refactor: move all multiplication dimensional analysis logic to place…

…holder function

Simplifies replace_placeholder_funcs function by removing a special case

public/dimensional_analysis.py

@@ -990,10 +990,32 @@ def custom_matmul(exp1: Expr, exp2: Expr):
     else:
         return Mul(exp1, exp2)
 
-def custom_matmul_dims(*args: Expr):
-    if len(args) == 2 and is_matrix(args[0]) and is_matrix(args[1]) and \
+def custom_multiply_dims(matmult: bool, *args: Expr):
+    matrix_args: list[Matrix] = []
+    scalar_args: list[Expr] = []
+    for arg in args:
+        if is_matrix(arg):
+            matrix_args.append(arg)
+        else:
+            scalar_args.append(arg)
+
+    if len(matrix_args) > 0 and len(scalar_args) > 0:
+        first_matrix = matrix_args[0]
+        scalar = Mul(*scalar_args)
+        new_rows = []
+        for i in range(first_matrix.rows):
+            new_row = []
+            new_rows.append(new_row)
+            for j in range(first_matrix.cols):
+                new_row.append(scalar*first_matrix[i,j]) # type: ignore
+
+        matrix_args[0] = Matrix(new_rows)
+        args = cast(tuple[Expr], matrix_args)
+
+    if matmult and len(args) == 2 and is_matrix(args[0]) and is_matrix(args[1]) and \
        (((args[0].rows == 3 and args[0].cols == 1) and (args[1].rows == 3 and args[1].cols == 1)) or \
         ((args[0].rows == 1 and args[0].cols == 3) and (args[1].rows == 1 and args[1].cols == 3))):
+        # cross product detected for matrix multiplication operator
 
         result = Matrix([Add(Mul(args[0][1],args[1][2]),Mul(args[0][2],args[1][1])),
                          Add(Mul(args[0][2],args[1][0]),Mul(args[0][0],args[1][2])),
@@ -1455,8 +1477,8 @@ def get_next_id(self):
     cast(Function, Function('_Inverse')) : {"dim_func": ensure_inverse_dims, "sympy_func": UniversalInverse},
     cast(Function, Function('_Transpose')) : {"dim_func": custom_transpose, "sympy_func": custom_transpose},
     cast(Function, Function('_Determinant')) : {"dim_func": custom_determinant, "sympy_func": custom_determinant},
-    cast(Function, Function('_mat_multiply')) : {"dim_func": custom_matmul_dims, "sympy_func": custom_matmul},
-    cast(Function, Function('_multiply')) : {"dim_func": Mul, "sympy_func": Mul},
+    cast(Function, Function('_mat_multiply')) : {"dim_func": partial(custom_multiply_dims, True), "sympy_func": custom_matmul},
+    cast(Function, Function('_multiply')) : {"dim_func": partial(custom_multiply_dims, False), "sympy_func": Mul},
     cast(Function, Function('_IndexMatrix')) : {"dim_func": IndexMatrix, "sympy_func": IndexMatrix},
     cast(Function, Function('_Eq')) : {"dim_func": Eq, "sympy_func": Eq},
     cast(Function, Function('_norm')) : {"dim_func": custom_norm, "sympy_func": custom_norm},
@@ -1506,32 +1528,7 @@ def replace_placeholder_funcs(expr: Expr,
     if len(expr.args) == 0:
         return expr
 
-    if func_key == "dim_func" and expr.func in multiply_placeholder_set:
-        processed_args = [replace_placeholder_funcs(cast(Expr, arg), func_key, placeholder_map, placeholder_set, data_table_subs) for arg in expr.args]
-        matrix_args = []
-        scalar_args = []
-        for arg in processed_args:
-            if is_matrix(cast(Expr, arg)):
-                matrix_args.append(arg)
-            else:
-                scalar_args.append(arg)
-
-        if len(matrix_args) > 0 and len(scalar_args) > 0:
-            first_matrix = matrix_args[0]
-            scalar = math.prod(scalar_args)
-            new_rows = []
-            for i in range(first_matrix.rows):
-                new_row = []
-                new_rows.append(new_row)
-                for j in range(first_matrix.cols):
-                    new_row.append(scalar*first_matrix[i,j])
-
-            matrix_args[0] = Matrix(new_rows)
-
-            return cast(Expr, cast(Callable, placeholder_map[expr.func][func_key])(*matrix_args))
-        else:
-            return cast(Expr, cast(Callable, placeholder_map[expr.func][func_key])(*processed_args))
-    elif expr.func in dummy_var_placeholder_set and func_key == "dim_func":
+    if expr.func in dummy_var_placeholder_set and func_key == "dim_func":
         return cast(Expr, cast(Callable, placeholder_map[expr.func][func_key])(*(replace_placeholder_funcs(cast(Expr, arg), func_key, placeholder_map, placeholder_set, data_table_subs) if index > 0 else arg for index, arg in enumerate(expr.args))))
     elif expr.func in placeholder_set:
         return cast(Expr, cast(Callable, placeholder_map[expr.func][func_key])(*(replace_placeholder_funcs(cast(Expr, arg), func_key, placeholder_map, placeholder_set, data_table_subs) for arg in expr.args)))