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VectorUtil.h
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1 // @(#)root/mathcore:$Id: 9ef2a4a7bd1b62c1293920c2af2f64791c75bdd8 $
2 // Authors: W. Brown, M. Fischler, L. Moneta 2005
3 
4 
5 /**********************************************************************
6  * *
7  * Copyright (c) 2005 , LCG ROOT MathLib Team *
8  * *
9  * *
10  **********************************************************************/
11 
12 // Header file for Vector Utility functions
13 //
14 // Created by: moneta at Tue May 31 21:10:29 2005
15 //
16 // Last update: Tue May 31 21:10:29 2005
17 //
18 #ifndef ROOT_Math_GenVector_VectorUtil
19 #define ROOT_Math_GenVector_VectorUtil 1
20 
21 #include "Math/Math.h"
22 
23 
24 #include "Math/GenVector/Boost.h"
25 
26 namespace ROOT {
27 
28  namespace Math {
29 
30 
31  // utility functions for vector classes
32 
33 
34 
35  /**
36  Global Helper functions for generic Vector classes. Any Vector classes implementing some defined member functions,
37  like Phi() or Eta() or mag() can use these functions.
38  The functions returning a scalar value, returns always double precision number even if the vector are
39  based on another precision type
40 
41  @ingroup GenVector
42  */
43 
44 
45  namespace VectorUtil {
46 
47 
48  // methods for 3D vectors
49 
50  /**
51  Find aximutal Angle difference between two generic vectors ( v2.Phi() - v1.Phi() )
52  The only requirements on the Vector classes is that they implement the Phi() method
53  \param v1 Vector of any type implementing the Phi() operator
54  \param v2 Vector of any type implementing the Phi() operator
55  \return Phi difference
56  \f[ \Delta \phi = \phi_2 - \phi_1 \f]
57  */
58  template <class Vector1, class Vector2>
59  inline typename Vector1::Scalar DeltaPhi( const Vector1 & v1, const Vector2 & v2) {
60  typename Vector1::Scalar dphi = v2.Phi() - v1.Phi();
61  if ( dphi > M_PI ) {
62  dphi -= 2.0*M_PI;
63  } else if ( dphi <= -M_PI ) {
64  dphi += 2.0*M_PI;
65  }
66  return dphi;
67  }
68 
69 
70 
71  /**
72  Find square of the difference in pseudorapidity (Eta) and Phi betwen two generic vectors
73  The only requirements on the Vector classes is that they implement the Phi() and Eta() method
74  \param v1 Vector 1
75  \param v2 Vector 2
76  \return Angle between the two vectors
77  \f[ \Delta R2 = ( \Delta \phi )^2 + ( \Delta \eta )^2 \f]
78  */
79  template <class Vector1, class Vector2>
80  inline typename Vector1::Scalar DeltaR2( const Vector1 & v1, const Vector2 & v2) {
81  typename Vector1::Scalar dphi = DeltaPhi(v1,v2);
82  typename Vector1::Scalar deta = v2.Eta() - v1.Eta();
83  return dphi*dphi + deta*deta;
84  }
85 
86  /**
87  Find difference in pseudorapidity (Eta) and Phi betwen two generic vectors
88  The only requirements on the Vector classes is that they implement the Phi() and Eta() method
89  \param v1 Vector 1
90  \param v2 Vector 2
91  \return Angle between the two vectors
92  \f[ \Delta R = \sqrt{ ( \Delta \phi )^2 + ( \Delta \eta )^2 } \f]
93  */
94  template <class Vector1, class Vector2>
95  inline typename Vector1::Scalar DeltaR( const Vector1 & v1, const Vector2 & v2) {
96  return std::sqrt( DeltaR2(v1,v2) );
97  }
98 
99 
100 
101  /**
102  Find CosTheta Angle between two generic 3D vectors
103  pre-requisite: vectors implement the X(), Y() and Z()
104  \param v1 Vector v1
105  \param v2 Vector v2
106  \return cosine of Angle between the two vectors
107  \f[ \cos \theta = \frac { \vec{v1} \cdot \vec{v2} }{ | \vec{v1} | | \vec{v2} | } \f]
108  */
109  // this cannot be made all generic since Mag2() for 2, 3 or 4 D is different
110  // need to have a specialization for polar Coordinates ??
