如何使用smooth.spline()函数使单调(增加)的平滑样条曲线? [英] How to make monotonic (increasing) smooth spline with smooth.spline() function?

问题描述

我有严格增加的数据，并且由于容易使用，希望使用smooth.spline()函数使平滑样条也单调增加.

例如，可以使用以下示例有效地复制我的数据:

testx <- 1:100
testy <- abs(rnorm(length(testx)))^3
testy <- cumsum(testy)
plot(testx,testy)
sspl <- smooth.spline(testx,testy)
lines(sspl,col="blue")

不一定到处都在增加.有什么建议吗?

解决方案

这不使用smooth.spline()，但是splinefun(..., method="hyman")将适合单调递增的样条线，并且易于使用.例如:

testx <- 1:100
testy <- abs(rnorm(length(testx)))^3
testy <- cumsum(testy)
plot(testx,testy)
sspl <- smooth.spline(testx,testy)
lines(sspl,col="blue")
tmp <- splinefun(x=testx, y=cumsum(testy), method="hyman")
lines(testx[-1], diff(tmp(testx)), col="red")

产生下图(红色是单调递增的样条曲线的值)

从splinefun的帮助文件中:方法"hyman"使用Hyman滤波来计算单调三次样条，该方法="fmm"适用于严格单调的输入.(在R 2.15.2中添加.)

I have data that are strictly increasing and would like to fit a smoothing spline that is monotonically increasing as well with the smooth.spline() function if possible, due to the ease of use of this function.

For example, my data can be effectively reproduced with the example:

testx <- 1:100
testy <- abs(rnorm(length(testx)))^3
testy <- cumsum(testy)
plot(testx,testy)
sspl <- smooth.spline(testx,testy)
lines(sspl,col="blue")

which is not necessarily increasing everywhere. Any suggestions?

解决方案

This doesn't use smooth.spline() but the splinefun(..., method="hyman") will fit a monotonically increasing spline and is also easy to use. So for example:

testx <- 1:100
testy <- abs(rnorm(length(testx)))^3
testy <- cumsum(testy)
plot(testx,testy)
sspl <- smooth.spline(testx,testy)
lines(sspl,col="blue")
tmp <- splinefun(x=testx, y=cumsum(testy), method="hyman")
lines(testx[-1], diff(tmp(testx)), col="red")

Yields the following figure (red are the values from the monotonically increasing spline)

From the help file of splinefun: "Method "hyman" computes a monotone cubic spline using Hyman filtering of an method = "fmm" fit for strictly monotonic inputs. (Added in R 2.15.2.)"

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