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mathcoreGenVector.C File Reference
Tutorials » Math tutorials

Detailed Description

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Example macro testing available methods and operation of the GenVector classes.

The results are compared and check at the numerical precision levels. Some small discrepancy can appear when the macro is executed on different architectures where it has been calibrated (Power PC G5) The macro is divided in 4 parts:

  • testVector3D : tests of the 3D Vector classes
  • testPoint3D : tests of the 3D Point classes
  • testLorentzVector : tests of the 4D LorentzVector classes
  • testVectorUtil : tests of the utility functions of all the vector classes

To execute the macro type in:

root[0] .x mathcoreGenVector.C
************************************************************************
Vector 3D Test
************************************************************************
Test Cartesian-Polar : ........ OK
Test Cartesian-CylindricalEta : ........ OK
Test Cartesian-Cylindrical : ........ OK
Test Operations : ............. OK
Test Setters : ...... OK
Test Linear Algebra conversion: . OK
************************************************************************
Point 3D Tests
************************************************************************
Test Cartesian-Polar : ........ OK
Test Polar-CylindricalEta : ........ OK
Test operations : ..... OK
************************************************************************
Lorentz Vector Tests
************************************************************************
Test XYZT - PtEtaPhiE Vectors: .......... OK
Test XYZT - PtEtaPhiM Vectors: .......... OK
Test PtEtaPhiE - PxPyPzM Vect.: .......... OK
Test operations : ............ OK
Test Setters : ........ OK
************************************************************************
Utility Function Tests
************************************************************************
Test Vector utility functions : .... OK
Test Point utility functions : .... OK
LorentzVector utility funct.: ... OK
************************************************************************
Rotation and Transformation Tests
************************************************************************
Test Vector Rotations : ............... OK
Test Axial Rotations : ............... OK
Test Rotations by a PI angle : ....... OK
Test Inversions : ............... OK
Test rectify : . OK
Test Transform3D : .............. OK
Test Plane3D : ........ OK
Test LorentzRotation : .......... OK
Test Boost : ............. OK
Number of tests 224 failed = 0
#include "TMatrixD.h"
#include "TVectorD.h"
#include "TMath.h"
#include "Math/Point3D.h"
#include "Math/Vector3D.h"
#include "Math/Vector4D.h"
#include "Math/GenVector/Rotation3D.h"
#include "Math/GenVector/EulerAngles.h"
#include "Math/GenVector/AxisAngle.h"
#include "Math/GenVector/Quaternion.h"
#include "Math/GenVector/RotationX.h"
#include "Math/GenVector/RotationY.h"
#include "Math/GenVector/RotationZ.h"
#include "Math/GenVector/RotationZYX.h"
#include "Math/GenVector/LorentzRotation.h"
#include "Math/GenVector/Boost.h"
#include "Math/GenVector/BoostX.h"
#include "Math/GenVector/BoostY.h"
#include "Math/GenVector/BoostZ.h"
#include "Math/GenVector/Transform3D.h"
#include "Math/GenVector/Plane3D.h"
#include "Math/GenVector/VectorUtil.h"
using namespace ROOT::Math;
int ntest = 0;
int nfail = 0;
int ok = 0;
int compare( double v1, double v2, const char* name, double Scale = 1.0) {
ntest = ntest + 1;
// numerical double limit for epsilon
double eps = Scale* 2.22044604925031308e-16;
int iret = 0;
