R Language definition

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安装 R 包获取数据统计绘图统计计算 R 语言定义
R Language Definition
OOP
黄湘云
Department of Statistics
China University of Mining & Technology,Beijing
May 4, 2016

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目录
1 安装 R 包
2 获取数据
3 统计绘图
4 统计计算
5 R 语言定义

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安装 R 包
从指定网站安装 R 包
install.packages("ggplot2",repos = "https://mirrors.tuna.tsinghua.edu.cn/CRAN/")
install.packages("pim",repos = "http://www.r-forge.r-project.org/",lib = "D:/library/")
一行命令安装 cran 上所有的 Packages
install.packages(setdiff(available.packages()[,1],
.packages(all.available = TRUE)))
安装 Bioconductor 上的 R 包
source("https://bioconductor.org/biocLite.R")
library(BiocInstaller)
biocLite("ggtree")
安装 Github 上的 R 包
library(devtools)
install_github("ropensci/aRxiv")

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安装注意几项
依赖问题主要针对离线安装和源码编译安装
平台问题有些 R 包只能装在类 unix 操作系统上
软件问题有些 R 包要求相应 R 软件版本
特定库依赖如 gputools 包依赖 cuda 库
# OS information
Sys.info()
sysname release version nodename
"Windows" "10 x64" "build 10586" "LENOVO-PC"
machine login user effective_user
"x86-64" "Xiangyun Huang" "Xiangyun Huang" "Xiangyun Huang"

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R 软件信息
> version
_
platform x86_64-w64-mingw32
arch x86_64
os mingw32
system x86_64, mingw32
status
major 3
minor 2.5
year 2016
month 04
day 14
svn rev 70478
language R
version.string R version 3.2.5 (2016-04-14)
nickname Very, Very Secure Dishes

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R 软件系统自带的数据集
# view R data sets
length(data(package = .packages(all.available = TRUE))$results[,3])
## [1] 20969
# extended packages
library(ggplot2)
data("diamonds")
head(diamonds)
## carat cut color clarity depth table price x y z
## 1 0.23 Ideal E SI2 61.5 55 326 3.95 3.98 2.43
## 2 0.21 Premium E SI1 59.8 61 326 3.89 3.84 2.31
## 3 0.23 Good E VS1 56.9 65 327 4.05 4.07 2.31
## 4 0.29 Premium I VS2 62.4 58 334 4.20 4.23 2.63
## 5 0.31 Good J SI2 63.3 58 335 4.34 4.35 2.75
## 6 0.24 Very Good J VVS2 62.8 57 336 3.94 3.96 2.48

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plot 函数–pch
点
26 shaps of points

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plot 函数–lty–lwd
线
0 10 20 30 40 50
−1.5−1.0−0.50.00.51.01.52.0
Simple Use of Color In a Plot
Just a Whisper of a Label

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调色板–连续型
Blues
BuGn
BuPu
GnBu
Greens
Greys
Oranges
OrRd
PuBu
PuBuGn
PuRd
Purples
RdPu
Reds
YlGn
YlGnBu
YlOrBr
YlOrRd

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调色板–极端型
BrBG
PiYG
PRGn
PuOr
RdBu
RdGy
RdYlBu
RdYlGn
Spectral

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调色板–离散型
Accent
Dark2
Paired
Pastel1
Pastel2
Set1
Set2
Set3

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举个栗子
barplot(sample(seq(20),6,replace = T),col=brewer.pal(11, "BrBG")[3:8])
05101520

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再举个栗子
Set3 3 colors
VADeaths
Frequency
10 20 30 40 50 60 70
0.00.51.01.52.02.53.0
Set2 3 colors
VADeaths
Frequency
0 20 40 60 8002468
Set1 3 colors
VADeaths
Frequency
0 20 40 60 80
0123456
Set3 8 colors
VADeaths
Frequency
0 20 40 60 80 100
051015
Greys 8 colors
VADeaths
Frequency
0 20 40 60 80
0123456
Greens 8 colors
VADeaths
Frequency
0 20 40 60 80
0123456

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继续举个栗子
Sepal.Length
2.0 2.5 3.0 3.5 4.0 0.5 1.0 1.5 2.0 2.5
4.55.56.57.5
2.03.04.0
Sepal.Width
Petal.Length
1234567
0.51.52.5
Petal.Width
4.5 5.5 6.5 7.5 1 2 3 4 5 6 7 1.0 1.5 2.0 2.5 3.0
1.02.03.0
Species

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三维图–persp
X
−10
−5
0
5
10
Y
−10
−5
0
5
10
Z
−2
0
2
4
6
8
.
z = Sinc( x2
+ y2
)

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添加数学公式
−3 −2 −1 0 1 2 3
0.00.10.20.30.4
Normal Probability Density Function
x
dnorm(x)
f(x) =
1
2πσ2
e
−(x−µ)2
2σ2
−3 −2 −1 0 1 2 3
0.00.20.40.60.81.0
Normal Cumulative Distribution Function
x
cumsum(x)/sum(x)
φ(x) =
1
2π
⌠
⌡−∞
x
e(−t2
2)
dt

