#include "TEveTrackPropagator.h"
#include "TEveTrack.h"
#include "TMath.h"
#include <cassert>
namespace
{
const Float_t kBMin = 1e-6;
const Float_t kPtMinSqr = 1e-20;
const Float_t kAMin = 1e-10;
const Float_t kStepEps = 1e-3;
}
TEveTrackPropagator::Helix_t::Helix_t() :
fCharge(0), fMinAng(45), fDelta(0.1),
fMaxStep(20.f), fCurrentStep(20.f),
fPhi(0), fValid(kFALSE),
fLam(-1), fR(-1), fPhiStep(-1), fSin(-1), fCos(-1),
fPtMag(-1), fPlDir(-1), fLStep(-1)
{
}
void TEveTrackPropagator::Helix_t::UpdateHelix(const TEveVector& p, const TEveVector& b, Bool_t fullUpdate)
{
fB = b;
fE1 = b;
fE1.Normalize();
fPlDir = p.Dot(fE1);
fPl = fE1*fPlDir;
fPt = p - fPl;
fPtMag = fPt.Mag();
fE2 = fPt;
fE2.Normalize();
TMath::Cross(fE1.Arr(), fE2.Arr(), fE3.Arr());
if (fCharge < 0) fE3.NegateXYZ();
if (fullUpdate)
{
using namespace TMath;
Float_t a = fgkB2C * b.Mag() * Abs(fCharge);
if (a > kAMin && fPtMag*fPtMag > kPtMinSqr)
{
fValid = kTRUE;
fR = Abs(fPtMag / a);
fLam = fPl.Mag() / fPtMag;
if (fPlDir < 0) fLam = - fLam;
fPhiStep = fMinAng * DegToRad();
if (fDelta < fR)
{
Float_t ang = 2*ACos(1 - fDelta/fR);
if (ang < fPhiStep) fPhiStep = ang;
}
fCurrentStep = fR*fPhiStep*(1 + fLam*fLam);
if (fCurrentStep > fMaxStep)
fPhiStep *= (fMaxStep/fCurrentStep);
fLStep = fR*fPhiStep*fLam;
fSin = Sin(fPhiStep);
fCos = Cos(fPhiStep);
}
else
{
fValid = kFALSE;
}
}
}
void TEveTrackPropagator::Helix_t::Step(const TEveVector4& v, const TEveVector& p,
TEveVector4& vOut, TEveVector& pOut)
{
vOut = v;
if (fValid)
{
TEveVector d = fE2*(fR*fSin) + fE3*(fR*(1-fCos)) + fE1*fLStep;
vOut += d;
vOut.fT += fLStep;
pOut = fPl + fE2*(fPtMag*fCos) + fE3*(fPtMag*fSin);
fPhi += fPhiStep;
}
else
{
vOut += p * (fMaxStep / p.Mag());
pOut = p;
}
}
void TEveTrackPropagator::Helix_t::UpdateRK(const TEveVector& p, const TEveVector& b)
{
if (fCharge)
{
fValid = kTRUE;
fB = b;
fPlDir = p.Dot(fB);
}
else
{
fValid = kFALSE;
}
}
ClassImp(TEveTrackPropagator);
Float_t TEveTrackPropagator::fgDefMagField = 0.5;
const Float_t TEveTrackPropagator::fgkB2C = 0.299792458e-2;
TEveTrackPropagator TEveTrackPropagator::fgDefStyle;
TEveTrackPropagator::TEveTrackPropagator(const char* n, const char* t,
TEveMagField *field) :
TEveElementList(n, t),
TEveRefBackPtr(),
fStepper(kHelix),
fMagFieldObj(field),
fMaxR (350),
fMaxZ (450),
fNMax (4096),
fMaxOrbs (0.5),
fEditPathMarks (kTRUE),
fFitDaughters (kTRUE),
fFitReferences (kTRUE),
fFitDecay (kTRUE),
fFitCluster2Ds (kTRUE),
fRnrDaughters (kFALSE),
fRnrReferences (kFALSE),
fRnrDecay (kFALSE),
fRnrFV (kFALSE),
fPMAtt(),
fFVAtt(),
fV()
{
fPMAtt.SetMarkerColor(kYellow);
fPMAtt.SetMarkerStyle(2);
fPMAtt.SetMarkerSize(2);
