# Initial guess Error using fsolve

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Shailee Yagnik on 23 Aug 2019
Commented: Walter Roberson on 29 Aug 2019
This is my code
clear all
tic
% fun= @(x)qfunc(2-0.5*x)*exp(-x^2);
% %
P0=0.5;
P1=1-P0;
P=P0/P1;
rho=0.3; %covariance
s1=0.5; %mean of sensor 1
s2=1;%mean of sensor 2
Sm=max(s1,s2);
t1=-20:0.01:20 ; %threhsold for sensor 1
stop=0;
stop_1=0;
for i=1:length(t1)
fun= @(x2) exp(-s2.^2./2).*exp(x2.*s2).*qfunc((t1(i)-s1-rho.*x2+rho.*s2)./sqrt(1-rho.^2))-P.*qfunc((t1(i)-rho.*x2)./sqrt(1-rho.^2))
myfun= @(y) exp(-s2^2./2).*exp(y*s2)*(1-qfunc((t1(i)-s1-rho*y+rho*s2)./sqrt(1-rho^2)))./(1-qfunc((t1(i)-rho.*y)./sqrt(1-rho^2)))-P;
y0=rand;
tw0=fsolve(myfun,y0);
end
I get this error msg ''Objective function is returning undefined values at initial point. fsolve cannot
continue.''
I think the function handle becomes of 0/0 form for initial guess because of qfunc of what I have underlined. How do I put a condtion to use the approximate of qfunc whenever the fsolve counters 0/0 form?

Walter Roberson on 23 Aug 2019
Array indices must be positive integers or logical values.
Error in @(y)exp(-s2^2./2).*exp(y*s2)*(1-qfunc((t1(i)-s1-rho*y+rho*s2)./sqrt(1-rho^2)))./(1-qfunc((t1(i)-rho.*y)./sqrt(1-rho^2)))-P
Your t1 is a vector, but your i is not defined so it defaults to being sqrt(-1) which is not a valid index.
Shailee Yagnik on 23 Aug 2019
Hello,
I have editted the above code in question kindly go through it. It still gives the error: ''Objective function is returning undefined values at initial point. fsolve cannot continue''

Walter Roberson on 23 Aug 2019
NZ = @(a,b) a ./ (b + (a==0 & b == 0));
myfun=@(y) exp(-s2^2./2).*exp(y*s2).*NZ(1-qfunc((t1(i)-s1-rho*y+rho*s2)./sqrt(1-rho^2)),1-qfunc((t1(i)-rho.*y)./sqrt(1-rho^2)))-P;
This detects the case where numerator and denominator are both 0, and substitutes 1 for the denominator in that case, giving a 0/1 result. Perhaps you might prefer
NZ = @(a,b) (a + (a==0 & b == 0)) ./ (b + (a==0 & b == 0));

Shailee Yagnik on 24 Aug 2019
Thank You. It solved the problem.
Shailee Yagnik on 29 Aug 2019
NEED Help!
is it correct to write and execute the function in context to the above problem:
NZ = @(a,b,y) ( (a+ (a==0 & b==0).*(1-1./(sqrt(2.*pi).*(t1-s1-rho.*y+rho.*s2)./sqrt(1-rho.^2))).*exp(-((t1-s1-rho.*y+rho.*s2)./sqrt(1-rho.^2)).^2./2))./ (b + (a==0 & b==0 )*(1-1./(sqrt(2.*pi).*(t1-rho.*y)./sqrt(1-rho.^2))).*exp(-((t1-rho.*y)./sqrt(1-rho.^2)).^2./2)));
myfun= @(y) (exp(-s2^2./2).*exp(y*s2)*NZ(qfunc(-(t1(i)-s1-rho*y+rho*s2)./sqrt(1-rho^2)),qfunc(-(t1(i)-rho.*y)./sqrt(1-rho^2)),y))-(P);
Walter Roberson on 29 Aug 2019
Possibly. However for clarity I would probably move some of that expressions into helper functions; in its current form, it is difficult to read.