注册 登录  
 加关注
   显示下一条  |  关闭
温馨提示!由于新浪微博认证机制调整,您的新浪微博帐号绑定已过期,请重新绑定!立即重新绑定新浪微博》  |  关闭

云之南

风声,雨声,读书声,声声入耳;家事,国事,天下事,事事关心

 
 
 

日志

 
 
关于我

专业背景:计算机科学 研究方向与兴趣: JavaEE-Web软件开发, 生物信息学, 数据挖掘与机器学习, 智能信息系统 目前工作: 基因组, 转录组, NGS高通量数据分析, 生物数据挖掘, 植物系统发育和比较进化基因组学

网易考拉推荐

R 平滑曲线画法 Interpolating Splines  

2011-06-10 22:56:18|  分类: R&Bioconductor |  标签: |举报 |字号 订阅

  下载LOFTER 我的照片书  |
> require(graphics)
> n <- 9
> x <- 1:n
> y <- rnorm(n)
> plot(x, y, main = paste("spline[fun](.) through", n, "points"))
> lines(spline(x, y))
> lines(spline(x, y, n = 201), col = 2)

Description

Perform cubic (or Hermite) spline interpolation of given data points, returning either a list of points obtained by the interpolation or a function performing the interpolation.

Usage

splinefun(x, y = NULL, method = c("fmm", "periodic", "natural", "monoH.FC"),
ties = mean)

spline(x, y = NULL, n = 3*length(x), method = "fmm",
xmin = min(x), xmax = max(x), xout, ties = mean)

splinefunH(x, y, m)

Arguments

x,y vectors giving the coordinates of the points to be interpolated. Alternatively a single plotting structure can be specified: see xy.coords.
m (for splinefunH()): vector of slopes m[i] at the points (x[i],y[i]); these together determine the Hermite “spline” which is piecewise cubic, (only) once differentiable continuously.
method specifies the type of spline to be used. Possible values are "fmm", "natural", "periodic" and "monoH.FC".
n if xout is left unspecified, interpolation takes place at n equally spaced points spanning the interval [xmin, xmax].
xmin, xmax left-hand and right-hand endpoint of the interpolation interval (when xout is unspecified).
xout an optional set of values specifying where interpolation is to take place.
ties Handling of tied x values. Either a function with a single vector argument returning a single number result or the string "ordered".

Details

The inputs can contain missing values which are deleted, so at least one complete (x, y) pair is required. If method = "fmm", the spline used is that of Forsythe, Malcolm and Moler (an exact cubic is fitted through the four points at each end of the data, and this is used to determine the end conditions). Natural splines are used when method = "natural", and periodic splines when method = "periodic".

The new (R 2.8.0) method "monoH.FC" computes a monotone Hermite spline according to the method of Fritsch and Carlson. It does so by determining slopes such that the Hermite spline, determined by (x[i],y[i],m[i]), is monotone (increasing or decreasing) iff the data are.

These interpolation splines can also be used for extrapolation, that is prediction at points outside the range of x. Extrapolation makes little sense for method = "fmm"; for natural splines it is linear using the slope of the interpolating curve at the nearest data point.

Value

spline returns a list containing components x and y which give the ordinates where interpolation took place and the interpolated values.

splinefun returns a function with formal arguments x and deriv, the latter defaulting to zero. This function can be used to evaluate the interpolating cubic spline (deriv=0), or its derivatives (deriv=1,2,3) at the points x, where the spline function interpolates the data points originally specified. This is often more useful than spline.

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

Forsythe, G. E., Malcolm, M. A. and Moler, C. B. (1977) Computer Methods for Mathematical Computations.

Fritsch, F. N. and Carlson, R. E. (1980) Monotone piecewise cubic interpolation, SIAM Journal on Numerical Analysis 17, 238–246.

See Also

approx and approxfun for constant and linear interpolation.

Package splines, especially interpSpline and periodicSpline for interpolation splines. That package also generates spline bases that can be used for regression splines.

smooth.spline for smoothing splines.

Examples

require(graphics)

op <- par(mfrow = c(2,1), mgp = c(2,.8,0), mar = .1+c(3,3,3,1))
n <- 9
x <- 1:n
y <- rnorm(n)
plot(x, y, main = paste("spline[fun](.) through", n, "points"))
lines(spline(x, y))
lines(spline(x, y, n = 201), col = 2)

y <- (x-6)^2
plot(x, y, main = "spline(.) -- 3 methods")
lines(spline(x, y, n = 201), col = 2)
lines(spline(x, y, n = 201, method = "natural"), col = 3)
lines(spline(x, y, n = 201, method = "periodic"), col = 4)
legend(6,25, c("fmm","natural","periodic"), col=2:4, lty=1)

y <- sin((x-0.5)*pi)
f <- splinefun(x, y)
ls(envir = environment(f))
splinecoef <- get("z", envir = environment(f))
curve(f(x), 1, 10, col = "green", lwd = 1.5)
points(splinecoef, col = "purple", cex = 2)
curve(f(x, deriv=1), 1, 10, col = 2, lwd = 1.5)
curve(f(x, deriv=2), 1, 10, col = 2, lwd = 1.5, n = 401)
curve(f(x, deriv=3), 1, 10, col = 2, lwd = 1.5, n = 401)
par(op)

## Manual spline evaluation --- demo the coefficients :
.x <- splinecoef$x
u <- seq(3,6, by = 0.25)
(ii <- findInterval(u, .x))
dx <- u - .x[ii]
f.u <- with(splinecoef,
y[ii] + dx*(b[ii] + dx*(c[ii] + dx* d[ii])))
stopifnot(all.equal(f(u), f.u))

## An example with ties (non-unique x values):
set.seed(1); x <- round(rnorm(30), 1); y <- sin(pi * x) + rnorm(30)/10
plot(x,y, main="spline(x,y) when x has ties")
lines(spline(x,y, n= 201), col = 2)
## visualizes the non-unique ones:
tx <- table(x); mx <- as.numeric(names(tx[tx > 1]))
ry <- matrix(unlist(tapply(y, match(x,mx), range, simplify=FALSE)),
ncol=2, byrow=TRUE)
segments(mx, ry[,1], mx, ry[,2], col = "blue", lwd = 2)

## An example of monotone interpolation
n <- 20
set.seed(11)
x. <- sort(runif(n)) ; y. <- cumsum(abs(rnorm(n)))
plot(x.,y.)
curve(splinefun(x.,y.)(x), add=TRUE, col=2, n=1001)
curve(splinefun(x.,y., method="mono")(x), add=TRUE, col=3, n=1001)
legend("topleft", paste("splinefun( \"", c("fmm", "monoH.CS"), "\" )", sep=''),
col=2:3, lty=1)
  评论这张
 
阅读(2649)| 评论(0)
推荐 转载

历史上的今天

在LOFTER的更多文章

评论

<#--最新日志,群博日志--> <#--推荐日志--> <#--引用记录--> <#--博主推荐--> <#--随机阅读--> <#--首页推荐--> <#--历史上的今天--> <#--被推荐日志--> <#--上一篇,下一篇--> <#-- 热度 --> <#-- 网易新闻广告 --> <#--右边模块结构--> <#--评论模块结构--> <#--引用模块结构--> <#--博主发起的投票-->
 
 
 
 
 
 
 
 
 
 
 
 
 
 

页脚

网易公司版权所有 ©1997-2016