vpasolve returns empty sym 0-by-1

Hi,

I have written a function that has been working consistently. This is the function below, and I will describe its procedure and aim. The important section is for k(2) -> k(n). There is an equation w^2=-g*k*tan(kd) which has infinite solutions due to the periodicity of the tangens. I am trying to find each of these solutions. However today I changed a few values, namely d and n, and I have been getting the error: In an assignment A(:) = B, the number of elements in A and B must be the same (Error in k_construct (line 19) kx(h)=vpasolve(f2, k, kx(h-1));). I have worked out that the vpasolve(f2, k, kx(h-1)) is returning Empty sym: 0-by-1. I cannot understand why it is doing this as there must be solutions as a parabola must intersect the tangens. It is working for d = 0.07 but not d = 0.17 or d = 0.27. It is working for d = 0.5, d = 0.6 and so on. I can't seem to find any problem with my code, any help would be greatly appreciated. Thanks so much !!

function [kx] = k_construct(w, d, n, L)
%Function determines the k column vector with n solutions and then
%constructs a matrice with i and j values of k

%Constants
g=9.81; %m s^-2 (Gravitational Constant)

%First Term

syms k
f1=(w^2)-(g*k*tanh(k*d));
kx(1)=vpasolve(f1, k, [0 Inf]);

%Other solutions in column vector
f2=(w^2)+(g*abs(k)*tan(abs(k)*d));
h = 2;
while h <= n
    vpasolve(f2, k, kx(h-1))
    kx(h)=vpasolve(f2, k, kx(h-1));
    q = 1;
    while (((kx(h) - kx(h-1)) < (d*pi/(2*L))) | (kx(h) < 0))
        kx(h) = vpasolve(f2, k, kx(h-1)+q);
        q = q+1;
    end
    h = h + 1;
end
kx;
end

[Alex Wylie]

I would really appreciate an answer asap as I thought my code was working and I have a deadline for a paper coming up very soon .. I was really surprised when this error came up and it threw a significant spanner in the works. Thanks so much for your time, Alex

[John D'Errico]

http://www.mathworks.com/matlabcentral/answers/29922-why-your-question-is-not-urgent-or-an-emergency

Everyone wants an answer to their question immediately. YESSIR! We will get right to it.

Of course not all problems as posed have a solution.

[Alex Wylie]

Yeah fair enough, sorry for being greedy. I appreciate everyone that spends any time trying to solve this problem. I have spent countless hours and any external insight is greatly appreciated. Sorry

[Karan Gill]

Did you try plotting the equation to ensure a solution does indeed exists? (i.e. the plot of "f2" crosses the zero line)

The vpasolve page has an example that shows the use of a plot to verify if a solution exists: https://www.mathworks.com/help/symbolic/vpasolve.html#bt51ety-1_1

Answer 1

[John D'Errico]

Ok, I really think the answer is that not all problems have a solution.

I don't see a value for n or w or L, as I could then give you a better answer. A parabola need not intersect a line always.

So my suggestion is to plot the curve. There is only one unknown. So plot the function for the values of d where it fails. My guess is you will see no solution.

If you DO see a solution in the plot, then it should give you an idea of a starting value for vpasolve, telling it where to look. Or, if you can provide all of the constants, then I can take a better look at it. I'll check back in an hour.