Jungfraujoch/image_analysis/structure_refinement/ModelScaling.cpp

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

#include "ModelScaling.h"

#include <algorithm>
#include <cmath>
#include <vector>

#include "../../common/ParallelFor.h"

namespace {

// gemmi::Scaling<float> as a grid point fits it: the same parameters, model values, derivatives
// and R. The solvent pair is fixed there, so |Fcalc + k_sol exp(-b_sol s^2) Fmask| of a reflection
// is the same at every evaluation of the solver; it is taken once per grid point here rather than
// at every evaluation, where it was most of the cost of the fit. Every expression is the one
// scaling.hpp evaluates, in the same types, so every number is the same to the bit.
struct FixedSolventFit {
    struct Point {
        gemmi::Miller hkl;
        float fobs;
        float fcalc_abs;   // std::abs(Scaling::get_fcalc(p))
        double get_y() const { return fobs; }
        double get_weight() const { return 1.0; }
    };
    const std::vector<gemmi::Vec6> &constraint_matrix;
    double k_overall = 1.0;
    gemmi::SMat33<double> b_star{0, 0, 0, 0, 0, 0};
    std::vector<Point> points;

    explicit FixedSolventFit(const gemmi::Scaling<float> &s) : constraint_matrix(s.constraint_matrix) {}

    // The reflections at the solvent pair of `s`, and its scale as the start of the fit.
    void Start(const gemmi::Scaling<float> &s) {
        k_overall = s.k_overall;
        b_star = s.b_star;
        points.resize(s.points.size());
        for (size_t i = 0; i < points.size(); ++i)
            points[i] = {s.points[i].hkl, s.points[i].fobs, std::abs(s.get_fcalc(s.points[i]))};
    }

    // Scaling::get_parameters(), set_parameters(), get_overall_scale_factor(), compute_value() and
    // compute_value_and_derivatives(), with k_sol and b_sol fixed.
    std::vector<double> get_parameters() const {
        std::vector<double> ret;
        ret.push_back(k_overall);
        for (const gemmi::Vec6 &v : constraint_matrix)
            ret.push_back(gemmi::vec6_dot(v, b_star));
        return ret;
    }
    void set_parameters(const double *p) {
        k_overall = p[0];
        int n = 0;
        b_star = {0, 0, 0, 0, 0, 0};
        for (const gemmi::Vec6 &row : constraint_matrix) {
            double d = p[++n];
            b_star.u11 += row[0] * d;
            b_star.u22 += row[1] * d;
            b_star.u33 += row[2] * d;
            b_star.u12 += row[3] * d;
            b_star.u13 += row[4] * d;
            b_star.u23 += row[5] * d;
        }
    }
    void set_parameters(const std::vector<double> &p) { set_parameters(p.data()); }
    double get_overall_scale_factor(const gemmi::Miller &hkl) const {
        return k_overall * std::exp(-0.25 * b_star.r_u_r(hkl));
    }
    double compute_value(const Point &p) const {
        return p.fcalc_abs * (float) get_overall_scale_factor(p.hkl);
    }
    double compute_value_and_derivatives(const Point &p, std::vector<double> &dy_da) const {
        gemmi::Vec3 h(p.hkl);
        double kaniso = std::exp(-0.25 * b_star.r_u_r(h));
        double fcalc_abs = p.fcalc_abs;
        int n = 1;
        double fe = fcalc_abs * kaniso;
        double y = k_overall * fe;
        dy_da[0] = fe;
        gemmi::SMat33<double> du = {
            -0.25 * y * (h.x * h.x),
            -0.25 * y * (h.y * h.y),
            -0.25 * y * (h.z * h.z),
            -0.5 * y * (h.x * h.y),
            -0.5 * y * (h.x * h.z),
            -0.5 * y * (h.y * h.z),
        };
        for (size_t j = 0; j < constraint_matrix.size(); ++j)
            dy_da[n + j] = gemmi::vec6_dot(constraint_matrix[j], du);
        return y;
    }
};

// R-factor of the current parameters over the fitted reflections. This is what the grid is
// selected on, and it is the quantity the scale exists to make small.
double RFactor(const FixedSolventFit &fit) {
    double num = 0, den = 0;
    for (const auto &p : fit.points) {
        num += std::fabs(p.fobs - fit.compute_value(p));
        den += p.fobs;
    }
    return den > 0 ? num / den : 1.0;
}

