// SPDX-FileCopyrightText: 2026 Filip Leonarski, Paul Scherrer Institute <filip.leonarski@psi.ch>
// SPDX-License-Identifier: GPL-3.0-only

#include <catch2/catch_all.hpp>

#include <algorithm>
#include <atomic>
#include <cmath>
#include <map>
#include <random>
#include <vector>

#include <gemmi/mmread_gz.hpp>
#include <gemmi/symmetry.hpp>

#include "../common/CUDAWrapper.h"
#include "../common/Logger.h"
#include "../image_analysis/structure_refinement/MonomerLibrary.h"
#include "../image_analysis/structure_refinement/Refinement.h"
#include "../image_analysis/structure_refinement/RefinementMath.h"
#include "../image_analysis/structure_refinement/RefinementMinimiser.h"
#include "../image_analysis/structure_refinement/RefinementRestraints.h"
#include "../image_analysis/structure_refinement/RefinementXray.h"
#ifdef JFJOCH_USE_CUDA
#include "../image_analysis/structure_refinement/RefinementGPU.h"
#endif

namespace {

// Copies of residue `code` at the embedded dictionary's ideal coordinates (hydrogens left out), each turned and
// moved to a place of its own in the cell.
gemmi::Structure residue_crystal(const std::vector<std::string> &codes, const gemmi::UnitCell &cell, const char *group,
                                 unsigned seed) {
    std::mt19937 rng(seed);
    std::uniform_real_distribution<double> frac(0.0, 1.0), angle(-3.1, 3.1);
    gemmi::Structure st;
    st.cell = cell;
    st.spacegroup_hm = group;
    st.setup_cell_images();
    gemmi::Model model(1);
    gemmi::Chain chain("A");
    int seq = 1;
    for (const std::string &code : codes) {
        const gemmi::ChemComp &cc = EmbeddedMonomerLibrary().monomers.at(code);
        gemmi::Residue res;
        res.name = code;
        res.seqid = gemmi::SeqId(seq++, ' ');
        res.het_flag = 'H';
        res.entity_type = gemmi::EntityType::NonPolymer;
        const gemmi::Position centre = cell.orthogonalize(gemmi::Fractional(frac(rng), frac(rng), frac(rng)));
        const double ax = angle(rng), ay = angle(rng), az = angle(rng);
        const gemmi::Mat33 rot = gemmi::Mat33(1, 0, 0, 0, std::cos(ax), -std::sin(ax), 0, std::sin(ax), std::cos(ax))
                                     .multiply(gemmi::Mat33(std::cos(ay), 0, std::sin(ay), 0, 1, 0, -std::sin(ay), 0, std::cos(ay)))
                                     .multiply(gemmi::Mat33(std::cos(az), -std::sin(az), 0, std::sin(az), std::cos(az), 0, 0, 0, 1));
        for (const gemmi::ChemComp::Atom &ca : cc.atoms) {
            if (ca.is_hydrogen())
                continue;
            gemmi::Atom a;
            a.name = ca.id;
            a.element = ca.el;
            a.pos = gemmi::Position(rot.multiply(ca.xyz)) + centre;
            a.b_iso = 20.0f;
            a.occ = 1.0f;
            res.atoms.push_back(a);
        }
        chain.residues.push_back(res);
    }
    model.chains.push_back(chain);
    st.models.push_back(model);
    return st;
}

// Atoms of a few elements scattered over the cell.
gemmi::Structure random_crystal(const gemmi::UnitCell &cell, const char *group, int n, unsigned seed) {
    std::mt19937 rng(seed);
    std::uniform_real_distribution<double> frac(0.0, 1.0), b(10.0, 40.0);
    const gemmi::El elements[] = {gemmi::El::C, gemmi::El::N, gemmi::El::O, gemmi::El::S};
    gemmi::Structure st;
    st.cell = cell;
    st.spacegroup_hm = group;
    st.setup_cell_images();
    gemmi::Model model(1);
    gemmi::Chain chain("A");
    gemmi::Residue res;
    res.name = "UNK";
    res.seqid = gemmi::SeqId(1, ' ');
    for (int i = 0; i < n; i++) {
        gemmi::Atom a;
        a.name = "X";
        a.element = elements[i % 4];
        a.pos = cell.orthogonalize(gemmi::Fractional(frac(rng), frac(rng), frac(rng)));
        a.b_iso = static_cast<float>(b(rng));
        a.occ = 1.0f;
        res.atoms.push_back(a);
    }
    chain.residues.push_back(res);
    model.chains.push_back(chain);
    st.models.push_back(model);
    return st;
}

// Every reflection of the group's ASU to d_min, amplitude 1, one in twenty free.
std::vector<MergedReflection> asu_reflections(const gemmi::UnitCell &cell, const gemmi::SpaceGroup &sg, double d_min) {
    std::vector<MergedReflection> out;
    const gemmi::ReciprocalAsu asu(&sg);
    const gemmi::GroupOps gops = sg.operations();
    const gemmi::Miller lim = cell.get_hkl_limits(d_min);
    int i = 0;
    for (int h = -lim[0]; h <= lim[0]; h++)
        for (int k = -lim[1]; k <= lim[1]; k++)
            for (int l = -lim[2]; l <= lim[2]; l++) {
                const gemmi::Miller m{{h, k, l}};
                if ((h == 0 && k == 0 && l == 0) || !asu.is_in(m) || gops.is_systematically_absent(m))
                    continue;
                const double d = cell.calculate_d(m);
                if (d < d_min)
                    continue;
                MergedReflection r;
                r.h = h;
                r.k = k;
                r.l = l;
                r.d = static_cast<float>(d);
                r.F = 1.0f;
                r.sigmaF = 0.05f;
                r.rfree_flag = (i++ % 20) == 0;
                out.push_back(r);
            }
    return out;
}