111  template <class Vector1, class Vector2>
112  double CosTheta( const Vector1 & v1, const Vector2 & v2) {
113  double arg;
114  double v1_r2 = v1.X()*v1.X() + v1.Y()*v1.Y() + v1.Z()*v1.Z();
115  double v2_r2 = v2.X()*v2.X() + v2.Y()*v2.Y() + v2.Z()*v2.Z();
116  double ptot2 = v1_r2*v2_r2;
117  if(ptot2 <= 0) {
118  arg = 0.0;
119  }else{
120  double pdot = v1.X()*v2.X() + v1.Y()*v2.Y() + v1.Z()*v2.Z();
121  arg = pdot/std::sqrt(ptot2);
122  if(arg > 1.0) arg = 1.0;
123  if(arg < -1.0) arg = -1.0;
124  }
125  return arg;
126  }
127 
128 
129  /**
130  Find Angle between two vectors.
131  Use the CosTheta() function
132  \param v1 Vector v1
133  \param v2 Vector v2
134  \return Angle between the two vectors
135  \f[ \theta = \cos ^{-1} \frac { \vec{v1} \cdot \vec{v2} }{ | \vec{v1} | | \vec{v2} | } \f]
136  */
137  template <class Vector1, class Vector2>
138  inline double Angle( const Vector1 & v1, const Vector2 & v2) {
139  return std::acos( CosTheta(v1, v2) );
140  }
141 
142  /**
143  Find the projection of v along the given direction u.
144  \param v Vector v for which the propjection is to be found
145  \param u Vector specifying the direction
146  \return Vector projection (same type of v)
147  \f[ \vec{proj} = \frac{ \vec{v} \cdot \vec{u} }{|\vec{u}|}\vec{u} \f]
148  Precondition is that Vector1 implements Dot function and Vector2 implements X(),Y() and Z()
149  */
150  template <class Vector1, class Vector2>
151  Vector1 ProjVector( const Vector1 & v, const Vector2 & u) {
152  double magU2 = u.X()*u.X() + u.Y()*u.Y() + u.Z()*u.Z();
153  if (magU2 == 0) return Vector1(0,0,0);
154  double d = v.Dot(u)/magU2;
155  return Vector1( u.X() * d, u.Y() * d, u.Z() * d);
156  }
157 
158  /**
159  Find the vector component of v perpendicular to the given direction of u
160  \param v Vector v for which the perpendicular component is to be found
161  \param u Vector specifying the direction
162  \return Vector component of v which is perpendicular to u
163  \f[ \vec{perp} = \vec{v} - \frac{ \vec{v} \cdot \vec{u} }{|\vec{u}|}\vec{u} \f]
164  Precondition is that Vector1 implements Dot function and Vector2 implements X(),Y() and Z()
165  */
166  template <class Vector1, class Vector2>
167  inline Vector1 PerpVector( const Vector1 & v, const Vector2 & u) {
168  return v - ProjVector(v,u);
169  }
170 
171  /**
172  Find the magnitude square of the vector component of v perpendicular to the given direction of u
173  \param v Vector v for which the perpendicular component is to be found
174  \param u Vector specifying the direction
175  \return square value of the component of v which is perpendicular to u
176  \f[ perp = | \vec{v} - \frac{ \vec{v} \cdot \vec{u} }{|\vec{u}|}\vec{u} |^2 \f]
177  Precondition is that Vector1 implements Dot function and Vector2 implements X(),Y() and Z()
178  */
179  template <class Vector1, class Vector2>
180  inline double Perp2( const Vector1 & v, const Vector2 & u) {
181  double magU2 = u.X()*u.X() + u.Y()*u.Y() + u.Z()*u.Z();
182  double prjvu = v.Dot(u);
183  double magV2 = v.Dot(v);
184  return magU2 > 0.0 ? magV2-prjvu*prjvu/magU2 : magV2;
185  }
186 
187  /**
188  Find the magnitude of the vector component of v perpendicular to the given direction of u
189  \param v Vector v for which the perpendicular component is to be found
190  \param u Vector specifying the direction
191  \return value of the component of v which is perpendicular to u
192  \f[ perp = | \vec{v} - \frac{ \vec{v} \cdot \vec{u} }{|\vec{u}|}\vec{u} | \f]
193  Precondition is that Vector1 implements Dot function and Vector2 implements X(),Y() and Z()
194  */
195  template <class Vector1, class Vector2>
196  inline double Perp( const Vector1 & v, const Vector2 & u) {
197  return std::sqrt(Perp2(v,u) );
