How could be possible to represent (plot and numerically) a sawthooth signal in R from:
y <- c(NA,NA,NA,NA,1,NA,NA,NA,1,NA,NA,NA,NA,NA,1,NA,NA,NA,NA,1,NA)
where 1 represents in y the time points when the sawtooth achieves a peak (obviously to 1). Note that the distance between peaks are unequal.
I thought about using interpolation but maybe it is unnecessary.
Thank you,
You can create a sequence of falling numbers like this:
peaks <- c(0, which(!is.na(y)), length(y))
drop <- -1/max(diff(peaks))
df <- do.call(rbind, lapply(diff(peaks), function(x) {
data.frame(x = c(0, rep(1, x)),
y = c(1, seq(1 + drop, by = drop, length.out = x)))
}))
df$x <- cumsum(df$x)
Which gives this result:
plot(df$x, df$y, type = "l")
Or if you want to be fancy...
library(ggplot2)
ggplot(df, aes(x, y)) +
geom_line(col = "deepskyblue4", size = 1.5) +
theme_bw()
Created on 2020-09-18 by the reprex package (v0.3.0)
Related
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.
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$y)) > minimal_change)[1] + 1 # Step 3
df <- df[left:right, ] # Step 4
Now we can plot the result:
ggplot(df, aes(x, y)) +
geom_line()+
geom_point(data = data.frame("x" = c(50, 250), "y" = c(25.91818, 25.91818)),
mapping = aes(x, y), colour = "red") +
scale_y_continuous(limits = c(0, 101)) +
scale_x_continuous(limits = c(0, 300))
Similar questions have been asked before in other forms. Some can be found here and here. However, I cant seem to adapt them when using a facet wrap displaying multiple density plots.
I tried adapting the other examples, but failed... I also tried using the ggpattern package, but when there is a large amount of data, it takes several minutes on my machine to create a plot.
I am trying to create a gradient under the density curve... but with the gradient pointing down. Something like in the example image below:
Some example data to work with:
library(ggplot2)
set.seed(321)
# create data
varNames <- c("x1", "x2", "x3")
df <- data.frame(
var = sample(varNames, 100, replace = T),
val = runif(100)
)
# create plot
ggplot(df, aes(x = val)) +
geom_density(aes(colour = var, fill = var)) +
facet_wrap(~var) +
theme_bw() +
theme(legend.position = "none")
You can use teunbrand's function, but you will need to apply it to each facet. Here simply looping over it with lapply
library(tidyverse)
library(polyclip)
#> polyclip 1.10-0 built from Clipper C++ version 6.4.0
## This is teunbrands function copied without any change!!
## from https://stackoverflow.com/a/64695516/7941188
fade_polygon <- function(x, y, n = 100) {
poly <- data.frame(x = x, y = y)
# Create bounding-box edges
yseq <- seq(min(poly$y), max(poly$y), length.out = n)
xlim <- range(poly$x) + c(-1, 1)
# Pair y-edges
grad <- cbind(head(yseq, -1), tail(yseq, -1))
# Add vertical ID
grad <- cbind(grad, seq_len(nrow(grad)))
# Slice up the polygon
grad <- apply(grad, 1, function(range) {
# Create bounding box
bbox <- data.frame(x = c(xlim, rev(xlim)),
y = c(range[1], range[1:2], range[2]))
# Do actual slicing
slice <- polyclip::polyclip(poly, bbox)
# Format as data.frame
for (i in seq_along(slice)) {
slice[[i]] <- data.frame(
x = slice[[i]]$x,
y = slice[[i]]$y,
value = range[3],
id = c(1, rep(0, length(slice[[i]]$x) - 1))
)
}
slice <- do.call(rbind, slice)
})
# Combine slices
grad <- do.call(rbind, grad)
# Create IDs
grad$id <- cumsum(grad$id)
return(grad)
}
## now here starts the change, loop over your variables. I'm creating the data frame directly instead of keeping the density object
dens <- lapply(split(df, df$var), function(x) {
dens <- density(x$val)
data.frame(x = dens$x, y = dens$y)
}
)
## we need this one for the plot, but still need the list
dens_df <- bind_rows(dens, .id = "var")
grad <- bind_rows(lapply(dens, function(x) fade_polygon(x$x, x$y)), .id = "var")
ggplot(grad, aes(x, y)) +
geom_line(data = dens_df) +
geom_polygon(aes(alpha = value, group = id),
fill = "blue") +
facet_wrap(~var) +
scale_alpha_continuous(range = c(0, 1))
Created on 2021-12-05 by the reprex package (v2.0.1)
I frequently use kernel density plots to illustrate distributions. These are easy and fast to create in R like so:
set.seed(1)
draws <- rnorm(100)^2
dens <- density(draws)
plot(dens)
#or in one line like this: plot(density(rnorm(100)^2))
Which gives me this nice little PDF:
I'd like to shade the area under the PDF from the 75th to 95th percentiles. It's easy to calculate the points using the quantile function:
q75 <- quantile(draws, .75)
q95 <- quantile(draws, .95)
But how do I shade the the area between q75 and q95?
