[R] using integrate with optimize nested in the integration
Hi guys im having a problem getting R to numerically integrate for some function, say f(bhat)*optimize(G(bhat)), over bhat. Where id like to integrate this over some finite range, so that here as we integrate over bhat optimize would return a different optimum. For instance consider this simple example for which I cannot get R to return the desired result: f - function(bhat) exp(bhat) g - function(bhat) optimize(f,c(0,15),maximum=TRUE)$maximum*bhat integrate(g,lower=0,upper=5) which returns: 187.499393759 with absolute error 2.1e-12 However this is an approximation of : 15*(5^2/2 - 0)=187.5, not what I intended on getting. Its not identifying that f is a function of bhat ... any advice or ways I can get integrate to not treat this as a constant? Any help is appreciated. Gregoy Gentlemen __ [[alternative HTML version deleted]] __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] using integrate with optimize nested in the integration
In your example, f is a function, but optimize(f,c(0,15),maximum=TRUE)$maximum is just a number (the point at which f reaches its maximum value). I'm not sure what you want, but if you had say f - function(x,y) x^3 + yx + 1 and defined g - function(y) optimize(f,c(0,5),maximum=TRUE,y)$maximum then g(t) is the x-value at which the function f(x,t) (over x in (0,5)) reaches its maximum for this fixed t. That could then be integrated. Reid Huntsinger -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Gregory Gentlemen Sent: Thursday, July 28, 2005 3:58 PM To: r-help@stat.math.ethz.ch Subject: [R] using integrate with optimize nested in the integration Hi guys im having a problem getting R to numerically integrate for some function, say f(bhat)*optimize(G(bhat)), over bhat. Where id like to integrate this over some finite range, so that here as we integrate over bhat optimize would return a different optimum. For instance consider this simple example for which I cannot get R to return the desired result: f - function(bhat) exp(bhat) g - function(bhat) optimize(f,c(0,15),maximum=TRUE)$maximum*bhat integrate(g,lower=0,upper=5) which returns: 187.499393759 with absolute error 2.1e-12 However this is an approximation of : 15*(5^2/2 - 0)=187.5, not what I intended on getting. Its not identifying that f is a function of bhat ... any advice or ways I can get integrate to not treat this as a constant? Any help is appreciated. Gregoy Gentlemen __ [[alternative HTML version deleted]] __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] using integrate with optimize nested in the integration
Gregory Gentlemen wrote:
Hi guys
im having a problem getting R to numerically integrate for some function,
say f(bhat)*optimize(G(bhat)), over bhat. Where id like to integrate this
over some finite range, so that here as we integrate over bhat optimize would
return a different optimum.
For instance consider this simple example for which I cannot get R to return
the desired result:
f - function(bhat) exp(bhat)
g - function(bhat) optimize(f,c(0,15),maximum=TRUE)$maximum*bhat
integrate(g,lower=0,upper=5)
which returns:
187.499393759 with absolute error 2.1e-12
However this is an approximation of : 15*(5^2/2 - 0)=187.5, not what I
intended on getting. Its not identifying that f is a function of bhat ... any
advice or ways I can get integrate to not treat this as a constant?
Any help is appreciated.
Gregoy Gentlemen
Hi, Gregory,
Your example is not very useful here since the optimize function is
constant.
I think you want something more like:
f - function(bhat, x) {
exp(bhat * x)
}
g - function(bhat) {
o - vector(numeric, length(bhat))
for(i in seq(along = bhat))
o[i] - optimize(f, c(0,15), maximum = TRUE, x = bhat[i])$maximum
bhat * o
}
integrate(g, lower = 0, upper = 5)
Because of the way integrate works, g(bhat) will always return a vector.
HTH,
--sundar
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] using integrate with optimize nested in the integration
Thanks for the prompt reply. Your right, that was a weak example. Consider this one though: f - function(n,x) (x-2.5)^2*n g - function(y) optimize(f,c(0,15), maximum=TRUE,x=y)$maximum*y then if you try: integrate(g,lower=0,upper=5) it produces: Error in optimize(f, c(0, 15), maximum = TRUE, x = y) : invalid function value in 'optimize' Any ideas? My problem is a similar more complex function in which optimizaiton depends on the value of the integrator. Huntsinger, Reid [EMAIL PROTECTED] wrote: In your example, f is a function, but optimize(f,c(0,15),maximum=TRUE)$maximum is just a number (the point at which f reaches its maximum value). I'm not sure what you want, but if you had say f - function(x,y) x^3 + yx + 1 and defined g - function(y) optimize(f,c(0,5),maximum=TRUE,y)$maximum then g(t) is the x-value at which the function f(x,t) (over x in (0,5)) reaches its maximum for this fixed t. That could then be integrated. Reid Huntsinger -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Gregory Gentlemen Sent: Thursday, July 28, 2005 3:58 PM To: r-help@stat.math.ethz.ch Subject: [R] using integrate with optimize nested in the integration Hi guys im having a problem getting R to numerically integrate for some function, say f(bhat)*optimize(G(bhat)), over bhat. Where id like to integrate this over some finite range, so that here as we integrate over bhat optimize would return a different optimum. For instance consider this simple example for which I cannot get R to return the desired result: f - function(bhat) exp(bhat) g - function(bhat) optimize(f,c(0,15),maximum=TRUE)$maximum*bhat integrate(g,lower=0,upper=5) which returns: 187.499393759 with absolute error 2.1e-12 However this is an approximation of : 15*(5^2/2 - 0)=187.5, not what I intended on getting. Its not identifying that f is a function of bhat ... any advice or ways I can get integrate to not treat this as a constant? Any help is appreciated. Gregoy Gentlemen __ [[alternative HTML version deleted]] __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html -- -- __ [[alternative HTML version deleted]] __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] using integrate with optimize nested in the integration
Again, not a good example, since f is linear in n so the max will always
be at 15.
