Remove data to the left and right of local minima - r

Question

I have a lot of measurements where I get data that looks something like this:
# Generate example data
x <- 1:100
y <- 100*(1-exp(-0.3*x))
x2 <- 101:200
y2 <- rev(y)
df <- data.frame("x" = c(x, x2),
"y" = c(y, y2))
df$x <- df$x + 50
rm(x, x2, y, y2)
x <- 1:50
y <- 25.91818
x2 <- 251:300
y2 <- 25.91818
df2 <- data.frame("x" = c(x, x2),
"y" = c(y, y2))
rm(x, x2, y, y2)
df <- rbind(df, df2)
rm(df2)
If I plot this I can see that there are left-most and right-most local minima.
library(ggplot2)
p <- ggplot(df, aes(x,y))+
geom_line()+
geom_point(data = data.frame("x" = c(50, 250), "y" = c(25.91818, 25.91818)),
mapping = aes(x, y), colour = "red")+
scale_y_continuous(limits = c(0, 101))
p + annotate("text", label = "minimum 1", x = 50, y = 20) +
annotate("text", label = "minimum 2", x = 250, y = 20)
What I would like to do is trim those data that are to the left of minimum 1 and right of minimum 2. It's not super straightforward as there may also be local minima between those two points, because the real data doesn't look this ideal. I would also need to apply this process to many many samples, but I think this may be trivial because I could use e.g. dplyr and group_by().
I had some luck plotting the local minima using the ggpmisc package, but I'm not sure how I can use that to actually subset my data. Just for clarity I included the code to do so below, and with the real data it looks a little better:
library(ggpmisc)
p2 <- ggplot(df, aes(x, y))+
geom_line()+
ggpmisc::stat_peaks(col="red", span=3)
p2
I hope this is clear and I'm happy to clarify any questions. Thank you in advance.

Answer 1

You could do this using the following steps:
Sort your data according to its x co-ordinates
On your sorted data, find the diff of the y co-ordinates, which will be 0 (or close to 0) for the flat sections at either end (as well as any flat sections in between)
Starting from the left, find the first point where the diff is not zero (or at least is above a minimal threshold). Store this index as a variable called left
Starting from the right, find the first point where the diff is not zero (or at least is above a minimal threshold). Store this index as a variable called right
Subset your data frame so it only contains the data between rows left:right
So, in your example we would have:
# Define a minimal threshold above which we are not at the minimum line
minimal_change <- 1e-6
df <- df[order(df$x),] # Step 1
left <- which(diff(df$y) > minimal_change)[1] # Step 2
right <- nrow(df) - which(diff(rev(df$y)) > minimal_change)[1] + 1 # Step 3
df <- df[left:right, ] # Step 4
Now we can plot the result:
ggplot(df, aes(x, y)) +
geom_line()+
geom_point(data = data.frame("x" = c(50, 250), "y" = c(25.91818, 25.91818)),
mapping = aes(x, y), colour = "red") +
scale_y_continuous(limits = c(0, 101)) +
scale_x_continuous(limits = c(0, 300))