| 1 | // -*- C++ -*-
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| 2 | // CLASSDOC OFF
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| 3 | // $Id: LorentzRotation.h,v 1.1 2008-06-04 14:14:58 demin Exp $
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| 4 | // ---------------------------------------------------------------------------
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| 5 | // CLASSDOC ON
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| 6 | //
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| 7 | // This file is a part of the CLHEP - a Class Library for High Energy Physics.
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| 8 | //
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| 9 | // This is the definition of the HepLorentzRotation class for performing
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| 10 | // Lorentz transformations (rotations and boosts) on objects of the
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| 11 | // HepLorentzVector class.
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| 12 | //
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| 13 | // HepLorentzRotation is a concrete implementation of Hep4RotationInterface.
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| 14 | //
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| 15 | // .SS See Also
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| 16 | // RotationInterfaces.h
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| 17 | // ThreeVector.h, LorentzVector.h
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| 18 | // Rotation.h, Boost.h
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| 19 | //
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| 20 | // .SS Author
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| 21 | // Leif Lonnblad, Mark Fischler
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| 22 |
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| 23 | #ifndef HEP_LORENTZROTATION_H
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| 24 | #define HEP_LORENTZROTATION_H
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| 25 |
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| 26 | #ifdef GNUPRAGMA
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| 27 | #pragma interface
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| 28 | #endif
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| 29 |
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| 30 | #include "CLHEP/Vector/defs.h"
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| 31 | #include "CLHEP/Vector/RotationInterfaces.h"
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| 32 | #include "CLHEP/Vector/Rotation.h"
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| 33 | #include "CLHEP/Vector/Boost.h"
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| 34 | #include "CLHEP/Vector/LorentzVector.h"
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| 35 |
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| 36 | namespace CLHEP {
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| 37 |
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| 38 | // Global methods
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| 39 |
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| 40 | inline HepLorentzRotation inverseOf ( const HepLorentzRotation & lt );
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| 41 | HepLorentzRotation operator * (const HepRotation & r,
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| 42 | const HepLorentzRotation & lt);
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| 43 | HepLorentzRotation operator * (const HepRotationX & r,
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| 44 | const HepLorentzRotation & lt);
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| 45 | HepLorentzRotation operator * (const HepRotationY & r,
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| 46 | const HepLorentzRotation & lt);
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| 47 | HepLorentzRotation operator * (const HepRotationZ & r,
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| 48 | const HepLorentzRotation & lt);
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| 49 |
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| 50 | /**
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| 51 | * @author
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| 52 | * @ingroup vector
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| 53 | */
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| 54 | class HepLorentzRotation {
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| 55 |
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| 56 | public:
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| 57 | // ---------- Identity HepLorentzRotation:
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| 58 |
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| 59 | static const HepLorentzRotation IDENTITY;
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| 60 |
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| 61 | // ---------- Constructors and Assignment:
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| 62 |
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| 63 | inline HepLorentzRotation();
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| 64 | // Default constructor. Gives a unit matrix.
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| 65 |
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| 66 | inline HepLorentzRotation (const HepLorentzRotation & r);
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| 67 | // Copy constructor.
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| 68 |
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| 69 | inline HepLorentzRotation (const HepRotation & r);
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| 70 | inline explicit HepLorentzRotation (const HepRotationX & r);
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| 71 | inline explicit HepLorentzRotation (const HepRotationY & r);
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| 72 | inline explicit HepLorentzRotation (const HepRotationZ & r);
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| 73 | inline HepLorentzRotation (const HepBoost & b);
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| 74 | inline explicit HepLorentzRotation (const HepBoostX & b);
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| 75 | inline explicit HepLorentzRotation (const HepBoostY & b);
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| 76 | inline explicit HepLorentzRotation (const HepBoostZ & b);
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| 77 | // Constructors from special cases.
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| 78 |
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| 79 | inline HepLorentzRotation & operator = (const HepLorentzRotation & m);
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| 80 | inline HepLorentzRotation & operator = (const HepRotation & m);
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| 81 | inline HepLorentzRotation & operator = (const HepBoost & m);
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| 82 | // Assignment.
