I'm trying to create an animation in Julia where a satellite orbits Earth. Earth in this case is represented by a static circle and the satellite's trajectory is a path extending from the launch point to the satellite's current position.
If I understand the process correctly, to create a gif in Julia, I need to use the #gif macro with a loop and create the next gif frame on each iteration of the loop. I've been attempting to plot Earth, then plot the launch point, then push the next position in the satellite's trajectory on each loop iteration, but it's pushing data to the Earth dataset.
I also have other plots that I would like to animate, but the animation examples that use multiple data series don't specify any x values. I need to specify x and y values for each datapoint in each series.
How can I specify the series to push a new point to?
Well, while trying to put together a small example script, I figured it out.
To begin, the conditions under which you can use push! with a plot are fairly specific. You can't use an Int64 (or any other type of integer) as an x value or push! will try to access the plot like an array at the "index" specified by your x data. This means you have to ensure every input is a Float (I didn't try this with more exotic data types for plotting like Bools, but I assume that that wouldn't go well either).
Also, the x and y (and z) data in a plot can't be something that push! doesn't work on normally, like a StepRangeLen (e.g. t = 0:10). Unfortunately this introduces an extra layer of complexity; if you need to use StepRangeLens in your plots, you'll have to convert them to Arrays: t = Array{Float64}(0:10).
Finally, it's probably good practice to pass in as many x and y values on each call to push! as you have series (if this wording is awkward, see the example below). Some of the examples for the Plots package add complexity in specifying a single x value for multiple y values, which is fine if your x values are the same for both series, but becomes a problem if they're different.
Putting all of this together, here's a minimal example of pushing to different series:
using Plots
# Let x and z be two different-valued, different-length vectors
x = Array{Float64}(range(0, stop=π, length=30))
z = Array{Float64}(range(0, stop=-π, length=20))
p = plot(x,sin.(x))
plot!(p, z, cos.(z))
# Pushing a single x,y pair goes to the first series:
push!(p, 0.0, -0.5)
# Pushing a single x value and a 2x1 Array sends the x value to
# both series, the first y value to the first series, and the
# second y value to the second series.
push!(p, -0.2, [-0.75, 0.2])
# Note: comma ^ is important
# Pushing two x values and two y values sends the first x value to
# the first series and the second x value to the second series.
# Same for the y values, which is the same as the previous example
push!(p, [-π/4, π/4], [0.1, 0.2])
# If you want to push only to one series, send a NaN to the others:
push!(p, [NaN, -3π/2], [NaN, 1.0])
display(p)
The plot is pretty incoherent if you run this as-is. I recommend commenting out each of the push! statements and uncommenting each one individually to see its effect on the plot.
Related
I'm rather new to programming and the site so let me know if I screw up on this explanation.
I have a rather long series of x, y coordinates representing a character in 2d space. Let's say that space is 200 x 400. I want to represent the amount of time the character is in each x, y coordinate by means of a pretty chloropleth.
I want to use heatmaply for this because I think the output is pretty and I want my audience to be able to zoom in on the data. It isn't really meant to do density estimation (I think?) so I'm trying to work around it.
I suppose the way to do this is to fill a 200x400 dataframe with counts of the number of occurrences of each x, y coordinate in the data at each x, y coordinate in the frame. Essentially, to build a 2d map out of the data frame and impose the counts upon it
So, I suppose my questions are:
1). How do I get the count of each unique x, y coordinate in my set
2). How might I pass those counts easily to the matching x, y cell in my 200x400 dataframe full of zeroes?
This seems like it should be easy but I can't seem to figure it out! I'm a novice to r and can't see the shape of what I need to do.
You can use the table function to get your matrix of counts.
table(X,Y)
X and Y should be columns of coordinates.
Output based on some sample data
I am having issues trying to generate a code that will cleanly produce a mean (specifically a weighted average) based on a simple plot of points using interpolation.
For Example;
ex=c(1,2,3,4,5)
why=c(2,5,9,15,24)
This shows the kind of information I am working with.
plot(ex, why, type="o")
At this point, I want to actually have each point "binned" so the lines between them are straight. To do this, I have been adding points to the x values manually in excel as (x+0.01).
This is the new output:
why=c(2,2,5,5,9,9,15,15,24,24)
ex=c(1,2,2.01,3,3.01,4,4.01,5,5.01,6)
plot(ex, why, type="o")
So this is where my question comes in to play. I have to do this many times and do not want to generate a ton of new vectors and objects. To get a weighted average, I have been interpolating y values for increments of x at 0.01 using interpolation into a new object. I am then able to go into this new object and get a mean when a point falls between the actual ex values, i.e.
mean(newy[1:245])
Because I made new y values for 100 increments of x that (basically) follow a straight line, I am getting a weighted average here for x= 1 to 2.45.
