Creating a row vector of combinations?

Question

Ali Almakhmari 2023-1-24

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https://ww2.mathworks.cn/matlabcentral/answers/1899390-creating-a-row-vector-of-combinations

评论： Dyuman Joshi 2023-1-27

I have a row vector that 1 by 4. And I know that the minimum and maximum values of the elements in this vector to be -15 and 15. How can I make a matrix that is N by 4 that contains all possible combinations of ALL values?

Let me given an example: min = -15, max = 15, so the result of the code should be a matrix that is N by 4 that will look something like this

A = [[-15,0,0,0];[-14,0,0,0];[-13,0,0,0];[-12,0,0,0];[-11,0,0,0];[-10,0,0,0];[-9,0,0,0];....and so on until the final value vector to be[15,15,15,15]];

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Answer 1

Davide Masiello 2023-1-24

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You could use nchoosek. The example below is from -3 to 3 for memory issues (you'll generate a humongous matrix). Just substitute -15:15 and the trick is done.

A = nchoosek(-3:3,4)
A = 35×4
    -3    -2    -1     0
    -3    -2    -1     1
    -3    -2    -1     2
    -3    -2    -1     3
    -3    -2     0     1
    -3    -2     0     2
    -3    -2     0     3
    -3    -2     1     2
    -3    -2     1     3
    -3    -2     2     3

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Davide Masiello 2023-1-25

编辑：Davide Masiello 2023-1-25

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@Dyuman Joshi thanks for pointing that out, I had missed it completely.

I think I came up with a solution, albeit slightly convoluted.

Some time ago I learned about a function on the File Exchange called allVL1.

It performs all combinations of integer vector that must verify a criteria on the sum.

I embedded this function in a loop to obtain the desired result.

The logic is as such.

1 - I define the maximum value, in this example 3 (or 15 in @Ali Almakhmari's problem).

2 - I establish the maximum sum achievable which is the maximum value times the number of columns of the output matrix (i.e., 3x4=12 in this case).

3 - Then, I loop for every combination leading to a sum of the row vector that goes from 0 to the maximum achievable sum and I concatenate the result to matrix A each time.

4 - Since this is done for positive integers, after the loop I concatenate -A with A to make it symmetric around zero.

5 - I perform a unique operation to remove the duplicated [0 0 0 0] row.

Please find the result attached below (full A matrix).

I still supect there might be a much easier way to do this.

maxN = 3;
ncol = 4;
A = [];
for sum = 0:maxN*ncol
    a = allVL1(ncol,sum);
    a = a(all(a<=maxN,2),:);
    A = [A;a];
end
A = [-A;A]