With the polygon() function, see its help page and I believe we had similar questions here too.
You need to find the index of the quantile values to get the actual (x,y) pairs.
Edit: Here you go:
x1 <- min(which(dens$x >= q75))
x2 <- max(which(dens$x < q95))
with(dens, polygon(x=c(x[c(x1,x1:x2,x2)]), y= c(0, y[x1:x2], 0), col="gray"))
Output (added by JDL)
Another solution:
dd <- with(dens,data.frame(x,y))
library(ggplot2)
qplot(x,y,data=dd,geom="line")+
geom_ribbon(data=subset(dd,x>q75 & x<q95),aes(ymax=y),ymin=0,
fill="red",colour=NA,alpha=0.5)
Result:
An expanded solution:
If you wanted to shade both tails (copy & paste of Dirk's code) and use known x values:
set.seed(1)
draws <- rnorm(100)^2
dens <- density(draws)
plot(dens)
q2 <- 2
q65 <- 6.5
qn08 <- -0.8
qn02 <- -0.2
x1 <- min(which(dens$x >= q2))
x2 <- max(which(dens$x < q65))
x3 <- min(which(dens$x >= qn08))
x4 <- max(which(dens$x < qn02))
with(dens, polygon(x=c(x[c(x1,x1:x2,x2)]), y= c(0, y[x1:x2], 0), col="gray"))
with(dens, polygon(x=c(x[c(x3,x3:x4,x4)]), y= c(0, y[x3:x4], 0), col="gray"))
Result:
This question needs a lattice answer. Here's a very basic one, simply adapting the method employed by Dirk and others:
#Set up the data
set.seed(1)
draws <- rnorm(100)^2
dens <- density(draws)
#Put in a simple data frame
d <- data.frame(x = dens$x, y = dens$y)
#Define a custom panel function;
# Options like color don't need to be hard coded
shadePanel <- function(x,y,shadeLims){
panel.lines(x,y)
m1 <- min(which(x >= shadeLims[1]))
m2 <- max(which(x <= shadeLims[2]))
tmp <- data.frame(x1 = x[c(m1,m1:m2,m2)], y1 = c(0,y[m1:m2],0))
panel.polygon(tmp$x1,tmp$y1,col = "blue")
}
#Plot
xyplot(y~x,data = d, panel = shadePanel, shadeLims = c(1,3))
Here's another ggplot2 variant based on a function that approximates the kernel density at the original data values:
approxdens <- function(x) {
dens <- density(x)
f <- with(dens, approxfun(x, y))
f(x)
}
Using the original data (rather than producing a new data frame with the density estimate's x and y values) has the benefit of also working in faceted plots where the quantile values depend on the variable by which the data is being grouped:
Code used
library(tidyverse)
library(RColorBrewer)
# dummy data
set.seed(1)
n <- 1e2
dt <- tibble(value = rnorm(n)^2)
# function that approximates the density at the provided values
approxdens <- function(x) {
dens <- density(x)
f <- with(dens, approxfun(x, y))
f(x)
}
probs <- c(0.75, 0.95)
dt <- dt %>%
mutate(dy = approxdens(value), # calculate density
p = percent_rank(value), # percentile rank
pcat = as.factor(cut(p, breaks = probs, # percentile category based on probs
include.lowest = TRUE)))
ggplot(dt, aes(value, dy)) +
geom_ribbon(aes(ymin = 0, ymax = dy, fill = pcat)) +
geom_line() +
scale_fill_brewer(guide = "none") +
theme_bw()
# dummy data with 2 groups
dt2 <- tibble(category = c(rep("A", n), rep("B", n)),
value = c(rnorm(n)^2, rnorm(n, mean = 2)))
dt2 <- dt2 %>%
group_by(category) %>%
mutate(dy = approxdens(value),
p = percent_rank(value),
pcat = as.factor(cut(p, breaks = probs,
include.lowest = TRUE)))
# faceted plot
ggplot(dt2, aes(value, dy)) +
geom_ribbon(aes(ymin = 0, ymax = dy, fill = pcat)) +
geom_line() +
facet_wrap(~ category, nrow = 2, scales = "fixed") +
scale_fill_brewer(guide = "none") +
theme_bw()
Created on 2018-07-13 by the reprex package (v0.2.0).
