From b7f7b29e48274b98136519e4b076812eb06acda8 Mon Sep 17 00:00:00 2001
From: NicklasXYZ <18580183+NicklasXYZ@users.noreply.github.com>
Date: Sat, 13 Apr 2024 23:38:39 +0200
Subject: [PATCH] Add canberra and bary-curtis distance

---
 src/gleam_community/maths/arithmetics.gleam   |  77 +++--
 src/gleam_community/maths/metrics.gleam       | 309 +++++++++++++-----
 .../maths/arithmetics_test.gleam              |  19 +-
 test/gleam_community/maths/metrics_test.gleam | 165 ++++++++--
 4 files changed, 432 insertions(+), 138 deletions(-)

diff --git a/src/gleam_community/maths/arithmetics.gleam b/src/gleam_community/maths/arithmetics.gleam
index dbd3ffe..b37a067 100644
--- a/src/gleam_community/maths/arithmetics.gleam
+++ b/src/gleam_community/maths/arithmetics.gleam
@@ -44,6 +44,9 @@
 
 import gleam/int
 import gleam/list
+import gleam/option
+import gleam/pair
+import gleam/result
 import gleam_community/maths/conversion
 import gleam_community/maths/elementary
 import gleam_community/maths/piecewise
@@ -289,29 +292,32 @@ pub fn proper_divisors(n: Int) -> List(Int) {
 ///     </a>
 /// </div>
 ///
-/// Calculate the sum of the elements in a list:
+/// Calculate the (weighted) sum of the elements in a list:
 ///
 /// \\[
-/// \sum_{i=1}^n x_i
+/// \sum_{i=1}^n w_i x_i
 /// \\]
 ///
-/// In the formula, $$n$$ is the length of the list and $$x_i \in \mathbb{R}$$ is the value in the input list indexed by $$i$$.
+/// In the formula, $$n$$ is the length of the list and $$x_i \in \mathbb{R}$$ is
+/// the value in the input list indexed by $$i$$, while $$w_i \in \mathbb{R}$$ is
+/// a corresponding weight ($$w_i = 1.0\;\forall i=1...n$$ by default).
 ///
 /// <details>
 ///     <summary>Example:</summary>
 ///
 ///     import gleeunit/should
+///     import gleam/option
 ///     import gleam_community/maths/arithmetics
 ///
 ///     pub fn example () {
 ///       // An empty list returns an error
 ///       []
-///       |> arithmetics.float_sum()
+///       |> arithmetics.float_sum(option.None)
 ///       |> should.equal(0.0)
 ///
 ///       // Valid input returns a result
 ///       [1.0, 2.0, 3.0]
-///       |> arithmetics.float_sum()
+///       |> arithmetics.float_sum(option.None)
 ///       |> should.equal(6.0)
 ///     }
 /// </details>
@@ -322,12 +328,18 @@ pub fn proper_divisors(n: Int) -> List(Int) {
 ///     </a>
 /// </div>
 ///
-pub fn float_sum(arr: List(Float)) -> Float {
-  case arr {
-    [] -> 0.0
-    _ ->
+pub fn float_sum(arr: List(Float), weights: option.Option(List(Float))) -> Float {
+  case arr, weights {
+    [], _ -> 0.0
+    _, option.None ->
       arr
       |> list.fold(0.0, fn(acc: Float, a: Float) -> Float { a +. acc })
+    _, option.Some(warr) -> {
+      list.zip(arr, warr)
+      |> list.fold(0.0, fn(acc: Float, a: #(Float, Float)) -> Float {
+        pair.first(a) *. pair.second(a) +. acc
+      })
+    }
   }
 }
 
