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randadjustIf

Random variables can be adjusted to satisfy a specific constraint.
For example we might adjust the variable x to be always greater than the variable y by using the command \randadjustIf{x,y}{x<=y}

The command \randadjustIf has the syntax \randadjustIf{[varlist]}{[relation]} .

  • varlist comma separated list of variables to be adjusted
  • relation a relation that defines an avoidance condition under which the variables in varlist should be adjusted.
\begin{question}

    \begin{variables}
        \randint[Z]{x}{-10}{10}
        \randint[Z]{y}{-10}{10}
        \drawFromSet{a}{1,2,3}
        \drawFromSet{b}{1,2,3}
        \randadjustIf{x,y}{x <= y} %adjust x and y if x is not greater than y
        \randadjustIf{b}{a = b}    %adjust b if b equals a
    \end{variables}

\end{question}

The avoidance_relation has to be a logical (boolean) combination (use \(NOT\), \(AND\), \(OR\)) of simple comparison relations \((=, !=, <, <=, >, >=)\) between expressions in the variables.

These expressions may include random and non-random variables defined in the same variable environment.

See Expressions And Relations for a more detailed description.

Hint:

  • Make sure that the avoidance relation can be avoided at all for the random variables with the ranges given. The \randint commands jointly define a product set which has to have a non-empty intersection with the complement of the avoidance set. Otherwise you get a runtime error when the problem is run.

  • Even if the intersection is non-empty but has a equi-distribution probability being too small, a runtime error might be the result, though the algorithm tries its best to find an admissible point.

\randadjustIf on a variable defined by \drawFromSet only works for (the default) type number

calling \randadjustIf multiple times

You may call randadjustIf multiple times to adjust disjoint lists of variables as in the following example: 

\begin{question}
    \begin{variables}
        \randint[Z]{x}{-10}{10}
        \randint[Z]{y}{-10}{10}
        \randint[Z]{c}{-10}{10}
        \randint[Z]{d}{-10}{10}
        \randadjustIf{x,y}{x <= y} %adjust x and y if x is not greater than y
        \randadjustIf{c,d}{c = d OR c = x}
    \end{variables}

\end{question}

You should NEVER adjust a variable that has impact to the constraint of a previous \randadjustIf. The following example might lead to problems:

\begin{question}

    \begin{variables}
        \randint[Z]{x}{-10}{10}
        \randint[Z]{y}{-10}{10}
        \randint[Z]{c}{-10}{10}
        \randint[Z]{d}{-10}{10}
        \function[calculate]{x2}{x+2}
        \randadjustIf{y}{x2 <= y} %adjust y if x+2 is not greater than y
        \randadjustIf{c,x}{c = d OR c = x} % here the variable x will be re-adjusted, the value of x2 changed
                                           % and the constraint from previous randadjustIf might be broken.
    \end{variables}

\end{question}

Adjusting global variables

Just as random variables defined inside the question environment, global variables (which are defined in the problem environment) can be adjusted, too.

You may use \randadjustIf in the same manner as explained above, also multiple times for disjoint sets of global variables. You should NOT adjust global variables within a question, but only in the problem environment where they are defined.

Alternatively use a switch/case statement