def run(self): """A function to run a shower for the given LHEF file.""" ##For e+e- -> qqBar (massless). __reader = LHEFHandlers.LHEFReader(self.__toLoad) self.__numEvents = __reader.get_number_events() __writer = LHEFHandlers.LHEFShowerWriter(__reader,self.__numEvents) __alertEvery = self.__numEvents/10 if __alertEvery > 1000: ##Slow enough to want to see something is happening! __alertEvery = 1000 elif (__alertEvery == 0): ##i.e < 10 events. __alertEvery = 1 for __eventIndex in range(self.__numEvents): if (__eventIndex%__alertEvery == 0): if (__eventIndex == 0): print "Begin showering...\n" else: print "Showering event", __eventIndex __MEParticle1 = __reader.get_event_particle(__eventIndex,0) __MEParticle2 = __reader.get_event_particle(__eventIndex,1) __EIn = __MEParticle1[0] + __MEParticle2[0] __S123In = kinematics.Sijk([__MEParticle1.get_four_momentum(), __MEParticle2.get_four_momentum()]) __particlesIn = [__MEParticle1,__MEParticle2] __showerParticle1 = __reader.get_event_particle(__eventIndex,2) __showerParticle2 = __reader.get_event_particle(__eventIndex,3) __showeri = showers.qqBarShower(__showerParticle1,__showerParticle2,self.__activeQCodes) __showeri.run_shower() __particlesOut = __showeri.export_results() __EOut = 0.0 __fourVectorsOut = [] for __p in __particlesOut: __ePV = __p.get_four_momentum() __EOut += __ePV[0] __fourVectorsOut.append(__ePV) assert precision.check_numbers_equal(kinematics.Sijk(__fourVectorsOut),__S123In) assert precision.check_numbers_equal(__EIn,__EOut) __trials, __muf2, __mur2 = __reader.get_event_trials(__eventIndex), __reader.get_event_muf2(__eventIndex), __reader.get_event_mur2(__eventIndex) __processID, __weight = __reader.get_event_process_ID(__eventIndex), __reader.get_event_weight(__eventIndex) __scale, __alphaEM = __reader.get_event_scale(__eventIndex), __reader.get_event_alphaEM(__eventIndex) __alphaS = __reader.get_event_alphaS(__eventIndex) __writer.add_event(__trials,__muf2,__mur2,__processID,__weight,__scale,__alphaEM,__alphaS,__particlesIn,__particlesOut) __writer.save() __numGluonsSplit = counters.gluonSplitCounter.counted() print "\nThere were", counters.gluonProdCounter.counted(), "gluons produced!" print "\nThere were", __numGluonsSplit, "gluons split!" print "\nThere were", counters.photonProdCounter.counted(), "photons produced!" print "\nThere were", counters.kPerpProdWarningCounter.counted(), "warnings for E1 or E3 < E2!\n" print "\n---------------------" print "Quark content report:" print "---------------------" __sumPercent = 0.0 for __aQCode in [1,2,3,4,5,6]: __qName = particleData.knownParticles.get_name_from_code(__aQCode) if precision.check_numbers_equal(__numGluonsSplit,0.0): __qPercent = 0.0 else: __qPercent = chains.producedQuarkCodes.output().count(__aQCode)*100.0/__numGluonsSplit __sumPercent += __qPercent print str(__qPercent) + "% are " + __qName + "s." print "This adds up to " + str(__sumPercent) + "%." assertions.pause(__name__)
def produce_new_vectors(v1, v3, PperpSquared, y):
"""A function to boost two vectors, perform the kinematics and return the tResults after boosting back."""
##Requires v3 to be the recoiling vector, consistent with all kinematics in this project.
assert (fourVectors.check_is_fourVector(v1)
and fourVectors.check_is_fourVector(v3))
assert (v1.__nonzero__() and v3.__nonzero__())
assert assertions.all_are_numbers([PperpSquared, y])
__energyIn = v1[0] + v3[
0] ##This is in the 'lab frame' as these are never actually boosted in the code.
__S123, __Pperp = Sijk([v1.copy(), v3.copy()]), math.sqrt(PperpSquared)
__boostRotate = lorentz.boostAndRotate(
v1.copy(), v3.copy(),
1) ##Given v3 as vector to recoil so need index 1 here.
__nBRV1, __nBRV2, __nBRV3 = calculate_split_ps(__S123, __Pperp, y)
assert precision.check_numbers_equal(0.0,
__nBRV1[3] + __nBRV2[3] + __nBRV3[3])
__nV1, __nV2, __nV3 = __boostRotate / __nBRV1, __boostRotate / __nBRV2, __boostRotate / __nBRV3
##Must also check energy out in the 'lab' frame too as not a Lorentz invariant quantity.
__energyOut = __nV1[0] + __nV2[0] + __nV3[0]
__energyDifference = __energyIn - __energyOut
__nV2 = fix_energy_difference(__energyDifference, __nV2)
##Check conservation rules:
assert precision.check_numbers_equal(__energyIn, __energyOut)
assert precision.check_numbers_equal(
__S123, Sijk([__nV1.copy(), __nV2.copy(),
__nV3.copy()]))
##No check for any momentums here as no longer have to sum to zero in this frame.
return __nV1, __nV2, __nV3
def calculate_split_ps(S123, Pperp, y):
"""A function to calculate the new p1,p2,p3 four-vectors following a dipole splitting."""
##Letting p2 take +Pperp and p1 take -Pperp by convention.
