/[PAMELA software]/DarthVader/TrackerLevel2/src/F77/grkuta.f
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Annotation of /DarthVader/TrackerLevel2/src/F77/grkuta.f

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Revision 1.2 - (hide annotations) (download)
Thu Jun 1 09:03:09 2006 UTC (18 years, 6 months ago) by pam-fi
Branch: MAIN
CVS Tags: v0r02, v1r01beta, v1r00, v1r01, v2r00BETA
Changes since 1.1: +270 -1 lines
Tracking routine updated in order to get track projected angles and track length

1 mocchiut 1.1 **********************************************************************
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 pam-fi 1.2 PARAMETER (IX=1,IY=2,IZ=3,IPX=4,IPY=5,IPZ=6)
45 mocchiut 1.1
46     *.
47     *. ------------------------------------------------------------------
48     *.
49     * This constant is for units CM,GEV/C and KGAUSS
50     *
51     ITER = 0
52     NCUT = 0
53     DO 10 J=1,7
54     VOUT(J)=VECT(J)
55     10 CONTINUE
56     PINV = EC * CHARGE / VECT(7)
57     TL = 0.
58     H = STEP
59     *
60     *
61     20 REST = STEP-TL
62     IF (DABS(H).GT.DABS(REST)) H = REST
63     DO I=1,3
64     VVV(I)=SNGL(VOUT(I))
65     ENDDO
66    
67     CALL GUFLD(VVV,FFF)
68     * print*,'GRKUTA Bx,By,Bz: ',(FFF(i),i=1,3)
69     DO I=1,3
70     F(I)=DBLE(FFF(I))
71     ENDDO
72     *
73     * Start of integration
74     *
75     X = VOUT(1)
76     Y = VOUT(2)
77     Z = VOUT(3)
78     A = VOUT(4)
79     B = VOUT(5)
80     C = VOUT(6)
81     *
82     H2 = HALF * H
83     H4 = HALF * H2
84     PH = PINV * H
85     PH2 = HALF * PH
86     SECXS(1) = (B * F(3) - C * F(2)) * PH2
87     SECYS(1) = (C * F(1) - A * F(3)) * PH2
88     SECZS(1) = (A * F(2) - B * F(1)) * PH2
89     ANG2 = (SECXS(1)**2 + SECYS(1)**2 + SECZS(1)**2)
90     IF (ANG2.GT.PISQUA) GO TO 40
91     DXT = H2 * A + H4 * SECXS(1)
92     DYT = H2 * B + H4 * SECYS(1)
93     DZT = H2 * C + H4 * SECZS(1)
94     XT = X + DXT
95     YT = Y + DYT
96     ZT = Z + DZT
97     *
98     * Second intermediate point
99     *
100     EST = DABS(DXT)+DABS(DYT)+DABS(DZT)
101     IF (EST.GT.H) GO TO 30
102    
103     DO I=1,3
104     VVV(I)=SNGL(XYZT(I))
105     ENDDO
106     CALL GUFLD(VVV,FFF)
107     DO I=1,3
108     F(I)=DBLE(FFF(I))
109     ENDDO
110     C CALL GUFLD(XYZT,F)
111     AT = A + SECXS(1)
112     BT = B + SECYS(1)
113     CT = C + SECZS(1)
114     *
115     SECXS(2) = (BT * F(3) - CT * F(2)) * PH2
116     SECYS(2) = (CT * F(1) - AT * F(3)) * PH2
117     SECZS(2) = (AT * F(2) - BT * F(1)) * PH2
118     AT = A + SECXS(2)
119     BT = B + SECYS(2)
120     CT = C + SECZS(2)
121     SECXS(3) = (BT * F(3) - CT * F(2)) * PH2
122     SECYS(3) = (CT * F(1) - AT * F(3)) * PH2
123     SECZS(3) = (AT * F(2) - BT * F(1)) * PH2
124     DXT = H * (A + SECXS(3))
125     DYT = H * (B + SECYS(3))
126     DZT = H * (C + SECZS(3))
127     XT = X + DXT
128     YT = Y + DYT
129     ZT = Z + DZT
130     AT = A + TWO*SECXS(3)
131     BT = B + TWO*SECYS(3)
132     CT = C + TWO*SECZS(3)
133     *
134     EST = ABS(DXT)+ABS(DYT)+ABS(DZT)
135     IF (EST.GT.2.*ABS(H)) GO TO 30
136    
137     DO I=1,3
138     VVV(I)=SNGL(XYZT(I))
