BASIC MATHEMATICAL FUNCTIONS AND LOGICAL OPERATORS IN R:
5-3## [1] 22^3## [1] 864^(1/3)## [1] 464^(1/2)## [1] 8sqrt(64)## [1] 8abs(5.6-8.9)/.5 #abs() is for absolute value## [1] 6.6log(12,4) # log of 12 at base 4## [1] 1.792481log10(12) # log of 12 at base 10## [1] 1.079181factorial(5)## [1] 120choose(10,4) # choosing 4 things out of 10## [1] 21025%/%7 # this is quotient ## [1] 325%%7 # this is remainder## [1] 4floor(6.3) # this will round down - greatest integer < 6.3## [1] 6ceiling(6.3) # this will round up - smallest integer > 6.3## [1] 7round(7.9956725,digits = 4) # this rounds a float to to given decimal places## [1] 7.9957signif(7.9956725,digits = 4) # this gives x to 4 digits in scientific notation## [1] 7.996runif(5) # this generates 5 random numbers between 0 and 1, distributed uniformly## [1] 0.08012073 0.20590587 0.64536359 0.39489703 0.54440751sin(45)## [1] 0.8509035tan(30)## [1] -6.405331GENERATING SEQUENCES IN R:
3:25## [1] 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25seq(3,25,3) #this generates a sequence from arg1 to arg2 with step=arg3## [1] 3 6 9 12 15 18 21 24seq(25,3,-3) # can also go backwards when generating a seq with negative step## [1] 25 22 19 16 13 10 7 4seq(from=7, by=2, along=1:10) # this generates a set of total 20 numbers, starting with 7, step=2## [1] 7 9 11 13 15 17 19 21 23 25rep(4.615,15) # this will repeat a single number (=4.615) for a total of 15 times## [1] 4.615 4.615 4.615 4.615 4.615 4.615 4.615 4.615 4.615 4.615 4.615 4.615
## [13] 4.615 4.615 4.615rep(1:5,4) # this will repeat a sequence (1:5) for a total of 4 times## [1] 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5rep(1:5,rep(2,5)) # this will repeat each number in the 1:5 sequence "twice" - since the second rep() repeats 2 for total 5 times## [1] 1 1 2 2 3 3 4 4 5 5rep(1:5,c(1,2,3,4,5)) # this is a more customized way of letting R know which specific number to repeat how many times## [1] 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5rep(c("Mon", "Tue", "Wed", "Thur"),c(3,1,4,2)) # the first c() gives list of arguments to be repeated, the second c() gives the number of times each argument in the previous function needs repeating## [1] "Mon" "Mon" "Mon" "Tue" "Wed" "Wed" "Wed" "Wed" "Thur" "Thur"VECTORS IN R:
y = c(2,4,6,8) # the concatenate() creates lists in R
x = c(y,y) # this function can also take in different lists as arguments and join them to create a new list
x## [1] 2 4 6 8 2 4 6 8n = length(x)
xmean = mean(x)
variance = sum((x-xmean)^2)/(n-1) #calculating variiance using sum(), length(), mean()
variance## [1] 5.714286var(x) # calculating variance in y using an in-built function## [1] 5.714286a = c(3,7,2,5,4,5,6,9,1,8)
quantile(a) # outputs avector containing - min 0%, lower quartile 25%, median 50%, upper quartile 75%, max 100% - of a)## 0% 25% 50% 75% 100%
## 1.00 3.25 5.00 6.75 9.00rank(a) # this outputs ranks of individual elements in the same order as they are present in the vector## [1] 3.0 8.0 2.0 5.5 4.0 5.5 7.0 10.0 1.0 9.0sort(a) # this outputs individual elements in a sorted order## [1] 1 2 3 4 5 5 6 7 8 9order(a) # this outputs the positions to fetch individual elements from to create an ascending list. Here, smallest element is at position 9, next element at position 3, and so on.## [1] 9 3 1 5 4 6 7 2 10 8newdtframe = data.frame(a,rank(a),sort(a),order(a)) # this creates a data frame which contains lists generated by above functions. We can use this specific data frame to view the results easily.
newdtframe## a rank.a. sort.a. order.a.
