leonarski_fandClaude Opus 4.8
6df657fe62
The monoclinic 2_1 screw was missed on EP_cs_02-10 and EP_cs_01-17 (adopted P2 instead of P2_1). The 0k0-odd reflections are correctly measured as weak (~0.1-1% of 0k0-even, matching XDS), but their merged sigmas are ~2x too small, so their I/sigma clears the present_i_over_sigma cut and they count as screw-axis violations - the search then falls back to the symmorphic group. Add a resolution-normalised intensity E^2 = I / <I>(shell), computed from equal-count resolution shells, and require a reflection to reach present_e_squared (0.3) as well as present_i_over_sigma before it counts as violating a predicted absence. This only tightens "present", so it cannot manufacture a screw whose predicted-absent class carries real intensity (a symmorphic crystal's axial reflections sit at E^2 ~ 1 and still register as violations). On the 18-crystal rotation battery this recovers the screw on EP_cs_02-10 and EP_cs_01-17 (-> P2_1) and, as a side effect, on MyoB (-> P2_1), pding4_001 (-> P4_122/P4_322) and pding4_003 (-> P2_2_2_1) - all confirmed by genuine absences in the reference intensities (absent class at 0.02-0.76% of the allowed class), which the old sigma-only test also missed. The other 13 crystals, indexing rate and ISa are unchanged; the screw-free control (Ins_I -> I23/I2_13) is unaffected. Add a regression test that reproduces the under-estimated-sigma screw and checks the gate recovers it (and that disabling the gate reproduces the miss). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
513 lines
23 KiB
C++
513 lines
23 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 "SearchSpaceGroup.h"
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#include <algorithm>
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#include <array>
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#include <cmath>
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#include <cstdint>
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#include <iomanip>
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#include <limits>
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#include <map>
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#include <sstream>
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#include <tuple>
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#include <unordered_map>
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#include <vector>
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namespace {
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// A merged reflection, folded onto the +/- Friedel-equivalent it represents, used as a
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// hash key to match symmetry-related reflections.
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struct HKLKey {
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int h = 0, k = 0, l = 0;
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bool operator==(const HKLKey& o) const noexcept { return h == o.h && k == o.k && l == o.l; }
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};
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struct HKLKeyHash {
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size_t operator()(const HKLKey& key) const noexcept {
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auto mix = [](uint64_t x) {
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x ^= x >> 33; x *= 0xff51afd7ed558ccdULL;
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x ^= x >> 33; x *= 0xc4ceb9fe1a85ec53ULL;
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x ^= x >> 33; return x;
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};
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return static_cast<size_t>(mix(static_cast<uint64_t>(key.h)) ^
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(mix(static_cast<uint64_t>(key.k)) << 1) ^
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(mix(static_cast<uint64_t>(key.l)) << 2));
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}
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};
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HKLKey Canonicalize(int h, int k, int l, bool merge_friedel) {
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if (merge_friedel && std::make_tuple(-h, -k, -l) < std::make_tuple(h, k, l))
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return {-h, -k, -l};
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return {h, k, l};
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}
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double PearsonCC(const std::vector<double>& x, const std::vector<double>& y) {
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if (x.size() < 2)
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return std::numeric_limits<double>::quiet_NaN();
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double sx = 0, sy = 0, sxx = 0, syy = 0, sxy = 0;
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for (size_t i = 0; i < x.size(); ++i) {
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sx += x[i]; sy += y[i];
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sxx += x[i] * x[i]; syy += y[i] * y[i]; sxy += x[i] * y[i];
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}
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const double n = static_cast<double>(x.size());
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const double vx = sxx - sx * sx / n;
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const double vy = syy - sy * sy / n;
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if (vx <= 0 || vy <= 0)
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return std::numeric_limits<double>::quiet_NaN();
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return (sxy - sx * sy / n) / std::sqrt(vx * vy);
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}
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// A reflection is extinct from lattice centering alone (independent of any screw/glide) when a
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// centering translation makes its structure factor cancel. Mirrors the centering half of
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// gemmi::GroupOps::is_systematically_absent, so screw absences can be judged separately.
