how to solve a cubic equation where the last term is an array

I have an equation with a set of constants in it and one array, I would like to solve the cubic equation for each of the V_total values which there are 365 of, and return the real roots for each V_total value into a single array of real solutions. I have tried using root() as well as fsolve() and in both cases it doesnt work. In the case of fsolve() i get the following message:

'fsolve' requires Optimization Toolbox.

Error in Hydroplant_Power_Calculation (line 28)

sol_x(i) = fsolve(@(V_total) fun(h, V_total(i)), rand());

Pasting my code below:

%declaring variables

Q_in = a column vector imported into matlab with 365 values

z = 70;

top_width = 223.6;

bottom_width = 61.6;

reservoir_length = 1;

%calculating reservoir volume

trapezium_area = ((top_width + bottom_width)/2)*z;

total_reservoir_volume = trapezium_area * reservoir_length *(1/2);

%now we need to find the volume added for each day

volume_added = Q_in.*86400; %in cubic meters

Q_out = 3; %metres cubed

volume_removed = Q_out * 86400;

V_total = volume_added - volume_removed; % volume at any given day

%EVERYTHING UP TO HERE IS FINE, NOW I TRY TO SOLVE THE CUBIC:

% Solving the cubic equation for h

%a = (1/19600)*top_width * reservoir_length;

%b = (1/280)*bottom_width*reservoir_length;

%c = 0;

%d = V_total;

%p = [a b c -d];

%h = roots(p)

%my second attempt:

fun = @(h, V_total) (1/19600)*top_width * reservoir_length*h.^3.+(1/280)*bottom_width*reservoir_length*h.^2-V_total

sol_x = zeros(size(V_total));

for i=1:numel(V_total)

sol_x(i) = fsolve(@(V_total) fun(h, V_total(i)), rand());

end

[Torsten]

It seems you don't have a valid licence for the Optimization Toolbox which is required to use "fsolve".

Answer 1

[Alan Weiss]

Try this instead of your code after %EVERYTHING UP TO HERE IS FINE:

sol_x = zeros(size(V_total));
for i = 1:numel(V_total)
    fun = @(h)(1/19600)*top_width * reservoir_length*h^3.+(1/280)*bottom_width*reservoir_length*h^2-V_total(i);
    sol_x(i) = fzero(fun,1);
end

Alan Weiss

MATLAB mathematical toolbox documentation

[Ryszard Nowacki]

Hi,

Thanks, at the end the problem was i didint realise i need to download the optimisation toolbox for it, the code seems to work now. Thanks for your time anyway!

[Alan Weiss]

If you use my answer you don't need Optimization Toolbox, only fzero, which is available in all MATLAB installations.

Alan Weiss

MATLAB mathematical toolbox documentation