1 * One step extrapolation routines in Fortran:
2 * EXTRAP_ONESTEP_HELIX, EXTRAP_ONESTEP_HELIX3, EXTRAP_ONESTEP_RUNGEKUTTA.
3 * Taken respectively from Geant (gtrak) routines:
4 * GHELIX, GHELIX3, GRKUTA.
5 * Everything in double precision,
6 * in order that the track fit with Minuit is converging.
7 * Modifications from Geant are indicated with "Cmodif".
9 Cmodif: SUBROUTINE GHELIX (CHARGE, STEP, VECT, VOUT) changed into:
10 SUBROUTINE EXTRAP_ONESTEP_HELIX (CHARGE, STEP, VECT, VOUT)
12 C. ******************************************************************
14 C. * Performs the tracking of one step in a magnetic field *
15 C. * The trajectory is assumed to be a helix in a constant field *
16 C. * taken at the mid point of the step. *
19 C. * STEP =arc length of the step asked *
20 C. * VECT =input vector (position,direction cos and momentum) *
21 C. * CHARGE= electric charge of the particle *
23 C. * VOUT = same as VECT after completion of the step *
25 C. * ==>Called by : <USER>, GUSWIM *
26 C. * Author M.Hansroul ********* *
27 C. * Modified S.Egli, S.V.Levonian *
28 C. * Modified V.Perevoztchikov
30 C. ******************************************************************
33 Cmodif: everything in double precision
34 IMPLICIT DOUBLE PRECISION(A-H,O-Z)
36 DIMENSION VECT(7),VOUT(7)
37 DIMENSION XYZ(3),H(4),HXP(3)
38 PARAMETER (IX=1,IY=2,IZ=3,IPX=4,IPY=5,IPZ=6,IPP=7)
39 PARAMETER (SIXTH = 1./6.)
40 PARAMETER (EC=2.9979251E-4)
42 C. ------------------------------------------------------------------
44 C units are kgauss,centimeters,gev/c
47 IF (CHARGE.EQ.0.) GO TO 10
48 XYZ(1) = VECT(IX) + 0.5 * STEP * VECT(IPX)
49 XYZ(2) = VECT(IY) + 0.5 * STEP * VECT(IPY)
50 XYZ(3) = VECT(IZ) + 0.5 * STEP * VECT(IPZ)
52 Cmodif: CALL GUFLD (XYZ, H) changed into:
53 CALL GUFLD_DOUBLE (XYZ, H)
55 H2XY = H(1)**2 + H(2)**2
57 IF (H(4).LE.1.E-12) GO TO 10
58 IF (H2XY.LE.1.E-12*H(4)) THEN
59 Cmodif: CALL GHELX3 (CHARGE*H(3), STEP, VECT, VOUT) changed into:
60 CALL EXTRAP_ONESTEP_HELIX3 (CHARGE*H(3), STEP, VECT, VOUT)
69 HXP(1) = H(2)*VECT(IPZ) - H(3)*VECT(IPY)
70 HXP(2) = H(3)*VECT(IPX) - H(1)*VECT(IPZ)
71 HXP(3) = H(1)*VECT(IPY) - H(2)*VECT(IPX)
73 HP = H(1)*VECT(IPX) + H(2)*VECT(IPY) + H(3)*VECT(IPZ)
75 RHO = -CHARGE*H(4)/VECT(IPP)
77 IF (ABS(TET).GT.0.15) THEN
80 TSINT = (TET-SINT)/TET
81 COS1T = 2.*(SIN(0.5*TET))**2/TET
91 F3 = STEP * TSINT * HP
96 VOUT(IX) = VECT(IX) + (F1*VECT(IPX) + F2*HXP(1) + F3*H(1))
97 VOUT(IY) = VECT(IY) + (F1*VECT(IPY) + F2*HXP(2) + F3*H(2))
98 VOUT(IZ) = VECT(IZ) + (F1*VECT(IPZ) + F2*HXP(3) + F3*H(3))
100 VOUT(IPX) = VECT(IPX) + (F4*VECT(IPX) + F5*HXP(1) + F6*H(1))
101 VOUT(IPY) = VECT(IPY) + (F4*VECT(IPY) + F5*HXP(2) + F6*H(2))
102 VOUT(IPZ) = VECT(IPZ) + (F4*VECT(IPZ) + F5*HXP(3) + F6*H(3))
108 VOUT(I) = VECT(I) + STEP * VECT(I+3)
109 VOUT(I+3) = VECT(I+3)
114 Cmodif: SUBROUTINE GHELX3 (FIELD, STEP, VECT, VOUT) changed into:
115 SUBROUTINE EXTRAP_ONESTEP_HELIX3 (FIELD, STEP, VECT, VOUT)
117 C. ******************************************************************
