leonarski_fandClaude Opus 5.5
d271a55a74
All exact to the bit (bench against the previous FitModelScale on P1, P2_1, P2_12_12_1, P4_32_12, P6_122, P2_13, I23 and the dependent n<=5 path; the ModelScaling cases; validation outputs identical on real data): - the start of a grid point (fit_isotropic_b_approximately) is computed from the same |Fcalc| the fit takes, once instead of twice, and without copying the Scaling's points per chunk; - gemmi's Levenberg-Marquardt is followed in a copy (LevMarFit) whose compute_lm_matrices is templated on the parameter count (2..7), so alpha/beta stay in registers; a zero derivative row adds +0 instead of being skipped (alpha/beta are never -0), and the full square is summed (the lower half is gemmi's, the upper is its mirror) - branch-free and vectorised; - grid points are scheduled one per task (ParallelFor) instead of fixed chunks; - a fine-pass pair bit-identical to a coarse-pass pair reuses that fit. Bench (single thread, 48k reflections, P2_1): 1.58 -> 1.33 s; ~15-25% on the other groups. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01SVmAWnzCmRKAXVUCdc4iNi
383 lines
17 KiB
C++
383 lines
17 KiB
C++
// SPDX-FileCopyrightText: 2026 Filip Leonarski, Paul Scherrer Institute <filip.leonarski@psi.ch>
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// SPDX-License-Identifier: GPL-3.0-only
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// FixedSolventFit follows the scaling target of GEMMI's scaling.hpp
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// (https://github.com/project-gemmi/gemmi/blob/master/include/gemmi/scaling.hpp), and
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// ComputeLMMatrices / LevMarFit the Levenberg-Marquardt of GEMMI's levmar.hpp
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// (https://github.com/project-gemmi/gemmi/blob/master/include/gemmi/levmar.hpp)
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// (c) Global Phasing Ltd., Mozilla Public License Version 2.0
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#include "ModelScaling.h"
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#include <algorithm>
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#include <cmath>
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#include <complex>
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#include <vector>
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#include "../../common/ParallelFor.h"
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namespace {
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// gemmi::Scaling<float> as a grid point fits it: the same starting point, parameters, model values,
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// derivatives and R. The solvent pair is fixed there, so |Fcalc + k_sol exp(-b_sol s^2) Fmask| of a
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// reflection is the same at every evaluation of the solver; it is taken once per grid point here rather than
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// at every evaluation, where it was most of the cost of the fit. Every expression is the one
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// scaling.hpp evaluates, in the same types, so every number is the same to the bit.
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struct FixedSolventFit {
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struct Point {
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gemmi::Miller hkl;
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float fobs;
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float fcalc_abs; // std::abs(Scaling::get_fcalc(p))
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double get_y() const { return fobs; }
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double get_weight() const { return 1.0; }
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};
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const std::vector<gemmi::Vec6> &constraint_matrix;
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double k_overall = 1.0;
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gemmi::SMat33<double> b_star{0, 0, 0, 0, 0, 0};
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std::vector<Point> points;
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explicit FixedSolventFit(const gemmi::Scaling<float> &s) : constraint_matrix(s.constraint_matrix) {}
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// The reflections of `s` at the solvent pair (k_sol, b_sol), and the start of the fit there: what
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// Scaling::fit_isotropic_b_approximately() sets, from the same |Fcalc|, taken once for both. Where
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// that finds five or fewer reflections to fit on it sets nothing, and the fit starts from
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// (k_start, b_start) - the scale gemmi's would have been left at.