Is there an easier and more elegant way to embed the interpolate code into the mean code so I could just say "average of interpolated y for nonreal x to nonreal x?"
It doesn't do exactly what you want, but you should consider the stepfun function -- this creates a step function out of two series.
plot(stepfun(ex[-1], why))
stepfun is handy because it gives you a function defined over that interval, so you can easily interpolate just by evaluating anywhere. The downside to it is that it is not strictly defined on the range given (which is why we have to cut off the first value in ex).
Based on your second plotting example, I think you are probably looking for this:
library(ggplot2)
qplot(ex, why, geom="step")
this gives:
Or if you want the line to go vertical first, you can use:
qplot(ex, why, geom="step", direction = "vh")
which gives:
I am able to create a 2-D plot using two parameters in IDL, i.e., star formation rate (y-axis) vs. time (x-axis).
But I would like to include the redshift (another variable) corresponding to each data point, say, as the top x-axis. It didn't work when I tried adding the third variable to PLOT procedure, and I have not been able to find any discussion on how to accomplish this online. Any help is appreciated.
First run PLOT.PRO with the NODATA keyword set and XAXIS=4 and YAXIS=4 to suppress each axis. Then you can use the AXIS.PRO program to define each axis. Then you can use OPLOT.PRO to draw the points of Z vs. X and Z vs. Y, where Z = star formation rate, X = time, and Y = redshift. Look up details on the [XYZ]AXIS keywords to determine which axis to draw at each time. You can even color each axis using the COLOR keyword with the AXIS.PRO program.
The only trick is that you will have to scale the Y data points to the X-axis scale prior to plotting because you will explicitly define the [XYZ]RANGE when calling PLOT.PRO (well you could do the converse and scale it to Y and redefine X, it's your choice). You need to do this scaling because OPLOT.PRO and, say, PLOTS.PRO use the original [XYZ]RANGE defined when calling PLOT.PRO to convert device coordinates to data coordinates.
Does that make sense?
first call PLOT, TIME, SFR with XSTYLE=9 to force exact range and suppress the top x-axis
then use the AXIS procedure to create the top x-axis
be careful with the ticks of that axis, which you want to correspond to a REDSHIFT that you compute from the TIME variable
example with a bottom x-axis in velocity and a top y-axis in frequency:
> plot, vel, spec, xsty=9, xtick_get=xtick, xtit='Velocity (km/s)', ytit='Antenna Temperature (K)'
> axis, !x.crange[0], !y.crange[1], xaxis=1, xtickv=((ref_freq - ref_freq/299792.458*xtick)), xtickformat='(F8.3)', xticks=n_elements(xtick)-1, xrange=(ref_freq - ref_freq/299792.458*minmax(!x.crange)), chars=1.5
You could always set the color to be the third dimension (ie. color or size).
I am trying to convey the concentration of lines in 2D space by showing the number of crossings through each pixel in a grid. I am picturing something similar to a density plot, but with more intuitive units. I was drawn to the spatstat package and its line segment class (psp) as it allows you to define line segments by their end points and incorporate the entire line in calculations. However, I'm struggling to find the right combination of functions to tally these counts and would appreciate any suggestions.
As shown in the example below with 50 lines, the density function produces values in (0,140), the pixellate function tallies the total length through each pixel and takes values in (0, 0.04), and as.mask produces a binary indictor of whether a line went through each pixel. I'm hoping to see something where the scale takes integer values, say 0..10.
require(spatstat)
set.seed(1234)
numLines = 50
# define line segments
L = psp(runif(numLines),runif(numLines),runif(numLines),runif(numLines), window=owin())
# image with 2-dimensional kernel density estimate
D = density.psp(L, sigma=0.03)
# image with total length of lines through each pixel
P = pixellate.psp(L)
# binary mask giving whether a line went through a pixel
B = as.mask.psp(L)
par(mfrow=c(2,2), mar=c(2,2,2,2))
plot(L, main="L")
plot(D, main="density.psp(L)")
plot(P, main="pixellate.psp(L)")
plot(B, main="as.mask.psp(L)")
The pixellate.psp function allows you to optionally specify weights to use in the calculation. I considered trying to manipulate this to normalize the pixels to take a count of one for each crossing, but the weight is applied uniquely to each line (and not specific to the line/pixel pair). I also considered calculating a binary mask for each line and adding the results, but it seems like there should be an easier way. I know that you can sample points along a line, and then do a count of the points by pixel. However, I am concerned about getting the sampling right so that there is one and only one point per line crossing of a pixel.
