# install package
> install.packages()
# load the package into the current session
> library(splines)
# update package
> update.packages()
# close the session
> q()
# more info about a function
> ?mean
> help(mean)
# store a value in a variable
> x = 6 # the value of x is 6
> assign("x", 5) # the value of x is 5
> x <- 4 # the value of x is 4
> 3 -> x # the value of x is 3
# كانو قاعدين يقترحوا أكتر من سينتكس وعملوهم كلهم عشان محدش يزعل
# list all current objects (variables/arrays/defined-functions..)
> ls()
> objects ()
# remove object
> rm(y, z)
# working directory
> getwd() # print the current working directory
> setwd("D:\\work") # navigate to the given working directory> 5 + 2 # 7
> 5 - 2 # 3
> 5 * 2 # 10
> 2 ^ 5 # 32 // to the power
> 5 / 2 # 2.5 // division
> 5 %/% 2 # 2 // integer division
> 2 %% 5 # 1 // remainder> 5 * exp(-2) * (cos(2 * pi / 6) + atan(1)) # 0.8697986> 1 == 1 # True
> 1 != 1 # False
> 2 < 2 # False
> 2 <= 2 # True
> T & F # False
> T | F # True
> is.na(NA) # True
> is.na(1) # False
> is.na(c(1, NA)) # False True> round(1.6) # 2
> sqrt(9) # 3
> sqrt(c(4, 9)) # 3
> abs(c(1, -1)) # 1 1
> exp(1) # 2.718282 // Exponential function *e to the power 1*
> log(exp(1)) # 1 // base-e logarithm
> log10(100) # 2 // base-10 logarithm
> sin(0) # 0
> cos(0) # 1
> tan(0) # 0
> asin(0) # 0
> acos(1) # 0
> atan(0) # 0
> min(c(1, 2)) # 1
> max(c(1, 2)) # 2
> min(1, 2) # 1
> max(1, 2) # 2
> length(c(1, 3, 8)) # 3
> sum(c(1, 3, 8)) # 12
> ceiling(c(1.8, -1.2)) # 2 -1
> floor(c(1.8, -1.2)) # 1 -2
> trunc(c(1.8, -1.2)) # 1 -1 // trunc always rounds toward 0
> pmin(c(1, 22, 3), c(5, 6, 7)) # 1 6 3 // the min between each element
> pmax(c(1, 22, 3), c(5, 6, 7)) # 5 22 7 // the max between each element> x = c(3, 3, 1, 5)
> mean(x) # 3
> median(x) # 3
> range(c(1, 3, 8)) # 1 8
> var(x) # 2.66667
> sd(x) # 1.632993
> quantile(x, 0.5) # 3
> cor(x, y)Example:
# random generation for a random sample of size 6 from the normal distribution
> x = rnorm(6)
# mean
> sum(x) / length(x) # 0.0883872
> mean(x) # 0.0883872
# standard deviation
> sqrt(sum((x - mean(x)) ^ 2) / (length(x) - 1)) # 0.9295404
> sd(x) # 0.9295404Types of vector:
-
numeric vector (array of numbers)
x = c(10.4, 5.6, 3.1, 6.4)
-
character vector (array of text strings)
x = c("Jan","Apr", "Jul", "Oct")
-
logical vector (array of TRUE / FALSE value)
x = c(T,T,F,T)
Creating vectors using concatenate function c:
# regular c
> a = c(1, 3, 4)
> a
1 2 3
# adding names
> b = c("i", "j", "k")
> names(a) = b
> a
i j k
1 3 4
# specifing vector names directly
> c(x=1, y=3, z=4)
x y z
1 3 4Creating vectors using sequence function seq:
> seq(1, 12) # from 1 to 12 including 1 and 12
1 2 3 4 5 6 7 8 9 10 11 12
> 1:12 # the same
1 2 3 4 5 6 7 8 9 10 11 12
> seq(1, 12, 2) # step is +2 not the default +1
1 3 5 7 9 11
> seq(-1, 1, 0.2) # step is +0.2
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
# working with letters vector
> letters # print the vector letters from "a" to "z"
> letters[10:15] # print "6" letters
"j" "k" "l" "m" "n" "o"Creating vectors using replicate function rep:
# repeat the vector [1, 2, 2] => 2 times
> rep(c(1, 2, 2), 2)
1 2 8 1 2 8
# repeat the generated vector [1 2 3] => 3 times
> rep(seq(1, 3), 3)
1 2 3 1 2 3 1 2 3
# repeat each element in the vector [7 6 8] => [1 2 3] times
> rep(c(7, 8, 9), c(1, 2, 3))
7 8 8 9 9 9
# repeat the generated vector [9 10 11] => [2 3 4] times
> rep(9:11, 2:4)
9 9 10 10 10 11 11 11 11Working with paste function:
> paste(c("X","Y"), 1:10, sep="")
