leonarski_f
8a123e794d
--mode scale re-measured the rocking width on the stored reflections, so on any file whose frames were predicted through the run's curve it merged with a different curve than the mx run did. The curve the post-refinement used (formula, table, radial scale) is now carried in the EndMessage (StillsRunWidth) and written to the master: /entry/MX/stillsRockingWidthFormula [gamma0 1/A, gamma_e rad, bandwidth sigma], /entry/MX/stillsRadialScale, /entry/MX/stillsRockingWidthTableDstar and /entry/MX/stillsRockingWidthTable (1/A). The reader returns it, and --mode scale passes it to the post-refinement. A file without it is re-measured as before. MeasureRunWidth grouped each frame's reflections by the frame's window, taken as the largest excitation error it predicted. With a window that follows sigma(d*) that is the high-resolution window, applied to the frame's low-resolution reflections too. Given the curve the frames were predicted through, the window is now that curve at the reflection's own resolution; without one, the frame's largest excitation error as before. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_015CeEGgpKdfkCTJb3YNMJcu (cherry picked from commit 992343d0206489991880bb927efc79131134a1d9)
794 lines
40 KiB
C++
794 lines
40 KiB
C++
// SPDX-FileCopyrightText: 2025 Filip Leonarski, Paul Scherrer Institute <filip.leonarski@psi.ch>
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// SPDX-License-Identifier: GPL-3.0-only
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#include "StillsPartialityRefine.h"
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#include <algorithm>
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#include <array>
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#include <atomic>
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#include <cmath>
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#include <future>
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#include <thread>
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#include <vector>
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#include <Eigen/Dense>
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#include <ceres/rotation.h>
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#include "Merge.h"
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#include "../../common/Logger.h"
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#include "../../common/ThreadAffinity.h"
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namespace {
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constexpr size_t MIN_FIT_REFLECTIONS = 20;
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constexpr double kRadToDeg = 180.0 / 3.14159265358979323846;
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// Model error of the per-crystal scale fit, as a fraction of the predicted intensity - ScaleOnTheFly's.
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constexpr double SCALE_MODEL_ERROR = 0.3;
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double SafeInv(double x, double fallback) {
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if (!std::isfinite(x) || x == 0.0)
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return fallback;
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return 1.0 / x;
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}
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// One accepted reflection reduced to the physical partiality fit: the base reciprocal vector q (crystal
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// frame at the stored per-image orientation), the reference full intensity, the measured intensity, the
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// reciprocal of the prescaling correction (the factor that turns a true intensity back into counts),
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// the measured variance and its background part, and the weight the tilt is refined with.
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// dist_ewald / partiality are recomputed from q under the refined tilt.
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struct FitObs {
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double qx, qy, qz;
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double Iref;
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double Iobs;
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double inv_corr; // 1 / (prescaling_corr * qe_corr * flight_corr)
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double sigma2;
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double var_bkg;
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double weight; // 1 / sqrt(variance at the current model), set with each G
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};
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// The variance of an observation at the model m: background, the counting noise of m and the model error.
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double ModelVariance(const FitObs &o, double m) {
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return o.var_bkg + std::max(0.0, m) + SCALE_MODEL_ERROR * SCALE_MODEL_ERROR * m * m;
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}
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double VecLen(double x, double y, double z) { return std::sqrt(x * x + y * y + z * z); }
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// The rocking width sigma^2 at a reflection of resolution d* (and |q_z|, for the bandwidth term): the
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// run's table where there is one - linear in d* between its shells, held beyond the outermost - else
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// the three-term formula.
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struct Width {
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double gamma0, gamma_e, bw;
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const std::vector<double> *table_dstar = nullptr, *table_s = nullptr;
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double Sigma2(double dstar, double qz) const {
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if (table_dstar && !table_dstar->empty()) {
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const auto &x = *table_dstar;
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const auto &y = *table_s;
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double s = y.front();
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if (dstar >= x.back())
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s = y.back();
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else if (dstar > x.front()) {
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const size_t i = std::upper_bound(x.begin(), x.end(), dstar) - x.begin();
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s = y[i - 1] + (dstar - x[i - 1]) / (x[i] - x[i - 1]) * (y[i] - y[i - 1]);
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}
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return s * s;
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}
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const double sig_ang = gamma_e * dstar;
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const double sbw = bw * std::fabs(qz);
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return gamma0 * gamma0 + sig_ang * sig_ang + sbw * sbw;
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}
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};
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// Analytic partiality for a reflection whose base reciprocal vector is q, tilted by (psi_x, psi_y).
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// Mirrors BraggPrediction: dist_ewald = |S| - 1/lambda with S = q_rot + S0, and
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// p = exp(-dist_ewald^2 / 2 sigma^2), sigma^2 = gamma0^2 + (gamma_e*d*)^2 + (bw*|q_z|)^2 - three
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// independent broadenings added in quadrature: the reciprocal-lattice point's own radius (gamma0,
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// ~1/domain size, resolution-INdependent), the mosaic/divergence spread (gamma_e*d*, proportional to
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// d*) and the bandwidth smear along the beam. In practice the fit below returns gamma_e ~ 0 and the
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// width is essentially gamma0 - see there.
