MeanField_SERiF/tests/solver/nonlinear.cpp

#include "serif/tests/solver/native_problem.hpp"
#include <cmath>
#include <expected>
#include <functional>
#include <limits>
#include <memory>
#include <span>
#include <string>
#include <vector>

#include <catch2/catch_test_macros.hpp>
#include <catch2/matchers/catch_matchers_floating_point.hpp>
#include <catch2/matchers/catch_matchers_string.hpp>
#include "mfem/linalg/densemat.hpp"
#include "serif/solver/nonlinear/newton.hpp"
#include "serif/solver/normalization/diagonal.hpp"

namespace {
    namespace solver = serif::solver;
    using Catch::Matchers::WithinAbs;

    /** @brief A one-coordinate physical state exercises the same owning-candidate contract as a star. */
    struct State {
        std::vector<double> coefficients;
        /** @brief Edit the sole physical unknown. */
        std::span<double> values() { return coefficients; }
        /** @brief Inspect immutable accepted physical coordinates. */
        std::span<const double> values() const { return coefficients; }
    };

    /** @brief Freeze a nonlinear residual and derivative in deliberately nontrivial coordinates. */
    struct System {
        std::vector<double> residual_values;
        ::mfem::DenseMatrix derivative{1};
        solver::normalization::DiagonalNormalization normalization;
        /** @brief Use state factor two and residual factor three to detect coordinate mixups. */
        System(const double residual, const double jacobian) : residual_values{3.0 * residual},
            normalization(*solver::normalization::make_diagonal_normalization({2.0}, {3.0})) {
            derivative(0, 0) = 1.5 * jacobian;
        }
        /** @brief Read the immutable normalized residual. */
        const std::vector<double>& residual() const { return residual_values; }
        /** @brief Read the matching normalized derivative. */
        const ::mfem::Operator& jacobian() const { return derivative; }
        /** @brief Recover physical trial steps with the accepted coordinate factors. */
        const auto& coordinates() const { return normalization; }
    };

    /** @brief A scalar inverse keeps this regression independent of stellar preconditioning quality. */
    struct Inverse : ::mfem::Solver {
        double reciprocal;
        /** @brief Freeze the inverse derivative belonging to one prepared state. */
        explicit Inverse(const double value) : ::mfem::Solver(1), reciprocal(1.0 / value) {}
        /** @brief Reject rebinding, which would violate frozen preparation ownership. */
        void SetOperator(const ::mfem::Operator&) override {}
        /** @brief Apply the exact scalar inverse. */
        void Mult(const ::mfem::Vector& input, ::mfem::Vector& output) const override { output[0] = reciprocal * input[0]; }
    };

    struct Prepared {
        std::shared_ptr<const System> owner;
        mutable Inverse inverse;
        /** @brief Retain the system before borrowing its derivative. */
        explicit Prepared(std::shared_ptr<const System> system) : owner(std::move(system)), inverse(owner->derivative(0, 0)) {}
        /** @brief Inspect the matching frozen residual and Jacobian. */
        const auto& system() const { return owner; }
        /** @brief Borrow the inverse while its owner remains alive. */
        ::mfem::Solver& preconditioner() const { return inverse; }
        /** @brief This scalar inverse has a fixed linear application. */
        auto contract() const { return solver::preconditioner::ApplicationContract::fixed_linear; }
    };

    /** @brief A positive-domain scalar equation reproduces numerical rejections and preparation failures. */
    struct Problem : serif::tests::solver::NativeProblem {
        using System = ::System;
        using Model = solver::NoModel;
        std::function<std::pair<double, double>(double)> equation = [](const double x) { return std::pair{x * x - 2.0, 2.0 * x}; };
        std::function<bool(double)> preparation_allowed = [](double) { return true; };
        int evaluations{0};
        bool numerical_rejections{true};
        /** @brief Algebraic tests have no descriptive stellar model. */
        std::shared_ptr<const Model> model_owner() const { return {}; }
        /** @brief Reject nonfinite or negative candidates before publication. */
        std::expected<std::shared_ptr<const System>, std::string> evaluate(const State& state) {
            ++evaluations;
            const double x = state.values()[0];
            if (!std::isfinite(x) || x < 0.0) {
                return std::unexpected("outside physical domain");
            }
            const auto [residual, derivative] = equation(x);
            return std::make_shared<const System>(residual, derivative);
        }
        /** @brief Inject inverse preparation failure without destroying accepted residual handles. */
        std::expected<std::shared_ptr<const Prepared>, std::string> prepare(const State& state) {
            if (!preparation_allowed(state.values()[0])) {
                return std::unexpected("injected preparation failure");
            }
            const auto evaluated = evaluate(state);
            if (!evaluated) { return std::unexpected(evaluated.error()); }
            return std::make_shared<const Prepared>(*evaluated);
        }
        /** @brief Preserve the physical candidate diagnostic. */
        std::string failure_message(const std::string& failure) const { return failure; }
        /** @brief A shorter scalar trial can reenter the positive domain. */
        bool recoverable(const std::string&) const { return numerical_rejections; }
    };

