Julia plots heatmap

Julia plots heatmap DEFAULT

Analyzing Wombat Data

 

We are using Julia to post-process Wombat simulations and produce publication ready plots. Julia offers native parallelism and near C speed in loops with the convenience of Python and IDL. It also interfaces very well with Wombat's Fortran 2008 (e.g. same array order and indexing) and exposes key HPC concepts like vectorization (dot syntax) and parallelization. However, it is structured in many ways like Python (modules, encapsulation), which makes for a very productive to work environment and a great playground to learn programming. Differently to Python, loops are fast and can be parallelized without much work.

Julia has reached version 1.0 end of 2018, which broke some of our code. Until everything is fixed, you can use 0.7 which shows deprecation warnings. 

Start Julia like this to optimize for your machine, in this case Intel haswell architecture with 4 cores and -O3 flag:

Available architectures are shown with 

Our Julia library including serial snapshot reading & plotting examples are part of the wombat source tree and can be found in the "lib/julia/" directory. 

You first want to add the Wombat julia library to your search path in your ~/.julia/config/startup.jl

Reading Wombat Data

In Julia the next command reads the whole grid density into an array 'rho' and the simulation properties into a structure 'sim': 

ReadSnap also takes the "sim" structure as an input to avoid processing the manifest every time you're reading data from the same simulation. "sim" carries all info necessary to read the patch data and can become large (10MB). It carries all snapshot information, except the actual data.

We plan to implement parallel analysis using the same patch based approach to the data as Wombat does internally. N Julia tasks read M patches in parallel, resolve boundaries if necessary, compute on every patch and reduce the result (e.g. projection & map making). This should make for an efficient post processing pipeline.

Dot Syntax

Notice in this example the dot . syntax in the example above. The dot tells Julia to operate element wise on an array. This seems dumb, if you're used to Python or IDL, until you realize that Julia is as fast as C because of this. If you're operating on pre-defined arrays you can replace all dots with a macro:

This expression will SIMD vectorize and approach C with gcc compiler (not Fortran though). 

You can introspect functions and check SIMD vectorization :

The last command will show the assembler output of the function test(). There should be vector instructions starting with "v" operating on xmm or ymm registers. Try doing this with Python !

Plots for Analysis and Animations

We recommend the Plots package with the GR backend to make quick plots for analysis and animations/movies. GR is the fastest backend and is being continuously improved. It now plots millions of points in less than a second inlined into iTerm.

Then plot something: 

The following code will produce an mp4 movie of an image sequence generated from Wombat data with Kovesi's colormaps: 

Plots is a very powerful generic package. Refer to the Plots documentation here for more examples and color palette definition. 

What if it doesn't work ?

  • If you get errors like this: 

then you are on a remote machine and GR cannot use the X-forwarding. You may try: 

Another workaround is to let xterm handle the forwarding. To do this open an xterm on the remote machine:

and then start julia inside this xterm. Alternatively, you can tell GR's GKS window system that it is "headless" with before starting julia:

It will then not attempt to output to a window, and you will have to save your plots into a png file:

A Word on Colors

The visual representation of data is a non-trivial undertaking. Colors in particular can bias the impression the viewer has on the data. Additionally, there are issues regarding black & white conversion (lines still distinguishable ?), reproduction on a printer and color blind viewers.

We recommend, colormaps either from the ColorBrewer package (lines in plots) or the Perceptual Colormaps (images). These maps are well behave and ensure good readability of results. They are also very pretty. See colorbrewer2.org and this paper.

The Color Brewer packages are available in julialang via

and can be made available in the Plots package and the gr backend via: 

and in PGF via our PGFTools (in wombat/lib/julia/misc) package:

which has to be called only once per julia session. 

The perceptual Color maps are available in Plots via 

The list of available colors is here. :colorcet is the perceptually uniform palette recommended above.

Plots for Publications

Highest quality plots for papers can be made with PGFPlots. It generates native LaTex code from the plot commands. This stunning in papers, which are all LaTeX, but the syntax takes some time to learn and is not very intuitive. 

A PGF example: 

Consult the PGFPlots documentation or directly the PGF manual. For more examples, you can get the plotting scripts for one of our papers. The MHD-Weno paper contains lots of examples. The Julia source code for the plots is available from the website in the Publications section under the "Source" button.

Sours: https://wombatcode.org/data-analysis-with-julia

jlgr Reference¶

This module offers a simple, matlab-style API built on top of the GR package.

Output Functions¶

Line Plots¶

function (args::PlotArg...; kv...)¶

Draw one or more line plots.

