EigenRefinement.h

Go to the documentation of this file.

#ifndef INCLUDE_MOLASSEMBLER_DG_EIGEN_REFINEMENT_PROBLEM_H
#define INCLUDE_MOLASSEMBLER_DG_EIGEN_REFINEMENT_PROBLEM_H

#include <Eigen/Dense>

#include "Molassembler/DistanceGeometry/DistanceBoundsMatrix.h"

namespace Scine {
namespace Molassembler {
namespace DistanceGeometry {

template<unsigned dimensionality, typename FloatType, bool SIMD>
class EigenRefinementProblem {
  static_assert(
    dimensionality == 3 || dimensionality == 4,
    "EigenRefinementProblem is only suitable for three or four dimensions"
  );

public:
  using VectorType = Eigen::Matrix<FloatType, Eigen::Dynamic, 1>;

  using ThreeDimensionalVector = Eigen::Matrix<FloatType, 3, 1>;
  using FullDimensionalVector = Eigen::Matrix<FloatType, dimensionality, 1>;

  using ThreeDimensionalMatrixType = Eigen::Matrix<FloatType, 3, Eigen::Dynamic>;
  using FullDimensionalMatrixType = Eigen::Matrix<FloatType, dimensionality, Eigen::Dynamic>;
  using FloatingPointType = FloatType;

  struct DefaultTermVisitor {
    void distanceTerm(unsigned /* i */, unsigned /* j */, double /* value */) {}
    void chiralTerm(const ChiralConstraint::SiteSequence& /* sites */, double /* value */) {}
    void dihedralTerm(const DihedralConstraint::SiteSequence& /* sites */, double /* value */) {}
    void fourthDimensionTerm(unsigned /* i */, double /* value */) {}
  };


  static std::string name() {
    std::string name = "Eigen";

    name += "RefinementProblem<dimensionality=";
    name += std::to_string(dimensionality);
    name += ", ";

    if(std::is_same<FloatType, float>::value) {
      name += "float";
    } else {
      name += "double";
    }

    if(SIMD) {
      name += ", SIMD=true>";
    } else {
      name += ", SIMD=false>";
    }

    return name;
  }

  inline static FullDimensionalVector getPosition(
    const VectorType& positions,
    const AtomIndex index
  ) {
    return positions.template segment<dimensionality>(dimensionality * index);
  }

  inline static ThreeDimensionalVector getPosition3D(
    const VectorType& positions,
    const AtomIndex index
  ) {
    return positions.template segment<3>(dimensionality * index);
  }

  static FullDimensionalVector getAveragePosition(
    const VectorType& positions,
    const ChiralConstraint::AtomListType& atomList
  ) {
    if(atomList.size() == 1) {
      return getPosition(positions, atomList.front());
    }

    FullDimensionalVector sum = FullDimensionalVector::Zero();
    for(const AtomIndex i : atomList) {
      sum += positions.template segment<dimensionality>(dimensionality * i);
    }

    return sum / atomList.size();
  }

  static ThreeDimensionalVector getAveragePosition3D(
    const VectorType& positions,
    const ChiralConstraint::AtomListType& atomList
  ) {
    if(atomList.size() == 1) {
      return getPosition3D(positions, atomList.front());
    }

    ThreeDimensionalVector sum = ThreeDimensionalVector::Zero();
    for(const AtomIndex i : atomList) {
      sum += positions.template segment<3>(dimensionality * i);
    }

    return sum / atomList.size();
  }

  VectorType upperDistanceBoundsSquared;
  VectorType lowerDistanceBoundsSquared;
  VectorType chiralUpperConstraints;
  VectorType chiralLowerConstraints;
  VectorType dihedralConstraintSumsHalved;
  VectorType dihedralConstraintDiffsHalved;
  std::vector<ChiralConstraint> chiralConstraints;
  std::vector<DihedralConstraint> dihedralConstraints;
  bool compressFourthDimension = false;
  bool dihedralTerms = false;

  mutable double proportionChiralConstraintsCorrectSign = 0.0;

