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25 //
26 // G4MagInt_Driver implementation
27 //
28 // V.Grichine, 07.10.1996 - Created
29 // W.Wander, 28.01.1998 - Added ability for low order integrators
30 // J.Apostolakis, 08.11.2001 - Respect minimum step in AccurateAdvance
31 // --------------------------------------------------------------------
32
33 #include <iomanip>
34
35 #include "globals.hh"
36 #include "G4SystemOfUnits.hh"
37 #include "G4GeometryTolerance.hh"
38 #include "G4MagIntegratorDriver.hh"
39 #include "G4FieldTrack.hh"
40
41 #ifdef G4DEBUG_FIELD
42 #include "G4DriverReporter.hh"
43 #endif
44
45 // ---------------------------------------------------------
46
47 // Constructor
48 //
49 G4MagInt_Driver::G4MagInt_Driver( G4double hminimum,
50 G4MagIntegratorStepper* pStepper,
51 G4int numComponents,
52 G4int statisticsVerbose)
53 : fNoIntegrationVariables(numComponents),
54 fNoVars( std::max( fNoIntegrationVariables, fMinNoVars )),
55 fStatisticsVerboseLevel(statisticsVerbose)
56 {
57 // In order to accomodate "Laboratory Time", which is [7], fMinNoVars=8
58 // is required. For proper time of flight and spin, fMinNoVars must be 12
59
60 RenewStepperAndAdjust( pStepper );
61 fMinimumStep = hminimum;
62
63 fMaxNoSteps = fMaxStepBase / pIntStepper->IntegratorOrder();
64 #ifdef G4DEBUG_FIELD
65 fVerboseLevel=2;
66 #endif
67
68 if( (fVerboseLevel > 0) || (fStatisticsVerboseLevel > 1) )
69 {
70 G4cout << "MagIntDriver version: Accur-Adv: "
71 << "invE_nS, QuickAdv-2sqrt with Statistics "
72 #ifdef G4FLD_STATS
73 << " enabled "
74 #else
75 << " disabled "
76 #endif
77 << G4endl;
78 }
79 }
80
81 // ---------------------------------------------------------
82
83 // Destructor
84 //
85 G4MagInt_Driver::~G4MagInt_Driver()
86 {
87 if( fStatisticsVerboseLevel > 1 )
88 {
89 PrintStatisticsReport();
90 }
91 }
92
93 // ---------------------------------------------------------
94
95 G4bool
96 G4MagInt_Driver::AccurateAdvance(G4FieldTrack& y_current,
97 G4double hstep,
98 G4double eps,
99 G4double hinitial )
100 {
101 // Runge-Kutta driver with adaptive stepsize control. Integrate starting
102 // values at y_current over hstep x2 with accuracy eps.
103 // On output ystart is replaced by values at the end of the integration
104 // interval. RightHandSide is the right-hand side of ODE system.
105 // The source is similar to odeint routine from NRC p.721-722 .
106
107 G4int nstp, i;
108 G4double x, hnext, hdid, h;
109
110 #ifdef G4DEBUG_FIELD
111 G4int no_warnings = 0;
112 static G4int dbg = 1;
113 static G4int nStpPr = 50; // For debug printing of long integrations
114 G4double ySubStepStart[G4FieldTrack::ncompSVEC];
115 G4FieldTrack yFldTrkStart(y_current);
116 #endif
117
118 G4double y[G4FieldTrack::ncompSVEC] = {0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.};
119 G4double dydx[G4FieldTrack::ncompSVEC] = {0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.};
120 G4double ystart[G4FieldTrack::ncompSVEC] = {0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.};
121 G4double yEnd[G4FieldTrack::ncompSVEC] = {0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.};
122 G4double x1, x2;
123 G4bool succeeded = true;
124
125 G4double startCurveLength;
126
127 const G4int nvar = fNoVars;
128
129 G4FieldTrack yStartFT(y_current);
130
131 // Ensure that hstep > 0
132 //
133 if( hstep <= 0.0 )
134 {
135 if( hstep == 0.0 )
136 {
137 std::ostringstream message;
138 message << "Proposed step is zero; hstep = " << hstep << " !";
139 G4Exception("G4MagInt_Driver::AccurateAdvance()",
140 "GeomField1001", JustWarning, message);
141 return succeeded;
142 }
143
144 std::ostringstream message;
145 message << "Invalid run condition." << G4endl
146 << "Proposed step is negative; hstep = " << hstep << "." << G4endl
147 << "Requested step cannot be negative! Aborting event.";
148 G4Exception("G4MagInt_Driver::AccurateAdvance()",
149 "GeomField0003", EventMustBeAborted, message);
150 return false;
151 }
152
153 y_current.DumpToArray( ystart );
154
155 startCurveLength= y_current.GetCurveLength();
156 x1= startCurveLength;
157 x2= x1 + hstep;
158
159 if ( (hinitial > 0.0) && (hinitial < hstep)
160 && (hinitial > perMillion * hstep) )
161 {
162 h = hinitial;
163 }
164 else // Initial Step size "h" defaults to the full interval
165 {
166 h = hstep;
167 }
168
169 x = x1;
170
171 for ( i=0; i<nvar; ++i) { y[i] = ystart[i]; }
172
173 G4bool lastStep= false;
174 nstp = 1;
175
176 do
177 {
178 G4ThreeVector StartPos( y[0], y[1], y[2] );
179
180 #ifdef G4DEBUG_FIELD
181 G4double xSubStepStart= x;
182 for (i=0; i<nvar; ++i) { ySubStepStart[i] = y[i]; }
183 yFldTrkStart.LoadFromArray(y, fNoIntegrationVariables);
184 yFldTrkStart.SetCurveLength(x);
185 #endif
186
187 pIntStepper->RightHandSide( y, dydx );
188 ++fNoTotalSteps;
189
190 // Perform the Integration
191 //
192 if( h > fMinimumStep )
193 {
194 OneGoodStep(y,dydx,x,h,eps,hdid,hnext) ;
195 //--------------------------------------
196 #ifdef G4DEBUG_FIELD
197 if (dbg>2)
