Stacking on a multi-variable function

So, I am trying to build a plot from a multi-variable function. I plan to hold 2 variables constant while indexing the 3rd variable, but then for each index of the 3rd variable, i hold that 3rd variable constant and index the 2nd, so on and so forth for the first variable.

For example,

f(x,y,z) = x + y + z
f = x(1) + y(1) + z(1:10)

then, for each z index...

f = x(1) + y(1:10) + z(1)

and then...

f = x(1:10) + y(1) + z(1)

so essentially for this example, I would have 1000 data points. My idea was to do nested for loops, however I don't think this is the right approach.

[the cyclist]

I'm not quite sure what the inputs and outputs should be.

Is the input only the function itself? But you say you "have 1000 data points".

What is the output? A single plot? Three plots, one for each variable? Or do you need a plot for

f = x(1:10) + y(1) + z(1)

and

f = x(1:10) + y(2) + z(1)

and so on such that you have a thousand plots in total?

I, for one, need a lot of clarification before I could provide any help.

[Brett]

The inputs will be the 3 variables with specific ranges. The output will be the function itself, a singular number from the result of the 3 inputs.

You described it correctly, in that I will have 1000 points total for this example. From the plots I am ultimately trying to optimize the best combination of x,y,z for the highest output achievable.

I believe this might be possible in a mesh/surf plot and the highest point on the 3-d plot will be the most optimized combination, but I am not sure.

Answer 1

[Walter Roberson]

[X, Y, Z] = ndgrid(x, y, z);
F = X + Y + Z;

F will now be numel(x) by numel(y) by numel(z) . You can extract parts of it such as

squeeze(F(7,:,2))

You might also want to look at slice() or isosurface()

[Walter Roberson]

Optimizing:

[maxF, maxidx] = max(F(:));
best_x = X(maxidx);
best_y = Y(maxidx);
best_z = Z(maxidx);

[Brett]

I'm confused where I would put my range of inputs and the equation in this

[Walter Roberson]

Before the line

[X, Y, Z] = ndgrid(x, y, z);

you would have set x, y, and z to be the values you were talking about in z(1:10) and so on -- the coordinates that you want to evaluate at.

Your equation is expressed at the line

F = X + Y + Z;

If you are writing a function that is passed a function handle such as

f = @(x,y,z) x+y+z;

then

F = f(X, Y, Z);

provide that f is vectorized. For example,

f = @(x,y,z) x.^2 - 3.*y.*z + x.*z;

[Brett]

Thank you, this has worked. Is there a way to plot the matrix I have recieved? It has given me a 2x24x24

[Walter Roberson]

You can extract parts of it such as

squeeze(F(2,:,7))

You might also want to look at slice() or isosurface()