#include <FastCircleFit.h>

Public Member Functions
float	chi2 () const

template<typename P , typename E >
	FastCircleFit (const P &points, const E &errors)

template<size_t N>
	FastCircleFit (const std::array< GlobalPoint, N > &points, const std::array< GlobalError, N > &errors)

float	rho () const

float	x0 () const

float	y0 () const

	~FastCircleFit ()=default

Private Member Functions
template<typename P , typename E , typename C >
void	calculate (const P &points, const E &errors, C &x, C &y, C &z, C &weight)

template<typename T >
T	sqr (T t)

Private Attributes
float	chi2_

float	rho_

float	x0_

float	y0_

Detailed Description

Same (almost) as FastCircle but with arbitrary number of hits.

Strandlie, Wroldsen, Frühwirth NIM A 488 (2002) 332-341. Frühwirth, Strandlie, Waltenberger NIM A 490 (2002) 366-378.

Definition at line 27 of file FastCircleFit.h.

Constructor & Destructor Documentation

template<typename P , typename E >

FastCircleFit::FastCircleFit	(	const P &	points,
		const E &	errors
	)

inline

Constructor for containers of GlobalPoint and GlobalError

Template Parameters

P	Container of GlobalPoint
E	Container of GlobalError

Container can be e.g. std::vector or DynArray.

Definition at line 38 of file FastCircleFit.h.

References calculate(), declareDynArray, N, histoStyle::weight, x, y, and z.

                                                   {
     const auto N = points.size();
     declareDynArray(float, N, x);
     declareDynArray(float, N, y);
     declareDynArray(float, N, z);
     declareDynArray(float, N, weight); // 1/sigma^2
     calculate(points, errors, x, y, z, weight);
   }

template<size_t N>

FastCircleFit::FastCircleFit	(	const std::array< GlobalPoint, N > &	points,
		const std::array< GlobalError, N > &	errors
	)

inline

Constructor for std::array of GlobalPoint and GlobalError

Definition at line 51 of file FastCircleFit.h.

References calculate(), histoStyle::weight, x, y, and z.

                                                                                                 {
     std::array<float, N> x;
     std::array<float, N> y;
     std::array<float, N> z;
     std::array<float, N> weight; // 1/sigma^2
     calculate(points, errors, x, y, z, weight);
   }

FastCircleFit::~FastCircleFit ( )

default

Member Function Documentation

template<typename P , typename E , typename C >

void FastCircleFit::calculate	(	const P &	points,
		const E &	errors,
		C &	x,
		C &	y,
		C &	z,
		C &	weight
	)

private

Definition at line 82 of file FastCircleFit.h.

References funct::A, EnergyCorrector::c, chi2_, HLT_FULL_cff::distance, i, timingPdfMaker::mean, N, gen::n, AlCaHLTBitMon_ParallelJobs::p, point, PRINT, rho_, S(), sqr(), mathSSE::sqrt(), tmp, w, x0_, and y0_.

Referenced by FastCircleFit().

                                                                                            {
   const auto N = points.size();
 
   // transform
   for(size_t i=0; i<N; ++i) {
     const auto& point = points[i];
     const auto p = point.basicVector();
     x[i] = p.x();
     y[i] = p.y();
     z[i] = sqr(p.x()) + sqr(p.y());
 
     // TODO: The following accounts only the hit uncertainty in phi.
     // Albeit it "works nicely", should we account also the
     // uncertainty in r in FPix (and the correlation between phi and r)?
     const float phiErr2 = errors[i].phierr(point);
     const float w = 1.f/(point.perp2()*phiErr2);
     weight[i] = w;
 
     PRINT << " point " << p.x()
           << " " << p.y()
           << " transformed " << x[i]
           << " " << y[i]
           << " " << z[i]
           << " weight " << w
           << std::endl;
   }
   const float invTotWeight = 1.f/std::accumulate(weight.begin(), weight.end(), 0.f);
   PRINT << " invTotWeight " << invTotWeight;
 