I frequently use kernel density plots to illustrate distributions. These are easy and fast to create in R like so:
set.seed(1)
draws <- rnorm(100)^2
dens <- density(draws)
plot(dens)
#or in one line like this: plot(density(rnorm(100)^2))
Which gives me this nice little PDF:
I'd like to shade the area under the PDF from the 75th to 95th percentiles. It's easy to calculate the points using the quantile function:
q75 <- quantile(draws, .75)
q95 <- quantile(draws, .95)
But how do I shade the the area between q75 and q95?
With the polygon() function, see its help page and I believe we had similar questions here too.
You need to find the index of the quantile values to get the actual (x,y) pairs.
Edit: Here you go:
x1 <- min(which(dens$x >= q75))
x2 <- max(which(dens$x < q95))
with(dens, polygon(x=c(x[c(x1,x1:x2,x2)]), y= c(0, y[x1:x2], 0), col="gray"))
Output (added by JDL)
Another solution:
dd <- with(dens,data.frame(x,y))
library(ggplot2)
qplot(x,y,data=dd,geom="line")+
geom_ribbon(data=subset(dd,x>q75 & x<q95),aes(ymax=y),ymin=0,
fill="red",colour=NA,alpha=0.5)
Result:
An expanded solution:
If you wanted to shade both tails (copy & paste of Dirk's code) and use known x values:
set.seed(1)
draws <- rnorm(100)^2
dens <- density(draws)
plot(dens)
q2 <- 2
q65 <- 6.5
qn08 <- -0.8
qn02 <- -0.2
x1 <- min(which(dens$x >= q2))
x2 <- max(which(dens$x < q65))
x3 <- min(which(dens$x >= qn08))
x4 <- max(which(dens$x < qn02))
with(dens, polygon(x=c(x[c(x1,x1:x2,x2)]), y= c(0, y[x1:x2], 0), col="gray"))
with(dens, polygon(x=c(x[c(x3,x3:x4,x4)]), y= c(0, y[x3:x4], 0), col="gray"))
Result:
This question needs a lattice answer. Here's a very basic one, simply adapting the method employed by Dirk and others:
#Set up the data
set.seed(1)
draws <- rnorm(100)^2
dens <- density(draws)
#Put in a simple data frame
d <- data.frame(x = dens$x, y = dens$y)
#Define a custom panel function;
# Options like color don't need to be hard coded
shadePanel <- function(x,y,shadeLims){
panel.lines(x,y)
m1 <- min(which(x >= shadeLims[1]))
m2 <- max(which(x <= shadeLims[2]))
tmp <- data.frame(x1 = x[c(m1,m1:m2,m2)], y1 = c(0,y[m1:m2],0))
panel.polygon(tmp$x1,tmp$y1,col = "blue")
}
#Plot
xyplot(y~x,data = d, panel = shadePanel, shadeLims = c(1,3))
Here's another ggplot2 variant based on a function that approximates the kernel density at the original data values:
approxdens <- function(x) {
dens <- density(x)
f <- with(dens, approxfun(x, y))
f(x)
}
Using the original data (rather than producing a new data frame with the density estimate's x and y values) has the benefit of also working in faceted plots where the quantile values depend on the variable by which the data is being grouped:
Code used
library(tidyverse)
library(RColorBrewer)
# dummy data
set.seed(1)
n <- 1e2
dt <- tibble(value = rnorm(n)^2)
# function that approximates the density at the provided values
approxdens <- function(x) {
dens <- density(x)
f <- with(dens, approxfun(x, y))
f(x)
}
probs <- c(0.75, 0.95)
dt <- dt %>%
mutate(dy = approxdens(value), # calculate density
p = percent_rank(value), # percentile rank
pcat = as.factor(cut(p, breaks = probs, # percentile category based on probs
include.lowest = TRUE)))
ggplot(dt, aes(value, dy)) +
geom_ribbon(aes(ymin = 0, ymax = dy, fill = pcat)) +
geom_line() +
scale_fill_brewer(guide = "none") +
theme_bw()
# dummy data with 2 groups
dt2 <- tibble(category = c(rep("A", n), rep("B", n)),
value = c(rnorm(n)^2, rnorm(n, mean = 2)))
dt2 <- dt2 %>%
group_by(category) %>%
mutate(dy = approxdens(value),
p = percent_rank(value),
pcat = as.factor(cut(p, breaks = probs,
include.lowest = TRUE)))
# faceted plot
ggplot(dt2, aes(value, dy)) +
geom_ribbon(aes(ymin = 0, ymax = dy, fill = pcat)) +
geom_line() +
facet_wrap(~ category, nrow = 2, scales = "fixed") +
scale_fill_brewer(guide = "none") +
theme_bw()
Created on 2018-07-13 by the reprex package (v0.2.0).
