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	/**
	* @file cell_base.cc
	*
	* @author Till Junge <till.junge@epfl.ch>
	*
	* @date 01 Nov 2017
	*
	* @brief Implementation for cell base class
	*
	* Copyright © 2017 Till Junge
	*
	* µSpectre is free software; you can redistribute it and/or
	* modify it under the terms of the GNU Lesser General Public License as
	* published by the Free Software Foundation, either version 3, or (at
	* your option) any later version.
	*
	* µSpectre is distributed in the hope that it will be useful, but
	* WITHOUT ANY WARRANTY; without even the implied warranty of
	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
	* General Public License for more details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with µSpectre; see the file COPYING. If not, write to the
	* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
	* * Boston, MA 02111-1307, USA.
	*
	* Additional permission under GNU GPL version 3 section 7
	*
	* If you modify this Program, or any covered work, by linking or combining it
	* with proprietary FFT implementations or numerical libraries, containing parts
	* covered by the terms of those libraries' licenses, the licensors of this
	* Program grant you additional permission to convey the resulting work.
	*/

	#include "cell/cell_base.hh"
	#include "common/ccoord_operations.hh"
	#include "common/iterators.hh"
	#include "common/tensor_algebra.hh"

	#include <sstream>
	#include <algorithm>
	#include <set>
	#include <functional>

	namespace muSpectre {

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	CellBase<DimS, DimM>::CellBase(Projection_ptr projection_)
	: subdomain_resolutions{projection_->get_subdomain_resolutions()},
	subdomain_locations{projection_->get_subdomain_locations()},
	domain_resolutions{projection_->get_domain_resolutions()},
	pixels(subdomain_resolutions, subdomain_locations),
	domain_lengths{projection_->get_domain_lengths()},
	fields{std::make_unique<FieldCollection_t>()},
	F{make_field<StrainField_t>("Gradient", *this->fields)},
	P{make_field<StressField_t>("Piola-Kirchhoff-1", *this->fields)},
	projection{std::move(projection_)} {
	// resize all global fields (strain, stress, etc)
	this->fields->initialise(this->subdomain_resolutions,
	this->subdomain_locations);
	}

	/**
	* turns out that the default move container in combination with
	* clang segfaults under certain (unclear) cicumstances, because the
	* move constructor of the optional appears to be busted in gcc
	* 7.2. Copying it (K) instead of moving it fixes the issue, and
	* since it is a reference, the cost is practically nil
	*/
	template <Dim_t DimS, Dim_t DimM>
	CellBase<DimS, DimM>::CellBase(CellBase && other)
	: subdomain_resolutions{std::move(other.subdomain_resolutions)},
	subdomain_locations{std::move(other.subdomain_locations)},
	domain_resolutions{std::move(other.domain_resolutions)},
	pixels{std::move(other.pixels)}, domain_lengths{std::move(
	other.domain_lengths)},
	fields{std::move(other.fields)}, F{other.F}, P{other.P},
	K{other.K}, // this seems to segfault under clang if it's not a move
	materials{std::move(other.materials)}, projection{std::move(
	other.projection)} {}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	typename CellBase<DimS, DimM>::Material_t &
	CellBase<DimS, DimM>::add_material(Material_ptr mat) {
	this->materials.push_back(std::move(mat));
	return *this->materials.back();
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	auto CellBase<DimS, DimM>::get_strain_vector() -> Vector_ref {
	return this->get_strain().eigenvec();
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	auto CellBase<DimS, DimM>::get_stress_vector() const -> ConstVector_ref {
	return this->get_stress().eigenvec();
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	void CellBase<DimS, DimM>::set_uniform_strain(
	const Eigen::Ref<const Matrix_t> & strain) {
	this->F.get_map() = strain;
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	auto CellBase<DimS, DimM>::evaluate_stress() -> ConstVector_ref {
	if (not this->initialised) {
	this->initialise();
	}
	for (auto & mat : this->materials) {
	mat->compute_stresses(this->F, this->P, this->get_formulation());
	}

	return this->P.const_eigenvec();
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	auto CellBase<DimS, DimM>::evaluate_stress_tangent()
	-> std::array<ConstVector_ref, 2> {
	if (not this->initialised) {
	this->initialise();
	}

