I'm having difficulties trying to plot the reciprocal of a basic sine wave within MatLab. The tutorial I'm following (not a MatLab tutorial) is plotting it by hand by placing a few points between each vertical asymptote to give you an idea of what the graph will look like. I've tried using MatLab's csc() function, and the graph when plotted along side x is nothing like the drawn example. The drawn example from 0 to pi looks similar to a big U and from pi to 2*pi is a negative version (upside down). Here is all the different combinations of code I've tried:
x = 0:0.01:100;
y = 5*csc(x); % amplitude of -5 to 5
plot(x,y)
Then I tried:
x = 0:0.01:100;
y = 1 / 5*sin(x); % amplitude of -5 to 5
plot(x,y)
Both results are dramatically different. I was wondering if using the vector x was okay as I was under the impression after one of my previous posts that the standard MatLab trig functions are setup to take radians rather than degrees?
Can you try this -
x = 0 : 0.01 : 2*pi;
y = csc(x);
plot(x,y)
ylim([-10, 10])
Is that what you expected?
Related
I have a problem in matlab.
I used a ksdensity function on a vector of deltaX, which was my computed X minus actual X.
And I did the same on deltaY.
Then I used plot on that data. This gave me two 2d plots.
As I have two plots showing how (in)accurate was my system in computing X and Y (something like gaussian bell it was). Now I would like to have one plot but in 3d.
The code was just like that:
[f,xi] = ksdensity(deltaX);
figure;
plot(xi,f)
Ok what I'm about to show is probably not the correct way to visualize your problem, mostly because I'm not quite sure I understand what you're up to. But this will show you an example of how to make the Z matrix as discussed in the comments to your question.
Here's the code:
x = wgn(1000,1,5);%create x and y variables, just noise
y = wgn(1000,1,10);
[f,xi] = ksdensity(x);%compute the ksdensity (no idea if this makes real-world sense)
[f2,xi2] = ksdensity(y);
%create the Z matrix by adding together the densities at each x,y pair
%I doubt this makes real-world sense
for z=1:length(xi)
for zz = 1:length(xi2)
Z(z,zz) = f(z)+f2(zz);
end
end
figure(1)
mesh(xi,xi2,Z)
Here's the result:
I leave it up to you to determine the correct way to visualize your density functions in 3D, this is just how you could make the Z matrix. In short, the Z matrix contains the plot elevation at each x,y coordinate. Hope this helps a little.
I need to be able to do a surface plot using data from 3 vectors. I found similar information, but no method seems to work with my data. My X and Y columns are evenly spaced, but not in increasing order. I tried different methods, but none of them seem to give me what I want, which is a simple surface linking close points together. I tried the following:
[X Y]=meshgrid(x,y);
Z=griddata(x,y,z, X,Y);
surf(X,Y,Z);
This is not exactly what I want, because it creates a surface at z=0 and makes it look more like a volume plot than just a surface. It also runs very slowly on my computer (probably from creating all the gridpoints). If I could get something that doesn't require as much memory it would be ideal (my vectors have about 20k values each), but this is not a necessity.
***Edit: I also tried using the scatteredInterpolant method found here,but the function doesn't seem to be recognized by MATLAB and I get this error:
Undefined function 'scatteredInterpolant' for input arguments of type 'double'.
Also here is an image of my problem:
You can see that we can't see under the surface, there is some z=0 plane blocking it.
If you have anything for me, any help is appreciated.
Thanks in advance.
**Edit 2: I added sample vectors, they're my x,y and z values from left to right.
***Edit 3: Here's an image of the triangulation I get. As you can see some points are being ignored for some reason, which gives those long and weird looking blue triangles.
Mike
As conventional methods seem to fail, I would suggest you to do it manually.
Create a Z matrix full of NaN values. The size of the matrix should be dependant on your x and y values.
Loop over all occuring x,y, pairs and put their (average?) z value in the right position of your Z matrix.
Loop over all NaN values and interpolate their value. Perhaps using filter2.
Use surf to plot the resulting surface
If you have points which are described by vectors, and you want to plot them you could always use a Delauny triangulation. The function in matlab is called Tri=delauny(X,Y,Z). The data generated by this function can be shown with either trimesh(Tri,X,Y,Z) or trisurf(Tri,X,Y,Z). Keep in mind trisurf is only for 3D data. If you want to adjust the transparancy of plots in your graph use the alpha setting.
I hope this helps
To me it looks like you just need to sort your data before plotting.
Here is an example which I believe is similar to your case (since I could not download your data).
x = [2 1 4 3 -1 -3 -4 -2];
y = [1 2 3 4 -1 -2 -3 -4];
z = 32 - x.*x - y.*y;
[X1 Y1] = meshgrid(x,y);
Z1 = 32 - X1.*X1 -Y1.*Y1;
surf(X1,Y1,Z1)
aux = sort([x;y],2);
x = aux(1,:);
y = aux(2,:);
[X2 Y2] = meshgrid(x,y);
Z2 = 32 - X.*X - Y.*Y;
figure()
surf(X2,Y2,Z2)
The first figure results in a very problematic surface:
The second figure contains the desired surface:
So I plot sine(w*time) vs cosine(w*time)
w being angular frequency.
Hope I'm not wasting anyone's time if I ask:
Would this look like a circle?
I've researched a whole bunch but most websites only graph sine and cosine side-by-side and show comparisons.
I got it to look like a circle and I was just wondering if this is correct.
Also, What can I call this plot? I just gave it a title "plot of a circle". But I am wondering if that is professional enough since I am doing it for class.
Thanks for your time and answers. Greatly appreciated.