119 C. * Tracking routine in a constant field oriented *
121 C. * Tracking is performed with a conventional *
122 C. * helix step method *
124 C. * ==>Called by : <USER>, GUSWIM *
125 C. * Authors R.Brun, M.Hansroul ********* *
126 C * Rewritten V.Perevoztchikov
128 C. ******************************************************************
131 Cmodif: everything in double precision
132 IMPLICIT DOUBLE PRECISION(A-H,O-Z)
134 DIMENSION VECT(7),VOUT(7),HXP(3)
135 PARAMETER (IX=1,IY=2,IZ=3,IPX=4,IPY=5,IPZ=6,IPP=7)
136 PARAMETER (SIXTH = 1./6.)
137 PARAMETER (EC=2.9979251E-4)
139 C. ------------------------------------------------------------------
141 C units are kgauss,centimeters,gev/c
143 VOUT(IPP) = VECT(IPP)
153 IF (ABS(TET).GT.0.15) THEN
156 TSINT = (TET-SINT)/TET
157 COS1T = 2.*(SIN(0.5*TET))**2/TET
167 F3 = STEP * TSINT * HP
170 F6 = TET * COS1T * HP
172 VOUT(IX) = VECT(IX) + (F1*VECT(IPX) + F2*HXP(1))
173 VOUT(IY) = VECT(IY) + (F1*VECT(IPY) + F2*HXP(2))
174 VOUT(IZ) = VECT(IZ) + (F1*VECT(IPZ) + F3)
176 VOUT(IPX) = VECT(IPX) + (F4*VECT(IPX) + F5*HXP(1))
177 VOUT(IPY) = VECT(IPY) + (F4*VECT(IPY) + F5*HXP(2))
178 VOUT(IPZ) = VECT(IPZ) + (F4*VECT(IPZ) + F6)
183 Cmodif: SUBROUTINE GRKUTA (CHARGE,STEP,VECT,VOUT) changed into:
184 SUBROUTINE EXTRAP_ONESTEP_RUNGEKUTTA (CHARGE,STEP,VECT,VOUT)
186 C. ******************************************************************
188 C. * Runge-Kutta method for tracking a particle through a magnetic *
189 C. * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
190 C. * Standards, procedure 25.5.20) *
192 C. * Input parameters *
193 C. * CHARGE Particle charge *
194 C. * STEP Step size *
195 C. * VECT Initial co-ords,direction cosines,momentum *
196 C. * Output parameters *
197 C. * VOUT Output co-ords,direction cosines,momentum *
198 C. * User routine called *
199 C. * CALL GUFLD(X,F) *
201 C. * ==>Called by : <USER>, GUSWIM *
202 C. * Authors R.Brun, M.Hansroul ********* *
203 C. * V.Perevoztchikov (CUT STEP implementation) *
206 C. ******************************************************************
208 Cmodif: no condition from CERNLIB_SINGLE for double precision
209 IMPLICIT DOUBLE PRECISION(A-H,O-Z)
210 Cmodif: REAL changed into DOUBLE PRECISION in following 2 lines
211 DOUBLE PRECISION CHARGE, STEP, VECT(*), VOUT(*), F(4)
212 DOUBLE PRECISION XYZT(3), XYZ(3), X, Y, Z, XT, YT, ZT
213 DIMENSION SECXS(4),SECYS(4),SECZS(4),HXP(3)
214 EQUIVALENCE (X,XYZ(1)),(Y,XYZ(2)),(Z,XYZ(3)),
215 + (XT,XYZT(1)),(YT,XYZT(2)),(ZT,XYZT(3))
217 PARAMETER (MAXIT = 1992, MAXCUT = 11)
218 PARAMETER (EC=2.9979251D-4,DLT=1D-4,DLT32=DLT/32)
219 PARAMETER (ZERO=0, ONE=1, TWO=2, THREE=3)
220 PARAMETER (THIRD=ONE/THREE, HALF=ONE/TWO)
221 PARAMETER (PISQUA=.986960440109D+01)
222 PARAMETER (IX=1,IY=2,IZ=3,IPX=4,IPY=5,IPZ=6)
224 *. ------------------------------------------------------------------
226 * This constant is for units CM,GEV/C and KGAUSS
233 PINV = EC * CHARGE / VECT(7)
