Combine Vectors Into Matrix - NOT ALL Possible Combinations from baseline

Hello All,

I have come across ways of combining vectors into a single matrix with all possbile matrices, however I am looking to step through changes for a DOE for example, so order matters and I only want to change one parameter at a time.

So if I have

A = {1, 2, 3, 4};

B = {7, 8, 9};

C = {10, 11, 12, 13};

D = {14, 15, 16};

It would yeild

Consider { 1 7 10 14} as a "baseline" and then the full DOE would look like...

The number of vectors would be dynamic and the length of the vectors as well.

Combs = 1 7 10 14

2 7 10 14

3 7 10 14

4 7 10 14

1 8 10 14

1 9 10 14

1 7 11 14

1 7 12 14

1 7 13 14

1 7 10 15

1 7 10 16

Any syntax help is greatly apperciated!

[Mark Sherstan]

Have you considered using the built in DOE functions? fullfact and fracfactgen might be useful. More info here: https://www.mathworks.com/help/stats/design-of-experiments-1.html

[AJ Foyt]

Thank you Mark, That is an interesting toolbox I was not aware of. Unfortunately I do not have the licensing for that toolbox.

Answer 1

[Guillaume]

allpoints = {[1 2 3 4], [7 8 9], [10 11 12 13], [14 15 16]}; %can be as many vectors of any length
baseline = [1 7 10 14];
assert(isequal(size(baseline), size(allpoints)), 'Shape and size of baseline doesn''t match allpoints');
assert(all(cellfun(@ismember, num2cell(baseline), allpoints)), 'Some points in baseline are not in allpoints');

result = cell(size(allpoints));  
for vecidx = 1:numel(allpoints)  %iterate over the test vectors
    testmatrix = repmat(baseline, numel(allpoints{vecidx}), 1);  %replicate baseline to number of elements in current vector
    testmatrix(:, vecidx) = allpoints{vecidx}(:);  %and replace test column by all the points in that vector
    result{vecidx} = testmatrix;
end
result = vertcat(result{:}) %concatenate the whole lot

Generates only the required combinations so should be a lot faster than generating all combinations and then discarding the unwanted ones.

[Stephan]

Just recognized that my approach would fail in cases where the content of allpoints is repeated in some entries. Nice solution!

[AJ Foyt]

Thank you Guillaume!!! That is a perfect solution.