double delta = v2 - v1;
double d = 0;
if (delta < 0 ) delta = - delta;
if (v1 == 0 || v2 == 0) {
if (delta > eps ) {
iret = 1;
}
}
// skip case v1 or v2 is infinity
else {
d = v1;
if ( v1 < 0) d = -d;
// add also case when delta is small by default
if ( delta/d > eps && delta > eps )
iret = 1;
}
if (iret == 0)
std::cout << ".";
else {
int pr = std::cout.precision (18);
int discr;
if (d != 0)
discr = int(delta/d/eps);
else
discr = int(delta/eps);
std::cout << "\nDiscrepancy in " << name << "() : " << v1 << " != " << v2 << " discr = " << discr
<< " (Allowed discrepancy is " << eps << ")\n";
std::cout.precision (pr);
nfail = nfail + 1;
}
return iret;
}
int testVector3D() {
std::cout << "\n************************************************************************\n "
<< " Vector 3D Test"
<< "\n************************************************************************\n";
XYZVector v1(0.01, 0.02, 16);
std::cout << "Test Cartesian-Polar : " ;
Polar3DVector v2(v1.R(), v1.Theta(), v1.Phi() );
ok = 0;
ok+= compare(v1.X(), v2.X(), "x");
ok+= compare(v1.Y(), v2.Y(), "y");
ok+= compare(v1.Z(), v2.Z(), "z");
ok+= compare(v1.Phi(), v2.Phi(), "phi");
ok+= compare(v1.Theta(), v2.Theta(), "theta");
ok+= compare(v1.R(), v2.R(), "r");
ok+= compare(v1.Eta(), v2.Eta(), "eta");
ok+= compare(v1.Rho(), v2.Rho(), "rho");
if (ok == 0) std::cout << "\t OK " << std::endl;
std::cout << "Test Cartesian-CylindricalEta : ";
RhoEtaPhiVector v3( v1.Rho(), v1.Eta(), v1.Phi() );
ok = 0;
ok+= compare(v1.X(), v3.X(), "x");
ok+= compare(v1.Y(), v3.Y(), "y");
ok+= compare(v1.Z(), v3.Z(), "z");
ok+= compare(v1.Phi(), v3.Phi(), "phi");
ok+= compare(v1.Theta(), v3.Theta(), "theta");
ok+= compare(v1.R(), v3.R(), "r");
ok+= compare(v1.Eta(), v3.Eta(), "eta");
ok+= compare(v1.Rho(), v3.Rho(), "rho");
if (ok == 0) std::cout << "\t OK " << std::endl;
std::cout << "Test Cartesian-Cylindrical : ";
RhoZPhiVector v4( v1.Rho(), v1.Z(), v1.Phi() );
ok = 0;
ok+= compare(v1.X(), v4.X(), "x");
ok+= compare(v1.Y(), v4.Y(), "y");
ok+= compare(v1.Z(), v4.Z(), "z");
ok+= compare(v1.Phi(), v4.Phi(), "phi");
ok+= compare(v1.Theta(), v4.Theta(), "theta");
ok+= compare(v1.R(), v4.R(), "r");
ok+= compare(v1.Eta(), v4.Eta(), "eta");
ok+= compare(v1.Rho(), v4.Rho(), "rho");
if (ok == 0) std::cout << "\t OK " << std::endl;
std::cout << "Test Operations : " ;
ok = 0;
double Dot = v1.Dot(v2);
ok+= compare( Dot, v1.Mag2(),"dot" );
XYZVector vcross = v1.Cross(v2);
ok+= compare( vcross.R(), 0,"cross" );
XYZVector vscale1 = v1*10;
XYZVector vscale2 = vscale1/10;
ok+= compare( v1.R(), vscale2.R(), "scale");
XYZVector vu = v1.Unit();
ok+= compare(v2.Phi(),vu.Phi(),"unit Phi");
ok+= compare(v2.Theta(),vu.Theta(),"unit Theta");
ok+= compare(1.0,vu.R(),"unit ");
XYZVector q1 = v1;
RhoEtaPhiVector q2(1.0,1.0,1.0);
XYZVector q3 = q1 + q2;
XYZVector q4 = q3 - q2;
ok+= compare( q4.X(), q1.X(), "op X" );
ok+= compare( q4.Y(), q1.Y(), "op Y" );
ok+= compare( q4.Z(), q1.Z(), "op Z" );
// test operator ==
XYZVector w1 = v1;
Polar3DVector w2 = v2;
RhoEtaPhiVector w3 = v3;
RhoZPhiVector w4 = v4;
ok+= compare( w1 == v1, static_cast<double>(true), "== XYZ");
ok+= compare( w2 == v2, static_cast<double>(true), "== Polar");
ok+= compare( w3 == v3, static_cast<double>(true), "== RhoEtaPhi");
ok+= compare( w4 == v4, static_cast<double>(true), "== RhoZPhi");
if (ok == 0) std::cout << "\t OK " << std::endl;
//test setters
std::cout << "Test Setters : " ;
q2.SetXYZ(q1.X(), q1.Y(), q1.Z() );
ok+= compare( q2.X(), q1.X(), "setXYZ X" );
ok+= compare( q2.Y(), q1.Y(), "setXYZ Y" );
ok+= compare( q2.Z(), q1.Z(), "setXYZ Z" );
q2.SetCoordinates( 2.0*q1.Rho(), q1.Eta(), q1.Phi() );
XYZVector q1s = 2.0*q1;
