How to align and scale plots of different dimensions with ggplot2, gridExtra? - r

I'm trying to produce side by side tile plots using ggplot2 and gridExtra.
However, the plots produced are not scaled/aligned, see the picture and code below.
How can I produce this figure such that the cells are aligned and of the same dimensions?
Code
library(ggplot2)
library(gridExtra)
## make date frames
one <- floor(runif(56, min=0, max=5))
data.one<- cbind(one,expand.grid(h = seq(1,8,1), w = seq(1,7,1)))
two <- floor(runif(35, min=0, max=5))
data.two <- cbind(two,expand.grid(h = seq(1,7,1), w = seq(1,5,1)))
## gridExtra layout
lay <- rbind(c(1,1,1,1,1,1,1,NA,NA,NA,NA,NA),
c(1,1,1,1,1,1,1,2,2,2,2,2),
c(1,1,1,1,1,1,1,2,2,2,2,2),
c(1,1,1,1,1,1,1,2,2,2,2,2),
c(1,1,1,1,1,1,1,2,2,2,2,2),
c(1,1,1,1,1,1,1,2,2,2,2,2),
c(1,1,1,1,1,1,1,2,2,2,2,2),
c(1,1,1,1,1,1,1,2,2,2,2,2))
##plots
plot.one<-ggplot(data=data.one)+
geom_tile(aes(x=w,y=h,fill=one),colour = "grey50")+
scale_fill_gradient(low = "white", high = "blue")+
theme(legend.position= "none")
plot.two<-ggplot(data=data.two)+
geom_tile(aes(y=h,x=w,fill=two),colour = "grey50")+
scale_fill_gradient(low = "white", high = "red")+
theme(legend.position= "none")
grid.arrange(plot.one,plot.two, layout_matrix = lay)

ggplot2 doesn't assign fixed sizes to the plot panels, so you need to go to a rather low-level, find out the number of bins in each plot, and use this to set the appropriate panel size in the gtable object. The other complication is that "null" units are a bit special in grid, so to have something that scales with them it needs to be a null unit itself, as in this dummy rectGrob squeezing the second plot panel from the top,
b1 <- ggplot_build(p1)
b2 <- ggplot_build(p2)
n <- function(b) length(unique(b[["data"]][[1]][["y"]]))
library(egg)
library(grid)
gf1 <- gtable_frame(ggplot_gtable(b1))
gf2 <- gtable_frame(ggplot_gtable(b2))
gf2$grobs[[5]][["grobs"]][[1]] <- arrangeGrob(
rectGrob(gp=gpar(fill="grey95", col=NA)), gf2$grobs[[5]][["grobs"]][[1]],
heights = unit.c(unit(1 - n(b2) / n(b1), "null"), unit(n(b2) / n(b1),"null")))
grid.arrange(gf1, gf2, ncol=2)

Related

How to arrange `ggplot2` objects side-by-side and ensure equal plotting areas?