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anscombe 数据
4 6 8 10 12 14
4567891011
x1
y1
y1 = 3 + 0.5x1
4 6 8 10 12 14
3456789
x1
y2
y2 = 3 + 0.5x1
4 6 8 10 12 14
681012
x1
y3
y3 = 3 + 0.5x1
8 10 12 14 16 18
681012
x4
y4
y4 = 3 + 0.5x4
σ^2
= 1.531,Multiple R2
= 0.667,Adjusted R2
= 0.629

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barplot
cardiothoracic gastrointestinal neuro other trauma
Types of surgery
Absolutefrequency
050100150200

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barplot
0
10
20
30
40
cardiothoracic gastrointestinal neuro other trauma
surgery
Relativefrequencyin%
Types of surgery

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多元概率分布函数
The multivariate t distribution (MVT) is given by
T(a, b, Σ, ν) =
21− ν
2
Γ(ν
2 )
∫ ∞
0
sν−1
e− s2
2 Φ(
sa
√
ν
,
sb
√
ν
, Σ)ds
multivariate normal distribution function (MVN)
Φ(a, b, Σ) =
1
√
|Σ|(2π)m
∫ b1
a1
∫ b2
a2
· · ·
∫ bm
am
e−1
2
x⊤Σ−1x
dx
x = (x1, x2, . . . , xm)⊤, −∞ ≤ ai ≤ bi ≤ ∞ for all i, and Σ is a
positive semi-definite symmetric m × m matrix

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计算多元正态分布的概率
library(mvtnorm)
library(matrixcalc)
path<-"C:/Users/Xiangyun Huang/Desktop/LanguageDefinitionR/"
setwd(path)
sigma <- read.csv(file="data/sigma1.csv",header=F, sep=",")
mat<-matrix(0,nrow = nrow(sigma),ncol = ncol(sigma))
sigma <- as.matrix(sigma)
attributes(sigma)<-attributes(mat)
# str(sigma)
# is.symmetric.matrix(sigma)
# is.positive.definite(sigma)
m = nrow(sigma)
Fn = pmvnorm(lower=rep(-Inf, m), upper=rep(0, m),
mean=rep(0, m), sigma =sigma)
Fn
## [1] 6.748008e-29
## attr(,"error")
## [1] 2.48407e-31
## attr(,"msg")
## [1] "Normal Completion"

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多元 t 分布分位数计算
n <- c(26, 24, 20, 33, 32)
V <- diag(1/n); df <- 130
C <- matrix(c(1,1,1,0,0,-1,0,0,1,0,
0,-1,0,0,1,0,0,0,-1,-1,
0,0,-1,0,0),ncol=5)
cv <- C %*% V %*% t(C) ## covariance matrix
dv <- t(1/sqrt(diag(cv)))
cr <- cv * (t(dv) %*% dv) ## correlation matrix
delta <- rep(0,5)
Tn<-qmvt(0.95, df = df, delta = delta, corr = cr,
abseps = 0.0001,maxpts = 100000, tail = "both")
Tn
## $quantile
## [1] 2.560946
##
## $f.quantile
## [1] 1.523691e-07
##
## attr(,"message")
## [1] "Normal Completion"

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谈谈对象
class(sigma) #Object Classes
## [1] "matrix"
str(sigma) #Compactly Display the Structure of an Arbitrary R Object
## num [1:83, 1:83] 0.3806 -0.0104 0 0 0 ...
mode(sigma) #The (Storage) Mode of an Object
## [1] "numeric"
typeof(sigma) #The Type of an Object
## [1] "double"
attributes(sigma) #Object Attribute Lists
## $dim
## [1] 83 83

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pryr 包撬开 R 的底层
pryr: Useful tools to pry back the covers of R and understand
the language at a deeper level.
c(is.list(sigma),is.matrix(sigma))
## [1] FALSE TRUE
c(is.vector(sigma),is.numeric(sigma))
## [1] FALSE TRUE
c(is.array(sigma),is.data.frame(sigma))
## [1] TRUE FALSE

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撬开 tabulate 函数
tabulate
## function (bin, nbins = max(1L, bin, na.rm = TRUE))
## {
## if (!is.numeric(bin) && !is.factor(bin))
## stop("'bin' must be numeric or a factor")
## if (typeof(bin) != "integer")
## bin <- as.integer(bin)
## if (nbins > .Machine$integer.max)
## stop("attempt to make a table with >= 2^31 elements")
## nbins <- as.integer(nbins)
## if (is.na(nbins))
## stop("invalid value of 'nbins'")
## .Internal(tabulate(bin, nbins))
## }
## <bytecode: 0x0000000016e96018>
## <environment: namespace:base>

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撬开 tabulate 函数
library(pryr)
show_c_source(.Internal(tabulate(bin,nbins)))
SEXP attribute_hidden do_tabulate(SEXP call, SEXP op, SEXP args, SEXP rho)
{
checkArity(op, args);
SEXP in = CAR(args), nbin = CADR(args);
if (TYPEOF(in) != INTSXP) error("invalid input");
R_xlen_t n = XLENGTH(in);
/* FIXME: could in principle be a long vector */
int nb = asInteger(nbin);
if (nb == NA_INTEGER || nb < 0)
error(_("invalid '%s' argument"), "nbin");
SEXP ans = allocVector(INTSXP, nb);
int *x = INTEGER(in), *y = INTEGER(ans);
if (nb) memset(y, 0, nb * sizeof(int));
for(R_xlen_t i = 0 ; i < n ; i++)
if (x[i] != NA_INTEGER && x[i] > 0 && x[i] <= nb) y[x[i] - 1]++;
return ans;
}

