I've got 3 vectors
x =[10^(-10) 10^(-9) 10^(-8) 10^(-7) 10^(-6) 10^(-5) 10^(-4) 10^(-3) 10^(-2)]
y =[10^(-10) 10^(-9) 10^(-8) 10^(-7) 10^(-6) 10^(-5) 10^(-4) 10^(-3) 10^(-2)]
and z which is the error that takes values from 5 to 0.01.
I need to create a contour plot. However, I cannot use meshgrid, as the step on my x and y axis should be very small and Matlab crashes when I'm trying that.
Any ideas about resolving it?
You can use meshgrid to produce the required mesh and replace the labels later on. The properties you are looking for are called XTick and XTickLabel. See for example: http://www.mathworks.com/matlabcentral/answers/92565
You need to use a logarithmic scale to see the results in any sensible way. Practically, this means you should probably do
x = logspace(-10, -2, 9);
y = logspace(-10, -2, 9);
logX = log(x);
logY = log(y);
[lxx lyy]=meshgrid(logX, logY);
and then plot contours as usual with
contour(lxx, lyy, reshape(z, [9 9]));
Finally, you would want to annotate your axes to show you are using a log scale - or you can turn off the tick labels and replace them with your own values.
Alternatively, I wonder if you could use the grid you have
[xx yy] = meshgrid(x, y);
and after plotting the contour, doing
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
I can't test this right now, so this may be bad advice. Let me know how it works for you.
Related
I need to plot a parabola and ellipse. However the ellipse is giving me trouble. Can anyone help? The equations are: y = -5*x^2 + 2 and (x^2/16) + (y^2/2) = 4
I've tried this code but obviously I feel like like it isn't right.
x = linspace(-5, 5);
y1 = (x.^2/16) + (y.^2/2) - 1;
y2 = -5*x.^2 +2;
figure(1)
plot(x, y1)
hold on
plot(x, y2)
hold off
Firstly, you did not define a range variable x. Secondly, the ellipse won't pass the vertical line test and can't be plotted like a regular function f(x). Thirdly, your equation y1 = (x.^2/16) + (y.^2/2) - 1; is non-sensical because you have y on each side.
You could correct your method by defining a range variable x1 and x2 that each have appropriate ranges for the functions your plotting. What I mean by this is that you probably don't want the same range for each function, because the ellipse is undefined over most of the range that the parabola is defined. To plot the ellipse using f(x) you could observe that there are + and - values that are identical, using this fact you could plot your ellipse by two functions one to represent the top half and one to represent the bottom half, each of these would pass the vertical line test.
OR
You could utilize ezplot and have a nice time with it because it makes your life easier. Here is a solution.
ezplot('x^2/16+y^2/2-4'); axis equal; hold on
ezplot('-5*x^2+2-y')
There are multiple ways to plot an ellipse, e.g. you could also use a parametric representation of the equation.
In your approach though, when plotting functions using plot(x,y) command, you need to express your dependent variable (y) through independent variable (x). You defined the range for x, which is what you substitute into your equations in order to find y's. While for the parabola, the dependency of y from x is obvious, you forgot to derive such a relationship for the ellipse. In this case it will be +-sqrt((1 - x^2/16)*2). So in your approach, you'll have to take into account both negative and positive y's for the same value of x. Also there's discrepancy in your written equation for the ellipse (=4) and the one in Matlab code (=1).
x = linspace(-5, 5);
y1 = sqrt((1 - x.^2/16)*2);
y2 = -5*x.^2 +2;
figure(1)
plot(x, real(y1), 'r', x, -real(y1), 'r')
hold on
plot(x, y2)
hold off
Since the ellipse has real y's not on the whole x domain, if you want to plot only real parts, specify real(y1) or abs(y1) (even though Matlab does it for you, too). You can also dismiss complex numbers for certain x when computing y1, but you'll need a for-loop for that.
In order to make things simpler, you can check the function fimplicit, ezplot is not recommended according to Matlab's documentation. Or if you want to plot the ellipse in a parametric way, fplot will work, too.
Another (more classic) approach for parametric plotting is given here already, then you don't need any other functions than what you already use. I think it is the simplest and most elegant way to plot an ellipse.
