# Fun with LoKi Functors

Learning objectives

• Understand what LoKi functors are
• Use LoKi functors interactively
• Be able to find functors that do what we want

LoKi functors are designed to flexibly compute and compare properties of the current decay, from simple quantities such as the transverse momentum of a particle to complicated ones like helicity angles. Internally, functors are implemented as C++ classes that take an object of type TYPE1 and return another of TYPE2. They can be used both in C++ and in Python code, and can be combined with each other using logical operations.

According to TYPE2 there are 3 types of functors:

• Functions, which return double.
• Predicates, which return a bool.
• Streamers, which return a std::vector of some other type TYPE3.

When filling tuples, the most used functors are functions, while predicates are typically used for selections.

According to TYPE1, there are many types of functors, the most important of which are (you can find a full list in the LoKi FAQ):

• Particle functors, which take LHCb::Particle* as input.
• Vertex functors, which take LHCb::VertexBase* as input.
• MC particle functors, which take LHCb::MCParticle* as input.
• MC vertex functors, which take LHCb::MCVertex* as input.
• Array particle functors, which take a LoKi::Range_ (an array of particles) as input.
• Track functors, which take LHCb::Track as input.
C++ classes
Things like LHCb::Particle are C++ classes that usually represent some physical object. You will interact with the C++ objects directly very rarely, if ever.

To understand what we can do with LoKi functors, we will pick up from where we left off exploring a DST interactively. Open the DST and get the first candidate in the D2hhCompleteEventPromptDst2D2RS line:

cands = evt['/Event/AllStreams/Phys/D2hhCompleteEventPromptDst2D2RSLine/Particles']
cand = cands[0]


We can now try to get very simple properties of the ${\displaystyle D^{*+}}$ candidate, such as its transverse momentum and measured mass.

from LoKiPhys.decorators import PT, MM
print PT(cand)
print MM(cand)


LoKiSvc.REPORT      ERROR LoKi::AuxDesktopBase:     loadDesktop(): unable to load IPhysDesktop! StatusCode=FAILURE
LoKiSvc.REPORT      ERROR The   ERROR message is suppressed : 'LoKi::AuxDesktopBase:    loadDesktop(): unable to load IPhysDesktop!' StatusCode=FAILURE

This is related to the fact that some functors need to run in the DaVinci ‘scope’, and they are all loaded in the LoKiPhys.decorators module. It's harmless in the examples we will use. If the import is made before the instantiation of the ApplicationMgr, there will be no warnings.

Math operations are also allowed:

from LoKiPhys.decorators import PX, PY, PZ
p_components_sum = PX + PY + PZ
p_components_sum(cand)

Challenge! - Does it make sense?
Retrieve the momentum magnitude ${\displaystyle p}$ and see if you can get the same answer with the PX, PY, PZ functors. Also compute the invariant mass ${\displaystyle m}$ and see if it matches what the MM functor returned.

If we want to get the properties of the ${\displaystyle D^{*+}}$ vertex, for example its fit quality (${\displaystyle \chi ^{2}}$), we need to pass an object to the functor.

from LoKiPhys.decorators import VCHI2
print VCHI2(cand.endVertex())


This is inconvenient when running DaVinci with Python options files, since in that case we don't have any way of calling the endVertex method. Instead, we can use the VFASPF adaptor functor, which allows us to use vertex functors as if they were particle functors (note how the functor is built by combining two functors).

from LoKiPhys.decorators import VFASPF
VCHI2(cand.endVertex()) == VFASPF(VCHI2)(cand)


ns of functions of functions of...

Challenge! - {{{title}}}
Make sure you understand what VFASPF(VCHI2)(cand) means. It may help to play around in Python, creating a function that takes another function as an argument, for example:

def create_greeting(salutation):
def greet(name):
print '{0}, {1}!'.format(salutation, name)
return greet

What would create_greeting('Hello') return? What about create_greeting('Howdy')('partner')? Why is doing this useful?

The calculation of some of the properties, such as the impact parameter (IP) or direction angle (DIRA), require the knowledge of the primary vertex (PV) associated to the candidate. In GaudiPython, we can get the PVs ourselves.

pv_finder_tool = appMgr.toolsvc().create(
'GenericParticle2PVRelator<_p2PVWithIPChi2, OfflineDistanceCalculatorName>/P2PVWithIPChi2',
interface='IRelatedPVFinder'
)
pvs = evt['/Event/AllStreams/Rec/Vertex/Primary']
best_pv = pv_finder_tool.relatedPV(cand, pvs)
from LoKiPhys.decorators import DIRA
print DIRA(best_pv)(cand)


Given that this is a very common operation, we have the possibility of using, in the context of a DaVinci application (Stripping, for example), a special set of functors, starting with the BPV prefix (for Best PV), which will get the PV for us. Some functors also end with the suffix DV, which means they can only be used in the DaVinci context.