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bool CenteringAbsent(const gemmi::GroupOps& gops, const gemmi::Op::Miller& hkl) {
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for (size_t i = 1; i < gops.cen_ops.size(); ++i) {
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const auto& t = gops.cen_ops[i];
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if ((t[0] * hkl[0] + t[1] * hkl[1] + t[2] * hkl[2]) % gemmi::Op::DEN != 0)
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return true;
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}
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return false;
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}
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std::array<int, 9> RotKey(const gemmi::Op& op) {
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std::array<int, 9> out{};
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for (int i = 0; i < 3; ++i)
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for (int j = 0; j < 3; ++j)
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out[i * 3 + j] = op.rot[i][j];
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return out;
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}
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// The rotation part of a space group in the reference setting (identity included), as a
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// sorted list of matrices - the key that groups space groups into a candidate point group.
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// It must be the rotation SET, not gemmi's PointGroup enum: P321 and P312 are both "32" yet
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// have their 2-folds along different directions, and only the matrices tell them apart.
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using RotationSet = std::vector<std::array<int, 9>>;
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RotationSet RotationSetOf(const gemmi::SpaceGroup& sg) {
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RotationSet out;
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for (const auto& op : sg.operations().derive_symmorphic().sym_ops)
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out.push_back(RotKey(op));
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std::sort(out.begin(), out.end());
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return out;
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}
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// Proper rotations of a crystal system's holohedry (the highest lattice symmetry it can host),
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// in the reference setting. Any candidate point group must be a subgroup of this.
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RotationSet HolohedryRotationSet(gemmi::CrystalSystem system) {
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int number = 0;
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switch (system) {
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case gemmi::CrystalSystem::Triclinic: number = 1; break; // P1
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case gemmi::CrystalSystem::Monoclinic: number = 3; break; // P2 (unique axis b)
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case gemmi::CrystalSystem::Orthorhombic: number = 16; break; // P222
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case gemmi::CrystalSystem::Tetragonal: number = 89; break; // P422
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case gemmi::CrystalSystem::Trigonal: number = 155; break; // R32
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case gemmi::CrystalSystem::Hexagonal: number = 177; break; // P622
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case gemmi::CrystalSystem::Cubic: number = 207; break; // P432
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}
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const auto* sg = gemmi::find_spacegroup_by_number(number);
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return sg ? RotationSetOf(*sg) : RotationSet{};
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}
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// A candidate point group: its proper rotations (reference setting) and a representative
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// symmorphic space group (used when only the point group is wanted, or for display).
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struct PointGroupInfo {
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RotationSet rotation_set;
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std::vector<gemmi::Op> rotations; // non-identity proper rotations
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const gemmi::SpaceGroup* representative = nullptr;
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};
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// Enumerate candidate point groups. When a holohedry is given (from the lattice metric), keep
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// only its subgroups - this both skips operators the lattice forbids and avoids accepting a
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// coincidental higher symmetry; all subgroups down to P1 are still candidates.
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std::vector<PointGroupInfo> EnumeratePointGroups(const std::optional<RotationSet>& holohedry) {
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std::vector<PointGroupInfo> out;
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std::map<RotationSet, size_t> index;
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for (const auto& sg : gemmi::spacegroup_tables::main) {
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if (!sg.is_sohncke() || !sg.is_reference_setting())
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continue;
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RotationSet rs = RotationSetOf(sg);
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if (holohedry.has_value() &&
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!std::includes(holohedry->begin(), holohedry->end(), rs.begin(), rs.end()))
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continue;
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auto it = index.find(rs);
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size_t pos;
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if (it == index.end()) {
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PointGroupInfo info;
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for (const auto& op : sg.operations().derive_symmorphic().sym_ops) {
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if (op.rot == gemmi::Op::identity().rot)
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continue;
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info.rotations.push_back(gemmi::Op{op.rot, {0, 0, 0}, op.notation});
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}
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info.rotation_set = rs;
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pos = out.size();
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index[rs] = pos;
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out.push_back(std::move(info));
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} else {
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pos = it->second;
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}
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// Prefer a symmorphic representative (the plain point-group setting).
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auto& info = out[pos];
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if (info.representative == nullptr ||
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(!info.representative->is_symmorphic() && sg.is_symmorphic()))
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info.representative = &sg;
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}
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return out;
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}
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}
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SearchSpaceGroupResult SearchSpaceGroup(
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const std::vector<MergedReflection>& merged,
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const SearchSpaceGroupOptions& opt) {
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SearchSpaceGroupResult result;
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if (merged.empty())
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return result;
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const size_t n = merged.size();
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// Flatten the reflections and mark which ones each stage may use. The correlation stage drops
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// weak reflections; the absence stage must keep them - that is where the screw-axis signal is.