I am trying to arrange two ggplot2 plots side by side, i.e., in a two-column
layout using the package gridExtra. I am interested in ensuring that both
plots have equal plotting area (i.e., the gray plot panel is the same for both
plots) regardless of the height of the x-axis labels. As you can see in the
example below, when longer x-axis labels are used, gridExtra::grid.arrange()
seems to compensate this by adjusting the plotting area (i.e., the grayed out
part of the plot).
# Dummy data.
data <- data.frame(x = 1:10, y = rnorm(10))
# Dummy labels.
x_labels_short <- 1:10
x_labels_long <- 100001:100010
# Common settings for both `ggplot2` plots.
layers <- list(
labs(
x = "Plot title"
),
theme(
axis.text.x = element_text(
angle = 90,
vjust = 0.5,
hjust = 1
)
)
)
# `ggplot2 plot (a).
plot_a <- ggplot(data, aes(x, y)) +
scale_x_continuous(breaks = 1:10, labels = x_labels_short) +
layers
# `ggplo2` plot (b).
plot_b <- ggplot(data, aes(x, y)) +
scale_x_continuous(breaks = 1:10, labels = x_labels_long) +
layers
# Showing the plots side by side.
gridExtra::grid.arrange(
plot_a,
plot_b,
ncol = 2
)
Output:
What I want is for both plots to (1) have equal plotting area and (b) the x-axis
title of plot_a to be aligned with that of plot_b (i.e., the x-axis title of
plot_a to be offset based on the length of of the x-axis labels of plot_b).
If this is not clear, this is what I want to achieve would look like with base
R.
# Wrapper for convenience.
plot_gen <- function(data, labels) {
plot(
NULL,
xlim = c(1, 10),
ylim = c(min(data$y), max(data$y)),
xlab = "",
ylab = "y",
xaxt = "n"
)
axis(
side = 1,
at = 1:10,
labels = labels,
las = 2
)
title(
xlab = "Plot title",
line = 4.5
)
}
# Get `par`.
old_par = par(no.readonly = TRUE)
# Set the two-column layout.
layout(matrix(1:2, ncol = 2))
# Adjust margins.
par(mar = old_par$mar + c(1.5, 0, 0, 0))
# Plot base plot one.
plot_gen(data, x_labels_short)
# Plot base plot two.
plot_gen(data, x_labels_long)
# Restore `par`.
par(old_par)
# Restore layout.
layout(1:1)
Output:
Quick mention. I found a similar question on SO (i.e.,
How to specify the size of a graph in ggplot2 independent of axis labels), however I fail to see how the
answers address the problem. Also, the plots I am trying to arrange are based
on different data and I don't think I can use a facet_wrap approach.
One suggestion: the patchwork package.
library(patchwork)
plot_a + plot_b
It also works for more complex layouts, e.g.:
(plot_a | plot_b) / plot_a

Extend axis limits without plotting (in order to align two plots by x-unit)

