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# How to evaluate functions for every possible input parameter combination?

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Craig Atkinson 15 Feb 2021
댓글: Craig Atkinson 15 Feb 2021
So I have a script set up for scalar inputs currently, but I want to change them to vectors and I want to generate a solution vector for every combination of inputs. For example, I have several expressions that can be calculated based on some inputs, but I don't know which combination of those inputs gives me the value that I desire the most (I'm not looking for a specific value, exactly, but I want to plot all out the outputs so I can look at the graph and determine which I think would be a good solution). Let's say I have three input vectors X, Y, and Z, and I have have a bunch of formulas such as f = x^2 + y, g = y^2 + z, h = x + y + z^3 etc etc. I'm not really sure how to go about obtaining vectors for f, g, or h while also having those values tied to their input parameters, if that makes sense.
X = linspace(0,10,1000);
Y = linspace(0,10,1000);
Z = linspace(0,10,1000);
F = X.^2 + Y;
G = Y.^2 + Z;
H = X + Y + Z.^3;
plot(F,G);
This is what I would do for a very simple example, but here I don't want to step through X, Y, and Z at the same rate. By doing this, everytime that X is 1, so are Y and Z, and everytime X is 10, so are Y and Z. I want those values, but I also want the values for when [X, Y, Z] = [1 7 4] and any other possible combination. But, I also need to be able to note which input conditions caused an output I like. If I am searching for a specific value, and I see that F = 5 somewhere (just a random number) how would I be able to tell what the values of X, Y, and Z were that caused F = 5?
This way, I could come back and alter the plots and filter all the results so that I only see a range of F, G, or H values that I'm looking for, but that's a different issue and I will ask another question if I cannot figure it out. If a very similar question has already been asked, I could not find it and I would appreciate being pointed in that direction as well.
If you know of a toolbox that simplifies this, I can also download that. Any solution is appreciated.

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### 채택된 답변

Matt J 15 Feb 2021
편집: Matt J 15 Feb 2021
You can use ndgrid,
[X,Y,Z]=ndgrid( 0:5:1000);
F = X.^2 + Y;
G = Y.^2 + Z;
H = X + Y + Z.^3;
idx=(F<=5);
locations = [X(idx),Y(idx),Z(idx)] %locations where F<=5;
locations = 402×3
0 0 0 0 5 0 0 0 5 0 5 5 0 0 10 0 5 10 0 0 15 0 5 15 0 0 20 0 5 20
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Craig Atkinson 15 Feb 2021
Ahh, I should have known that. Thank you both

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