How to map points in Vector A with points in vector B?

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Rayan Glus 2021-3-10

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https://ww2.mathworks.cn/matlabcentral/answers/767997-how-to-map-points-in-vector-a-with-points-in-vector-b

评论： Rayan Glus 2021-3-13

采纳的回答： Steven Lord

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Hi,

I have two row vectors with the same size.

A = randi(100,1,100);
B = randi([101, 200],1,100);

I want to have another row vector AB where :

AB(i) = j ;% i and j are elements in A and B respectively 
AB(j) = i;

AB's length supposed to be length of A + length of B, correct? What if in one case i and j happens to have the same value when both A and B are :

A = randi(100,1,100);
B = randi(100,1,100);

Thanks!

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Jorg Woehl 2021-3-10

编辑：Jorg Woehl 2021-3-10

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Rayan, can you clarify what you mean with AB(i)=j and AB(j)=i where "i and j are elements in A and B respectively"? Or, more precisely, what is the link between i and j?

Taking a simple example:

A = randi(100,1,5)
A =
    21    31    48    24    85
    
B = randi([101, 200],1,5)
B =
   120   123   118   123   144

Do you now want AB(21)=120, and AB(120)=21, meaning that i and j are the corresponding elements in A and B? Or, expressed mathematically: i=A(k) and j=B(k) for a given k?

If that's the case, the vector AB cannot be constructed, because several elements of A can have the same value, let's say "19". That means that A(19) cannot be uniquely defined. And the same argument holds for vector B. (I think this is the question that you were pondering,too.)

Rayan Glus 2021-3-10

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Thanks for your reply Jorg.

So, A and B are basically, vectors of cities. And I want to map between these cities. Let's say that city 21 in A is mapped to city 120 in B and vice versa.

If that's the case, the vector AB cannot be constructed.

I agree with you. But what if we define:

A = 1:100;
B = 101:200;

Would it be possible then to map between the i's and j's?

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Answer 1

Steven Lord 2021-3-10

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https://ww2.mathworks.cn/matlabcentral/answers/767997-how-to-map-points-in-vector-a-with-points-in-vector-b#answer_643707

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So you want something like this?

v = randperm(10) % Shuffle the numbers from 1 to 10
v = 1×10
     7     3     9     4     6     1    10     2     5     8
A = v(1:5) % Cut the "deck"
A = 1×5
     7     3     9     4     6
B = v(6:10)
B = 1×5
     1    10     2     5     8
AB = zeros(1, 10);
AB(A) = B;
AB(B) = A
AB = 1×10
     7     9    10     5     4     8     1     6     2     3