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 // This file is part of the ACTS project.
 //
 // Copyright (C) 2016 CERN for the benefit of the ACTS project
 //
 // This Source Code Form is subject to the terms of the Mozilla Public
 // License, v. 2.0. If a copy of the MPL was not distributed with this
 // file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
 #include "Acts/Geometry/Extent.hpp"
 #include "Acts/Seeding/SeedFilter.hpp"
 #include "Acts/Seeding/SeedFinder.hpp"
 #include "Acts/Seeding/SeedFinderOrthogonalConfig.hpp"
 #include "Acts/Seeding/SeedFinderUtils.hpp"
 #include "Acts/Utilities/AxisDefinitions.hpp"
 
 #include <algorithm>
 #include <cmath>
 #include <functional>
 #include <numeric>
 #include <type_traits>
 
 namespace Acts {
 template <typename external_spacepoint_t>
 auto SeedFinderOrthogonal<external_spacepoint_t>::validTupleOrthoRangeLH(
     const external_spacepoint_t &low) const -> typename tree_t::range_t {
   float colMin = m_config.collisionRegionMin;
   float colMax = m_config.collisionRegionMax;
   float pL = low.phi();
   float rL = low.radius();
   float zL = low.z();
 
   typename tree_t::range_t res;
 
   /*
    * Cut: Ensure that we search only in φ_min ≤ φ ≤ φ_max, as defined by the
    * seeding configuration.
    */
   res[DimPhi].shrinkMin(m_config.phiMin);
   res[DimPhi].shrinkMax(m_config.phiMax);
 
   /*
    * Cut: Ensure that we search only in r ≤ r_max, as defined by the seeding
    * configuration.
    */
   res[DimR].shrinkMax(m_config.rMax);
 
   /*
    * Cut: Ensure that we search only in z_min ≤ z ≤ z_max, as defined by the
    * seeding configuration.
    */
   res[DimZ].shrinkMin(m_config.zMin);
   res[DimZ].shrinkMax(m_config.zMax);
 
   /*
    * Cut: Ensure that we search only in Δr_min ≤ r - r_L ≤ Δr_max, as defined
    * by the seeding configuration and the given lower spacepoint.
    */
   res[DimR].shrinkMin(rL + m_config.deltaRMinTopSP);
   res[DimR].shrinkMax(rL + m_config.deltaRMaxTopSP);
 
   /*
    * Cut: Now that we have constrained r, we can use that new r range to
    * further constrain z.
    */
   float zMax = (res[DimR].max() / rL) * (zL - colMin) + colMin;
   float zMin = colMax - (res[DimR].max() / rL) * (colMax - zL);
 
   /*
    * This cut only works if z_low is outside the collision region for z.
    */
   if (zL > colMin) {
     res[DimZ].shrinkMax(zMax);
   } else if (zL < colMax) {
     res[DimZ].shrinkMin(zMin);
   }
 
   /*
    * Cut: Shrink the z-range using the maximum cot(θ).
    */
   res[DimZ].shrinkMin(zL - m_config.cotThetaMax * (res[DimR].max() - rL));
   res[DimZ].shrinkMax(zL + m_config.cotThetaMax * (res[DimR].max() - rL));
 
   /*
    * Cut: Shrink the φ range, such that Δφ_min ≤ φ - φ_L ≤ Δφ_max
    */
   res[DimPhi].shrinkMin(pL - m_config.deltaPhiMax);
   res[DimPhi].shrinkMax(pL + m_config.deltaPhiMax);
 
   // Cut: Ensure that z-distance between SPs is within max and min values.
   res[DimZ].shrinkMin(zL - m_config.deltaZMax);
   res[DimZ].shrinkMax(zL + m_config.deltaZMax);
 
   return res;
 }
 
 template <typename external_spacepoint_t>
 auto SeedFinderOrthogonal<external_spacepoint_t>::validTupleOrthoRangeHL(
     const external_spacepoint_t &high) const -> typename tree_t::range_t {
   float pM = high.phi();
   float rM = high.radius();
   float zM = high.z();
 
   typename tree_t::range_t res;
 
