R help - Apr 2013 - Solving an integral in R gives the error “The integral is probably divergent”

I am trying to solve an integral in R. However, I am getting an error when
I am trying to solve for that integral.

The equation that I am trying to solve is as follows:

$$ C_m = \frac{{abs{x}}e^{2x}}{\pi^{1/2}}\int_0^t t^{-3/2}e^{-x^2/t-t}dt $$

[image: enter image description here]

The code that I am using is as follows:

a <- seq(from=-10, by=0.5,length=100)
## Create a function to compute integrationCfun <- function(XX, upper){
  integrand <- function(x)x^(-0.5)*exp((-XX^2/x)-x)
  integrated <- integrate(integrand, lower=0, upper=upper)$value
  (final <- abs(XX)*pi^(-0.5)*exp(2*XX)*integrated) }


b<- sapply(a, Cfun, upper=1)

The error that I am getting is as follows:

Error in integrate(integrand, lower = 0, upper = upper) :
  the integral is probably divergent

Does this mean I cannot solve the integral ?

Any possible ways to fix this problem will be highly appreciated.The
question can be found on
http://stackoverflow.com/questions/15892586/solving-an-integral-in-r-gives-error-the-integral-is-probably-divergent
 also.

Thanks.

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I don't get an error message (after I correct the missing line break after
the comment
> b<- sapply(a, Cfun, upper=1)
> b
  [1]  1.583458e-54  7.768026e-50  2.317562e-45  4.206260e-41  4.645737e-37
 3.123801e-33  1.279358e-29  3.193257e-26  4.860876e-23
 [10]  4.516582e-20  2.564400e-17  8.908932e-15  1.896996e-12  2.481084e-10
 1.998561e-08  9.946570e-07  3.067751e-05  5.862075e-04
 [19]  6.818952e-03  4.297061e-02  0.000000e+00  3.175122e-01  3.723022e-01
 2.364930e-01  9.144836e-02  2.190878e-02  3.252754e-03
 [28]  2.983763e-04  1.685692e-05  5.849602e-07  1.244158e-08  1.619155e-10
 1.287603e-12  6.250149e-15  1.850281e-17  3.338241e-20
 [37]  3.668412e-23  2.454192e-26  9.991546e-30  2.474577e-33  3.727226e-37
 3.413319e-41  1.900112e-45  6.428505e-50  1.321588e-54
 [46]  1.650722e-59  1.252524e-64  5.772750e-70  1.615916e-75  2.746972e-81
 2.835655e-87  1.777399e-93 6.764271e-100 1.562923e-106
 [55] 2.192373e-113 1.866955e-120 9.651205e-128 3.028623e-135 5.769185e-143
6.670835e-151 4.682023e-159 1.994643e-167 5.157808e-176
 [64] 8.095084e-185 7.711162e-194 4.458042e-203 1.564139e-212 3.330362e-222
4.302974e-232 3.373500e-242 1.604721e-252 4.631224e-263
 [73] 8.108474e-274 8.611898e-285 5.547745e-296  0.000000e+00  0.000000e+00
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 [82]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 [91]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
[100]  0.000000e+00


  -thomas



On Tue, Apr 9, 2013 at 3:14 PM, Janesh Devkota
<janesh.devkota@gmail.com>wrote:
> I am trying to solve an integral in R. However, I am getting an error when
> I am trying to solve for that integral.
>
> The equation that I am trying to solve is as follows:
>
> $$ C_m = \frac{{abs{x}}e^{2x}}{\pi^{1/2}}\int_0^t t^{-3/2}e^{-x^2/t-t}dt $$
>
> [image: enter image description here]
>
> The code that I am using is as follows:
>
> a <- seq(from=-10, by=0.5,length=100)
> ## Create a function to compute integrationCfun <- function(XX, upper){
>   integrand <- function(x)x^(-0.5)*exp((-XX^2/x)-x)
>   integrated <- integrate(integrand, lower=0, upper=upper)$value
>   (final <- abs(XX)*pi^(-0.5)*exp(2*XX)*integrated) }
>
>
> b<- sapply(a, Cfun, upper=1)
>
> The error that I am getting is as follows:
>
> Error in integrate(integrand, lower = 0, upper = upper) :
>   the integral is probably divergent
>
> Does this mean I cannot solve the integral ?
>
> Any possible ways to fix this problem will be highly appreciated.The
> question can be found on
>
>
http://stackoverflow.com/questions/15892586/solving-an-integral-in-r-gives-error-the-integral-is-probably-divergent
>  also.
>
> Thanks.
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help@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.
>


-- 
Thomas Lumley
Professor of Biostatistics
University of Auckland

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