Implement elastic alignment

Cargo.toml

@@ -23,6 +23,8 @@ indicatif = { version = "0.17.8", optional = true }
 ndarray-npy ="0.8.1"
 itertools = "0.12.1"
 thiserror = { version = "1.0.58", optional = true }
+dtw = { git = "https://github.com/Ledger-Donjon/dtw.git", rev = "0f8d7ec3bbdf2ca4ec8ea35feddb8d1db73e7d54" }
+num-traits = "0.2.19"
 
 [dev-dependencies]
 criterion = "0.5.1"

src/preprocessors.rs

@@ -1,6 +1,10 @@
 use itertools::Itertools;
 use ndarray::{s, Array1, ArrayView1};
-use std::ops::Range;
+use num_traits::{AsPrimitive, One, Zero};
+use std::{
+    cmp::Ordering,
+    ops::{Div, Range},
+};
 
 use crate::processors::MeanVar;
 
@@ -148,12 +152,103 @@ impl StandardScaler {
     }
 }
 
+pub use dtw::dist;
+
+/// Align traces using elastic alignment [1]. Elastic alignment is a dynamic alignment algorithm
+/// based on FastDTW.
+///
+/// # Examples
+/// ```rust
+/// use muscat::preprocessors::{ElasticAlignment, dist::euclidean_distance};
+/// use ndarray::array;
+///
+/// let reference_trace = array![77, 117, 5, 51, 91, -12, -33];
+/// let trace_to_align = array![77, 117, 13, 15, 5, 51, 91];
+/// let elastic_alignment = ElasticAlignment::new(reference_trace, 1, euclidean_distance);
+///
+/// let aligned_trace = elastic_alignment.align(trace_to_align.view());
+/// ```
+///
+/// # References
+/// [1] van Woudenberg, J.G.J., Witteman, M.F., Bakker, B. (2011). Improving Differential Power
+/// Analysis by Elastic Alignment. In: Kiayias, A. (eds) Topics in Cryptology – CT-RSA 2011. CT-RSA
+/// 2011. Lecture Notes in Computer Science, vol 6558. Springer, Berlin, Heidelberg.
+/// https://doi.org/10.1007/978-3-642-19074-2_8
+pub struct ElasticAlignment<T, D>
+where
+    D: Fn(T, T) -> T,
+{
+    reference_trace: Array1<T>,
+    /// FastDTW radius
+    radius: usize,
+    /// Distance function
+    dist: D,
+}
+
+impl<T, D> ElasticAlignment<T, D>
+where
+    T: dtw::Average + dtw::SumContainer + Copy + Zero + 'static,
+    T::Container: Zero + One + Div<Output = T::Container> + AsPrimitive<T>,
+    D: Fn(T, T) -> T,
+{
+    /// Creates a new [`ElasticAlignment`] with the given reference trace and distance function.
+    pub fn new(reference_trace: Array1<T>, radius: usize, dist: D) -> Self {
+        Self {
+            reference_trace,
+            radius,
+            dist,
+        }
+    }
+
+    /// Align given trace using elastic alignment (see [`ElasticAlignment`]).
+    pub fn align_with_cmp<C>(&self, trace: ArrayView1<T>, cmp: &C) -> Array1<T>
+    where
+        C: Fn(&T::Container, &T::Container) -> Ordering,
+    {
+        let warp_path = dtw::fast_dtw_with_cmp(
+            self.reference_trace.as_slice().unwrap(),
+            trace.as_slice().unwrap(),
+            self.radius,
+            &self.dist,
+            cmp,
+        );
+
+        let mut aligned_trace = Array1::zeros([trace.len()]);
+        let mut k = 0;
+        for j in 0..trace.len() {
+            let mut count = T::Container::zero();
+            let mut sum = T::Container::zero();
+
+            while k < warp_path.len() && warp_path[k].0 == j {
+                count = count + T::Container::one();
+                sum = sum + T::Container::from(trace[warp_path[k].1]);
+                k += 1;
+            }
+
+            aligned_trace[j] = (sum / count).as_();
+        }
+
+        aligned_trace
+    }
+}
+
+impl<T, D> ElasticAlignment<T, D>
+where
+    T: dtw::Average + dtw::SumContainer + Copy + Zero + 'static,
+    T::Container: Zero + One + Div<Output = T::Container> + AsPrimitive<T> + Ord,
+    D: Fn(T, T) -> T,
+{
+    /// Align given trace using elastic alignment (see [`ElasticAlignment`]).
+    ///
+    /// NOTE: See [`ElasticAlignment::align_with_cmp`] for type than do not implement [`Ord`].
+    pub fn align(&self, trace: ArrayView1<T>) -> Array1<T> {
+        self.align_with_cmp(trace, &T::Container::cmp)
+    }
+}
+
 #[cfg(test)]
 mod tests {
-    use crate::preprocessors::StandardScaler;
-
-    use super::CenteredProduct;
-    use super::Power;
+    use crate::preprocessors::{dist, CenteredProduct, ElasticAlignment, Power, StandardScaler};
     use ndarray::array;
 
     fn round_to_2_digits(x: f64) -> f64 {
@@ -285,4 +380,29 @@ mod tests {
             );
         }
     }
+
+    #[test]
+    fn test_elastic_align() {
+        let reference_trace = array![77, 117, 5, 51, 91, -12, -33];
+        let trace = array![77, 117, 13, 15, 5, 51, 91];
+
+        let elastic_alignment =
+            ElasticAlignment::new(reference_trace.clone(), 1, dist::euclidean_distance);
+        assert_eq!(
+            elastic_alignment.align(trace.view()),
+            array![77, 117, 11, 51, 51, 51, 91]
+        );
+    }
+
+    #[test]
+    fn test_elastic_align_same_trace() {
+        let reference_trace = array![77, 117, 5, 51, 91, -12, -33];
+
+        let elastic_alignment =
+            ElasticAlignment::new(reference_trace.clone(), 1, dist::euclidean_distance);
+        assert_eq!(
+            elastic_alignment.align(reference_trace.view()),
+            reference_trace
+        );
+    }
 }