Finding the highest and lowest rates of increase at specific x value across several time series in R

Hi Alexander,

Yes, you're right - that approach would be much faster and much less subject to error. The method that I was using worked as intended, but I am more than happy to try to learn this arguably more effective way. My only question in that regard is the defining of the object "df" in:

ExtractFirstMin<- function(df){
  df$abs_diff<- abs(df$em-1)
  min_rate<- df$pct[which.min(df$abs_diff)]
  return(min_rate)
}

Is object "df" in your example above coming from this?

#Generate data
set.seed(5)
for (i in 1:10) {
  assign(x = paste0("df", i),
         value = data.frame(Time = sort(rnorm(n = 10, mean = 1, sd = 0.1)),
                            Rate= rnorm(n = 10, mean = 30, sd = 1)))
} # Create 10 Data Frames

If so, how would I approach placing all 10 of my dataframes (i.e. df1, df2, df3, df4...df10) in that command?

Thanks, again, and sorry if I missed this previously in your explanation! In any case, at least I am able to obtain the results that I was looking for!

-----Original Message-----
From: Alexander Ilich <ailich at usf.edu>
To: r-sig-geo at r-project.org <r-sig-geo at r-project.org>; rain1290 at aim.com <rain1290 at aim.com>
Sent: Wed, May 17, 2023 10:16 am
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

Awesome, glad you were able to get the result you needed. Just to be clear though, you shouldn't need to manually copy the code "df$pct[which.min(df$abs_diff)]" repeatedly for each dataframe. That I sent just to explain what internally was happening when using sapply and the function. If you replace "$x" with "$em" and $y" with "$pct" you can automatically iterate through as many dataframes as you want as long as they are in df_list.

# Define Functions (two versions based on how you want to deal with ties)
ExtractFirstMin<- function(df){
  df$abs_diff<- abs(df$em-1)
  min_rate<- df$pct[which.min(df$abs_diff)]
  return(min_rate)
}

# Put all dataframes into a list
df_list<- list(df1,df2,df3,df4,df5,df6,df7,df8,df9,df10)

# Apply function across list
w<- sapply(df_list, ExtractFirstMin)
w
#>  [1] 29.40269 32.21546 30.75330 30.12109 30.38361 28.64928 30.45568 29.66190
#>  [9] 31.57229 31.33907
________________________________
From: rain1290 at aim.com <rain1290 at aim.com>
Sent: Tuesday, May 16, 2023 11:13 PM
To: Alexander Ilich <ailich at usf.edu>; r-sig-geo at r-project.org <r-sig-geo at r-project.org>
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

Hi Alexander,

Oh, wow...you are absolutely right - I cannot believe that I did not notice that previously! Thank you so much, yet again, including for the insight on what "numeric(0)" signifies! Indeed, it all works just fine now!

I am now able to flexibly achieve the goal of deriving the range of these values across the 10 dataframes using the "range" function!

I cannot thank you enough, including for your tireless efforts to explain everything step-by-step throughout all of this, though I do apologize for the time spent on this!



-----Original Message-----
From: Alexander Ilich <ailich at usf.edu>
To: r-sig-geo at r-project.org <r-sig-geo at r-project.org>; rain1290 at aim.com <rain1290 at aim.com>
Sent: Tue, May 16, 2023 10:24 pm
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

I believe you didn't clear your environment and that's why df1 works. All should evaluate to "numeric(0) with the current code. You call df2$abs_diff, but you never defined that variable. You assigned that result to an object called diff2 which is not used anywhere else in your code. If you type in df2$abs_diff, you'll see it evaluates to NULL and that caries through the rest of your code. numeric(0) means that it's a variable of type numeric but it's empty (zero in length).

set.seed(5)
df2<- data.frame(em= rnorm(10), pct=rnorm(10))

diff2 <- abs(df2$em-1) #You defined diff2
df2$abs_diff #This was never defined so it evalues to NULL
#> NULL

which.min(df2$abs_diff) #can't find position of min since df2$abs_diff was never defined
#> integer(0)

df2$pct[which.min(df2$abs_diff)] #cannot subset df2$pct since which.min(df2$abs_diff) evaluates to integer(0)
#> numeric(0)