@@ -385,29 +397,32 @@ pub fn int_sum(arr: List(Int)) -> Int {
 ///     </a>
 /// </div>
 ///
-/// Calculate the product of the elements in a list:
+/// Calculate the (weighted) product of the elements in a list:
 ///
 /// \\[
-/// \prod_{i=1}^n x_i
+/// \prod_{i=1}^n x_i^{w_i}
 /// \\]
 ///
-/// In the formula, $$n$$ is the length of the list and $$x_i \in \mathbb{R}$$ is the value in the input list indexed by $$i$$.
-///
+/// In the formula, $$n$$ is the length of the list and $$x_i \in \mathbb{R}$$ is
+/// the value in the input list indexed by $$i$$, while $$w_i \in \mathbb{R}$$ is
+/// a corresponding weight ($$w_i = 1.0\;\forall i=1...n$$ by default).
+/// 
 /// <details>
 ///     <summary>Example:</summary>
 ///
 ///     import gleeunit/should
+///     import gleam/option
 ///     import gleam_community/maths/arithmetics
 ///
 ///     pub fn example () {
 ///       // An empty list returns 0.0
 ///       []
-///       |> arithmetics.float_product()
+///       |> arithmetics.float_product(option.None)
 ///       |> should.equal(0.0)
 ///
 ///       // Valid input returns a result
 ///       [1.0, 2.0, 3.0]
-///       |> arithmetics.float_product()
+///       |> arithmetics.float_product(option.None)
 ///       |> should.equal(6.0)
 ///     }
 /// </details>
@@ -418,12 +433,36 @@ pub fn int_sum(arr: List(Int)) -> Int {
 ///     </a>
 /// </div>
 ///
-pub fn float_product(arr: List(Float)) -> Float {
-  case arr {
-    [] -> 1.0
-    _ ->
+pub fn float_product(
+  arr: List(Float),
+  weights: option.Option(List(Float)),
+) -> Result(Float, String) {
+  case arr, weights {
+    [], _ ->
+      1.0
+      |> Ok
+    _, option.None ->
       arr
       |> list.fold(1.0, fn(acc: Float, a: Float) -> Float { a *. acc })
+      |> Ok
+    _, option.Some(warr) -> {
+      let results =
+        list.zip(arr, warr)
+        |> list.map(fn(a: #(Float, Float)) -> Result(Float, String) {
+          pair.first(a)
+          |> elementary.power(pair.second(a))
+        })
+        |> result.all
+      case results {
+        Ok(prods) ->
+          prods
+          |> list.fold(1.0, fn(acc: Float, a: Float) -> Float { a *. acc })
+          |> Ok
+        Error(msg) ->
+          msg
+          |> Error
+      }
+    }
   }
 }
 
diff --git a/src/gleam_community/maths/metrics.gleam b/src/gleam_community/maths/metrics.gleam
index 237b900..84cb8b2 100644
--- a/src/gleam_community/maths/metrics.gleam
+++ b/src/gleam_community/maths/metrics.gleam
@@ -33,6 +33,8 @@
 ////   * [`chebyshev_distance`](#chebyshev_distance)
 ////   * [`minkowski_distance`](#minkowski_distance)
 ////   * [`cosine_similarity`](#cosine_similarity)
+////   * [`canberra_distance`](#canberra_distance)
+////   * [`braycurtis_distance`](#braycurtis_distance)
 //// * **Set & string similarity measures**
 ////   * [`jaccard_index`](#jaccard_index)
 ////   * [`sorensen_dice_coefficient`](#sorensen_dice_coefficient)
@@ -57,6 +59,48 @@ import gleam/set
 import gleam/float
 import gleam/int
 import gleam/string
+import gleam/option
+
+/// Utility function that checks all lists have the expected length
+/// Primarily used by all distance measures taking List(Float) as input
+fn check_lists(
+  xarr: List(Float),
+  yarr: List(Float),
+  weights: option.Option(List(Float)),
+) -> Result(Bool, String) {
+  case xarr, yarr {
+    [], _ ->
+      "Invalid input argument: The list xarr is empty."
+      |> Error
+    _, [] ->
+      "Invalid input argument: The list yarr is empty."
+      |> Error
+    _, _ -> {
+      let xlen: Int = list.length(xarr)
+      let ylen: Int = list.length(yarr)
+      case xlen == ylen, weights {
+        False, _ ->
+          "Invalid input argument: length(xarr) != length(yarr). Valid input is when length(xarr) == length(yarr)."
+          |> Error
+        True, option.None -> {
+          True
+          |> Ok
+        }
+        True, option.Some(warr) -> {
+          let wlen: Int = list.length(warr)
+          case xlen == wlen {
+            True ->
+              True
+              |> Ok
+            False ->
+              "Invalid input argument: length(weights) != length(xarr) and length(weights) != length(yarr). Valid input is when length(weights) == length(xarr) == length(yarr)."
+              |> Error
+          }
+        }
+      }
+    }
+  }
+}
 
