| 1 |
********************************************************************** |
| 2 |
* |
| 3 |
* |
| 4 |
* routine per tracciare la particella di uno STEP |
| 5 |
* |
| 6 |
SUBROUTINE GRKUTA (CHARGE,STEP,VECT,VOUT) |
| 7 |
C. |
| 8 |
C. ****************************************************************** |
| 9 |
C. * * |
| 10 |
C. * Runge-Kutta method for tracking a particle through a magnetic * |
| 11 |
C. * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of * |
| 12 |
C. * Standards, procedure 25.5.20) * |
| 13 |
C. * * |
| 14 |
C. * Input parameters * |
| 15 |
C. * CHARGE Particle charge * |
| 16 |
C. * STEP Step size * |
| 17 |
C. * VECT Initial co-ords,direction cosines,momentum * |
| 18 |
C. * Output parameters * |
| 19 |
C. * VOUT Output co-ords,direction cosines,momentum * |
| 20 |
C. * User routine called * |
| 21 |
C. * CALL GUFLD(X,F) * |
| 22 |
C. * * |
| 23 |
C. * ==>Called by : <USER>, GUSWIM * |
| 24 |
C. * Authors R.Brun, M.Hansroul ********* * |
| 25 |
C. * V.Perevoztchikov (CUT STEP implementation) * |
| 26 |
C. * * |
| 27 |
C. * * |
| 28 |
C. ****************************************************************** |
| 29 |
C. |
| 30 |
IMPLICIT DOUBLE PRECISION(A-H,O-Z) |
| 31 |
* |
| 32 |
REAL VVV(3),FFF(3) |
| 33 |
REAL*8 CHARGE, STEP, VECT(*), VOUT(*), F(4) |
| 34 |
REAL*8 XYZT(3), XYZ(3), X, Y, Z, XT, YT, ZT |
| 35 |
DIMENSION SECXS(4),SECYS(4),SECZS(4),HXP(3) |
| 36 |
EQUIVALENCE (X,XYZ(1)),(Y,XYZ(2)),(Z,XYZ(3)), |
| 37 |
+ (XT,XYZT(1)),(YT,XYZT(2)),(ZT,XYZT(3)) |
| 38 |
* |
| 39 |
PARAMETER (MAXIT = 1992, MAXCUT = 11) |
| 40 |
PARAMETER (EC=2.9979251D-4,DLT=1D-4,DLT32=DLT/32) |
| 41 |
PARAMETER (ZERO=0, ONE=1, TWO=2, THREE=3) |
| 42 |
PARAMETER (THIRD=ONE/THREE, HALF=ONE/TWO) |
| 43 |
PARAMETER (PISQUA=.986960440109D+01) |
| 44 |
PARAMETER (IX=1,IY=2,IZ=3,IPX=4,IPY=5,IPZ=6) |
| 45 |
|
| 46 |
*. |
| 47 |
*. ------------------------------------------------------------------ |
| 48 |
*. |
| 49 |
* This constant is for units CM,GEV/C and KGAUSS |
| 50 |
* |
| 51 |
c print *,'GRKUTA+++++ charge ',charge,' step ',step,' vect(3) ', |
| 52 |
c & vect(3) |
| 53 |
ITER = 0 |
| 54 |
NCUT = 0 |
| 55 |
DO 10 J=1,7 |
| 56 |
VOUT(J)=VECT(J) |
| 57 |
c print *,' grkuta j ',j,' vout ',vout(j) |
| 58 |
c print *,' grkuta j ',j,' vect ',vect(j) |
| 59 |
10 CONTINUE |
| 60 |
PINV = EC * CHARGE / VECT(7) |
| 61 |
TL = 0. |
| 62 |
H = STEP |
| 63 |
* |
| 64 |
* |
| 65 |
20 REST = STEP-TL |
| 66 |
IF (DABS(H).GT.DABS(REST)) H = REST |
| 67 |
DO I=1,3 |
| 68 |
VVV(I)=SNGL(VOUT(I)) |
| 69 |
c print *,'grkuta i ',i,' vvv ',vvv(i) |
