
			scalar_t sum = 0.0;
			for (index_t m: m_data->range_mineral())
			{
			if (ideq_min(m) == no_equation or m_data->nu_mineral(m, component) == 0.0) continue;
			const auto concentration = saturation_mineral(x, m)/molar_volume_mineral(m);
			sum += m_data->nu_mineral(m, component)*concentration;
			}
			return sum;
			}


			scalar_t AdimensionalSystem::weigthed_sum_gas(index_t component) const
			{
			scalar_t sum = 0.0;
			for (index_t k: m_data->range_gas())
			{
			if (not is_active_gas(k) or m_data->nu_gas(k, component) == 0.0) continue;
			sum += m_data->nu_gas(k, component)*gas_concentration(k);
			}
			return sum;
			}


			scalar_t AdimensionalSystem::diff_weigthed_sum_gas(index_t diff_component, index_t component) const
			{
			scalar_t sum = 0.0;
			for (index_t k: m_data->range_gas())
			{
			if (not is_active_gas(k) or m_data->nu_gas(k, component) == 0.0) continue;
			sum += log10m_data->nu_gas(k, diff_component)m_data->nu_gas(k, component)*gas_concentration(k);
			}
			return sum;
			}


			scalar_t AdimensionalSystem::residual_water(const Vector& x) const
			{
			scalar_t res {0.0};
			if (water_equation_type() == WaterEquationType::MassConservation)
			{
			const scalar_t conc_w = density_water()*saturation_water(x);
			res = total_concentration_bc(0);
			res -= conc_w/m_data->molar_mass_basis_si(0);
			res -= conc_w*weigthed_sum_aqueous(0);
			if (ideq_surf() != no_equation)
			res -= conc_w*weigthed_sum_sorbed(0);
			res -= weigthed_sum_mineral(x, 0);
			if (m_data->nb_gas() > 0)
			res -= weigthed_sum_gas(0);
			res /= total_concentration_bc(0);
			}
			else if (water_equation_type() == WaterEquationType::SaturatedSystem)
			{
			res = 1 - saturation_water(x) - m_inert_volume_fraction;
			for (index_t mineral: m_data->range_mineral())
			{
			res -= saturation_mineral(x, mineral);
			}
			}
			return res;
			}


			scalar_t AdimensionalSystem::residual_component(const Vector &x, index_t component) const
			{
			specmicp_assert(aqueous_component_equation_type(component)
			== AqueousComponentEquationType::MassConservation);
			const scalar_t conc_w = density_water()*saturation_water(x);
			scalar_t res = total_concentration_bc(component);
			res -= conc_w*component_molality(x, component);
			res -= conc_w*weigthed_sum_aqueous(component);
			if (ideq_surf() != no_equation)
			res -= conc_w*weigthed_sum_sorbed(component);
			res -= weigthed_sum_mineral(x, component);
			if (m_data->nb_gas() > 0)
			res -= weigthed_sum_gas(component);
			res /= total_concentration_bc(component);
			return res;
			}

			scalar_t AdimensionalSystem::residual_fixed_activity(const Vector& x, index_t component) const
			{
			specmicp_assert(aqueous_component_equation_type(component)
			== AqueousComponentEquationType::FixedActivity);
			scalar_t res = (fixed_activity_bc(component)
			- log_gamma_component(component)
			- log_component_molality(x, component)
			);
			res /= fixed_activity_bc(component);
			return res;
			}

			scalar_t AdimensionalSystem::residual_fixed_fugacity(const Vector& x, index_t component) const
			{
			specmicp_assert(aqueous_component_equation_type(component)
			== AqueousComponentEquationType::FixedFugacity);
			index_t id_g = m_equations.fixed_activity_species[component];
			scalar_t res = fixed_fugacity_bc(component) + m_data->logk_gas(id_g);
			for (index_t component: m_data->range_aqueous_component())
			{
			if (m_data->nu_gas(id_g, component) == 0) continue;
			res -= m_data->nu_gas(id_g, component)*( log_gamma_component(component)
			+ log_component_molality(x, component));
			}
			res /= fixed_fugacity_bc(component);
			return res;
			}

