On Dec 17, 2013, at 8:53 AM, Aur?lien Philippot wrote:
> Dear R experts,
>
> I am trying to find numerical solutions for an integral equation.
>
>
> Here is an example:
>
> I started by defining the integrand, as a function of x and C, where x is
> the variable of integration and C is the parameter I am interested in:
>
>
> integrand<- function(C,x){-((100000*x)^(-1)-(1000*x+C)^(-1))*
> 1/(0.20*sqrt(2*pi))*exp(-0.5*(x-0.10)/(0.20))^2)}
Error: unexpected ')' in:
"integrand<- function(C,x){-((100000*x)^(-1)-(1000*x+C)^(-1))*
1/(0.20*sqrt(2*pi))*exp(-0.5*(x-0.10)/(0.20))^2)"
Taking out the last parenthesis resulted in a variety of error messages
including:
> output(0)
Error in integrate(integrand, C = C, lower = 0, upper = Inf) :
extremely bad integrand behaviour> output(-10)
Error in integrate(integrand, C = C, lower = 0, upper = Inf) :
the integral is probably divergent
> Then, I integrate with respect to x, and define an objective function
> (output) with respect to C:
>
>
> output<- function(C) integrate(integrand, C=C, lower=0, upper=Inf)$value
>
>
Generally these problems are solved with the use of something along the lines of
sapply( seq(...), output) # across an appropriate domain
Or using the `Vectorize` function.
But since you did not supply tested code for the integrand, I am not proceeding
further.
--
david.
> I would like all the values of C (if any) for which the integral is equal
> to 0.
>
> I did the following:
>
>
> library(rootSolve)
>
> uniroot.all(output, c(0,1000000))
>
>
> but that does not work ("evaluation of function gave a result of wrong
> length"). I cannot either plot the function using plot or curve. I
don't
> understand what is going on?
>
> Thanks in advance for any advice!
>
> Aurelien
--
David Winsemius
Alameda, CA, USA