Jungfraujoch/image_analysis/scale_merge/Merge.cpp

// SPDX-FileCopyrightText: 2025 Filip Leonarski, Paul Scherrer Institute <filip.leonarski@psi.ch>
// SPDX-License-Identifier: GPL-3.0-only

#include "Merge.h"

#include <algorithm>
#include <cmath>
#include <limits>
#include <unordered_map>

#include <spdlog/fmt/fmt.h>

#include <gemmi/reciproc.hpp>

#include "../../common/CorrelationCoefficient.h"
#include "../../common/ResolutionShells.h"
#include "../../common/Definitions.h"
#include "HKLKey.h"
#include "RfreeFlags.h"
#include "FrenchWilson.h"

namespace {
    // Deterministic CC1/2 half-set assignment: a splitmix64 bit-mix of the image's stable index.
    // A pure function of image identity (not a draw from a shared RNG in call order) keeps the split
    // reproducible run-to-run, independent of AddImage call order, and safe under concurrent merging.
    int HalfForImage(int64_t image_id) {
        uint64_t z = static_cast<uint64_t>(image_id) + 0x9e3779b97f4a7c15ULL;
        z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9ULL;
        z = (z ^ (z >> 27)) * 0x94d049bb133111ebULL;
        z = z ^ (z >> 31);
        return static_cast<int>(z & 1ULL);
    }
}

MergeOnTheFly::MergeOnTheFly(const DiffractionExperiment &x)
    : space_group_number(x.GetSpaceGroupNumber().value_or(1)),
      scaling_settings(x.GetScalingSettings()),
      indexing_settings(x.GetIndexingSettings()),
      high_resolution_limit(scaling_settings.GetHighResolutionLimit_A()),
      low_resolution_limit(scaling_settings.GetLowResolutionLimit_A()),
      // A min-image-CC of 0 (the default) means "no limit": leave the optional
      // empty so the per-image CC cut is inactive. Otherwise a 0.0 threshold
      // would silently drop every image with a non-positive per-image CC.
      image_cc_limit(scaling_settings.GetMinCCForImage() > 0.0
                         ? std::optional<double>(scaling_settings.GetMinCCForImage())
                         : std::nullopt),
      min_partiality(scaling_settings.GetMinPartiality()),
      generator(scaling_settings.GetMergeFriedel(), space_group_number),
      reject_outliers(scaling_settings.GetOutlierRejectNsigma() > 0.0),
      reject_nsigma(scaling_settings.GetOutlierRejectNsigma()) {
}

MergeOnTheFly &MergeOnTheFly::ReferenceCell(const std::optional<UnitCell> &cell) {
    reference_cell = cell;
    return *this;
}

void MergeOnTheFly::AddImage(const IntegrationOutcome &outcome, int64_t image_id) {
    std::unique_lock ul(merged_mutex);

    if (Mask(outcome))
        return;

    const int half = HalfForImage(image_id);

    for (const auto &r: outcome.reflections) {
        if (generator.IsSystematicallyAbsent(r))
            continue;

        if (r.image_scale_corr <= 0.0 || !std::isfinite(r.image_scale_corr))
            continue;
        if (!AcceptReflection(r, high_resolution_limit, low_resolution_limit))
            continue;
        if (exclude_ice_rings && r.on_ice_ring)
            continue;
        if (r.partiality < min_partiality)
            continue;

        const float I_corr = r.I * r.image_scale_corr;
        float sigma_corr = r.sigma * r.image_scale_corr;
        if (!std::isfinite(I_corr) || !std::isfinite(sigma_corr) || sigma_corr <= 0.0)
            continue;
        auto hkl = generator(r);
        auto hkl_key = hkl.pack();
        sigma_corr = CorrectedSigma(I_corr, sigma_corr, r.image_scale_corr, r.var_bkg, hkl_key);

