MATLAB: How to reconstruct a matrix form a vector and a mask matrix

reconstruct a matrix

I am using a mask matrix to reduce the size and remove not relevant part, but I cannot reconstruct the matrix back.
i.e.
a =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
M =
0 0 0 0 0
0 1 1 1 0
0 1 1 1 0
0 1 1 1 0
0 0 0 0 0
>> B=a(M>0)’
B =
5 6 12 7 13 19 14 20 21
Now what I need is a way to go back i.e
>> A=(??M??B??)
A=
0 0 0 0 0
0 5 7 14 0
0 6 13 20 0
0 12 19 21 0
0 0 0 0 0
thanks

Best Answer

No need for the intermediate step there. Just directly use element-wise multiplication to create A matrix
a = [
    17    24     1     8    15
    23     5     7    14    16
     4     6    13    20    22
    10    12    19    21     3
    11    18    25     2     9];
M = [
     0     0     0     0     0
     0     1     1     1     0
     0     1     1     1     0
     0     1     1     1     0
     0     0     0     0     0];
 
A = a.*M
Result
>> A
A =
     0     0     0     0     0
     0     5     7    14     0
     0     6    13    20     0
     0    12    19    21     0
     0     0     0     0     0
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