Given scatter data, or a matrix, I would like to generate a nice plot such as the one shown below, with all 3 histograms and a colored matrix. I'm specifically interested in the diagonal histogram, which ideally, would correspond to the diagonals of a matrix:
Source figure: www.med.upenn.edu/mulab/jpst.html
The existing command scatterhist is not that powerful to generate this type of graph. Any ideas?
Thanks!
EDIT:
Following #Cris Luengo's hints, I came up with the following code which does some first work at the inclined histogram: WORK IN PROGRESS (HELP WELCOME)!!
b = [0 1 2 3 4 5 6 7 8 9 10];
h = [0.33477 0.40166 0.20134 0.053451 0.008112 0.000643 2.7e-05 0 0 0 0];
wid = 0.25; bb = sort([b-wid b-wid b+wid b+wid]);
kk = [zeros(numel(h),1) h(:) h(:) zeros(numel(h),1)];
kk = reshape(kk',[1,numel(kk)]);
pp=patch(bb,kk,'b');axis([-.5 5 0 .5])
set(gca,'CameraUpVector',[-1,.08,0]);axis square
EDIT 2: Using rotation
phi = pi/4;
R = [cos(phi),-sin(phi);sin(phi),cos(phi)];
rr = [bb' kk'] * R;
bb = rr(:,1); kk = rr(:,2);
patch(bb,kk,'b'); axis([-.5 3 -4 .5])
Here is a recipe to plot the diagonal histogram, if you can do that I’m sure you can figure out the rest too.
Compute the histogram, the bin counts are h, the bin centers are b.
Build a coordinate matrix, attaching the coordinates of a point on the x-axis at the left and right ends of the histogram:
coords = [b(:),h(:)];
coords = [coord;b(end),0;b(1),0];
Using patch you can now plot the histogram as follows:
patch(coords(1,:),coords(2,:));
To plot a rotated histogram you can simply multiply the coords matrix with a rotation matrix, before using patch:
phi = pi/4;
R = [cos(phi),-sin(phi);sin(phi),cos(phi)];
coords = R * coords;
You might need to shift the plot to place it at the right location w.r.t. the other elements.
I recommend that you place all these graphic elements in the same axes object; you can set the axes’ visibility to 'off' so that it works only as a canvas for the other elements.
It will be a bit of work to get everything placed as in the plot you show, but none of it is difficult. Use the low-level image, line,patch and text to place those types of elements, don’t try to use the higher-level plotting functions such as plot, they don’t provide any benefits over the low-level ones in this case.
Related
I want to make a figure in MATLAB as described in the following image
What I did is the following:
x = [1 2 3];
y = [2 2 4];
radius = [1 1.2 2.2];
theta = [-pi 0 pi];
figure;
scatter(x,y,radius)
How do I add an angle theta to the plot to represent a complex number z = radius.*exp(1j*theta) at every spacial coordinates?
Technically speaking, those are only circles if x and y axes are scaled equally. That is because scatter always plots circles, independently of the scales (and they remain circles if you zoom in nonuniformly. + you have the problem with the line, which should indicate the angle...
You can solve both issues by drawing the circles:
function plotCirc(x,y,r,theta)
% calculate "points" where you want to draw approximate a circle
ang = 0:0.01:2*pi+.01;
xp = r*cos(ang);
yp = r*sin(ang);
% calculate start and end point to indicate the angle (starting at math=0, i.e. right, horizontal)
xt = x + [0 r*sin(theta)];
yt = y + [0 r*cos(theta)];
% plot with color: b-blue
plot(x+xp,y+yp,'b', xt,yt,'b');
end
having this little function, you can call it to draw as many circles as you want
x = [1 2 3];
y = [2 2 4];
radius = [1 1.2 2.2];
theta = [-pi 0 pi];
figure
hold on
for i = 1:length(x)
plotCirc(x(i),y(i),radius(i),theta(i))
end
I went back over scatter again, and it looks like you can't get that directly from the function. Hopefully there's a clean built-in way to do this, and someone else will chime in with it, but as a backup plan, you can just add the lines yourself.
You'd want a number of lines that's the same as the length of your coordinate set, from the center point to the edge at the target angle, and fortunately 'line' does multiple lines if you feed it a matrix.
You could just tack this on to the end of your code to get the angled line:
x_lines = [x; x + radius.*cos(theta)];
y_lines = [y; y + radius.*sin(theta)];
line(x_lines, y_lines, 'Color', 'b')
I had to assign the color specifically, since otherwise 'line' makes each new line cycle through the default colors, but that also means you could easily change the line color to stand out more. There's also no center dot, but that'd just be a second scatter plot with tiny radius. Should plot most of what you're looking for, at least.
