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use crate::math::distances::WeightedDistances;
use ebi_objects::{
anyhow::{Context, Result, anyhow},
ebi_arithmetic::{
One,
exact::{MaybeExact, is_exact_globally},
fraction::{fraction_enum::FractionEnum, signed::Numerator},
malachite::{
Integer,
base::num::basic::traits::{One as MOne, Zero as MZero},
rational::Rational,
},
},
};
use ebi_optimisation::network_simplex::NetworkSimplex;
use rayon::prelude::*;
/// Authored by Leonhard Mühlmeyer (2024)
/// Implementation of the Earth Movers Stochastic Conformance Cheching (EMSC) described in
/// Leemans et al. *Earth movers’ stochastic conformance checking.* BPM Forum 2019.
/// Leemans et al. *Stochastic process mining: Earth movers’ stochastic conformance.* Information Systems 102 2021.
impl dyn WeightedDistances {
/// # Algorithm
/// 1. **Compute all pairwise distances** between the traces of the two languages (parallelized, see `DistanceMatrix`).
///
/// 2. **Is exact arithmetic required?**<br>
/// a. Calculate the Least Common Multiple (LCM) of all denominators of distances (i.e., the elements in the `DistanceMatrix`).<br>
/// b. Calculate the Least Common Multiple (LCM) of all denominators of trace probabilities from both stochastic languages.<br>
/// c. If the LCMs are within the range of `i64`, use `i64` for the `NetworkSimplex` computation (remains exact but faster).
/// If the LCMs are within the range of `i128`, use `i128` for the `NetworkSimplex` computation.
/// Otherwise, use `BigInt`.<br>
/// d. Scale the distances and probabilities by the respective identified LCM to retrieve integer values.<br>
/// e. Create a network graph with the scaled distances and probabilities:<br>
/// i. For each trace in the first language, create a supply node with the corresponding trace probability as supply.<br>
/// ii. For each trace in the second language, create a demand node with the corresponding trace probability as demand (i.e., negative supply).<br>
/// iii. Create an edge between each pair of traces with the respective scaled distance as cost.<br>
/// f. Run the `NetworkSimplex` algorithm to find the optimal flow between the supply and demand nodes.<br>
/// g. Calculate the EMSC value as `1 - (result / (LCM of distances * LCM of probabilities))` (i.e., undo the scaling trick).<br>
///
/// 3. **If exact arithmetic is not required**, use `f64` for the `NetworkSimplex` computation.<br>
/// a. Create a network graph with the scaled distances and probabilities:<br>
/// i. For each trace in the first language, create a supply node with the corresponding trace probability as supply.<br>
/// ii. For each trace in the second language, create a demand node with the corresponding trace probability as demand (i.e., negative supply).<br>
/// iii. Create an edge between each pair of traces with the respective distance as cost.<br>
/// b. Run the `NetworkSimplex` algorithm to find the optimal flow between the supply and demand nodes.<br>
/// c. Calculate the EMSC value as `1 - result`.
pub fn earth_movers_stochastic_conformance(&self) -> Result<FractionEnum> {
if self.len_a() == 0 || self.len_b() == 0 {
return Err(anyhow!("One of the languages is empty."));
}
if is_exact_globally() {
//exact mode
// 2. Is exact arithmetic required?
log::info!("Calculating exact EMSC value");
// 2a. Calculate the Least Common Multiple (LCM) of all denominators of distances (i.e. the elements in the DistanceMatrix).
let lcm_distances = self.lowest_common_multiple_denominators_distances()?;
let lcm_probabilities = self.lowest_common_multiple_denominators_weights()?;
// 2b. Calculate the Least Common Multiple (LCM) of all denominators of trace probabilities from both stochastic languages.
let n = self.len_a();
let m = self.len_b();
let lcm_distance_fraction = FractionEnum::Exact(Rational::from(lcm_distances.clone()));
let lcm_probability_fraction =
FractionEnum::Exact(Rational::from(lcm_probabilities.clone()));
log::debug!(
"LCM of distances: {:?} \n LCM of probabilities {:?}",
lcm_distances,
lcm_probabilities
);
// 2c. If the LCMs are within the range of i64, use i64 for the NetworkSimplex computation (remains exact but faster). Otherwise use BigInt.
