If this is posted elsewhere I cannot find it. I need to perform multiple
integration where some of the variables are in the bounds of the other
variables. I was trying to use R2Cuba function but cannot set the upper and
lower bounds. My code so far is :
int <- function(y){
u2 = y[1]
z2 = y[2]
u1 =y[3]
z1 = y[4]
ff <- u1*(z1-u1)*u2*(z2-u2)*exp(-0.027*(12-z2))
return(ff)
}
cuhre(4,1,int,rel.tol=1e-3,lower=c(y[4],y[4],4,4),upper=c(12,y[4],12,y[2]),abs.tol1e-12,flags=
list(verbose=2, final=0))
I know that code is wrong but it shows that variables are in both the upper
and lower bounds.
Thanks.
Dustin Long
UNC-Chapel Hill
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One useful trick is to use the indicator function in your integrand to define
regions where the integrand is non-zero.
int <- function(y){
u2 = y[1]
z2 = y[2]
u1 =y[3]
z1 = y[4]
reg.nonzero <- (u2 > z1 & u2 <= 12) & (z2 > z1 & z2
<= 12) & (u1 > 4 & u1 <= z2) & (u2 > 4 & u2 <=
z2)
ff <- ifelse (reg.nonzero, u1*(z1-u1)*u2*(z2-u2)*exp(-0.027*(12-z2)), 0)
return(ff)
}
Ravi.
____________________________________________________________________
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University
Ph. (410) 502-2619
email: rvaradhan at jhmi.edu
----- Original Message -----
From: Dmlong21 <dmlong at bios.unc.edu>
Date: Tuesday, March 29, 2011 3:05 am
Subject: [R] Integration with variable bounds
To: r-help at r-project.org
> If this is posted elsewhere I cannot find it. I need to perform multiple
> integration where some of the variables are in the bounds of the other
> variables. I was trying to use R2Cuba function but cannot set the
> upper and
> lower bounds. My code so far is :
>
> int <- function(y){
> u2 = y[1]
> z2 = y[2]
> u1 =y[3]
> z1 = y[4]
>
> ff <- u1*(z1-u1)*u2*(z2-u2)*exp(-0.027*(12-z2))
> return(ff)
> }
>
>
>
cuhre(4,1,int,rel.tol=1e-3,lower=c(y[4],y[4],4,4),upper=c(12,y[4],12,y[2]),abs.tol>
1e-12,flags= list(verbose=2, final=0))
>
>
> I know that code is wrong but it shows that variables are in both the
> upper
> and lower bounds.
> Thanks.
>
> Dustin Long
> UNC-Chapel Hill
>
> --
> View this message in context:
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help at r-project.org mailing list
>
> PLEASE do read the posting guide
> and provide commented, minimal, self-contained, reproducible code.
Thanks for the tip but all I get is 0 for the integral. Any other
suggestions?
int <- function(y){
u2 = y[1]
z2 = y[2]
u1 =y[3]
z1 = y[4]
reg.nonzero <- (u2 > z1 & u2 < z2) & (z2 > z1 & z2 <
12) & (u1 > 4 & u1 <
z1) & (z1 > 4 & z1 < 12)
ff <- ifelse (reg.nonzero, u1*(z1-u1)*u2*(z2-u2)*exp(-0.027*(12-z2)), 0)
return(ff)
}
cuhre(4,1,int)
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You get 0 because you did not specify lower and upper bounds that define the hyper-rectangle; therefore, the default is used which is (0,1)^4. Specify the proper lower and upper bounds. Ravi. ____________________________________________________________________ Ravi Varadhan, Ph.D. Assistant Professor, Division of Geriatric Medicine and Gerontology School of Medicine Johns Hopkins University Ph. (410) 502-2619 email: rvaradhan at jhmi.edu ----- Original Message ----- From: Dmlong21 <dmlong at bios.unc.edu> Date: Tuesday, March 29, 2011 3:11 pm Subject: Re: [R] Integration with variable bounds To: r-help at r-project.org> Thanks for the tip but all I get is 0 for the integral. Any other > suggestions? > > int <- function(y){ > u2 = y[1] > z2 = y[2] > u1 =y[3] > z1 = y[4] > > reg.nonzero <- (u2 > z1 & u2 < z2) & (z2 > z1 & z2 < 12) & (u1 > 4 & > u1 < > z1) & (z1 > 4 & z1 < 12) > > > ff <- ifelse (reg.nonzero, u1*(z1-u1)*u2*(z2-u2)*exp(-0.027*(12-z2)), > 0) > > > return(ff) > > > } > > > cuhre(4,1,int) > > -- > View this message in context: > Sent from the R help mailing list archive at Nabble.com. > > ______________________________________________ > R-help at r-project.org mailing list > > PLEASE do read the posting guide > and provide commented, minimal, self-contained, reproducible code.
Try this: require(R2Cuba) ans <- divonne(4,1,int, lower=c(4,4,4,4), upper=c(12,12,12,12), max.eval=1e06, rel.tol=1.e-04)> ansintegral: 15663.04 (+-1.6) nregions: 182; number of evaluations: 910834; probability: 1.478672e-09>I am not sure if this answer is correct. Ravi. ____________________________________________________________________ Ravi Varadhan, Ph.D. Assistant Professor, Division of Geriatric Medicine and Gerontology School of Medicine Johns Hopkins University Ph. (410) 502-2619 email: rvaradhan at jhmi.edu ----- Original Message ----- From: Ravi Varadhan <rvaradhan at jhmi.edu> Date: Tuesday, March 29, 2011 9:13 pm Subject: Re: [R] Integration with variable bounds To: Dmlong21 <dmlong at bios.unc.edu> Cc: r-help at r-project.org> You get 0 because you did not specify lower and upper bounds that > define the hyper-rectangle; therefore, the default is used which is (0,1)^4. > > Specify the proper lower and upper bounds. > > Ravi. > > ____________________________________________________________________ > > Ravi Varadhan, Ph.D. > Assistant Professor, > Division of Geriatric Medicine and Gerontology > School of Medicine > Johns Hopkins University > > Ph. (410) 502-2619 > email: rvaradhan at jhmi.edu > > > ----- Original Message ----- > From: Dmlong21 <dmlong at bios.unc.edu> > Date: Tuesday, March 29, 2011 3:11 pm > Subject: Re: [R] Integration with variable bounds > To: r-help at r-project.org > > > > Thanks for the tip but all I get is 0 for the integral. Any other > > suggestions? > > > > int <- function(y){ > > u2 = y[1] > > z2 = y[2] > > u1 =y[3] > > z1 = y[4] > > > > reg.nonzero <- (u2 > z1 & u2 < z2) & (z2 > z1 & z2 < 12) & (u1 > 4 & > > > u1 < > > z1) & (z1 > 4 & z1 < 12) > > > > > > ff <- ifelse (reg.nonzero, > u1*(z1-u1)*u2*(z2-u2)*exp(-0.027*(12-z2)), > > 0) > > > > > > return(ff) > > > > > > } > > > > > > cuhre(4,1,int) > > > > -- > > View this message in context: > > Sent from the R help mailing list archive at Nabble.com. > > > > ______________________________________________ > > R-help at r-project.org mailing list > > > > PLEASE do read the posting guide > > and provide commented, minimal, self-contained, reproducible code. > > ______________________________________________ > R-help at r-project.org mailing list > > PLEASE do read the posting guide > and provide commented, minimal, self-contained, reproducible code.