Feature non linear time averaged msd

package/AUTHORS

@@ -258,7 +258,7 @@ Chronological list of authors
   - Abdulrahman Elbanna
   - Tulga-Erdene Sodjargal
   - Gareth Elliott
-
+  - Sirsha Ganguly
 
 External code
 -------------

package/MDAnalysis/analysis/msd.py

@@ -1,3 +1,25 @@
+######## Documentation
+#
+# Issue: The default '_conclude_simple()' function previously calculated time-averaged mean squared displacement considering linear timespacing between the frames even when a dump file with non-linear timestep gap is provided
+#
+#   Modified by Sirsha Ganguly
+#
+# Modification:
+# '_conclude_modified()' is the new function added to calculate time-averaged mean squared displacement of non-linear dumps
+    # Note: This new function is generalized for non-linear dumps.
+    #       Moreover, if you use this function to calculate for linear timedump this gives same result as '_conclude_simple()' which is implemented in the default version.
+    #       So, I believe the algorithm in '_conclude_modified()' can potentially be used to calculate time-averaged msd in future.
+    #       For now it only executes when the dump is non-linear. [ This is determined by the added function is_linear() ]
+    #       It is tested with a .dump file of a Coarse Grained system of single type 
+#
+# General Algorithm of '_conclude_modified()' to calculate time-averaged msd:
+    # It creates a dictionary/hash-map with the key being the time difference between the frames (Delta t) and value being a list containing the frame to frame MSD values [msd1, msd2, .....] for that particular Delta t
+        # Dictionary to collect MSDs: {Δt: [msd1, msd2, ...]}
+    # The reference frame is changed with each iteration and each time a new Key (i.e, Delta t) is found it is appended in the dictionary/hash-map
+    # If a duplicate Delta_t is found it is added to the value (msd list) of that specefic Key in the dictionary/hash-map
+    # Lastly in the dictionary/hash-map for each Delta_t the msd values inside the list are averaged
+#
+
 # -*- Mode: python; tab-width: 4; indent-tabs-mode:nil; coding:utf-8 -*-
 # vim: tabstop=4 expandtab shiftwidth=4 softtabstop=4
 #
@@ -263,7 +285,17 @@
 del Doi
 
 
+
 class EinsteinMSD(AnalysisBase):
+
+    @staticmethod
+    def is_linear(sequence): # This function is to check if the timesteps in the array is linear or not! If it's linear default MDA code will carry-out other wise the modified code carries!
+        if len(sequence) < 2:
+            return True
+        step = sequence[1] - sequence[0]
+        return all(sequence[i+1] - sequence[i] == step for i in range(len(sequence) - 1))
+
+
     r"""Class to calculate Mean Squared Displacement by the Einstein relation.
 
     Parameters
@@ -386,7 +418,10 @@
         if self.fft:
             self._conclude_fft()
         else:
-            self._conclude_simple()
+            if self.is_linear([ts.time for ts in self._trajectory]):
+                self._conclude_simple()
+            else:
+                self._conclude_modified() # New modified code
 
     def _conclude_simple(self):
         r"""Calculates the MSD via the simple "windowed" algorithm."""
@@ -421,3 +456,46 @@
                 positions[:, n, :]
             )
         self.results.timeseries = self.results.msds_by_particle.mean(axis=1)
+
+
+    def _conclude_modified(self):
+        from collections import defaultdict
+        print("The Dump file has non-linear time spacing")
+
+        dump_times = [ts.time for ts in self._trajectory]
+        # print(dump_times)
+        n_frames = len(dump_times)
+        n_atoms = self.n_particles
+        positions = np.zeros((n_frames, n_atoms, 3))
+        positions = self._position_array.astype(np.float64)
+
+        msd_dict = defaultdict(list) # Dictionary to collect MSDs: {Δt: [msd1, msd2, ...]}
+
+        # Looping over all the frames as if the referenced gets shifted frame to frame
+        for i in range(n_frames):
+            for j in range(i + 1, n_frames):
+                delta_t = dump_times[j] - dump_times[i]
+
+                # Compute displacement and squared displacement
+                disp = positions[j] - positions[i]
+                squared_disp = np.sum(disp ** 2, axis=1)
+                msd = np.mean(squared_disp)
+
+                # Store MSD under corresponding Δt
+                msd_dict[delta_t].append(msd)
+
+        msd_dict[0] = [0]
+
+        # Prepare averaged results
+        delta_t_values = []
+        avg_msds = []
+        for delta_t in sorted(msd_dict.keys()):
+            msd_list = msd_dict[delta_t]
+            avg_msd = np.mean(msd_list)
+            delta_t_values.append(delta_t)
+            avg_msds.append(avg_msd)
+
+        self.results.timeseries = delta_t_values
+        self.results.msds_by_particle = avg_msds
+
+        # self.results.timeseries = self.results.msds_by_particle.mean(axis=1)