| 70 |
ENDDO |
| 71 |
c print *,'grkuta pinv ',pinv,' h ',h,' rest ',rest |
| 72 |
|
| 73 |
CALL GUFLD(VVV,FFF) |
| 74 |
DO I=1,3 |
| 75 |
F(I)=DBLE(FFF(I)) |
| 76 |
c print *,'grkuta i ',i,' f ',f(i) |
| 77 |
ENDDO |
| 78 |
* |
| 79 |
* Start of integration |
| 80 |
* |
| 81 |
X = VOUT(1) |
| 82 |
Y = VOUT(2) |
| 83 |
Z = VOUT(3) |
| 84 |
A = VOUT(4) |
| 85 |
B = VOUT(5) |
| 86 |
C = VOUT(6) |
| 87 |
c print *,' QUI A ',A,' B ',B,' C ',C |
| 88 |
c print *,' QUI x ',x,' y ',y,' z ',z |
| 89 |
* |
| 90 |
H2 = HALF * H |
| 91 |
H4 = HALF * H2 |
| 92 |
PH = PINV * H |
| 93 |
PH2 = HALF * PH |
| 94 |
SECXS(1) = (B * F(3) - C * F(2)) * PH2 |
| 95 |
SECYS(1) = (C * F(1) - A * F(3)) * PH2 |
| 96 |
SECZS(1) = (A * F(2) - B * F(1)) * PH2 |
| 97 |
ANG2 = (SECXS(1)**2 + SECYS(1)**2 + SECZS(1)**2) |
| 98 |
IF (ANG2.GT.PISQUA) GO TO 40 |
| 99 |
DXT = H2 * A + H4 * SECXS(1) |
| 100 |
DYT = H2 * B + H4 * SECYS(1) |
| 101 |
DZT = H2 * C + H4 * SECZS(1) |
| 102 |
XT = X + DXT |
| 103 |
YT = Y + DYT |
| 104 |
ZT = Z + DZT |
| 105 |
* |
| 106 |
* Second intermediate point |
| 107 |
* |
| 108 |
EST = DABS(DXT)+DABS(DYT)+DABS(DZT) |
| 109 |
IF (EST.GT.H) GO TO 30 |
| 110 |
|
| 111 |
DO I=1,3 |
| 112 |
VVV(I)=SNGL(XYZT(I)) |
| 113 |
ENDDO |
| 114 |
CALL GUFLD(VVV,FFF) |
| 115 |
DO I=1,3 |
| 116 |
F(I)=DBLE(FFF(I)) |
| 117 |
c print *,'2grkuta i ',i,' f ',f(i) |
| 118 |
ENDDO |
| 119 |
C CALL GUFLD(XYZT,F) |
| 120 |
AT = A + SECXS(1) |
| 121 |
BT = B + SECYS(1) |
| 122 |
CT = C + SECZS(1) |
| 123 |
* |
| 124 |
SECXS(2) = (BT * F(3) - CT * F(2)) * PH2 |
| 125 |
SECYS(2) = (CT * F(1) - AT * F(3)) * PH2 |
| 126 |
SECZS(2) = (AT * F(2) - BT * F(1)) * PH2 |
| 127 |
c print *,'1 at ',xt,' bt ',yt,' ct ',zt |
| 128 |
AT = A + SECXS(2) |
| 129 |
BT = B + SECYS(2) |
| 130 |
CT = C + SECZS(2) |
| 131 |
c print *,'2 at ',xt,' bt ',yt,' ct ',zt |
| 132 |
SECXS(3) = (BT * F(3) - CT * F(2)) * PH2 |
| 133 |
SECYS(3) = (CT * F(1) - AT * F(3)) * PH2 |
| 134 |
SECZS(3) = (AT * F(2) - BT * F(1)) * PH2 |
| 135 |
DXT = H * (A + SECXS(3)) |
| 136 |
DYT = H * (B + SECYS(3)) |
| 137 |
DZT = H * (C + SECZS(3)) |
| 138 |
XT = X + DXT |
| 139 |
YT = Y + DYT |
| 140 |
ZT = Z + DZT |
| 141 |
c print *,' xt ',xt,' yt ',yt,' zt ',zt |
| 142 |
c print *,' dxt ',xt,' dyt ',yt,' dzt ',zt |
| 143 |
c print *,' at ',xt,' bt ',yt,' ct ',zt |
| 144 |
AT = A + TWO*SECXS(3) |
| 145 |
BT = B + TWO*SECYS(3) |
| 146 |
CT = C + TWO*SECZS(3) |
| 147 |
* |
| 148 |
EST = ABS(DXT)+ABS(DYT)+ABS(DZT) |
| 149 |
IF (EST.GT.2.*ABS(H)) GO TO 30 |
| 150 |
|
| 151 |
DO I=1,3 |
| 152 |
VVV(I)=SNGL(XYZT(I)) |
