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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 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 """


        # Possible cases:
        # 1) Z given, rest can be None and calculated
        # 2) A and x given, rest can be calculated
        # 3) A and Y , calc L (if not given) - calc x and the rest

        # this catches case 3
        if self.x is None and self.Z is None:
            # in that case we need L or at least A to calculate it
            if self.L is None:
                self.L = calc_L(self.A)
                logging.info('Leontief matrix L calculated')
            self.x = calc_x_from_L(self.L, self.Y.sum(axis=1))
            self.meta._add_modify('Industry Output x calculated')

        # this chains of ifs catch cases 1 and 2
        if self.Z is None:
            self.Z = calc_Z(self.A, self.x)
            self.meta._add_modify('Flow matrix Z calculated')

        if self.x is None:
            self.x = calc_x(self.Z, self.Y)
            self.meta._add_modify('Industry output x calculated')

        if self.A is None:
                self.A = calc_A(self.Z, self.x)
                self.meta._add_modify('Coefficient matrix A calculated')

        if self.L is None:
                self.L = calc_L(self.A)
                self.meta._add_modify('Leontief matrix L calculated')

        return self