        // Robust outlier rejection: drop this observation if it sits more than
        // reject_nsigma error-model sigmas from the reflection's median. Needs the active
        // error model so sigma_corr reflects the real scatter (else the threshold is the
        // bare counting sigma and would cull good partials).
        if (reject_outliers && error_model_active) {
            const auto mit = reject_median_I.find(hkl_key);
            if (mit != reject_median_I.end() &&
                std::fabs(I_corr - mit->second) > reject_nsigma * sigma_corr) {
                ++reject_count;
                continue;
            }
        }

        auto it = accumulator.find(hkl_key);
        if (it == accumulator.end())
            it = accumulator.emplace(hkl_key, MergeAccum{
                                 .h = hkl.plus ? hkl.h : -hkl.h,
                                 .k = hkl.plus ? hkl.k : -hkl.k,
                                 .l = hkl.plus ? hkl.l : -hkl.l,
                             }).first;

        const float w = 1.0f / (sigma_corr * sigma_corr);
        const float wI = w * I_corr;

        it->second.sum_wI += wI;
        it->second.sum_w += w;

        it->second.sum_wI_half[half] += wI;
        it->second.sum_w_half[half] += w;
        it->second.n_half[half]++;

        if (!std::isfinite(it->second.d) && std::isfinite(r.d) && r.d > 0.0f)
            it->second.d = r.d;
    }
}

float MergeOnTheFly::CorrectedSigma(float I_corr, float sigma_corr, float image_scale_corr,
                                    float var_bkg,
                                    uint64_t hkl_key) const {
    if (!error_model_active)
        return sigma_corr;

    // Intensity for the (b*I)^2 term: the reflection's mean (constant over its
    // observations), falling back to this observation only if the mean is unknown.
    const auto it = error_model_mean_I.find(hkl_key);
    const double I_for_b = (it != error_model_mean_I.end()) ? it->second : I_corr;

    // Base variance for the a*sigma^2 term. A weak observation's sigma^2 = a background/read part plus a
    // Poisson signal part proportional to its OWN intensity; weighting the merge by 1/sigma^2 with that
    // per-observation sigma biases the inverse-variance mean low at <1 photon (an up-fluctuated observation
    // gets a larger sigma and is over-downweighted, so the weighted mean drifts below <I>). Rebuild the
    // signal part at the reflection's EXPECTED intensity <I> instead - decompose out the background part
    // and re-add corr*<I> - so the weight no longer correlates with the observation's own fluctuation. This
    // mirrors the rotation combine in RotationScaleMerge::process_rawrun and is bit-identical when the
    // observation sits at its reflection mean.
    // The signal part removed here is the one the observation's own sigma actually carries, so it is
    // taken at max(0, I): a negative intensity has no Poisson signal to subtract, and subtracting it
    // anyway ADDS to the background part and inflates the weight of exactly the down-fluctuated
    // observations this correction exists to stop being mistreated.
    double a_var = static_cast<double>(sigma_corr) * sigma_corr;
    if (scaling_settings.GetExpectedVarianceMerge()) {
        const double bkg_var = static_cast<double>(image_scale_corr) * image_scale_corr * var_bkg;
        const double base = bkg_var + static_cast<double>(image_scale_corr) * std::max(0.0, I_for_b);
        if (base > 0.0)
            a_var = base;
    }

    const double v = error_model_a * a_var
                     + (error_model_b * I_for_b) * (error_model_b * I_for_b);
    return (v > 0.0) ? static_cast<float>(std::sqrt(v)) : sigma_corr;
}

void MergeOnTheFly::RefineErrorModel(const std::vector<IntegrationOutcome> &outcomes) {
    // Reset to identity up front: every early return below then leaves the model
    // inactive (CorrectedSigma returns sigma unchanged) rather than keeping a stale
    // a/b from a previous call alongside a freshly-cleared mean map.
    // Median of the chi-square(1) distribution: a single observation's squared deviation from its
    // reflection mean, divided by its variance, is chi-square(1)-distributed, so its median is this
    // fraction of its mean. Used both to de-bias the median-based variance fit and to normalize the
    // reported median reduced chi^2 so that honestly calibrated sigmas give 1.0 (not 0.4549).
    constexpr double CHI2_1_MEDIAN = 0.454936;

    error_model_active = false;
    error_model_a = 1.0;
    error_model_b = 0.0;
    error_model_chi2 = 0.0;
    error_model_mean_I.clear();
    reject_median_I.clear();
    reject_count = 0;

