Related
I'm trying to make a figure similar to this in R. Basically X and Y represent coordinates (e.g. lon/lat) and Z represents elevation. I want to plot a 3D bar chart with a elevation as the bar height, and then show a smooth curve of fitted Z values going through the bars. I am able to get a 3d barplot with barplot3d but I'm not sure if it's possible to add the fitted curve on top of that. Does anyone know how to do this? I have some example code below demonstrating what I've tried so far.
library(rgl)
library(barplot3d)
library(tidyverse)
x_mat<- matrix(rep(-1:1, each=3),nrow = 3) #x coordinates
y_mat<- matrix(rev(rep(-1:1, each=3)),nrow = 3, byrow = TRUE) #y coordinates
df<- data.frame(x = as.vector(x_mat), y = as.vector(y_mat)) #dataframe
set.seed(5)
df<- df %>% mutate(z= x^2+ y^2 + rnorm(n = 9, mean = 0, sd = 0.1)) #add elevation values
m<- lm(z ~ I(x^2)+I(y^2)+I(x*y)+x+y, data = df) #fitted curve
rgl.open()
rgl::plot3d(m)
barplot3d(rows=3,cols=3, z=df$z,scalexy=1, gap=0, alpha=0.4,theta=30,phi=50,
topcolors = "gray", gridlines = TRUE)
Update: More complicated example
The curve doesn't seem to intersect the bars properly with current solution for a non-symmetrical curve (fixed in most updated answer).
library(rgl)
library(barplot3d)
library(tidyverse)
x_mat<- matrix(rep(-1:1, each=3),nrow = 3) #x coordinates
y_mat<- matrix(rev(rep(-1:1, each=3)),nrow = 3, byrow = TRUE) #y coordinates
A<- 0.2
B<- 0.2
C<- 0.4
D<- 0.4
E<- 0
df<- data.frame(x = as.vector(x_mat), y = as.vector(y_mat)) #dataframe
df<- df %>% mutate(z= A*x^2 + B*y^2 + C*x*y + D*x + E*y) #add elevation values
z_mat<- matrix(data = df$z, nrow=3)
m<- lm(z ~ I(x^2)+I(y^2)+I(x*y)+x+y, data = df) #fitted curve
df$zpred<- predict(m, data.frame(x=df$x, y=df$y))
round(df$z-df$zpred,10) #Predictions should fit observations almost exactly (i.e. intersect exactly with bars)
#0 0 0 0 0 0 0 0 0
n<- 10
xvals <- seq(-1, 1, len = n)
xmat <- replicate(n, seq(1.5, 3.5, len = n))
ymat <- t(xmat)
pred <- expand.grid(x = xvals, y = xvals)
zmat <- matrix(predict(m, pred), nrow = n, ncol = n)
barplot3d(rows=3,cols=3, z=df$z, gap=0, alpha=0.4, phi = 45,
topcolors = "gray", sidecolors = "cyan", linecolors= "blue", gridlines = FALSE, zlabels = FALSE)
surface3d(x = xmat, y = zmat, z = ymat-5, color = "purple", alpha = 0.7)
axes3d()
As you can probably tell, your 3d surface is rotated 90 degrees relative to where it should be. This is not your fault; it is just a difference between the way barplot3d is drawn compared to the other rgl shapes. You also need a bit of shifting and rescaling to get it to fit.
