#pragma once
#include <adelie_core/optimization/search_pivot.hpp>
#include <adelie_core/solver/utils.hpp>
#include <adelie_core/util/algorithm.hpp>
#include <adelie_core/util/exceptions.hpp>
#include <adelie_core/util/macros.hpp>
#include <adelie_core/util/omp.hpp>
#include <adelie_core/util/stopwatch.hpp>
#include <adelie_core/util/tqdm.hpp>

namespace adelie_core {
namespace solver {

/**
 * Updates absolute gradient in the base state.
 * The state DOES NOT have to be in its invariance. 
 * After the function finishes, abs_grad will reflect the correct value
 * respective to grad.
 */
template <class StateType, class ValueType>
inline void update_abs_grad(
    StateType& state,
    ValueType lmda
)
{
    using state_t = std::decay_t<StateType>;
    using value_t = typename state_t::value_t;
    using vec_value_t = typename state_t::vec_value_t;
    using rowmat_uint64_t = util::rowmat_type<uint64_t>;

    const auto& constraints = state.constraints;
    const auto& groups = state.groups;
    const auto& group_sizes = state.group_sizes;
    const auto& penalty = state.penalty;
    const auto& grad = state.grad;
    const auto& screen_set = state.screen_set;
    const auto& screen_hashset = state.screen_hashset;
    const auto& screen_begins = state.screen_begins;
    const auto& screen_beta = state.screen_beta;
    const auto alpha = state.alpha;
    const auto constraint_buffer_size = state.constraint_buffer_size;
    const auto n_threads = state.n_threads;
    auto& abs_grad = state.abs_grad;

    const auto is_screen = [&](auto i) {
        return screen_hashset.find(i) != screen_hashset.end();
    };

    vec_value_t buff(group_sizes.maxCoeff());
    rowmat_uint64_t constraint_buffer(std::max<size_t>(1, n_threads), constraint_buffer_size);

    // do not parallelize since it may result in large false sharing 
    // (access to abs_grad[i] is random order)
    for (size_t ss_idx = 0; ss_idx < screen_set.size(); ++ss_idx) 
    {
        const auto i = screen_set[ss_idx];
        const auto b = screen_begins[ss_idx]; 
        const auto k = groups[i];
        const auto size_k = group_sizes[i];
        const auto pk = penalty[i];
        const auto regul = ((1-alpha) * lmda) * pk;
        const auto constraint = constraints[i];
        const Eigen::Map<const vec_value_t> sbeta(
            screen_beta.data() + b,
            size_k
        );
        const auto common_expr = grad.segment(k, size_k) - regul * sbeta;

        if (constraint == nullptr) {
            abs_grad[i] = common_expr.matrix().norm();
        } else {
            auto vbuff = buff.head(size_k);
            constraint->gradient(sbeta, vbuff);
            abs_grad[i] = (common_expr - vbuff).matrix().norm();
        }
    }

    // can be parallelized since access is in linear order.
    // any false sharing is happening near the beginning/ends of the block of indices.
    std::atomic_bool try_failed = false; 
    const auto routine = [&](int i) {
        if (try_failed.load(std::memory_order_relaxed) || is_screen(i)) return;
        auto cbuff = constraint_buffer.row(util::omp_get_thread_num());
        const auto k = groups[i];
        const auto size_k = group_sizes[i];
        const auto constraint = constraints[i];
        const auto v_k = grad.segment(k, size_k);
        try {
            abs_grad[i] = (
                constraint ?
                constraint->solve_zero(v_k, cbuff) :
                v_k.matrix().norm()
            );
        } catch (...) {
            try_failed = true;
        }
    };
    const bool is_not_all_none = util::rowvec_type<bool>::NullaryExpr(
        constraints.size(), 
        [&](auto i) { return constraints[i] != nullptr; }
    ).any();
    const size_t n_bytes = sizeof(value_t) * abs_grad.size();
    util::omp_parallel_for(routine, 0, groups.size(), n_threads * (is_not_all_none || (n_bytes > Configs::min_bytes)));
    if (try_failed) {
        throw util::adelie_core_solver_error(
            "exception raised in constraint->solve_zero(). "
            "Try changing the configurations such as convergence tolerance that affect solve_zero(). "
        );
    }
}

