I'm trying to plot the gradient of the real part of a complex function, however what I get is a blank figure. I do not understand what I am doing wrong since the code works with other functions (such as the imaginary part)
% Set up
x = -3:0.2:3;
y1 = (-3:0.2:3);
y = (-3:0.2:3)*1i;
[X, Y]= meshgrid(x,y);
% Complex variable s
s = X + Y;
% Complex function f(z)
z = s + 1./s;
figure
subplot(1,2,1);
[Dx, Dy] = gradient(real(z),.2,.5);
quiver(x,y1,Dx,Dy)
title('u(x,y) gradient, vector field');
%%Imaginary part
subplot(1,2,2)
contour(x,y1,imag(z),linspace(-10,10,100)); title('Contour of Im(f)');
xlabel('x'); ylabel('y'); %clabel(C3);
title('Imaginary part');
Here below is the image I get
I tried to rescale and resize the picture, the domain etc... but couldn't get the gradient to display (the arrows). What am I doing wrong here?
EDIT:
I found out it displays blank perhaps because there are some Inf and -Inf values in the Dy and Dx variables, is there an option to ignore these values or set them to 0?
It looks to me like it works, but the line width of your arrows is too small for you to see.
You can increase it by assigning a handle to the quiver plot like so:
hQuiver = quiver(x,y1,Dx,Dy);
And then, after the plot is created, change any of its many properties like so:
set(hQuiver,'LineWidth',4)
or do it all in the call to quiver:
hQuiver = quiver(x,y1,Dx,Dy,'LineWidth',4);
In this case it gives the following:
EDIT:
To answer your secondary question, you can set elements that are equal to +Inf or -Inf to any value you want using isinf:
Dx(isinf(Dx)) = 0;
and
Dy(isinf(Dy)) = 0;
It is not blank. You've plotted the quiver diagram (usually used in optical flow diagrams). It is giving an inward pointing arrow at each of the locations formed by the grid with points in x and y1.
Related
Question:
Write a function called point_cloud that takes one scalar as an input argument (the function does not have to check the format of the input) and has no output argument.
If it is called like this, point_cloud(100), then it plots 100 points. Each point has a random x coordinate and a random y coordinate, each of which is gotten by a call to randn, which uses a normal distribution with a standard deviation equal to 1. The range of the plot axes should be −5 to 5 in both the x and y dimensions. The grid should be turned off. The points should be plotted and displayed one at a time by calling plot with only one point specified and, following the call of plot, by a call of drawnow, which causes the point to be plotted immediately. The command hold on should be included so that all previous points are retained when a new point is plotted.
Figure 2.41 shows an example view of the plot after point_cloud(100000) has completed its point-by-point plotting on a Mac. (Note that on Windows the points are much larger. Also note that it takes a long time to plot this many points with drawnow. Finally, try zooming in the middle.)
Figure 2.41
My Code:
function point_cloud(N)
hold on
grid off
axis([-5,5,-5,5])
for ii = 1:N
plot(randn(ii));
drawnow;
end
I know this is wrong, but I'm not sure how to solve this problem. Can someone help?
Solved code:
function point_cloud(N)
figure
hold on
grid off
axis([-5,5,-5,5])
x = randn(N,1);
y = randn(N,1);
for ii = 1:N
plot(x(ii),y(ii),'b.');
drawnow;
end
You do not need the for loop at all. And drawing the plot each iteration is very time consuming. How about rather using the scatter function.
figure
hold on
grid off
axis([-5,5,-5,5])
x = randn(N,1);
y = randn(N,1);
scatter(x,y,'b.')
This will be a lot faster.
To add to the other answer, here is the code as a function, with the added functionality that the points are one pixel on Windows as well:
function point_cloud(N)
f = figure;
x = randn(N,1);
y = randn(N,1);
scatter(x,y,1/36,'b.');
f.GraphicsSmoothing = 'off';
grid off
axis([-5,5,-5,5])
axis equal
end
The size of the markers is set with the third parameter of scatter: 1/36. The graphics smoothing of the figure needs to be set to 'off' as well, to make sure that the pixels don't become blurry or lighter.
Here's a 3D version:
function point_cloud3D(N)
f = figure;
x = randn(N,1);
y = randn(N,1);
z = randn(N,1);
scatter3(x,y,z,1/36,'b.');
f.GraphicsSmoothing = 'off';
grid off
axis([-5,5,-5,5,-5,5])
axis square
view(3)
end
I wanted to generate a plot (X vs Y), and Z values depend on the Y. The example is shown in the figure below. The matrix size of X is same with Z but not Y. I can plot Z against X, but I wanted to combine all the plot into a single plot and become Y against X. I can plot multiple plots into a single plot but the plot is overlapping each other.
