Why is this for loop not producing unique values for each index of the calculated matrix?

This is the part of the script I am having trouble with:

 load('DENS.mat')
 for i = 1:151
    Vsto(i) = sqrt(2*2800/(DENS(i)*180*1.7));
    Vlof(i) = 1.15*Vsto(i);
    Vavg(i) = sqrt((Vlof(i))^2/2);
    Davg(i) = 0.5*DENS(i)*Vavg(i)^2*(180)*(0.0870);
 end

The DENS matrix is a 1x151 double which I have attached to this post. I want to produce a 1x151 matrix called Davg with values corresponding to Vavg and DENS. The problem is that when I run this part of my script I get a 1x151 matrix with 151 values which are the same and correspond to DENS(151) and Vavg(151) for every value within Davg. If you remove the square (the ^2 beside Vavg(i)), however, this problem goes away and I get 151 unique, but wrong, values within Davg. The other matrices Vsto, Vlof, and Vavg produce correct values.

What is wrong with this code? I think it has something to do with the square in Davg and the sqrt function in Vavg but I don't know how.

Thank you

[Bob Thompson]

I can't say I know why the problem is happening, but what happens if you do (Vavg(i))^2?

[Polus Patrus]

Nothing changes, it's still the same wrong output.

Answer 1

[Jan]

Why do you assume, that the output is wrong? Numerically it is correct and Matlab calculates exactly what it is instructed to do.

A simplified version of the code:

load('DENS.mat')
for i = 1:151
   Vsto(i) = sqrt(2 * 2800 / (DENS(i) * 180 * 1.7));
   Vlof(i) = 1.15 * Vsto(i);
   Vavg(i) = sqrt(Vlof(i) ^ 2 / 2);
   Davg(i) = 0.5 * DENS(i)*Vavg(i)^2 * 180 * 0.0870;
end

Now vectorize this instead of the loop:

Vsto = sqrt(2 * 2800 ./ (DENS * 180 * 1.7));
Vlof = 1.15 * Vsto;
Vavg = abs(Vlof) / sqrt(2);  % Cheaper than: sqrt(Vlof(i) ^ 2 / 2)
Davg = 0.5 * DENS .* Vavg .^ 2 * 180 * 0.0870;

These terms can be combined:

Davg = 0.5 * DENS .* ...
       (abs(1.15 * sqrt(5600 ./ (DENS * 180 * 1.7))) / sqrt(2)) .^ 2 * ...
       180 * 0.0870

Then DENS ./ (sqrt(DENS) .^ 2) removes the dependency to the input and you get a constant. To be exact:

Davg = repmat(0.25 * 180 * 0.0870 * 1.3225 * 5600 / (180 * 1.7), size(DENS))

[Polus Patrus]

Thank you, this helps very much. I appreciate you showing me how to vectorize rather than using a loop.

Answer 2

[Image Analyst]

If you just plug each term into the following one, you'll see that DENS completely cancels out and all you're left with is the constants, hence Davg is a constant.

[Polus Patrus]

Thank you.

Answer 3

[Bob Thompson]

After expanding and simplifying your equations I can safely say that when Vavg^2 is used then Davg(i) = 94.753... because you are effectively taking DENS(i)/DENS(i) multiplied by a series of constants which end up being 94.753. Double check your equations.

[Polus Patrus]

Thank you.