// The observations set to |F| of `truth`, and a row model with no scale, no solvent and the likelihood's
// parameters estimated against `model`.
void set_observations(RefinementEngine &engine, RefinementReflections &refl, const gemmi::Model &truth,
                      const gemmi::Model &model) {
    std::vector<std::complex<float>> f;
    engine.Fcalc(truth, f);
    for (size_t m = 0; m < refl.Size(); m++)
        refl.fo[m] = std::abs(f[m]);
    engine.Fcalc(model, f);
    XrayRowModel rows;
    rows.k_total.assign(refl.Size(), 1.0f);
    rows.fmask.assign(refl.Size(), {0, 0});
    EstimateLikelihoodParameters(refl, f, rows);
    engine.SetRowModel(rows);
}

gemmi::Model shaken(const gemmi::Model &model, double sigma, double b_sigma, unsigned seed) {
    std::mt19937 rng(seed);
    std::normal_distribution<double> d(0, sigma), db(0, b_sigma);
    gemmi::Model out = model;
    for (gemmi::Chain &ch : out.chains)
        for (gemmi::Residue &r : ch.residues)
            for (gemmi::Atom &a : r.atoms) {
                a.pos += gemmi::Position(d(rng), d(rng), d(rng));
                a.b_iso = static_cast<float>(std::max(5.0, a.b_iso + db(rng)));
            }
    return out;
}

std::vector<gemmi::Atom *> atoms_of(gemmi::Model &model) {
    std::vector<gemmi::Atom *> out;
    for (gemmi::Chain &ch : model.chains)
        for (gemmi::Residue &r : ch.residues)
            for (gemmi::Atom &a : r.atoms)
                out.push_back(&a);
    return out;
}

// The engine's gradient of a few atoms against central differences of its own target.
void check_xray_gradient(RefinementEngine &engine, gemmi::Model model, double tolerance) {
    std::vector<std::array<double, 4>> grad;
    engine.Evaluate(model, &grad);
    std::vector<gemmi::Atom *> atoms = atoms_of(model);
    const double hx = 2e-3, hb = 2e-2;
    double max_g = 0;
    for (const auto &g : grad)
        for (int c = 0; c < 4; c++)
            max_g = std::max(max_g, std::fabs(g[c]));
    for (size_t i = 0; i < atoms.size(); i += atoms.size() / 7) {
        for (int c = 0; c < 4; c++) {
            const gemmi::Position p0 = atoms[i]->pos;
            const float b0 = atoms[i]->b_iso;
            const double h = c < 3 ? hx : hb;
            auto set = [&](double s) {
                atoms[i]->pos = p0;
                atoms[i]->b_iso = b0;
                if (c < 3)
                    atoms[i]->pos.at(c) += s;
                else
                    atoms[i]->b_iso = static_cast<float>(b0 + s);
            };
            set(h);
            const double fp = engine.Evaluate(model, nullptr);
            set(-h);
            const double fm = engine.Evaluate(model, nullptr);
            set(0);
            const double fd = (fp - fm) / (2 * h);
            CAPTURE(i, c, fd, grad[i][c], max_g);
            CHECK(std::fabs(fd - grad[i][c]) < tolerance * std::max(std::fabs(fd), 0.05 * max_g));
        }
    }
}

}  // namespace

TEST_CASE("RefinementLikelihood_derivative", "[Refinement]") {
    for (bool centric : {false, true})
        for (double fc : {0.3, 2.0, 9.0}) {
            double dfc = 0, dummy = 0;
            const double f0 = refine_math::AmplitudeNegLogLikelihood<double>(4.0, fc, 0.8, 2.5, centric, dfc);
            const double h = 1e-5;
            const double fp = refine_math::AmplitudeNegLogLikelihood<double>(4.0, fc + h, 0.8, 2.5, centric, dummy);
            const double fm = refine_math::AmplitudeNegLogLikelihood<double>(4.0, fc - h, 0.8, 2.5, centric, dummy);
            CAPTURE(centric, fc, f0);
            CHECK(dfc == Catch::Approx((fp - fm) / (2 * h)).epsilon(1e-5));
        }
    // the Bessel approximation on both sides of its switch
    double l0, r0, l1, r1;
    refine_math::BesselI0I1(3.75 * (1 - 1e-12), l0, r0);
    refine_math::BesselI0I1(3.75 * (1 + 1e-12), l1, r1);
    CHECK(l0 == Catch::Approx(l1).epsilon(1e-5));
    CHECK(r0 == Catch::Approx(r1).epsilon(1e-5));
}

TEST_CASE("RefinementMonomerLibrary_embedded", "[Refinement]") {
    const gemmi::MonLib &monlib = EmbeddedMonomerLibrary();
    for (const char *code : {"ALA", "PRO", "MSE", "DA", "U", "ATP", "GOL", "SO4", "HOH", "ZN"})
        CHECK(InEmbeddedMonomerLibrary(code));
    CHECK_FALSE(InEmbeddedMonomerLibrary("XYZ"));
    for (const char *link : {"TRANS", "CIS", "PTRANS", "p", "SS"})
        CHECK(monlib.links.count(link) == 1);
    CHECK(monlib.modifications.count("NH3") == 1);
    CHECK(monlib.ener_lib.atoms.count("CH1") == 1);
}