I am trying to combine two ggplot objects with patchwork - two plots with different subsets of data, but the same x variable (and therefore same unit). I would like to align the plots according to the x values - Each x unit should have the same physical width in the final plot.
This is very easy when actually plotting the entire width of the larger data set (see plot below) - but I struggle to plot only parts of the data and keeping the same alignment.
library(ggplot2)
library(patchwork)
library(dplyr)
p1 <-
ggplot(mtcars, aes(mpg)) +
geom_density(trim = TRUE) +
scale_x_continuous(limits = c(10,35))
p2 <-
ggplot(filter(mtcars, mpg < 20), aes(mpg)) +
geom_histogram(binwidth = 1, boundary = 1) +
scale_x_continuous(limits = c(10,35))
p1/p2
Created on 2019-08-07 by the reprex package (v0.3.0)
The desired output
That's photoshopped
adding coord_cartesian(xlim = c(10,(20 or 35)), clip = 'off'), and/or changing scale_x limits to c(0,(20 or 35)) doesn't work.
patchwork also won't let me set the widths of both plots when they are in two rows, which makes sense in a way. So I could create an empty plot for the second row and set the widths for those, but this seems a terrible hack and I feel there must be a much easier solution.
I am not restricted to patchwork, but any solution allowing to use it would be very welcome.
I modified the align_plots function from the cowplot package for this, so that its plot_grid function can now support adjustments to the dimensions of each plot.
(The main reason I went with cowplot rather than patchwork is that I haven't had much tinkering experience with the latter, and overloading common operators like + makes me slightly nervous.)
Demonstration of results
# x / y axis range of p1 / p2 have been changed for illustration purpose
p1 <- ggplot(mtcars, aes(mpg, 1 + stat(count))) +
geom_density(trim = TRUE) +
scale_x_continuous(limits = c(10,35)) +
coord_cartesian(ylim = c(1, 3.5))
p2 <- ggplot(filter(mtcars, mpg >= 15 & mpg < 30), aes(mpg)) +
geom_histogram(binwidth = 1, boundary = 1)
plot_grid(p1, p2, ncol = 1, align = "v") # plots in 1 column, x-axes aligned
plot_grid(p1, p2, nrow = 1, align = "h") # plots in 1 row, y-axes aligned
Plots in 1 column (x-axes aligned for 15-28 range):
Plots in 1 row (y-axes aligned for 1 - 3.5 range):
Caveats
This hack assumes the plots that the user intends to align (either horizontally or vertically) have reasonably similar axes of comparable magnitude. I haven't tested it on more extreme cases.
This hack expects simple non-faceted plots in Cartesian coordinates. I'm not sure what one could expect from aligning faceted plots. Similarly, I'm not considering polar coordinates (what's there to align?) or map projections (haven't looked into this, but they feel rather complicated).
This hack expects the gtable cell containing the plot panel to be in the 7th row / 5th column of the gtable object, which is based on my understanding of how ggplot objects are typically converted to gtables, and may not survive changes to the underlying code.
Code
Modified version of cowplot::align_plots:
align_plots_modified <- function (..., plotlist = NULL, align = c("none", "h", "v", "hv"),
axis = c("none", "l", "r", "t", "b", "lr", "tb", "tblr"),
greedy = TRUE) {
plots <- c(list(...), plotlist)
num_plots <- length(plots)
grobs <- lapply(plots, function(x) {
if (!is.null(x)) as_gtable(x)
else NULL
})
halign <- switch(align[1], h = TRUE, vh = TRUE, hv = TRUE, FALSE)
valign <- switch(align[1], v = TRUE, vh = TRUE, hv = TRUE, FALSE)
vcomplex_align <- hcomplex_align <- FALSE
if (valign) {
# modification: get x-axis value range associated with each plot, create union of
# value ranges across all plots, & calculate the proportional width of each plot
# (with white space on either side) required in order for the plots to align
plot.x.range <- lapply(plots, function(x) ggplot_build(x)$layout$panel_params[[1]]$x.range)
full.range <- range(plot.x.range)
plot.x.range <- lapply(plot.x.range,
function(x) c(diff(c(full.range[1], x[1]))/ diff(full.range),
diff(x)/ diff(full.range),
diff(c(x[2], full.range[2]))/ diff(full.range)))
num_widths <- unique(lapply(grobs, function(x) {
length(x$widths)
}))
num_widths[num_widths == 0] <- NULL
if (length(num_widths) > 1 || length(grep("l|r", axis[1])) > 0) {
vcomplex_align = TRUE
warning("Method not implemented for faceted plots. Placing unaligned.")
valign <- FALSE
}
else {
max_widths <- list(do.call(grid::unit.pmax,
lapply(grobs, function(x) {x$widths})))
}
}
if (halign) {
# modification: get y-axis value range associated with each plot, create union of
# value ranges across all plots, & calculate the proportional width of each plot
# (with white space on either side) required in order for the plots to align
plot.y.range <- lapply(plots, function(x) ggplot_build(x)$layout$panel_params[[1]]$y.range)
full.range <- range(plot.y.range)
plot.y.range <- lapply(plot.y.range,
function(x) c(diff(c(full.range[1], x[1]))/ diff(full.range),
diff(x)/ diff(full.range),
diff(c(x[2], full.range[2]))/ diff(full.range)))
num_heights <- unique(lapply(grobs, function(x) {
length(x$heights)
}))
num_heights[num_heights == 0] <- NULL
if (length(num_heights) > 1 || length(grep("t|b", axis[1])) > 0) {
hcomplex_align = TRUE
warning("Method not implemented for faceted plots. Placing unaligned.")
halign <- FALSE
}
else {
max_heights <- list(do.call(grid::unit.pmax,
lapply(grobs, function(x) {x$heights})))
}
}
for (i in 1:num_plots) {
if (!is.null(grobs[[i]])) {
if (valign) {
grobs[[i]]$widths <- max_widths[[1]]
# modification: change panel cell's width to a proportion of unit(1, "null"),
# then add whitespace to the left / right of the plot's existing gtable
grobs[[i]]$widths[[5]] <- unit(plot.x.range[[i]][2], "null")
grobs[[i]] <- gtable::gtable_add_cols(grobs[[i]],
widths = unit(plot.x.range[[i]][1], "null"),
pos = 0)
grobs[[i]] <- gtable::gtable_add_cols(grobs[[i]],
widths = unit(plot.x.range[[i]][3], "null"),
pos = -1)
}
if (halign) {
grobs[[i]]$heights <- max_heights[[1]]
# modification: change panel cell's height to a proportion of unit(1, "null"),
# then add whitespace to the bottom / top of the plot's existing gtable
grobs[[i]]$heights[[7]] <- unit(plot.y.range[[i]][2], "null")
grobs[[i]] <- gtable::gtable_add_rows(grobs[[i]],
heights = unit(plot.y.range[[i]][1], "null"),
pos = -1)
grobs[[i]] <- gtable::gtable_add_rows(grobs[[i]],
heights = unit(plot.y.range[[i]][3], "null"),
pos = 0)
}
}
}
grobs
}
Utilising the above modified function with cowplot package's plot_grid:
# To start using (in current R session only; effect will not carry over to subsequent session)
trace(cowplot::plot_grid, edit = TRUE)
# In the pop-up window, change `grobs <- align_plots(...)` (at around line 27) to
# `grobs <- align_plots_modified(...)`
# To stop using
untrace(cowplot::plot_grid)
(Alternatively, we can define a modified version of plot_grid function that uses align_plots_modified instead of cowplot::align_plots. Results would be the same either way.)
Here is an option with grid.arrange that does not use a blank plot, but requires a manual of adjustment of:
plot margin
x axis expansion
number of decimal places in y axis labels
library(ggplot2)
library(dplyr)
library(gridExtra)
p1 <-
ggplot(mtcars, aes(mpg)) +
geom_density(trim = TRUE) +
scale_x_continuous(limits = c(10,35), breaks=seq(10,35,5), expand = expand_scale(add=c(0,0)))
p2 <-
ggplot(filter(mtcars, mpg < 20), aes(mpg)) +
geom_histogram(binwidth = 1, boundary = 1) +
scale_x_continuous(limits = c(10,20), breaks=seq(10,20,5), expand = expand_scale(add=c(0,0))) +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01)) +
theme(plot.margin = unit(c(0,1,0,0), "cm"))
grid.arrange(p1, p2,
layout_matrix = rbind(c(1, 1), c(2, NA))
)
Should make this plot:

Customize breaks on a color gradient legend using base R

Here is a sample script using random numbers instead of real elevation data.
library(gridExtra)
library(spatstat) #im function
elevation <- runif(500, 0, 10)
B <- matrix(elevation, nrow = 20, ncol = 25)
Elevation_Map <- im(B)
custom <- colorRampPalette(c("cyan","green", "yellow", "orange", "red"))
plot(Elevation_Map, col = custom(10), main = NULL)
This is the plot and legend that I get:
This is the legend that I am trying to recreate in R (this one made in Word):
I know this is possible and its probably a simple solution but I've tried using some examples I found online to no avail.
This plot (with real elevation data) is an art piece that will be hung in a gallery, with the elevation plot on 1 board and the legend on a separate board. I tried to get R to plot just the plot without the legend using
plot(Elevation_Map, col = custom(10), main = NULL, legend = NULL)
like I have in the past but for some reason it always plots the legend with the plot. As of right now I'm planning on just cropping the .pdf into 2 separate files to achieve this.
Here are two ways of doing it using other packages:
# example data, set seed to reproduce.
set.seed(1); elevation <- runif(500, 0, 10)
B <- matrix(elevation, nrow = 20, ncol = 25)
#Elevation_Map <- im(B)
custom <- colorRampPalette(c("cyan","green", "yellow", "orange", "red"))
1) Using fields package, image.plot(), it is same "base" graphics::image.default() plot but with more arguments for customisation (but couldn't remove the ticks from legend):
library(fields)
image.plot(B, nlevel = 10, col = custom(10),
breaks = 1:11,
lab.breaks = c("Low Elevation", rep("", 9), "High Elevation"),
legend.mar = 10)
2) Using ggplot package, geom_raster function:
library(ggplot2)
library(reshape) # convert matrix to long dataframe: melt
B_melt <- reshape2::melt(B)
head(B_melt)
ggplot(B_melt, aes(X1, X2, fill = value)) +
geom_raster() +
theme_void() +
scale_fill_gradientn(name = element_blank(),
breaks = c(1, 9),
labels = c("Low Elevation", "High Elevation"),
colours = custom(10))
The code in the original post is using the im class from the spatstat package. The plot command is dispatched to plot.im. Simply look at help(plot.im) to figure out how to control the colour ribbon. The relevant argument is ribargs. Here is a solution:
plot(Elevation_Map, col=custom(10), main="",
ribargs=list(at=Elevation_Map$yrange,
labels=c("Low Elevation", "High Elevation"),
las=1))