(My version of Matlab is old enough that scatter behaves differently, so I can only check the line part, but they have the right length and location.)
Edit: Other answer makes a good point on whether scatter is appropriate here. Probably better to draw the circle too.
MATLAB's surf command allows you to pass it optional X and Y data that specify non-cartesian x-y components. (they essentially change the basis vectors). I desire to pass similar arguments to a function that will draw a line.
How do I plot a line using a non-cartesian coordinate system?
My apologies if my terminology is a little off. This still might technically be a cartesian space but it wouldn't be square in the sense that one unit in the x-direction is orthogonal to one unit in the y-direction. If you can correct my terminology, I would really appreciate it!
EDIT:
Below better demonstrates what I mean:
The commands:
datA=1:10;
datB=1:10;
X=cosd(8*datA)'*datB;
Y=datA'*log10(datB*3);
Z=ones(size(datA'))*cosd(datB);
XX=X./(1+Z);
YY=Y./(1+Z);
surf(XX,YY,eye(10)); view([0 0 1])
produces the following graph:
Here, the X and Y dimensions are not orthogonal nor equi-spaced. One unit in x could correspond to 5 cm in the x direction but the next one unit in x could correspond to 2 cm in the x direction + 1 cm in the y direction. I desire to replicate this functionality but drawing a line instead of a surf For instance, I'm looking for a function where:
straightLine=[(1:10)' (1:10)'];
my_line(XX,YY,straightLine(:,1),straightLine(:,2))
would produce a line that traced the red squares on the surf graph.
I'm still not certain of what your input data are about, and what you want to plot. However, from how you want to plot it, I can help.
When you call
surf(XX,YY,eye(10)); view([0 0 1]);
and want to get only the "red parts", i.e. the maxima of the function, you are essentially selecting a subset of the XX, YY matrices using the diagonal matrix as indicator. So you could select those points manually, and use plot to plot them as a line:
Xplot = diag(XX);
Yplot = diag(YY);
plot(Xplot,Yplot,'r.-');
The call to diag(XX) will take the diagonal elements of the matrix XX, which is exactly where you'll get the red patches when you use surf with the z data according to eye().
Result:
Also, if you're just trying to do what your example states, then there's no need to use matrices just to take out the diagonal eventually. Here's the same result, using elementwise operations on your input vectors:
datA = 1:10;
datB = 1:10;
X2 = cosd(8*datA).*datB;
Y2 = datA.*log10(datB*3);
Z2 = cosd(datB);
XX2 = X2./(1+Z2);
YY2 = Y2./(1+Z2);
plot(Xplot,Yplot,'rs-',XX2,YY2,'bo--','linewidth',2,'markersize',10);
legend('original','vector')
Result:
Matlab has many built-in function to assist you.
In 2D the easiest way to do this is polar that allows you to make a graph using theta and rho vectors:
theta = linspace(0,2*pi,100);
r = sin(2*theta);
figure(1)
polar(theta, r), grid on
So, you would get this.
There also is pol2cart function that would convert your data into x and y format:
[x,y] = pol2cart(theta,r);
figure(2)
plot(x, y), grid on
This would look slightly different
Then, if we extend this to 3D, you are only left with plot3. So, If you have data like:
theta = linspace(0,10*pi,500);
r = ones(size(theta));
z = linspace(-10,10,500);
you need to use pol2cart with 3 arguments to produce this:
[x,y,z] = pol2cart(theta,r,z);
figure(3)
plot3(x,y,z),grid on
Finally, if you have spherical data, you have sph2cart:
theta = linspace(0,2*pi,100);
phi = linspace(-pi/2,pi/2,100);
rho = sin(2*theta - phi);
[x,y,z] = sph2cart(theta, phi, rho);
figure(4)
plot3(x,y,z),grid on
view([-150 70])
That would look this way
I am trying to create my own voronoi diagram. I have an arbitrary shape defined by their x and y coordinates stored in separate vectors. Inside this shape are some points of interest (with known coordinates) that belong to two different groups and act as seeds to the voronoi diagram. As an example, the whole diagram ranges from x=-10 to x=90 and y=-20 to y=60. The boundary shape is not rectangular but falls within the axes range above.
What I have done so far is to create a 3D matrix (100 X 80 X 3), C, with all ones so that the default colour will be white. I then looped through from i=1:100, j=1:80, testing individual pixels to see if they fall within the shape using inpolygon. If they do, I then find out which point is the pixel closest to and assign it a colour based on whether the closest point belongs to group 1 or 2.
All is good so far. I then used imagesc to display the image with a custom axis range. The problem is that the voronoi diagram has the general shape but it is off in terms of position as the pixel coordinates are different from the actual world coordinates.