This function can receive one or more of the following:

  • x values and y values, or

  • x values and a callable to determine y values, or

  • y values only, with their indices as x values

Parameters

args – the data to plot

Usage examples:

julia> # Create example data julia> x = LinRange(-2, 2, 40) julia> y = 2 .* x .+ 4 julia> # Plot x and y julia> plot(x, y) julia> # Plot x and a callable julia> plot(x, t -> t^3 + t^2 + t) julia> # Plot y, using its indices for the x values julia> plot(y)
_images/plot.png
function (args::PlotArg...; kv...)¶

Draw one or more line plots over another plot.

This function can receive one or more of the following:

  • x values and y values, or

  • x values and a callable to determine y values, or

  • y values only, with their indices as x values

Parameters

args – the data to plot

Usage examples:

julia># Create example datajulia>x=LinRange(-2,2,40)julia>y=2.*x.+4julia># Draw the first plotjulia>plot(x,y)julia># Plot graph over itjulia>oplot(x,x->x^3+x^2+x)
_images/oplot.png
function (args...; kv...)¶

Draw one or more three-dimensional line plots.

Parameters
  • x – the x coordinates to plot

  • y – the y coordinates to plot

  • z – the z coordinates to plot

Usage examples:

julia># Create example datajulia>x=LinRange(0,30,1000)julia>y=cos.(x).*xjulia>z=sin.(x).*xjulia># Plot the pointsjulia>plot3(x,y,z)
_images/plot3.png
function (args...; kv...)¶

Draw one or more polar plots.

This function can receive one or more of the following:

  • angle values and radius values, or

  • angle values and a callable to determine radius values

Parameters

args – the data to plot

Usage examples:

julia># Create example datajulia>angles=LinRange(0,2pi,40)julia>radii=LinRange(0,2,40)julia># Plot angles and radiijulia>polar(angles,radii)julia># Plot angles and a callablejulia>polar(angles,r->cos(r)^2)
_images/polar.png

Scatter Plots¶

function (args...; kv...)¶

Draw one or more scatter plots.

This function can receive one or more of the following:

  • x values and y values, or

  • x values and a callable to determine y values, or

  • y values only, with their indices as x values

Additional to x and y values, you can provide values for the markers’ size and color. Size values will determine the marker size in percent of the regular size, and color values will be used in combination with the current colormap.

Parameters

args – the data to plot

Usage examples:

julia># Create example datajulia>x=LinRange(-2,2,40)julia>y=0.2.*x.+0.4julia># Plot x and yjulia>scatter(x,y)julia># Plot x and a callablejulia>scatter(x,x->0.2*x+0.4)julia># Plot y, using its indices for the x valuesjulia>scatter(y)julia># Plot a diagonal with increasing size and colorjulia>x=LinRange(0,1,11)julia>y=LinRange(0,1,11)julia>s=LinRange(50,400,11)julia>c=LinRange(0,255,11)julia>scatter(x,y,s,c)
_images/scatter.png
function (args...; kv...)¶

Draw one or more three-dimensional scatter plots.

Additional to x, y and z values, you can provide values for the markers’ color. Color values will be used in combination with the current colormap.

Parameters
  • x – the x coordinates to plot

  • y – the y coordinates to plot

  • z – the z coordinates to plot

  • c – the optional color values to plot

Usage examples:

julia># Create example datajulia>x=2.*rand(100).-1julia>y=2.*rand(100).-1julia>z=2.*rand(100).-1julia>c=999.*rand(100).+1julia># Plot the pointsjulia>scatter3(x,y,z)julia># Plot the points with colorsjulia>scatter3(x,y,z,c)
_images/scatter3.png

Stem Plots¶

function (args...; kv...)¶

Draw a stem plot.

This function can receive one or more of the following:

  • x values and y values, or

  • x values and a callable to determine y values, or

  • y values only, with their indices as x values

Parameters

args – the data to plot

Usage examples:

julia># Create example datajulia>x=LinRange(-2,2,40)julia>y=0.2.*x.+0.4julia># Plot x and yjulia>stem(x,y)julia># Plot x and a callablejulia>stem(x,x->x^3+x^2+x+6)julia># Plot y, using its indices for the x valuesjulia>stem(y)
_images/stem.png

Histograms¶

function (x; kv...)¶

Draw a histogram.

If nbins is Nothing or 0, this function computes the number of bins as 3.3 * log10(n) + 1, with n as the number of elements in x, otherwise the given number of bins is used for the histogram.

Parameters
  • x – the values to draw as histogram

  • num_bins – the number of bins in the histogram

Usage examples:

julia># Create example datajulia>x=2.*rand(100).-1julia># Draw the histogramjulia>histogram(x)julia># Draw the histogram with 19 binsjulia>histogram(x,nbins=19)
_images/histogram1.png
function (args...; kv...)¶

Draw a hexagon binning plot.

