在R中求解积分给出误差“积分可能是发散的".

问题描述

我正在尝试求解R中的一个积分.但是，当我尝试求解该积分时遇到错误.

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

我要求解的方程式如下:

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

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

我正在使用的代码如下:

The code that I am using is as follows:

a <- seq(from=-10, by=0.5,length=100)

## Create a function to compute integration
Cfun <- function(XX, upper){
  integrand <- function(x)x^(-1.5)*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)

我得到的错误如下:

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

这是否意味着我无法求解积分?

Does this mean I cannot solve the integral ?

任何解决此问题的方法将受到高度赞赏.

Any possible ways to fix this problem will be highly appreciated.

谢谢.

推荐答案

您可以在try语句中将对Cfun的调用包装起来

You could wrap the call to Cfun in a try statement

# note using `lapply` so errors don't coerce the result to character
b <- lapply(a, function(x,...) try(Cfun(x, ...), silent = TRUE), upper = 1)

如果您想将错误替换为NA值并打印警告，说明集成引发了错误

If you wanted to replace the errors with NA values and print a warning that the integration threw an error

Cfun <- function(XX, upper){
  integrand <- function(x)x^(-1.5)*exp((-XX^2/x)-x)
  int <- try(integrate(integrand, lower=0, upper=upper), silent = TRUE)
  if(inherits(int ,'try-error')){
    warning(as.vector(int))
    integrated <- NA_real_
  } else {
    integrated <- int$value
  }
  (final <- abs(XX)*pi^(-0.5)*exp(2*XX)*integrated) }

---

编辑(facepalm时刻)

出现错误是因为在t=0时未定义函数(在被积数内除以t).

---

Edit (facepalm moment)

Your error arises because your function is not defined when t=0 (you divide by t within the integrand).

Cfun <- function(XX, upper){
  integrand <- function(x)x^(-1.5)*exp((-XX^2/x)-x)
  # deal with xx=0
  if(isTRUE(all.equal(XX, 0)){
      warning('The integrand is not defined at XX = 0')
      return(NA_real_)
  }
  # deal with other integration errors
  int <- try(integrate(integrand, lower=0, upper=upper), silent = TRUE)
  if(inherits(int ,'try-error')){
    warning(as.vector(int))
    integrated <- NA_real_
  } else {
    integrated <- int$value
  }
  (final <- abs(XX)*pi^(-0.5)*exp(2*XX)*integrated) }

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