barplot3d(rows=3,cols=3, z=df$z, gap=0, alpha=0.4, phi = 45,
topcolors = "gray", gridlines = TRUE)
xvals <- seq(-1.5, 1.5, len = 10)
xmat <- replicate(10, seq(1, 4, len = 10))
ymat <- t(xmat)
pred <- expand.grid(x = xvals, y = xvals)
zmat <- matrix(predict(m, pred), 10, 10)
surface3d(xmat, zmat, color = "gold", alpha = 0.5, ymat - 5)
Update
To remove the points above the highest bar, just set them to NA. You probably want to increase the resolution when you do this though:
xvals <- seq(-1.5, 1.5, len = 100)
xmat <- replicate(100, seq(1, 4, len = 100))
ymat <- t(xmat) - 5
pred <- expand.grid(x = xvals, y = xvals)
zmat <- matrix(predict(m, pred), 100, 100)
zmat[zmat > 2] <- NA
barplot3d(rows=3,cols=3, z=df$z, gap=0, alpha=0.4, phi = 45,
topcolors = "gray", gridlines = TRUE)
surface3d(xmat, zmat, color = "gold", alpha = 0.5, ymat)
Note that this gives an unavoidably ragged edge to the graphic
An alternative is to shrink the x, y grids at which z is calculated:
xvals <- seq(-1, 1, len = 100)
xmat <- replicate(100, seq(1.5, 3.5, len = 100))
ymat <- t(xmat) - 5
pred <- expand.grid(x = xvals, y = xvals)
zmat <- matrix(predict(m, pred), 100, 100)
barplot3d(rows=3,cols=3, z=df$z, gap=0, alpha=0.4, phi = 45,
topcolors = "gray", gridlines = TRUE)
surface3d(xmat, zmat, ymat, color = "gray20", alpha = 0.5)
Further update
It looks as though we need a double flip to get the z values correct:
barplot3d(rows=3,cols=3, z=df$z, gap=0, alpha=0.4, phi = 45,
topcolors = "gray", sidecolors = "cyan", linecolors= "blue",
gridlines = FALSE, zlabels = FALSE)
surface3d(x = xmat, y = t(apply(t(apply(zmat, 1, rev)), 2, rev)),
z = ymat-5, color = "purple", alpha = 0.7)
axes3d()
I want to make contour levels of bivariate normal density plotted in base persp function. Here is the code:
###############
library(pacman)
p_load(tidyverse)
p_load(mvtnorm)
p_load(GA)
my_mean<-c(25,65)
mycors<-seq(-1,1,by=.25)
sd_vec<-c(5,7)
i<-3
temp_cor<-matrix(c(1,mycors[i],
mycors[i],1),
byrow = T,ncol=2)
V<-sd_vec %*% t(sd_vec) *temp_cor
my_x<-seq(my_mean[1]-3*sd_vec[1], my_mean[1]+3*sd_vec[1], length.out=20)
my_y<-seq(my_mean[2]-3*sd_vec[2], my_mean[2]+3*sd_vec[2], length.out=20)
temp_f<-function(a,b){dmvnorm(cbind(a,b), my_mean,V)}
my_z<-outer(my_x, my_y,temp_f)
nlevels<-20
my_zlim <- range(my_z, finite = TRUE)
my_levels <- pretty(my_zlim, nlevels)
zz <- (my_z[-1, -1] + my_z[-1, -ncol(my_z)] + my_z[-nrow(my_z), -1] + my_z[-nrow(my_z),
-ncol(my_z)])/4
cols <- jet.colors(length(my_levels) - 1)
zzz <- cut(zz, breaks = my_levels, labels = cols)
persp(my_x, my_y, my_z, theta = -25, phi = 45, expand = 0.5,xlab="x",ylab="y",zlab="f(x,y)",col = as.character(zzz))
data.grid <- expand.grid(x = seq(my_mean[1]-3*sd_vec[1], my_mean[1]+3*sd_vec[1], length.out=200),
y = seq(my_mean[2]-3*sd_vec[2], my_mean[2]+3*sd_vec[2], length.out=200))
q.samp <- cbind(data.grid, prob = dmvnorm(data.grid, mean = my_mean, sigma = V))
ggplot(q.samp, aes(x=x, y=y, z=prob)) +
geom_contour( aes(z=prob, color=..level..)) +
#scale_color_gradient(level = jet.colors(length(my_levels) - 1))+
theme_bw()
Created on 2020-10-31 by the reprex package (v0.3.0)
Since the color palette of the persp graph seems to be discrete, I want to give colors to the contours which approximately resembles the colors in persp graph.
