I have two representations of the same function. The one shows it as a function of voltage, the other as a function of depth (a monotonous but complicated function). Depth can be expressed as a function of voltage. I would like to add something like a voltage axis to the depth representation but this does not seem to be possible.
How can I add vertical lines at increments of the voltage like -0.5, -1.0, -1.5, ... on the depth plot?
I found that it is indeed possible to create a custom second axis on the top. The result looks like this: https://dl.dropbox.com/u/226980/solved.jpg
This works by using FixedLocator.
The whole code looks like this:
f = subplot(111)
p1 = plot(depth_samples,NtNdbulk, label = "relative concentration")
xlabel("depth [um]")
ylabel("N_trap/N_bulk")
twinx()
p2 = plot(depth_samples,Nt, color='r', label = "absolute concentration")
p = p1 + p2
ylabel("N_trap")
labs = [l.get_label() for l in p]
legend(p, labs, loc=0)
ax2 = twiny()
p1 = plot(depth_samples,NtNdbulk, alpha = 0) #invisible
l = matplotlib.ticker.FixedLocator(tick_depth*1e4) # Positions of the ticks
ax2.get_xaxis().set_major_locator(l)
ax2.get_xaxis().set_ticklabels(ticks) # Voltages as displayed
xlabel("DLTS voltage during pulse")
show()
Related
I have been trying to add a bell curve to my histogram an outline it with a color so that it is more pleasing. enter image description here
I have added what my histogram looks like to give someone an idea on what I am working with, also here is my code thus far, thank you in advance.
ggplot(data = mammal.data.22.select2)+
geom_histogram(aes(x=Time, fill=Species))+
scale_fill_manual(values=c("paleturquoise4", "turquoise2"))+
facet_wrap(~Species, nrow=1)+
ylab("Observations")+
xlab("Time of Day")+
theme(strip.text.x = element_blank())
Let's build a histogram with a build-in dataset that seems similar-ish to your data structure.
library(ggplot2)
binwidth <- 0.25
p <- ggplot(iris, aes(Petal.Length)) +
geom_histogram(
aes(fill = Species),
binwidth = binwidth,
alpha = 0.5
) +
facet_wrap(~ Species)
You can use stat_bin() + geom_step() to give an outline to the histogram, without colouring the edge of every rectangle in the histogram. The only downside is that the first and last bins don't touch the x-axis.
p + stat_bin(
geom = "step", direction = "mid",
aes(colour = Species), binwidth = binwidth
)
To overlay a density function with a histogram, you could calculate the relevant parameters yourself and use stat_function() with fun = dnorm repeatedly. Alternatively, you can use ggh4x::stat_theodensity() to achieve a similar thing. Note that whether you use stat_function() or stat_theodensity(), you should scale the density back to the counts that your histogram uses (or scale histogram to density). In the example below, we do that by using after_stat(count * binwidth).
p + ggh4x::stat_theodensity(
aes(colour = Species,
y = after_stat(count * binwidth))
)
Created on 2022-04-15 by the reprex package (v2.0.1)
(disclaimer: I'm the author of ggh4x)
def signed_angle_between_vecs(target_vec, start_vec, plane_normal=None):
start_vec = np.array(start_vec)
target_vec = np.array(target_vec)
start_vec = start_vec/np.linalg.norm(start_vec)
target_vec = target_vec/np.linalg.norm(target_vec)
if plane_normal is None:
arg1 = np.dot(np.cross(start_vec, target_vec), np.cross(start_vec, target_vec))
else:
arg1 = np.dot(np.cross(start_vec, target_vec), plane_normal)
arg2 = np.dot(start_vec, target_vec)
return np.arctan2(arg1, arg2)
from scipy.spatial.transform import Rotation as R
world_frame_axis = input_rotation_object.apply(canonical_axis)
angle = signed_angle_between_vecs(canonical_axis, world_frame_axis)
axis_angle = np.cross(world_frame_axis, canonical_axis) * angle
C = R.from_rotvec(axis_angle)
transformed_world_frame_axis_to_canonical = C.apply(world_frame_axis)
I am trying to align world_frame_axis to canonical_axis by performing a rotation around the normal vector generated by the cross product between the two vectors, using the signed angle between the two axes.
However, this code does not work. If you start with some arbitrary rotation as input_rotation_object you will see that transformed_world_frame_axis_to_canonical does not match canonical_axis.