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double ComputeP(double qx, double qy, double qz,
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double psi_x, double psi_y,
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double s0x, double s0y, double s0z, double inv_lambda,
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const Width &width) {
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double aa[3] = {psi_x, psi_y, 0.0};
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double q[3] = {qx, qy, qz};
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double qr[3];
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ceres::AngleAxisRotatePoint(aa, q, qr);
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const double Sx = qr[0] + s0x, Sy = qr[1] + s0y, Sz = qr[2] + s0z;
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const double de = std::sqrt(Sx * Sx + Sy * Sy + Sz * Sz) - inv_lambda;
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const double dstar = std::sqrt(qr[0] * qr[0] + qr[1] * qr[1] + qr[2] * qr[2]);
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const double sig2 = width.Sigma2(dstar, qr[2]);
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if (!(sig2 > 0.0))
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return 1.0;
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return std::exp(-0.5 * de * de / sig2);
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}
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// The prediction window cuts the rocking curve. Reflections fill a window of half-width W evenly, so
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// their plain moment of de is u = W^2 / 3, and the intensity-weighted moment m of a Gaussian of width
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// s cut at +-W is u * g(a), a = W / s, with g(a) = 3/a^2 (1 - 2 a phi(a) / erf(a / sqrt 2)): 1 for a
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// curve much wider than the window, s^2 / u for a much narrower one. Solves g(a) = m / u for s^2 by
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// bisection (g falls with a). A curve wider than the window cannot be measured through it: empty.
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std::optional<double> UntruncatedVariance(double m, double u) {
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auto g = [](double a) {
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const double phi = std::exp(-0.5 * a * a) / std::sqrt(2.0 * 3.14159265358979323846);
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return 3.0 / (a * a) * (1.0 - 2.0 * a * phi / std::erf(a / std::sqrt(2.0)));
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};
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const double t = m / u;
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double lo = 1.0, hi = 50.0;
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if (!(t < g(lo)))
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return std::nullopt;
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for (int i = 0; i < 60; ++i) {
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const double mid = 0.5 * (lo + hi);
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(g(mid) > t ? lo : hi) = mid;
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}
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const double a = 0.5 * (lo + hi);
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return 3.0 * u / (a * a);
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}
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// Robust per-crystal scale G (linear in G given the model coefficients), the objective of
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// ScaleOnTheFly::SolveScaleIRLS: minimise sum Cauchy_k( (G*coeff - Iobs) / sqrt(var(G*coeff)) ) over G >= 0,
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// the variances re-evaluated at each step's G.
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double SolveScaleIRLS(const std::vector<FitObs> &obs, const std::vector<double> &coeff, double robust_k) {
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double num = 0.0, den = 0.0;
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for (size_t i = 0; i < obs.size(); ++i) {
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num += coeff[i] * obs[i].Iobs / obs[i].sigma2;
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den += coeff[i] * coeff[i] / obs[i].sigma2;
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}
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if (!(den > 0.0) || !std::isfinite(num / den))
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return 1.0;
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double G = std::max(0.0, num / den);
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const double k2 = robust_k * robust_k;
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for (int iter = 0; iter < 30; ++iter) {
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num = den = 0.0;
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for (size_t i = 0; i < obs.size(); ++i) {
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const double res = G * coeff[i] - obs[i].Iobs;
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const double w = 1.0 / (ModelVariance(obs[i], G * coeff[i]) + res * res / k2);
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num += w * coeff[i] * obs[i].Iobs;
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den += w * coeff[i] * coeff[i];
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}
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if (!(den > 0.0) || !std::isfinite(num / den))
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break;
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const double G_prev = G;
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G = std::max(0.0, num / den);
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if (std::abs(G - G_prev) <= 1e-7 * std::max(G, 1.0))
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break;
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}
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return G;
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}
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// The rotation by the angle-axis vector (psi_x, psi_y, 0) as a matrix (Rodrigues), so that one tilt
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// is applied to all the reflections of a crystal by a matrix product each.
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std::array<double, 9> TiltMatrix(double psi_x, double psi_y) {
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const double theta = std::sqrt(psi_x * psi_x + psi_y * psi_y);
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if (theta < 1e-15)
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return {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
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const double kx = psi_x / theta, ky = psi_y / theta;
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const double c = std::cos(theta), s = std::sin(theta), t = 1.0 - c;
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return {c + t * kx * kx, t * kx * ky, s * ky,
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t * kx * ky, c + t * ky * ky, -s * kx,
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-s * ky, s * kx, c};
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}
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// ComputeP with the tilt given as its rotation matrix.
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struct TiltModel {
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double s0x, s0y, s0z, inv_lambda;
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Width width;
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double P(const std::array<double, 9> &R, const FitObs &o) const {
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const double qx = R[0] * o.qx + R[1] * o.qy + R[2] * o.qz;
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const double qy = R[3] * o.qx + R[4] * o.qy + R[5] * o.qz;
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const double qz = R[6] * o.qx + R[7] * o.qy + R[8] * o.qz;
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const double de = VecLen(qx + s0x, qy + s0y, qz + s0z) - inv_lambda;
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const double sig2 = width.Sigma2(VecLen(qx, qy, qz), qz);
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if (!(sig2 > 0.0))
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return 1.0;
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return std::exp(-0.5 * de * de / sig2);
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}
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};
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// Refine the orientation tilt (psi_x, psi_y) holding the scale G fixed: minimise
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// sum_i rho(r_i^2) / 2 + |psi / sigma_prior|^2 / 2, r_i = weight_i (G p_i(psi) Iref_i / corr_i - Iobs_i),
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// with the Cauchy rho(s) = k^2 log(1 + s / k^2) - the intensity-space objective of ScaleOnTheFly, and
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// the Gaussian prior a proper MAP term since r_i is already in sigma units. Levenberg-Marquardt on the
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// normal equations reweighted by rho', the Jacobian by central differences, every trial tilt held inside
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// the bound. Returns false when the cost cannot be evaluated, leaving psi as it came in.
