Crate laddu

Expand description

laddu (/ˈlʌduː/) is a library for analysis of particle physics data. It is intended to be a simple and efficient alternative to some of the other tools out there. laddu is written in Rust with bindings to Python via PyO3 and maturin and is the spiritual successor to rustitude, one of my first Rust projects. The goal of this project is to allow users to perform complex amplitude analyses (like partial-wave analyses) without complex code or configuration files.

This crate is still in an early development phase, and the API is not stable. It can (and likely will) be subject to breaking changes before the 1.0.0 version release (and hopefully not many after that).

§Table of Contents

Key Features
Installation
Quick Start
- Writing a New Amplitude
- Calculating a Likelihood
Data Format
MPI Support
Future Plans
Alternatives

§Key Features

A simple interface focused on combining Amplitudes into models which can be evaluated over Datasets.
A single Amplitude trait which makes it easy to write new amplitudes and integrate them into the library.
Easy interfaces to precompute and cache values before the main calculation to speed up model evaluations.
Efficient parallelism using rayon.
Python bindings to allow users to write quick, easy-to-read code that just works.

§Installation

laddu can be added to a Rust project with cargo:

cargo add laddu

The library’s Python bindings are located in a library by the same name, which can be installed simply with your favorite Python package manager:

pip install laddu

§Quick Start

§Rust

§Writing a New Amplitude

At the time of writing, Rust is not a common language used by particle physics, but this tutorial should hopefully convince the reader that they don’t have to know the intricacies of Rust to write performant amplitudes. As an example, here is how one might write a Breit-Wigner, parameterized as follows:

I_{\ell}(m; m_0, \Gamma_0, m_1, m_2) =  \frac{1}{\pi}\frac{m_0 \Gamma_0 B_{\ell}(m, m_1, m_2)}{(m_0^2 - m^2) - \imath m_0 \Gamma}

where

\Gamma = \Gamma_0 \frac{m_0}{m} \frac{q(m, m_1, m_2)}{q(m_0, m_1, m_2)} \left(\frac{B_{\ell}(m, m_1, m_2)}{B_{\ell}(m_0, m_1, m_2)}\right)^2

is the relativistic width correction, $q(m_a, m_b, m_c)$ is the breakup momentum of a particle with mass $m_a$ decaying into two particles with masses $m_b$ and $m_c$, $B_{\ell}(m_a, m_b, m_c)$ is the Blatt-Weisskopf barrier factor for the same decay assuming particle $a$ has angular momentum $\ell$, $m_0$ is the mass of the resonance, $\Gamma_0$ is the nominal width of the resonance, $m_1$ and $m_2$ are the masses of the decay products, and $m$ is the “input” mass.

Although this particular amplitude is already included in laddu, let’s assume it isn’t and imagine how we would write it from scratch:

use laddu::{
   ParameterLike, Event, Cache, Resources, Mass,
   ParameterID, Parameters, Float, LadduError, PI, AmplitudeID, Complex,
};
use laddu::traits::*;
use laddu::utils::functions::{blatt_weisskopf, breakup_momentum};
use laddu::{Deserialize, Serialize, typetag};

#[derive(Clone, Serialize, Deserialize)]
pub struct MyBreitWigner {
    name: String,
    mass: ParameterLike,
    width: ParameterLike,
    pid_mass: ParameterID,
    pid_width: ParameterID,
    l: usize,
    daughter_1_mass: Mass,
    daughter_2_mass: Mass,
    resonance_mass: Mass,
}
impl MyBreitWigner {
    pub fn new(
        name: &str,
        mass: ParameterLike,
        width: ParameterLike,
        l: usize,
        daughter_1_mass: &Mass,
        daughter_2_mass: &Mass,
        resonance_mass: &Mass,
    ) -> Box<Self> {
        Self {
            name: name.to_string(),
            mass,
            width,
            pid_mass: ParameterID::default(),
            pid_width: ParameterID::default(),
            l,
            daughter_1_mass: daughter_1_mass.clone(),
            daughter_2_mass: daughter_2_mass.clone(),
            resonance_mass: resonance_mass.clone(),
        }
        .into()
    }
}