if lcm_probabilities <= Integer::from(i64::MAX)
&& (Into::<Integer>::into(lcm_distances.clone()) + Integer::ONE)
* Integer::from(n + m)
<= Integer::from(i64::MAX)
{
log::info!("Using i64 for NetworkSimplex computation.");
// (i64) 2e. Create a network graph with the scaled distances and probabilities:
// (i64) 2e(i). For each trace in the first language, create a supply node with the corresponding trace probability as supply.
// (i64) 2e(ii). For each trace in the second language, create a demand node with the corresponding trace probability as demand (i.e. negative supply).
let mut supply = vec![0i64; n + m];
supply
.par_chunks_mut(1024)
.enumerate()
.for_each(|(chunk_idx, chunk)| {
chunk.iter_mut().enumerate().for_each(|(i, s)| {
let idx = chunk_idx * 1024 + i;
*s = if idx < n {
(self.weight_a(idx) * &lcm_probability_fraction)
.exact_ref()
.unwrap()
.numerator_ref()
.try_into()
.unwrap()
} else if idx < n + m {
-TryInto::<i64>::try_into(
(self.weight_b(idx - n) * &lcm_probability_fraction)
.exact_ref()
.unwrap()
.numerator_ref(),
)
.unwrap()
} else {
0
};
});
});
// (i64) 2d. Scale the distances and probabilities by the respective identified LCM to retrieve integer values.
// (i64) 2e(iii). Create an edge between each pair of traces with the respective scaled distance as cost.
let mut graph_and_costs = vec![vec![None; n + m]; n + m];
for i in 0..n {
for j in 0..m {
let product = self.distance(i, j) * &lcm_distance_fraction;
let i64 = product
.exact_ref()
.unwrap()
.numerator_ref()
.try_into()
.unwrap();
graph_and_costs[i][j + n] = Some(i64);
}
}
// (i64) 2f. Run the NetworkSimplex algorithm to find the optimal flow between the supply and demand nodes.
log::info!("Starting Network Simplex.");
let mut ns = NetworkSimplex::new(&graph_and_costs, &supply, false, false);
ns.run(false);
let ns_result = ns
.get_bigint_result()
.context("NetworkSimplex did not return a result, cannot calculate EMSC")?;
log::debug!("NetworkSimplex result: {:?}", ns_result);
// (i64) 2g. Calculate the EMSC value as 1 - (result / (LCM of distances * LCM of probabilities)) (i.e. undo the scaling trick).
let mut result = FractionEnum::one();
let mut distance = FractionEnum::Exact(Rational::from(ns_result));
distance /= FractionEnum::Exact(Rational::from(lcm_distances));
distance /= FractionEnum::Exact(Rational::from(lcm_probabilities));
result -= distance;
return Ok(result);
} else if lcm_probabilities <= Integer::from(i128::MAX)
&& (Into::<Integer>::into(lcm_distances.clone()) + Integer::ONE)
* Integer::from(n + m)
<= Integer::from(i128::MAX)
{
log::info!("Using i128 for NetworkSimplex computation.");
// (i128) 2e. Create a network graph with the scaled distances and probabilities:
// (i128) 2e(i). For each trace in the first language, create a supply node with the corresponding trace probability as supply.
// (i128) 2e(ii). For each trace in the second language, create a demand node with the corresponding trace probability as demand (i.e. negative supply).
let mut supply = vec![0i128; n + m];
supply
.par_chunks_mut(1024)
.enumerate()
.for_each(|(chunk_idx, chunk)| {
chunk.iter_mut().enumerate().for_each(|(i, s)| {
let idx = chunk_idx * 1024 + i;
*s = if idx < n {
(self.weight_a(idx) * &lcm_probability_fraction)
.exact_ref()
.unwrap()
.numerator_ref()
.try_into()
.unwrap()
} else if idx < n + m {
-TryInto::<i128>::try_into(
(self.weight_b(idx - n) * &lcm_probability_fraction)
.exact_ref()
.unwrap()
.numerator_ref(),
)
.unwrap()
} else {
0
};
});
});
// (i128) 2d. Scale the distances and probabilities by the respective identified LCM to retrieve integer values.