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bool RefineTilt(const std::vector<FitObs> &obs, const TiltModel &model, double G, double robust_k,
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double inv_sigma_prior, double max_tilt, double psi[2]) {
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constexpr int MAX_ITERATIONS = 25;
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constexpr double STEP = 1e-7; // rad, for the central differences
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const double k2 = robust_k * robust_k;
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const double prior2 = inv_sigma_prior * inv_sigma_prior;
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auto cost = [&](const double p[2]) {
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const auto R = TiltMatrix(p[0], p[1]);
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double c = 0.5 * prior2 * (p[0] * p[0] + p[1] * p[1]);
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for (const auto &o: obs) {
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const double r = o.weight * (G * model.P(R, o) * o.inv_corr * o.Iref - o.Iobs);
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c += 0.5 * k2 * std::log1p(r * r / k2);
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}
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return c;
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};
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double current = cost(psi);
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if (!std::isfinite(current))
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return false;
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double lambda = 1e-4;
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for (int iter = 0; iter < MAX_ITERATIONS; ++iter) {
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const auto R = TiltMatrix(psi[0], psi[1]);
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const auto Rxp = TiltMatrix(psi[0] + STEP, psi[1]), Rxm = TiltMatrix(psi[0] - STEP, psi[1]);
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const auto Ryp = TiltMatrix(psi[0], psi[1] + STEP), Rym = TiltMatrix(psi[0], psi[1] - STEP);
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double A00 = prior2, A01 = 0.0, A11 = prior2;
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double b0 = prior2 * psi[0], b1 = prior2 * psi[1];
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for (const auto &o: obs) {
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const double a = o.weight * G * o.inv_corr * o.Iref;
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const double r = a * model.P(R, o) - o.weight * o.Iobs;
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const double jx = a * (model.P(Rxp, o) - model.P(Rxm, o)) / (2.0 * STEP);
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const double jy = a * (model.P(Ryp, o) - model.P(Rym, o)) / (2.0 * STEP);
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const double w = 1.0 / (1.0 + r * r / k2); // rho'
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A00 += w * jx * jx;
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A01 += w * jx * jy;
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A11 += w * jy * jy;
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b0 += w * jx * r;
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b1 += w * jy * r;
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}
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bool accepted = false;
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double trial[2] = {psi[0], psi[1]};
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double trial_cost = current;
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while (lambda < 1e10) {
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const double M00 = A00 * (1.0 + lambda), M11 = A11 * (1.0 + lambda);
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const double det = M00 * M11 - A01 * A01;
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if (!(det > 0.0))
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break;
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trial[0] = std::clamp(psi[0] - (M11 * b0 - A01 * b1) / det, -max_tilt, max_tilt);
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trial[1] = std::clamp(psi[1] - (M00 * b1 - A01 * b0) / det, -max_tilt, max_tilt);
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trial_cost = cost(trial);
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if (std::isfinite(trial_cost) && trial_cost < current) {
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accepted = true;
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lambda = std::max(lambda / 10.0, 1e-12);
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break;
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}
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lambda *= 10.0;
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}
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if (!accepted)
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break;
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const double step = std::hypot(trial[0] - psi[0], trial[1] - psi[1]);
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const double decrease = current - trial_cost;
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psi[0] = trial[0];
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psi[1] = trial[1];
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current = trial_cost;
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if (decrease <= 1e-6 * current || step <= 1e-10)
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break;
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}
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return true;
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}
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}
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StillsPartialityRefine::StillsPartialityRefine(const DiffractionExperiment &x)
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: experiment_(x),
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hkl_key_generator_(x.GetScalingSettings().GetMergeFriedel(), x.GetSpaceGroupOrP1()),
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d_min_limit_(x.GetScalingSettings().GetHighResolutionLimit_A()),
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d_max_limit_(x.GetScalingSettings().GetLowResolutionLimit_A()),
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min_partiality_(x.GetScalingSettings().GetMinPartiality()),
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bandwidth_sigma_(x.GetBandwidthFWHM().value_or(0.0f) / 2.3548f) {}
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double StillsPartialityRefine::RefineOne(IntegrationOutcome &outcome,
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const std::map<HKLKey, double> &reference,
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const std::optional<RunWidth> &run_width,
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double radial_scale) const {
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if (outcome.reflections.empty())
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return 0.0;
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const Coord Astar = outcome.latt.Astar();
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const Coord Bstar = outcome.latt.Bstar();
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const Coord Cstar = outcome.latt.Cstar();
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const Coord S0 = outcome.geom.GetScatteringVector();
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const double inv_lambda = 1.0 / outcome.geom.GetWavelength_A();
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auto base_q = [&](const Reflection &r) {
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return (Astar * static_cast<float>(r.h) + Bstar * static_cast<float>(r.k)
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+ Cstar * static_cast<float>(r.l)) * static_cast<float>(radial_scale);
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};
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// Collect the reflections that constrain the fit (accepted, non-ice, finite, present in the reference).
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std::vector<FitObs> obs;
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obs.reserve(outcome.reflections.size());
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// Moments of the excitation error against resolution: de^2 ~ gamma0^2 + gamma_e^2 * d*^2, fitted per
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// crystal by ordinary least squares on (d*^2, de^2). Both components come out of the data.
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double m_n = 0.0, m_x = 0.0, m_xx = 0.0, m_y = 0.0, m_xy = 0.0;
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size_t n_de = 0;
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for (const Reflection &r: outcome.reflections) {
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if (r.on_ice_ring || !AcceptReflection(r, d_min_limit_, d_max_limit_))
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continue;
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if (!std::isfinite(r.I) || !std::isfinite(r.sigma) || r.sigma <= 0.0f)
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continue;
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const auto it = reference.find(hkl_key_generator_(r));
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if (it == reference.end() || !std::isfinite(it->second))
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continue;
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const Coord q = base_q(r);
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obs.push_back(FitObs{
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.qx = q.x, .qy = q.y, .qz = q.z,
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.Iref = it->second,
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.Iobs = static_cast<double>(r.I),
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.inv_corr = SafeInv(r.prescaling_corr * r.qe_corr * r.flight_corr, 1.0),
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.sigma2 = static_cast<double>(r.sigma) * r.sigma,
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.var_bkg = std::isfinite(r.var_bkg) && r.var_bkg > 0.0f ? r.var_bkg : static_cast<double>(r.sigma) * r.sigma,
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.weight = SafeInv(r.sigma, 1.0),
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});
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// Excitation error at the stored orientation (psi = 0), collected as the moments of de^2 against
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// d*^2, so BOTH width components are fitted rather than one being forced to zero. Forcing the
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// width to be purely angular (gamma0 = 0) pins it to the high-resolution edge - it is fitted over
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// a d*^2-dense population - and it then collapses at low d*, giving p ~ 0 for reflections that
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// were plainly recorded, which inflated the merged low-resolution intensity scale ~3.6x.