   Eigen::Vector3f mean = Eigen::Vector3f::Zero();
   for(size_t i=0; i<N; ++i) {
     const float w = weight[i];
     mean[0] += w*x[i];
     mean[1] += w*y[i];
     mean[2] += w*z[i];
   }
   mean *= invTotWeight;
   PRINT << " mean " << mean[0] << " " << mean[1] << " " << mean[2] << std::endl;
 
   Eigen::Matrix3f A = Eigen::Matrix3f::Zero();
   for(size_t i=0; i<N; ++i) {
     const auto diff_x = x[i] - mean[0];
     const auto diff_y = y[i] - mean[1];
     const auto diff_z = z[i] - mean[2];
     const auto w = weight[i];
 
     // exploit the fact that only lower triangular part of the matrix
     // is used in the eigenvalue calculation
     A(0,0) += w * diff_x * diff_x;
     A(1,0) += w * diff_y * diff_x;
     A(1,1) += w * diff_y * diff_y;
     A(2,0) += w * diff_z * diff_x;
     A(2,1) += w * diff_z * diff_y;
     A(2,2) += w * diff_z * diff_z;
     PRINT << " i " << i << " A " << A(0,0) << " " << A(0,1) << " " << A(0,2) << std::endl
           << "     " << A(1,0) << " " << A(1,1) << " " << A(1,2) << std::endl
           << "     " << A(2,0) << " " << A(2,1) << " " << A(2,2) << std::endl;
   }
   A *= 1./static_cast<float>(N);
 
   PRINT << " A " << A(0,0) << " " << A(0,1) << " " << A(0,2) << std::endl
         << "   " << A(1,0) << " " << A(1,1) << " " << A(1,2) << std::endl
         << "   " << A(2,0) << " " << A(2,1) << " " << A(2,2) << std::endl;
 
   // find eigenvalues and vectors
   Eigen::SelfAdjointEigenSolver<Eigen::Matrix3f> eigen(A);
   const auto& eigenValues = eigen.eigenvalues();
   const auto& eigenVectors = eigen.eigenvectors();
 
   // in Eigen the first eigenvalue is the smallest
   PRINT << " eigenvalues " << eigenValues[0]
         << " " << eigenValues[1]
         << " " << eigenValues[2]
         << std::endl;
 
   PRINT << " eigen " << eigenVectors(0,0) << " " << eigenVectors(0,1) << " " << eigenVectors(0,2) << std::endl
         << "       " << eigenVectors(1,0) << " " << eigenVectors(1,1) << " " << eigenVectors(1,2) << std::endl
         << "       " << eigenVectors(2,0) << " " << eigenVectors(2,1) << " " << eigenVectors(2,2) << std::endl;
 
   // eivenvector corresponding smallest eigenvalue
   auto n = eigenVectors.col(0);
   PRINT << " n (unit) " << n[0] << " " << n[1] << " " << n[2] << std::endl;
 
   const float c = -1.f * (n[0]*mean[0] + n[1]*mean[1] + n[2]*mean[2]);
 
   PRINT << " c " << c << std::endl;
 
   // calculate fit parameters
   const auto tmp = 0.5f * 1.f/n[2];
   x0_ = -n[0]*tmp;
   y0_ = -n[1]*tmp;
   const float rho2 = (1 - sqr(n[2]) - 4*c*n[2]) * sqr(tmp);
   rho_ = std::sqrt(rho2);
 
   // calculate square sum
   float S = 0;
   for(size_t i=0; i<N; ++i) {
     const float incr = sqr(c + n[0]*x[i] + n[1]*y[i] + n[2]*z[i]) * weight[i];
 #if defined(MK_DEBUG) || defined(EDM_ML_DEBUG)
     const float distance = std::sqrt(sqr(x[i]-x0_) + sqr(y[i]-y0_)) - rho_;
     PRINT << " i " << i
           << " chi2 incr " << incr
           << " d(hit, circle) " << distance
           << " sigma " << 1.f/std::sqrt(weight[i])
           << std::endl;
 #endif
     S += incr;
   }
   chi2_ = S;
 }