 /// <div style="text-align: right;">
 ///     <a href="https://github.com/gleam-community/maths/issues">
@@ -169,8 +213,9 @@ pub fn norm(arr: List(Float), p: Float) -> Float {
 pub fn manhattan_distance(
   xarr: List(Float),
   yarr: List(Float),
+  weights: option.Option(List(Float)),
 ) -> Result(Float, String) {
-  minkowski_distance(xarr, yarr, 1.0)
+  minkowski_distance(xarr, yarr, 1.0, weights)
 }
 
 /// <div style="text-align: right;">
@@ -231,34 +276,24 @@ pub fn minkowski_distance(
   xarr: List(Float),
   yarr: List(Float),
   p: Float,
+  weights: option.Option(List(Float)),
 ) -> Result(Float, String) {
-  case xarr, yarr {
-    [], _ ->
-      "Invalid input argument: The list xarr is empty."
+  case check_lists(xarr, yarr, weights) {
+    Error(msg) ->
+      msg
       |> Error
-    _, [] ->
-      "Invalid input argument: The list yarr is empty."
-      |> Error
-    _, _ -> {
-      let xlen: Int = list.length(xarr)
-      let ylen: Int = list.length(yarr)
-      case xlen == ylen {
-        False ->
-          "Invalid input argument: length(xarr) != length(yarr). Valid input is when length(xarr) == length(yarr)."
-          |> Error
+    Ok(_) -> {
+      case p <. 1.0 {
         True ->
-          case p <. 1.0 {
-            True ->
-              "Invalid input argument: p < 1. Valid input is p >= 1."
-              |> Error
-            False ->
-              list.zip(xarr, yarr)
-              |> list.map(fn(tuple: #(Float, Float)) -> Float {
-                pair.first(tuple) -. pair.second(tuple)
-              })
-              |> norm(p)
-              |> Ok
-          }
+          "Invalid input argument: p < 1. Valid input is p >= 1."
+          |> Error
+        False ->
+          list.zip(xarr, yarr)
+          |> list.map(fn(tuple: #(Float, Float)) -> Float {
+            pair.first(tuple) -. pair.second(tuple)
+          })
+          |> norm(p)
+          |> Ok
       }
     }
   }
@@ -314,8 +349,9 @@ pub fn minkowski_distance(
 pub fn euclidean_distance(
   xarr: List(Float),
   yarr: List(Float),
+  weights: option.Option(List(Float)),
 ) -> Result(Float, String) {
-  minkowski_distance(xarr, yarr, 2.0)
+  minkowski_distance(xarr, yarr, 2.0, weights)
 }
 