ok+= compare( q2.X(), q1s.X(), "set X" );
ok+= compare( q2.Y(), q1s.Y(), "set Y" );
ok+= compare( q2.Z(), q1s.Z(), "set Z" );
if (ok == 0) std::cout << "\t\t OK " << std::endl;
std::cout << "Test Linear Algebra conversion: " ;
XYZVector vxyz1(1.,2.,3.);
TVectorD vla1(3);
vxyz1.Coordinates().GetCoordinates(vla1.GetMatrixArray() );
TVectorD vla2(3);
vla2[0] = 1.; vla2[1] = -2.; vla2[2] = 1.;
XYZVector vxyz2;
vxyz2.SetCoordinates(&vla2[0]);
ok = 0;
double prod1 = vxyz1.Dot(vxyz2);
double prod2 = vla1*vla2;
ok+= compare( prod1, prod2, "la test" );
if (ok == 0) std::cout << "\t\t OK " << std::endl;
return ok;
}
int testPoint3D() {
std::cout << "\n************************************************************************\n "
<< " Point 3D Tests"
<< "\n************************************************************************\n";
XYZPoint p1(1.0, 2.0, 3.0);
std::cout << "Test Cartesian-Polar : ";
Polar3DPoint p2(p1.R(), p1.Theta(), p1.Phi() );
ok = 0;
ok+= compare(p1.x(), p2.X(), "x");
ok+= compare(p1.y(), p2.Y(), "y");
ok+= compare(p1.z(), p2.Z(), "z");
ok+= compare(p1.phi(), p2.Phi(), "phi");
ok+= compare(p1.theta(), p2.Theta(), "theta");
ok+= compare(p1.r(), p2.R(), "r");
ok+= compare(p1.eta(), p2.Eta(), "eta");
ok+= compare(p1.rho(), p2.Rho(), "rho");
if (ok == 0) std::cout << "\t OK " << std::endl;
std::cout << "Test Polar-CylindricalEta : ";
RhoEtaPhiPoint p3( p2.Rho(), p2.Eta(), p2.Phi() );
ok = 0;
ok+= compare(p2.X(), p3.X(), "x");
ok+= compare(p2.Y(), p3.Y(), "y");
ok+= compare(p2.Z(), p3.Z(), "z",3);
ok+= compare(p2.Phi(), p3.Phi(), "phi");
ok+= compare(p2.Theta(), p3.Theta(), "theta");
ok+= compare(p2.R(), p3.R(), "r");
ok+= compare(p2.Eta(), p3.Eta(), "eta");
ok+= compare(p2.Rho(), p3.Rho(), "rho");
if (ok == 0) std::cout << "\t OK " << std::endl;
std::cout << "Test operations : ";
//std::cout << "\nTest Dot and Cross products with Vectors : ";
Polar3DVector vperp(1.,p1.Theta() + TMath::PiOver2(),p1.Phi() );
double Dot = p1.Dot(vperp);
ok+= compare( Dot, 0.0,"dot", 10 );
XYZPoint vcross = p1.Cross(vperp);
ok+= compare( vcross.R(), p1.R(),"cross mag" );
ok+= compare( vcross.Dot(vperp), 0.0,"cross dir" );
XYZPoint pscale1 = 10*p1;
XYZPoint pscale2 = pscale1/10;
ok+= compare( p1.R(), pscale2.R(), "scale");
// test operator ==
ok+= compare( p1 == pscale2, static_cast<double>(true), "== Point");
//RhoEtaPhiPoint q1 = p1; ! constructor yet not working in CLING
RhoEtaPhiPoint q1; q1 = p1;
q1.SetCoordinates(p1.Rho(),2.0, p1.Phi() );
Polar3DVector v2(p1.R(), p1.Theta(),p1.Phi());
if (ok == 0) std::cout << "\t OK " << std::endl;
return ok;
}
int testLorentzVector() {
std::cout << "\n************************************************************************\n "
<< " Lorentz Vector Tests"
<< "\n************************************************************************\n";
XYZTVector v1(1.0, 2.0, 3.0, 4.0);
std::cout << "Test XYZT - PtEtaPhiE Vectors: ";
PtEtaPhiEVector v2( v1.Rho(), v1.Eta(), v1.Phi(), v1.E() );
ok = 0;
ok+= compare(v1.Px(), v2.X(), "x");
ok+= compare(v1.Py(), v2.Y(), "y");
ok+= compare(v1.Pz(), v2.Z(), "z", 2);
ok+= compare(v1.E(), v2.T(), "e");
ok+= compare(v1.Phi(), v2.Phi(), "phi");
ok+= compare(v1.Theta(), v2.Theta(), "theta");
ok+= compare(v1.Pt(), v2.Pt(), "pt");
ok+= compare(v1.M(), v2.M(), "mass", 5);
ok+= compare(v1.Et(), v2.Et(), "et");
ok+= compare(v1.Mt(), v2.Mt(), "mt", 3);
if (ok == 0) std::cout << "\t OK " << std::endl;
std::cout << "Test XYZT - PtEtaPhiM Vectors: ";
PtEtaPhiMVector v3( v1.Rho(), v1.Eta(), v1.Phi(), v1.M() );
ok = 0;
ok+= compare(v1.Px(), v3.X(), "x");
ok+= compare(v1.Py(), v3.Y(), "y");
ok+= compare(v1.Pz(), v3.Z(), "z", 2);
