How to draw several graphics in one picture in Mathematica? - matlab

Just like hold on in Matlab.
I met this problem when i want to draw several lines in one picture.
The number of lines varies.

Mathematica has a lot of constructs allowing you to combine plots, graphics and images.
I'll give you several examples. You can search the help system to find out more and understand the subtleties of the examples bellow:
Edit
If you want to read/write from/to files, the following code may serve you as a starting guide:
(*Create data*)
data = RandomReal[1, {8, 2}];
(*Put into a file*)
Export["c:\\test.tab", data, "Table"];
(*Read the file into another list*)
rdat = Import["c:\\test.tab", "Table"];
(*And Plot it like before*)
Graphics[{Line##, Red, PointSize[Large], Point /# #} &#rdat]

Mathematica 8 introduced a new versatile function Overlay, which can be used to graphically overlay any type of expression:
Overlay[{Graphics[{Yellow, Disk[]}], "Sun"}]

Use Show to combine graphics objects.
Show[Plot[Sin[x],{x,0,10}], Plot[Cos[x],{x,0,10}]]
EDIT If you want to draw several lines, then build your Graphics object out of several lines:
Graphics[ Table[ Line[{{0,0}, {Cos[x],Sin[x]}}], {x,0,Pi,Pi/10} ] ]

combine graphics primitives like Szabolcs said:
Graphics[ Table[ Line[{{0,0}, {Cos[x],Sin[x]}}], {x,0,Pi,Pi/10} ] ]
but if you are using plot then what you need to do is:
Show[Table[Plot[A Sin[x],{x,0,2 Pi}],{A,0.1,10}]]
Show command allows you to combine the graphics Table produces varying A, each one of them a Plot over x.

Related

How to add title to graph_tool plot?

I'm using graph_tool to draw some graphs, and I don't see an obvious way to add a title to the output image.
If it is possible, how do I add a title?
The code I have right now draws a nice-looking graph, and I have added annotations to the vertices. But I haven't found a way to annotate the graph as a whole (like a title).
import graph_tool as gt
def draw_graph(g:gt.Graph):
ebet = gt.centrality.betweenness(g)[1]
pos = gt.draw.arf_layout(g)
gt.draw.graph_draw(
g,
pos=pos,
vertex_text=g.vertex_index,
edge_color=ebet,
vertex_size=gt.draw.prop_to_size(g.vertex_properties['size'], ma=50,log=False, power=1),
# vertex_fill_color=g.vertex_properties['size'],
output='tiny.pdf')
Graph-tool is not a full-fledged plot library, it focuses only on drawing graphs. To display titles, axes, legends, etc, it should be used together with matplotlib, as explained here: https://graph-tool.skewed.de/static/doc/demos/matplotlib/matplotlib.html

add simple geometric elements to GUIDE GUI

I am desiging a simple GUI application in Matlab using GUIDE.
I am displayed a number of axis - and I would like to add some simple design elements to make the interface clearer. I would like to draw a colored rectangle around an axis (seperate from the axis)... there are two such axes, each displaying details of some things shown in a third plot, and I would like this color clue to link the details to the overview.
So is it possible to add simple geometric shape objects to a Matlab GUI? I don't see anything but controls in GUIDE but perhaps its possible to add them manually with an explicit command?
It is generally difficult to draw any random shape. Except Square & rectangle, for which you can create panels and change the properties like BorderWidth and HighlightColor.
Since MATLAB GUI is based on Java, you can create any object in MATLAB GUI which can be created in Java. You can refer to this website [1] for further learning.
[1] http://undocumentedmatlab.com/matlab-java-book/

