MATLAB: How to evaluate a unknown variable

matlab functionvariable

I am trying to evaluate a specific variable, i.e., lambda from the following expression:
alpha=0.9;
g=[3, 2, 1];
N=10;
P=5;
sum(( lambda*(2-alpha)-sqrt(lambda*alpha*(lambda*alpha+g.*4*(1-alpha))) ) ./ ( g.*2*lambda*(alpha-1) )) = N*P
Which function shall I use to find the value of lambda that satisfies the equality above, since it is the only unknown variable?

Best Answer

Using fsolve: 
alpha=0.9;
g=[3, 2, 1];
N=10;
P=5;
f = @(lambda) sum(( lambda*(2-alpha)-sqrt(lambda*alpha*(lambda*alpha+g.*4*(1-alpha))) ) ...
    ./ ( g.*2*lambda*(alpha-1) )) - N*P;
lambda0 = 1;
options = optimoptions('fsolve','Display','iter','Algorithm','levenberg-marquardt');
lambda = fsolve(f, lambda0, options);
Learn more at https://www.mathworks.com/help/optim/ug/fsolve.html
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