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const double dstar = VecLen(q.x, q.y, q.z);
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const double de0 = VecLen(q.x + S0.x, q.y + S0.y, q.z + S0.z) - inv_lambda;
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if (dstar > 1e-9) {
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const double x = dstar * dstar, y = de0 * de0;
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m_n += 1.0;
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m_x += x;
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m_xx += x * x;
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m_y += y;
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m_xy += x * y;
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++n_de;
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}
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}
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if (obs.size() < MIN_FIT_REFLECTIONS || n_de == 0)
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return 0.0;
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// Without the run's measured width (too few reflections in the run to measure it), the width comes
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// from this crystal's own reflections. Solve the 2x2 normal equations for de^2 = A + B d*^2. A degenerate spread in d* (all reflections in
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// one shell) leaves B undetermined, so fall back to the pure angular width there; a negative fitted
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// component is unphysical and is clamped to zero, which reduces to the previous model.
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//
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// Measured outcome, worth knowing before touching this: the fit does NOT split the width between the
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// two terms - it returns gamma0 ~ 4e-4 1/A and gamma_e ~ 0 (their cross-over sits at d = 0.3 A, far
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// outside any measured range), i.e. a width constant in the LINEAR Ewald distance. That is
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// structural, not a fluke: prediction accepts reflections on a fixed linear |dist_ewald| cutoff, so
|
|
// the accepted population's de^2 is flat in d*^2 by construction and the slope is genuinely ~0. The
|
|
// truncated population cannot constrain an angular term, and its width is the window's, not the
|
|
// crystal's - which is why the run's measured width is used wherever there is one.
|
|
const double det = m_n * m_xx - m_x * m_x;
|
|
double A = 0.0, B = 0.0;
|
|
if (std::fabs(det) > 1e-30) {
|
|
A = (m_xx * m_y - m_x * m_xy) / det;
|
|
B = (m_n * m_xy - m_x * m_y) / det;
|
|
} else {
|
|
B = m_x > 0.0 ? m_y / m_x : 0.0;
|
|
}
|
|
double gamma0 = std::sqrt(std::max(0.0, A));
|
|
const double gamma_e_fit = std::max(std::sqrt(std::max(0.0, B)), 1e-9);
|
|
double gamma_e = settings_.gamma_e > 0.0 ? settings_.gamma_e : gamma_e_fit;
|
|
double bw = bandwidth_sigma_;
|
|
if (run_width) {
|
|
gamma0 = run_width->gamma0;
|
|
gamma_e = std::max(run_width->gamma_e, 1e-9);
|
|
bw = run_width->bandwidth_sigma;
|
|
}
|
|
const Width width{.gamma0 = gamma0, .gamma_e = gamma_e, .bw = bw,
|
|
.table_dstar = run_width ? &run_width->table_dstar : nullptr,
|
|
.table_s = run_width ? &run_width->table_s : nullptr};
|
|
|
|
double psi[2] = {0.0, 0.0};
|
|
double G = 1.0;
|
|
|
|
const TiltModel model{.s0x = S0.x, .s0y = S0.y, .s0z = S0.z, .inv_lambda = inv_lambda,
|
|
.width = width};
|
|
const bool refine_tilt = obs.size() >= settings_.min_reflections;
|
|
const int inner = refine_tilt ? settings_.inner_iterations : 1;
|
|
|
|
for (int it = 0; it < inner; ++it) {
|
|
// (1) Solve G given the current partialities, and weight the tilt fit by the variances at that model.
|
|
std::vector<double> coeff(obs.size());
|
|
for (size_t j = 0; j < obs.size(); ++j) {
|
|
const double p = ComputeP(obs[j].qx, obs[j].qy, obs[j].qz, psi[0], psi[1],
|
|
S0.x, S0.y, S0.z, inv_lambda, width);
|
|
coeff[j] = p * obs[j].inv_corr * obs[j].Iref;
|
|
}
|
|
G = SolveScaleIRLS(obs, coeff, settings_.robust_k);
|
|
if (!(G > 0.0) || !std::isfinite(G))
|
|
return 0.0;
|
|
for (size_t j = 0; j < obs.size(); ++j)
|
|
obs[j].weight = 1.0 / std::sqrt(ModelVariance(obs[j], G * coeff[j]));
|
|
|
|
if (!refine_tilt)
|
|
break;
|
|
|
|
// (2) Refine the tilt holding G fixed. A cost that cannot be evaluated keeps the tilt this crystal
|
|
// came in with and stops refining it - G alone is still a usable model.
|
|
const double inv_sigma_prior = settings_.prior_sigma_deg > 0.0 ? kRadToDeg / settings_.prior_sigma_deg : 0.0;
|
|
if (!RefineTilt(obs, model, G, settings_.robust_k, inv_sigma_prior, settings_.max_tilt_rad, psi))
|
|
break;
|
|
}
|
|
|
|
// Write the refined partiality + scale correction onto every reflection of the crystal (not only the
|
|
// fit subset), so the merge sees a consistent model. image_scale_corr = prescaling_corr * qe_corr * flight_corr /
|
|
// (partiality * G), the same composition ScaleOnTheFly writes.