________________________________
From: rain1290 at aim.com <rain1290 at aim.com>
Sent: Tuesday, May 16, 2023 8:29 PM
To: Alexander Ilich <ailich at usf.edu>; r-sig-geo at r-project.org <r-sig-geo at r-project.org>
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

Hi Alexander,

I am receiving that for my real data, which is, indeed, odd. It works just fine with my very first dataframe, but for all other dataframes, it returns "numeric(0)". I did the following to organize each dataframe accordingly (note that I renamed my dataframes to "df1" through to "df10" for simplicity):

diff1 <- abs(df1$em-1)
w1 <- df1$pct[which.min(df1$abs_diff)]

diff2 <- abs(df2$em-1)
w2 <- df2$pct[which.min(df2$abs_diff)]

diff3 <- abs(df3$em-1)
w3 <- df3$pct[which.min(df3$abs_diff)]

diff4 <- abs(df4$em-1)
w4 <- df4$pct[which.min(df4$abs_diff)]

diff5 <- abs(df5$em-1)
w5 <- df5$pct[which.min(df5$abs_diff)]

diff6 <- abs(df6$em-1)
w6 <- df6$pct[which.min(df6$abs_diff)]

diff7 <- abs(df7$em-1)
w7 <- df7$pct[which.min(df7$abs_diff)]

diff8 <- abs(df8$em-1)
w8 <- df8$pct[which.min(df8$abs_diff)]

diff9 <- abs(df9$em-1)
w9 <- df9$pct[which.min(df9$abs_diff)]

diff10 <- abs(df10$em-1)
w10 <- df10$pct[which.min(df10$abs_diff)]

This is what object "df2" looks like (the first 21 rows are displayed - there are 140 rows in total). All dataframes are structured the same way, including "df1" (which, as mentioned previously, worked just fine). All begin with "0.000000000" in the first row. "em" is my x-column name, and "pct" is my y-column name, as shown in the image below:

[df2.jpg]

What could make the other dataframes so different from "df1" to cause "numeric(0)"? Essentially, why would "df1" be fine, and not the other 9 dataframes? Unless my code for the other dataframes is flawed somehow?

Thanks, again,

-----Original Message-----
From: Alexander Ilich <ailich at usf.edu>
To: rain1290 at aim.com <rain1290 at aim.com>; r-sig-geo at r-project.org <r-sig-geo at r-project.org>
Sent: Tue, May 16, 2023 7:38 pm
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

It's not clear to me why that would be happening. Are you getting that with your real data or the example data generated in the code I sent? The only reasons I can think of for that happening is if you're trying to access the zeroeth element of a vector which would require which.min(df2$abs_diff) to somehow evaluating to zero (which I don't see how it could) or if your dataframe is zero rows.
________________________________
From: rain1290 at aim.com <rain1290 at aim.com>
Sent: Tuesday, May 16, 2023 5:58:22 PM
To: Alexander Ilich <ailich at usf.edu>; r-sig-geo at r-project.org <r-sig-geo at r-project.org>
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

Hi Alexander,
Thank you so much, once again! Very, very helpful explanations.

I experimented with this method:

df1$abs_diff<- abs(df1$x-1)
min_rate[1]<- df1$y[which.min(df1$abs_diff)]

df2$abs_diff<- abs(df2$x-1)
min_rate[2]<- df2$y[which.min(df2$abs_diff)]


For the first dataframe, it correctly returned the first y-value where x = ~1. However, for dataframe2 to dataframe9, I strangely received: "numeric(0)".  Everything is correctly placed. It does not appear to be an error per se, but is there a way around that to avoid that message and see the correct value?

Thanks, again,

-----Original Message-----
From: Alexander Ilich <ailich at usf.edu>
To: r-sig-geo at r-project.org <r-sig-geo at r-project.org>; rain1290 at aim.com <rain1290 at aim.com>
Sent: Tue, May 16, 2023 2:03 pm
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

sapply goes element by element in your list, where each element is one of your dataframes. So mydata starts out as dataframe1, then dataframe2, then dataframe3, etc. It is never all of them at once. It goes through the list sequentially. So, at the end of the sapply call, you have a vector of length 10 where the first element corresponds to the rate closest to x=1 in dataframe 1, and the tenth element corresponds to the rate closest to x=1 in dataframe 10. If your columns are not named x and y, then the function should be edited accordingly based on the names. It does assume the "x" and "y" have the same name across dataframes. For example, if x was actually "Time" and y was "Rate", you could use