}  // namespace

// Following the phenix bulk-solvent and scaling procedure: k_sol and b_sol by a grid search, with
// the overall scale and the anisotropic B refitted at every grid point - Afonine, Grosse-Kunstleve
// & Adams, Acta Cryst. D61, 850-855, 2005, which searches b_sol over 10-80 A^2 in steps of 5.
// The fit is unweighted, as in both phenix and Refmac (Murshudov, Skubak, Lebedev, Pannu, Steiner,
// Nicholls, Winn, Long & Vagin, Acta Cryst. D67, 355-367, 2011, eq. 11). The physical range and the
// starting values are those of Fokine & Urzhumtsev, Acta Cryst. D58, 1387-1392, 2002.
//
// The point of the grid is that k_sol and b_sol cannot leave the physical box: gemmi's own
// fit_parameters() is an unbounded Levenberg-Marquardt, and on this corpus it reached b_sol of
// 1707 A^2 - a solvent term switched off in all but the lowest-resolution shell. Here the solvent
// pair is held fixed at each grid point and only the overall scale and the symmetry-constrained
// anisotropic B are refined, which is the well-conditioned half of the problem and is left to
// gemmi's solver rather than reimplemented.
//
// Every grid point is its own fit: fit_isotropic_b_approximately() sets k_overall and b_star from the
// data and the point's solvent pair alone, so a point does not depend on the one fitted before it, and
// the points run in parallel, each chunk on its own copy of `scaling`. The winner is then read off in
// grid order with the serial rule (lowest finite R, the first on a tie), so the answer is the serial
// loop's bit for bit. The one exception is fit_isotropic_b_approximately() finding five or fewer
// reflections to fit on - it then returns without setting anything and a point WOULD start from where
// the previous one ended - so there the grid is walked in order, on `scaling` itself, as it always was.
ModelScaleReport FitModelScale(gemmi::Scaling<float> &scaling, ModelScaleBox box, size_t nthreads) {
    ModelScaleReport report;
    report.n_points = static_cast<int>(scaling.points.size());
    if (scaling.points.size() < 20)
        return report;

    const bool had_solvent = scaling.use_solvent;
    scaling.fix_k_sol = true;      // the grid owns the solvent pair; the solver never sees it
    scaling.fix_b_sol = true;

    // The reflections fit_isotropic_b_approximately() fits on (its own filter).
    int n_isotropic = 0;
    for (const auto &p : scaling.points)
        if (!(p.fobs < 1 || p.fobs < p.sigma))
            ++n_isotropic;
    const bool independent = n_isotropic > 5;

    double best_r = -1, best_k_sol = 0.35, best_b_sol = 46.0, best_k_overall = 1.0;
    gemmi::SMat33<double> best_b_star{0, 0, 0, 0, 0, 0};

    struct PointFit { double k_sol, b_sol, r = NAN, k_overall = 1.0; gemmi::SMat33<double> b_star{0, 0, 0, 0, 0, 0}; };
    auto fit_point = [](gemmi::Scaling<float> &s, FixedSolventFit &fit, PointFit &pf) {
        s.k_sol = pf.k_sol;
        s.b_sol = pf.b_sol;
        s.fit_isotropic_b_approximately();   // a fresh starting point for this solvent pair
        fit.Start(s);
        gemmi::LevMar levmar;
        levmar.fit(fit);                     // k_overall + anisotropic B only
        s.k_overall = fit.k_overall;
        s.b_star = fit.b_star;
        pf.r = RFactor(fit);
        pf.k_overall = fit.k_overall;
        pf.b_star = fit.b_star;
    };
    auto try_points = [&](std::vector<PointFit> &pts) {
        if (independent)
            ParallelChunks(static_cast<int>(pts.size()), nthreads, [&](int lo, int hi) {
                gemmi::Scaling<float> local = scaling;
                FixedSolventFit fit(local);
                for (int i = lo; i < hi; ++i)
                    fit_point(local, fit, pts[i]);
            });
        else {
            FixedSolventFit fit(scaling);
            for (auto &pf : pts)
                fit_point(scaling, fit, pf);
        }
        for (const auto &pf : pts) {
            ++report.n_grid;
            // A diverged fit gives r = NaN; latched as best_r it wins every later r < best_r.
            if (std::isfinite(pf.r) && (best_r < 0 || pf.r < best_r)) {
                best_r = pf.r;
                best_k_sol = pf.k_sol;
                best_b_sol = pf.b_sol;
                best_k_overall = pf.k_overall;
                best_b_star = pf.b_star;
            }
        }
    };

    // Coarse pass over the whole box, then one refinement pass around the winner.
    std::vector<PointFit> coarse;
    for (double ks = box.k_lo; ks <= box.k_hi + 1e-9; ks += 0.05)
        for (double bs = box.b_lo; bs <= box.b_hi + 1e-9; bs += 10.0)
            coarse.push_back(PointFit{ks, bs});
    try_points(coarse);
    const double k0 = best_k_sol, b0 = best_b_sol;
    const double k_hi2 = std::min(box.k_hi, k0 + 0.05);
    const double b_hi2 = std::min(box.b_hi, b0 + 10.0);
    std::vector<PointFit> fine;
    for (double ks = std::max(box.k_lo, k0 - 0.05); ks <= k_hi2 + 1e-9; ks += 0.025)
        for (double bs = std::max(box.b_lo, b0 - 10.0); bs <= b_hi2 + 1e-9; bs += 5.0)
            fine.push_back(PointFit{ks, bs});
    try_points(fine);

    scaling.k_sol = best_k_sol;
    scaling.b_sol = best_b_sol;
    scaling.k_overall = best_k_overall;
    scaling.b_star = best_b_star;
    scaling.use_solvent = had_solvent;
    report.r_work_fit = best_r;
    return report;
}