[ENH] Implement DTW with Global alignment (aeon-toolkit#2565)

* Implements Dynamic Time Warping with Global Invariances

* Adds Numba JIT compilation support

* Adds docs and numba support for dtw_gi and test_distance fixed

* Fixes doctests

* Automatic `pre-commit` fixes

* Minor changes

* Minor changes

* Remove dtw_gi function and combine with private method _dtw_gi

* Adds parameter tests

* Fixes doctests

* Minor changes

Author: tanishy7777

aeon/distances/__init__.py

@@ -18,6 +18,10 @@
     "dtw_pairwise_distance",
     "dtw_cost_matrix",
     "dtw_alignment_path",
+    "dtw_gi_distance",
+    "dtw_gi_pairwise_distance",
+    "dtw_gi_cost_matrix",
+    "dtw_gi_alignment_path",
     "ddtw_distance",
     "ddtw_pairwise_distance",
     "ddtw_alignment_path",
@@ -111,6 +115,10 @@
     dtw_alignment_path,
     dtw_cost_matrix,
     dtw_distance,
+    dtw_gi_alignment_path,
+    dtw_gi_cost_matrix,
+    dtw_gi_distance,
+    dtw_gi_pairwise_distance,
     dtw_pairwise_distance,
     edr_alignment_path,
     edr_cost_matrix,

aeon/distances/_distance.py

@@ -24,6 +24,10 @@
     dtw_alignment_path,
     dtw_cost_matrix,
     dtw_distance,
+    dtw_gi_alignment_path,
+    dtw_gi_cost_matrix,
+    dtw_gi_distance,
+    dtw_gi_pairwise_distance,
     dtw_pairwise_distance,
     edr_alignment_path,
     edr_cost_matrix,
@@ -447,6 +451,7 @@ def get_distance_function(method: Union[str, DistanceFunction]) -> DistanceFunct
     method          Distance Function
     =============== ========================================
     'dtw'           distances.dtw_distance
+    'dtw_gi'        distances.dtw_gi_distance
     'shape_dtw'     distances.shape_dtw_distance
     'ddtw'          distances.ddtw_distance
     'wdtw'          distances.wdtw_distance
@@ -728,6 +733,16 @@ class DistanceType(Enum):
         "symmetric": True,
         "unequal_support": True,
     },
+    {
+        "name": "dtw_gi",
+        "distance": dtw_gi_distance,
+        "pairwise_distance": dtw_gi_pairwise_distance,
+        "cost_matrix": dtw_gi_cost_matrix,
+        "alignment_path": dtw_gi_alignment_path,
+        "type": DistanceType.ELASTIC,
+        "symmetric": False,
+        "unequal_support": True,
+    },
     {
         "name": "ddtw",
         "distance": ddtw_distance,

aeon/distances/elastic/__init__.py

@@ -10,6 +10,10 @@
     "dtw_pairwise_distance",
     "dtw_cost_matrix",
     "dtw_alignment_path",
+    "dtw_gi_distance",
+    "dtw_gi_pairwise_distance",
+    "dtw_gi_cost_matrix",
+    "dtw_gi_alignment_path",
     "ddtw_distance",
     "ddtw_pairwise_distance",
     "ddtw_alignment_path",
@@ -71,6 +75,12 @@
     dtw_distance,
     dtw_pairwise_distance,
 )
+from aeon.distances.elastic._dtw_gi import (
+    dtw_gi_alignment_path,
+    dtw_gi_cost_matrix,
+    dtw_gi_distance,
+    dtw_gi_pairwise_distance,
+)
 from aeon.distances.elastic._edr import (
     edr_alignment_path,
     edr_cost_matrix,