TEST_CASE("RefinementRestraints_ideal_residues", "[Refinement]") {
    const gemmi::UnitCell cell(60, 65, 70, 90, 90, 90);
    gemmi::Structure st = residue_crystal({"PHE", "DA", "ATP", "HOH", "ZN"}, cell, "P 21 21 21", 3);
    const RefinementTopology topo = BuildRefinementTopology(st);
    CHECK(topo.restrained_residues == 5);
    CHECK(topo.fixed_residues == 0);
    CHECK(topo.bonds > 60);
    CHECK(topo.planes >= 3);
    CHECK(topo.chirals >= 4);
    std::vector<std::array<double, 4>> xyzb;
    for (gemmi::Atom *a : atoms_of(st.models[0]))
        xyzb.push_back({a->pos.x, a->pos.y, a->pos.z, a->b_iso});
    const GeometryStatistics g = MeasureGeometry(topo.geometry, {}, xyzb);
    CHECK(g.rmsd_bonds < 0.02);
    CHECK(g.rmsd_angles < 2.5);
    CHECK(g.rmsd_chirals < 0.2);
}

// A zinc bound by four cysteines (the dictionary's own ZN-CYS link) and a magnesium by six waters (links made from
// the library's metal-site statistics), both from LINK records: the bonds come out at the expected distances,
// and a metal set off its site returns there under them alone.
TEST_CASE("RefinementRestraints_metal_links", "[Refinement]") {
    const gemmi::UnitCell cell(40, 40, 40, 90, 90, 90);
    gemmi::Structure st = residue_crystal({"CYS", "CYS", "CYS", "CYS", "ZN", "HOH", "HOH", "HOH", "HOH", "HOH", "HOH",
                                           "MG"}, cell, "P 1", 11);
    double mg_o = 0, mg_sigma = 0;
    REQUIRE(EmbeddedMetalDistance(gemmi::El::Mg, gemmi::El::O, 6, mg_o, mg_sigma));
    CHECK(mg_o == Catch::Approx(2.07).margin(0.02));   // Mg-O of an octahedral site
    constexpr double ZN_S = 2.34;                      // the ZN-CYS link
    std::vector<gemmi::Residue> &res = st.models[0].chains[0].residues;
    // the donors on a tetrahedron and an octahedron around their sites, each residue moved as a whole
    const gemmi::Position zn_site(10, 10, 10), mg_site(25, 25, 25);
    const double t = 1.0 / std::sqrt(3.0);
    const gemmi::Position tetra[4] = {{t, t, t}, {t, -t, -t}, {-t, t, -t}, {-t, -t, t}};
    const gemmi::Position octa[6] = {{1, 0, 0}, {-1, 0, 0}, {0, 1, 0}, {0, -1, 0}, {0, 0, 1}, {0, 0, -1}};
    auto donor_to = [](gemmi::Residue &r, const std::string &atom, const gemmi::Position &target) {
        const gemmi::Position shift = target - r.find_atom(atom, '*')->pos;
        for (gemmi::Atom &a : r.atoms)
            a.pos += shift;
    };
    for (int k = 0; k < 4; k++)
        donor_to(res[k], "SG", zn_site + tetra[k] * ZN_S);
    for (int k = 0; k < 6; k++)
        donor_to(res[5 + k], "O", mg_site + octa[k] * mg_o);
    // the metals off their sites by 0.3 A
    res[4].atoms[0].pos = zn_site + gemmi::Position(0.2, -0.15, 0.17);
    res[11].atoms[0].pos = mg_site + gemmi::Position(-0.1, 0.25, 0.12);
    auto link = [&](int metal, int donor, const char *atom) {
        gemmi::Connection c;
        c.type = gemmi::Connection::MetalC;
        c.asu = gemmi::Asu::Same;
        c.partner1 = gemmi::AtomAddress("A", res[donor].seqid, res[donor].name, atom);
        c.partner2 = gemmi::AtomAddress("A", res[metal].seqid, res[metal].name, res[metal].atoms[0].name);
        st.connections.push_back(c);
    };
    for (int k = 0; k < 4; k++)
        link(4, k, "SG");
    for (int k = 0; k < 6; k++)
        link(11, 5 + k, "O");

    const RefinementTopology topo = BuildRefinementTopology(st);
    CHECK(topo.metal_links == 6);   // the Mg-O links; Zn-S is the dictionary's
    std::vector<gemmi::Atom *> atoms = atoms_of(st.models[0]);
    const int zn = static_cast<int>(std::find(atoms.begin(), atoms.end(), &res[4].atoms[0]) - atoms.begin());
    const int mg = static_cast<int>(std::find(atoms.begin(), atoms.end(), &res[11].atoms[0]) - atoms.begin());
    // the metals' bonds kept apart from the covalent ones, none left among them
    for (const RestraintRecord &r : topo.geometry.records)
        CHECK_FALSE((r.kind == static_cast<int>(RestraintKind::Bond) &&
                     (r.atom[0] == zn || r.atom[1] == zn || r.atom[0] == mg || r.atom[1] == mg)));
    const RestraintSet &metal_bonds = topo.metal_bonds;
    REQUIRE(metal_bonds.records.size() == 10);
    for (const RestraintRecord &r : metal_bonds.records) {
        const bool is_zn = r.atom[0] == zn || r.atom[1] == zn;
        CHECK((is_zn || r.atom[0] == mg || r.atom[1] == mg));
        CHECK(r.ideal == Catch::Approx(is_zn ? ZN_S : mg_o).margin(1e-4));
    }

