Merge vector and matrix with duplicated common values

I have a large size of matrix and here is the sample. I have an another vector,B.

 A = 
  1  1  2  3  …
  1  2  3  5  
  1  3  4  2  
  2  4  5  5  
  2  5  1  6  
  2  6  4  3  
  3  7  5  1  
  3  7  3  2  
  3  8  2  1  
  4  9  5  4  
  4  9  6  1  
  4  0  2  5  
...

B = 
1
2
1
1

I would like to merge the vector and the matrix by matching first column of A and the vector B. Because there are multiple rows with the each value of first column (e.g., 4 rows for value 1, 3 rows of value 2 and so on), all of rows for each value should be merged for a new dataset (C as below), and duplicated value in vector B (as shown, 1 is duplicated), it seems to be challenging.

Here is what I want to have

C = 

 1  1  2  3
1  2  3  5
1  3  4  2
2  4  5  5
2  5  1  6
2  6  4  3
1  1  2  3
1  2  3  5
1  3  4  2
1  1  2  3
1  2  3  5
1  3  4  2

[Stephen23]

@Boram Lim: please explain how C is derived from A and B. It is not clear from your question what their relationship is.

[Boram Lim]

It is like stacking

Part of A, rows with 1 in the first column
1  1  2  3
1  2  3  5
1  3  4  2

 Part of B, rows with 1 in the first column

2  4  5  5
2  5  1  6
2  6  4  3

 Part of A, rows with 1 in the first column
1  1  2  3
1  2  3  5
1  3  4  2

 Part of A, rows with 1 in the first column
1  1  2  3
1  2  3  5
1  3  4  2

[Boram Lim]

Because vector B has (1 ,2 1, 1), I want to have C by stacking rows with each of B values in the first column of A. I can do it by using innerjoin(B,A,'Key','name of common variable'). However, how to do it without using innerjoin?

[Stephen23]

@Boram Lim: then the C in your question is different to the one in your comment above (see "part B"). Which is correct?

[Boram Lim]

Oh, I made a mistake. you are right. I just updated. Thank you

Answer 1

[Stephen23]

One solution using accumarray:

>> A = [1,1,2,3;1,2,3,5;1,3,4,2;2,4,5,5;2,5,1,6;2,6,4,3;3,7,5,1;3,7,3,2;3,8,2,1;4,9,5,4;4,9,6,1;4,0,2,5];
>> B = [1;2;1;1];
>> R = 1:size(A,1);
>> Z = accumarray(A(:,1),R.',[],@(r){A(r,:)});
>> C = vertcat(Z{B})
C =
     1     1     2     3
     1     2     3     5
     1     3     4     2
     2     4     5     5
     2     5     1     6
     2     6     4     3
     1     1     2     3
     1     2     3     5
     1     3     4     2
     1     1     2     3
     1     2     3     5
     1     3     4     2