Visualize a function using double integration in R - Wacky Result - r

I am trying to visualize a curve for pollination distribution. I am very new to R so please don't be upset by my stupidity.
llim <- 0
ulim <- 6.29
f <- function(x,y) {(.156812/((2*pi)*(.000005^2)*(gamma(2/.156812)))*exp(-((sqrt(x^2+y^2))/.000005)^.156812))}
integrate(function(y) {
sapply(y, function(y) {
integrate(function(x) f(x,y), llim, ulim)$value
})
}, llim, ulim)
fv <- Vectorize(f)
curve(fv, from=0, to=1000)
And I get:
Error in y^2 : 'y' is missing

I'm not quite sure what you're asking to plot. But I know you want to visualise your scalar function of two arguments.
Here are some approaches. First we define your function.
llim <- 0
ulim <- 6.29
f <- function(x,y) {
(.156812/((2*pi)*(.000005^2)*(gamma(2/.156812)))*exp(-((sqrt(x^2+y^2))/.000005)^.156812))
}
From your title I thought of the following. The function defined below intf integrates your function over the square [0,ul] x [0,ul] and return the value. We then vectorise and plot the integral over the square as a function the length of the side of the square.
intf <- function(ul) {
integrate(function(y) {
sapply(y, function(y) {
integrate(function(x) f(x,y), 0, ul)$value
})
}, 0, ul)$value
}
fv <- Vectorize(intf)
curve(fv, from=0, to=1000)
If f is a distribution, I guess you can make your (somewhat) nice probability interpretation of this curve. (I.e. ~20 % probability of pollination(?) in the 200 by 200 meter square.)
However, you can also do a contour plot (of the log-transformed values) which illustrate the function we are integrating above:
logf <- function(x, y) log(f(x, y))
x <- y <- seq(llim, ulim, length.out = 100)
contour(x, y, outer(x, y, logf), lwd = 2, drawlabels = FALSE)
You can also plot some profiles of the surface:
plot(1, xlim = c(llim, ulim), ylim = c(0, 0.005), xlab = "x", ylab = "f")
y <- seq(llim, ulim, length.out = 6)
for (i in seq_along(y)) {
tmp <- function(x) f(x, y = y[i])
curve(tmp, llim, ulim, add = TRUE, col = i)
}
legend("topright", lty = 1, col = seq_along(y),
legend = as.expression(paste("y = ",y)))
They need to be modified a bit to make them publication worthy, but you get the idea. Lastly, you can do some 3d plots as others have suggested.
EDIT
As per your comments, you can also do something like this:
# Define the function times radius (this time with general a and b)
# The default of a and b is as before
g <- function(z, a = 5e-6, b = .156812) {
z * (b/(2*pi*a^2*gamma(2/b)))*exp(-(z/a)^b)
}
# A function that integrates g from 0 to Z and rotates
# As g is not dependent on the angle we just multiply by 2pi
intg <- function(Z, ...) {
2*pi*integrate(g, 0, Z, ...)$value
}
# Vectorize the Z argument of intg
gv <- Vectorize(intg, "Z")
# Plot
Z <- seq(0, 1000, length.out = 100)
plot(Z, gv(Z), type = "l", lwd = 2)
lines(Z, gv(Z, a = 5e-5), col = "blue", lwd = 2)
lines(Z, gv(Z, b = .150), col = "red", lwd = 2)
lines(Z, gv(Z, a = 1e-4, b = .2), col = "orange", lwd = 2)
You can then plot the curves for the a and b you want. If either is not specified, the default is used.
Disclaimer: my calculus is rusty and I just did off this top of my head. You should verify that I've done the rotation of the function around the axis properly.

The lattice package has several functions that can help you draw 3 dimensional plots, including wireframe() and persp(). If you prefer not to use a 3d-plot, you can create a contour plot using contour().
Note: I don't know if this is intentional, but your data produces a very large spike in one corner of the plot. This produces a plot that is for all intents flat, with a barely noticable spike in one corner. This is particularly problematic with the contour plot below.
library(lattice)
x <- seq(0, 1000, length.out = 50)
y <- seq(0, 1000, length.out = 50)
First the wire frame plot:
df <- expand.grid(x=x, y=y)
df$z <- with(df, f(x, y))
wireframe(z ~ x * y, data = df)
Next the perspective plot:
dm <- outer(x, y, FUN=f)
persp(x, y, dm)
The contour plot:
contour(x, y, dm)

Related

Using base R, how to create a "joy plot" (aka ridgeline plots), with many distributions on top of each other with vertical offset?