|
|
for (auto &r: outcome.reflections) {
|
|
const Coord q = base_q(r);
|
|
const double p = ComputeP(q.x, q.y, q.z, psi[0], psi[1], S0.x, S0.y, S0.z, inv_lambda, width);
|
|
r.partiality = static_cast<float>(p);
|
|
const float corr = r.prescaling_corr * r.qe_corr * r.flight_corr;
|
|
const double denom = p * G;
|
|
r.image_scale_corr = (std::isfinite(corr) && std::isfinite(denom) && denom > 0.0)
|
|
? static_cast<float>(corr / denom)
|
|
: NAN;
|
|
}
|
|
outcome.image_scale_g = static_cast<float>(G);
|
|
|
|
// The corrections just changed, so the CC that ScaleOnTheFly measured no longer describes them.
|
|
// Refresh it here: it is reported per image and --min-image-cc drops images by it, so it has to be
|
|
// the CC of the data that is actually merged.
|
|
const auto [cc, cc_n] = ImageReferenceCC(outcome.reflections, reference, hkl_key_generator_,
|
|
d_min_limit_, d_max_limit_, min_partiality_);
|
|
|
|
outcome.image_scale_cc = cc;
|
|
outcome.image_scale_cc_n = cc_n;
|
|
|
|
const double tilt_deg = std::sqrt(psi[0] * psi[0] + psi[1] * psi[1]) * kRadToDeg;
|
|
return tilt_deg;
|
|
}
|
|
|
|
double StillsPartialityRefine::MeasureRadialScale(const std::vector<IntegrationOutcome> &outcomes,
|
|
const std::optional<UnitCell> &reference_cell,
|
|
double radial_scale) const {
|
|
// A scale of the reciprocal lattice - a wavelength, or a cell, a little off - leaves every spot where
|
|
// it was (positions fix only lambda d*), but moves each reflection's excitation error by
|
|
// eps lambda d*^2 / 2 for q -> (1 + eps) q, so the run's rocking curve sits off zero by an amount
|
|
// growing as d*^2. The prediction window is symmetric in de, so the intensity-weighted mean de of a
|
|
// shell is that offset, and a line through the origin in lambda d*^2 / 2 gives eps. A window that cuts
|
|
// an off-centre curve pulls the mean toward zero, so the caller iterates from the scale found.
|
|
const auto &indexing = experiment_.GetIndexingSettings();
|
|
struct Point { double x, de, w; };
|
|
std::vector<Point> pts;
|
|
double max_x = 0.0;
|
|
for (const auto &o: outcomes) {
|
|
if (!o.image_scale_g || !(*o.image_scale_g > 0.0))
|
|
continue;
|
|
if (reference_cell && !o.latt.GetUnitCell().is_close(*reference_cell, indexing.GetUnitCellDistTolerance(),
|
|
indexing.GetUnitCellAngleTolerance_deg()))
|
|
continue;
|
|
const Coord S0 = o.geom.GetScatteringVector();
|
|
const double inv_lambda = 1.0 / o.geom.GetWavelength_A();
|
|
for (const auto &r: o.reflections) {
|
|
if (r.on_ice_ring || !AcceptReflection(r, d_min_limit_, d_max_limit_) || !(r.d > 0.0f))
|
|
continue;
|
|
const double w = r.I * r.prescaling_corr * r.qe_corr * r.flight_corr / *o.image_scale_g;
|
|
if (!std::isfinite(w))
|
|
continue;
|
|
const Coord q = (o.latt.Astar() * static_cast<float>(r.h) + o.latt.Bstar() * static_cast<float>(r.k)
|
|
+ o.latt.Cstar() * static_cast<float>(r.l)) * static_cast<float>(radial_scale);
|
|
const double x = 0.5 / (inv_lambda * r.d * r.d);
|
|
pts.push_back({x, VecLen(q.x + S0.x, q.y + S0.y, q.z + S0.z) - inv_lambda, w});
|
|
max_x = std::max(max_x, x);
|
|
}
|
|
}
|
|
constexpr int N_SHELLS = 8;
|
|
if (pts.size() < 100 * N_SHELLS)
|
|
return radial_scale;
|
|
std::array<double, N_SHELLS> sw{}, swde{}, swx{};
|
|
for (const auto &p: pts) {
|
|
const int b = std::min(N_SHELLS - 1, static_cast<int>(p.x / max_x * N_SHELLS));
|
|
sw[b] += p.w;
|
|
swde[b] += p.w * p.de;
|
|
swx[b] += p.w * p.x;
|
|
}
|
|
double sxy = 0.0, sxx = 0.0;
|
|
for (int b = 0; b < N_SHELLS; ++b) {
|
|
if (!(sw[b] > 0.0))
|
|
continue;
|
|
const double x = swx[b] / sw[b], y = swde[b] / sw[b];
|
|
sxy += sw[b] * x * y;
|
|
sxx += sw[b] * x * x;
|
|
}
|
|
if (!(sxx > 0.0) || !std::isfinite(sxy))
|
|
return radial_scale;
|
|
// the slope is eps, removed by scaling q by (1 - eps)
|
|
return radial_scale * (1.0 - sxy / sxx);
|
|
}
|
|
|
|
std::optional<StillsPartialityRefine::RunWidth> StillsPartialityRefine::MeasureRunWidth(
|
|
const std::vector<IntegrationOutcome> &outcomes, const std::optional<UnitCell> &reference_cell,
|
|
double radial_scale, const RunWidth *window_width) const {
|
|
// The rocking width measured on the crystals rather than on the prediction window. A lattice point
|
|
// sits anywhere across the window with equal likelihood, while what it records is I_full * p(de), so
|
|
// the intensity-weighted second moment of the excitation error, sum I de^2 / sum I, is the width s^2
|
|
// of a Gaussian p - corrected for the window cutting the curve's tails (UntruncatedVariance). The
|
|
// plain moment of de over the predicted reflections, which the per-crystal fit in RefineOne uses, is
|
|
// instead the window's own (W^2 / 3). Measured in shells of d*^2 over the whole run, where the
|
|
// intensities of thousands of crystals average out, and fitted as s^2 = gamma0^2 + gamma_e^2 d*^2 +
|
|
// (bandwidth_sigma lambda d*^2 / 2)^2.