			scalar_t AdimensionalSystem::residual_mineral(const Vector& x, index_t m) const
			{
			specmicp_assert(ideq_min(m) != no_equation);
			scalar_t res = m_data->logk_mineral(m);
			for (index_t i: m_data->range_aqueous_component())
			{
			if (m_data->nu_mineral(m, i) != 0)
			{
			const auto log_activity_i = log_component_molality(x, i) + log_gamma_component(i);
			res -= m_data->nu_mineral(m, i)*log_activity_i;
			}
			}
			if (ideq_electron() != no_equation and m_data->is_mineral_half_cell_reaction(m))
			res -= m_data->nu_mineral(m, m_data->electron_index())*log_activity_electron(x);
			return res;
			}

			scalar_t AdimensionalSystem::residual_charge_conservation(const Vector& x) const
			{
			scalar_t res = 0.0;
			for (index_t i: m_data->range_aqueous_component())
			{
			if (m_data->charge_component(i) != 0 and ideq_paq(i) != no_equation)
			res += m_data->charge_component(i)*component_molality(x, i);
			}
			for (index_t j: m_data->range_aqueous())
			{
			if (m_data->charge_aqueous(j) == 0 and not is_aqueous_active(j)) continue;
			res += m_data->charge_aqueous(j)*secondary_molality(j);
			}
			return res;
			}

			scalar_t AdimensionalSystem::residual_surface(const Vector &x) const
			{
			specmicp_assert(ideq_surf() != no_equation);
			const scalar_t conc_w = density_water()*saturation_water(x);
			scalar_t res = surface_total_concentration() - conc_w*free_sorption_site_concentration(x);
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			res -= conc_wm_data->nb_sorption_sites(s)sorbed_species_concentration(s);
			}
			return res/surface_total_concentration();
			}

			scalar_t AdimensionalSystem::residual_electron(const Vector &x) const
			{
			specmicp_assert(electron_equation_type() == ElectronEquationType::Equilibrium);
			const scalar_t conc_w = density_water()*saturation_water(x);
			scalar_t res = 0.0;
			res -= conc_w * weigthed_sum_aqueous(m_data->electron_index());
			if (ideq_surf() != no_equation)
			res -= conc_w * weigthed_sum_sorbed(m_data->electron_index());
			res -= weigthed_sum_mineral(x, m_data->electron_index());
			if (m_data->nb_gas() > 0)
			res -= weigthed_sum_gas(m_data->electron_index());
			return res/get_options().scaling_electron;
			}

			void AdimensionalSystem::get_residuals(const Vector& x, Vector& residual)
			{
			residual.resize(total_variables());
			// initialisation of 'main' secondary variables
			// They are especially nessary if the finite difference jacobian is used
			// and for the linesearch
			set_secondary_concentration(x);
			set_sorbed_concentrations(x);
			//
			// water
			if (ideq_w() != no_equation) residual(ideq_w()) = residual_water(x);
			// aqueous component
			for (index_t i: m_data->range_aqueous_component())
			{
			switch (aqueous_component_equation_type(i))
			{
			case AqueousComponentEquationType::NoEquation:
			break;
			case AqueousComponentEquationType::MassConservation:
			residual(ideq_paq(i)) = residual_component(x, i);
			break;
			case AqueousComponentEquationType::ChargeBalance:
			residual(ideq_paq(i)) = residual_charge_conservation(x);
			break;
			case AqueousComponentEquationType::FixedActivity:
			residual(ideq_paq(i)) = residual_fixed_activity(x, i);
			break;
			case AqueousComponentEquationType::FixedFugacity:
			residual(ideq_paq(i)) = residual_fixed_fugacity(x, i);
			break;
			}
			}
			// surface
			if (ideq_surf() != no_equation) residual(ideq_surf()) = residual_surface(x);
			// mineral
			for (index_t m: m_data->range_mineral())
			{
			if (ideq_min(m) != no_equation) residual(ideq_min(m)) = residual_mineral(x, m);
			}
			// electron
			if (ideq_electron() != no_equation ) residual(ideq_electron()) = residual_electron(x);
			// std::cout << residual << std::endl;
			}

