add an example to study the _recoding inbreeding_ phenomenon

this MR adds examples/inbreeding.rs which allows to do two things

• naive recoding: in order to generate a new random shard, we first k-decode the whole data and then 1-encode a single shard
• true recoding: to achieve the same goal, we directly k-recode shards into a new one

the scenario

regardless of the recoding strategy, the scenario is the same

1. data is split into k shards and n original shards are generated
2. for a given number of steps s, k shards are drawn randomly with replacement and we count the number of successful decoding, given a measure of the diversity, \delta = \frac{\#success}{\#attempts}
3. create a new recoded shard and add it to the n previous ones, i.e. n increases by one
4. repeat steps 2. and 3. as long as you want

results

examples/inbreeding.rs

@@ -5,7 +5,7 @@
 /// const K = 10
 /// const N = 2 * $K
 /// const NB_MEASUREMENTS = 100
-/// const MAX_T = 50
+/// const MAX_T = 150
 ///
 /// cargo run --example inbreeding -- ...[
 ///     $NB_BYTES,
@@ -16,7 +16,7 @@
 ///     --test-case end-to-end
 /// ] | lines | into float | save --force baseline.nuon
 ///
-/// 0..3 | each {|i|
+/// seq 2 $K | reverse | each {|r|
 ///     let inbreeding = cargo run --example inbreeding -- ...[
 ///         $NB_BYTES,
 ///         -k $K
@@ -24,28 +24,31 @@
 ///         --nb-measurements $NB_MEASUREMENTS
 ///         -t $MAX_T
 ///         --test-case recoding
-///         -r ($K - $i)
+///         -r $r
 ///     ] | lines | into float
 ///
 ///     {
-///         r: ($K - $i),
+///         r: $r,
 ///         inbreeding: $inbreeding,
 ///     }
-/// } | save --force res.nuon
+/// } | save --force inbreeding.nuon
 /// ```
 /// - plot the results
 /// ```nushell
 /// let data = open inbreeding.nuon
 /// let k = $data.r | math max
-/// let w = 10
+/// let w = 3
 /// let l = $data.inbreeding.0 | length
 ///
+/// use std repeat
+///
 /// let raw = $data | update inbreeding { take ($l - $w + 1)}
-/// let smooth = $data | update inbreeding { window $w | each { math avg } }
+/// let smooth = $data | update inbreeding { prepend (1 | repeat $w) | window $w | each { math avg } }
 ///
 /// $smooth
 ///     | insert name {|it|
-///         if $it.r == $k { "$k$" }  else { $"$k - ($k - $it.r)$" }
+///        let r = if $it.r == $k { "k" }  else { $"k - ($k - $it.r)" }
+///        $"$r = ($r)$"
 ///     }
 ///     | append ($raw | insert name null | insert style { line: { alpha: 0.1 } })
 ///     | update inbreeding {|it|