ok+= compare(v1.E(), v3.T(), "e");
ok+= compare(v1.Phi(), v3.Phi(), "phi");
ok+= compare(v1.Theta(), v3.Theta(), "theta");
ok+= compare(v1.Pt(), v3.Pt(), "pt");
ok+= compare(v1.M(), v3.M(), "mass", 5);
ok+= compare(v1.Et(), v3.Et(), "et");
ok+= compare(v1.Mt(), v3.Mt(), "mt", 3);
if (ok == 0) std::cout << "\t OK " << std::endl;
std::cout << "Test PtEtaPhiE - PxPyPzM Vect.: ";
PxPyPzMVector v4( v3.X(), v3.Y(), v3.Z(), v3.M() );
ok = 0;
ok+= compare(v4.Px(), v3.X(), "x");
ok+= compare(v4.Py(), v3.Y(), "y");
ok+= compare(v4.Pz(), v3.Z(), "z",2);
ok+= compare(v4.E(), v3.T(), "e");
ok+= compare(v4.Phi(), v3.Phi(), "phi");
ok+= compare(v4.Theta(), v3.Theta(), "theta");
ok+= compare(v4.Pt(), v3.Pt(), "pt");
ok+= compare(v4.M(), v3.M(), "mass",5);
ok+= compare(v4.Et(), v3.Et(), "et");
ok+= compare(v4.Mt(), v3.Mt(), "mt",3);
if (ok == 0) std::cout << "\t OK " << std::endl;
std::cout << "Test operations : ";
ok = 0;
double Dot = v1.Dot(v2);
ok+= compare( Dot, v1.M2(),"dot" , 10 );
XYZTVector vscale1 = v1*10;
XYZTVector vscale2 = vscale1/10;
ok+= compare( v1.M(), vscale2.M(), "scale");
XYZTVector q1 = v1;
PtEtaPhiEVector q2(1.0,1.0,1.0,5.0);
XYZTVector q3 = q1 + q2;
XYZTVector q4 = q3 - q2;
ok+= compare( q4.x(), q1.X(), "op X" );
ok+= compare( q4.y(), q1.Y(), "op Y" );
ok+= compare( q4.z(), q1.Z(), "op Z" );
ok+= compare( q4.t(), q1.E(), "op E" );
// test operator ==
XYZTVector w1 = v1;
PtEtaPhiEVector w2 = v2;
PtEtaPhiMVector w3 = v3;
PxPyPzMVector w4 = v4;
ok+= compare( w1 == v1, static_cast<double>(true), "== PxPyPzE");
ok+= compare( w2 == v2, static_cast<double>(true), "== PtEtaPhiE");
ok+= compare( w3 == v3, static_cast<double>(true), "== PtEtaPhiM");
ok+= compare( w4 == v4, static_cast<double>(true), "== PxPyPzM");
// test gamma beta and boost
XYZVector b = q1.BoostToCM();
double beta = q1.Beta();
double gamma = q1.Gamma();
ok += compare( b.R(), beta, "beta" );
ok += compare( gamma, 1./sqrt( 1 - beta*beta ), "gamma");
if (ok == 0) std::cout << "\t OK " << std::endl;
//test setters
std::cout << "Test Setters : " ;
q2.SetXYZT(q1.Px(), q1.Py(), q1.Pz(), q1.E() );
ok+= compare( q2.X(), q1.X(), "setXYZT X" );
ok+= compare( q2.Y(), q1.Y(), "setXYZT Y" );
ok+= compare( q2.Z(), q1.Z(), "setXYZT Z" ,2);
ok+= compare( q2.T(), q1.E(), "setXYZT E" );
q2.SetCoordinates( 2.0*q1.Rho(), q1.Eta(), q1.Phi(), 2.0*q1.E() );
XYZTVector q1s = q1*2.0;
ok+= compare( q2.X(), q1s.X(), "set X" );
ok+= compare( q2.Y(), q1s.Y(), "set Y" );
ok+= compare( q2.Z(), q1s.Z(), "set Z" ,2);
ok+= compare( q2.T(), q1s.T(), "set E" );
if (ok == 0) std::cout << "\t OK " << std::endl;
return ok;
}
int testVectorUtil() {
std::cout << "\n************************************************************************\n "
<< " Utility Function Tests"
<< "\n************************************************************************\n";
std::cout << "Test Vector utility functions : ";
XYZVector v1(1.0, 2.0, 3.0);
Polar3DVector v2pol(v1.R(), v1.Theta()+TMath::PiOver2(), v1.Phi() + 1.0);
// mixedmethods not yet impl.
XYZVector v2; v2 = v2pol;
ok = 0;
ok += compare( VectorUtil::DeltaPhi(v1,v2), 1.0, "deltaPhi Vec");
RhoEtaPhiVector v2cyl(v1.Rho(), v1.Eta() + 1.0, v1.Phi() + 1.0);
v2 = v2cyl;
ok += compare( VectorUtil::DeltaR(v1,v2), sqrt(2.0), "DeltaR Vec");
XYZVector vperp = v1.Cross(v2);
ok += compare( VectorUtil::CosTheta(v1,vperp), 0.0, "costheta Vec");
ok += compare( VectorUtil::Angle(v1,vperp), TMath::PiOver2(), "angle Vec");
if (ok == 0) std::cout << "\t\t OK " << std::endl;
std::cout << "Test Point utility functions : ";
XYZPoint p1(1.0, 2.0, 3.0);
Polar3DPoint p2pol(p1.R(), p1.Theta()+TMath::PiOver2(), p1.Phi() + 1.0);
// mixedmethods not yet impl.