I tried to map it using imref2d but I do not know how it really works or how to display the image after using imref2d. Please help me on this.
I am open to other methods too!
Thank you!
Edit:
As requested, let me give a more detailed example and explanation of my problem.
Let us assume a simple diamond shape boundary with the following vectors and 4 points with the following coordinate vectors:
%Boundary vectors
Boundary_X = [-5 40 85 40 -5];
Boundary_Y = [20 50 20 -10 20];
%Point vectors
Group_One_X = [20 30];
Group_One_Y = [10 40];
Group_Two_X = [50 70];
Group_Two_Y = [5 20];
Next I plot all of them, with different groups having different colours.
%Plot boundary and points
hold on
plot(Boundary_X,Boundary_Y)
scatter(Group_One_X,Group_One_Y,10,'MarkerFaceColor','Black',...
'MarkerEdgeColor','Black')
scatter(Group_Two_X,Group_Two_Y,10,'MarkerFaceColor','Red',...
'MarkerEdgeColor','Red')
hold off
axis([-10, 90, -20, 60])
This is the result:
Boundary with points
Next I test the whole graph area pixel by pixel, and colour them either cyan or yellow depending on whether they are closer to group 1 or 2 points.
%Create pixel vector with default white colour
C=ones(100,80,3);
Colour_One = [0 1 1];
Colour_Two = [1 1 0];
%Loop through whole diagram
for i=1:100
for j=1:80
x=i;
y=j
if inpolygon(x,y,Boundary_X,Boundary_Y)
%Code for testing which point is pixel closest to
%If closest to group 1, assign group 1 colour, else group 2
%colour
end
end
end
%Display image
hold on
imagesc(C)
hold off
This is the result
Failed Voronoi Diagram
The shape is somewhat correct for the right side but not for the others. I understand that this because my world coordinates start from negative values but the pixel coordinates start from 1.
Hence I am at a lost as to how can I solve this problem.
Thank you!
One thing to notice is that you have to convert between image and plot coordinates. The plot coordinates are (x,y) where x goes to the right, and y goes up. The matrix coordinates are (i,j) where i goes down, and j to the right. An easy way to do this is with the use of vec_X,vec_Y as shown below.
Another solution for the newer Matlab versions would be - as you said - using imref2d but unfortunately I have no experience with that command.
%Boundary vectors
Boundary_X = [-5 40 85 40 -5];
Boundary_Y = [20 50 20 -10 20];
%Point vectors
Group_One_X = [20 30];
Group_One_Y = [10 40];
Group_Two_X = [50 70];
Group_Two_Y = [5 20];
%Coordinate system
min_X = -10;
max_X = 90;
min_Y = -20;
max_Y = 60;
axis([min_X, max_X, min_Y, max_Y])
%Create pixel vector with default white colour
rows_N = 100;
columns_N = 80;
C=ones(rows_N,columns_N,3);
%These vectors say where each of the pixels is in the plot coordinate
%system
vec_X = linspace(min_X,max_X,columns_N);
vec_Y = linspace(min_Y,max_Y,rows_N);
Colour_One = [0 1 1];
Colour_Two = [1 1 0];
%Loop through whole diagram
for i=1:100
for j=1:80
if inpolygon(vec_X(j),vec_Y(i),Boundary_X,Boundary_Y)
%calculate distance to each point
Distances_One = zeros(size(Group_One_X));
Distances_Two = zeros(size(Group_Two_X));
for k=1:numel(Group_One_X);
Distances_One(k) = norm([Group_One_X(k),Group_One_Y(k)]-[vec_X(j),vec_Y(i)]);%assuming euclidean norm, but can be adjusted to whatever norm you need
end
for k=1:numel(Group_Two_X);
Distances_Two(k) = norm([Group_Two_X(k),Group_Two_Y(k)]-[vec_X(j),vec_Y(i)]);%assuming euclidean norm, but can be adjusted to whatever norm you need
end
if min(Distances_One) < min(Distances_Two);
C(i,j,:) = Colour_One;
else
C(i,j,:) = Colour_Two;
end
end
end
end
%Display image
imagesc(vec_X,vec_Y,C) %lets you draw the image according to vec_X and vec_Y
%Plot boundary and points
hold on
plot(Boundary_X,Boundary_Y)
scatter(Group_One_X,Group_One_Y,10,'MarkerFaceColor','Black',...
'MarkerEdgeColor','Black')
scatter(Group_Two_X,Group_Two_Y,10,'MarkerFaceColor','Red',...
'MarkerEdgeColor','Red')
hold off
I have two datasets, one of which is a target position, and the other is the actual position. I would like to plot the target with a +/- acceptable range and then overlay with the actual. This question is only concerning the target position however.