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std::vector<int> H(n), K(n), L(n);
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std::vector<double> I(n), Sigma(n), IoverSigma(n);
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std::vector<HKLKey> key(n);
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std::vector<char> pass_absence(n, 0), pass_cc(n, 0);
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for (size_t i = 0; i < n; ++i) {
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const auto& r = merged[i];
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H[i] = r.h; K[i] = r.k; L[i] = r.l;
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I[i] = r.I;
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Sigma[i] = std::isfinite(r.sigma) && r.sigma > 0 ? r.sigma : 0.0;
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key[i] = Canonicalize(r.h, r.k, r.l, opt.merge_friedel);
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const bool finite = std::isfinite(r.I) && std::isfinite(r.sigma) && r.sigma > 0 &&
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std::isfinite(r.d) && r.d > 0;
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const bool in_range = finite && (opt.d_min_limit_A <= 0 || r.d >= opt.d_min_limit_A);
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IoverSigma[i] = finite ? r.I / r.sigma : 0.0;
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pass_absence[i] = in_range;
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// The correlation stage uses only genuinely-present reflections. Near-zero (systematically
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// absent) reflections would otherwise form a second cluster at the origin and fake a high
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// correlation for false operators - fatal on centered lattices, where half the reflections
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// are extinct.
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pass_cc[i] = in_range && IoverSigma[i] >= opt.present_i_over_sigma &&
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(opt.min_i_over_sigma <= 0 || IoverSigma[i] >= opt.min_i_over_sigma);
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}
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// Resolution-normalised intensity E^2 = I / <I>(shell), from equal-count resolution shells over
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// the reflections the absence test uses. Lets the absence test judge "present" by intensity
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// magnitude, not by a possibly under-estimated sigma (see present_e_squared).
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std::vector<double> Esq(n, 0.0);
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{
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std::vector<size_t> order;
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order.reserve(n);
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for (size_t i = 0; i < n; ++i)
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if (pass_absence[i])
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order.push_back(i);
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std::sort(order.begin(), order.end(),
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[&](size_t a, size_t b) { return merged[a].d > merged[b].d; }); // low res -> high res
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const int bins = std::clamp(static_cast<int>(order.size() / 100), 1, 25);
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const size_t per = (order.size() + bins - 1) / std::max(1, bins);
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for (size_t b = 0; b * per < order.size(); ++b) {
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const size_t lo = b * per, hi = std::min(order.size(), lo + per);
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double sum = 0.0;
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for (size_t j = lo; j < hi; ++j)
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sum += I[order[j]];
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const double mean = (hi > lo) ? sum / static_cast<double>(hi - lo) : 0.0;
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for (size_t j = lo; j < hi; ++j)
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Esq[order[j]] = mean > 0.0 ? I[order[j]] / mean : 0.0;
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}
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}
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std::unordered_map<HKLKey, int, HKLKeyHash> key_to_index;
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key_to_index.reserve(n * 2);
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for (size_t i = 0; i < n; ++i)
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if (pass_absence[i])
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key_to_index.emplace(key[i], static_cast<int>(i));
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// --- Stage A: score each distinct rotation operator once ---
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std::vector<uint32_t> visited(n, 0);
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uint32_t epoch = 0;
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auto score_operator = [&](const gemmi::Op& op) -> SpaceGroupOperatorScore {
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++epoch;
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std::vector<double> x, y;
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for (size_t i = 0; i < n; ++i) {
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if (!pass_cc[i] || visited[i] == epoch)
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continue;
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const auto m2 = op.apply_to_hkl(gemmi::Op::Miller{{H[i], K[i], L[i]}});
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const HKLKey k2 = Canonicalize(m2[0], m2[1], m2[2], opt.merge_friedel);
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if (k2 == key[i])
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continue; // reflection lies on this rotation axis
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const auto it = key_to_index.find(k2);
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if (it == key_to_index.end())
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continue;
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const int j = it->second;
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if (!pass_cc[j])
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continue;
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x.push_back(I[i]);
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y.push_back(I[j]);
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visited[i] = epoch;
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visited[j] = epoch;
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}
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SpaceGroupOperatorScore s;
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s.op_triplet_hkl = op.as_hkl().triplet('h');
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s.n_pairs = static_cast<int>(x.size());
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s.cc = PearsonCC(x, y);
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s.present = s.n_pairs >= opt.min_pairs_per_operator && std::isfinite(s.cc) &&