    // the two metals moved down the gradient of their bonds, everything else held
    std::vector<std::array<double, 4>> xyzb;
    for (gemmi::Atom *a : atoms)
        xyzb.push_back({a->pos.x, a->pos.y, a->pos.z, a->b_iso});
    double e = EvaluateRestraints(metal_bonds, xyzb, nullptr), step = 1e-4;
    for (int it = 0; it < 2000 && step > 1e-12; it++) {
        std::vector<std::array<double, 4>> grad(xyzb.size(), {0, 0, 0, 0}), trial = xyzb;
        EvaluateRestraints(metal_bonds, xyzb, &grad);
        for (int a : {zn, mg})
            for (int k = 0; k < 3; k++)
                trial[a][k] -= step * grad[a][k];
        const double e_trial = EvaluateRestraints(metal_bonds, trial, nullptr);
        if (e_trial < e) {
            xyzb = trial;
            e = e_trial;
            step *= 1.5;
        } else
            step *= 0.5;
    }
    for (const RestraintRecord &r : metal_bonds.records)
        CHECK(RestraintValue(metal_bonds, r, xyzb) == Catch::Approx(r.ideal).margin(0.005));
}

// Deposited models cut down to a ligand and the residues within 4.2 A of it (test_data/ligands, from the PDB entries
// their names start with; the tRNA as its modified nucleotides and their neighbours in the chain): every ligand is
// restrained, its own restraints included, the deposited geometry agrees with the dictionary, and the links the
// ligands need are made - the RNA backbone to and from each modified nucleotide, the iron of a heme to its histidine
// (and a heme C's to its methionine) from the LINK records, and a heme C's two thioethers to its cysteines.
TEST_CASE("RefinementRestraints_deposited_ligands", "[Refinement]") {
    const std::vector<std::string> modified_nucleotides = {"PSU", "5MC", "1MA", "OMG", "OMC", "H2U", "M2G", "7MG",
                                                           "2MG", "5MU"};
    const std::vector<std::pair<std::string, std::vector<std::string>>> cases = {
        {"1ehz_psu", modified_nucleotides}, {"8bkh_hem", {"HEM"}}, {"6k9i_hec", {"HEC"}}, {"2w3v_ndp", {"NDP"}},
        {"5vml_nap", {"NAP"}}, {"6f3p_nad", {"NAD"}}, {"8con_nai", {"NAI"}}, {"3tk0_fad", {"FAD"}},
        {"7tcd_fmn", {"FMN"}}, {"6w4h_sam", {"SAM"}}, {"5epe_sah", {"SAH"}}};
    for (const auto &[name, ligands] : cases) {
        DYNAMIC_SECTION(name) {
            gemmi::Structure st = gemmi::read_structure_gz("../../tests/test_data/ligands/" + name + ".pdb.gz");
            const RefinementTopology topo = BuildRefinementTopology(st);
            std::vector<gemmi::Atom *> atoms = atoms_of(st.models[0]);
            std::vector<const gemmi::Residue *> residue_of;
            for (const gemmi::Chain &ch : st.models[0].chains)
                for (const gemmi::Residue &r : ch.residues)
                    for (size_t k = 0; k < r.atoms.size(); k++)
                        residue_of.push_back(&r);
            auto index_of = [&](const gemmi::Residue &r, const char *atom) {
                const gemmi::Atom *a = r.find_atom(atom, '*');
                return a == nullptr ? -1 : static_cast<int>(std::find(atoms.begin(), atoms.end(), a) - atoms.begin());
            };
            auto bonded = [&](const RestraintSet &set, int i, int j) {
                for (const RestraintRecord &r : set.records)
                    if (r.kind == static_cast<int>(RestraintKind::Bond) &&
                        ((r.atom[0] == i && r.atom[1] == j) || (r.atom[0] == j && r.atom[1] == i)))
                        return true;
                return false;
            };

            std::map<std::string, int> restraints, found;
            for (const RestraintRecord &r : topo.geometry.records)
                if (r.kind != static_cast<int>(RestraintKind::Plane))
                    restraints[residue_of[r.atom[0]]->name]++;
            for (size_t i = 0; i < atoms.size(); i++)
                if (std::find(ligands.begin(), ligands.end(), residue_of[i]->name) != ligands.end()) {
                    found[residue_of[i]->name]++;
                    CHECK(topo.refinable[i]);
                }
            for (const std::string &code : ligands) {
                INFO(code);
                CHECK(found[code] > 0);
                CHECK(restraints[code] > 0);
                CHECK(std::find(topo.fixed_names.begin(), topo.fixed_names.end(), code) == topo.fixed_names.end());
            }

            std::vector<std::array<double, 4>> xyzb;
            for (gemmi::Atom *a : atoms)
                xyzb.push_back({a->pos.x, a->pos.y, a->pos.z, a->b_iso});
            const GeometryStatistics g = MeasureGeometry(topo.geometry, {}, xyzb, &topo.metal_bonds);
            CHECK(g.rmsd_bonds < 0.03);
            CHECK(g.rmsd_angles < 3.0);
            CHECK(g.rmsd_metal < 0.1);