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void Start(const gemmi::Scaling<float> &s, double k_sol, double b_sol,
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double k_start, const gemmi::SMat33<double> &b_start) {
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k_overall = k_start;
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b_star = b_start;
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points.resize(s.points.size());
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double sx = 0, sy = 0, sxx = 0, sxy = 0;
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int n = 0;
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for (size_t i = 0; i < points.size(); ++i) {
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const auto &p = s.points[i];
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// Scaling::get_fcalc() at (k_sol, b_sol)
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const std::complex<float> fcalc =
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s.use_solvent ? p.fcmol + (float) (k_sol * std::exp(-b_sol * p.stol2)) * p.fmask : p.fcmol;
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points[i] = {p.hkl, p.fobs, std::abs(fcalc)};
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if (p.fobs < 1 || p.fobs < p.sigma) // skip weak reflections
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continue;
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double fcalc_abs = points[i].fcalc_abs;
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double x = p.stol2;
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double y = std::log(static_cast<float>(p.fobs / fcalc_abs));
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sx += x;
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sy += y;
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sxx += x * x;
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sxy += x * y;
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n += 1;
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}
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if (n <= 5)
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return;
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double slope = (n * sxy - sx * sy) / (n * sxx - sx * sx);
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double intercept = (sy - slope * sx) / n;
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double b_iso = -slope;
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k_overall = std::exp(intercept);
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b_star = gemmi::SMat33<double>{b_iso, b_iso, b_iso, 0, 0, 0}.transformed_by(s.cell.frac.mat);
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}
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// Scaling::get_parameters(), set_parameters(), get_overall_scale_factor(), compute_value() and
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// compute_value_and_derivatives(), with k_sol and b_sol fixed.
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std::vector<double> get_parameters() const {
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std::vector<double> ret;
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ret.push_back(k_overall);
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for (const gemmi::Vec6 &v : constraint_matrix)
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ret.push_back(gemmi::vec6_dot(v, b_star));
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return ret;
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}
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void set_parameters(const double *p) {
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k_overall = p[0];
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int n = 0;
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b_star = {0, 0, 0, 0, 0, 0};
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for (const gemmi::Vec6 &row : constraint_matrix) {
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double d = p[++n];
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b_star.u11 += row[0] * d;
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b_star.u22 += row[1] * d;
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b_star.u33 += row[2] * d;
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b_star.u12 += row[3] * d;
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b_star.u13 += row[4] * d;
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b_star.u23 += row[5] * d;
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}
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}
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void set_parameters(const std::vector<double> &p) { set_parameters(p.data()); }
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double get_overall_scale_factor(const gemmi::Miller &hkl) const {
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return k_overall * std::exp(-0.25 * b_star.r_u_r(hkl));
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}
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double compute_value(const Point &p) const {
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return p.fcalc_abs * (float) get_overall_scale_factor(p.hkl);
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}
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// For NA parameters: the B components are NA - 1 constraint rows.
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template <int NA>
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double compute_value_and_derivatives(const Point &p, double *dy_da) const {
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gemmi::Vec3 h(p.hkl);
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double kaniso = std::exp(-0.25 * b_star.r_u_r(h));
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double fcalc_abs = p.fcalc_abs;
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int n = 1;
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double fe = fcalc_abs * kaniso;
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double y = k_overall * fe;
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dy_da[0] = fe;
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gemmi::SMat33<double> du = {
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-0.25 * y * (h.x * h.x),
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-0.25 * y * (h.y * h.y),
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-0.25 * y * (h.z * h.z),
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-0.5 * y * (h.x * h.y),
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-0.5 * y * (h.x * h.z),
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-0.5 * y * (h.y * h.z),
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};
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for (int j = 0; j < NA - 1; ++j)
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dy_da[n + j] = gemmi::vec6_dot(constraint_matrix[j], du);
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return y;
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}
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};
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// R-factor of the current parameters over the fitted reflections. This is what the grid is
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// selected on, and it is the quantity the scale exists to make small.