XYZPoint p2; p2 = p2pol;
ok = 0;
ok += compare( VectorUtil::DeltaPhi(p1,p2), 1.0, "deltaPhi Point");
RhoEtaPhiPoint p2cyl(p1.Rho(), p1.Eta() + 1.0, p1.Phi() + 1.0);
p2 = p2cyl;
ok += compare( VectorUtil::DeltaR(p1,p2), sqrt(2.0), "DeltaR Point");
XYZPoint pperp(vperp.X(), vperp.Y(), vperp.Z());
ok += compare( VectorUtil::CosTheta(p1,pperp), 0.0, "costheta Point");
ok += compare( VectorUtil::Angle(p1,pperp), TMath::PiOver2(), "angle Point");
if (ok == 0) std::cout << "\t\t OK " << std::endl;
std::cout << "LorentzVector utility funct.: ";
XYZTVector q1(1.0, 2.0, 3.0,4.0);
PtEtaPhiEVector q2cyl(q1.Pt(), q1.Eta()+1.0, q1.Phi() + 1.0, q1.E() );
XYZTVector q2; q2 = q2cyl;
ok = 0;
ok += compare( VectorUtil::DeltaPhi(q1,q2), 1.0, "deltaPhi LVec");
ok += compare( VectorUtil::DeltaR(q1,q2), sqrt(2.0), "DeltaR LVec");
XYZTVector qsum = q1+q2;
ok += compare( VectorUtil::InvariantMass(q1,q2), qsum.M(), "InvMass");
if (ok == 0) std::cout << "\t\t OK " << std::endl;
return ok;
}
int testRotation() {
std::cout << "\n************************************************************************\n "
<< " Rotation and Transformation Tests"
<< "\n************************************************************************\n";
std::cout << "Test Vector Rotations : ";
ok = 0;
XYZPoint v(1.,2,3.);
double pi = TMath::Pi();
// initiate rotation with some non -trivial angles to test all matrix
EulerAngles r1( pi/2.,pi/4., pi/3 );
Rotation3D r2(r1);
// only operator= is in CLING for the other rotations
Quaternion r3; r3 = r2;
AxisAngle r4; r4 = r3;
RotationZYX r5; r5 = r2;
XYZPoint v1 = r1 * v;
XYZPoint v2 = r2 * v;
XYZPoint v3 = r3 * v;
XYZPoint v4 = r4 * v;
XYZPoint v5 = r5 * v;
ok+= compare(v1.X(), v2.X(), "x",2);
ok+= compare(v1.Y(), v2.Y(), "y",2);
ok+= compare(v1.Z(), v2.Z(), "z",2);
ok+= compare(v1.X(), v3.X(), "x",2);
ok+= compare(v1.Y(), v3.Y(), "y",2);
ok+= compare(v1.Z(), v3.Z(), "z",2);
ok+= compare(v1.X(), v4.X(), "x",5);
ok+= compare(v1.Y(), v4.Y(), "y",5);
ok+= compare(v1.Z(), v4.Z(), "z",5);
ok+= compare(v1.X(), v5.X(), "x",2);
ok+= compare(v1.Y(), v5.Y(), "y",2);
ok+= compare(v1.Z(), v5.Z(), "z",2);
// test with matrix
double rdata[9];
r2.GetComponents(rdata, rdata+9);
TMatrixD m(3,3,rdata);
double vdata[3];
v.GetCoordinates(vdata);
TVectorD q(3,vdata);
TVectorD q2 = m*q;
XYZPoint v6;
v6.SetCoordinates( q2.GetMatrixArray() );
ok+= compare(v1.X(), v6.X(), "x");
ok+= compare(v1.Y(), v6.Y(), "y");
ok+= compare(v1.Z(), v6.Z(), "z");
if (ok == 0) std::cout << "\t OK " << std::endl;
else std::cout << std::endl;
std::cout << "Test Axial Rotations : ";
ok = 0;
RotationX rx( pi/3);
RotationY ry( pi/4);
RotationZ rz( 4*pi/5);
Rotation3D r3x(rx);
Rotation3D r3y(ry);
Rotation3D r3z(rz);
Quaternion qx; qx = rx;
Quaternion qy; qy = ry;
Quaternion qz; qz = rz;
RotationZYX rzyx( rz.Angle(), ry.Angle(), rx.Angle() );
XYZPoint vrot1 = rx * ry * rz * v;
XYZPoint vrot2 = r3x * r3y * r3z * v;
ok+= compare(vrot1.X(), vrot2.X(), "x");
ok+= compare(vrot1.Y(), vrot2.Y(), "y");
ok+= compare(vrot1.Z(), vrot2.Z(), "z");
vrot2 = qx * qy * qz * v;
ok+= compare(vrot1.X(), vrot2.X(), "x",2);
ok+= compare(vrot1.Y(), vrot2.Y(), "y",2);
ok+= compare(vrot1.Z(), vrot2.Z(), "z",2);
vrot2 = rzyx * v;
ok+= compare(vrot1.X(), vrot2.X(), "x");
ok+= compare(vrot1.Y(), vrot2.Y(), "y");
ok+= compare(vrot1.Z(), vrot2.Z(), "z");
// now inverse (first x then y then z)
