combine
Description
joins the parameter spaces sp_new
= combine(sp1
,sp2
)sp1
and sp2
into a
composite parameter space that contains sp1
and
sp2
as subspaces. You can combine gridded parameter spaces, random
parameter spaces, or both. You can use composite parameter spaces to generate sample sets
containing both gridded and randomly sampled parameters.
Examples
Generate Samples with Both Gridded and Random Parameters
If your model contains some parameters you want to sample across a grid and others from which you want to draw random samples, you can combine gridded and random parameter spaces.
This example uses the sdoCSTR
model discussed in detail in Design Exploration Using Parameter Sampling (Code). Open the model.
mdl = "sdoCSTR";
open_system(mdl)
Among the parameters in this model are the reactor cylinder area A
, height h
, and the feed temperature and concentration, FeedCon0
and FeedTemp0
. Suppose that you want to explore the sensitivity of your design constraint to these four parameters, sampling across a grid of A
and h
values while drawing FeedCon0
and FeedTemp0
from random distributions.
First, define a gridded parameter space for A
and h
. Use sdo.getParameterFromModel
to create an array of param.Continuous
objects representing A
and h
. Then, specify values for the grid, and create the parameter space.
pg = sdo.getParameterFromModel(mdl,{'A','h'}); Avals = {0.2 0.6 1.0 1.4 1.8}; hvals = {0.5 1.5 2.5}; gspace = sdo.GriddedSpace(pg,{Avals,hvals});
Next, define a random parameter space for FeedCon0
and FeedTemp0
. Create an array of param.Continuous
objects and specify the probability distributions for each parameter. For this example, assign both variables a normal distribution where the mean is the current parameter value in the model and the variance is 5% of the mean. Then, create the parameter space.
pr = sdo.getParameterFromModel(mdl,{'FeedCon0','FeedTemp0'}); distCon = makedist('normal',pr(1).Value,0.05*pr(1).Value); distTemp = makedist('normal',pr(2).Value,0.05*pr(2).Value); rspace = sdo.ParameterSpace(pr); rspace = setDistribution(rspace,'FeedCon0',distCon); rspace = setDistribution(rspace,'FeedTemp0',distTemp);
Finally, combine the two parameter spaces into a new parameter space.
cspace = combine(gspace,rspace)
cspace = GriddedSpace with properties: ParameterValues: {{1x4 cell} {1x4 cell} [1x1 prob.NormalDistribution] [1x1 prob.NormalDistribution]} Notes: [] Spaces: {[1x1 sdo.GriddedSpace] [1x1 sdo.ParameterSpace]} ParameterNames: {'A' 'h' 'FeedCon0' 'FeedTemp0'} Options: [1x1 sdo.GriddingOptions]
The combined space is represented by a sdo.GriddedSpace
object. The property cspace.Spaces
shows that cspace
contains the two subspaces, one gridded space and one random parameter space. The property cspace.ParameterValues
shows that the space includes the finite grid for A
and H
, and the probability distributions for the random variables FeedCon0
and FeedTemp0
.
You can now use sdo.sample
to draw sets of sampled values from the combined space. By default, the samples are exhaustive over the grid, meaning every possible combination of grid values is included in the sampled set. Suppose that for each combination, you want to sample the random parameters ten times. Provide that value to sdo.sample
in the NumSample
argument.
cspace.Options.Method = 'exhaustive';
NumSample = 10;
evalues = sdo.sample(cspace,NumSample)
evalues=150×4 table
A h FeedCon0 FeedTemp0
___ ___ ________ _________
0.2 0.5 10.269 275.09
0.6 0.5 10.269 275.09
1 0.5 10.269 275.09
1.4 0.5 10.269 275.09
1.8 0.5 10.269 275.09
0.2 1.5 10.269 275.09
0.6 1.5 10.269 275.09
1 1.5 10.269 275.09
1.4 1.5 10.269 275.09
1.8 1.5 10.269 275.09
0.2 2.5 10.269 275.09
0.6 2.5 10.269 275.09
1 2.5 10.269 275.09
1.4 2.5 10.269 275.09
1.8 2.5 10.269 275.09
0.2 0.5 10.917 339.77
⋮
Here, for each of the fifteen combinations of (A
, h
) values, sdo.sample
assigns ten random values for (Feedcon0
, FeedTemp0
), resulting in 150 sets of (A
, h
, FeedCon0
, FeedTemp0
) samples.