What am I doing wrong?
not a python coder so I might be wrong but this looks suspicious:
start_vec = start_vec/np.linalg.norm(start_vec)
from the names I would expect that np.linalg.norm normalizes the vector already so the line should be:
start_vec = np.linalg.norm(start_vec)
and all the similar lines too ...
Also the atan2 operands are not looking right to me. I would (using math):
a = start_vec / |start_vec | // normalized start
b = target_vec / |target_vec| // normalized end
u = a // normalized one axis of plane
v = cross(u ,b)
v = cross(v ,u)
v = v / |v| // normalized second axis of plane perpendicular to u
dx = dot(u,b) // target vector in 2D aligned to start
dy = dot(v,b)
ang = atan2(dy,dx)
beware the ang might negated (depending on your notations) if the case either add minus sign or reverse the order in cross(u,v) to cross(v,u) Also you can do sanity check with comparing result to unsigned:
ang' = acos(dot(a,b))
in absolute values they should be the same (+/- rounding error).
I have a M vs N curve (let's take it to be a sigmoid, for ease of understanding) for a given value of parameters P and Q. I need to visualise the M vs N curves for a range of values of P and Q (assume 10 values in 0 to 1, i.e. 0.1, 0.2, ..., 0.9 for both P and Q)
The only solution that I've found for this problem is a Trellis plot (essentially a matrix of plots). I'd like to know if there any other method to visualise this sort of a 4d(?) relationship besides the Trellis plots. Thanks.
I'm not sure I understand what you're hoping for, so let me know if this is on the right track. Below are three examples using R.
The first is indeed a matrix of plots where each panel represents a different value of q and, within each panel, each curve represents a different value of p. The second is a 3D plot which looks at a surface based on three of the variables with the fourth fixed. The third is a Shiny app that creates the same interactive plot as in the second example but also provides a slider that allows you to change p and see how the plot changes. Unfortunately, I'm not sure how to embed the interactive plots in Stackoverflow so I've just provided the code.
I'm not sure if there's an elegant way to look at all four variables at the same time, but maybe someone will come along with additional options.
Matrix of plots for various values of p and q
library(tidyverse)
theme_set(theme_classic())
# Function to plot
my_fun = function(x, p, q) {
1/(1 + exp(p + q*x))
}
# Parameters
params = expand.grid(p=seq(-2,2,length=6), q=seq(-1,1,length=11))
# x-values to feed to my_fun
x = seq(-10,10,0.1)
# Generate data frame for plotting
dat = map2_df(params$p, params$q, function(p, q) {
data.frame(p=p, q=q, x, y=my_fun(x, p, q))
})
ggplot(dat, aes(x,y,colour=p, group=p)) +
geom_line() +
facet_grid(. ~ q, labeller=label_both) +
labs(colour="p") +
scale_colour_gradient(low="red", high="blue") +
theme(legend.position="bottom")
3D plot with one variable fixed
The code below will produce an interactive 3D plot that you can zoom and rotate. I've fixed the value of p and drawn a plot of the y surface for a grid of x and q values.
library(rgl)
x = seq(-10,10,0.1)
q = seq(-1,1,0.01)
y = outer(x, q, function(a, b) 1/(1 + exp(1 + b*a)))
persp3d(x, q, y, col=hcl(240,80,65), specular="grey20",
xlab = "x", ylab = "q", zlab = "y")
I'm not sure how to embed the interactive plot, but here's a static image of one viewing angle:
Shiny app
The code below will create the same plot as above, but with the added ability to vary p with a slider and see how the plot changes.
Open an R script file and paste in the code below. Save it as app.r in its own directory then run the code. Both an rgl window and the Shiny app page with the slider for controlling the value of p should open. Resize the windows as desired and then move the slider to see how the function surface changes for various values of p.
library(shiny)
# Define UI for application that draws an interactive plot
ui <- fluidPage(
# Application title
titlePanel("Plot the function 1/(1 + exp(p + q*x))"),
# Sidebar with a slider input for number of bins
sidebarLayout(
sidebarPanel(
sliderInput("p",
"Vary the value of p and see how the plot changes",
min = -2,
max = 2,
value = 1,
step=0.2)
),
# Show a plot of the generated distribution
mainPanel(
plotOutput("distPlot")
)
)
)
# Define server logic required to draw the plot
server <- function(input, output) {
output$distPlot <- renderPlot({
library(rgl)
x = seq(-10,10,0.1)
q = seq(-1,1,0.01)
y = outer(x, q, function(a, b) 1/(1 + exp(input$p + b*a)))
persp3d(x, q, y, col=hcl(240,50,65), specular="grey20",
xlab = "x", ylab = "q", zlab = "y")
})
}
# Run the application
shinyApp(ui = ui, server = server)
Can anyone help me with parameters for SetGeoTransform? I'm creating raster layers with GDAL, but I can't find description of 3rd and 5th parameter for SetGeoTransform. It should be definition of x and y axis for cells. I try to find something about it here and here, but nothing.
