R中矩阵运算
# 数据产生
# rnorm(n, mean = 0, sd = 1) 正态分布的随机数（r 代表随机，可以替换成dnorm, pnorm, qnorm 作不同计算。r= random = 随机， d= density = 密度， p= probability = 概率 ， q =quantile = 分位）
# runif(n, min = 0, max = 1) 平均分布的随机数
# rep(1,5) 把1重复5次
# scale(1:5) 标准化数据
> a <- c(rnorm(5), rnorm(5,1), runif(5), runif(5,-1,1), 1:5, rep(0,5), c(2,10,11,13,4), scale(1:5)[1:5])
> a
[1] -0.41253556 0.12192929 -0.47635888 -0.97171653 1.09162243 1.87789657
[7] -0.11717937 2.92953522 1.33836620 -0.03269026 0.87540920 0.13005744
[13] 0.11900686 0.76663940 0.28407356 -0.91251181 0.17997973 0.50452258
[19] 0.25961316 -0.58052230 1.00000000 2.00000000 3.00000000 4.00000000
[25] 5.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
[31] 2.00000000 10.00000000 11.00000000 13.00000000 4.00000000 -1.26491106
[37] -0.63245553 0.00000000 0.63245553 1.26491106
> a <- matrix(a, ncol=5, byrow=T)
> a
[,1] [,2] [,3] [,4] [,5]
[1,] -0.4125356 0.1219293 -0.4763589 -0.9717165 1.09162243
[2,] 1.8778966 -0.1171794 2.9295352 1.3383662 -0.03269026
[3,] 0.8754092 0.1300574 0.1190069 0.7666394 0.28407356
[4,] -0.9125118 0.1799797 0.5045226 0.2596132 -0.58052230
[5,] 1.0000000 2.0000000 3.0000000 4.0000000 5.00000000
[6,] 0.0000000 0.0000000 0.0000000 0.0000000 0.00000000
[7,] 2.0000000 10.0000000 11.0000000 13.0000000 4.00000000
[8,] -1.2649111 -0.6324555 0.0000000 0.6324555 1.26491106
# 求行的加和
> rowSums(a)
[1] -0.6470593 5.9959284 2.1751865 -0.5489186 15.0000000 0.0000000 40.0000000
[8] 0.0000000
# 去除全部为0的行
> a <- a[rowSums(abs(a))!=0,]
> a
[,1] [,2] [,3] [,4] [,5]
[1,] -0.4125356 0.1219293 -0.4763589 -0.9717165 1.09162243
[2,] 1.8778966 -0.1171794 2.9295352 1.3383662 -0.03269026
[3,] 0.8754092 0.1300574 0.1190069 0.7666394 0.28407356
[4,] -0.9125118 0.1799797 0.5045226 0.2596132 -0.58052230
[5,] 1.0000000 2.0000000 3.0000000 4.0000000 5.00000000
[6,] 2.0000000 10.0000000 11.0000000 13.0000000 4.00000000
[7,] -1.2649111 -0.6324555 0.0000000 0.6324555 1.26491106
# 矩阵运算，R默认针对整个数据进行常见运算
# 所有值都乘以2
> a * 2
[,1] [,2] [,3] [,4] [,5]
[1,] -0.8250711 0.2438586 -0.9527178 -1.9434331 2.18324487
[2,] 3.7557931 -0.2343587 5.8590704 2.6767324 -0.06538051
[3,] 1.7508184 0.2601149 0.2380137 1.5332788 0.56814712
[4,] -1.8250236 0.3599595 1.0090452 0.5192263 -1.16104460
[5,] 2.0000000 4.0000000 6.0000000 8.0000000 10.00000000