A = [

0 0 0 -1

0 0 -1 0

0 -1 0 0

-1 0 0 0

0 0 0 -2

0 0 -1 -1

0 0 -2 0

0 -1 0 -1

0 -1 -1 0

0 -2 0 0

-1 0 0 -1

-1 0 -1 0

-1 -1 0 0

-2 0 0 0

0 0 0 -3

0 0 -1 -2

0 0 -2 -1

0 0 -3 0

0 -1 0 -2

0 -1 -1 -1

0 -1 -2 0

0 -2 0 -1

0 -2 -1 0

0 -3 0 0

-1 0 0 -2

-1 0 -1 -1

-1 0 -2 0

-1 -1 0 -1

-1 -1 -1 0

-1 -2 0 0

-2 0 0 -1

-2 0 -1 0

-2 -1 0 0

-3 0 0 0

0 0 -1 -3

0 0 -2 -2

0 0 -3 -1

0 -1 0 -3

0 -1 -1 -2

0 -1 -2 -1

0 -1 -3 0

0 -2 0 -2

0 -2 -1 -1

0 -2 -2 0

0 -3 0 -1

0 -3 -1 0

-1 0 0 -3

-1 0 -1 -2

-1 0 -2 -1

-1 0 -3 0

-1 -1 0 -2

-1 -1 -1 -1

-1 -1 -2 0

-1 -2 0 -1

-1 -2 -1 0

-1 -3 0 0

-2 0 0 -2

-2 0 -1 -1

-2 0 -2 0

-2 -1 0 -1

-2 -1 -1 0

-2 -2 0 0

-3 0 0 -1

-3 0 -1 0

-3 -1 0 0

0 0 -2 -3

0 0 -3 -2

0 -1 -1 -3

0 -1 -2 -2

0 -1 -3 -1

0 -2 0 -3

0 -2 -1 -2

0 -2 -2 -1

0 -2 -3 0

0 -3 0 -2

0 -3 -1 -1

0 -3 -2 0

-1 0 -1 -3

-1 0 -2 -2

-1 0 -3 -1

-1 -1 0 -3

-1 -1 -1 -2

-1 -1 -2 -1

-1 -1 -3 0

-1 -2 0 -2

-1 -2 -1 -1

-1 -2 -2 0

-1 -3 0 -1

-1 -3 -1 0

-2 0 0 -3

-2 0 -1 -2

-2 0 -2 -1

-2 0 -3 0

-2 -1 0 -2

-2 -1 -1 -1

-2 -1 -2 0

-2 -2 0 -1

-2 -2 -1 0

-2 -3 0 0

-3 0 0 -2

-3 0 -1 -1

-3 0 -2 0

-3 -1 0 -1

-3 -1 -1 0

-3 -2 0 0

0 0 -3 -3

0 -1 -2 -3

0 -1 -3 -2

0 -2 -1 -3

0 -2 -2 -2

0 -2 -3 -1

0 -3 0 -3

0 -3 -1 -2

0 -3 -2 -1

0 -3 -3 0

-1 0 -2 -3

-1 0 -3 -2

-1 -1 -1 -3

-1 -1 -2 -2

-1 -1 -3 -1

-1 -2 0 -3

-1 -2 -1 -2

-1 -2 -2 -1

-1 -2 -3 0

-1 -3 0 -2

-1 -3 -1 -1

-1 -3 -2 0

-2 0 -1 -3

-2 0 -2 -2

-2 0 -3 -1

-2 -1 0 -3

-2 -1 -1 -2

-2 -1 -2 -1

-2 -1 -3 0

-2 -2 0 -2

-2 -2 -1 -1

-2 -2 -2 0

-2 -3 0 -1

-2 -3 -1 0

-3 0 0 -3

-3 0 -1 -2

-3 0 -2 -1

-3 0 -3 0

-3 -1 0 -2

-3 -1 -1 -1

-3 -1 -2 0

-3 -2 0 -1

-3 -2 -1 0

-3 -3 0 0

0 -1 -3 -3

0 -2 -2 -3

0 -2 -3 -2

0 -3 -1 -3

0 -3 -2 -2

0 -3 -3 -1

-1 0 -3 -3

-1 -1 -2 -3

-1 -1 -3 -2

-1 -2 -1 -3

-1 -2 -2 -2

-1 -2 -3 -1

-1 -3 0 -3

-1 -3 -1 -2

-1 -3 -2 -1

-1 -3 -3 0

-2 0 -2 -3

-2 0 -3 -2

-2 -1 -1 -3

-2 -1 -2 -2

-2 -1 -3 -1

-2 -2 0 -3

-2 -2 -1 -2

-2 -2 -2 -1

-2 -2 -3 0

-2 -3 0 -2

-2 -3 -1 -1

-2 -3 -2 0

-3 0 -1 -3

-3 0 -2 -2

-3 0 -3 -1

-3 -1 0 -3

-3 -1 -1 -2

-3 -1 -2 -1

-3 -1 -3 0

-3 -2 0 -2

-3 -2 -1 -1

-3 -2 -2 0

-3 -3 0 -1

-3 -3 -1 0

0 -2 -3 -3

0 -3 -2 -3

0 -3 -3 -2

-1 -1 -3 -3

-1 -2 -2 -3

-1 -2 -3 -2

-1 -3 -1 -3

-1 -3 -2 -2

-1 -3 -3 -1

-2 0 -3 -3

-2 -1 -2 -3

-2 -1 -3 -2

-2 -2 -1 -3

-2 -2 -2 -2

-2 -2 -3 -1

-2 -3 0 -3

-2 -3 -1 -2

-2 -3 -2 -1

-2 -3 -3 0

-3 0 -2 -3

-3 0 -3 -2

-3 -1 -1 -3

-3 -1 -2 -2

-3 -1 -3 -1

-3 -2 0 -3