198 {
199 // PrintStatus( ySubStepStart, xSubStepStart, y, x, h, nstp); // Only
200 G4DriverReporter::PrintStatus( ySubStepStart, xSubStepStart, y, x, h, nstp, nvar);
201 }
202 #endif
203 }
204 else
205 {
206 G4FieldTrack yFldTrk( G4ThreeVector(0,0,0),
207 G4ThreeVector(0,0,0), 0., 0., 0., 0. );
208 G4double dchord_step, dyerr, dyerr_len; // What to do with these ?
209 yFldTrk.LoadFromArray(y, fNoIntegrationVariables);
210 yFldTrk.SetCurveLength( x );
211
212 QuickAdvance( yFldTrk, dydx, h, dchord_step, dyerr_len );
213 //-----------------------------------------------------
214
215 yFldTrk.DumpToArray(y);
216
217 #ifdef G4FLD_STATS
218 ++fNoSmallSteps;
219 if ( dyerr_len > fDyerr_max ) { fDyerr_max = dyerr_len; }
220 fDyerrPos_smTot += dyerr_len;
221 fSumH_sm += h; // Length total for 'small' steps
222 if (nstp==1) { ++fNoInitialSmallSteps; }
223 #endif
224 #ifdef G4DEBUG_FIELD
225 if (dbg>1)
226 {
227 if(fNoSmallSteps<2) { PrintStatus(ySubStepStart, x1, y, x, h, -nstp); }
228 G4cout << "Another sub-min step, no " << fNoSmallSteps
229 << " of " << fNoTotalSteps << " this time " << nstp << G4endl;
230 PrintStatus( ySubStepStart, x1, y, x, h, nstp); // Only this
231 G4cout << " dyerr= " << dyerr_len << " relative = " << dyerr_len / h
232 << " epsilon= " << eps << " hstep= " << hstep
233 << " h= " << h << " hmin= " << fMinimumStep << G4endl;
234 }
235 #endif
236 if( h == 0.0 )
237 {
238 G4Exception("G4MagInt_Driver::AccurateAdvance()",
239 "GeomField0003", FatalException,
240 "Integration Step became Zero!");
241 }
242 dyerr = dyerr_len / h;
243 hdid = h;
244 x += hdid;
245
246 // Compute suggested new step
247 hnext = ComputeNewStepSize( dyerr/eps, h);
248 }
249
250 G4ThreeVector EndPos( y[0], y[1], y[2] );
251
252 #ifdef G4DEBUG_FIELD
253 if( (dbg>0) && (dbg<=2) && (nstp>nStpPr))
254 {
255 if( nstp==nStpPr ) { G4cout << "***** Many steps ****" << G4endl; }
256 G4cout << "MagIntDrv: " ;
257 G4cout << "hdid=" << std::setw(12) << hdid << " "
258 << "hnext=" << std::setw(12) << hnext << " "
259 << "hstep=" << std::setw(12) << hstep << " (requested) "
260 << G4endl;
261 PrintStatus( ystart, x1, y, x, h, (nstp==nStpPr) ? -nstp: nstp);
262 }
263 #endif
264
265 // Check the endpoint
266 G4double endPointDist= (EndPos-StartPos).mag();
267 if ( endPointDist >= hdid*(1.+perMillion) )
268 {
269 ++fNoBadSteps;
270
271 // Issue a warning only for gross differences -
272 // we understand how small difference occur.
273 if ( endPointDist >= hdid*(1.+perThousand) )
274 {
275 #ifdef G4DEBUG_FIELD
276 if (dbg)
277 {
278 WarnEndPointTooFar ( endPointDist, hdid, eps, dbg );
279 G4cerr << " Total steps: bad " << fNoBadSteps
280 << " current h= " << hdid << G4endl;
281 PrintStatus( ystart, x1, y, x, hstep, no_warnings?nstp:-nstp);
282 }
283 ++no_warnings;
284 #endif
285 }
286 }
287
288 // Avoid numerous small last steps
289 if( (h < eps * hstep) || (h < fSmallestFraction * startCurveLength) )
290 {
291 // No more integration -- the next step will not happen
292 lastStep = true;
293 }
294 else
295 {
296 // Check the proposed next stepsize
297 if(std::fabs(hnext) <= Hmin())
298 {
299 #ifdef G4DEBUG_FIELD
300 // If simply a very small interval is being integrated, do not warn
301 if( (x < x2 * (1-eps) ) && // The last step can be small: OK
302 (std::fabs(hstep) > Hmin()) ) // and if we are asked, it's OK
303 {
304 if(dbg>0)
305 {
306 WarnSmallStepSize( hnext, hstep, h, x-x1, nstp );
307 PrintStatus( ystart, x1, y, x, hstep, no_warnings?nstp:-nstp);
308 }
309 ++no_warnings;
310 }
311 #endif
312 // Make sure that the next step is at least Hmin.
