feat: add solver core skeleton

tests/CMakeLists.txt

@@ -0,0 +1,2 @@
+add_subdirectory(unit)
+add_subdirectory(integration)

tests/integration/CMakeLists.txt

@@ -0,0 +1,8 @@
+file(GLOB FESA_INTEGRATION_TEST_SOURCES CONFIGURE_DEPENDS "${CMAKE_CURRENT_SOURCE_DIR}/*_test.cpp")
+
+foreach(test_source IN LISTS FESA_INTEGRATION_TEST_SOURCES)
+    get_filename_component(test_name "${test_source}" NAME_WE)
+    add_executable("${test_name}" "${test_source}")
+    target_link_libraries("${test_name}" PRIVATE fesa_core)
+    add_test(NAME "${test_name}" COMMAND "${test_name}")
+endforeach()

tests/integration/solver_core_skeleton_integration_test.cpp

@@ -0,0 +1,64 @@
+#include <fesa/analysis/linear_static_analysis.hpp>
+#include <fesa/results/results.hpp>
+
+namespace {
+
+int fail()
+{
+    return 1;
+}
+
+fesa::model::Domain make_domain()
+{
+    fesa::model::Domain domain;
+    domain.add_node({fesa::core::NodeId{1}, {0.0, 0.0, 0.0}});
+    domain.add_node({fesa::core::NodeId{2}, {1.0, 0.0, 0.0}});
+    domain.add_material({fesa::core::MaterialId{3}, "steel"});
+    domain.add_property({fesa::core::PropertyId{4}, "bar", fesa::core::MaterialId{3}});
+    domain.add_element({
+        fesa::core::ElementId{5},
+        fesa::model::ElementTopology::truss2,
+        {fesa::core::NodeId{1}, fesa::core::NodeId{2}},
+        fesa::core::PropertyId{4}
+    });
+    fesa::model::AnalysisStep step{fesa::core::StepId{6}, "static-step"};
+    step.add_boundary_condition({fesa::core::NodeId{1}, fesa::model::DofComponent::ux, 0.0});
+    step.add_load({fesa::core::NodeId{2}, fesa::model::DofComponent::ux, 10.0});
+    domain.add_step(step);
+    return domain;
+}
+
+} // namespace
+
+int main()
+{
+    const auto domain = make_domain();
+    fesa::analysis::LinearStaticAnalysis analysis{domain, fesa::core::StepId{6}};
+    analysis.run();
+
+    if (analysis.analysis_model() == nullptr || analysis.state() == nullptr) {
+        return fail();
+    }
+    if (analysis.analysis_model()->active_elements().size() != 1 ||
+        analysis.analysis_model()->active_boundary_conditions().size() != 1 ||
+        analysis.analysis_model()->active_loads().size() != 1) {
+        return fail();
+    }
+
+    fesa::results::ResultStep result_step{"static-step"};
+    auto& frame = result_step.add_frame(0, 0.0);
+    frame.add_field_output({
+        "U",
+        fesa::results::FieldLocation::nodal,
+        {"ux", "uy", "uz"},
+        {1, 2},
+        {0.0, 0.0, 0.0, 0.0, 0.0, 0.0}
+    });
+
+    if (result_step.frames().size() != 1 ||
+        result_step.frames()[0].field_outputs().size() != 1) {
+        return fail();
+    }
+
+    return 0;
+}

tests/unit/CMakeLists.txt

@@ -0,0 +1,8 @@
+file(GLOB FESA_UNIT_TEST_SOURCES CONFIGURE_DEPENDS "${CMAKE_CURRENT_SOURCE_DIR}/*_test.cpp")
+
+foreach(test_source IN LISTS FESA_UNIT_TEST_SOURCES)
+    get_filename_component(test_name "${test_source}" NAME_WE)
+    add_executable("${test_name}" "${test_source}")
+    target_link_libraries("${test_name}" PRIVATE fesa_core)
+    add_test(NAME "${test_name}" COMMAND "${test_name}")
+endforeach()