    /** @brief Model an affine element determinant using the same physical coordinate as the scalar equation. */
    struct GeometryProblem : Problem {
        double determinant_direction{0.0};
        int inverted_trials{0};
        int limit_calls{0};
        /** @brief Validate every candidate even when proactive geometry checks are disabled. */
        std::expected<std::shared_ptr<const System>, std::string> evaluate(const State& state) {
            if (state.values()[0] <= 0.0) {
                ++inverted_trials;
                return std::unexpected("inverted element");
            }
            return Problem::evaluate(state);
        }
        /** @brief Capture a physical tangent and return the last safe rung before its determinant vanishes. */
        std::expected<serif::geometry::deformation::GeometryStepLimit, std::string> geometry_limit(
            const State&, std::span<const double> direction, double maximum, double safety, bool) {
            ++limit_calls;
            determinant_direction = direction[0];
            CHECK(maximum == 1.0);
            CHECK(safety == 0.9);
            return serif::geometry::deformation::GeometryStepLimit{.step = 0.25, .boundary_step = 1.0 / 3.0, .limited_by_geometry = true};
        }
        /** @brief Use the same determinant estimate to skip unsafe backtracking rungs after an actual rejection. */
        double next_step(double step, const solver::Backtracking& options, const auto& evaluation) const {
            REQUIRE_FALSE(evaluation);
            CHECK(evaluation.error() == "inverted element");
            return solver::next_backtracking_step(step, 1.0, 1.0 + determinant_direction * step, true, options);
        }
    };

    /** @brief Inject a failed strategy evaluation to check numerical versus configuration errors. */
    struct FailedInitialization : solver::StandardNewton {
        /** @brief Mimic a strategy replacing the initial evaluation with a rejected candidate. */
        solver::TrialAssessment initialize(Problem&, State&, std::expected<std::shared_ptr<const System>, std::string>& evaluation, const auto&) {
            evaluation = std::unexpected("injected initialization failure");
            return {.usable = false};
        }
    };

    /** @brief Return prescribed corrections to isolate orchestration from linear convergence. */
    struct ScriptedBackend {
        std::shared_ptr<std::vector<double>> guesses{std::make_shared<std::vector<double>>()};
        std::function<void(int, ::mfem::Vector&)> correction;
        /** @brief Capture the safeguarded remainder carried between accepted nonlinear iterations. */
        solver::linear::Report solve(const ::mfem::Operator&, ::mfem::Solver&, solver::preconditioner::ApplicationContract,
            const ::mfem::Vector&, ::mfem::Vector& output, solver::linear::Control) const {
            guesses->push_back(output[0]);
            correction(static_cast<int>(guesses->size()), output);
            return {.status = solver::linear::Status::converged};
        }
    };
}

TEST_CASE("Newton converges in physical coordinates and owns its accepted checkpoint", "[solver][nonlinear]") {
    std::shared_ptr<const System> first;
    Problem problem;
    const auto observer = [&](const solver::SolveEvent& event, const State&, const auto& system) {
        if (event.kind == solver::EventKind::initial) { first = system; }
    };
    auto result = solver::solve_newton(problem, State{{1.0}}, solver::SolverOptions{}, observer);
    REQUIRE(result.converged());
    REQUIRE(result.has_state());
    CHECK_THAT(result.state().values()[0], WithinAbs(std::sqrt(2.0), 1.0e-8));
    CHECK(first->residual()[0] == -3.0);
    CHECK(result.system() != first);
    CHECK(result.diagnostics().accepted_iterations > 0);
    CHECK(*result.diagnostics().final_residual_norm <= *result.diagnostics().convergence_threshold);
}

