# To what function's outputs do these numbers belong?

I have a sequence of numbers which have been used in an open source R Package. I am trying to understand how the package is accomplishing its objectives. So i need to know the function to whose set of outputs these belong:

    -3.075163e-07,
2.186369e-07,
2.960645e-07,
-2.101838e-07,
-2.844124e-07,
2.015925e-07,
2.725605e-07,
-1.928639e-07,
-2.605095e-07,
1.839984e-07,
2.482599e-07,
-1.749968e-07,
-2.358125e-07,
1.658597e-07,
2.231680e-07,
-1.565879e-07,
-2.103273e-07,
1.471821e-07,


There are a lot more of these in the actual source but in the interest o keeping the question short i have only given these few numbers. If you want to see all of them: R Package

Download the source. Extract it. There will be a folder called R in the extracted files. In that folder there will be a Source file called identify_quantify.R

In line 27 the numbers start and go on till line 13109.

EDIT: If you want to see the file with only the values then it can be found at: link

I think these are the outputs of some trigonometric function. I am not sure though. I dont know what tag to give to this question so i am tagging it as trignometry. Please correct if it is wrong.

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Looks like noise. Did you plot it? – draks ... Jan 17 '12 at 10:19
Can you make it more convenient to access the data? Not everyone has the ability/can be bothered to uncompress gzipped files. – Chris Taylor Jan 17 '12 at 10:20
I dont think it is noise. Though i might be wrong. I have not plotted it. I should have mentioned, i am not a mathematician. I really dont have any experience regarding this. So i ask the question: How can these values be plotted without doing it manually? Is there any online application for this? – guy Jan 17 '12 at 10:25
@ChrisTaylor Okay. give me 5 minutes. I will upload the file to some site. – guy Jan 17 '12 at 10:26
@ChrisTaylor I have added the file. Please see it. – guy Jan 17 '12 at 10:33

Your data is actually four separate series, which will become obvious if you plot it. You can use the following R code to extract the individual series:

x <- read.csv('identify_quantify.r')
x <- x[[1]]

idx1 <- seq(1,13082,by=4)
idx2 <- seq(2,13082,by=4)
idx3 <- seq(3,13082,by=4)
idx4 <- seq(4,13082,by=4)

x1 <- x[idx1]
x2 <- x[idx2]
x3 <- x[idx3]
x4 <- x[idx4]


It looks to me like the functions are trigonometric, inside an exponential envelope, for example:

$$f(x) = A\cos(x) \exp(-bx^2)$$

for suitable values of $A$ and $b$. You can plot a function like this in R with the code:

> x <- seq(-6*pi, 6*pi, length=1000)
> A <- 1
> b <- 0.02
> f <- A * cos(x) * exp(-b*x^2)
> plot(x,f)


and see if you can make it fit.

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