#Generate data
set.seed(5)
for (i in 1:10) {
  assign(x = paste0("df", i),
         value = data.frame(Time = sort(rnorm(n = 10, mean = 1, sd = 0.1)),
                            Rate= rnorm(n = 10, mean = 30, sd = 1)))
} # Create 10 Data Frames

# Define Functions (two versions based on how you want to deal with ties)
ExtractFirstMin<- function(df){
  df$abs_diff<- abs(df$Time-1)
  min_rate<- df$Rate[which.min(df$abs_diff)]
  return(min_rate)
}

# Put all dataframes into a list
df_list<- list(df1,df2,df3,df4,df5,df6,df7,df8,df9,df10)

# Apply function across list
sapply(df_list, ExtractFirstMin)
________________________________
From: rain1290 at aim.com <rain1290 at aim.com>
Sent: Tuesday, May 16, 2023 12:46 PM
To: Alexander Ilich <ailich at usf.edu>; r-sig-geo at r-project.org <r-sig-geo at r-project.org>
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

Hi Alexander,

Wow, thank you so very much for taking the time to articulate this answer! It really gives a good understanding of what is going on at each stage in the coding!

And sorry if I missed this previously, but the object "mydata" is defined based on the incorporation of all dataframes? Since it is designed to swiftly obtain the first minimum at y = ~1 across each dataframe, "mydata" must take into account "dataframe1" to dataframe10", correct?

Also, the "x" is simply replaced with the name of the x-column and the "y" with the y-column name, if I understand correctly?

Again, sorry if I overlooked this, but that would be all, and thank you so very much, once again for your help and time with this! Much appreciated!

~Trav.~


-----Original Message-----
From: Alexander Ilich <ailich at usf.edu>
To: r-sig-geo at r-project.org <r-sig-geo at r-project.org>; rain1290 at aim.com <rain1290 at aim.com>
Sent: Tue, May 16, 2023 11:42 am
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

The only spot you'll need to change the names for is when putting all of your dataframes in a list as that is based on the names you gave them in your script when reading in the data. In the function, you don't need to change the input to "dataframe1", and naming it that way could be confusing since you are applying the function to more than just dataframe1 (you're applying it to all 10 of your dataframes). I named the argument df to indicate that you should supply your dataframe as the input to the function, but you could name it anything you want. For example, you could call it "mydata" and define the function this way if you wanted to.

ExtractFirstMin<- function(mydata){
  mydata$abs_diff<- abs(mydata$x-1)
  min_rate<- mydata$y[which.min(mydata$abs_diff)]
  return(min_rate)
}

#The function has its own environment of variables that is separate from the global environment of variables you've defined in your script.
#When we supply one of your dataframes to the function, we are assigning that information to a variable in the function's environment called "mydata". Functions allow you to generalize your code so that you're not required to name your variables a certain way. Note here, we do assume that "mydata" has a "$x" and "$y" slot though.

#Without generalizing the code using a function, we'd need to copy and paste the code over and over again and make sure to change the name of the dataframe each time. This is very time consuming and error prone. Here's an example for the first 3 dataframes.

min_rate<- rep(NA_real_, 10) #initialize empty vector
df1$abs_diff<- abs(df1$x-1)
min_rate[1]<- df1$y[which.min(df1$abs_diff)]

df2$abs_diff<- abs(df2$x-1)
min_rate[2]<- df2$y[which.min(df2$abs_diff)]

df3$abs_diff<- abs(df3$x-1)
min_rate[3]<- df3$y[which.min(df3$abs_diff)]

print(min_rate)
#>  [1] 29.40269 32.21546 30.75330       NA       NA       NA       NA       NA
#>  [9]       NA       NA

#With the function defined we can run that it for each individual dataframe, which is less error prone than copying and pasting but still fairly repetitive
ExtractFirstMin(mydata = df1) # You can explicitly say "mydata ="
#> [1] 29.40269
ExtractFirstMin(df2) # Or equivalently it will be based on the order arguments when you defined the function. Since there is just one argument, then what you supply is assigned to "mydata"
#> [1] 32.21546
ExtractFirstMin(df3)
#> [1] 30.7533