            if (name == "1ehz_psu") {
                // each modified nucleotide bonded to the residue before it in the chain, where that one is there
                int links = 0;
                for (const gemmi::Residue &r : st.models[0].chains[0].residues) {
                    const gemmi::Residue *prev = &r == &st.models[0].chains[0].residues.front() ? nullptr : &r - 1;
                    if (prev == nullptr || prev->seqid.num != r.seqid.num - 1 ||
                        std::find(ligands.begin(), ligands.end(), r.name) == ligands.end())
                        continue;
                    INFO(r.name << " " << *r.seqid.num);
                    CHECK(bonded(topo.geometry, index_of(*prev, "O3'"), index_of(r, "P")));
                    links++;
                }
                CHECK(links >= 10);
            }
            if (name == "8bkh_hem" || name == "6k9i_hec") {
                const gemmi::Residue *heme = nullptr, *his = nullptr;
                for (const gemmi::Residue &r : st.models[0].chains[0].residues) {
                    if (r.name == ligands[0])
                        heme = &r;
                    if (r.name == "HIS" && r.seqid.num == (name == "8bkh_hem" ? 93 : 18))
                        his = &r;
                }
                REQUIRE(heme != nullptr);
                REQUIRE(his != nullptr);
                const int fe = index_of(*heme, "FE");
                CHECK(topo.metal[fe]);
                CHECK(topo.metal_links == (name == "8bkh_hem" ? 1 : 2));   // the histidine; and the methionine
                CHECK(bonded(topo.metal_bonds, fe, index_of(*his, "NE2")));
                CHECK(bonded(topo.metal_bonds, fe, index_of(*heme, "NA")));   // the porphyrin's own, among the metal's
                if (name == "6k9i_hec")
                    for (auto [cys, carbon] : {std::pair{14, "CAB"}, std::pair{17, "CAC"}})
                        for (const gemmi::Residue &r : st.models[0].chains[0].residues)
                            if (r.name == "CYS" && r.seqid.num == cys)
                                CHECK(bonded(topo.geometry, index_of(r, "SG"), index_of(*heme, carbon)));
            }
        }
    }
}

TEST_CASE("RefinementRestraints_gradient", "[Refinement]") {
    const gemmi::UnitCell cell(14, 15, 16, 90, 90, 90);
    gemmi::Structure st = residue_crystal({"TYR", "DG"}, cell, "P 21 21 21", 5);
    st.models[0] = shaken(st.models[0], 0.15, 3.0, 2);
    const RefinementTopology topo = BuildRefinementTopology(st);
    // the geometry, the B similarity and the repulsions (symmetry mates included, at a contact distance that
    // makes every pair within reach count)
    RestraintSet set = topo.geometry;
    set.Append(topo.adp);
    RefinementTopology wide = topo;
    for (float &r : wide.vdw_radius)
        r = 2.5f;
    std::fill(wide.hbond.begin(), wide.hbond.end(), 0);
    const RestraintSet rep = BuildRepulsions(wide, st.models[0], cell, *st.find_spacegroup(), 0.0);
    REQUIRE(rep.records.size() > 10);
    bool image = false;
    for (const RestraintRecord &r : rep.records)
        image = image || r.rot[0] != 1.0f || r.tran[0] != 0.0f || r.tran[1] != 0.0f || r.tran[2] != 0.0f;
    CAPTURE(rep.records.size());
    CHECK(image);
    set.Append(rep);
    set.Finalize(atoms_of(st.models[0]).size());

    std::vector<std::array<double, 4>> xyzb;
    for (gemmi::Atom *a : atoms_of(st.models[0]))
        xyzb.push_back({a->pos.x, a->pos.y, a->pos.z, a->b_iso});
    // each kind of restraint on its own, against central differences
    for (int kind = 0; kind <= static_cast<int>(RestraintKind::BSimilarity); kind++) {
        RestraintSet one;
        for (const RestraintRecord &r : set.records)
            if (r.kind == kind) {
                RestraintRecord copy = r;
                if (kind == static_cast<int>(RestraintKind::Plane)) {
                    copy.atom[0] = static_cast<int>(one.plane_atoms.size());
                    for (int k = 0; k < r.atom[1]; k++)
                        one.plane_atoms.push_back(set.plane_atoms[r.atom[0] + k]);
                }
                one.Add(copy, kind == static_cast<int>(RestraintKind::Plane) ? r.atom[1] : 4);
            }
        CAPTURE(kind, one.records.size());
        std::vector<std::array<double, 4>> grad(xyzb.size(), {0, 0, 0, 0});
        EvaluateRestraints(one, xyzb, &grad);
        const double h = 1e-6;
        for (size_t i = 0; i < xyzb.size(); i++)
            for (int c = 0; c < 4; c++) {
                auto x = xyzb;
                x[i][c] += h;
                const double fp = EvaluateRestraints(one, x, nullptr);
                x[i][c] -= 2 * h;
                const double fm = EvaluateRestraints(one, x, nullptr);
                CAPTURE(i, c);
                CHECK(grad[i][c] == Catch::Approx((fp - fm) / (2 * h)).epsilon(1e-4).margin(1e-3));
            }
    }

#ifdef JFJOCH_USE_CUDA
    if (get_gpu_count() > 0) {
        // the GPU's float evaluation of the same set
        // (the engine is made for a cell wide enough for its gather; the restraints do not read the cell)
        const gemmi::UnitCell wide_cell(40, 40, 40, 90, 90, 90);
        std::vector<MergedReflection> merged = asu_reflections(wide_cell, *st.find_spacegroup(), 3.0);
        RefinementReflections refl = PrepareRefinementReflections(merged, wide_cell, *st.find_spacegroup(), 3.0);
        auto gpu = MakeRefinementEngineGPU(0, wide_cell, *st.find_spacegroup(), 3.0, refl, st.models[0], 100.0, SIZE_MAX);
        REQUIRE(gpu);
        gpu->SetRestraints(0, set);
        std::vector<std::array<double, 4>> ggpu;
        const double egpu = gpu->EvaluateRestraints(0, xyzb, &ggpu);
        std::vector<std::array<double, 4>> gcpu(xyzb.size(), {0, 0, 0, 0});
        const double ecpu = EvaluateRestraints(set, xyzb, &gcpu);
        CHECK(egpu == Catch::Approx(ecpu).epsilon(1e-4));
        for (size_t i = 0; i < xyzb.size(); i++)
            for (int c = 0; c < 4; c++)
                CHECK(ggpu[i][c] == Catch::Approx(gcpu[i][c]).epsilon(2e-3).margin(2e-2));
    }
#endif
}