|
|
//
|
|
// Each frame predicts through a window of its own (twice its profile radius), and these differ by an
|
|
// order of magnitude within a run. Pooled, the frames with the widest windows decide both moments, and
|
|
// the correction then reads their window: on a run whose windows are mostly narrower than the curve at
|
|
// high resolution, the pooled measurement came out as the window at every resolution, a width constant
|
|
// in d* that is several times too wide at low resolution. So within a shell the frames are taken in
|
|
// WINDOW_GROUPS groups of similar window, each measured against its own, and the shell's width is the
|
|
// median of the groups whose curve is narrower than their window; a shell where no group can see the
|
|
// curve is left out.
|
|
//
|
|
// A frame's window is the largest excitation error it predicted where it predicted through one width.
|
|
// Predicted through the run's width (window_width), the window is its formula at the reflection's own
|
|
// resolution: the frame's largest excitation error is then the high-resolution window, and taken as the
|
|
// window of its low-resolution reflections it put them in the wrong group.
|
|
const auto &indexing = experiment_.GetIndexingSettings();
|
|
struct Point { double x, de2, w, var_w, window; };
|
|
std::vector<Point> pts;
|
|
for (const auto &o: outcomes) {
|
|
if (!o.image_scale_g || !(*o.image_scale_g > 0.0))
|
|
continue;
|
|
if (reference_cell && !o.latt.GetUnitCell().is_close(*reference_cell, indexing.GetUnitCellDistTolerance(),
|
|
indexing.GetUnitCellAngleTolerance_deg()))
|
|
continue;
|
|
float frame_window = 0.0f; // the largest excitation error the frame predicted
|
|
for (const auto &r: o.reflections)
|
|
if (std::isfinite(r.dist_ewald))
|
|
frame_window = std::max(frame_window, std::fabs(r.dist_ewald));
|
|
for (const auto &r: o.reflections) {
|
|
if (r.on_ice_ring || !AcceptReflection(r, d_min_limit_, d_max_limit_))
|
|
continue;
|
|
const double corr = r.prescaling_corr * r.qe_corr * r.flight_corr / *o.image_scale_g;
|
|
const double w = r.I * corr, sigma_w = r.sigma * corr;
|
|
if (!std::isfinite(w) || !std::isfinite(sigma_w) || !std::isfinite(r.dist_ewald) || !(r.d > 0.0f))
|
|
continue;
|
|
// The excitation error the window was cut in is the prediction's; the curve's is taken at the
|
|
// run's radial scale (MeasureRadialScale), recomputed from the lattice when that is not one.
|
|
double de = r.dist_ewald;
|
|
if (radial_scale != 1.0) {
|
|
const Coord q = (o.latt.Astar() * static_cast<float>(r.h) + o.latt.Bstar() * static_cast<float>(r.k)
|
|
+ o.latt.Cstar() * static_cast<float>(r.l)) * static_cast<float>(radial_scale);
|
|
const Coord S0 = o.geom.GetScatteringVector();
|
|
de = VecLen(q.x + S0.x, q.y + S0.y, q.z + S0.z) - 1.0 / o.geom.GetWavelength_A();
|
|
}
|
|
double window = frame_window;
|
|
if (window_width) {
|
|
// the formula at the reflection's d*, its bandwidth term at |q_z| = lambda d*^2 / 2
|
|
const double dstar = 1.0 / r.d;
|
|
const double a = window_width->gamma_e * dstar;
|
|
const double b = window_width->bandwidth_sigma * o.geom.GetWavelength_A() * dstar * dstar / 2.0;
|
|
window = std::sqrt(window_width->gamma0 * window_width->gamma0 + a * a + b * b);
|
|
}
|
|
pts.push_back({1.0 / (static_cast<double>(r.d) * r.d), de * de, w, sigma_w * sigma_w, window});
|
|
}
|
|
}
|
|
constexpr size_t N_SHELLS = 8;
|
|
constexpr size_t WINDOW_GROUPS = 4;
|
|
if (pts.size() < 100 * N_SHELLS)
|
|
return std::nullopt;
|
|
std::sort(pts.begin(), pts.end(), [](const Point &a, const Point &b) { return a.x < b.x; });
|
|
|
|
Logger logger("StillsPartialityRefine");
|
|
// A group's moment is no better than the summed intensity it is weighted by, so a group is used only
|
|
// where that sum is measured to 10 % (sum I / sigma(sum I) >= 10): beyond the diffraction limit the
|
|
// sum is noise and can even be negative, and says nothing about the width.
|
|
constexpr double MIN_SHELL_SIGNAL = 10.0;
|
|
// The width of the points [lo, hi) of pts (sorted by d*): the median of the window groups' widths.
|
|
auto shell_width = [&](size_t lo, size_t hi) -> std::optional<double> {
|
|
std::vector<Point> shell(pts.begin() + lo, pts.begin() + hi);
|
|
std::sort(shell.begin(), shell.end(), [](const Point &a, const Point &b) { return a.window < b.window; });
|
|
std::vector<double> widths;
|
|
for (size_t g = 0; g < WINDOW_GROUPS; ++g) {
|
|
const size_t glo = g * shell.size() / WINDOW_GROUPS, ghi = (g + 1) * shell.size() / WINDOW_GROUPS;
|
|
double sw = 0.0, svar = 0.0, swde2 = 0.0, sde2 = 0.0;
|
|
for (size_t i = glo; i < ghi; ++i) {
|
|
sw += shell[i].w;
|
|
svar += shell[i].var_w;
|
|
swde2 += shell[i].w * shell[i].de2;
|
|
sde2 += shell[i].de2;
|
|
}
|
|
if (!(sw >= MIN_SHELL_SIGNAL * std::sqrt(svar)) || !(swde2 > 0.0))
|
|
continue;
|
|
if (const auto v = UntruncatedVariance(swde2 / sw, sde2 / static_cast<double>(ghi - glo)))
|
|
widths.push_back(*v);
|
|
}
|
|
if (widths.empty())
|
|
return std::nullopt;
|
|
std::sort(widths.begin(), widths.end());
|
|
const size_t m = widths.size();
|
|
return m % 2 ? widths[m / 2] : 0.5 * (widths[m / 2 - 1] + widths[m / 2]);
|
|
};
|
|
|
|
// For the three-term formula (the prediction window): shells of equal count in d*^2.