You can also have sdo.sample
choose only one random (FeedCon0
,FeedTemp0
) value for each (A
,h
) pair. To do so, set the sampling method of cspace
to sequential. Note that in this case, you created cspace
using a gridded space gspace
that had gspace.Options.Method = 'exhaustive'
. Thus, when you sample cspace
, the (A
,h
) pairs are still exhaustive.
cspace.Options.Method = 'sequential';
svalues = sdo.sample(cspace)
svalues=15×4 table
A h FeedCon0 FeedTemp0
___ ___ ________ _________
0.2 0.5 9.5682 296.27
0.6 0.5 10.039 273
1 0.5 9.3929 284.05
1.4 0.5 9.4432 279.34
1.8 0.5 9.9966 329.67
0.2 1.5 10.766 285.92
0.6 1.5 9.6152 306.03
1 1.5 10.186 292.16
1.4 1.5 9.8872 308.11
1.8 1.5 10.559 283.72
0.2 2.5 9.4555 274.32
0.6 2.5 10.016 274.02
1 2.5 10.276 302.2
1.4 2.5 10.55 292.38
1.8 2.5 10.772 292.11
Use values
with sdo.evalute
to evaluate your design objectives at each of the sampled parameter values. For instance, if you have defined a cost function design
, you can use values
in a call to sdo.evluate
as follows.
[yR,infoR] = sdo.evaluate(@design,p,values);
Input Arguments
sp1
, sp2
— Parameter spaces to combine
sdo.ParameterSpace
object | sdo.GriddedSpace
object
Parameter spaces to combine, specified as sdo.ParameterSpace
objects, sdo.GriddedSpace
objects, or one of each.
method
— Sampling method
'exhaustive'
(default) | "exhaustive"
| 'sequential'
| "sequential"
Sampling method of the combined space, specified as one of the following:
'exhaustive'
or"exhaustive"
— Samples drawn withsdo.sample
include all possible combinations of values from each subspace.'sequential'
or"sequential"
— Samples drawn withsdo.sample
include pairwise combinations of values from each subspace.
The method
argument sets the method property of the composite
space, sp_new.Option.Method
. If both sp1
and
sp2
are random parameter spaces
(sdo.ParameterSpace
), then method
is
ignored.
Output Arguments
sp_new
— Combined parameter space
sdo.GriddedSpace
object | sdo.ParameterSpace
object
Combined parameter space, returned as an sdo.GriddedSpace
object or
sdo.ParameterSpace
object.
If
sp1
andsp2
are both random parameter spaces (sdo.ParameterSpace
), thensp_new
is ansdo.ParameterSpace
object. Combining two random parameter spaces is equivalent to adding the parameters of one random space to the other usingaddParameter
.If either
sp1
orsp2
is a gridded parameter space (sdo.GriddedSpace
), thensp_new
is a composite space. The composite space is returned as ansdo.GriddedSpace
object that contains the combined spaces as subspaces in theSpaces
property.You can think of a composite space as tree of spaces that contain subspaces. Use
combine
to construct the tree one space at a time. A composite gridded parameter space contains at most one random parameter space at the top level of the composite space. When you combine a composite parameter space that has a random parameter subspace with another random parameter space, the random parameter spaces are combined into a single parameter space at the top level of the composite space.
Version History
Introduced in R2023a
See Also
sdo.ParameterSpace
| sdo.GriddedSpace
| sdo.sample
| addParameter
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