#[typetag::serde]
impl Amplitude for MyBreitWigner {
    fn register(&mut self, resources: &mut Resources) -> Result<AmplitudeID, LadduError> {
        self.pid_mass = resources.register_parameter(&self.mass);
        self.pid_width = resources.register_parameter(&self.width);
        resources.register_amplitude(&self.name)
    }

    fn compute(&self, parameters: &Parameters, event: &Event, _cache: &Cache) -> Complex<Float> {
        let mass = self.resonance_mass.value(event);
        let mass0 = parameters.get(self.pid_mass);
        let width0 = parameters.get(self.pid_width);
        let mass1 = self.daughter_1_mass.value(event);
        let mass2 = self.daughter_2_mass.value(event);
        let q0 = breakup_momentum(mass0, mass1, mass2);
        let q = breakup_momentum(mass, mass1, mass2);
        let f0 = blatt_weisskopf(mass0, mass1, mass2, self.l);
        let f = blatt_weisskopf(mass, mass1, mass2, self.l);
        let width = width0 * (mass0 / mass) * (q / q0) * (f / f0).powi(2);
        let n = Float::sqrt(mass0 * width0 / PI);
        let d = Complex::new(mass0.powi(2) - mass.powi(2), -(mass0 * width));
        Complex::from(f * n) / d
    }
}

While it isn’t shown here, we can often be more efficient when implementing Amplitudes by precomputing values which do not depend on the free parameters. See the Amplitude::precompute method for more details.

§Calculating a Likelihood

We could then write some code to use this amplitude. For demonstration purposes, let’s just calculate an extended unbinned negative log-likelihood, assuming we have some data and Monte Carlo in the proper parquet format:


use laddu::{Scalar, Mass, Manager, NLL, parameter, open};
let ds_data = open("test_data/data.parquet").unwrap();
let ds_mc = open("test_data/mc.parquet").unwrap();

let resonance_mass = Mass::new([2, 3]);
let p1_mass = Mass::new([2]);
let p2_mass = Mass::new([3]);
let mut manager = Manager::default();
let bw = manager.register(MyBreitWigner::new(
    "bw",
    parameter("mass"),
    parameter("width"),
    2,
    &p1_mass,
    &p2_mass,
    &resonance_mass,
)).unwrap();
let mag = manager.register(Scalar::new("mag", parameter("magnitude"))).unwrap();
let expr = (mag * bw).norm_sqr();
let model = manager.model(&expr);

let nll = NLL::new(&model, &ds_data, &ds_mc);
println!("Parameters names and order: {:?}", nll.parameters());
let result = nll.evaluate(&[1.27, 0.120, 100.0]);
println!("The extended negative log-likelihood is {}", result);

In practice, amplitudes can also be added together, their real and imaginary parts can be taken, and evaluators should mostly take the real part of whatever complex value comes out of the model.

§Data Format

The data format for laddu is a bit different from some of the alternatives like AmpTools. Since ROOT doesn’t yet have bindings to Rust and projects to read ROOT files are still largely works in progress (although I hope to use oxyroot in the future when I can figure out a few bugs), the primary interface for data in laddu is Parquet files. These are easily accessible from almost any other language and they don’t take up much more space than ROOT files. In the interest of future compatibility with any number of experimental setups, the data format consists of an arbitrary number of columns containing the four-momenta of each particle, the polarization vector of each particle (optional) and a single column for the weight. These columns all have standardized names. For example, the following columns would describe a dataset with four particles, the first of which is a polarized photon beam, as in the GlueX experiment:

Column name	Data Type	Interpretation
`p4_0_E`	`Float32`	Beam Energy
`p4_0_Px`	`Float32`	Beam Momentum (x-component)
`p4_0_Py`	`Float32`	Beam Momentum (y-component)
`p4_0_Pz`	`Float32`	Beam Momentum (z-component)
`aux_0_x`	`Float32`	Beam Polarization (x-component)
`aux_0_y`	`Float32`	Beam Polarization (y-component)
`aux_0_z`	`Float32`	Beam Polarization (z-component)
`p4_1_E`	`Float32`	Recoil Proton Energy
`p4_1_Px`	`Float32`	Recoil Proton Momentum (x-component)
`p4_1_Py`	`Float32`	Recoil Proton Momentum (y-component)
`p4_1_Pz`	`Float32`	Recoil Proton Momentum (z-component)
`p4_2_E`	`Float32`	Decay Product 1 Energy
`p4_2_Px`	`Float32`	Decay Product 1 Momentum (x-component)
`p4_2_Py`	`Float32`	Decay Product 1 Momentum (y-component)
`p4_2_Pz`	`Float32`	Decay Product 1 Momentum (z-component)
`p4_3_E`	`Float32`	Decay Product 2 Energy
`p4_3_Px`	`Float32`	Decay Product 2 Momentum (x-component)
`p4_3_Py`	`Float32`	Decay Product 2 Momentum (y-component)
`p4_3_Pz`	`Float32`	Decay Product 2 Momentum (z-component)
`weight`	`Float32`	Event Weight

To make it easier to get started, we can directly convert from the AmpTools format using the provided [amptools-to-laddu] script (see the bin directory of this repository). This is not bundled with the Python library (yet) but may be in the future.

