how to use optimization iterative display

how would i use optimization iterative display to display the value of Ein after each iteration?

clc
close all
clear all


gam = 10e-3; % damping frequency
f = 8.8e-3; % oscillator strength
eb = 11.2; % background epsilon
x = 5.0; %constant
om = 1.5;  % frequency array;%frequency array om=1.4:0.001:1.6
syms hw0 k wp Ein er

V = [hw0, k ,wp, Ein, er ];
eq1=hw0 - 1i*((gam+sqrt(-(gam*gam)-(4*k*k)))/(2)); % resonant frequency
eq2=k - sqrt((wp*wp)/(1+2*eb) ); %to find resonant frequency
eq3=wp - sqrt(hw0^2+x*Ein*Ein);%plasma frequency
eq4=Ein - (eb-er)/(er+2*eb);%internal electric field
eq5=er - 1- ( ( f * wp*wp )./ (hw0*hw0-om.*om-1i.*om*gam));%reletive permittivity
eqs = matlabFunction([eq1;eq2;eq3;eq4;eq5], 'Vars', {[hw0 k wp Ein er ].'});
initialguess=[1.5; 2.5 ;1.4; 0.436 - 1i*0.00000112 ; -16.5-1i*1.06 ];

options = optimoptions('fsolve','Display','none','PlotFcn',@optimplotfirstorderopt,'MaxFunctionEvaluations',100);
sol=fsolve(eqs,initialguess,options);

hw0=sol(1);
k=sol(2);
wp=sol(3);
Ein=sol(4);
er=sol(5);

Answer 1

[Ameer Hamza]

This shows how to print value of Ein in each iteration using OutputFcn

clc
close all
clear all


gam = 10e-3; % damping frequency
f = 8.8e-3; % oscillator strength
eb = 11.2; % background epsilon
x = 5.0; %constant
om = 1.5;  % frequency array;%frequency array om=1.4:0.001:1.6
syms hw0 k wp Ein er

V = [hw0, k ,wp, Ein, er ];
eq1=hw0 - 1i*((gam+sqrt(-(gam*gam)-(4*k*k)))/(2)); % resonant frequency
eq2=k - sqrt((wp*wp)/(1+2*eb) ); %to find resonant frequency
eq3=wp - sqrt(hw0^2+x*Ein*Ein);%plasma frequency
eq4=Ein - (eb-er)/(er+2*eb);%internal electric field
eq5=er - 1- ( ( f * wp*wp )./ (hw0*hw0-om.*om-1i.*om*gam));%reletive permittivity
eqs = matlabFunction([eq1;eq2;eq3;eq4;eq5], 'Vars', {[hw0 k wp Ein er ].'});
initialguess=[1.5; 2.5 ;1.4; 0.436 - 1i*0.00000112 ; -16.5-1i*1.06 ];

options = optimoptions('fsolve','Display','none', 'OutputFcn', @outFcn, 'PlotFcn',@optimplotfirstorderopt,'MaxFunctionEvaluations',100);
sol=fsolve(eqs,initialguess,options);

hw0=sol(1);
k=sol(2);
wp=sol(3);
Ein=sol(4);
er=sol(5);

function y = outFcn(x, ~, s)
    if strcmp(s, 'iter') % only print value when the current iteration finishes
        fprintf('Ein=%f\n', x(4));
    end
    y = 0;
end

[Anushka Deshpandey]

also how would i plot Ein against the range 1.4:1.6?

[Ameer Hamza]

Can you explain what do you mean by "range 1.4:1.6"?

[Anushka Deshpandey]

I want for the value of om to be an array from 1.4 to 1.6 instead of the constant 1.5. After that i need to plot Ein vs om

[Ameer Hamza]

You can write a for loop. Following code is untested, but it gives a general idea

clc
close all
clear all


gam = 10e-3; % damping frequency
f = 8.8e-3; % oscillator strength
eb = 11.2; % background epsilon
x = 5.0; %constant
OM = 1.4:0.01:1.6;  % frequency array;%frequency array om=1.4:0.001:1.6

Ein_sol = zeros(size(OM));
for i = 1:numel(OM)
    om = OM(i);
    syms hw0 k wp Ein er
    V = [hw0, k ,wp, Ein, er ];
    eq1=hw0 - 1i*((gam+sqrt(-(gam*gam)-(4*k*k)))/(2)); % resonant frequency
    eq2=k - sqrt((wp*wp)/(1+2*eb) ); %to find resonant frequency
    eq3=wp - sqrt(hw0^2+x*Ein*Ein);%plasma frequency
    eq4=Ein - (eb-er)/(er+2*eb);%internal electric field
    eq5=er - 1- ( ( f * wp*wp )./ (hw0*hw0-om.*om-1i.*om*gam));%reletive permittivity
    eqs = matlabFunction([eq1;eq2;eq3;eq4;eq5], 'Vars', {[hw0 k wp Ein er ].'});
    initialguess=[1.5; 2.5 ;1.4; 0.436 - 1i*0.00000112 ; -16.5-1i*1.06 ];
    
    options = optimoptions('fsolve','Display','none', 'OutputFcn', @outFcn, 'PlotFcn',@optimplotfirstorderopt,'MaxFunctionEvaluations',100);
    sol=fsolve(eqs,initialguess,options);
    
    hw0_sol=sol(1);
    k_sol=sol(2);
    wp_sol=sol(3);
    Ein_sol(i)=sol(4);
    er_sol=sol(5);
end

figure()
axes();
plot(OM, Ein_sol)

function y = outFcn(x, ~, s)
    if strcmp(s, 'iter') % only print value when the current iteration finishes
        fprintf('Ein=%f\n', x(4));
    end
    y = 0;
end

[Anushka Deshpandey]

can i store sym variables in a double array?

[Ameer Hamza]

No, they cannot be used in same array. I have fixed the issue with my code. Try the updated code.

[Anushka Deshpandey]

thanks a lot!!it worked

[Ameer Hamza]

I am glad to be of help!

Answer 2

[Mario Malic]

Edit: Display does not return values of variables in iterations, my bad. Ameer's answer should get you what you wanted.

Go to documentations on fsolve, see the left section and find Input Arguments -> Options, find Display option and set it appropriately.