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s.cc >= opt.min_operator_cc;
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return s;
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};
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std::map<std::array<int, 9>, SpaceGroupOperatorScore> op_cache;
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auto operator_score = [&](const gemmi::Op& op) -> const SpaceGroupOperatorScore& {
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const auto rk = RotKey(op);
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auto it = op_cache.find(rk);
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if (it != op_cache.end())
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return it->second;
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return op_cache.emplace(rk, score_operator(op)).first->second;
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};
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std::optional<RotationSet> holohedry;
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if (opt.lattice_system.has_value())
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holohedry = HolohedryRotationSet(opt.lattice_system.value());
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const auto point_groups = EnumeratePointGroups(holohedry);
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// Reduced chi^2 of the intensities merged under a point group's rotations - how well its symmetry
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// equivalents agree RELATIVE TO THEIR ERRORS. A real point group gives ~1; a false operator forces
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// non-equivalent reflections together, so they disagree by many sigma and chi^2 blows up. This is
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// more sensitive than R-meas to a strong pseudo-symmetry (where the intensities still correlate well
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// - high operator CC - but not within their errors). Inverse-variance weighted mean per orbit, over
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// the present (pass_cc) reflections.
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auto chi2_under = [&](const std::vector<gemmi::Op>& rotations) -> double {
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struct Acc { double sw = 0.0, swI = 0.0; int n = 0; };
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std::unordered_map<HKLKey, Acc, HKLKeyHash> grp;
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std::vector<HKLKey> rep(n);
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for (size_t i = 0; i < n; ++i) {
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if (!pass_cc[i] || !(Sigma[i] > 0.0))
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continue;
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HKLKey best = key[i];
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for (const auto& op : rotations) {
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const auto m = op.apply_to_hkl(gemmi::Op::Miller{{H[i], K[i], L[i]}});
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const HKLKey k2 = Canonicalize(m[0], m[1], m[2], opt.merge_friedel);
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if (std::make_tuple(k2.h, k2.k, k2.l) < std::make_tuple(best.h, best.k, best.l))
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best = k2;
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}
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rep[i] = best;
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auto& g = grp[best];
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const double w = 1.0 / (Sigma[i] * Sigma[i]);
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g.sw += w; g.swI += w * I[i]; g.n += 1;
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}
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double chi2 = 0.0;
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long dof = 0;
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for (size_t i = 0; i < n; ++i) {
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if (!pass_cc[i] || !(Sigma[i] > 0.0))
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continue;
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const auto& g = grp[rep[i]];
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if (g.n < 2)
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continue;
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const double mean = g.swI / g.sw, dev = I[i] - mean;
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chi2 += dev * dev / (Sigma[i] * Sigma[i]);
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}
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for (const auto& [k, g] : grp)
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if (g.n >= 2)
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dof += g.n - 1;
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return dof > 0 ? chi2 / static_cast<double>(dof) : std::numeric_limits<double>::quiet_NaN();
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};
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// Operator-CC-confirmed candidates, each with its merge chi^2; chi2_ref = the most consistent.
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struct PGCand { const PointGroupInfo* pg; int order; double min_cc; double chi2; };
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std::vector<PGCand> pg_cands;
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double chi2_ref = std::numeric_limits<double>::infinity();
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for (const auto& pg : point_groups) {
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bool all_present = true;
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double min_cc = pg.rotations.empty() ? 1.0 : std::numeric_limits<double>::infinity();
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for (const auto& op : pg.rotations) {
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const auto& s = operator_score(op);
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all_present = all_present && s.present;
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min_cc = std::min(min_cc, s.cc);
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}
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if (!all_present)
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continue;
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const double ch = pg.rotations.empty() ? std::numeric_limits<double>::quiet_NaN()
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: chi2_under(pg.rotations);
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pg_cands.push_back({&pg, static_cast<int>(pg.rotations.size()) + 1, min_cc, ch});
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if (!pg.rotations.empty() && std::isfinite(ch))
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chi2_ref = std::min(chi2_ref, ch);
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}
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// Choose the largest point group that is both operator-confirmed AND self-consistent (its merge
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// chi^2 is not inflated past max_merge_chi2_ratio x the most-consistent candidate; ties -> higher
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// min CC). Identity (no operators) is always consistent, so it stays the P1 fallback.