I have unsuccessfully attempted the built in area, fill, and rectangle functions. Using code found on stackoverflow here, it is only correct in certain areas.
For example
y = [1 1 1 2 1 1 3 3 1 1 1 1 1 1 1]; % Target datum
y1 = y+1; %variation in target size
y2 = y-1;
t = 1:15;
X=[t,fliplr(t)]; %create continuous x value array for plotting
Y=[y1,fliplr(y2)]; %create y values for out and then back
fill(X,Y,'b');
The figure produced looks like this:
I would prefer it to be filled within the red boxes drawn on here:
Thank you!
If you would just plot a function y against x, then you could use a stairs plot. Luckily for us, you can use the stairs function like:
[xs,ys] = stairs(x,y);
to create the vectors xs, ys which generate a stairs-plot when using the plot function. We can now use these vectors to generate the correct X and Y vectors for the fill function. Note that stairs generates column vectors, so we have to transpose them first:
y = [1 1 1 2 1 1 3 3 1 1 1 1 1 1 1]; % Target datum
y1 = y+1; %variation in target size
y2 = y-1;
t = 1:15;
[ts,ys1] = stairs(t,y1);
[ts,ys2] = stairs(t,y2);
X=[ts.',fliplr(ts.')]; %create continuous x value array for plotting
Y=[ys1.',fliplr(ys2.')]; %create y values for out and then back
fill(X,Y,'b');
Again, thank you hbaderts. You answered my question perfectly, however when I applied it to the large data set I needed for, I obtained this image
https://dl.dropboxusercontent.com/u/37982601/stair%20fill.png
I think it is because the fill function connects vertices to fill?
In any case, for the potential solution of another individual, combined your suggested code with the stair function and used the area function.
By plotting them on top of one another and setting the color of the lower area to be white, it appears as the rectangular figures I was after.
%sample code. produces image similar to o.p.
y = [1 1 1 2 1 1 3 3 1 1 1 1 1 1 1];
y1 = y+1;
y2 = y-1;
t = 1:15;
[ts,ys1] = stairs(t,y1);
[ts,ys2] = stairs(t,y2);
area(ts,ys1,'FaceColor','b','EdgeColor','none')
hold on
area(ts,ys2,'FaceColor','w','EdgeColor','none')
https://dl.dropboxusercontent.com/u/37982601/stair%20area.png
Thanks again for your help and for pointing me in the right direction!
I'm looking to create a "web" between a set of points where the data tells whether there is a link between any two points.
The way I thought of would be by plotting every couple points, and overlaying each couple on top of eachother.
However, if there is a way to just simple draw a line between two points that would be much easier.
Any help would be appreciated!
If you can organize the x and y coordinates of your line segments into 2-by-N arrays, you can use the function PLOT to plot each column of the matrices as a line. Here's a simple example to draw the four lines of a unit square:
x = [0 1 1 0; ...
1 1 0 0];
y = [0 0 1 1; ...
0 1 1 0];
plot(x,y);
This will plot each line in a different color. To plot all of the lines as black, do this:
plot(x,y,'k');
Use plot. Suppose your two points are a = [x1 y1] and b = [x2 y2], then:
plot([x1 x2],[y1 y2]);
If you meant by I'm looking to create a "web" between a set of points where the data tells whether there is a link between any two points actually some kind of graph represented by its adjacency matrix (opposite to other answers simple means to connect points), then:
this gplot function may indeed be the proper tool for you. It's the basic visualization tool to plot nodes and links of a graph represented as a adjacency matrix.
use this function:
function [] = drawline(p1, p2 ,color)
%enter code here
theta = atan2( p2(2) - p1(2), p2(1) - p1(1));
r = sqrt( (p2(1) - p1(1))^2 + (p2(2) - p1(2))^2);
line = 0:0.01: r;
x = p1(1) + line*cos(theta);
y = p1(2) + line*sin(theta);
plot(x, y , color)
call it like:
drawline([fx(i) fy(i)] ,[y(i,1) y(i,2)],'red')
Credit: http://www.mathworks.com/matlabcentral/answers/108652-draw-lines-between-points#answer_139175
Lets say you want a line with coordinates (x1,y1) and (x2,y2). Then you make a vector with the x and y coordinates: x = [x1 x2] and y=[y1 y2].
Matlab has a function called 'Line', this is used in this way:
line(x,y)
If you want to see the effect of drawing lines, you can use plot inside for loop note that data is a n*2 matrix containing the 'x,y' of 'n' points
clf(figure(3))
for i = 1 : length(data)-1
plot([data(i,1),data(i+1,1)], [data(i,2),data(i+1,2)], '-*');
hold on
end
hold off
Or can use this statement to draw it in one step
plot(data(:,1), data(:,2), '-*');