  EigenRefinementProblem(
    const Eigen::MatrixXd& squaredBounds,
    std::vector<ChiralConstraint> passChiralConstraints,
    std::vector<DihedralConstraint> passDihedralConstraints
  ) : chiralConstraints(std::move(passChiralConstraints)),
      dihedralConstraints(std::move(passDihedralConstraints))
  {
    const unsigned N = squaredBounds.cols();
    const unsigned strictlyUpperTriangularElements = N * (N - 1) / 2;

    // Lineize upper distance bounds squared
    upperDistanceBoundsSquared.resize(strictlyUpperTriangularElements);
    lowerDistanceBoundsSquared.resize(strictlyUpperTriangularElements);
    for(unsigned linearIndex = 0, i = 0; i < N; ++i) {
      for(unsigned j = i + 1; j < N; ++j, ++linearIndex) {
        upperDistanceBoundsSquared(linearIndex) = squaredBounds(i, j);
        lowerDistanceBoundsSquared(linearIndex) = squaredBounds(j, i);
      }
    }

    // Vectorize chiral constraint bounds
    const unsigned C = chiralConstraints.size();
    chiralUpperConstraints.resize(C);
    chiralLowerConstraints.resize(C);
    for(unsigned i = 0; i < C; ++i) {
      const ChiralConstraint& constraint = chiralConstraints[i];
      chiralUpperConstraints(i) = constraint.upper;
      chiralLowerConstraints(i) = constraint.lower;
    }

    // Vectorize dihedral constraint bounds sum halves and diff halves
    const unsigned D = dihedralConstraints.size();
    dihedralConstraintSumsHalved.resize(D);
    dihedralConstraintDiffsHalved.resize(D);
    for(unsigned i = 0; i < D; ++i) {
      const DihedralConstraint& constraint = dihedralConstraints[i];
      dihedralConstraintSumsHalved(i) = (constraint.upper + constraint.lower) / 2;
      dihedralConstraintDiffsHalved(i) = (constraint.upper - constraint.lower) / 2;
    }
  }


  void distanceContributions(
    const VectorType& positions,
    FloatType& error,
    Eigen::Ref<VectorType> gradient
  ) const {
    // Delegate to SIMD or non-SIMD implementation
    distanceContributionsImpl(positions, error, gradient, DefaultTermVisitor {});
  }

  void chiralContributions(
    const VectorType& positions,
    FloatType& error,
    Eigen::Ref<VectorType> gradient
  ) const {
    chiralContributionsImpl(positions, error, gradient, DefaultTermVisitor {});
  }

  void dihedralContributions(
    const VectorType& positions,
    FloatType& error,
    Eigen::Ref<VectorType> gradient
  ) const {
    if(dihedralTerms) {
      dihedralContributionsImpl(positions, error, gradient, DefaultTermVisitor {});
    }
  }

  void fourthDimensionContributions(
    const VectorType& positions,
    FloatType& error,
    Eigen::Ref<VectorType> gradient
  ) const {
    fourthDimensionContributionsImpl(positions, error, gradient, DefaultTermVisitor {});
  }

  void operator() (const VectorType& parameters, FloatType& value, Eigen::Ref<VectorType> gradient) const {
    assert(parameters.size() == gradient.size());
    assert(parameters.size() % dimensionality == 0);

    value = 0;
    gradient.setZero();

    fourthDimensionContributions(parameters, value, gradient);
    dihedralContributions(parameters, value, gradient);
    distanceContributions(parameters, value, gradient);
    chiralContributions(parameters, value, gradient);
  }

  double calculateProportionChiralConstraintsCorrectSign(const VectorType& positions) const {
    unsigned nonZeroChiralConstraints = 0;
    unsigned incorrectNonZeroChiralConstraints = 0;

    for(const auto& constraint : chiralConstraints) {
      /* Make sure that chiral constraints meant to cause coplanarity of
       * four indices aren't counted here - Their volume bounds are
       * usually so tight that they might be slightly outside in any given
       * refinement step. If they are outside their target values by a large
       * amount, that is caught by finalStructureAcceptable anyway.
       */
      if(!constraint.targetVolumeIsZero()) {
        nonZeroChiralConstraints += 1;