			// ================ //
			// //
			// Jacobian //
			// //
			// ================ //


			void AdimensionalSystem::get_jacobian(Vector& x, Matrix& jacobian)
			// //non-optimized Finite difference, for test only
			#ifdef SPECMICP_DEBUG_EQUATION_FD_JACOBIAN
			{
			finite_difference_jacobian(x, jacobian);
			return;
			}
			#else // analytical jacobian
			{
			analytical_jacobian(x, jacobian);
			return;
			}
			#endif


			void AdimensionalSystem::finite_difference_jacobian(Vector& x, Matrix& jacobian)
			{
			const int neq = total_variables();
			Eigen::VectorXd res(neq);
			Eigen::VectorXd perturbed_res(neq);

			jacobian.setZero(neq, neq);

			get_residuals(x, res);
			for (int j=0; j<neq; ++j)
			{
			double h = 1e-8*std::abs(x(j));
			if (h==0) h = 1e-8;
			double tmp = x(j);
			x(j) += h;
			h = x(j) - tmp;
			get_residuals(x, perturbed_res);
			for (int i=0; i<neq; ++i)
			{
			jacobian(i, j) = (perturbed_res(i) - res(i))/h;
			}
			x(j) = tmp;
			}
			}


			void AdimensionalSystem::analytical_jacobian(Vector& x, Matrix& jacobian)
			{
			const int neq = total_variables();
			jacobian.setZero(neq, neq);
			// water
			jacobian_water(x, jacobian);
			// aqueous component
			jacobian_aqueous_components(x, jacobian);
			// surface
			if (ideq_surf() != no_equation) jacobian_surface(x, jacobian);
			// mineral equilibrium
			jacobian_minerals(x, jacobian);
			// electron
			if (ideq_electron() != no_equation) jacobian_electron(x, jacobian);
			}

			void AdimensionalSystem::jacobian_water(Vector& x, Matrix& jacobian)
			{
			if (water_equation_type() == WaterEquationType::MassConservation)
			{
			const index_t idw = ideq_w();
			const scalar_t rho_w = density_water();
			const scalar_t factor = total_concentration_bc(0);
			scalar_t tmp = -1.0/m_data->molar_mass_basis_si(0);
			tmp -= weigthed_sum_aqueous(0);
			tmp -= weigthed_sum_sorbed(0);
			tmp *= rho_w;
			jacobian(idw, idw) = tmp/factor;
			const scalar_t conc_w = density_water()*saturation_water(x);
			for (index_t k: m_data->range_aqueous_component())
			{
			if (ideq_paq(k) == no_equation) continue;
			scalar_t tmp = 0.0;
			tmp -= diff_weigthed_sum_aqueous(k, 0);
			tmp -= diff_weigthed_sum_sorbed(k, 0);
			// fixme gas
			tmp *= conc_w;
			tmp -= diff_weigthed_sum_gas(k, 0);
			jacobian(idw, ideq_paq(k)) = tmp/factor;
			}
			if (ideq_electron() != no_equation)
			{
			scalar_t tmp = 0.0;
			tmp -= diff_weigthed_sum_aqueous(m_data->electron_index(), 0);
			tmp -= diff_weigthed_sum_sorbed(m_data->electron_index(), 0);
			tmp*= conc_w;
			tmp -= diff_weigthed_sum_gas(m_data->electron_index(), 0);
			jacobian(idw, ideq_electron()) = tmp/factor;
			}
			for (index_t m: m_data->range_mineral())
			{
			if (ideq_min(m) == no_equation) continue;
			jacobian(idw, ideq_min(m)) = -m_data->nu_mineral(m, 0)/molar_volume_mineral(m)/factor;
			}
			}
			else if (water_equation_type() == WaterEquationType::SaturatedSystem)
			{
			const index_t idw = ideq_w();
			jacobian(idw, idw) = -1;
			for (index_t m: m_data->range_mineral())
			{
			if (ideq_min(m) == no_equation) continue;
			jacobian(idw, ideq_min(m)) = -1;
			}
			}
			}

