Uncertain real parameters have a name (the
and a nominal value (the
Several other properties (
describe the uncertainty in parameter values.
All properties of a
be accessed through
The properties are:
Nominal value of element
Signifies which description (from
Additive variation (% of absolute value of nominal)
all automatically synchronized. If the nominal value is 0, then the
controls what aspect of the uncertainty remains unchanged when
changed. Assigning to any of
the value, but does not change the mode.
AutoSimplify property controls how expressions
involving the real parameter are simplified. Its default value is
which means elementary methods of simplification are applied as operations
are completed. Other values for
simplification performed) and
techniques are applied). See Simplifying Representation of Uncertain Objects to learn
more about the
AutoSimplify property and the command
If no property/value pairs are specified, default values are
used. The default
and the default value of
1]. Some examples are shown below. In many cases, the full
property name is not specified, taking advantage of the case-insensitive,
partial name property matching.
This example shows how to create uncertain real parameters, modify properties such as range of uncertainty, and sample uncertain parameters.
Create an uncertain real parameter, nominal value 3, with default values for all unspecified properties (including plus/minus variability of 1).
a = ureal('a',3)
a = Uncertain real parameter "a" with nominal value 3 and variability [-1,1].
View the properties and their values, and note that the
Percentage descriptions of variability are automatically maintained.
Name: 'a' NominalValue: 3 Mode: 'PlusMinus' Range: [2 4] PlusMinus: [-1 1] Percentage: [-33.3333 33.3333] AutoSimplify: 'basic'
Create an uncertain real parameter, nominal value 2, with 20% variability. Again, view the properties, and note that the
PlusMinus descriptions of variability are automatically maintained.
b = ureal('b',2,'Percentage',20) get(b)
b = Uncertain real parameter "b" with nominal value 2 and variability [-20,20]%. Name: 'b' NominalValue: 2 Mode: 'Percentage' Range: [1.6000 2.4000] PlusMinus: [-0.4000 0.4000] Percentage: [-20 20] AutoSimplify: 'basic'
Change the range of the parameter. All descriptions of variability are automatically updated, while the nominal value remains fixed. Although the change in variability was accomplished by specifying the
Mode is unaffected, and remains
b.Range = [1.9 2.3]; get(b)
Name: 'b' NominalValue: 2 Mode: 'Percentage' Range: [1.9000 2.3000] PlusMinus: [-0.1000 0.3000] Percentage: [-5.0000 15.0000] AutoSimplify: 'basic'
As mentioned, the
Mode property signifies what aspect of the uncertainty remains unchanged when
NominalValue is modified. Hence, if a real parameter is in
Percentage mode, then the
PlusMinus properties are determined from the
Percentage property and
NominalValue preserves the
Percentage property, and automatically updates the
b.NominalValue = 2.2; get(b)
Name: 'b' NominalValue: 2.2000 Mode: 'Percentage' Range: [2.0900 2.5300] PlusMinus: [-0.1100 0.3300] Percentage: [-5.0000 15.0000] AutoSimplify: 'basic'
Create an uncertain parameter with an asymmetric variation about its nominal value. Examine the properties to confirm the asymmetric range.
c = ureal('c',-5,'Percentage',[-20 30]); get(c)
Name: 'c' NominalValue: -5 Mode: 'Percentage' Range: [-6 -3.5000] PlusMinus: [-1 1.5000] Percentage: [-20 30] AutoSimplify: 'basic'
Create an uncertain parameter, specifying variability with
Percentage, but force the
Mode to be
d = ureal('d',-1,'Mode','Range','Percentage',[-40 60]); get(d)
Name: 'd' NominalValue: -1 Mode: 'Range' Range: [-1.4000 -0.4000] PlusMinus: [-0.4000 0.6000] Percentage: [-40 60] AutoSimplify: 'basic'
Finally, create an uncertain real parameter, and set the
AutoSimplify property to
e = ureal('e',10,'PlusMinus',[-23],'Mode','Percentage','AutoSimplify','Full') get(e)
e = Uncertain real parameter "e" with nominal value 10 and variability [-230,230]%. Name: 'e' NominalValue: 10 Mode: 'Percentage' Range: [-13 33] PlusMinus: [-23 23] Percentage: [-230 230] AutoSimplify: 'full'
Specifying conflicting values for
Range/Percentage/PlusMinus when creating a
ureal element does not result in an error. In this case, the last specified property is used. This last occurrence also determines the
Mode is explicitly specified, in which case that is used, regardless of the property/value pairs ordering.
f = ureal('f',3,'PlusMinus',[-2 1],'Percentage',40) g = ureal('g',2,'PlusMinus',[-2 1],'Mode','Range','Percentage',40) g.Mode
f = Uncertain real parameter "f" with nominal value 3 and variability [-40,40]%. g = Uncertain real parameter "g" with nominal value 2 and range [1.2,2.8]. ans = Range
Create an uncertain real parameter, use
usample to generate 1000 instances (resulting in a 1-by-1-by-1000 array), reshape the array, and plot a histogram, with 20 bins (within the range of 2 to 4).
h = ureal('h',3); hsample = usample(h,1000); hist(reshape(hsample,[1000 1]),20);
Make the range unsymmetric about the nominal value, and repeat the sampling, and histogram plot (with 40 bins over the range of 2-to-6)
h.Range = [2 6]; hsample = usample(h,1000); hist(reshape(hsample,[1000 1]),40);
Note that the distribution is skewed. However, the number of samples less than the nominal value and the number of samples greater than the nominal value are equal (on average). Verify this.
length(find(hsample(:) < h.NominalValue))
ans = 482
length(find(hsample(:) > h.NominalValue))
ans = 518
The distribution used in usample is uniform in the normalized description of the uncertain real parameter. See Decomposing Uncertain Objects to learn more about the normalized description.
There is no notion of an empty
ureal (or any other uncertain element, for that matter).
ureal, by itself, creates an element named
'UNNAMED', with default property values.