# Rather than manually typing out to tun the function on eeach dataframe and bringing it together, we can instead use sapply.
# Sapply takes a list of inputs and a function as arguments. It then applies the function to every element in the list and returns a vector (i.e. goes through each dataframe in your list, applies the function to each one individually, and then records the result for each one in a single variable).
sapply(df_list, ExtractFirstMin)
#>  [1] 29.40269 32.21546 30.75330 30.12109 30.38361 28.64928 30.45568 29.66190
#>  [9] 31.57229 31.33907


________________________________
From: rain1290 at aim.com <rain1290 at aim.com>
Sent: Monday, May 15, 2023 4:44 PM
To: Alexander Ilich <ailich at usf.edu>; r-sig-geo at r-project.org <r-sig-geo at r-project.org>
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

Hi Alexander and everyone,

I hope that all is well! Just to follow up with this, I recently was able to try the following code that you had kindly previously shared:

ExtractFirstMin<- function(df){
  df$abs_diff<- abs(df$x-1)
  min_rate<- df$y[which.min(df$abs_diff)]
  return(min_rate)
} #Get first y value of closest to x=1

Just to be clear, do I simply replace the "df" in that code with the name of my individual dataframes? For example, here is the name of my 10 dataframes, which are successfully placed in a list (i.e. df_list), as you showed previously:

dataframe1
dataframe2
dataframe3
dataframe4
dataframe5
dataframe6
dataframe7
dataframe8
dataframe9
dataframe10

Thus, using your example above, using the first dataframe listed there, would this become:

ExtractFirstMin<- function(dataframe1){
  dataframe1$abs_diff<- abs(dataframe1$x-1)
  min_rate<- dataframe1$y[which.min(dataframe1$abs_diff)]
  return(min_rate)
} #Get first y value of closest to x=1

df_list<- list(dataframe1, dataframe2, dataframe3, dataframe4, dataframe5, dataframe6, dataframe7, dataframe8, dataframe9, dataframe10)

# Apply function across list
sapply(df_list, ExtractFirstMin)


Am I doing this correctly?

Thanks, again!


-----Original Message-----
From: Alexander Ilich <ailich at usf.edu>
To: rain1290 at aim.com <rain1290 at aim.com>
Sent: Thu, May 11, 2023 1:48 am
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

Sure thing. Glad I could help!
________________________________
From: rain1290 at aim.com <rain1290 at aim.com>
Sent: Thursday, May 11, 2023 12:17:12 AM
To: Alexander Ilich <ailich at usf.edu>
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

Hi Alexander,

Many thanks for sharing this! It was really helpful!


-----Original Message-----
From: Alexander Ilich <ailich at usf.edu>
To: rain1290 at aim.com <rain1290 at aim.com>
Sent: Wed, May 10, 2023 2:05 pm
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

One way to do this would be to put all your dataframes in a list, make one of the code implementation I put earlier into a function, and then use sapply to apply it across all the data frames.

#Generate data
set.seed(5)
for (i in 1:10) {
  assign(x = paste0("df", i),
         value = data.frame(x = sort(rnorm(n = 10, mean = 1, sd = 0.1)),
                            y= rnorm(n = 10, mean = 30, sd = 1)))
  } # Create 10 Data Frames

# Define Functions (two versions based on how you want to deal with ties)
ExtractFirstMin<- function(df){
  df$abs_diff<- abs(df$x-1)
  min_rate<- df$y[which.min(df$abs_diff)]
  return(min_rate)
} #Get first y value of closest to x=1

ExtractAvgMin<- function(df){
  df$abs_diff<- abs(df$x-1)
  min_rate<- mean(df$y[df$abs_diff==min(df$abs_diff)])
  return(min_rate)
} #Average all y values that are closest to x=1

# Put all dataframes into a list
df_list<- list(df1,df2,df3,df4,df5,df6,df7,df8,df9,df10)

# Apply function across list
sapply(df_list, ExtractFirstMin)
#>  [1] 29.40269 32.21546 30.75330 30.12109 30.38361 28.64928 30.45568 29.66190
#>  [9] 31.57229 31.33907

sapply(df_list, ExtractAvgMin)
#>  [1] 29.40269 32.21546 30.75330 30.12109 30.38361 28.64928 30.45568 29.66190
#>  [9] 31.57229 31.33907
________________________________
From: rain1290 at aim.com <rain1290 at aim.com>
Sent: Wednesday, May 10, 2023 1:40 PM
To: Alexander Ilich <ailich at usf.edu>; r-sig-geo at r-project.org <r-sig-geo at r-project.org>
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

Hi Alexander,

Thank you so much for taking the time to outline these suggestions!

