Jungfraujoch/image_analysis/geom_refinement/XtalOptimizer.cpp

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

#include "XtalOptimizer.h"
#include "ceres/ceres.h"
#include "ceres/rotation.h"

struct XtalResidual {
    XtalResidual(double x, double y,
                 double lambda,
                 double pixel_size,
                 double angle_rad,
                 double exp_h, double exp_k,
                 double exp_l,
                 gemmi::CrystalSystem symmetry)
        : obs_x(x), obs_y(y),
          lambda(lambda),
          pixel_size(pixel_size),
          exp_h(exp_h),
          exp_k(exp_k),
          exp_l(exp_l),
          angle_rad(angle_rad),
          symmetry(symmetry) {
    }

    template<typename T>
    bool operator()(const T *const beam_x,
                    const T *const beam_y,
                    const T *const distance_mm,
                    const T *const detector_rot,
                    const T *const rotation_axis,
                    const T *const p0,
                    const T *const p1,
                    const T *const p2,
                    T *residual) const {
        T c1 = ceres::cos(T(detector_rot[0]));
        T c2 = ceres::cos(T(detector_rot[1]));
        T s1 = ceres::sin(T(detector_rot[0]));
        T s2 = ceres::sin(T(detector_rot[1]));

        // x_lab in mm
        T x_lab = (T(obs_x) - beam_x[0]) * T(pixel_size);
        T y_lab = (T(obs_y) - beam_y[0]) * T(pixel_size);
        T z_lab = T(distance_mm[0]);

        // apply rotations
        T x = x_lab * c1 + z_lab * s1;
        T y = y_lab * c2 + (-x_lab * s1 + z_lab * c1) * s2;
        T z = -y_lab * s2 + (-x_lab * s1 + z_lab * c1) * c2;

        // convert to recip space
        T lab_norm = ceres::sqrt(x * x + y * y + z * z);

        T recip[3];
        recip[0] = x / (lab_norm * T(lambda));
        recip[1] = y / (lab_norm * T(lambda));
        recip[2] = (z / lab_norm - T(1.0)) / T(lambda);

        Eigen::Map<const Eigen::Matrix<T, 3, 1>> e_obs_recip_raw(recip);

        // Apply goniometer "back-to-start" rotation:
        // brings observed reciprocal from image orientation into reference crystal frame
        T v[3], rot_arr[9];
        v[0] = T(angle_rad) * rotation_axis[0];
        v[1] = T(angle_rad) * rotation_axis[1];
        v[2] = T(angle_rad) * rotation_axis[2];
        ceres::AngleAxisToRotationMatrix(v, rot_arr);

        Eigen::Matrix<T, 3, 3> R_gonio_back(rot_arr);
        Eigen::Matrix<T, 3, 1> e_obs_recip = R_gonio_back * e_obs_recip_raw;

        Eigen::Matrix<T, 3, 1> e_pred;
        Eigen::Matrix<T, 3, 3> e_latt;

        T uc_rot_matrix[9];
        ceres::AngleAxisToRotationMatrix(p0, uc_rot_matrix);

        Eigen::Map<const Eigen::Matrix<T, 3, 3>> e_uc_rot_matrix(uc_rot_matrix);
        Eigen::Matrix<T, 3, 1> e_uc_len = Eigen::Matrix<T, 3, 1>::Zero();
        Eigen::Matrix<T, 3, 3> B = Eigen::Matrix<T, 3, 3>::Identity();

        if (symmetry == gemmi::CrystalSystem::Hexagonal) {
            e_uc_len << p1[0], p1[0], p1[2];
            B(0, 1) = T(-0.5); // cos(120)
            B(1, 1) = T(sqrt(3.0) / 2.0); // sin(120)
        } else if (symmetry == gemmi::CrystalSystem::Orthorhombic) {
            e_uc_len << p1[0], p1[1], p1[2];
        } else if (symmetry == gemmi::CrystalSystem::Tetragonal) {
            e_uc_len << p1[0], p1[0], p1[2];
        } else if (symmetry == gemmi::CrystalSystem::Cubic) {
            e_uc_len << p1[0], p1[0], p1[0];
        } else if (symmetry == gemmi::CrystalSystem::Monoclinic) {
            // Unique axis b: alpha = gamma = 90°, beta free (angle between a and c)
            e_uc_len << p1[0], p1[1], p1[2];
            B(0, 2) = ceres::cos(p2[0]);
            B(2, 2) = ceres::sin(p2[0]);
        } else {
            // Triclinic: p1 = (a,b,c), p2 = (alpha, beta, gamma) in radians
            const T ca = ceres::cos(p2[0]);
            const T cb = ceres::cos(p2[1]);
            const T cg = ceres::cos(p2[2]);
            const T sg = ceres::sin(p2[2]);

            e_uc_len << p1[0], p1[1], p1[2];