// (i128) 2e(iii). Create an edge between each pair of traces with the respective scaled distance as cost.
let mut graph_and_costs = vec![vec![None; n + m]; n + m];
for i in 0..n {
for j in 0..m {
let product = self.distance(i, j) * &lcm_distance_fraction;
let i128 = product
.exact_ref()
.unwrap()
.numerator_ref()
.try_into()
.unwrap();
graph_and_costs[i][j + n] = Some(i128);
}
}
// 2f. Run the NetworkSimplex algorithm to find the optimal flow between the supply and demand nodes.
log::info!("Starting Network Simplex.");
let mut ns = NetworkSimplex::new(&graph_and_costs, &supply, false, false);
ns.run(false);
let ns_result = ns
.get_bigint_result()
.context("NetworkSimplex did not return a result, cannot calculate EMSC")?;
log::debug!("NetworkSimplex result: {:?}", ns_result);
// (i128) 2g. Calculate the EMSC value as 1 - (result / (LCM of distances * LCM of probabilities)) (i.e. undo the scaling trick).
let mut result = FractionEnum::one();
let mut distance = FractionEnum::Exact(Rational::from(ns_result));
distance /= FractionEnum::Exact(Rational::from(lcm_distances));
distance /= FractionEnum::Exact(Rational::from(lcm_probabilities));
result -= distance;
return Ok(result);
} else {
log::info!("Using BigInt for NetworkSimplex computation.");
// (BigInt) 2e. Create a network graph with the scaled distances and probabilities:
// (BigInt) 2e(i). For each trace in the first language, create a supply node with the corresponding trace probability as supply.
// (BigInt) 2e(ii). For each trace in the second language, create a demand node with the corresponding trace probability as demand (i.e. negative supply).
let mut supply = vec![Integer::ZERO; n + m];
supply
.par_chunks_mut(1024)
.enumerate()
.for_each(|(chunk_idx, chunk)| {
chunk.iter_mut().enumerate().for_each(|(i, s)| {
let idx = chunk_idx * 1024 + i;
*s = if idx < n {
(self.weight_a(idx) * &lcm_probability_fraction)
.exact_ref()
.unwrap()
.to_numerator()
.into()
} else if idx < n + m {
-(self.weight_b(idx - n) * &lcm_probability_fraction)
.exact_ref()
.unwrap()
.to_numerator()
} else {
Integer::ZERO
};
});
});
// 2d(BigInt). Scale the distances and probabilities by the respective identified LCM to retrieve integer values.
// (BigInt) 2e(iii). Create an edge between each pair of traces with the respective scaled distance as cost.
let mut graph_and_costs = vec![vec![None; n + m]; n + m];
for index_a in 0..n {
for index_b in 0..m {
let product = self.distance(index_a, index_b) * &lcm_distance_fraction;
let bigint = product.exact_ref().unwrap().signed_numerator();
graph_and_costs[index_a][index_b + n] = Some(bigint);
}
}
// 2f. Run the NetworkSimplex algorithm to find the optimal flow between the supply and demand nodes.
log::info!("Starting Network Simplex.");
let mut ns = NetworkSimplex::new(&graph_and_costs, &supply, false, false);
ns.run(false);
let ns_result = ns
.get_result()
.context("NetworkSimplex did not return a result, cannot calculate EMSC")?;
log::debug!("NetworkSimplex result: {:?}", ns_result);
// 2g. Calculate the EMSC value as 1 - (result / (LCM of distances * LCM of probabilities)) (i.e. undo the scaling trick).
let mut result = FractionEnum::one();
let mut distance = FractionEnum::Exact(Rational::from(ns_result));
distance /= FractionEnum::Exact(Rational::from(lcm_distances));
distance /= FractionEnum::Exact(Rational::from(lcm_probabilities));
result -= distance;
return Ok(result);
}
} else {
//approximate mode
// 2. Is exact arithmetic required?
