There are likely many ways to do this without a for loop. One way is to cast the first column of matrix to a Categorical data type. We can think of the first column as a discrete set of categories rather than a numeric datatype. Then by specifying these categories as ordinals, we can rank them, and use this information to sort. See the below steps to do this using the example:
% The example data:
A=[3 1 5]; %the indexing vector
B=[5 55;3 33;1 11;3 333;5 555;1 111]; %the matrix to be sorted
% Step 1 convert the first row of B to a categorical datatype and save to a
% temporary variable.
B_Cat = categorical(B(:,1),A,'Ordinal',true);
% Note: We use A to define the category names. By also
% specifying it as an Ordinal, the order of categories specified in A
% determines the ranking used when sorting or comparing.
% Step 2: sort the temporary variable, save the indices for rearranging B.
[~,I] = sort(B_Cat);
% Step 3: Rearrange B by using the indices from the previous step to create
% the desired C matrix
C = B(I,:)
The output is:
C =
3 33
3 333
1 11
1 111
5 55
5 555