   /*
    * Cut: Ensure that we search only in φ_min ≤ φ ≤ φ_max, as defined by the
    * seeding configuration.
    */
   res[DimPhi].shrinkMin(m_config.phiMin);
   res[DimPhi].shrinkMax(m_config.phiMax);
 
   /*
    * Cut: Ensure that we search only in r ≤ r_max, as defined by the seeding
    * configuration.
    */
   res[DimR].shrinkMax(m_config.rMax);
 
   /*
    * Cut: Ensure that we search only in z_min ≤ z ≤ z_max, as defined by the
    * seeding configuration.
    */
   res[DimZ].shrinkMin(m_config.zMin);
   res[DimZ].shrinkMax(m_config.zMax);
 
   /*
    * Cut: Ensure that we search only in Δr_min ≤ r_H - r ≤ Δr_max, as defined
    * by the seeding configuration and the given higher spacepoint.
    */
   res[DimR].shrinkMin(rM - m_config.deltaRMaxBottomSP);
   res[DimR].shrinkMax(rM - m_config.deltaRMinBottomSP);
 
   /*
    * Cut: Now that we have constrained r, we can use that new r range to
    * further constrain z.
    */
   float fracR = res[DimR].min() / rM;
 
   float zMin =
       (zM - m_config.collisionRegionMin) * fracR + m_config.collisionRegionMin;
   float zMax =
       (zM - m_config.collisionRegionMax) * fracR + m_config.collisionRegionMax;
 
   res[DimZ].shrinkMin(std::min(zMin, zM));
   res[DimZ].shrinkMax(std::max(zMax, zM));
 
   /*
    * Cut: Shrink the φ range, such that Δφ_min ≤ φ - φ_H ≤ Δφ_max
    */
   res[DimPhi].shrinkMin(pM - m_config.deltaPhiMax);
   res[DimPhi].shrinkMax(pM + m_config.deltaPhiMax);
 
   // Cut: Ensure that z-distance between SPs is within max and min values.
   res[DimZ].shrinkMin(zM - m_config.deltaZMax);
   res[DimZ].shrinkMax(zM + m_config.deltaZMax);
 
   return res;
 }
 
 template <typename external_spacepoint_t>
 bool SeedFinderOrthogonal<external_spacepoint_t>::validTuple(
     const SeedFinderOptions &options, const external_spacepoint_t &low,
     const external_spacepoint_t &high, bool isMiddleInverted) const {
   float rL = low.radius();
   float rH = high.radius();
 
   float zL = low.z();
   float zH = high.z();
 
   float deltaR = rH - rL;
 
   float deltaZ = (zH - zL);
   float cotTheta = deltaZ / deltaR;
   /*
    * Cut: Ensure that the origin of the dublet (the intersection of the line
    * between them with the z axis) lies within the collision region.
    */
   float zOrigin = zL - rL * cotTheta;
   if (zOrigin < m_config.collisionRegionMin ||
       zOrigin > m_config.collisionRegionMax) {
     return false;
   }
 
   // cut on the max curvature calculated from dublets
   // first transform the space point coordinates into a frame such that the
   // central space point SPm is in the origin of the frame and the x axis
   // points away from the interaction point in addition to a translation
   // transformation we also perform a rotation in order to keep the
   // curvature of the circle tangent to the x axis
   if (m_config.interactionPointCut) {
     float xVal = (high.x() - low.x()) * (low.x() / rL) +
                  (high.y() - low.y()) * (low.y() / rL);
     float yVal = (high.y() - low.y()) * (low.x() / rL) -
                  (high.x() - low.x()) * (low.y() / rL);
 
     const int sign = isMiddleInverted ? -1 : 1;
 