[6,] 4.0000000 20.0000000 22.0000000 26.0000000 8.00000000
[7,] -2.5298221 -1.2649111 0.0000000 1.2649111 2.52982213
# 所有值取绝对值，再取对数 （取对数前一般加一个数避免对0或负值取对数）
> log2(abs(a)+1)
[,1] [,2] [,3] [,4] [,5]
[1,] 0.4982872 0.1659818 0.5620435 0.9794522 1.0646224
[2,] 1.5250147 0.1598608 1.9743587 1.2255009 0.0464076
[3,] 0.9072054 0.1763961 0.1622189 0.8210076 0.3607278
[4,] 0.9354687 0.2387621 0.5893058 0.3329807 0.6604014
[5,] 1.0000000 1.5849625 2.0000000 2.3219281 2.5849625
[6,] 1.5849625 3.4594316 3.5849625 3.8073549 2.3219281
[7,] 1.1794544 0.7070437 0.0000000 0.7070437 1.1794544
# 取出最大值、最小值、行数、列数
> max(a)
[1] 13
> min(a)
[1] -1.264911
> nrow(a)
[1] 7
> ncol(a)
[1] 5
# 增加一列或一行
# cbind: column bind
> cbind(a, 1:7)
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] -0.4125356 0.1219293 -0.4763589 -0.9717165 1.09162243 1
[2,] 1.8778966 -0.1171794 2.9295352 1.3383662 -0.03269026 2
[3,] 0.8754092 0.1300574 0.1190069 0.7666394 0.28407356 3
[4,] -0.9125118 0.1799797 0.5045226 0.2596132 -0.58052230 4
[5,] 1.0000000 2.0000000 3.0000000 4.0000000 5.00000000 5
[6,] 2.0000000 10.0000000 11.0000000 13.0000000 4.00000000 6
[7,] -1.2649111 -0.6324555 0.0000000 0.6324555 1.26491106 7
> cbind(a, seven=1:7)
seven
[1,] -0.4125356 0.1219293 -0.4763589 -0.9717165 1.09162243 1
[2,] 1.8778966 -0.1171794 2.9295352 1.3383662 -0.03269026 2
[3,] 0.8754092 0.1300574 0.1190069 0.7666394 0.28407356 3
[4,] -0.9125118 0.1799797 0.5045226 0.2596132 -0.58052230 4
[5,] 1.0000000 2.0000000 3.0000000 4.0000000 5.00000000 5
[6,] 2.0000000 10.0000000 11.0000000 13.0000000 4.00000000 6
[7,] -1.2649111 -0.6324555 0.0000000 0.6324555 1.26491106 7
# rbind: row bind
> rbind(a,1:5)
[,1] [,2] [,3] [,4] [,5]
[1,] -0.4125356 0.1219293 -0.4763589 -0.9717165 1.09162243
[2,] 1.8778966 -0.1171794 2.9295352 1.3383662 -0.03269026
[3,] 0.8754092 0.1300574 0.1190069 0.7666394 0.28407356
[4,] -0.9125118 0.1799797 0.5045226 0.2596132 -0.58052230
[5,] 1.0000000 2.0000000 3.0000000 4.0000000 5.00000000
[6,] 2.0000000 10.0000000 11.0000000 13.0000000 4.00000000
[7,] -1.2649111 -0.6324555 0.0000000 0.6324555 1.26491106
[8,] 1.0000000 2.0000000 3.0000000 4.0000000 5.00000000
# 计算每一行的mad (中值绝对偏差，一般认为比方差的鲁棒性更强，更少受异常值的影响，更能反映数据间的差异)1表示矩阵行，2表示矩阵列，也可以是c(1,2)
> apply(a,1,mad)
[1] 0.7923976 2.0327283 0.2447279 0.4811672 1.4826000 4.4478000 0.9376786