//not applicable in this compilation mode
// 3. Exact arithmetic is not required, use f64 for the NetworkSimplex computation.
log::info!(
"Calculating approximate EMSC value. Using f64 for NetworkSimplex computation."
);
// 3a. Create a network graph with the scaled distances and probabilities:
let n = self.len_a();
let m = self.len_b();
// 3a(i). For each trace in the first language, create a supply node with the corresponding trace probability as supply.
let mut supply = vec![0.0; n + m];
supply
.par_iter_mut()
.enumerate()
.take(n)
.for_each(|(i, supply)| {
*supply = *self.weight_a(i).approx_ref().unwrap();
});
// 3a(ii). For each trace in the second language, create a demand node with the corresponding trace probability as demand (i.e. negative supply).
supply
.par_iter_mut()
.enumerate()
.skip(n)
.take(m)
.for_each(|(i, supply)| {
*supply = -self.weight_b(i - n).approx_ref().unwrap();
});
// 3a(iii). Create an edge between each pair of traces with the respective distance as cost.
let mut graph_and_costs = vec![vec![None; n + m]; n + m];
// Populate the top-right n x m part of graph_and_costs with scaled_distances
self.iter()
.for_each(|(i, j, f)| graph_and_costs[i][j + n] = Some(*f.approx_ref().unwrap()));
// 3b. Run the NetworkSimplex algorithm to find the optimal flow between the supply and demand nodes.
let mut ns = NetworkSimplex::new(&graph_and_costs, &supply, false, true);
log::info!("Starting Network Simplex.");
ns.run(true);
let ns_result = match ns.get_result() {
Some(result) => result,
None => {
log::info!(
"NetworkSimplex did not return a result, retrying with adjusted parameters."
);
let mut retry_ns = NetworkSimplex::new(&graph_and_costs, &supply, false, false);
retry_ns.run(true);
retry_ns
.get_result()
.context("NetworkSimplex did not return a result, cannot calculate EMSC")?
}
};
log::debug!("NetworkSimplex result: {:?}", ns_result);
// 3c. Calculate the EMSC value as 1 - result.
let result = 1.0 - ns_result;
Ok(FractionEnum::Approx(result))
}
}
}
#[cfg(test)]
mod tests {
use crate::{
ebi_traits::ebi_trait_finite_stochastic_language::EbiTraitFiniteStochasticLanguage,
techniques::earth_movers_stochastic_conformance::EarthMoversStochasticConformance,
};
use ebi_objects::{
FiniteStochasticLanguage,
ebi_arithmetic::{Fraction, One, Zero},
};
use std::fs;
#[test]
fn emsc_one() {
let fin1 = fs::read_to_string("testfiles/aa.slang").unwrap();
let mut slang1: Box<dyn EbiTraitFiniteStochasticLanguage> =
Box::new(fin1.parse::<FiniteStochasticLanguage>().unwrap());
let fin2 = fs::read_to_string("testfiles/aa.slang").unwrap();
let mut slang2 = fin2.parse::<FiniteStochasticLanguage>().unwrap();
let emsc = slang1
.earth_movers_stochastic_conformance(&mut slang2)
.unwrap();
assert_eq!(emsc, Fraction::one());
}
#[test]
fn emsc_zero() {
let fin1 = fs::read_to_string("testfiles/aa.slang").unwrap();
let mut slang1: Box<dyn EbiTraitFiniteStochasticLanguage> =
Box::new(fin1.parse::<FiniteStochasticLanguage>().unwrap());
let fin2 = fs::read_to_string("testfiles/bb.slang").unwrap();
let mut slang2 = fin2.parse::<FiniteStochasticLanguage>().unwrap();
let emsc = slang1
.earth_movers_stochastic_conformance(&mut slang2)
.unwrap();
assert_eq!(emsc, Fraction::zero());
}
}