            // B_triclinic builds lattice from lengths+angles in crystallographic convention
            // columns correspond to a, b, c in Cartesian frame prior to global rotation
            B(0, 0) = T(1);
            B(1, 0) = T(0);
            B(2, 0) = T(0);
            B(0, 1) = cg;
            B(1, 1) = sg;
            B(2, 1) = T(0);
            // c vector components:
            T cx = cb;
            T cy = (ca - cb * cg) / sg;
            T v = T(1) - cx * cx - cy * cy;
            T cz;
            if (v >= T(0))
                cz = ceres::sqrt(v);
            else
                cz = T(0);

            B(0, 2) = cx;
            B(1, 2) = cy;
            B(2, 2) = cz;
        }

        e_latt = e_uc_rot_matrix * e_uc_len.asDiagonal() * B;

        Eigen::Matrix<T, 3, 1> e_hkl;
        e_hkl << T(exp_h), T(exp_k), T(exp_l);

        auto e_pred_hkl = e_latt.transpose() * e_obs_recip;

        residual[0] = exp_h - e_pred_hkl[0];
        residual[1] = exp_k - e_pred_hkl[1];
        residual[2] = exp_l - e_pred_hkl[2];

        return true;
    }

    const double obs_x, obs_y;
    const double lambda;
    const double pixel_size;
    const double exp_h;
    const double exp_k;
    const double exp_l;
    const double angle_rad;
    gemmi::CrystalSystem symmetry;
};

inline void LatticeToRodriguesAndLengths_GS(const CrystalLattice &latt,
                                            double rod[3],
                                            double lengths[3]) {
    // Load lattice columns
    const Coord a = latt.Vec0();
    const Coord b = latt.Vec1();
    const Coord c = latt.Vec2();

    Eigen::Vector3d A(a[0], a[1], a[2]);
    Eigen::Vector3d B(b[0], b[1], b[2]);
    Eigen::Vector3d C(c[0], c[1], c[2]);

    // Lengths = column norms (orthorhombic assumption)
    lengths[0] = A.norm();
    lengths[1] = B.norm();
    lengths[2] = C.norm();

    auto safe_unit = [](const Eigen::Vector3d &v, double eps = 1e-15) -> Eigen::Vector3d {
        double n = v.norm();
        return (n > eps) ? (v / n) : Eigen::Vector3d(1.0, 0.0, 0.0);
    };

    // Gram–Schmidt with original order: x from A, y from B orthogonalized vs x
    Eigen::Vector3d e1 = safe_unit(A);
    Eigen::Vector3d y = B - (e1.dot(B)) * e1;
    Eigen::Vector3d e2 = safe_unit(y);

    // z from cross to ensure right-handed basis
    Eigen::Vector3d e3 = e1.cross(e2);
    double n3 = e3.norm();
    if (n3 < 1e-15) {
        // Degenerate case: B nearly collinear with A → use C instead
        y = C - (e1.dot(C)) * e1;
        e2 = safe_unit(y);
        e3 = e1.cross(e2);
        n3 = e3.norm();
        if (n3 < 1e-15) {
            // Still degenerate: pick any perpendicular to e1
            e2 = safe_unit((std::abs(e1.x()) < 0.9)
                               ? Eigen::Vector3d::UnitX().cross(e1)
                               : Eigen::Vector3d::UnitY().cross(e1));
            e3 = e1.cross(e2);
        }
    } else {
        e3 /= n3;
    }

    Eigen::Matrix3d R;
    R.col(0) = e1;
    R.col(1) = e2;
    R.col(2) = e3;

    // Convert rotation to Rodrigues (axis * angle)
    Eigen::AngleAxisd aa(R);
    Eigen::Vector3d r = aa.angle() * aa.axis();
    rod[0] = r.x();
    rod[1] = r.y();
    rod[2] = r.z();
}

void LatticeToRodriguesAndLengths_Hex(const CrystalLattice &latt, double rod[3], double ac[3]) {
    const Coord a = latt.Vec0();
    const Coord b = latt.Vec1();
    const Coord c = latt.Vec2();