assert assertions.all_are_numbers([S123, Pperp, y])
assert ((S123 > 0.0) and (Pperp > 0.0))
__E1, __E2 = calculate_E1(S123, Pperp, y), calculate_E2(S123, Pperp, y)
__E3, __kPerp = calculate_E3(S123, Pperp,
y), calculate_kPerp(S123, Pperp, y)
##Store all energies produced for plotting graphs after showering:
e1s.store(__E1)
e2s.store(__E2)
e3s.store(__E3)
__randomPhi, __newP1 = get_random_phi(), fourVectors.fourVector(
0.0, 0.0, 0.0, 0.0)
__newP2, __newP3 = fourVectors.fourVector(0.0, 0.0, 0.0,
0.0), fourVectors.fourVector(
0.0, 0.0, 0.0, 0.0)
assert (0.0 < __randomPhi and __randomPhi < 2.0 * math.pi)
##Populate the first vector:
__newP1[0] = __E1
__newP1[1] = (-1.0) * __kPerp * math.cos(__randomPhi)
__newP1[2] = (-1.0) * __kPerp * math.sin(__randomPhi)
__newP1[3] = math.sqrt((__E1 * __E1) - (__kPerp * __kPerp))
assert ((__newP1[0] > 0.0) and (__newP1[3] > 0.0))
##Populate the second vector:
__newP2[0] = __E2
__newP2[1] = __kPerp * math.cos(__randomPhi)
__newP2[2] = __kPerp * math.sin(__randomPhi)
__newP2[3] = math.sqrt((__E2 * __E2) - (__kPerp * __kPerp))
assert (__newP2[0] > 0.0)
##Populate the third vector. Entries 1 & 2 already 0 as required:
__newP3[0] = __E3
__newP3[3] = (-1.0) * __E3
assert ((__newP3[0] > 0.0) and (__newP3[3] < 0.0))
##Log x's for a produced particle for plotting after showering:
tX1s.store(calculate_x1(S123, Pperp, y))
tX3s.store(calculate_x3(S123, Pperp, y))
##Check the direction of the produced particle is consistent with parallel momentum conservation.
##This allows for different recoil configurations.
if precision.check_numbers_equal(0.0,
__newP1[3] + __newP2[3] + __newP3[3]):
return __newP1, __newP2, __newP3
elif precision.check_numbers_equal(0.0,
__newP1[3] - __newP2[3] + __newP3[3]):
__newP2[3] = -__newP2[3]
return __newP1, __newP2, __newP3
elif precision.check_numbers_equal(0.0,
-__newP1[3] + __newP2[3] + __newP3[3]):
__newP1[3] = -__newP1[3]
return __newP1, __newP2, __newP3
def scaled_quark_directions(S123,theta): """A function to return two quark directional vectors scaled to match a given S123 value.""" __cE = constants.cut_off_energy() assert ((type(S123) == float) and (S123 > __cE*__cE)) assert((type(theta) == float) and (0.0 <= theta) and (theta <= math.pi)) __E = math.sqrt(S123)/2.0 __dV1, __dV2 = produce_quark_directions(S123,theta) __magnitude = __dV1.calculate_cartesian_magnitude() __scale = __E/__magnitude __dV1 *= __scale __dV2 *= __scale __dV1[0], __dV2[0] = __E, __E ##Check massless: assert (precision.check_numbers_equal(__dV1*__dV1,0.0) and precision.check_numbers_equal(__dV2*__dV2,0.0)) return __dV1, __dV2
def get_quark_weights(S123, posQuarkCodes, cosTheta=None):
"""A function to calculate the quark weights to beused by the ME generator."""
__cE = constants.cut_off_energy()
assert ((type(S123) == float) and (S123 > __cE * __cE))
assert (type(posQuarkCodes) == list)
assert (((type(cosTheta) == float) and (-1.0 <= cosTheta) and
(cosTheta <= 1.0)) or (cosTheta == None))
##Using dictionary not list so you don't have to assume an order of the quark codes.
__hardCodedQWeights = {
1: 16.05764282,
2: 11.94029851,
3: 16.05764282,
4: 24.32321153,
5: 31.62120432
}
__qWeights = {} ##Empty dictionary initiated.
for __qCode in posQuarkCodes: ##Uses the quark codes given to weight for the chosen set.
if (cosTheta == None):
__qWeights[__qCode] = __hardCodedQWeights[
__qCode] ##Only take the hard coded ones required so normalisation works.
else:
__qWeights[__qCode] = calc_f_for_cos_theta(S123, __qCode, cosTheta)
__total = sum(__qWeights.itervalues())
__qWeights.update(
(x, y / __total) for x, y in __qWeights.items()) ##Normalise them
assert precision.check_numbers_equal(
sum(__qWeights.itervalues()),
1.0) ##i.e they should now be normalised to 1.
return __qWeights
def scaled_quark_directions(S123, theta):
"""A function to return two quark directional vectors scaled to match a given S123 value."""
__cE = constants.cut_off_energy()
assert ((type(S123) == float) and (S123 > __cE * __cE))
assert ((type(theta) == float) and (0.0 <= theta) and (theta <= math.pi))
__E = math.sqrt(S123) / 2.0
__dV1, __dV2 = produce_quark_directions(S123, theta)
__magnitude = __dV1.calculate_cartesian_magnitude()
__scale = __E / __magnitude
__dV1 *= __scale
__dV2 *= __scale
__dV1[0], __dV2[0] = __E, __E
##Check massless:
assert (precision.check_numbers_equal(__dV1 * __dV1, 0.0)
and precision.check_numbers_equal(__dV2 * __dV2, 0.0))
return __dV1, __dV2
def __eq__(self, other):
"""A function to check whether two four-vectors are equal up to the code precision."""
assert check_is_fourVector(other)
assert (self.__nonzero__() and other.__nonzero__())
for __i11 in range(4):
if not precision.check_numbers_equal(self[__i11], other[__i11]):
return False
return True
def zero_or(value): """A function to see if a value can be set to 0.0 when writing an LHEF file.""" ##Main use is to remove -ve energies that are actually zero with the code precision. assert (type(value) == float) if precision.check_numbers_equal(value,0.0): return 0.0 else: return value
def __eq__(self,other): """A function to check whether two four-vectors are equal up to the code precision.""" assert check_is_fourVector(other) assert (self.__nonzero__() and other.__nonzero__()) for __i11 in range(4): if not precision.check_numbers_equal(self[__i11],other[__i11]): return False return True
def zero_or(value):
"""A function to see if a value can be set to 0.0 when writing an LHEF file."""
##Main use is to remove -ve energies that are actually zero with the code precision.
assert (type(value) == float)
if precision.check_numbers_equal(value, 0.0):
return 0.0
else:
return value
def add_event(self,trials,muf2,mur2,processID,weight,scale,alphaEM,alphaS,particlesIn,particlesOut):
"""A function to convert a produced particles data to LHEF and add to the writer."""
assert ((type(trials) == int) or (isinstance(trials, basestring)))
assert ((type(muf2) == int) or (type(muf2) == float) or (isinstance(muf2, basestring)))
assert ((type(mur2) == int) or (type(mur2) == float) or (isinstance(mur2, basestring)))
assert ((type(processID) == int) or (isinstance(processID, basestring)))
assert ((type(weight) == float) or (type(weight) == int) or (isinstance(weight, basestring)))
assert ((type(scale) == float) or (isinstance(scale, basestring)))
assert ((type(alphaEM) == float) or (isinstance(alphaEM, basestring)))
assert ((type(alphaS) == float) or (isinstance(alphaS, basestring)))
self.__numProdLogger.store(len(particlesOut) - 2) ##Log number of produced partons per event.
if (self.__topWritten == False):
self.write_top()
self.__haveEvents = True ##Only called once here.