## 1 3 3.0 1 9
## 2 7 8.0 2 3
## 3 2 2.0 3 1
## 4 5 5.5 4 5
## 5 4 4.0 5 4
## 6 5 5.5 5 6
## 7 6 7.0 6 7
## 8 9 10.0 7 2
## 9 1 1.0 8 10
## 10 8 9.0 9 8DATAFRAMES IN R:
worms = read.csv("C:\\temp\\Course Data\\worms.csv",header=T,row.names=1)
worms## Area Slope Vegetation Soil.pH Damp Worm.density
## Nashs.Field 3.6 11 Grassland 4.1 FALSE 4
## Silwood.Bottom 5.1 2 Arable 5.2 FALSE 7
## Nursery.Field 2.8 3 Grassland 4.3 FALSE 2
## Rush.Meadow 2.4 5 Meadow 4.9 TRUE 5
## Gunness.Thicket 3.8 0 Scrub 4.2 FALSE 6
## Oak.Mead 3.1 2 Grassland 3.9 FALSE 2
## Church.Field 3.5 3 Grassland 4.2 FALSE 3
## Ashurst 2.1 0 Arable 4.8 FALSE 4
## The.Orchard 1.9 0 Orchard 5.7 FALSE 9
## Rookery.Slope 1.5 4 Grassland 5.0 TRUE 7
## Garden.Wood 2.9 10 Scrub 5.2 FALSE 8
## North.Gravel 3.3 1 Grassland 4.1 FALSE 1
## South.Gravel 3.7 2 Grassland 4.0 FALSE 2
## Observatory.Ridge 1.8 6 Grassland 3.8 FALSE 0
## Pond.Field 4.1 0 Meadow 5.0 TRUE 6
## Water.Meadow 3.9 0 Meadow 4.9 TRUE 8
## Cheapside 2.2 8 Scrub 4.7 TRUE 4
## Pound.Hill 4.4 2 Arable 4.5 FALSE 5
## Gravel.Pit 2.9 1 Grassland 3.5 FALSE 1
## Farm.Wood 0.8 10 Scrub 5.1 TRUE 3names(worms) # gives a list of variable/column names## [1] "Area" "Slope" "Vegetation" "Soil.pH" "Damp"
## [6] "Worm.density"attach(worms) # makes accessible names accessible in this code
summary(worms) # summary stats. "Field.Name" clumn was not summarized since it contains row names (unique data points).## Area Slope Vegetation Soil.pH
## Min. :0.800 Min. : 0.00 Length:20 Min. :3.500
## 1st Qu.:2.175 1st Qu.: 0.75 Class :character 1st Qu.:4.100
## Median :3.000 Median : 2.00 Mode :character Median :4.600
## Mean :2.990 Mean : 3.50 Mean :4.555
## 3rd Qu.:3.725 3rd Qu.: 5.25 3rd Qu.:5.000
## Max. :5.100 Max. :11.00 Max. :5.700
## Damp Worm.density
## Mode :logical Min. :0.00
## FALSE:14 1st Qu.:2.00
## TRUE :6 Median :4.00
## Mean :4.35
## 3rd Qu.:6.25
## Max. :9.00worms[2,4] # different ways to use "subscripts" to access data in specific dataframe locations## [1] 5.2worms[,4]## [1] 4.1 5.2 4.3 4.9 4.2 3.9 4.2 4.8 5.7 5.0 5.2 4.1 4.0 3.8 5.0 4.9 4.7 4.5 3.5
## [20] 5.1worms[3,]## Area Slope Vegetation Soil.pH Damp Worm.density
## Nursery.Field 2.8 3 Grassland 4.3 FALSE 2worms[1:3,c(1,2,4,6)]## Area Slope Soil.pH Worm.density
## Nashs.Field 3.6 11 4.1 4
## Silwood.Bottom 5.1 2 5.2 7
## Nursery.Field 2.8 3 4.3 2worms[Soil.pH>4 & Worm.density>5,] #using subscripts and logical operators (to set conditions) together## Area Slope Vegetation Soil.pH Damp Worm.density
## Silwood.Bottom 5.1 2 Arable 5.2 FALSE 7
## Gunness.Thicket 3.8 0 Scrub 4.2 FALSE 6
## The.Orchard 1.9 0 Orchard 5.7 FALSE 9
## Rookery.Slope 1.5 4 Grassland 5.0 TRUE 7
## Garden.Wood 2.9 10 Scrub 5.2 FALSE 8
## Pond.Field 4.1 0 Meadow 5.0 TRUE 6
## Water.Meadow 3.9 0 Meadow 4.9 TRUE 8worms[order(worms[,1]),] # ordering all rows by "Area", i.e., column 1## Area Slope Vegetation Soil.pH Damp Worm.density
## Farm.Wood 0.8 10 Scrub 5.1 TRUE 3
## Rookery.Slope 1.5 4 Grassland 5.0 TRUE 7
## Observatory.Ridge 1.8 