I need to find description of these two parameters... It's a value in degrees, radians, meters? Or something else?
The geotransform is used to convert from map to pixel coordinates and back using an affine transformation. The 3rd and 5th parameter are used (together with the 2nd and 4th) to define the rotation if your image doesn't have 'north up'.
But most images are north up, and then both the 3rd and 5th parameter are zero.
The affine transform consists of six coefficients returned by
GDALDataset::GetGeoTransform() which map pixel/line coordinates into
georeferenced space using the following relationship:
Xgeo = GT(0) + Xpixel*GT(1) + Yline*GT(2)
Ygeo = GT(3) + Xpixel*GT(4) + Yline*GT(5)
See the section on affine geotransform at:
https://gdal.org/tutorials/geotransforms_tut.html
I did do like below code.
As a result I was able to do same with SetGeoTransform.
# new file
dst = gdal.GetDriverByName('GTiff').Create(OUT_PATH, xsize, ysize, band_num, dtype)
# old file
ds = gdal.Open(fpath)
wkt = ds.GetProjection()
gcps = ds.GetGCPs()
dst.SetGCPs(gcps, wkt)
...
dst.FlushCache()
dst = Nonet
Given information from the aforementioned gdal datamodel docs, the 3rd & 5th parameters of SatGeoTransform (x_skew and y_skew respectively) can be calculated from two control points (p1, p2) with known x and y in both "geo" and "pixel" coordinate spaces. p1 should be above-left of p2 in pixelspace.
x_skew = sqrt((p1.geox-p2.geox)**2 + (p1.geoy-p2.geoy)**2) / (p1.pixely - p2.pixely)`
y_skew = sqrt((p1.geox-p2.geox)**2 + (p1.geoy-p2.geoy)**2) / (p1.pixelx - p2.pixelx)`
In short this is the ratio of Euclidean distance between the points in geospace to the height (or width) of the image in pixelspace.
The units of the parameters are "geo"length/"pixel"length.
Here is a demonstration using the corners of the image stored as control points (gcps):
import gdal
from math import sqrt
ds = gdal.Open(fpath)
gcps = ds.GetGCPs()
assert gcps[0].Id == 'UpperLeft'
p1 = gcps[0]
assert gcps[2].Id == 'LowerRight'
p2 = gcps[2]
y_skew = (
sqrt((p1.GCPX-p2.GCPX)**2 + (p1.GCPY-p2.GCPY)**2) /
(p1.GCPPixel - p2.GCPPixel)
)
x_skew = (
sqrt((p1.GCPX-p2.GCPX)**2 + (p1.GCPY-p2.GCPY)**2) /
(p1.GCPLine - p2.GCPLine)
)
x_res = (p2.GCPX - p1.GCPX) / ds.RasterXSize
y_res = (p2.GCPY - p1.GCPY) / ds.RasterYSize
ds.SetGeoTransform([
p1.GCPX,
x_res,
x_skew,
p1.GCPY,
y_skew,
y_res,
])
I asked this question yesterday about storing a plot within an object. I tried implementing the first approach (aware that I did not specify that I was using qplot() in my original question) and noticed that it did not work as expected.
library(ggplot2) # add ggplot2
string = "C:/example.pdf" # Setup pdf
pdf(string,height=6,width=9)
x_range <- range(1,50) # Specify Range
# Create a list to hold the plot objects.
pltList <- list()
pltList[]
for(i in 1 : 16){
# Organise data
y = (1:50) * i * 1000 # Get y col
x = (1:50) # get x col
y = log(y) # Use natural log
# Regression
lm.0 = lm(formula = y ~ x) # make linear model
inter = summary(lm.0)$coefficients[1,1] # Get intercept
slop = summary(lm.0)$coefficients[2,1] # Get slope
# Make plot name
pltName <- paste( 'a', i, sep = '' )
# make plot object
p <- qplot(
x, y,
xlab = "Radius [km]",
ylab = "Services [log]",
xlim = x_range,
main = paste("Sample",i)
) + geom_abline(intercept = inter, slope = slop, colour = "red", size = 1)
print(p)
pltList[[pltName]] = p
}
# close the PDF file
dev.off()
I have used sample numbers in this case so the code runs if it is just copied. I did spend a few hours puzzling over this but I cannot figure out what is going wrong. It writes the first set of pdfs without problem, so I have 16 pdfs with the correct plots.
