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1 // -*- C++ -*- 1 // -*- C++ -*-
>> 2 // $Id:$
2 // ------------------------------------------- 3 // ---------------------------------------------------------------------------
3 // 4 //
4 // This file is a part of the CLHEP - a Class 5 // This file is a part of the CLHEP - a Class Library for High Energy Physics.
5 // 6 //
6 // This is the implementation basic parts of t 7 // This is the implementation basic parts of the HepLorentzRotation class.
7 // 8 //
8 // Some ZOOM methods involving construction fr 9 // Some ZOOM methods involving construction from columns and decomposition
9 // into boost*rotation are split off into Lore 10 // into boost*rotation are split off into LorentzRotationC and LorentzRotationD
10 11
>> 12 #ifdef GNUPRAGMA
>> 13 #pragma implementation
>> 14 #endif
>> 15
11 #include "CLHEP/Vector/LorentzRotation.h" 16 #include "CLHEP/Vector/LorentzRotation.h"
12 17
13 #include <cmath> <<
14 #include <iomanip> <<
15 #include <iostream> 18 #include <iostream>
>> 19 #include <iomanip>
16 20
17 namespace CLHEP { 21 namespace CLHEP {
18 22
19 // ---------- Constructors and Assignment: 23 // ---------- Constructors and Assignment:
20 24
21 25
22 HepLorentzRotation & HepLorentzRotation::set 26 HepLorentzRotation & HepLorentzRotation::set
23 (double bx, double by, double bz) { 27 (double bx, double by, double bz) {
24 double bp2 = bx*bx + by*by + bz*bz; 28 double bp2 = bx*bx + by*by + bz*bz;
25 // if (bp2 >= 1) { 29 // if (bp2 >= 1) {
26 // std::cerr << "HepLorentzRotation::set() 30 // std::cerr << "HepLorentzRotation::set() - "
27 // << "Boost Vector supplied to set HepLo 31 // << "Boost Vector supplied to set HepLorentzRotation represents speed >= c."
28 // << std::endl; 32 // << std::endl;
29 // } 33 // }
30 double gamma = 1.0 / std::sqrt(1.0 - bp2); 34 double gamma = 1.0 / std::sqrt(1.0 - bp2);
31 double bgamma = gamma * gamma / (1.0 + gamma 35 double bgamma = gamma * gamma / (1.0 + gamma);
32 mxx = 1.0 + bgamma * bx * bx; 36 mxx = 1.0 + bgamma * bx * bx;
33 myy = 1.0 + bgamma * by * by; 37 myy = 1.0 + bgamma * by * by;
34 mzz = 1.0 + bgamma * bz * bz; 38 mzz = 1.0 + bgamma * bz * bz;
35 mxy = myx = bgamma * bx * by; 39 mxy = myx = bgamma * bx * by;
36 mxz = mzx = bgamma * bx * bz; 40 mxz = mzx = bgamma * bx * bz;
37 myz = mzy = bgamma * by * bz; 41 myz = mzy = bgamma * by * bz;
38 mxt = mtx = gamma * bx; 42 mxt = mtx = gamma * bx;
39 myt = mty = gamma * by; 43 myt = mty = gamma * by;
40 mzt = mtz = gamma * bz; 44 mzt = mtz = gamma * bz;
41 mtt = gamma; 45 mtt = gamma;
42 return *this; 46 return *this;
43 } 47 }
44 48
45 HepLorentzRotation & HepLorentzRotation::set 49 HepLorentzRotation & HepLorentzRotation::set
46 (const HepBoost & B, const HepRotation & R 50 (const HepBoost & B, const HepRotation & R) {
47 set (B.rep4x4()); 51 set (B.rep4x4());
48 *this = matrixMultiplication ( R.rep4x4() ); 52 *this = matrixMultiplication ( R.rep4x4() );
49 return *this; 53 return *this;
50 } 54 }
51 55
52 HepLorentzRotation & HepLorentzRotation::set 56 HepLorentzRotation & HepLorentzRotation::set