313 h = Hmin();
314 }
315 else
316 {
317 h = hnext;
318 }
319
320 // Ensure that the next step does not overshoot
321 if ( x+h > x2 )
322 { // When stepsize overshoots, decrease it!
323 h = x2 - x ; // Must cope with difficult rounding-error
324 } // issues if hstep << x2
325
326 if ( h == 0.0 )
327 {
328 // Cannot progress - accept this as last step - by default
329 lastStep = true;
330 #ifdef G4DEBUG_FIELD
331 if (dbg>2)
332 {
333 int prec= G4cout.precision(12);
334 G4cout << "Warning: G4MagIntegratorDriver::AccurateAdvance"
335 << G4endl
336 << " Integration step 'h' became "
337 << h << " due to roundoff. " << G4endl
338 << " Calculated as difference of x2= "<< x2 << " and x=" << x
339 << " Forcing termination of advance." << G4endl;
340 G4cout.precision(prec);
341 }
342 #endif
343 }
344 }
345 } while ( ((++nstp)<=fMaxNoSteps) && (x < x2) && (!lastStep) );
346 // Loop checking, 07.10.2016, J. Apostolakis
347
348 // Have we reached the end ?
349 // --> a better test might be x-x2 > an_epsilon
350
351 succeeded = (x>=x2); // If it was a "forced" last step
352
353 for (i=0; i<nvar; ++i) { yEnd[i] = y[i]; }
354
355 // Put back the values.
356 y_current.LoadFromArray( yEnd, fNoIntegrationVariables );
357 y_current.SetCurveLength( x );
358
359 if(nstp > fMaxNoSteps)
360 {
361 succeeded = false;
362 #ifdef G4DEBUG_FIELD
363 ++no_warnings;
364 if (dbg)
365 {
366 WarnTooManyStep( x1, x2, x ); // Issue WARNING
367 PrintStatus( yEnd, x1, y, x, hstep, -nstp);
368 }
369 #endif
370 }
371
372 #ifdef G4DEBUG_FIELD
373 if( dbg && no_warnings )
374 {
375 G4cerr << "G4MagIntegratorDriver exit status: no-steps " << nstp << G4endl;
376 PrintStatus( yEnd, x1, y, x, hstep, nstp);
377 }
378 #endif
379
380 return succeeded;
381 } // end of AccurateAdvance ...........................
382
383 // ---------------------------------------------------------
384
385 void
386 G4MagInt_Driver::WarnSmallStepSize( G4double hnext, G4double hstep,
387 G4double h, G4double xDone,
388 G4int nstp)
389 {
390 static G4ThreadLocal G4int noWarningsIssued = 0;
391 const G4int maxNoWarnings = 10; // Number of verbose warnings
392 std::ostringstream message;
393 if( (noWarningsIssued < maxNoWarnings) || fVerboseLevel > 10 )
394 {
395 message << "The stepsize for the next iteration, " << hnext
396 << ", is too small - in Step number " << nstp << "." << G4endl
397 << "The minimum for the driver is " << Hmin() << G4endl
398 << "Requested integr. length was " << hstep << " ." << G4endl
399 << "The size of this sub-step was " << h << " ." << G4endl
400 << "The integrations has already gone " << xDone;
401 }
402 else
403 {
404 message << "Too small 'next' step " << hnext
405 << ", step-no: " << nstp << G4endl
406 << ", this sub-step: " << h
407 << ", req_tot_len: " << hstep
408 << ", done: " << xDone << ", min: " << Hmin();
409 }
410 G4Exception("G4MagInt_Driver::WarnSmallStepSize()", "GeomField1001",
411 JustWarning, message);
412 ++noWarningsIssued;
413 }
414
415 // ---------------------------------------------------------
416
417 void
418 G4MagInt_Driver::WarnTooManyStep( G4double x1start,
419 G4double x2end,
420 G4double xCurrent )
421 {
422 std::ostringstream message;
423 message << "The number of steps used in the Integration driver"
424 << " (Runge-Kutta) is too many." << G4endl
425 << "Integration of the interval was not completed !" << G4endl
426 << "Only a " << (xCurrent-x1start)*100/(x2end-x1start)
427 << " % fraction of it was done.";
428 G4Exception("G4MagInt_Driver::WarnTooManyStep()", "GeomField1001",
429 JustWarning, message);
430 }
431
432 // ---------------------------------------------------------
433
434 void
435 G4MagInt_Driver::WarnEndPointTooFar (G4double endPointDist,
436 G4double h ,
437 G4double eps,
438 G4int dbg)
439 {
440 static G4ThreadLocal G4double maxRelError = 0.0;
441 G4bool isNewMax, prNewMax;
442
443 isNewMax = endPointDist > (1.0 + maxRelError) * h;
444 prNewMax = endPointDist > (1.0 + 1.05 * maxRelError) * h;
445 if( isNewMax ) { maxRelError= endPointDist / h - 1.0; }
446
447 if( (dbg != 0) && (h > G4GeometryTolerance::GetInstance()->GetSurfaceTolerance())
448 && ( (dbg>1) || prNewMax || (endPointDist >= h*(1.+eps) ) ) )
449 {
450 static G4ThreadLocal G4int noWarnings = 0;
451 std::ostringstream message;
452 if( (noWarnings++ < 10) || (dbg>2) )
453 {
454 message << "The integration produced an end-point which " << G4endl
455 << "is further from the start-point than the curve length."
