R and Data analysis old notes (i) Use of basic mathematical functions

• Creating a vector matrix

> X1=c (2,3,6,8) > X2=c (1,2,3,4) > a1= (1:100) > length (A1) [1] 100> Length (x1) [1] 4> mode (x1) [1] "Numeric" > Rbind (x1,x2)   [, 1] [, 2] [, 3] [, 4]x1    2    3    6    8x2    1    2    3    4> cbind (x1,x2)     X1 x2[1,]  2  1[2,]  3  2[3,]  6  3[4,]  8  4

• Averaging, and, multiplication, max, variance, standard deviation

> Mean (x1) [1] 4.75> sum (x1) [1] 19> max (x1) [1] 8> min (x1) [1] 2> var (x1) [1] 7.583333> prod (x1) [1] 288> SD (x1) [1] 2.753785

• Generating vectors

> 1:10 [1] 1 2 3 4 5 6 7 8 9 10> 1:10-1 [1] 0 1 2 3 4 5 6 7 8 9> 1:10*2 [1] 2 4 6 8 10 12 14 16 18 2   0> a=2:60*2+1> A [1] 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41[20] 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79[39] 81 83 85 87 89 91 93 95 97 99 101 103 105 107 1 111 113 117[58] 119 121> a[5][1] 13> a[-5] [1] 5 7 9 11 15 17 19 21 23 25 27 29 31 33 35 3  7 39 41 43[20] 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81[39] 83 85 87 89 91 93 103 107 109 111 113 101 117 119[58] 121> a[c (2,3,8)][1] 7 9 19> a[a<20][1] 5 7 9 11 13 1   5 19> a[a[3]][1] 21> seq (6,20) [1] 6 7 8 9 ten each (20>) [1] 5 7   9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41[20] 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79[About] Bayi-----The 101 103 107 109 111 113, 117[58] 119 121> seq (5,121,length=10) [1] 5.00000 17.88889 30.77778 43.66667 56.55556 69.44444 82.33333 [8] 95.22222 108.11111 121.00000

• New Vector

> A=c (2,3,4,2,3,2,1,4,3,2,1) > Which.max (a) [1] 3> A[which.max (a)][1] 4> which (a==2) [1]  1  4  6 10> A[which (a==2)][1] 2 2 2 2> which (a>5) integer (0) > A[which (a>5)]numeric (0) > A=1:20> A [1]  1<  C5/>2  3  4  5  6  7  8 9  Ten (a) 20> rev (a) [1] 20 19 18 17 16 15 14 13  9  8  7  6  5  4 3  2  1> a=c (2,3,4,5,6,6,7,8,3,2) > sort (a) [1 ] 2 2 3 3 4 5 6 6 7 8> Rev (sort (a)) [1] 8 7 6 6 5 4 3 3 2 2

• Build matrix

> A1=c (1:12) > Matrix (a1,nrow=3,ncol=4)     [, 1] [, 2] [, 3] [, 4][1,]    1    4    7   10[2,]    2    5    8   11[3,]    3    6    9   12> Matrix (a1,nrow=4,ncol=3)     [, 1] [, 2] [, 3][1,]    1    5    9[2,]    2    6   10[3,]    3    7   11[4,]    4    8   12> Matrix (a1,nrow=4,ncol =3,byrow=t)     [, 1] [, 2] [, 3][1,]    1    2    3[2,]    4    5    6[3,]    7    8    9[4,]   12

• Matrix operations

Matrix addition

> A=matrix (1:12,nrow=3,ncol=4) > t (a)     [, 1] [, 2] [, 3][1,]    1    2    3[2,]    4    5    6[3 ,]    7    8    9[4,]   ten   12> A=b=matrix (1:12,nrow=3,ncol=4) > A+b     [, 1] [, 2] [, 3] [, 4] [1,]    2    8   20[2,]    4   22[3,] 6 24> A-b     [, 1 ] [, 2] [, 3] [, 4][1,]    0    0    0    0[2,]    0    0    0    0[3,]    0    0    0    0

Matrix multiplication

> A=matrix (1:12,nrow=3,ncol=4) > B=matrix (1:12,nrow=4,ncol=3) > A%*%b     [, 1] [, 2] [, 3][1,]  158  246[2,]  184  288[3,]  330> a=matrix (1:16,nrow=4,ncol=4) > A     [, 1] [ , 2] [, 3] [, 4][1,]    1    5    9   13[2,]    2    6   14[3,]    3    7   15[4,]    4    8   16> diag (a) [1]  1  6 16> diag (Diag (a))     [, 1] [, 2] [, 3] [, 4][1, ]    1    0    0    0[2,]    0    6    0    0[3,]    0    0    0[4,]    0    0    0   16> diag (4)     [, 1] [, 2] [, 3] [, 4][1,]    1    0    0    0[2,]    0    1    0    0[3,]    0    0    1    0[4,]    0    0    0    1