 /// <div style="text-align: right;">
@@ -364,32 +400,21 @@ pub fn euclidean_distance(
 pub fn chebyshev_distance(
   xarr: List(Float),
   yarr: List(Float),
+  weights: option.Option(List(Float)),
 ) -> Result(Float, String) {
-  case xarr, yarr {
-    [], _ ->
-      "Invalid input argument: The list xarr is empty."
+  case check_lists(xarr, yarr, weights) {
+    Error(msg) ->
+      msg
       |> Error
-    _, [] ->
-      "Invalid input argument: The list yarr is empty."
-      |> Error
-    _, _ -> {
-      let xlen: Int = list.length(xarr)
-      let ylen: Int = list.length(yarr)
-      case xlen == ylen {
-        False ->
-          "Invalid input argument: length(xarr) != length(yarr). Valid input is when length(xarr) == length(yarr)."
-          |> Error
-        True -> {
-          let differences =
-            list.zip(xarr, yarr)
-            |> list.map(fn(tuple: #(Float, Float)) -> Float {
-              { pair.first(tuple) -. pair.second(tuple) }
-              |> piecewise.float_absolute_value()
-            })
-          differences
-          |> piecewise.list_maximum(float.compare)
-        }
-      }
+    Ok(_) -> {
+      let differences =
+        list.zip(xarr, yarr)
+        |> list.map(fn(tuple: #(Float, Float)) -> Float {
+          { pair.first(tuple) -. pair.second(tuple) }
+          |> piecewise.float_absolute_value()
+        })
+      differences
+      |> piecewise.list_maximum(float.compare)
     }
   }
 }
@@ -441,7 +466,7 @@ pub fn mean(arr: List(Float)) -> Result(Float, String) {
       |> Error
     _ ->
       arr
-      |> arithmetics.float_sum()
+      |> arithmetics.float_sum(option.None)
       |> fn(a: Float) -> Float {
         a /. conversion.int_to_float(list.length(arr))
       }
@@ -579,7 +604,7 @@ pub fn variance(arr: List(Float), ddof: Int) -> Result(Float, String) {
             let assert Ok(result) = elementary.power(a -. mean, 2.0)
             result
           })
-          |> arithmetics.float_sum()
+          |> arithmetics.float_sum(option.None)
           |> fn(a: Float) -> Float {
             a
             /. {
@@ -969,34 +994,23 @@ pub fn overlap_coefficient(xset: set.Set(a), yset: set.Set(a)) -> Float {
 pub fn cosine_similarity(
   xarr: List(Float),
   yarr: List(Float),
+  weights: option.Option(List(Float)),
 ) -> Result(Float, String) {
-  case xarr, yarr {
-    [], _ ->
-      "Invalid input argument: The list xarr is empty."
+  case check_lists(xarr, yarr, weights) {
+    Error(msg) ->
+      msg
       |> Error
-    _, [] ->
-      "Invalid input argument: The list yarr is empty."
-      |> Error
-    _, _ -> {
-      let xlen: Int = list.length(xarr)
-      let ylen: Int = list.length(yarr)
-      case xlen == ylen {
-        False ->
-          "Invalid input argument: length(xarr) != length(yarr). Valid input is when length(xarr) == length(yarr)."
-          |> Error
-        True -> {
-          list.fold(
-            list.zip(xarr, yarr),
-            0.0,
-            fn(acc: Float, a: #(Float, Float)) -> Float {
-              let result: Float = pair.first(a) *. pair.second(a)
-              result +. acc
-            },
-          )
-          /. { norm(xarr, 2.0) *. norm(yarr, 2.0) }
-          |> Ok
-        }
-      }
+    Ok(_) -> {
+      list.fold(
+        list.zip(xarr, yarr),
+        0.0,
+        fn(acc: Float, a: #(Float, Float)) -> Float {
+          let result: Float = pair.first(a) *. pair.second(a)
+          result +. acc
+        },
+      )
+      /. { norm(xarr, 2.0) *. norm(yarr, 2.0) }
+      |> Ok
     }
   }
 }
@@ -1119,3 +1133,140 @@ fn distance_list_helper(
     }
   }
 }
+
+/// <div style="text-align: right;">
+///     <a href="https://github.com/gleam-community/maths/issues">
+///         <small>Spot a typo? Open an issue!</small>
+///     </a>
+/// </div>
+/// 
+/// <details>
+///     <summary>Example:</summary>
+///
+///     import gleeunit/should
+///     import gleam_community/maths/metrics
+///
+///     pub fn example () {
+///     }
+/// </details>
+///
+/// <div style="text-align: right;">
+///     <a href="#">
+///         <small>Back to top ↑</small>
+///     </a>
+/// </div>
+///
+///
+pub fn canberra_distance(
+  xarr: List(Float),
+  yarr: List(Float),
+  weights: option.Option(List(Float)),
+) -> Result(Float, String) {
+  case check_lists(xarr, yarr, weights) {
+    Error(msg) ->
+      msg
+      |> Error
+    Ok(_) -> {
+      let arr: List(Float) =
+        list.zip(xarr, yarr)
+        |> list.map(canberra_distance_helper)
+      case weights {
+        option.None -> {
+          arr
+          |> arithmetics.float_sum(option.None)
+          |> Ok
+        }
+        _ -> {
+          arr
+          |> arithmetics.float_sum(weights)
+          |> Ok
+        }
+      }
+    }
+  }
+}
+
+fn canberra_distance_helper(tuple: #(Float, Float)) -> Float {
+  let numerator: Float =
+    piecewise.float_absolute_value({ pair.first(tuple) -. pair.second(tuple) })
+  let denominator: Float = {
+    piecewise.float_absolute_value(pair.first(tuple))
+    +. piecewise.float_absolute_value(pair.second(tuple))
+  }
+  numerator /. denominator
+}
+
+/// <div style="text-align: right;">
+///     <a href="https://github.com/gleam-community/maths/issues">
+///         <small>Spot a typo? Open an issue!</small>
+///     </a>
+/// </div>
+/// 
+/// <details>
+///     <summary>Example:</summary>
+///
+///     import gleeunit/should
+///     import gleam_community/maths/metrics
+///
+///     pub fn example () {
+///     }
+/// </details>
+///
+/// <div style="text-align: right;">
+///     <a href="#">
+///         <small>Back to top ↑</small>
+///     </a>
+/// </div>
+///
+///
+pub fn braycurtis_distance(
+  xarr: List(Float),
+  yarr: List(Float),
+  weights: option.Option(List(Float)),
+) -> Result(Float, String) {
+  case check_lists(xarr, yarr, weights) {
+    Error(msg) ->
+      msg
+      |> Error
+    Ok(_) -> {
+      let zipped_arr: List(#(Float, Float)) = list.zip(xarr, yarr)
+      let numerator_elements: List(Float) =
+        zipped_arr
+        |> list.map(fn(tuple: #(Float, Float)) -> Float {
+          piecewise.float_absolute_value({
+            pair.first(tuple) -. pair.second(tuple)
+          })
+        })
+      let denominator_elements: List(Float) =
+        zipped_arr
+        |> list.map(fn(tuple: #(Float, Float)) -> Float {
+          piecewise.float_absolute_value({
+            pair.first(tuple) +. pair.second(tuple)
+          })
+        })
+
+      case weights {
+        option.None -> {
+          let numerator =
+            numerator_elements
+            |> arithmetics.float_sum(option.None)
+          let denominator =
+            denominator_elements
+            |> arithmetics.float_sum(option.None)
+          { numerator /. denominator }
+          |> Ok
+        }
+        _ -> {
+          let numerator =
+            numerator_elements
+            |> arithmetics.float_sum(weights)
+          let denominator =
+            denominator_elements
+            |> arithmetics.float_sum(weights)
+          { numerator /. denominator }
+          |> Ok
+        }
+      }
+    }
+  }
+}
diff --git a/test/gleam_community/maths/arithmetics_test.gleam b/test/gleam_community/maths/arithmetics_test.gleam
index aa694b7..7ec5ad5 100644
--- a/test/gleam_community/maths/arithmetics_test.gleam
+++ b/test/gleam_community/maths/arithmetics_test.gleam
@@ -1,5 +1,6 @@
 import gleam_community/maths/arithmetics
 import gleeunit/should
+import gleam/option
 