__listOfParticles = particlesIn + particlesOut
#Currently not sorting by order of production.
#__listOfIDs = [x.get_unique_ID() for x in __listOfParticles]
#__sortedListOfParticles = [x for (y,x) in sorted(zip(__listOfIDs,__listOfParticles), key=lambda pair: pair[0])]
__sortedListOfParticles = __listOfParticles ##Replacement line to keep the chain ordering.
for particle in __sortedListOfParticles:
assert particles.check_is_particle(particle)
assert particle.__nonzero__()
__numberParticles = len(particlesIn) + len(particlesOut)
__line1 = "\n<event>" # trials='" + str(trials) + "' muf2='" + str(muf2) + "' mur2='" + str(mur2) + "'>"
__line2 = ("\n\t\t" + str(__numberParticles) + "\t" + str(processID) + "\t" + str(weight) + "\t" + str(scale))
__line2 += ("\t" + str(alphaEM) + "\t" + str(alphaS))
__inLines, __outLines = "", ""
__endLine = "\n</event>"
__zO = zero_or
__pHS = "{:." + str(constants.LHEF_DS_number_decimal_places()) + "e}"
for i, p in enumerate(__sortedListOfParticles): ##Iterate through both at once, but with particlesIn first!
if not precision.check_numbers_equal(p.get_four_momentum()*p.get_four_momentum(),0.0):
fFV = kinematics.fix_not_massless(p.get_four_momentum()) ##Adjust to make sure they are exactly massless for Pythia.
else:
fFV = p.get_four_momentum()
if i <= 1: ##Carry on as normal for first two (initial-state) particles.
__mum1, __mum2 = p.get_mother(0), p.get_mother(1)
else: ##Set all mother values to 1 and 2 as required by Pythia 8.2.
__mum1, __mum2 = 1, 2
__newLine = ("\n\t\t\t" + str(p.get_code()) + "\t" + str(p.get_status_code()) + "\t" + str(__mum1))
__newLine += ("\t" + str(__mum2) + "\t" + str(p.get_colour(0)) + "\t\t" + str(p.get_colour(1)))
__newLine += ("\t\t" + __pHS.format(__zO(fFV[1])) + "\t" + __pHS.format(__zO(fFV[2])) + "\t")
__newLine += (__pHS.format(__zO(fFV[3])) + "\t" + __pHS.format(__zO(fFV[0])) + "\t")
__newLine += (__pHS.format(__zO(p.get_mass())) + "\t" + str(__zO(p.get_width())) + "\t\t" + str(p.get_spin()))
__inLines += __newLine
__toSave = __line1 + __line2 + __inLines + __outLines + __endLine
__file = open(self.__saveName,'a') ##'a' means append to.
__file.write(__toSave)
__file.close()
self.__numberEventsSaved += 1
def get_quark_weights(S123,posQuarkCodes,cosTheta = None):
"""A function to calculate the quark weights to beused by the ME generator."""
__cE = constants.cut_off_energy()
assert ((type(S123) == float) and (S123 > __cE*__cE))
assert (type(posQuarkCodes) == list)
assert (((type(cosTheta) == float) and (-1.0 <= cosTheta) and (cosTheta <= 1.0)) or (cosTheta == None))
##Using dictionary not list so you don't have to assume an order of the quark codes.
__hardCodedQWeights = {1:16.05764282,2:11.94029851,3:16.05764282,4:24.32321153,5:31.62120432}
__qWeights = {} ##Empty dictionary initiated.
for __qCode in posQuarkCodes: ##Uses the quark codes given to weight for the chosen set.
if (cosTheta == None):
__qWeights[__qCode] = __hardCodedQWeights[__qCode] ##Only take the hard coded ones required so normalisation works.
else:
__qWeights[__qCode] = calc_f_for_cos_theta(S123,__qCode,cosTheta)
__total = sum(__qWeights.itervalues())
__qWeights.update((x, y/__total) for x, y in __qWeights.items()) ##Normalise them
assert precision.check_numbers_equal(sum(__qWeights.itervalues()),1.0) ##i.e they should now be normalised to 1.
return __qWeights
def add_event(self,trials,muf2,mur2,processID,weight,scale,alphaEM,alphaS,particlesIn,particlesOut):
"""A function to convert a produced particles data to LHEF and add to the writer."""
assert ((type(trials) == int) or (isinstance(trials, basestring)))
assert ((type(muf2) == int) or (type(muf2) == float) or (isinstance(muf2, basestring)))
assert ((type(mur2) == int) or (type(mur2) == float) or (isinstance(mur2, basestring)))
assert ((type(processID) == int) or (isinstance(processID, basestring)))
assert ((type(weight) == float) or (type(weight) == int) or (isinstance(weight, basestring)))
assert ((type(scale) == float) or (isinstance(scale, basestring)))
assert ((type(alphaEM) == float) or (isinstance(alphaEM, basestring)))
assert ((type(alphaS) == float) or (isinstance(alphaS, basestring)))
if (self.__topWritten == False):
self.write_top()
self.__haveEvents = True ##Only called once here.
