function [p_in,lim_lower,lim_upper]=initParamExponential(x,y)
%Assumes form a*exp(-bx)+c

%Setting upper and lower limits
[amp_max,ind_max]=max(y);
[amp_min,ind_min]=min(y);

lim_upper=[Inf,Inf,Inf];
lim_lower=-lim_upper;

%Fix to avoid unphysical offsets on data where all y values exceed 0.
if all(y>0)
    lim_lower(3)=0;
end

if abs(amp_max)>abs(amp_min)
    lim_upper(1)=Inf;
    lim_lower(1)=0;
else
    lim_upper(1)=0;
    lim_lower(1)=-Inf;
end

if (ind_max>ind_min && abs(amp_max)>abs(amp_min))...
        || (ind_max<ind_min && abs(amp_max)<abs(amp_min))
    lim_upper(2)=Inf;
    lim_lower(2)=0;
else
    lim_upper(2)=0;
    lim_lower(2)=-Inf;
end

%Method for estimating initial parameters taken from 
%http://www.matrixlab-examples.com/exponential-regression.html. Some
%modifications required to account for negative y values
% y=y-amp_min;
if all(y>0)
    y=y-amp_min+eps;
    n=length(x);
    y2=log(y);
    j=sum(x);
    k=sum(y2);
    l=sum(x.^2);
    r2=sum(x .* y2);
    p_in(2)=(n * r2 - k * j)/(n * l - j^2);
    p_in(1)=exp((k-p_in(2)*j)/n);
    y=y+amp_min-eps;
elseif abs(amp_max)>abs(amp_min) && amp_max>0
    p_in(1)=amp_max;
    p_in(2)=-1;
else
    p_in(1)=amp_min;
    p_in(2)=-1;
end

if abs(amp_max)>abs(amp_min)
    p_in(3)=amp_min;
else
    p_in(3)=amp_max;
end

end