# Find values that put equation to zero

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MARCO FORTI on 9 Apr 2021
Commented: MARCO FORTI on 10 Apr 2021
In this model: where all the variables are of dymension TX1, I need to find all the (T) values of gamma that put the equation to zero.
I tryed with the following code, but the program returns me all NAN, how can I fix the code to get it?
j=1; %increment level. The loop will work for j>1 as well.
for i=1:j:T;
fnc = @(gamma,C,S) 1./(1+gamma).*(C(i)-(S(i)*gamma)) - M(i); % Model function
rn = @(gamma) norm(M - fnc(gamma,C,S)); % Residual norm
gamma0 = ; % Inizializzazione
[gamma, ResNorm] = fzero(rn, gamma0);
end

Matt J on 10 Apr 2021
Edited: Matt J on 10 Apr 2021
gamma=nan(T,1);
j=1; %increment level. The loop will work for j>1 as well.
for i=1:j:T;
ci=C(i); si=S(i); mi=M(i);
fnc = @(gamma) 1./(1+gamma).*(ci-(si*gamma)) - mi;
gamma0 = 15;
[gamma(i), ResNorm] = fzero(fcn, gamma0);
end
MARCO FORTI on 10 Apr 2021
It works, thanks!

Alan Stevens on 9 Apr 2021
Edited: Alan Stevens on 9 Apr 2021
If your expression is equal to zero, then you can rearrange it to get gamma directly. A little algebra gives
gamma = (C-M)./(S+M);
No need for fzero at all.
MARCO FORTI on 10 Apr 2021
Sorry, I mispelled the formula, now I corrected fixed it.
However I would like to understand how to develope a proper matlab code for this (or other similar) situations. Could you help?