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1 // -*- C++ -*- 1 // -*- C++ -*-
2 // ------------------------------------------- 2 // ---------------------------------------------------------------------------
3 // 3 //
4 // This file is a part of the CLHEP - a Class 4 // This file is a part of the CLHEP - a Class Library for High Energy Physics.
5 // 5 //
6 // This is the implementation of those parts o 6 // This is the implementation of those parts of the HepLorentzRotation class
7 // which involve decomposition into Boost*Rota 7 // which involve decomposition into Boost*Rotation.
8 8
9 #include "CLHEP/Vector/LorentzRotation.h" << 9 #ifdef GNUPRAGMA
>> 10 #pragma implementation
>> 11 #endif
10 12
11 #include <cmath> << 13 #include "CLHEP/Vector/LorentzRotation.h"
12 #include <iostream> <<
13 14
14 namespace CLHEP { 15 namespace CLHEP {
15 16
16 // ---------- Decomposition: 17 // ---------- Decomposition:
17 18
18 void HepLorentzRotation::decompose 19 void HepLorentzRotation::decompose
19 (HepBoost & bboost, HepRotation & rotation) 20 (HepBoost & bboost, HepRotation & rotation) const {
20 21
21 // The boost will be the pure boost based on 22 // The boost will be the pure boost based on column 4 of the transformation
22 // matrix. Since the constructor takes the 23 // matrix. Since the constructor takes the beta vector, and not beta*gamma,
23 // we first divide through by gamma = the tt 24 // we first divide through by gamma = the tt element. This of course can
24 // never be zero since the last row has t**2 25 // never be zero since the last row has t**2 - v**2 = +1.
25 26
26 Hep3Vector betaVec ( xt(), yt(), zt() ); 27 Hep3Vector betaVec ( xt(), yt(), zt() );
27 betaVec *= 1.0 / tt(); 28 betaVec *= 1.0 / tt();
28 bboost.set( betaVec ); 29 bboost.set( betaVec );
29 30
30 // The rotation will be inverse of B times T 31 // The rotation will be inverse of B times T.
31 32
32 HepBoost B( -betaVec ); 33 HepBoost B( -betaVec );
33 HepLorentzRotation R( B * *this ); 34 HepLorentzRotation R( B * *this );
34 35
35 HepRep3x3 m1 ( R.xx(), R.xy(), R.xz(), 36 HepRep3x3 m1 ( R.xx(), R.xy(), R.xz(),
36 R.yx(), R.yy(), R.yz(), 37 R.yx(), R.yy(), R.yz(),
37 R.zx(), R.zy(), R.zz() ); 38 R.zx(), R.zy(), R.zz() );
38 rotation.set( m1 ); 39 rotation.set( m1 );
39 rotation.rectify(); 40 rotation.rectify();
40 41
41 return; 42 return;
42 43
43 } 44 }
44 45
45 void HepLorentzRotation::decompose 46 void HepLorentzRotation::decompose
46 (Hep3Vector & bboost, HepAxisAngle & rotatio 47 (Hep3Vector & bboost, HepAxisAngle & rotation) const {
47 HepRotation r; 48 HepRotation r;
48 HepBoost b; 49 HepBoost b;
49 decompose(b,r); 50 decompose(b,r);
50 bboost = b.boostVector(); 51 bboost = b.boostVector();
51 rotation = r.axisAngle(); 52 rotation = r.axisAngle();
52 return; 53 return;
53 } 54 }
54 55
55 void HepLorentzRotation::decompose 56 void HepLorentzRotation::decompose
56 (HepRotation & rotation, HepBoost & bboost) 57 (HepRotation & rotation, HepBoost & bboost) const {
57 58
58 // In this case the pure boost is based on r 59 // In this case the pure boost is based on row 4 of the matrix.
59 60
60 Hep3Vector betaVec( tx(), ty(), tz() ); 61 Hep3Vector betaVec( tx(), ty(), tz() );
61 betaVec *= 1.0 / tt(); 62 betaVec *= 1.0 / tt();
62 bboost.set( betaVec ); 63 bboost.set( betaVec );
63 64
64 // The rotation will be T times the inverse 65 // The rotation will be T times the inverse of B.
