Full workflow from raw data to pixel tracks and vertices on GPUs (#216)

Port and optimise the full workflow from pixel raw data to pixel tracks and vertices to GPUs.
Clean the pixel n-tuplets with the "fishbone" algorithm (only on GPUs).

Other changes:
  - recover the Riemann fit updates lost during the merge with CMSSW 10.4.x;
  - speed up clustering and track fitting;
  - minor bug fix to avoid trivial regression with the optimized fit.

RecoPixelVertexing/PixelTrackFitting/interface/FitResult.h

@@ -0,0 +1,112 @@
+#ifndef RecoPixelVertexing_PixelTrackFitting_interface_FitResult_h
+#define RecoPixelVertexing_PixelTrackFitting_interface_FitResult_h
+
+#include <cmath>
+
+#include <cuda_runtime.h>
+#include <Eigen/Core>
+#include <Eigen/Eigenvalues>
+
+#include "HeterogeneousCore/CUDAUtilities/interface/cuda_assert.h"
+
+namespace Rfit
+{
+
+constexpr double d = 1.e-4;          //!< used in numerical derivative (J2 in Circle_fit())
+constexpr unsigned int max_nop = 4;  //!< In order to avoid use of dynamic memory
+
+
+using VectorXd = Eigen::VectorXd;
+using MatrixXd = Eigen::MatrixXd;
+template<int N>
+using MatrixNd = Eigen::Matrix<double, N, N>;
+template<int N>
+using ArrayNd = Eigen::Array<double, N, N>;
+template<int N>
+using Matrix2Nd = Eigen::Matrix<double, 2 * N, 2 * N>;
+template<int N>
+using Matrix3Nd = Eigen::Matrix<double, 3 * N, 3 * N>;
+template<int N>
+using Matrix2xNd = Eigen::Matrix<double, 2, N>;
+template<int N>
+using Array2xNd = Eigen::Array<double, 2, N>;
+template<int N>
+using Matrix3xNd = Eigen::Matrix<double, 3, N>;
+template<int N>
+using MatrixNx3d = Eigen::Matrix<double, N, 3>;
+template<int N>
+using MatrixNx5d = Eigen::Matrix<double, N, 5>;
+template<int N>
+using VectorNd = Eigen::Matrix<double, N, 1>;
+template<int N>
+using Vector2Nd = Eigen::Matrix<double, 2 * N, 1>;
+template<int N>
+using Vector3Nd = Eigen::Matrix<double, 3 * N, 1>;
+template<int N>
+using RowVectorNd = Eigen::Matrix<double, 1, 1, N>;
+template<int N>
+using RowVector2Nd = Eigen::Matrix<double, 1, 2 * N>;
+
+
+
+using Vector2d = Eigen::Vector2d;
+using Vector3d = Eigen::Vector3d;
+using Vector4d = Eigen::Vector4d;
+using Matrix2d = Eigen::Matrix2d;
+using Matrix3d = Eigen::Matrix3d;
+using Matrix4d = Eigen::Matrix4d;
+using Matrix5d = Eigen::Matrix<double, 5, 5>;
+using Matrix6d = Eigen::Matrix<double, 6, 6>;
+using Vector5d = Eigen::Matrix<double, 5, 1>;
+
+using Matrix3f = Eigen::Matrix3f;
+using Vector3f = Eigen::Vector3f;
+using Vector4f = Eigen::Vector4f;
+using Vector6f = Eigen::Matrix<double, 6, 1>;
+
+using u_int = unsigned int;
+
+
+struct circle_fit
+{
+    Vector3d par;  //!< parameter: (X0,Y0,R)
+    Matrix3d cov;
+    /*!< covariance matrix: \n
+      |cov(X0,X0)|cov(Y0,X0)|cov( R,X0)| \n
+      |cov(X0,Y0)|cov(Y0,Y0)|cov( R,Y0)| \n
+      |cov(X0, R)|cov(Y0, R)|cov( R, R)|
+  */
+    int32_t q;  //!< particle charge
+    float chi2 = 0.0;
+};
+
+struct line_fit
+{
+    Vector2d par;  //!<(cotan(theta),Zip)
+    Matrix2d cov;
+    /*!<
+      |cov(c_t,c_t)|cov(Zip,c_t)| \n
+      |cov(c_t,Zip)|cov(Zip,Zip)|
+  */
+    double chi2 = 0.0;
+};
+
+struct helix_fit
+{
+    Vector5d par;  //!<(phi,Tip,pt,cotan(theta)),Zip)
+    Matrix5d cov;
+    /*!< ()->cov() \n
+      |(phi,phi)|(Tip,phi)|(p_t,phi)|(c_t,phi)|(Zip,phi)| \n
+      |(phi,Tip)|(Tip,Tip)|(p_t,Tip)|(c_t,Tip)|(Zip,Tip)| \n
+      |(phi,p_t)|(Tip,p_t)|(p_t,p_t)|(c_t,p_t)|(Zip,p_t)| \n
+      |(phi,c_t)|(Tip,c_t)|(p_t,c_t)|(c_t,c_t)|(Zip,c_t)| \n
+      |(phi,Zip)|(Tip,Zip)|(p_t,Zip)|(c_t,Zip)|(Zip,Zip)|
+  */
+    float chi2_circle;
+    float chi2_line;
+//    Vector4d fast_fit;
+    int32_t q;  //!< particle charge
+} __attribute__((aligned(16)));
+
+} // namespace RFit
+#endif