fFVAtt.SetMarkerColor(kRed);
fFVAtt.SetMarkerStyle(4);
fFVAtt.SetMarkerSize(1.5);
if (fMagFieldObj == 0)
fMagFieldObj = new TEveMagFieldConst(0., 0., fgDefMagField);
}
TEveTrackPropagator::~TEveTrackPropagator()
{
delete fMagFieldObj;
}
void TEveTrackPropagator::OnZeroRefCount()
{
CheckReferenceCount("TEveTrackPropagator::OnZeroRefCount ");
}
void TEveTrackPropagator::CheckReferenceCount(const TEveException& eh)
{
if (fRefCount <= 0)
{
TEveElementList::CheckReferenceCount(eh);
}
}
void TEveTrackPropagator::ElementChanged(Bool_t update_scenes, Bool_t redraw)
{
TEveTrack* track;
std::list<TEveElement*>::iterator i = fBackRefs.begin();
while (i != fBackRefs.end())
{
track = dynamic_cast<TEveTrack*>(*i);
track->StampObjProps();
++i;
}
TEveElementList::ElementChanged(update_scenes, redraw);
}
void TEveTrackPropagator::InitTrack(TEveVector &v, Int_t charge)
{
fV.fX = v.fX;
fV.fY = v.fY;
fV.fZ = v.fZ;
fPoints.push_back(fV);
fH.fPhi = 0;
fH.fCharge = charge;
}
void TEveTrackPropagator::ResetTrack()
{
fPoints.clear();
fH.fPhi = 0;
}
Bool_t TEveTrackPropagator::GoToVertex(TEveVector& v, TEveVector& p)
{
if (fStepper == kHelix)
fH.UpdateHelix(p, fMagFieldObj->GetField(fV), kTRUE);
else
fH.UpdateRK(p, fMagFieldObj->GetField(fV));
if ((v-fV).Mag() < kStepEps)
{
fPoints.push_back(v);
return kTRUE;
}
return fH.fValid ? LoopToVertex(v, p): LineToVertex(v);
}
void TEveTrackPropagator::GoToBounds(TEveVector& p)
{
if (fStepper == kHelix)
fH.UpdateHelix(p, fMagFieldObj->GetField(fV), kTRUE);
else
fH.UpdateRK(p, fMagFieldObj->GetField(fV));
fH.fValid ? LoopToBounds(p): LineToBounds(p);
}
void TEveTrackPropagator::Step(TEveVector4 &v, TEveVector &p, TEveVector4 &vOut, TEveVector &pOut)
{
if (fStepper == kHelix)
{
fH.UpdateHelix(p, fMagFieldObj->GetField(v), !fMagFieldObj->IsConst());
fH.Step(v, p, vOut, pOut);
}
else
{
fH.UpdateRK(p, fMagFieldObj->GetField(v));
Double_t vecRKIn[7];
vecRKIn[0] = v.fX;
vecRKIn[1] = v.fY;
vecRKIn[2] = v.fZ;
Float_t nm = 1/p.Mag();
vecRKIn[3] = p.fX*nm;
vecRKIn[4] = p.fY*nm;
vecRKIn[5] = p.fZ*nm;
vecRKIn[6] = p.Mag();
Double_t vecRKOut[7];
OneStepRungeKutta(fH.fCharge, fH.fMaxStep, vecRKIn, vecRKOut);
vOut.fX = vecRKOut[0];
vOut.fY = vecRKOut[1];
vOut.fZ = vecRKOut[2];
vOut.fT += fH.fMaxStep;
Double_t pm = vecRKOut[6];
pOut.fX = vecRKOut[3]*pm;
pOut.fY = vecRKOut[4]*pm;
pOut.fZ = vecRKOut[5]*pm;
}
}
void TEveTrackPropagator::LoopToBounds(TEveVector& p)
{
const Float_t maxRsq = fMaxR*fMaxR;
TEveVector4 currV(fV);
TEveVector4 forwV(fV);
TEveVector forwP (p);
Int_t np = fPoints.size();
Float_t maxPhi = fMaxOrbs*TMath::TwoPi();
while (fH.fPhi < maxPhi && np<fNMax)
{
Step(currV, p, forwV, forwP);