    Eigen::Vector3d A(a[0], a[1], a[2]);
    Eigen::Vector3d B(b[0], b[1], b[2]);
    Eigen::Vector3d C(c[0], c[1], c[2]);

    const double a_len = A.norm();
    const double b_len = B.norm();
    const double c_len = C.norm();

    ac[0] = (a_len + b_len) / 2.0;
    ac[1] = (a_len + b_len) / 2.0;
    ac[2] = c_len;

    Eigen::Vector3d e1;
    Eigen::Vector3d e3;

    if (a_len > 0.0)
        e1 = A / a_len;
    else
        e1 = Eigen::Vector3d::UnitX();

    if (c_len > 0.0)
        e3 = C / c_len;
    else
        e3 = Eigen::Vector3d::UnitZ();

    Eigen::Vector3d e2 = e3.cross(e1);
    if (e2.norm() < 1e-15) {
        e2 = (std::abs(e1.x()) < 0.9)
                 ? Eigen::Vector3d::UnitX().cross(e1)
                 : Eigen::Vector3d::UnitY().cross(e1);
    }
    e2.normalize();
    e3 = e1.cross(e2).normalized();

    Eigen::Matrix3d R;
    R.col(0) = e1;
    R.col(1) = e2;
    R.col(2) = e3;

    Eigen::AngleAxisd aa(R);
    Eigen::Vector3d r = aa.angle() * aa.axis();
    rod[0] = r.x();
    rod[1] = r.y();
    rod[2] = r.z();
}

// Extract rotation (Rodrigues), lengths (a,b,c) and beta (rad) for monoclinic (unique axis b).
// Frame choice: e2 aligned with b; e1 from a projected orthogonal to e2; e3 = e1 x e2.
inline void LatticeToRodriguesLengthsBeta_Mono(const CrystalLattice &latt,
                                               double rod[3],
                                               double lengths[3],
                                               double &beta_rad) {
    const Coord a = latt.Vec0();
    const Coord b = latt.Vec1();
    const Coord c = latt.Vec2();

    Eigen::Vector3d A(a[0], a[1], a[2]);
    Eigen::Vector3d B(b[0], b[1], b[2]);
    Eigen::Vector3d C(c[0], c[1], c[2]);

    const double a_len = A.norm();
    const double b_len = B.norm();
    const double c_len = C.norm();

    lengths[0] = a_len;
    lengths[1] = b_len;
    lengths[2] = c_len;

    // beta = angle between a and c
    double cos_beta = 0.0;
    if (a_len > 0.0 && c_len > 0.0)
        cos_beta = std::max(-1.0, std::min(1.0, A.dot(C) / (a_len * c_len)));
    beta_rad = std::acos(cos_beta);
    Eigen::Vector3d e2, ax;

    // e2 along b (unique axis)
    if (b_len > 0.0)
        e2 = B / b_len;
    else
        e2 = Eigen::Vector3d::UnitY();

    if (a_len > 0.0)
        ax = A / a_len;
    else
        ax = Eigen::Vector3d::UnitX();

    Eigen::Vector3d e1 = ax - (ax.dot(e2)) * e2;
    double n1 = e1.norm();
    if (n1 < 1e-15) {
        // Fallback: use any perpendicular to e2
        e1 = (std::abs(e2.x()) < 0.9
                  ? Eigen::Vector3d::UnitX().cross(e2)
                  : Eigen::Vector3d::UnitY().cross(e2));
    }
    e1.normalize();
    // e3 completes the right-handed frame
    Eigen::Vector3d e3 = e1.cross(e2).normalized();

    Eigen::Matrix3d R;
    R.col(0) = e1;
    R.col(1) = e2;
    R.col(2) = e3;

    Eigen::AngleAxisd aa(R);
    Eigen::Vector3d r = aa.angle() * aa.axis();
    rod[0] = r.x();
    rod[1] = r.y();
    rod[2] = r.z();
}

CrystalLattice AngleAxisAndLengthsToLattice(const double rod[3], const double lengths[3], bool hex) {
    const Eigen::Vector3d r(rod[0], rod[1], rod[2]);
    const double angle = r.norm();
    Eigen::Matrix3d R = Eigen::Matrix3d::Identity();
    if (angle > 0.0)
        R = Eigen::AngleAxisd(angle, r / angle).toRotationMatrix();
    const Eigen::DiagonalMatrix<double, 3> D(lengths[0], lengths[1], lengths[2]);