The type of plot I am trying to achieve in R seems to have been known as either as moving distribution, as joy plot or as ridgeline plot:
There is already a question in Stackoverflow whose recorded answer explains how to do it using ggplot: How to reproduce this moving distribution plot with R?
However, for learning purposes, I am trying to achieve the same using only base R plots (no lattice, no ggplot, no any plotting package).
In order to get started, I generated the following fake data to play with:
set.seed(2020)
shapes <- c(0.1, 0.5, 1, 2, 4, 5, 6)
dat <- lapply(shapes, function(x) rbeta(1000, x, x))
names(dat) <- letters[1:length(shapes)]
Then using mfrow I can achieve this:
par(mfrow=c(length(shapes), 1))
par(mar=c(1, 5, 1, 1))
for(i in 1:length(shapes))
{
values <- density(dat[[names(dat)[i]]])
plot(NA,
xlim=c(min(values$x), max(values$x)),
ylim=c(min(values$y), max(values$y)),
axes=FALSE,
main="",
xlab="",
ylab=letters[i])
polygon(values, col="light blue")
}
The result I get is:
Clearly, using mfrow (or even layout) here is not flexible enough and also does allow for the overlaps between the distributions.
Then, the question: how can I reproduce that type of plot using only base R plotting functions?
Here's a base R solution. First, we calculate all the density values and then manually offset off the y axis
vals <- Map(function(x, g, i) {
with(density(x), data.frame(x,y=y+(i-1), g))
}, dat, names(dat), seq_along(dat))
Then, to plot, we calculate the overall range, draw an empty plot, and the draw the densities (in reverse so they stack)
xrange <- range(unlist(lapply(vals, function(d) range(d$x))))
yrange <- range(unlist(lapply(vals, function(d) range(d$y))))
plot(0,0, type="n", xlim=xrange, ylim=yrange, yaxt="n", ylab="", xlab="Value")
for(d in rev(vals)) {
with(d, polygon(x, y, col="light blue"))
}
axis(2, at=seq_along(dat)-1, names(dat))
d = lapply(dat, function(x){
tmp = density(x)
data.frame(x = tmp$x, y = tmp$y)
})
d = lapply(seq_along(d), function(i){
tmp = d[[i]]
tmp$grp = names(d)[i]
tmp
})
d = do.call(rbind, d)
grp = unique(d$grp)
n = length(grp)
spcx = 5
spcy = 3
rx = range(d$x)
ry = range(d$y)
rx[2] = rx[2] + n/spcx
ry[2] = ry[2] + n/spcy
graphics.off()
plot(1, type = "n", xlim = rx, ylim = ry, axes = FALSE, ann = FALSE)
lapply(seq_along(grp), function(i){
x = grp[i]
abline(h = (n - i)/spcy, col = "grey")
axis(2, at = (n - i)/spcy, labels = grp[i])
polygon(d$x[d$grp == x] + (n - i)/spcx,
d$y[d$grp == x] + (n - i)/spcy,
col = rgb(0.5, 0.5, 0.5, 0.5))
})