Is there is a straight-forward way to do this in R? Otherwise would this be an appropriate suggestion for a future package enhancement? Is this more easily accomplished in another language such as python or matlab?
The example above and my testing has been with spatstat 1.40-0, R 3.1.2, on x86_64-w64-mingw32.
You are absolutely right that this is something to put in as a future enhancement. It will be done in one of the next versions of spatstat. It will probably be an option in pixellate.psp to count the number of crossing lines rather than measure the total length.
For now you have to do something a bit convoluted as e.g:
require(spatstat)
set.seed(1234)
numLines = 50
# define line segments
L <- psp(runif(numLines),runif(numLines),runif(numLines),runif(numLines), window=owin())
# split into individual lines and use as.mask.psp on each
masklist <- lapply(1:nsegments(L), function(i) as.mask.psp(L[i]))
# convert to 0-1 image for easy addition
imlist <- lapply(masklist, as.im.owin, na.replace = 0)
rslt <- Reduce("+", imlist)
# plot
plot(rslt, main = "")
I am trying to plot large amounts of points using some library. The points are ordered by time and their values can be considered unpredictable.
My problem at the moment is that the sheer number of points makes the library take too long to render. Many of the points are redundant (that is - they are "on" the same line as defined by a function y = ax + b). Is there a way to detect and remove redundant points in order to speed rendering ?
Thank you for your time.
The following is a variation on the Ramer-Douglas-Peucker algorithm for 1.5d graphs:
Compute the line equation between first and last point
Check all other points to find what is the most distant from the line
If the worst point is below the tolerance you want then output a single segment
Otherwise call recursively considering two sub-arrays, using the worst point as splitter
In python this could be
def simplify(pts, eps):
if len(pts) < 3:
return pts
x0, y0 = pts[0]
x1, y1 = pts[-1]
m = float(y1 - y0) / float(x1 - x0)
q = y0 - m*x0
worst_err = -1
worst_index = -1
for i in xrange(1, len(pts) - 1):
x, y = pts[i]
err = abs(m*x + q - y)
if err > worst_err:
worst_err = err
worst_index = i
if worst_err < eps:
return [(x0, y0), (x1, y1)]
else:
first = simplify(pts[:worst_index+1], eps)
second = simplify(pts[worst_index:], eps)
return first + second[1:]
print simplify([(0,0), (10,10), (20,20), (30,30), (50,0)], 0.1)
The output is [(0, 0), (30, 30), (50, 0)].
About python syntax for arrays that may be non obvious:
x[a:b] is the part of array from index a up to index b (excluded)
x[n:] is the array made using elements of x from index n to the end
x[:n] is the array made using first n elements of x
a+b when a and b are arrays means concatenation
x[-1] is the last element of an array
An example of the results of running this implementation on a graph with 100,000 points with increasing values of eps can be seen here.
I came across this question after I had this very idea. Skip redundant points on plots. I believe I came up with a far better and simpler solution and I'm happy to share as my first proposed solution on SO. I've coded it and it works well for me. It also takes into account the screen scale. There may be 100 points in value between those plot points, but if the user has a chart sized small, they won't see them.
So, iterating through your data/plot loop, before you draw/add your next data point, look at the next value ahead and calculate the change in screen scale (or value, but I think screen scale for the above-mentioned reason is better). Now do the same for the next value ahead (getting these values is just a matter of peeking ahead in your array/collection/list/etc adding the for next step increment (probably 1/2) to the current for value whilst in the loop). If the 2 values are the same (or perhaps very minor change, per your own preference), you can skip this one point in your chart by simply adding 'continue' in the loop, skipping adding the data point as the point lies exactly on the slope between the point before and after it.
Using this method, I reduce a chart from 963 points to 427 for example, with absolutely zero visual change.
I think you might need to perhaps read this a couple of times to understand, but it's far simpler than the other best solution mentioned here, much lighter weight, and has zero visual effect on your plot.
I would probably apply a "least squares" algorithm to obtain a line of best fit. You can then go through your points and downfilter consecutive points that lie close to the line. You only need to plot the outliers, and the points that take the curve back to the line of best fit.
Edit: You may not need to employ "least squares"; if your input is expected to hover around "y=ax+b" as you say, then that's already your line of best fit and you can just use that. :)