Replace one element of a column in another - matlab

Question

Let A and B be column vectors:
A = (1:6).'; %'// [1;2;3;4;5;6]
B = (7:12).'; %'// [7;8;9;10;11;12]
How do I construct a matrix such that one element of A is replaced each time by an element from B to get C as:
C = [...
7 1 1 1 1 1
2 8 2 2 2 2
3 3 9 3 3 3
4 4 4 10 4 4
5 5 5 5 11 5
6 6 6 6 6 12];
If C is to be indexed as index = [1 1 1 2 2 3 3]', how is it possible to produce
c1 = [...
1 7 1 1
1 2 8 2
1 3 3 9];
c2 = [...
2 10 4
2 5 11];
c3 = [3 6]; %// either this
c3 = [3 12]; %// or this

Answer 1

Problem #1:
C = bsxfun(#plus,A.',-diag(A)+diag(B));
gives:
7 2 3 4 5 6
1 8 3 4 5 6
1 2 9 4 5 6
1 2 3 10 5 6
1 2 3 4 11 6
1 2 3 4 5 12
Problem #2:
As far as I understand, you want to extract blocks out of the previously found C matrix, in the following fashion:
Where c1, c2, c3 are the green, red and blue blocks, repectively; and "missing" elements are replaced with NaN (in the initial version of your question).
index = [1 1 1 2 2 3 3]; %// Block definition
[blkSz,~] = histcounts(index,numel(unique(index))); %// Conversion...
paddedC = padarray(C,numel(index)-numel(diag(C))*[1 1],NaN,'post');
blocks = mat2cell(paddedC,blkSz,blkSz);
This results in a cell-array blocks with the following contents:
blocks =
[3x3 double] [3x2 double] [3x2 double]
[2x3 double] [2x2 double] [2x2 double]
[2x3 double] [2x2 double] [2x2 double]
Where for example blocks{1,1} is:
ans =
7 2 3
1 8 3
1 2 9
Then you can pad the array using the index of the loop, to get the c cell, like so:
c = cell(numel(blkSz),1); %// Preallocation
for ind1 = 1:numel(blkSz)
c{ind1} = padarray(blocks{ind1,ind1},1,ind1,'pre');
end
Note that c1 is found in c{1} etc.
Addition:
In the case when you don't want c1...c3 to be (possibly) padded with NaNs, the best way in my opinion would be trimming the index vector to the length of A or B ("length(C)"). This ensures you won't access blocks outside your square matrix. For example:
newIdx = index(1:numel(A));
Then just use newIdx instead of index in the rest of the code.