    Eigen::Matrix3d Bhex = Eigen::Matrix3d::Identity();
    if (hex) {
        Bhex(0, 1) = -1 / 2.0;
        Bhex(1, 1) = sqrt(3) / 2;
    }

    auto latt = R * D * Bhex;
    return CrystalLattice(Coord(latt(0, 0), latt(1, 0), latt(2, 0)),
                          Coord(latt(0, 1), latt(1, 1), latt(2, 1)),
                          Coord(latt(0, 2), latt(1, 2), latt(2, 2)));
}

inline CrystalLattice AngleAxisLengthsBetaToLattice_Mono(const double rod[3],
                                                         const double lengths[3],
                                                         double beta_rad) {
    const Eigen::Vector3d r(rod[0], rod[1], rod[2]);
    const double angle = r.norm();
    Eigen::Matrix3d R = Eigen::Matrix3d::Identity();
    if (angle > 0.0)
        R = Eigen::AngleAxisd(angle, r / angle).toRotationMatrix();

    const Eigen::DiagonalMatrix<double, 3> D(lengths[0], lengths[1], lengths[2]);

    Eigen::Matrix3d B = Eigen::Matrix3d::Identity();
    // Bmono = [[1,0,cosβ],[0,1,0],[0,0,sinβ]]
    B(0, 2) = std::cos(beta_rad);
    B(2, 2) = std::sin(beta_rad);

    Eigen::Matrix3d latt = R * D * B;
    return CrystalLattice(Coord(latt(0, 0), latt(1, 0), latt(2, 0)),
                          Coord(latt(0, 1), latt(1, 1), latt(2, 1)),
                          Coord(latt(0, 2), latt(1, 2), latt(2, 2)));
}

bool XtalOptimizerInternal(XtalOptimizerData &data,
                           const std::vector<SpotToSave> &spots,
                           const float tolerance) {
    try {
        data.latt.Regularize(data.crystal_system);

        Coord vec0 = data.latt.Vec0();
        Coord vec1 = data.latt.Vec1();
        Coord vec2 = data.latt.Vec2();
        double beta = data.latt.GetUnitCell().beta;

        // Initial guess for the parameters
        double beam_x = data.geom.GetBeamX_pxl();
        double beam_y = data.geom.GetBeamY_pxl();
        double distance_mm = data.geom.GetDetectorDistance_mm();

        double detector_rot[2] = {data.geom.GetPoniRot1_rad(), data.geom.GetPoniRot2_rad()};

        ceres::Problem problem;

        double latt_vec0[3], latt_vec1[3], latt_vec2[3];

        double rot_vec[3] = {1, 0, 0};

        switch (data.crystal_system) {
            case gemmi::CrystalSystem::Orthorhombic:
                LatticeToRodriguesAndLengths_GS(data.latt, latt_vec0, latt_vec1);
                break;
            case gemmi::CrystalSystem::Tetragonal:
                LatticeToRodriguesAndLengths_GS(data.latt, latt_vec0, latt_vec1);
                latt_vec1[0] = (latt_vec1[0] + latt_vec1[1]) / 2.0;
                break;
            case gemmi::CrystalSystem::Cubic:
                LatticeToRodriguesAndLengths_GS(data.latt, latt_vec0, latt_vec1);
                latt_vec1[0] = (latt_vec1[0] + latt_vec1[1] + latt_vec1[2]) / 3.0;
                break;
            case gemmi::CrystalSystem::Hexagonal:
                LatticeToRodriguesAndLengths_Hex(data.latt, latt_vec0, latt_vec1);
                break;
            case gemmi::CrystalSystem::Monoclinic:
                LatticeToRodriguesLengthsBeta_Mono(data.latt, latt_vec0, latt_vec1, beta);
                latt_vec2[0] = beta;
                latt_vec2[1] = 0.0;
                latt_vec2[2] = 0.0;
                break;
            default:
                // Triclinic: initialize a,b,c and α,β,γ from current unit cell
                LatticeToRodriguesAndLengths_GS(data.latt, latt_vec0, latt_vec1);
                auto uc = data.latt.GetUnitCell();
                latt_vec2[0] = uc.alpha * M_PI / 180.0;
                latt_vec2[1] = uc.beta * M_PI / 180.0;
                latt_vec2[2] = uc.gamma * M_PI / 180.0;
                break;
        }

        if (data.axis) {
            rot_vec[0] = data.axis->GetAxis().x;
            rot_vec[1] = data.axis->GetAxis().y;
            rot_vec[2] = data.axis->GetAxis().z;
        }

        const float tolerance_sq = tolerance * tolerance;