    // --- 1. Collect accepted, scaled observations grouped by symmetry-equivalent hkl,
    //        applying exactly the filters AddImage uses. ---
    struct Obs { float I, sigma; };
    std::unordered_map<uint64_t, std::vector<Obs>> groups;

    for (const auto &outcome: outcomes) {
        if (Mask(outcome))
            continue;
        for (const auto &r: outcome.reflections) {
            if (generator.IsSystematicallyAbsent(r))
                continue;
            if (r.image_scale_corr <= 0.0 || !std::isfinite(r.image_scale_corr))
                continue;
            if (!AcceptReflection(r, high_resolution_limit, low_resolution_limit))
                continue;
            if (exclude_ice_rings && r.on_ice_ring)
                continue;
            if (r.partiality < min_partiality)
                continue;
            const float I_corr = r.I * r.image_scale_corr;
            const float sigma_corr = r.sigma * r.image_scale_corr;
            if (!std::isfinite(I_corr) || !std::isfinite(sigma_corr) || sigma_corr <= 0.0f)
                continue;
            groups[generator(r).pack()].push_back({I_corr, sigma_corr});
        }
    }

    // --- 2. One global pool of (sigma^2, <I>^2, bias-corrected squared deviation). For an
    //        observation in a group of n, the residual from the inverse-variance mean has
    //        E[(I_i - <I>)^2] = sigma_i^2 (1 - h_i), h_i = w_i / sum_w (its leverage). The
    //        (b*I)^2 term uses the reflection mean, so the mean (not I_i) is the abscissa. ---
    struct Sample { double s2, I2, dev2; };
    std::vector<Sample> samples;

    for (const auto &[key, obs]: groups) {
        if (obs.size() < 2)
            continue;
        double sum_w = 0.0, sum_wI = 0.0;
        for (const auto &o: obs) {
            const double w = 1.0 / (static_cast<double>(o.sigma) * o.sigma);
            sum_w += w;
            sum_wI += w * o.I;
        }
        if (!(sum_w > 0.0))
            continue;
        const double mean = sum_wI / sum_w;
        error_model_mean_I[key] = static_cast<float>(mean);
        // Robust centre for outlier rejection: the median intensity (resists the very
        // outliers the inverse-variance mean is being protected from). Only when active.
        if (reject_outliers) {
            std::vector<float> iv;
            iv.reserve(obs.size());
            for (const auto &o: obs)
                iv.push_back(o.I);
            std::nth_element(iv.begin(), iv.begin() + iv.size() / 2, iv.end());
            reject_median_I[key] = iv[iv.size() / 2];
        }
        const double I2 = mean * mean;
        for (const auto &o: obs) {
            const double w = 1.0 / (static_cast<double>(o.sigma) * o.sigma);
            const double factor = 1.0 - w / sum_w;
            if (factor < 0.05)
                continue;
            const double resid = static_cast<double>(o.I) - mean;
            samples.push_back({static_cast<double>(o.sigma) * o.sigma, I2, resid * resid / factor});
        }
    }

    // --- 3. Fit global dev2 = a*sigma^2 + b^2*<I>^2. Bin by intensity (the per-observation
    //        dev2 is chi-square-1 noisy) and take medians; weight the bins by 1/dev2^2 so it
    //        is a *relative* fit - otherwise the strong bins (which fix b) swamp the weak
    //        bins (which fix a) and the weak sigmas stay over-confident. ---
    constexpr int n_bins = 16;
    if (samples.size() < static_cast<size_t>(8 * n_bins))
        return; // too little multiplicity to fit -> leave identity

    std::sort(samples.begin(), samples.end(),
              [](const Sample &p, const Sample &q) { return p.I2 < q.I2; });

    auto median = [](std::vector<double> &v) {
        std::nth_element(v.begin(), v.begin() + v.size() / 2, v.end());
        return v[v.size() / 2];
    };

    // Per-intensity-bin medians of (sigma^2, <I>^2, dev2).
    std::vector<double> bs2, bI2, bd2;
    bs2.reserve(n_bins); bI2.reserve(n_bins); bd2.reserve(n_bins);
    const size_t per = samples.size() / n_bins;
    for (int bin = 0; bin < n_bins; ++bin) {
        const size_t lo = bin * per;
        const size_t hi = (bin == n_bins - 1) ? samples.size() : lo + per;
        std::vector<double> vs2, vI2, vd2;
        vs2.reserve(hi - lo); vI2.reserve(hi - lo); vd2.reserve(hi - lo);
        for (size_t i = lo; i < hi; ++i) {
            vs2.push_back(samples[i].s2);
            vI2.push_back(samples[i].I2);
            vd2.push_back(samples[i].dev2);
        }
        bs2.push_back(median(vs2));
        bI2.push_back(median(vI2));
        // The per-observation dev2 is sigma^2 * chi-square(1)-distributed, whose MEDIAN is 0.4549 of
        // its mean. Fitting the model to the robust median would therefore calibrate the variances to
        // 0.4549x their true value (reduced chi^2 ~ 1/0.4549 = 2.2). Divide the median by that constant
        // to recover an unbiased estimate of the mean (E[dev2] = sigma^2), keeping the robustness of
        // the median while targeting reduced chi^2 = 1.
        bd2.push_back(median(vd2) / CHI2_1_MEDIAN);
    }