			void AdimensionalSystem::jacobian_aqueous_components(Vector& x, Matrix& jacobian)
			{
			for (index_t i: m_data->range_aqueous_component())
			{
			const index_t idp = ideq_paq(i);
			if (idp == no_equation) continue;
			switch (aqueous_component_equation_type(i))
			{
			case AqueousComponentEquationType::NoEquation:
			continue;
			// Mass balance equation
			// =====================
			case AqueousComponentEquationType::MassConservation:
			{
			const scalar_t conc_w = density_water()*saturation_water(x);
			const scalar_t factor = total_concentration_bc(i);
			// Aqueous components
			for (index_t k: m_data->range_aqueous_component())
			{
			if (ideq_paq(k) == no_equation) continue;
			scalar_t tmp_iip = 0;
			if (k == i) tmp_iip -= component_molality(x, i)*log10;
			tmp_iip -= diff_weigthed_sum_aqueous(k, i);
			tmp_iip -= diff_weigthed_sum_sorbed(k, i);
			tmp_iip *= conc_w;
			tmp_iip -= diff_weigthed_sum_gas(k, i);
			jacobian(idp, ideq_paq(k)) = tmp_iip/factor;
			}
			// Minerals
			for (index_t m: m_data->range_mineral())
			{
			if (ideq_min(m) == no_equation) continue;
			jacobian(idp, ideq_min(m)) = - m_data->nu_mineral(m, i)/molar_volume_mineral(m)/factor;
			}
			// Water
			if (ideq_w() != no_equation)
			{
			scalar_t tmp_iw = -component_molality(x, i);
			tmp_iw -= weigthed_sum_aqueous(i);
			tmp_iw -= weigthed_sum_sorbed(i);
			tmp_iw *= density_water();
			jacobian(idp, ideq_w()) = tmp_iw/factor;
			}
			// Surface
			if (ideq_surf() != no_equation)
			{
			scalar_t tmp_s = -conc_w*diff_surface_weigthed_sum_sorbed(i);
			jacobian(idp, ideq_surf()) = tmp_s/factor;
			}
			// Electron
			if (ideq_electron() != no_equation)
			{
			scalar_t tmp = 0.0;
			tmp -= diff_weigthed_sum_aqueous(m_data->electron_index(), i);
			tmp -= diff_weigthed_sum_sorbed(m_data->electron_index(), i);
			tmp*= conc_w;
			tmp -= diff_weigthed_sum_gas(m_data->electron_index(), i);
			jacobian(idp, ideq_electron()) = tmp/factor;
			}
			break;
			}
			// Charge balance equation
			// =======================
			case AqueousComponentEquationType::ChargeBalance:
			{
			// Aqueous components
			for (index_t k: m_data->range_aqueous_component())
			{
			const index_t idc = ideq_paq(k);
			if (idc == no_equation) continue;
			scalar_t tmp_drdb = 0.0;
			if (m_data->charge_component(k) != 0.0)
			tmp_drdb = m_data->charge_component(k);
			// Secondary species
			for (index_t j: m_data->range_aqueous())
			{
			if ( not is_aqueous_active(j)
			or m_data->nu_aqueous(j, k) == 0.0
			or m_data->charge_aqueous(j) == 0.0
			)
			continue;
			scalar_t tmp_value = m_data->nu_aqueous(j, k)*m_data->charge_aqueous(j);
			tmp_value *= secondary_molality(j)/component_molality(x, k);
			tmp_drdb += tmp_value;
			}
			jacobian(idp, idc) += component_molality(x,k)log10tmp_drdb;
			}
			break;
			}
			// Fixed activity equation
			// =======================
			case AqueousComponentEquationType::FixedActivity:
			jacobian(idp, idp) = -1.0/fixed_activity_bc(i);
			break;
			// Fixed fugacity equation
			// =======================
			case AqueousComponentEquationType::FixedFugacity:
			{
			index_t id_g = m_equations.fixed_activity_species[i];
			for (index_t k: m_data->range_aqueous_component())
			{
			if (ideq_paq(k) == no_equation or m_data->nu_gas(id_g, k) == 0.0) continue;
			jacobian(idp, ideq_paq(k)) = -m_data->nu_gas(id_g, k)/fixed_fugacity_bc(i);
			}
			break;
			} // end case
			} // end switch
			}
			}

