Evaluating Formulas

Unlike a program written in a programming language, a modelx Model does not have a single entry point, such as the main function in C. And modelx also differs from Excel, in a sence that modelx does not populate its Model with calculated values upon opening the Model. modelx evaluates a Formula when its value is requested by the user directly or indirectly through Formulas depending on the Fromula’s value.

The Fibo Cells in the sample below is taken from the earlier section:

>>> Fibo.formula
def Fibo(n):
    if n > 1:
        return Fibo(n-1) + Fibo(n-2)
    else:
        return n

Initially, Fibo does not have any values. You can check Fibo’s values by converting it to dict:

>>> dict(Fibo)
{}

When you request the value of Fibo for n=5, the values of Fibo for n=0 through n=4 are also calculated:

>>> Fibo(5)
5

>>> dict(Fibo)
{1: 1, 0: 0, 2: 1, 3: 2, 4: 3, 5: 5}

Namespaces for Formulas

Most Formulas need to reference values of other Cells and References to calculate their own values. Unlike Python functions, the name binding for modelx Formulas is independent from Python modules. Each Space has its own namespace associated with itself, and the names in the Formulas of child Cells in the Space are bound in the namespace associated with the Space. The names defined in the associated namespace are the names of the child objects of the Space, such as child Cells, Spaces and References. In addition to the child objects’ names, global References, special names and built-in names are defined in the associated namespace. The global References are the References defined at the containing Model level, as attributes of the Model. The special names are defiend by modelx, and the names start with “_”. Currently there is only one special name, _space, which refers to the Space itself. The list below summarizes the kind of names defined in the namespace associated with a UserSpace.

• The child Cells, Spaces and References

• The global References defined in the Model

• The special names (_space)

• The Python built-in names

The sample code below is taken from the mortgage loan example we have seen earlier. The Balance global variable refers to a Cells object Balance, but the name of the variable does not need to be the same as the Cells’ name:

>>> Balance.formula
def Balance(t):

    if t > 0:
        return Balance(t-1) * (1+Rate) - Payment()
    else:
        return Principal

>>> Balance(30)
1.2096279533579946e-10

If Balance was a Python function, then the names in the Balance definition, such as Balance, Rate, Payment, Principal would refer to global variables defined in the module that the function was defined in. However, as explained above, the Formula of Balance is evaluated in the namespace associated with its parent Space Fixed. The Fixed Space has child Cells, such as Payment and Balance. It also has child References, such as Principal and Rate. So, the names in the Balance definition refer to those child Cells and Referneces of the Fixed Space. To get all the names defined in the Fixed name space, use the Python built-in function dict. The code below assumes that the Fixed variable refers to the Fixed Space:

>>> dir(Fixed)
['Balance',
 'Payment',
 'Principal',
 'Rate',
 'Term',
 '__builtins__',
 '_self',
 '_space']

(Note: _self in the list above is deprecated and should not be used.)

Analyzing Formula dependency

<<TODO>>