My question is there any method I can merge multiple plots into a single plot without overlapping each plot as the difference between each plot is very small (e.g Z1=1,2,3,4,5 and Z2=1.0001,2.0002,3.0001,4.0002,5.0001). So, I wanted to set each Z plot at different Y axis. (e.g Z1 at Y=0, Z2 at Y=2 ...)
Does anyone have any suggestions or idea?
Thank You
I'll clarify the ideas I wrote in a comment.
First, let's get some data:
x = 470:0.1:484;
z1 = cos(x)/2;
z2 = sin(x)/3;
z3 = cos(x+0.2)/2.3;
I'll plot just three data sets, all of this is trivial to extend to any number of data sets.
Idea 1: multiple axes
The idea here is simply to use subplot to create a small-multiple type plot:
ytick = [-0.5,0.0,0.5];
ylim = [-0.9,0.9]);
figure
h1 = subplot(3,1,1);
plot(x,z1);
set(h1,'ylim',ylim,'ytick',ytick);
title('z1')
h2 = subplot(3,1,2);
plot(x,z2);
set(h2,'ylim',ylim,'ytick',ytick);
title('z2')
h3 = subplot(3,1,3);
plot(x,z3);
set(h3,'ylim',ylim,'ytick',ytick);
title('z3')
Note that it is possible to, e.g., remove the tick labels from the top two plot, leaving only labels on the bottom one. You can then also move the axes so that they are closer together (which might be necessary if there are lots of these lines in the same plot):
set(h1,'xticklabel',[],'box','off')
set(h2,'xticklabel',[],'box','off')
set(h3,'box','off')
set(h1,'position',[0.13,0.71,0.8,0.24])
set(h2,'position',[0.13,0.41,0.8,0.24])
set(h3,'position',[0.13,0.11,0.8,0.24])
axes(h1)
title('')
ylabel('z1')
axes(h2)
title('')
ylabel('z2')
axes(h3)
title('')
ylabel('z3')
Idea 2: same axes, plot with offset
This is the simpler approach, as you're dealing only with a single axis. #Zizy Archer already showed how easy it is to shift data if they're all in a single 2D matrix Z. Here I'll just plot z1, z2+2, and z3+4. Adjust the offsets to your liking. Next, I set the 'ytick' property to create the illusion of separate graphs, and set the 'yticklabel' property so that the numbers along the y-axis match the actual data plotted. The end result is similar to the multiple axes plots above, but they're all in a single axes:
figure
plot(x,z1);
hold on
plot(x,z2+2);
plot(x,z3+4);
ytick = [-0.5,0.0,0.5];
set(gca,'ytick',[ytick,ytick+2,ytick+4]);
set(gca,'yticklabel',[ytick,ytick,ytick]);
text(484.5,0,'z1')
text(484.5,2,'z2')
text(484.5,4,'z3')
The simplest would be to shift Z data. But note that Z2 would look like to be oscillating around 1 - so this is a neat visual representation, but might mislead.
% Simple version - shift Z curves by 0, 1, ... (as recommended by #Cris Luengo)
shiftMat = repmat(0 : size(Z, 2)-1, size(Z,1), 1);
Z = Z + shiftMat;
%Min shift up to have non-overlapping - curves touching
for i = 2 : size(Z, 2)
Zdif = (Z(:, i-1) - Z(:, i));
Z(:, i) = Z(:, i) + max(Zdif); % + 0.01 to separate them a little bit.
end
%Bigger shift up, to have all points of Z(2) equal or above all points of z1.
for i = 2 : numZ
Zdif = max(Z(:, i-1))-min(Z(:, i));
Z(:, i) = Z(:, i) + Zdif;
end
Another possibility is to have multiple Y axis and each Z curve plotted against its own Y axis. This is likely fancier and shouldn't mislead, but it is way more work, even after you grab the function, as you still need to position all those axes. MATLAB by default lets you use only 2 axes, so grab a function from fileexchange to add more: https://www.mathworks.com/matlabcentral/fileexchange/9016-addaxis
Question
When using polarhistogram(theta) to plot a dataset containing azimuths from 0-360 degrees. Is it possible to specify colours for given segments?
Example
In the plot bellow for example would it be possible to specify that all bars between 0 and 90 degrees (and thus 180-270 degrees also) are red? whilst the rest remains blue?
Reference material
I think if it exists it will be within here somewhere but I am unable to figure out which part exactly:
https://www.mathworks.com/help/matlab/ref/polaraxes-properties.html
If you use rose, you can extract the edges of the histogram and plot each bar one by one. It's a bit of a hack but it works, looks pretty and does not require Matlab 2016b.
theta = atan2(rand(1e3,1)-0.5,2*(rand(1e3,1)-0.5));
n = 25;
colours = hsv(n);
figure;
rose(theta,n); cla; % Use this to initialise polar axes
[theta,rho] = rose(theta,n); % Get the histogram edges
theta(end+1) = theta(1); % Wrap around for easy interation
rho(end+1) = rho(1);
hold on;
for j = 1:floor(length(theta)/4)
k = #(j) 4*(j-1)+1; % Change of iterator
h = polar(theta(k(j):k(j)+3),rho(k(j):k(j)+3));
set(h,'color',colours(j,:)); % Set the color
[x,y] = pol2cart(theta(k(j):k(j)+3),rho(k(j):k(j)+3));
h = patch(x,y,'');
set(h,'FaceColor',colours(j,:),'FaceAlpha',0.2);
uistack(h,'down');
end
grid on; axis equal;
title('Coloured polar histogram')
Result
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
Can someone share a technique using MATLAB to plot the surface f(x,y)=(21/4)x^2y over the region x^2 <= y <= 1?