What if I wanted to only isolate the y-value at x = 1.0 across all of my 10 dataframes? That way, I could quickly see what the highest and lowest y-value is at x = 1.0? That said, in reality, not all x values are precisely 1.0 (it can be something like 0.99 to 1.02), but the idea is to target the y-value at x = ~1.0. Is that at all possible?

Thanks, again!

-----Original Message-----
From: Alexander Ilich <ailich at usf.edu>
To: r-sig-geo at r-project.org <r-sig-geo at r-project.org>; rain1290 at aim.com <rain1290 at aim.com>
Sent: Wed, May 10, 2023 10:31 am
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

So using your data but removing x=1, 0.8 and 1.2 would be equally close. Two potential options are to choose the y value corresponding to the first minimum difference (in this case x=0.8, y=39), or average the y values for all that are equally close (in this case average the y values for x=0.8 and x=1.2). I think the easiest wayodo that would to first calculate a column of the absolute value of differences between x and 1 and then subset the dataframe to the minimum of that column to extract the y values. Here's a base R and tidyverse implementation to do that.

#Base R
df<- data.frame(x=c(0,0.2,0.4,0.6,0.8,1.2,1.4),
                y= c(0,27,31,32,39,34,25))
df$abs_diff<- abs(df$x-1)

df$y[which.min(df$abs_diff)] #Get first y value of closest to x=1
#> [1] 39
mean(df$y[df$abs_diff==min(df$abs_diff)]) #Average all y values that are closest to x=1
#> [1] 36.5

#tidyverse
rm(list=ls())
library(dplyr)

df<- data.frame(x=c(0,0.2,0.4,0.6,0.8,1.2,1.4),
                y= c(0,27,31,32,39,34,25))
df<- df %>% mutate(abs_diff = abs(x-1))

df %>% filter(abs_diff==min(abs_diff)) %>% pull(y) %>% head(1) #Get first y value of closest to x=1
#> [1] 39

df %>% filter(abs_diff==min(abs_diff)) %>% pull(y) %>% mean() #Average all y values that are closest to x=1
#> [1] 36.5
________________________________
From: rain1290 at aim.com <rain1290 at aim.com>
Sent: Wednesday, May 10, 2023 8:13 AM
To: Alexander Ilich <ailich at usf.edu>; r-sig-geo at r-project.org <r-sig-geo at r-project.org>
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

Hi Alex and everyone,

My apologies for the confusion and this double message (I just noticed that the example dataset appeared distorted)! Let me try to simplify here again.

My dataframes are structured in the following way: an x column and y column, like this:

[X]


Now, let's say that I want to determine the rate of increase at about x = 1.0, relative to the beginning of the period (i.e. 0 at the beginning). We can see clearly here that the answer would be y = 43. My question is would it be possible to quickly determine the value at around x = 1.0 across the 10 dataframes that I have like this without having to manually check them? The idea is to determine the range of values for y at around x = 1.0 across all dataframes. Note that it's not perfectly x = 1.0 in all dataframes - some could be 0.99 or 1.01.

I hope that this is clearer!

Thanks,


-----Original Message-----
From: Alexander Ilich <ailich at usf.edu>
To: r-sig-geo at r-project.org <r-sig-geo at r-project.org>; rain1290 at aim.com <rain1290 at aim.com>
Sent: Tue, May 9, 2023 2:23 pm
Subject: Re: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

I'm currently having a bit of difficultly following. Rather than using your actual data, perhaps you could include code to generate a smaller dataset with the same structure with clear definitions of what is contained within each (r faq - How to make a great R reproducible example - Stack Overflow<https://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example>). You can design that dataset to be small with a known answer and the describe how you got to that answer and then others could help determine some code to accomplish that task.