How to visualize correlation matrix as a schemaball in Matlab

I have 42 variables and I have calculated the correlation matrix for them in Matlab. Now I would like to visualize it with a schemaball. Does anyone have any suggestions / experiences how this could be done in Matlab? The following pictures will explain my point better:
In the pictures each parabola between variables would mean the strength of correlation between them. The thicker the line is, the more correlation. I prefer the style of picture 1 more than the style in picture 2 where I have used different colors to highlight the strength of correlation.
Kinda finished I guess.. code can be found here at github.
Documentation is included in the file.
The yellow/magenta color (for positive/negative correlation) is configurable, as well as the fontsize of the labels and the angles at which the labels are plotted, so you can get fancy if you want and not distribute them evenly along the perimeter/group some/...
If you want to actually print these graphs or use them outside matlab, I suggest using vector formats (eg eps). It's also annoying that the text resizes when you zoom in/out, but I don't know of any way to fix that without hacking the zoom function :/
schemaball % demo
schemaball(arrayfun(#num2str,1:10,'uni',false), rand(10).^8,11,[0.1587 0.8750],[0.8333 1],2*pi*sin(linspace(0,pi/2-pi/20,10)))
schemaball(arrayfun(#num2str,1:50,'uni',false), rand(50).^50,9)
I finished and submitted my version to the FEX: schemaball and will update the link asap.
There are a some differences with Gunther Struyf's contribution:
You can return the handles to the graphic object for full manual customization
Labels are oriented to allow maximum left-to-rigth readability
The figure stretches to fit labels in, leaving the axes unchanged
Syntax requires only correlations matrix (but allows optional inputs)
Optimized for performance.
Follow examples of demo, custom labels and creative customization.
Note: the first figure was exported with saveas(), all others with export_fig.
schemaball
x = rand(10).^3;
x(:,3) = 1.3*mean(x,2);
schemaball(x, {'Hi','how','is','your','day?', 'Do','you','like','schemaballs?','NO!!'})
h = schemaball;
set(h.l(~isnan(h.l)), 'LineWidth',1.2)
set(h.s, 'MarkerEdgeColor','red','LineWidth',2,'SizeData',100)
set(h.t, 'EdgeColor','white','LineWidth',1)
The default colormap:
To improve on screen rendering you can launch MATLAB with the experimental -hgVersion 2 switch which produces anti/aliased graphics by default now (source: HG2 update | Undocumented Matlab). However, if you try to save the figure, the file will have the usual old anti-aliased rendering, so here's a printscreen image of Gunther's schemaball:
Important update:
You can do this in Matlab now with the FileExchange submission:
http://www.mathworks.com/matlabcentral/fileexchange/48576-circulargraph
There is an exmample by Matlab in here:
http://uk.mathworks.com/examples/matlab/3859-circular-graph-examples
Which gives this kind of beautiful plots:
Coincidentally, Cleve Moler (MathWorks Chief Mathematician) showed an example of just this sort of plot on his most recent blog post (not nearly as beautiful as the ones in your example, and the connecting lines are straight rather than parabolic, but it looks functional). Unfortunately he didn't include the code directly, but if you leave him a comment on the post he's usually very willing to share things.
What might be even nicer for you is that he also applies (and this time includes) code to permute the rows/columns of the array in order to maximize the spatial proximity of highly connected nodes, rather than randomly ordering them around the circumference. You end up with a 'crescent'-shaped envelope of connecting lines, with the thick bit of the crescent representing the most highly connected nodes.
Unfortunately however, I suspect that if you need to enhance his code to get the very narrow, high-resolution lines in your example plots, then MATLAB's currently non-anti-aliased graphics aren't quite up to it yet.
I've recently been experimenting with MATLAB data and the D3 visualization library for similar graphs - there are several related types of circular visualizations you may be interested in and many of them are interactive. Another helpful, well-baked, and freely available option is Circos which is probably responsible for most of the prettier versions of these graphs you've seen in popular press.

Perl - Ratio of homogeneous areas of an image

I would like to check whether an image has a lot of homogeneous areas. Therefore I would like to get some kind of value of an image that declares a ratio for images depending on the amount/size of homogeneous areas (e.g. that value could have a range from 0 to 5).
Instead of a value there could be some kind of classification as well.
[many homogeneous areas -> value/class 5 ; few homogeneous areas -> value/class 0]
I would like to do that in perl. Is there a package/function or something like that?
What you want seems to be an area of image processing research which I am not familiar with. However, GraphicsMagick's mogrify utility has a -segment option:
Use -segment to segment an image by analyzing the histograms of the color components and identifying units that are homogeneous with the fuzzy c-means technique. The scale-space filter analyzes the histograms of the three color components of the image and identifies a set of classes. The extents of each class is used to coarsely segment the image with thresholding. The color associated with each class is determined by the mean color of all pixels within the extents of a particular class. Finally, any unclassified pixels are assigned to the closest class with the fuzzy c-means technique.
I don't know if this is any use to you. You might have to hit the library on this one, and read some research. You do have access to this through PerlMagick as well. However, it does not look like it gives access to the internals, but just produces an image based on parameters.
In my tests (without really understanding what the parameters do), photos turned entirely black, whereas PNG images with large areas of similar colors were reduced to a sort of an average color. Whether you can use that fact to develop a measure is an open question I am not going to investigate ;-)

Using imtophat in MATLAB

I'm trying to do top hat filtering in MATLAB. The imtophat function looks promising, but I have no idea how to use it. I don't have a lot of work with MATLAB before. I am trying to look find basically small spots several pixels wide that are local maxima in my 2 dimensional array.
I think you have more problem undertanding how to use STREL, than IMTOPHAT. The later can be described as simple threshold but per structural element, not the whole image.
Here is another good examples of using STREL and IMTOPHAT:
http://www.mathworks.com/matlabcentral/fx_files/2573/1/content/html/R14_MicroarrayImage_CaseStudy.html
This series of posts on Steve Eddins blog might be useful for you:
http://blogs.mathworks.com/steve/category/dilation-algorithms/
tophat is basically an "opening" procedure followed by a subtraction of the result from the original image. the best and most helpful explanation of opening I've found here:
http://homepages.inf.ed.ac.uk/rbf/HIPR2/morops.htm
"The effect of opening can be quite easily visualized. Imagine taking
the structuring element and sliding it around inside each foreground
region, without changing its orientation. All pixels which can be
covered by the structuring element with the structuring element being
entirely within the foreground region will be preserved. However, all
foreground pixels which cannot be reached by the structuring element
without parts of it moving out of the foreground region will be eroded
away."
The documentation on imtophat has an example .. did you try it? The following images are from the MATLAB documentation.
Code
I = imread('rice.png');
imshow(I)
se = strel('disk',12);
J = imtophat(I,se);
figure, imshow(J,[])
Original
(image source: mathworks.com)
Top Hat with a disk structuring element
(image source: mathworks.com)