generate a specific matrix in matlab

Question

I have matrix: x=[0 0 0;5 8 0; 7 6 0]

I want matrix: m=[0 0 0;5 8 0;7 6 0; 0 0 8;5 8 8;7 6 8; 0 0 16;5 8 16;7 6 16]

I want that the third column of matrix x gets multiplied each time by 8 while other two columns remain same. I want this to continue until the value in third column reaches 72.

How can I do it with bsxfun or any other way?

Answer 1

Assuming the following two assumptions, you could try an approach listed thereafter -

1. Keep on adding rather than multiplying.
2. All final elements in column-3 to reach at least 72.

Approach #1 [With bsxfun]

stopn = 72; %// stop adding till this number
add_factor = 8; %// Add factor to be added at each iteration to get to 72
ntimes = ceil(max((stopn - x(:,3))/add_factor)) %// no. of iterations needed

%// Get the starting 2d version of matrix to be added to x iteratively
x_add_2d = zeros(size(x)); %//
x_add_2d(:,3) = add_factor;

%// Get the complete version of matrix to be added (in 3d), then add to x
x_add_3d = bsxfun(@plus,x,bsxfun(@times,x_add_2d,permute([0:ntimes],[1 3 2])))

%// Concatenate along rows to form a 2D array as the final output
out = reshape(permute(x_add_3d,[1 3 2]),size(x_add_3d,1)*(ntimes+1),[])

Approach #2 [With repmat]

stopn = 72; %// stop adding till this number
add_factor = 8; %// Add factor to be added at each iteration to get to 72
ntimes = ceil(max((stopn - x(:,3))/add_factor)); %// no. of iterations needed

out = repmat(x,[ntimes+1 1]) %// replicated version of x
add_col3 = repmat([0:8:ntimes*8],size(x,1),1) %// column-3 values to be added
out(:,3) =  out(:,3) + add_col3(:) %// add those for the final output

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Sample run -

x =
    52    43    57
    41    40    48
    41    49    50
out =
    52    43    57
    41    40    48
    41    49    50
    52    43    65
    41    40    56
    41    49    58
    52    43    73
    41    40    64
    41    49    66
    52    43    81
    41    40    72
    41    49    74