139     ENDDO
140     CALL GUFLD(VVV,FFF)
141     DO I=1,3
142     F(I)=DBLE(FFF(I))
143     ENDDO
144     C CALL GUFLD(XYZT,F)
145     *
146     Z = Z + (C + (SECZS(1) + SECZS(2) + SECZS(3)) * THIRD) * H
147     Y = Y + (B + (SECYS(1) + SECYS(2) + SECYS(3)) * THIRD) * H
148     X = X + (A + (SECXS(1) + SECXS(2) + SECXS(3)) * THIRD) * H
149     *
150     SECXS(4) = (BT*F(3) - CT*F(2))* PH2
151     SECYS(4) = (CT*F(1) - AT*F(3))* PH2
152     SECZS(4) = (AT*F(2) - BT*F(1))* PH2
153     A = A+(SECXS(1)+SECXS(4)+TWO * (SECXS(2)+SECXS(3))) * THIRD
154     B = B+(SECYS(1)+SECYS(4)+TWO * (SECYS(2)+SECYS(3))) * THIRD
155     C = C+(SECZS(1)+SECZS(4)+TWO * (SECZS(2)+SECZS(3))) * THIRD
156     *
157     EST = ABS(SECXS(1)+SECXS(4) - (SECXS(2)+SECXS(3)))
158     ++ ABS(SECYS(1)+SECYS(4) - (SECYS(2)+SECYS(3)))
159     ++ ABS(SECZS(1)+SECZS(4) - (SECZS(2)+SECZS(3)))
160     *
161     IF (EST.GT.DLT .AND. ABS(H).GT.1.E-4) GO TO 30
162     ITER = ITER + 1
163     NCUT = 0
164     * If too many iterations, go to HELIX
165     IF (ITER.GT.MAXIT) GO TO 40
166     *
167     TL = TL + H
168     IF (EST.LT.(DLT32)) THEN
169     H = H*TWO
170     ENDIF
171     CBA = ONE/ SQRT(A*A + B*B + C*C)
172     VOUT(1) = X
173     VOUT(2) = Y
174     VOUT(3) = Z
175     VOUT(4) = CBA*A
176     VOUT(5) = CBA*B
177     VOUT(6) = CBA*C
178     REST = STEP - TL
179     IF (STEP.LT.0.) REST = -REST
180     IF (REST .GT. 1.E-5*DABS(STEP)) GO TO 20
181     *
182     GO TO 999
183     *
184     ** CUT STEP
185     30 NCUT = NCUT + 1
186     * If too many cuts , go to HELIX
187     IF (NCUT.GT.MAXCUT) GO TO 40
188     H = H*HALF
189     GO TO 20
190     *
191     ** ANGLE TOO BIG, USE HELIX
192     40 F1 = F(1)
193     F2 = F(2)
194     F3 = F(3)
195     F4 = DSQRT(F1**2+F2**2+F3**2)
196     RHO = -F4*PINV
197     TET = RHO * STEP
198     IF(TET.NE.0.) THEN
199     HNORM = ONE/F4
200     F1 = F1*HNORM
201     F2 = F2*HNORM
202     F3 = F3*HNORM
203     *
204     HXP(1) = F2*VECT(IPZ) - F3*VECT(IPY)
205     HXP(2) = F3*VECT(IPX) - F1*VECT(IPZ)
206     HXP(3) = F1*VECT(IPY) - F2*VECT(IPX)
207    
208     HP = F1*VECT(IPX) + F2*VECT(IPY) + F3*VECT(IPZ)
209     *
210     RHO1 = ONE/RHO
211     SINT = DSIN(TET)
212     COST = TWO*DSIN(HALF*TET)**2
213     *
214     G1 = SINT*RHO1
215     G2 = COST*RHO1
216     G3 = (TET-SINT) * HP*RHO1
217     G4 = -COST
218     G5 = SINT
219     G6 = COST * HP
220    
221     VOUT(IX) = VECT(IX) + (G1*VECT(IPX) + G2*HXP(1) + G3*F1)
222     VOUT(IY) = VECT(IY) + (G1*VECT(IPY) + G2*HXP(2) + G3*F2)
223     VOUT(IZ) = VECT(IZ) + (G1*VECT(IPZ) + G2*HXP(3) + G3*F3)
224    
225     VOUT(IPX) = VECT(IPX) + (G4*VECT(IPX) + G5*HXP(1) + G6*F1)
226     VOUT(IPY) = VECT(IPY) + (G4*VECT(IPY) + G5*HXP(2) + G6*F2)
227     VOUT(IPZ) = VECT(IPZ) + (G4*VECT(IPZ) + G5*HXP(3) + G6*F3)
228     *
229     ELSE
230     VOUT(IX) = VECT(IX) + STEP*VECT(IPX)
231     VOUT(IY) = VECT(IY) + STEP*VECT(IPY)
232     VOUT(IZ) = VECT(IZ) + STEP*VECT(IPZ)
233     *
234     ENDIF
235     *
236     999 END
237     *
238     *
239    
240 pam-fi 1.2 **********************************************************************
