如何对R中特定范围内的函数求和? [英] How to sum a function over a specific range in R?
问题描述
这里是三列:
indx vehID LocalY
1 2 35.381
2 2 39.381
3 2 43.381
4 2 47.38
5 2 51.381
6 2 55.381
7 2 59.381
8 2 63.379
9 2 67.383
10 2 71.398
11 2 75.401
12 2 79.349
13 2 83.233
14 2 87.043
15 2 90.829
16 2 94.683
17 2 98.611
18 2 102.56
19 2 106.385
20 2 110.079
21 2 113.628
22 2 117.118
23 2 120.6
24 2 124.096
25 2 127.597
26 2 131.099
27 2 134.595
28 2 138.081
29 2 141.578
30 2 145.131
31 2 148.784
32 2 152.559
33 2 156.449
34 2 160.379
35 2 164.277
36 2 168.15
37 2 172.044
38 2 176
39 2 179.959
40 2 183.862
41 2 187.716
42 2 191.561
43 2 195.455
44 2 199.414
45 2 203.417
46 2 207.43
47 2 211.431
48 2 215.428
49 2 219.427
50 2 223.462
51 2 227.422
52 2 231.231
53 2 235.001
54 2 238.909
55 2 242.958
56 2 247.137
57 2 251.247
58 2 255.292
59 2 259.31
60 2 263.372
61 2 267.54
62 2 271.842
63 2 276.256
64 2 280.724
65 2 285.172
我想通过应用以下公式创建一个名为Smoothed Y"的新列:
I want to create a new column called 'Smoothed Y' by applying the following formula:
D=15, delta (三角形符号) = 5, i = indx, x_alpha(tk) = LocalY, x_alpha(ti) = 平滑值
D=15, delta (triangular symbol) = 5, i = indx, x_alpha(tk) = LocalY, x_alpha(ti) = smoothed value
我尝试使用以下代码来首先计算 Z:(下面的内核表示 exp 函数)
I have tried using following code for first calculating Z: (Kernel below means the exp function)
t <- 0.5
dt <- 0.1
delta <- t/dt
d <- 3*delta
indx <- a$indx
for (i in indx) {
initial <- i-d
end <- i+d
k <- c(initial:end)
for (n in k) {
kernel <- exp(-abs(i-n)/delta)
z <- sum(kernel)
}
}
a$z <- z
print (a)
注意:'a' 是包含上述三列的导入数据框.
NOTE: 'a' is the imported data frame containing the three columns above.
尽管计算函数的值很好，但它不会对变量 z 中的值求和.如何对每个 indx 值 i 在 i-d 到 i+d 范围内求和?
Although the values of computed function are fine but it doesn't sum up the values in variable z. How can I do summation over the range i-d to i+d for every indx value i?
推荐答案
您可以使用 convolve 函数.您需要决定的一件事是，对于比卷积核的宽度更接近数组任一端的索引，该怎么做.一种选择是简单地使用部分内核，重新缩放以使权重总和仍为 1.
You can use the convolve function. One thing you need to decide is what to do for indices closer to either end of the array than width of the convolution kernel. One option is to simply use the partial kernel, rescaled so the weights still sum to 1.
smooth<-function(x,D,delta){
z<-exp(-abs(-D:D)/delta)
r<-convolve(x,z,type="open")/convolve(rep(1,length(x)),z,type="open")
r<-head(tail(r,-D),-D)
r
}
将数组设为 y，结果如下:
With your array as y, the result is this:
> yy<-smooth(y,15,5)
> yy
[1] 50.70804 52.10837 54.04788 56.33651 58.87682 61.61121 64.50214
[8] 67.52265 70.65186 73.87197 77.16683 80.52193 83.92574 87.36969
[15] 90.84850 94.35809 98.15750 101.93317 105.67833 109.38989 113.06889
[22] 116.72139 120.35510 123.97707 127.59293 131.20786 134.82720 138.45720
[29] 142.10507 145.77820 149.48224 153.21934 156.98794 160.78322 164.60057
[36] 168.43699 172.29076 176.15989 180.04104 183.93127 187.83046 191.74004
[43] 195.66223 199.59781 203.54565 207.50342 211.46888 215.44064 219.41764
[50] 223.39908 227.05822 230.66813 234.22890 237.74176 241.20236 244.60039
[57] 247.91917 251.14346 254.25876 257.24891 260.09121 262.74910 265.16057
[64] 267.21598 268.70276
当然，问题在于内核最终不在边缘处居中.这是一个众所周知的问题，有办法处理它，但它使问题复杂化.绘制数据将向您展示这种非居中的影响:
Of course, the problem with this is that the kernel ends up non-centered at the edges. This is a well-known problem, and there are ways to deal with it but it complicates the problem. Plotting the data will show you the effects of this non-centering:
plot(y)
lines(yy)
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