tests/unit/analysis_flow_linear_static_analysis_test.cpp

@@ -0,0 +1,37 @@
+#include <fesa/analysis/linear_static_analysis.hpp>
+
+namespace {
+
+fesa::model::Domain make_domain()
+{
+    fesa::model::Domain domain;
+    domain.add_node({fesa::core::NodeId{1}, {0.0, 0.0, 0.0}});
+    domain.add_node({fesa::core::NodeId{2}, {1.0, 0.0, 0.0}});
+    domain.add_material({fesa::core::MaterialId{3}, "steel"});
+    domain.add_property({fesa::core::PropertyId{4}, "bar", fesa::core::MaterialId{3}});
+    domain.add_element({
+        fesa::core::ElementId{5},
+        fesa::model::ElementTopology::truss2,
+        {fesa::core::NodeId{1}, fesa::core::NodeId{2}},
+        fesa::core::PropertyId{4}
+    });
+    fesa::model::AnalysisStep step{fesa::core::StepId{6}, "static"};
+    step.add_boundary_condition({fesa::core::NodeId{1}, fesa::model::DofComponent::ux, 0.0});
+    step.add_load({fesa::core::NodeId{2}, fesa::model::DofComponent::ux, 10.0});
+    domain.add_step(step);
+    return domain;
+}
+
+} // namespace
+
+int main()
+{
+    const auto domain = make_domain();
+    fesa::analysis::LinearStaticAnalysis analysis{domain, fesa::core::StepId{6}};
+    analysis.run();
+
+    if (analysis.analysis_model() == nullptr || analysis.state() == nullptr) {
+        return 1;
+    }
+    return analysis.state()->displacement().size() == 6 ? 0 : 1;
+}

tests/unit/analysis_flow_template_test.cpp

@@ -0,0 +1,44 @@
+#include <fesa/analysis/analysis.hpp>
+
+#include <string>
+#include <vector>
+
+class RecordingAnalysis : public fesa::analysis::Analysis {
+public:
+    const std::vector<std::string>& calls() const
+    {
+        return calls_;
+    }
+
+protected:
+    void initialize() override { calls_.push_back("initialize"); }
+    void build_analysis_model() override { calls_.push_back("build_analysis_model"); }
+    void build_dof_map() override { calls_.push_back("build_dof_map"); }
+    void build_sparse_pattern() override { calls_.push_back("build_sparse_pattern"); }
+    void assemble() override { calls_.push_back("assemble"); }
+    void apply_boundary_conditions() override { calls_.push_back("apply_boundary_conditions"); }
+    void solve() override { calls_.push_back("solve"); }
+    void update_state() override { calls_.push_back("update_state"); }
+    void write_results() override { calls_.push_back("write_results"); }
+
+private:
+    std::vector<std::string> calls_;
+};
+
+int main()
+{
+    RecordingAnalysis analysis;
+    analysis.run();
+    const std::vector<std::string> expected{
+        "initialize",
+        "build_analysis_model",
+        "build_dof_map",
+        "build_sparse_pattern",
+        "assemble",
+        "apply_boundary_conditions",
+        "solve",
+        "update_state",
+        "write_results"
+    };
+    return analysis.calls() == expected ? 0 : 1;
+}

tests/unit/analysis_model_view_test.cpp

@@ -0,0 +1,73 @@
+#include <fesa/analysis/analysis_model.hpp>
+
+#include <stdexcept>
+
+namespace {
+
+fesa::model::Domain make_domain()
+{
+    fesa::model::Domain domain;
+    domain.add_node({fesa::core::NodeId{1}, {0.0, 0.0, 0.0}});
+    domain.add_node({fesa::core::NodeId{2}, {1.0, 0.0, 0.0}});
+    domain.add_material({fesa::core::MaterialId{3}, "steel"});
+    domain.add_property({fesa::core::PropertyId{4}, "bar", fesa::core::MaterialId{3}});
+    domain.add_element({
+        fesa::core::ElementId{5},
+        fesa::model::ElementTopology::truss2,
+        {fesa::core::NodeId{1}, fesa::core::NodeId{2}},
+        fesa::core::PropertyId{4}
+    });
+
+    fesa::model::AnalysisStep step{fesa::core::StepId{6}, "static"};
+    step.add_boundary_condition({fesa::core::NodeId{1}, fesa::model::DofComponent::ux, 0.0});
+    step.add_load({fesa::core::NodeId{2}, fesa::model::DofComponent::ux, 10.0});
+    domain.add_step(step);
+    return domain;
+}
+
+int fail()
+{
+    return 1;
+}
+
+} // namespace
+
+int main()
+{
+    const auto domain = make_domain();
+    const fesa::analysis::AnalysisModel model{domain, fesa::core::StepId{6}};
+
+    if (&model.domain() != &domain) {
+        return fail();
+    }
+    if (&model.step() != domain.find_step(fesa::core::StepId{6})) {
+        return fail();
+    }
+    if (model.active_elements().size() != 1 ||
+        model.active_elements()[0] != domain.find_element(fesa::core::ElementId{5})) {
+        return fail();
+    }
+    if (model.active_boundary_conditions().size() != 1 ||
+        model.active_loads().size() != 1) {
+        return fail();
+    }
+
+    const auto* property = model.property_for(*model.active_elements()[0]);
+    if (property == nullptr || property != domain.find_property(fesa::core::PropertyId{4})) {
+        return fail();
+    }
+
+    const auto* material = model.material_for(*property);
+    if (material == nullptr || material != domain.find_material(fesa::core::MaterialId{3})) {
+        return fail();
+    }
+
+    try {
+        const fesa::analysis::AnalysisModel missing{domain, fesa::core::StepId{99}};
+        (void)missing;
+        return fail();
+    } catch (const std::invalid_argument&) {
+    }
+
+    return 0;
+}

