Summation using For Loop

I have to solve the equation for 'a'.

Now x are the elements in the following array:

x=[0.56746089 0.60481729 0.622521 0.53714241 0.60310756 1.07806689 1.19968209 1.05637284 1.14618436 0.94031809];

My problem is that I do not know how to call the elements in the array in a function.

Answer 1

[Brian Voke]

To call a specific element from an array or matrix you can use this notation: for matrix x the first element would be x(1), the second element would be x(2) and so on. If you're just trying to find the solution to that equation where each element in a corresponds to a solution with a single element in x then you can write the equation using element wise operators to multiply matrices element wise the operator is preceded with period. (So a times x would be written as a .*x). Then you could solve the equation using the solve function.

[J.Cam]

Thanks for the reply, I tried this but I kept having an error.

x=[0.7569

0.69956496

0.60109009

0.67519089

0.14676561

0.72607441

0.65302561

0.40106889

0.71284249

0.69022864];

syms a

m=((x(i,1)).*cos(a.*(x(i,1)))./(sin(a.*((x(i,1))))));

ftn = 10/a + symsum(m,1,10)

value=vpasolve(ftn==0,a)

[Brian Voke]

I'm not sure exactly how you'd format this to work, but I believe your current error is that your trying to use symsum to sum the variable i, but you do not have i as a symbolic variable. Including i as a symbolic variable is a step in the right direction, but I think you may have to look more into the inputs and setup for symsum before you'll get this working right.

[J.Cam]

What's the best way to go about it? Is there an easier way?

[Brian Voke]

I would double check to make sure I didn't mess up any parantheses but I think this is a solution. This works because there's only 10 elements in the x matrix so it's not like you need to specify which elements you want to run then sum. The elementwise multiplication makes it so that the resulting m matrix has 10 elements each corresponding to an element in x. So the normal sum function should work.

x=[0.7569
0.69956496
0.60109009
0.67519089
0.14676561
0.72607441
0.65302561
0.40106889
0.71284249
0.69022864];
syms a
m=(x.*cos(a.*(x))./(sin(a.*x)));
ms=sum(m);
ftn = 10/a + ms;

value=vpasolve(ftn==0,a)

[J.Cam]

This worked! Thank you!

[Brian Voke]

No problemo