53 (const HepRotation & R, const HepBoost & B 57 (const HepRotation & R, const HepBoost & B) {
54 set (R.rep4x4()); 58 set (R.rep4x4());
55 *this = matrixMultiplication ( B.rep4x4() ); 59 *this = matrixMultiplication ( B.rep4x4() );
56 return *this; 60 return *this;
57 } 61 }
58 62
59 // ---------- Accessors: 63 // ---------- Accessors:
60 64
61 // ------------ Subscripting: 65 // ------------ Subscripting:
62 66
63 double HepLorentzRotation::operator () (int i, 67 double HepLorentzRotation::operator () (int i, int j) const {
64 if (i == 0) { 68 if (i == 0) {
65 if (j == 0) { return xx(); } 69 if (j == 0) { return xx(); }
66 if (j == 1) { return xy(); } 70 if (j == 1) { return xy(); }
67 if (j == 2) { return xz(); } 71 if (j == 2) { return xz(); }
68 if (j == 3) { return xt(); } 72 if (j == 3) { return xt(); }
69 } else if (i == 1) { 73 } else if (i == 1) {
70 if (j == 0) { return yx(); } 74 if (j == 0) { return yx(); }
71 if (j == 1) { return yy(); } 75 if (j == 1) { return yy(); }
72 if (j == 2) { return yz(); } 76 if (j == 2) { return yz(); }
73 if (j == 3) { return yt(); } 77 if (j == 3) { return yt(); }
74 } else if (i == 2) { 78 } else if (i == 2) {
75 if (j == 0) { return zx(); } 79 if (j == 0) { return zx(); }
76 if (j == 1) { return zy(); } 80 if (j == 1) { return zy(); }
77 if (j == 2) { return zz(); } 81 if (j == 2) { return zz(); }
78 if (j == 3) { return zt(); } 82 if (j == 3) { return zt(); }
79 } else if (i == 3) { 83 } else if (i == 3) {
80 if (j == 0) { return tx(); } 84 if (j == 0) { return tx(); }
81 if (j == 1) { return ty(); } 85 if (j == 1) { return ty(); }
82 if (j == 2) { return tz(); } 86 if (j == 2) { return tz(); }
83 if (j == 3) { return tt(); } 87 if (j == 3) { return tt(); }
84 } 88 }
85 std::cerr << "HepLorentzRotation subscriptin << 89 std::cerr << "HepLorentzRotation subscripting: bad indeces "
86 << "(" << i << "," << j << ")\n"; 90 << "(" << i << "," << j << ")\n";
87 return 0.0; 91 return 0.0;
88 } 92 }
89 93
90 // ---------- Application: 94 // ---------- Application:
91 95
92 96
93 // ---------- Comparison: 97 // ---------- Comparison:
94 98
95 int HepLorentzRotation::compare( const HepLore 99 int HepLorentzRotation::compare( const HepLorentzRotation & m1 ) const {
96 if (mtt<m1.mtt) return -1; else if (mtt 100 if (mtt<m1.mtt) return -1; else if (mtt>m1.mtt) return 1;
97 else if (mtz<m1.mtz) return -1; else if (mtz 101 else if (mtz<m1.mtz) return -1; else if (mtz>m1.mtz) return 1;
98 else if (mty<m1.mty) return -1; else if (mty 102 else if (mty<m1.mty) return -1; else if (mty>m1.mty) return 1;
99 else if (mtx<m1.mtx) return -1; else if (mtx 103 else if (mtx<m1.mtx) return -1; else if (mtx>m1.mtx) return 1;
100 104
101 else if (mzt<m1.mzt) return -1; else if (mzt 105 else if (mzt<m1.mzt) return -1; else if (mzt>m1.mzt) return 1;
102 else if (mzz<m1.mzz) return -1; else if (mzz 106 else if (mzz<m1.mzz) return -1; else if (mzz>m1.mzz) return 1;
103 else if (mzy<m1.mzy) return -1; else if (mzy 107 else if (mzy<m1.mzy) return -1; else if (mzy>m1.mzy) return 1;