__listOfParticles = particlesIn + particlesOut
__listOfIDs = [x.get_unique_ID() for x in __listOfParticles]
__sortedListOfParticles = [x for (y,x) in sorted(zip(__listOfIDs,__listOfParticles), key=lambda pair: pair[0])]
for particle in __sortedListOfParticles:
assert particles.check_is_particle(particle)
assert particle.__nonzero__()
__numberParticles = len(particlesIn) + len(particlesOut)
__line1 = "\n<event>" #trials='" + str(trials) + "' muf2='" + str(muf2) + "' mur2='" + str(mur2) + "'>"
__line2 = ("\n\t\t" + str(__numberParticles) + "\t" + str(processID) + "\t" + str(weight) + "\t" + str(scale))
__line2 += ("\t" + str(alphaEM) + "\t" + str(alphaS))
__inLines, __outLines = "", ""
__endLine = "\n</event>"
__zO = zero_or
__pHS = "{:." + str(constants.LHEF_ME_number_decimal_places()) + "e}"
for p in __sortedListOfParticles: ##Iterate through both at once, but with particlesIn first!
if not precision.check_numbers_equal(p.get_four_momentum()*p.get_four_momentum(),0.0): ##Shouldn't ever need to call it.
fFV = kinematics.fix_not_massless(p.get_four_momentum()) ##Adjust to make sure they are exactly massless for Pythia.
else:
fFV = p.get_four_momentum()
__newLine = ("\n\t\t\t" + str(p.get_code()) + "\t" + str(p.get_status_code()) + "\t" + str(p.get_mother(0)))
__newLine += ("\t" + str(p.get_mother(1)) + "\t" + str(p.get_colour(0)) + "\t\t" + str(p.get_colour(1)))
__newLine += ("\t\t" + __pHS.format(__zO(fFV[1])) + "\t" + __pHS.format(__zO(fFV[2])) + "\t")
__newLine += (__pHS.format(__zO(fFV[3])) + "\t" + __pHS.format(__zO(fFV[0])) + "\t")
__newLine += (__pHS.format(__zO(p.get_mass())) + "\t" + str(__zO(p.get_width())) + "\t\t" + str(p.get_spin()))
__inLines += __newLine
__toSave = __line1 + __line2 + __inLines + __outLines + __endLine
__file = open(self.__saveName,'a') ##'a' means append to.
__file.write(__toSave)
__file.close()
self.__numberEventsSaved += 1
def solve_sudakovs(PperpSquaredMax,S123,difCrossSecIds,code1,code2,logCrosSecs = None):
"""A function to generate a PperpSquared and y for an emission or splitting, using the Sudakov form factor."""
##Codes 1,2 still needed to get the charges for EM radiation.
##Using veto algorithm in "PYTHIA 6.0 Physics and Manual".
##And p198 of "Monte Carlo simulations of hard QCD radiation" for bivariant algorithm.
##And p16 of "Initial-state showering based on colour dipoles connected to incoming parton lines" for real y limits.
##And p5 of "Fooling around with the Sudakov veto algorithm" for multiple emission form.
assert assertions.all_are_numbers([PperpSquaredMax,S123])
assert (type(difCrossSecIds) == list)
__kQs = particleData.knownParticles.get_known_quarks()
__gC = particleData.knownParticles.get_code_from_name('gluon')
__expectedCodes = __kQs + [-x for x in __kQs] + [__gC]
assert ((code1 in __expectedCodes) and (code2 in __expectedCodes))
__cutOff = constants.cut_off_energy()*constants.cut_off_energy()
if (PperpSquaredMax < __cutOff):
return None, None, None
__notChosen1, __y, __PperpSquaredi = True, 0, assertions.force_float_number(PperpSquaredMax)
__PperpSquarediMinus1 = __PperpSquaredi
while __notChosen1: ##i += 1
__notChosen2 = True
while __notChosen2:
__R1 = random.random()
__PperpSquaredi = calc_inv_G((math.log(__R1) + calc_G(__PperpSquarediMinus1,S123)),S123)
if (__PperpSquaredi > S123/4.0): ##The maximum physically possible!
__notChosen2 = True
__PperpSquarediMinus1 = __PperpSquaredi
continue #Re-run the while loop
if (__PperpSquaredi <= __PperpSquarediMinus1): ##Don't update __PperpSquaredi if fails as would start allowing higher values!
__notChosen2 = False ##Move on
if (__PperpSquaredi < __cutOff):
return None, None, None
__R2 = random.random()
__ymin, __ymax = -0.5*math.log(S123/__PperpSquaredi), 0.5*math.log(S123/__PperpSquaredi)
__yi = calc_inv_G2(__R2*(calc_G2(__ymax) - calc_G2(__ymin)) + calc_G2(__ymin))
if not check_rapidity_allowed(S123,__PperpSquaredi,__yi): ##Veto incorrect y-range. On the boundary is allowed.
__PperpSquarediMinus1 = __PperpSquaredi
continue ##Don't accept, notChosen1 == True, while will run again.
__R3 = random.random()
__numberCSIds = len(difCrossSecIds)
__ratio = sum_cSs(difCrossSecIds,S123,__PperpSquaredi,__yi,code1,code2) / __numberCSIds*calc_g(__PperpSquaredi,__yi)
if (__ratio <= __R3):
__PperpSquarediMinus1 = __PperpSquaredi
continue ##Don't accept, notChosen1 == True, while will run again.
else:
__notChosen1 = False ##Accept.
##Prepare weights for choosing Id of process occuring:
__idWeights = {} ##Empty dictionary initiated.
for __difCrossSecId in difCrossSecIds: ##Uses the Ids given so will weight for the chosen set.
__idWeights[__difCrossSecId] = sum_cSs([__difCrossSecId],S123,__PperpSquaredi,__yi,code1,code2)
__total = sum(__idWeights.itervalues())
__idWeights.update((x, y/__total) for x, y in __idWeights.items()) ##Normalise them
assert precision.check_numbers_equal(sum(__idWeights.itervalues()),1.0) ##i.e they should now be normalised to 1.
##Choose which process:
__R4 = random.random() ##Doesn't include 1 -> using < not <= for checks is fair.
__sumSoFar = 0.0
__chosenId = None
__chosen = False
if (logCrosSecs == 1):
crossSecsGluSplit.store(qg_to_qQQBar_cS(S123,__PperpSquaredi,__yi))
crossSecsGluProd.store(qg_to_qgg_cS(S123,__PperpSquaredi,__yi))
for __difCrossSecId in difCrossSecIds:
if (not __chosen):
__sumSoFar += __idWeights[__difCrossSecId]
if (__R4 < __sumSoFar):
__chosenId = __difCrossSecId
__chosen = True
assert (not (__chosenId == None)) ##Should have chosen by now!
return __PperpSquaredi, __yi, __chosenId
pyplot.xlim(0.001, 10**6)
assertions.show_graph()
print "\nFinished testing Nf function."
assertions.pause(__name__)
##Test beta0 function:##
print "\n--------------------------------------------------\n"
print "Testing beta0 function:"
##Using N=3 version from four-loop paper which is the same as Krauss'.
for tNf1 in range(0, 7):
if (tNf1 == 4):
assertions.pause(__name__)
tExpectedBeta0 = 11.0 - (2.0 / 3.0) * tNf1
print "\nbeta0(" + str(tNf1) + ") returns:", beta0(tNf1)
print "The expected value is:", tExpectedBeta0
if precision.check_numbers_equal(beta0(tNf1), tExpectedBeta0):
print "These are equal within the code precision: Test successful!"