456 << G4endl;
457 }
458 message << " Distance of endpoints = " << endPointDist
459 << ", curve length = " << h << G4endl
460 << " Difference (curveLen-endpDist)= " << (h - endPointDist)
461 << ", relative = " << (h-endPointDist) / h
462 << ", epsilon = " << eps;
463 G4Exception("G4MagInt_Driver::WarnEndPointTooFar()", "GeomField1001",
464 JustWarning, message);
465 }
466 }
467
468 // ---------------------------------------------------------
469
470 void
471 G4MagInt_Driver::OneGoodStep( G4double y[], // InOut
472 const G4double dydx[],
473 G4double& x, // InOut
474 G4double htry,
475 G4double eps_rel_max,
476 G4double& hdid, // Out
477 G4double& hnext ) // Out
478
479 // Driver for one Runge-Kutta Step with monitoring of local truncation error
480 // to ensure accuracy and adjust stepsize. Input are dependent variable
481 // array y[0,...,5] and its derivative dydx[0,...,5] at the
482 // starting value of the independent variable x . Also input are stepsize
483 // to be attempted htry, and the required accuracy eps. On output y and x
484 // are replaced by their new values, hdid is the stepsize that was actually
485 // accomplished, and hnext is the estimated next stepsize.
486 // This is similar to the function rkqs from the book:
487 // Numerical Recipes in C: The Art of Scientific Computing (NRC), Second
488 // Edition, by William H. Press, Saul A. Teukolsky, William T.
489 // Vetterling, and Brian P. Flannery (Cambridge University Press 1992),
490 // 16.2 Adaptive StepSize Control for Runge-Kutta, p. 719
491
492 {
493 G4double errmax_sq;
494 G4double h, htemp, xnew ;
495
496 G4double yerr[G4FieldTrack::ncompSVEC], ytemp[G4FieldTrack::ncompSVEC];
497
498 h = htry ; // Set stepsize to the initial trial value
499
500 G4double inv_eps_vel_sq = 1.0 / (eps_rel_max*eps_rel_max);
501
502 G4double errpos_sq = 0.0; // square of displacement error
503 G4double errvel_sq = 0.0; // square of momentum vector difference
504 G4double errspin_sq = 0.0; // square of spin vector difference
505
506 const G4int max_trials=100;
507
508 G4ThreeVector Spin(y[9],y[10],y[11]);
509 G4double spin_mag2 = Spin.mag2();
510 G4bool hasSpin = (spin_mag2 > 0.0);
511
512 for (G4int iter=0; iter<max_trials; ++iter)
513 {
514 pIntStepper-> Stepper(y,dydx,h,ytemp,yerr);
515 // *******
516 G4double eps_pos = eps_rel_max * std::max(h, fMinimumStep);
517 G4double inv_eps_pos_sq = 1.0 / (eps_pos*eps_pos);
518
519 // Evaluate accuracy
520 //
521 errpos_sq = sqr(yerr[0]) + sqr(yerr[1]) + sqr(yerr[2]) ;
522 errpos_sq *= inv_eps_pos_sq; // Scale relative to required tolerance
523
524 // Accuracy for momentum
525 G4double magvel_sq= sqr(y[3]) + sqr(y[4]) + sqr(y[5]) ;
526 G4double sumerr_sq = sqr(yerr[3]) + sqr(yerr[4]) + sqr(yerr[5]) ;
527 if( magvel_sq > 0.0 )
528 {
529 errvel_sq = sumerr_sq / magvel_sq;
530 }
531 else
532 {
533 std::ostringstream message;
534 message << "Found case of zero momentum." << G4endl
535 << "- iteration= " << iter << "; h= " << h;
536 G4Exception("G4MagInt_Driver::OneGoodStep()",
537 "GeomField1001", JustWarning, message);
538 errvel_sq = sumerr_sq;
539 }
540 errvel_sq *= inv_eps_vel_sq;
541 errmax_sq = std::max( errpos_sq, errvel_sq ); // Square of maximum error
542
543 if( hasSpin )
544 {
545 // Accuracy for spin
546 errspin_sq = ( sqr(yerr[9]) + sqr(yerr[10]) + sqr(yerr[11]) )
547 / spin_mag2; // ( sqr(y[9]) + sqr(y[10]) + sqr(y[11]) );
548 errspin_sq *= inv_eps_vel_sq;
549 errmax_sq = std::max( errmax_sq, errspin_sq );
550 }
551
552 if ( errmax_sq <= 1.0 ) { break; } // Step succeeded.
553
554 // Step failed; compute the size of retrial Step.