/**
 * Updates all derived quantities from screen_set in the base class. 
 * The state must be such that only the screen_set is either unchanged from invariance,
 * or appended with new groups.
 * After the function finishes, all screen quantities in the base class
 * will be consistent with screen_set, and the state is otherwise effectively
 * unchanged in the sense that other quantities dependent on screen states are unchanged.
 */
template <class StateType>
inline void update_screen_derived_base(
    StateType& state
)
{
    const auto& group_sizes = state.group_sizes;
    const auto& screen_set = state.screen_set;
    auto& screen_hashset = state.screen_hashset;
    auto& screen_begins = state.screen_begins;
    auto& screen_beta = state.screen_beta;
    auto& screen_is_active = state.screen_is_active;

    /* update screen_hashset */
    const auto old_screen_size = screen_begins.size();
    const auto screen_set_new_begin = std::next(screen_set.begin(), old_screen_size);
    screen_hashset.insert(screen_set_new_begin, screen_set.end());

    /* update screen_begins */
    size_t screen_value_size = (
        (old_screen_size == 0) ? 
        0 : (screen_begins.back() + group_sizes[screen_set[old_screen_size-1]])
    );
    for (size_t i = old_screen_size; i < screen_set.size(); ++i) {
        const auto curr_size = group_sizes[screen_set[i]];
        screen_begins.push_back(screen_value_size);
        screen_value_size += curr_size;
    }

    /* update screen_beta */
    screen_beta.resize(screen_value_size, 0);

    /* update screen_is_active */
    screen_is_active.resize(screen_set.size(), false);
}

// TODO: 
// It might be too much to save all of them though especially if we have a lot of active constraints.
// Then, state.dual is going to be super dense and we have 100 rows of such dense vectors.
// Nonetheless, it's still useful to have this for diagnostic purposes... maybe a flag to control whether this gets saved?
template <class StateType, class VecIndexType, class VecValueType>
inline typename StateType::sp_vec_value_t sparsify_dual(
    const StateType& state,
    VecIndexType& indices,
    VecValueType& values
)
{
    using index_t = typename StateType::index_t;
    using value_t = typename StateType::value_t;
    using vec_index_t = typename StateType::vec_index_t;
    using vec_value_t = typename StateType::vec_value_t;
    using sp_vec_value_t = typename StateType::sp_vec_value_t;

    const auto& constraints = state.constraints;
    const auto& dual_groups = state.dual_groups;
    const auto n_threads = state.n_threads;

    const auto n_constraints = constraints.size();
    vec_index_t begins(n_constraints+1);
    begins[0] = 0;
    begins.tail(n_constraints) = vec_index_t::NullaryExpr(
        n_constraints, 
        [&](auto i) {
            const auto constraint = constraints[i];
            return constraint ? constraint->duals_nnz() : 0;
        }
    );
    for (Eigen::Index i = 1; i < begins.size(); ++i) {
        begins[i] += begins[i-1];
    }
    indices.resize(begins[n_constraints]); 
    values.resize(begins[n_constraints]);

    if (begins[n_constraints]) {
        const auto routine = [&](auto i) {
            const auto b = begins[i];
            const auto nnz = begins[i+1] - b;
            if (nnz <= 0) return;
            const auto constraint = constraints[i];
            Eigen::Map<vec_index_t> indices_v(indices.data() + b, nnz);
            Eigen::Map<vec_value_t> values_v(values.data() + b, nnz);
            constraint->dual(indices_v, values_v);
            indices_v += dual_groups[i];
        };
        const bool is_not_all_none = util::rowvec_type<bool>::NullaryExpr(
            constraints.size(), 
            [&](auto i) { return constraints[i] != nullptr; }
        ).any();
        const size_t n_bytes = (sizeof(index_t) + sizeof(value_t)) * indices.size();
        util::omp_parallel_for(routine, 0, n_constraints, n_threads * (is_not_all_none || (n_bytes > Configs::min_bytes)));
    }

