feat: add Mash distance metric and rolling entropy support

Implement the Mash distance metric across the CLI, index, and compact vector traits. This includes adding a `Mash` variant to the `DistanceMetric` enum and `MetricArg` CLI argument, implementing the conversion from Jaccard distances using the standard mutation-rate estimator formula, and updating documentation with supported metrics and algorithmic references. Additionally, add an `entropy` method to rolling statistics for computing order-specific entropy.

src/obicompactvec/src/traits.rs

@@ -1,5 +1,16 @@
 use ndarray::{Array1, Array2};
 
+/// Convert a Jaccard distance matrix (`1 - J`) into a Mash distance matrix, per
+/// https://mash.readthedocs.io/en/latest/distances.html:
+/// `D = -1/k * ln(2J / (1+J))`.
+fn jaccard_to_mash(d_jaccard: &Array2<f64>, k: usize) -> Array2<f64> {
+    d_jaccard.mapv(|d| {
+        let j = 1.0 - d;
+        if j <= 0.0 { 1.0 }
+        else { -1.0 / k as f64 * (2.0 * j / (1.0 + j)).ln() }
+    })
+}
+
 // ── Column-level weight statistic — total count or presence count per column.
 /// Additive across layers and partitions; used as denominator in normalised distances.
 ///
@@ -74,6 +85,12 @@ pub trait CountPartials: ColumnWeights {
         m
     }
 
+    /// Mash distance (https://mash.readthedocs.io/en/latest/distances.html), derived
+    /// from the presence-threshold Jaccard distance.
+    fn threshold_mash_dist_matrix(&self, k: usize, threshold: u32) -> Array2<f64> {
+        jaccard_to_mash(&self.threshold_jaccard_dist_matrix(threshold), k)
+    }
+
     fn relfreq_bray_dist_matrix(&self) -> Array2<f64> {
         let global = self.col_weights();
         let mut m = self.partial_relfreq_bray(&global).mapv(|v| 1.0 - v);
@@ -126,6 +143,12 @@ pub trait BitPartials: ColumnWeights {
         m
     }
 
+    /// Mash distance (https://mash.readthedocs.io/en/latest/distances.html), derived
+    /// from the Jaccard distance.
+    fn mash_dist_matrix(&self, k: usize) -> Array2<f64> {
+        jaccard_to_mash(&self.jaccard_dist_matrix(), k)
+    }
+
     fn hamming_dist_matrix(&self) -> Array2<u64> {
         self.partial_hamming()
     }

src/obikindex/src/distance.rs

@@ -14,6 +14,8 @@ pub enum DistanceMetric {
     Jaccard,
     /// Hamming distance (number of differing kmer positions) on presence/absence data.
     Hamming,
+    /// Mash distance on presence/absence data (Jaccard-derived mutation-rate estimate).
+    Mash,
     /// Bray-Curtis dissimilarity on raw counts.
     BrayCurtis,
     /// Bray-Curtis dissimilarity normalised by per-genome total counts.
@@ -84,6 +86,7 @@ impl KmerIndex {
                 DistanceMetric::Hellinger         => CountPartials::hellinger_dist_matrix(&global),
                 DistanceMetric::HellingerEuclidean => CountPartials::hellinger_euclidean_dist_matrix(&global),
                 DistanceMetric::Jaccard           => CountPartials::threshold_jaccard_dist_matrix(&global, presence_threshold),
+                DistanceMetric::Mash              => CountPartials::threshold_mash_dist_matrix(&global, self.kmer_size(), presence_threshold),
                 DistanceMetric::Hamming           => {
                     return Err(OKIError::InvalidInput(
                         "Hamming is only available for presence/absence indexes".into(),
@@ -108,6 +111,7 @@ impl KmerIndex {
 
             let matrix = match metric {
                 DistanceMetric::Jaccard => BitPartials::jaccard_dist_matrix(&global),
+                DistanceMetric::Mash    => BitPartials::mash_dist_matrix(&global, self.kmer_size()),
                 DistanceMetric::Hamming => {
                     BitPartials::hamming_dist_matrix(&global).mapv(|v| v as f64)
                 }

src/obikmer/src/cmd/distance.rs

@@ -10,6 +10,7 @@ use tracing::info;
 #[derive(clap::ValueEnum, Clone, Copy, Debug)]
 pub enum MetricArg {
     Jaccard,
+    Mash,
     Hamming,
     BrayCurtis,
     #[value(name = "relfreq-bray-curtis")]
@@ -26,6 +27,7 @@ impl From<MetricArg> for DistanceMetric {
     fn from(m: MetricArg) -> Self {
         match m {
             MetricArg::Jaccard            => DistanceMetric::Jaccard,
+            MetricArg::Mash               => DistanceMetric::Mash,
             MetricArg::Hamming            => DistanceMetric::Hamming,
             MetricArg::BrayCurtis         => DistanceMetric::BrayCurtis,
             MetricArg::RelfreqBrayCurtis  => DistanceMetric::RelfreqBrayCurtis,

src/obiskbuilder/src/rolling_stat.rs

@@ -196,13 +196,6 @@ impl RollingStat {
             .map(|raw| Minimizer::from_raw_unchecked(raw << (64 - self.m * 2)))
     }
 
-    pub fn entropy(&self, order: usize) -> Option<f64> {
-        if !self.ready() {
-            return None;
-        }
-        Some(self.entropy.entropy(order))
-    }
-
     pub fn normalized_entropy(&self) -> Option<f64> {
         if !self.ready() {
             return None;