vrot1 = rz * ry * rx * v;
vrot2 = r3z * r3y * r3x * v;
ok+= compare(vrot1.X(), vrot2.X(), "x");
ok+= compare(vrot1.Y(), vrot2.Y(), "y");
ok+= compare(vrot1.Z(), vrot2.Z(), "z");
XYZPoint vinv1 = rx.Inverse()*ry.Inverse()*rz.Inverse()*vrot1;
ok+= compare(vinv1.X(), v.X(), "x",2);
ok+= compare(vinv1.Y(), v.Y(), "y");
ok+= compare(vinv1.Z(), v.Z(), "z");
if (ok == 0) std::cout << "\t OK " << std::endl;
else std::cout << std::endl;
std::cout << "Test Rotations by a PI angle : ";
ok = 0;
double b[4] = { 6,8,10,3.14159265358979323 };
AxisAngle arPi(b,b+4 );
Rotation3D rPi(arPi);
AxisAngle a1; a1 = rPi;
ok+= compare(arPi.Axis().X(), a1.Axis().X(),"x");
ok+= compare(arPi.Axis().Y(), a1.Axis().Y(),"y");
ok+= compare(arPi.Axis().Z(), a1.Axis().Z(),"z");
ok+= compare(arPi.Angle(), a1.Angle(),"angle");
EulerAngles ePi; ePi=rPi;
EulerAngles e1; e1=Rotation3D(a1);
ok+= compare(ePi.Phi(), e1.Phi(),"phi");
ok+= compare(ePi.Theta(), e1.Theta(),"theta");
ok+= compare(ePi.Psi(), e1.Psi(),"ps1");
if (ok == 0) std::cout << "\t\t OK " << std::endl;
else std::cout << std::endl;
std::cout << "Test Inversions : ";
ok = 0;
EulerAngles s1 = r1.Inverse();
Rotation3D s2 = r2.Inverse();
Quaternion s3 = r3.Inverse();
AxisAngle s4 = r4.Inverse();
RotationZYX s5 = r5.Inverse();
// Euler angles not yet impl.
XYZPoint p = s2 * r2 * v;
ok+= compare(p.X(), v.X(), "x",10);
ok+= compare(p.Y(), v.Y(), "y",10);
ok+= compare(p.Z(), v.Z(), "z",10);
p = s3 * r3 * v;
ok+= compare(p.X(), v.X(), "x",10);
ok+= compare(p.Y(), v.Y(), "y",10);
ok+= compare(p.Z(), v.Z(), "z",10);
p = s4 * r4 * v;
// axis angle inversion not very precise
ok+= compare(p.X(), v.X(), "x",1E9);
ok+= compare(p.Y(), v.Y(), "y",1E9);
ok+= compare(p.Z(), v.Z(), "z",1E9);
p = s5 * r5 * v;
ok+= compare(p.X(), v.X(), "x",10);
ok+= compare(p.Y(), v.Y(), "y",10);
ok+= compare(p.Z(), v.Z(), "z",10);
Rotation3D r6(r5);
Rotation3D s6 = r6.Inverse();
p = s6 * r6 * v;
ok+= compare(p.X(), v.X(), "x",10);
ok+= compare(p.Y(), v.Y(), "y",10);
ok+= compare(p.Z(), v.Z(), "z",10);
if (ok == 0) std::cout << "\t OK " << std::endl;
else std::cout << std::endl;
// test Rectify
std::cout << "Test rectify : ";
ok = 0;
XYZVector u1(0.999498,-0.00118212,-0.0316611);
XYZVector u2(0,0.999304,-0.0373108);
XYZVector u3(0.0316832,0.0372921,0.998802);
Rotation3D rr(u1,u2,u3);
// check orto-normality
XYZPoint vrr = rr* v;
ok+= compare(v.R(), vrr.R(), "R",1.E9);
if (ok == 0) std::cout << "\t\t OK " << std::endl;
else std::cout << std::endl;
std::cout << "Test Transform3D : ";
ok = 0;
XYZVector d(1.,-2.,3.);
Transform3D t(r2,d);
XYZPoint pd = t * v;
// apply directly rotation
XYZPoint vd = r2 * v + d;
ok+= compare(pd.X(), vd.X(), "x");
ok+= compare(pd.Y(), vd.Y(), "y");
ok+= compare(pd.Z(), vd.Z(), "z");
// test with matrix
double tdata[12];
t.GetComponents(tdata);
TMatrixD mt(3,4,tdata);
double vData[4]; // needs a vector of dim 4
v.GetCoordinates(vData);
vData[3] = 1;
TVectorD q0(4,vData);
TVectorD qt = mt*q0;
ok+= compare(pd.X(), qt(0), "x");
ok+= compare(pd.Y(), qt(1), "y");
ok+= compare(pd.Z(), qt(2), "z");
// test inverse
Transform3D tinv = t.Inverse();
p = tinv * t * v;
ok+= compare(p.X(), v.X(), "x",10);
ok+= compare(p.Y(), v.Y(), "y",10);
ok+= compare(p.Z(), v.Z(), "z",10);
// test construct inverse from translation first
Transform3D tinv2 ( r2.Inverse(), r2.Inverse() *( -d) ) ;