This function uses hexagonal binning and the the current colormap to display a series of points. It can receive one or more of the following:

  • x values and y values, or

  • x values and a callable to determine y values, or

  • y values only, with their indices as x values

Parameters

args – the data to plot

Usage examples:

julia># Create example datajulia>x=randn(100000)julia>y=randn(100000)julia># Draw the hexbin plotjulia>hexbin(x,y)
_images/hexbin.png

Contour Plots¶

function (args...; kv...)¶

Draw a contour plot.

This function uses the current colormap to display a either a series of points or a two-dimensional array as a contour plot. It can receive one or more of the following:

  • x values, y values and z values, or

  • M x values, N y values and z values on a NxM grid, or

  • M x values, N y values and a callable to determine z values

If a series of points is passed to this function, their values will be interpolated on a grid. For grid points outside the convex hull of the provided points, a value of 0 will be used.

Parameters

args – the data to plot

Usage examples:

julia># Create example point datajulia>x=8.*rand(100).-4julia>y=8.*rand(100).-4julia>z=sin.(x).+cos.(y)julia># Draw the contour plotjulia>contour(x,y,z)julia># Create example grid datajulia>x=LinRange(-2,2,40)julia>y=LinRange(0,pi,20)julia>z=sin.(x').+cos.(y)julia># Draw the contour plotjulia>contour(x,y,z)julia># Draw the contour plot using a callablejulia>contour(x,y,(x,y)->sin(x)+cos(y))
_images/contour1.png
function (args...; kv...)¶

Draw a filled contour plot.

This function uses the current colormap to display a either a series of points or a two-dimensional array as a filled contour plot. It can receive one or more of the following:

  • x values, y values and z values, or

  • M x values, N y values and z values on a NxM grid, or

  • M x values, N y values and a callable to determine z values

If a series of points is passed to this function, their values will be interpolated on a grid. For grid points outside the convex hull of the provided points, a value of 0 will be used.

Parameters

args – the data to plot

Usage examples:

julia># Create example point datajulia>x=8.*rand(100).-4julia>y=8.*rand(100).-4julia>z=sin.(x).+cos.(y)julia># Draw the contour plotjulia>contourf(x,y,z)julia># Create example grid datajulia>x=LinRange(-2,2,40)julia>y=LinRange(0,pi,20)julia>z=sin.(x').+cos.(y)julia># Draw the contour plotjulia>contourf(x,y,z)julia># Draw the contour plot using a callablejulia>contourf(x,y,(x,y)->sin(x)+cos(y))
_images/contourf.png
function (args...; kv...)¶

Draw a triangular contour plot.

This function uses the current colormap to display a series of points as a triangular contour plot. It will use a Delaunay triangulation to interpolate the z values between x and y values. If the series of points is concave, this can lead to interpolation artifacts on the edges of the plot, as the interpolation may occur in very acute triangles.

Parameters
  • x – the x coordinates to plot

  • y – the y coordinates to plot

  • z – the z coordinates to plot

Usage examples:

julia># Create example point datajulia>x=8.*rand(100).-4julia>y=8.*rand(100).-4julia>z=sin.(x)+cos.(y)julia># Draw the triangular contour plotjulia>tricont(x,y,z)
_images/tricont.png

Surface Plots¶

function (args...; kv...)¶

Draw a three-dimensional surface plot.

This function uses the current colormap to display a either a series of points or a two-dimensional array as a surface plot. It can receive one or more of the following:

  • x values, y values and z values, or

  • M x values, N y values and z values on a NxM grid, or

  • M x values, N y values and a callable to determine z values

If a series of points is passed to this function, their values will be interpolated on a grid. For grid points outside the convex hull of the provided points, a value of 0 will be used.

Parameters

args – the data to plot

Usage examples:

julia># Create example point datajulia>x=8.*rand(100).-4julia>y=8.*rand(100).-4julia>z=sin.(x).+cos.(y)julia># Draw the surface plotjulia>surface(x,y,z)julia># Create example grid datajulia>x=LinRange(-2,2,40)julia>y=LinRange(0,pi,20)julia>z=sin.(x').+cos.(y)julia># Draw the surface plotjulia>surface(x,y,z)julia># Draw the surface plot using a callablejulia>surface(x,y,(x,y)->sin(x)+cos(y))
_images/surface.png
function (args...; kv...)¶

Draw a triangular surface plot.

This function uses the current colormap to display a series of points as a triangular surface plot. It will use a Delaunay triangulation to interpolate the z values between x and y values. If the series of points is concave, this can lead to interpolation artifacts on the edges of the plot, as the interpolation may occur in very acute triangles.