TEST_CASE("A converged terminal root needs no inverse of its singular Jacobian", "[solver][nonlinear]") {
    Problem problem;
    problem.equation = [](double value) {
        return std::pair{(value - 1.0) * (value - 1.0) * (value + 1.0), 3.0 * value * value - 2.0 * value - 1.0};
    };
    int preparations = 0;
    problem.preparation_allowed = [&](double value) {
        ++preparations;
        return value != 1.0;
    };
    const State original{{0.0}};
    const auto result = solver::solve_newton(problem, original);
    REQUIRE(result.converged());
    CHECK(result.state().values()[0] == 1.0);
    CHECK(result.system()->residual()[0] == 0.0);
    CHECK(result.system()->derivative(0, 0) == 0.0);
    CHECK(result.diagnostics().accepted_iterations == 1);
    CHECK(result.diagnostics().attempted_iterations == 1);
    CHECK(preparations == 1);
    CHECK(original.values()[0] == 0.0);
}

TEST_CASE("Newton separates rejected initial guesses from accepted iteration-limit checkpoints", "[solver][nonlinear]") {
    Problem problem;
    SECTION("rejected initial state") {
        const auto result = solver::solve_newton(problem, State{{-1.0}});
        CHECK(result.status() == solver::SolveStatus::initial_state_rejected);
        CHECK_FALSE(result.has_state());
        CHECK_THROWS_AS(result.state(), std::logic_error);
    }
    SECTION("zero budget") {
        problem.preparation_allowed = [](double) { return false; };
        const auto result = solver::solve_newton(problem, State{{1.0}}, solver::SolverOptions{.method = {.maximum_iterations = 0}});
        CHECK(result.status() == solver::SolveStatus::maximum_iterations);
        CHECK(result.state().values()[0] == 1.0);
        CHECK(result.diagnostics().attempted_iterations == 0);
    }
    SECTION("last accepted iteration") {
        const auto result = solver::solve_newton(problem, State{{1.0}}, solver::SolverOptions{.method = {.maximum_iterations = 1}});
        CHECK(result.status() == solver::SolveStatus::maximum_iterations);
        CHECK(result.state().values()[0] == 1.5);
        CHECK(result.diagnostics().accepted_iterations == 1);
    }
}

TEST_CASE("Newton retains the accepted state when preparing an otherwise acceptable candidate fails", "[solver][nonlinear]") {
    Problem problem;
    SECTION("a numerical rejection returns the accepted checkpoint") {
        problem.preparation_allowed = [](double x) { return x == 1.0; };
        const auto result = solver::solve_newton(problem, State{{1.0}});
        CHECK(result.status() == solver::SolveStatus::preparation_failure);
        CHECK(result.state().values()[0] == 1.0);
        CHECK(result.system()->residual()[0] == -3.0);
        CHECK(result.diagnostics().accepted_iterations == 0);
    }
    SECTION("a preparation exception propagates before any candidate is accepted") {
        const State original{{1.0}};
        std::shared_ptr<const System> checkpoint;
        int preparations = 0;
        int accepted = 0;
        problem.preparation_allowed = [&](double x) {
            ++preparations;
            serif::utils::errors::serif_ensure<serif::utils::errors::SERiFErrorCode::INVALID_ARGUMENT, std::runtime_error>(
                x == 1.0, "injected preconditioner refresh failure");
            return true;
        };
        const auto observe = [&](const solver::SolveEvent& event, const State&, const auto& system) {
            if (event.kind == solver::EventKind::initial) {
                checkpoint = system;
            }
            if (event.kind == solver::EventKind::accepted) {
                ++accepted;
            }
        };
        CHECK_THROWS_WITH(solver::solve_newton(problem, original, solver::SolverOptions{}, observe),
            Catch::Matchers::ContainsSubstring("injected preconditioner refresh failure"));
        REQUIRE(checkpoint);
        CHECK(preparations == 2);
        CHECK(accepted == 0);
        CHECK(original.values()[0] == 1.0);
        CHECK(checkpoint->residual()[0] == -3.0);
        problem.preparation_allowed = [](double) { return true; };
        CHECK(solver::solve_newton(problem, original).converged());
        CHECK(checkpoint->residual()[0] == -3.0);
    }
}

