Using fzero solving function between two bounds

Hi all.

I have tried to search up this issue I am having with the search function and have tried to find similar implementations but so far turned up nothing! This is my first time asking a question on here so please feel free to ask anything I haven't offered to help solve the issue.

I am trying to solve for an angle phistar between two bounds, sim,epsilon (1e-6) and pi/2 if f_func @ pi/2 > 0.

f_func is a function containing more than just the angle variable.

f_func returns decimals, both positive and negative of magnitude less than 2 when I run the main script.

When I run my main code, I get this error. This doesn't make sense to me as my interval endpoints are finite and real?!?

I have tried implementing fsolve, lsqnonlin and fminsearch but to no avail.

Can anyone suggest an alternative solving function or see any errors in the function syntax?

function [phistar] = BEMSOLVE(phiv,rotor,sim)
%%% Function to solve Blade Element Momentum Theory Equations via Ning's Implementation



if  f_func(pi/2,rotor,sim) > 0 
           
    phistar =  fzero(@(phiv) f_func(phiv,rotor,sim),[sim.epsilon,pi/2]);
   
elseif (fPB_func(-pi/4,rotor,sim) < 0 && fPB_func(sim.epsilon,rotor,sim) > 0)

    phistar = fzero(@(phiv) fPB_func(phiv,rotor,sim),[-pi/4,-sim.epsilon]);
  
else
     phistar = fzero(@(phiv) f_func(phiv,rotor,sim),[pi/2,pi]);               
end

[darova]

Can you attach f_func?

[Johnny Dewhurst]

function [f] = f_func(phiv,rotor,sim)
%%% Function to return f

a          = a_func(phiv,rotor);
kappaprime = kappaprime_func(phiv,rotor);

f          = (sin(phiv)./(1-a))-(cos(phiv).*(1-kappaprime)./(sim.lambda));

end

[Johnny Dewhurst]

I think the problem may be that I am trying to use fzero to solve an array? Is fzero capable of this, or is there another function I should be using?

[darova]

fzero can return only one root. YOu can use addition for loop for finding several solutions

[John D'Errico]

fzero CANNOT solve an array. You could use arrayfun, if you know what you are doing, but it is simpler to just use a loop.

[Johnny Dewhurst]

The solution I came up with was to use a temporary input for each iteration, ensuring I was passing a single element, rather than an array to fzero as below. I hope this comes in handy for others!

phistar = cell(1,sim.N);                            % Allocating phistar
for i = 1:sim.N                                     % Looping elements radially
            
rotor.spani        = linspace(turbine.hub,turbine.tip-0.1,sim.N);                            
rotor.solidityi(i) = interp1(input.span,input.solidity,rotor.spani(i),'linear','extrap');                
rotor.twisti(i)    = interp1(input.span,input.twist,rotor.spani(i),'linear','extrap');   
rotor.Ci(i)        = rotor.solidityi(i)*2*pi.*rotor.spani(i)/turbine.B;                   
rotor.alphav(i)    = phi(i)-rotor.twisti(i);                                              

temp_rotor.spani      = rotor.spani(i);             % Interpolated span     [m]  
temp_rotor.solidityi  = rotor.solidityi(i);         % Interpolated solidity [-]            
temp_rotor.twisti     = rotor.twisti(i);            % Interpolated twist    [radians] 
temp_rotor.Ci         = rotor.Ci(i);                % Interpolated Chord    [m]
temp_rotor.alphav     = rotor.alphav(i);            % Local AoA             [radians]

phistar{i}            = BEMSOLVE(phi(i),rotor,temp_rotor,sim);                
clear i                   
end