You will not be able to generate points for the ellipse using a function f(x) from a Cartesian linspace range. Instead, you can still use linspace but for the angle in a polar notation, from 0 to 2*pi. You should also be able to easily adjust radius and offset on both axis on the cos and sin expressions.
x = linspace(-5, 5);
y2 = -5*x.^2 +2;
figure(1)
clf;
plot(x, y2)
hold on
a = linspace(0,2*pi);
x2 = 4*cos(a);
y2 = sqrt(2)*sin(a);
plot(x2, y2)
xlim([-5,5]);
ylim([-5,5]);
hold off
I'm trying to plot two lines (data and linear fit) in a single graph with logarithmic scale. My code:
Iots = I_An./Temp.^2; % I Over T Squared
Oot = 1./Temp; % One Over T
[p,~] = polyfit(Oot,Iots,1);
linfit = polyval(p,Oot);
figure('color','w','units','normalized','outerposition',[0 0 1 1]);
hold on
loglog(Oot,Iots,'.','LineWidth',2);
loglog(Oot,linfit,':r','LineWidth',2);
The result is not a logarithmic scale graph:
If I run just one of the plot lines, it works on its own. What should I do? Are there any contradicting commands?
You want to call hold on after creating your first loglog plot. Also, you only need to use loglog on the first plot to create the logarithmic axes. After than you can just call normal plot and it will use the logarithmic axes.
x = linspace(0, 100);
loglog(x, x, '.', 'LineWidth', 2);
hold on
plot(x, x.^2, '.r', 'LineWidth',2);
Environment: Windows 7 64 bit, Matlab 2014a
Objective:
To draw a heatmap of errors for two parameters to be optimized.
To put proper tick marks and tick values
Draw the grid lines in the correct place
Problem: Arranging the X and Y tick positions and values. When the last ("end") value of the vectors in x and y axes are the same, the code I use puts the ticks and values properly. However, when the end values are different it does not, and produces something really weird.
Below I have included the code which I have modified so that you can run it without the need of adding anything. Of course in my case the error vector are the error values, not random numbers. To see the problem of "end value" use the second b vector.
fontsize = 20
k = [2^-5, 2^-3, 2^-1, 2^0, 2^1, 2^3, 2^5, 2^7, 2^9, 2^11, 2^13, 2^15]
b = [2^-5, 2^-3, 2^-1, 2^0, 2^1, 2^3, 2^5, 2^7, 2^8, 2^9, 2^10, 2^11, 2^13, 2^15]
% b = [2^-5, 2^-3, 2^-1, 2^0, 2^1, 2^3, 2^5, 2^7, 2^8, 2^9, 2^10, 2^11, 2^13, 2^19]
errorVector = randi(20, 1, length(b)*length(k))'
figure
% Create a matrix from error vector (size of error vector is [length(k)*length(b),1])
B = reshape(errorVector, [length(b), length(k)])
B = flipud(B)
% imagesc(x,y,C)
imagesc(b, k, B)
title('Heatmap Parameters Percent Error', 'FontSize', fontsize);
% Set colorbar limits
caxis([0 15])
colorbar;
ax1 = gca;
xTickLabel = (k)'
xTick = linspace(k(1), k(end), numel(xTickLabel))';
set(ax1, 'XTick', xTick, 'XTickLabel', xTickLabel)
xlabel('k parameter', 'FontSize', fontsize)
yTickLabel = (b)'
yTick = linspace(b(1), b(end), numel(yTickLabel))';
set(ax1, 'YTick', yTick, 'YTickLabel', flipud(yTickLabel(:)))
ylabel('b parameter', 'FontSize', fontsize)
set(ax1,'FontSize', fontsize)
Here, change any of the end values of b or k vectors, and the program will output a graph where the X and Y ticks are totally wrong.
Also, I would like to draw grid lines. When I use "grid on" it draws grid lines right on the tick marks which is not correct in the case of heatmap. Because tick marks will be in the center of the columns -or rows- but the grid lines should be at the boundaries between the columns -or rows.
By the way if you know a better way to plot a heatmap in Matlab, please do tell.
Please help me solve this problem. Any help is appreciated,
Ilyas
First of all - you don't need to flipud the B matrix - by default imagesc plots the y-data inversed, but you can fix this with the following statement:
set(gca,'ydir','normal');
This also means you don't have to mess around with flipping the tick-labels. You can get the labels right by doing the following:
% replace the imagesc call with:
imagesc(B);
set(gca,'ydir','normal');
% formatting stuff
...
% replace the set commands with:
set(ax1, 'XTick', 1:length(k), 'XTickLabel', k)
set(ax1, 'YTick', 1:length(b), 'YTickLabel', b)
By default, if you don't provide x and y data to the imagesc command, it will number them linearly (1,2,3...). Basically what we've done here is make sure that it has ticks for each of the elements of b and k, and then set the labels to the values of the respective vectors.
Unfortunately, I'm not sure if there is a way to get the grid spacing right with imagesc or not. You could try using pcolor instead, which has it's own set of issues, but allows you to get grid lines (of sorts) between the elements. It also allows you to use an interpolated shading mode, which will make your plot look more like a typical heat map.