if (forwV.Perp2() > maxRsq)
{
Float_t t = (fMaxR - currV.R()) / (forwV.R() - currV.R());
if (t < 0 || t > 1)
{
Warning("TEveTrackPropagator::HelixToBounds",
"In MaxR crossing expected t>=0 && t<=1: t=%f, r1=%f, r2=%f, MaxR=%f.",
t, currV.R(), forwV.R(), fMaxR);
return;
}
TEveVector d(forwV);
d -= currV;
d *= t;
d += currV;
fPoints.push_back(d);
return;
}
else if (TMath::Abs(forwV.fZ) > fMaxZ)
{
Float_t t = (fMaxZ - TMath::Abs(currV.fZ)) / TMath::Abs((forwV.fZ - currV.fZ));
if (t < 0 || t > 1)
{
Warning("TEveTrackPropagator::HelixToBounds",
"In MaxZ crossing expected t>=0 && t<=1: t=%f, z1=%f, z2=%f, MaxZ=%f.",
t, currV.fZ, forwV.fZ, fMaxZ);
return;
}
TEveVector d(forwV -currV);
d *= t;
d +=currV;
fPoints.push_back(d);
return;
}
currV = forwV;
p = forwP;
fPoints.push_back(currV);
np++;
}
}
Bool_t TEveTrackPropagator::LoopToVertex(TEveVector& v, TEveVector& p)
{
const Float_t maxRsq = fMaxR*fMaxR;
TEveVector4 currV(fV);
TEveVector4 forwV(fV);
TEveVector forwP(p);
Int_t first_point = fPoints.size();
Int_t np = first_point;
do
{
Step(currV, p, forwV, forwP);
if (PointOverVertex(v, forwV))
break;
if (IsOutsideBounds(forwV, maxRsq, fMaxZ))
{
fV = currV;
return kFALSE;
}
fPoints.push_back(forwV);
currV = forwV;
p = forwP;
++np;
} while (np < fNMax);
if (np > first_point)
{
TEveVector d1 = v; d1 -= currV;
TEveVector d2 = forwV; d2 -= currV;
TEveVector pln = fH.fPl;
pln.Normalize();
if (d1.Mag() > kStepEps)
{
Float_t origMaxStep = fH.fMaxStep;
fH.fMaxStep = d1.Mag();
if (fStepper == kHelix)
fH.UpdateHelix(p, fMagFieldObj->GetField(fV), kTRUE);
else
fH.UpdateRK(p, fMagFieldObj->GetField(fV));
Step(currV, p, forwV, forwP);
p = forwP;
currV = forwV;
fPoints.push_back(currV); np++;
fH.fMaxStep = origMaxStep;
TEveVector off(v); off -= currV;
off *= 1.0f / currV.fT;
for (Int_t i = first_point; i < np; ++i)
{
fPoints[i] += off * fPoints[i].fT;
}
fV = v;
return kTRUE;
}
}
fPoints.push_back(v);
fV = v;
return kTRUE;
}
Bool_t TEveTrackPropagator::LineToVertex(TEveVector& v)
{
TEveVector4 currV = v;
currV.fX = v.fX;
currV.fY = v.fY;
currV.fZ = v.fZ;
fPoints.push_back(currV);
fV = v;
return kTRUE;
}
void TEveTrackPropagator::LineToBounds(TEveVector& p)
{
Float_t tZ = 0, tR = 0, tB = 0;
if (p.fZ > 0) {
tZ = (fMaxZ - fV.fZ)/p.fZ;
}
else if (p.fZ < 0 ) {
tZ = (-1)*(fMaxZ + fV.fZ)/p.fZ;
}
Double_t a = p.fX*p.fX + p.fY*p.fY;
Double_t b = 2*(fV.fX*p.fX + fV.fY*p.fY);
Double_t c = fV.fX*fV.fX + fV.fY*fV.fY - fMaxR*fMaxR;
Double_t d = b*b - 4*a*c;
if (d >= 0) {
Double_t sqrtD=TMath::Sqrt(d);
tR = ( -b - sqrtD )/(2*a);
if (tR < 0) {
tR = ( -b + sqrtD )/(2*a);
}
tB = tR < tZ ? tR : tZ;
} else {
tB = tZ;