        const ThreeDimensionalVector delta = getAveragePosition3D(positions, constraint.sites[3]);

        const double volume = (
          getAveragePosition3D(positions, constraint.sites[0]) - delta
        ).dot(
          (
            getAveragePosition3D(positions, constraint.sites[1]) - delta
          ).cross(
            getAveragePosition3D(positions, constraint.sites[2]) - delta
          )
        );

        if( // can this be simplified? -> sign bit XOR?
          (volume < 0 && constraint.lower > 0)
          || (volume > 0 && constraint.lower < 0)
        ) {
          incorrectNonZeroChiralConstraints += 1;
        }
      }
    }

    if(nonZeroChiralConstraints == 0) {
      proportionChiralConstraintsCorrectSign = 1.0;
    } else {
      proportionChiralConstraintsCorrectSign = static_cast<double>(
        nonZeroChiralConstraints - incorrectNonZeroChiralConstraints
      ) / nonZeroChiralConstraints;
    }

    return proportionChiralConstraintsCorrectSign;
  }

  template<typename Visitor>
  auto visitTerms(const VectorType& positions, Visitor&& visitor) const {
    FloatType dummyValue = 0;
    VectorType dummyGradient;
    dummyGradient.resize(positions.size());
    dummyGradient.setZero();

    fourthDimensionContributionsImpl(positions, dummyValue, dummyGradient, visitor);
    dihedralContributionsImpl(positions, dummyValue, dummyGradient, visitor);
    distanceContributionsImpl(positions, dummyValue, dummyGradient, visitor);
    chiralContributionsImpl(positions, dummyValue, dummyGradient, visitor);
  }

  template<typename Visitor>
  auto visitUnfulfilledConstraints(
    const DistanceBoundsMatrix& bounds,
    const VectorType& positions,
    Visitor&& visitor
  ) const {
    const unsigned N = positions.size() / dimensionality;

    // Distance bounds deviations
    for(unsigned i = 0; i < N; ++i) {
      for(unsigned j = i + 1; j < N; ++j) {
        const double ijDistance = (
          positions.template segment<dimensionality>(dimensionality * j)
          - positions.template segment<dimensionality>(dimensionality * i)
        ).norm();

        if(
          ijDistance - bounds.upperBound(i, j) > visitor.deviationThreshold
          || bounds.lowerBound(i, j) - ijDistance > visitor.deviationThreshold
        ) {
          visitor.distanceOverThreshold(i, j, ijDistance);
          if(visitor.earlyExit) {
            return visitor.value;
          }
        }
      }
    }

    // Check chiral bound deviations
    for(const auto& constraint : chiralConstraints) {
      const double volume = (
        getAveragePosition3D(positions, constraint.sites[0])
        - getAveragePosition3D(positions, constraint.sites[3])
      ).dot(
        (
          getAveragePosition3D(positions, constraint.sites[1])
          - getAveragePosition3D(positions, constraint.sites[3])
        ).cross(
          getAveragePosition3D(positions, constraint.sites[2])
          - getAveragePosition3D(positions, constraint.sites[3])
        )
      );

      if(
        volume - constraint.upper > visitor.deviationThreshold
        || constraint.lower - volume > visitor.deviationThreshold
      ) {
        visitor.chiralOverThreshold(constraint, volume);
        if(visitor.earlyExit) {
          return visitor.value;
        }
      }
    }