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| 83 |
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| 84 | HepLorentzRotation & set (double bx, double by, double bz);
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| 85 | inline HepLorentzRotation & set (const Hep3Vector & p);
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| 86 | inline HepLorentzRotation & set (const HepRotation & r);
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| 87 | inline HepLorentzRotation & set (const HepRotationX & r);
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| 88 | inline HepLorentzRotation & set (const HepRotationY & r);
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| 89 | inline HepLorentzRotation & set (const HepRotationZ & r);
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| 90 | inline HepLorentzRotation & set (const HepBoost & boost);
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| 91 | inline HepLorentzRotation & set (const HepBoostX & boost);
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| 92 | inline HepLorentzRotation & set (const HepBoostY & boost);
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| 93 | inline HepLorentzRotation & set (const HepBoostZ & boost);
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| 94 | inline HepLorentzRotation (double bx, double by, double bz);
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| 95 | inline HepLorentzRotation (const Hep3Vector & p);
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| 96 | // Other Constructors giving a Lorentz-boost.
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| 97 |
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| 98 | HepLorentzRotation & set( const HepBoost & B, const HepRotation & R );
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| 99 | inline HepLorentzRotation ( const HepBoost & B, const HepRotation & R );
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| 100 | // supply B and R: T = B R:
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| 101 |
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| 102 | HepLorentzRotation & set( const HepRotation & R, const HepBoost & B );
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| 103 | inline HepLorentzRotation ( const HepRotation & R, const HepBoost & B );
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| 104 | // supply R and B: T = R B:
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| 105 |
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| 106 | HepLorentzRotation ( const HepLorentzVector & col1,
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| 107 | const HepLorentzVector & col2,
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| 108 | const HepLorentzVector & col3,
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| 109 | const HepLorentzVector & col4 );
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| 110 | // Construct from four *orthosymplectic* LorentzVectors for the columns:
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| 111 | // NOTE:
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| 112 | // This constructor, and the two set methods below,
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| 113 | // will check that the columns (or rows) form an orthosymplectic
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| 114 | // matrix, and will adjust values so that this relation is
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| 115 | // as exact as possible.
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| 116 | // Orthosymplectic means the dot product USING THE METRIC
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| 117 | // of two different coumns will be 0, and of a column with
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| 118 | // itself will be one.
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| 119 |
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| 120 | HepLorentzRotation & set( const HepLorentzVector & col1,
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| 121 | const HepLorentzVector & col2,
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| 122 | const HepLorentzVector & col3,
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| 123 | const HepLorentzVector & col4 );
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| 124 | // supply four *orthosymplectic* HepLorentzVectors for the columns
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| 125 |
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| 126 | HepLorentzRotation & setRows( const HepLorentzVector & row1,
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| 127 | const HepLorentzVector & row2,
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| 128 | const HepLorentzVector & row3,
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| 129 | const HepLorentzVector & row4 );
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| 130 | // supply four *orthosymplectic* HepLorentzVectors for the columns
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| 131 |
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| 132 | inline HepLorentzRotation & set( const HepRep4x4 & rep );
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| 133 | inline HepLorentzRotation ( const HepRep4x4 & rep );
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| 134 | // supply a HepRep4x4 structure (16 numbers)
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| 135 | // WARNING:
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| 136 | // This constructor and set method will assume the
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| 137 | // HepRep4x4 supplied is in fact an orthosymplectic matrix.
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| 138 | // No checking or correction is done. If you are
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| 139 | // not certain the matrix is orthosymplectic, break it
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| 140 | // into four HepLorentzVector columns and use the form
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| 141 | // HepLorentzRotation (col1, col2, col3, col4)
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| 142 |
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| 143 | // ---------- Accessors:
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| 144 |
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| 145 | inline double xx() const;
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| 146 | inline double xy() const;
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| 147 | inline double xz() const;
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| 148 | inline double xt() const;
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| 149 | inline double yx() const;
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| 150 | inline double yy() const;
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| 151 | inline double yz() const;
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| 152 | inline double yt() const;
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| 153 | inline double zx() const;
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| 154 | inline double zy() const;
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| 155 | inline double zz() const;
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| 156 | inline double zt() const;
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| 157 | inline double tx() const;
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| 158 | inline double ty() const;
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| 159 | inline double tz() const;
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| 160 | inline double tt() const;
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| 161 | // Elements of the matrix.
