MATLAB: Does the function give weird outputs?

functionsvectors

I am trying to create a code to calculate work. I have a vector for n and when I run the script I keep getting numbers that don't make sense such as a zero for the estimated integral when using the vector. when I run the script without the n vector and just input n I get more logical answers but they still seem off.
function [ w,Ws,error ] = trap_wfp610( ~ )
% Calculates the work done using numerical integration and the trapezoidal rule
% Detailed explanation goes here
n=[1,11,21,3,1,41,51]';
h=(5*10^-2)/n;
a=0;
b=5*10^-2;
f=@(a)(5*(10^5)*a+10^5)*pi*(5*10^-2)^2;
g=@(b)(5*(10^5)*b+10^5)*pi*(5*10^-2)^2;
w=h/2*(f(a)+g(b));
syms x
k1=500000;
k2=10^5;
p=(k1*x+k2)*pi*.05^2;
Ws=int(p,x,0,5*10^-2);
error=abs((w-Ws)/Ws)*100;
disp('Work Trap Rule');
disp(w);
disp('Work Actual');
disp(Ws);
disp('Error');
disp(error);
plot(w,n)
plot(error,n)
end
These are my outputs
>> trap_wfp610
Work Trap Rule
         0         0         0         0         0         0    0.8662
Work Actual
(225*pi)/16
Error
[ 100, 100, 100, 100, 100, 100, 5000/51]
ans =
           0         0         0         0         0         0    0.8662
which seem illogical.

Best Answer

Now that I can read your post, having had to edit it myself to make it readable...
It gives weird outputs because you do not understand many basics of MATLAB, from what I can see so far. For example...
n=[1,11,21,31,41,51]';
h=(5*10^-2)/n;
So you create a vector, then do a divide. Great, except you have not bothered to check that what you thought you did and what you actually did were two totally different things. You need to learn how to use element-wise division, NOT just use the / operator. That is, use ./ instead. There is a difference.
So, lets see what happens when you execute the first two lines of your code.
h
h =
     0    0    0    0    0   0.00098039
Hmm. Not what you expected, I suppose. But had you bothered to read the tutorials, you would have learned that element-wise division (and often multiplication) requires the use of the ./ operator.
h=(5*10^-2)./n
h =
         0.05
    0.0045455
     0.002381
    0.0016129
    0.0012195
   0.00098039
Forward slash does a linear algebra operation, that is NOT what you expected to see. The way I did it does what I'll bet you expected to see.
In the future, I suggest that you don't just throw down a pile of code, and hope that it does what you expected, that MATLAB would have read your mind and did what you wanted, rather than what you told it to do. Until you learn what the basic operators do, test each line of code to verify that you got what you expected.
Next, it looks like you are trying to do an n-point trapezoidal rule, with n varying over the set [1,11,21,3,1,41,51]. A good idea on the face of it, but then you don't generate any set of points on that interval, no loops, no implicit loops in your code. You just subtracted two numbers. I'm not sure how MATLAB is supposed to know what you wanted to do here. How is MATLAB supposed to interpret n?
What MATLAB just did was what you TOLD it to do, which in this case, was apparently to produce somewhat random looking garbage.
There are other things I could comment on. For example, while I see while you have learned the basic syntax of function handles, my guess is you do not understand them at all. In your code, you created f and g as identically the same functions, one is a function of a, and one a function of b. But inside, they are identical.
I could go further, but it looks like you mainly need to start learning the basics. For example, suppose you want to perform a basic trapezoidal rule on the function x.^2, over the interval [0,1]. See that I used .^, to allow the operation to work for a vector of inputs, an element-wise exponentiation. (Addition and subtraction do not need element-wise operators. * and / also sometimes do what you will have expected, but until you learn how they work, it is best to be careful.)
f = @(x) x.^2;
n = 11;
xi = linspace(0,1,n);
yi = f(xi);
trapz(xi,yi)
ans =
                   0.335
Not too bad, since 1 / 3 is the correct answer. The 11 point trapezoidal approximation seems about right. I could have done the trapezoidal rule by computing the weights myself, and writing it as a weighted sum, but why bother?
Be careful though, since I'll bet that you think you could have used
n = [1 11 21 31 41 51];
in the above example, and that MATLAB would have known you wanted to do the same operation for each value of n. Sorry, but MATLAB will get that wrong, and your next post will be you wailing "why did this fail?"
As it turns out, I COULD have written somewhat more sophisticated code that would compute n point trapezoidal rule estimates for each of those values of n, but it would just introduce a nifty trick to you that would be confusing to you at this point in your quest to learn MATLAB as fast as you possibly can do so. SLOW DOWN.
So, you need to spend some time learning how to use MATLAB, rather than skimming through, skipping the basics, but learning some random advanced stuff, then trying to throw it all together and hoping that MATLAB will know what you WANT to do. MATLAB cannot read your mind.
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