}
TEveVector nv(fV.fX + p.fX*tB, fV.fY + p.fY*tB, fV.fZ+ p.fZ*tB);
LineToVertex(nv);
}
Bool_t TEveTrackPropagator::HelixIntersectPlane(const TEveVector& p,
const TEveVector& point,
const TEveVector& normal,
TEveVector& itsect)
{
TEveVector pos(fV);
TEveVector mom(p);
if (fMagFieldObj->IsConst())
fH.UpdateHelix(mom, fMagFieldObj->GetField(pos), kFALSE);
TEveVector n(normal);
TEveVector delta = pos - point;
Float_t d = delta.Dot(n);
if (d > 0) {
n.NegateXYZ();
d = -d;
}
TEveVector4 forwV;
TEveVector forwP;
TEveVector4 pos4(pos);
while (1)
{
Step(pos4, mom, forwV , forwP);
Float_t new_d = (forwV - point).Dot(n);
if (new_d < d)
{
Warning("TEveTrackPropagator::HelixIntersectPlane", "going away from the plane.");
return kFALSE;
}
if (new_d > 0)
{
delta = forwV - pos;
itsect = pos + delta * (d / (d - new_d));
return kTRUE;
}
pos4 = forwV;
mom = forwP;
}
}
Bool_t TEveTrackPropagator::LineIntersectPlane(const TEveVector& p,
const TEveVector& point,
const TEveVector& normal,
TEveVector& itsect)
{
TEveVector pos(fV.fX, fV.fY, fV.fZ);
TEveVector delta = pos - point;
Float_t d = delta.Dot(normal);
if (d == 0) {
itsect = pos;
return kTRUE;
}
Float_t t = (p.Dot(normal)) / d;
if (t < 0) {
return kFALSE;
} else {
itsect = pos + p*t;
return kTRUE;
}
}
Bool_t TEveTrackPropagator::IntersectPlane(const TEveVector& p,
const TEveVector& point,
const TEveVector& normal,
TEveVector& itsect)
{
if (fH.fCharge && fMagFieldObj && p.Perp2() > kPtMinSqr)
return HelixIntersectPlane(p, point, normal, itsect);
else
return LineIntersectPlane(p, point, normal, itsect);
}
void TEveTrackPropagator::FillPointSet(TEvePointSet* ps) const
{
Int_t size = TMath::Min(fNMax, (Int_t)fPoints.size());
ps->Reset(size);
for (Int_t i = 0; i < size; ++i)
{
const TEveVector4& v = fPoints[i];
ps->SetNextPoint(v.fX, v.fY, v.fZ);
}
}
void TEveTrackPropagator::RebuildTracks()
{
TEveTrack* track;
std::list<TEveElement*>::iterator i = fBackRefs.begin();
while (i != fBackRefs.end())
{
track = dynamic_cast<TEveTrack*>(*i);
track->MakeTrack();
track->StampObjProps();
++i;
}
}
void TEveTrackPropagator::SetMagField(Float_t bX, Float_t bY, Float_t bZ)
{
if (fMagFieldObj) delete fMagFieldObj;
fMagFieldObj = new TEveMagFieldConst(bX, bY, bZ);
RebuildTracks();
}
void TEveTrackPropagator::SetMagFieldObj(TEveMagField *mff)
{
if (fMagFieldObj) delete fMagFieldObj;
fMagFieldObj = mff;
RebuildTracks();
}
void TEveTrackPropagator::PrintMagField(Float_t x, Float_t y, Float_t z) const
{
if (fMagFieldObj) fMagFieldObj->PrintField(x, y, z);
}
void TEveTrackPropagator::SetMaxR(Float_t x)
{
fMaxR = x;
RebuildTracks();
}
void TEveTrackPropagator::SetMaxZ(Float_t x)