Then when I use this piece of code:
string = "C:/test_tabloid.pdf"
pdf(string, height = 11, width = 17)
grid.newpage()
pushViewport( viewport( layout = grid.layout(3, 3) ) )
vplayout <- function(x, y){viewport(layout.pos.row = x, layout.pos.col = y)}
counter = 1
# Page 1
for (i in 1:3){
for (j in 1:3){
pltName <- paste( 'a', counter, sep = '' )
print( pltList[[pltName]], vp = vplayout(i,j) )
counter = counter + 1
}
}
dev.off()
the result I get is the last linear model line (abline) on every graph, but the data does not change. When I check my list of plots, it seems that all of them become overwritten by the most recent plot (with the exception of the abline object).
A less important secondary question was how to generate a muli-page pdf with several plots on each page, but the main goal of my code was to store the plots in a list that I could access at a later date.
Ok, so if your plot command is changed to
p <- qplot(data = data.frame(x = x, y = y),
x, y,
xlab = "Radius [km]",
ylab = "Services [log]",
xlim = x_range,
ylim = c(0,10),
main = paste("Sample",i)
) + geom_abline(intercept = inter, slope = slop, colour = "red", size = 1)
then everything works as expected. Here's what I suspect is happening (although Hadley could probably clarify things). When ggplot2 "saves" the data, what it actually does is save a data frame, and the names of the parameters. So for the command as I have given it, you get
> summary(pltList[["a1"]])
data: x, y [50x2]
mapping: x = x, y = y
scales: x, y
faceting: facet_grid(. ~ ., FALSE)
-----------------------------------
geom_point:
stat_identity:
position_identity: (width = NULL, height = NULL)
mapping: group = 1
geom_abline: colour = red, size = 1
stat_abline: intercept = 2.55595281266726, slope = 0.05543539319091
position_identity: (width = NULL, height = NULL)
However, if you don't specify a data parameter in qplot, all the variables get evaluated in the current scope, because there is no attached (read: saved) data frame.
data: [0x0]
mapping: x = x, y = y
scales: x, y
faceting: facet_grid(. ~ ., FALSE)
-----------------------------------
geom_point:
stat_identity:
position_identity: (width = NULL, height = NULL)
mapping: group = 1
geom_abline: colour = red, size = 1
stat_abline: intercept = 2.55595281266726, slope = 0.05543539319091
position_identity: (width = NULL, height = NULL)
So when the plot is generated the second time around, rather than using the original values, it uses the current values of x and y.
I think you should use the data argument in qplot, i.e., store your vectors in a data frame.
See Hadley's book, Section 4.4:
The restriction on the data is simple: it must be a data frame. This is restrictive, and unlike other graphics packages in R. Lattice functions can take an optional data frame or use vectors directly from the global environment. ...
The data is stored in the plot object as a copy, not a reference. This has two
important consequences: if your data changes, the plot will not; and ggplot2 objects are entirely self-contained so that they can be save()d to disk and later load()ed and plotted without needing anything else from that session.
There is a bug in your code concerning list subscripting. It should be
pltList[[pltName]]
not
pltList[pltName]
Note:
class(pltList[1])
[1] "list"
pltList[1] is a list containing the first element of pltList.
class(pltList[[1]])
[1] "ggplot"
pltList[[1]] is the first element of pltList.
For your second question: Multi-page pdfs are easy -- see help(pdf):
onefile: logical: if true (the default) allow multiple figures in one
file. If false, generate a file with name containing the
page number for each page. Defaults to ‘TRUE’.
For your main question, I don't understand if you want to store the plot inputs in a list for later processing, or the plot outputs. If it is the latter, I am not sure that plot() returns an object you can store and retrieve.
Another suggestion regarding your second question would be to use either Sweave or Brew as they will give you complete control over how you display your multi-page pdf.
Have a look at this related question.