        // Add residuals for each point
        for (const auto &pt: spots) {
            if (!data.index_ice_rings && pt.ice_ring)
                continue;

            Eigen::Matrix3d gonio_back_rot = Eigen::Matrix3d::Identity();

            Coord axis = Coord(1,0,0);
            float angle_rad = 0.0;

            Coord recip = data.geom.DetectorToRecip(pt.x, pt.y);

            if (data.axis) {
                const float angle_deg = data.axis->GetAngle_deg(pt.image) + data.axis->GetWedge_deg() / 2.0f;
                auto rot = data.axis->GetTransformationAngle(angle_deg);
                recip = rot * recip;

                angle_rad = angle_deg * M_PI / 180.0;
                axis = data.axis->GetAxis();
            }

            double h_fp = recip * vec0;
            double k_fp = recip * vec1;
            double l_fp = recip * vec2;

            double h = std::round(h_fp);
            double k = std::round(k_fp);
            double l = std::round(l_fp);

            double norm_sq = (h - h_fp) * (h - h_fp) + (k - k_fp) * (k - k_fp) + (l - l_fp) * (l - l_fp);

            if (norm_sq > tolerance_sq)
                continue;

            problem.AddResidualBlock(
                new ceres::AutoDiffCostFunction<XtalResidual, 3, 1, 1, 1, 2, 3, 3, 3, 3>(
                    new XtalResidual(pt.x, pt.y,
                                     data.geom.GetWavelength_A(),
                                     data.geom.GetPixelSize_mm(),
                                     angle_rad,
                                     h, k, l,
                                     data.crystal_system)),
                nullptr,
                &beam_x,
                &beam_y,
                &distance_mm,
                detector_rot,
                rot_vec,
                latt_vec0,
                latt_vec1,
                latt_vec2
            );
        }

        if (problem.NumResidualBlocks() < data.min_spots)
            return false;

        if (!data.refine_distance_mm)
            problem.SetParameterBlockConstant(&distance_mm);
        else {
            const double dist_range = 0.1;
            problem.SetParameterLowerBound(&distance_mm, 0, distance_mm * (1.0 - dist_range));
            problem.SetParameterLowerBound(&distance_mm, 0, distance_mm * (1.0 + dist_range));
        }

        if (!data.refine_beam_center) {
            problem.SetParameterBlockConstant(&beam_x);
            problem.SetParameterBlockConstant(&beam_y);
        }

        if (!data.refine_detector_angles) {
            problem.SetParameterBlockConstant(detector_rot);
        } else {
            const double rot_range = 3.0 / 180.0 * M_PI;
            for (int i = 0; i < 2; ++i) {
                problem.SetParameterLowerBound(detector_rot, i, detector_rot[i] - rot_range);
                problem.SetParameterUpperBound(detector_rot, i, detector_rot[i] + rot_range);
            }
        }

        if (!data.refine_rotation_axis) {
            problem.SetParameterBlockConstant(rot_vec);
        }

        if (!data.refine_unit_cell) {
            problem.SetParameterBlockConstant(latt_vec1);
            problem.SetParameterBlockConstant(latt_vec2);
        } else {
            // Parameter bounds
            // Lengths
            for (int i = 0; i < 3; ++i) {
                problem.SetParameterLowerBound(latt_vec1, i, data.min_length_A);
                problem.SetParameterUpperBound(latt_vec1, i, data.max_length_A);
            }

            if (data.crystal_system == gemmi::CrystalSystem::Monoclinic) {
                const double beta_lo = std::max(1e-6, M_PI * (data.min_angle_deg / 180.0));
                const double beta_hi = std::min(M_PI - 1e-6, M_PI * (data.max_angle_deg / 180.0));
                problem.SetParameterLowerBound(latt_vec2, 0, beta_lo);
                problem.SetParameterUpperBound(latt_vec2, 0, beta_hi);
            } else if (data.crystal_system == gemmi::CrystalSystem::Triclinic) {
                // α, β, γ bounds (radians)
                const double alo = M_PI * (data.min_angle_deg / 180.0);
                const double ahi = M_PI * (data.max_angle_deg / 180.0);
                for (int i = 0; i < 3; ++i) {
                    problem.SetParameterLowerBound(latt_vec2, i, alo);
                    problem.SetParameterUpperBound(latt_vec2, i, ahi);
                }
            }
        }

