finding a coefficient from an equation

Hello, i m a beginner on matlab and i would need some help. I have 2 vectors x and z with 10 values each and the equation z=c*sqrt(x). I have to find the value of c. Help please.

[Adam Danz]

This is more of a math problem than a Matlab problem.

In essence, you have to solve for c. Then you just have to plug in your vectors.

Since this is likely homework, I'd be glad to help you solve.

Hint #1:

y = x*A  --->  y/A = x

Hint #2:

To divide two vectors element-wise, use q./r

[Ana Monea]

I forgot to mention that c is a constant. So i guess that i need to find just one value for c even if i have 10 values in each vector. I think i habe to use a command but i don t know which one.

[Walter Roberson]

In that case either use / or \ operators with appropriate arguments. They will do a least-squared fitting to find the best value for c.

Answer 1

[Ang Feng]

(1)If your vectors x and x follows exactly z=c*sqrt(x), then the constant c can be calculated, as mentioned by Adam Danz,

c = sqrt(x)./z

You have a vector c which has 10 identical value which is what you are looking for.

(2) In the case x, and z just follow then trend of z=c*sqrt(x), you are actually asking for a constant c that minimize some function of the error vector. Normally, we minimize norm of the square of the error . This is a least square problem. You can actually use the curve fitting tool box to fit the function.

sqrtX = sqrt(x);
f = fit(sqrtX,z,'poly1');
c = f.p1;

Here is my little example.

x = (1:10)';sqrtX = sqrt(x);
z = 2*sqrtX+0.05*randn(10,1);% add some noise
f = fit(sqrtX,z,'poly1');
c = f.p1
ans = 
    1.9725

The parameter c = 2 was calculated to be 1.9725.

[Ana Monea]

Thanks for the help