    // Check dihedral constraints
    for(const auto& constraint : dihedralConstraints) {
      const ThreeDimensionalVector alpha = getAveragePosition3D(positions, constraint.sites[0]);
      const ThreeDimensionalVector beta = getAveragePosition3D(positions, constraint.sites[1]);
      const ThreeDimensionalVector gamma = getAveragePosition3D(positions, constraint.sites[2]);
      const ThreeDimensionalVector delta = getAveragePosition3D(positions, constraint.sites[3]);

      const ThreeDimensionalVector f = alpha - beta;
      const ThreeDimensionalVector g = beta - gamma;
      const ThreeDimensionalVector h = delta - gamma;

      const ThreeDimensionalVector a = f.cross(g);
      const ThreeDimensionalVector b = h.cross(g);

      const double dihedral = std::atan2(
        a.cross(b).dot(-g.normalized()),
        a.dot(b)
      );

      const double constraintSumHalved = (constraint.lower + constraint.upper) / 2;

      double phi;
      if(dihedral < constraintSumHalved - M_PI) {
        phi = dihedral + 2 * M_PI;
      } else if(dihedral > constraintSumHalved + M_PI) {
        phi = dihedral - 2 * M_PI;
      } else {
        phi = dihedral;
      }

      const double term = std::fabs(phi - constraintSumHalved) - (constraint.upper - constraint.lower) / 2;

      if(term > visitor.deviationThreshold) {
        visitor.dihedralOverThreshold(constraint, dihedral, term);
        if(visitor.earlyExit) {
          return visitor.value;
        }
      }
    }

    return visitor.value;
  }

private:

  template<class Visitor, bool dependent = SIMD, std::enable_if_t<!dependent, int>...>
  void distanceContributionsImpl(
    const VectorType& positions,
    FloatType& error,
    Eigen::Ref<VectorType> gradient,
    Visitor&& visitor
  ) const {
    assert(positions.size() == gradient.size());
    const unsigned N = positions.size() / dimensionality;

    for(unsigned linearIndex = 0, i = 0; i < N - 1; ++i) {
      for(unsigned j = i + 1; j < N; ++j, ++linearIndex) {
        const FloatType lowerBoundSquared = lowerDistanceBoundsSquared(linearIndex);
        const FloatType upperBoundSquared = upperDistanceBoundsSquared(linearIndex);
        assert(lowerBoundSquared <= upperBoundSquared);

        // For both
        const FullDimensionalVector positionDifference = (
          positions.template segment<dimensionality>(dimensionality * i)
          - positions.template segment<dimensionality>(dimensionality * j)
        );

        const FloatType squareDistance = positionDifference.squaredNorm();

        // Upper term
        const FloatType upperTerm = squareDistance / upperBoundSquared - 1;

        if(upperTerm > 0) {
          const FloatType value = upperTerm * upperTerm;
          error += value;
          visitor.distanceTerm(i, j, value);

          const FullDimensionalVector f = 4 * positionDifference * upperTerm / upperBoundSquared;

          gradient.template segment<dimensionality>(dimensionality * i) += f;
          gradient.template segment<dimensionality>(dimensionality * j) -= f;
        } else {
          // Lower term is only possible if the upper term does not contribute
          const FloatType quotient = lowerBoundSquared + squareDistance;
          const FloatType lowerTerm = 2 * lowerBoundSquared / quotient - 1;

          if(lowerTerm > 0) {
            const FloatType value = lowerTerm * lowerTerm;
            error += value;
            visitor.distanceTerm(i, j, value);

            const FullDimensionalVector g = 8 * lowerBoundSquared * positionDifference * lowerTerm / (
              quotient * quotient
            );

            /* We use -= because the lower term needs the position vector
             * difference (j - i), so we reuse positionDifference and just subtract
             * from the gradient instead of adding to it
             */
            gradient.template segment<dimensionality>(dimensionality * i) -= g;
            gradient.template segment<dimensionality>(dimensionality * j) += g;
          } else {
            visitor.distanceTerm(i, j, 0.0);
          }
        }
      }
    }
  }