        // Configure solver
        ceres::Solver::Options options;
        options.linear_solver_type = ceres::DENSE_QR;
        options.minimizer_progress_to_stdout = false;
        options.max_solver_time_in_seconds = data.max_time;
        options.logging_type = ceres::LoggingType::SILENT;
        ceres::Solver::Summary summary;

        // Run optimization
        ceres::Solve(options, &problem, &summary);

        if (data.refine_beam_center) {
            data.beam_corr_x = data.geom.GetBeamX_pxl() - beam_x;
            data.beam_corr_y = data.geom.GetBeamY_pxl() - beam_y;
            data.geom.BeamX_pxl(beam_x).BeamY_pxl(beam_y);
        }

        if (data.refine_distance_mm)
            data.geom.DetectorDistance_mm(distance_mm);

        if (data.refine_detector_angles)
            data.geom.PoniRot1_rad(detector_rot[0]).PoniRot2_rad(detector_rot[1]);

        if (data.axis && data.refine_rotation_axis)
            data.axis.value().Axis(Coord(rot_vec[0], rot_vec[1], rot_vec[2]));

        if (data.crystal_system == gemmi::CrystalSystem::Orthorhombic)
            data.latt = AngleAxisAndLengthsToLattice(latt_vec0, latt_vec1, false);
        else if (data.crystal_system == gemmi::CrystalSystem::Tetragonal) {
            latt_vec1[1] = latt_vec1[0];
            data.latt = AngleAxisAndLengthsToLattice(latt_vec0, latt_vec1, false);
        } else if (data.crystal_system == gemmi::CrystalSystem::Cubic) {
            latt_vec1[1] = latt_vec1[0];
            latt_vec1[2] = latt_vec1[0];
            data.latt = AngleAxisAndLengthsToLattice(latt_vec0, latt_vec1, false);
        } else if (data.crystal_system == gemmi::CrystalSystem::Hexagonal) {
            latt_vec1[1] = latt_vec1[0];
            data.latt = AngleAxisAndLengthsToLattice(latt_vec0, latt_vec1, true);
        } else if (data.crystal_system == gemmi::CrystalSystem::Monoclinic) {
            data.latt = AngleAxisLengthsBetaToLattice_Mono(latt_vec0, latt_vec1, latt_vec2[0]);
        } else {
            // Triclinic: reconstruct with generic B from α,β,γ
            const Eigen::Vector3d r(latt_vec0[0], latt_vec0[1], latt_vec0[2]);
            const double angle = r.norm();
            Eigen::Matrix3d R = Eigen::Matrix3d::Identity();
            if (angle > 0.0)
                R = Eigen::AngleAxisd(angle, r / angle).toRotationMatrix();

            Eigen::Matrix3d B = Eigen::Matrix3d::Identity();
            const double ca = std::cos(latt_vec2[0]);
            const double cb = std::cos(latt_vec2[1]);
            const double cg = std::cos(latt_vec2[2]);
            const double sg = std::sin(latt_vec2[2]);

            // a along x, b in x-y, c general
            B(0, 0) = 1.0;
            B(1, 0) = 0.0;
            B(2, 0) = 0.0;
            B(0, 1) = cg;
            B(1, 1) = sg;
            B(2, 1) = 0.0;

            const double cx = cb;
            const double cy = (ca - cb * cg) / sg;
            const double cz = std::sqrt(std::max(0.0, 1.0 - cx * cx - cy * cy));

            B(0, 2) = cx;
            B(1, 2) = cy;
            B(2, 2) = cz;

            Eigen::DiagonalMatrix<double, 3> D(latt_vec1[0], latt_vec1[1], latt_vec1[2]);
            Eigen::Matrix3d latt = R * D * B;

            data.latt = CrystalLattice(Coord(latt(0, 0), latt(1, 0), latt(2, 0)),
                                       Coord(latt(0, 1), latt(1, 1), latt(2, 1)),
                                       Coord(latt(0, 2), latt(1, 2), latt(2, 2)));
        }
        data.latt.Regularize(data.crystal_system);

        return true;
    } catch (...) {
        // Convergence problems, likely not updated
        return false;
    }
}

bool XtalOptimizer(XtalOptimizerData &data, const std::vector<SpotToSave> &spots) {
    if (!XtalOptimizerInternal(data, spots, 0.3))
        return false;
    XtalOptimizerInternal(data, spots, 0.2);
    return XtalOptimizerInternal(data, spots, 0.1);
}