			void AdimensionalSystem::jacobian_minerals(Vector& x, Matrix& jacobian)
			{
			for (index_t m: m_data->range_mineral())
			{
			const index_t idm = ideq_min(m);
			if (idm == no_equation) continue;
			for (index_t i: m_data->range_aqueous_component())
			{
			if (ideq_paq(i) == no_equation) continue;
			jacobian(idm, ideq_paq(i)) = -m_data->nu_mineral(m, i);
			}
			if (ideq_electron() != no_equation and m_data->is_mineral_half_cell_reaction(m))
			jacobian(idm, ideq_electron()) = -m_data->nu_mineral(m, m_data->electron_index());

			}
			}

			void AdimensionalSystem::jacobian_surface(Vector& x, Matrix& jacobian)
			{
			const index_t ids = ideq_surf();
			const scalar_t factor = surface_total_concentration();
			const scalar_t conc_w = density_water()*saturation_water(x);
			specmicp_assert(ids != no_equation);
			scalar_t tmp_s = - free_sorption_site_concentration(x);
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			tmp_s -= m_data->nb_sorption_sites(s)* m_data->nb_sorption_sites(s)*sorbed_species_concentration(s);
			}
			jacobian(ids, ids) = conc_wlog10 tmp_s / factor;

			// water
			const index_t idw = ideq_w();
			if (idw != no_equation)
			{
			const scalar_t rho_w = density_water();
			scalar_t tmp_w = - free_sorption_site_concentration(x);
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			tmp_w -= m_data->nb_sorption_sites(s)*sorbed_species_concentration(s);
			}
			jacobian(ids, idw) = rho_w * tmp_w / factor;
			}
			// component

			for (index_t k: m_data->range_aqueous_component())
			{
			const index_t idk = ideq_paq(k);
			if (idk == no_equation) continue;
			scalar_t tmp_k = - conc_w*diff_surface_weigthed_sum_sorbed(k);
			jacobian(ids, idk) = tmp_k/factor;
			}
			if (ideq_electron() != no_equation)
			{
			scalar_t tmp_e = - conc_w*diff_surface_weigthed_sum_sorbed(m_data->electron_index());
			jacobian(ids, ideq_electron()) = tmp_e/factor;
			}
			// water
			}


			void AdimensionalSystem::jacobian_electron(Vector& x, Matrix& jacobian)
			{
			const auto ide = ideq_electron();
			const auto dofe = m_data->electron_index();
			const scalar_t conc_w = density_water()*saturation_water(x);
			const scalar_t factor = get_options().scaling_electron;
			// Aqueous components
			for (index_t k: m_data->range_aqueous_component())
			{
			if (ideq_paq(k) == no_equation) continue;
			scalar_t tmp_eip = 0;
			tmp_eip -= diff_weigthed_sum_aqueous(k, dofe);
			tmp_eip -= diff_weigthed_sum_sorbed(k, dofe);
			tmp_eip *= conc_w;
			tmp_eip -= diff_weigthed_sum_gas(k, dofe);
			jacobian(ide, ideq_paq(k)) = tmp_eip/factor;
			}
			// Minerals
			for (index_t m: m_data->range_mineral())
			{
			if (ideq_min(m) == no_equation) continue;
			jacobian(ide, ideq_min(m)) = - m_data->nu_mineral(m, dofe)/molar_volume_mineral(m)/factor;
			}
			// Water
			if (ideq_w() != no_equation)
			{
			scalar_t tmp_iw = 0;
			tmp_iw -= weigthed_sum_aqueous(dofe);
			tmp_iw -= weigthed_sum_sorbed(dofe);
			tmp_iw *= density_water();
			jacobian(ide, ideq_w()) = tmp_iw/factor;
			}
			// Surface
			if (ideq_surf() != no_equation)
			{
			scalar_t tmp_s = -conc_w*diff_surface_weigthed_sum_sorbed(dofe);
			jacobian(ide, ideq_surf()) = tmp_s/factor;
			}
			// Electron
			if (ideq_electron() != no_equation)
			{
			scalar_t tmp = 0.0;
			tmp -= diff_weigthed_sum_aqueous(dofe, dofe);
			tmp -= diff_weigthed_sum_sorbed(dofe, dofe);
			tmp*= conc_w;
			tmp -= diff_weigthed_sum_gas(dofe, dofe);
			jacobian(ide, ide) = tmp/factor;
			}
			}