TEST_CASE("Newton rejects trials without altering accepted handles and reuses its damped correction", "[solver][nonlinear]") {
    Problem problem;
    problem.equation = [](double x) { return std::pair{x, 1.0}; };
    ScriptedBackend backend{.correction = [](int call, ::mfem::Vector& correction) { correction[0] = call == 1 ? -6.0 : -0.5; }};
    std::vector<double> accepted_steps;
    std::shared_ptr<const System> initial;
    const auto observer = [&](const solver::SolveEvent& event, const State&, const auto& system) {
        if (event.kind == solver::EventKind::initial) { initial = system; }
        if (event.kind == solver::EventKind::trial_rejected) {
            CHECK(initial->residual()[0] == 3.0);
            CHECK_FALSE(system);
            CHECK_FALSE(event.metric.has_value());
        }
        if (event.kind == solver::EventKind::accepted) {
            REQUIRE(event.metric.has_value());
            CHECK(event.metric->valid());
            accepted_steps.push_back(event.step);
        }
    };
    const auto result = solver::solve_newton(problem, State{{1.0}},
        solver::SolverOptions{.method = {.relative_tolerance = 0.0, .absolute_tolerance = 1.0e-12, .maximum_iterations = 2}, .linear_solver = backend}, observer);
    REQUIRE(accepted_steps.size() == 2);
    CHECK(accepted_steps[0] == 0.25);
    CHECK(accepted_steps[1] == 0.5);
    REQUIRE(backend.guesses->size() == 2);
    CHECK((*backend.guesses)[0] == 0.0);
    CHECK((*backend.guesses)[1] == -4.5);
    CHECK(result.diagnostics().rejected_trials == 2);
    CHECK(result.state().values()[0] == 0.125);
}

TEST_CASE("Newton reports metric failures without accepting the failed metric", "[solver][nonlinear]") {
    Problem problem;
    int calls = 0;
    SECTION("initial nonfinite norm") {
        const auto metric = [](std::span<const double>) { return solver::MetricEvaluation{.residual_norm = std::numeric_limits<double>::quiet_NaN()}; };
        const auto result = solver::solve_newton(problem, State{{1.0}}, solver::SolverOptions{.metric = metric});
        CHECK(result.status() == solver::SolveStatus::invalid_metric);
        CHECK_FALSE(result.has_state());
    }
    SECTION("one nonfinite trial merit") {
        const auto metric = [&](std::span<const double> residual) {
            if (++calls == 2) { return solver::MetricEvaluation{.merit = std::numeric_limits<double>::infinity()}; }
            return solver::NormalizedResidualMetric{}(residual);
        };
        const auto result = solver::solve_newton(problem, State{{1.0}}, solver::SolverOptions{.metric = metric});
        CHECK(result.converged());
        CHECK(result.diagnostics().rejected_trials >= 1);
    }
}

TEST_CASE("Newton checks custom correction dimensions and finiteness", "[solver][nonlinear]") {
    Problem problem;
    SECTION("nonfinite correction is numerical failure") {
        ScriptedBackend backend{.correction = [](int, ::mfem::Vector& correction) { correction[0] = std::numeric_limits<double>::infinity(); }};
        const auto result = solver::solve_newton(problem, State{{1.0}}, solver::SolverOptions{.linear_solver = backend});
        CHECK(result.status() == solver::SolveStatus::linear_solve_failure);
        CHECK(result.state().values()[0] == 1.0);
    }
    SECTION("wrong correction size is a backend contract error") {
        ScriptedBackend backend{.correction = [](int, ::mfem::Vector& correction) { correction.SetSize(2); }};
        CHECK_THROWS_AS(solver::solve_newton(problem, State{{1.0}}, solver::SolverOptions{.linear_solver = backend}), std::logic_error);
    }
}