 pub fn int_gcd_test() {
   arithmetics.gcd(1, 1)
@@ -100,16 +101,16 @@ pub fn int_divisors_test() {
 pub fn float_list_sum_test() {
   // An empty list returns 0
   []
-  |> arithmetics.float_sum()
+  |> arithmetics.float_sum(option.None)
   |> should.equal(0.0)
 
   // Valid input returns a result
   [1.0, 2.0, 3.0]
-  |> arithmetics.float_sum()
+  |> arithmetics.float_sum(option.None)
   |> should.equal(6.0)
 
   [-2.0, 4.0, 6.0]
-  |> arithmetics.float_sum()
+  |> arithmetics.float_sum(option.None)
   |> should.equal(8.0)
 }
 
@@ -132,17 +133,17 @@ pub fn int_list_sum_test() {
 pub fn float_list_product_test() {
   // An empty list returns 0
   []
-  |> arithmetics.float_product()
-  |> should.equal(1.0)
+  |> arithmetics.float_product(option.None)
+  |> should.equal(Ok(1.0))
 
   // Valid input returns a result
   [1.0, 2.0, 3.0]
-  |> arithmetics.float_product()
-  |> should.equal(6.0)
+  |> arithmetics.float_product(option.None)
+  |> should.equal(Ok(6.0))
 
   [-2.0, 4.0, 6.0]
-  |> arithmetics.float_product()
-  |> should.equal(-48.0)
+  |> arithmetics.float_product(option.None)
+  |> should.equal(Ok(-48.0))
 }
 
 pub fn int_list_product_test() {
diff --git a/test/gleam_community/maths/metrics_test.gleam b/test/gleam_community/maths/metrics_test.gleam
index e5888a0..3ccf758 100644
--- a/test/gleam_community/maths/metrics_test.gleam
+++ b/test/gleam_community/maths/metrics_test.gleam
@@ -3,6 +3,7 @@ import gleam_community/maths/metrics
 import gleam_community/maths/predicates
 import gleeunit/should
 import gleam/set
+import gleam/option
 
 pub fn float_list_norm_test() {
   let assert Ok(tol) = elementary.power(-10.0, -6.0)
@@ -54,15 +55,16 @@ pub fn float_list_manhattan_test() {
   let assert Ok(tol) = elementary.power(-10.0, -6.0)
 