Parameters
  • x – the x coordinates to plot

  • y – the y coordinates to plot

  • z – the z coordinates to plot

Usage examples:

julia># Create example point datajulia>x=8.*rand(100).-4julia>y=8.*rand(100).-4julia>z=sin.(x).+cos.(y)julia># Draw the triangular surface plotjulia>trisurf(x,y,z)
_images/trisurf.png
function (args...; kv...)¶

Draw a three-dimensional wireframe plot.

This function uses the current colormap to display a either a series of points or a two-dimensional array as a wireframe plot. It can receive one or more of the following:

  • x values, y values and z values, or

  • M x values, N y values and z values on a NxM grid, or

  • M x values, N y values and a callable to determine z values

If a series of points is passed to this function, their values will be interpolated on a grid. For grid points outside the convex hull of the provided points, a value of 0 will be used.

Parameters

args – the data to plot

Usage examples:

julia># Create example point datajulia>x=8.*rand(100).-4julia>y=8.*rand(100).-4julia>z=sin.(x).+cos.(y)julia># Draw the wireframe plotjulia>wireframe(x,y,z)julia># Create example grid datajulia>x=LinRange(-2,2,40)julia>y=LinRange(0,pi,20)julia>z=sin.(x').+cos.(y)julia># Draw the wireframe plotjulia>wireframe(x,y,z)julia># Draw the wireframe plot using a callablejulia>wireframe(x,y,(x,y)->sin(x)+cos(y))
_images/wireframe.png

Heatmaps¶

function (D; kv...)¶

Draw a heatmap.

This function uses the current colormap to display a two-dimensional array as a heatmap. The array is drawn with its first value in the bottom left corner, so in some cases it may be neccessary to flip the columns (see the example below).

By default the function will use the column and row indices for the x- and y-axes, respectively, so setting the axis limits is recommended. Also note that the values in the array must lie within the current z-axis limits so it may be neccessary to adjust these limits or clip the range of array values.

Parameters

data – the heatmap data

Usage examples:

julia># Create example datajulia>x=LinRange(-2,2,40)julia>y=LinRange(0,pi,20)julia>z=sin.(x').+cos.(y)julia># Draw the heatmapjulia>heatmap(z)
function (x, y, z; kv...)¶
_images/heatmap.png

Images¶

function (I; kv...)¶

Draw an image.

This function can draw an image either from reading a file or using a two-dimensional array and the current colormap.

Parameters

image – an image file name or two-dimensional array

Usage examples:

julia># Create example datajulia>x=LinRange(-2,2,40)julia>y=LinRange(0,pi,20)julia>z=sin.(x').+cos.(y)julia># Draw an image from a 2d arrayjulia>imshow(z)julia># Draw an image from a filejulia>imshow("example.png")
_images/imshow.png

Isosurfaces¶

function (V; kv...)¶

Draw an isosurface.

This function can draw an image either from reading a file or using a two-dimensional array and the current colormap. Values greater than the isovalue will be seen as outside the isosurface, while values less than the isovalue will be seen as inside the isosurface.

Parameters
  • v – the volume data

  • isovalue – the isovalue

Usage examples:

julia># Create example datajulia>s=LinRange(-1,1,40)julia>v=1.-(s.^2.+(s.^2)'.+reshape(s,1,1,:).^2).^0.5julia># Draw an image from a 2d arrayjulia>isosurface(v,isovalue=0.2)
_images/isosurface.png

Attribute Functions¶

function (s

Set the plot title.

The plot title is drawn using the extended text function GR.textext. You can use a subset of LaTeX math syntax, but will need to escape certain characters, e.g. parentheses. For more information see the documentation of GR.textext.

Parameters

title – the plot title

Usage examples:

julia># Set the plot title to "Example Plot"julia>title("Example Plot")julia># Clear the plot titlejulia>title("")
function (args::AbstractString...; kv...)¶

Set the legend of the plot.

The plot legend is drawn using the extended text function GR.textext. You can use a subset of LaTeX math syntax, but will need to escape certain characters, e.g. parentheses. For more information see the documentation of GR.textext.

Parameters

args – The legend strings

Usage examples:

julia># Set the legends to "a" and "b"julia>legend("a","b")
function (s

Set the x-axis label.

The axis labels are drawn using the extended text function GR.textext. You can use a subset of LaTeX math syntax, but will need to escape certain characters, e.g. parentheses. For more information see the documentation of GR.textext.

Parameters

x_label – the x-axis label

Usage examples:

julia># Set the x-axis label to "x"julia>xlabel("x")julia># Clear the x-axis labeljulia>xlabel("")
function (s

Set the y-axis label.

The axis labels are drawn using the extended text function GR.textext. You can use a subset of LaTeX math syntax, but will need to escape certain characters, e.g. parentheses. For more information see the documentation of GR.textext.

