How can I fill a matrix column with dta coming from another matrix according to index

I need to fill a large matrix with data coming from a smaller matrix. Both matrices contains a first column with an index and a second column with the results of an experiment. I need to combine the results according to their index. For example I have a matrix A:

1 1
2 1
3 1
4 1
5 1
6 1
7 1
8 1
9 1

And a matrix B

1 10
2 10
4 10
7 10

I would like to combine them to obtain the matrix C with 3 columns (column 1 for index, column 2 results from A, column 3 results from B)

1 1 10
2 1 10
3 1 NaN
4 1 10
5 1 NaN
6 1 NaN
7 1 10
8 1 NaN
9 1 NaN

I have to do that on matrices with millions of rows, therefore methods limiting calculation time would be welcome. Thank you very much for any help.

Answer 1

[Matz Johansson Bergström]

Without knowing the size of the matrix, it might be a good idea to use a sparse matrix, instead of filling the non existant elements with NaN. Now, this is not exactly what you did, but it will give you a good hint of what you can accomplish with a sparse structure.

I did this fairly quick, because it is late where I live, but it should work fine

%create the example vectors
A = [(1:9)',ones(9,1)];
B = [1,2,4,7]';
B = [B, 10+0*B];

%putting the data into a sparse matrix 
M = sparse([]);
M(A(:,1), 1) = A(:,2);
M(B(:,1), 2) = B(:,2);

Note that I use the first column in A as an index in M and the same goes for B. When I add the elements I add them in the first column of M, then the second column, separating where the values come frome.

I hope this helps.

[olivier espeli]

thank you very much for your help

Answer 2

[Shoaibur Rahman]

A = [(1:9)' ones(9,1)];
B = [1 10; 2 10; 4 10; 7 10];
C = NaN(size(A,1),1);
C(B(:,1)) = B(:,2);
C = [A C]

[olivier espeli]

Thank you very much for you help

Answer 3

[Image Analyst]

Try this:

A = [...
1 1
2 1
3 1
4 5
5 1
6 1
7 9
8 1
9 1]

B = [...
1 10
2 20
4 70
7 90]

% Find  out what the max index could possibly be.
maxRow = max([A(:,1); B(:,1)])
C = zeros(maxRow, 3); % Preallocate C.
% Assign all possible indices to column 1 of C.
C(:,1)=1:maxRow;
% Assign column 2 of A to column 2 of C.
C(A(:,1),2) = A(:, 2);
% Assign column 2 of B to column 3 of C.
C(B(:,1), 3) = B(:, 2)

In the command window:

C =
     1     1    10
     2     1    20
     3     1     0
     4     5    70
     5     1     0
     6     1     0
     7     9    90
     8     1     0
     9     1     0

It's vectorized so it should be pretty fast. Anyway, a million rows is not that many. Here it is with a million rows and it took 0.03 seconds:

numberOfRows = 1000000;
A = int32(randi(99, [numberOfRows, 2]));
B = int32(randi(99, [numberOfRows, 2]));
tic;
% Find  out what the max index could possibly be.
maxRow = max([A(:,1); B(:,1)]);
C = zeros(maxRow, 3); % Preallocate C.
% Assign all possible indices to column 1 of C.
C(:,1)=1:maxRow;
% Assign column 2 of A to column 2 of C.
C(A(:,1),2) = A(:, 2);
% Assign column 2 of B to column 3 of C.
C(B(:,1), 3) = B(:, 2);
toc;

[olivier espeli]

Thank you very much, very helpful.