Obtaining the minimum value of solutions

Hello,

I would like to collect the "minimum value" of each positive solution corresponding to each "n". After running the program, there are series of solutions for each "n". Would you let me know the way of obtaining the minimum value among the series of solution?

format long e
T=0.1;
k=1.0;        
k_1=0.2;      
k_2=0.1;    
a_p=0.0001;    
k_p=a_p/10;    
a_q=0.00015;   
k_q=0.00002;   
theta=0.01;               
m1=0.0000005;            
m2=0.0000002;             
W=0.00002;                
syms x
gamma=(a_p*k*k_2)/(k_p*m1*k_1);

for n=1:1:10
equation=[(1+sqrt(gamma*theta^n))/sqrt(gamma+sqrt(theta^n))]^2-[(theta+x)/(1+x)]^(n+1)==0;  
sol=vpasolve(equation,x);
fprintf('%d\n',n);
fprintf('%.10e\n',sol(sol>0.0));   <======= Any additional command to take "minimum value" of the solution?
end

Answer 1

[Star Strider]

The ‘minimum’ depends on how you want to define it. Most of the results returned in ‘sol’ are complex, and the min function will return the value with the smallest magnitude (absolute value).

See the documentation section on Smallest Complex Element (link) for details.

In the interim, see if this will do what you want:

fprintf('%.10e\n',min(sol(sol>0.0)));

Experiment to get the result you want.

[onsagerian]

Thank you for your explanation!

[Star Strider]

As always, my pleasure!