Parameters

y_label – the y-axis label

function ()¶

Control Functions¶

function (; kv...)¶

Create a new figure with the given settings.

Settings like the current colormap, title or axis limits as stored in the current figure. This function creates a new figure, restores the default settings and applies any settings passed to the function as keyword arguments.

Usage examples:

julia># Restore all default settingsjulia>figure()julia># Restore all default settings and set the titlejulia>figure(title="Example Figure")
function (nr, nc, p

Set current subplot index.

By default, the current plot will cover the whole window. To display more than one plot, the window can be split into a number of rows and columns, with the current plot covering one or more cells in the resulting grid.

Subplot indices are one-based and start at the upper left corner, with a new row starting after every num_columns subplots.

Parameters
  • num_rows – the number of subplot rows

  • num_columns – the number of subplot columns

  • subplot_indices

- the subplot index to be used by the current plot - a pair of subplot indices, setting which subplots should be covered by the current plot

Usage examples:

julia># Set the current plot to the second subplot in a 2x3 gridjulia>subplot(2,3,2)julia># Set the current plot to cover the first two rows of a 4x2 gridjulia>subplot(4,2,(1,4))julia># Use the full window for the current plotjulia>subplot(1,1,1)
function (filename; kv...)¶

Save the current figure to a file.

This function draw the current figure using one of GR’s workstation types to create a file of the given name. Which file types are supported depends on the installed workstation types, but GR usually is built with support for .png, .jpg, .pdf, .ps, .gif and various other file formats.

Parameters

filename – the filename the figure should be saved to

Usage examples:

julia># Create a simple plotjulia>x=1:100julia>plot(x,1./(x.+1))julia># Save the figure to a filejulia>savefig("example.png")
function (flag

Set the hold flag for combining multiple plots.

The hold flag prevents drawing of axes and clearing of previous plots, so that the next plot will be drawn on top of the previous one.

Parameters

flag – the value of the hold flag

Usage examples:

julia># Create example datajulia>x=LinRange(0,1,100)julia># Draw the first plotjulia>plot(x,x.^2)julia># Set the hold flagjulia>hold(true)julia># Draw additional plotsjulia>plot(x,x.^4)julia>plot(x,x.^8)julia># Reset the hold flagjulia>hold(false)

Hosted by PGI-JCNS-TA
Sours: https://gr-framework.org/julia-jlgr.html
  1. Skullcandy replacement cable
  2. Etsy outdoor mats
  3. Tangled dress pattern

tbreloff/Plots.jl

Hi guys :wave: I just recently started using and my experience is mixed so far. Hope I can help out in some way :pray:

In particular, I like to plot everything as I'm coding (habit harking back to Matlab days), so I am constantly edited and plotting. I am also using and I suspect there may be some issues with the interplay, but not sure.

In my function, I am calling etc repeatedly using the backend on Windows (Julia v0.6.2).

The first couple of times, it worked, but then it just stopped plotting with no error messages or anything. Just no plots happening.

Even closing the REPL has no impact, so I started calling directly from the REPL. This again worked the first couple times, but then mysterious stops. No error messages. Nothing.

Then I back up and instead of , I try just and it works. Then I add the next plot back and it works. I then got back to all working from the REPL. Kind of strange.

Then, even these plots stopped working altogether and now even after rebooting, I cannot get with to work reliably.

Is this a known issue? Given the nature of thing just mysteriously stop working, I think it will be impossible for me to find a repeatable example.

Sours: https://gitter.im/tbreloff/Plots.jl?at=5a4e19e768d092bb622219ae
JuliaCon 2016 - Plots with Plots.jl (Workshop) - Tom Breloff

Some Visualization Libraries to Choose From

A quick reference on the many options to visualize data with Julia.

by Martin D. Maas, Ph.D

@MartinDMaas

Last updated: 2021-08-02

There are multiple plotting packages for Julia worth checking:

Detailed documentation can be found in each package, and in the referenced tutorials and examples pages.

To keep this tutorial series as much as self-contained as reasonably possible, let’s go over a few examples here:

Plotting a Function with Plots.jl

Julia Line Plot

Displaying a Pseudocolor Plot of a 2D Array

One way of doing a 2d pseudocolor plot with Julia is to use the ‘heatmap’ function.

Julia Heatmap

Calling Matplotlib’s PyPlot with PyPlot.jl

Alternatively, we could also use the PyPlot package, which provides a direct interface to Matplotlib’s Pyplot via PyCall, namely to the matplotlib.pyplot module.

For example, the above example can be modified as follows:

to produce the following plot:

Julia Pseudolocor Plot

Note that using both PyPlot and Plots could result in errors, so native Julia libraries should be preferred.