TEST_CASE("Newton propagates observer errors while previously published snapshots remain valid", "[solver][nonlinear]") {
    for (const auto failure_phase : {solver::EventKind::initial, solver::EventKind::before_iteration,
        solver::EventKind::trial_rejected, solver::EventKind::before_accept, solver::EventKind::accepted, solver::EventKind::finished}) {
        CAPTURE(static_cast<int>(failure_phase));
        Problem problem;
        problem.equation = [](double value) { return std::pair{value, 1.0}; };
        const State original{{1.0}};
        std::shared_ptr<const System> checkpoint;
        bool reached_failure = false;
        auto observer = [&, token = std::make_unique<int>(19)](const solver::SolveEvent& event, const State&, const auto& system) {
            CHECK(*token == 19);
            if (event.kind == solver::EventKind::initial) {
                checkpoint = system;
            }
            if (event.kind == failure_phase) {
                reached_failure = true;
                serif::utils::errors::serif_error<std::runtime_error, serif::utils::errors::SERiFErrorCode::INVALID_ARGUMENT>(
                    "injected observer local cause at phase {}", static_cast<int>(failure_phase));
            }
        };
        ScriptedBackend backend{.correction = [](int, ::mfem::Vector& correction) { correction[0] = -6.0; }};
        const auto options = solver::SolverOptions{.method = {.maximum_iterations = 1}, .linear_solver = backend};
        CHECK_THROWS_WITH(solver::solve_newton(problem, original, options, std::move(observer)),
            Catch::Matchers::ContainsSubstring("injected observer local cause at phase"));
        CHECK(reached_failure);
        REQUIRE(checkpoint);
        CHECK(checkpoint->residual()[0] == 3.0);
        CHECK(original.values()[0] == 1.0);
        const auto recovered = solver::solve_newton(problem, original);
        CHECK(recovered.converged());
        CHECK(recovered.state().values()[0] == 0.0);
        CHECK(checkpoint->residual()[0] == 3.0);
    }
}

TEST_CASE("Backtracking geometry estimates skip only unsafe ladder rungs", "[solver][nonlinear][geometry]") {
    const solver::Backtracking options;
    CHECK(solver::next_backtracking_step(1.0, 1.0, -9.0, true, options) == 0.0625);
    CHECK(solver::next_backtracking_step(1.0, 1.0, -9.0, false, options) == 0.5);
    CHECK(solver::next_backtracking_step(1.0, 1.0, std::numeric_limits<double>::quiet_NaN(), true, options) == 0.5);
    CHECK_THROWS_AS(solver::Backtracking{.contraction = 1.0}.validate(), std::logic_error);
    CHECK_THROWS_AS(solver::Newton{.relative_tolerance = -1.0}.validate(), std::logic_error);
}

TEST_CASE("Newton distinguishes strategy initialization rejection from invalid configuration", "[solver][nonlinear]") {
    Problem problem;
    const solver::SolverOptions options{.strategies = FailedInitialization{}};
    SECTION("numerical rejection returns an unsuccessful result") {
        const auto result = solver::solve_newton(problem, State{{1.0}}, options);
        CHECK(result.status() == solver::SolveStatus::initial_state_rejected);
        CHECK(result.message() == "injected initialization failure");
        CHECK_FALSE(result.has_state());
    }
    SECTION("configuration failure propagates") {
        problem.numerical_rejections = false;
        CHECK_THROWS_AS(solver::solve_newton(problem, State{{1.0}}, options), std::logic_error);
    }
}

TEST_CASE("Newton geometry safeguards use physical directions and retain validation when preflight is disabled", "[solver][nonlinear][geometry]") {
    for (const bool proactive : {false, true}) {
        GeometryProblem problem;
        problem.equation = [](double value) { return std::pair{value, 1.0}; };
        ScriptedBackend backend{.correction = [](int, ::mfem::Vector& correction) { correction[0] = -6.0; }};
        std::shared_ptr<const System> first;
        const auto observe = [&](const solver::SolveEvent& event, const State&, const auto& system) {
            if (event.kind == solver::EventKind::initial) {
                first = system;
            }
        };
        const auto result = solver::solve_newton(problem, State{{1.0}},
            solver::SolverOptions{.method = {.maximum_iterations = 1}, .linear_solver = backend,
                .line_search = {.geometry_preflight = proactive}}, observe);
        CHECK(problem.limit_calls == 1);
        CHECK(problem.determinant_direction == -3.0);
        CHECK(problem.inverted_trials == static_cast<int>(!proactive));
        CHECK(result.diagnostics().rejected_trials == static_cast<int>(!proactive));
        CHECK(result.diagnostics().geometry_limited_iterations == static_cast<int>(proactive));
        CHECK(result.diagnostics().last_accepted_step == 0.25);
        CHECK(result.state().values()[0] == 0.25);
        REQUIRE(first);
        CHECK(first->residual()[0] == 3.0);
    }
}

namespace {
    /** @brief Reject one otherwise evaluable trial explicitly, without retaining hidden rejection state. */
    struct RejectFirstTrial : solver::StandardNewton {
        int attempts{0};
        /** @brief The second trial uses the original checked direction and may be accepted normally. */
        solver::TrialAssessment trial(auto&, const auto&, const auto&, const auto&, double, auto&, auto&, const auto&, double) {
            if (++attempts == 1) { return {.usable = false, .message = "injected numerical trial rejection"}; }
            return {};
        }
    };
}