     if (std::abs(rL * yVal) > sign * m_config.impactMax * xVal) {
       // conformal transformation u=x/(x²+y²) v=y/(x²+y²) transform the
       // circle into straight lines in the u/v plane the line equation can
       // be described in terms of aCoef and bCoef, where v = aCoef * u +
       // bCoef
       float uT = xVal / (xVal * xVal + yVal * yVal);
       float vT = yVal / (xVal * xVal + yVal * yVal);
       // in the rotated frame the interaction point is positioned at x = -rM
       // and y ~= impactParam
       float uIP = -1. / rL;
       float vIP = m_config.impactMax / (rL * rL);
       if (sign * yVal > 0.) {
         vIP = -vIP;
       }
       // we can obtain aCoef as the slope dv/du of the linear function,
       // estimated using du and dv between the two SP bCoef is obtained by
       // inserting aCoef into the linear equation
       float aCoef = (vT - vIP) / (uT - uIP);
       float bCoef = vIP - aCoef * uIP;
       // the distance of the straight line from the origin (radius of the
       // circle) is related to aCoef and bCoef by d^2 = bCoef^2 / (1 +
       // aCoef^2) = 1 / (radius^2) and we can apply the cut on the curvature
       if ((bCoef * bCoef) > (1 + aCoef * aCoef) / options.minHelixDiameter2) {
         return false;
       }
     }
   }
 
   /*
    * Cut: Ensure that the forward angle (z / r) lies within reasonable bounds,
    * which is to say the absolute value must be smaller than the max cot(θ).
    */
   if (std::abs(cotTheta) > m_config.cotThetaMax) {
     return false;
   }
 
   /*
    * Cut: Ensure that inner-middle dublet is in a certain (r, eta) region of the
    * detector according to detector specific cuts.
    */
   const float rInner = (isMiddleInverted) ? rH : rL;
   if (!m_config.experimentCuts(rInner, cotTheta)) {
     return false;
   }
 
   return true;
 }
 
 template <typename external_spacepoint_t>
 SeedFinderOrthogonal<external_spacepoint_t>::SeedFinderOrthogonal(
     const SeedFinderOrthogonalConfig<external_spacepoint_t> &config,
     std::unique_ptr<const Acts::Logger> logger)
     : m_config(config), m_logger(std::move(logger)) {
   if (!config.isInInternalUnits) {
     throw std::runtime_error(
         "SeedFinderOrthogonalConfig not in ACTS internal units in "
         "SeedFinderOrthogonal");
   }
 }
 
 template <typename external_spacepoint_t>
 void SeedFinderOrthogonal<external_spacepoint_t>::filterCandidates(
     const SeedFinderOptions &options, Acts::SpacePointMutableData &mutableData,
     const external_spacepoint_t &middle,
     const std::vector<const external_spacepoint_t *> &bottom,
     const std::vector<const external_spacepoint_t *> &top,
     SeedFilterState seedFilterState,
     CandidatesForMiddleSp<const external_spacepoint_t> &candidates_collector)
     const {
   float rM = middle.radius();
   float zM = middle.z();
   float varianceRM = middle.varianceR();
   float varianceZM = middle.varianceZ();
 
   // apply cut on the number of top SP if seedConfirmation is true
   if (m_config.seedConfirmation == true) {
     // check if middle SP is in the central or forward region
     SeedConfirmationRangeConfig seedConfRange =
         (zM > m_config.centralSeedConfirmationRange.zMaxSeedConf ||
          zM < m_config.centralSeedConfirmationRange.zMinSeedConf)
             ? m_config.forwardSeedConfirmationRange
             : m_config.centralSeedConfirmationRange;
     // set the minimum number of top SP depending on whether the middle SP is
     // in the central or forward region
     seedFilterState.nTopSeedConf = rM > seedConfRange.rMaxSeedConf
                                        ? seedConfRange.nTopForLargeR
                                        : seedConfRange.nTopForSmallR;
     // set max bottom radius for seed confirmation
     seedFilterState.rMaxSeedConf = seedConfRange.rMaxSeedConf;
     // continue if number of top SPs is smaller than minimum
     if (top.size() < seedFilterState.nTopSeedConf) {
       return;
     }
   }
 
   std::vector<const external_spacepoint_t *> top_valid;
   std::vector<float> curvatures;
   std::vector<float> impactParameters;
 
   // contains parameters required to calculate circle with linear equation
   // ...for bottom-middle
   std::vector<LinCircle> linCircleBottom;
   // ...for middle-top
   std::vector<LinCircle> linCircleTop;
 