|
|
std::vector<double> sx, sy;
|
|
for (size_t k = 0; k < N_SHELLS; ++k) {
|
|
const size_t lo = k * pts.size() / N_SHELLS, hi = (k + 1) * pts.size() / N_SHELLS;
|
|
const auto y = shell_width(lo, hi);
|
|
if (!y)
|
|
continue;
|
|
double sumx = 0.0;
|
|
for (size_t i = lo; i < hi; ++i)
|
|
sumx += pts[i].x;
|
|
const double x = sumx / static_cast<double>(hi - lo);
|
|
sx.push_back(x);
|
|
sy.push_back(*y);
|
|
logger.Debug("Stills rocking width at d = {:.2f} A: {:.2e} 1/A ({:.3f} deg)",
|
|
1.0 / std::sqrt(x), std::sqrt(*y), std::sqrt(*y / x) * kRadToDeg);
|
|
}
|
|
|
|
// For the partiality: shells of equal width in d*, kept as a table. Equal-count shells crowd where
|
|
// the reflections are - on a run predicting ~1000 reflections a frame, all eight sat at 3.8-1.8 A, so
|
|
// the low-resolution width was the formula's extrapolation, and the three-term fit flipped between
|
|
// forms with the number of frames (to a pure bandwidth at 50k frames). Measured where it is used and
|
|
// interpolated, the width needs no form. A wider curve at finer resolution is the physics (every term
|
|
// grows with d*), so the table is made non-decreasing (pool adjacent violators, weighted by the
|
|
// shells' summed signal).
|
|
std::vector<double> table_dstar, table_s, table_weight;
|
|
{
|
|
const double lo_d = std::sqrt(pts.front().x), hi_d = std::sqrt(pts.back().x);
|
|
size_t lo = 0;
|
|
for (size_t k = 0; k < N_SHELLS; ++k) {
|
|
const double edge = lo_d + (hi_d - lo_d) * static_cast<double>(k + 1) / N_SHELLS;
|
|
size_t hi = lo;
|
|
while (hi < pts.size() && (k + 1 == N_SHELLS || std::sqrt(pts[hi].x) < edge))
|
|
++hi;
|
|
double sw = 0.0, svar = 0.0, sds = 0.0;
|
|
for (size_t i = lo; i < hi; ++i) {
|
|
sw += pts[i].w;
|
|
svar += pts[i].var_w;
|
|
sds += std::sqrt(pts[i].x);
|
|
}
|
|
if (hi - lo >= 400 && sw >= MIN_SHELL_SIGNAL * std::sqrt(svar))
|
|
if (const auto y = shell_width(lo, hi)) {
|
|
table_dstar.push_back(sds / static_cast<double>(hi - lo));
|
|
table_s.push_back(std::sqrt(*y));
|
|
table_weight.push_back(sw / std::sqrt(svar));
|
|
}
|
|
lo = hi;
|
|
}
|
|
std::vector<double> block_s, block_w;
|
|
std::vector<size_t> block_n;
|
|
for (size_t i = 0; i < table_s.size(); ++i) {
|
|
block_s.push_back(table_s[i]);
|
|
block_w.push_back(table_weight[i]);
|
|
block_n.push_back(1);
|
|
while (block_s.size() > 1 && block_s[block_s.size() - 2] > block_s.back()) {
|
|
const size_t j = block_s.size() - 2;
|
|
block_s[j] = (block_s[j] * block_w[j] + block_s.back() * block_w.back()) / (block_w[j] + block_w.back());
|
|
block_w[j] += block_w.back();
|
|
block_n[j] += block_n.back();
|
|
block_s.pop_back();
|
|
block_w.pop_back();
|
|
block_n.pop_back();
|
|
}
|
|
}
|
|
table_s.clear();
|
|
for (size_t j = 0; j < block_s.size(); ++j)
|
|
table_s.insert(table_s.end(), block_n[j], block_s[j]);
|
|
if (table_dstar.size() < 3) {
|
|
table_dstar.clear();
|
|
table_s.clear();
|
|
}
|
|
}
|
|
|
|
if (sx.size() < 3)
|
|
return std::nullopt;
|
|
|
|
// Least squares for s^2 = A + B d*^2 + C d*^4 over the shells. Every term is a variance, so a negative
|
|
// one is unphysical: of the fits on each subset of the three terms, the best with none negative is kept.