Also, if anyone is aware of some tutorials or links that would help with this type of problem, could you please share them?
Thanks.
Here is another approach:
%%
close all
x=linspace(-1,1,40);
g1=x.^2;
g2=ones(1,40);
y=[];
n=20;
for k=0:n
y=[y;g1+(g2-g1)*k/n];
end
x=x(ones(1,n+1),:);
z=21/4*x.^2.*y;
meshz(x,y,z)
axis tight
xlabel('x-axis')
ylabel('y-axis')
view(136,42)
And the result:
And finally, you can map the region (-1,1)x(0,1) in the uv-plane into the region bounded by $y=x^2 and y=1 in the xy-plane with the parametrization:
f(u,v) = (u\sqrt{v},v)
Capture from: https://math.stackexchange.com/questions/823168/transform-rectangular-region-to-region-bounded-by-y-1-and-y-x2
This code produces the same image shown above:
close all
[u,v]=meshgrid(linspace(-1,1,40),linspace(0,1,20));
x=u.*sqrt(v);
y=v;
z=21/4*x.^2.*y;
meshz(x,y,z)
axis tight
xlabel('x-axis')
ylabel('y-axis')
view(136,42)
First off, let's look at your valid region of values. This is telling us that y >= x^2 and also y <= 1. This means that your y values need to be on the positive plane bounded by the parabola x^2 and they also must be less than or equal to 1. In other words, your y values must be bound within the area dictated from y = x^2 to y = 1. Pictorially, your y values are bounded within this shape:
As such, your x values must also be bound between -1 and 1. Therefore, your actual boundaries are: -1 <= x <= 1 and 0 <= y <= 1. However, this only locates our boundaries for x and y but it doesn't handle where the plot has valid values. We'll tackle that later.
Now that we have that established, you can use ezsurf to plot surface plots in MATLAB that are dictated by a 2D equation.
You call ezsurf like so:
ezsurf(FUN, [XMIN,XMAX,YMIN,YMAX]);
FUN is a function or a string that contains the equation you want, and XMIN,XMAX,YMIN,YMAX contain the lowest and highest x and y values you want to plot. Plotting without these values assumes a span from -2*pi to 2*pi in both dimensions. As such, let's create a new function that will handle when we have valid values, and when we don't. Use this code, and save it to a new file called myfun.m. Make sure you save this to your current Working Directory.
function z = myfun(x,y)
z = (21/4)*x.^2.*y;
z(~(x.^2 <= y & y <= 1)) = nan;
end
This will allow you to take a series of x and y values and output values that are dictated by the 2D equation that you have given us. Any values that don't satisfy the condition of x^2 <= y <= 1, you set them to NaN. ezsurf will not plot NaN values.
Now, call ezsurf like so:
ezsurf(#myfun, [-1,1,0,1]);
You thus get:
This will spawn a new figure for you, and there are some tools at the top that will allow you interact with your 3D plot. For instance, you can use the rotation tool that's at the top bar beside the hand to rotate your figure around and see what this looks like. Click on this tool, then left click your mouse and hold the left mouse button anywhere within the surface plot. You can drag around, changing the azimuth and the latitude to get the perspective that you want.
Edit: June 4th, 2014
Noting your comments, we can decrease the jagged edges by increasing the number of points in the plot. As such, you can append a final parameter to ezsurf which is N, the number of points to add in each dimension. Increasing the number of points will decrease the width in between each point and so the plot will look smoother. The default value of N is 60 in both dimensions. Let's try increasing the amount of points in each dimension to 100.
ezsurf(#myfun, [-1,1,0,1], 100);
Your plot will look like:
Hope this helps!
Try the following to make the required function, compute the values, and plot only the region that is desired:
% Make the function. You could put this in a file by itself, if you wanted.
f = #(x,y) (21/4)*x.^2.*y;
[X Y] = meshgrid(linspace(0,1));
Z = f(X,Y);
% compute the values we want to plot:
valsToPlot = (X.^2 <= Y) & (Y <= 1);
% remove the values that we don't want to plot:
X(~valsToPlot) = nan;
Y(~valsToPlot) = nan;
Z(~valsToPlot) = nan;
% And... plot.
figure(59382);
clf;
surf(X,Y,Z);