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

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Ryszard Nowacki
Ryszard Nowacki 2021-12-9
评论： Alan Weiss 2021-12-12
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

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采纳的回答

Alan Weiss
Alan Weiss 2021-12-9
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
  2 个评论
Ryszard Nowacki
Ryszard Nowacki 2021-12-12
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
Alan Weiss 2021-12-12
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

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