Cartesian product of list

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laurent jalabert 2019-1-14

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https://ww2.mathworks.cn/matlabcentral/answers/439668-cartesian-product-of-list

评论： laurent jalabert 2019-1-14

采纳的回答： Guillaume

在 MATLAB Online 中打开

Hello,

I have 4 vectors A, B, C, D with

A=1:6; B=1:5; C=1:10; D=1:4; % in real case, the max values i.e 6, 5, 10 and 4, are not always equal to those values but always integers

ADBC = allcomb(A,D,B,C); % each row corresponds to an experimental condition involving one of each parameter A, B, C, D

Now, I want to reorganize ADBC elements (row) in order to build a new matrix ABCD = allcomb(A,B,C,D);

As an example, I have ADBC = [2 2 3 1], which means A=2, B=3, C=1 and D=2;

The question is what is the row of ABCD corresponding to the same condition (A=2, B=3, C=1, D=2) if it was organized as ABCD, i.e [2 3 1 2] ?

Here is the answer :

A=1:6; B=1:5; C=1:10; D=1:4; % in real case, the max values i.e 6, 5, 10 and 4, are not always equal to those values but always integers
ABCD = allcomb(A,B,C,D); % https://fr.mathworks.com/matlabcentral/fileexchange/10064-allcomb-varargin
ADBC = allcomb(A,D,B,C); % each row corresponds to an experimental condition involving one of each parameter A, B, C, D
 i = 0; crush = 1;
 while  crush ~= 4 % because I seek for 4 values [i j k m]
     i=i+1;
     check = find(ADBC(i,:) == [2 2 3 1]); % in order "ADBC"
     crush = length(check);
 end
ADBC(i,:)
i % 271
 i = 0; crush2 = 1;
 while  crush2 ~= 4 % because I seek for 4 values [i j k m]
     i=i+1;
     check2 = find(ABCD(i,:) == [2 3 1 2]); % after sorting ex1 elements in order"ABCD"
     crush2 = length(check2); 
 end
ABCD(i,:)
i % 282

So I would like to rebuilt the transfer function between the known ADBC and the rebuilt ABCD.

So, I guess I should write a loop (from 1 to 6*5*10*4=1200) to scan each ADBC element (ex1), get the old position (271 in the example), then sort the element with respect to "ABCD" order, then get the new position in case of ABCD vector (282 in the example).

So ABCD(282) = ADBC(271).

Can anyone simplify this approach ?

How to generalize to any ACBD, ADBC, ABDC, ... (24 cases) to rebuild ABCD in any case ? ABCD is my goal.