Minor suggestions in docstr

pymrio/core/mriosystem.py

@@ -1388,7 +1388,7 @@ def file_name_nr(a, c):
             plt.ion()
 
     def get_rows(self):
-        """ Returns the name of the rows of the extension"""
+        """ Returns the name of the rows of the extension """
         possible_dataframes = [
             "F",
             "F_Y",
@@ -1518,9 +1518,9 @@ class IOSystem(CoreSystem):
         final demand with MultiIndex with index.names = (['region', 'sector'])
         and column.names = (['region', 'category'])
     A : pandas.DataFrame
-        coefficient input output table, MultiTndex as Z
+        coefficient input output table, MultiIndex as Z
     L : pandas.DataFrame
-        Leontief, MultiTndex as Z
+        Leontief (= inv(I-A)), MultiIndex as Z
     unit : pandas.DataFrame
         Unit for each row of Z
     system : string
@@ -1642,7 +1642,13 @@ def calc_system(self):
         """
         Calculates the missing part of the core IOSystem
 
-        The method checks Z, x, A, L and calculates all which are None
+        The method checks Z, A, x, L and calculates all which are None
+
+        The possible cases are:
+            Case    Provided    Calculated
+            1)      Z           A, x, L
+            2)      A, x        Z, L
+            3)      A, Y        L, x, Z
         """
 
         # Possible cases:

pymrio/tools/iomath.py

@@ -19,6 +19,8 @@
 def calc_x(Z, Y):
     """Calculate the industry output x from the Z and Y matrix
 
+    industry output (x) = flows (sum_columns(Z)) + final demand (sum_columns(Y))
+
     Parameters
     ----------
     Z : pandas.DataFrame or numpy.array
@@ -46,6 +48,10 @@ def calc_x(Z, Y):
 def calc_x_from_L(L, y):
     """Calculate the industry output x from L and a y vector
 
+    x = Ly
+
+    The industry output x is computed from a demand vector y
+
     Parameters
     ----------
     L : pandas.DataFrame or numpy.array
@@ -71,6 +77,11 @@ def calc_x_from_L(L, y):
 def calc_Z(A, x):
     """calculate the Z matrix (flows) from A and x
 
+    A = Z / x[None, :]  =>  Z = A * x[None, :]
+
+    By definition, the coefficient matrix A is basically the normalized flows
+    So Z is just derived from A by un-normalizing using the industrial output x
+
     Parameters
     ----------
     A : pandas.DataFrame or numpy.array
@@ -101,6 +112,8 @@ def calc_Z(A, x):
 def calc_A(Z, x):
     """Calculate the A matrix (coefficients) from Z and x
 
+    A is a normalized version of the industrial flows Z
+
     Parameters
     ----------
     Z : pandas.DataFrame or numpy.array
@@ -140,6 +153,19 @@ def calc_A(Z, x):
 def calc_L(A):
     """Calculate the Leontief L from A
 
+    L = inverse matrix of (I - A)
+
+    Where I is an identity matrix of same shape as A
+
+    Comes from:
+        x = Ax + y  =>  (I-A)x = y
+    Where:
+        A: coefficient input () - output () table
+        x: output vector
+        y: final demand vector
+
+    Hence, L allows to derive a required output vector x for a given demand y
+
     Parameters
     ----------
     A : pandas.DataFrame or numpy.array