arithmetic_analysis/jacobi_iteration_method.py

@@ -116,6 +116,19 @@ def jacobi_iteration_method(
     strictly_diagonally_dominant(table)
 
     """
+    denom - a list of values along the diagonal
+    val - values of the last column of the table array
+
+    masks - boolean mask of all strings without diagonal
+    elements array coefficient_matrix
+
+    ttt - coefficient_matrix array values without diagonal elements
+    ind - column indexes for each row without diagonal elements
+    arr - list obtained by column indexes from the list init_val
+
+    the code below uses vectorized operations based on
+    the previous algorithm on loopss:
+
     # Iterates the whole matrix for given number of times
     for _ in range(iterations):
         new_val = []
@@ -133,40 +146,18 @@ def jacobi_iteration_method(
         init_val = new_val
     """
 
-    """
-    denom - a list of values along the diagonal
-    """
     denom = np.diag(coefficient_matrix)
-    """
-    val_last - values of the last column of the table array
-    """
-    val_last = table[:, -1]
-    """
-    masks - boolean mask of all strings without diagonal
-    elements array coefficient_matrix
-    """
+    val = table[:, -1]
     masks = ~np.eye(coefficient_matrix.shape[0], dtype=bool)
-    """
-    no_diag - coefficient_matrix array values without diagonal elements
-    """
-    no_diag = coefficient_matrix[masks].reshape(-1, rows - 1)
-    """
-    Here we get 'i_col' - these are the column numbers, for each row
-    without diagonal elements, except for the last column.
-    """
+    ttt = coefficient_matrix[masks].reshape(-1, rows - 1)
     i_row, i_col = np.where(masks)
     ind = i_col.reshape(-1, rows - 1)
-    """
-    'i_col' is converted to a two-dimensional list 'ind',
-    which will be used to make selections from 'init_val'
-    ('arr' array see below).
-    """
 
     # Iterates the whole matrix for given number of times
     for _ in range(iterations):
         arr = np.take(init_val, ind)
-        temp = np.sum((-1) * no_diag * arr, axis=1)
-        new_val = (temp + val_last) / denom
+        temp = np.sum((-1) * ttt * arr, axis=1)
+        new_val = (temp + val) / denom
         init_val = new_val
 
     return new_val.tolist()