555 htemp = GetSafety() * h * std::pow( errmax_sq, 0.5*GetPshrnk() );
556
557 if (htemp >= 0.1*h) { h = htemp; } // Truncation error too large,
558 else { h = 0.1*h; } // reduce stepsize, but no more
559 // than a factor of 10
560 xnew = x + h;
561 if(xnew == x)
562 {
563 std::ostringstream message;
564 message << "Stepsize underflow in Stepper !" << G4endl
565 << "- Step's start x=" << x << " and end x= " << xnew
566 << " are equal !! " << G4endl
567 << " Due to step-size= " << h
568 << ". Note that input step was " << htry;
569 G4Exception("G4MagInt_Driver::OneGoodStep()",
570 "GeomField1001", JustWarning, message);
571 break;
572 }
573 }
574
575 // Compute size of next Step
576 if (errmax_sq > errcon*errcon)
577 {
578 hnext = GetSafety()*h*std::pow(errmax_sq, 0.5*GetPgrow());
579 }
580 else
581 {
582 hnext = max_stepping_increase*h ; // No more than a factor of 5 increase
583 }
584 x += (hdid = h);
585
586 for(G4int k=0; k<fNoIntegrationVariables; ++k) { y[k] = ytemp[k]; }
587
588 return;
589 }
590
591 //----------------------------------------------------------------------
592
593 // QuickAdvance just tries one Step - it does not ensure accuracy
594 //
595 G4bool G4MagInt_Driver::QuickAdvance(G4FieldTrack& y_posvel, // INOUT
596 const G4double dydx[],
597 G4double hstep, // In
598 G4double& dchord_step,
599 G4double& dyerr_pos_sq,
600 G4double& dyerr_mom_rel_sq )
601 {
602 G4Exception("G4MagInt_Driver::QuickAdvance()", "GeomField0001",
603 FatalException, "Not yet implemented.");
604
605 // Use the parameters of this method, to please compiler
606 //
607 dchord_step = dyerr_pos_sq = hstep * hstep * dydx[0];
608 dyerr_mom_rel_sq = y_posvel.GetPosition().mag2();
609 return true;
610 }
611
612 //----------------------------------------------------------------------
613
614 G4bool G4MagInt_Driver::QuickAdvance(G4FieldTrack& y_posvel, // INOUT
615 const G4double dydx[],
616 G4double hstep, // In
617 G4double& dchord_step,
618 G4double& dyerr )
619 {
620 G4double dyerr_pos_sq, dyerr_mom_rel_sq;
621 G4double yerr_vec[G4FieldTrack::ncompSVEC],
622 yarrin[G4FieldTrack::ncompSVEC], yarrout[G4FieldTrack::ncompSVEC];
623 G4double s_start;
624 G4double dyerr_mom_sq, vel_mag_sq, inv_vel_mag_sq;
625
626 // Move data into array
627 y_posvel.DumpToArray( yarrin ); // yarrin <== y_posvel
628 s_start = y_posvel.GetCurveLength();
629
630 // Do an Integration Step
631 pIntStepper-> Stepper(yarrin, dydx, hstep, yarrout, yerr_vec) ;
632
633 // Estimate curve-chord distance
634 dchord_step= pIntStepper-> DistChord();
635
636 // Put back the values. yarrout ==> y_posvel
637 y_posvel.LoadFromArray( yarrout, fNoIntegrationVariables );
638 y_posvel.SetCurveLength( s_start + hstep );
639
640 #ifdef G4DEBUG_FIELD
641 if(fVerboseLevel>2)
642 {
643 G4cout << "G4MagIntDrv: Quick Advance" << G4endl;
644 PrintStatus( yarrin, s_start, yarrout, s_start+hstep, hstep, 1);
645 }
646 #endif
647
648 // A single measure of the error
649 // TO-DO : account for energy, spin, ... ?
650 vel_mag_sq = ( sqr(yarrout[3])+sqr(yarrout[4])+sqr(yarrout[5]) );
651 inv_vel_mag_sq = 1.0 / vel_mag_sq;
652 dyerr_pos_sq = ( sqr(yerr_vec[0])+sqr(yerr_vec[1])+sqr(yerr_vec[2]));
653 dyerr_mom_sq = ( sqr(yerr_vec[3])+sqr(yerr_vec[4])+sqr(yerr_vec[5]));
654 dyerr_mom_rel_sq = dyerr_mom_sq * inv_vel_mag_sq;
655
656 // Calculate also the change in the momentum squared also ???
657 // G4double veloc_square = y_posvel.GetVelocity().mag2();
658 // ...
659
660 #ifdef RETURN_A_NEW_STEP_LENGTH
661 // The following step cannot be done here because "eps" is not known.
662 dyerr_len = std::sqrt( dyerr_len_sq );
663 dyerr_len_sq /= eps ;
664
665 // Look at the velocity deviation ?