    const auto last_constraint = constraints[n_constraints-1];
    const auto n_duals = (
        dual_groups[n_constraints-1] + 
        (last_constraint ? last_constraint->duals() : 0)
    );
    Eigen::Map<const sp_vec_value_t> dual_map(
        n_duals,
        indices.size(),
        indices.data(),
        values.data()
    );
    return dual_map;
}

template <class StateType, class PBType>
ADELIE_CORE_STRONG_INLINE
void pb_add_suffix(
    const StateType& state,
    PBType& pb
)
{
    const auto& devs = state.devs;
    // current training % dev explained
    pb << " [dev:" 
        << std::fixed << std::setprecision(1) 
        << ((devs.size() == 0) ? 0.0 : devs.back()) * 100
        << "%]"
        ; 
}

template <class StateType>
ADELIE_CORE_STRONG_INLINE
bool early_exit(
    const StateType& state
)
{
    const auto early_exit = state.early_exit;
    const auto& devs = state.devs;

    if (!early_exit || !devs.size()) return false;

    const auto adev_tol = state.adev_tol;
    const auto ddev_tol = state.ddev_tol;

    const auto dev_u = devs[devs.size()-1];
    if (dev_u >= adev_tol) return true;
    if (devs.size() == 1) return false;

    const auto dev_m = devs[devs.size()-2];
    if (std::abs(dev_u-dev_m) < ddev_tol) return true;

    return false;
}

/**
 * Screens for new variables to include in the screen set
 * for fitting with lmda = lmda_next.
 * 
 * State MUST be a valid state satisfying its invariance.
 * Note that only the screen set is modified!
 * All derived screen quantities must be updated afterwards. 
 */
template <class StateType, class ValueType>
inline void screen(
    StateType& state,
    ValueType lmda_next,
    bool all_kkt_passed,
    int n_new_active
)
{
    using state_t = std::decay_t<StateType>;
    using vec_value_t = typename state_t::vec_value_t;
    using vec_index_t = typename state_t::vec_index_t;

    const auto& abs_grad = state.abs_grad;
    const auto lmda = state.lmda;
    const auto alpha = state.alpha;
    const auto& penalty = state.penalty;
    const auto& screen_hashset = state.screen_hashset;
    const auto max_screen_size = state.max_screen_size;
    const auto screen_rule = state.screen_rule;
    const auto pivot_subset_ratio = state.pivot_subset_ratio;
    const auto pivot_subset_min = state.pivot_subset_min;
    const auto pivot_slack_ratio = state.pivot_slack_ratio;

    // may get modified
    auto& screen_set = state.screen_set;

    const int old_screen_set_size = screen_set.size();

    assert(screen_set.size() <= abs_grad.size());

    const auto is_screen = [&](auto i) { 
        return screen_hashset.find(i) != screen_hashset.end(); 
    };

    const auto do_pivot = [&]() {
        // Only compute pivot rule if new active variables entered.
        // The pivot rule doesn't include new screen variables otherwise,
        // so no need to do any computations.
        if (n_new_active) {
            const int G = abs_grad.size();
            vec_index_t order = vec_index_t::LinSpaced(G, 0, G-1);
            vec_value_t weights = vec_value_t::NullaryExpr(
                G, [&](auto i) { 
                    return (penalty[i] <= 0) ? 
                        alpha * lmda : std::min(abs_grad[i] / penalty[i], alpha * lmda); 
                }
            );
            std::sort(
                order.data(), 
                order.data() + order.size(), 
                [&](auto i, auto j) { 
                    return weights[i] < weights[j]; 
                }
            );
            const int subset_size = std::min<int>(std::max<int>(
                old_screen_set_size * (1 + pivot_subset_ratio),
                pivot_subset_min
            ), G);
            // top largest subset_size number of weights
            vec_value_t weights_sorted_sub = vec_value_t::NullaryExpr(
                subset_size,
                [&](auto i) { return weights[order[G-subset_size+i]]; } 
            );

            vec_value_t mses(subset_size);
            vec_value_t indices = vec_value_t::LinSpaced(subset_size, 0, subset_size-1);
            const int pivot_idx = optimization::search_pivot(
                indices, 
                weights_sorted_sub, 
                mses
            );
            const int full_pivot_idx = G - subset_size + pivot_idx;