	constexpr bool create_tangent{true};
	this->get_tangent(create_tangent);

	for (auto & mat : this->materials) {
	mat->compute_stresses_tangent(this->F, this->P, this->K.value(),
	this->get_formulation());
	}
	const TangentField_t & k = this->K.value();
	return std::array<ConstVector_ref, 2>{this->P.const_eigenvec(),
	k.const_eigenvec()};
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	auto CellBase<DimS, DimM>::evaluate_projected_directional_stiffness(
	Eigen::Ref<const Vector_t> delF) -> Vector_ref {
	// the following const_cast should be safe, as long as the
	// constructed delF_field is const itself
	const TypedField<FieldCollection_t, Real> delF_field(
	"Proxied raw memory for strain increment", *this->fields,
	Eigen::Map<Vector_t>(const_cast<Real *>(delF.data()), delF.size()),
	this->F.get_nb_components());

	if (!this->K) {
	throw std::runtime_error(
	"currently only implemented for cases where a stiffness matrix "
	"exists");
	}

	if (delF.size() != this->get_nb_dof()) {
	std::stringstream err{};
	err << "input should be of size ndof = ¶(" << this->subdomain_resolutions
	<< ") × " << DimS << "² = " << this->get_nb_dof() << " but I got "
	<< delF.size();
	throw std::runtime_error(err.str());
	}

	const std::string out_name{"δP; temp output for directional stiffness"};
	auto & delP = this->get_managed_T2_field(out_name);

	auto Kmap{this->K.value().get().get_map()};
	auto delPmap{delP.get_map()};
	MatrixFieldMap<FieldCollection_t, Real, DimM, DimM, true> delFmap(
	delF_field);

	for (auto && tup : akantu::zip(Kmap, delFmap, delPmap)) {
	auto & k = std::get<0>(tup);
	auto & df = std::get<1>(tup);
	auto & dp = std::get<2>(tup);
	dp = Matrices::tensmult(k, df);
	}

	return Vector_ref(this->project(delP).data(), this->get_nb_dof());
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	std::array<Dim_t, 2> CellBase<DimS, DimM>::get_strain_shape() const {
	return this->projection->get_strain_shape();
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	void CellBase<DimS, DimM>::apply_projection(Eigen::Ref<Vector_t> vec) {
	TypedField<FieldCollection_t, Real> field("Proxy for projection",
	*this->fields, vec,
	this->F.get_nb_components());
	this->projection->apply_projection(field);
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	typename CellBase<DimS, DimM>::FullResponse_t
	CellBase<DimS, DimM>::evaluate_stress_tangent(StrainField_t & grad) {
	if (this->initialised == false) {
	this->initialise();
	}
	//! High level compatibility checks
	if (grad.size() != this->F.size()) {
	throw std::runtime_error("Size mismatch");
	}
	constexpr bool create_tangent{true};
	this->get_tangent(create_tangent);

	for (auto & mat : this->materials) {
	mat->compute_stresses_tangent(grad, this->P, this->K.value(),
	this->get_formulation());
	}
	return std::tie(this->P, this->K.value());
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	typename CellBase<DimS, DimM>::StressField_t &
	CellBase<DimS, DimM>::directional_stiffness(const TangentField_t & K,
	const StrainField_t & delF,
	StressField_t & delP) {
	for (auto && tup :
	akantu::zip(K.get_map(), delF.get_map(), delP.get_map())) {
	auto & k = std::get<0>(tup);
	auto & df = std::get<1>(tup);
	auto & dp = std::get<2>(tup);
	dp = Matrices::tensmult(k, df);
	}
	return this->project(delP);
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	typename CellBase<DimS, DimM>::Vector_ref
	CellBase<DimS, DimM>::directional_stiffness_vec(
	const Eigen::Ref<const Vector_t> & delF) {
	if (!this->K) {
	throw std::runtime_error(
	"currently only implemented for cases where a stiffness matrix "
	"exists");
	}
	if (delF.size() != this->get_nb_dof()) {
	std::stringstream err{};
	err << "input should be of size ndof = ¶(" << this->subdomain_resolutions
	<< ") × " << DimS << "² = " << this->get_nb_dof() << " but I got "
	<< delF.size();
	throw std::runtime_error(err.str());
	}
	const std::string out_name{"temp output for directional stiffness"};
	const std::string in_name{"temp input for directional stiffness"};