666 // sqr(yerr_vec[3])+sqr(yerr_vec[4])+sqr(yerr_vec[5]));
667
668 // Set suggested new step
669 hstep = ComputeNewStepSize( dyerr_len, hstep);
670 #endif
671
672 if( dyerr_pos_sq > ( dyerr_mom_rel_sq * sqr(hstep) ) )
673 {
674 dyerr = std::sqrt(dyerr_pos_sq);
675 }
676 else
677 {
678 // Scale it to the current step size - for now
679 dyerr = std::sqrt(dyerr_mom_rel_sq) * hstep;
680 }
681
682 return true;
683 }
684
685 // --------------------------------------------------------------------------
686
687 #ifdef QUICK_ADV_ARRAY_IN_AND_OUT
688 G4bool G4MagInt_Driver::QuickAdvance(G4double yarrin[], // In
689 const G4double dydx[],
690 G4double hstep, // In
691 G4double yarrout[],
692 G4double& dchord_step,
693 G4double& dyerr ) // In length
694 {
695 G4Exception("G4MagInt_Driver::QuickAdvance()", "GeomField0001",
696 FatalException, "Not yet implemented.");
697 dyerr = dchord_step = hstep * yarrin[0] * dydx[0];
698 yarrout[0]= yarrin[0];
699 }
700 #endif
701
702 // --------------------------------------------------------------------------
703
704 // This method computes new step sizes - but does not limit changes to
705 // within certain factors
706 //
707 G4double G4MagInt_Driver::
708 ComputeNewStepSize_WithoutReductionLimit(G4double errMaxNorm, // max error (normalised)
709 G4double hstepCurrent) // current step size
710 {
711 G4double hnew;
712
713 // Compute size of next Step for a failed step
714 if(errMaxNorm > 1.0 )
715 {
716 // Step failed; compute the size of retrial Step.
717 hnew = GetSafety()*hstepCurrent*std::pow(errMaxNorm,GetPshrnk()) ;
718 }
719 else if(errMaxNorm > 0.0 )
720 {
721 // Compute size of next Step for a successful step
722 hnew = GetSafety()*hstepCurrent*std::pow(errMaxNorm,GetPgrow()) ;
723 }
724 else
725 {
726 // if error estimate is zero (possible) or negative (dubious)
727 hnew = max_stepping_increase * hstepCurrent;
728 }
729
730 return hnew;
731 }
732
733 // ---------------------------------------------------------------------------
734
735 G4double
736 G4MagInt_Driver::ComputeNewStepSize(
737 G4double errMaxNorm, // max error (normalised)
738 G4double hstepCurrent) // current step size
739 {
740 // Legacy behaviour:
741 return ComputeNewStepSize_WithoutReductionLimit( errMaxNorm, hstepCurrent );
742 // 'Improved' behaviour - at least more consistent with other step estimates:
743 // return ComputeNewStepSize_WithinLimits( errMaxNorm, hstepCurrent );
744 }
745
746 // This method computes new step sizes limiting changes within certain factors
747 //
748 // It shares its logic with AccurateAdvance.
749 // They are kept separate currently for optimisation.
750 //
751 G4double
752 G4MagInt_Driver::ComputeNewStepSize_WithinLimits(
753 G4double errMaxNorm, // max error (normalised)
754 G4double hstepCurrent) // current step size
755 {
756 G4double hnew;
757
758 // Compute size of next Step for a failed step
759 if (errMaxNorm > 1.0 )
760 {
761 // Step failed; compute the size of retrial Step.
762 hnew = GetSafety()*hstepCurrent*std::pow(errMaxNorm,GetPshrnk()) ;
763
764 if (hnew < max_stepping_decrease*hstepCurrent)
765 {
766 hnew = max_stepping_decrease*hstepCurrent ;
767 // reduce stepsize, but no more
768 // than this factor (value= 1/10)
769 }
770 }
771 else
772 {
773 // Compute size of next Step for a successful step
774 if (errMaxNorm > errcon)
775 { hnew = GetSafety()*hstepCurrent*std::pow(errMaxNorm,GetPgrow()); }
776 else // No more than a factor of 5 increase
777 { hnew = max_stepping_increase * hstepCurrent; }
778 }
779 return hnew;
780 }
781
782 // ---------------------------------------------------------------------------
783
784 void G4MagInt_Driver::PrintStatus( const G4double* StartArr,
785 G4double xstart,
786 const G4double* CurrentArr,
787 G4double xcurrent,
788 G4double requestStep,
789 G4int subStepNo )
790 // Potentially add as arguments:
791 // <dydx> - as Initial Force
792 // stepTaken(hdid) - last step taken
793 // nextStep (hnext) - proposal for size
794 {
795 G4FieldTrack StartFT(G4ThreeVector(0,0,0),
796 G4ThreeVector(0,0,0), 0., 0., 0., 0. );
797 G4FieldTrack CurrentFT (StartFT);
798
799 StartFT.LoadFromArray( StartArr, fNoIntegrationVariables);
800 StartFT.SetCurveLength( xstart);
801 CurrentFT.LoadFromArray( CurrentArr, fNoIntegrationVariables);
802 CurrentFT.SetCurveLength( xcurrent );
803