Matrix inversion

> A=matrix (rnorm) > A             [, 1]        [, 2]       [, 3]       [, 4][1,] -1.604650746-2.22482987  1.5094439  1.0070701[2,]  0.006409861-0.01506928-0.6651050-1.9342548[3,] -1.606959408-0.49430092-0.9376593  0.1979031[4,]  0.422441416-0.33201336  0.3848287  1.1256368> Solve (a)           [, 1]       [, 2]       [, 3 ]       [, 4][1,] -0.1426715  0.5944611-0.1676185  1.1786143[2,] -0.1804919-0.9604913-0.2055298-1.4528592[ 3,]  0.3168603-0.5776493-0.6252734-1.1661647[4,] -0.1080209-0.3089139  0.2160497  0.4162172

Solving systems of linear equations

> A=matrix (Rnorm (16), BIS)
> A
[, 1]       [, 2]       [, 3] [, 4]
[1,] -1.604650746-2.22482987 1.5094439 1.0070701
[2,] 0.006409861-0.01506928-0.6651050-1.9342548
[3,] -1.606959408-0.49430092-0.9376593 0.1979031
[4,] 0.422441416-0.33201336 0.3848287 1.1256368
> Solve (a)
[, 1]       [, 2]       [, 3] [, 4]
[1,]-0.1426715 0.5944611-0.1676185 1.1786143
[2,] -0.1804919-0.9604913-0.2055298-1.4528592
[3,] 0.3168603-0.5776493-0.6252734-1.1661647
[4,] -0.1080209-0.3089139 0.2160497 0.4162172
> A=matrix (Rnorm (16), BIS)
> A
[, 1]        [, 2]        [, 3] [, 4]
[1,] 1.0451867-0.2426553-0.51232551-0.12062549
[2,] -1.5518006-0.1333096 0.03677731-0.10715366
[3,] -1.0620249-1.3160312 0.01713207 0.09320016
[4,]-0.6664664 2.2398778 1.94861889 0.01788447
> B=c (1:4)
> b
[1] 1 2 3 4
> Solve (A, B)
[1] 0.9840158-4.6924392 8.0064010-24.3295023

Eigenvalues and eigenvectors of matrices

> A=diag (4) +1> a     [, 1] [, 2] [, 3] [, 4][1,]    2    1    1    1[2,]    1    2    1    1[3,]    1    1    2    1[4,]    1    1    1    2> A.e=eigen (a,symmetric=t) > A.e$values[1] 5 1 1 1$vectors     [, 1]       [, 2]       [, 3]       [, 4] [1,] -0.5  0.8660254  0.0000000  0.0000000[2,] -0.5-0.2886751-0.5773503-0.5773503[3,] -0.5-0.2886751- 0.2113249  0.7886751[4,] -0.5-0.2886751  0.7886751-0.2113249> a.e$vectors%*%diag (a.e$values)%*%t (a.e$ Vectors)     [, 1] [, 2] [, 3] [, 4][1,]    2    1    1    1[2,]    1    2    1    1[3,]    1    1    2    1[4,]    1    1    1    2

• Data frame

> X1=c (10,13,14,23,43) > X2=c (12,35,35,67,54) > X=data.frame (x1,x2) > x  x1 x21 10 122 13 353 14 354 23 675 4 3 54> Plot (x) #散点图

• Read text file

(X=read.table ("Abc.txt")) #读剪贴板y =read.table ("clipboard", Header=f) yz=read.table ("clipboard", header=t) Z

• Looping statements

For statement

> for (i-in 1:59) {a[i]=1*2+3}> a [1] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5[39] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5> > b=0> for (i in 1:59) {a[i]=i*2+3;b[i]=i*5-4}> b [1]   1   6
   11-----  -  Bayi  91[20]  96 101 106 111 116 121 126 131 136 141 146 151 156 161 166 171 176 181 186[39] 191 196 201 206 211 216 221 226 231 236 241 246 251 256 261 266 271 276 281[58] 286 291

While statement

A[1]=5> i=1> while (a[i]<121) {i=i+1;a[i]=a[i-1]+2}> A [1]   5   7   9  17 43 of the above-the-  41[20]  All in all, a  .  79[39-------  97  99 101 103 105 107 109 111 113 115 117[58] 119 121

• R Script Reference

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R and Data analysis old notes (i) Use of basic mathematical functions