241     *
242     *
243     * routine per tracciare la particella di uno STEP
244     * *** extended version ***
245     * it return also the track-length
246     *
247     SUBROUTINE GRKUTA2 (CHARGE,STEP,VECT,VOUT)
248     C.
249     C. ******************************************************************
250     C. * *
251     C. * Runge-Kutta method for tracking a particle through a magnetic *
252     C. * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
253     C. * Standards, procedure 25.5.20) *
254     C. * *
255     C. * Input parameters *
256     C. * CHARGE Particle charge *
257     C. * STEP Step size *
258     C. * VECT Initial co-ords,direction cosines,momentum *
259     C. * Output parameters *
260     C. * VOUT Output co-ords,direction cosines,momentum *
261     C. * User routine called *
262     C. * CALL GUFLD(X,F) *
263     C. * *
264     C. * ==>Called by : <USER>, GUSWIM *
265     C. * Authors R.Brun, M.Hansroul ********* *
266     C. * V.Perevoztchikov (CUT STEP implementation) *
267     C. * *
268     C. * *
269     C. ******************************************************************
270     C.
271     IMPLICIT DOUBLE PRECISION(A-H,O-Z)
272     *
273     REAL VVV(3),FFF(3)
274     REAL*8 CHARGE, STEP, VECT(*), VOUT(*), F(4)
275     REAL*8 XYZT(3), XYZ(3), X, Y, Z, XT, YT, ZT
276     DIMENSION SECXS(4),SECYS(4),SECZS(4),HXP(3)
277     EQUIVALENCE (X,XYZ(1)),(Y,XYZ(2)),(Z,XYZ(3)),
278     + (XT,XYZT(1)),(YT,XYZT(2)),(ZT,XYZT(3))
279     *
280     PARAMETER (MAXIT = 1992, MAXCUT = 11)
281     PARAMETER (EC=2.9979251D-4,DLT=1D-4,DLT32=DLT/32)
282     PARAMETER (ZERO=0, ONE=1, TWO=2, THREE=3)
283     PARAMETER (THIRD=ONE/THREE, HALF=ONE/TWO)
284     PARAMETER (PISQUA=.986960440109D+01)
285     PARAMETER (IX=1,IY=2,IZ=3,IPX=4,IPY=5,IPZ=6)
286    
287     * track length
288     REAL*8 DL
289    
290     *.
291     *. ------------------------------------------------------------------
292     *.