// Contacts with other copies of the molecule: in P1 two waters 2.4 A apart across the a face (17.6 A apart within
// the cell) repel each other once, and a water 1.4 A from a 3-fold axis, 2.4 A from its images x -> T x and
// x -> T^-1 x (one contact per asymmetric unit), repels its image once.
TEST_CASE("RefinementRestraints_lattice_and_symmetry_contacts", "[Refinement]") {
    auto oxygens = [](gemmi::Structure &st, const std::vector<gemmi::Fractional> &where) {
        std::vector<gemmi::Atom *> atoms = atoms_of(st.models[0]);
        REQUIRE(atoms.size() == where.size());
        for (size_t i = 0; i < where.size(); i++)
            atoms[i]->pos = st.cell.orthogonalize(where[i]);
    };
    {
        const gemmi::UnitCell cell(20, 21, 22, 90, 90, 90);
        gemmi::Structure st = residue_crystal({"HOH", "HOH"}, cell, "P 1", 1);
        oxygens(st, {gemmi::Fractional(0.01, 0.5, 0.5), gemmi::Fractional(0.89, 0.5, 0.5)});
        const RefinementTopology topo = BuildRefinementTopology(st);
        const RestraintSet rep = BuildRepulsions(topo, st.models[0], cell, *st.find_spacegroup(), 0.0);
        REQUIRE(rep.records.size() == 1);
        CHECK(rep.records[0].tran[0] == Catch::Approx(-20.0f));
        CHECK(BuildBContacts(topo, st.models[0], cell, *st.find_spacegroup()).records.size() == 1);
    }
    {
        const gemmi::UnitCell cell(20, 20, 22, 90, 90, 120);
        gemmi::Structure st = residue_crystal({"HOH"}, cell, "P 3", 1);
        oxygens(st, {cell.fractionalize(gemmi::Position(1.4, 0.0, 11.0))});
        const RefinementTopology topo = BuildRefinementTopology(st);
        const RestraintSet rep = BuildRepulsions(topo, st.models[0], cell, *st.find_spacegroup(), 0.0);
        CHECK(rep.records.size() == 1);
    }
}

// A complete model whose every atom is off by a Gaussian error of sigma_x per axis: D(s) = <cos(2 pi s.dx)> =
// exp(-2 pi^2 sigma_x^2 s^2) (Luzzati). With a negligible measurement error D comes out at that; with an error of
// half the rms amplitude of the outermost shell it falls below it there, where the error is a large part of the
// spread and is counted twice, and stays where the amplitudes are strong.
TEST_CASE("RefinementLikelihood_D_coordinate_error", "[Refinement]") {
    const char *group = "P 1";
    const gemmi::SpaceGroup &sg = *gemmi::find_spacegroup_by_name(group);
    const gemmi::UnitCell cell(40, 45, 50, 90, 90, 90);
    const double d_min = 1.5, sigma_x = 0.25;
    gemmi::Structure truth = random_crystal(cell, group, 1500, 3);
    gemmi::Model model = truth.models[0];
    std::mt19937 rng(4);
    std::normal_distribution<double> dx(0, sigma_x);
    for (gemmi::Atom &a : model.chains[0].residues[0].atoms)
        a.pos += gemmi::Position(dx(rng), dx(rng), dx(rng));
    RefinementReflections refl = PrepareRefinementReflections(asu_reflections(cell, sg, d_min), cell, sg, d_min);
    auto cpu = MakeRefinementEngineCPU(cell, sg, d_min, refl, 4);
    cpu->SetBlur(RefinementBlur(cell, sg, d_min, 5.0));
    std::vector<std::complex<float>> f;
    cpu->Fcalc(truth.models[0], f);
    for (size_t m = 0; m < refl.Size(); m++)
        refl.fo[m] = std::abs(f[m]);
    cpu->Fcalc(model, f);

    // mean D and mean Luzzati D in five shells of 1/d^2
    constexpr int SHELLS = 5;
    const double s2_max = 1.0 / (d_min * d_min);
    auto shells = [&](const XrayRowModel &rows, std::vector<double> &d, std::vector<double> &luzzati) {
        std::vector<int> n(SHELLS, 0);
        d.assign(SHELLS, 0);
        luzzati.assign(SHELLS, 0);
        for (size_t m = 0; m < refl.Size(); m++) {
            const int k = std::min(SHELLS - 1, static_cast<int>(refl.inv_d2[m] / s2_max * SHELLS));
            d[k] += rows.d[m];
            luzzati[k] += std::exp(-2 * M_PI * M_PI * sigma_x * sigma_x * refl.inv_d2[m]);
            n[k]++;
        }
        for (int k = 0; k < SHELLS; k++) {
            d[k] /= n[k];
            luzzati[k] /= n[k];
        }
    };
    XrayRowModel rows;
    rows.k_total.assign(refl.Size(), 1.0f);
    rows.fmask.assign(refl.Size(), {0, 0});
    for (float &s : refl.sigma)
        s = 0.01f;
    EstimateLikelihoodParameters(refl, f, rows);
    std::vector<double> d_clean, luzzati;
    shells(rows, d_clean, luzzati);
    for (int k = 0; k < SHELLS; k++) {
        CAPTURE(k, d_clean[k], luzzati[k]);
        CHECK(std::fabs(d_clean[k] - luzzati[k]) < 0.05);
    }
    CHECK(luzzati[SHELLS - 1] < 0.65);