198  }
199 
200 
201 
202  // Lorentz Vector functions
203 
204 
205  /**
206  return the invariant mass of two LorentzVector
207  The only requirement on the LorentzVector is that they need to implement the
208  X() , Y(), Z() and E() methods.
209  \param v1 LorenzVector 1
210  \param v2 LorenzVector 2
211  \return invariant mass M
212  \f[ M_{12} = \sqrt{ (\vec{v1} + \vec{v2} ) \cdot (\vec{v1} + \vec{v2} ) } \f]
213  */
214  template <class Vector1, class Vector2>
215  inline typename Vector1::Scalar InvariantMass( const Vector1 & v1, const Vector2 & v2) {
216  typedef typename Vector1::Scalar Scalar;
217  Scalar ee = (v1.E() + v2.E() );
218  Scalar xx = (v1.X() + v2.X() );
219  Scalar yy = (v1.Y() + v2.Y() );
220  Scalar zz = (v1.Z() + v2.Z() );
221  Scalar mm2 = ee*ee - xx*xx - yy*yy - zz*zz;
222  return mm2 < 0.0 ? -std::sqrt(-mm2) : std::sqrt(mm2);
223  // PxPyPzE4D<double> q(xx,yy,zz,ee);
224  // return q.M();
225  //return ( v1 + v2).mag();
226  }
227 
228  template <class Vector1, class Vector2>
229  inline typename Vector1::Scalar InvariantMass2( const Vector1 & v1, const Vector2 & v2) {
230  typedef typename Vector1::Scalar Scalar;
231  Scalar ee = (v1.E() + v2.E() );
232  Scalar xx = (v1.X() + v2.X() );
233  Scalar yy = (v1.Y() + v2.Y() );
234  Scalar zz = (v1.Z() + v2.Z() );
235  Scalar mm2 = ee*ee - xx*xx - yy*yy - zz*zz;
236  return mm2 ; // < 0.0 ? -std::sqrt(-mm2) : std::sqrt(mm2);
237  // PxPyPzE4D<double> q(xx,yy,zz,ee);
238  // return q.M();
239  //return ( v1 + v2).mag();
240  }
241 
242  // rotation and transformations
243 
244 
245 #ifndef __CINT__
246  /**
247  rotation along X axis for a generic vector by an Angle alpha
248  returning a new vector.
249  The only pre requisite on the Vector is that it has to implement the X() , Y() and Z()
250  and SetXYZ methods.
251  */
252  template <class Vector>
253  Vector RotateX(const Vector & v, double alpha) {
254  double sina = sin(alpha);
255  double cosa = cos(alpha);
256  double y2 = v.Y() * cosa - v.Z()*sina;
257  double z2 = v.Z() * cosa + v.Y() * sina;
258  Vector vrot;
259  vrot.SetXYZ(v.X(), y2, z2);
260  return vrot;
261  }
262 
263  /**
264  rotation along Y axis for a generic vector by an Angle alpha
265  returning a new vector.
266  The only pre requisite on the Vector is that it has to implement the X() , Y() and Z()
267  and SetXYZ methods.
268  */
269  template <class Vector>
270  Vector RotateY(const Vector & v, double alpha) {
271  double sina = sin(alpha);
272  double cosa = cos(alpha);
273  double x2 = v.X() * cosa + v.Z() * sina;
274  double z2 = v.Z() * cosa - v.X() * sina;
275  Vector vrot;
276  vrot.SetXYZ(x2, v.Y(), z2);
277  return vrot;
278  }
279 
280  /**
281  rotation along Z axis for a generic vector by an Angle alpha
282  returning a new vector.
283  The only pre requisite on the Vector is that it has to implement the X() , Y() and Z()
284  and SetXYZ methods.
285  */
286  template <class Vector>
287  Vector RotateZ(const Vector & v, double alpha) {
288  double sina = sin(alpha);
289  double cosa = cos(alpha);
290  double x2 = v.X() * cosa - v.Y() * sina;
291  double y2 = v.Y() * cosa + v.X() * sina;
292  Vector vrot;
293  vrot.SetXYZ(x2, y2, v.Z());
294  return vrot;
295  }
296 
297 
298  /**
299  rotation on a generic vector using a generic rotation class.