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const PointGroupInfo* best_pg = nullptr;
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int best_pg_order = 0;
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double best_pg_min_cc = -2.0;
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for (const auto& c : pg_cands) {
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const bool consistent = c.pg->rotations.empty() || !std::isfinite(c.chi2) ||
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!std::isfinite(chi2_ref) || c.chi2 <= chi2_ref * opt.max_merge_chi2_ratio;
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if (!consistent)
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continue;
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if (c.order > best_pg_order || (c.order == best_pg_order && c.min_cc > best_pg_min_cc)) {
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best_pg = c.pg;
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best_pg_order = c.order;
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best_pg_min_cc = c.min_cc;
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}
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}
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for (const auto& [rk, s] : op_cache)
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result.operator_scores.push_back(s);
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std::sort(result.operator_scores.begin(), result.operator_scores.end(),
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[](const auto& a, const auto& b) { return a.cc > b.cc; });
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if (best_pg == nullptr) // should not happen (C1 always qualifies)
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return result;
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if (best_pg->representative)
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result.point_group_hm = best_pg->representative->point_group_hm();
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// --- Stage B: pick the space group within the point group ---
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// Without screw/centering determination, return the symmorphic representative.
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if (!opt.determine_space_group || best_pg->rotations.empty()) {
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if (best_pg->representative)
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result.best_space_group = *best_pg->representative;
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return result;
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}
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for (const auto& sg : gemmi::spacegroup_tables::main) {
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if (!sg.is_sohncke() || !sg.is_reference_setting() || RotationSetOf(sg) != best_pg->rotation_set)
|
|
continue;
|
|
|
|
const gemmi::GroupOps gops = sg.operations();
|
|
SpaceGroupCandidateScore s{.space_group = sg};
|
|
double absent_sum = 0, present_sum = 0;
|
|
int present_n = 0;
|
|
|
|
// Judge centering and screw/glide absences on separate reflection sets. Lumping them lets
|
|
// a large, correct centering-absent set hide a few strong screw violations and over-claim
|
|
// screw axes (e.g. I4_132 on I432 data).
|
|
int centering_absent = 0, centering_violations = 0;
|
|
int screw_absent = 0, screw_violations = 0;
|
|
|
|
for (size_t i = 0; i < n; ++i) {
|
|
if (!pass_absence[i])
|
|
continue;
|
|
const gemmi::Op::Miller hkl{{H[i], K[i], L[i]}};
|
|
// Present := statistically significant AND intensity-significant. The E^2 gate keeps a
|
|
// weak axial reflection with an under-estimated sigma (fake high I/sigma) from faking a
|
|
// screw-axis violation; it only relaxes "present", so it cannot over-call a screw whose
|
|
// predicted-absent class carries real intensity.
|
|
const bool present = IoverSigma[i] > opt.present_i_over_sigma &&
|
|
(opt.present_e_squared <= 0.0 || Esq[i] > opt.present_e_squared);
|
|
|
|
if (CenteringAbsent(gops, hkl)) {
|
|
s.absent_observed += 1;
|
|
absent_sum += IoverSigma[i];
|
|
centering_absent += 1;
|
|
if (present) { s.absent_violations += 1; centering_violations += 1; }
|
|
} else if (gops.is_systematically_absent(hkl)) {
|
|
s.absent_observed += 1;
|
|
absent_sum += IoverSigma[i];
|
|
screw_absent += 1;
|
|
if (present) { s.absent_violations += 1; screw_violations += 1; }
|
|
} else {
|
|
present_n += 1;
|
|
present_sum += IoverSigma[i];
|
|
}
|
|
}
|
|
|
|
if (s.absent_observed > 0)
|
|
s.absent_mean_i_over_sigma = absent_sum / s.absent_observed;
|
|
if (present_n > 0)
|
|
s.present_mean_i_over_sigma = present_sum / present_n;
|
|
|
|
const bool centering_ok = centering_absent == 0 ||
|
|
centering_violations <= opt.max_absent_violation_fraction * centering_absent;
|
|
const bool screw_ok = screw_absent == 0 ||
|
|
screw_violations <= opt.max_absent_violation_fraction * screw_absent;
|
|
s.consistent = centering_ok && screw_ok;
|
|
result.candidates.push_back(std::move(s));
|
|
}
|
|
|
|
// A candidate is eligible when its absences are confirmed and there are enough of them to
|
|
// trust (the symmorphic group, with no absences, is always eligible as the fallback). Rank
|
|
// eligible candidates by how many absences they explain - the screw/centering content that is
|
|
// both real and maximal wins, instead of defaulting to the symmorphic group.