I frequently use kernel density plots to illustrate distributions. These are easy and fast to create in R like so:
set.seed(1)
draws <- rnorm(100)^2
dens <- density(draws)
plot(dens)
#or in one line like this: plot(density(rnorm(100)^2))
Which gives me this nice little PDF:
I'd like to shade the area under the PDF from the 75th to 95th percentiles. It's easy to calculate the points using the quantile function:
q75 <- quantile(draws, .75)
q95 <- quantile(draws, .95)
But how do I shade the the area between q75 and q95?
With the polygon() function, see its help page and I believe we had similar questions here too.
You need to find the index of the quantile values to get the actual (x,y) pairs.
Edit: Here you go:
x1 <- min(which(dens$x >= q75))
x2 <- max(which(dens$x < q95))
with(dens, polygon(x=c(x[c(x1,x1:x2,x2)]), y= c(0, y[x1:x2], 0), col="gray"))
Output (added by JDL)
Another solution:
dd <- with(dens,data.frame(x,y))
library(ggplot2)
qplot(x,y,data=dd,geom="line")+
geom_ribbon(data=subset(dd,x>q75 & x<q95),aes(ymax=y),ymin=0,
fill="red",colour=NA,alpha=0.5)
Result:
An expanded solution:
If you wanted to shade both tails (copy & paste of Dirk's code) and use known x values:
set.seed(1)
draws <- rnorm(100)^2
dens <- density(draws)
plot(dens)
q2 <- 2
q65 <- 6.5
qn08 <- -0.8
qn02 <- -0.2
x1 <- min(which(dens$x >= q2))
x2 <- max(which(dens$x < q65))
x3 <- min(which(dens$x >= qn08))
x4 <- max(which(dens$x < qn02))
with(dens, polygon(x=c(x[c(x1,x1:x2,x2)]), y= c(0, y[x1:x2], 0), col="gray"))
with(dens, polygon(x=c(x[c(x3,x3:x4,x4)]), y= c(0, y[x3:x4], 0), col="gray"))
Result:
This question needs a lattice answer. Here's a very basic one, simply adapting the method employed by Dirk and others:
#Set up the data
set.seed(1)
draws <- rnorm(100)^2
dens <- density(draws)
#Put in a simple data frame
d <- data.frame(x = dens$x, y = dens$y)
#Define a custom panel function;
# Options like color don't need to be hard coded
shadePanel <- function(x,y,shadeLims){
panel.lines(x,y)
m1 <- min(which(x >= shadeLims[1]))
m2 <- max(which(x <= shadeLims[2]))
tmp <- data.frame(x1 = x[c(m1,m1:m2,m2)], y1 = c(0,y[m1:m2],0))
panel.polygon(tmp$x1,tmp$y1,col = "blue")
}
#Plot
xyplot(y~x,data = d, panel = shadePanel, shadeLims = c(1,3))
Here's another ggplot2 variant based on a function that approximates the kernel density at the original data values:
approxdens <- function(x) {
dens <- density(x)
f <- with(dens, approxfun(x, y))
f(x)
}
Using the original data (rather than producing a new data frame with the density estimate's x and y values) has the benefit of also working in faceted plots where the quantile values depend on the variable by which the data is being grouped:
Code used
library(tidyverse)
library(RColorBrewer)
# dummy data
set.seed(1)
n <- 1e2
dt <- tibble(value = rnorm(n)^2)
# function that approximates the density at the provided values
approxdens <- function(x) {
dens <- density(x)
f <- with(dens, approxfun(x, y))
f(x)
}
probs <- c(0.75, 0.95)
dt <- dt %>%
mutate(dy = approxdens(value), # calculate density
p = percent_rank(value), # percentile rank
pcat = as.factor(cut(p, breaks = probs, # percentile category based on probs
include.lowest = TRUE)))
ggplot(dt, aes(value, dy)) +
geom_ribbon(aes(ymin = 0, ymax = dy, fill = pcat)) +
geom_line() +
scale_fill_brewer(guide = "none") +
theme_bw()
# dummy data with 2 groups
dt2 <- tibble(category = c(rep("A", n), rep("B", n)),
value = c(rnorm(n)^2, rnorm(n, mean = 2)))
dt2 <- dt2 %>%
group_by(category) %>%
mutate(dy = approxdens(value),
p = percent_rank(value),
pcat = as.factor(cut(p, breaks = probs,
include.lowest = TRUE)))
# faceted plot
ggplot(dt2, aes(value, dy)) +
geom_ribbon(aes(ymin = 0, ymax = dy, fill = pcat)) +
geom_line() +
facet_wrap(~ category, nrow = 2, scales = "fixed") +
scale_fill_brewer(guide = "none") +
theme_bw()
Created on 2018-07-13 by the reprex package (v0.2.0).