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double RFactor(const FixedSolventFit &fit) {
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double num = 0, den = 0;
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for (const auto &p : fit.points) {
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num += std::fabs(p.fobs - fit.compute_value(p));
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den += p.fobs;
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}
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return den > 0 ? num / den : 1.0;
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}
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// gemmi's compute_lm_matrices() (levmar.hpp) on a FixedSolventFit of NA parameters. With the count
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// known to the compiler the matrices are held in registers rather than written to memory at every
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// reflection; the operations are gemmi's, in gemmi's order, so the matrices are gemmi's to the bit.
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// A reflection's weight is 1 (FixedSolventFit::Point::get_weight), which gemmi multiplies by.
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// gemmi skips the row of a derivative that is exactly 0; here the row gets +0 instead, which keeps the
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// loop free of branches and changes nothing: an element of alpha or beta is never -0, the one value
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// adding +0 would change, since it starts at +0 and a sum is only -0 when both its terms are. And
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// where gemmi fills the lower half of alpha, the whole square is summed here, a rectangle the compiler
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// can vectorise; the lower half is gemmi's, and the upper is replaced by it at the end, as in gemmi.
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template <int NA>
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double ComputeLMMatrices(const FixedSolventFit &fit, double *alpha_out, double *beta_out) {
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long double wssr = 0; // long double here notably increases the accuracy
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double alpha[NA * NA] = {}, beta[NA] = {};
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double dy_da[NA];
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for (const auto &p : fit.points) {
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double y = fit.compute_value_and_derivatives<NA>(p, dy_da);
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double dy_sig = p.get_y() - y;
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for (int j = 0; j != NA; ++j) {
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const bool used = dy_da[j] != 0;
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for (int k = 0; k < NA; ++k) {
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const double a = dy_da[j] * dy_da[k];
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alpha[NA * j + k] += used ? a : 0.0;
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}
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const double b = dy_sig * dy_da[j];
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beta[j] += used ? b : 0.0;
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}
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wssr += gemmi::sq(dy_sig);
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}
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// The upper half of alpha is the lower half's mirror, as in gemmi.
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for (int j = 1; j < NA; j++)
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for (int k = 0; k < j; k++)
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alpha[NA * k + j] = alpha[NA * j + k];
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std::copy(alpha, alpha + NA * NA, alpha_out);
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std::copy(beta, beta + NA, beta_out);
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return (double) wssr;
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}
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// gemmi's LevMar::fit() (levmar.hpp) with its default settings, on ComputeLMMatrices<NA>() - the same
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// iterations to the same answer, bit for bit.
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template <int NA>
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void LevMarFit(FixedSolventFit &target) {
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const int eval_limit = 100;
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const double lambda_limit = 1e+15;
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const double stop_rel_change = 1e-5;
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const double lambda_up_factor = 10;
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const double lambda_down_factor = 0.1;
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const double lambda_start = 0.001;
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std::vector<double> initial_a = target.get_parameters();
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std::vector<double> best_a = initial_a;
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double lambda = lambda_start;
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double alpha[NA * NA], beta[NA], temp_alpha[NA * NA];
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std::vector<double> temp_beta(NA);
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const double initial_wssr = ComputeLMMatrices<NA>(target, alpha, beta);
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double wssr = initial_wssr;
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int small_change_counter = 0;
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int eval_count = 1; // number of function evaluations so far
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for (;;) {
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if (eval_limit > 0 && eval_count >= eval_limit)
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break;
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// prepare next parameters -> temp_beta
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std::copy(alpha, alpha + NA * NA, temp_alpha);
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// Using '*=' not '+=' below applies the dampling factor as:
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// J^T J + lambda * diag(J^T J); not ... + lambda * I.