104 else if (mzx<m1.mzx) return -1; else if (mzx 108 else if (mzx<m1.mzx) return -1; else if (mzx>m1.mzx) return 1;
105 109
106 else if (myt<m1.myt) return -1; else if (myt 110 else if (myt<m1.myt) return -1; else if (myt>m1.myt) return 1;
107 else if (myz<m1.myz) return -1; else if (myz 111 else if (myz<m1.myz) return -1; else if (myz>m1.myz) return 1;
108 else if (myy<m1.myy) return -1; else if (myy 112 else if (myy<m1.myy) return -1; else if (myy>m1.myy) return 1;
109 else if (myx<m1.myx) return -1; else if (myx 113 else if (myx<m1.myx) return -1; else if (myx>m1.myx) return 1;
110 114
111 else if (mxt<m1.mxt) return -1; else if (mxt 115 else if (mxt<m1.mxt) return -1; else if (mxt>m1.mxt) return 1;
112 else if (mxz<m1.mxz) return -1; else if (mxz 116 else if (mxz<m1.mxz) return -1; else if (mxz>m1.mxz) return 1;
113 else if (mxy<m1.mxy) return -1; else if (mxy 117 else if (mxy<m1.mxy) return -1; else if (mxy>m1.mxy) return 1;
114 else if (mxx<m1.mxx) return -1; else if (mxx 118 else if (mxx<m1.mxx) return -1; else if (mxx>m1.mxx) return 1;
115 119
116 else return 0; 120 else return 0;
117 } 121 }
118 122
119 123
120 // ---------- Operations in the group of 4-Rot 124 // ---------- Operations in the group of 4-Rotations
121 125
122 HepLorentzRotation 126 HepLorentzRotation
123 HepLorentzRotation::matrixMultiplication(const 127 HepLorentzRotation::matrixMultiplication(const HepRep4x4 & m1) const {
124 return HepLorentzRotation( 128 return HepLorentzRotation(
125 mxx*m1.xx_ + mxy*m1.yx_ + mxz*m1.zx_ + mxt 129 mxx*m1.xx_ + mxy*m1.yx_ + mxz*m1.zx_ + mxt*m1.tx_,
126 mxx*m1.xy_ + mxy*m1.yy_ + mxz*m1.zy_ + mxt 130 mxx*m1.xy_ + mxy*m1.yy_ + mxz*m1.zy_ + mxt*m1.ty_,
127 mxx*m1.xz_ + mxy*m1.yz_ + mxz*m1.zz_ + mxt 131 mxx*m1.xz_ + mxy*m1.yz_ + mxz*m1.zz_ + mxt*m1.tz_,
128 mxx*m1.xt_ + mxy*m1.yt_ + mxz*m1.zt_ + mxt 132 mxx*m1.xt_ + mxy*m1.yt_ + mxz*m1.zt_ + mxt*m1.tt_,
129 133
130 myx*m1.xx_ + myy*m1.yx_ + myz*m1.zx_ + myt 134 myx*m1.xx_ + myy*m1.yx_ + myz*m1.zx_ + myt*m1.tx_,
131 myx*m1.xy_ + myy*m1.yy_ + myz*m1.zy_ + myt 135 myx*m1.xy_ + myy*m1.yy_ + myz*m1.zy_ + myt*m1.ty_,
132 myx*m1.xz_ + myy*m1.yz_ + myz*m1.zz_ + myt 136 myx*m1.xz_ + myy*m1.yz_ + myz*m1.zz_ + myt*m1.tz_,
133 myx*m1.xt_ + myy*m1.yt_ + myz*m1.zt_ + myt 137 myx*m1.xt_ + myy*m1.yt_ + myz*m1.zt_ + myt*m1.tt_,
134 138
135 mzx*m1.xx_ + mzy*m1.yx_ + mzz*m1.zx_ + mzt 139 mzx*m1.xx_ + mzy*m1.yx_ + mzz*m1.zx_ + mzt*m1.tx_,
136 mzx*m1.xy_ + mzy*m1.yy_ + mzz*m1.zy_ + mzt 140 mzx*m1.xy_ + mzy*m1.yy_ + mzz*m1.zy_ + mzt*m1.ty_,
137 mzx*m1.xz_ + mzy*m1.yz_ + mzz*m1.zz_ + mzt 141 mzx*m1.xz_ + mzy*m1.yz_ + mzz*m1.zz_ + mzt*m1.tz_,
138 mzx*m1.xt_ + mzy*m1.yt_ + mzz*m1.zt_ + mzt 142 mzx*m1.xt_ + mzy*m1.yt_ + mzz*m1.zt_ + mzt*m1.tt_,
139 143
140 mtx*m1.xx_ + mty*m1.yx_ + mtz*m1.zx_ + mtt 144 mtx*m1.xx_ + mty*m1.yx_ + mtz*m1.zx_ + mtt*m1.tx_,
141 mtx*m1.xy_ + mty*m1.yy_ + mtz*m1.zy_ + mtt 145 mtx*m1.xy_ + mty*m1.yy_ + mtz*m1.zy_ + mtt*m1.ty_,
142 mtx*m1.xz_ + mty*m1.yz_ + mtz*m1.zz_ + mtt 146 mtx*m1.xz_ + mty*m1.yz_ + mtz*m1.zz_ + mtt*m1.tz_,
143 mtx*m1.xt_ + mty*m1.yt_ + mtz*m1.zt_ + mtt 147 mtx*m1.xt_ + mty*m1.yt_ + mtz*m1.zt_ + mtt*m1.tt_ );