   // transform coordinates
   transformCoordinates(mutableData, bottom, middle, true, linCircleBottom);
   transformCoordinates(mutableData, top, middle, false, linCircleTop);
 
   // sort: make index vector
   std::vector<std::size_t> sorted_bottoms(linCircleBottom.size());
   for (std::size_t i(0); i < sorted_bottoms.size(); ++i) {
     sorted_bottoms[i] = i;
   }
 
   std::vector<std::size_t> sorted_tops(linCircleTop.size());
   for (std::size_t i(0); i < sorted_tops.size(); ++i) {
     sorted_tops[i] = i;
   }
 
   std::ranges::sort(sorted_bottoms, {},
                     [&linCircleBottom](const std::size_t s) {
                       return linCircleBottom[s].cotTheta;
                     });
 
   std::ranges::sort(sorted_tops, {}, [&linCircleTop](const std::size_t s) {
     return linCircleTop[s].cotTheta;
   });
 
   std::vector<float> tanMT;
   tanMT.reserve(top.size());
 
   std::size_t numTopSP = top.size();
   for (std::size_t t = 0; t < numTopSP; t++) {
     tanMT.push_back(
         std::atan2(top[t]->radius() - middle.radius(), top[t]->z() - zM));
   }
 
   std::size_t t0 = 0;
 
   for (const std::size_t b : sorted_bottoms) {
     // break if we reached the last top SP
     if (t0 == numTopSP) {
       break;
     }
 
     auto lb = linCircleBottom[b];
 
     // 1+(cot^2(theta)) = 1/sin^2(theta)
     float iSinTheta2 = (1. + lb.cotTheta * lb.cotTheta);
     float sigmaSquaredPtDependent = iSinTheta2 * options.sigmapT2perRadius;
     // calculate max scattering for min momentum at the seed's theta angle
     // scaling scatteringAngle^2 by sin^2(theta) to convert pT^2 to p^2
     // accurate would be taking 1/atan(thetaBottom)-1/atan(thetaTop) <
     // scattering
     // but to avoid trig functions we approximate cot by scaling by
     // 1/sin^4(theta)
     // resolving with pT to p scaling --> only divide by sin^2(theta)
     // max approximation error for allowed scattering angles of 0.04 rad at
     // eta=infinity: ~8.5%
     float scatteringInRegion2 = options.multipleScattering2 * iSinTheta2;
 
     // minimum number of compatible top SPs to trigger the filter for a certain
     // middle bottom pair if seedConfirmation is false we always ask for at
     // least one compatible top to trigger the filter
     std::size_t minCompatibleTopSPs = 2;
     if (!m_config.seedConfirmation ||
         bottom[b]->radius() > seedFilterState.rMaxSeedConf) {
       minCompatibleTopSPs = 1;
     }
     if (m_config.seedConfirmation &&
         candidates_collector.nHighQualityCandidates()) {
       minCompatibleTopSPs++;
     }
 
     // clear all vectors used in each inner for loop
     top_valid.clear();
     curvatures.clear();
     impactParameters.clear();
 
     float tanLM = std::atan2(rM - bottom[b]->radius(), zM - bottom[b]->z());
 
     for (std::size_t index_t = t0; index_t < numTopSP; index_t++) {
       const std::size_t t = sorted_tops[index_t];
       auto lt = linCircleTop[t];
 
       if (std::abs(tanLM - tanMT[t]) > 0.005) {
         continue;
       }
 
       // add errors of spB-spM and spM-spT pairs and add the correlation term
       // for errors on spM
       float error2 = lt.Er + lb.Er +
                      2 * (lb.cotTheta * lt.cotTheta * varianceRM + varianceZM) *
                          lb.iDeltaR * lt.iDeltaR;
 
       float deltaCotTheta = lb.cotTheta - lt.cotTheta;
       float deltaCotTheta2 = deltaCotTheta * deltaCotTheta;
 