    // Relative-weighted (1/dev2^2) least squares for (a, b^2). Floor the weight's dev2 at a
    // small fraction of the typical bin dev2: an absolute floor (1e-30) does not stop a
    // near-zero-scatter bin from acquiring a runaway weight and hijacking the fit, so the
    // floor must scale with the data. The regression target keeps the unfloored dev2.
    std::vector<double> bd2_sorted = bd2;
    const double dev2_floor = std::max(1e-30, 1e-3 * median(bd2_sorted));
    double Ass = 0, AsI = 0, AII = 0, Bs = 0, BI = 0;
    for (int bin = 0; bin < n_bins; ++bin) {
        const double s2 = bs2[bin], I2 = bI2[bin], d2 = bd2[bin];
        const double d2w = std::max(d2, dev2_floor);
        const double wgt = 1.0 / (d2w * d2w);
        Ass += wgt * s2 * s2;
        AsI += wgt * s2 * I2;
        AII += wgt * I2 * I2;
        Bs  += wgt * s2 * d2;
        BI  += wgt * I2 * d2;
    }

    // Reject a near-collinear (ill-conditioned) system *relatively*: det lies in
    // [0, Ass*AII] by Cauchy-Schwarz, so compare against that scale rather than 1e-30.
    const double det = Ass * AII - AsI * AsI;
    if (!(det > 1e-10 * Ass * AII))
        return;
    const double a  = std::clamp((Bs * AII - BI * AsI) / det, 0.25, 100.0);
    const double b2 = std::max((Ass * BI - AsI * Bs) / det, 0.0);

    error_model_a = a;
    error_model_b = std::sqrt(b2);
    error_model_active = true;

    // Achieved goodness of fit: the median of the per-observation dev2/(a*sigma^2 + (b*<I>)^2). That
    // ratio is chi-square(1)-distributed (median 0.4549) when the sigmas are correct, so normalize by
    // CHI2_1_MEDIAN to report a median reduced chi^2 that targets 1.0. The median (not mean) keeps it
    // robust to the heavy outlier tail of serial data.
    std::vector<double> chi2;
    chi2.reserve(samples.size());
    for (const auto &s: samples) {
        const double v = a * s.s2 + b2 * s.I2;
        if (v > 0.0)
            chi2.push_back(s.dev2 / v);
    }
    error_model_chi2 = chi2.empty() ? 0.0 : median(chi2) / CHI2_1_MEDIAN;
}

bool MergeOnTheFly::Mask(const IntegrationOutcome &outcome) {
    if (reference_cell) {
        auto cell = outcome.latt.GetUnitCell();
        if (!cell.is_close(*reference_cell,
                          indexing_settings.GetUnitCellDistTolerance(),
                          indexing_settings.GetUnitCellAngleTolerance_deg()))
            return true;
    }

    if (filter_by_image_cc && image_cc_limit) {
        if (!outcome.image_scale_cc
            || std::isnan(outcome.image_scale_cc.value())
            || outcome.image_scale_cc.value() < image_cc_limit.value())
            return true;
    }
    return false;
}

std::vector<MergedReflection> MergeOnTheFly::ExportReflections() {
    std::unique_lock ul(merged_mutex);

    std::vector<MergedReflection> out;
    out.reserve(accumulator.size());
    for (const auto &accum: accumulator | std::views::values) {
        if (accum.sum_w <= 0.0)
            continue;

