Fun with LoKi Functors

Learning Objectives

  • Find out how the physics information can be obtained from the DST

  • Understand what LoKi functors are

  • Use LoKi functors interactively

  • Be able to find functors that do what we want

Probably most of you have seen somewhere in a Stripping line, a Run 1-2 trigger line or a DaVinci options file an expression like this:

'(PT > 750*MeV) & (P > 4000*MeV) & (MIPCHI2DV(PRIMARY) > 4)'.

Usually these strings represent so-called LoKi functors. In this lesson we will explore why they exist, how one can use them interactively and some of the technical details behind them.

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 or the impact parameter with respect to the primary vertex to even more complicated ones like helicity angles in a multi-body decay. 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, also due to the existence of LoKi functors.

To understand what we can do with LoKi functors, we will pick up from where we left off exploring a DST interactively. First open the DST as we did previously:

$ lb-run --ext=ipython DaVinci/v45r8 ipython -i explore.py 00070793_00000001_7.AllStreams.dst

Get the first candidate in the D2hhPromptDst2D2KKLine line:

advance('D2hhPromptDst2D2KKLine')
candidates = evt['/Event/AllStreams/Phys/D2hhPromptDst2D2KKLine/Particles']
candidate = candidates[0]

The object candidate , loaded from the DST, is of type LHCb::Particle and we are looking at its representation via python bindings. We can do help(candidate) to find out which functions are available. We can try to get very simple properties of the \(` D^{* +} `\) candidate. Let’s start from the components of its momentum. This can be done calling the function momentum() for our candidate in the following way:

p_x = candidate.momentum().X()
p_y = candidate.momentum().Y()
p_z = candidate.momentum().Z()
print (p_x, p_y, p_z)

This is inconvenient when running DaVinci with Python options files: there’s no way of calling the momentum() method. Instead, we can use the corresponding LoKi particle functors:

from LoKiPhys.decorators import PX, PY, PZ
print (PX(candidate))
print (PY(candidate))
print (PZ(candidate))

You will see an error when loading the functors:

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.

Does it make sense?

Compare the output of PX functor with the result of calling the function candidate.momentum().X().

Math operations are also allowed:

p_components_sum = PX + PY + PZ
p_components_sum(candidate)

There exist specific LoKi functors for all the most important properties of the particle. For example, the transverse momentum and mass:

from LoKiPhys.decorators import PT, M
print (PT(candidate))
print (M(candidate))

Some practice

Retrieve the momentum magnitude using functors PX, PY and PZ. There is also a specific functor P which does the job. Compare the results.

Now, retrieve the transverse momentum and invariant mass (you will probably need the energy functor E), and see if it matches what the PT and M functors return.

A note about units

By the convention, the LHCb default units are MeV, millimeters and nanoseconds. It is easy to print the values of interest in other units:

from LoKiPhys.decorators import GeV
print (PT(candidate)/GeV)

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

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

Again, 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(candidate.endVertex()) == VFASPF(VCHI2)(candidate)

Functions of functions of functions of…

Make sure you understand what VFASPF(VCHI2)(candidate) 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?

Recently, there has been some effort to simplify the LoKi syntax. In particular, the new functor CHI2VX was introduced which is equivalent to VFASPF(VCHI2). However, in pretty much all code used during Runs 1 and 2 of LHCb you will only see the old syntax.

Calculation of some of the properties, such as the impact parameter (IP) or cosine of the direction angle (DIRA), requires 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/Rec/Vertex/Primary']
best_pv = pv_finder_tool.relatedPV(candidate, pvs)

Now, we can get the cosine of the direction angle for the candidate given the primary vertex:

from LoKiPhys.decorators import DIRA
print (DIRA(best_pv)(candidate))

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.

To get the quality of impact parameter of the candidate, one needs as well to call a distance calculator:

from GaudiPython.Bindings import gbl
distCal = appMgr.toolSvc().create("LoKi::DistanceCalculator", interface=gbl.IDistanceCalculator)
ipTool = gbl.LoKi.Vertices.ImpactParamTool(distCal)

Now, we evaluate the quality of impact parameter of the candidate, given the primary vertex, and using the provided calculator:

from LoKiPhys.decorators import IPCHI2
print (IPCHI2(best_pv, ipTool)(candidate))

In the context of DaVinci application, e.g. the Stripping, the things become much simplier since the calculator instances are loaded automatically, and the syntax for calling the IPCHI2 functor becomes IPCHI2(best_pv,geo())(candidate), where geo() is the geometry calculator tool.