       // Apply a cut on the compatibility between the r-z slope of the two
       // seed segments. This is done by comparing the squared difference
       // between slopes, and comparing to the squared uncertainty in this
       // difference - we keep a seed if the difference is compatible within
       // the assumed uncertainties. The uncertainties get contribution from
       // the  space-point-related squared error (error2) and a scattering term
       // calculated assuming the minimum pt we expect to reconstruct
       // (scatteringInRegion2). This assumes gaussian error propagation which
       // allows just adding the two errors if they are uncorrelated (which is
       // fair for scattering and measurement uncertainties)
       if (deltaCotTheta2 > (error2 + scatteringInRegion2)) {
         // skip top SPs based on cotTheta sorting when producing triplets
         // break if cotTheta from bottom SP < cotTheta from top SP because
         // the SP are sorted by cotTheta
         if (deltaCotTheta < 0) {
           break;
         }
         t0 = index_t + 1;
         continue;
       }
 
       float dU = lt.U - lb.U;
 
       // A and B are evaluated as a function of the circumference parameters
       // x_0 and y_0
       float A = (lt.V - lb.V) / dU;
       float S2 = 1. + A * A;
       float B = lb.V - A * lb.U;
       float B2 = B * B;
       // sqrt(S2)/B = 2 * helixradius
       // calculated radius must not be smaller than minimum radius
       if (S2 < B2 * options.minHelixDiameter2) {
         continue;
       }
 
       // 1/helixradius: (B/sqrt(S2))*2 (we leave everything squared)
       // convert p(T) to p scaling by sin^2(theta) AND scale by 1/sin^4(theta)
       // from rad to deltaCotTheta
       float p2scatterSigma = B2 / S2 * sigmaSquaredPtDependent;
       if (!std::isinf(m_config.maxPtScattering)) {
         // if pT > maxPtScattering, calculate allowed scattering angle using
         // maxPtScattering instead of pt.
         if (B2 == 0 || options.pTPerHelixRadius * std::sqrt(S2 / B2) >
                            2. * m_config.maxPtScattering) {
           float pTscatterSigma =
               (m_config.highland / m_config.maxPtScattering) *
               m_config.sigmaScattering;
           p2scatterSigma = pTscatterSigma * pTscatterSigma * iSinTheta2;
         }
       }
       // if deltaTheta larger than allowed scattering for calculated pT, skip
       if (deltaCotTheta2 > (error2 + p2scatterSigma)) {
         if (deltaCotTheta < 0) {
           break;
         }
         t0 = index_t;
         continue;
       }
 
       // A and B allow calculation of impact params in U/V plane with linear
       // function
       // (in contrast to having to solve a quadratic function in x/y plane)
       float Im = std::abs((A - B * rM) * rM);
 
       if (Im <= m_config.impactMax) {
         top_valid.push_back(top[t]);
         // inverse diameter is signed depending on if the curvature is
         // positive/negative in phi
         curvatures.push_back(B / std::sqrt(S2));
         impactParameters.push_back(Im);
       }
     }
 
     // continue if number of top SPs is smaller than minimum required for filter
     if (top_valid.size() < minCompatibleTopSPs) {
       continue;
     }
 
     seedFilterState.zOrigin = zM - rM * lb.cotTheta;
 
     m_config.seedFilter->filterSeeds_2SpFixed(
         mutableData, *bottom[b], middle, top_valid, curvatures,
         impactParameters, seedFilterState, candidates_collector);
 
   }  // loop on bottoms
 }
 
 template <typename external_spacepoint_t>
 template <typename output_container_t>
 void SeedFinderOrthogonal<external_spacepoint_t>::processFromMiddleSP(
     const SeedFinderOptions &options, Acts::SpacePointMutableData &mutableData,
     const tree_t &tree, output_container_t &out_cont,
     const typename tree_t::pair_t &middle_p) const {
   using range_t = typename tree_t::range_t;
   const external_spacepoint_t &middle = *middle_p.second;
 
   /*
    * Prepare four output vectors for seed candidates:
    *
    * bottom_lh_v denotes the candidates bottom seed points, assuming that the
    * track has monotonically _increasing_ z position. bottom_hl_v denotes the
    * candidate bottom points assuming that the track has monotonically
    * _decreasing_ z position. top_lh_v are the candidate top points for an
    * increasing z track, and top_hl_v are the candidate top points for a
    * decreasing z track.
    */
   std::vector<const external_spacepoint_t *> bottom_lh_v, bottom_hl_v, top_lh_v,
       top_hl_v;
 