Plot vertical surface below function

I'm trying to create a very simple 3D plot using the rgl package: I have a function that just maps x values into y values. For a given z (in my example: z = 1), I can plot this function in a 3D plot:
library(rgl)
mycurve <- function(x) { return (1/x)}
myx <- seq(1, 10, by = 0.1)
plot3d(x = NA, xlim = c(0, 10), ylim = c(0, 10), zlim = c(0, 5),
xlab = "x", ylab = "y", zlab = "height")
lines3d(x = myx, y = mycurve(myx), z = 1)
However, even after hours of trying to understand the documentation of ?persp3d and ?surface3d, I still have no idea how to add a surface to my plot that "connects" my line to the x-y plane – like this:
(To generate this image, I cheated by plotting many lines: for (i in seq(0, 1, by = 0.01)) { lines3d(x = myx, y = mycurve(myx), z = i) }.)
I suppose that I need to supply the correct values to surface3d somehow. From ?surface3d:
The surface is defined by the matrix of height values in z, with rows corresponding to the values in x and columns corresponding to the values in y.
Given that my space curve is "vertical", each value of x corresponds to only 1 value of y. Still, I need to specify two z values for each xy pair, which is why I do not know how to proceed.
How can I plot a space curve as shown in the second image?
In persp3d, all 3 arguments can be matrices, so you can plot arbitrary surfaces. For your needs, this works:
mycurve <- function(x) { return (1/x)}
myx <- seq(1, 10, by = 0.1)
xmat <- matrix(NA, 2, length(myx))
ymat <- matrix(NA, 2, length(myx))
zmat <- matrix(NA, 2, length(myx))
for (i in 0:1) {
xmat[i+1,] <- myx
ymat[i+1,] <- mycurve(myx)
zmat[i+1,] <- i
}
library(rgl)
persp3d(x = xmat, y = ymat, z = zmat, xlim = c(0, 10), ylim = c(0, 10), zlim = c(0, 5),
xlab = "x", ylab = "y", zlab = "height", col = "gray")
The image produced looks like this:
If you want z to depend on x or y, you'll likely want a smaller step size, but this works for the surface you're after.
To use the persp3d function one needs to create a matrix for z to correspond to all of the x and y values in the desired range.
I revised your function to take both the x and y parameters and return the desired z value. The outer function will call the function repeatedly to fill the matrix. Then plot, with the defined x and y axis and z (from the outer function)
library(rgl)
mycurve <- function(x, y) { return (1/x)}
myx <- seq(1, 10, by = 0.4)
myy <-seq(1, 10, by =0.4)
#create matrix
data<-outer(myx, myy, mycurve)
#plot points
persp3d(x=myx, y=myy, z=data,
xlab = "x", ylab = "y", zlab = "height")

Conway Maxwell Distribution Density Plot

I have written my own code to simulate the Conway maxwell distribution sample.
This is the pmf (Guikema & Goffelt, 2008):
However, I have met some problem to plot the density plot.
rcomp <- function(n,lamb,v)
{
u <- runif(n)
w <- integer(n)
for(i in 1:n) {
z=sum(sapply( 0:100, function(j) (( ((lamb)^j) / (factorial(j)) )^v) ))
x <- seq(1, 50, 1) #seq of 1 to 50, increase by 1
px <- (((lamb^x)/factorial(x))^v)/z
# px is pmf of re-parameter conway maxwell
w[i] <- if (u[i] < px[1]) 0 else (max (which (cumsum(px) <= u[i])))
}
return (w)
}
dcomp <- function(x,lamb,v) {
z=sum(sapply( 0:100, function(j) (( ((lamb)^j) / (factorial(j)) )^v) ))
px <- (((lamb^x)/factorial(x))^v)/z
return(px)
}
As I wanna plot the density plot to check whether lamb or v is location parameter, the plot I get is weird.
x = rcomp(100,6,0.2); pdf = dcomp(x,6,0.2)
x1 = rcomp(100,6,0.5); pdf1 = dcomp(x1,6,0.5)
x2 = rcomp(100,6,0.7); pdf2 = dcomp(x2,6,0.7)
plot(x2, pdf2, type="l", lwd=1,lty=1,col="blue")
How could I solve this problem?
Source: Guikema & Goffelt (2008), A Flexible Count Data Regression Model for Risk Analysis. Risk Analysis 28(1): 215.
You have to sort the values of the x coordinate if you want a graph to connect the points in their axis order.
Note, however, that there might be better ways to graph the density you want. See the red curve. I first create a vector x of values within a certain range and then compute the PDF for those values. These pairs (x, y) are what function lines plots.
set.seed(2673) # Make the results reproducible
x2 <- rcomp(100, 6, 0.7)
x2 <- sort(x2)
pdf2 <- dcomp(x2, 6, 0.7)
plot(x2, pdf2, type = "l", lwd = 1, lty = 1, col = "blue")
x <- seq(0, 50, length.out = 100)
y <- dcomp(x, 6, 0.2)
lines(x, y, type = "l", col = "red")