| 153 |
c print *,'3grkuta i ',i,' vvv ',vvv(i) |
| 154 |
c print *,'3grkuta i ',i,' xyzt ',xyzt(i) |
| 155 |
ENDDO |
| 156 |
CALL GUFLD(VVV,FFF) |
| 157 |
DO I=1,3 |
| 158 |
F(I)=DBLE(FFF(I)) |
| 159 |
c print *,'3grkuta i ',i,' f ',f(i) |
| 160 |
c print *,'3grkuta i ',i,' fff ',fff(i) |
| 161 |
ENDDO |
| 162 |
C CALL GUFLD(XYZT,F) |
| 163 |
* |
| 164 |
Z = Z + (C + (SECZS(1) + SECZS(2) + SECZS(3)) * THIRD) * H |
| 165 |
Y = Y + (B + (SECYS(1) + SECYS(2) + SECYS(3)) * THIRD) * H |
| 166 |
X = X + (A + (SECXS(1) + SECXS(2) + SECXS(3)) * THIRD) * H |
| 167 |
* |
| 168 |
SECXS(4) = (BT*F(3) - CT*F(2))* PH2 |
| 169 |
c print *,'secxs4 bt ',bt,' ct ',ct,' ph2 ',ph2 |
| 170 |
SECYS(4) = (CT*F(1) - AT*F(3))* PH2 |
| 171 |
SECZS(4) = (AT*F(2) - BT*F(1))* PH2 |
| 172 |
A = A+(SECXS(1)+SECXS(4)+TWO * (SECXS(2)+SECXS(3))) * THIRD |
| 173 |
c print *,'=> a ',a,' secxs 1 ',SECXS(1),' 4 ',SECXS(4),' 2 ', |
| 174 |
c & SECXS(2),' 3 ',SECXS(3),' third ',third |
| 175 |
B = B+(SECYS(1)+SECYS(4)+TWO * (SECYS(2)+SECYS(3))) * THIRD |
| 176 |
C = C+(SECZS(1)+SECZS(4)+TWO * (SECZS(2)+SECZS(3))) * THIRD |
| 177 |
* |
| 178 |
EST = ABS(SECXS(1)+SECXS(4) - (SECXS(2)+SECXS(3))) |
| 179 |
++ ABS(SECYS(1)+SECYS(4) - (SECYS(2)+SECYS(3))) |
| 180 |
++ ABS(SECZS(1)+SECZS(4) - (SECZS(2)+SECZS(3))) |
| 181 |
* |
| 182 |
IF (EST.GT.DLT .AND. ABS(H).GT.1.E-4) GO TO 30 |
| 183 |
ITER = ITER + 1 |
| 184 |
NCUT = 0 |
| 185 |
* If too many iterations, go to HELIX |
| 186 |
IF (ITER.GT.MAXIT) GO TO 40 |
| 187 |
* |
| 188 |
TL = TL + H |
| 189 |
IF (EST.LT.(DLT32)) THEN |
| 190 |
H = H*TWO |
| 191 |
ENDIF |
| 192 |
CBA = ONE/ SQRT(A*A + B*B + C*C) |
| 193 |
VOUT(1) = X |
| 194 |
VOUT(2) = Y |
| 195 |
VOUT(3) = Z |
| 196 |
VOUT(4) = CBA*A |
| 197 |
VOUT(5) = CBA*B |
| 198 |
VOUT(6) = CBA*C |
| 199 |
REST = STEP - TL |
| 200 |
IF (STEP.LT.0.) REST = -REST |
| 201 |
IF (REST .GT. 1.E-5*DABS(STEP)) GO TO 20 |
| 202 |
* |
| 203 |
c print *,' x ',x,' y ',y,' z ',z,' cba ',cba, |
| 204 |
c & ' a ',a,' b ',b,' c ',c,' step ',step, |
| 205 |
c & ' tl ',tl,' rest ',rest,' est ',est, |
| 206 |
c & ' h ',h,' two ',two,' one ',one |
| 207 |
GO TO 999 |
| 208 |
* |
| 209 |
** CUT STEP |
| 210 |
30 NCUT = NCUT + 1 |
| 211 |
* If too many cuts , go to HELIX |
| 212 |
IF (NCUT.GT.MAXCUT) GO TO 40 |
| 213 |
H = H*HALF |
| 214 |
GO TO 20 |
| 215 |
* |
| 216 |
** ANGLE TOO BIG, USE HELIX |
| 217 |
40 F1 = F(1) |
| 218 |
F2 = F(2) |
| 219 |
F3 = F(3) |
| 220 |
F4 = DSQRT(F1**2+F2**2+F3**2) |
| 221 |
RHO = -F4*PINV |
| 222 |
TET = RHO * STEP |
| 223 |
IF(TET.NE.0.) THEN |
| 224 |