239 IF (ABS(H).GT.ABS(REST)) H = REST
240 Cmodif: CALL GUFLD(VOUT,F) changed into:
241 CALL GUFLD_DOUBLE(VOUT,F)
243 * Start of integration
256 SECXS(1) = (B * F(3) - C * F(2)) * PH2
257 SECYS(1) = (C * F(1) - A * F(3)) * PH2
258 SECZS(1) = (A * F(2) - B * F(1)) * PH2
259 ANG2 = (SECXS(1)**2 + SECYS(1)**2 + SECZS(1)**2)
260 IF (ANG2.GT.PISQUA) GO TO 40
261 DXT = H2 * A + H4 * SECXS(1)
262 DYT = H2 * B + H4 * SECYS(1)
263 DZT = H2 * C + H4 * SECZS(1)
268 * Second intermediate point
270 EST = ABS(DXT)+ABS(DYT)+ABS(DZT)
271 IF (EST.GT.H) GO TO 30
273 Cmodif: CALL GUFLD(XYZT,F) changed into:
274 CALL GUFLD_DOUBLE(XYZT,F)
279 SECXS(2) = (BT * F(3) - CT * F(2)) * PH2
280 SECYS(2) = (CT * F(1) - AT * F(3)) * PH2
281 SECZS(2) = (AT * F(2) - BT * F(1)) * PH2
285 SECXS(3) = (BT * F(3) - CT * F(2)) * PH2
286 SECYS(3) = (CT * F(1) - AT * F(3)) * PH2
287 SECZS(3) = (AT * F(2) - BT * F(1)) * PH2
288 DXT = H * (A + SECXS(3))
289 DYT = H * (B + SECYS(3))
290 DZT = H * (C + SECZS(3))
294 AT = A + TWO*SECXS(3)
295 BT = B + TWO*SECYS(3)
296 CT = C + TWO*SECZS(3)
298 EST = ABS(DXT)+ABS(DYT)+ABS(DZT)
299 IF (EST.GT.2.*ABS(H)) GO TO 30
301 Cmodif: CALL GUFLD(XYZT,F) changed into:
302 CALL GUFLD_DOUBLE(XYZT,F)
304 Z = Z + (C + (SECZS(1) + SECZS(2) + SECZS(3)) * THIRD) * H
305 Y = Y + (B + (SECYS(1) + SECYS(2) + SECYS(3)) * THIRD) * H
306 X = X + (A + (SECXS(1) + SECXS(2) + SECXS(3)) * THIRD) * H
308 SECXS(4) = (BT*F(3) - CT*F(2))* PH2
309 SECYS(4) = (CT*F(1) - AT*F(3))* PH2
310 SECZS(4) = (AT*F(2) - BT*F(1))* PH2
311 A = A+(SECXS(1)+SECXS(4)+TWO * (SECXS(2)+SECXS(3))) * THIRD
312 B = B+(SECYS(1)+SECYS(4)+TWO * (SECYS(2)+SECYS(3))) * THIRD
313 C = C+(SECZS(1)+SECZS(4)+TWO * (SECZS(2)+SECZS(3))) * THIRD
315 EST = ABS(SECXS(1)+SECXS(4) - (SECXS(2)+SECXS(3)))
316 ++ ABS(SECYS(1)+SECYS(4) - (SECYS(2)+SECYS(3)))
317 ++ ABS(SECZS(1)+SECZS(4) - (SECZS(2)+SECZS(3)))
319 IF (EST.GT.DLT .AND. ABS(H).GT.1.E-4) GO TO 30
322 * If too many iterations, go to HELIX
323 IF (ITER.GT.MAXIT) GO TO 40
326 IF (EST.LT.(DLT32)) THEN
329 CBA = ONE/ SQRT(A*A + B*B + C*C)
337 IF (STEP.LT.0.) REST = -REST
338 IF (REST .GT. 1.E-5*ABS(STEP)) GO TO 20
344 * If too many cuts , go to HELIX
345 IF (NCUT.GT.MAXCUT) GO TO 40
349 ** ANGLE TOO BIG, USE HELIX
353 F4 = SQRT(F1**2+F2**2+F3**2)
362 HXP(1) = F2*VECT(IPZ) - F3*VECT(IPY)
363 HXP(2) = F3*VECT(IPX) - F1*VECT(IPZ)
364 HXP(3) = F1*VECT(IPY) - F2*VECT(IPX)
366 HP = F1*VECT(IPX) + F2*VECT(IPY) + F3*VECT(IPZ)
370 COST = TWO*SIN(HALF*TET)**2
374 G3 = (TET-SINT) * HP*RHO1
379 VOUT(IX) = VECT(IX) + (G1*VECT(IPX) + G2*HXP(1) + G3*F1)
380 VOUT(IY) = VECT(IY) + (G1*VECT(IPY) + G2*HXP(2) + G3*F2)
381 VOUT(IZ) = VECT(IZ) + (G1*VECT(IPZ) + G2*HXP(3) + G3*F3)
383 VOUT(IPX) = VECT(IPX) + (G4*VECT(IPX) + G5*HXP(1) + G6*F1)
384 VOUT(IPY) = VECT(IPY) + (G4*VECT(IPY) + G5*HXP(2) + G6*F2)
385 VOUT(IPZ) = VECT(IPZ) + (G4*VECT(IPZ) + G5*HXP(3) + G6*F3)
388 VOUT(IX) = VECT(IX) + STEP*VECT(IPX)
389 VOUT(IY) = VECT(IY) + STEP*VECT(IPY)
390 VOUT(IZ) = VECT(IZ) + STEP*VECT(IPZ)