13.1.2 Constraint Inspection

When an expression in a Mech model is supposed to evaluate to a number but it does not, it can often be caught by the CheckSystem function. CheckSystem evaluates the constraint expressions in the current model, subject to the current initial guesses and parameters, and reports any nonnumeric expressions found. Consider the following simple model of a reciprocating slider. If CheckSystem is run before the symbols amp and freq are defined, they are identified.

Here is a reciprocating slider model.

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If the symbols amp and freq are defined at runtime, but not defined in such a way that the expression amp Sin[freq T] evaluates to a number, CheckSystem cannot determine exactly what is wrong.

Here is a bogus definition for the symbol freq.

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The constraint inspection function.

Constraints is a Mech function that is used to return all or part of the vector of constraint expressions in the current model. Often, direct inspection of the constraints immediately gives a clue as to the cause of an error. Usually, the constraints are inspected subject to the values of the current guesses and parameters, which shows exactly what CheckSystem saw to be an error.

Here is the entire current constraint vector.

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In all cases, input such as this should return a vector of numbers. In this case, the third constraint expression evaluates to a list of numbers, instead of a single number. Obviously this is due to the bogus definition of freq = {2, 4} in the example.

We can repair the bogus definition and try again.

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Now the constraints evaluate to a list of numbers, as is required. The fact that each of the constraint expressions evaluates to zero simply means that all of the constraints are perfectly satisfied at the current values of the initial guesses, which is not usually the case.