§MPI Support

The latest version of laddu supports the Message Passing Interface (MPI) protocol for distributed computing. MPI-compatible versions of the core laddu methods have been written behind the mpi feature gate. To build laddu with MPI compatibility, it can be added with the mpi feature via cargo add laddu --features mpi. Note that this requires a working MPI installation, and OpenMPI or MPICH are recommended, as well as LLVM/Clang. The installation of these packages differs by system, but are generally available via each system’s package manager.

To use MPI in Rust, one must simply surround their main analysis code with a call to laddu::mpi::use_mpi(true) and laddu::mpi::finalize_mpi(). The first method has a boolean flag which allows for runtime switching of MPI use (for example, disabling MPI with an environment variable).

§Future Plans

GPU integration (this is incredibly difficult to do right now, but it’s something I’m looking into).
As always, more tests and documentation.

§Alternatives

While this is likely the first Rust project (aside from my previous attempt, rustitude), there are several other amplitude analysis programs out there at time of writing. This library is a rewrite of rustitude which was written when I was just learning Rust and didn’t have a firm grasp of a lot of the core concepts that are required to make the analysis pipeline memory- and CPU-efficient. In particular, rustitude worked well, but ate up a ton of memory and did not handle precalculation as nicely.

§AmpTools

The main inspiration for this project is the library most of my collaboration uses, AmpTools. AmpTools has several advantages over laddu: it’s probably faster for almost every use case, but this is mainly because it is fully integrated with MPI and GPU support. I’m not actually sure if there’s a fair benchmark between the two libraries, but I’d wager AmpTools would still win. AmpTools is a much older, more developed project, dating back to 2010. However, it does have its disadvantages. First and foremost, the primary interaction with the library is through configuration files which are not really code and sort of represent a domain specific language. As such, there isn’t really a way to check if a particular config will work before running it. Users could technically code up their analyses in C++ as well, but I think this would generally be more work for very little benefit. AmpTools primarily interacts with Minuit, so there aren’t simple ways to perform alternative optimization algorithms, and the outputs are a file which must also be parsed by code written by the user. This usually means some boilerplate setup for each analysis, a slew of input and output files, and, since it doesn’t ship with any amplitudes, integration with other libraries. The data format is also very rigid, to the point where including beam polarization information feels hacked on (see the Zlm implementation here which requires the event-by-event polarization to be stored in the beam’s four-momentum). While there isn’t an official Python interface, Lawrence Ng has made some progress porting the code here.

§PyPWA

PyPWA is a library written in pure Python. While this might seem like an issue for performance (and it sort of is), the library has several features which encourage the use of JIT compilers. The upside is that analyses can be quickly prototyped and run with very few dependencies, it can even run on GPUs and use multiprocessing. The downside is that recent development has been slow and the actual implementation of common amplitudes is, in my opinion, messy. I don’t think that’s a reason to not use it, but it does make it difficult for new users to get started.

§ComPWA

ComPWA is a newcomer to the field. It’s also a pure Python implementation and is comprised of three separate libraries. QRules can be used to validate and generate particle reaction topologies using conservation rules. AmpForm uses SymPy to transform these topologies into mathematical expressions, and it can also simplify the mathematical forms through the built-in CAS of SymPy. Finally, TensorWaves connects AmpForm to various fitting methods. In general, these libraries have tons of neat features, are well-documented, and are really quite nice to use. I would like to eventually see laddu as a companion to ComPWA (rather than direct competition), but I don’t really know enough about the libraries to say much more than that.

§Others

It could be the case that I am leaving out software with which I am not familiar. If so, I’d love to include it here for reference. I don’t think that laddu will ever be the end-all-be-all of amplitude analysis, just an alternative that might improve on existing systems. It is important for physicists to be aware of these alternatives. For example, if you really don’t want to learn Rust but need to implement an amplitude which isn’t already included here, laddu isn’t for you, and one of these alternatives might be best.

Re-exports§

pub use typetag;

Modules§

amplitudes: Amplitudes and methods for making and evaluating them.
breit_wigner: The Breit-Wigner amplitude.
common: Common amplitudes (like a scalar value which just contains a single free parameter).
data: Methods for loading and manipulating Event-based data.
experimental
extensions: Module for likelihood-related structures and methods
ganesh_ext: A module containing the laddu interface with the ganesh library
kmatrix: Amplitudes related to the K-Matrix formalism.
likelihoods: Extended maximum likelihood cost functions with support for additive terms
phase_space: A phase space factor for $a+b\to c+d$ with $c\to 1+2$ .
piecewise: Piecewise functions as amplitudes.
resources: Structures for manipulating the cache and free parameters.
traits: Useful traits for all crate structs
utils: Utility functions, enums, and traits
ylm: A spherical harmonic amplitude.
zlm: A polarized spherical harmonic amplitude.