    // a measurement error of half the rms amplitude of the outermost shell
    double fo2 = 0;
    int n = 0;
    for (size_t m = 0; m < refl.Size(); m++)
        if (refl.inv_d2[m] > s2_max * (SHELLS - 1) / SHELLS) {
            fo2 += double(refl.fo[m]) * refl.fo[m];
            n++;
        }
    for (float &s : refl.sigma)
        s = static_cast<float>(0.5 * std::sqrt(fo2 / n));
    EstimateLikelihoodParameters(refl, f, rows);
    std::vector<double> d_noisy;
    shells(rows, d_noisy, luzzati);
    CHECK(d_noisy[0] > d_clean[0] - 0.03);
    CHECK(d_noisy[SHELLS - 1] < d_clean[SHELLS - 1] - 0.1);
}

TEST_CASE("RefinementXray_gradient_CPU", "[Refinement]") {
    for (const char *group : {"P 1", "P 21 21 21", "C 1 2 1", "P 61 2 2"}) {
        CAPTURE(group);
        const gemmi::SpaceGroup &sg = *gemmi::find_spacegroup_by_name(group);
        const gemmi::UnitCell cell = sg.crystal_system() == gemmi::CrystalSystem::Hexagonal
                                         ? gemmi::UnitCell(30, 30, 45, 90, 90, 120)
                                         : gemmi::UnitCell(28, 31, 34, 90, sg.number == 5 ? 104 : 90, 90);
        gemmi::Structure truth = random_crystal(cell, group, 240, 7);
        gemmi::Model model = shaken(truth.models[0], 0.3, 4.0, 8);
        RefinementReflections refl = PrepareRefinementReflections(asu_reflections(cell, sg, 2.2), cell, sg, 2.2);
        REQUIRE(refl.Size() > 500);
        auto cpu = MakeRefinementEngineCPU(cell, sg, 2.2, refl, 4);
        cpu->SetBlur(RefinementBlur(cell, sg, 2.2, 5.0));
        set_observations(*cpu, refl, truth.models[0], model);
        check_xray_gradient(*cpu, model, 0.03);
    }
}

#ifdef JFJOCH_USE_CUDA
TEST_CASE("RefinementXray_gradient_GPU", "[Refinement]") {
    if (get_gpu_count() == 0)
        return;
    for (const char *group : {"P 1", "P 21 21 21", "C 1 2 1", "P 61 2 2"}) {
        CAPTURE(group);
        const gemmi::SpaceGroup &sg = *gemmi::find_spacegroup_by_name(group);
        const gemmi::UnitCell cell = sg.crystal_system() == gemmi::CrystalSystem::Hexagonal
                                         ? gemmi::UnitCell(30, 30, 45, 90, 90, 120)
                                         : gemmi::UnitCell(28, 31, 34, 90, sg.number == 5 ? 104 : 90, 90);
        gemmi::Structure truth = random_crystal(cell, group, 240, 7);
        gemmi::Model model = shaken(truth.models[0], 0.3, 4.0, 8);
        RefinementReflections refl = PrepareRefinementReflections(asu_reflections(cell, sg, 2.2), cell, sg, 2.2);
        auto cpu = MakeRefinementEngineCPU(cell, sg, 2.2, refl, 4);
        cpu->SetBlur(RefinementBlur(cell, sg, 2.2, 5.0));
        set_observations(*cpu, refl, truth.models[0], model);
        // the GPU engine sees the same observations: it is made after they are set
        auto gpu = MakeRefinementEngineGPU(0, cell, sg, 2.2, refl, model, 300.0, SIZE_MAX);
        REQUIRE(gpu);
        gpu->SetBlur(RefinementBlur(cell, sg, 2.2, 5.0));
        std::vector<std::complex<float>> f;
        cpu->Fcalc(model, f);
        XrayRowModel rows;
        rows.k_total.assign(refl.Size(), 1.0f);
        rows.fmask.assign(refl.Size(), {0, 0});
        EstimateLikelihoodParameters(refl, f, rows);
        cpu->SetRowModel(rows);
        gpu->SetRowModel(rows);

        std::vector<std::complex<float>> fg;
        gpu->Fcalc(model, fg);
        double num = 0, den = 0;
        for (size_t m = 0; m < f.size(); m++) {
            num += std::abs(f[m] - fg[m]);
            den += std::abs(f[m]);
        }
        CHECK(num / den < 1e-3);

        std::vector<std::array<double, 4>> gc, gg;
        const double tc = cpu->Evaluate(model, &gc);
        const double tg = gpu->Evaluate(model, &gg);
        CHECK(tg == Catch::Approx(tc).epsilon(1e-4));
        double max_g = 0;
        for (const auto &g : gc)
            for (int c = 0; c < 4; c++)
                max_g = std::max(max_g, std::fabs(g[c]));
        for (size_t i = 0; i < gc.size(); i++)
            for (int c = 0; c < 4; c++) {
                CAPTURE(i, c);
                CHECK(std::fabs(gg[i][c] - gc[i][c]) < 0.01 * max_g);
            }
        check_xray_gradient(*gpu, model, 0.05);
    }
}
#endif