Finding LoKi functors
The full list of defined LoKi functors can be found in the LoKi::Cuts namespace in the doxygen. They are quite well documented with examples on how to use them. The list can be overwhelming, so it's also worth checking a more curated selection of functors in the TWiki, here and here.

So far we've only looked at the properties of the head of the decay (that is, the ${\displaystyle D^{*+}}$), but what if we want to get information about its daughters? As an example, let's get the largest transverse momentum of the final state particles. A simple solution would be to navigate the tree and calculate the maximum ${\displaystyle p_{\text{T}}}$.

def find_tracks(particle):
tracks = []
if particle.isBasicParticle():
proto = particle.proto()
if proto:
track = proto.track()
if track:
tracks.append(particle.data())
else:
for child in particle.daughters():
tracks.extend(find_tracks(child))
return tracks

max_pt = max([PT(child) for child in find_tracks(cand)])


However, LoKi offers functions for performing such operations, namely MAXTREE and MINTREE, which get as parameters the selection criteria, the functor to calculate and a default value. In our example,

from LoKiPhys.decorators import MAXTREE, ISBASIC, HASTRACK
MAXTREE(ISBASIC & HASTRACK, PT, -1)(cand) == max_pt


In this example, we have used two selection functors, ISBASIC and HASTRACK, which return true if the particle doesn't have children and is made up by a track, respectively. We can see that they do the same thing as particle.isBasicParticle() and particle.proto().track() in a more compact way.

Similarly, the SUMTREE functor allows us to accumulate quantities for those children that pass a certain selection:

from LoKiPhys.decorators import SUMTREE, ABSID
print SUMTREE(211 == ABSID, PT)(cand)
print SUMTREE('pi+' == ABSID, PT)(cand)


In this case, we have summed the transverse momentum of the pions in the tree. Note the usage of the ABSID functor, which selects particles from the decay tree using either their PDG Monte Carlo ID or their name.

Another very useful LoKi functor is CHILD, which allows us to access a property of a single children of the particle. To specify which child we want, its order is used, so we need to know how the candidate was built. For example, from

In [10]: cand.daughtersVector()
Out[10]:

0 |->D0                           M/PT/E/PX/PY/PZ: 1.8624/ 6.4521/ 47.44/-4.939/-4.152/ 46.96 [GeV]  #  0
EndVertex  X/Y/Z:0.2911/-0.2378/-14.38 [mm]  Chi2/nDoF 0.4039/1 #  0
1    |->K-                        M/PT/E/PX/PY/PZ: 0.4937/ 2.8013/ 25.45/-1.799/-2.147/ 25.29 [GeV]  # 19
1    |->pi+                       M/PT/E/PX/PY/PZ: 0.1396/ 3.7258/ 21.99/-3.141/-2.004/ 21.67 [GeV]  # 22
0 |->pi+                          M/PT/E/PX/PY/PZ: 0.1396/ 0.3701/ 2.678/-0.2873/-0.2333/ 2.649 [GeV]  # 10

we know that D0 is the first child and pi+ is the second. Therefore, to access the ${\displaystyle p_{\text{T}}}$ of the ${\displaystyle D^{0}}$ we have 2 options.

from LoKiPhys.decorators import CHILD
# Option 1
mass = MM(cand.daughtersVector()[0])
# Option 2
mass_child = CHILD(MM, 1)(cand)
# Do they agree?
mass == mass_child


The usage of LoKi functors extends much further than in the interactive GaudiPython world we've been exploring here.

They constitute the basis of particle filtering in the selection framework, discussed in the Building your own decay chain lesson in second-analysis-steps. Selecting particles means using LoKi predicates, functors that give a bool output, like ISBASIC and HASTRACK. Amongst these, a key functor is in_range, which returns True if the value of the given function functor (that is, the functor that returns a double) is within the given lower and upper limit. It helps writing CPU-efficient functors and thus is very important when building time-critical software like trigger or stripping lines.

from LoKiCore.functions import in_range
in_range(2000, MM, 2014)(cand)
in_range(1860, CHILD(MM, 1), 1870)(cand)


Additionally, LoKi functors can be used directly inside our DaVinci jobs to store specific bits of information in our ntuples without the need for a complicated C++-based algorithms. This second option will be discussed in the TupleTools and branches lesson.

Debugging LoKi functors

If you write complicated LoKi functors, typically in the context of selections, you need functions for debugging when things go wrong. LoKi provides wrapper functors that evaluate a functor (or functor expression), print debugging information and return the result; the most important of these are:

• dump1, which prints the input object and returns the calculated functor value,

from LoKiCore.functions import dump1
debug_p_components_sum = dump1(p_components_sum)
debug_p_components_sum(cand)

• monitor which prints the input the functor string and returns the calculated functor value,

from LoKiCore.functions import monitor
monitor_p_components_sum = monitor(p_components_sum)
monitor_p_components_sum(cand)