Locally Overriding Units

Locally overriding units

In some rare occasions the unit specified in the declaration of a particular identifier does not necessarily have to match with the unit of the data for that identifier. In that case, AIMMS allows you just to override the unit of a particular expression locally. Such a local unit override of an expression always takes the simple form

(expression) [simple-unit-expression]

where expression is some AIMMS expression, and simple-unit-expression is a simple unit expression as explained in Unit Expressions. If expression solely consists of a numeric constant, AIMMS allows you to omit the parentheses around it.

Where to use

You can use local unit overrides in a variety of data I/O related situations.

  • In a WRITE, DISPLAY or PUT statement, you can use a local unit override to specify the particular unit in which data must be written to a file, database table or window.

  • In the FormatString function, you can use a local unit override to specify the unit in which a numeric argument corresponding to a %n format specifier must be formatted.

  • On the left side of a data assignment, in the header of a composite table, or in a READ statement, you can use a local unit override to specify the unit in which the supplied data to be provided.

Commensurate requirement

In all these data I/O statements and expressions, AIMMS requires that the unit provided in the override is commensurate with the original unit that can be associated with the expression.

Example

Given the declarations of the examples in the Unit Analysis, the following data I/O statements locally override the default unit [km/h] of the identifier VelocityOfItem with the commensurate unit [mph].

  • Override per identifier:

    (VelocityOfItem) [mph] := DATA { car: 55, truck: 45 };
read (VelocityOfItem) [mph] from table VelocityTable;
display (VelocityOfItem) [mph];

  • Override per individual entry:

    put (VelocityOfItem('car')) [mph];
StringVal := FormatString("Speed in [mph]: %n", (VelocityOfItem('car')) [mph]);

Recall that parentheses are always required when you want to override the default unit in expressions and statements, unless the overridden expression is a simple numeric constant.

Override for consistency

In addition to overriding units during a data exchange, you can also override the unit of a (sub)expression in an assignment with the purpose of enforcing unit consistency of all terms in the assignment. This is especially useful when there are numeric constants inside your expressions. AIMMS will add the appropriate scale factor if the specified unit override does not match with the corresponding atomic unit expression.

Examples

The following examples illustrate unit overrides with the purpose of enforcing unit consistency.

  • Consider the assignment

    SoundIntensity := (10 * log10( SoundLevel / ReferenceLevel )) [dB];

    If SoundIntensity has an associated unit of [dB], the right hand side of the assignment, which by itself is unitless, must be locally overridden to make the entire assignment unit consistent.

  • Consider the assignment

    a := b + 10 [km];

    where both a and b are measured in terms of length. As discussed in Unit Analysis, AIMMS will make no assumption about the unit associated with the numerical constant 10 in the expression on the right-hand side of the assignment. In order to make the assignment unit consistent, an explicit unit override of the constant term is required. If the associated base unit is [m], AIMMS will automatically add a scale factor of 1000, whence the assignment will numerically evaluate to a := b + 10*1000.

Caution is needed

If you explicitly associate a unit with an expression which already contains one or more identifiers with associated units, the numerical result can be unexpected. This is due to fact that AIMMS, during expression evaluation, uses the unscaled numerical values with respect to the associated atomic units of each identifier. To illustrate, reconsider the assignment

a := (b * c) [km];

but now assume that the identifiers a, b, and c have units [km], [km], and [10*m]. If the values of b and c are 1 [km](=1000 [m]) and 50 [10*m](=500 [m]), respectively, the numerical result of a after the assignment will amount to (500 * 1000)*1000 [m]= 500000 [km], which may not be the result that you intended.