Are you looking for geom_contour_fill with a scale_fill_discrete according to the interpolated values of cols?
ggplot(q.samp, aes(x, y, z = prob)) +
geom_contour_filled( aes(fill = ..level..), col = "black", bins = 11) +
scale_fill_discrete(type = jet.colors(11)) +
theme_bw()
Or if you are looking for colored lines instead of fills you can use scale_gradientn
ggplot(q.samp, aes(x, y, z = prob)) +
geom_contour(aes(color = ..level..), bins = 11, size = 1) +
scale_color_gradientn(colours = jet.colors(11)) +
theme_bw()
I am trying to create a scatterplot that is summarized by hexagon bins of counts. I would like the user to be able to define the count breaks for the color scale. I have this working, using scale_fill_manual(). Oddly, however, it only works sometimes. In the MWE below, using the given seed value, if xbins=10, there are issues resulting in a plot as follows:
However, if xbins=20 or 40, for example, the plot doesn't seem to have problems:
My MWE is as follows:
library(ggplot2)
library(hexbin)
library(RColorBrewer)
set.seed(1)
xbins <- 20
x <- abs(rnorm(10000))
y <- abs(rnorm(10000))
minVal <- min(x, y)
maxVal <- max(x, y)
maxRange <- c(minVal, maxVal)
buffer <- (maxRange[2] - maxRange[1]) / (xbins / 2)
h <- hexbin(x = x, y = y, xbins = xbins, shape = 1, IDs = TRUE,
xbnds = maxRange, ybnds = maxRange)
hexdf <- data.frame (hcell2xy(h), hexID = h#cell, counts = h#count)
my_breaks <- c(2, 4, 6, 8, 20, 1000)
clrs <- brewer.pal(length(my_breaks) + 3, "Blues")
clrs <- clrs[3:length(clrs)]
hexdf$countColor <- cut(hexdf$counts, breaks = c(0, my_breaks, Inf),
labels = rev(clrs))
ggplot(hexdf, aes(x = x, y = y, hexID = hexID, fill = countColor)) +
scale_fill_manual(values = levels(hexdf$countColor)) +
geom_hex(stat = "identity") +
geom_abline(intercept = 0, color = "red", size = 0.25) +
coord_fixed(xlim = c(-0.5, (maxRange[2] + buffer)),
ylim = c(-0.5, (maxRange[2] + buffer))) +
theme(aspect.ratio=1)
My goal is to tweak this code so that the plot does not have problems (where suddenly certain hexagons are different sizes and shapes than the rest) regardless of the value assigned to xbins. However, I am puzzled what may be causing this problem for certain xbins values. Any advice would be greatly appreciated.
EDIT:
I am updating the example code after taking into account comments by #bdemarest and #Axeman. I followed the most popular answer in the link #Axeman recommends, and believe it is more useful when you are working with scale_fill_continuous() on an integer vector. Here, I am working on scale_fill_manual() on a factor vector. As a result, I am still unable to get this goal to work. Thank you.
library(ggplot2)
library(hexbin)
library(RColorBrewer)
set.seed(1)
xbins <- 10
x <- abs(rnorm(10000))
y <- abs(rnorm(10000))
minVal <- min(x, y)
maxVal <- max(x, y)
maxRange <- c(minVal, maxVal)
buffer <- (maxRange[2] - maxRange[1]) / (xbins / 2)
bindata = data.frame(x=x,y=y,factor=as.factor(1))
h <- hexbin(bindata, xbins = xbins, IDs = TRUE, xbnds = maxRange, ybnds = maxRange)
counts <- hexTapply (h, bindata$factor, table)
counts <- t (simplify2array (counts))
counts <- melt (counts)
colnames (counts) <- c ("factor", "ID", "counts")
counts$factor =as.factor(counts$factor)
hexdf <- data.frame (hcell2xy (h), ID = h#cell)
hexdf <- merge (counts, hexdf)
my_breaks <- c(2, 4, 6, 8, 20, 1000)
clrs <- brewer.pal(length(my_breaks) + 3, "Blues")
clrs <- clrs[3:length(clrs)]
hexdf$countColor <- cut(hexdf$counts, breaks = c(0, my_breaks, Inf), labels = rev(clrs))
ggplot(hexdf, aes(x = x, y = y, fill = countColor)) +
scale_fill_manual(values = levels(hexdf$countColor)) +
geom_hex(stat = "identity") +
geom_abline(intercept = 0, color = "red", size = 0.25) +
coord_cartesian(xlim = c(-0.5, maxRange[2]+buffer), ylim = c(-0.5, maxRange[2]+ buffer)) + theme(aspect.ratio=1)
you can define colors in 'geom' instead of 'scale' that modifies the scale of plot:
ggplot(hexdf, aes(x = x, y = y)) +
geom_hex(stat = "identity",fill =hexdf$countColor)
The question R interpolated polar contour plot shows an excellent way to produce interpolated polar plots in R. I include the very slightly modified version I'm using:
PolarImageInterpolate <- function(
### Plotting data (in cartesian) - will be converted to polar space.
x, y, z,
### Plot component flags
contours=TRUE, # Add contours to the plotted surface
legend=TRUE, # Plot a surface data legend?
axes=TRUE, # Plot axes?
points=TRUE, # Plot individual data points
extrapolate=FALSE, # Should we extrapolate outside data points?
### Data splitting params for color scale and contours
col_breaks_source = 1, # Where to calculate the color brakes from (1=data,2=surface)
# If you know the levels, input directly (i.e. c(0,1))
col_levels = 10, # Number of color levels to use - must match length(col) if
#col specified separately
col = rev(heat.colors(col_levels)), # Colors to plot
# col = rev(heat.colors(col_levels)), # Colors to plot
contour_breaks_source = 1, # 1=z data, 2=calculated surface data
# If you know the levels, input directly (i.e. c(0,1))
contour_levels = col_levels+1, # One more contour break than col_levels (must be
# specified correctly if done manually
### Plotting params
outer.radius = ceiling(max(sqrt(x^2+y^2))),
circle.rads = pretty(c(0,outer.radius)), #Radius lines
spatial_res=1000, #Resolution of fitted surface
single_point_overlay=0, #Overlay "key" data point with square
#(0 = No, Other = number of pt)
### Fitting parameters
interp.type = 1, #1 = linear, 2 = Thin plate spline
lambda=0){ #Used only when interp.type = 2
minitics <- seq(-outer.radius, outer.radius, length.out = spatial_res)
# interpolate the data
if (interp.type ==1 ){
Interp <- akima:::interp(x = x, y = y, z = z,
extrap = extrapolate,
xo = minitics,
yo = minitics,
linear = FALSE)
Mat <- Interp[[3]]
}
else if (interp.type == 2){
library(fields)
grid.list = list(x=minitics,y=minitics)
t = Tps(cbind(x,y),z,lambda=lambda)
tmp = predict.surface(t,grid.list,extrap=extrapolate)
Mat = tmp$z
}
else {stop("interp.type value not valid")}
# mark cells outside circle as NA
markNA <- matrix(minitics, ncol = spatial_res, nrow = spatial_res)
Mat[!sqrt(markNA ^ 2 + t(markNA) ^ 2) < outer.radius] <- NA
### Set contour_breaks based on requested source
if ((length(contour_breaks_source == 1)) & (contour_breaks_source[1] == 1)){
contour_breaks = seq(min(z,na.rm=TRUE),max(z,na.rm=TRUE),
by=(max(z,na.rm=TRUE)-min(z,na.rm=TRUE))/(contour_levels-1))
}
else if ((length(contour_breaks_source == 1)) & (contour_breaks_source[1] == 2)){
contour_breaks = seq(min(Mat,na.rm=TRUE),max(Mat,na.rm=TRUE),
by=(max(Mat,na.rm=TRUE)-min(Mat,na.rm=TRUE))/(contour_levels-1))
}
else if ((length(contour_breaks_source) == 2) & (is.numeric(contour_breaks_source))){
contour_breaks = pretty(contour_breaks_source,n=contour_levels)
contour_breaks = seq(contour_breaks_source[1],contour_breaks_source[2],