   // Empty lists returns an error
-  metrics.manhattan_distance([], [])
+  metrics.manhattan_distance([], [], option.None)
   |> should.be_error()
 
   // Differing lengths returns error
-  metrics.manhattan_distance([], [1.0])
+  metrics.manhattan_distance([], [1.0], option.None)
   |> should.be_error()
 
   // manhattan distance (p = 1)
-  let assert Ok(result) = metrics.manhattan_distance([0.0, 0.0], [1.0, 2.0])
+  let assert Ok(result) =
+    metrics.manhattan_distance([0.0, 0.0], [1.0, 2.0], option.None)
   result
   |> predicates.is_close(3.0, 0.0, tol)
   |> should.be_true()
@@ -72,53 +74,53 @@ pub fn float_list_minkowski_test() {
   let assert Ok(tol) = elementary.power(-10.0, -6.0)
 
   // Empty lists returns an error
-  metrics.minkowski_distance([], [], 1.0)
+  metrics.minkowski_distance([], [], 1.0, option.None)
   |> should.be_error()
 
   // Differing lengths returns error
-  metrics.minkowski_distance([], [1.0], 1.0)
+  metrics.minkowski_distance([], [1.0], 1.0, option.None)
   |> should.be_error()
 
   // Test order < 1
-  metrics.minkowski_distance([0.0, 0.0], [0.0, 0.0], -1.0)
+  metrics.minkowski_distance([0.0, 0.0], [0.0, 0.0], -1.0, option.None)
   |> should.be_error()
 
   // Check that the function agrees, at some arbitrary input
   // points, with known function values
   let assert Ok(result) =
-    metrics.minkowski_distance([1.0, 1.0], [1.0, 1.0], 1.0)
+    metrics.minkowski_distance([1.0, 1.0], [1.0, 1.0], 1.0, option.None)
   result
   |> predicates.is_close(0.0, 0.0, tol)
   |> should.be_true()
 
   let assert Ok(result) =
-    metrics.minkowski_distance([0.0, 0.0], [1.0, 1.0], 10.0)
+    metrics.minkowski_distance([0.0, 0.0], [1.0, 1.0], 10.0, option.None)
   result
   |> predicates.is_close(1.0717734625362931, 0.0, tol)
   |> should.be_true()
 
   let assert Ok(result) =
-    metrics.minkowski_distance([0.0, 0.0], [1.0, 1.0], 100.0)
+    metrics.minkowski_distance([0.0, 0.0], [1.0, 1.0], 100.0, option.None)
   result
   |> predicates.is_close(1.0069555500567189, 0.0, tol)
   |> should.be_true()
 
   let assert Ok(result) =
-    metrics.minkowski_distance([0.0, 0.0], [1.0, 1.0], 10.0)
+    metrics.minkowski_distance([0.0, 0.0], [1.0, 1.0], 10.0, option.None)
   result
   |> predicates.is_close(1.0717734625362931, 0.0, tol)
   |> should.be_true()
 
   // Euclidean distance (p = 2)
   let assert Ok(result) =
-    metrics.minkowski_distance([0.0, 0.0], [1.0, 2.0], 2.0)
+    metrics.minkowski_distance([0.0, 0.0], [1.0, 2.0], 2.0, option.None)
   result
   |> predicates.is_close(2.23606797749979, 0.0, tol)
   |> should.be_true()
 
   // Manhattan distance (p = 1)
   let assert Ok(result) =
-    metrics.minkowski_distance([0.0, 0.0], [1.0, 2.0], 1.0)
+    metrics.minkowski_distance([0.0, 0.0], [1.0, 2.0], 1.0, option.None)
   result
   |> predicates.is_close(3.0, 0.0, tol)
   |> should.be_true()
@@ -128,15 +130,16 @@ pub fn float_list_euclidean_test() {
   let assert Ok(tol) = elementary.power(-10.0, -6.0)
 
   // Empty lists returns an error
-  metrics.euclidean_distance([], [])
+  metrics.euclidean_distance([], [], option.None)
   |> should.be_error()
 
   // Differing lengths returns error
-  metrics.euclidean_distance([], [1.0])
+  metrics.euclidean_distance([], [1.0], option.None)
   |> should.be_error()
 