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| 162 |
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| 163 | inline HepLorentzVector col1() const;
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| 164 | inline HepLorentzVector col2() const;
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| 165 | inline HepLorentzVector col3() const;
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| 166 | inline HepLorentzVector col4() const;
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| 167 | // orthosymplectic column vectors
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| 168 |
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| 169 | inline HepLorentzVector row1() const;
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| 170 | inline HepLorentzVector row2() const;
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| 171 | inline HepLorentzVector row3() const;
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| 172 | inline HepLorentzVector row4() const;
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| 173 | // orthosymplectic row vectors
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| 174 |
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| 175 | inline HepRep4x4 rep4x4() const;
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| 176 | // 4x4 representation:
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| 177 |
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| 178 | // ------------ Subscripting:
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| 179 |
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| 180 | class HepLorentzRotation_row {
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| 181 | public:
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| 182 | inline HepLorentzRotation_row(const HepLorentzRotation &, int);
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| 183 | inline double operator [] (int) const;
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| 184 | private:
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| 185 | const HepLorentzRotation & rr;
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| 186 | int ii;
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| 187 | };
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| 188 | // Helper class for implemention of C-style subscripting r[i][j]
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| 189 |
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| 190 | inline const HepLorentzRotation_row operator [] (int) const;
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| 191 | // Returns object of the helper class for C-style subscripting r[i][j]
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| 192 |
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| 193 | double operator () (int, int) const;
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| 194 | // Fortran-style subscripting: returns (i,j) element of the matrix.
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| 195 |
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| 196 | // ---------- Decomposition:
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| 197 |
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| 198 | void decompose (Hep3Vector & boost, HepAxisAngle & rotation) const;
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| 199 | void decompose (HepBoost & boost, HepRotation & rotation) const;
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| 200 | // Find B and R such that L = B*R
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| 201 |
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| 202 | void decompose (HepAxisAngle & rotation, Hep3Vector & boost) const;
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| 203 | void decompose (HepRotation & rotation, HepBoost & boost) const;
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| 204 | // Find R and B such that L = R*B
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| 205 |
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| 206 | // ---------- Comparisons:
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| 207 |
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| 208 | int compare( const HepLorentzRotation & m ) const;
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| 209 | // Dictionary-order comparison, in order tt,tz,...zt,zz,zy,zx,yt,yz,...,xx
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| 210 | // Used in operator<, >, <=, >=
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| 211 |
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| 212 | inline bool operator == (const HepLorentzRotation &) const;
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| 213 | inline bool operator != (const HepLorentzRotation &) const;
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| 214 | inline bool operator <= (const HepLorentzRotation &) const;
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| 215 | inline bool operator >= (const HepLorentzRotation &) const;
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| 216 | inline bool operator < (const HepLorentzRotation &) const;
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| 217 | inline bool operator > (const HepLorentzRotation &) const;
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| 218 |
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| 219 | inline bool isIdentity() const;
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| 220 | // Returns true if the Identity matrix.
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| 221 |
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| 222 | double distance2( const HepBoost & b ) const;
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| 223 | double distance2( const HepRotation & r ) const;
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| 224 | double distance2( const HepLorentzRotation & lt ) const;
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| 225 | // Decomposes L = B*R, returns the sum of distance2 for B and R.
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| 226 |
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| 227 | double howNear( const HepBoost & b ) const;
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| 228 | double howNear( const HepRotation & r) const;
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| 229 | double howNear( const HepLorentzRotation & lt ) const;
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| 230 |
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| 231 | bool isNear(const HepBoost & b,
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| 232 | double epsilon=Hep4RotationInterface::tolerance) const;
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| 233 | bool isNear(const HepRotation & r,
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| 234 | double epsilon=Hep4RotationInterface::tolerance) const;
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| 235 | bool isNear(const HepLorentzRotation & lt,
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| 236 | double epsilon=Hep4RotationInterface::tolerance) const;
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| 237 |
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| 238 | // ---------- Properties:
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| 239 |
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| 240 | double norm2() const;
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| 241 | // distance2 (IDENTITY), which involves decomposing into B and R and summing
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| 242 | // norm2 for the individual B and R parts.
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| 243 |
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| 244 | void rectify();
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| 245 | // non-const but logically moot correction for accumulated roundoff errors
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| 246 | // rectify averages the matrix with the orthotranspose of its actual
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| 247 | // inverse (absent accumulated roundoff errors, the orthotranspose IS
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| 248 | // the inverse)); this removes to first order those errors.
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| 249 | // Then it formally decomposes that, extracts axis and delta for its
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| 250 | // Rotation part, forms a LorentzRotation from a true HepRotation
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| 251 | // with those values of axis and delta, times the true Boost
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| 252 | // with that boost vector.
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| 253 |
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| 254 | // ---------- Application:
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| 255 |
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| 256 | inline HepLorentzVector vectorMultiplication(const HepLorentzVector&) const;
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| 257 | inline HepLorentzVector operator()( const HepLorentzVector & w ) const;
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| 258 | inline HepLorentzVector operator* ( const HepLorentzVector & p ) const;
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| 259 | // Multiplication with a Lorentz Vector.
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| 260 |
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| 261 | // ---------- Operations in the group of 4-Rotations
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| 262 |
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| 263 | HepLorentzRotation matrixMultiplication(const HepRep4x4 & m) const;
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| 264 |
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| 265 | inline HepLorentzRotation operator * (const HepBoost & b) const;
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| 266 | inline HepLorentzRotation operator * (const HepRotation & r) const;
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| 267 | inline HepLorentzRotation operator * (const HepLorentzRotation & lt) const;
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| 268 | // Product of two Lorentz Rotations (this) * lt - matrix multiplication
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| 269 |
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| 270 | inline HepLorentzRotation & operator *= (const HepBoost & b);
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| 271 | inline HepLorentzRotation & operator *= (const HepRotation & r);
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| 272 | inline HepLorentzRotation & operator *= (const HepLorentzRotation & lt);
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| 273 | inline HepLorentzRotation & transform (const HepBoost & b);
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| 274 | inline HepLorentzRotation & transform (const HepRotation & r);
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| 275 | inline HepLorentzRotation & transform (const HepLorentzRotation & lt);
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| 276 | // Matrix multiplication.
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| 277 | // Note a *= b; <=> a = a * b; while a.transform(b); <=> a = b * a;
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| 278 |
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| 279 | // Here there is an opportunity for speedup by providing specialized forms
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| 280 | // of lt * r and lt * b where r is a RotationX Y or Z or b is a BoostX Y or Z
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| 281 | // These are, in fact, provided below for the transform() methods.
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| 282 |
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| 283 | HepLorentzRotation & rotateX(double delta);
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| 284 | // Rotation around the x-axis; equivalent to LT = RotationX(delta) * LT
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| 285 |
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| 286 | HepLorentzRotation & rotateY(double delta);
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| 287 | // Rotation around the y-axis; equivalent to LT = RotationY(delta) * LT
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| 288 |
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| 289 | HepLorentzRotation & rotateZ(double delta);
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| 290 | // Rotation around the z-axis; equivalent to LT = RotationZ(delta) * LT
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| 291 |
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| 292 | inline HepLorentzRotation & rotate(double delta, const Hep3Vector& axis);
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| 293 | inline HepLorentzRotation & rotate(double delta, const Hep3Vector *axis);
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| 294 | // Rotation around specified vector - LT = Rotation(delta,axis)*LT
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| 295 |
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| 296 | HepLorentzRotation & boostX(double beta);
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| 297 | // Pure boost along the x-axis; equivalent to LT = BoostX(beta) * LT
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| 298 |
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| 299 | HepLorentzRotation & boostY(double beta);
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| 300 | // Pure boost along the y-axis; equivalent to LT = BoostX(beta) * LT
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| 301 |
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| 302 | HepLorentzRotation & boostZ(double beta);
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| 303 | // Pure boost along the z-axis; equivalent to LT = BoostX(beta) * LT
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| 304 |
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| 305 | inline HepLorentzRotation & boost(double, double, double);
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| 306 | inline HepLorentzRotation & boost(const Hep3Vector &);
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| 307 | // Lorenz boost.