# 计算每一行的var (方差)
# apply表示对数据（第一个参数）的每一行 (第二个参数赋值为1) 或每一列 (2)操作。最后返回一个列表
> apply(a,1,var)
[1] 0.6160264 1.6811161 0.1298913 0.3659391 2.5000000 22.5000000 1.0000000
# 计算每一列的平均值
> apply(a,2,mean)
[1] 0.4519068 1.6689045 2.4395294 2.7179083 1.5753421
# 取出中值绝对偏差大于0.5的行
> b = a[apply(a,1,mad)>0.5,]
> b
[,1] [,2] [,3] [,4] [,5]
[1,] -0.4125356 0.1219293 -0.4763589 -0.9717165 1.09162243
[2,] 1.8778966 -0.1171794 2.9295352 1.3383662 -0.03269026
[3,] 1.0000000 2.0000000 3.0000000 4.0000000 5.00000000
[4,] 2.0000000 10.0000000 11.0000000 13.0000000 4.00000000
[5,] -1.2649111 -0.6324555 0.0000000 0.6324555 1.26491106
# 矩阵按照mad的大小降序排列
> c = b[order(apply(b,1,mad), decreasing=T),]
> c
[,1] [,2] [,3] [,4] [,5]
[1,] 2.0000000 10.0000000 11.0000000 13.0000000 4.00000000
[2,] 1.8778966 -0.1171794 2.9295352 1.3383662 -0.03269026
[3,] 1.0000000 2.0000000 3.0000000 4.0000000 5.00000000
[4,] -1.2649111 -0.6324555 0.0000000 0.6324555 1.26491106
[5,] -0.4125356 0.1219293 -0.4763589 -0.9717165 1.09162243
> rownames(c) <- paste('Gene', letters[1:5], sep="_")
> colnames(c) <- toupper(letters[1:5])
> c
A B C D E
Gene_a 2.0000000 10.0000000 11.0000000 13.0000000 4.00000000
Gene_b 1.8778966 -0.1171794 2.9295352 1.3383662 -0.03269026
Gene_c 1.0000000 2.0000000 3.0000000 4.0000000 5.00000000
Gene_d -1.2649111 -0.6324555 0.0000000 0.6324555 1.26491106
Gene_e -0.4125356 0.1219293 -0.4763589 -0.9717165 1.09162243
# 矩阵转置
> expr = t(c)
> expr
Gene_a Gene_b Gene_c Gene_d Gene_e
A 2 1.87789657 1 -1.2649111 -0.4125356
B 10 -0.11717937 2 -0.6324555 0.1219293
C 11 2.92953522 3 0.0000000 -0.4763589
D 13 1.33836620 4 0.6324555 -0.9717165
E 4 -0.03269026 5 1.2649111 1.0916224
# 矩阵值的替换
> expr2 = expr
> expr2[expr2<0] = 0
> expr2
Gene_a Gene_b Gene_c Gene_d Gene_e
A 2 1.877897 1 0.0000000 0.0000000
B 10 0.000000 2 0.0000000 0.1219293
C 11 2.929535 3 0.0000000 0.0000000
D 13 1.338366 4 0.6324555 0.0000000
E 4 0.000000 5 1.2649111 1.0916224
# 矩阵中只针对某一列替换
# expr2是个矩阵不是数据框，不能使用列名字索引
> expr2[expr2$Gene_b<1, "Gene_b"] <- 1
Error in expr2$Gene_b : $ operator is invalid for atomic vectors
# str是一个最为常用、好用的查看变量信息的工具，尤其是对特别复杂的变量，可以看清其层级结构，便于提取数据
> str(expr2)
num [1:5, 1:5] 2 10 11 13 4 ...
- attr(*, "dimnames")=List of 2
..$ : chr [1:5] "A" "B" "C" "D" ...
..$ : chr [1:5] "Gene_a" "Gene_b" "Gene_c" "Gene_d" ...