My MATLAB code for anyone interested:
clear all; clc; % clear the Workspace and the Command Window
f = 2; w = 2*pi*f; % specify a frequency in Hz and convert to rad/sec
T = 0.01; % specify a time increment
time = 0 : T : 0.5; % specify a vector of time points
x = sin(w*time); % evaluate the sine function for each element of the vector time
y = cos(w*time);
plot(x,y)
axis equal
grid on
xlabel('sin(w*time)');ylabel('cos(w*time)');title('Plot of a Circle');
axis([-1.1 1.1 -1.1 1.1]);
print
Here is a link to a Wolfram Alpha query I just did:
http://www.wolframalpha.com/input/?i=x%3Dsin%28t%29%2C+y%3Dcos%28t%29
I am not sure if it what you want to see, but that site (WolframAlpha.com) is a great place to explore and challenge mathematical concepts that are new to you.
Also, I would call it a plot of a circle since that is what the output looks like.
You are making a Lissajous curve. Keep in mind that a cosine is just a sine offset by pi/2 radians, and so plotting a sine against a cosine will indeed result in a circle. Changing the frequency and/or relative phase between x(t) and y(t) will result in many different interesting patterns.
I have various plots (with hold on) as show in the following figure:
I would like to know how to find equations of these six curves in Matlab. Thanks.
I found interactive fitting tool in Matlab simple and helpful, though somewhat limited in scope:
The graph above seems to be linear interpolation. Given vectors X and Y of data, where X contains the arguments and Y the function points, you could do
f = interp1(X, Y, x)
to get the linearly interpolated value f(x). For example if the data is
X = [0 1 2 3 4 5];
Y = [0 1 4 9 16 25];
then
y = interp1(X, Y, 1.5)
should give you a very rough approximation to 1.5^2. interp1 will match the graph exactly, but you might be interested in fancier curve-fitting operations, like spline approximations etc.
Does rxns stand for reactions? In that case, your curves are most likely exponential. An exponential function has the form: y = a*exp(b * x) . In your case, y is the width of mixing zone, and x is the time in years. Now, all you need to do is run exponential regression in Matlab to find the optimal values of parameters a and b, and you'll have your equations.
The advice, though there might be better answer, from me is: try to see the rate of increase in the curve. For example, cubic is more representative than quadratic if the rate of increase seems fast and find the polynomial and compute the deviation error. For irregular curves, you might try spline fitting. I guess there is also a toolbox in matlab for spline fitting.
There is a way to extract information with the current figure handle (gcf) from you graph.
For example, you can get the series that were plotted in a graph:
% Some figure is created and data are plotted on it
figure;
hold on;
A = [ 1 2 3 4 5 7] % Dummy data
B = A.*A % Some other dummy data
plot(A,B);
plot(A.*3,B-1);
% Those three lines of code will get you series that were plotted on your graph
lh=findall(gcf,'type','line'); % Extract the plotted line from the figure handle
xp=get(lh,'xdata'); % Extract the Xs
yp=get(lh,'ydata'); % Extract the Ys
There must be other informations that you can get from the "findall(gcf,...)" methods.
I 'm having a problem with creating a joint density function from data. What I have is queue sizes from a stock as two vectors saved as:
X = [askQueueSize bidQueueSize];
I then use the hist3-function to create a 3D histogram. This is what I get:
http://dl.dropbox.com/u/709705/hist-plot.png
What I want is to have the Z-axis normalized so that it goes from [0 1].
How do I do that? Or do someone have a great joint density matlab function on stock?
This is similar (How to draw probability density function in MatLab?) but in 2D.
What I want is 3D with x:ask queue, y:bid queue, z:probability.
Would greatly appreciate if someone could help me with this, because I've hit a wall over here.
I couldn't see a simple way of doing this. You can get the histogram counts back from hist3 using
[N C] = hist3(X);
and the idea would be to normalise them with:
N = N / sum(N(:));
but I can't find a nice way to plot them back to a histogram afterwards (You can use bar3(N), but I think the axes labels will need to be set manually).
The solution I ended up with involves modifying the code of hist3. If you have access to this (edit hist3) then this may work for you, but I'm not really sure what the legal situation is (you need a licence for the statistics toolbox, if you copy hist3 and modify it yourself, this is probably not legal).
Anyway, I found the place where the data is being prepared for a surf plot. There are 3 matrices corresponding to x, y, and z. Just before the contents of the z matrix were calculated (line 256), I inserted:
n = n / sum(n(:));
which normalises the count matrix.
Finally once the histogram is plotted, you can set the axis limits with:
xlim([0, 1]);
if necessary.
With help from a guy at mathworks forum, this is the great solution I ended up with:
(data_x and data_y are values, which you want to calculate at hist3)
x = min_x:step:max_x; % axis x, which you want to see
y = min_y:step:max_y; % axis y, which you want to see
[X,Y] = meshgrid(x,y); *%important for "surf" - makes defined grid*
pdf = hist3([data_x , data_y],{x y}); %standard hist3 (calculated for yours axis)
pdf_normalize = (pdf'./length(data_x)); %normalization means devide it by length of
%data_x (or data_y)
figure()
surf(X,Y,pdf_normalize) % plot distribution
This gave me the joint density plot in 3D. Which can be checked by calculating the integral over the surface with:
integralOverDensityPlot = sum(trapz(pdf_normalize));
When the variable step goes to zero the variable integralOverDensityPlot goes to 1.0
Hope this help someone!
There is a fast way how to do this with hist3 function:
[bins centers] = hist3(X); % X should be matrix with two columns
c_1 = centers{1};
c_2 = centers{2};
pdf = bins / (sum(sum(bins))*(c_1(2)-c_1(1)) * (c_2(2)-c_2(1)));
If you "integrate" this you will get 1.
sum(sum(pdf * (c_1(2)-c_1(1)) * (c_2(2)-c_2(1))))