Try this:
f - function(x, n) -(x - 2.5 * n)^2 # max is at 2.5*n
g - function(n) {
o - vector(numeric, length(n))
for(i in seq(along = n))
o[i] - optimize(f, c(0, 15), maximum = TRUE, n = n[i])$maximum
n * o
}
integrate(g, lower = 0, upper = 5)
# int_0^5 (2.5 * n^2) dn = 2.5/3 * 5^3 = 104.1667
--sundar
Gregory Gentlemen wrote:
Thanks for the prompt reply.
Your right, that was a weak example.
Consider this one though:
f - function(n,x) (x-2.5)^2*n
g - function(y) optimize(f,c(0,15), maximum=TRUE,x=y)$maximum*y
then if you try:
integrate(g,lower=0,upper=5)
it produces:
Error in optimize(f, c(0, 15), maximum = TRUE, x = y) :
invalid function value in 'optimize'
Any ideas?
My problem is a similar more complex function in which optimizaiton depends
on the value of the integrator.
Huntsinger, Reid [EMAIL PROTECTED] wrote:
In your example, f is a function, but
optimize(f,c(0,15),maximum=TRUE)$maximum is just a number (the point at
which f reaches its maximum value). I'm not sure what you want, but if you
had say
f - function(x,y) x^3 + yx + 1
and defined
g - function(y) optimize(f,c(0,5),maximum=TRUE,y)$maximum
then g(t) is the x-value at which the function f(x,t) (over x in (0,5))
reaches its maximum for this fixed t. That could then be integrated.
Reid Huntsinger
-Original Message-
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of Gregory Gentlemen
Sent: Thursday, July 28, 2005 3:58 PM
To: r-help@stat.math.ethz.ch
Subject: [R] using integrate with optimize nested in the integration
Hi guys
im having a problem getting R to numerically integrate for some function,
say f(bhat)*optimize(G(bhat)), over bhat. Where id like to integrate this
over some finite range, so that here as we integrate over bhat optimize
would return a different optimum.
For instance consider this simple example for which I cannot get R to return
the desired result:
f - function(bhat) exp(bhat)
g - function(bhat) optimize(f,c(0,15),maximum=TRUE)$maximum*bhat
integrate(g,lower=0,upper=5)
which returns:
187.499393759 with absolute error 2.1e-12
However this is an approximation of : 15*(5^2/2 - 0)=187.5, not what I
intended on getting. Its not identifying that f is a function of bhat ...
any advice or ways I can get integrate to not treat this as a constant?
Any help is appreciated.
Gregoy Gentlemen
__
[[alternative HTML version deleted]]
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
--
--
__
[[alternative HTML version deleted]]
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] using integrate with optimize nested in the integration
Integrate needs a vectorized function. For your example,
integrate(function(x) sapply(x,g),lower=0,upper=5)
187.4994 with absolute error 2.1e-12
Reid Huntsinger
-Original Message-
From: Gregory Gentlemen [mailto:[EMAIL PROTECTED]
Sent: Thursday, July 28, 2005 4:37 PM
To: Huntsinger, Reid; r-help@stat.math.ethz.ch
Subject: RE: [R] using integrate with optimize nested in the integration
Thanks for the prompt reply.
Your right, that was a weak example.
Consider this one though:
f - function(n,x) (x-2.5)^2*n
g - function(y) optimize(f,c(0,15), maximum=TRUE,x=y)$maximum*y
then if you try:
integrate(g,lower=0,upper=5)
it produces:
Error in optimize(f, c(0, 15), maximum = TRUE, x = y) :
invalid function value in 'optimize'
Any ideas?
My problem is a similar more complex function in which optimizaiton depends
on the value of the integrator.
Huntsinger, Reid [EMAIL PROTECTED] wrote:
In your example, f is a function, but
optimize(f,c(0,15),maximum=TRUE)$maximum is just a number (the point at
which f reaches its maximum value). I'm not sure what you want, but if you
had say
f - function(x,y) x^3 + yx + 1
and defined
g - function(y) optimize(f,c(0,5),maximum=TRUE,y)$maximum
then g(t) is the x-value at which the function f(x,t) (over x in (0,5))
reaches its maximum for this fixed t. That could then be integrated.
Reid Huntsinger
-Original Message-
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of Gregory Gentlemen
Sent: Thursday, July 28, 2005 3:58 PM
To: r-help@stat.math.ethz.ch
Subject: [R] using integrate with optimize nested in the integration
Hi guys
im having a problem getting R to numerically integrate for some function,
say f(bhat)*optimize(G(bhat)), over bhat. Where id like to integrate this
over some finite range, so that here as we integrate over bhat optimize
would return a different optimum.
For instance consider this simple example for which I cannot get R to return
the desired result:
f - function(bhat) exp(bhat)
g - function(bhat) optimize(f,c(0,15),maximum=TRUE)$maximum*bhat
integrate(g,lower=0,upper=5)
which returns:
187.499393759 with absolute error 2.1e-12
However this is an approximation of : 15*(5^2/2 - 0)=187.5, not what I
intended on getting. Its not identifying that f is a function of bhat ...
any advice or ways I can get integrate to not treat this as a constant?
Any help is appreciated.
Gregoy Gentlemen
__
[[alternative HTML version deleted]]
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
--
Notice: This e-mail message, together with any attachments, ...{{dropped}}
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