804 PrintStatus(StartFT, CurrentFT, requestStep, subStepNo );
805 }
806
807 // ---------------------------------------------------------------------------
808
809 void G4MagInt_Driver::PrintStatus(const G4FieldTrack& StartFT,
810 const G4FieldTrack& CurrentFT,
811 G4double requestStep,
812 G4int subStepNo)
813 {
814 G4int verboseLevel= fVerboseLevel;
815 const G4int noPrecision = 5;
816 G4long oldPrec= G4cout.precision(noPrecision);
817 // G4cout.setf(ios_base::fixed,ios_base::floatfield);
818
819 const G4ThreeVector StartPosition= StartFT.GetPosition();
820 const G4ThreeVector StartUnitVelocity= StartFT.GetMomentumDir();
821 const G4ThreeVector CurrentPosition= CurrentFT.GetPosition();
822 const G4ThreeVector CurrentUnitVelocity= CurrentFT.GetMomentumDir();
823
824 G4double DotStartCurrentVeloc= StartUnitVelocity.dot(CurrentUnitVelocity);
825
826 G4double step_len= CurrentFT.GetCurveLength() - StartFT.GetCurveLength();
827 G4double subStepSize = step_len;
828
829 if( (subStepNo <= 1) || (verboseLevel > 3) )
830 {
831 subStepNo = - subStepNo; // To allow printing banner
832
833 G4cout << std::setw( 6) << " " << std::setw( 25)
834 << " G4MagInt_Driver: Current Position and Direction" << " "
835 << G4endl;
836 G4cout << std::setw( 5) << "Step#" << " "
837 << std::setw( 7) << "s-curve" << " "
838 << std::setw( 9) << "X(mm)" << " "
839 << std::setw( 9) << "Y(mm)" << " "
840 << std::setw( 9) << "Z(mm)" << " "
841 << std::setw( 8) << " N_x " << " "
842 << std::setw( 8) << " N_y " << " "
843 << std::setw( 8) << " N_z " << " "
844 << std::setw( 8) << " N^2-1 " << " "
845 << std::setw(10) << " N(0).N " << " "
846 << std::setw( 7) << "KinEner " << " "
847 << std::setw(12) << "Track-l" << " " // Add the Sub-step ??
848 << std::setw(12) << "Step-len" << " "
849 << std::setw(12) << "Step-len" << " "
850 << std::setw( 9) << "ReqStep" << " "
851 << G4endl;
852 }
853
854 if( (subStepNo <= 0) )
855 {
856 PrintStat_Aux( StartFT, requestStep, 0.,
857 0, 0.0, 1.0);
858 }
859
860 if( verboseLevel <= 3 )
861 {
862 G4cout.precision(noPrecision);
863 PrintStat_Aux( CurrentFT, requestStep, step_len,
864 subStepNo, subStepSize, DotStartCurrentVeloc );
865 }
866
867 G4cout.precision(oldPrec);
868 }
869
870 // ---------------------------------------------------------------------------
871
872 void G4MagInt_Driver::PrintStat_Aux(const G4FieldTrack& aFieldTrack,
873 G4double requestStep,
874 G4double step_len,
875 G4int subStepNo,
876 G4double subStepSize,
877 G4double dotVeloc_StartCurr)
878 {
879 const G4ThreeVector Position = aFieldTrack.GetPosition();
880 const G4ThreeVector UnitVelocity = aFieldTrack.GetMomentumDir();
881
882 if( subStepNo >= 0)
883 {
884 G4cout << std::setw( 5) << subStepNo << " ";
885 }
886 else
887 {
888 G4cout << std::setw( 5) << "Start" << " ";
889 }
890 G4double curveLen= aFieldTrack.GetCurveLength();
891 G4cout << std::setw( 7) << curveLen;
892 G4cout << std::setw( 9) << Position.x() << " "
893 << std::setw( 9) << Position.y() << " "
894 << std::setw( 9) << Position.z() << " "
895 << std::setw( 8) << UnitVelocity.x() << " "
896 << std::setw( 8) << UnitVelocity.y() << " "
897 << std::setw( 8) << UnitVelocity.z() << " ";
898 G4long oldprec= G4cout.precision(3);
899 G4cout << std::setw( 8) << UnitVelocity.mag2()-1.0 << " ";
900 G4cout.precision(6);
901 G4cout << std::setw(10) << dotVeloc_StartCurr << " ";
902 G4cout.precision(oldprec);
903 G4cout << std::setw( 7) << aFieldTrack.GetKineticEnergy();
904 G4cout << std::setw(12) << step_len << " ";
905
906 static G4ThreadLocal G4double oldCurveLength = 0.0;
907 static G4ThreadLocal G4double oldSubStepLength = 0.0;
908 static G4ThreadLocal G4int oldSubStepNo = -1;
909
910 G4double subStep_len = 0.0;
911 if( curveLen > oldCurveLength )
912 {
913 subStep_len= curveLen - oldCurveLength;
914 }
915 else if (subStepNo == oldSubStepNo)
916 {
917 subStep_len= oldSubStepLength;
918 }
919 oldCurveLength= curveLen;
920 oldSubStepLength= subStep_len;
921
922 G4cout << std::setw(12) << subStep_len << " ";
923 G4cout << std::setw(12) << subStepSize << " ";
924 if( requestStep != -1.0 )
925 {
926 G4cout << std::setw( 9) << requestStep << " ";
927 }
928 else
929 {
930 G4cout << std::setw( 9) << " InitialStep " << " ";
931 }
932 G4cout << G4endl;
933 }
934
935 // ---------------------------------------------------------------------------
936
