How to sum a function in a certain range in R?

Question

Here are three columns:

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 

I want to create a new Smooth Y column using the following formula:

D = 15, triangle (triangular symbol) = 5, i = indx, x_alpha (tk) = LocalY, x_alpha (ti) = smoothed value

I tried using the following code for the first calculation of Z: (The core below means the exp function)

 t <- 0.5 dt <- 0.1 delta <- t/dt d <- 3*delta indx <- a$indx for (i in indx) { initial <- id end <- i+d k <- c(initial:end) for (n in k) { kernel <- exp(-abs(in)/delta) z <- sum(kernel) } } a$z <- z print (a) 

NOTE: “a” is an imported data frame containing the three columns above.

Although the values ​​of the calculated function are accurate, they do not summarize the values ​​in the variable z. How can I sum over the range of id to i + d for each indx i value?

Answer 1

You can use the convolve function. The only thing you need to decide is to make for indices closer to either end of the array than the width of the convolution kernel. One option is to simply use a partial kernel that is scalable so that the balance can still add up 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 } 

With your array as y result is as follows:

 > 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 

Of course, the problem is that the core ends off-center at the edges. This is a well-known problem, and there are ways to deal with it, but it complicates the problem. Building data will show you the effect of this non-centering:

 plot(y) lines(yy)