        MergedReflection mr{
            .h = accum.h,
            .k = accum.k,
            .l = accum.l,
            .I = static_cast<float>(accum.sum_wI / accum.sum_w),
            .sigma = static_cast<float>(1.0 / std::sqrt(accum.sum_w)),
            .I_half = {NAN, NAN},
            .sigma_half = {NAN, NAN},
            .d = accum.d
        };

        if (accum.n_half[0] + accum.n_half[1] > 0 && accum.sum_w_half[0] > 0.0 && accum.sum_w_half[1] > 0.0) {
            for (int i = 0; i < 2; ++i) {
                mr.I_half[i] = static_cast<float>(accum.sum_wI_half[i] / accum.sum_w_half[i]);
                mr.sigma_half[i] = static_cast<float>(1.0 / std::sqrt(accum.sum_w_half[i]));
            }
        }

        if (!std::isfinite(accum.d) || accum.d <= 0.0f)
            continue;

        out.emplace_back(mr);
    }

    AssignRfreeFlags(out, space_group_number, scaling_settings.GetRfreeFraction());
    ApplyFrenchWilson(out, space_group_number);
    return out;
}

std::vector<MergedReflection> MergeAll(const DiffractionExperiment &x,
                                       const std::vector<IntegrationOutcome> &integration_outcome) {
    MergeOnTheFly merge(x);
    for (size_t i = 0; i < integration_outcome.size(); ++i)
        merge.AddImage(integration_outcome[i], static_cast<int64_t>(i));
    return merge.ExportReflections();
}

struct ShellAccum {
    int total_obs = 0;
    int unique = 0;
    int possible = 0;

    double sum_i_over_sigma = 0.0;
    int n_i_over_sigma = 0;

    CorrelationCoefficient cc_half;
    CorrelationCoefficient cc_ref;
};

std::pair<double, size_t> ImageReferenceCC(const std::vector<Reflection> &reflections,
                                           const std::map<HKLKey, double> &reference,
                                           const HKLKeyGenerator &generator,
                                           std::optional<double> d_min_limit,
                                           std::optional<double> d_max_limit,
                                           double min_partiality) {
    constexpr size_t MIN_REFLECTIONS = 20;

    double sum_x = 0.0;
    double sum_y = 0.0;
    double sum_x2 = 0.0;
    double sum_y2 = 0.0;
    double sum_xy = 0.0;
    size_t n = 0;

    for (const auto &r: reflections) {
        if (r.on_ice_ring)
            continue;
        if (!AcceptReflection(r, d_min_limit, d_max_limit))
            continue;
        if (r.partiality < min_partiality)
            continue;
        if (!std::isfinite(r.I) || !std::isfinite(r.image_scale_corr) || r.image_scale_corr <= 0.0f)
            continue;
        if (!std::isfinite(r.sigma) || r.sigma <= 0.0f)
            continue;

        const auto it = reference.find(generator(r));
        if (it == reference.end())
            continue;

        const double image_i = static_cast<double>(r.I) * static_cast<double>(r.image_scale_corr);
        const double ref_i = it->second;

        if (!std::isfinite(image_i) || !std::isfinite(ref_i))
            continue;

        sum_x += image_i;
        sum_y += ref_i;
        sum_x2 += image_i * image_i;
        sum_y2 += ref_i * ref_i;
        sum_xy += image_i * ref_i;
        ++n;
    }

    if (n < MIN_REFLECTIONS)
        return {NAN, n};

    const double nd = static_cast<double>(n);
    const double cov = sum_xy - sum_x * sum_y / nd;
    const double var_x = sum_x2 - sum_x * sum_x / nd;
    const double var_y = sum_y2 - sum_y * sum_y / nd;

    if (!(var_x > 0.0 && var_y > 0.0))
        return {NAN, n};

    return {cov / std::sqrt(var_x * var_y), n};
}

void CalcPossibleReflections(int space_group_number ,
                             const UnitCell &cell,
                             double d_min,
                             double d_max,
                             const ResolutionShells &shells,
                             std::vector<ShellAccum> &acc,
                             bool merge_friedel) {
    gemmi::UnitCell gemmi_cell = cell;
    const gemmi::SpaceGroup *sg = gemmi::find_spacegroup_by_number(space_group_number);
    if (sg == nullptr)
        throw JFJochException(JFJochExceptionCategory::InputParameterInvalid,
            "Invalid space group number " + std::to_string(space_group_number));