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for (int j = 0; j < NA; j++)
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temp_alpha[NA * j + j] *= (1.0 + lambda);
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std::copy(beta, beta + NA, temp_beta.begin());
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// Matrix solution (Ax=b) temp_alpha * da == temp_beta
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gemmi::jordan_solve(temp_alpha, temp_beta.data(), NA);
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for (int i = 0; i < NA; i++)
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// put new a[] into temp_beta[]
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temp_beta[i] += best_a[i];
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target.set_parameters(temp_beta);
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double new_wssr = gemmi::compute_wssr(target);
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++eval_count;
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if (new_wssr < wssr) {
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double rel_change = (wssr - new_wssr) / wssr;
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wssr = new_wssr;
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best_a = temp_beta;
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if (wssr == 0)
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break;
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// termination criterion: negligible change of wssr
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if (rel_change < stop_rel_change) {
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if (++small_change_counter >= 2)
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break;
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} else {
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small_change_counter = 0;
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}
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ComputeLMMatrices<NA>(target, alpha, beta);
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++eval_count;
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lambda *= lambda_down_factor;
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} else { // worse fitting
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if (lambda > lambda_limit) // termination criterion: large lambda
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break;
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lambda *= lambda_up_factor;
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}
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}
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target.set_parameters(wssr < initial_wssr ? best_a : initial_a);
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}
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// LevMarFit() at the fit's parameter count: k_overall and one per symmetry-allowed component of B,
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// which is one (cubic) to six (triclinic).
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void LevMarFit(FixedSolventFit &fit) {
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switch (fit.constraint_matrix.size()) {
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case 1: LevMarFit<2>(fit); break;
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case 2: LevMarFit<3>(fit); break;
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case 3: LevMarFit<4>(fit); break;
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case 4: LevMarFit<5>(fit); break;
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case 5: LevMarFit<6>(fit); break;
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default: LevMarFit<7>(fit); break;
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}
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}
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} // namespace
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// Following the phenix bulk-solvent and scaling procedure: k_sol and b_sol by a grid search, with
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// the overall scale and the anisotropic B refitted at every grid point - Afonine, Grosse-Kunstleve
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// & Adams, Acta Cryst. D61, 850-855, 2005, which searches b_sol over 10-80 A^2 in steps of 5.
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// The fit is unweighted, as in both phenix and Refmac (Murshudov, Skubak, Lebedev, Pannu, Steiner,
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// Nicholls, Winn, Long & Vagin, Acta Cryst. D67, 355-367, 2011, eq. 11). The physical range and the
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// starting values are those of Fokine & Urzhumtsev, Acta Cryst. D58, 1387-1392, 2002.
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//
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// The point of the grid is that k_sol and b_sol cannot leave the physical box: gemmi's own
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// fit_parameters() is an unbounded Levenberg-Marquardt, and on this corpus it reached b_sol of
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// 1707 A^2 - a solvent term switched off in all but the lowest-resolution shell. Here the solvent
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// pair is held fixed at each grid point and only the overall scale and the symmetry-constrained
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// anisotropic B are refined, which is the well-conditioned half of the problem and is left to
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// gemmi's solver rather than reimplemented.
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//
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// Every grid point is its own fit: fit_isotropic_b_approximately() sets k_overall and b_star from the
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// data and the point's solvent pair alone, so a point does not depend on the one fitted before it, and
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// the points run in parallel, one point per task, each on a FixedSolventFit of its own. The winner is
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// then read off in grid order with the serial rule (lowest finite R, the first on a tie), so the answer
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// is the serial loop's bit for bit. For the same reason a pair the refinement pass shares with the
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// coarse one - the same two numbers, to the bit - is the same fit, and is taken from there rather than
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// made again. The one exception is fit_isotropic_b_approximately() finding five or fewer reflections to
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// fit on - it then returns without setting anything and a point WOULD start from where the previous one
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// ended - so there the grid is walked in order, each point from where the last ended, as it always was.
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ModelScaleReport FitModelScale(gemmi::Scaling<float> &scaling, ModelScaleBox box, size_t nthreads) {
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ModelScaleReport report;
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report.n_points = static_cast<int>(scaling.points.size());
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if (scaling.points.size() < 20)
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return report;
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const bool had_solvent = scaling.use_solvent;
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scaling.fix_k_sol = true; // the grid owns the solvent pair; the solver never sees it
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scaling.fix_b_sol = true;
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// The reflections fit_isotropic_b_approximately() fits on (its own filter).
