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Combining Matlab's `repmat` with R's `rep` for tensors of arbitrary order
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function repeat{T}(v::Array{T}, | |
dims::Integer...; | |
repetitions::Integer = 1) | |
n = length(v) | |
n_res = n * repetitions * prod(dims) | |
res = Array(T, tuple(repetitions * n * dims[1], dims[2:end]...)...) | |
for i in 0:(n_res - 1) | |
index = mod(fld(i, repetitions), n) | |
res[i + 1] = v[index + 1] | |
end | |
return res | |
end | |
myrepmat{T}(v::Vector{T}, a::Integer, b::Integer) = repeat(v, a, b) | |
myrepmat{T}(m::Matrix{T}, a::Integer, b::Integer) = repeat(m, a, b) | |
@assert isequal(repeat(["A", "B"], 1, repetitions = 1), | |
["A", "B"]) | |
@assert isequal(repeat(["A", "B"], 2, repetitions = 1), | |
["A", "B", "A", "B"]) | |
@assert isequal(repeat(["A", "B"], 1, repetitions = 2), | |
["A", "A", "B", "B"]) | |
@assert isequal(repeat(["A", "B"], 2, repetitions = 2), | |
["A", "A", "B", "B", "A", "A", "B", "B"]) | |
@assert isequal(repeat(["A", "B"], 1, 1, repetitions = 1), | |
["A", "B"]'') | |
@assert isequal(repeat(["A", "B"], 1, 2, repetitions = 1), | |
["A" "A"; | |
"B" "B"]) | |
@assert isequal(repeat(["A", "B"], 2, 1, repetitions = 1), | |
["A"; | |
"B"; | |
"A"; | |
"B";]'') | |
@assert isequal(repeat(["A", "B"], 2, 2, repetitions = 1), | |
["A" "A"; | |
"B" "B"; | |
"A" "A"; | |
"B" "B";]) | |
@assert isequal(repeat(["A", "B"], 2, 2, repetitions = 2), | |
["A" "A"; | |
"A" "A"; | |
"B" "B"; | |
"B" "B"; | |
"A" "A"; | |
"A" "A"; | |
"B" "B"; | |
"B" "B";]) | |
for i in 1:3 | |
for j in 1:3 | |
@assert isequal(myrepmat(["A", "B"], i, j), | |
repmat(["A", "B"], i, j)) | |
end | |
end | |
for i in 1:3 | |
for j in 1:3 | |
@assert isequal(myrepmat(["A", "B"]'', i, j), | |
repmat(["A", "B"]'', i, j)) | |
end | |
end |
While it's easy to see how to hardcode the vector and matrix cases, it's not clear to me how to generalize repmat
to produce sane behavior for tensors or under repetitions.
Next set of ideas:
repeat(A, inner = [a1, a2, a3], outer = [b1, b2, b3])
# order_res = max(length(inner), length(outer))
# Retain specified singleton dimensions
# Order of Result >= Order of Input
repeat([1, 2, 3], inner = [1], outer = [1])
=> [1, 2, 3]
repeat([1, 2, 3], inner = [1], outer = [1, 1])
<=> repeat([1, 2, 3], inner = [1, 1], outer = [1, 1])
=> [1;
2;
3;]
repeat([1, 2, 3], inner = [2], outer = [1])
=> [1, 1, 2, 2, 3, 3]
repeat([1, 2, 3], inner = [1], outer = [2])
=> [1, 2, 3, 1, 2, 3]
repeat([1 2;
3 4], inner = [1, 1], outer = [1, 1])
=> [1 2;
3 4;]
repeat([1 2;
3 4], inner = [2, 1], outer = [1, 1])
=> [1 2;
1 2;
3 4;
3 4;]
repeat([1 2;
3 4], inner = [1, 2], outer = [1, 1])
=> [1 1 2 2;
3 3 4 4;]