			// ========================== //
			// //
			// Secondary variables //
			// //
			// ========================== //

			void AdimensionalSystem::set_secondary_variables(const Vector& x)
			{
			set_saturation_gas_phase(x);
			set_pressure_fugacity(x);
			if (ideq_surf() != no_equation) set_sorbed_concentrations(x);
			set_secondary_concentration(x);
			compute_log_gamma(x);
			}

			void AdimensionalSystem::set_saturation_gas_phase(const Vector& x)
			{
			m_second.saturation_gas = 1 - saturation_water(x) - sum_saturation_minerals(x) - m_inert_volume_fraction;
			}

			void AdimensionalSystem::set_pressure_fugacity(const Vector& x)
			{
			const auto rt = constants::gas_constant*temperature();
			for (index_t k: m_data->range_gas())
			{
			if (not is_active_gas(k)) continue;
			scalar_t logp = -m_data->logk_gas(k);
			for (index_t i: m_data->range_aqueous_component())
			{
			if (m_data->nu_gas(k, i) == 0.0) continue;
			const auto log_activity_i = log_component_molality(x, i) + log_gamma_component(i);
			logp += m_data->nu_gas(k, i) * log_activity_i;
			}
			if (ideq_electron() != no_equation and m_data->is_gas_half_cell_reaction(k))
			logp += m_data->nu_gas(k, m_data->electron_index())*log_activity_electron(x);
			m_second.gas_fugacity(k) = pow10(logp);
			const scalar_t pressure = gas_fugacity(k)*gas_total_pressure();
			const scalar_t concentration = saturation_gas_phase()*pressure/rt;
			m_second.gas_concentration(k) = concentration;
			}
			}

			void AdimensionalSystem::set_secondary_concentration(const Vector& x)
			{
			for (index_t j: m_data->range_aqueous())
			{
			if (not is_aqueous_active(j))
			{
			m_second.secondary_molalities(j) = 0.0;
			continue;
			}
			scalar_t logconc = -m_data->logk_aqueous(j) - log_gamma_secondary(j);
			for (index_t k: m_data->range_aqueous_component())
			{
			if (m_data->nu_aqueous(j, k) == 0) continue;
			const auto log_activity_k = log_component_molality(x, k) + log_gamma_component(k);
			logconc += m_data->nu_aqueous(j, k)*log_activity_k;
			}
			if (ideq_electron() != no_equation and m_data->is_half_cell_reaction(j))
			logconc += m_data->nu_aqueous(j, m_data->electron_index())*log_activity_electron(x);
			m_second.secondary_molalities(j) = pow10(logconc);
			}
			}