"X1" "Y2" "X3" "Y4" "X5" "Y6" "X7" "Y8" "X9" "Y10"print the following output using
repandpastefunctions:
"X1Y1" "X2Y2" "X3Y3" "X4Y4" "X5Y5" "X6Y6" "X7Y7" "X8Y8" "X9Y9" "X10Y10"
> Xs = paste(c("X"), 1:10, sep="")
> Ys = paste(c("Y"), 1:10, sep="")
> paste(Xs, Ys, sep="")# by default the matrix will be filled in a columnwise fashion
> matrix(1:12, nrow=3)
[,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
# to fill the matrix in a rowwise fashion we add byrow=T
> x = matrix(1:12, nrow=3, byrow=T)
> x
[,1] [,2] [,3] [,4]
[1,] 1 2 3 4
[2,] 5 6 7 8
[3,] 9 10 11 12
# using transposition function
> y = t(x)
> y
[,1] [,2] [,3]
[1,] 1 5 9
[2,] 2 6 10
[3,] 3 7 11
[4,] 4 8 12
# accessing the matrix elements
> y[2, 2]
6
> y[2,]
2 6 10
> y[,2]
5 6 7 8
# matrix info
> dim(y)
4 2
> length(y)
12
> colMeans(y) # means of the columns
2.5 6.5 10.5
> rowMeans(y) # means of the rows
5 6 7 8
# using dim to generate matix (not recommended)
> m = 1:9
> dim(m) = c(3,3)
> m # the matrix will be filled in a columnwise fashion
[,1] [,2] [,3]
[1,] 1 4 7
[2,] 2 5 8
[3,] 3 6 9
> det(m) # calculate the determinant
0
# using the diagonal function
> diag(m)
1 5 9
> sum(diag(m)) # the trace of matrix m
15
> diag(c(1, 5, 9))
[,1] [,2] [,3]
[1,] 1 0 0
[2,] 0 5 0
[3,] 0 0 9
> diag(3) # identity matrix of order 3
[,1] [,2] [,3]
[1,] 1 0 0
[2,] 0 1 0
[3,] 0 0 1
# combining matrices by joining rows / columns
> a = matrix(1:6, nrow=2)
> b = matrix(11:16, nrow=2)
> a
[,1] [,2] [,3]
[1,] 1 3 5
[2,] 2 4 6
> b
[,1] [,2] [,3]
[1,] 11 13 15
[2,] 12 14 16
> rbind(a, b)
[,1] [,2] [,3]
[1,] 1 3 5
[2,] 2 4 6
[3,] 11 13 15
[4,] 12 14 16
> rbind(4, 1, b, a, c(22, 23, 24))
[,1] [,2] [,3]
[1,] 4 4 4
[2,] 1 1 1
[3,] 11 13 15
[4,] 12 14 16
[5,] 1 3 5
[6,] 2 4 6
[7,] 22 23 24
> cbind(a, b)
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1 3 5 11 13 15
[2,] 2 4 6 12 14 16
# math operations
> a + b # element by element addition
> a - b # element by element subtraction
> a * b # element by element product
> a / b # element by element division
# matrix multiplication
> a %*% b # can't multiply: size (2*3) %*% (2*3)
{Error in a %*% b : non-conformable arguments}
> a %*% t(b) # it's ok: size (2*3) %*% (3*2)
[,1] [,2]
[1,] 125 134
[2,] 164 176Working with crossproduct & outer-product
# crossproduct
> crossprod(1:4, 4:7) # 1*4 + 2*5 + 3*6 + 4*7
60
> crossprod(1:4) # same as crossprod(1:4, 1:4)
# outer-product
> a = c(1,2, 3)
> b = c(4, 5, 6, 7)
> outer(a, b, '*') # each matrix[i,j] element = a[i] "*" b[j]
[,1] [,2] [,3] [,4]
[1,] 4 5 6 7
[2,] 8 10 12 14
[3,] 12 15 18 21
# we can change the '*' operator by using a defined function with 2 parameters
> anotherFunction <- function(x, y) y^x
> outer(a, b, anotherFunction)
[,1] [,2] [,3] [,4]
[1,] 4 5 6 7
[2,] 16 25 36 49
[3,] 64 125 216 343Calculating the eigenvalues and eigenvectors of a symmetric matrix
> m = matrix(c(10, 2, 1, 2, 20, 6, 1, 6, 30), nrow=3)
> m
[,1] [,2] [,3]
[1,] 10 2 1
[2,] 2 20 6
[3,] 1 6 30
> resultObject = eigen(m)
# to get the vector of eigenvalues
> resultObject$val
32.94503 17.44151 9.61346
# to get the matrix of eigenvectors
> resultObject$vec
[,1] [,2] [,3]
[1,] -0.07662051 -0.1785530 0.980942473
[2,] -0.42900733 -0.8822029 -0.194089574
[3,] -0.90004556 0.4357028 0.009005696Solve Function: solves the equation a %*% x = b’ for ‘x’ where b can be either a vector or a matrix.
find the value of x & y
we can think of it as the following:
> A = matrix(c(1, 1, 1, -1), 2, 2, byrow=T)
> b = c(5,1)
> solve(A) %*% b
3 2
# instead of solve(A) %*% b we can use
> solve(A, b)
3 2