All possible combinations of variables

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Josep 2014-8-5

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https://ww2.mathworks.cn/matlabcentral/answers/146404-all-possible-combinations-of-variables

编辑： Star Strider 2014-8-13

Hey everybody,

I have a system with x variables and I want to obtain by using MATLAB a combination of all of them in all the possible groups. Let me introduce you an example:

Lets suppose I have 6 variables for example(1,2,3,4,5,6), it means there will be 63 combinations without repeating any. My aim is to achieve all the combinations like this:

[1] [2] [3] [4] [5] [6]

[1,2] [1,3] [1,4] [1,5] [1,6] [2,3] [2,4] ...

[1,2,3] [1,2,4] [1,2,5] [1,2,6] [1,3,4] [1,3,5] [1,3,6] [1,4,5] [1,4,6] [1,5,6] [2,3,4] ....

and the same for groups of 4, 5 and 6 variables.

Does anybody know how to do it for X number of variables? I need to do this to compute an statistics equation in order to detect errors in the measured values of the system.

Thank you for your attention!

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Andrew Reibold 2014-8-5

Do you just need to know 'how many' combinations there are, or do you need all of the combinations output. If you need them output, how should they be displayed or stored?

Josep 2014-8-5

No, I need all of the combinations output. Could I email you in order to be more explicit?

Thank you!

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Star Strider 2014-8-5

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/146404-all-possible-combinations-of-variables#answer_147481

编辑：Star Strider 2014-8-5

在 MATLAB Online 中打开

If you have the Statistics Toolbox, use the combnk function:

v = 1:6;
c2 = combnk(v,2)
c3 = combnk(v,3)

... and so on for 4, 5, and 6.

According to Wikipedia, Data validation and reconciliation is at least initially an optimisation problem. You can probably do that with fminsearch, but will need the Optimization Toolbox for the other optimisation functions. There are no MATLAB functions that will do data reconciliation (at least that I could find), although I’m certain you can use existing MATLAB functions to do what you want. I can’t find anything in the File Exchange when I did a search on ‘data reconciliation’.

Since the PDF data you posted likely come from previous studies, I suggest you consult that paper for the procedures it uses. Code them yourself in MATLAB, test your code, preferably using the data it used (if available), and see how the results compare. Use your code on the individual streams first. If that is successful, then combine them according to the established procedures (in the paper you quoted the PDF from), and go from there. I have never needed to do data reconciliation and so have no experience with it, I know essentially nothing about hydrology, and I have no idea how you combine your streamflow data.

If you have problems getting your code to run or give the correct results, return here with a full description of what you want to do, what you did, what you want your code to do, what it did or did not do that you wanted it to, and the full text of any error messages it threw, along with the line that threw the error. It would likely help to attach a PDF of the paper you used as your reference for your code.

Star Strider 2014-8-7

在 MATLAB Online 中打开

I don’t understand how your definition of the covariance matrix H. You are correct that the diagonals are the squared values of the standard deviations, but it is not a diagonal matrix. It contains the covariances of the various components of whatever data created it. The cov function can do that for you.

What is r? It must be a (2x1) vector, but how is it calculated?

It will likely not be difficult to calculate your T statistic, but it will be tedious, since it will involve looping over several combinations of variables. You will have to index it in the loop over the variables that are used to create it, so T will be a matrix. The link to the File Exchange function I sent you earlier will generate the combinations for you.

Given Fk, H, and r, the T calculation is straightforward:

T = (Fk'*inv(H)*Fk)\(Fk'*inv(H)*r);

Using the inv function is not considered good programming practice, but I don’t see how to avoid it here.

You would have to index T in a loop to save it for the various combinations of variables you’re using to generate it, but that would not be difficult.

Star Strider 2014-8-8

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For the situation involving the two-variable combinations, COMBINATOR would return a (15x2) matrix (6 numbers taken 2 at at time). The loop might go like this:

N = 2;
combs = COMBINATOR MATRIX OUTPUT FOR 6 NUMBERS TAKEN N AT A TIME;
for k2 = 1:size(combs,1)
    % Calculate data for this combination of (combs(k1,1),combs(k1,2),...) —> |Fk|,|H|,|r|
    T(combs(k1,1),combs(k1,2),...) = ...     % Calculate T for these data;
end

At the end of the loop, you will have a matrix of T values whose subscripts are the values for the various combinations of variables. The same goes for the three-variable situation, except that instead of (combs(k1,1),combs(k1,2)) you will have (combs(k1,1),combs(k1,2),combs(k1,3)), and so on for the others. You will have to store the T matrix as a ‘.mat’ file after the end of each loop, first renaming it T2 for the two-variable run, T3 for the three-variable run, and so for the rest. (This prevents you from overwriting a generic T matrix if you load all into your workspace at the same time.)

You could do the same thing with nested for loops, but that would quickly get cumbersome with six nested loops. I would use the method I outlined here. You can use one loop for all runs.

Obviously, this is simply an outline of one way you might do it.

Josep 2014-8-13

I have done this:

function combo = combs(6,2)

combinator(n,k,'c'); % Combinations without repetition

combo = ans;

end

And I still have an error message:

>> combs(6, 2) Error: File: combs.m Line: 2 Column: 24 Unexpected MATLAB expression.

Star Strider 2014-8-13

编辑：Star Strider 2014-8-13

在 MATLAB Online 中打开

That’s strange. Line 2 is the combinator call, and column 24 is in the comment!

I’ll download combinator in a few minutes to see if I can replicate your error.

Later that same day ...

I downloaded combinator, saved it to my user directory, and ran this code:

combinator(6,2,'c'); % Combinations without repetition
combo = ans;

without problems, returning combo as a (15x2) double matrix. I have no idea what may be the problem with your code, or perhaps with your MATLAB installation.

I still suggest you run this command from the Command Window:

which combinator -all

and copy the results to a comment to this thread.

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