    // Generate unique reflections
    std::vector<gemmi::Miller> possible_hkls = gemmi::make_miller_vector(gemmi_cell, sg, d_min, d_max, true);
    const gemmi::GroupOps gops = sg->operations();
    CrystalLattice lattice(cell);
    const auto astar = lattice.Astar();
    const auto bstar = lattice.Bstar();
    const auto cstar = lattice.Cstar();

    for (const auto &hkl: possible_hkls) {
        const auto q = hkl[0] * astar + hkl[1] * bstar + hkl[2] * cstar;
        const auto qlen = q.Length();
        if (qlen < 1e-6)
            continue;
        const auto d = 1.0 / qlen;
        const auto shell = shells.GetShell(d);
        if (!shell.has_value())
            continue;
        const int s = *shell;
        if (s >= 0 && s < acc.size())
            // Anomalous (no Friedel merge): an acentric reflection has two unique members (I+ and I-),
            // a centric one only one — match how unique_reflections is counted, so completeness stays
            // <=100% instead of approaching 200%.
            acc[s].possible += (merge_friedel || gops.is_reflection_centric(hkl)) ? 1 : 2;
    }
}


MergeStatistics MergeOnTheFly::MergeStats(const std::vector<MergedReflection> &merged,
                           const std::vector<IntegrationOutcome > &integration_outcome,
                           const std::vector<MergedReflection> &reference,
                           std::optional<double> d_min_override) {

    const int n_shells = scaling_settings.GetReportShellCount();

    auto d_min_limit_A = d_min_override.has_value()
        ? d_min_override : scaling_settings.GetHighResolutionLimit_A();
    const auto d_max_limit_A = scaling_settings.GetLowResolutionLimit_A();

    std::unordered_map<uint64_t, float> reference_intensities;
    if (!reference.empty()) {
        reference_intensities.reserve(reference.size());
        for (const auto &r: reference) {
            if (!std::isfinite(r.I))
                continue;

            const auto hkl = generator(r);
            reference_intensities[hkl.pack()] = r.I;
        }
    }

    float d_min = std::numeric_limits<float>::max();
    float d_max = 0.0f;

    for (const auto &m: merged) {
        if (!std::isfinite(m.d) || m.d <= 0.0f)
            continue;
        if (d_min_limit_A && m.d < d_min_limit_A)
            continue;
        if (d_max_limit_A && m.d > d_max_limit_A)
            continue;

        d_min = std::min(d_min, m.d);
        d_max = std::max(d_max, m.d);
    }

    if (!(d_min < d_max && d_min > 0.0f))
        throw JFJochException(JFJochExceptionCategory::InputParameterInvalid,
            "MergeStats: Error in resolution calculation");

    const float d_min_pad = d_min * 0.999f;
    const float d_max_pad = d_max * 1.001f;

    ResolutionShells shells(d_min_pad, d_max_pad, n_shells);
    const auto shell_mean_1_d2 = shells.GetShellMeanOneOverResSq();
    const auto shell_min_res = shells.GetShellMinRes();

    std::vector<ShellAccum> acc(n_shells);

    if (reference_cell.has_value())
        CalcPossibleReflections(space_group_number, reference_cell.value(),
            d_min_pad, d_max_pad, shells, acc, scaling_settings.GetMergeFriedel());

    CorrelationCoefficient cc_half_overall;
    CorrelationCoefficient cc_ref_overall;

    for (const auto &m: merged) {
        const auto shell = shells.GetShell(m.d);
        if (!shell.has_value())
            continue;

        const int s = *shell;
        if (s >= 0 && s < n_shells) {
            if (std::isfinite(m.I) && std::isfinite(m.sigma) && m.sigma > 0.0) {
                acc[s].unique++;
                acc[s].sum_i_over_sigma += m.I / m.sigma;
                ++acc[s].n_i_over_sigma;

                if (!reference_intensities.empty()) {
                    const auto hkl = generator(m);
                    const auto ref_it = reference_intensities.find(hkl.pack());
                    if (ref_it != reference_intensities.end() && std::isfinite(ref_it->second)) {
                        acc[s].cc_ref.Add(m.I, ref_it->second);
                        cc_ref_overall.Add(m.I, ref_it->second);
                    }
                }

                if (std::isfinite(m.I_half[0]) && std::isfinite(m.I_half[1])) {
                    acc[s].cc_half.Add(m.I_half[0], m.I_half[1]);
                    cc_half_overall.Add(m.I_half[0], m.I_half[1]);
                }

