1 | #ifndef MATHEMATICALTOOLS_SEEN |
---|
2 | #define MATHEMATICALTOOLS_SEEN |
---|
3 | #include <iostream> |
---|
4 | #include <fstream> |
---|
5 | #include <sstream> |
---|
6 | #include <vector> |
---|
7 | #include <cmath> |
---|
8 | |
---|
9 | |
---|
10 | |
---|
11 | using namespace std; |
---|
12 | |
---|
13 | |
---|
14 | |
---|
15 | |
---|
16 | class mathTools |
---|
17 | { |
---|
18 | |
---|
19 | |
---|
20 | public : |
---|
21 | // return the index K such that : |
---|
22 | // vec[K] <= xx < vec[K+1] |
---|
23 | // vec is assumed to be increasingly ordered |
---|
24 | // if xx is outside , return -1 |
---|
25 | static int locateInVector(const vector<double>& vec, double xx) |
---|
26 | { |
---|
27 | int n= vec.size(); |
---|
28 | int jl = 0; |
---|
29 | int ju = n+1; |
---|
30 | int jm; |
---|
31 | if ( vec[0] == xx ) return 0; |
---|
32 | if ( vec.back() <= xx || vec[0] > xx) return -1; |
---|
33 | while ( ju - jl > 1 ) |
---|
34 | { |
---|
35 | jm = (ju + jl)/2; |
---|
36 | if ( vec[jm-1] <= xx ) jl = jm; |
---|
37 | else ju = jm; |
---|
38 | } |
---|
39 | return jl - 1; |
---|
40 | } |
---|
41 | |
---|
42 | |
---|
43 | |
---|
44 | |
---|
45 | // algo. Boris (Birdsall p. 356) in 2D |
---|
46 | // 'tgArcMoitie' is equal to tg(theta/2), if theta is |
---|
47 | // the desired rotation angle. |
---|
48 | // if tg(theta/2) is given exactly, the rotation is 'exact' |
---|
49 | // |
---|
50 | static void borisBunemanRotation(double tgArcMoitie, double& vz, double& vx) |
---|
51 | { |
---|
52 | double t2 = tgArcMoitie * tgArcMoitie; |
---|
53 | double sinAngle = 2.0 * tgArcMoitie / ( 1 + t2 ); |
---|
54 | double vauxz = vz + vx*tgArcMoitie; |
---|
55 | vx = vx - vauxz*sinAngle; |
---|
56 | vz = vauxz + vx*tgArcMoitie; |
---|
57 | } |
---|
58 | |
---|
59 | }; |
---|
60 | |
---|
61 | |
---|
62 | |
---|
63 | |
---|
64 | class TRIDVECTOR |
---|
65 | { |
---|
66 | double vec_[3]; |
---|
67 | |
---|
68 | public : |
---|
69 | |
---|
70 | TRIDVECTOR() |
---|
71 | { |
---|
72 | int k; |
---|
73 | for (k=0; k<3; k++) vec_[k] = 0.0; |
---|
74 | } |
---|
75 | |
---|
76 | TRIDVECTOR( const TRIDVECTOR& triv) |
---|
77 | { |
---|
78 | setComponents( triv.vec_[0],triv.vec_[1], triv.vec_[2]); |
---|
79 | } |
---|
80 | |
---|
81 | |
---|
82 | |
---|
83 | TRIDVECTOR(double x,double y,double z) |
---|
84 | { |
---|
85 | vec_[0] = x; |
---|
86 | vec_[1] = y; |
---|
87 | vec_[2] = z; |
---|
88 | } |
---|
89 | |
---|
90 | inline double& operator() (int index) { return vec_[index]; } |
---|
91 | inline const double& operator() (int index) const { return vec_[index]; } |
---|
92 | |
---|
93 | inline TRIDVECTOR& operator= (const TRIDVECTOR& triv) |
---|
94 | { |
---|
95 | setComponents( triv.vec_[0],triv.vec_[1], triv.vec_[2]); |
---|
96 | return *this; |
