Lua函数泛化n维数组

以下的MWE初始化、递增和打印2-D和3-D数值数组。它很容易扩展到处理4-D等数组，但是更优雅的做法是创建一个接受维数（最多7维）为参数或根据输入参数数量确定维数的通用函数。如何实现一个好的方式？

MWE：

local i_low, i_high = 2, 4
local i_range = i_high - i_low - 1

local j_low, j_high = 3, 7
local j_range = j_high - j_low - 1

local k_low, k_high = 1, 3
local k_range = k_high - k_low - 1

local myArray_two = {}
local myArray_three = {}

function initArray_two(t, i_low, i_high, j_low, j_high, value)
    local i, j = 0, 0

    for i = i_low, i_high, 1 do
        for j = j_low, j_high, 1 do
            local idx = j * i_range + i
            t[idx] = value
        end
    end
end

function initArray_three(t, i_low, i_high, j_low, j_high, k_low, k_high, value)
    local i, j, k = 0, 0, 0

    for i = i_low, i_high, 1 do
        for j = j_low, j_high, 1 do
            for k = k_low, k_high, 1 do
                local idx = k*j_range*i_range + j*i_range + i
                t[idx] = value
            end
        end
    end
end

function incrValue_two(t, i, j, value)
    assert(i>i_low and i <= i_high)
    assert(j>j_low and j <= j_high)

    local idx = j * i_range + i
    t[idx] = t[idx] + value
end

function incrValue_three(t, i, j, k, value)
    assert(i>i_low and i <= i_high)
    assert(j>j_low and j <= j_high)
    assert(k>k_low and k <= k_high)

    local idx = k*j_range*i_range + j*i_range + i
    t[idx] = t[idx] + value
end

function printArray_two(t, title, i_low, i_high, j_low, j_high)
    local i, j = 0, 0
    print(title.."\n")

    for i = i_low, i_high, 1 do
        for j = j_low, j_high, 1 do
            local idx = j * i_range + i
            print(i.."\t"..j.."\t"..t[idx])
        end
        print("\n")
    end

end

function printArray_three(t, title, i_low, i_high, j_low, j_high, k_low, k_high)
    local i, j, k = 0, 0, 0
    print(title.."\n")

    for i = i_low, i_high, 1 do
        for j = j_low, j_high, 1 do
            for k = k_low, k_high, 1 do
                local idx = k*j_range*i_range + j*i_range + i
                print(i.."\t"..j.."\t"..k.."\t"..t[idx].."\n")
            end
        end
    end

end

initArray_two(myArray_two, i_low, i_high, j_low, j_high, 0)
initArray_three(myArray_three, i_low, i_high, j_low, j_high, k_low, k_high, 1)

incrValue_two(myArray_two, 2, 3, 11)
incrValue_two(myArray_two, 2, 3, 13)
incrValue_two(myArray_two, 4, 7, 5)
printArray_two(myArray_two, "一个二维数组", i_low, i_high, j_low, j_high)

incrValue_three(myArray_three, 2, 3, 1, 9)
incrValue_three(myArray_three, 2, 3, 1, 17)
printArray_three(myArray_three, "一个三维数组", i_low, i_high, j_low, j_high, k_low, k_high)