65 66
66 HepBoost B( -betaVec ); 67 HepBoost B( -betaVec );
67 HepLorentzRotation R( *this * B ); 68 HepLorentzRotation R( *this * B );
68 69
69 HepRep3x3 m1 ( R.xx(), R.xy(), R.xz(), 70 HepRep3x3 m1 ( R.xx(), R.xy(), R.xz(),
70 R.yx(), R.yy(), R.yz(), 71 R.yx(), R.yy(), R.yz(),
71 R.zx(), R.zy(), R.zz() ); 72 R.zx(), R.zy(), R.zz() );
72 rotation.set( m1 ); 73 rotation.set( m1 );
73 rotation.rectify(); 74 rotation.rectify();
74 return; 75 return;
75 76
76 } 77 }
77 78
78 void HepLorentzRotation::decompose 79 void HepLorentzRotation::decompose
79 (HepAxisAngle & rotation, Hep3Vector & bboos 80 (HepAxisAngle & rotation, Hep3Vector & bboost) const {
80 HepRotation r; 81 HepRotation r;
81 HepBoost b; 82 HepBoost b;
82 decompose(r,b); 83 decompose(r,b);
83 rotation = r.axisAngle(); 84 rotation = r.axisAngle();
84 bboost = b.boostVector(); 85 bboost = b.boostVector();
85 return; 86 return;
86 } 87 }
87 88
88 double HepLorentzRotation::distance2( const He 89 double HepLorentzRotation::distance2( const HepBoost & b ) const {
89 HepBoost b1; 90 HepBoost b1;
90 HepRotation r1; 91 HepRotation r1;
91 decompose( b1, r1 ); 92 decompose( b1, r1 );
92 double db2 = b1.distance2( b ); 93 double db2 = b1.distance2( b );
93 double dr2 = r1.norm2(); 94 double dr2 = r1.norm2();
94 return ( db2 + dr2 ); 95 return ( db2 + dr2 );
95 } 96 }
96 97
97 double HepLorentzRotation::distance2( const He 98 double HepLorentzRotation::distance2( const HepRotation & r ) const {
98 HepBoost b1; 99 HepBoost b1;
99 HepRotation r1; 100 HepRotation r1;
100 decompose( b1, r1 ); 101 decompose( b1, r1 );
101 double db2 = b1.norm2( ); 102 double db2 = b1.norm2( );
102 double dr2 = r1.distance2( r ); 103 double dr2 = r1.distance2( r );
103 return ( db2 + dr2 ); 104 return ( db2 + dr2 );
104 } 105 }
105 106
106 double HepLorentzRotation::distance2( 107 double HepLorentzRotation::distance2(
107 const HepLorentzRotation & lt ) co 108 const HepLorentzRotation & lt ) const {
108 HepBoost b1; 109 HepBoost b1;
109 HepRotation r1; 110 HepRotation r1;
110 decompose( b1, r1 ); 111 decompose( b1, r1 );
111 HepBoost b2; 112 HepBoost b2;
112 HepRotation r2; 113 HepRotation r2;
113 lt.decompose (b2, r2); 114 lt.decompose (b2, r2);
114 double db2 = b1.distance2( b2 ); 115 double db2 = b1.distance2( b2 );
115 double dr2 = r1.distance2( r2 ); 116 double dr2 = r1.distance2( r2 );
116 return ( db2 + dr2 ); 117 return ( db2 + dr2 );
117 } 118 }
118 119
119 double HepLorentzRotation::howNear( const HepB 120 double HepLorentzRotation::howNear( const HepBoost & b ) const {
120 return std::sqrt( distance2( b ) ); 121 return std::sqrt( distance2( b ) );
121 } 122 }
122 double HepLorentzRotation::howNear( const HepR 123 double HepLorentzRotation::howNear( const HepRotation & r ) const {
123 return std::sqrt( distance2( r ) ); 124 return std::sqrt( distance2( r ) );
124 } 125 }
125 double HepLorentzRotation::howNear( const HepL 126 double HepLorentzRotation::howNear( const HepLorentzRotation & lt )const {
126 return std::sqrt( distance2( lt ) ); 127 return std::sqrt( distance2( lt ) );
127 } 128 }
128 129
129 bool HepLorentzRotation::isNear( 130 bool HepLorentzRotation::isNear(
130 const HepBoost & b, double epsilon ) const 131 const HepBoost & b, double epsilon ) const {
131 HepBoost b1; 132 HepBoost b1;
132 HepRotation r1; 133 HepRotation r1;
133 decompose( b1, r1 ); 134 decompose( b1, r1 );
134 double db2 = b1.distance2(b); 135 double db2 = b1.distance2(b);
135 if ( db2 > epsilon*epsilon ) { 136 if ( db2 > epsilon*epsilon ) {
136 return false; // Saves the time-con 137 return false; // Saves the time-consuming Rotation::norm2
137 } 138 }
138 double dr2 = r1.norm2(); 139 double dr2 = r1.norm2();
139 return ( (db2 + dr2) <= epsilon*epsilon ); 140 return ( (db2 + dr2) <= epsilon*epsilon );
140 } 141 }
141 142
142 bool HepLorentzRotation::isNear( 143 bool HepLorentzRotation::isNear(
143 const HepRotation & r, double epsilon ) co 144 const HepRotation & r, double epsilon ) const {
