sdo.GriddedSpace

This example uses the sdoCSTR model discussed in detail in Design Exploration Using Parameter Sampling (Code). Among the parameters in this model are the reactor cylinder area A and height h. Suppose that you want to test the sensitivity of your design objectives over a grid of values for these parameters. To start, open the model and create param.Continuous objects to represent the two parameters.

mdl = "sdoCSTR";
open_system(mdl);
p = sdo.getParameterFromModel(mdl,{'A','h'});

Specify the grid of values for each parameter by placing the values in a cell array. The grids in this example are uniformly spaced, but you can also use nonuniformly spaced values.

Avals = {0.2 0.6 1.0 1.4 1.8 2.2};
hvals = {0.5 1.5 2.5 3.5};

Define the gridded parameter space using this grid.

gp = sdo.GriddedSpace(p,{Avals,hvals});

Sample the parameter space to generate all the combinations to use for sensitivity analysis. By default, sdo.sample generates an exhaustive list of all possible combinations in the parameter space, (Avals,hvals) = (0.2,0.5), (0.6,0.5), (1.0,0.5), ..., (1.4,3.5), (1.8,3.5), (2.2,3.5). Thus, the sampled values make up a table of 24 rows.

values = sdo.sample(gp)

values=24×2 table
     A      h 
    ___    ___

    0.2    0.5
    0.6    0.5
      1    0.5
    1.4    0.5
    1.8    0.5
    2.2    0.5
    0.2    1.5
    0.6    1.5
      1    1.5
    1.4    1.5
    1.8    1.5
    2.2    1.5
    0.2    2.5
    0.6    2.5
      1    2.5
    1.4    2.5
      ⋮

You can visualize the sampled values for a view of the distribution of samples.

 sdo.scatterPlot(values)

Use values with sdo.evaluate to evaluate your design objectives at the sampled parameter values. For instance, if you have defined a cost function design.m to capture your design objectives, you can use values in a call to sdo.evaluate as follows.

[yR,infoR] = sdo.evaluate(@design,p,values);

The example Exhaustive Sampling Across a Grid of Parameter Values shows how to create exhaustive grids of parameter values. Suppose instead that you want to create a set of specified pairs of parameter values (A1,h1), (A2,h2), and so on. To do so, use the sequential method of sampling the gridded parameter space. Open the model and create param.Continuous objects to represent the two parameters.

mdl = "sdoCSTR";
open_system(mdl);
p = sdo.getParameterFromModel(mdl,{'A','h'});

Specify the values (A1, A2, ...) and (h1, h2, ...). For sequential sampling, use the same number of values for each parameter.

Avals = {0.2 0.6 1.0 1.4 1.8};
hvals = {0.5 1.0 1.5 2.0 2.5};

Define the gridded parameter space using this grid.

gp = sdo.GriddedSpace(p,{Avals,hvals});

Specify sequential sampling using the Method property of the Options property of gp.

gp.Options.Method = 'sequential';

Finally, sample the parameter space to generate the parameter samples (Avals,hvals) = (0.2,0.5), (0.6,1.0), ..., (1.8,2.5).

values = sdo.sample(gp)

values=5×2 table
     A      h 
    ___    ___

    0.2    0.5
    0.6      1
      1    1.5
    1.4      2
    1.8    2.5

You can visualize the sampled values for a view of the set of samples.

sdo.scatterPlot(values)

Use values with sdo.evaluate to evaluate your design objectives at the sampled parameter values. For instance, if you have defined a cost function design.m to capture your design objectives, you can use values in a call to sdo.evaluate as follows.

[yR,infoR] = sdo.evaluate(@design,p,values);

You can sample discrete parameters across their full gird of allowed values or across a subset of those values. As with continuous parameters, sampling can be exhaustive or sequential.

The sdoMotorPosition model includes a resistor network containing resistors R1, R2, R3, and R4. Open the model, and create a vector of param.Discrete objects to represent the resistor values.

mdl = "sdoMotorPosition";
open_system(mdl)
params = sdo.getParameterFromModel(mdl,[],{'R1','R2','R3','R4'});

Specify sets of allowed values and current values for these parameters,

% R1 values
params(1).ValueSet = [39 43 47 51 56];
params(1).Value    = 47;
% R2 values
params(2).ValueSet = [150 160 180 200 220];
params(2).Value    = 180;
% R3 values
params(3).ValueSet = [8.2 9.1 10 11 12];
params(3).Value    = 10;
% R4 values
params(4).ValueSet = [8.2 9.1 10 11 12];
params(4).Value    = 10;

To generate samples using the full set of allowed values, create the gridded parameter space without specifying any values.

gspace = sdo.GriddedSpace(params)

gspace = 
  GriddedSpace with properties:

    ParameterValues: {{1x5 cell}  {1x5 cell}  {1x5 cell}  {1x5 cell}}
              Notes: []
             Spaces: {1x0 cell}
     ParameterNames: {'R1'  'R2'  'R3'  'R4'}
            Options: [1x1 sdo.GriddingOptions]

Generate a sequential sample set, (R1_1, R2_1, R3_1, R4_1), ..., (R1_5, R2_5, R3_5, R4_5), by setting the sampling method of gspace.

gspace.Options.Method = 'sequential';
svalues = sdo.sample(gspace)

svalues=5×4 table
    R1    R2     R3     R4 
    __    ___    ___    ___

    39    150    8.2    8.2
    43    160    9.1    9.1
    47    180     10     10
    51    200     11     11
    56    220     12     12

To draw samples from a subset of the allowed parameter values, reset the values in gspace using setValues. Alternatively, specify the subsets when you create the gridded parameter space. The values you specify must be subsets of the ValueSet property of params and must include the current value of each parameter.

gsubspace = sdo.GriddedSpace(params,...
            {{39 43 47},{150 160 180},{8.2 9.1 10},{8.2 9.1 10}});

Suppose that you want an exhaustive of every possible combination of R1, R2, R3, and R4 values in these subsets. Use sdo.sample to obtain these samples.

gsubspace.Options.Method = 'exhaustive';
evalues = sdo.sample(gsubspace)

evalues=81×4 table
    R1    R2     R3     R4 
    __    ___    ___    ___

    39    150    8.2    8.2
    43    150    8.2    8.2
    47    150    8.2    8.2
    39    160    8.2    8.2
    43    160    8.2    8.2
    47    160    8.2    8.2
    39    180    8.2    8.2
    43    180    8.2    8.2
    47    180    8.2    8.2
    39    150    9.1    8.2
    43    150    9.1    8.2
    47    150    9.1    8.2
    39    160    9.1    8.2
    43    160    9.1    8.2
    47    160    9.1    8.2
    39    180    9.1    8.2
      ⋮