From 00237cd2b2decfe3dd2f4afbcc56dfde65e876ed Mon Sep 17 00:00:00 2001
From: dbring <dbring@gmail.com>
Date: Sun, 8 Oct 2023 14:16:31 -0700
Subject: [PATCH 1/3] Added the Minkowski distance function

---
 maths/minkowski_distance.py | 41 +++++++++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)
 create mode 100644 maths/minkowski_distance.py

diff --git a/maths/minkowski_distance.py b/maths/minkowski_distance.py
new file mode 100644
index 000000000000..3043ffabfb1b
--- /dev/null
+++ b/maths/minkowski_distance.py
@@ -0,0 +1,41 @@
+def minkowski_distance(
+    point_a: list[float],
+    point_b: list[float],
+    order: int,
+) -> float:
+    """
+    This function calculates the Minkowski distance for a given order between
+    two n-dimensional points represented as lists. For the case of order = 1,
+    the Minkowski distance degenerates to the Manhattan distance. For
+    order = 2, the usual Euclidean distance is obtained.
+
+    https://en.wikipedia.org/wiki/Minkowski_distance
+
+    >>> minkowski_distance([1.0, 1.0], [2.0, 2.0], 1)
+    2.0
+    >>> minkowski_distance([1.0, 2.0, 3.0, 4.0], [5.0, 6.0, 7.0, 8.0], 2)
+    8.0
+    >>> minkowski_distance([1.0], [2.0], -1)
+    Traceback (most recent call last):
+        ...
+    Exception: The order must be greater than or equal to 1.
+    >>> minkowski_distance([1.0], [1.0, 2.0], 1)
+    Traceback (most recent call last):
+        ...
+    Exception: Both points must have the same dimension.
+    """
+    if order < 1:
+        raise Exception("The order must be greater than or equal to 1.")
+
+    if len(point_a) != len(point_b):
+        raise Exception("Both points must have the same dimension.")
+
+    return float(
+        sum(abs(a - b) ** order for a, b in zip(point_a, point_b)) ** (1 / order)
+    )
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

From 8789275cf9716cfa13c7801b3eed9354e1d294c5 Mon Sep 17 00:00:00 2001
From: dbring <dbring@gmail.com>
Date: Mon, 9 Oct 2023 12:59:10 -0700
Subject: [PATCH 2/3] Made error handling more precise

---
 maths/minkowski_distance.py | 12 +++++-------
 1 file changed, 5 insertions(+), 7 deletions(-)

diff --git a/maths/minkowski_distance.py b/maths/minkowski_distance.py
index 3043ffabfb1b..ffc239e7d1e3 100644
--- a/maths/minkowski_distance.py
+++ b/maths/minkowski_distance.py
@@ -18,21 +18,19 @@ def minkowski_distance(
     >>> minkowski_distance([1.0], [2.0], -1)
     Traceback (most recent call last):
         ...
-    Exception: The order must be greater than or equal to 1.
+    ValueError: The order must be greater than or equal to 1.
     >>> minkowski_distance([1.0], [1.0, 2.0], 1)
     Traceback (most recent call last):
         ...
-    Exception: Both points must have the same dimension.
+    ValueError: Both points must have the same dimension.
     """
     if order < 1:
-        raise Exception("The order must be greater than or equal to 1.")
+        raise ValueError("The order must be greater than or equal to 1.")
 
     if len(point_a) != len(point_b):
-        raise Exception("Both points must have the same dimension.")
+        raise ValueError("Both points must have the same dimension.")
 
-    return float(
-        sum(abs(a - b) ** order for a, b in zip(point_a, point_b)) ** (1 / order)
-    )
+    return sum(abs(a - b) ** order for a, b in zip(point_a, point_b)) ** (1 / order)
 
 
 if __name__ == "__main__":

From d9472f75fab296818b275c10fa80e9280b011852 Mon Sep 17 00:00:00 2001
From: dbring <dbring@gmail.com>
Date: Mon, 9 Oct 2023 15:30:01 -0700
Subject: [PATCH 3/3] Added note about floating point errors and corresponding
 doctest

---
 maths/minkowski_distance.py | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/maths/minkowski_distance.py b/maths/minkowski_distance.py
index ffc239e7d1e3..3237124e8d36 100644
--- a/maths/minkowski_distance.py
+++ b/maths/minkowski_distance.py
@@ -11,10 +11,16 @@ def minkowski_distance(
 
     https://en.wikipedia.org/wiki/Minkowski_distance
 
+    Note: due to floating point calculation errors the output of this
+    function may be inaccurate.
+
     >>> minkowski_distance([1.0, 1.0], [2.0, 2.0], 1)
     2.0
     >>> minkowski_distance([1.0, 2.0, 3.0, 4.0], [5.0, 6.0, 7.0, 8.0], 2)
     8.0
+    >>> import numpy as np
+    >>> np.isclose(5.0, minkowski_distance([5.0], [0.0], 3))
+    True
     >>> minkowski_distance([1.0], [2.0], -1)
     Traceback (most recent call last):
         ...