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撬开 plot
methods(plot)
## [1] plot,ANY-method plot,color-method plot.acf*
## [4] plot.data.frame* plot.decomposed.ts* plot.default
## [7] plot.dendrogram* plot.density* plot.ecdf
## [10] plot.factor* plot.formula* plot.function
## [13] plot.ggplot* plot.gtable* plot.hclust*
## [16] plot.histogram* plot.HoltWinters* plot.isoreg*
## [19] plot.lm* plot.medpolish* plot.mlm*
## [22] plot.ppr* plot.prcomp* plot.princomp*
## [25] plot.profile.nls* plot.raster* plot.spec*
## [28] plot.stepfun plot.stl* plot.table*
## [31] plot.ts plot.tskernel* plot.TukeyHSD*
## see '?methods' for accessing help and source code

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visible from generic isS4
plot,ANY-method TRUE graphics plot TRUE
plot,color-method TRUE colorspace plot TRUE
plot.acf FALSE registered S3method for plot plot FALSE
plot.data.frame FALSE registered S3method for plot plot FALSE
plot.decomposed.ts FALSE registered S3method for plot plot FALSE
plot.default TRUE graphics plot FALSE
plot.dendrogram FALSE registered S3method for plot plot FALSE
plot.density FALSE registered S3method for plot plot FALSE
plot.ecdf TRUE stats plot FALSE
plot.factor FALSE registered S3method for plot plot FALSE
plot.formula FALSE registered S3method for plot plot FALSE
plot.function TRUE graphics plot FALSE
plot.ggplot FALSE registered S3method for plot plot FALSE
plot.gtable FALSE registered S3method for plot plot FALSE
plot.hclust FALSE registered S3method for plot plot FALSE
plot.histogram FALSE registered S3method for plot plot FALSE
plot.HoltWinters FALSE registered S3method for plot plot FALSE
plot.isoreg FALSE registered S3method for plot plot FALSE
plot.lm FALSE registered S3method for plot plot FALSE
plot.medpolish FALSE registered S3method for plot plot FALSE
plot.mlm FALSE registered S3method for plot plot FALSE
plot.ppr FALSE registered S3method for plot plot FALSE
plot.prcomp FALSE registered S3method for plot plot FALSE
plot.princomp FALSE registered S3method for plot plot FALSE
plot.profile.nls FALSE registered S3method for plot plot FALSE
plot.raster FALSE registered S3method for plot plot FALSE
plot.spec FALSE registered S3method for plot plot FALSE
plot.stepfun TRUE stats plot FALSE
plot.stl FALSE registered S3method for plot plot FALSE
plot.table FALSE registered S3method for plot plot FALSE
plot.ts TRUE stats plot FALSE
plot.tskernel FALSE registered S3method for plot plot FALSE
plot.TukeyHSD FALSE registered S3method for plot plot FALSE

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统计计算环境
> devtools::session_info()$packages
package * version date source
colorspace 1.2-6 2015-03-11 CRAN (R 3.2.4)
devtools 1.11.0 2016-04-12 CRAN (R 3.2.4)
digest 0.6.9 2016-01-08 CRAN (R 3.2.4)
evaluate 0.9 2016-04-29 CRAN (R 3.2.5)
formatR 1.3 2016-03-05 CRAN (R 3.2.4)
ggplot2 * 2.1.0 2016-03-01 CRAN (R 3.2.4)
gtable 0.2.0 2016-02-26 CRAN (R 3.2.4)
highr 0.5.1 2015-09-18 CRAN (R 3.2.4)
knitr * 1.12.27 2016-05-01 Github (yihui/knitr@5a0a689)
labeling 0.3 2014-08-23 CRAN (R 3.2.3)
magrittr 1.5 2014-11-22 CRAN (R 3.2.3)
matrixcalc * 1.0-3 2012-09-15 CRAN (R 3.2.3)
memoise 1.0.0 2016-01-29 CRAN (R 3.2.3)
munsell 0.4.3 2016-02-13 CRAN (R 3.2.3)
mvtnorm * 1.0-5 2016-02-02 CRAN (R 3.2.3)
plyr 1.8.3 2015-06-12 CRAN (R 3.2.3)
RColorBrewer * 1.1-2 2014-12-07 CRAN (R 3.2.3)
Rcpp 0.12.4 2016-03-26 CRAN (R 3.2.4)
scales 0.4.0 2016-02-26 CRAN (R 3.2.3)
stringi 1.0-1 2015-10-22 CRAN (R 3.2.3)
stringr 1.0.0 2015-04-30 CRAN (R 3.2.3)
withr 1.0.1 2016-02-04 CRAN (R 3.2.3)

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