Positioning of grobs

I want to plot data for a linear model in a main plot and a plot of the effects (forest plot) as a subplot using arrangeGrob.
Here are the data:
set.seed(1)
main.df <- data.frame(sample=c(paste("E.plus.A.plus",1:3,sep="_"),paste("E.minus.A.plus",1:3,sep="_"),paste("E.plus.A.minus",1:3,sep="_"),paste("E.minus.A.minus",1:3,sep="_")),
replicate=rep(1:3,4),cpm=c(rnorm(12)),
factor.level=factor(c(rep("E.plus.A.plus",3),rep("E.minus.A.plus",3),rep("E.plus.A.minus",3),rep("E.minus.A.minus",3)),
levels=c("E.plus.A.plus","E.minus.A.plus","E.plus.A.minus","E.minus.A.minus")))
effects.df <- data.frame(factor.level=c("E.plus.A.plus-E.minus.A.plus","E.plus.A.plus-E.plus.A.minus","E.plus.A.plus-E.minus.A.minus",
"E.minus.A.plus-E.plus.A.minus","E.minus.A.plus-E.minus.A.minus","E.plus.A.minus-E.minus.A.minus"),
effect=rnorm(6),effect.df=runif(6,0,0.5),p.value=runif(6,0,1),y=1:6+0.2)
effects.df$effect.high <- effects.df$effect+effects.df$effect.df
effects.df$effect.low <- effects.df$effect-effects.df$effect.df
effects.df$factor.level <- factor(effects.df$factor.level,levels=effects.df$factor.level)
The ggplots:
require(ggplot2)
require(grid)
require(gridExtra)
main.plot <- ggplot(main.df,aes(x=replicate,y=cpm,color=factor.level))+geom_point(size=3)+
facet_wrap(~factor.level,ncol=length(levels(main.df$factor.level)))+
labs(x="replicate",y="cpm")+scale_x_continuous(breaks=unique(main.df$replicate))+theme_bw()+
theme(legend.key=element_blank(),panel.border=element_blank(),strip.background=element_blank(),axis.title=element_text(size=8),plot.title=element_text(size=9,hjust=0.5))
Which is:
sub.plot <- ggplot(effects.df,aes(x=effect,y=factor.level,color=factor.level))+geom_point(size=2.5,shape=19)+geom_errorbarh(aes(xmax=effect.high,xmin=effect.low),height=0.1)+
geom_vline(xintercept=0,linetype="longdash",colour="black",size=0.25)+theme_bw()+theme(legend.key=element_blank(),panel.border=element_blank(),strip.background=element_blank(),axis.title=element_text(size=7),axis.text=element_text(size=7),legend.text=element_text(size=7),legend.title=element_text(size=7))+
geom_text(aes(x=effects.df$effect,y=effects.df$y,label=format(signif(effects.df$p.value,2),scientific=T)),size=2.5)
And is:
And here's how I try to combine them into a single plot:
if(!is.null(dev.list())) dev.off()
blank <- grid.rect(gp = gpar(col = "white"))
sub.plot.grob <- arrangeGrob(blank,sub.plot,ncol=1)
combined.plot <- arrangeGrob(main.plot,sub.plot,ncol=2,widths=c(1,1))
grid.arrange(combined.plot)
which gives:
How do I adjust the position and dimensions so that sub.plot is smaller (all layers, e.g., text are reduced proportionally), and is positioned below the legend of main.plot?
I strongly recommend the package cowplot for this sort of task. Here, I am building three nested sets (the main plot to the left, then the two legends together at the top right, then the sub plot at the bottom right). Note the wonderful get_legend function that make pulling the legends incredibly easy.
plot_grid(
main.plot + theme(legend.position = "none")
, plot_grid(
plot_grid(
get_legend(main.plot)
, get_legend(sub.plot)
, nrow = 1
)
, sub.plot + theme(legend.position = "none")
, nrow = 2
)
, nrow = 1
)
gives:
Obviously I'd recommend changing one (or both) of the color palettes, but that should give what you want.
If you really want the legend with the sub.plot, instead of with the other legend, you could skip the get_legend.
You can also adjust the width/height of the sets using rel_widths and rel_heights if you want something other than the even sizes.
As an additional note, cowplot sets its own default theme on load. I generally revert to what I like by running theme_set(theme_minimal()) right after loading it.
here's a grid.arrange solution,
grid.arrange(grobs = replicate(4, ggplot(), simplify = FALSE),
layout_matrix = cbind(c(1,1), c(3,2), c(4, 2)),
widths = c(2,1,1))
with those bits and pieces,
get_legend <- function(p) {
g <- ggplotGrob(p)
id <- grep("guide", g$layout$name)
g$grobs[[id]]
}
leg1 <- get_legend(main.plot); leg2 <- get_legend(sub.plot)
gl <- list(main.plot + theme(legend.position = "none"),
sub.plot + theme(legend.position = "none"), leg1, leg2)
grid.arrange(grobs = gl,
layout_matrix = cbind(c(1,1), c(3,2), c(4, 2)),
widths = c(2,1,1))