|
|
std::array<double, 3> best{};
|
|
double best_residual = INFINITY;
|
|
for (int mask = 1; mask < 8; ++mask) {
|
|
std::vector<int> terms;
|
|
for (int t = 0; t < 3; ++t)
|
|
if (mask & (1 << t))
|
|
terms.push_back(t);
|
|
const int m = static_cast<int>(terms.size());
|
|
Eigen::MatrixXd M = Eigen::MatrixXd::Zero(m, m);
|
|
Eigen::VectorXd v = Eigen::VectorXd::Zero(m);
|
|
for (size_t k = 0; k < sx.size(); ++k)
|
|
for (int i = 0; i < m; ++i) {
|
|
const double fi = std::pow(sx[k], terms[i]);
|
|
v(i) += fi * sy[k];
|
|
for (int j = 0; j < m; ++j)
|
|
M(i, j) += fi * std::pow(sx[k], terms[j]);
|
|
}
|
|
const Eigen::VectorXd c = M.ldlt().solve(v);
|
|
if (!c.allFinite() || (c.array() < 0.0).any())
|
|
continue;
|
|
std::array<double, 3> coef{};
|
|
for (int i = 0; i < m; ++i)
|
|
coef[terms[i]] = c(i);
|
|
double residual = 0.0;
|
|
for (size_t k = 0; k < sx.size(); ++k) {
|
|
const double r = sy[k] - coef[0] - coef[1] * sx[k] - coef[2] * sx[k] * sx[k];
|
|
residual += r * r;
|
|
}
|
|
if (residual < best_residual) {
|
|
best_residual = residual;
|
|
best = coef;
|
|
}
|
|
}
|
|
if (!std::isfinite(best_residual) || !(best[0] + best[1] + best[2] > 0.0))
|
|
return std::nullopt;
|
|
// The d*^4 term is a bandwidth: its radial smear bw |q_z|, with |q_z| = lambda d*^2 / 2 on the sphere.
|
|
const RunWidth width{.gamma0 = std::sqrt(best[0]), .gamma_e = std::sqrt(best[1]),
|
|
.bandwidth_sigma = 2.0 * std::sqrt(best[2]) / experiment_.GetWavelength_A(),
|
|
.radial_scale = radial_scale, .table_dstar = table_dstar, .table_s = table_s};
|
|
logger.Info("Stills rocking width measured: {:.2e} 1/A + {:.3f} deg angular + {:.4f} bandwidth (FWHM)",
|
|
width.gamma0, width.gamma_e * kRadToDeg, width.bandwidth_sigma * 2.3548);
|
|
std::string table;
|
|
for (size_t i = 0; i < table_dstar.size(); ++i)
|
|
table += fmt::format(" {:.2f} A {:.2e}", 1.0 / table_dstar[i], table_s[i]);
|
|
logger.Info("Stills rocking width for the partiality, against resolution (1/A):{}",
|
|
table.empty() ? " none, the formula is used" : table);
|
|
return width;
|
|
}
|
|
|
|
double StillsPartialityRefine::Run(std::vector<IntegrationOutcome> &outcomes, size_t nthreads,
|
|
const std::optional<UnitCell> &reference_cell,
|
|
const std::optional<RunWidth> &given_width,
|
|
std::optional<RunWidth> *used_width) const {
|
|
const auto &indexing = experiment_.GetIndexingSettings();
|
|
auto merged_crystal = [&](const IntegrationOutcome &o) {
|
|
return !reference_cell || o.latt.GetUnitCell().is_close(*reference_cell,
|
|
indexing.GetUnitCellDistTolerance(),
|
|
indexing.GetUnitCellAngleTolerance_deg());
|
|
};
|
|
if (nthreads == 0)
|
|
nthreads = AvailableCpus();
|
|
nthreads = std::max<size_t>(1, nthreads);
|
|
|
|
double last_mean_tilt = 0.0;
|
|
// Where the frames were predicted through a curve measured before the image pass, the partialities use
|
|
// that same curve. Measured again here, through windows that follow it, the width reads narrower at low
|
|
// resolution (its constant term falls to about zero), and the merge it gave moved R-free against the
|
|
// models by up to +-0.015 per run in both directions, where the one curve moved it by at most +0.008.
|
|
std::optional<RunWidth> run_width = given_width;
|
|
if (!run_width) {
|
|
double radial_scale = 1.0;
|
|
for (int i = 0; i < 3; ++i)
|
|
radial_scale = MeasureRadialScale(outcomes, reference_cell, radial_scale);
|
|
Logger("StillsPartialityRefine").Info("Stills rocking curve centre: reciprocal lattice scaled by {:+.2e}",
|
|
radial_scale - 1.0);
|
|
run_width = MeasureRunWidth(outcomes, reference_cell, radial_scale);
|
|
}
|
|
const double radial_scale = run_width ? run_width->radial_scale : 1.0;
|
|
if (used_width)
|
|
*used_width = run_width;
|
|
|
|
for (int outer = 0; outer < settings_.outer_iterations; ++outer) {
|
|
// Reference full intensities from the current corrections.
|
|
const std::vector<MergedReflection> merged = MergeAll(experiment_, outcomes, nthreads, reference_cell);
|
|
std::map<HKLKey, double> reference;
|
|
for (const auto &m: merged)
|
|
reference[hkl_key_generator_(m)] = m.I;
|
|
|
|
std::atomic<double> tilt_sum{0.0};
|
|
std::atomic<size_t> tilt_n{0};
|
|
std::atomic<size_t> next{0};
|
|
|
|
auto worker = [&]() {
|
|
size_t i = next.fetch_add(1);
|
|
while (i < outcomes.size()) {
|
|
const double t = merged_crystal(outcomes[i]) ? RefineOne(outcomes[i], reference, run_width, radial_scale) : 0.0;
|
|
if (t > 0.0) {
|
|
double prev = tilt_sum.load();
|
|
while (!tilt_sum.compare_exchange_weak(prev, prev + t)) {}
|
|
tilt_n.fetch_add(1);
|
|
}
|
|
i = next.fetch_add(1);
|
|
}
|
|
};
|
|
|
|
const size_t nt = std::min(nthreads, std::max<size_t>(1, outcomes.size()));
|
|
if (nt <= 1) {
|
|
worker();
|
|
} else {
|
|
std::vector<std::future<void>> futures;
|
|
futures.reserve(nt);
|
|
for (size_t t = 0; t < nt; ++t)
|
|
futures.emplace_back(std::async(std::launch::async, worker));
|
|
for (auto &f: futures)
|
|
f.get();
|
|
}
|
|
|
|
last_mean_tilt = tilt_n > 0 ? tilt_sum.load() / static_cast<double>(tilt_n.load()) : 0.0;
|
|
}
|
|
|
|
return last_mean_tilt;
|
|
}
|