Sours: https://www.matecdev.com/posts/julia-plotting.html

Heatmap julia plots

“how to plot heatmap for a given matrix in python” Code Answer





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Sours: https://www.codegrepper.com/code-examples/python/how+to+plot+heatmap+for+a+given+matrix+in+python
Introduction to plots in Julia

Plotting Thematic Maps using Shapefiles in Julia

To keep things organized, we will create some directories in our project environment.

For mapping actual values to colors, we need to normalize those values. Here we create a function to normalize a vector to values between 0 and 1.

We will download the shapefiles to our directory.

The shapefiles came down zipped. So we will unzip them to the directory before we can read them.

Now they are unzipped, we can read the shapefiles. This is done in a few steps:

  1. Read the data table that came with the shapefile into a dataframe;
  2. Add the municipality shapes to the dataframe;
  3. Select only those shapes that represent land (not water).

Now we are going to download data on the number of Covid-19 cases per municipality per day to our directory.

Reading the data into a dataframe is pretty straightforward.

The dataframe contains data for multiple days. For our plot we are only interested in the data for the most recent day. And we select only those rows for which a municipality is known.

Because some municipalities have more than one data point for a day, we will sum those values.

Now we have the municipality shapes and data in one dataframe and the Covid-19 data in a separate dataframe, we will join them together.

For a meaningful plot we not only need the cases for a day per municipality, but also the population per municipality (variable ). Based on those variables we can calculate the number of Covid-19 cases per 100 000 inhabitants.

We need to normalize the calculated values before we van convert them to colors bases on a gradient colormap. For our plot we will use the colormap because our plot is basically a geospatial heatmap.

Other nice colormaps your can experiment with are , , , , , , , and .

After all data preparation is done, plotting the thematic map is easy.

I’m planning to work on a Julia package for plotting thematic maps like the Python package to simplify things. As afar as I know there are no Julia equivalents for . The package — which I love — does has support for the format but not for shapefiles. An other option is to use the from the package. Let me know your thoughts.

Sours: https://towardsdatascience.com/plotting-thematic-maps-using-shapefiles-in-julia-6a926ef77721

You will also like:

StatsPlots

Build Statusproject chat

Original author: Thomas Breloff (@tbreloff), maintained by the JuliaPlots members

This package is a drop-in replacement for Plots.jl that contains many statistical recipes for concepts and types introduced in the JuliaStats organization.

It is thus slightly less lightweight, but has more functionality. Main documentation is found in the Plots.jl documentation (https://juliaplots.github.io).

Initialize:

#]add StatsPlots # install the package if it isn't installedusing StatsPlots # no need for `using Plots` as that is reexported heregr(size=(400,300))

Table-like data structures, including , , , etc... (see here for an exhaustive list), are supported thanks to the macro which allows passing columns as symbols. Those columns can then be manipulated inside the call, like normal :

using DataFrames, IndexedTables df =DataFrame(a =1:10, b =10.*rand(10), c =10.*rand(10)) @df df plot(:a, [:b:c], colour = [:red:blue]) @df df scatter(:a, :b, markersize =4.*log.(:c.+0.1)) t =table(1:10, rand(10), names = [:a, :b]) # [email protected] t scatter(2.*:b)

Inside a macro call, the utility function can be used to refer to a range of columns:

@df df plot(:a, cols(2:3), colour = [:red:blue])

or to refer to a column whose symbol is represented by a variable:

s =:[email protected] df plot(:a, cols(s))

will refer to all columns of the data table.

In case of ambiguity, symbols not referring to columns must be escaped by :

df[:red] =rand(10) @df df plot(:a, [:b:c], colour =^([:red:blue]))

The macro plays nicely with the new syntax of the Query.jl data manipulation package (v0.8 and above), in that a plot command can be added at the end of a query pipeline, without having to explicitly collect the outcome of the query first:

using Query, StatsPlots df |>@filter(_.a >5) |>@map({_.b, d = _.c-10}) |>@dfscatter(:b, :d)

The syntax is also compatible with the Plots.jl grouping machinery:

using RDatasets school = RDatasets.dataset("mlmRev","Hsb82") @df school density(:MAch, group =:Sx)

To group by more than one column, use a tuple of symbols:

@df school density(:MAch, group = (:Sx, :Sector), legend =:topleft)

grouped

To name the legend entries with custom or automatic names (i.e. ) use the curly bracket syntax . Entries with get the custom name you give, whereas entries without take the name of the column.


The old syntax, passing the as the first argument to the call is no longer supported.