  template<class Visitor, bool dependent = SIMD, std::enable_if_t<dependent, int>...>
  void distanceContributionsImpl(
    const VectorType& positions,
    FloatType& error,
    Eigen::Ref<VectorType> gradient,
    Visitor&& /* visitor */
  ) const {
    assert(positions.size() == gradient.size());
    /* Using the squared distance bounds to avoid unneeded square-root calculations
     *
     * NOTE: positions are full-dimensional
     *
     * for each nonredundant pair of atoms (i < j)
     *   Calculate a squared vector distance:
     *   sq_distance = (position[j] - position[i]).array().square().sum()
     *
     *   upper_term = (sq_distance / upperBoundSquared) - 1
     *
     *   if upper_term > 0:
     *     error += upper_term.square()
     *
     *   lower_term = (
     *    2 * lowerBoundSquared / (lowerBoundSquared + sq_distance)
     *   ) - 1
     *
     *   if lowerTerm > 0:
     *     error += lower_term.square()
     *
     * SIMDize:
     *   sq_distances = list of upper triangular square distance terms
     *   upper_bounds_sq = list of corresponding upper bounds (identical across runs, no need to gather multiple times)
     *   lower_bounds_sq = list of corresponding lower bounds (same as above)
     *
     *   upper_terms = (sq_distances / upper_bounds_sq) - 1
     *   error += upper_terms.max(0.0).square().sum()
     *
     *   lower_terms = (2 * lower_bounds_sq / (lower_bounds_sq + sq_distances)) - 1
     *   error += lower_terms.max(0.0).square().sum()
     *
     */

    // Calculate all full-dimensional N(N-1) / 2 position differences
    const unsigned N = positions.size() / dimensionality;
    const unsigned differencesCount = N * (N - 1) / 2;

    FullDimensionalMatrixType positionDifferences(dimensionality, differencesCount);
    {
      unsigned offset = 0;
      for(unsigned i = 0; i < N - 1; ++i) {
        auto iPosition = positions.template segment<dimensionality>(dimensionality * i);
        for(unsigned j = i + 1; j < N; ++j) {
          positionDifferences.col(offset) = (
            iPosition
            - positions.template segment<dimensionality>(dimensionality * j)
          );
          ++offset;
        }
      }
    }

    // SIMD
    const VectorType squareDistances = positionDifferences.colwise().squaredNorm();

    // SIMD
    const VectorType upperTerms = squareDistances.array() / upperDistanceBoundsSquared.array() - 1;

#ifndef NDEBUG
    {
      // Check correctness of results so far
      unsigned offset = 0;
      for(unsigned i = 0; i < N - 1; ++i) {
        for(unsigned j = i + 1; j < N; ++j) {
          const FullDimensionalVector positionDifference = (
            positions.template segment<dimensionality>(dimensionality * i)
            - positions.template segment<dimensionality>(dimensionality * j)
          );

          assert(positionDifferences.col(offset) == positionDifference);

          const FloatType squareDistance = positionDifference.squaredNorm();

          assert(squareDistance == squareDistances(offset));

          // Upper term
          const FloatType upperTerm = squareDistance / upperDistanceBoundsSquared(offset) - 1;

          assert(upperTerm == upperTerms(offset));

          ++offset;
        }
      }
    }
#endif

    // Traverse upper terms and calculate gradients
    for(unsigned iOffset = 0, i = 0; i < N - 1; ++i) {
      const unsigned crossTerms = N - i - 1;
      for(unsigned jOffset = 0, j = i + 1;  j < N; ++j, ++jOffset) {
        const FloatType upperTerm = upperTerms(iOffset + jOffset);
        if(upperTerm > 0) {
          error += upperTerm * upperTerm;

          /* This i-j combination has an upper value contribution
           *
           * calculate gradient and apply to i and j
           */
          const FullDimensionalVector f = (
            4 * positionDifferences.col(iOffset + jOffset) * upperTerm
            / upperDistanceBoundsSquared(iOffset + jOffset)
          );

          // position difference is i - j, not j - i (!)
          gradient.template segment<dimensionality>(dimensionality * i) += f;
          gradient.template segment<dimensionality>(dimensionality * j) -= f;
        } else {
          /* This i-j combination MAYBE has a lower value contribution
           */
          const auto& lowerBoundSquared = lowerDistanceBoundsSquared(iOffset + jOffset);
          const FloatType quotient = lowerBoundSquared + squareDistances(iOffset + jOffset);
          const FloatType lowerTerm = 2 * lowerBoundSquared / quotient - 1;

          if(lowerTerm > 0) {
            // Add it to the error
            error += lowerTerm * lowerTerm;