   // Euclidean distance (p = 2)
-  let assert Ok(result) = metrics.euclidean_distance([0.0, 0.0], [1.0, 2.0])
+  let assert Ok(result) =
+    metrics.euclidean_distance([0.0, 0.0], [1.0, 2.0], option.None)
   result
   |> predicates.is_close(2.23606797749979, 0.0, tol)
   |> should.be_true()
@@ -266,65 +269,69 @@ pub fn overlap_coefficient_test() {
 
 pub fn cosine_similarity_test() {
   // Empty lists returns an error
-  metrics.cosine_similarity([], [])
+  metrics.cosine_similarity([], [], option.None)
   |> should.be_error()
 
   // One empty list returns an error
-  metrics.cosine_similarity([1.0, 2.0, 3.0], [])
+  metrics.cosine_similarity([1.0, 2.0, 3.0], [], option.None)
   |> should.be_error()
 
   // One empty list returns an error
-  metrics.cosine_similarity([], [1.0, 2.0, 3.0])
+  metrics.cosine_similarity([], [1.0, 2.0, 3.0], option.None)
   |> should.be_error()
 
   // Different sized lists returns an error
-  metrics.cosine_similarity([1.0, 2.0], [1.0, 2.0, 3.0, 4.0])
+  metrics.cosine_similarity([1.0, 2.0], [1.0, 2.0, 3.0, 4.0], option.None)
   |> should.be_error()
 
   // Two orthogonal vectors (represented by lists)
-  metrics.cosine_similarity([-1.0, 1.0, 0.0], [1.0, 1.0, -1.0])
+  metrics.cosine_similarity([-1.0, 1.0, 0.0], [1.0, 1.0, -1.0], option.None)
   |> should.equal(Ok(0.0))
 
   // Two identical (parallel) vectors (represented by lists)
-  metrics.cosine_similarity([1.0, 2.0, 3.0], [1.0, 2.0, 3.0])
+  metrics.cosine_similarity([1.0, 2.0, 3.0], [1.0, 2.0, 3.0], option.None)
   |> should.equal(Ok(1.0))
 
   // Two parallel, but oppositely oriented vectors (represented by lists)
-  metrics.cosine_similarity([-1.0, -2.0, -3.0], [1.0, 2.0, 3.0])
+  metrics.cosine_similarity([-1.0, -2.0, -3.0], [1.0, 2.0, 3.0], option.None)
   |> should.equal(Ok(-1.0))
 }
 
 pub fn chebyshev_distance_test() {
   // Empty lists returns an error
-  metrics.chebyshev_distance([], [])
+  metrics.chebyshev_distance([], [], option.None)
   |> should.be_error()
 
   // One empty list returns an error
-  metrics.chebyshev_distance([1.0, 2.0, 3.0], [])
+  metrics.chebyshev_distance([1.0, 2.0, 3.0], [], option.None)
   |> should.be_error()
 
   // One empty list returns an error
-  metrics.chebyshev_distance([], [1.0, 2.0, 3.0])
+  metrics.chebyshev_distance([], [1.0, 2.0, 3.0], option.None)
   |> should.be_error()
 
   // Different sized lists returns an error
-  metrics.chebyshev_distance([1.0, 2.0], [1.0, 2.0, 3.0, 4.0])
+  metrics.chebyshev_distance([1.0, 2.0], [1.0, 2.0, 3.0, 4.0], option.None)
   |> should.be_error()
 
   // Try different types of valid input
-  metrics.chebyshev_distance([1.0, 0.0], [0.0, 2.0])
+  metrics.chebyshev_distance([1.0, 0.0], [0.0, 2.0], option.None)
   |> should.equal(Ok(2.0))
 
-  metrics.chebyshev_distance([1.0, 0.0], [2.0, 0.0])
+  metrics.chebyshev_distance([1.0, 0.0], [2.0, 0.0], option.None)
   |> should.equal(Ok(1.0))
 
-  metrics.chebyshev_distance([1.0, 0.0], [-2.0, 0.0])
+  metrics.chebyshev_distance([1.0, 0.0], [-2.0, 0.0], option.None)
   |> should.equal(Ok(3.0))
 
-  metrics.chebyshev_distance([-5.0, -10.0, -3.0], [-1.0, -12.0, -3.0])
+  metrics.chebyshev_distance(
+    [-5.0, -10.0, -3.0],
+    [-1.0, -12.0, -3.0],
+    option.None,
+  )
   |> should.equal(Ok(4.0))
 