tests/unit/analysis_state_vectors_test.cpp

@@ -0,0 +1,80 @@
+#include <fesa/analysis/analysis_state.hpp>
+
+#include <stdexcept>
+#include <vector>
+
+namespace {
+
+int fail()
+{
+    return 1;
+}
+
+bool all_zero(const std::vector<double>& values)
+{
+    for (const double value : values) {
+        if (value != 0.0) {
+            return false;
+        }
+    }
+    return true;
+}
+
+} // namespace
+
+int main()
+{
+    fesa::analysis::AnalysisState state{3};
+    if (state.displacement().size() != 3 ||
+        state.velocity().size() != 3 ||
+        state.acceleration().size() != 3 ||
+        state.temperature().size() != 3 ||
+        state.external_force().size() != 3 ||
+        state.internal_force().size() != 3 ||
+        state.residual().size() != 3) {
+        return fail();
+    }
+    if (!all_zero(state.displacement()) || !all_zero(state.residual())) {
+        return fail();
+    }
+
+    state.set_displacement({1.0, 2.0, 3.0});
+    if (state.displacement()[2] != 3.0) {
+        return fail();
+    }
+
+    state.set_external_force({10.0, 20.0, 30.0});
+    state.set_internal_force({1.0, 2.0, 3.0});
+    state.update_residual();
+    if (state.residual()[0] != 9.0 ||
+        state.residual()[1] != 18.0 ||
+        state.residual()[2] != 27.0) {
+        return fail();
+    }
+
+    try {
+        state.set_displacement({1.0});
+        return fail();
+    } catch (const std::invalid_argument&) {
+    }
+
+    state.iteration_state().time = 1.25;
+    state.iteration_state().increment = 2;
+    state.iteration_state().iteration = 3;
+    if (state.iteration_state().time != 1.25 ||
+        state.iteration_state().increment != 2 ||
+        state.iteration_state().iteration != 3) {
+        return fail();
+    }
+
+    state.set_element_state(fesa::core::ElementId{7}, {4.0, 5.0});
+    const auto* element_state = state.element_state(fesa::core::ElementId{7});
+    if (element_state == nullptr || element_state->size() != 2 || (*element_state)[1] != 5.0) {
+        return fail();
+    }
+    if (state.element_state(fesa::core::ElementId{8}) != nullptr) {
+        return fail();
+    }
+
+    return 0;
+}

tests/unit/core_diagnostic_test.cpp

@@ -0,0 +1,11 @@
+#include <fesa/core/diagnostic.hpp>
+
+int main()
+{
+    const fesa::core::Diagnostic diagnostic{
+        fesa::core::Severity::info,
+        "core.info",
+        "diagnostic"
+    };
+    return diagnostic.code == "core.info" ? 0 : 1;
+}

tests/unit/core_ids_test.cpp

@@ -0,0 +1,9 @@
+#include <fesa/core/ids.hpp>
+
+#include <type_traits>
+
+int main()
+{
+    static_assert(!std::is_same_v<fesa::core::NodeId, fesa::core::ElementId>);
+    return fesa::core::NodeId{7}.value == 7 ? 0 : 1;
+}