Visualizing a table interactively

A GUI based on the Interact package is available to create plots from a table interactively, using any of the recipes defined below. This small app can be deployed in a Jupyter lab / notebook, Juno plot pane, a Blink window or in the browser, see here for instructions.

import RDatasets iris = RDatasets.dataset("datasets", "iris") using StatsPlots, Interact using Blink w =Window() body!(w, dataviewer(iris))

dataviewer

marginalhist with DataFrames

using RDatasets iris =dataset("datasets","iris") @df iris marginalhist(:PetalLength, :PetalWidth)

marginalhist


marginalscatter with DataFrames

using RDatasets iris =dataset("datasets","iris") @df iris marginalscatter(:PetalLength, :PetalWidth)

marginalscatter


marginalkde

x =randn(1024) y =randn(1024) marginalkde(x, x+y)

correlated-marg

  • can be used to set the number of contour levels (default 10); levels are evenly-spaced in the cumulative probability mass.
  • (default ) can be used to adjust the bounds of the plot. Clip values are expressed as multiples of the and percentiles of the underlying 1D distributions (these would be 1-sigma ranges for a Gaussian).

corrplot and cornerplot

This plot type shows the correlation among input variables. The marker color in scatter plots reveal the degree of correlation. Pass the desired colorgradient to . With the default gradient positive correlations are blue, neutral are yellow and negative are red. In the 2d-histograms the color gradient show the frequency of points in that bin (as usual controlled by ).

then

@df iris corrplot([:SepalLength:SepalWidth:PetalLength:PetalWidth], grid =false)

or also:

@df iris corrplot(cols(1:4), grid =false)

corrplot

A correlation plot may also be produced from a matrix:

M =randn(1000,4) M[:,2] .+=0.8sqrt.(abs.(M[:,1])) .-0.5M[:,3] .+5 M[:,3] .-=0.7M[:,1].^2.+2corrplot(M, label = ["x$i"for i=1:4])

cornerplot(M, compact=true)


boxplot, dotplot, and violin

import RDatasets singers = RDatasets.dataset("lattice", "singer") @df singers violin(string.(:VoicePart), :Height, linewidth=0) @df singers boxplot!(string.(:VoicePart), :Height, fillalpha=0.75, linewidth=2) @df singers dotplot!(string.(:VoicePart), :Height, marker=(:black, stroke(0)))

violin

Asymmetric violin or dot plots can be created using the keyword ( - default, or ), e.g.:

singers_moscow =deepcopy(singers) singers_moscow[:Height] = singers_moscow[:Height] [email protected] singers violin(string.(:VoicePart), :Height, side=:right, linewidth=0, label="Scala") @df singers_moscow violin!(string.(:VoicePart), :Height, side=:left, linewidth=0, label="Moscow") @df singers dotplot!(string.(:VoicePart), :Height, side=:right, marker=(:black,stroke(0)), label="") @df singers_moscow dotplot!(string.(:VoicePart), :Height, side=:left, marker=(:black,stroke(0)), label="")

Dot plots can spread their dots over the full width of their column , or restricted to the kernel density (i.e. width of violin plot) with (default). Horizontal position is random, so dots are repositioned each time the plot is recreated. keeps the dots along the center.

violin2


Equal-area histograms

The ea-histogram is an alternative histogram implementation, where every 'box' in the histogram contains the same number of sample points and all boxes have the same area. Areas with a higher density of points thus get higher boxes. This type of histogram shows spikes well, but may oversmooth in the tails. The y axis is not intuitively interpretable.

a = [randn(100); randn(100) .+3; randn(100) ./2.+3] ea_histogram(a, bins =:scott, fillalpha =0.4)

equal area histogram


AndrewsPlot

AndrewsPlots are a way to visualize structure in high-dimensional data by depicting each row of an array or table as a line that varies with the values in columns. https://en.wikipedia.org/wiki/Andrews_plot

using RDatasets iris =dataset("datasets", "iris") @df iris andrewsplot(:Species, cols(1:4), legend =:topleft)

iris_andrews_curve


Distributions

using Distributions plot(Normal(3,5), fill=(0, .5,:orange))

dist =Gamma(2) scatter(dist, leg=false) bar!(dist, func=cdf, alpha=0.3)

Quantile-Quantile plots

The function compares the quantiles of two distributions, and accepts either a vector of sample values or a . The is a shorthand for comparing a distribution to the normal distribution. If the distributions are similar the points will be on a straight line.