TEST_CASE("Explicit numerical trial rejection cannot invalidate the following candidate", "[solver][nonlinear]") {
    Problem problem;
    int rejections = 0;
    const auto observe = [&](const solver::SolveEvent& event, const State&, const auto& system) {
        if (event.kind == solver::EventKind::trial_rejected) {
            ++rejections;
            CHECK(event.message == "injected numerical trial rejection");
            CHECK(system != nullptr);
            CHECK_FALSE(event.metric.has_value());
        }
    };
    const auto result = solver::solve_newton(problem, State{{1.0}},
        solver::SolverOptions{.strategies = RejectFirstTrial{}}, observe);
    CHECK(result.converged());
    CHECK(rejections == 1);
    CHECK_THAT(result.state().values()[0], WithinAbs(std::sqrt(2.0), 1.0e-8));
}

TEST_CASE("Newton resumes the original accepted boundary including damped correction carry", "[solver][nonlinear][restart]") {
    Problem uninterrupted_problem;
    const solver::SolverOptions options{.method = {.relative_tolerance = 1.0e-10, .maximum_iterations = 20,
        .linear_solve = {.relative_tolerance = 1.0e-12}}};
    const auto uninterrupted = solver::solve_newton(uninterrupted_problem, State{{0.1}}, options);
    REQUIRE(uninterrupted.converged());
    Problem interrupted_problem;
    const auto stop = [](const solver::SolveEvent& event, const auto&, const auto&) {
        return event.kind == solver::EventKind::accepted ? solver::SolveControl::stop : solver::SolveControl::continue_solve;
    };
    solver::SolveTiming timing;
    const auto interrupted = solver::solve_newton(interrupted_problem, State{{0.1}}, options, solver::TimedObserver{timing, stop});
    const double interrupted_seconds = timing.seconds;
    REQUIRE(interrupted.status() == solver::SolveStatus::stopped);
    REQUIRE(interrupted.has_checkpoint());
    const auto checkpoint = interrupted.checkpoint();
    REQUIRE(checkpoint.progress.diagnostics.accepted_iterations == 1);
    CHECK(checkpoint.progress.diagnostics.last_accepted_step < 1.0);
    CHECK(checkpoint.progress.correction[0] != 0.0);
    CHECK(checkpoint.progress.next_step == checkpoint.progress.diagnostics.last_accepted_step / options.line_search.contraction);
    Problem restored_problem;
    const auto resumed = solver::resume_newton(restored_problem, checkpoint, options, solver::TimedObserver{timing});
    CHECK(timing.seconds >= interrupted_seconds);
    REQUIRE(resumed.converged());
    CHECK(resumed.state().values()[0] == uninterrupted.state().values()[0]);
    CHECK(resumed.diagnostics().initial_residual_norm == uninterrupted.diagnostics().initial_residual_norm);
    CHECK(resumed.diagnostics().convergence_threshold == uninterrupted.diagnostics().convergence_threshold);
    CHECK(resumed.diagnostics().attempted_iterations == uninterrupted.diagnostics().attempted_iterations);
    CHECK(resumed.diagnostics().line_search_trials == uninterrupted.diagnostics().line_search_trials);
    CHECK(resumed.diagnostics().total_linear_iterations == uninterrupted.diagnostics().total_linear_iterations);
    CHECK(resumed.diagnostics().rejected_trials == uninterrupted.diagnostics().rejected_trials);
}