144 } 148 }
145 149
146 HepLorentzRotation & HepLorentzRotation::rotat 150 HepLorentzRotation & HepLorentzRotation::rotateX(double delta) {
147 double c1 = std::cos (delta); 151 double c1 = std::cos (delta);
148 double s1 = std::sin (delta); 152 double s1 = std::sin (delta);
149 HepLorentzVector rowy = row2(); 153 HepLorentzVector rowy = row2();
150 HepLorentzVector rowz = row3(); 154 HepLorentzVector rowz = row3();
151 HepLorentzVector r2 = c1 * rowy - s1 * rowz; 155 HepLorentzVector r2 = c1 * rowy - s1 * rowz;
152 HepLorentzVector r3 = s1 * rowy + c1 * rowz; 156 HepLorentzVector r3 = s1 * rowy + c1 * rowz;
153 myx = r2.x(); myy = r2.y(); myz = r2.z() 157 myx = r2.x(); myy = r2.y(); myz = r2.z(); myt = r2.t();
154 mzx = r3.x(); mzy = r3.y(); mzz = r3.z() 158 mzx = r3.x(); mzy = r3.y(); mzz = r3.z(); mzt = r3.t();
155 return *this; 159 return *this;
156 } 160 }
157 161
158 HepLorentzRotation & HepLorentzRotation::rotat 162 HepLorentzRotation & HepLorentzRotation::rotateY(double delta) {
159 double c1 = std::cos (delta); 163 double c1 = std::cos (delta);
160 double s1 = std::sin (delta); 164 double s1 = std::sin (delta);
161 HepLorentzVector rowx = row1(); 165 HepLorentzVector rowx = row1();
162 HepLorentzVector rowz = row3(); 166 HepLorentzVector rowz = row3();
163 HepLorentzVector r1 = c1 * rowx + s1 * rowz 167 HepLorentzVector r1 = c1 * rowx + s1 * rowz;
164 HepLorentzVector r3 = -s1 * rowx + c1 * rowz 168 HepLorentzVector r3 = -s1 * rowx + c1 * rowz;
165 mxx = r1.x(); mxy = r1.y(); mxz = r1.z() 169 mxx = r1.x(); mxy = r1.y(); mxz = r1.z(); mxt = r1.t();
166 mzx = r3.x(); mzy = r3.y(); mzz = r3.z() 170 mzx = r3.x(); mzy = r3.y(); mzz = r3.z(); mzt = r3.t();
167 return *this; 171 return *this;
168 } 172 }
169 173
170 HepLorentzRotation & HepLorentzRotation::rotat 174 HepLorentzRotation & HepLorentzRotation::rotateZ(double delta) {
171 double c1 = std::cos (delta); 175 double c1 = std::cos (delta);
172 double s1 = std::sin (delta); 176 double s1 = std::sin (delta);
173 HepLorentzVector rowx = row1(); 177 HepLorentzVector rowx = row1();
174 HepLorentzVector rowy = row2(); 178 HepLorentzVector rowy = row2();
175 HepLorentzVector r1 = c1 * rowx - s1 * rowy; 179 HepLorentzVector r1 = c1 * rowx - s1 * rowy;
176 HepLorentzVector r2 = s1 * rowx + c1 * rowy; 180 HepLorentzVector r2 = s1 * rowx + c1 * rowy;
177 mxx = r1.x(); mxy = r1.y(); mxz = r1.z() 181 mxx = r1.x(); mxy = r1.y(); mxz = r1.z(); mxt = r1.t();
178 myx = r2.x(); myy = r2.y(); myz = r2.z() 182 myx = r2.x(); myy = r2.y(); myz = r2.z(); myt = r2.t();
179 return *this; 183 return *this;
180 } 184 }
181 185
182 HepLorentzRotation & HepLorentzRotation::boost 186 HepLorentzRotation & HepLorentzRotation::boostX(double beta) {
183 double b2 = beta*beta; 187 double b2 = beta*beta;
184 // if (b2 >= 1) { 188 // if (b2 >= 1) {
185 // std::cerr << "HepLorentzRotation::boostX 189 // std::cerr << "HepLorentzRotation::boostX() - "
186 // << "Beta supplied to HepLorentzRotatio 190 // << "Beta supplied to HepLorentzRotation::boostX represents speed >= c."