300  The only requirement on the vector is that implements the
301  X(), Y(), Z() and SetXYZ methods.
302  The requirement on the rotation matrix is that need to implement the
303  (i,j) operator returning the matrix element with R(0,0) = xx element
304  */
305  template<class Vector, class RotationMatrix>
306  Vector Rotate(const Vector &v, const RotationMatrix & rot) {
307  double xX = v.X();
308  double yY = v.Y();
309  double zZ = v.Z();
310  double x2 = rot(0,0)*xX + rot(0,1)*yY + rot(0,2)*zZ;
311  double y2 = rot(1,0)*xX + rot(1,1)*yY + rot(1,2)*zZ;
312  double z2 = rot(2,0)*xX + rot(2,1)*yY + rot(2,2)*zZ;
313  Vector vrot;
314  vrot.SetXYZ(x2,y2,z2);
315  return vrot;
316  }
317 
318  /**
319  Boost a generic Lorentz Vector class using a generic 3D Vector class describing the boost
320  The only requirement on the vector is that implements the
321  X(), Y(), Z(), T() and SetXYZT methods.
322  The requirement on the boost vector is that needs to implement the
323  X(), Y() , Z() retorning the vector elements describing the boost
324  The beta of the boost must be <= 1 or a nul Lorentz Vector will be returned
325  */
326  template <class LVector, class BoostVector>
327  LVector boost(const LVector & v, const BoostVector & b) {
328  double bx = b.X();
329  double by = b.Y();
330  double bz = b.Z();
331  double b2 = bx*bx + by*by + bz*bz;
332  if (b2 >= 1) {
333  GenVector::Throw ( "Beta Vector supplied to set Boost represents speed >= c");
334  return LVector();
335  }
336  double gamma = 1.0 / std::sqrt(1.0 - b2);
337  double bp = bx*v.X() + by*v.Y() + bz*v.Z();
338  double gamma2 = b2 > 0 ? (gamma - 1.0)/b2 : 0.0;
339  double x2 = v.X() + gamma2*bp*bx + gamma*bx*v.T();
340  double y2 = v.Y() + gamma2*bp*by + gamma*by*v.T();
341  double z2 = v.Z() + gamma2*bp*bz + gamma*bz*v.T();
342  double t2 = gamma*(v.T() + bp);
343  LVector lv;
344  lv.SetXYZT(x2,y2,z2,t2);
345  return lv;
346  }
347 
348 
349  /**
350  Boost a generic Lorentz Vector class along the X direction with a factor beta
351  The only requirement on the vector is that implements the
352  X(), Y(), Z(), T() and SetXYZT methods.
353  The beta of the boost must be <= 1 or a nul Lorentz Vector will be returned
354  */
355  template <class LVector, class T>
356  LVector boostX(const LVector & v, T beta) {
357  if (beta >= 1) {
358  GenVector::Throw ("Beta Vector supplied to set Boost represents speed >= c");
359  return LVector();
360  }
361  T gamma = 1.0/ std::sqrt(1.0 - beta*beta);
362  typename LVector::Scalar x2 = gamma * v.X() + gamma * beta * v.T();
363  typename LVector::Scalar t2 = gamma * beta * v.X() + gamma * v.T();
364 
365  LVector lv;
366  lv.SetXYZT(x2,v.Y(),v.Z(),t2);
367  return lv;
368  }
369 
370  /**
371  Boost a generic Lorentz Vector class along the Y direction with a factor beta
372  The only requirement on the vector is that implements the
373  X(), Y(), Z(), T() methods and be constructed from x,y,z,t values
374  The beta of the boost must be <= 1 or a nul Lorentz Vector will be returned
375  */
376  template <class LVector>
377  LVector boostY(const LVector & v, double beta) {
378  if (beta >= 1) {
379  GenVector::Throw ("Beta Vector supplied to set Boost represents speed >= c");
380  return LVector();
381  }
382  double gamma = 1.0/ std::sqrt(1.0 - beta*beta);
383  double y2 = gamma * v.Y() + gamma * beta * v.T();
384  double t2 = gamma * beta * v.Y() + gamma * v.T();
385  LVector lv;
386  lv.SetXYZT(v.X(),y2,v.Z(),t2);
387  return lv;
388  }
389 
390  /**
391  Boost a generic Lorentz Vector class along the Z direction with a factor beta
392  The only requirement on the vector is that implements the
393  X(), Y(), Z(), T() methods and be constructed from x,y,z,t values
394  The beta of the boost must be <= 1 or a nul Lorentz Vector will be returned
395  */
396  template <class LVector>
397  LVector boostZ(const LVector & v, double beta) {
398  if (beta >= 1) {
399  GenVector::Throw ( "Beta Vector supplied to set Boost represents speed >= c");
400  return LVector();
401  }
402  double gamma = 1.0/ std::sqrt(1.0 - beta*beta);
403  double z2 = gamma * v.Z() + gamma * beta * v.T();
404  double t2 = gamma * beta * v.Z() + gamma * v.T();
405  LVector lv;
406  lv.SetXYZT(v.X(),v.Y(),z2,t2);
407  return lv;