            // Calculate gradient and apply
            const FullDimensionalVector g = (
              8 * lowerBoundSquared * positionDifferences.col(iOffset + jOffset) * lowerTerm / (
                quotient * quotient
              )
            );

            // position difference is i - j, not j - i (!)
            gradient.template segment<dimensionality>(dimensionality * i) -= g;
            gradient.template segment<dimensionality>(dimensionality * j) += g;
          }
        }
      }

      iOffset += crossTerms;
    }
  }

  template<typename Visitor>
  void chiralContributionsImpl(
    const VectorType& positions,
    FloatType& error,
    Eigen::Ref<VectorType> gradient,
    Visitor&& visitor
  ) const {
    unsigned nonZeroChiralConstraints = 0;
    unsigned incorrectNonZeroChiralConstraints = 0;

    for(const auto& constraint : chiralConstraints) {
      const ThreeDimensionalVector alpha = getAveragePosition3D(positions, constraint.sites[0]);
      const ThreeDimensionalVector beta = getAveragePosition3D(positions, constraint.sites[1]);
      const ThreeDimensionalVector gamma = getAveragePosition3D(positions, constraint.sites[2]);
      const ThreeDimensionalVector delta = getAveragePosition3D(positions, constraint.sites[3]);

      const ThreeDimensionalVector alphaMinusDelta = alpha - delta;
      const ThreeDimensionalVector betaMinusDelta = beta - delta;
      const ThreeDimensionalVector gammaMinusDelta = gamma - delta;

      const FloatType volume = (alphaMinusDelta).dot(
        betaMinusDelta.cross(gammaMinusDelta)
      );

      if(!constraint.targetVolumeIsZero()) {
        ++nonZeroChiralConstraints;
        if(
          ( volume < 0 && constraint.lower > 0)
          || (volume > 0 && constraint.lower < 0)
        ) {
          ++incorrectNonZeroChiralConstraints;
        }
      }

      // Upper bound term
      const FloatType upperTerm = static_cast<FloatType>(constraint.weight) * (volume - static_cast<FloatType>(constraint.upper));
      if(upperTerm > 0) {
        const FloatType value = upperTerm * upperTerm;
        error += value;
        visitor.chiralTerm(constraint.sites, value);
      }

      // Lower bound term
      const FloatType lowerTerm = static_cast<FloatType>(constraint.weight) * (static_cast<FloatType>(constraint.lower) - volume);
      if(lowerTerm > 0) {
        const FloatType value = lowerTerm * lowerTerm;
        error += value;
        visitor.chiralTerm(constraint.sites, value);
      }

      const FloatType factor = 2 * (
        std::max(FloatType {0}, upperTerm)
        - std::max(FloatType {0}, lowerTerm)
      );

      /* Make sure computing all cross products is worth it by checking that
       * one of both terms is actually greater than 0
       */
      if(factor != 0) {
        // Specific to deltaI only but still repeated
        const ThreeDimensionalVector alphaMinusGamma = alpha - gamma;
        const ThreeDimensionalVector betaMinusGamma = beta - gamma;

        const ThreeDimensionalVector iContribution = (
          factor * betaMinusDelta.cross(gammaMinusDelta)
          / constraint.sites[0].size()
        );

        const ThreeDimensionalVector jContribution = (
          factor * gammaMinusDelta.cross(alphaMinusDelta)
          / constraint.sites[1].size()
        );

        const ThreeDimensionalVector kContribution = (
          factor * alphaMinusDelta.cross(betaMinusDelta)
          / constraint.sites[2].size()
        );

        const ThreeDimensionalVector lContribution = (
          factor * betaMinusGamma.cross(alphaMinusGamma)
          / constraint.sites[3].size()
        );

