最大样本 [英] Sample with a max
问题描述
如果我想对数字进行采样以创建向量，我会这样做:
If I want to sample numbers to create a vector I do:
set.seed(123)
x <- sample(1:100,200, replace = TRUE)
sum(x)
# [1] 10228
如果我想抽取 20 个总和为 100 的随机数，然后抽取 30 个数字但总和仍然为 100，该怎么办.我想这将比看起来更具挑战性.?sample 并在 Google 上搜索并没有为我提供线索.如果与所需的总和不够接近(例如在 5 以内)，我想可能需要一些时间来进行采样然后拒绝.
What if I want to sample 20 random numbers that sum to 100, and then 30 numbers but still sum to 100. This I imagine will be more of a challenge than it seems. ?sample and searching Google has not provided me with a clue. And a loop to sample then reject if not close enough( e.g. within 5) of the desired sum I guess may take some time.
有没有更好的方法来实现这一目标?
Is there a better way to achieve this?
一个例子是:
foo(10,100) # ten random numbers that sum to 100. (not including zeros)
# 10,10,20,7,8,9,4,10,2,20
推荐答案
这是另一种尝试.它不使用sample，而是使用runif.我在显示总和的输出中添加了一个可选的消息"，可以使用 showSum 参数触发.还有一个 Tolerance 参数指定需要多接近目标.
Here's another attempt. It doesn't use sample, but uses runif. I've added an optional "message" to the output showing the sum, which can be triggered using the showSum argument. There is also a Tolerance argument that specifies how close to the target is required.
SampleToSum <- function(Target = 100, VecLen = 10,
InRange = 1:100, Tolerance = 2,
showSum = TRUE) {
Res <- vector()
while ( TRUE ) {
Res <- round(diff(c(0, sort(runif(VecLen - 1)), 1)) * Target)
if ( all(Res > 0) &
all(Res >= min(InRange)) &
all(Res <= max(InRange)) &
abs((sum(Res) - Target)) <= Tolerance ) { break }
}
if (isTRUE(showSum)) cat("Total = ", sum(Res), "\n")
Res
}
这里有一些例子.
注意默认设置和设置Tolerance = 0
set.seed(1)
SampleToSum()
# Total = 101
# [1] 20 6 11 20 6 3 24 1 4 6
SampleToSum(Tolerance=0)
# Total = 100
# [1] 19 15 4 10 1 11 7 16 4 13
您可以使用 replicate 验证此行为.这是设置 Tolerance = 0 并运行该函数 5 次的结果.
You can verify this behavior by using replicate. Here's the result of setting Tolerance = 0 and running the function 5 times.
system.time(output <- replicate(5, SampleToSum(
Target = 1376,
VecLen = 13,
InRange = 10:200,
Tolerance = 0)))
# Total = 1376
# Total = 1376
# Total = 1376
# Total = 1376
# Total = 1376
# user system elapsed
# 0.144 0.000 0.145
output
# [,1] [,2] [,3] [,4] [,5]
# [1,] 29 46 11 43 171
# [2,] 103 161 113 195 197
# [3,] 145 134 91 131 147
# [4,] 154 173 138 19 17
# [5,] 197 62 173 11 87
# [6,] 101 142 87 173 99
# [7,] 168 61 97 40 121
# [8,] 140 121 99 135 117
# [9,] 46 78 31 200 79
# [10,] 140 168 146 17 56
# [11,] 21 146 117 182 85
# [12,] 63 30 180 179 78
# [13,] 69 54 93 51 122
同样设置Tolerance = 5并运行该函数5次.
And the same for setting Tolerance = 5 and running the function 5 times.
system.time(output <- replicate(5, SampleToSum(
Target = 1376,
VecLen = 13,
InRange = 10:200,
Tolerance = 5)))
# Total = 1375
# Total = 1376
# Total = 1374
# Total = 1374
# Total = 1376
# user system elapsed
# 0.060 0.000 0.058
output
# [,1] [,2] [,3] [,4] [,5]
# [1,] 65 190 103 15 47
# [2,] 160 95 98 196 183
# [3,] 178 169 134 15 26
# [4,] 49 53 186 48 41
# [5,] 104 81 161 171 180
# [6,] 54 126 67 130 182
# [7,] 34 131 49 113 76
# [8,] 17 21 107 62 95
# [9,] 151 136 132 195 169
# [10,] 194 187 91 163 22
# [11,] 23 69 54 97 30
# [12,] 190 14 134 43 150
# [13,] 156 104 58 126 175
毫不奇怪，将容差设置为 0 会使函数变慢.
Not surprisingly, setting the tolerance to 0 would make the function slower.
请注意，由于这是一个随机"过程，因此很难猜测找到正确的数字组合需要多长时间.例如，使用set.seed(123)，我连续运行了3次以下测试:
Note that since this is a "random" process, it's hard to guess how long it would take to find the right combination of numbers. For example, using set.seed(123), I ran the following test three times in a row:
system.time(SampleToSum(Target = 1163,
VecLen = 15,
InRange = 50:150))
第一次运行只用了 9 秒多一点.第二个只用了 7.5 秒多一点.第三个花了……不到 381 秒！这是一个很大的变化！
The first run took just over 9 seconds. The second took just over 7.5 seconds. The third took... just under 381 seconds! That's a lot of variation!
出于好奇，我在函数中添加了一个计数器，第一次运行需要 55026 次尝试才能得到满足我们所有条件的向量！(我没有费心尝试第二次和第三次尝试.)
Out of curiosity, I added a counter into the function, and the first run took 55026 attempts to arrive at a vector that satisfied all of our conditions! (I didn't bother trying for the second and third attempts.)
在函数中添加一些错误或健全性检查以确保输入合理可能会很好.例如，您不应该输入 SampleToSum(Target = 100, VecLen = 10, InRange = 15:50) 因为范围是 15 到 50，所以无法达到 100 AND向量中有 10 个值.
It might be good to add some error or sanity checking into the function to make sure the inputs are reasonable. For example, one should not be able to enter SampleToSum(Target = 100, VecLen = 10, InRange = 15:50) since with a range of 15 to 50, there's no way to get to 100 AND have 10 values in your vector.
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