			void AdimensionalSystem::set_sorbed_concentrations(const Vector& x)
			{
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s))
			{
			m_second.sorbed_concentrations(s) = 0.0;
			continue;
			}
			scalar_t logconc = -m_data->logk_sorbed(s) +
			m_data->nb_sorption_sites(s)*(log_free_sorption_site_concentration(x));
			for (index_t k: m_data->range_aqueous_component())
			{
			if (m_data->nu_sorbed(s, k) == 0.0) continue;
			const auto activity_k = log_component_molality(x, k) + log_gamma_component(k);
			logconc += m_data->nu_sorbed(s, k)*activity_k;
			}
			if (ideq_electron() != no_equation and m_data->is_sorbed_half_cell_reaction(s))
			logconc += m_data->nu_sorbed(s, m_data->electron_index())*log_activity_electron(x);
			m_second.sorbed_concentrations(s) = pow10(logconc);
			}
			}

			void AdimensionalSystem::set_ionic_strength(const Vector& x)
			{
			scalar_t ionic = 0;
			for (index_t i: m_data->range_aqueous_component())
			{
			if (ideq_paq(i) == no_equation or m_data->charge_component(i) == 0) continue;
			ionic += component_molality(x, i)*std::pow(m_data->charge_component(i),2);
			}
			for (index_t j: m_data->range_aqueous())
			{
			if (not is_aqueous_active(j) or m_data->charge_aqueous(j) == 0) continue;
			ionic += secondary_molality(j)*std::pow(m_data->charge_aqueous(j),2);
			}
			ionic_strength() = ionic/2;
			}

			void AdimensionalSystem::compute_log_gamma(const Vector& x)
			{
			set_ionic_strength(x);
			const scalar_t sqrti = std::sqrt(ionic_strength());
			for (index_t i: m_data->range_aqueous_component())
			{
			if (ideq_paq(i) == no_equation)
			{
			log_gamma_component(i) = 0.0;
			continue;
			}
			log_gamma_component(i) = laws::extended_debye_huckel(
			ionic_strength(), sqrti,
			m_data->charge_component(i),
			m_data->a_debye_component(i),
			m_data->b_debye_component(i)
			);
			}
			for (index_t j: m_data->range_aqueous())
			{
			if (not is_aqueous_active(j))
			{
			log_gamma_secondary(j) = 0.0;
			continue;
			}
			log_gamma_secondary(j) = laws::extended_debye_huckel(
			ionic_strength(), sqrti,
			m_data->charge_aqueous(j),
			m_data->a_debye_aqueous(j),
			m_data->b_debye_aqueous(j)
			);
			}
			}

			bool AdimensionalSystem::hook_start_iteration(const Vector& x, scalar_t norm_residual)
			{
			if (not get_options().non_ideality)
			{
			set_secondary_variables(x);
			// we still need to compute secondary species !
			// if (norm_residual < nb_free_variables()*get_options().start_non_ideality_computation)
			// {
			// set_secondary_variables(x);
			// }
			return true;
			}

			not_in_linesearch = true;
			scalar_t previous_norm = m_second.loggamma.norm();
			bool may_have_converged = false;
			if (norm_residual < nb_free_variables()*get_options().start_non_ideality_computation)
			{
			// Use fixed point iterations for non-ideality
			for (int i=0; i<get_options().non_ideality_max_iter; ++i)
			{
			set_secondary_variables(x);
			compute_log_gamma(x);
			// convergence check
			if (std::abs(previous_norm - m_second.loggamma.norm())/previous_norm <
			get_options().non_ideality_tolerance) {
			may_have_converged = true;
			break;
			}
			previous_norm = m_second.loggamma.norm();
			}
			}
			return may_have_converged;
			}

			double AdimensionalSystem::max_lambda(const Vector& x, const Vector& update)
			{
			if (ideq_w() != no_equation)
			{
			return 1.0/std::max(1.0, -update(0)/(get_options().under_relaxation_factor*x(0)));
			}
			else
			{
			return 1.0;
			}
			}