-3 -2 -1 -2

-3 -2 -2 -1

-3 -2 -3 0

-3 -3 0 -2

-3 -3 -1 -1

-3 -3 -2 0

0 -3 -3 -3

-1 -2 -3 -3

-1 -3 -2 -3

-1 -3 -3 -2

-2 -1 -3 -3

-2 -2 -2 -3

-2 -2 -3 -2

-2 -3 -1 -3

-2 -3 -2 -2

-2 -3 -3 -1

-3 0 -3 -3

-3 -1 -2 -3

-3 -1 -3 -2

-3 -2 -1 -3

-3 -2 -2 -2

-3 -2 -3 -1

-3 -3 0 -3

-3 -3 -1 -2

-3 -3 -2 -1

-3 -3 -3 0

-1 -3 -3 -3

-2 -2 -3 -3

-2 -3 -2 -3

-2 -3 -3 -2

-3 -1 -3 -3

-3 -2 -2 -3

-3 -2 -3 -2

-3 -3 -1 -3

-3 -3 -2 -2

-3 -3 -3 -1

-2 -3 -3 -3

-3 -2 -3 -3

-3 -3 -2 -3

-3 -3 -3 -2

-3 -3 -3 -3

0 0 0 0

0 0 0 1

0 0 1 0

0 1 0 0

1 0 0 0

0 0 0 2

0 0 1 1

0 0 2 0

0 1 0 1

0 1 1 0

0 2 0 0

1 0 0 1

1 0 1 0

1 1 0 0

2 0 0 0

0 0 0 3

0 0 1 2

0 0 2 1

0 0 3 0

0 1 0 2

0 1 1 1

0 1 2 0

0 2 0 1

0 2 1 0

0 3 0 0

1 0 0 2

1 0 1 1

1 0 2 0

1 1 0 1

1 1 1 0

1 2 0 0

2 0 0 1

2 0 1 0

2 1 0 0

3 0 0 0

0 0 1 3

0 0 2 2

0 0 3 1

0 1 0 3

0 1 1 2

0 1 2 1

0 1 3 0

0 2 0 2

0 2 1 1

0 2 2 0

0 3 0 1

0 3 1 0

1 0 0 3

1 0 1 2

1 0 2 1

1 0 3 0

1 1 0 2

1 1 1 1

1 1 2 0

1 2 0 1

1 2 1 0

1 3 0 0

2 0 0 2

2 0 1 1

2 0 2 0

2 1 0 1

2 1 1 0

2 2 0 0

3 0 0 1

3 0 1 0

3 1 0 0

0 0 2 3

0 0 3 2

0 1 1 3

0 1 2 2

0 1 3 1

0 2 0 3

0 2 1 2

0 2 2 1

0 2 3 0

0 3 0 2

0 3 1 1

0 3 2 0

1 0 1 3

1 0 2 2

1 0 3 1

1 1 0 3

1 1 1 2

1 1 2 1

1 1 3 0

1 2 0 2

1 2 1 1

1 2 2 0

1 3 0 1

1 3 1 0

2 0 0 3

2 0 1 2

2 0 2 1

2 0 3 0

2 1 0 2

2 1 1 1

2 1 2 0

2 2 0 1

2 2 1 0

2 3 0 0

3 0 0 2

3 0 1 1

3 0 2 0

3 1 0 1

3 1 1 0

3 2 0 0

0 0 3 3

0 1 2 3

0 1 3 2

0 2 1 3

0 2 2 2

0 2 3 1

0 3 0 3

0 3 1 2

0 3 2 1

0 3 3 0

1 0 2 3

1 0 3 2

1 1 1 3

1 1 2 2

1 1 3 1

1 2 0 3

1 2 1 2

1 2 2 1

1 2 3 0

1 3 0 2

1 3 1 1

1 3 2 0

2 0 1 3

2 0 2 2

2 0 3 1

2 1 0 3

2 1 1 2

2 1 2 1

2 1 3 0

2 2 0 2

2 2 1 1

2 2 2 0

2 3 0 1

2 3 1 0

3 0 0 3

3 0 1 2

3 0 2 1

3 0 3 0

3 1 0 2

3 1 1 1

3 1 2 0

3 2 0 1

3 2 1 0

3 3 0 0

0 1 3 3

0 2 2 3

0 2 3 2

0 3 1 3

0 3 2 2

0 3 3 1

1 0 3 3

1 1 2 3

1 1 3 2

1 2 1 3

1 2 2 2

1 2 3 1

1 3 0 3

1 3 1 2

1 3 2 1

1 3 3 0

2 0 2 3

2 0 3 2

2 1 1 3

2 1 2 2

2 1 3 1

2 2 0 3

2 2 1 2

2 2 2 1

2 2 3 0

2 3 0 2

2 3 1 1

2 3 2 0

3 0 1 3

3 0 2 2

3 0 3 1

3 1 0 3

3 1 1 2

3 1 2 1

3 1 3 0

3 2 0 2

3 2 1 1

3 2 2 0

3 3 0 1

3 3 1 0

0 2 3 3

0 3 2 3

0 3 3 2

1 1 3 3

1 2 2 3

1 2 3 2

1 3 1 3

1 3 2 2

1 3 3 1

2 0 3 3

2 1 2 3

2 1 3 2

2 2 1 3

2 2 2 2

2 2 3 1

2 3 0 3

2 3 1 2

2 3 2 1

2 3 3 0

3 0 2 3

3 0 3 2

3 1 1 3

3 1 2 2

3 1 3 1

3 2 0 3

3 2 1 2

3 2 2 1

3 2 3 0

3 3 0 2

3 3 1 1

3 3 2 0

0 3 3 3

1 2 3 3

1 3 2 3

1 3 3 2