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 \(` D^{* +} `\)), but what if we want to get information about its decay products? 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 \(` p_{\text{T}} `\).

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

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

A note about the try/except

If you import LoKi before running this example, it magically removes the .data() function and allows the particle to be used directly. The code above is made general using the try/except block and will work in either case.

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)(candidate) == 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.

Combining LoKi cuts

You might have noticed above we used the & operator (bitwise AND) to combine the ISBASIC and HASTRACK cuts above. This is because Python doesn’t allow LoKi to override the behaviour of and and or (”logical AND/OR”), so if we use them the Python interpreter tries to combine the two cuts straight away, before we have even passed in our candidate:

In [1]: ((M>1200) or (PT > 500))
Out[1]:  (M>1200)

the result is that our PT cut vanishes! If we use the | operator (”bitwise OR”) then LoKi correctly builds a functor representing the OR of our cuts:

In [2]: ((M>1200) | (PT > 500))
Out[2]:  ( (M>1200) | (PT>500) )

This is why you should always use & and | when combining LoKi functors, and never use and and or.

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(321 == ABSID, PT)(candidate))
print (SUMTREE('K+' == ABSID, PT)(candidate))

In this case, we have summed the transverse momentum of the charged kaons 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. If you would like to consider only the kaons of one specific charge in the selection requirement, consider the ID functor which does exactly the same thing, however has a sign which is positive for particles and negative for antiparticles.

Another very useful LoKi functor is CHILD, which allows us to access a property of a single child 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]: candidate.daughtersVector()
Out[10]:

 0 |->D0                           M/PT/E/PX/PY/PZ: 1.8653/ 2.5848/ 31.32/ 2.508/-0.6267/ 31.15 [GeV]  #  0 
                                       EndVertex  X/Y/Z: 1.053/-0.2006/-29.13 [mm]  Chi2/nDoF 0.2349/1 #  0 
 1    |->K+                        M/PT/E/PX/PY/PZ: 0.4937/ 2.1334/ 20.26/ 2.129/0.1371/ 20.14 [GeV]  #  5 
 1    |->K-                        M/PT/E/PX/PY/PZ: 0.4937/ 0.8534/ 11.06/0.3795/-0.7643/ 11.01 [GeV]  # 10 
 0 |->pi+                          M/PT/E/PX/PY/PZ: 0.1396/ 0.2558/ 3.101/0.2451/-0.0733/ 3.088 [GeV]  #  4

we know that D0 is the first child and pi+ is the second. Therefore, to access the mass of the \(` D^{0} `\) we have 2 options:

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

Child vertex?

Evaluate the quality of the D0 decay vertex.

In the similar way, we may access properties of child of the child: for example, a kaon from the \(` D^{0} `\) decay:

from LoKiPhys.decorators import CHILD
mass_kaon = CHILD(CHILD(M, 1),1)(candidate)

Tracks and PID

For the particles having tracks, we may exploit track functors to get the corresponding track properties. For instance, the track quality is given by functor TRCHI2.

What happens if we call TRCHI2(candidate)? Explain the result.

Evaluate the track quality for the first and second kaon, also independently of that retrieve (in a single line) the worst of two.

Then, evaluate the probability that each kaon is really a kaon (PROBNNk) or rather a misidentified pion (PROBNNpi).

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, M, 2014)(candidate)
in_range(1860, CHILD(M, 1), 1870)(candidate)

Understanding the cuts in the stripping lines

Have a look at the stripping line D2hhPromptDst2D2KKLine which is used in our example. Open a CombineParticles/D2hhPromptDst2D2KKLine section, and explain which requirements are coded in the ‘MotherCut’, ‘DaughterCuts’ and ‘CombinationCut’ sections. (More details about CombineParticles algorithm are explained in the lesson of second analysis steps.)

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(candidate)

  • 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(candidate)

A word on the Run 3

In the Run 3, we introduce a more performant set of throughput-oriented functors, known as ThOr functors. While they have certain conceptual similarities to the LoKi functors, they are designed to work in a more efficient manner for multithreaded execution.