TEST_CASE("RefinementMinimiser_quadratic", "[Refinement]") {
    // f = sum a_k (x_k - 1)^2 with curvatures spread over two decades
    const size_t n = 50;
    std::vector<double> a(n);
    for (size_t k = 0; k < n; k++)
        a[k] = std::pow(100.0, static_cast<double>(k) / (n - 1));
    const RefinementMinimiser::Target target = [&](const std::vector<double> &x, double &f, std::vector<double> &g) {
        f = 0;
        for (size_t k = 0; k < n; k++) {
            f += a[k] * (x[k] - 1) * (x[k] - 1);
            g[k] = 2 * a[k] * (x[k] - 1);
        }
        return true;
    };
    auto distance = [&](const std::vector<double> &x) {
        double d = 0;
        for (double v : x)
            d = std::max(d, std::fabs(v - 1));
        return d;
    };

    // the exact diagonal: one step
    RefinementMinimiser exact;
    std::vector<double> h(n);
    for (size_t k = 0; k < n; k++)
        h[k] = 2 * a[k];
    exact.SetDiagonal(h);
    std::vector<double> x(n, 0.0);
    exact.Minimise(target, x, 1, 0.0, 10.0);
    CHECK(distance(x) < 1e-9);

    // without it, the memory carried from one call to the next does what one long call does
    RefinementMinimiser split, whole;
    std::vector<double> xs(n, 0.0), xw(n, 0.0);
    for (int call = 0; call < 6; call++)
        split.Minimise(target, xs, 10, 0.0, 10.0);
    whole.Minimise(target, xw, 60, 0.0, 10.0);
    CHECK(distance(xw) < 1e-3);
    for (size_t k = 0; k < n; k++)
        CHECK(xs[k] == Catch::Approx(xw[k]).margin(1e-12));
}

TEST_CASE("Refinement_restrained_recovers_model", "[Refinement]") {
    const gemmi::UnitCell cell(36, 40, 44, 90, 90, 90);
    const gemmi::SpaceGroup &sg = *gemmi::find_spacegroup_by_name("P 21 21 21");
    gemmi::Structure truth = residue_crystal({"PHE", "TRP", "DA", "DG", "TYR", "HOH", "HOH", "HOH"}, cell,
                                             "P 21 21 21", 11);
    gemmi::Structure start = truth;
    start.models[0] = shaken(truth.models[0], 0.25, 5.0, 12);
    std::vector<MergedReflection> merged = asu_reflections(cell, sg, 1.8);
    {
        RefinementReflections refl = PrepareRefinementReflections(merged, cell, sg, 1.8 * 0.999);
        auto cpu = MakeRefinementEngineCPU(cell, sg, 1.8 * 0.999, refl, 4);
        cpu->SetBlur(RefinementBlur(cell, sg, 1.8, 5.0));
        std::vector<std::complex<float>> f;
        cpu->Fcalc(truth.models[0], f);
        std::map<gemmi::Miller, double> amplitude;
        for (size_t m = 0; m < refl.Size(); m++)
            amplitude[refl.hkl[m]] = std::abs(f[m]);
        std::mt19937 rng(3);
        std::normal_distribution<double> noise(0.0, 0.03);
        for (MergedReflection &r : merged) {
            const auto it = amplitude.find(gemmi::Miller{{r.h, r.k, r.l}});
            r.F = it == amplitude.end() ? NAN : static_cast<float>(it->second * (1 + noise(rng)));
            r.sigmaF = 0.03f * r.F + 0.01f;
        }
    }
    Logger logger("RefinementTest");
    for (bool gpu : {false, true}) {
        if (gpu && get_gpu_count() == 0)
            continue;
        CAPTURE(gpu);
        RefinementSettings settings;
        settings.gpu = gpu;
        settings.nthreads = 4;
        settings.weight_ladder = {0.0625};
        settings.adp_ladder = {4.0};
        settings.max_steps = 2;
        settings.final_ladder = {1.0};
        settings.riding_hydrogens = false;   // the data were made without them
        const RefinementResult r = RefineModel(start, merged, cell, sg, 1.0, logger, settings);
        REQUIRE(r.ok);
        CHECK(r.on_gpu == gpu);
        CHECK(r.restrained_residues == 8);
        CHECK(r.r_free < 0.6 * r.r_free_start);
        CHECK(r.geometry.rmsd_bonds < r.geometry_start.rmsd_bonds);
        double rms = 0;
        std::vector<gemmi::Atom *> refined = atoms_of(r.model->models[0]);
        std::erase_if(refined, [](const gemmi::Atom *a) { return a->is_hydrogen(); });   // the riding hydrogens
        const std::vector<gemmi::Atom *> ref = atoms_of(truth.models[0]);
        REQUIRE(refined.size() == ref.size());
        for (size_t i = 0; i < ref.size(); i++)
            rms += refined[i]->pos.dist_sq(ref[i]->pos);
        rms = std::sqrt(rms / ref.size());
        CHECK(rms < 0.15);

        // cut short before the first weight trial: the model as placed comes back, no trial chosen
        const std::atomic<bool> cancel{true};
        settings.cancel = &cancel;
        const RefinementResult c = RefineModel(start, merged, cell, sg, 1.0, logger, settings);
        REQUIRE(c.ok);
        CHECK(c.cancelled);
        CHECK_FALSE(c.restrained);
        CHECK(c.trials.empty());
        CHECK(c.model != nullptr);
        CHECK_FALSE(r.cancelled);
    }
}