p = tinv2 * t * v;
ok+= compare(p.X(), v.X(), "x",10);
ok+= compare(p.Y(), v.Y(), "y",10);
ok+= compare(p.Z(), v.Z(), "z",10);
// test from only rotation and only translation
Transform3D ta( EulerAngles(1.,2.,3.) );
Transform3D tb( XYZVector(1,2,3) );
Transform3D tc( Rotation3D(EulerAngles(1.,2.,3.)) , XYZVector(1,2,3) );
Transform3D td( ta.Rotation(), ta.Rotation() * XYZVector(1,2,3) ) ;
ok+= compare( tc == tb*ta, static_cast<double>(true), "== Rot*Tra");
ok+= compare( td == ta*tb, static_cast<double>(true), "== Rot*Tra");
if (ok == 0) std::cout << "\t OK " << std::endl;
else std::cout << std::endl;
std::cout << "Test Plane3D : ";
ok = 0;
// test transform a 3D plane
XYZPoint p1(1,2,3);
XYZPoint p2(-2,-1,4);
XYZPoint p3(-1,3,2);
Plane3D plane(p1,p2,p3);
XYZVector n = plane.Normal();
// normal is perpendicular to vectors on the planes obtained from subtracting the points
ok+= compare(n.Dot(p2-p1), 0.0, "n.v12",10);
ok+= compare(n.Dot(p3-p1), 0.0, "n.v13",10);
ok+= compare(n.Dot(p3-p2), 0.0, "n.v23",10);
Plane3D plane1 = t(plane);
// transform the points
XYZPoint pt1 = t(p1);
XYZPoint pt2 = t(p2);
XYZPoint pt3 = t(p3);
Plane3D plane2(pt1,pt2,pt3);
XYZVector n1 = plane1.Normal();
XYZVector n2 = plane2.Normal();
ok+= compare(n1.X(), n2.X(), "a",10);
ok+= compare(n1.Y(), n2.Y(), "b",10);
ok+= compare(n1.Z(), n2.Z(), "c",10);
ok+= compare(plane1.HesseDistance(), plane2.HesseDistance(), "d",10);
// check distances
ok += compare(plane1.Distance(pt1), 0.0, "distance",10);
if (ok == 0) std::cout << "\t OK " << std::endl;
else std::cout << std::endl;
std::cout << "Test LorentzRotation : ";
ok = 0;
XYZTVector lv(1.,2.,3.,4.);
// test from rotx (using boosts and 3D rotations not yet impl.)
// rx,ry and rz already defined
Rotation3D r3d = rx*ry*rz;
LorentzRotation rlx(rx);
LorentzRotation rly(ry);
LorentzRotation rlz(rz);
LorentzRotation rl0 = rlx*rly*rlz;
LorentzRotation rl1( r3d);
XYZTVector lv0 = rl0 * lv;
XYZTVector lv1 = rl1 * lv;
XYZTVector lv2 = r3d * lv;
ok+= compare(lv1== lv2,true,"V0==V2");
ok+= compare(lv1== lv2,true,"V1==V2");
double rlData[16];
rl0.GetComponents(rlData);
TMatrixD ml(4,4,rlData);
double lvData[4];
lv.GetCoordinates(lvData);
TVectorD ql(4,lvData);
TVectorD qlr = ml*ql;
ok+= compare(lv1.X(), qlr(0), "x");
ok+= compare(lv1.Y(), qlr(1), "y");
ok+= compare(lv1.Z(), qlr(2), "z");
ok+= compare(lv1.E(), qlr(3), "t");
// test inverse
lv0 = rl0 * rl0.Inverse() * lv;
ok+= compare(lv0.X(), lv.X(), "x");
ok+= compare(lv0.Y(), lv.Y(), "y");
ok+= compare(lv0.Z(), lv.Z(), "z");
ok+= compare(lv0.E(), lv.E(), "t");
if (ok == 0) std::cout << "\t OK " << std::endl;
else std::cout << std::endl;
// test Boosts
std::cout << "Test Boost : ";
ok = 0;
Boost bst( 0.3,0.4,0.5); // boost (must be <= 1)
XYZTVector lvb = bst ( lv );
LorentzRotation rl2 (bst);
XYZTVector lvb2 = rl2 (lv);
// test with lorentz rotation
ok+= compare(lvb.X(), lvb2.X(), "x");
ok+= compare(lvb.Y(), lvb2.Y(), "y");
ok+= compare(lvb.Z(), lvb2.Z(), "z");
ok+= compare(lvb.E(), lvb2.E(), "t");
ok+= compare(lvb.M(), lv.M(), "m",50); // m must stay constant
// test inverse
lv0 = bst.Inverse() * lvb;
ok+= compare(lv0.X(), lv.X(), "x",5);
ok+= compare(lv0.Y(), lv.Y(), "y",5);
ok+= compare(lv0.Z(), lv.Z(), "z",3);
ok+= compare(lv0.E(), lv.E(), "t",3);
XYZVector brest = lv.BoostToCM();
bst.SetComponents( brest.X(), brest.Y(), brest.Z() );
XYZTVector lvr = bst * lv;