To use pcolor instead, you just have to replace imagesc:
% imagesc(B);
% set(gca,'ydir','normal');
pcolor(B);
% this uses a smoother shading method, for a more 'heatmap' like output
% shading interp
Everything else should work as intended, I believe.
I generated a 3D surface in matlab.
clear all;
close all;
clc;
x = [1:0.1:5];
y=[1:50];
[n1 n2] = size(x);
[m1, m2] = size(y);
for i = 1 : m2
for j = 1 : n2
z(i,j) = (x(1,j)) / (y(1,i));
end
end
[x, y] = meshgrid(x, y);
surf(y, x, z)
colorbar
xlabel('x')
ylabel('y')
zlabel('z')
I got the following plotted surface:
I am interested now to rotate the cube of a quarter turn in the clockwise direction. I know that I can use the "rotate3d on" and choose the best Az and EI, but I didn't understand what are Az and EI and how should be equal to respond to my need?
For example:
There also another function called camroll(). But I don't know what must the value in () in order to rotate the cube of a quarter turn in the clockwise direction. Does 90 degree is the correct answer?
Any help will be very appreciated!
To rotate the figure axis you can use the view command:
surf(rand(20))
for az = 360:-1:-0
view(az, 30)
pause(0.01)
end
Azimus has values in between 0° and 360°. To turn the axis figure by 90° in counter-clockwise direction you oculd choose the azimuths of: [270, 180, 90, 0]
as #ASantosRibeiro mentioned, the rotate function will produce the output you want. As an aside, here is a vectorized version of your code, which you might find useful if you have a significantly larger data set.
x = 1:0.1:5;
y=1:50;
X = repmat(x',1,size(y,2)).';
Y = repmat(y',1,size(x,2));
Z = X./Y;
figure
hSurf = surf(Y,X,Z);
rotate(hSurf,[1,0,0],45) % As proposed by #ASantosRibeiro
colorbar
xlabel('x')
ylabel('y')
zlabel('z')
The repmat function is used to replicate both x and y in order to form X and Y with correct sizes to be allowed to divide one by the other in order to form Z. This operation is quite similar to the call to meshgrid in your code. For a small dataset like the one in your example the running times are similar with both methods (on my laptop), however when I use x = 1:0.1:500 and y = 1:500 for example the vectorized version takes 3x less time, so it might be worthwhile to look at it.
Hope that helps you!
I apologize for asking this, I believe this is a simple task, but I don't know how to do it.
Suppose I have a formula y = (exp(-x) + x^2)/sqrt(pi(x) and I want to plot it as y versus x^2.
How does one do this?
Like this:
X = 0:0.1:5; %// Get the x values
x = X.^2; %// Square them
%// Your formula had errors, I fixed them but I could have misinterpreted here, please check
y = (exp(-x) + x.^2)./sqrt(pi*x); %// Calculate y at intervals based on the squared x. This is still y = f(x), I'm just calculating it at the points at which I want to plot it.
plot(x,y) %//Plot against the square X.
At this point this is no different to having just plotted it normally. What you want is to make the tickmarks go up in values of X.^2. This does not change the y-values nor distort the function, it just changes what it looks like visually. Similar to plotting against a log scale:
set(gca, 'XTick', X.^2) %//Set the tickmarks to be squared
The second method gives you a plot like
edit:
Actually I think you were asking for this:
x = 0:0.1:5;
y = x.^2; %// Put your function in here, I'm using a simple quadratic for illustrative purposes.
plot(x.^2,y) %//Plot against the square X. Now your y values a f(x^2) which is wrong, but we'll fix that later
set(gca, 'XTick', (0:0.5:5).^2) %//Set the tickmarks to be a nonlinear intervals
set(gca, 'XTickLabel', 0:0.5:5) %//Cahnge the labels to be the original x values, now accroding to the plot y = f(x) again but has the shape of f(x^2)
So here I'm plotting a simple quadratic, but if I plot it against a squared x it should become linear. However I still want to read off the graph that y=x^2, not y=x, I just want it to look like y=x. So if I read the y value for the x value of 4 on that graph i will get 16 which is still the same correct original y value.
Here's my answer: it is similar to Dan's one, but fundamentally different. You can calculate the values of y as a function of x, but plot them as a function of x^2, which is what the OP was asking, if my understanding is correct:
x = 0:0.1:5; %// Get the x values
x_squared = x.^2; %// Square them
%// Your formula had errors, I fixed them but I could have misinterpreted here, please check
y = (exp(-x) + x.^2)./sqrt(pi*x); %// Calculate y based on x, not the square of x
plot(x_squared,y) %//Plot against the square of x
As Dan mentioned, you can always change the tickmarks:
x_ticks = (0:0.5:5).^2; % coarser vector to avoid excessive number of ticks
set(gca, 'XTick', x_ticks) %//Set the tickmarks to be squared