187 // << std::endl; 191 // << std::endl;
188 // } 192 // }
189 double g1 = 1.0/std::sqrt(1.0-b2); 193 double g1 = 1.0/std::sqrt(1.0-b2);
190 double bg = beta*g1; 194 double bg = beta*g1;
191 HepLorentzVector rowx = row1(); 195 HepLorentzVector rowx = row1();
192 HepLorentzVector rowt = row4(); 196 HepLorentzVector rowt = row4();
193 HepLorentzVector r1 = g1 * rowx + bg * rowt 197 HepLorentzVector r1 = g1 * rowx + bg * rowt;
194 HepLorentzVector r4 = bg * rowx + g1 * rowt 198 HepLorentzVector r4 = bg * rowx + g1 * rowt;
195 mxx = r1.x(); mxy = r1.y(); mxz = r1.z() 199 mxx = r1.x(); mxy = r1.y(); mxz = r1.z(); mxt = r1.t();
196 mtx = r4.x(); mty = r4.y(); mtz = r4.z() 200 mtx = r4.x(); mty = r4.y(); mtz = r4.z(); mtt = r4.t();
197 return *this; 201 return *this;
198 } 202 }
199 203
200 HepLorentzRotation & HepLorentzRotation::boost 204 HepLorentzRotation & HepLorentzRotation::boostY(double beta) {
201 double b2 = beta*beta; 205 double b2 = beta*beta;
202 // if (b2 >= 1) { 206 // if (b2 >= 1) {
203 // std::cerr << "HepLorentzRotation::boostY 207 // std::cerr << "HepLorentzRotation::boostY() - "
204 // << "Beta supplied to HepLorentzRotatio 208 // << "Beta supplied to HepLorentzRotation::boostY represents speed >= c."
205 // << std::endl; 209 // << std::endl;
206 // } 210 // }
207 double g1 = 1.0/std::sqrt(1.0-b2); 211 double g1 = 1.0/std::sqrt(1.0-b2);
208 double bg = beta*g1; 212 double bg = beta*g1;
209 HepLorentzVector rowy = row2(); 213 HepLorentzVector rowy = row2();
210 HepLorentzVector rowt = row4(); 214 HepLorentzVector rowt = row4();
211 HepLorentzVector r2 = g1 * rowy + bg * rowt 215 HepLorentzVector r2 = g1 * rowy + bg * rowt;
212 HepLorentzVector r4 = bg * rowy + g1 * rowt 216 HepLorentzVector r4 = bg * rowy + g1 * rowt;
213 myx = r2.x(); myy = r2.y(); myz = r2.z() 217 myx = r2.x(); myy = r2.y(); myz = r2.z(); myt = r2.t();
214 mtx = r4.x(); mty = r4.y(); mtz = r4.z() 218 mtx = r4.x(); mty = r4.y(); mtz = r4.z(); mtt = r4.t();
215 return *this; 219 return *this;
216 } 220 }
217 221
218 HepLorentzRotation & HepLorentzRotation::boost 222 HepLorentzRotation & HepLorentzRotation::boostZ(double beta) {
219 double b2 = beta*beta; 223 double b2 = beta*beta;
220 // if (b2 >= 1) { 224 // if (b2 >= 1) {
221 // std::cerr << "HepLorentzRotation::boostZ 225 // std::cerr << "HepLorentzRotation::boostZ() - "
222 // << "Beta supplied to HepLorentzRotatio 226 // << "Beta supplied to HepLorentzRotation::boostZ represents speed >= c."
223 // << std::endl; 227 // << std::endl;
224 // } 228 // }
225 double g1 = 1.0/std::sqrt(1.0-b2); 229 double g1 = 1.0/std::sqrt(1.0-b2);
226 double bg = beta*g1; 230 double bg = beta*g1;
227 HepLorentzVector rowz = row3(); 231 HepLorentzVector rowz = row3();
228 HepLorentzVector rowt = row4(); 232 HepLorentzVector rowt = row4();
229 HepLorentzVector r3 = g1 * rowz + bg * rowt 233 HepLorentzVector r3 = g1 * rowz + bg * rowt;
230 HepLorentzVector r4 = bg * rowz + g1 * rowt 234 HepLorentzVector r4 = bg * rowz + g1 * rowt;
231 mtx = r4.x(); mty = r4.y(); mtz = r4.z() 235 mtx = r4.x(); mty = r4.y(); mtz = r4.z(); mtt = r4.t();
232 mzx = r3.x(); mzy = r3.y(); mzz = r3.z() 236 mzx = r3.x(); mzy = r3.y(); mzz = r3.z(); mzt = r3.t();
233 return *this; 237 return *this;
234 } 238 }
235 239
236 std::ostream & HepLorentzRotation::print( std: 240 std::ostream & HepLorentzRotation::print( std::ostream & os ) const {
237 os << "\n [ ( " << 241 os << "\n [ ( " <<
238 std::setw(11) << std::setprecision(6) 242 std::setw(11) << std::setprecision(6) << xx() << " " <<
239 std::setw(11) << std::setprecision(6) 243 std::setw(11) << std::setprecision(6) << xy() << " " <<
240 std::setw(11) << std::setprecision(6) 244 std::setw(11) << std::setprecision(6) << xz() << " " <<
241 std::setw(11) << std::setprecision(6) 245 std::setw(11) << std::setprecision(6) << xt() << ")\n"
242 << " ( " << 246 << " ( " <<
243 std::setw(11) << std::setprecision(6) 247 std::setw(11) << std::setprecision(6) << yx() << " " <<
244 std::setw(11) << std::setprecision(6) 248 std::setw(11) << std::setprecision(6) << yy() << " " <<
245 std::setw(11) << std::setprecision(6) 249 std::setw(11) << std::setprecision(6) << yz() << " " <<
246 std::setw(11) << std::setprecision(6) 250 std::setw(11) << std::setprecision(6) << yt() << ")\n"
247 << " ( " << 251 << " ( " <<
248 std::setw(11) << std::setprecision(6) 252 std::setw(11) << std::setprecision(6) << zx() << " " <<
249 std::setw(11) << std::setprecision(6) 253 std::setw(11) << std::setprecision(6) << zy() << " " <<
250 std::setw(11) << std::setprecision(6) 254 std::setw(11) << std::setprecision(6) << zz() << " " <<
251 std::setw(11) << std::setprecision(6) 255 std::setw(11) << std::setprecision(6) << zt() << ")\n"
252 << " ( " << 256 << " ( " <<
253 std::setw(11) << std::setprecision(6) 257 std::setw(11) << std::setprecision(6) << tx() << " " <<
254 std::setw(11) << std::setprecision(6) 258 std::setw(11) << std::setprecision(6) << ty() << " " <<
255 std::setw(11) << std::setprecision(6) 259 std::setw(11) << std::setprecision(6) << tz() << " " <<
