通过PCHIP功能进行集成 [英] Integrating over a PCHIP Function

问题描述

如何在R中的PCHIP(逐片三次Hermite插值多项式)函数上进行积分? pchip {pracma}返回内插的点数据，要集成，我们当然需要一个函数.我在pchip()的帮助菜单下看到待办事项:应提供一个'pchipfun'"，我不知道手动生成将有多困难?还有其他建议吗?您可以将n次多项式回归拟合到插值点并将其积分以获得大致的近似值，但这很快就很混乱...

How can I integrate over a PCHIP (Piecewise Cubic Hermite Interpolation Polynomial) function in R? pchip {pracma} returns interpolated point data, and to integrate we of course need a function. I see under the help menu for pchip(), "TODO: A `pchipfun' should be provided," I don't know how hard this would be to generate manually? Any other suggestions? You could fit an nth degree polynomial regression to the interpolated points and integrate off that to get a rough approximation, but that gets messy pretty quick...

这是pchip {pracma}的源代码，它返回点而不是函数，我想返回函数更多的是数学问题，而不是R问题，但是我愿意接受任何建议！拜托！

Here's the source code for pchip {pracma} which returns points and not a function, I suppose returning a function is more of a math question not an R question, but I'm open for any and all suggestions! Please!

function (xi, yi, x) 
{
    h <- diff(xi)
    delta <- diff(yi)/h
    d <- .pchipslopes(h, delta)
    n <- length(xi)
    a <- (3 * delta - 2 * d[1:(n - 1)] - d[2:n])/h
    b <- (d[1:(n - 1)] - 2 * delta + d[2:n])/h^2
    k <- rep(1, length(x))
    for (j in 2:(n - 1)) {
        k[xi[j] <= x] <- j
    }
    s <- x - xi[k]
    v <- yi[k] + s * (d[k] + s * (a[k] + s * b[k]))
    return(v)
}

谢谢！

推荐答案

什么对您不起作用?您必须像这样使用 pchipfun() 定义函数:

What does not work for you? You have to define a function using pchipfun() like this:

> library(pracma)

> xs <- linspace(0, pi, 10)
> ys <- sin(xs)

> pchipfun <- function(xi, yi) function(x) pchip(xi, yi, x)

> f <- pchipfun(xs, ys)
> integrate(f, 0, pi)
2.000749 with absolute error < 0.00017

我在R-Forge上更新了实践1.7.2，以包含pchipfun() 并向pchip()添加了一些错误检查.

I have updated pracma 1.7.2 on R-Forge to include pchipfun() and added some error checking to pchip().

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