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| 308 |
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| 309 | inline HepLorentzRotation inverse() const;
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| 310 | // Return the inverse.
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| 311 |
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| 312 | inline HepLorentzRotation & invert();
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| 313 | // Inverts the LorentzRotation matrix.
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| 314 |
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| 315 | // ---------- I/O:
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| 316 |
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| 317 | std::ostream & print( std::ostream & os ) const;
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| 318 | // Aligned six-digit-accurate output of the transformation matrix.
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| 319 |
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| 320 | // ---------- Tolerance
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| 321 |
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| 322 | static inline double getTolerance();
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| 323 | static inline double setTolerance(double tol);
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| 324 |
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| 325 | friend HepLorentzRotation inverseOf ( const HepLorentzRotation & lt );
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| 326 |
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| 327 | protected:
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| 328 |
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| 329 | inline HepLorentzRotation
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| 330 | (double mxx, double mxy, double mxz, double mxt,
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| 331 | double myx, double myy, double myz, double myt,
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| 332 | double mzx, double mzy, double mzz, double mzt,
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| 333 | double mtx, double mty, double mtz, double mtt);
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| 334 | // Protected constructor.
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| 335 | // DOES NOT CHECK FOR VALIDITY AS A LORENTZ TRANSFORMATION.
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| 336 |
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| 337 | inline void setBoost(double, double, double);
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| 338 | // Set elements according to a boost vector.
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| 339 |
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| 340 | double mxx, mxy, mxz, mxt,
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| 341 | myx, myy, myz, myt,
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| 342 | mzx, mzy, mzz, mzt,
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| 343 | mtx, mty, mtz, mtt;
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| 344 | // The matrix elements.
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| 345 |
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| 346 | }; // HepLorentzRotation
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| 347 |
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| 348 | inline std::ostream & operator<<
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| 349 | ( std::ostream & os, const HepLorentzRotation& lt )
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| 350 | {return lt.print(os);}
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| 351 |
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| 352 | inline bool operator==(const HepRotation &r, const HepLorentzRotation & lt)
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| 353 | { return lt==r; }
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| 354 | inline bool operator!=(const HepRotation &r, const HepLorentzRotation & lt)
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| 355 | { return lt!=r; }
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| 356 | inline bool operator<=(const HepRotation &r, const HepLorentzRotation & lt)
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| 357 | { return lt<=r; }
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| 358 | inline bool operator>=(const HepRotation &r, const HepLorentzRotation & lt)
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| 359 | { return lt>=r; }
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| 360 | inline bool operator<(const HepRotation &r, const HepLorentzRotation & lt)
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| 361 | { return lt<r; }
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| 362 | inline bool operator>(const HepRotation &r, const HepLorentzRotation & lt)
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| 363 | { return lt>r; }
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| 364 |
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| 365 | inline bool operator==(const HepBoost &b, const HepLorentzRotation & lt)
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| 366 | { return lt==b; }
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| 367 | inline bool operator!=(const HepBoost &b, const HepLorentzRotation & lt)
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| 368 | { return lt!=b; }
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| 369 | inline bool operator<=(const HepBoost &b, const HepLorentzRotation & lt)
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| 370 | { return lt<=b; }
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| 371 | inline bool operator>=(const HepBoost &b, const HepLorentzRotation & lt)
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| 372 | { return lt>=b; }
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| 373 | inline bool operator<(const HepBoost &b, const HepLorentzRotation & lt)
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| 374 | { return lt<b; }
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| 375 | inline bool operator>(const HepBoost &b, const HepLorentzRotation & lt)
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| 376 | { return lt>b; }
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| 377 |
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| 378 | } // namespace CLHEP
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| 379 |
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| 380 | #include "CLHEP/Vector/LorentzRotation.icc"
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| 381 |
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| 382 | #ifdef ENABLE_BACKWARDS_COMPATIBILITY
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| 383 | // backwards compatibility will be enabled ONLY in CLHEP 1.9
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| 384 | using namespace CLHEP;
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| 385 | #endif
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| 386 |
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| 387 | #endif /* HEP_LORENTZROTATION_H */
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| 388 |
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