else:
print "Not equal: Test failed!"
print "\nFinished testing beta0 function."
assertions.pause(__name__)
##Test beta1 function:##
print "\n--------------------------------------------------\n"
print "Testing beta1 function:"
##Using N=3 version from four-loop paper which is the same as Krauss'.
for tNf2 in range(0, 7):
if (tNf2 == 4):
assertions.pause(__name__)
tExpectedBeta1 = 102.0 - (38.0 / 3.0) * tNf2
print "\nbeta1(" + str(tNf2) + ") returns:", beta1(tNf2)
def add_event(self, trials, muf2, mur2, processID, weight, scale, alphaEM,
alphaS, particlesIn, particlesOut):
"""A function to convert a produced particles data to LHEF and add to the writer."""
assert ((type(trials) == int) or (isinstance(trials, basestring)))
assert ((type(muf2) == int) or (type(muf2) == float)
or (isinstance(muf2, basestring)))
assert ((type(mur2) == int) or (type(mur2) == float)
or (isinstance(mur2, basestring)))
assert ((type(processID) == int)
or (isinstance(processID, basestring)))
assert ((type(weight) == float) or (type(weight) == int)
or (isinstance(weight, basestring)))
assert ((type(scale) == float) or (isinstance(scale, basestring)))
assert ((type(alphaEM) == float) or (isinstance(alphaEM, basestring)))
assert ((type(alphaS) == float) or (isinstance(alphaS, basestring)))
if (self.__topWritten == False):
self.write_top()
self.__haveEvents = True ##Only called once here.
__listOfParticles = particlesIn + particlesOut
__listOfIDs = [x.get_unique_ID() for x in __listOfParticles]
__sortedListOfParticles = [
x for (y, x) in sorted(zip(__listOfIDs, __listOfParticles),
key=lambda pair: pair[0])
]
for particle in __sortedListOfParticles:
assert particles.check_is_particle(particle)
assert particle.__nonzero__()
__numberParticles = len(particlesIn) + len(particlesOut)
__line1 = "\n<event>" #trials='" + str(trials) + "' muf2='" + str(muf2) + "' mur2='" + str(mur2) + "'>"
__line2 = ("\n\t\t" + str(__numberParticles) + "\t" + str(processID) +
"\t" + str(weight) + "\t" + str(scale))
__line2 += ("\t" + str(alphaEM) + "\t" + str(alphaS))
__inLines, __outLines = "", ""
__endLine = "\n</event>"
__zO = zero_or
__pHS = "{:." + str(constants.LHEF_ME_number_decimal_places()) + "e}"
for p in __sortedListOfParticles: ##Iterate through both at once, but with particlesIn first!
if not precision.check_numbers_equal(
p.get_four_momentum() * p.get_four_momentum(),
0.0): ##Shouldn't ever need to call it.
fFV = kinematics.fix_not_massless(p.get_four_momentum(
)) ##Adjust to make sure they are exactly massless for Pythia.
else:
fFV = p.get_four_momentum()
__newLine = ("\n\t\t\t" + str(p.get_code()) + "\t" +
str(p.get_status_code()) + "\t" +
str(p.get_mother(0)))
__newLine += ("\t" + str(p.get_mother(1)) + "\t" +
str(p.get_colour(0)) + "\t\t" + str(p.get_colour(1)))
__newLine += ("\t\t" + __pHS.format(__zO(fFV[1])) + "\t" +
__pHS.format(__zO(fFV[2])) + "\t")
__newLine += (__pHS.format(__zO(fFV[3])) + "\t" +
__pHS.format(__zO(fFV[0])) + "\t")
__newLine += (__pHS.format(__zO(p.get_mass())) + "\t" +
str(__zO(p.get_width())) + "\t\t" +
str(p.get_spin()))
__inLines += __newLine
__toSave = __line1 + __line2 + __inLines + __outLines + __endLine
__file = open(self.__saveName, 'a') ##'a' means append to.
__file.write(__toSave)
__file.close()
self.__numberEventsSaved += 1
def solve_sudakovs(PperpSquaredMax,
S123,
difCrossSecIds,
code1,
code2,
logCrosSecs=None):
"""A function to generate a PperpSquared and y for an emission or splitting, using the Sudakov form factor."""
##Codes 1,2 still needed to get the charges for EM radiation.
##Using veto algorithm in "PYTHIA 6.0 Physics and Manual".
##And p198 of "Monte Carlo simulations of hard QCD radiation" for bivariant algorithm.
##And p16 of "Initial-state showering based on colour dipoles connected to incoming parton lines" for real y limits.
##And p5 of "Fooling around with the Sudakov veto algorithm" for multiple emission form.
assert assertions.all_are_numbers([PperpSquaredMax, S123])
assert (type(difCrossSecIds) == list)
__kQs = particleData.knownParticles.get_known_quarks()
__gC = particleData.knownParticles.get_code_from_name('gluon')
__expectedCodes = __kQs + [-x for x in __kQs] + [__gC]
assert ((code1 in __expectedCodes) and (code2 in __expectedCodes))
__cutOff = constants.cut_off_energy() * constants.cut_off_energy()
if (PperpSquaredMax < __cutOff):
return None, None, None
__notChosen1, __y, __PperpSquaredi = True, 0, assertions.force_float_number(
PperpSquaredMax)
__PperpSquarediMinus1 = __PperpSquaredi
while __notChosen1: ##i += 1
__notChosen2 = True
while __notChosen2:
__R1 = random.random()
__PperpSquaredi = calc_inv_G(
(math.log(__R1) + calc_G(__PperpSquarediMinus1, S123)), S123)
if (__PperpSquaredi >
S123 / 4.0): ##The maximum physically possible!
__notChosen2 = True
__PperpSquarediMinus1 = __PperpSquaredi
continue #Re-run the while loop
if (
__PperpSquaredi <= __PperpSquarediMinus1
): ##Don't update __PperpSquaredi if fails as would start allowing higher values!