x =rand(Normal(), 100) y =rand(Cauchy(), 100) plot( qqplot(x, y, qqline =:fit), # qqplot of two samples, show a fitted regression lineqqplot(Cauchy, y), # compare with a Cauchy distribution fitted to y; pass an instance (e.g. Normal(0,1)) to compare with a specific distributionqqnorm(x, qqline =:R) # the :R default line passes through the 1st and 3rd quartiles of the distribution )

skaermbillede 2017-09-28 kl 22 46 28

Grouped Bar plots

groupedbar(rand(10,3), bar_position =:stack, bar_width=0.7)

tmp

This is the default:

groupedbar(rand(10,3), bar_position =:dodge, bar_width=0.7)

tmp

The syntax is also possible in combination with :

ctg =repeat(["Category 1", "Category 2"], inner =5) nam =repeat("G".*string.(1:5), outer =2) groupedbar(nam, rand(5, 2), group = ctg, xlabel ="Groups", ylabel ="Scores", title ="Scores by group and category", bar_width =0.67, lw =0, framestyle =:box)

Grouped Histograms

dodge

stack

Dendrograms

using Clustering D =rand(10, 10) D += D' hc =hclust(D, linkage=:single) plot(hc)

dendrogram

The option in can be used to minimize the distance between neighboring leaves:

using Clustering using Distances using StatsPlots using Random n =40 mat =zeros(Int, n, n) # create banded matrixfor i in1:n last =minimum([i+Int(floor(n/5)), n]) for j in i:last mat[i,j] =1endend# randomize order mat = mat[:, randperm(n)] dm =pairwise(Euclidean(), mat, dims=2) # normal ordering hcl1 =hclust(dm, linkage=:average) plot( plot(hcl1, xticks=false), heatmap(mat[:, hcl1.order], colorbar=false, xticks=(1:n, ["$i"for i in hcl1.order])), layout=grid(2,1, heights=[0.2,0.8]) )

heatmap dendrogram non-optimal

Compare to:

# optimal ordering hcl2 =hclust(dm, linkage=:average, branchorder=:optimal) plot( plot(hcl2, xticks=false), heatmap(mat[:, hcl2.order], colorbar=false, xticks=(1:n, ["$i"for i in hcl2.order])), layout=grid(2,1, heights=[0.2,0.8]) )

heatmap dendrogram optimal

Dendrogram on the right side

using Distances using Clustering using StatsBase using StatsPlots pd=rand(Float64,16,7) dist_col=pairwise(CorrDist(),pd,dims=2) hc_col=hclust(dist_col, branchorder=:optimal) dist_row=pairwise(CorrDist(),pd,dims=1) hc_row=hclust(dist_row, branchorder=:optimal) pdz=similar(pd) for row in hc_row.order pdz[row,hc_col.order]=zscore(pd[row,hc_col.order]) end nrows=length(hc_row.order) rowlabels=(1:16)[hc_row.order] ncols=length(hc_col.order) collabels=(1:7)[hc_col.order] l =grid(2,2,heights=[0.2,0.8,0.2,0.8],widths=[0.8,0.2,0.8,0.2]) plot( layout = l, plot(hc_col,xticks=false), plot(ticks=nothing,border=:none), plot( pdz[hc_row.order,hc_col.order], st=:heatmap, #yticks=(1:nrows,rowlabels), yticks=(1:nrows,rowlabels), xticks=(1:ncols,collabels), xrotation=90, colorbar=false ), plot(hc_row,yticks=false,xrotation=90,orientation=:horizontal) )

heatmap with dendrograms on top and on the right

GroupedErrors.jl for population analysis

Population analysis on a table-like data structures can be done using the highly recommended GroupedErrors package.

This external package, in combination with StatsPlots, greatly simplifies the creation of two types of plots:

1. Subject by subject plot (generally a scatter plot)

Some simple summary statistics are computed for each experimental subject (mean is default but any scalar valued function would do) and then plotted against some other summary statistics, potentially splitting by some categorical experimental variable.

2. Population plot (generally a ribbon plot in continuous case, or bar plot in discrete case)

Some statistical analysis is computed at the single subject level (for example the density/hazard/cumulative of some variable, or the expected value of a variable given another) and the analysis is summarized across subjects (taking for example mean and s.e.m), potentially splitting by some categorical experimental variable.

For more information please refer to the README.

A GUI based on QML and the GR Plots.jl backend to simplify the use of StatsPlots.jl and GroupedErrors.jl even further can be found here (usable but still in alpha stage).

Ordinations

MDS from can be plotted as scatter plots.

using MultivariateStats, RDatasets, StatsPlots iris =dataset("datasets", "iris") X =convert(Matrix, iris[:, 1:4]) M =fit(MDS, X'; maxoutdim=2) plot(M, group=iris.Species)

MDS plot

PCA will be added once the API in MultivariateStats is changed. See https://github.com/JuliaStats/MultivariateStats.jl/issues/109 and https://github.com/JuliaStats/MultivariateStats.jl/issues/95.

Covariance ellipses

A 2×2 covariance matrix can be plotted as an ellipse, which is a contour line of a Gaussian density function with variance .

covariance ellipses

Sours: https://juliapackages.com/p/statplots


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