tests/unit/core_primitives_test.cpp

@@ -0,0 +1,50 @@
+#include <fesa/core/diagnostic.hpp>
+#include <fesa/core/ids.hpp>
+#include <fesa/core/status.hpp>
+
+#include <string>
+#include <type_traits>
+
+namespace {
+
+int fail()
+{
+    return 1;
+}
+
+} // namespace
+
+int main()
+{
+    static_assert(!std::is_same_v<fesa::core::NodeId, fesa::core::ElementId>);
+
+    const auto ok = fesa::core::Status::ok();
+    if (!ok.is_ok() || !ok.diagnostics().empty()) {
+        return fail();
+    }
+
+    fesa::core::Diagnostic error{
+        fesa::core::Severity::error,
+        "core.error",
+        "core failure"
+    };
+    auto failed = fesa::core::Status::failure(error);
+    if (failed.is_ok() || failed.diagnostics().size() != 1) {
+        return fail();
+    }
+    if (failed.diagnostics()[0].code != "core.error" ||
+        failed.diagnostics()[0].message != "core failure") {
+        return fail();
+    }
+
+    failed.add({fesa::core::Severity::warning, "core.warning", "check warning"});
+    if (failed.diagnostics().size() != 2) {
+        return fail();
+    }
+    if (failed.diagnostics()[0].code != "core.error" ||
+        failed.diagnostics()[1].code != "core.warning") {
+        return fail();
+    }
+
+    return 0;
+}

tests/unit/core_status_test.cpp

@@ -0,0 +1,7 @@
+#include <fesa/core/status.hpp>
+
+int main()
+{
+    const auto status = fesa::core::Status::ok();
+    return status.is_ok() ? 0 : 1;
+}

tests/unit/dof_manager_dof_key_test.cpp

@@ -0,0 +1,8 @@
+#include <fesa/fem/dof_key.hpp>
+
+int main()
+{
+    const fesa::fem::DofKey lhs{fesa::core::NodeId{1}, fesa::model::DofComponent::ux};
+    const fesa::fem::DofKey rhs{fesa::core::NodeId{1}, fesa::model::DofComponent::ux};
+    return lhs == rhs ? 0 : 1;
+}

tests/unit/dof_manager_numbering_test.cpp

@@ -0,0 +1,83 @@
+#include <fesa/fem/dof_manager.hpp>
+
+#include <stdexcept>
+#include <vector>
+
+namespace {
+
+int fail()
+{
+    return 1;
+}
+
+} // namespace
+
+int main()
+{
+    fesa::fem::DofManager dofs;
+    dofs.define_node_dofs(fesa::core::NodeId{2}, {
+        fesa::model::DofComponent::ux,
+        fesa::model::DofComponent::uy
+    });
+    dofs.define_node_dofs(fesa::core::NodeId{1}, {
+        fesa::model::DofComponent::uy,
+        fesa::model::DofComponent::ux
+    });
+    dofs.apply_boundary_condition({
+        fesa::core::NodeId{1},
+        fesa::model::DofComponent::ux,
+        0.0
+    });
+    dofs.number_equations();
+
+    const fesa::fem::DofKey n1ux{fesa::core::NodeId{1}, fesa::model::DofComponent::ux};
+    const fesa::fem::DofKey n1uy{fesa::core::NodeId{1}, fesa::model::DofComponent::uy};
+    const fesa::fem::DofKey n2ux{fesa::core::NodeId{2}, fesa::model::DofComponent::ux};
+    const fesa::fem::DofKey n2uy{fesa::core::NodeId{2}, fesa::model::DofComponent::uy};
+
+    if (dofs.total_dof_count() != 4 ||
+        dofs.constrained_dof_count() != 1 ||
+        dofs.free_dof_count() != 3) {
+        return fail();
+    }
+    if (dofs.equation_id(n1ux) != 0 ||
+        dofs.equation_id(n1uy) != 1 ||
+        dofs.equation_id(n2ux) != 2 ||
+        dofs.equation_id(n2uy) != 3) {
+        return fail();
+    }
+    if (!dofs.is_constrained(n1ux) ||
+        dofs.free_equation_id(n1ux).has_value()) {
+        return fail();
+    }
+    if (!dofs.free_equation_id(n1uy).has_value() ||
+        *dofs.free_equation_id(n1uy) != 0 ||
+        *dofs.free_equation_id(n2ux) != 1 ||
+        *dofs.free_equation_id(n2uy) != 2) {
+        return fail();
+    }
+
+    const auto full = dofs.expand_free_vector({11.0, 22.0, 33.0});
+    if (full.size() != 4 ||
+        full[0] != 0.0 ||
+        full[1] != 11.0 ||
+        full[2] != 22.0 ||
+        full[3] != 33.0) {
+        return fail();
+    }
+
+    const auto& pattern = dofs.sparse_pattern();
+    if (pattern.size() != 9 ||
+        pattern.front() != std::pair<int, int>{0, 0} ||
+        pattern.back() != std::pair<int, int>{2, 2}) {
+        return fail();
+    }
+
+    try {
+        (void)dofs.equation_id({fesa::core::NodeId{99}, fesa::model::DofComponent::ux});
+        return fail();
+    } catch (const std::invalid_argument&) {
+    }
+
+    return 0;
+}