{
fMaxZ = x;
RebuildTracks();
}
void TEveTrackPropagator::SetMaxOrbs(Float_t x)
{
fMaxOrbs = x;
RebuildTracks();
}
void TEveTrackPropagator::SetMinAng(Float_t x)
{
fH.fMinAng = x;
RebuildTracks();
}
void TEveTrackPropagator::SetDelta(Float_t x)
{
fH.fDelta = x;
RebuildTracks();
}
void TEveTrackPropagator::SetFitDaughters(Bool_t x)
{
fFitDaughters = x;
RebuildTracks();
}
void TEveTrackPropagator::SetFitReferences(Bool_t x)
{
fFitReferences = x;
RebuildTracks();
}
void TEveTrackPropagator::SetFitDecay(Bool_t x)
{
fFitDecay = x;
RebuildTracks();
}
void TEveTrackPropagator::SetFitCluster2Ds(Bool_t x)
{
fFitCluster2Ds = x;
RebuildTracks();
}
void TEveTrackPropagator::SetRnrDecay(Bool_t rnr)
{
fRnrDecay = rnr;
RebuildTracks();
}
void TEveTrackPropagator::SetRnrCluster2Ds(Bool_t rnr)
{
fRnrCluster2Ds = rnr;
RebuildTracks();
}
void TEveTrackPropagator::SetRnrDaughters(Bool_t rnr)
{
fRnrDaughters = rnr;
RebuildTracks();
}
void TEveTrackPropagator::SetRnrReferences(Bool_t rnr)
{
fRnrReferences = rnr;
RebuildTracks();
}
void TEveTrackPropagator::SetMaxStep(Float_t x)
{
fH.fMaxStep = x;
RebuildTracks();
}
void TEveTrackPropagator::OneStepRungeKutta(Double_t charge, Double_t step,
Double_t* vect, Double_t* vout)
{
Double_t h2, h4, f[4];
Double_t xyzt[3], a, b, c, ph,ph2;
Double_t secxs[4],secys[4],seczs[4],hxp[3];
Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
Double_t est, at, bt, ct, cba;
Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
Double_t x;
Double_t y;
Double_t z;
Double_t xt;
Double_t yt;
Double_t zt;
Double_t maxit = 10;
Double_t maxcut = 11;
const Double_t hmin = 1e-4;
const Double_t kdlt = 1e-3;
const Double_t kdlt32 = kdlt/32.;
const Double_t kthird = 1./3.;
const Double_t khalf = 0.5;
const Double_t kec = 2.9979251e-3;
const Double_t kpisqua = 9.86960440109;
const Int_t kix = 0;
const Int_t kiy = 1;
const Int_t kiz = 2;
const Int_t kipx = 3;
const Int_t kipy = 4;
const Int_t kipz = 5;
Int_t iter = 0;
Int_t ncut = 0;
for(Int_t j = 0; j < 7; j++)
vout[j] = vect[j];
Double_t pinv = kec * charge / vect[6];
Double_t tl = 0.;
Double_t h = step;
Double_t rest;
do {
rest = step - tl;
if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
f[0] = -fH.fB.fX;
f[1] = -fH.fB.fY;
f[2] = -fH.fB.fZ;
x = vout[0];
y = vout[1];
z = vout[2];
a = vout[3];
b = vout[4];
c = vout[5];
h2 = khalf * h;
h4 = khalf * h2;
ph = pinv * h;
ph2 = khalf * ph;
secxs[0] = (b * f[2] - c * f[1]) * ph2;
secys[0] = (c * f[0] - a * f[2]) * ph2;
seczs[0] = (a * f[1] - b * f[0]) * ph2;
ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
if (ang2 > kpisqua) break;
dxt = h2 * a + h4 * secxs[0];
dyt = h2 * b + h4 * secys[0];