by=(contour_breaks_source[2]-contour_breaks_source[1])/(contour_levels-1))
}
else {stop("Invalid selection for \"contour_breaks_source\"")}
### Set color breaks based on requested source
if ((length(col_breaks_source) == 1) & (col_breaks_source[1] == 1))
{zlim=c(min(z,na.rm=TRUE),max(z,na.rm=TRUE))}
else if ((length(col_breaks_source) == 1) & (col_breaks_source[1] == 2))
{zlim=c(min(Mat,na.rm=TRUE),max(Mat,na.rm=TRUE))}
else if ((length(col_breaks_source) == 2) & (is.numeric(col_breaks_source)))
{zlim=col_breaks_source}
else {stop("Invalid selection for \"col_breaks_source\"")}
# begin plot
Mat_plot = Mat
Mat_plot[which(Mat_plot<zlim[1])]=zlim[1]
Mat_plot[which(Mat_plot>zlim[2])]=zlim[2]
image(x = minitics, y = minitics, Mat_plot , useRaster = TRUE, asp = 1, axes = FALSE, xlab = "", ylab = "", zlim = zlim, col = col)
# add contours if desired
if (contours){
CL <- contourLines(x = minitics, y = minitics, Mat, levels = contour_breaks)
A <- lapply(CL, function(xy){
lines(xy$x, xy$y, col = gray(.2), lwd = .5)
})
}
# add interpolated point if desired
if (points){
points(x, y, pch = 21, bg ="blue")
}
# add overlay point (used for trained image marking) if desired
if (single_point_overlay!=0){
points(x[single_point_overlay],y[single_point_overlay],pch=0)
}
# add radial axes if desired
if (axes){
# internals for axis markup
RMat <- function(radians){
matrix(c(cos(radians), sin(radians), -sin(radians), cos(radians)), ncol = 2)
}
circle <- function(x, y, rad = 1, nvert = 500){
rads <- seq(0,2*pi,length.out = nvert)
xcoords <- cos(rads) * rad + x
ycoords <- sin(rads) * rad + y
cbind(xcoords, ycoords)
}
# draw circles
if (missing(circle.rads)){
circle.rads <- pretty(c(0,outer.radius))
}
for (i in circle.rads){
lines(circle(0, 0, i), col = "#66666650")
}
# put on radial spoke axes:
axis.rads <- c(0, pi / 6, pi / 3, pi / 2, 2 * pi / 3, 5 * pi / 6)
r.labs <- c(90, 60, 30, 0, 330, 300)
l.labs <- c(270, 240, 210, 180, 150, 120)
for (i in 1:length(axis.rads)){
endpoints <- zapsmall(c(RMat(axis.rads[i]) %*% matrix(c(1, 0, -1, 0) * outer.radius,ncol = 2)))
segments(endpoints[1], endpoints[2], endpoints[3], endpoints[4], col = "#66666650")
endpoints <- c(RMat(axis.rads[i]) %*% matrix(c(1.1, 0, -1.1, 0) * outer.radius, ncol = 2))
lab1 <- bquote(.(r.labs[i]) * degree)
lab2 <- bquote(.(l.labs[i]) * degree)
text(endpoints[1], endpoints[2], lab1, xpd = TRUE)
text(endpoints[3], endpoints[4], lab2, xpd = TRUE)
}
axis(2, pos = -1.25 * outer.radius, at = sort(union(circle.rads,-circle.rads)), labels = NA)
text( -1.26 * outer.radius, sort(union(circle.rads, -circle.rads)),sort(union(circle.rads, -circle.rads)), xpd = TRUE, pos = 2)
