Store trios of values from different vectors in an only vector

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ABG 2022-10-2

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评论： ABG 2022-10-4

Hi guys!

I am trying to store trios of values (intengers values from 1 to 100) which fulfill an equation. The equation in this case is z^2=x^2+y^2.

I have tried it many ways, but none of them have worked correctly.

Now I am trying to use a couple of FOR loops in order to analyze every value of x and y, and finally determine which values of z I need. I am trying to solve this part with an IF inside the two FOR loops, but it is not working.

I do not know how can I store the diferent trios of values inside an only vector.

I was wondering if you could help me. Thanks!

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ABG 2022-10-2

I don't understand why a^2+b^2 have to equal 0. Could you explain it to me please?

Torsten 2022-10-2

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You must check whether a^2+b^2 is a square. To do this, you take the squareroot and check whether it's an integer.

s = 14;
mod(sqrt(s),1)
ans = 0.7417
s = 25;
mod(sqrt(s),1)
ans = 0

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采纳的回答

John D'Errico 2022-10-2

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Please stop posting the same question multiple times. You made some effort though.

First, learn to use meshgrid.

[X,Y] = meshgrid(1:100);

Next, compute Z, for EVERY values of X and Y.

Z = sqrt(X.^2 + Y.^2);

A sample values of Z is

Z(5,8)
ans = 9.4340

Z(60,83)
ans = 102.4158

You have found a solution only when z is an integer, AND Z is no larger than 100.

Can you now test to see which elements of Z are both an integer, AND no larger than 100? Even better, can you do that without using loops? Can you use find? It might make sense to keep only the solutions where X<=Y, as the problem is symmetric. If (x,y,z) is a solution, then so is (y,x,z). So you should discard the cases that yield these replicate solutions.

Could you have done this using loops? OF COURSE!

XYZsolutions = zeros(0,3);
for x = 1:100
    for y = x:100
        % Note this automatically discards the cases where x is greater than y.
        % if you wanted to keep them, then have the y loop run form 1 to 100.
        z = sqrt(x^2 + y^2)
        
        % now you need to test to seee if z is an integer.
        % You need to test to see if z is not greater than 100.
        % You need to make some effort here, so why not think about how to perform those tests?
        if ???????????????????????????
            XYZsolutions(end+1,:) = [x,y,z];
        end
    end
end

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Torsten 2022-10-3

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You forgot the line

triplets = triplets(mod(triplets(:,3),1)==0,:)

:-)

Image Analyst 2022-10-3

OK, that extracts out only values where z is an integer. When I first read it, I saw that x and y were integers but I hadn't realized that z also had to be an integer also (but I do now). 😃

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更多回答（1 个）

Image Analyst 2022-10-2

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编辑：Image Analyst 2022-10-2

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Try using meshgrid

x = 1 : 100;

y = 1 : 100;

% Get an x and a y for every location.

[X, Y] = meshgrid(x, y);

% Construct the surface

z = sqrt(X .^ 2 + Y .^ 2);

% Display the surface

surf(z, 'EdgeColor','none')

colorbar

xlabel('x')

ylabel('y')

zlabel('z')

% Find x,y,z triplets

triplets = [X(:), Y(:), z(:)]

triplets = 10000×3

1.0000 1.0000 1.4142 1.0000 2.0000 2.2361 1.0000 3.0000 3.1623 1.0000 4.0000 4.1231 1.0000 5.0000 5.0990 1.0000 6.0000 6.0828 1.0000 7.0000 7.0711 1.0000 8.0000 8.0623 1.0000 9.0000 9.0554 1.0000 10.0000 10.0499