matlab: matrix construction

gistfile1.txt

expand(vec,dims)
    # split vec into layers
    ex:expand([1;2],[])   -> [1;2]
       expand([1;2],[2])  -> [1 2;
                              1 2]
       expand([1;2],[2 3]) -> 
            1 1 1    2 2 2
            1 1 1    2 2 2 (a 2*3*2 matrix)
       expand([1;2;3],[1 2]) ->
            1 1   2 2   3 3 (a 1*2*3 matrix)

rep(mat,dims)
    # induce on dims(a dimension range) with recursively calling repmat
    case dims of
        []        -> mat
        otherwise -> rep(repmat(mat,car(dims)),cdr(dims))
    where car([a b]) = a
          cdr([a b]) = [b]

    ex:
          rep([0;1], [2 3])
        = rep([0 0 , [3])
               1 1]
        = 0 0    0 0
          1 1    1 1 (a 2*2*2 matrix)

zipWith f mats
    # mats is a list of matrix with the same size
    # f is a function with arity = length(mats)
    ex: zipWith f [[1 2] [3 4]]
        = [f(1,3) f(2,4)]

#----------------------------------------------
for Vectors V = {Vi            | i=1:n}
        and L = {Li=length(Vi) | i=1:n}
        and f with arity = n

a matrix construction that interweaving V can be written as:

zipWith f [ rep(expand(Vi, [Li for i=1:i-1]), [i+1:n]) for i=1:n ]

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