HNORM = ONE/F4 |
| 225 |
F1 = F1*HNORM |
| 226 |
F2 = F2*HNORM |
| 227 |
F3 = F3*HNORM |
| 228 |
* |
| 229 |
HXP(1) = F2*VECT(IPZ) - F3*VECT(IPY) |
| 230 |
HXP(2) = F3*VECT(IPX) - F1*VECT(IPZ) |
| 231 |
HXP(3) = F1*VECT(IPY) - F2*VECT(IPX) |
| 232 |
|
| 233 |
HP = F1*VECT(IPX) + F2*VECT(IPY) + F3*VECT(IPZ) |
| 234 |
* |
| 235 |
RHO1 = ONE/RHO |
| 236 |
SINT = DSIN(TET) |
| 237 |
COST = TWO*DSIN(HALF*TET)**2 |
| 238 |
* |
| 239 |
G1 = SINT*RHO1 |
| 240 |
G2 = COST*RHO1 |
| 241 |
G3 = (TET-SINT) * HP*RHO1 |
| 242 |
G4 = -COST |
| 243 |
G5 = SINT |
| 244 |
G6 = COST * HP |
| 245 |
|
| 246 |
VOUT(IX) = VECT(IX) + (G1*VECT(IPX) + G2*HXP(1) + G3*F1) |
| 247 |
VOUT(IY) = VECT(IY) + (G1*VECT(IPY) + G2*HXP(2) + G3*F2) |
| 248 |
VOUT(IZ) = VECT(IZ) + (G1*VECT(IPZ) + G2*HXP(3) + G3*F3) |
| 249 |
c print *,' iz ',iz,' vect ',vect(iz),' g1 ',g1,' ipz ',ipz, |
| 250 |
c & ' vect ',vect(ipz),' g2 ',g2,' hxp ',hxp(3),' g3 ',g3, |
| 251 |
c & ' f3 ',f3 |
| 252 |
|
| 253 |
VOUT(IPX) = VECT(IPX) + (G4*VECT(IPX) + G5*HXP(1) + G6*F1) |
| 254 |
VOUT(IPY) = VECT(IPY) + (G4*VECT(IPY) + G5*HXP(2) + G6*F2) |
| 255 |
VOUT(IPZ) = VECT(IPZ) + (G4*VECT(IPZ) + G5*HXP(3) + G6*F3) |
| 256 |
* |
| 257 |
ELSE |
| 258 |
VOUT(IX) = VECT(IX) + STEP*VECT(IPX) |
| 259 |
VOUT(IY) = VECT(IY) + STEP*VECT(IPY) |
| 260 |
VOUT(IZ) = VECT(IZ) + STEP*VECT(IPZ) |
| 261 |
c print *,' iz ',iz,' vect ',vect(iz),' step ',step,' ipz ',ipz, |
| 262 |
c & ' vect ',vect(ipz) |
| 263 |
* |
| 264 |
ENDIF |
| 265 |
* |
| 266 |
999 END |
| 267 |
* |
| 268 |
* |
| 269 |
|
| 270 |
|
| 271 |
|
| 272 |
********************************************************************** |
| 273 |
* |
| 274 |
* gives the value of the magnetic field in the tracking point |
| 275 |
* |
| 276 |
********************************************************************** |
| 277 |
|
| 278 |
subroutine gufld(v,f) !coordinates in cm, B field in kGauss |
| 279 |
|
| 280 |
real v(3),f(3) !coordinates in cm, B field in kGauss, error in kGauss |
| 281 |
|
| 282 |
real*8 vv(3),ff(3) !inter_B.f works in double precision |
| 283 |
|
| 284 |
|
| 285 |
do i=1,3 |
| 286 |
vv(i)=v(i)/100. !inter_B.f works in meters |
| 287 |
c print *,'IN gufld i ',i,' v ',v(i) |
| 288 |
enddo |
| 289 |
c inter_B: coordinates in m, B field in Tesla |
| 290 |
call inter_B(vv(1),vv(2),vv(3),ff) |
| 291 |
do i=1,3 !change back the field in kGauss |
| 292 |
f(i)=ff(i)*10. |
| 293 |
enddo |
| 294 |
c do i=1,3 |
| 295 |
c print *,'OUT gufld i ',i,' v ',v(i) |
| 296 |
c enddo |
| 297 |
return |
| 298 |
end |
| 299 |
|
Parent Directory
| 
Revision Log