293     * This constant is for units CM,GEV/C and KGAUSS
294     *
295     ITER = 0
296     NCUT = 0
297     DO 10 J=1,8
298     VOUT(J)=VECT(J)
299     10 CONTINUE
300     PINV = EC * CHARGE / VECT(7)
301     TL = 0.
302     H = STEP
303    
304     c print*,'===================== START GRKUTA2'
305    
306     *
307     *
308     20 REST = STEP-TL
309     IF (DABS(H).GT.DABS(REST)) H = REST
310     DO I=1,3
311     VVV(I)=SNGL(VOUT(I))
312     ENDDO
313    
314     CALL GUFLD(VVV,FFF)
315     * print*,'GRKUTA Bx,By,Bz: ',(FFF(i),i=1,3)
316     DO I=1,3
317     F(I)=DBLE(FFF(I))
318     ENDDO
319     *
320     * Start of integration
321     *
322     X = VOUT(1)
323     Y = VOUT(2)
324     Z = VOUT(3)
325     A = VOUT(4)
326     B = VOUT(5)
327     C = VOUT(6)
328    
329     DL = VOUT(8)
330    
331     *
332     H2 = HALF * H
333     H4 = HALF * H2
334     PH = PINV * H
335     PH2 = HALF * PH
336     SECXS(1) = (B * F(3) - C * F(2)) * PH2
337     SECYS(1) = (C * F(1) - A * F(3)) * PH2
338     SECZS(1) = (A * F(2) - B * F(1)) * PH2
339     ANG2 = (SECXS(1)**2 + SECYS(1)**2 + SECZS(1)**2)
340     IF (ANG2.GT.PISQUA) GO TO 40
341     DXT = H2 * A + H4 * SECXS(1)
342     DYT = H2 * B + H4 * SECYS(1)
343     DZT = H2 * C + H4 * SECZS(1)
344     XT = X + DXT
345     YT = Y + DYT
346     ZT = Z + DZT
347     *
348     * Second intermediate point
349     *
350     EST = DABS(DXT)+DABS(DYT)+DABS(DZT)
351     IF (EST.GT.H) GO TO 30
352    
353     DO I=1,3
354     VVV(I)=SNGL(XYZT(I))
355     ENDDO
356     CALL GUFLD(VVV,FFF)
357     DO I=1,3
358     F(I)=DBLE(FFF(I))
359     ENDDO
360     C CALL GUFLD(XYZT,F)
361     AT = A + SECXS(1)
362     BT = B + SECYS(1)
363     CT = C + SECZS(1)
364     *
365     SECXS(2) = (BT * F(3) - CT * F(2)) * PH2
366     SECYS(2) = (CT * F(1) - AT * F(3)) * PH2
367     SECZS(2) = (AT * F(2) - BT * F(1)) * PH2
368     AT = A + SECXS(2)
369     BT = B + SECYS(2)
370     CT = C + SECZS(2)
371     SECXS(3) = (BT * F(3) - CT * F(2)) * PH2
372     SECYS(3) = (CT * F(1) - AT * F(3)) * PH2
373     SECZS(3) = (AT * F(2) - BT * F(1)) * PH2
374     DXT = H * (A + SECXS(3))
375     DYT = H * (B + SECYS(3))
376     DZT = H * (C + SECZS(3))
377     XT = X + DXT
378     YT = Y + DYT
379     ZT = Z + DZT
380     AT = A + TWO*SECXS(3)
381     BT = B + TWO*SECYS(3)
382     CT = C + TWO*SECZS(3)
383     *
384     EST = ABS(DXT)+ABS(DYT)+ABS(DZT)
385     IF (EST.GT.2.*ABS(H)) GO TO 30
386    
387     DO I=1,3
388     VVV(I)=SNGL(XYZT(I))
389     ENDDO
390     CALL GUFLD(VVV,FFF)
391     DO I=1,3
392     F(I)=DBLE(FFF(I))
393     ENDDO
394     C CALL GUFLD(XYZT,F)
395     *
396     Z = Z + (C + (SECZS(1) + SECZS(2) + SECZS(3)) * THIRD) * H
397     Y = Y + (B + (SECYS(1) + SECYS(2) + SECYS(3)) * THIRD) * H
398     X = X + (A + (SECXS(1) + SECXS(2) + SECXS(3)) * THIRD) * H
399     *
400     SECXS(4) = (BT*F(3) - CT*F(2))* PH2
401     SECYS(4) = (CT*F(1) - AT*F(3))* PH2
402     SECZS(4) = (AT*F(2) - BT*F(1))* PH2
403     A = A+(SECXS(1)+SECXS(4)+TWO * (SECXS(2)+SECXS(3))) * THIRD
404     B = B+(SECYS(1)+SECYS(4)+TWO * (SECYS(2)+SECYS(3))) * THIRD
405     C = C+(SECZS(1)+SECZS(4)+TWO * (SECZS(2)+SECZS(3))) * THIRD
406     *
407     EST = ABS(SECXS(1)+SECXS(4) - (SECXS(2)+SECXS(3)))
408     ++ ABS(SECYS(1)+SECYS(4) - (SECYS(2)+SECYS(3)))
409     ++ ABS(SECZS(1)+SECZS(4) - (SECZS(2)+SECZS(3)))
410     *
411     IF (EST.GT.DLT .AND. ABS(H).GT.1.E-4) GO TO 30
412 mocchiut 1.1
413 pam-fi 1.2 ITER = ITER + 1
414     NCUT = 0
415     * If too many iterations, go to HELIX
