By default, functions expect dimensionless inputs and provide dimensionless outputs. When such a function is called with arguments having well-defined units (except when explicitly dimensionless), it is called with the numerical value of the argument expressed in the current unit system for the context where the function is used. The return value from the unit handling perspective behaves like a number, adapting its unit to the context where it is used. An analytic function should be seen as a numerical “black box” evaluating only numerical expressions. The inputs to the function will be converted using the unit specified, so, for example, a value of 3 meters becomes 3000 if the argument’s unit is mm. The result from the evaluation uses the selected base unit. The analytic functions do not keep a unit consistency, so that you can define a function such as 1.23·x3 + 0.045·x2 + 0.345; the formula itself only evaluates a numerical expression.

In the Units section in the Settings window for the Analytic, Interpolation, and Piecewise function nodes, you can define units for the function’s inputs and output. The Arguments column shows the name of each input argument. In the corresponding text field in the Unit column, type a unit for that argument. In the Function field, type the unit for the function’s output.

For External functions and MATLAB functions, enter expressions for the partial derivatives of each function with respect to their input arguments. The derivative information is needed by the automatic Jacobian computation. In the Derivatives table, each row contains a partial derivative of a function with respect to one of its arguments:

Use this table to set the range for arguments in preview plots. For each argument, enter a Lower limit, and an Upper limit in the Plot Parameters table. There is also a Unit column that shows the unit of the argument. In Analytic function plot settings, the argument column is updated automatically and must always match the specified argument list. For External and MATLAB functions, the argument column is absent. Instead, the limits specified in the table are applied to in order from top to bottom to the arguments of the first function with a matching number of arguments. It is also this first matching function that is plotted when you click the Plot button () or the Create Plot button ().

For the Step, Triangle, and Rectangle functions, enter a value in the Size of transition zone field to control the amount of smoothing. Also, set the Number of continuous derivatives to 1 or 2. The default is to make derivatives continuous up to second order. For the Ramp function, additionally specify a value, if desired, for the Size of transition zone at start and, if desired and a cutoff is active, a value for the Size of transition zone at cutoff. For the Step function, the step is the same as for the flc1hs and flc2hs smoothed step functions, depending on the settings in the Number of continuous derivatives list (see Additional Smoothed Functions). The parameter d in flc1hs(x,d), for example, is set to half of the value in the Size of transition zone field,