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testMatVec.cc
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testMatVec.cc
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#include <iostream>
#include <limits>
#include <cassert>
#include "Rivet/Math/MathUtils.hh"
#include "Rivet/Math/Vectors.hh"
#include "Rivet/Math/Matrices.hh"
using namespace std;
using namespace Rivet;
int main() {
FourVector a(1,0,0,0);
cout << a << ": interval = " << a.invariant() << endl;
assert(fuzzyEquals(a.invariant(), 1));
a.setZ(1);
assert(isZero(a.invariant()));
cout << a << ": interval = " << a.invariant() << endl;
a.setY(2).setZ(3);
cout << a << ": interval = " << a.invariant() << endl;
assert(fuzzyEquals(a.invariant(), -12));
cout << a << ": vector = " << a.vector3() << endl << endl;
FourMomentum b(1,0,0,0);
cout << b << ": mass = " << b.mass() << endl;
assert(fuzzyEquals(b.mass2(), 1));
b.setPz(1);
cout << b << ": mass = " << b.mass() << endl;
assert(isZero(b.mass2()));
b.setPy(2).setPz(3).setE(6);
cout << b << ": mass = " << b.mass2() << endl;
assert(fuzzyEquals(b.mass2(), 23));
cout << b << ": vector = " << b.vector3() << endl << endl;
Matrix3 m;
m.set(0, 0, 7/4.0);
m.set(0, 1, 3 * sqrt(3)/4.0);
m.set(1, 0, 3 * sqrt(3)/4.0);
m.set(1, 1, 13/4.0);
m.set(2, 2, 9);
cout << m << endl << endl;
EigenSystem<3> es = diagonalize(m);
cout << "Matrices:" << endl;
cout << Matrix3() << endl;
cout << Matrix3::mkIdentity() << endl;
const Matrix3 I3 = Matrix3::mkIdentity();
cout << Matrix3::mkIdentity() * m * I3 << endl;
cout << "tr(0) & det(0): " << Matrix3().trace() << ", " << Matrix3().det() << endl;
cout << "tr(I3) & det(I3): " << I3.trace() << ", " << I3.det() << endl;
Matrix3 m1 = Matrix3::mkIdentity();
Matrix3 m2 = m1;
m1.setRow(1, Vector3(1,2,3));
m2.setColumn(1, Vector3(3,2,1));
Matrix3 m3 = Matrix3::mkZero();
cout << m1 << " + " << m2 << " = " << m1 + m2 << endl;
m3.setRow(0, Vector3(2,3,0)).setRow(1, Vector3(1,4,3)).setRow(2, Vector3(0,1,2));
cout << m1+m2 << " == " << m3 << ": " << (m1+m2 == m3 ? "true" : "false") << endl;
cout << endl;
Vector3 v3(1,2,3);
cout << "Vector: " << v3 << endl;
cout << "Invert: " << v3 << " --> " << -v3 << endl;
const Matrix3 rot90(Vector3(0,0,1), PI/2.0);
const Matrix3 rot90m(Vector3(0,0,1), -PI/2.0);
const Matrix3 rot180(Vector3(0,0,1), PI);
const Matrix3 rot180m(Vector3(0,0,1), -PI);
const Vector3 v3_90 = rot90*v3;
cout << "Rot 90: " << v3 << " ---> " << v3_90 << endl;
const Vector3 v3_90m = rot90m*v3;
cout << "Rot -90: " << v3 << " ---> " << v3_90m << endl;
const Vector3 v3_180 = rot180*v3;
cout << "Rot 180: " << v3 << " ---> " << v3_180 << endl;
const Vector3 v3_180m = rot180m*v3;
cout << "Rot -180: " << v3 << " ---> " << v3_180m << endl;
assert(fuzzyEquals(v3_180, v3_180m));
const Vector3 v3_9090 = rot90*rot90*v3;
cout << "Rot 2 x 90: " << v3 << " ---> " << v3_9090 << endl;
assert(fuzzyEquals(v3_180, v3_9090));
const Vector3 v3_90m90m = rot90m*rot90m*v3;
cout << "Rot 2 x -90: " << v3 << " ---> " << v3_90m90m << endl;
assert(fuzzyEquals(v3_180, v3_90m90m));
const Vector3 v3_9090m = rot90*rot90m*v3;
const Vector3 v3_90m90 = rot90m*rot90*v3;
cout << "Rot 90*-90: "<< v3 << " ---> " << v3_9090m << endl;
cout << "Rot -90*90: "<< v3 << " ---> " << v3_90m90 << endl;
assert(fuzzyEquals(v3, v3_9090m));
assert(fuzzyEquals(v3, v3_90m90));
const Vector3 v3_90i = rot90.inverse()*v3;
cout << "Rot (90)^-1: "<< v3 << " ---> " << v3_90i << endl;
assert(fuzzyEquals(v3_90i, v3_90m));
const Vector3 v3_9090i = rot90*rot90.inverse()*v3;
const Vector3 v3_90i90 = rot90.inverse()*rot90*v3;
cout << "Rot 90*(90)^-1: "<< v3 << " ---> " << v3_9090i << endl;
cout << "Rot (90)^-1*90: "<< v3 << " ---> " << v3_90i90 << endl;
assert(fuzzyEquals(v3, v3_9090i));
assert(fuzzyEquals(v3, v3_90i90));
const Matrix3 rot1(Vector3(0,1,0), PI/180.0);
cout << "Rot 0 x 45 x 1: " << v3 << endl;
for (size_t i = 0; i < 8; ++i) {
for (size_t j = 0; j < 45; ++j) {
v3 = rot1*v3;
}
cout << "Rot " << i+1 << " x 45 x 1: " << v3 << endl;
}
assert(fuzzyEquals(v3, Vector3(1,2,3)));
cout << endl;
cout << "Boosts:" << endl;
LorentzTransform ltX(0.5,0,0);
cout << "LTx: " << ltX << endl;
cout << "I on LTx: " << ltX.rotate(Matrix3::mkIdentity()) << endl;
cout << "Rot90 on LTx: " << ltX.rotate(rot90) << endl;
cout << endl;
cout << "X-boosts:" << endl;
const FourMomentum p1 = FourMomentum(10,0,0,1);
const FourMomentum p2 = ltX.transform(p1);
cout << p1 << " -> " << p2 << endl;
cout << p2 << " -> " << ltX.inverse().transform(p2) << endl;
//cout << p1.boostVector() << endl;
const FourMomentum p3 = LorentzTransform(-p1.boostVector()).transform(p1);
cout << p1 << " -> " << p3 << endl;
cout << endl;
LorentzTransform ltY(0,0.4,0);
cout << FourMomentum(1,0,0,1) << " -> " //<< "\n "
<< (ltX * ltY).transform(FourMomentum(1,0,0,1)) << endl;
cout << FourMomentum(1,0,0,1) << " -> " //<< "\n "
<< (ltY * ltX).transform(FourMomentum(1,0,0,1)) << endl;
cout << (ltX * ltY).boost() << endl;
cout << (ltY * ltX).boost() << endl;
cout << (ltX * ltX.inverse()).boost() << endl;
return EXIT_SUCCESS;
}

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