ok+= compare(lvr.X(), 0.0, "x",10);
ok+= compare(lvr.Y(), 0.0, "y",10);
ok+= compare(lvr.Z(), 0.0, "z",10);
ok+= compare(lvr.M(), lv.M(), "m",10);
if (ok == 0) std::cout << "\t OK " << std::endl;
else std::cout << std::endl;
return ok;
}
void mathcoreGenVector() {
testVector3D();
testPoint3D();
testLorentzVector();
testVectorUtil();
testRotation();
std::cout << "\n\nNumber of tests " << ntest << " failed = " << nfail << std::endl;
}
d
#define d(i)
Definition RSha256.hxx:102
b
#define b(i)
Definition RSha256.hxx:100
s1
#define s1(x)
Definition RSha256.hxx:91
TRangeDynCast
ROOT::Detail::TRangeCast< T, true > TRangeDynCast
TRangeDynCast is an adapter class that allows the typed iteration through a TCollection.
Definition TCollection.h:358
p
winID h TVirtualViewer3D TVirtualGLPainter p
Definition TGWin32VirtualGLProxy.cxx:51
name
char name[80]
Definition TGX11.cxx:110
q
float * q
Definition THbookFile.cxx:89
ROOT::Math::AxisAngle
AxisAngle class describing rotation represented with direction axis (3D Vector) and an angle of rotat...
Definition AxisAngle.h:42
ROOT::Math::Boost
Lorentz boost class with the (4D) transformation represented internally by a 4x4 orthosymplectic matr...
Definition Boost.h:47
ROOT::Math::EulerAngles
EulerAngles class describing rotation as three angles (Euler Angles).
Definition EulerAngles.h:45
ROOT::Math::Impl::Plane3D
Class describing a geometrical plane in 3 dimensions.
Definition Plane3D.h:53
ROOT::Math::Impl::Transform3D
Basic 3D Transformation class describing a rotation and then a translation The internal data are a 3D...
Definition Transform3D.h:80
ROOT::Math::LorentzRotation
Lorentz transformation class with the (4D) transformation represented by a 4x4 orthosymplectic matrix...
Definition LorentzRotation.h:55
ROOT::Math::Quaternion
Rotation class with the (3D) rotation represented by a unit quaternion (u, i, j, k).
Definition Quaternion.h:49
ROOT::Math::Rotation3D
Rotation class with the (3D) rotation represented by a 3x3 orthogonal matrix.
Definition Rotation3D.h:67
ROOT::Math::RotationX
Rotation class representing a 3D rotation about the X axis by the angle of rotation.
Definition RotationX.h:45
ROOT::Math::RotationY
Rotation class representing a 3D rotation about the Y axis by the angle of rotation.
Definition RotationY.h:45
ROOT::Math::RotationZYX
Rotation class with the (3D) rotation represented by angles describing first a rotation of an angle p...
Definition RotationZYX.h:63
ROOT::Math::RotationZ
Rotation class representing a 3D rotation about the Z axis by the angle of rotation.
Definition RotationZ.h:45
ROOT::Math::beta
double beta(double x, double y)
Calculates the beta function.
Definition SpecFuncMathCore.cxx:111
n
const Int_t n
Definition legend1.C:16
ROOT::Math::Cephes::gamma
double gamma(double x)
Definition SpecFuncCephes.cxx:339
TMath::PiOver2
constexpr Double_t PiOver2()
Definition TMath.h:51
TMath::Pi
constexpr Double_t Pi()
Definition TMath.h:37
Dot
#define Dot(u, v)
Definition normal.c:49
v2
@ v2
Definition rootcling_impl.cxx:3702
v
@ v
Definition rootcling_impl.cxx:3699
v4
@ v4
Definition rootcling_impl.cxx:3704
v3
@ v3
Definition rootcling_impl.cxx:3703
v1
@ v1
Definition rootcling_impl.cxx:3701
lv
TLine lv
Definition textalign.C:5
m
TMarker m
Definition textangle.C:8
Author
Lorenzo Moneta

Definition in file mathcoreGenVector.C.