        for(const AtomIndex alphaI : constraint.sites[0]) {
          gradient.template segment<3>(dimensionality * alphaI) += iContribution;
        }

        for(const AtomIndex betaI : constraint.sites[1]) {
          gradient.template segment<3>(dimensionality * betaI) += jContribution;
        }

        for(const AtomIndex gammaI : constraint.sites[2]) {
          gradient.template segment<3>(dimensionality * gammaI) += kContribution;
        }

        for(const AtomIndex deltaI : constraint.sites[3]) {
          gradient.template segment<3>(dimensionality * deltaI) += lContribution;
        }
      } else {
        visitor.chiralTerm(constraint.sites, 0.0);
      }
    }

    // Set signaling member
    if(nonZeroChiralConstraints == 0) {
      proportionChiralConstraintsCorrectSign = 1;
    } else {
      proportionChiralConstraintsCorrectSign = static_cast<double>(
        nonZeroChiralConstraints - incorrectNonZeroChiralConstraints
      ) / nonZeroChiralConstraints;
    }
  }

  template<class Visitor>
  void dihedralContributionsImpl(
    const VectorType& positions,
    FloatType& error,
    Eigen::Ref<VectorType> gradient,
    Visitor&& visitor
  ) const {
    assert(positions.size() == gradient.size());
    constexpr FloatType reductionFactor = 1.0 / 10;

    for(const DihedralConstraint& constraint : dihedralConstraints) {
      const ThreeDimensionalVector alpha = getAveragePosition3D(positions, constraint.sites[0]);
      const ThreeDimensionalVector beta = getAveragePosition3D(positions, constraint.sites[1]);
      const ThreeDimensionalVector gamma = getAveragePosition3D(positions, constraint.sites[2]);
      const ThreeDimensionalVector delta = getAveragePosition3D(positions, constraint.sites[3]);

      const ThreeDimensionalVector f = alpha - beta;
      const ThreeDimensionalVector g = beta - gamma;
      const ThreeDimensionalVector h = delta - gamma;

      ThreeDimensionalVector a = f.cross(g);
      ThreeDimensionalVector b = h.cross(g);

      // Calculate the dihedral angle
      FloatType phi = std::atan2(
        a.cross(b).dot(-g.normalized()),
        a.dot(b)
      );

      const FloatType constraintSumHalved = (static_cast<FloatType>(constraint.lower) + static_cast<FloatType>(constraint.upper)) / 2;

      constexpr FloatType pi {M_PI};

      if(phi < constraintSumHalved - pi) {
        phi += 2 * pi;
      } else if(phi > constraintSumHalved + pi) {
        phi -= 2 * pi;
      }

      const FloatType w_phi = phi - constraintSumHalved;

      FloatType h_phi = std::fabs(w_phi) - (static_cast<FloatType>(constraint.upper) - static_cast<FloatType>(constraint.lower)) / 2;

      /* "Apply the max function": If h <= 0, then the max function yields zero,
       * so we can skip this constraint
       */
      if(h_phi <= 0) {
        visitor.dihedralTerm(constraint.sites, 0.0);
        continue;
      }

      // Error contribution
      const FloatType errorContribution = h_phi * h_phi * reductionFactor;
      error += errorContribution;
      visitor.dihedralTerm(constraint.sites, errorContribution);

      // Multiply with sgn (w)
      h_phi *= static_cast<int>(0 < w_phi) - static_cast<int>(w_phi < 0);

      // Multiply in 2 and the reduction factor
      h_phi *= 2 * reductionFactor;

