How can I reconstruct a matrix form a vector and a mask 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

Answer 1

[Ameer Hamza]

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

[Itay Gdor]

first thanks,

I neet the intermidiat step as I only want to save matrix B (and M) in ordeer to save memory space (I have a lot of B matrixs and only one mask also the mask is not squer).

[Ameer Hamza]

In that case, try something like this

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)';
A = zeros(size(M));
A(M==1) = B;
A = reshape(A, size(M));

[Itay Gdor]

thanks you, that works well !!!

[Ameer Hamza]

I am glad to be of help!!!