}
# add legend if desired
# this could be sloppy if there are lots of breaks, and that's why it's optional.
# another option would be to use fields:::image.plot(), using only the legend.
# There's an example for how to do so in its documentation
if (legend){
library(fields)
image.plot(legend.only=TRUE, smallplot=c(.78,.82,.1,.8), col=col, zlim=zlim)
# ylevs <- seq(-outer.radius, outer.radius, length = contour_levels+ 1)
# #ylevs <- seq(-outer.radius, outer.radius, length = length(contour_breaks))
# rect(1.2 * outer.radius, ylevs[1:(length(ylevs) - 1)], 1.3 * outer.radius, ylevs[2:length(ylevs)], col = col, border = NA, xpd = TRUE)
# rect(1.2 * outer.radius, min(ylevs), 1.3 * outer.radius, max(ylevs), border = "#66666650", xpd = TRUE)
# text(1.3 * outer.radius, ylevs[seq(1,length(ylevs),length.out=length(contour_breaks))],round(contour_breaks, 1), pos = 4, xpd = TRUE)
}
}
Unfortunately, this function has a few bugs:
a) Even with a purely radial pattern, the produced plot has a distortion whose origin I don't understand:
#example
r <- rep(seq(0.1, 0.9, len = 8), each = 8)
theta <- rep(seq(0, 7/4*pi, by = pi/4), times = 8)
x <- r*sin(theta)
y <- r*cos(theta)
z <- z <- rep(seq(0, 1, len = 8), each = 8)
PolarImageInterpolate(x, y, z)
why the wiggles between 300° and 360°? The z function is constant in theta, so there's no reason why there should be wiggles.
b) After 4 years, some of the packages loaded have been modified and at least one functionality of the function is broken. Setting interp.type = 2 should use thin plate splines for interpolation instead than a basic linear interpolation, but it doesn't work:
> PolarImageInterpolate(x, y, z, interp.type = 2)
Warning:
Grid searches over lambda (nugget and sill variances) with minima at the endpoints:
(GCV) Generalized Cross-Validation
minimum at right endpoint lambda = 9.493563e-06 (eff. df= 60.80002 )
predict.surface is now the function predictSurface
Error in image.default(x = minitics, y = minitics, Mat_plot, useRaster = TRUE, :
'z' must be a matrix
the first message is a warning and doesn't worry me, but the second one is actually an error and prevents me from using thin plate splines. Can you help me solve these two problems?
Also, I'd like to "upgrade" to using ggplot2, so if you can give an answer which does that, it would be great. Otherwise, after the bugs are fixed, I'll try asking a specific question which only asks to modify the function so that it uses ggplot2.
For the ggplot2 solution, here is a start. geom_raster allows interpolation, but does not work for polar coordinates. Instead, you can use geom_tile, though then you may need to do the interpolation yourself before passing the values to ggplot.
Of important note: the example data you gave gives an error when working with geom_raster that I believe is caused by the spacing of the values. Here is an example set that works (note, used this blog as a guide, though it is now outdated):
dat_grid <-
expand.grid(x = seq(0,350,10), y = 0:10)
dat_grid$density <- runif(nrow(dat_grid))
ggplot(dat_grid
, aes(x = x, y = y, fill = density)) +
geom_tile() +
coord_polar() +
scale_x_continuous(breaks = seq(0,360,90)) +
scale_fill_gradient2(low = "white"
, mid = "yellow"
, high = "red3"
, midpoint = 0.5)
If you are working from raw data, you might be able to get ggplot to do the work for you. Here is an example working from raw data. There are a lot of manual tinkering things to do, but it is at least an optional starting point:
polarData <-
data.frame(
theta = runif(10000, 0, 2*pi)
, r = log(abs(rnorm(10000, 0, 10)))
)
toCart <-
data.frame(
x = polarData$r * cos(polarData$theta)
, y = polarData$r * sin(polarData$theta)
)
axisLines <-
data.frame(
x = 0
, y = 0
, xend = max(polarData$r)*cos(seq(0, 2*pi, pi/4))
, yend = max(polarData$r)*sin(seq(0, 2*pi, pi/4))
, angle = paste(seq(0, 2, 1/4), "pi") )
ticks <-
data.frame(
label = pretty(c(0, max(polarData$r)) )[-1]
)
ggplot(toCart) +
# geom_point(aes(x = x, y = y)) +
stat_density_2d(aes(x = x, y = y
, fill = ..level..)
, geom = "polygon") +
scale_fill_gradient(low = "white"
, high = "red3") +
theme(axis.text = element_blank()
, axis.title = element_blank()
, axis.line = element_blank()
, axis.ticks = element_blank()) +
geom_segment(data = axisLines
, aes(x = x, y = y
, xend = xend
, yend = yend)) +
geom_label(data = axisLines
, aes(x = xend, y = yend, label = angle)) +
geom_label(data = ticks
, aes(x = 0, y = label, label = label))
From an another post, I came to know that the fucnction predict.surface from package fields is deprecated whic is used for interp.type = 2 in PolarImageInterpolate. Instead, a new predictSurface function is introduced, which can be used here.