            // add everything beyond the cutoff index that isn't screen yet
            for (int ii = G-1; ii >= full_pivot_idx; --ii) {
                const auto i = order[ii];
                if (is_screen(i)) continue;
                screen_set.push_back(i); 
            }
            // add some slack of new groups below the pivot
            int count = 0;
            for (int ii = full_pivot_idx - 1; ii >= 0; --ii) {
                if (count >= pivot_slack_ratio * n_new_active) break;
                const auto i = order[ii]; 
                if (is_screen(i)) continue;
                screen_set.push_back(i);
                ++count;
            }
        }

        // this case should rarely happen, but we arrived here because
        // previous iteration added all pivot-rule predictions and KKT still failed.
        // In this case, do the most safe thing, which is to add all failed variables.
        if ((screen_set.size() == static_cast<size_t>(old_screen_set_size)) && !all_kkt_passed) {
            for (int i = 0; i < abs_grad.size(); ++i) {
                if (is_screen(i)) continue;
                if (abs_grad[i] > lmda_next * penalty[i] * alpha) {
                    screen_set.push_back(i);
                }
            }
        }
    };

    /* update screen_set */

    // KKT passed for some lambdas in the batch
    if (screen_rule == util::screen_rule_type::_strong) {
        const auto strong_rule_lmda = (2 * lmda_next - lmda) * alpha;

        for (int i = 0; i < abs_grad.size(); ++i) {
            if (is_screen(i)) continue;
            if (abs_grad[i] > strong_rule_lmda * penalty[i]) {
                screen_set.push_back(i);
            }
        }
    } else if (screen_rule == util::screen_rule_type::_pivot) {
        do_pivot();
    } else {
        throw util::adelie_core_solver_error("Unknown screen rule!");
    }

    // If adding new amount went over max screen size, 
    // undo the change to keep invariance from before, then throw exception.
    if (screen_set.size() > max_screen_size) {
        screen_set.erase(
            std::next(screen_set.begin(), old_screen_set_size),
            screen_set.end()
        );
        throw util::max_screen_set_error();
    }
}

/**
 * Checks the KKT condition for the current state at lmda.
 */
template <class StateType, class ValueType>
ADELIE_CORE_STRONG_INLINE
bool kkt(
    StateType& state,
    ValueType lmda
)
{
    const auto& groups = state.groups;
    const auto alpha = state.alpha;
    const auto& penalty = state.penalty;
    const auto& screen_hashset = state.screen_hashset;
    const auto& abs_grad = state.abs_grad;

    const auto is_screen = [&](auto i) {
        return screen_hashset.find(i) != screen_hashset.end();
    };

    for (int k = 0; k < groups.size(); ++k) {
        if (is_screen(k)) continue;
        const auto pk = penalty[k];
        const auto abs_grad_k = abs_grad[k];
        if (abs_grad_k > lmda * alpha * pk) return false;
    }

    return true;
}

template <
    class StateType,
    class PBType,
    class PBAddSuffixType,
    class UpdateLossNullType,
    class UpdateInvarianceType,
    class UpdateSolutionsType,
    class EarlyExitType,
    class ScreenType,
    class FitType
>
inline void solve_core(
    StateType&& state,
    PBType&& pb,
    PBAddSuffixType pb_add_suffix_f,
    UpdateLossNullType update_loss_null_f,
    UpdateInvarianceType update_invariance_f,
    UpdateSolutionsType update_solutions_f,
    EarlyExitType early_exit_f,
    ScreenType screen_f,
    FitType fit_f
)
{
    using state_t = std::decay_t<StateType>;
    using value_t = typename state_t::value_t;
    using vec_value_t = typename state_t::vec_value_t;
    using sw_t = util::Stopwatch;