TEST_CASE("Newton restart retains the consumed budget and validates checkpoint consistency", "[solver][nonlinear][restart]") {
    Problem problem;
    solver::SolverOptions options{.method = {.maximum_iterations = 1}};
    const auto limited = solver::solve_newton(problem, State{{0.1}}, options);
    REQUIRE(limited.status() == solver::SolveStatus::maximum_iterations);
    const auto checkpoint = limited.checkpoint();
    SECTION("Resuming consumes only the remaining total budget") {
        const auto no_budget = solver::resume_newton(problem, checkpoint, options);
        CHECK(no_budget.status() == solver::SolveStatus::maximum_iterations);
        CHECK(no_budget.diagnostics().attempted_iterations == 1);
        CHECK(no_budget.state().values()[0] == checkpoint.state.values()[0]);
        options.method.maximum_iterations = 20;
        const auto continued = solver::resume_newton(problem, checkpoint, options);
        CHECK(continued.converged());
        CHECK(continued.diagnostics().initial_residual_norm == checkpoint.progress.diagnostics.initial_residual_norm);
    }
    SECTION("Invalid carried coordinates are rejected before evaluation") {
        auto corrupted = checkpoint;
        corrupted.progress.correction.clear();
        const int before = problem.evaluations;
        CHECK_THROWS_AS(solver::resume_newton(problem, corrupted, options), std::logic_error);
        CHECK(problem.evaluations == before);
    }
    SECTION("Changed convergence tolerances cannot silently start a new convergence reference") {
        options.method.relative_tolerance *= 0.1;
        CHECK_THROWS_AS(solver::resume_newton(problem, checkpoint, options), std::logic_error);
    }
    SECTION("A changed physical problem cannot pass off its residual as the saved one") {
        problem.equation = [](double value) { return std::pair{value * value - 3.0, 2.0 * value}; };
        CHECK_THROWS_AS(solver::resume_newton(problem, checkpoint, options), std::logic_error);
    }
}

TEST_CASE("Newton stops only at accepted boundaries and does not silently discard strategy history", "[solver][nonlinear][restart]") {
    Problem problem;
    SECTION("An initial accepted state can be checkpointed before any linear solve") {
        const auto stop = [](const solver::SolveEvent&, const auto&, const auto&) { return solver::SolveControl::stop; };
        const auto stopped = solver::solve_newton(problem, State{{0.1}}, solver::SolverOptions{}, stop);
        CHECK(stopped.status() == solver::SolveStatus::stopped);
        REQUIRE(stopped.has_checkpoint());
        CHECK(stopped.checkpoint().progress.diagnostics.attempted_iterations == 0);
        CHECK(stopped.checkpoint().progress.correction[0] == 0.0);
    }
    SECTION("Existing void observers retain the temporary event calling convention") {
        int notifications = 0;
        const auto observe = [&](solver::SolveEvent&&, const auto&, const auto&) { ++notifications; };
        const auto result = solver::solve_newton(problem, State{{1.0}}, solver::SolverOptions{}, observe);
        CHECK(result.converged());
        CHECK(notifications > 0);
    }
    SECTION("Trial callbacks cannot interrupt an incomplete Newton step") {
        const auto stop = [](const solver::SolveEvent& event, const auto&, const auto&) {
            return event.kind == solver::EventKind::trial_rejected || event.kind == solver::EventKind::before_accept ?
                solver::SolveControl::stop : solver::SolveControl::continue_solve;
        };
        const auto result = solver::solve_newton(problem, State{{0.1}}, solver::SolverOptions{}, stop);
        CHECK(result.status() == solver::SolveStatus::stopped);
        CHECK(result.diagnostics().accepted_iterations == 1);
        CHECK(result.diagnostics().rejected_trials > 0);
        CHECK(result.has_checkpoint());
    }
    SECTION("A before-accept stop request survives a later continue response") {
        int accepted_notifications = 0;
        const auto stop = [&](const solver::SolveEvent& event, const auto&, const auto&) {
            if (event.kind == solver::EventKind::accepted) {
                ++accepted_notifications;
            }
            return event.kind == solver::EventKind::before_accept ? solver::SolveControl::stop : solver::SolveControl::continue_solve;
        };
        const auto result = solver::solve_newton(problem, State{{0.1}}, solver::SolverOptions{}, stop);
        CHECK(result.status() == solver::SolveStatus::stopped);
        CHECK(accepted_notifications == 1);
        REQUIRE(result.has_checkpoint());
        CHECK(result.checkpoint().progress.diagnostics.accepted_iterations == 1);
    }
    SECTION("Ordinary custom strategies still solve but cannot claim a complete restart") {
        struct CustomStrategy : solver::StandardNewton {
            int history{0};
        };
        const auto result = solver::solve_newton(problem, State{{1.0}}, solver::SolverOptions{.strategies = CustomStrategy{}});
        CHECK(result.converged());
        CHECK_FALSE(result.has_checkpoint());
        CHECK_THROWS_AS(result.checkpoint(), std::logic_error);
    }
}