# Documentation

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# ureal

Create uncertain real parameter

## Syntax

```p = ureal('name',nominalvalue)
p = ureal('name',nominalvalue,'Property1',Value1,...
'Property2',Value2,...)
```

## Description

An uncertain real parameter is used to represent a real number whose value is uncertain. Uncertain real parameters have a name (the `Name` property), and a nominal value (`NominalValue` property).

The uncertainty (potential deviation from `NominalValue`) is described (equivalently) in 3 different properties:

• `PlusMinus`: the additive deviation from `NominalValue`

• `Range`: the interval containing `NominalValue`

• `Percentage`: the percentage deviation from `NominalValue`

The `Mode` property specifies which one of these three descriptions remains unchanged if the `NominalValue` is changed (the other two descriptions are derived). The possible values for the `Mode` property are` 'Range', 'Percentage'` and `'PlusMinus'`.

The default `Mode` is `'PlusMinus'`, and `[-1 1]` is the default value for the `'PlusMinus'` property. The range of uncertainty need not be symmetric about `NominalValue`.

The property `AutoSimplify` controls how expressions involving the uncertain matrix are simplified. Its default value is` 'basic'`, which means elementary methods of simplification are applied as operations are completed. Other values for `AutoSimplify` are` 'off''`, no simplification performed, and` 'full'`, which applies model-reduction-like techniques to the uncertain object.

## Examples

### Example 1

Create an uncertain real parameter and use `get` to display the properties and their values. Create uncertain real parameter object` a` with the internal name `'a'` and nominal value` 5`.

```a = ureal('a',5) Uncertain Real Parameter: Name a, NominalValue 5, variability = [-1 1] get(a) Name: 'a' NominalValue: 5 Mode: 'PlusMinus' Range: [4 6] PlusMinus: [-1 1] Percentage: [-20 20] AutoSimplify: 'basic' ```

Note that the `Mode` is `'PlusMinus'`, and that the value of `PlusMinus` is indeed ```[-1 1]```. As expected, the range description of uncertainty is ```[4 6]```, while the percentage description of uncertainty is ```[-20 20]```.

Set the range to `[3 9]`. This leaves `Mode` and `NominalValue` unchanged, but all three descriptions of uncertainty have been modified.

```a.Range = [3 9]; get(a) Name: 'a' NominalValue: 5 Mode: 'PlusMinus' Range: [3 9] PlusMinus: [-2 4] Percentage: [-40 80] AutoSimplify: 'basic' ```

### Example 2

Property/Value pairs can also be specified at creation.

```b = ureal('b',6,'Percentage',[-30 40],'AutoSimplify','full'); get(b) Name: 'b' NominalValue: 6 Mode: 'Percentage' Range: [4.2000 8.4000] PlusMinus: [-1.8000 2.4000] Percentage: [-30.0000 40.0000] AutoSimplify: 'full' ```

Note that `Mode` is automatically set to `'Percentage'`.

### Example 3

Specify the uncertainty in terms of percentage, but force `Mode` to `'Range'`.

```c = ureal('c',4,'Mode','Range','Percentage',25); get(c) Name: 'c' NominalValue: 4 Mode: 'Range' Range: [3 5] PlusMinus: [-1 1] Percentage: [-25 25] AutoSimplify: 'basic' ```