144 HepBoost b1; 145 HepBoost b1;
145 HepRotation r1; 146 HepRotation r1;
146 decompose( b1, r1 ); 147 decompose( b1, r1 );
147 double db2 = b1.norm2(); 148 double db2 = b1.norm2();
148 if ( db2 > epsilon*epsilon ) { 149 if ( db2 > epsilon*epsilon ) {
149 return false; // Saves the time-con 150 return false; // Saves the time-consuming Rotation::distance2
150 } 151 }
151 double dr2 = r1.distance2(r); 152 double dr2 = r1.distance2(r);
152 return ( (db2 + dr2) <= epsilon*epsilon ); 153 return ( (db2 + dr2) <= epsilon*epsilon );
153 } 154 }
154 155
155 bool HepLorentzRotation::isNear( 156 bool HepLorentzRotation::isNear(
156 const HepLorentzRotation & lt, double epsi 157 const HepLorentzRotation & lt, double epsilon ) const {
157 HepBoost b1; 158 HepBoost b1;
158 HepRotation r1; 159 HepRotation r1;
159 decompose( b1, r1 ); 160 decompose( b1, r1 );
160 HepBoost b2; 161 HepBoost b2;
161 HepRotation r2; 162 HepRotation r2;
162 lt.decompose (b2, r2); 163 lt.decompose (b2, r2);
163 double db2 = b1.distance2(b2); 164 double db2 = b1.distance2(b2);
164 if ( db2 > epsilon*epsilon ) { 165 if ( db2 > epsilon*epsilon ) {
165 return false; // Saves the time-con 166 return false; // Saves the time-consuming Rotation::distance2
166 } 167 }
167 double dr2 = r1.distance2(r2); 168 double dr2 = r1.distance2(r2);
168 return ( (db2 + dr2) <= epsilon*epsilon ); 169 return ( (db2 + dr2) <= epsilon*epsilon );
169 } 170 }
170 171
171 double HepLorentzRotation::norm2() const { 172 double HepLorentzRotation::norm2() const {
172 HepBoost b; 173 HepBoost b;
173 HepRotation r; 174 HepRotation r;
174 decompose( b, r ); 175 decompose( b, r );
175 return b.norm2() + r.norm2(); 176 return b.norm2() + r.norm2();
176 } 177 }
177 178
178 void HepLorentzRotation::rectify() { 179 void HepLorentzRotation::rectify() {
179 180
180 // Assuming the representation of this is cl 181 // Assuming the representation of this is close to a true LT,
181 // but may have drifted due to round-off err 182 // but may have drifted due to round-off error from many operations,
182 // this forms an "exact" orthosymplectic mat 183 // this forms an "exact" orthosymplectic matrix for the LT again.
183 184
184 // There are several ways to do this, all eq 185 // There are several ways to do this, all equivalent to lowest order in
185 // the corrected error. We choose to form a 186 // the corrected error. We choose to form an LT based on the inverse boost
186 // extracted from row 4, and left-multiply b 187 // extracted from row 4, and left-multiply by LT to form what would be
187 // a rotation if the LT were kosher. We dro 188 // a rotation if the LT were kosher. We drop the possibly non-zero t
188 // components of that, rectify that rotation 189 // components of that, rectify that rotation and multiply back by the boost.
189 190
190 Hep3Vector beta (tx(), ty(), tz()); 191 Hep3Vector beta (tx(), ty(), tz());
191 double gam = tt(); // NaN-proofing 192 double gam = tt(); // NaN-proofing
192 if ( gam <= 0 ) { 193 if ( gam <= 0 ) {
193 std::cerr << "HepLorentzRotation::rectify( 194 std::cerr << "HepLorentzRotation::rectify() - "
194 << "rectify() on a transformation with tt() 195 << "rectify() on a transformation with tt() <= 0 - will not help!"
195 << std::endl; 196 << std::endl;
196 gam = 1; 197 gam = 1;
197 } 198 }
198 beta *= 1.0/gam; 199 beta *= 1.0/gam;
199 HepLorentzRotation R = (*this) * HepBoost(-b 200 HepLorentzRotation R = (*this) * HepBoost(-beta);
200 201
201 HepRep3x3 m1 ( R.xx(), R.xy(), R.xz(), 202 HepRep3x3 m1 ( R.xx(), R.xy(), R.xz(),
202 R.yx(), R.yy(), R.yz(), 203 R.yx(), R.yy(), R.yz(),
203 R.zx(), R.zy(), R.zz() ); 204 R.zx(), R.zy(), R.zz() );
204 205
205 HepRotation Rgood (m1); 206 HepRotation Rgood (m1);
206 Rgood.rectify(); 207 Rgood.rectify();
207 208
208 set ( Rgood, HepBoost(beta) ); 209 set ( Rgood, HepBoost(beta) );
209 } 210 }
210 211
211 } // namespace CLHEP 212 } // namespace CLHEP
212 213