            }
        }
    }

    // Per-reflection mean <I>, and a per-reflection accumulator for R_meas - it needs |I_i - <I>|,
    // so the observations are visited again now that the means are known.
    std::unordered_map<uint64_t, float> merged_I;
    merged_I.reserve(merged.size());
    for (const auto &m: merged)
        if (std::isfinite(m.I))
            merged_I[generator(m).pack()] = m.I;

    struct RmeasObs { double sum_abs_dev = 0.0; double sum_I = 0.0; int n = 0; int shell = -1; };
    std::unordered_map<uint64_t, RmeasObs> rmeas_obs;
    rmeas_obs.reserve(merged.size());

    for (int i = 0; i < integration_outcome.size(); ++i) {
        if (Mask(integration_outcome[i]))
            continue;

        for (const auto &r: integration_outcome[i].reflections) {
            if (generator.IsSystematicallyAbsent(r))
                continue;
            if (r.image_scale_corr <= 0.0 || !std::isfinite(r.image_scale_corr))
                continue;
            if (!AcceptReflection(r, d_min_limit_A, d_max_limit_A))
                continue;
            if (r.partiality < min_partiality)
                continue;

            const float I_corr = r.I * r.image_scale_corr;
            const float sigma_corr = r.sigma * r.image_scale_corr;
            if (!std::isfinite(I_corr) || !std::isfinite(sigma_corr) || sigma_corr <= 0.0f)
                continue;

            const auto shell = shells.GetShell(r.d);
            if (!shell.has_value())
                continue;
            const int s = *shell;
            if (s >= 0 && s < n_shells) {
                acc[s].total_obs++;
                const auto key = generator(r).pack();
                const auto mit = merged_I.find(key);
                if (mit != merged_I.end()) {
                    auto &ra = rmeas_obs[key];
                    ra.sum_abs_dev += std::abs(static_cast<double>(I_corr) - mit->second);
                    ra.sum_I += I_corr;
                    ra.n++;
                    ra.shell = s;
                }
            }
        }
    }

    // R_meas per shell: sum over reflections of sqrt(n/(n-1)) * sum_i|I_i - <I>|, over sum of I_i.
    std::vector<double> rmeas_num(n_shells, 0.0), rmeas_den(n_shells, 0.0);
    double rmeas_num_all = 0.0, rmeas_den_all = 0.0;
    for (const auto &[key, ra]: rmeas_obs) {
        if (ra.n < 2 || ra.shell < 0 || ra.shell >= n_shells)
            continue;
        const double factor = std::sqrt(static_cast<double>(ra.n) / (ra.n - 1));
        rmeas_num[ra.shell] += factor * ra.sum_abs_dev;
        rmeas_den[ra.shell] += ra.sum_I;
        rmeas_num_all += factor * ra.sum_abs_dev;
        rmeas_den_all += ra.sum_I;
    }

    MergeStatistics out;
    out.shells.resize(n_shells);

    for (int s = 0; s < n_shells; ++s) {
        const auto &sa = acc[s];
        auto &ss = out.shells[s];

        ss.mean_one_over_d2 = shell_mean_1_d2[s];
        ss.d_min = shell_min_res[s];
        ss.d_max = s == 0 ? d_max_pad : shell_min_res[s - 1];
        ss.total_observations = sa.total_obs;
        ss.unique_reflections = sa.unique;
        ss.possible_unique_reflections = sa.possible;
        ss.mean_i_over_sigma = sa.n_i_over_sigma > 0
                                   ? sa.sum_i_over_sigma / sa.n_i_over_sigma
                                   : 0.0;

        ss.cc_half = sa.cc_half.GetCC();
        ss.cc_ref = sa.cc_ref.GetCC();
        ss.r_meas = rmeas_den[s] > 0.0 ? rmeas_num[s] / rmeas_den[s] : NAN;
    }

    auto &overall = out.overall;
    overall.d_min = d_min;
    overall.d_max = d_max;

    int all_possible = 0;
    int all_unique = 0;
    double sum_i_over_sigma = 0.0;
    int n_i_over_sigma = 0;


    for (const auto &sa: acc) {
        overall.total_observations += sa.total_obs;
        all_unique += sa.unique;
        all_possible += sa.possible;
        sum_i_over_sigma += sa.sum_i_over_sigma;
        n_i_over_sigma += sa.n_i_over_sigma;

