# How to obtain a Matrix?

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Hi evreyone, I am trying to obtain a matrix [n,n] by a vector [n,1] in order that the total (sum) of each row must be equal to the vector's row. See the example

vector=[ 5; 10; 3] matrix=[1,2,1,1; 2,3,4,1; 3,0,0]

There is any funciont in matlab that do this? I need that the values in the matrix are not all equal.

it's okay if it gives (2,1,2) but if it does (2,2,2) it isn't what i am looking for. It would be even better if the values in the matrix changes evrey time I run the code. For example: [1 run]-> 5= [1,1,2,0,1] | [2 run]-> 5= [1,2,2,0,0] | [3 run]-> 5= [1,3,0,0,1] and so on

Hope you can help me

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### Answers (4)

Matt J
on 30 Jun 2021

Edited: Matt J
on 30 Jun 2021

Perhaps as follows?

vector=[ 5; 10; 3] ;

n=numel(vector);

matrix=zeros(n); %pre-allocate

s=vector;

for i=1:n

if i==n

col=s;

else

col=floor(rand*s);

end

matrix(:,i)=col;

s=max(s-col,0);

end

matrix,

check=all(sum(matrix,2)==vector)

##### 1 Comment

Matt J
on 1 Jul 2021

Matt's code with a large vector returns some numbers in the first columns, in the central columns a series of zeros and in the last column of the matrix a series of 1s.

Here is a modification that distributes the values a bit more evenly and randomly across the rows (note the attached file).

n=15;

vector=randi(3*n,n,1);

matrix=zeros(n); %pre-allocate

s=vector;

for i=1:n

if i==n

col=s;

else

factor=rand(size(s))./(sqrt(n-i));

col=floor(factor.*s);

end

matrix(:,i)=col;

s=max(s-col,0);

end

[~,perm]=sortlidx(rand(size(matrix)),2);

matrix=matrix(perm),

check=all(sum(matrix,2)==vector)

Image Analyst
on 1 Jul 2021

I don't believe it's a common enough thing to want to do that there is a built in function for it so you'll have to build it yourself.

If you're not restricting it to integers, this works:

vector = [5; 10; 3] % Column vector

matrix = repmat(vector', [length(vector), 1])

percentages = [0.5, 0.3, 0.2] % Fractions of number to appear in each row.

matrix(1,:) = matrix(1,:) * percentages(1);

matrix(2,:) = matrix(2,:) * percentages(2);

matrix(3,:) = matrix(3,:) * percentages(3)

matrix =

2.5 5 1.5

1.5 3 0.9

1 2 0.6

##### 0 Comments

Walter Roberson
on 5 Jul 2021

##### 0 Comments

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