tests/unit/harness_smoke_test.cpp

@@ -0,0 +1,7 @@
+#include <string>
+
+int main()
+{
+    const std::string project = "fesa";
+    return project.size() == 4 ? 0 : 1;
+}

tests/unit/model_analysis_step_test.cpp

@@ -0,0 +1,7 @@
+#include <fesa/model/analysis_step.hpp>
+
+int main()
+{
+    const fesa::model::AnalysisStep step{fesa::core::StepId{1}, "static"};
+    return step.name() == "static" ? 0 : 1;
+}

tests/unit/model_boundary_condition_test.cpp

@@ -0,0 +1,11 @@
+#include <fesa/model/boundary_condition.hpp>
+
+int main()
+{
+    const fesa::model::BoundaryCondition bc{
+        fesa::core::NodeId{1},
+        fesa::model::DofComponent::ux,
+        0.0
+    };
+    return bc.node_id().value == 1 ? 0 : 1;
+}

tests/unit/model_domain_test.cpp

@@ -0,0 +1,79 @@
+#include <fesa/model/domain.hpp>
+
+#include <array>
+#include <vector>
+
+namespace {
+
+int fail()
+{
+    return 1;
+}
+
+} // namespace
+
+int main()
+{
+    fesa::model::Domain domain;
+
+    domain.add_node(fesa::model::Node{fesa::core::NodeId{1}, {1.0, 2.0, 3.0}});
+    domain.add_element(fesa::model::Element{
+        fesa::core::ElementId{10},
+        fesa::model::ElementTopology::truss2,
+        {fesa::core::NodeId{1}, fesa::core::NodeId{2}},
+        fesa::core::PropertyId{20}
+    });
+    domain.add_material(fesa::model::Material{fesa::core::MaterialId{30}, "steel"});
+    domain.add_property(fesa::model::Property{
+        fesa::core::PropertyId{20},
+        "bar",
+        fesa::core::MaterialId{30}
+    });
+
+    fesa::model::AnalysisStep step{fesa::core::StepId{40}, "load"};
+    step.add_boundary_condition({fesa::core::NodeId{1}, fesa::model::DofComponent::ux, 0.0});
+    step.add_load({fesa::core::NodeId{2}, fesa::model::DofComponent::ux, 10.0});
+    domain.add_step(step);
+
+    const auto* node = domain.find_node(fesa::core::NodeId{1});
+    if (node == nullptr || node->coordinates()[2] != 3.0) {
+        return fail();
+    }
+
+    const auto* element = domain.find_element(fesa::core::ElementId{10});
+    if (element == nullptr ||
+        element->topology() != fesa::model::ElementTopology::truss2 ||
+        element->node_ids().size() != 2 ||
+        element->property_id().value != 20) {
+        return fail();
+    }
+
+    const auto* material = domain.find_material(fesa::core::MaterialId{30});
+    if (material == nullptr || material->name() != "steel") {
+        return fail();
+    }
+
+    const auto* property = domain.find_property(fesa::core::PropertyId{20});
+    if (property == nullptr ||
+        property->name() != "bar" ||
+        property->material_id().value != 30) {
+        return fail();
+    }
+
+    const auto* analysis_step = domain.find_step(fesa::core::StepId{40});
+    if (analysis_step == nullptr ||
+        analysis_step->boundary_conditions().size() != 1 ||
+        analysis_step->loads().size() != 1) {
+        return fail();
+    }
+
+    if (domain.find_node(fesa::core::NodeId{999}) != nullptr ||
+        domain.find_element(fesa::core::ElementId{999}) != nullptr ||
+        domain.find_material(fesa::core::MaterialId{999}) != nullptr ||
+        domain.find_property(fesa::core::PropertyId{999}) != nullptr ||
+        domain.find_step(fesa::core::StepId{999}) != nullptr) {
+        return fail();
+    }
+
+    return 0;
+}

