Store trios of values from different vectors in an only vector

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!

[Torsten]

Save them in a matrix with three columns for x, y and z.

[John D'Errico]

You want Pythagorean triplets. What code did you write? It is far better to help to correct code than it is to write complete code from scratch. Yes, I could write it for you, but that would be just doing an obvious homework assignment for you.

So if you want help, then show what you did.

[Torsten]

@John D'Errico

https://de.mathworks.com/matlabcentral/answers/1815495-check-what-values-of-three-variables-fulfill-a-certain-condition?s_tid=srchtitle

[ABG]

roots=[]; %stores the trios
x=[1:1:100]; % values of X
y=[1:1:100]; % values of Y
z=[1:1:100]; % values of Z
for i=1:length(x)
    for k=1:length(y)
       if z==sqrt(x.^2+y.^2)
          found=1;
       end
    end
end
if found==1
    disp(x,y,z)
end

[ABG]

This is the code I have written. Srry for not attaching it before, I am new in MATLAB forums...

I don't know if this code is well planned, or there is a big mistake on the approach.

Thanks!

[Torsten]

I don't understand exactly what you are trying to do.

Do you want to find all possible triples (x,y,z) with x^2+y^2=z^2 for 1<=x<=100, 1<=y<=100 ?

Or given z^2, do you want to find all possible x and y such that x^2+y^2=z^2 ?

Or ...

[ABG]

I want to find all the possible triplets that fulfill the equation, with the limits you wrote.

I don't know if the problem is that I am trying to find values of z when I have previously defined...

For me it is the same case in the two options, but i understand you're telling me that this are two different approaches?

[Dyuman Joshi]

Are you trying to find pythagorean triplets, with all values less than or equal to 100?

[ABG]

I just have searched information about it, and yes, it seems like it.

But the enunciate did not tell that exactly.

[Torsten]

Sure. For the first part, compute all sums a^2+b^2 and check whether mod(sqrt(a^2+b^2),1) == 0. If true, you found a triple.

[ABG]

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

[Torsten]

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

Answer 1

[John D'Errico]

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

or

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

[ABG]

I posted it two times just because i didn't receive much help, and I want to only improve and matlab.

Thank you so much John for the explanation! I will keep trying it.

[Image Analyst]

Did my solution below not produce the plot and triplets you wanted?

[Torsten]

You forgot the line

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

:-)

[Image Analyst]

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). 😃

Answer 2

[Image Analyst]

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

[ABG]

Appreciate your help man!