937 void G4MagInt_Driver::PrintStatisticsReport()
938 {
939 G4int noPrecBig = 6;
940 G4long oldPrec = G4cout.precision(noPrecBig);
941
942 G4cout << "G4MagInt_Driver Statistics of steps undertaken. " << G4endl;
943 G4cout << "G4MagInt_Driver: Number of Steps: "
944 << " Total= " << fNoTotalSteps
945 << " Bad= " << fNoBadSteps
946 << " Small= " << fNoSmallSteps
947 << " Non-initial small= " << (fNoSmallSteps-fNoInitialSmallSteps)
948 << G4endl;
949 G4cout.precision(oldPrec);
950 }
951
952 // ---------------------------------------------------------------------------
953
954 void G4MagInt_Driver::SetSmallestFraction(G4double newFraction)
955 {
956 if( (newFraction > 1.e-16) && (newFraction < 1e-8) )
957 {
958 fSmallestFraction= newFraction;
959 }
960 else
961 {
962 std::ostringstream message;
963 message << "Smallest Fraction not changed. " << G4endl
964 << " Proposed value was " << newFraction << G4endl
965 << " Value must be between 1.e-8 and 1.e-16";
966 G4Exception("G4MagInt_Driver::SetSmallestFraction()",
967 "GeomField1001", JustWarning, message);
968 }
969 }
970
971 void G4MagInt_Driver::
972 GetDerivatives(const G4FieldTrack& y_curr, G4double* dydx) const
973 {
974 G4double ytemp[G4FieldTrack::ncompSVEC];
975 y_curr.DumpToArray(ytemp);
976 pIntStepper->RightHandSide(ytemp, dydx);
977 // Avoid virtual call for GetStepper
978 // Was: GetStepper()->ComputeRightHandSide(ytemp, dydx);
979 }
980
981 void G4MagInt_Driver::GetDerivatives(const G4FieldTrack& track,
982 G4double dydx[],
983 G4double field[]) const
984 {
985 G4double ytemp[G4FieldTrack::ncompSVEC];
986 track.DumpToArray(ytemp);
987 pIntStepper->RightHandSide(ytemp, dydx, field);
988 }
989
990 G4EquationOfMotion* G4MagInt_Driver::GetEquationOfMotion()
991 {
992 return pIntStepper->GetEquationOfMotion();
993 }
994
995 void G4MagInt_Driver::SetEquationOfMotion(G4EquationOfMotion *equation)
996 {
997 pIntStepper->SetEquationOfMotion(equation);
998 }
999
1000 const G4MagIntegratorStepper* G4MagInt_Driver::GetStepper() const
1001 {
1002 return pIntStepper;
1003 }
1004
1005 G4MagIntegratorStepper* G4MagInt_Driver::GetStepper()
1006 {
1007 return pIntStepper;
1008 }
1009
1010 void G4MagInt_Driver::
1011 RenewStepperAndAdjust(G4MagIntegratorStepper* pItsStepper)
1012 {
1013 pIntStepper = pItsStepper;
1014 ReSetParameters();
1015 }
1016
1017 void G4MagInt_Driver::StreamInfo( std::ostream& os ) const
1018 {
1019 os << "State of G4MagInt_Driver: " << std::endl;
1020 os << " Max number of Steps = " << fMaxNoSteps
1021 << " (base # = " << fMaxStepBase << " )" << std::endl;
1022 os << " Safety factor = " << safety << std::endl;
1023 os << " Power - shrink = " << pshrnk << std::endl;
1024 os << " Power - grow = " << pgrow << std::endl;
1025 os << " threshold (errcon) = " << errcon << std::endl;
1026
1027 os << " fMinimumStep = " << fMinimumStep << std::endl;
1028 os << " Smallest Fraction = " << fSmallestFraction << std::endl;
1029
1030 os << " No Integrat Vars = " << fNoIntegrationVariables << std::endl;
1031 os << " Min No Vars = " << fMinNoVars << std::endl;
1032 os << " Num-Vars = " << fNoVars << std::endl;
1033
1034 os << " verbose level = " << fVerboseLevel << std::endl;
1035 os << " Reintegrates = " << DoesReIntegrate() << std::endl;
1036 }
1037
1038 void PrintInfo( const G4MagInt_Driver & magDrv, std::ostream& os )
1039 {
1040 os << "State of G4MagInt_Driver: " << std::endl;
1041 os << " Max number of Steps = " << magDrv.GetMaxNoSteps();
1042 // << " (base # = " << magDrv.fMaxStepBase << " )" << std::endl;
1043 os << " Safety factor = " << magDrv.GetSafety() << std::endl;
1044 os << " Power - shrink = " << magDrv.GetPshrnk() << std::endl;
1045 os << " Power - grow = " << magDrv.GetPgrow() << std::endl;
1046 os << " threshold (errcon) = " << magDrv.GetErrcon() << std::endl;
1047
1048 os << " fMinimumStep = " << magDrv.GetHmin() << std::endl;
1049 os << " Smallest Fraction = " << magDrv.GetSmallestFraction() << std::endl;
1050
1051 /*****
1052 os << " No Integrat Vars = " << magDrv.GetNoIntegrationVariables << std::endl;
1053 os << " Min No Vars = " << magDrv.GetMinNoVars << std::endl;
1054 os << " Num-Vars = " << magDrv.GetNoVars << std::endl;
1055 *****/
1056 os << " verbose level = " << magDrv.GetVerboseLevel() << std::endl;
1057 os << " Reintegrates = " << magDrv.DoesReIntegrate() << std::endl;
1058 }
1059