tests/unit/model_element_test.cpp

@@ -0,0 +1,12 @@
+#include <fesa/model/element.hpp>
+
+int main()
+{
+    const fesa::model::Element element{
+        fesa::core::ElementId{1},
+        fesa::model::ElementTopology::bar2,
+        {fesa::core::NodeId{1}, fesa::core::NodeId{2}},
+        fesa::core::PropertyId{3}
+    };
+    return element.node_ids().size() == 2 ? 0 : 1;
+}

tests/unit/model_load_test.cpp

@@ -0,0 +1,11 @@
+#include <fesa/model/load.hpp>
+
+int main()
+{
+    const fesa::model::Load load{
+        fesa::core::NodeId{2},
+        fesa::model::DofComponent::ux,
+        5.0
+    };
+    return load.value() == 5.0 ? 0 : 1;
+}

tests/unit/model_material_test.cpp

@@ -0,0 +1,7 @@
+#include <fesa/model/material.hpp>
+
+int main()
+{
+    const fesa::model::Material material{fesa::core::MaterialId{1}, "steel"};
+    return material.name() == "steel" ? 0 : 1;
+}

tests/unit/model_node_test.cpp

@@ -0,0 +1,7 @@
+#include <fesa/model/node.hpp>
+
+int main()
+{
+    const fesa::model::Node node{fesa::core::NodeId{1}, {0.0, 1.0, 2.0}};
+    return node.coordinates()[1] == 1.0 ? 0 : 1;
+}

tests/unit/model_property_test.cpp

@@ -0,0 +1,11 @@
+#include <fesa/model/property.hpp>
+
+int main()
+{
+    const fesa::model::Property property{
+        fesa::core::PropertyId{2},
+        "section",
+        fesa::core::MaterialId{3}
+    };
+    return property.material_id().value == 3 ? 0 : 1;
+}

tests/unit/results_containers_test.cpp

@@ -0,0 +1,69 @@
+#include <fesa/results/results.hpp>
+
+#include <stdexcept>
+
+namespace {
+
+int fail()
+{
+    return 1;
+}
+
+} // namespace
+
+int main()
+{
+    fesa::results::ResultStep step{"static"};
+    auto& frame = step.add_frame(1, 0.0);
+    if (step.name() != "static" ||
+        step.frames().size() != 1 ||
+        frame.frame_id() != 1 ||
+        frame.time() != 0.0) {
+        return fail();
+    }
+
+    frame.add_field_output({
+        "U",
+        fesa::results::FieldLocation::nodal,
+        {"ux", "uy"},
+        {1, 2},
+        {0.0, 0.1, 1.0, 1.1}
+    });
+    if (frame.field_outputs().size() != 1 ||
+        frame.field_outputs()[0].entity_ids[1] != 2 ||
+        frame.field_outputs()[0].values[3] != 1.1) {
+        return fail();
+    }
+
+    frame.add_history_output({"load-factor", {0.0, 1.0}, {0.0, 10.0}});
+    if (frame.history_outputs().size() != 1 ||
+        frame.history_outputs()[0].values[1] != 10.0) {
+        return fail();
+    }
+
+    try {
+        frame.add_field_output({
+            "bad",
+            fesa::results::FieldLocation::nodal,
+            {},
+            {1},
+            {0.0}
+        });
+        return fail();
+    } catch (const std::invalid_argument&) {
+    }
+
+    try {
+        frame.add_field_output({
+            "bad-shape",
+            fesa::results::FieldLocation::nodal,
+            {"ux", "uy"},
+            {1},
+            {0.0}
+        });
+        return fail();
+    } catch (const std::invalid_argument&) {
+    }
+
+    return 0;
+}