   /*
    * Storage for seed candidates
    */
   std::size_t max_num_quality_seeds_per_spm =
       m_config.seedFilter->getSeedFilterConfig().maxQualitySeedsPerSpMConf;
   std::size_t max_num_seeds_per_spm =
       m_config.seedFilter->getSeedFilterConfig().maxSeedsPerSpMConf;
 
   CandidatesForMiddleSp<const external_spacepoint_t> candidates_collector;
   candidates_collector.setMaxElements(max_num_seeds_per_spm,
                                       max_num_quality_seeds_per_spm);
 
   /*
    * Calculate the search ranges for bottom and top candidates for this middle
    * space point.
    */
   range_t bottom_r = validTupleOrthoRangeHL(middle);
   range_t top_r = validTupleOrthoRangeLH(middle);
 
   /*
    * Calculate the value of cot(θ) for this middle spacepoint.
    */
   float myCotTheta =
       std::max(std::abs(middle.z() / middle.radius()), m_config.cotThetaMax);
 
   /*
    * Calculate the maximum Δr, given that we have already constrained our
    * search space.
    */
   float deltaRMaxTop = top_r[DimR].max() - middle.radius();
   float deltaRMaxBottom = middle.radius() - bottom_r[DimR].min();
 
   /*
    * Create the search range for the bottom spacepoint assuming a
    * monotonically increasing z track, by calculating the minimum z value from
    * the cot(θ), and by setting the maximum to the z position of the middle
    * spacepoint - if the z position is higher than the middle point, then it
    * would be a decreasing z track!
    */
   range_t bottom_lh_r = bottom_r;
   bottom_lh_r[DimZ].shrink(middle.z() - myCotTheta * deltaRMaxBottom,
                            middle.z());
 
   /*
    * Calculate the search ranges for the other four sets of points in a
    * similar fashion.
    */
   range_t top_lh_r = top_r;
   top_lh_r[DimZ].shrink(middle.z(), middle.z() + myCotTheta * deltaRMaxTop);
 
   range_t bottom_hl_r = bottom_r;
   bottom_hl_r[DimZ].shrink(middle.z(),
                            middle.z() + myCotTheta * deltaRMaxBottom);
   range_t top_hl_r = top_r;
   top_hl_r[DimZ].shrink(middle.z() - myCotTheta * deltaRMaxTop, middle.z());
 
   /*
    * Make sure the candidate vectors are clear, in case we've used them
    * before.
    */
   bottom_lh_v.clear();
   bottom_hl_v.clear();
   top_lh_v.clear();
   top_hl_v.clear();
 
   /*
    * Now, we will actually search for the spaces. Remembering that we combine
    * bottom and top candidates for increasing and decreasing tracks
    * separately, we will first check whether both the search ranges for
    * increasing tracks are not degenerate - if they are, we will never find
    * any seeds and we do not need to bother doing the search.
    */
   if (!bottom_lh_r.degenerate() && !top_lh_r.degenerate()) {
     /*
      * Search the trees for points that lie in the given search range.
      */
     tree.rangeSearchMapDiscard(top_lh_r,
                                [this, &options, &middle, &top_lh_v](
                                    const typename tree_t::coordinate_t &,
                                    const typename tree_t::value_t &top) {
                                  if (validTuple(options, *top, middle, true)) {
                                    top_lh_v.push_back(top);
                                  }
                                });
   }
 
   /*
    * Perform the same search for candidate bottom spacepoints, but for
    * monotonically decreasing z tracks.
    */
   if (!bottom_hl_r.degenerate() && !top_hl_r.degenerate()) {
     tree.rangeSearchMapDiscard(top_hl_r,
                                [this, &options, &middle, &top_hl_v](
                                    const typename tree_t::coordinate_t &,
                                    const typename tree_t::value_t &top) {
                                  if (validTuple(options, middle, *top, false)) {
                                    top_hl_v.push_back(top);
                                  }
                                });
   }
 
