5

Can any one help how to find approximate area under the curve using Riemann Sums in R?

It seems we do not have any package in R which could help.

Sample data:

MNo1    X1  Y1    MNo2  X2  Y2
1   2981    -66287  1   595 -47797
1   2981    -66287  1   595 -47797
2   2973    -66087  2   541 -47597
2   2973    -66087  2   541 -47597
3   2963    -65887  3   485 -47397
3   2963    -65887  3   485 -47397
4   2952    -65687  4   430 -47197
4   2952    -65687  4   430 -47197
5   2942    -65486  5   375 -46998
5   2942    -65486  5   375 -46998
6   2935    -65286  6   322 -46798
6   2935    -65286  6   322 -46798
7   2932    -65086  7   270 -46598
7   2932    -65086  7   270 -46598
8   2936    -64886  8   222 -46398
8   2936    -64886  8   222 -46398
9   2948    -64685  9   176 -46198
9   2948    -64685  9   176 -46198
10  2968    -64485  10  135 -45999
10  2968    -64485  10  135 -45999
11  2998    -64284  11  97  -45799
11  2998    -64284  11  97  -45799
12  3035    -64084  12  65  -45599
12  3035    -64084  12  65  -45599
13  3077    -63883  13  37  -45399
13  3077    -63883  13  37  -45399
14  3122    -63683  14  14  -45199
14  3122    -63683  14  14  -45199
15  3168    -63482  15  -5  -44999
15  3168    -63482  15  -5  -44999
16  3212    -63282  16  -20 -44799
16  3212    -63282  16  -20 -44799
17  3250    -63081  17  -31 -44599
17  3250    -63081  17  -31 -44599
18  3280    -62881  18  -38 -44399
18  3280    -62881  18  -38 -44399
19  3301    -62680  19  -43 -44199
19  3301    -62680  19  -43 -44199
20  3313    -62480  20  -45 -43999
Arthur Ulfeldt
  • 90,827
  • 27
  • 201
  • 284
Manoj Kumar
  • 5,273
  • 1
  • 26
  • 33
  • 1
    Take a look at the `sintegral` function from the `Bolstad` package – Acarbalacar Oct 17 '16 at 07:53
  • This [discussion](https://chemicalstatistician.wordpress.com/2014/01/20/rectangular-integration-a-k-a-the-midpoint-rule/) may point you in the right direction. – Bhas Oct 17 '16 at 08:38

1 Answers1

8

Check this demo : 

> library(zoo)
> x <- 1:10
> y <- -x^2
> Result <- sum(diff(x[x]) * rollmean(y[x], 2))

> Result
[1] -334.5

After check this question, I found function trapz() from package pracma be more efficient:

> library(pracma)
> Result.2 <- trapz(x, y)
> Result.2
[1] -334.5
Community
  • 1
  • 1
xtluo
  • 1,961
  • 18
  • 26
  • Thanks so much @XiaotaoLuo .... any Idea, if I want, how can I generate a function for this data.. something like Y = f(x) where f(x) is the function generated using data above... – Manoj Kumar Oct 17 '16 at 16:37
  • Is there two piece of data above ？ Including Mno1 and Mno2. And I don't think generating function is a good choice， all you need is a list of variable X and a list of response value Y. By doing this， you can calculate approximate area under any curve . – xtluo Oct 17 '16 at 18:08
  • @XiaotaoLou.. yes dear. MNo1 and Mno2 are just the observation numbers, these are not important but X and Y sets are. your idea is well taken thanks. but I though of generating function, so that I am able to generalize that equation for all other sets of observations taken over different date time stamps. – Manoj Kumar Oct 17 '16 at 18:24