__notChosen2 = False ##Move on
if (__PperpSquaredi < __cutOff):
return None, None, None
__R2 = random.random()
__ymin, __ymax = -0.5 * math.log(
S123 / __PperpSquaredi), 0.5 * math.log(S123 / __PperpSquaredi)
__yi = calc_inv_G2(__R2 * (calc_G2(__ymax) - calc_G2(__ymin)) +
calc_G2(__ymin))
if not check_rapidity_allowed(
S123, __PperpSquaredi,
__yi): ##Veto incorrect y-range. On the boundary is allowed.
__PperpSquarediMinus1 = __PperpSquaredi
continue ##Don't accept, notChosen1 == True, while will run again.
__R3 = random.random()
__numberCSIds = len(difCrossSecIds)
__ratio = sum_cSs(difCrossSecIds, S123, __PperpSquaredi, __yi, code1,
code2) / __numberCSIds * calc_g(
__PperpSquaredi, __yi)
if (__ratio <= __R3):
__PperpSquarediMinus1 = __PperpSquaredi
continue ##Don't accept, notChosen1 == True, while will run again.
else:
__notChosen1 = False ##Accept.
##Prepare weights for choosing Id of process occuring:
__idWeights = {} ##Empty dictionary initiated.
for __difCrossSecId in difCrossSecIds: ##Uses the Ids given so will weight for the chosen set.
__idWeights[__difCrossSecId] = sum_cSs([__difCrossSecId], S123,
__PperpSquaredi, __yi, code1,
code2)
__total = sum(__idWeights.itervalues())
__idWeights.update(
(x, y / __total) for x, y in __idWeights.items()) ##Normalise them
assert precision.check_numbers_equal(
sum(__idWeights.itervalues()),
1.0) ##i.e they should now be normalised to 1.
##Choose which process:
__R4 = random.random(
) ##Doesn't include 1 -> using < not <= for checks is fair.
__sumSoFar = 0.0
__chosenId = None
__chosen = False
if (logCrosSecs == 1):
crossSecsGluSplit.store(qg_to_qQQBar_cS(S123, __PperpSquaredi, __yi))
crossSecsGluProd.store(qg_to_qgg_cS(S123, __PperpSquaredi, __yi))
for __difCrossSecId in difCrossSecIds:
if (not __chosen):
__sumSoFar += __idWeights[__difCrossSecId]
if (__R4 < __sumSoFar):
__chosenId = __difCrossSecId
__chosen = True
assert (not (__chosenId == None)) ##Should have chosen by now!
return __PperpSquaredi, __yi, __chosenId
def run(self):
"""A function to run a shower for the given LHEF file."""
##For e+e- -> qqBar (massless).
__reader = LHEFHandlers.LHEFReader(self.__toLoad)
self.__numEvents = __reader.get_number_events()
__writer = LHEFHandlers.LHEFShowerWriter(__reader, self.__numEvents)
__alertEvery = self.__numEvents / 10
if __alertEvery > 1000: ##Slow enough to want to see something is happening!
__alertEvery = 1000
elif (__alertEvery == 0): ##i.e < 10 events.
__alertEvery = 1
for __eventIndex in range(self.__numEvents):
if (__eventIndex % __alertEvery == 0):
if (__eventIndex == 0):
print "Begin showering...\n"
else:
print "Showering event", __eventIndex
__MEParticle1 = __reader.get_event_particle(__eventIndex, 0)
__MEParticle2 = __reader.get_event_particle(__eventIndex, 1)
__EIn = __MEParticle1[0] + __MEParticle2[0]
__S123In = kinematics.Sijk([
__MEParticle1.get_four_momentum(),
__MEParticle2.get_four_momentum()
])
__particlesIn = [__MEParticle1, __MEParticle2]
__showerParticle1 = __reader.get_event_particle(__eventIndex, 2)
__showerParticle2 = __reader.get_event_particle(__eventIndex, 3)
__showeri = showers.qqBarShower(__showerParticle1,
__showerParticle2,
self.__activeQCodes)
__showeri.run_shower()
__particlesOut = __showeri.export_results()
__EOut = 0.0
__fourVectorsOut = []
for __p in __particlesOut:
__ePV = __p.get_four_momentum()
__EOut += __ePV[0]
__fourVectorsOut.append(__ePV)
assert precision.check_numbers_equal(
kinematics.Sijk(__fourVectorsOut), __S123In)
assert precision.check_numbers_equal(__EIn, __EOut)
__trials, __muf2, __mur2 = __reader.get_event_trials(
__eventIndex), __reader.get_event_muf2(
__eventIndex), __reader.get_event_mur2(__eventIndex)
__processID, __weight = __reader.get_event_process_ID(
__eventIndex), __reader.get_event_weight(__eventIndex)
__scale, __alphaEM = __reader.get_event_scale(
__eventIndex), __reader.get_event_alphaEM(__eventIndex)
__alphaS = __reader.get_event_alphaS(__eventIndex)
__writer.add_event(__trials, __muf2, __mur2, __processID, __weight,
__scale, __alphaEM, __alphaS, __particlesIn,
__particlesOut)
__writer.save()
__numGluonsSplit = counters.gluonSplitCounter.counted()
print "\nThere were", counters.gluonProdCounter.counted(
), "gluons produced!"
print "\nThere were", __numGluonsSplit, "gluons split!"
print "\nThere were", counters.photonProdCounter.counted(
), "photons produced!"
print "\nThere were", counters.kPerpProdWarningCounter.counted(
), "warnings for E1 or E3 < E2!\n"
print "\n---------------------"
print "Quark content report:"
print "---------------------"
__sumPercent = 0.0
for __aQCode in [1, 2, 3, 4, 5, 6]:
__qName = particleData.knownParticles.get_name_from_code(__aQCode)
if precision.check_numbers_equal(__numGluonsSplit, 0.0):
__qPercent = 0.0
else:
__qPercent = chains.producedQuarkCodes.output().count(
__aQCode) * 100.0 / __numGluonsSplit
__sumPercent += __qPercent
print str(__qPercent) + "% are " + __qName + "s."
print "This adds up to " + str(__sumPercent) + "%."
assertions.pause(__name__)
pyplot.xlim(0.001,10**6)
assertions.show_graph()
print "\nFinished testing Nf function."
assertions.pause(__name__)
##Test beta0 function:##
print "\n--------------------------------------------------\n"
print "Testing beta0 function:"
##Using N=3 version from four-loop paper which is the same as Krauss'.