|
|
auto eligible = [&](const SpaceGroupCandidateScore& s) {
|
|
return s.consistent && (s.absent_observed == 0 || s.absent_observed >= opt.min_absent_observed);
|
|
};
|
|
std::sort(result.candidates.begin(), result.candidates.end(),
|
|
[&](const SpaceGroupCandidateScore& a, const SpaceGroupCandidateScore& b) {
|
|
if (eligible(a) != eligible(b))
|
|
return eligible(a);
|
|
if (a.absent_observed != b.absent_observed)
|
|
return a.absent_observed > b.absent_observed;
|
|
// Tie (e.g. I23 vs I2_13, indistinguishable by absences): lower space-group number.
|
|
return a.space_group.number < b.space_group.number;
|
|
});
|
|
|
|
if (!result.candidates.empty() && eligible(result.candidates.front())) {
|
|
const int best_absent = result.candidates.front().absent_observed;
|
|
for (auto& s : result.candidates) {
|
|
if (!eligible(s) || s.absent_observed != best_absent)
|
|
continue;
|
|
s.selected = true;
|
|
if (!result.best_space_group.has_value())
|
|
result.best_space_group = s.space_group; // representative (lowest number)
|
|
else
|
|
result.alternatives.push_back(s.space_group);
|
|
}
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
std::string SearchSpaceGroupResultToText(const SearchSpaceGroupResult& result,
|
|
size_t max_candidates_to_print) {
|
|
std::ostringstream os;
|
|
|
|
os << "Point group: " << (result.point_group_hm.empty() ? "?" : result.point_group_hm)
|
|
<< " (from intensity correlations)\n";
|
|
|
|
os << " " << std::setw(14) << std::left << "operator" << std::right
|
|
<< std::setw(9) << "CC" << std::setw(10) << "pairs" << std::setw(9) << "symm" << "\n";
|
|
for (const auto& s : result.operator_scores) {
|
|
os << " " << std::setw(14) << std::left << s.op_triplet_hkl << std::right
|
|
<< std::setw(9) << std::fixed << std::setprecision(3) << s.cc
|
|
<< std::setw(10) << s.n_pairs
|
|
<< std::setw(9) << (s.present ? "yes" : "no") << "\n";
|
|
}
|
|
|
|
os << "\nSpace-group candidates\n";
|
|
os << " " << std::setw(10) << std::left << "SG" << std::right
|
|
<< std::setw(9) << "absent" << std::setw(7) << "viol"
|
|
<< std::setw(11) << "<I/s>abs" << std::setw(11) << "<I/s>pres"
|
|
<< std::setw(6) << "OK" << "\n";
|
|
|
|
const size_t count = std::min(max_candidates_to_print, result.candidates.size());
|
|
for (size_t i = 0; i < count; ++i) {
|
|
const auto& c = result.candidates[i];
|
|
os << (c.selected ? "* " : " ")
|
|
<< std::setw(10) << std::left << c.space_group.short_name() << std::right
|
|
<< std::setw(9) << c.absent_observed << std::setw(7) << c.absent_violations
|
|
<< std::setw(11) << std::fixed << std::setprecision(2) << c.absent_mean_i_over_sigma
|
|
<< std::setw(11) << std::fixed << std::setprecision(2) << c.present_mean_i_over_sigma
|
|
<< std::setw(6) << (c.consistent ? "yes" : "no") << "\n";
|
|
}
|
|
|
|
if (result.best_space_group.has_value()) {
|
|
os << "Best space group: " << result.best_space_group->short_name();
|
|
for (const auto& alt : result.alternatives)
|
|
os << " or " << alt.short_name();
|
|
if (!result.alternatives.empty())
|
|
os << " (indistinguishable from these data)";
|
|
os << "\n";
|
|
} else {
|
|
os << "Best space group: none determined\n";
|
|
}
|
|
|
|
return os.str();
|
|
}
|