      // Precompute some reused expressions
      const FloatType gLength = g.norm();
      if(gLength == 0) {
        throw std::runtime_error("Encountered zero-length g vector in dihedral errors");
      }

      const FloatType aLengthSq = a.squaredNorm();
      if(aLengthSq == 0) {
        throw std::runtime_error("Encountered zero-length a vector in dihedral gradient contributions");
      }
      a /= aLengthSq;
      const FloatType bLengthSq = b.squaredNorm();
      if(bLengthSq == 0) {
        throw std::runtime_error("Encountered zero-length b vector in dihedral gradient contributions");
      }
      b /= bLengthSq;
      const FloatType fDotG = f.dot(g);
      const FloatType gDotH = g.dot(h);

      const ThreeDimensionalVector iContribution = (
        -(h_phi / constraint.sites[0].size()) * gLength * a
      );

      const ThreeDimensionalVector jContribution = (
        (h_phi / constraint.sites[1].size()) * (
          (gLength + fDotG / gLength) * a
          - (gDotH / gLength) * b
        )
      );

      const ThreeDimensionalVector kContribution = (
        (h_phi / constraint.sites[2].size()) * (
          (gDotH / gLength - gLength) * b
          - (fDotG / gLength) * a
        )
      );

      const ThreeDimensionalVector lContribution = (
        (h_phi / constraint.sites[3].size()) * gLength * b
      );

      if(
        !iContribution.array().isFinite().all()
        || !jContribution.array().isFinite().all()
        || !kContribution.array().isFinite().all()
        || !lContribution.array().isFinite().all()
      ) {
        throw std::runtime_error("Encountered non-finite dihedral gradient contributions");
      }

      /* Distribute contributions among constituting indices */
      for(const AtomIndex alphaConstitutingIndex : constraint.sites[0]) {
        gradient.template segment<3>(dimensionality * alphaConstitutingIndex) += iContribution;
      }

      for(const AtomIndex betaConstitutingIndex: constraint.sites[1]) {
        gradient.template segment<3>(dimensionality * betaConstitutingIndex) += jContribution;
      }

      for(const AtomIndex gammaConstitutingIndex : constraint.sites[2]) {
        gradient.template segment<3>(dimensionality * gammaConstitutingIndex) += kContribution;
      }

      for(const AtomIndex deltaConstitutingIndex : constraint.sites[3]) {
        gradient.template segment<3>(dimensionality * deltaConstitutingIndex) += lContribution;
      }
    }
  }

  template<class Visitor = DefaultTermVisitor>
  void fourthDimensionContributionsImpl(
    const VectorType& positions,
    FloatType& error,
    Eigen::Ref<VectorType> gradient,
    Visitor&& visitor = {}
  ) const {
    if(dimensionality != 4) {
      return;
    }

    // Collect all fourth dimension values, square and sum, add to error
    const unsigned N = positions.size() / dimensionality;
    if(compressFourthDimension) {
      for(unsigned i = 0; i < N; ++i) {
        const FloatType fourthDimensionalValue = positions(4 * i + 3);
        const FloatType value = fourthDimensionalValue * fourthDimensionalValue;
        error += value;
        visitor.fourthDimensionTerm(i, value);
        gradient(4 * i + 3) += 2 * fourthDimensionalValue;
      }
    } else {
      for(unsigned i = 0; i < N; ++i) {
        visitor.fourthDimensionTerm(i, 0.0);
      }
    }
  }
};

template<typename RefinementType>
struct RefinementTraits {
  // Trick to make the compiler tell me the template arguments to RefinementType
  template<
    template<unsigned, typename, bool> class BaseClass,
    unsigned dimensionality,
    typename FloatingPointType,
    bool SIMD
  > static auto templateArgumentHelper(BaseClass<dimensionality, FloatingPointType, SIMD> /* a */)
    -> std::tuple<
      std::integral_constant<unsigned, dimensionality>,
      FloatingPointType,
      std::integral_constant<bool, SIMD>
    >
  {
    return {};
  }

  using TemplateArgumentsTuple = decltype(templateArgumentHelper(std::declval<RefinementType>()));
  using DimensionalityConstant = std::tuple_element_t<0, TemplateArgumentsTuple>;
  using FloatingPointType = std::tuple_element_t<1, TemplateArgumentsTuple>;
  using SimdConstant = std::tuple_element_t<2, TemplateArgumentsTuple>;
};

} // namespace DistanceGeometry
} // namespace Molassembler
} // namespace Scine

#endif