for tNf1 in range(0,7):
if (tNf1 == 4):
assertions.pause(__name__)
tExpectedBeta0 = 11.0 - (2.0/3.0)*tNf1
print "\nbeta0("+str(tNf1)+") returns:" , beta0(tNf1)
print "The expected value is:" , tExpectedBeta0
if precision.check_numbers_equal(beta0(tNf1),tExpectedBeta0):
print "These are equal within the code precision: Test successful!"
else:
print "Not equal: Test failed!"
print "\nFinished testing beta0 function."
assertions.pause(__name__)
##Test beta1 function:##
print "\n--------------------------------------------------\n"
print "Testing beta1 function:"
##Using N=3 version from four-loop paper which is the same as Krauss'.
for tNf2 in range(0,7):
if (tNf2 == 4):
assertions.pause(__name__)
tExpectedBeta1 = 102.0 - (38.0/3.0)*tNf2
print "\nbeta1("+str(tNf2)+") returns:" , beta1(tNf2)
def add_event(self, trials, muf2, mur2, processID, weight, scale, alphaEM,
alphaS, particlesIn, particlesOut):
"""A function to convert a produced particles data to LHEF and add to the writer."""
assert ((type(trials) == int) or (isinstance(trials, basestring)))
assert ((type(muf2) == int) or (type(muf2) == float)
or (isinstance(muf2, basestring)))
assert ((type(mur2) == int) or (type(mur2) == float)
or (isinstance(mur2, basestring)))
assert ((type(processID) == int)
or (isinstance(processID, basestring)))
assert ((type(weight) == float) or (type(weight) == int)
or (isinstance(weight, basestring)))
assert ((type(scale) == float) or (isinstance(scale, basestring)))
assert ((type(alphaEM) == float) or (isinstance(alphaEM, basestring)))
assert ((type(alphaS) == float) or (isinstance(alphaS, basestring)))
self.__numProdLogger.store(
len(particlesOut) - 2) ##Log number of produced partons per event.
if (self.__topWritten == False):
self.write_top()
self.__haveEvents = True ##Only called once here.
__listOfParticles = particlesIn + particlesOut
#Currently not sorting by order of production.
#__listOfIDs = [x.get_unique_ID() for x in __listOfParticles]
#__sortedListOfParticles = [x for (y,x) in sorted(zip(__listOfIDs,__listOfParticles), key=lambda pair: pair[0])]
__sortedListOfParticles = __listOfParticles ##Replacement line to keep the chain ordering.
for particle in __sortedListOfParticles:
assert particles.check_is_particle(particle)
assert particle.__nonzero__()
__numberParticles = len(particlesIn) + len(particlesOut)
__line1 = "\n<event>" # trials='" + str(trials) + "' muf2='" + str(muf2) + "' mur2='" + str(mur2) + "'>"
__line2 = ("\n\t\t" + str(__numberParticles) + "\t" + str(processID) +
"\t" + str(weight) + "\t" + str(scale))
__line2 += ("\t" + str(alphaEM) + "\t" + str(alphaS))
__inLines, __outLines = "", ""
__endLine = "\n</event>"
__zO = zero_or
__pHS = "{:." + str(constants.LHEF_DS_number_decimal_places()) + "e}"
for i, p in enumerate(
__sortedListOfParticles
): ##Iterate through both at once, but with particlesIn first!
if not precision.check_numbers_equal(
p.get_four_momentum() * p.get_four_momentum(), 0.0):
fFV = kinematics.fix_not_massless(p.get_four_momentum(
)) ##Adjust to make sure they are exactly massless for Pythia.
else:
fFV = p.get_four_momentum()
if i <= 1: ##Carry on as normal for first two (initial-state) particles.
__mum1, __mum2 = p.get_mother(0), p.get_mother(1)
else: ##Set all mother values to 1 and 2 as required by Pythia 8.2.
__mum1, __mum2 = 1, 2
__newLine = ("\n\t\t\t" + str(p.get_code()) + "\t" +
str(p.get_status_code()) + "\t" + str(__mum1))
__newLine += ("\t" + str(__mum2) + "\t" + str(p.get_colour(0)) +
"\t\t" + str(p.get_colour(1)))
__newLine += ("\t\t" + __pHS.format(__zO(fFV[1])) + "\t" +
__pHS.format(__zO(fFV[2])) + "\t")
__newLine += (__pHS.format(__zO(fFV[3])) + "\t" +
__pHS.format(__zO(fFV[0])) + "\t")
__newLine += (__pHS.format(__zO(p.get_mass())) + "\t" +
str(__zO(p.get_width())) + "\t\t" +
str(p.get_spin()))
__inLines += __newLine
__toSave = __line1 + __line2 + __inLines + __outLines + __endLine
__file = open(self.__saveName, 'a') ##'a' means append to.
__file.write(__toSave)
__file.close()
self.__numberEventsSaved += 1
for fC in tFermionCodes:
for lI in tLowerIndices:
print "Calling with lower index", lI, "and upper index", tG_N(
fC), "returns:"
print neutral_weak_couplings(lI, fC)
results.append(neutral_weak_couplings(lI, fC))
assertions.pause(__name__)
tExpected = [
-0.34582666666, -0.5, 0.19165333333, 0.5, -0.34582666666, -0.5,
0.19165333333, 0.5, -0.34582666666, -0.5, 0.19165333333, 0.5
]
tExpected += [
-0.03748, -0.5, 0.5, 0.5, -0.03748, -0.5, 0.5, 0.5, -0.03748, -0.5,
0.5, 0.5
]
tSuccessful = True
for i, v in enumerate(results):
if not precision.check_numbers_equal(results[i], tExpected[i]):
tSuccessful = False
if tSuccessful:
print "\nTest successful!"
else:
print "\nTest failed!"
print "\nFinished testing neutral_weak_couplings."
assertions.pause(__name__)
##Done testing:##
print "\n---------------------------------------------\n"
print "///////////////////////////////////"
print "Finished checking constants module!"
