Generating Exaustive Parameter Combinations

Hi Everyone.

I want to create many Simulink.SimulationInput Objekts to simulate with many parameters.

To achieve this I am looking for a way to create exhaustive combinations of parameters.

I have not yet decided but thought, that structs might be usefull here. So far the Idea looks like this:

%function simIn = createSimIn(ModelName,Parameters)
%    ParameterNames = fieldnames(Parameters);
%    simIn(1:length(Parameters)) = Simulink.SimulationInput(ModelName);
%    for i = 1:length(Parameters)
%        for ii = 1:length(ParameterNames)
%            simIn(i) = simIn(i).setVariable(ParameterNames(ii),Paramters(i).(ParameterNames(ii)),'Workspace',simIn(i).ModelName);
%        end
%    end
%end

To get this running I would need a way to create a struct with and exhaustive combination of the parameters.

Lets say I have parameters:

a = 1:5;
b= 0:0.1:0.4;

Example = struct('a',num2cell(a),'b',num2cell(b))

Example = 1×5 struct array with fields:
    a
    b

I would want to create a struct that contains an exhaustive combinations, for a known number of parameters and equal lengths i can do:

Example = struct('a',num2cell(sort(repmat(a,1,length(b)))), ...
                 'b',num2cell(repmat(b,1,length(a),1)))

Example = 1×25 struct array with fields:
    a
    b

But I would want to do it for an arbitrary number of parameters and arbitrary multiplicities for the parameters. Is there an easier way to do this?

[Jan]

What about using meshgrid or loops?

[Florian Rössing]

Loops are my fallback option, but they are ugly, so i hoped there might be a nicer way to doing this.

Meshgrids i never heard of before, but I just looked it up, looks like you can only use that for 2 and 3D Data.

Answer 1

[Bruno Luong]

I start with a scalar structure s rather than the structure array, since paramereters might have different lengths

s=struct('a', 1:3, ...
    'b', 1:4, ...
    'c', 1:5)

s = struct with fields:
    a: [1 2 3]
    b: [1 2 3 4]
    c: [1 2 3 4 5]

c = struct2cell(s);
n = length(c);
[c{:}] = ndgrid(c{:});
A = reshape(cat(n+1,c{:}),[],n);
sarg = [fieldnames(s)'; num2cell(num2cell(A),1)];
Sexpand = struct(sarg{:})'

Sexpand = 1×60 struct array with fields:
    a
    b
    c

[Florian Rössing]

Thank You! I do not yet understand how it works, but it works perfectly.

How did you come up with this?

[Bruno Luong]

Practice.

[Florian Rössing]

Hey, I realized one quirk with your code.

When one parameter in s is a string, then the cat() turns everything into strings. I guess this is due to cats output beeing an array, that requires contents to have the same datatype.

Is there an easy work around?

Example:

s=struct('a', 1:3, ...
    'b', 1:4, ...
    'c', 1:5, ...
    'str', "Test")

s = struct with fields:
      a: [1 2 3]
      b: [1 2 3 4]
      c: [1 2 3 4 5]
    str: "Test"

c = struct2cell(s);
n = length(c);
[c{:}] = ndgrid(c{:});
A = reshape(cat(n+1,c{:}),[],n);
sarg = [fieldnames(s)'; num2cell(num2cell(A),1)];
Sexpand = struct(sarg{:})'

Sexpand = 1×60 struct array with fields:
    a
    b
    c
    str

Sexpand(2)

ans = struct with fields:
      a: "2"
      b: "1"
      c: "1"
    str: "Test"

[Bruno Luong]

Sorry my code is never intended to work on anything different than numerical data.

[Bruno Luong]

Here is the fix:

s=struct('a', 1:3, ...
    'b', 1:4, ...
    'c', 1:5, ...
    'str', "Test")

s = struct with fields:
      a: [1 2 3]
      b: [1 2 3 4]
      c: [1 2 3 4 5]
    str: "Test"

c = cellfun(@num2cell,struct2cell(s),'unif',0);
n = length(c);
[c{:}] = ndgrid(c{:});
A = reshape(cat(n+1,c{:}),[],n);
sarg = [fieldnames(s)'; num2cell(A,1)];
Sexpand = struct(sarg{:});
Sexpand(1)

ans = struct with fields:
      a: 1
      b: 1
      c: 1
    str: "Test"

Sexpand(end)

ans = struct with fields:
      a: 3
      b: 4
      c: 5
    str: "Test"