Structs§

AmplitudeID: A tag which refers to a registered Amplitude. This is the base object which can be used to build Expressions and should be obtained from the Manager::register method.
Angles: A struct for obtaining both spherical angles at the same time.
BinnedDataset: A list of Datasets formed by binning Events by some Variable.
BreitWigner: A relativistic Breit-Wigner Amplitude, parameterized as follows:
Cache: A single cache entry corresponding to precomputed data for a particular Event in a Dataset.
Complex: A complex number in Cartesian form.
ComplexScalar: A complex-valued Amplitude which just contains two parameters representing its real and imaginary parts.
CosTheta: A struct for obtaining the $\cos\theta$ (cosine of the polar angle) of a decay product in a given reference frame of its parent resonance.
Dataset: A collection of Events.
Ensemble: A collection of Walkers
Evaluator: A structure which can be used to evaluate the stored Expression built on registered Amplitudes. This contains a Resources struct which already contains cached values for precomputed Amplitudes and any relevant free parameters and constants.
Event: A single event in a Dataset containing all the relevant particle information.
LikelihoodEvaluator: A structure to evaluate and minimize combinations of LikelihoodTerms.
LikelihoodID: An identifier that can be used like an AmplitudeID to combine registered LikelihoodTerms.
LikelihoodManager: A Manager but for LikelihoodTerms.
LikelihoodScalar: A LikelihoodTerm which represents a single scaling parameter.
MCMCOptions: A set of options that are used when Markov Chain Monte Carlo samplings are performed.
Manager: A manager which can be used to register Amplitudes with Resources. This structure is essential to any analysis and should be constructed using the Manager::default() method.
Mandelstam: A struct used to calculate Mandelstam variables ($s$, $t$, or $u$).
Mass: A struct for obtaining the mass of a particle by indexing the four-momenta of an event, adding together multiple four-momenta if more than one index is given.
MinimizerOptions: A set of options that are used when minimizations are performed.
Model: A struct which contains a set of registerd Amplitudes (inside a Manager) and an Expression.
NLL: An extended, unbinned negative log-likelihood evaluator.
Parameters: This struct holds references to the constants and free parameters used in the fit so that they may be obtained from their corresponding ParameterID.
PhaseSpaceFactor: An Amplitude describing the phase space factor given in Equation A4 here
Phi: A struct for obtaining the $\phi$ angle (azimuthal angle) of a decay product in a given reference frame of its parent resonance.
PiecewiseComplexScalar: A piecewise complex-valued Amplitude which just contains two parameters representing its real and imaginary parts.
PiecewisePolarComplexScalar: A piecewise complex-valued Amplitude which just contains two parameters representing its magnitude and phase.
PiecewiseScalar: A piecewise scalar-valued Amplitude which just contains a single parameter for each bin as its value.
PolAngle: A struct defining the polarization angle for a beam relative to the production plane.
PolMagnitude: A struct defining the polarization magnitude for a beam relative to the production plane.
PolarComplexScalar: A complex-valued Amplitude which just contains two parameters representing its magnitude and phase.
Polarization: A struct for obtaining both the polarization angle and magnitude at the same time.
Resources: The main resource manager for cached values, amplitudes, parameters, and constants.
Scalar: A scalar-valued Amplitude which just contains a single parameter as its value.
Status: A status message struct containing all information about a minimization result.
Vec3: A vector with three components
Vec4: A vector with four components (a Lorentz vector)
Ylm: An Amplitude for the spherical harmonic function $Y_\ell^m(\theta, \phi)$.
Zlm: An Amplitude representing an extension of the Ylm Amplitude assuming a linearly polarized beam as described in Equation (D13) here

Enums§

Expression: An expression tree which contains AmplitudeIDs and operators over them.
LadduError: The error type used by all laddu internal methods
LikelihoodExpression: A combination of LikelihoodTerms as well as sums and products of them.
ParameterID: An object which acts as a tag to refer to either a free parameter or a constant value.
ParameterLike: An enum containing either a named free parameter or a constant value.

Constants§

PI: The mathematical constant $\pi$.

Traits§

Deserialize: A data structure that can be deserialized from any data format supported by Serde.
Serialize: A data structure that can be serialized into any data format supported by Serde.

Functions§

constant: Shorthand for generating a constant value (which acts like a fixed parameter).
open: Open a Parquet file and read the data into a Dataset.
parameter: Shorthand for generating a named free parameter.

Type Aliases§

DVector: A dynamically sized column vector.
Float: A floating-point number type (defaults to f64, see f32 feature).

Derive Macros§

Deserialize
Serialize

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