print "///////////////////////////////////"
def check_lightlike(pV): """A function to check whether a momentum vector is light-like (i.e P.P = M^2 = 0).""" assert fourVectors.check_is_fourVector(pV) assert pV.__nonzero__() __MinkowskiSP = pV * pV return precision.check_numbers_equal(__MinkowskiSP,0.0)
##Test neutral_weak_couplings:## print "\n--------------------------------------------------\n" print "Testing neutral_weak_couplings:\n" tFermionCodes = particleData.knownParticles.get_known_fermions() tG_N = particleData.knownParticles.get_name_from_code results = [] for fC in tFermionCodes: for lI in tLowerIndices: print "Calling with lower index", lI ,"and upper index", tG_N(fC), "returns:" print neutral_weak_couplings(lI,fC) results.append(neutral_weak_couplings(lI,fC)) assertions.pause(__name__) tExpected = [-0.34582666666,-0.5,0.19165333333,0.5,-0.34582666666,-0.5,0.19165333333,0.5,-0.34582666666,-0.5,0.19165333333,0.5] tExpected += [-0.03748,-0.5,0.5,0.5,-0.03748,-0.5,0.5,0.5,-0.03748,-0.5,0.5,0.5] tSuccessful = True for i, v in enumerate(results): if not precision.check_numbers_equal(results[i],tExpected[i]): tSuccessful = False if tSuccessful: print "\nTest successful!" else: print "\nTest failed!" print "\nFinished testing neutral_weak_couplings." assertions.pause(__name__) ##Done testing:## print "\n---------------------------------------------\n" print "///////////////////////////////////" print "Finished checking constants module!" print "///////////////////////////////////"
math.sqrt(1.2 * 1.2 + 4.5 * 4.5 + 3.2 * 3.2), 1.2, 4.5, 3.2)
tEdiff = 5.4
tEDiffVecOut = fix_energy_difference(tEdiff, tEDiffVector)
print "Generating test variables completed"
assertions.pause(__name__)
##Test Sijk function:##
print "\n--------------------------------------------------\n"
print "Testing Sijk function:\n"
for tFourVector in tFourVectors:
print "Momentum-" + tFourVector + " is:\n", tFourVectors[tFourVector]
assertions.pause(__name__)
print "\nFor a & b, Sijk returns:", Sijk(
[tFourVectors['a'], tFourVectors['b']])
print "Compared to the expected value of:", tExpectedSab
if precision.check_numbers_equal(
Sijk([tFourVectors['a'], tFourVectors['b']]), tExpectedSab):
print "\nFirst test, equal within the code precision: Test successful!"
else:
print "\nFirst test, not equal within the code precision: Test failed!"
print "Possibly just a precision error?\n"
print "{0:.20f}".format(Sijk([tFourVectors['a'], tFourVectors['b']]))
print "{0:.20f}".format(tExpectedSab)
print "\nFor a & b, Sijk returns:", Sijk(
[tFourVectors['c'], tFourVectors['d']])
print "Compared to the expected value of:", tExpectedScd
if precision.check_numbers_equal(
Sijk([tFourVectors['c'], tFourVectors['d']]), tExpectedScd):
print "\nSecond test, equal within the code precision: Test successful!"
else:
print "\nSecond test, not equal within the code precision: Test failed!"
print "Possibly just a precision error?\n"
if check_timelike(tLightlike):
tSuccessful = False
if tSuccessful:
print "\nTest successful!"
else:
print "\nTest failed!"
print "\nFinished testing check_timelike and check_lightlike."
assertions.pause(__name__)
##Test calculate_m_from_p_vector, check_v_not_faster_than_c and p_vector_to_v:##
print "\n--------------------------------------------------\n"
print "Testing calculate_m_from_p_vector, check_v_not_faster_than_c and p_vector_to_v:\n"
tSuccessful = True
print "Calling calculate_m_from_p_vector on tLightlike:", calculate_m_from_p_vector(
tLightlike)
if not precision.check_numbers_equal(calculate_m_from_p_vector(tLightlike),
0.0):
tSuccessful = False
print "Calling check_v_not_faster_than_c on", tNotTooFast1, ":", check_v_not_faster_than_c(
tNotTooFast1)
if not check_v_not_faster_than_c(tNotTooFast1):
tSuccessful = False
print "Calling check_v_not_faster_than_c on", tNotTooFast2, ":", check_v_not_faster_than_c(
tNotTooFast2)
if not check_v_not_faster_than_c(tNotTooFast2):
tSuccessful = False
print "Calling check_v_not_faster_than_c on", tTooFast1, ":", check_v_not_faster_than_c(
tTooFast1)
if check_v_not_faster_than_c(tTooFast1):
tSuccessful = False
print "Calling check_v_not_faster_than_c on", tTooFast2, ":", check_v_not_faster_than_c(
tTooFast2)
print "Calling check_timelike on tLightlike:" , check_timelike(tLightlike) if check_timelike(tLightlike): tSuccessful = False if tSuccessful: print "\nTest successful!" else: print "\nTest failed!" print "\nFinished testing check_timelike and check_lightlike." assertions.pause(__name__) ##Test calculate_m_from_p_vector, check_v_not_faster_than_c and p_vector_to_v:## print "\n--------------------------------------------------\n" print "Testing calculate_m_from_p_vector, check_v_not_faster_than_c and p_vector_to_v:\n" tSuccessful = True print "Calling calculate_m_from_p_vector on tLightlike:" , calculate_m_from_p_vector(tLightlike) if not precision.check_numbers_equal(calculate_m_from_p_vector(tLightlike),0.0): tSuccessful = False print "Calling check_v_not_faster_than_c on" , tNotTooFast1 , ":" , check_v_not_faster_than_c(tNotTooFast1) if not check_v_not_faster_than_c(tNotTooFast1): tSuccessful = False print "Calling check_v_not_faster_than_c on" , tNotTooFast2 , ":" , check_v_not_faster_than_c(tNotTooFast2) if not check_v_not_faster_than_c(tNotTooFast2): tSuccessful = False print "Calling check_v_not_faster_than_c on" , tTooFast1 , ":" , check_v_not_faster_than_c(tTooFast1) if check_v_not_faster_than_c(tTooFast1): tSuccessful = False print "Calling check_v_not_faster_than_c on" , tTooFast2 , ":" , check_v_not_faster_than_c(tTooFast2) if check_v_not_faster_than_c(tTooFast2): tSuccessful = False print "Using" , tMomentum4V1 , "which has mass:" , calculate_m_from_p_vector(tMomentum4V1) tExpected = math.sqrt((tMomentum4V1[1]*tMomentum4V1[1]) + (tMomentum4V1[2]*tMomentum4V1[2]) + (tMomentum4V1[3]*tMomentum4V1[3]))
def check_lightlike(pV):
"""A function to check whether a momentum vector is light-like (i.e P.P = M^2 = 0)."""
assert fourVectors.check_is_fourVector(pV)
assert pV.__nonzero__()
__MinkowskiSP = pV * pV
return precision.check_numbers_equal(__MinkowskiSP, 0.0)