Subtracting Matrices in Special way

I have a Matrices as:

A=[1 10 12;2 12 3; 3 15 4; 4 16 7; 5 18 9; 6 10 10; 7 12 9; 9 5 6];

B=[3 9 8; 4 8 3; 5 2 5; 7 10 2; 8 9 7; 8 9 7; 9 12 10; 10 5 6];

Where Colum 1 is the index Colum 2 is the x and Colum 3 is the y. I would like to match each index of the 2 matrices and subtract the x and y values. The solution should be something like this:

C=[1 10 12; 2 12 3; 3 6 -4; 4 8 4; 5 16 4; 6 10 10; 7 2 7; 8 -9 -7; 9 -7 -4; 10 -5 -6] 

How would I do this?

[Stephen23]

https://web.archive.org/web/20211202055613/https://www.mathworks.com/matlabcentral/answers/1600119-subtracting-matrices-in-special-way

Answer 1

[Ive J]

There should be a simpler way, but this works:

A=[1 10 12;2 12 3; 3 15 4; 4 16 7; 5 18 9; 6 10 10; 7 12 9; 9 5 6];
B=[3 9 8; 4 8 3; 5 2 5; 7 10 2; 8 9 7; 8 9 7; 9 12 10; 10 5 6];

% build a new matrix from union of indices
idx = union(A(:, 1), B(:, 1));
D = [idx, zeros(numel(idx), 2)]; 

% fill x and y for shared indices between A and B
[fa, fb] = ismember(A(:, 1), B(:, 1));
fd = ismember(idx, A(fa, 1)); 
D(fd, 2:3) = A(fa, 2:3) - B(fb(fa), 2:3);

% fill the remaining rows in D
A(fa, :) = []; B(fb(fa), :) = []; % don't need them anymore!
[fd, fa] = ismember(idx, A(:, 1)); 
D(fd, 2:3) = A(fa(fd), 2:3);

[fd, fb] = ismember(idx, B(:, 1));
D(fd, 2:3) = D(fd, 2:3) - B(fb(fd), 2:3);

% check if D is same as C
C=[1 10 12; 2 12 3; 3 6 -4; 4 8 4; 5 16 4; 6 10 10; 7 2 7; 8 -9 -7; 9 -7 -4; 10 -5 -6];
all(D == C, 'all')

ans = logical
   1

[A]

Thanks!!

Answer 2

[Stephen23]

If the A values are copied first then only two ISMEMBER are required (simpler, more efficient), nor any resizing or changing of the A & B arrays (more efficient, and in general changing raw input data is best avoided):

A = [1,10,12;2,12,3;3,15,4;4,16,7;5,18,9;6,10,10;7,12,9;9,5,6]

A = 8×3

1 10 12 2 12 3 3 15 4 4 16 7 5 18 9 6 10 10 7 12 9 9 5 6

B = [3,9,8;4,8,3;5,2,5;7,10,2;8,9,7;8,9,7;9,12,10;10,5,6]

B = 8×3

3 9 8 4 8 3 5 2 5 7 10 2 8 9 7 8 9 7 9 12 10 10 5 6

X = union(A(:,1), B(:,1));
D = [X,zeros(numel(X),2)];
% Copy A values:
[Xd,Xa] = ismember(X,A(:,1));
D(Xd,2:3) = A(Xa(Xd),2:3);
% Subtract B values:
[Xd,Xb] = ismember(X,B(:,1));
D(Xd,2:3) = D(Xd,2:3) - B(Xb(Xd),2:3)

D = 10×3

1 10 12 2 12 3 3 6 -4 4 8 4 5 16 4 6 10 10 7 2 7 8 -9 -7 9 -7 -4 10 -5 -6

% Compare:
C = [1,10,12;2,12,3;3,6,-4;4,8,4;5,16,4;6,10,10;7,2,7;8,-9,-7;9,-7,-4;10,-5,-6];
isequal(C,D)

ans = logical
   1