Best Regards,
Alex
________________________________
From: R-sig-Geo <r-sig-geo-bounces at r-project.org> on behalf of rain1290--- via R-sig-Geo <r-sig-geo at r-project.org>
Sent: Tuesday, May 9, 2023 1:01 PM
To: r-sig-geo at r-project.org <r-sig-geo at r-project.org>
Subject: [R-sig-Geo] Finding the highest and lowest rates of increase at specific x value across several time series in R

I would like to attempt to determine the difference between the highest and lowest rates of increase across a series of dataframes at a specified x value. As shown below, the dataframes have basic x and y columns, with emissions values in the x column, and precipitation values in the y column. Among the dataframes, the idea would be to determine the highest and lowest rates of precipitation increase at "approximately" 1 Terratons of emissions (TtC) relative to the first value of each time series. For example, I want to figure out which dataframe has the highest increase at 1 TtC, and which dataframe has the lowest increase at 1 TtC. at However, I am not sure if there is a way to quickly achieve this? Here are the dataframes that I created, followed by an example of how each dataframe is structured:
#Dataframe objects created:
    CanESMRCP8.5PL<-data.frame(get3.teratons, pland20)     IPSLLRRCP8.5PL<-data.frame(get6.teratons, pland21)    IPSLMRRCP8.5PL<-data.frame(get9.teratons, pland22)    IPSLLRBRCP8.5PL<-data.frame(get12.teratons, pland23)    MIROCRCP8.5PL<-data.frame(get15.teratons, pland24)    HadGEMRCP8.5PL<-data.frame(get18.teratons, pland25)    MPILRRCP8.5PL<-data.frame(get21.teratons, pland26)    GFDLGRCP8.5PL<-data.frame(get27.teratons, pland27)    GFDLMRCP8.5PL<-data.frame(get30.teratons, pland28)
#Example of what each of these look like:
    >CanESMRCP8.5PL
        get3.teratons   pland20    X1      0.4542249 13.252426    X2      0.4626662  3.766658    X3      0.4715780  2.220986    X4      0.4809204  8.495072    X5      0.4901427 10.206458    X6      0.4993126 10.942797    X7      0.5088599  6.592956    X8      0.5187588  2.435796    X9      0.5286758  2.275836    X10     0.5389284  5.051706    X11     0.5496212  8.313389    X12     0.5600628  9.007722    X13     0.5708608 11.905644    X14     0.5819234  6.126022    X15     0.5926283  9.883264    X16     0.6042306  7.699696    X17     0.6159752  5.614193    X18     0.6274483  6.681527    X19     0.6394011 10.112812    X20     0.6519496  8.721810    X21     0.6646344 10.315931    X22     0.6773436 11.372490    X23     0.6903203  8.662169    X24     0.7036479 10.106109    X25     0.7180955 10.990867    X26     0.7322746 13.491778    X27     0.7459771 17.256650    X28     0.7604589 12.040960    X29     0.7753096 10.638796    X30     0.7898374  7.889500    X31     0.8047258 11.757174    X32     0.8204160 15.060151    X33     0.8359387  9.822078    X34     0.8510721 11.388695    X35     0.8661237 10.271567    X36     0.8815913 13.224285    X37     0.8984146 15.584782    X38     0.9154501  9.320024    X39     0.9324529  9.187128    X40     0.9497379 12.919805    X41     0.9672824 15.190318    X42     0.9854439 12.098606    X43     1.0041460 16.758629    X44     1.0241779 17.435182    X45     1.0451656 15.323428    X46     1.0663605 18.292109    X47     1.0868977 12.625429    X48     1.1079376 17.318583    X49     1.1295719 14.056624    X50     1.1516720 18.239445    X51     1.1736696 16.312087    X52     1.1963065 18.683315    X53     1.2195753 20.364835    X54     1.2425277 14.337167    X55     1.2653873 16.072449    X56     1.2888002 14.870248    X57     1.3126799 18.431717    X58     1.3362459 19.873449    X59     1.3593610 17.278361    X60     1.3833589 18.532887    X61     1.4083234 16.178170    X62     1.4328881 17.689810    X63     1.4572568 21.395131    X64     1.4821021 20.154886    