MATLAB Plot function of two variables on 2D Grid

[etothex]

Hey all - this is my first post on the forum but I've browsed for help for a really long time on other topics. Any help would be greatly appreciated!

So I have a function, called stability.m that takes in two independent variables, say x and y, as input and outputs either a 1 or a 0 for each pairing of x and y. I would like to set up a plot as x versus y that plots each pairing as a colored dot (simply all 1's = black and all 0's = red, for instance). I would more or less rather like a grid/matrix so I can easily see what each possible pairing would represent for broad ranges of x and y (IE, x and y = 1x100 vectors).

I was wondering if this is even possible. I have read through tons of tutorials regarding mesh plots, scatter plots, etc and have found most to say that functions of two variables can only be plotted on a 3d graph. Is this true?

Thanks for the help
- etothex

 

[MisterX]

I would like to set up a plot as x versus y that plots each pairing as a colored dot

You can do that using http://www.mathworks.com/help/techdoc/ref/scatter.html", with C being vector with the same size as X and Y.

X = 0:7;
Y = 0:7;

colormap(hsv(256));
C = (0:7)/8;

scatter(X, Y, 4, C, 'filled');

You can also display 2D matrices using http://www.mathworks.com/help/techdoc/ref/image.html".

 

[etothex]

You can do that using http://www.mathworks.com/help/techdoc/ref/scatter.html", with C being vector with the same size as X and Y.

X = 0:7;
Y = 0:7;

colormap(hsv(256));
C = (0:7)/8;

scatter(X, Y, 4, C, 'filled');

You can also display 2D matrices using http://www.mathworks.com/help/techdoc/ref/image.html".

Okay got a little further with the image function. however, with scatter, the constraint that C needs to be of same length as X, Y won't be good here because if X and Y are length 4, then there will be 16 points that need to be plotted on the graph. (X=1, Y=1:4 then X=2, Y=1:4 and so on). Is there a way around this?

 

[MisterX]

The length of X and the length of Y and the length of C should all be equal to the number of points (since you want a different color for each point). By X, Y, and C, I mean the parameters to the scatter function.

So, using the example you gave, one might think of the probem as, given the two length 4 vectors, how does one use MATLAB to generate the two 16 length vectors. Here is one way to do it:

x = 1:4;
y = 1:4;

X = kron(x,ones(size(y))); %repeats each element (a bit like interpolation)
Y = repmat(y, size(x)); %repeats the whole vector

colormap(hsv(length(X)));

C = (0:(length(X) - 1))/length(X);
scatter(X, Y, 4, C, 'filled');

 

[alphy]

Hello etothex,

Yes, it is possible to plot a function of two variables on a 2D grid using MATLAB's plot function. You can use the meshgrid function to create a grid of x and y values, and then use the plot function to plot the output of your stability function for each combination of x and y as a colored dot.

Here is an example code:

% Define x and y as vectors
x = 1:100;
y = 1:100;

% Create a grid of x and y values
[X,Y] = meshgrid(x,y);

% Call the stability function for each combination of x and y
Z = stability(X,Y);

% Plot the result as a colored dot for each combination of x and y
plot(X(:),Y(:),'o','MarkerFaceColor',Z)

This will create a 2D plot with x and y on the axes and the output of your stability function represented by colored dots. You can adjust the colors and markers as desired to make the plot easier to interpret.

I hope this helps. Happy plotting!