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int n_isotropic = 0;
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for (const auto &p : scaling.points)
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if (!(p.fobs < 1 || p.fobs < p.sigma))
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++n_isotropic;
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const bool independent = n_isotropic > 5;
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double best_r = -1, best_k_sol = 0.35, best_b_sol = 46.0, best_k_overall = 1.0;
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gemmi::SMat33<double> best_b_star{0, 0, 0, 0, 0, 0};
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struct PointFit { double k_sol, b_sol, r = NAN, k_overall = 1.0; gemmi::SMat33<double> b_star{0, 0, 0, 0, 0, 0}; };
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// The scale the walk stands at, which a point starts from only where the data give it no start of its own.
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double k_last = scaling.k_overall;
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gemmi::SMat33<double> b_last = scaling.b_star;
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auto fit_point = [&scaling](FixedSolventFit &fit, PointFit &pf, double k_start,
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const gemmi::SMat33<double> &b_start) {
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fit.Start(scaling, pf.k_sol, pf.b_sol, k_start, b_start);
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LevMarFit(fit); // k_overall + anisotropic B only
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pf.r = RFactor(fit);
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pf.k_overall = fit.k_overall;
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pf.b_star = fit.b_star;
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};
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std::vector<PointFit> fitted; // every point fitted so far, in grid order
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auto try_points = [&](std::vector<PointFit> &pts) {
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if (independent) {
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std::vector<int> todo;
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for (int i = 0; i < static_cast<int>(pts.size()); ++i) {
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const auto same = std::find_if(fitted.begin(), fitted.end(), [&](const PointFit &f) {
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return f.k_sol == pts[i].k_sol && f.b_sol == pts[i].b_sol;
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});
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if (same != fitted.end())
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pts[i] = *same;
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else
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todo.push_back(i);
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}
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ParallelFor(static_cast<int>(todo.size()), nthreads, [&](int j) {
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FixedSolventFit fit(scaling);
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fit_point(fit, pts[todo[j]], k_last, b_last);
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});
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} else {
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FixedSolventFit fit(scaling);
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for (auto &pf : pts) {
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fit_point(fit, pf, k_last, b_last);
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k_last = pf.k_overall;
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b_last = pf.b_star;
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}
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}
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for (const auto &pf : pts) {
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++report.n_grid;
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// A diverged fit gives r = NaN; latched as best_r it wins every later r < best_r.
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if (std::isfinite(pf.r) && (best_r < 0 || pf.r < best_r)) {
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best_r = pf.r;
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best_k_sol = pf.k_sol;
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best_b_sol = pf.b_sol;
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best_k_overall = pf.k_overall;
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best_b_star = pf.b_star;
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}
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}
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fitted.insert(fitted.end(), pts.begin(), pts.end());
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};
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// Coarse pass over the whole box, then one refinement pass around the winner.
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std::vector<PointFit> coarse;
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for (double ks = box.k_lo; ks <= box.k_hi + 1e-9; ks += 0.05)
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for (double bs = box.b_lo; bs <= box.b_hi + 1e-9; bs += 10.0)
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coarse.push_back(PointFit{ks, bs});
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try_points(coarse);
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const double k0 = best_k_sol, b0 = best_b_sol;
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const double k_hi2 = std::min(box.k_hi, k0 + 0.05);
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const double b_hi2 = std::min(box.b_hi, b0 + 10.0);
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std::vector<PointFit> fine;
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for (double ks = std::max(box.k_lo, k0 - 0.05); ks <= k_hi2 + 1e-9; ks += 0.025)
|
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for (double bs = std::max(box.b_lo, b0 - 10.0); bs <= b_hi2 + 1e-9; bs += 5.0)
|
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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;
|
|
}
|