408  }
409 
410 #endif
411 
412 
413 
414 
415  // MATRIX VECTOR MULTIPLICATION
416  // cannot define an operator * otherwise conflicts with rotations
417  // operations like Rotation3D * vector use Mult
418 
419  /**
420  Multiplications of a generic matrices with a DisplacementVector3D of any coordinate system.
421  Assume that the matrix implements the operator( i,j) and that it has at least 3 columns and 3 rows. There is no check on the matrix size !!
422  */
423  template<class Matrix, class CoordSystem, class U>
424  inline
427  vret.SetXYZ( m(0,0) * v.x() + m(0,1) * v.y() + m(0,2) * v.z() ,
428  m(1,0) * v.x() + m(1,1) * v.y() + m(1,2) * v.z() ,
429  m(2,0) * v.x() + m(2,1) * v.y() + m(2,2) * v.z() );
430  return vret;
431  }
432 
433 
434  /**
435  Multiplications of a generic matrices with a generic PositionVector
436  Assume that the matrix implements the operator( i,j) and that it has at least 3 columns and 3 rows. There is no check on the matrix size !!
437  */
438  template<class Matrix, class CoordSystem, class U>
439  inline
442  pret.SetXYZ( m(0,0) * p.x() + m(0,1) * p.y() + m(0,2) * p.z() ,
443  m(1,0) * p.x() + m(1,1) * p.y() + m(1,2) * p.z() ,
444  m(2,0) * p.x() + m(2,1) * p.y() + m(2,2) * p.z() );
445  return pret;
446  }
447 
448 
449  /**
450  Multiplications of a generic matrices with a LorentzVector described
451  in any coordinate system.
452  Assume that the matrix implements the operator( i,j) and that it has at least 4 columns and 4 rows. There is no check on the matrix size !!
453  */
454  // this will not be ambigous with operator*(Scalar, LorentzVector) since that one // Scalar is passed by value
455  template<class CoordSystem, class Matrix>
456  inline
459  vret.SetXYZT( m(0,0)*v.x() + m(0,1)*v.y() + m(0,2)*v.z() + m(0,3)* v.t() ,
460  m(1,0)*v.x() + m(1,1)*v.y() + m(1,2)*v.z() + m(1,3)* v.t() ,
461  m(2,0)*v.x() + m(2,1)*v.y() + m(2,2)*v.z() + m(2,3)* v.t() ,
462  m(3,0)*v.x() + m(3,1)*v.y() + m(3,2)*v.z() + m(3,3)* v.t() );
463  return vret;
464  }
465 
466 
467 
468  // non-template utility functions for all objects
469 
470 
471  /**
472  Return a phi angle in the interval (0,2*PI]
473  */
474  double Phi_0_2pi(double phi);
475  /**
476  Returns phi angle in the interval (-PI,PI]
477  */
478  double Phi_mpi_pi(double phi);
479 
480 
481 
482  } // end namespace Vector Util
483 
484 
485 
486  } // end namespace Math
487 
488 } // end namespace ROOT
489 
490 
491 #endif /* ROOT_Math_GenVector_VectorUtil */
double Phi_0_2pi(double phi)
Return a phi angle in the interval (0,2*PI]
Definition: VectorUtil.cxx:22
Class describing a generic LorentzVector in the 4D space-time, using the specified coordinate syste...
Definition: LorentzVector.h:59
auto * m
Definition: textangle.C:8
DisplacementVector3D< CoordSystem, Tag > & SetXYZ(Scalar a, Scalar b, Scalar c)
set the values of the vector from the cartesian components (x,y,z) (if the vector is held in polar or...
Returns the available number of logical cores.
Definition: StringConv.hxx:21
Vector1::Scalar DeltaR2(const Vector1 &v1, const Vector2 &v2)
Find square of the difference in pseudorapidity (Eta) and Phi betwen two generic vectors The only re...
Definition: VectorUtil.h:80
double T(double x)
Definition: ChebyshevPol.h:34
LVector boostX(const LVector &v, T beta)
Boost a generic Lorentz Vector class along the X direction with a factor beta The only requirement o...
