Garden with Insight v1.0 Help: Numerical exceptions window

Garden with Insight is a numerical simulation, which means that it makes many calculations involving numbers to produce the results you see. Computers and software are wonderful tools for creating fast numerical simulations, but there are important limitations. In particular, most software programs can only reserve a limited amount of the computer's memory to store each number. This means that numbers can have only a certain range. For most of the model numbers used by Garden with Insight, these limits are from 1.5 x 10-45 to 3.4 x 10+38 in positive and negative numbers.

For most computer applications these ranges are more than adequate, and even in a numerical simulation normal conditions should not cause these bounds to be exceeded. However, if there is a problem with the simulation, the bounds can be exceeded, and this causes what is called a numerical exception. A numerical exception sometimes causes some values to be calculated incorrectly.

Problems with the simulation come from two sources: extreme input values (which cause the simulation to operate in an unrealistic boundary condition) and errors in the simulation itself. We have tried to minimize extreme input values by setting bounds on each of the hundreds of input parameters used by Garden with Insight. Simulation errors are minimized by repeated testing. However, it is difficult to find all errors because there are so many situations that can cause exceptions among the over 350 equations and 17,500 lines of model program code. Small errors that go undetected for a short time can accumulate and worsen over long periods of simulation. Also, the scientific assumptions underlying the models do not necessarily hold when several input values are at extreme values.

There are three basic types of numerical exception:

overflow: The number calculated has become too large for the computer to represent. In Garden with Insight this means that the number is greater than 3.4 x 10+38 or less than -3.4 x 10+38.

underflow: The number calculated is so close to zero that the computer cannot represent the number of digits after the decimal required to distinguish it from zero. In Garden with Insight this means that the number is less than 1.5 x 10-45 or greater than -1.5 x 10-45.

nonsensical value for a mathematical expression: The number input to a mathematical function is one for which the result is impossible to represent as a real number. For example, the natural log of a negative number is impossible for the computer to represent, as is the result of dividing any number by zero.

All numerical simulations have to deal with numerical exceptions. Some hide them from the user, some halt at the first exception, and some routinely round or limit numbers to avoid exceptions. In Garden with Insight numerical exceptions are presented in the Numerical exceptions window. When a numerical exception occurs, its description is added to the exception list in the Numerical exceptions window.

The numerical exceptions window

The numerical exceptions window has a list of exceptions and a few buttons you can use to manage the list and save information for technical support.

Save as: Save the list of exceptions as a numerical exceptions text file (.nex).

Clear: Empty the exception list.

The three check boxes under the exception list determine what the simulation should do when there is an exception.

appear: Check this check box to make the numerical exceptions window appear whenever a numerical exception occurs. Uncheck this check box if you don't want the numerical exceptions window to pop up when an error occurs. You can access the numerical exceptions window at any time by choosing it from the Window menu in the garden window.

log to file: Check this check box to start a log file of numerical exceptions (it will have the extension .nex), or to append to the file if it already exists. This option is useful if you think there is a problem and want to write out the errors as they happen instead of afterward. Uncheck this check box to stop logging errors to the file.

stop simulation: Check this box to have the simulation stop when it has finished simulating the day on which the exception occurs.

Click Close to close the numerical exceptions window.