   // apply cut on the number of top SP if seedConfirmation is true
   SeedFilterState seedFilterState;
   bool search_bot_hl = true;
   bool search_bot_lh = true;
   if (m_config.seedConfirmation) {
     // check if middle SP is in the central or forward region
     SeedConfirmationRangeConfig seedConfRange =
         (middle.z() > m_config.centralSeedConfirmationRange.zMaxSeedConf ||
          middle.z() < m_config.centralSeedConfirmationRange.zMinSeedConf)
             ? m_config.forwardSeedConfirmationRange
             : m_config.centralSeedConfirmationRange;
     // set the minimum number of top SP depending on whether the middle SP is
     // in the central or forward region
     seedFilterState.nTopSeedConf = middle.radius() > seedConfRange.rMaxSeedConf
                                        ? seedConfRange.nTopForLargeR
                                        : seedConfRange.nTopForSmallR;
     // set max bottom radius for seed confirmation
     seedFilterState.rMaxSeedConf = seedConfRange.rMaxSeedConf;
     // continue if number of top SPs is smaller than minimum
     if (top_lh_v.size() < seedFilterState.nTopSeedConf) {
       search_bot_lh = false;
     }
     if (top_hl_v.size() < seedFilterState.nTopSeedConf) {
       search_bot_hl = false;
     }
   }
 
   /*
    * Next, we perform a search for bottom candidates in increasing z tracks,
    * which only makes sense if we found any bottom candidates.
    */
   if (!top_lh_v.empty() && search_bot_lh) {
     tree.rangeSearchMapDiscard(
         bottom_lh_r, [this, &options, &middle, &bottom_lh_v](
                          const typename tree_t::coordinate_t &,
                          const typename tree_t::value_t &bottom) {
           if (validTuple(options, *bottom, middle, false)) {
             bottom_lh_v.push_back(bottom);
           }
         });
   }
 
   /*
    * And repeat for the top spacepoints for decreasing z tracks!
    */
   if (!top_hl_v.empty() && search_bot_hl) {
     tree.rangeSearchMapDiscard(
         bottom_hl_r, [this, &options, &middle, &bottom_hl_v](
                          const typename tree_t::coordinate_t &,
                          const typename tree_t::value_t &bottom) {
           if (validTuple(options, middle, *bottom, true)) {
             bottom_hl_v.push_back(bottom);
           }
         });
   }
 
   /*
    * If we have candidates for increasing z tracks, we try to combine them.
    */
   if (!bottom_lh_v.empty() && !top_lh_v.empty()) {
     filterCandidates(options, mutableData, middle, bottom_lh_v, top_lh_v,
                      seedFilterState, candidates_collector);
   }
   /*
    * Try to combine candidates for decreasing z tracks.
    */
   if (!bottom_hl_v.empty() && !top_hl_v.empty()) {
     filterCandidates(options, mutableData, middle, bottom_hl_v, top_hl_v,
                      seedFilterState, candidates_collector);
   }
   /*
    * Run a seed filter, just like in other seeding algorithms.
    */
   if ((!bottom_lh_v.empty() && !top_lh_v.empty()) ||
       (!bottom_hl_v.empty() && !top_hl_v.empty())) {
     m_config.seedFilter->filterSeeds_1SpFixed(mutableData, candidates_collector,
                                               out_cont);
   }
 }
 
 template <typename external_spacepoint_t>
 auto SeedFinderOrthogonal<external_spacepoint_t>::createTree(
     const std::vector<const external_spacepoint_t *> &spacePoints) const
     -> tree_t {
   std::vector<typename tree_t::pair_t> points;
   points.reserve(spacePoints.size());
 