	auto & out_tempref = this->get_managed_T2_field(out_name);
	auto & in_tempref = this->get_managed_T2_field(in_name);
	Vector_ref(in_tempref.data(), this->get_nb_dof()) = delF;

	this->directional_stiffness(this->K.value(), in_tempref, out_tempref);
	return Vector_ref(out_tempref.data(), this->get_nb_dof());
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	Eigen::ArrayXXd CellBase<DimS, DimM>::directional_stiffness_with_copy(
	Eigen::Ref<Eigen::ArrayXXd> delF) {
	if (!this->K) {
	throw std::runtime_error(
	"currently only implemented for cases where a stiffness matrix "
	"exists");
	}
	const std::string out_name{"temp output for directional stiffness"};
	const std::string in_name{"temp input for directional stiffness"};

	auto & out_tempref = this->get_managed_T2_field(out_name);
	auto & in_tempref = this->get_managed_T2_field(in_name);
	in_tempref.eigen() = delF;
	this->directional_stiffness(this->K.value(), in_tempref, out_tempref);
	return out_tempref.eigen();
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	typename CellBase<DimS, DimM>::StressField_t &
	CellBase<DimS, DimM>::project(StressField_t & field) {
	this->projection->apply_projection(field);
	return field;
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	typename CellBase<DimS, DimM>::StrainField_t &
	CellBase<DimS, DimM>::get_strain() {
	if (this->initialised == false) {
	this->initialise();
	}
	return this->F;
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	const typename CellBase<DimS, DimM>::StressField_t &
	CellBase<DimS, DimM>::get_stress() const {
	return this->P;
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	const typename CellBase<DimS, DimM>::TangentField_t &
	CellBase<DimS, DimM>::get_tangent(bool create) {
	if (!this->K) {
	if (create) {
	this->K =
	make_field<TangentField_t>("Tangent Stiffness", *this->fields);
	} else {
	throw std::runtime_error("K does not exist");
	}
	}
	return this->K.value();
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	typename CellBase<DimS, DimM>::StrainField_t &
	CellBase<DimS, DimM>::get_managed_T2_field(std::string unique_name) {
	if (!this->fields->check_field_exists(unique_name)) {
	return make_field<StressField_t>(unique_name, *this->fields);
	} else {
	return static_cast<StressField_t &>(this->fields->at(unique_name));
	}
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	auto CellBase<DimS, DimM>::get_managed_real_field(std::string unique_name,
	size_t nb_components)
	-> Field_t<Real> & {
	if (!this->fields->check_field_exists(unique_name)) {
	return make_field<Field_t<Real>>(unique_name, *this->fields,
	nb_components);
	} else {
	auto & ret_ref{Field_t<Real>::check_ref(this->fields->at(unique_name))};
	if (ret_ref.get_nb_components() != nb_components) {
	std::stringstream err{};
	err << "Field '" << unique_name << "' already exists and it has "
	<< ret_ref.get_nb_components()
	<< " components. You asked for a field "
	<< "with " << nb_components << "components.";
	throw std::runtime_error(err.str());
	}
	return ret_ref;
	}
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	auto CellBase<DimS, DimM>::get_globalised_internal_real_field(
	const std::string & unique_name) -> Field_t<Real> & {
	using LField_t = typename Field_t<Real>::LocalField_t;
	// start by checking that the field exists at least once, and that
	// it always has th same number of components
	std::set<Dim_t> nb_component_categories{};
	std::vector<std::reference_wrapper<LField_t>> local_fields;
	for (auto & mat : this->materials) {
	auto & coll = mat->get_collection();
	if (coll.check_field_exists(unique_name)) {
	auto & field{LField_t::check_ref(coll[unique_name])};
	local_fields.emplace_back(field);
	nb_component_categories.insert(field.get_nb_components());
	}
	}
	if (nb_component_categories.size() != 1) {
	const auto & nb_match{nb_component_categories.size()};
	std::stringstream err_str{};
	if (nb_match > 1) {
	err_str << "The fields named '" << unique_name << "' do not have the "
	<< "same number of components in every material, which is a "
	<< "requirement for globalising them! The following values "
	<< "were found by material:" << std::endl;
	for (auto & mat : this->materials) {
	auto & coll = mat->get_collection();
	if (coll.check_field_exists(unique_name)) {
	auto & field{LField_t::check_ref(coll[unique_name])};
	err_str << field.get_nb_components() << " components in material '"
	<< mat->get_name() << "'" << std::endl;
	}
	}
	} else {
	err_str << "The field named '" << unique_name << "' does not exist in "
	<< "any of the materials and can therefore not be globalised!";
	}
	throw std::runtime_error(err_str.str());
	}
	const Dim_t nb_components{*nb_component_categories.begin()};