Definition: VectorUtil.h:356
Vector1::Scalar InvariantMass2(const Vector1 &v1, const Vector2 &v2)
Definition: VectorUtil.h:229
Vector1 ProjVector(const Vector1 &v, const Vector2 &u)
Find the projection of v along the given direction u.
Definition: VectorUtil.h:151
Class describing a generic position vector (point) in 3 dimensions.
Vector RotateX(const Vector &v, double alpha)
rotation along X axis for a generic vector by an Angle alpha returning a new vector.
Definition: VectorUtil.h:253
LorentzVector< CoordSystem > & SetXYZT(Scalar xx, Scalar yy, Scalar zz, Scalar tt)
set the values of the vector from the cartesian components (x,y,z,t) (if the vector is held in anothe...
double cos(double)
double beta(double x, double y)
Calculates the beta function.
double sqrt(double)
static const double x2[5]
double acos(double)
Vector1::Scalar DeltaR(const Vector1 &v1, const Vector2 &v2)
Find difference in pseudorapidity (Eta) and Phi betwen two generic vectors The only requirements on ...
Definition: VectorUtil.h:95
double Perp2(const Vector1 &v, const Vector2 &u)
Find the magnitude square of the vector component of v perpendicular to the given direction of u ...
Definition: VectorUtil.h:180
Vector1::Scalar InvariantMass(const Vector1 &v1, const Vector2 &v2)
return the invariant mass of two LorentzVector The only requirement on the LorentzVector is that the...
Definition: VectorUtil.h:215
Vector RotateZ(const Vector &v, double alpha)
rotation along Z axis for a generic vector by an Angle alpha returning a new vector.
Definition: VectorUtil.h:287
double sin(double)
auto * lv
Definition: textalign.C:5
LVector boostZ(const LVector &v, double beta)
Boost a generic Lorentz Vector class along the Z direction with a factor beta The only requirement o...
Definition: VectorUtil.h:397
static constexpr double mm2
double gamma(double x)
Class describing a generic displacement vector in 3 dimensions.
Vector1::Scalar DeltaPhi(const Vector1 &v1, const Vector2 &v2)
Find aximutal Angle difference between two generic vectors ( v2.Phi() - v1.Phi() ) The only requirem...
Definition: VectorUtil.h:59
#define M_PI
Definition: Rotated.cxx:105
double Angle(const Vector1 &v1, const Vector2 &v2)
Find Angle between two vectors.
Definition: VectorUtil.h:138
LVector boost(const LVector &v, const BoostVector &b)
Boost a generic Lorentz Vector class using a generic 3D Vector class describing the boost The only r...
Definition: VectorUtil.h:327
Vector RotateY(const Vector &v, double alpha)
rotation along Y axis for a generic vector by an Angle alpha returning a new vector.
Definition: VectorUtil.h:270
double Phi_mpi_pi(double phi)
Returns phi angle in the interval (-PI,PI]
Definition: VectorUtil.cxx:36
Vector Rotate(const Vector &v, const RotationMatrix &rot)
rotation on a generic vector using a generic rotation class.
Definition: VectorUtil.h:306
#define d(i)
Definition: RSha256.hxx:102
DisplacementVector3D< CoordSystem, U > Mult(const Matrix &m, const DisplacementVector3D< CoordSystem, U > &v)
Multiplications of a generic matrices with a DisplacementVector3D of any coordinate system...
Definition: VectorUtil.h:425
Namespace for new Math classes and functions.
Vector1 PerpVector(const Vector1 &v, const Vector2 &u)
Find the vector component of v perpendicular to the given direction of u
Definition: VectorUtil.h:167
you should not use this method at all Int_t Int_t Double_t Double_t Double_t Int_t Double_t Double_t Double_t Double_t b
Definition: TRolke.cxx:630
void Throw(const char *)
function throwing exception, by creating internally a GenVector_exception only when needed ...
LVector boostY(const LVector &v, double beta)
Boost a generic Lorentz Vector class along the Y direction with a factor beta The only requirement o...
Definition: VectorUtil.h:377
double Perp(const Vector1 &v, const Vector2 &u)
Find the magnitude of the vector component of v perpendicular to the given direction of u ...
Definition: VectorUtil.h:196
Rotation3D::Scalar Scalar
double CosTheta(const Vector1 &v1, const Vector2 &v2)
Find CosTheta Angle between two generic 3D vectors pre-requisite: vectors implement the X()...
Definition: VectorUtil.h:112