R help - Dec 2007 - Integral implicit function

Hi,

Could somebody help me with the following. I want to calculate the integral over
an implicit function. I thought to integrate over a function depending on
uniroot. In previous topics I found a thread about finding the root of an
integral. And that works. But the other way around, does not work. Does R
support this?

I included the following example. The function in the example is very easy and
can be solved explicitly, but when it does not work for such an easy function it
will certainly not work for a more difficult function. First the root of an
integral (which works) and then the integral of a function dependent on uniroot:

# Calculating the root of an integral

a<- function(x,y)
    {x-y}

b<- function(y)
    {integrate(a,lower=1,upper=2,y=y)$value}

d<- uniroot(b,c(0,10))$root

print(d)

# Calculating the integral of a function dependent on uniroot

e<- function(u,v)
    {u-v}

f<- function(v)
    {uniroot(e,c(0,10),v=v)$root}

g<- integrate(f,lower=1,upper=2)$value

print(g)

Does anyone have suggestions how to proceed? By the way, the implicit function I
am targeting does have a unique solution, it is only not explicitly solvable,
i.e. in the example above, you cannot solve u as a function of v explicitly, so
as to substitute it in the integrand.


Thanks a lot in advance for your help,

Best regards,

Eddy Bekkers
Department of Economics
Erasmus University Rotterdam

Have you tried vectorizing the inner function? 
Hint: integrate() calls the integrand vectorwise... 
in your example,
      integrate(Vectorize(f),lower=1,upper=2)
should do what you expected.

Best,
Peter


Eddy H. G. Bekkers wrote:
> 
> Hi,
> 
> Could somebody help me with the following. I want to calculate the
> integral over an implicit function. I thought to integrate over a function
> depending on uniroot. In previous topics I found a thread about finding
> the root of an integral. And that works. But the other way around, does
> not work. Does R support this?
> 
> I included the following example. The function in the example is very easy
> and can be solved explicitly, but when it does not work for such an easy
> function it will certainly not work for a more difficult function. First
> the root of an integral (which works) and then the integral of a function
> dependent on uniroot:
> 
> # Calculating the root of an integral
> 
> a<- function(x,y)
>     {x-y}
> 
> b<- function(y)
>     {integrate(a,lower=1,upper=2,y=y)$value}
> 
> d<- uniroot(b,c(0,10))$root
> 
> print(d)
> 
> # Calculating the integral of a function dependent on uniroot
> 
> e<- function(u,v)
>     {u-v}
> 
> f<- function(v)
>     {uniroot(e,c(0,10),v=v)$root}
> 
> g<- integrate(f,lower=1,upper=2)$value
> 
> print(g)
> 
> Does anyone have suggestions how to proceed? By the way, the implicit
> function I am targeting does have a unique solution, it is only not
> explicitly solvable, i.e. in the example above, you cannot solve u as a
> function of v explicitly, so as to substitute it in the integrand. 
> 
> 
> Thanks a lot in advance for your help,
> 
> Best regards,
> 
> Eddy Bekkers
> Department of Economics
> Erasmus University Rotterdam
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 
> 
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