    const auto alpha = state.alpha;
    const auto& penalty = state.penalty;
    const auto& screen_set = state.screen_set;
    const auto max_screen_size = state.max_screen_size;
    const auto setup_lmda_max = state.setup_lmda_max;
    const auto setup_lmda_path = state.setup_lmda_path;
    const auto lmda_path_size = state.lmda_path_size;
    const auto min_ratio = state.min_ratio;
    const auto& active_set_size = state.active_set_size;
    const auto& abs_grad = state.abs_grad;
    auto& lmda_max = state.lmda_max;
    auto& lmda_path = state.lmda_path;
    auto& benchmark_screen = state.benchmark_screen;
    auto& benchmark_fit_screen = state.benchmark_fit_screen;
    auto& benchmark_fit_active = state.benchmark_fit_active;
    auto& benchmark_kkt = state.benchmark_kkt;
    auto& benchmark_invariance = state.benchmark_invariance;
    auto& n_valid_solutions = state.n_valid_solutions;
    auto& active_sizes = state.active_sizes;
    auto& screen_sizes = state.screen_sizes;

    // Manually set progress bar to iters_done_ == 1.
    // This ensures that until pb is properly initialized to the range of [0, lmda_path.size()),
    // if the function finishes earlier then pb will print "... 0/0 ..." instead of "... -1/0 ...".
    pb.manually_set_progress(1); 

    if (screen_set.size() > max_screen_size) throw util::max_screen_set_error();

    update_loss_null_f(state);

    // ==================================================================================== 
    // Initial fit for lambda ~ infinity to setup lmda_max
    // ==================================================================================== 
    // Only unpenalized (l1) groups are active in this case.
    // State must include all unpenalized groups.
    // We solve for large lambda, then back-track the KKT condition to find the lambda
    // that leads to that solution where all penalized variables have 0 coefficient.
    if (setup_lmda_max) {
        // Must divide by at least the max penalty amount
        // so that we don't overflow.
       // Just to be safe, we divide by at least a fixed constant > 1 as well.
        const value_t large_lmda = (
            1e-3 * std::numeric_limits<value_t>::max() /
            std::max<value_t>(1, penalty.maxCoeff())
        ); 

        auto tup = fit_f(state, large_lmda);
        auto&& state_gaussian_pin = std::get<0>(tup);

        update_invariance_f(state, state_gaussian_pin, large_lmda);

        lmda_max = compute_lmda_max(abs_grad, alpha, penalty);
    }

    // ==================================================================================== 
    // Generate lambda path if needed
    // ==================================================================================== 
    if (setup_lmda_path) {
        if (lmda_path_size <= 0) return;

        lmda_path.resize(lmda_path_size);

        compute_lmda_path(lmda_path, min_ratio, lmda_max);
    }

    // ==================================================================================== 
    // Initial fit for lambda > lambda_max
    // ==================================================================================== 
    // Only unpenalized (l1) groups are active in this case by definition of lmda_max.
    // Since state is in its invariance (solution at state.lmda) and unpenalized groups
    // are ALWAYS active, state includes all unpenalized groups.
    // If no lambda in lmda_path is > lmda_max and setup at lmda_max is not required, 
    // state is left unchanged.
    // Otherwise, it is in its invariance at lmda = lmda_max.
    // All solutions to lambda > lambda_max are saved.

    // initialize progress bar
    pb.set_range(
        util::tq::int_iterator<int>(0),
        util::tq::int_iterator<int>(lmda_path.size())
    );
    auto pb_it = pb.begin();

    // slice lambda_path up to lmda_max
    const auto large_lmda_path_size = std::find_if(
        lmda_path.data(), 
        lmda_path.data() + lmda_path.size(),
        [&](auto x) { return x <= lmda_max; }
    ) - lmda_path.data();

    if (large_lmda_path_size || setup_lmda_max) {
        // create a lambda path containing only lmdas > lambda_max
        // and additionally lambda_max at the end.
        // If large_lmda_path_size > 0, mind as well fit for lambda_max as well to go down the path.
        vec_value_t large_lmda_path(large_lmda_path_size + 1);
        large_lmda_path.head(large_lmda_path_size) = lmda_path.head(large_lmda_path_size);
        large_lmda_path[large_lmda_path_size] = lmda_max;

        for (int i = 0; i < large_lmda_path.size(); ++i) {
            if (i < large_lmda_path.size()-1) {
                // update progress bar
                static_cast<void>(pb_it != pb.end());
            }

            auto tup = fit_f(state, large_lmda_path[i]);
            auto&& state_gaussian_pin = std::get<0>(tup);