416     IF (ITER.GT.MAXIT) GO TO 40
417     *
418     DL = VOUT(8) +
419     $ DSQRT( 0
420     $ + (X-VOUT(1))**2
421     $ + (Y-VOUT(2))**2
422     $ + (Z-VOUT(3))**2
423     $ )
424     c print*,'- ',VOUT(3),z,VOUT(1),x,VOUT(2),y,DL
425     *
426     TL = TL + H
427     IF (EST.LT.(DLT32)) THEN
428     H = H*TWO
429     ENDIF
430     CBA = ONE/ SQRT(A*A + B*B + C*C)
431     VOUT(1) = X
432     VOUT(2) = Y
433     VOUT(3) = Z
434     VOUT(4) = CBA*A
435     VOUT(5) = CBA*B
436     VOUT(6) = CBA*C
437     VOUT(8) = DL
438     REST = STEP - TL
439     IF (STEP.LT.0.) REST = -REST
440     IF (REST .GT. 1.E-5*DABS(STEP)) GO TO 20
441     *
442     GO TO 999
443     *
444     ** CUT STEP
445     30 NCUT = NCUT + 1
446     * If too many cuts , go to HELIX
447     IF (NCUT.GT.MAXCUT) GO TO 40
448     H = H*HALF
449     GO TO 20
450     *
451     ** ANGLE TOO BIG, USE HELIX
452     40 F1 = F(1)
453     F2 = F(2)
454     F3 = F(3)
455     F4 = DSQRT(F1**2+F2**2+F3**2)
456     RHO = -F4*PINV
457     TET = RHO * STEP
458     IF(TET.NE.0.) THEN
459     HNORM = ONE/F4
460     F1 = F1*HNORM
461     F2 = F2*HNORM
462     F3 = F3*HNORM
463     *
464     HXP(1) = F2*VECT(IPZ) - F3*VECT(IPY)
465     HXP(2) = F3*VECT(IPX) - F1*VECT(IPZ)
466     HXP(3) = F1*VECT(IPY) - F2*VECT(IPX)
467    
468     HP = F1*VECT(IPX) + F2*VECT(IPY) + F3*VECT(IPZ)
469     *
470     RHO1 = ONE/RHO
471     SINT = DSIN(TET)
472     COST = TWO*DSIN(HALF*TET)**2
473     *
474     G1 = SINT*RHO1
475     G2 = COST*RHO1
476     G3 = (TET-SINT) * HP*RHO1
477     G4 = -COST
478     G5 = SINT
479     G6 = COST * HP
480    
481     VOUT(IX) = VECT(IX) + (G1*VECT(IPX) + G2*HXP(1) + G3*F1)
482     VOUT(IY) = VECT(IY) + (G1*VECT(IPY) + G2*HXP(2) + G3*F2)
483     VOUT(IZ) = VECT(IZ) + (G1*VECT(IPZ) + G2*HXP(3) + G3*F3)
484    
485     VOUT(IPX) = VECT(IPX) + (G4*VECT(IPX) + G5*HXP(1) + G6*F1)
486     VOUT(IPY) = VECT(IPY) + (G4*VECT(IPY) + G5*HXP(2) + G6*F2)
487     VOUT(IPZ) = VECT(IPZ) + (G4*VECT(IPZ) + G5*HXP(3) + G6*F3)
488     *
489     ELSE
490     VOUT(IX) = VECT(IX) + STEP*VECT(IPX)
491     VOUT(IY) = VECT(IY) + STEP*VECT(IPY)
492     VOUT(IZ) = VECT(IZ) + STEP*VECT(IPZ)
493     *
494     ENDIF
495     * TEMP !!! TEMP !!! TEMP !!! TEMP !!! TEMP !!! TEMP !!!
496     * devo mettere la lunghezza dell'elica!!!!!!!!!!!!!!
497     * ma non mi riesce :-(
498     VOUT(8) = DSQRT( 0
499     $ +(VOUT(IX)-VECT(IX))**2
500     $ +(VOUT(IY)-VECT(IY))**2
501     $ +(VOUT(IZ)-VECT(IZ))**2
502     $ )
503     print*,'WARNING: GRKUTA2 --> '
504     $ ,'helix :-( ... length evaluated with straight line'
505    
506     *
507     999 END
508     *
509     *
510 mocchiut 1.1
511     **********************************************************************
512     *
513     * gives the value of the magnetic field in the tracking point
514     *
515     **********************************************************************
516    
517     subroutine gufld(v,f) !coordinates in cm, B field in kGauss
518    
519     real v(3),f(3) !coordinates in cm, B field in kGauss, error in kGauss
520    
521     real*8 vv(3),ff(3) !inter_B.f works in double precision
522    
523    
524     do i=1,3
525     vv(i)=v(i)/100. !inter_B.f works in meters
526     enddo
527     c inter_B: coordinates in m, B field in Tesla
528     call inter_B(vv(1),vv(2),vv(3),ff)
529     do i=1,3 !change back the field in kGauss
530     f(i)=ff(i)*10.
531     enddo
532    
533     return
534     end
535    

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