---|
97 | } |
---|
98 | |
---|
99 | |
---|
100 | inline TRIDVECTOR& operator = (double value) |
---|
101 | { |
---|
102 | setComponents( value,value, value); |
---|
103 | return *this; |
---|
104 | } |
---|
105 | |
---|
106 | inline void operator *= (const double& factor) |
---|
107 | { |
---|
108 | int k; |
---|
109 | for (k=0; k < 3; k++) vec_[k] *= factor; |
---|
110 | // return *this; |
---|
111 | } |
---|
112 | |
---|
113 | |
---|
114 | |
---|
115 | inline TRIDVECTOR operator + (const TRIDVECTOR& v2) |
---|
116 | { |
---|
117 | // int k; |
---|
118 | return TRIDVECTOR(vec_[0] + v2.vec_[0], vec_[1] + v2.vec_[1], vec_[2] + v2.vec_[2]); |
---|
119 | // for (k=0; k < 3; k++) vec_[k] += v2.vec_[k]; |
---|
120 | // return *this; |
---|
121 | } |
---|
122 | |
---|
123 | inline void operator += (const TRIDVECTOR& v2) |
---|
124 | { |
---|
125 | int k; |
---|
126 | for (k=0; k < 3; k++) vec_[k] += v2.vec_[k]; |
---|
127 | // return *this; |
---|
128 | } |
---|
129 | |
---|
130 | |
---|
131 | inline TRIDVECTOR operator * (const double& facteur) const |
---|
132 | { |
---|
133 | return TRIDVECTOR( vec_[0] * facteur, vec_[1] * facteur, vec_[2] * facteur); |
---|
134 | } |
---|
135 | |
---|
136 | |
---|
137 | inline TRIDVECTOR operator * (const TRIDVECTOR& v2) |
---|
138 | { |
---|
139 | double auxx, auxy, auxz; |
---|
140 | // for ( k=0; k<3; k++) aux[k] = vec_[k]; |
---|
141 | auxx = vec_[1] * v2.vec_[2] - vec_[2] * v2.vec_[1]; |
---|
142 | auxy = vec_[2] * v2.vec_[0] - vec_[0] * v2.vec_[2]; |
---|
143 | auxz = vec_[0] * v2.vec_[1] - vec_[1] * v2.vec_[0]; |
---|
144 | // return *this; |
---|
145 | return TRIDVECTOR(auxx, auxy, auxz); |
---|
146 | } |
---|
147 | |
---|
148 | |
---|
149 | |
---|
150 | inline double getComponent(int index ) const {return vec_[index];} |
---|
151 | |
---|
152 | inline void setComponent(int index, double value ) {vec_[index] = value;} |
---|
153 | |
---|
154 | inline void incrementComponent(int index, double value ) {vec_[index] += value;} |
---|
155 | |
---|
156 | |
---|
157 | inline void getComponents(double& x,double& y,double& z) const |
---|
158 | { |
---|
159 | x = vec_[0]; |
---|
160 | y = vec_[1]; |
---|
161 | z = vec_[2]; |
---|
162 | } |
---|
163 | |
---|
164 | inline void setComponents(double x, double y, double z) |
---|
165 | { |
---|
166 | vec_[0] = x; |
---|
167 | vec_[1] = y; |
---|
168 | vec_[2] = z; |
---|
169 | } |
---|
170 | |
---|
171 | |
---|
172 | |
---|
173 | // algo. Boris (Birdsall p. 356) |
---|
174 | // the input vector 'tgArcMoitie' is in the direction of the axis of |
---|
175 | // rotation. Its module is equal to tg(theta/2), if theta is |
---|
176 | // the desired rotation angle. |
---|
177 | // if tg(theta/2) is given exactly, the rotation is 'exact' |
---|