# Index in original to indices in result
#1 -> 1, 3
#2 -> 2, 4
# ...
#4 -> 6, 8
repeat([1 2;
3 4], inner = [1, 1], outer = [2, 1])
=> [1 2;
3 4;
1 2;
3 4;]
# Index in original to indices in result
#1 -> 1, 3
#2 -> 2, 4
# ...
#4 -> 6, 8
repeat([1 2;
3 4], inner = [1, 1], outer = [1, 2])
=> [1 2 1 2;
3 4 3 4;]
# Index in original to indices in result
#1 -> 1, 5
#2 -> 2, 6
# ...
#4 -> 4, 8
repeat([1 2;
3 4;
5 6;], inner = [1, 1], outer = [2, 1])
=> [1 2;
3 4;
5 6;
1 2;
3 4;
5 6;]
# Index in original to indices in result
#1 -> 1, 4
#2 -> 2, 5
# ...
#4 -> 7, 10
# mod(7, 6) = mod(7, outer[1] * sizes[0])
# Distance between successive slots is
# outer[i] * sizes[i - 1]
# outer[i - 2] * sizes[i - 1]
# Offset?
# Output Sizes:
# output_sizes[i] = sizes[i] * inner[i] * outer[i]
repeat([1 2;
3 4;
5 6;], inner = [1, 1], outer = [1, 2])
=> [1 2 1 2;
3 4 3 4;
5 6 5 6;]
# Index in original to indices in result
#1 -> 1, 7
#2 -> 2, 6
# ...
#4 -> 4, 8
# sum_over_i(outer[i] * size(A, i - 1))???
repeat([:, :, 1][1 2;
3 4;],
[:, :, 2][5 6;
7 8;], inner = [1, 1, 2], outer = [1, 1, 1])
=> [:, :, 1][1 2;
3 4;]
[:, :, 2][1 2;
3 4;]
[:, :, 3][5 6;
7 8;]
[:, :, 4][5 6;
7 8;]
#1 -> 1, 5
#2 -> 2, 6
#3 -> 3, 7
# ...
#5 -> 9, 13
# ...
#8 -> 12, 16
# i -> i + intervenors_along_previous_dimensions, ... distances
repeat([1 2], inner = [1, 1], outer = [2, 1])
=> [1 2;
1 2;]
sizes = [1, 2]
# If you had full index set, [i, j]
# you would do:
# i, j -> ??
#1, 1 -> 1, 1 AND 2, 1
#1, 2 -> 2, 1 AND 2, 2
repeat([1 2;
3 4;], inner = [2, 2], outer = [2, 2])
=> [1 1 2 2 1 1 2 2;
1 1 2 2 1 1 2 2;
3 3 4 4 3 3 4 4;
3 3 4 4 3 3 4 4;
1 1 2 2 1 1 2 2;
1 1 2 2 1 1 2 2;
3 3 4 4 3 3 4 4;
3 3 4 4 3 3 4 4;]
# Input Index -> Output Indices
#1 -> 1, 2, 5, 6, 9, 10, 13, 14, 33, 34, 37, 38, 41, 42, 45, 46
#2 -> 3, 4, 7, 8, 11, 12, 15, 16, 35, 36, 39, 40, 43, 44, 47, 48
#3 -> 17, 18, 21, 22, 25, 26, 29, 30, 49, 50, 53, 54, 57, 58, 61, 62
#4 -> 19, 20, 23, 24, 27, 28, 31, 32, 51, 52, 55, 56, 59, 60, 63, 64
#
# Observations
# * All sequences have same gaps
# * Estimate sequence 1, 2, 5, 6, 9, 10, 13, 14, 33, 34, 37, 38, 41, 42, 45, 46
# * Offsets are 0, 2, 16, 18
# * Need rule to produce gap sequences and offsets
# i, j -> i:SF1:max_i, j:SF2:max_j ???
# inner increases offsets, but decreases distance between successors
# outer "maintains" offsets???
# i -> inner[1] * sizes[1]
#
repeat([1, 2], inner = [1, 1], outer = [2, 1])
=> [1;
2;
1;
2;]
sizes = [2, 1]
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The problem with this approach is that it doesn't give the right answer for matrices. The behavior it should have is:
In contrast, it has this behavior: