Matrices in a matrix.

Hi,

I have 4 matrices: X1=[1;2;3;4] X2=[ 5,6,7,8] X3=[9,10,11,12] X4=[13,14,15,16]

I would like to compare these matrices to each other and i want to create a new matrix depending on this comparison.

So I want to create a Y=[yij] 4x4 matrix which consists of matrices.

Now i'll explain the comparing rule with an example.

Here min(X1)= 1 and the max(X1)=4

Let's take x ∈ X2.

If x satisfy min(X1) <= x <= max(X1) it should be 1 in a new matrix , if it does not satisfy min(X1)<= x <= max(X1) it should be 0 in a new matrix.

So in this example i need a matrix :[ 0; 0; 0; 0 ]

According to this rule, i want to create a matrix Y=[yij] which consist of these comparison matrices.

So the first row of Y should consist of 4 elements in other words 4 different matrices related to X1. ( comparison of X1 with itself and others )

• First element of this matrix is y11 which consists of comparing X1 with itself. ( y11= [1;1;1;1], since every element satisfies the rule)
• Second element is y12 which consists of comparing X1 with X2. (y12=[0;0;0;0], since none of the elements satisfies the rule)
• Third element is y13 which consists of comparing X1 with X3.
• Last element of the first row is y14 which consists of comparing X1 with X4.

In this way, i want to create a 4x4 matrix Y.

Is there any way to do this with for loop?

Thanks.

Answer 1

[Guillaume]

First thing: a matrix of matrices does not exist mathematically, so what you're asking is an impossibility. In matlab, you can store matrices in a cell array. cell arrays are not matrices and work differently so may not be what you want. For example you can't perform mathematical operations on a cell array.

Second thing: Numbered variables are always a bad idea and will greatly complicate your code. You're embedding an index in the variable name which is problematic. Instead you should be using a cell array or a 2D matrix to store your vectors. Either way, you then use standard matlab indexing to refer to each vector.

I would recommend you store your X vectors as rows of a matrix:

X = [1 2 3 4      
     5 6 7 8
     9 10 11 12
     13 14 15 16];

X(1, :) is your original X1, etc.

With that storage, what you want can be done easily without a loop. As said it can't be stored as a 2D matrix. I'd recommend a 3D matrix instead

%Better X for demo
X = [1 2 3 4 5;    ... x1
     3 5 7 9 11;   ... x2
     2 4 6 8 10;   ... x3
     3 9 12 15 18];  % x4
 
 minx = min(X, [], 2);  %min of each vector
 maxx = max(X, [], 2);  %max of each vector
 result = X >= reshape(minx, 1, 1, []) & X <= reshape(maxx, 1, 1, []) 

result is a numvector x numcolumn x numvector matrix, where result(r, :, p) is the comparison of X(r, :) with X(p, :).

[Serra Aksoy]

Thank you very much for your quick response.

But i have a question.

X = [1 2 3 4 5

3 5 7 9 11

2 4 6 8 10

3 9 12 15 18];

Here when i compare X1 with itself, for a result i need [1 1 1 1 1] ( Since every element of X1 satisfies min(X1)<= x <=max(X1))

or when i compare X1 with X2, the result should be [ 1 1 0 0 0 ] ( Since only the first two elements of X2, 3 and 5, satisfy the condition: min(X1) <= x <= max (X1) )

So in your code, when i try to compare X1 with X1 using result(1, :, 1), i cant get the result i want.

[Guillaume]

After fixing several typos in the code, you'll find it works properly. Sorry, I should have tested it first.

You'll see that result(1, :, 1) (X1 compared with X1) is indeed [1 1 1 1 1] and result(1, :, 2) (X1 compared with X2) is indeed [1 1 0 0 0]

[Serra Aksoy]

Thank you very much for your help. But i have one more queistion.

I asked here : https://www.mathworks.com/matlabcentral/answers/504269-calculating-the-sum-of-each-row-in-a-matrix

Could you please just take a look at it? Thanks.