178 | // |
---|
179 | void borisBunemanRotation(const TRIDVECTOR& tgArcMoitie) |
---|
180 | { |
---|
181 | double t2 = tgArcMoitie.norm2(); |
---|
182 | double fac = 2.0 / ( 1.0 + t2); |
---|
183 | TRIDVECTOR sinArc = tgArcMoitie * fac; |
---|
184 | TRIDVECTOR vecPrim(*this); |
---|
185 | vecPrim += (*this) * tgArcMoitie; |
---|
186 | (*this) += vecPrim * sinArc; |
---|
187 | } |
---|
188 | |
---|
189 | |
---|
190 | |
---|
191 | |
---|
192 | // rotation in ZX plane |
---|
193 | inline void rotateZXComponentsBuneman(double tgAngleMoitie ) |
---|
194 | { |
---|
195 | mathTools::borisBunemanRotation(tgAngleMoitie, vec_[2], vec_[0]); |
---|
196 | } |
---|
197 | |
---|
198 | // transform the vector Er, Etheta, Ez to a vector Ex,Ey,Ez, assuming the end |
---|
199 | // of the vector at (x,y) in the plane (X,Y) |
---|
200 | inline void fromCylindricalToCartesian(double costet, double sintet) |
---|
201 | { |
---|
202 | double auxr = vec_[0]; |
---|
203 | double auxtet = vec_[1]; |
---|
204 | vec_[0] = auxr * costet - auxtet * sintet; |
---|
205 | vec_[1] = auxr * sintet + auxtet * costet; |
---|
206 | } |
---|
207 | |
---|
208 | |
---|
209 | inline void clear() |
---|
210 | { |
---|
211 | vec_[0] = 0.0; |
---|
212 | vec_[1] = 0.0; |
---|
213 | vec_[2] = 0.0; |
---|
214 | } |
---|
215 | |
---|
216 | inline double norm2() const |
---|
217 | { |
---|
218 | return vec_[0]*vec_[0] + vec_[1]*vec_[1] + vec_[2]*vec_[2]; |
---|
219 | } |
---|
220 | inline double norm() const |
---|
221 | { |
---|
222 | return sqrt(abs(norm2())); |
---|
223 | } |
---|
224 | |
---|
225 | inline void renormalize() |
---|
226 | { |
---|
227 | int k; |
---|
228 | double normeInv = 1.0/norm(); |
---|
229 | for (k=0; k< 3 ; k++) vec_[k] *= normeInv; |
---|
230 | } |
---|
231 | |
---|
232 | inline void opposite() |
---|
233 | { |
---|
234 | int k; |
---|
235 | for (k=0; k< 3 ; k++) vec_[k] = -vec_[k]; |
---|
236 | } |
---|
237 | |
---|
238 | inline void print() const |
---|
239 | { |
---|
240 | cout << " x comp. = " << vec_[0] << " y comp. = " << vec_[1] << " z comp. = " << vec_[2] << endl; |
---|
241 | cout << " norme = " << norm() << endl; |
---|
242 | } |
---|
243 | |
---|
244 | string output_flow() const |
---|
245 | { |
---|
246 | ostringstream sortie; |
---|
247 | sortie << " " << vec_[0] << " " << vec_[1] << " " << vec_[2]; |
---|
248 | return sortie.str(); |
---|
249 | } |
---|
250 | |
---|
251 | bool input_flow( ifstream& ifs) |
---|
252 | { |
---|
253 | bool test; |
---|
254 | if ( ifs >> vec_[0] >> vec_[1] >> vec_[2]) test= true; |
---|
255 | else test = false; |
---|
256 | return test; |
---|
257 | } |
---|
258 | |
---|
259 | |
---|
260 | }; |
---|
261 | |
---|
262 | |
---|
263 | |
---|
264 | |
---|
265 | |
---|
266 | |
---|
267 | |
---|
268 | #endif |
---|