            /* Invariance */
            // save only the solutions that the user asked for (up to and not including lmda_max)
            if (i < large_lmda_path.size()-1) {
                update_solutions_f(
                    state, 
                    state_gaussian_pin,
                    large_lmda_path[i]
                );
                pb_add_suffix_f(state, pb);
                ++pb_it;

                if (early_exit_f(state)) {
                    if (!(pb_it != pb.end())) return;
                    pb_add_suffix_f(state, pb);
                    return;
                }
            // otherwise, put the state at the last fitted lambda (lmda_max)
            } else {
                update_invariance_f(state, state_gaussian_pin, large_lmda_path[i]);
            }
        }
    }

    size_t lmda_path_idx = large_lmda_path_size; // next index into lmda_path to fit

    // ==================================================================================== 
    // BASIL iterations for lambda <= lambda_max
    // ==================================================================================== 
    // In this case, screen_set may not contain the true active set.
    // We must go through BASIL iterations to solve each lambda.
    sw_t sw;
    int current_active_size = active_set_size;
    bool kkt_passed = true;
    int n_new_active = 0;

    for (; pb_it != pb.end(); ++pb_it)
    {
        // batch the next set of lambdas
        const auto lmda_curr = lmda_path[lmda_path_idx];

        // keep doing screen-fit-kkt until KKT passes
        while (1) {
            try {
                // ==================================================================================== 
                // Screening step
                // ==================================================================================== 
                sw.start();
                screen_f(state, lmda_curr, kkt_passed, n_new_active);
                benchmark_screen.push_back(sw.elapsed());

                // ==================================================================================== 
                // Fit step
                // ==================================================================================== 
                auto tup = fit_f(state, lmda_curr);
                auto&& state_gaussian_pin = std::get<0>(tup);
                benchmark_fit_screen.push_back(std::get<1>(tup));
                benchmark_fit_active.push_back(std::get<2>(tup));

                // ==================================================================================== 
                // Invariance step
                // ==================================================================================== 
                sw.start();
                update_invariance_f(state, state_gaussian_pin, lmda_curr);
                benchmark_invariance.push_back(sw.elapsed());

                // ==================================================================================== 
                // KKT step
                // ==================================================================================== 
                sw.start();
                kkt_passed = kkt(state, lmda_curr);
                n_valid_solutions.push_back(kkt_passed);
                lmda_path_idx += kkt_passed;
                if (kkt_passed) {
                    update_solutions_f(
                        state, 
                        state_gaussian_pin,
                        lmda_curr
                    );
                }
                benchmark_kkt.push_back(sw.elapsed());

                // ==================================================================================== 
                // Diagnostic step
                // ==================================================================================== 
                if (kkt_passed) {
                    active_sizes.push_back(active_set_size);
                    screen_sizes.push_back(state.screen_set.size());
                }
                // compute the number of new active groups 
                n_new_active = (
                    kkt_passed ?
                    (active_sizes.back() - current_active_size) : n_new_active
                );
                current_active_size = (
                    kkt_passed ?
                    active_sizes.back() : current_active_size
                );
            } catch (...) {
                pb_add_suffix_f(state, pb);
                throw;
            }

            if (kkt_passed) break;
        } // end while(1)

        pb_add_suffix_f(state, pb);

        // Early exit condition must be here to ensure that 
        // it is called after processing each lambda (including the last lambda).
        if (early_exit_f(state)) {
            // must add one more bar
            ++pb_it;
            if (!(pb_it != pb.end())) break;
            pb_add_suffix_f(state, pb);
            break;
        }
    } // end for-loop over progress bar
}

} // namespace solver
} // namespace adelie_core 