Multiple plots lay out as upper triangle matrix and formatted as scatter plots

I am doing a Bayesian modeling and I have 8 variables, for each variable there is a correlation parameter, and each pair of variables have a correlation parameter. All those parameters have their posterior density plot. I would like to arrange those plots in a upper triangle layout, and I used the result from
Upper triangle layout
However, it would be better if I can title/label the plots in the same fashion as what scatter plot does, i.e., I will only have titles(variable names) in the top and in the right, and by checking the corresponding titles on the top and right of each sub figure, people will know what the correlation parameter is standing for.
Here is minimum example I have achieved, where I only used 3 variables for illustration.
require(ggplot2)
corr_1 = rnorm(100)
corr_2 = rnorm(100)
corr_12 = rnorm(100)
corr_list = list(corr_1, corr_2, corr_12)
ttls = c('variance within variable 1',
'correlation within variable 1 & 2',
'variance within variable 2')
plots = list()
for(i in 1:3){
temp_df = data.frame(x=corr_list[[i]])
temp = ggplot(data=temp_df, aes(x=x)) +
geom_density()+
ggtitle(ttls[i])
plots[[i]] = temp
}
library(gridExtra) ## for grid.arrange()
library(grid)
ng <- nullGrob()
grid.arrange(plots[[1]], plots[[2]],
ng, plots[[3]])
So what I want is instead of explicitly stating what the correlation means, having labels in the top of the plot. I should have title "variable1" and "variable2" on top, and on the right of the plot, I have title "variable1" and "variable2" vertically, just like what the scatter plots does.
The final layout I'd like to have is similar to this one:
However, the difference is that mine plots requires the off diagonal parts to be all density plot, and all the density plots are independent, i.e., the data does not depend on other variables, as in my minimum example, I have independent plots stored in a list( while in a pairwise scatter plot, each subplot is using one variable as x, one as y).
I'm assuming that you have your plots appropriately arranged, and that all you need is to add the variable labels. I've made a couple of changes to the plot function to remove titles and axis labels.
arrangeGrob returns a grob which is also a gtable. Thus, gtable functions can be applied to add the labels. I've added some comments below.
library(ggplot2)
library(gridExtra)
library(grid)
library(gtable)
corr_1 = rnorm(100)
corr_2 = rnorm(100)
corr_12 = rnorm(100)
corr_list = list(corr_1, corr_2, corr_12)
ttls = c('variance within variable 1',
'correlation within variable 1 & 2',
'variance within variable 2')
plots = list()
for(i in 1:3){
temp_df = data.frame(x=corr_list[[i]])
temp = ggplot(data=temp_df, aes(x=x)) +
geom_density() +
theme(axis.title = element_blank()) #+
# ggtitle(ttls[i])
plots[[i]] = temp
}
ng <- nullGrob()
gp <- arrangeGrob(plots[[1]], plots[[2]],
ng, plots[[3]])
# The gp object is a gtable;
# thus gtable functions can be applied to add the the necessary labels
# A list of text grobs - the labels
vars <- list(textGrob("Variable 1"), textGrob("Variable 2"))
# So that there is space for the labels,
# add a row to the top of the gtable,
# and a column to the left of the gtable.
gp <- gtable_add_cols(gp, unit(1.5, "lines"), 0)
gp <- gtable_add_rows(gp, unit(1.5, "lines"), 0)
# Add the label grobs.
# The labels on the left should be rotated; hence the edit.
# t and l refer to cells in the gtable layout.
# gtable_show_layout(gp) shows the layout.
gp <- gtable_add_grob(gp, lapply(vars, editGrob, rot = 90), t = 2:3, l = 1)
gp <- gtable_add_grob(gp, vars, t = 1, l = 2:3)
# Draw it
grid.newpage()
grid.draw(gp)

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