dzt = h2 * c + h4 * seczs[0];
xt = x + dxt;
yt = y + dyt;
zt = z + dzt;
est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
if (est > h) {
if (ncut++ > maxcut) break;
h *= khalf;
continue;
}
xyzt[0] = xt;
xyzt[1] = yt;
xyzt[2] = zt;
fH.fB = fMagFieldObj->GetField(xt, yt, zt);
f[0] = -fH.fB.fX;
f[1] = -fH.fB.fY;
f[2] = -fH.fB.fZ;
at = a + secxs[0];
bt = b + secys[0];
ct = c + seczs[0];
secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
secys[1] = (ct * f[0] - at * f[2]) * ph2;
seczs[1] = (at * f[1] - bt * f[0]) * ph2;
at = a + secxs[1];
bt = b + secys[1];
ct = c + seczs[1];
secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
secys[2] = (ct * f[0] - at * f[2]) * ph2;
seczs[2] = (at * f[1] - bt * f[0]) * ph2;
dxt = h * (a + secxs[2]);
dyt = h * (b + secys[2]);
dzt = h * (c + seczs[2]);
xt = x + dxt;
yt = y + dyt;
zt = z + dzt;
at = a + 2.*secxs[2];
bt = b + 2.*secys[2];
ct = c + 2.*seczs[2];
est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
if (est > 2.*TMath::Abs(h)) {
if (ncut++ > maxcut) break;
h *= khalf;
continue;
}
xyzt[0] = xt;
xyzt[1] = yt;
xyzt[2] = zt;
fH.fB = fMagFieldObj->GetField(xt, yt, zt);
f[0] = -fH.fB.fX;
f[1] = -fH.fB.fY;
f[2] = -fH.fB.fZ;
z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
secxs[3] = (bt*f[2] - ct*f[1])* ph2;
secys[3] = (ct*f[0] - at*f[2])* ph2;
seczs[3] = (at*f[1] - bt*f[0])* ph2;
a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
+ TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
+ TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
if (est > kdlt && TMath::Abs(h) > hmin) {
if (ncut++ > maxcut) break;
h *= khalf;
continue;
}
ncut = 0;
if (iter++ > maxit) break;
tl += h;
if (est < kdlt32)
h *= 2.;
cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
vout[0] = x;
vout[1] = y;
vout[2] = z;
vout[3] = cba*a;
vout[4] = cba*b;
vout[5] = cba*c;
rest = step - tl;
if (step < 0.) rest = -rest;
if (rest < 1.e-5*TMath::Abs(step)) return;
} while(1);
f1 = f[0];
f2 = f[1];
f3 = f[2];
f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
rho = -f4*pinv;
tet = rho * step;
hnorm = 1./f4;
f1 = f1*hnorm;
f2 = f2*hnorm;
f3 = f3*hnorm;
hxp[0] = f2*vect[kipz] - f3*vect[kipy];
hxp[1] = f3*vect[kipx] - f1*vect[kipz];
hxp[2] = f1*vect[kipy] - f2*vect[kipx];
hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
rho1 = 1./rho;
sint = TMath::Sin(tet);
cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
g1 = sint*rho1;
g2 = cost*rho1;
g3 = (tet-sint) * hp*rho1;
g4 = -cost;
g5 = sint;
g6 = cost * hp;
vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
fH.fPhi += tet;
}
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