	// get and prepare the field
	auto & field{this->get_managed_real_field(unique_name, nb_components)};
	field.set_zero();

	// fill it with local internal values
	for (auto & local_field : local_fields) {
	field.fill_from_local(local_field);
	}
	return field;
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	auto CellBase<DimS, DimM>::get_managed_real_array(std::string unique_name,
	size_t nb_components)
	-> Array_ref<Real> {
	auto & field{this->get_managed_real_field(unique_name, nb_components)};
	return Array_ref<Real>{field.data(), Dim_t(nb_components),
	Dim_t(field.size())};
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	auto CellBase<DimS, DimM>::get_globalised_internal_real_array(
	const std::string & unique_name) -> Array_ref<Real> {
	auto & field{this->get_globalised_internal_real_field(unique_name)};
	return Array_ref<Real>{field.data(), Dim_t(field.get_nb_components()),
	Dim_t(field.size())};
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	void CellBase<DimS, DimM>::initialise(FFT_PlanFlags flags) {
	// check that all pixels have been assigned exactly one material
	this->check_material_coverage();
	for (auto && mat : this->materials) {
	mat->initialise();
	}
	// initialise the projection and compute the fft plan
	this->projection->initialise(flags);
	this->initialised = true;
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	void CellBase<DimS, DimM>::save_history_variables() {
	for (auto && mat : this->materials) {
	mat->save_history_variables();
	}
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	typename CellBase<DimS, DimM>::iterator CellBase<DimS, DimM>::begin() {
	return this->pixels.begin();
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	typename CellBase<DimS, DimM>::iterator CellBase<DimS, DimM>::end() {
	return this->pixels.end();
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	auto CellBase<DimS, DimM>::get_adaptor() -> Adaptor {
	return Adaptor(*this);
	}

	/* ---------------------------------------------------------------------- */
	template <Dim_t DimS, Dim_t DimM>
	void CellBase<DimS, DimM>::check_material_coverage() {
	auto nb_pixels = CcoordOps::get_size(this->subdomain_resolutions);
	std::vector<MaterialBase<DimS, DimM> *> assignments(nb_pixels, nullptr);
	for (auto & mat : this->materials) {
	for (auto & pixel : *mat) {
	auto index = CcoordOps::get_index(this->subdomain_resolutions,
	this->subdomain_locations, pixel);
	auto & assignment{assignments.at(index)};
	if (assignment != nullptr) {
	std::stringstream err{};
	err << "Pixel " << pixel << "is already assigned to material '"
	<< assignment->get_name()
	<< "' and cannot be reassigned to material '" << mat->get_name();
	throw std::runtime_error(err.str());
	} else {
	assignments[index] = mat.get();
	}
	}
	}

	// find and identify unassigned pixels
	std::vector<Ccoord> unassigned_pixels;
	for (size_t i = 0; i < assignments.size(); ++i) {
	if (assignments[i] == nullptr) {
	unassigned_pixels.push_back(CcoordOps::get_ccoord(
	this->subdomain_resolutions, this->subdomain_locations, i));
	}
	}

	if (unassigned_pixels.size() != 0) {
	std::stringstream err{};
	err << "The following pixels have were not assigned a material: ";
	for (auto & pixel : unassigned_pixels) {
	err << pixel << ", ";
	}
	err << "and that cannot be handled";
	throw std::runtime_error(err.str());
	}
	}

	template class CellBase<twoD, twoD>;
	template class CellBase<threeD, threeD>;

	} // namespace muSpectre

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