    }

    overall.possible_unique_reflections = all_possible;
    overall.unique_reflections = all_unique;
    overall.mean_i_over_sigma = n_i_over_sigma > 0 ? sum_i_over_sigma / n_i_over_sigma : 0.0;
    overall.cc_half = cc_half_overall.GetCC();
    overall.cc_ref = cc_ref_overall.GetCC();
    overall.r_meas = rmeas_den_all > 0.0 ? rmeas_num_all / rmeas_den_all : NAN;

    return out;
}

const char *SweepQualityReasonCode(SweepQualityReason reason) {
    switch (reason) {
        case SweepQualityReason::NoDiffraction:    return "no_diffraction";
        case SweepQualityReason::CrystalOutOfBeam: return "crystal_out_of_beam";
        case SweepQualityReason::WeakDiffraction:  return "weak_diffraction";
        case SweepQualityReason::LossOfCentring:   return "loss_of_centring";
        case SweepQualityReason::RadiationDamage:  return "radiation_damage";
    }
    return "unknown";
}

const char *SweepQualityReasonText(SweepQualityReason reason) {
    switch (reason) {
        case SweepQualityReason::NoDiffraction:    return "no diffraction";
        case SweepQualityReason::CrystalOutOfBeam: return "out of beam";
        case SweepQualityReason::WeakDiffraction:  return "weak diffraction";
        case SweepQualityReason::LossOfCentring:   return "loss of centring";
        case SweepQualityReason::RadiationDamage:  return "radiation damage";
    }
    return "unknown";
}

std::ostream &operator<<(std::ostream &output, const MergeStatisticsShell &in) {
    double completeness = in.possible_unique_reflections > 0
        ? static_cast<double>(in.unique_reflections) / in.possible_unique_reflections * 100.0 : 0.0;
    double multiplicity = in.unique_reflections > 0
        ? static_cast<double>(in.total_observations) / in.unique_reflections : 0.0;

    output << fmt::format("{:8d} {:8d} {:8d} {:7.1f}% {:7.1f} {:8.1f} {:7.1f}% {:7.1f}% {:7.1f}% {:8.2f}",
                in.total_observations,
                in.unique_reflections,
                in.possible_unique_reflections,
                completeness,
                multiplicity,
                in.mean_i_over_sigma,
                in.r_meas*100.0,
                in.cc_half*100.0,
                in.cc_ref*100.0,
                in.abs_diff_over_sigma_anomalous);
    return output;
}

std::ostream &operator<<(std::ostream &output, const MergeStatistics &in) {
    output << std::endl;
    output << fmt::format("  {:>8s} {:>8s} {:>8s} {:>8s} {:>8s} {:>7s} {:>8s} {:>8s} {:>8s} {:>8s} {:>8s}",
        "d_min", "N_obs", "N_uniq", "N_possib", "Compl", "Mult", "<I/sig>", "R_meas", "CC1/2", "CCref", "SigAno")
    << std::endl;
    output << fmt::format("  {:->8s} {:->8s} {:->8s} {:->8s} {:->8s} {:->7s} {:->8s} {:->8s} {:->8s} {:->8s} {:->8s}",
        "", "", "", "", "", "", "", "", "", "", "") << std::endl;
    for (const auto &sh: in.shells) {
        if (sh.unique_reflections == 0)
            continue;
        output << fmt::format("  {:8.2f} ", sh.d_min);
        output << sh;
        output << std::endl;
    }
    output << fmt::format("  {:->8s} {:->8s} {:->8s} {:->8s} {:->8s} {:->7s} {:->8s} {:->8s} {:->8s} {:->8s} {:->8s}",
        "", "", "", "", "", "", "", "", "", "", "") << std::endl;

    output << fmt::format("  {:>8s} ", "Overall");
    output << in.overall;
    output << std::endl;
    if (std::isfinite(in.wilson_b) && in.wilson_b > 0.0)
        output << fmt::format("  Wilson B-factor estimate: {:.2f} A^2 (correlation {:.3f})",
                              in.wilson_b, in.wilson_b_correlation) << std::endl;
    if (std::isfinite(in.radiation_damage_delta_b))
        output << fmt::format("  Radiation damage: relative B-factor change over run = {:+.2f} A^2 "
                              "(first->last, {} batches)",
                              in.radiation_damage_delta_b, in.radiation_damage_b_batch.size()) << std::endl;
    output << std::endl;
    return output;
}