   /*
    * For every input point, we create a coordinate-pointer pair, which we then
    * linearly pass to the k-d tree constructor. That constructor will take
    * care of sorting the pairs and splitting the space.
    */
   for (const external_spacepoint_t *sp : spacePoints) {
     typename tree_t::coordinate_t point;
 
     point[DimPhi] = sp->phi();
     point[DimR] = sp->radius();
     point[DimZ] = sp->z();
 
     points.emplace_back(point, sp);
   }
 
   ACTS_VERBOSE("Created k-d tree populated with " << points.size()
                                                   << " space points");
   return tree_t(std::move(points));
 }
 
 template <typename external_spacepoint_t>
 template <typename input_container_t, typename output_container_t>
 void SeedFinderOrthogonal<external_spacepoint_t>::createSeeds(
     const Acts::SeedFinderOptions &options,
     const input_container_t &spacePoints, output_container_t &out_cont) const {
   ACTS_VERBOSE("Creating seeds with Orthogonal strategy");
   if (!options.isInInternalUnits) {
     throw std::runtime_error(
         "SeedFinderOptions not in ACTS internal units in "
         "SeedFinderOrthogonal");
   }
   /*
    * The template parameters we accept are a little too generic, so we want to
    * run some basic checks to make sure the containers have the correct value
    * types.
    */
   static_assert(std::is_same_v<typename output_container_t::value_type,
                                Seed<external_spacepoint_t>>,
                 "Output iterator container type must accept seeds.");
   static_assert(std::is_same_v<typename input_container_t::value_type,
                                external_spacepoint_t>,
                 "Input container must contain external spacepoints.");
 
   /*
    * Sadly, for the time being, we will need to construct our internal space
    * points on the heap. This adds some additional overhead and work. Here we
    * take each external spacepoint, allocate a corresponding internal space
    * point, and save it in a vector.
    */
   ACTS_VERBOSE("Running on " << spacePoints.size() << " input space points");
   Acts::Extent rRangeSPExtent;
   std::vector<const external_spacepoint_t *> internal_sps;
   internal_sps.reserve(spacePoints.size());
 
   Acts::SpacePointMutableData mutableData;
   mutableData.resize(spacePoints.size());
 
   for (const external_spacepoint_t &p : spacePoints) {
     // store x,y,z values in extent
     rRangeSPExtent.extend({p.x(), p.y(), p.z()});
     internal_sps.push_back(&p);
   }
   ACTS_VERBOSE(rRangeSPExtent);
 
   // variable middle SP radial region of interest
   const Acts::Range1D<float> rMiddleSPRange(
       std::floor(rRangeSPExtent.min(Acts::AxisDirection::AxisR) / 2) * 2 +
           m_config.deltaRMiddleMinSPRange,
       std::floor(rRangeSPExtent.max(Acts::AxisDirection::AxisR) / 2) * 2 -
           m_config.deltaRMiddleMaxSPRange);
 
   /*
    * Construct the k-d tree from these points. Note that this not consume or
    * take ownership of the points.
    */
   tree_t tree = createTree(internal_sps);
   /*
    * Run the seeding algorithm by iterating over all the points in the tree
    * and seeing what happens if we take them to be our middle spacepoint.
    */
   for (const typename tree_t::pair_t &middle_p : tree) {
     const external_spacepoint_t &middle = *middle_p.second;
     auto rM = middle.radius();
 
     /*
      * Cut: Ensure that the middle spacepoint lies within a valid r-region for
      * middle points.
      */
     if (m_config.useVariableMiddleSPRange) {
       if (rM < rMiddleSPRange.min() || rM > rMiddleSPRange.max()) {
         continue;
       }
     } else {
       if (rM > m_config.rMaxMiddle || rM < m_config.rMinMiddle) {
         continue;
       }
     }
 
     // remove all middle SPs outside phi and z region of interest
     if (middle.z() < m_config.zOutermostLayers.first ||
         middle.z() > m_config.zOutermostLayers.second) {
       continue;
     }
     float spPhi = middle.phi();
     if (spPhi > m_config.phiMax || spPhi < m_config.phiMin) {
       continue;
     }
 
     processFromMiddleSP(options, mutableData, tree, out_cont, middle_p);
   }
 }
 
 template <typename external_spacepoint_t>
 template <typename input_container_t>
 std::vector<Seed<external_spacepoint_t>>
 SeedFinderOrthogonal<external_spacepoint_t>::createSeeds(
     const Acts::SeedFinderOptions &options,
     const input_container_t &spacePoints) const {
   std::vector<seed_t> r;
   createSeeds(options, spacePoints, r);
   return r;
 }
 
 }  // namespace Acts

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