2 1 3 3

2 2 2 3

2 2 3 2

2 3 1 3

2 3 2 2

2 3 3 1

3 0 3 3

3 1 2 3

3 1 3 2

3 2 1 3

3 2 2 2

3 2 3 1

3 3 0 3

3 3 1 2

3 3 2 1

3 3 3 0

1 3 3 3

2 2 3 3

2 3 2 3

2 3 3 2

3 1 3 3

3 2 2 3

3 2 3 2

3 3 1 3

3 3 2 2

3 3 3 1

2 3 3 3

3 2 3 3

3 3 2 3

3 3 3 2

3 3 3 3 ];

Dyuman Joshi 2023-1-25

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Nice work, Davide! I sometimes forget that FEx is an amazing resource as well

And the solution checks out, there should be 7^4 rows total for [-3 3]

7^4
ans = 2401

@Ali Almakhmari, you can obtain the desired solution for the intended range, but it would contain

fprintf('%d rows', 31^4)
923521 rows

so it would be difficult to go through all of them.

Ali Almakhmari 2023-1-25

Thank you all for your help. You have been amazing!

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Answer 2

Stephen23 2023-1-25

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One simple aprpoach is to download this FEX submission:

https://www.mathworks.com/matlabcentral/fileexchange/24325-combinator-combinations-and-permutations

but you will need plenty of memory:

V = -3:3
V = 1×7
    -3    -2    -1     0     1     2     3
X = combinator(numel(V),4,'p','r');
M = V(X)
M = 2401×4
    -3    -3    -3    -3
    -3    -3    -3    -2
    -3    -3    -3    -1
    -3    -3    -3     0
    -3    -3    -3     1
    -3    -3    -3     2
    -3    -3    -3     3
    -3    -3    -2    -3
    -3    -3    -2    -2
    -3    -3    -2    -1

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Stephen23 2023-1-26

编辑：Stephen23 2023-1-26

"What do you mean by copy them?"

Perhaps COPYFILE or one of the WEB* or URL* functions lets you copy from the FEX location to the Answers environment, from whence you could run it. Go and read the documentation and do some experiments. I can't help you with this, I have never tried.

"Also, how did you run the function?"

I downloaded it from FEX, uploaded it here, ran the code, then (out of respect for the submitter's license conditions) deleted the function before submitting my answer. You can delete uploaded files by clicking on the little red "x":

Dyuman Joshi 2023-1-27

Okay, I'll try it. Thanks for replying.

"I downloaded it from FEX, uploaded it here, ran the code, then (out of respect for the submitter's license conditions) deleted the function before submitting my answer."

Fair enough.

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Creating a row vector of combinations?

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