X65     1.5072721 15.655971    X66     1.5325393 21.692028    X67     1.5581797 23.258303    X68     1.5842384 23.802459    X69     1.6108635 15.824673    X70     1.6365393 19.016228    X71     1.6618322 20.957593    X72     1.6876948 19.105363    X73     1.7134712 19.759288    X74     1.7392598 27.315595    X75     1.7652725 24.882263    X76     1.7913807 25.813408    X77     1.8173818 23.658997    X78     1.8434211 24.223432    X79     1.8695911 23.560818    X80     1.8960611 28.057708    X81     1.9228969 26.996265    X82     1.9493552 26.659719    X83     1.9759324 22.723687    X84     2.0026666 30.977267    X85     2.0290137 29.384326    X86     2.0549359 24.840383    X87     2.0811679 26.952620    X88     2.1081763 29.894790    X89     2.1349227 25.224040    X90     2.1613017 27.722623
    >IPSLLRRCP8.5PL
        get6.teratons   pland21    X1      0.5300411  8.128827    X2      0.5401701  6.683660    X3      0.5503503 12.344974    X4      0.5607762 11.322411    X5      0.5714146 14.250646    X6      0.5825357 10.013592    X7      0.5937966  9.437394    X8      0.6051673  8.138396    X9      0.6168960  9.767765    X10     0.6290367  8.166579    X11     0.6413864 12.307348    X12     0.6539184 12.623931    X13     0.6667360 11.182448    X14     0.6800060 12.585040    X15     0.6935350 13.408614    X16     0.7071757  9.352335    X17     0.7211951 12.743725    X18     0.7356089 11.625612    X19     0.7502665 10.240418    X20     0.7650959 12.394282    X21     0.7800845 16.963066    X22     0.7953119 16.380090    X23     0.8107459 10.510501    X24     0.8260236 12.645911    X25     0.8414439 14.134851    X26     0.8572960 18.924963    X27     0.8732313 17.849050    X28     0.8892344 10.941533    X29     0.9057380 12.034925    X30     0.9223530 15.897904    X31     0.9391578 19.707692    X32     0.9563358 16.690375    X33     0.9738711 18.098571    X34     0.9916517 16.588447    X35     1.0096934 16.125172    X36     1.0279473 19.108647    X37     1.0463864 16.972994    X38     1.0653421 22.869403    X39     1.0842487 21.228874    X40     1.1035309 25.509754    X41     1.1230403 15.579367    X42     1.1426743 21.259726    X43     1.1626806 26.061262    X44     1.1833831 21.918530    X45     1.2045888 22.369094    X46     1.2262981 21.480456    X47     1.2481395 20.503543    X48     1.2703019 27.717028    X49     1.2929382 26.295449    X50     1.3157745 28.271455    X51     1.3390449 31.595651    X52     1.3626052 26.188018    X53     1.3863833 26.326999    X54     1.4102701 26.902272    X55     1.4343871 25.308764    X56     1.4584666 23.789699    X57     1.4831504 26.916504    X58     1.5080384 32.921638    X59     1.5331210 29.753267    X60     1.5582794 29.567720    X61     1.5832585 31.454097    X62     1.6085002 26.602191    X63     1.6339502 35.873728    X64     1.6594560 34.222654    X65     1.6851070 36.290959    X66     1.7109757 31.623912    X67     1.7368503 31.965520    X68     1.7626750 41.490310    X69     1.7883216 35.645934    X70     1.8141292 35.639422    X71     1.8405670 37.085608    X72     1.8672313 44.812777    X73     1.8939987 40.044602    X74     1.9208222 37.834526    X75     1.9478806 44.497335    X76     1.9750195 39.839740    X77     2.0024118 38.300529    X78     2.0302205 52.116649    X79     2.0581589 59.189047    X80     2.0861536 51.559857    X81     2.1141780 43.305779    X82     2.1421791 47.950074    X83     2.1703249 46.252149    X84     2.1985953 47.536605    X85     2.2266540 49.422466    X86     2.2547762 44.577399    X87     2.2827062 49.720523    X88     2.3102098 47.138244    X89     2.3379090 51.882832    X90     2.3656370 51.413472
Etc...
Any help with this would be greatly appreciated!
Thanks,
        [[alternative HTML version deleted]]

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