# 转换为数据框，再进行相应的操作
> expr2 <- as.data.frame(expr2)
> str(expr2)
'data.frame': 5 obs. of 5 variables:
$ Gene_a: num 2 10 11 13 4
$ Gene_b: num 1.88 1 2.93 1.34 1
$ Gene_c: num 1 2 3 4 5
$ Gene_d: num 0 0 0 0.632 1.265
$ Gene_e: num 0 0.122 0 0 1.092
> expr2[expr2$Gene_b<1, "Gene_b"] <- 1
> expr2
Gene_a Gene_b Gene_c Gene_d Gene_e
A 2 1.877897 1 0.0000000 0.0000000
B 10 1.000000 2 0.0000000 0.1219293
C 11 2.929535 3 0.0000000 0.0000000
D 13 1.338366 4 0.6324555 0.0000000
E 4 1.000000 5 1.2649111 1.0916224
R中矩阵筛选合并
# 读入样品信息
> sampleInfo = "Samp;Group;Genotype
+ A;Control;WT
+ B;Control;WT
+ D;Treatment;Mutant
+ C;Treatment;Mutant
+ E;Treatment;WT
+ F;Treatment;WT"
> phenoData = read.table(text=sampleInfo, sep=";", header=T, row.names=1, quote="")
> phenoData
Group Genotype
A Control WT
B Control WT
D Treatment Mutant
C Treatment Mutant
E Treatment WT
F Treatment WT
# 把样品信息按照基因表达矩阵中的样品信息排序，并只保留有基因表达信息的样品
> phenoData[match(rownames(expr), rownames(phenoData)),]
Group Genotype
A Control WT
B Control WT
C Treatment Mutant
D Treatment Mutant
E Treatment WT
# 注意顺序，%in%比match更好理解一些
> phenoData = phenoData[rownames(phenoData) %in% rownames(expr),]
> phenoData
Group Genotype
A Control WT
B Control WT
C Treatment Mutant
D Treatment Mutant
E Treatment WT
# 合并矩阵
# by=0 表示按照行的名字排序
# by=columnname 表示按照共有的某一列排序
# 合并后多出了新的一列Row.names
> merge_data = merge(expr, phenoData, by=0, all.x=T)
> merge_data
Row.names Gene_a Gene_b Gene_c Gene_d Gene_e Group Genotype
1 A 2 1.87789657 1 -1.2649111 -0.4125356 Control WT
2 B 10 -0.11717937 2 -0.6324555 0.1219293 Control WT
3 C 11 2.92953522 3 0.0000000 -0.4763589 Treatment Mutant
4 D 13 1.33836620 4 0.6324555 -0.9717165 Treatment Mutant
5 E 4 -0.03269026 5 1.2649111 1.0916224 Treatment WT
> rownames(merge_data) <- merge_data$Row.names
> merge_data
Row.names Gene_a Gene_b Gene_c Gene_d Gene_e Group Genotype
A A 2 1.87789657 1 -1.2649111 -0.4125356 Control WT
B B 10 -0.11717937 2 -0.6324555 0.1219293 Control WT
C C 11 2.92953522 3 0.0000000 -0.4763589 Treatment Mutant
D D 13 1.33836620 4 0.6324555 -0.9717165 Treatment Mutant
E E 4 -0.03269026 5 1.2649111 1.0916224 Treatment WT
# 去除一列；-1表示去除第一列
> merge_data = merge_data[,-1]
> merge_data
Gene_a Gene_b Gene_c Gene_d Gene_e Group Genotype
A 2 1.87789657 1 -1.2649111 -0.4125356 Control WT
B 10 -0.11717937 2 -0.6324555 0.1219293 Control WT
C 11 2.92953522 3 0.0000000 -0.4763589 Treatment Mutant
D 13 1.33836620 4 0.6324555 -0.9717165 Treatment Mutant
E 4 -0.03269026 5 1.2649111 1.0916224 Treatment WT
# 提取出所有的数值列。sapply()对列表或者向量使用函数
> merge_data[sapply(merge_data, is.numeric)]
Gene_a Gene_b Gene_c Gene_d Gene_e
A 2 1.87789657 1 -1.2649111 -0.4125356
B 10 -0.11717937 2 -0.6324555 0.1219293
C 11 2.92953522 3 0.0000000 -0.4763589
D 13 1.33836620 4 0.6324555 -0.9717165
E 4 -0.03269026 5 1.2649111 1.0916224