-  metrics.chebyshev_distance([1.0, 2.0, 3.0], [1.0, 2.0, 3.0])
+  metrics.chebyshev_distance([1.0, 2.0, 3.0], [1.0, 2.0, 3.0], option.None)
   |> should.equal(Ok(0.0))
 }
 
@@ -367,3 +374,99 @@ pub fn levenshtein_distance_test() {
   )
   |> should.equal(10)
 }
+
+pub fn canberra_distance_test() {
+  // Empty lists returns an error
+  metrics.canberra_distance([], [], option.None)
+  |> should.be_error()
+
+  // One empty list returns an error
+  metrics.canberra_distance([1.0, 2.0, 3.0], [], option.None)
+  |> should.be_error()
+
+  // One empty list returns an error
+  metrics.canberra_distance([], [1.0, 2.0, 3.0], option.None)
+  |> should.be_error()
+
+  // Different sized lists returns an error
+  metrics.canberra_distance([1.0, 2.0], [1.0, 2.0, 3.0, 4.0], option.None)
+  |> should.be_error()
+
+  // Try different types of valid input
+  metrics.canberra_distance([0.0, 0.0], [0.0, 0.0], option.None)
+  |> should.equal(Ok(0.0))
+
+  metrics.canberra_distance([1.0, 2.0], [-2.0, -1.0], option.None)
+  |> should.equal(Ok(2.0))
+
+  metrics.canberra_distance([1.0, 0.0], [0.0, 2.0], option.None)
+  |> should.equal(Ok(2.0))
+
+  metrics.canberra_distance([1.0, 0.0], [2.0, 0.0], option.None)
+  |> should.equal(Ok(1.0 /. 3.0))
+
+  metrics.canberra_distance([1.0, 0.0], [0.0, 2.0], option.Some([1.0, 1.0]))
+  |> should.equal(Ok(2.0))
+
+  metrics.canberra_distance([1.0, 0.0], [0.0, 2.0], option.Some([1.0, 0.5]))
+  |> should.equal(Ok(1.5))
+
+  metrics.canberra_distance([1.0, 0.0], [0.0, 2.0], option.Some([0.5, 0.5]))
+  |> should.equal(Ok(1.0))
+
+  // Different sized lists (weights) returns an error
+  metrics.canberra_distance(
+    [1.0, 2.0, 3.0],
+    [1.0, 2.0, 3.0],
+    option.Some([1.0]),
+  )
+  |> should.be_error()
+}
+
+pub fn braycurtis_distance_test() {
+  // Empty lists returns an error
+  metrics.braycurtis_distance([], [], option.None)
+  |> should.be_error()
+
+  // One empty list returns an error
+  metrics.braycurtis_distance([1.0, 2.0, 3.0], [], option.None)
+  |> should.be_error()
+
+  // One empty list returns an error
+  metrics.braycurtis_distance([], [1.0, 2.0, 3.0], option.None)
+  |> should.be_error()
+
+  // Different sized lists returns an error
+  metrics.braycurtis_distance([1.0, 2.0], [1.0, 2.0, 3.0, 4.0], option.None)
+  |> should.be_error()
+
+  // Try different types of valid input
+  metrics.braycurtis_distance([0.0, 0.0], [0.0, 0.0], option.None)
+  |> should.equal(Ok(0.0))
+
+  metrics.braycurtis_distance([1.0, 2.0], [-2.0, -1.0], option.None)
+  |> should.equal(Ok(3.0))
+
+  metrics.braycurtis_distance([1.0, 0.0], [0.0, 2.0], option.None)
+  |> should.equal(Ok(1.0))
+
+  metrics.braycurtis_distance([1.0, 2.0], [3.0, 4.0], option.None)
+  |> should.equal(Ok(0.4))
+
+  metrics.braycurtis_distance([1.0, 2.0], [3.0, 4.0], option.Some([1.0, 1.0]))
+  |> should.equal(Ok(0.4))
+
+  metrics.braycurtis_distance([1.0, 2.0], [3.0, 4.0], option.Some([0.5, 1.0]))
+  |> should.equal(Ok(0.375))
+
+  metrics.braycurtis_distance([1.0, 2.0], [3.0, 4.0], option.Some([0.25, 0.25]))
+  |> should.equal(Ok(0.4))
+
+  // Different sized lists (weights) returns an error
+  metrics.braycurtis_distance(
+    [1.0, 2.0, 3.0],
+    [1.0, 2.0, 3.0],
+    option.Some([1.0]),
+  )
+  |> should.be_error()
+}