Facet_wrap like plot using R base graphics

I want to compare two datasets with same x and y variables. However, not all X variable points are present on both. As a toy example say this is what I have:
position.x <- c(1,2,3)
score.x <- c(450,220,330)
x <- data.frame(position,score.x)
position.y <- c(2,3,5)
score.y <- c(333,423,988)
y<- data.frame(position.y,score.y)
par(mfrow = c(2,1))
plot(x, pch = 19)
plot(y, pch = 19)
X axes are not comparable. I found some post explaining how to do it on ggplot using facet_wrap but I would like to do it using base graph.
Thank you in advance.
you could specify the range of the x and y axises by xlim and slim
position.x <- c(1,2,3)
score.x <- c(450,220,330)
x <- data.frame(position,score.x)
position.y <- c(2,3,5)
score.y <- c(333,423,988)
y<- data.frame(position.y,score.y)
par(mfrow = c(2,1))
plot(x, pch = 19, xlim=c(1,5))
plot(y, pch = 19, xlim=c(1,5))
if you are going to repeat this, you might as well write some kind of function (which is one of the benefits of ggplot--it takes care of all the set-up for you):
## data needs to be in a long format
dat <- data.frame(position = c(1,2,3,2,3,5),
score = c(450,220,330,333,423,988),
z = c('x','x','x','y','y','y'))
facet_wrap <- function(data, x, y, z, horiz = TRUE, ...) {
## save current par settings and return after finished
op <- par(no.readonly = TRUE)
on.exit(par(op))
zz <- unique(data[, z])
## sets up the layout to cascade horizontally or vertically
## and sets xlim and ylim appropriately
if (horiz) {
par(mfrow = c(1, length(zz)), ...)
ylim <- range(data[, y])
xlim <- NULL
} else {
par(mfrow = c(length(zz), 1), ...)
xlim <- range(data[, x])
ylim <- NULL
}
## make a subset of data for each unique by variable
## and draw a basic plot for each one
for (ii in zz) {
tmp <- data[data[, z] %in% ii, ]
plot(tmp[, x], tmp[, y], xlim = xlim, ylim = ylim)
}
}
facet_wrap(dat, 'position', 'score', 'z', mar = c(5,4,2,2))
facet_wrap(dat, 'position', 'score', 'z', mar = c(5,4,1,2), horiz = FALSE)

How to make 3D line plot in R (waterfall plot)

I would like to create a waterfall plot in R (XYYY) from my data.
So far, I use this code:
load("myData.RData")
ls()
dim(data)
##matrix to xyz coords
library(reshape2)
newData <- melt(data, id="Group.1")
dim(newData)
head(newData)
tail(newData)
newDataO <- newData[c(2,1,3)]
head(newDataO)
##color scale for z axis
myColorRamp <- function(colors, values) {
v <- (values - min(values))/diff(range(values))
x <- colorRamp(colors)(v)
rgb(x[,1], x[,2], x[,3], maxColorValue = 255)
}
cols <- myColorRamp(c("darkblue","yellow","darkorange","red","darkred"),newDataO$value)
##3D scatter
library(rgl)
plot3d(newDataO$variable, newDataO$Group.1, newDataO$value, xlab="", ylab="", zlab="", type="p", col=cols, box=FALSE, axes=FALSE)
rgl.postscript("persptrial_060514.eps","eps")
to get this plot:
https://dl.dropboxusercontent.com/u/14906265/persptrial_060514.jpg
I have also use this option in 2d with polygon but the result does not properly show the differential effect between both plots (left vs right).
I do not know whether something like persp3d could do the job but I am not familiar enough with writing code to achieve it. Any help will be very much appreciated.
It seems to me that the simplest way of doing a waterfall plot in R is to add all the lines manually in a loop.
library(rgl)
# Function to plot
f <- function(x, y) sin(10 * x * y) * cos(4 * y^3) + x
nx <- 30
ny <- 100
x <- seq(0, 1, length = nx)
y <- seq(0, 1, length = ny)
z <- outer(x, y, FUN = f)
# Plot function and add lines manually
surface3d(x, y, z, alpha = 0.4)
axes3d()
for (i in 1:nx) lines3d(x[i], y, z[i, ], col = 'white', lwd = 2)

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