Example:
r <- rep(seq(0.1, 0.9, len = 8), each = 8)
theta <- rep(seq(0, 7/4*pi, by = pi/4), times = 8)
x <- r*sin(theta)
y <- r*cos(theta)
z <- z <- rep(seq(0, 1, len = 8), each = 8)
PolarImageInterpolate(x, y, z, interp.type = 2)
I've code gradient descent algorithm in R and now I'm trying to "draw" the path of the vectors.
I've got draw points in my contour plot, but it's not correct because nobody knows what happened first.
In my algorith always I have an previous state P=(Xi,Yi) and a later state L=(Xi+1,Yi+1), so, How can I draw the vector PL in a contour or a persp plot?
I only got this with contour, where the red point is the convergence:
The same for persp:
Thanks all!
EDIT:
Graphics can be obtanined respectively:
f<-function(u,v){
u*u*exp(2*v)+4*v*v*exp(-2*u)-4*u*v*exp(v-u)
}
x = seq(-2, 2, by = 0.5)
y = seq(-2, 2, by = 0.5)
z <- outer(x,y,f)
#Contour plot
contour(x,y,z)
#Persp plot
persp(x, y, z, phi = 25, theta = 55, xlim=c(-2,2), ylim=c(-2,2),
xlab = "U", ylab = "V",
main = "F(u,v)", col="yellow", ticktype = "detailed"
) -> res
Taking Himmelblau's function as a test example:
f <- function(x, y) { (x^2+y-11)^2 + (x+y^2-7)^2 }
Its partial derivatives:
dx <- function(x,y) {4*x**3-4*x*y-42*x+4*x*y-14}
dy <- function(x,y) {4*y**3+2*x**2-26*y+4*x*y-22}
Running the gradient descent:
# gradient descent parameters
num_iter <- 100
learning_rate <- 0.001
x_val <- 6
y_val <- 6
updates_x <- vector("numeric", length = num_iter)
updates_y <- vector("numeric", length = num_iter)
updates_z <- vector("numeric", length = num_iter)
# parameter updates
for (i in 1:num_iter) {
dx_val = dx(x_val,y_val)
dy_val = dy(x_val,y_val)
x_val <- x_val-learning_rate*dx_val
y_val <- y_val-learning_rate*dx_val
z_val <- f(x_val, y_val)
updates_x[i] <- x_val
updates_y[i] <- y_val
updates_z[i] <- z_val
}
Plotting:
x <- seq(-6, 6, length = 100)
y <- x
z <- outer(x, y, f)
plt <- persp(x, y, z,
theta = -50-log(i), phi = 20+log(i),
expand = 0.5,
col = "lightblue", border = 'lightblue',
axes = FALSE, box = FALSE,
ltheta = 60, shade = 0.90
)
points(trans3d(updates_x[1:i], updates_y[1:i], updates_z[1:i],pmat = plt),
col = c(rep('white', num_iter-1), 'blue'),
pch = 16,
cex = c(rep(0.5, num_iter-1), 1))
There's a trick to plotting points using persp, as mentioned in ?persp. By employing the power of trans3d, you can successfully put points and lines on a perspective plot.
f<-function(u,v){
u*u*exp(2*v)+4*v*v*exp(-2*u)-4*u*v*exp(v-u)
}
x = seq(-2, 2, by = 0.5)
y = seq(-2, 2, by = 0.5)
z <- scale(outer(x,y,f))
view <- persp(x, y, z, phi = 30, theta = 30, xlim=c(-2,2), ylim=c(-2,2),
xlab = "X", ylab = "Y", zlab = "Z", scale = FALSE,
main = "F(u,v)", col="yellow", ticktype = "detailed")
set.seed(2)
pts <- data.frame(x = sample(x, 3),
y = sample(y, 3),
z = sample(z, 3))
points(trans3d(x = pts$x, y = pts$y, z = pts$z, pmat = view), pch = 16)
lines(trans3d(x = pts$x, y = pts$y, z = pts$z, pmat = view))