这是我的矩阵
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12.9701665831908), .Dim = c(99L, 11L))
每列对我来说都是要集成的函数，并将值放在我的
integr矩阵中： integr=matrix(0,11)
for (t in 1:11){
integrating = approxfun(thau,func[,t],rule=2)
integr[t,1]=integrate(integrating, lower = 0.01, upper = 0.5,subdivisions = 1000)$value
}
我有此错误信息：
Error in integrate(integrating, lower = 0.01, upper = 0.5, subdivisions = 1000) :
extremely bad integrand behaviour
如何解决此问题并继续在R中使用函数
integrate。我需要做一些非线性方法吗？如果是这样，我该怎么办？非常感谢。
最佳答案
首先，很有趣的是，在最近的10天左右的时间内，有很多关于分位数函数的数值积分问题。例如：
Building a function by defining X and Y and then Integrating in R
Standard Normal Quantile Function Integration in R
Understanding and implementing numerical integration with a quantile function in R
请注意，这个问题与第一个问题有何相似之处。尽管您没有提到thau是什么，但我相信它是thau <- seq(0.01, 0.99, 0.01)。让我们针对func绘制thau矩阵：
matplot(thau, func, type = "l")
同样，让我们验证
func的所有列是否单调递增：all(diff(func) > 0)
# [1] TRUE
基本上，您的问题使用的是我在第一个链接问题中提供的答案（但是，在第三个链接问题中给出了
rule = 2的理由）。但是感谢您的问题；我现在意识到背后存在一些潜在的数值缺陷。由于我不是该领域的专家，所以我很难在有限的时间内了解Adaptive Quadrature背后的数学原理。但是令我感到惊讶的是，它有时会在如此琐碎的任务上失败。
正如我在第二个链接问题中提到的那样，我们甚至可以使用梯形规则。
当我测试
integrate时，它是func的第一列，而不是您报告失败的第五列。## get interpolation function for all columns in a list
flst <- lapply(1:ncol(func), function (i) approxfun(thau, func[,i], rule = 2))
## all OK excluding the 1st column
sapply(flst[-1], function (fun) integrate(fun, 0.01, 0.5)$value)
# [1] -2.010421 -2.088981 -2.114083 -2.000653 -2.015932 -1.986130 -1.912076
# [8] -1.877459 -1.892291 -1.921983
## the 1st one fails
integrate(flst[[1]], 0.01, 0.5)
# extremely bad integrand behaviour
如前所述，我认为这种故障是由于问题的简单性造成的。实际上，让我们考虑
integrate(flst[[1]], 0.01 + .Machine$double.eps ^ 0.25, 0.5)
# -2.13653 with absolute error < 8.7e-05
integrate(flst[[1]], 0, 0.5)
# -2.286034 with absolute error < 0.00027
他们都工作。
据我了解，
integrate函数正在使用两个Fortran子例程：dqags用于确定积分，能够处理端点奇点；dqagi用于不定积分。integrate的R文档没有对这些例程的错误处理做太多解释，但是Fortran页面做了些许工作。不幸的是，还不清楚“不良行为”是什么。但是很明显，无论错误代码是什么，那些Fortran子例程将始终返回积分结果。查看
integrate的源代码可以验证这一点。积分结果存储在变量wk中，然后使用swtich语句解释存储在wk$ierr中的整数错误代码：res$message <- switch(wk$ierr + 1L, "OK", "maximum number of subdivisions reached",
"roundoff error was detected", "extremely bad integrand behaviour",
"roundoff error is detected in the extrapolation table",
"the integral is probably divergent", "the input is invalid")
if (wk$ierr == 6L || (wk$ierr > 0L && stop.on.error))
stop(res$message)
if之后的switch语句决定我们是否要忽略任何错误。注意，在stop.on.error中有一个integrate参数。如果我们将其设置为FALSE而不是默认的TRUE，则integrate将始终有效。因此，让我们做z <- integrate(flst[[1]], 0.01, 0.5, stop.on.error = FALSE)
str(z)
# $ value : num -2.14
# $ abs.error : num 0.000446
# $ subdivisions: int 69
# $ message : chr "extremely bad integrand behaviour"
# $ call : language integrate(f = flst[[1]], lower = 0.01, upper = 0.5, stop.on.error = FALSE)
# - attr(*, "class")= chr "integrate"
z$value
# [1] -2.138348
目前，这就是我所能做的。我相信在不久的将来，我将有机会阅读有关“自适应正交”的文章。