256 std::setw(11) << std::setprecision(6) 260 std::setw(11) << std::setprecision(6) << tt() << ") ]\n";
257 return os; 261 return os;
258 } 262 }
259 263
260 HepLorentzRotation operator* ( const HepRotati 264 HepLorentzRotation operator* ( const HepRotation & r,
261 const HepLorent 265 const HepLorentzRotation & lt) {
262 r.rep4x4(); 266 r.rep4x4();
263 lt.rep4x4(); 267 lt.rep4x4();
264 return HepLorentzRotation( HepRep4x4( 268 return HepLorentzRotation( HepRep4x4(
265 r.xx()*lt.xx() + r.xy()*lt.yx() + r.x 269 r.xx()*lt.xx() + r.xy()*lt.yx() + r.xz()*lt.zx() + r.xt()*lt.tx(),
266 r.xx()*lt.xy() + r.xy()*lt.yy() + r.xz()*lt 270 r.xx()*lt.xy() + r.xy()*lt.yy() + r.xz()*lt.zy() + r.xt()*lt.ty(),
267 r.xx()*lt.xz() + r.xy()*lt.yz() + r.xz()*lt 271 r.xx()*lt.xz() + r.xy()*lt.yz() + r.xz()*lt.zz() + r.xt()*lt.tz(),
268 r.xx()*lt.xt() + r.xy()*lt.yt() + r.xz()*lt 272 r.xx()*lt.xt() + r.xy()*lt.yt() + r.xz()*lt.zt() + r.xt()*lt.tt(),
269 273
270 r.yx()*lt.xx() + r.yy()*lt.yx() + r.y 274 r.yx()*lt.xx() + r.yy()*lt.yx() + r.yz()*lt.zx() + r.yt()*lt.tx(),
271 r.yx()*lt.xy() + r.yy()*lt.yy() + r.y 275 r.yx()*lt.xy() + r.yy()*lt.yy() + r.yz()*lt.zy() + r.yt()*lt.ty(),
272 r.yx()*lt.xz() + r.yy()*lt.yz() + r.y 276 r.yx()*lt.xz() + r.yy()*lt.yz() + r.yz()*lt.zz() + r.yt()*lt.tz(),
273 r.yx()*lt.xt() + r.yy()*lt.yt() + r.y 277 r.yx()*lt.xt() + r.yy()*lt.yt() + r.yz()*lt.zt() + r.yt()*lt.tt(),
274 278
275 r.zx()*lt.xx() + r.zy()*lt.yx() + r.z 279 r.zx()*lt.xx() + r.zy()*lt.yx() + r.zz()*lt.zx() + r.zt()*lt.tx(),
276 r.zx()*lt.xy() + r.zy()*lt.yy() + r.z 280 r.zx()*lt.xy() + r.zy()*lt.yy() + r.zz()*lt.zy() + r.zt()*lt.ty(),
277 r.zx()*lt.xz() + r.zy()*lt.yz() + r.z 281 r.zx()*lt.xz() + r.zy()*lt.yz() + r.zz()*lt.zz() + r.zt()*lt.tz(),
278 r.zx()*lt.xt() + r.zy()*lt.yt() + r.z 282 r.zx()*lt.xt() + r.zy()*lt.yt() + r.zz()*lt.zt() + r.zt()*lt.tt(),
279 283
280 r.tx()*lt.xx() + r.ty()*lt.yx() + r.t 284 r.tx()*lt.xx() + r.ty()*lt.yx() + r.tz()*lt.zx() + r.tt()*lt.tx(),
281 r.tx()*lt.xy() + r.ty()*lt.yy() + r.t 285 r.tx()*lt.xy() + r.ty()*lt.yy() + r.tz()*lt.zy() + r.tt()*lt.ty(),
282 r.tx()*lt.xz() + r.ty()*lt.yz() + r.t 286 r.tx()*lt.xz() + r.ty()*lt.yz() + r.tz()*lt.zz() + r.tt()*lt.tz(),
283 r.tx()*lt.xt() + r.ty()*lt.yt() + r.t 287 r.tx()*lt.xt() + r.ty()*lt.yt() + r.tz()*lt.zt() + r.tt()*lt.tt() ) );
284 } 288 }
285 289
286 290
287 const HepLorentzRotation HepLorentzRotation::I 291 const HepLorentzRotation HepLorentzRotation::IDENTITY;
288 292
289 } // namespace CLHEP 293 } // namespace CLHEP
290 294