			AdimensionalSystemSolution AdimensionalSystem::get_solution(Vector& xtot, const Vector& x)
			{
			double previous_norm = m_second.loggamma.norm();
			set_saturation_gas_phase(x);
			set_pressure_fugacity(x);
			set_secondary_concentration(x);
			if (ideq_surf() != no_equation) set_sorbed_concentrations(x);
			if (get_options().non_ideality)
			{
			compute_log_gamma(x);
			if (std::abs(previous_norm - m_second.loggamma.norm()) > 1e-6)
			{
			WARNING << "Activity coefficient have not converged !" << std::endl
			<< "output can not be trusted\n Difference : "
			+std::to_string(std::abs(previous_norm - m_second.loggamma.norm()));
			}
			}
			// Set the correct value for the water total saturation
			if (ideq_w() == no_equation)
			{
			xtot(dof_water()) = saturation_water(x);
			}
			return AdimensionalSystemSolution(xtot,
			m_second.secondary_molalities,
			m_second.loggamma,
			m_second.ionic_strength,
			m_second.gas_fugacity,
			m_second.sorbed_concentrations,
			m_inert_volume_fraction);
			}

			// Water, saturation and density
			// ==============================

			scalar_t AdimensionalSystem::density_water() const {
			return laws::density_water(units::celsius(25.0), length_unit(), mass_unit());
			}


			scalar_t AdimensionalSystem::saturation_water(const Vector& x) const
			{
			if (ideq_w() != no_equation)
			return x(ideq_w());
			else
			return 1.0 - sum_saturation_minerals(x) - m_inert_volume_fraction;
			}

			scalar_t AdimensionalSystem::saturation_mineral(const Vector& x, index_t mineral) const
			{
			specmicp_assert(mineral >= 0 and mineral < m_data->nb_mineral());
			if (ideq_min(mineral) == no_equation) return 0.0;
			else return x(ideq_min(mineral));
			}

			scalar_t AdimensionalSystem::sum_saturation_minerals(const Vector& x) const
			{
			scalar_t sum_saturations = 0.0;
			for (index_t mineral: m_data->range_mineral())
			{
			sum_saturations += saturation_mineral(x, mineral);
			}
			return sum_saturations;
			}

			// Starting guess
			// ==============

			void AdimensionalSystem::reasonable_starting_guess(Vector &xtot)
			{
			xtot.resize(total_dofs());
			xtot(dof_water()) = 0.8;
			for (index_t i: m_data->range_aqueous_component())
			{
			xtot(dof_component(i)) = -4.0;
			}
			if (ideq_surf() != no_equation)
			xtot(dof_surface()) = std::log10(0.8*surface_total_concentration());
			else
			xtot(dof_surface()) = -HUGE_VAL;
			if (ideq_electron() != no_equation)
			xtot(dof_electron()) = -4;
			else
			xtot(dof_electron()) = -HUGE_VAL;
			xtot.segment(offset_minerals(), m_data->nb_mineral()).setZero();
			m_second = SecondaryVariables(m_data);
			}

			void AdimensionalSystem::reasonable_restarting_guess(Vector& xtot)
			{
			std::random_device rd;
			std::mt19937 gen(rd());
			std::uniform_real_distribution<> dis(-2, 2);

			xtot(dof_water()) = 0.5;
			for (index_t i: m_data->range_aqueous_component())
			{
			//if (xtot(dof_component(i)) > 0 or xtot(dof_component(i)) < -9)
			xtot(i) = get_options().restart_concentration + dis(gen);
			}
			if (ideq_surf() != no_equation)
			xtot(dof_surface()) = std::log10(0.8*surface_total_concentration());
			else
			xtot(dof_surface()) = -HUGE_VAL;
			if (ideq_electron() != no_equation)
			xtot(dof_electron()) = -4;
			else
			xtot(dof_electron()) = -HUGE_VAL;
			xtot.segment(offset_minerals(), m_data->nb_mineral()).setZero();

			m_second = SecondaryVariables(m_data);
			}

			} // end namespace specmicp

specmicp/src/specmicp/adimensional/adimensional_system.cppda87eb82fc39reactmicp/unsaturated

adimensional_system.cppView Options

specmicp/src/specmicp/adimensional/adimensional_system.cpp
da87eb82fc39reactmicp/unsaturated

adimensional_system.cpp
View Options