6 Grassland 3.8 FALSE 0
## The.Orchard 1.9 0 Orchard 5.7 FALSE 9
## Ashurst 2.1 0 Arable 4.8 FALSE 4
## Cheapside 2.2 8 Scrub 4.7 TRUE 4
## Rush.Meadow 2.4 5 Meadow 4.9 TRUE 5
## Nursery.Field 2.8 3 Grassland 4.3 FALSE 2
## Garden.Wood 2.9 10 Scrub 5.2 FALSE 8
## Gravel.Pit 2.9 1 Grassland 3.5 FALSE 1
## Oak.Mead 3.1 2 Grassland 3.9 FALSE 2
## North.Gravel 3.3 1 Grassland 4.1 FALSE 1
## Church.Field 3.5 3 Grassland 4.2 FALSE 3
## Nashs.Field 3.6 11 Grassland 4.1 FALSE 4
## South.Gravel 3.7 2 Grassland 4.0 FALSE 2
## Gunness.Thicket 3.8 0 Scrub 4.2 FALSE 6
## Water.Meadow 3.9 0 Meadow 4.9 TRUE 8
## Pond.Field 4.1 0 Meadow 5.0 TRUE 6
## Pound.Hill 4.4 2 Arable 4.5 FALSE 5
## Silwood.Bottom 5.1 2 Arable 5.2 FALSE 7worms[rev(order(worms[,1])),] # same as above, but in descending order, rev() reverses the argument.## Area Slope Vegetation Soil.pH Damp Worm.density
## Silwood.Bottom 5.1 2 Arable 5.2 FALSE 7
## Pound.Hill 4.4 2 Arable 4.5 FALSE 5
## Pond.Field 4.1 0 Meadow 5.0 TRUE 6
## Water.Meadow 3.9 0 Meadow 4.9 TRUE 8
## Gunness.Thicket 3.8 0 Scrub 4.2 FALSE 6
## South.Gravel 3.7 2 Grassland 4.0 FALSE 2
## Nashs.Field 3.6 11 Grassland 4.1 FALSE 4
## Church.Field 3.5 3 Grassland 4.2 FALSE 3
## North.Gravel 3.3 1 Grassland 4.1 FALSE 1
## Oak.Mead 3.1 2 Grassland 3.9 FALSE 2
## Gravel.Pit 2.9 1 Grassland 3.5 FALSE 1
## Garden.Wood 2.9 10 Scrub 5.2 FALSE 8
## Nursery.Field 2.8 3 Grassland 4.3 FALSE 2
## Rush.Meadow 2.4 5 Meadow 4.9 TRUE 5
## Cheapside 2.2 8 Scrub 4.7 TRUE 4
## Ashurst 2.1 0 Arable 4.8 FALSE 4
## The.Orchard 1.9 0 Orchard 5.7 FALSE 9
## Observatory.Ridge 1.8 6 Grassland 3.8 FALSE 0
## Rookery.Slope 1.5 4 Grassland 5.0 TRUE 7
## Farm.Wood 0.8 10 Scrub 5.1 TRUE 3order(Area)## [1] 20 10 14 9 8 17 4 3 11 19 6 12 7 1 13 5 16 15 18 2Vegetation[order(Slope)] # this outputs vegetation names ordered by slope. can use rev() to order descending## [1] "Scrub" "Arable" "Orchard" "Meadow" "Meadow" "Grassland"
## [7] "Grassland" "Arable" "Grassland" "Grassland" "Arable" "Grassland"
## [13] "Grassland" "Grassland" "Meadow" "Grassland" "Scrub" "Scrub"
## [19] "Scrub" "Grassland"LOGICAL SUBSCRIPTS IN R DATAFRAMES:
x = 0:10
sum(x) # this sums all values of x## [1] 55x<7 # this outputs results of T/F operation applied to individual elements of x## [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE1*(x<7) # this converts T/F results of above statement to numeric 1/0## [1] 1 1 1 1 1 1 1 0 0 0 0sum(x<7) # this sums the no. of occurences when x<7## [1] 7sum(x[x<7]) # this sums up all numbers in x that are <7## [1] 21y = c(8,5,3,9,1,0,4,2,7,6) # find the top 3 elements of vector y
rev(sort(y))[1:3] # this outputs top 3 elements## [1] 9 8 7sum(rev(sort(y))[1:3])# this outputs sum of top 3 elements## [1] 24which(y>5) # this outputs positions of elements satisfying y>5 in y## [1] 1 4 9 10y[(y>5)] # this outputs the the exact elements satisfying y>5## [1] 8 9 7 6sample(y) # sampling without replacement## [1] 7 8 0 6 3 1 2 4 5 9sample(y,replace=T) # sampling with replacement## [1] 7 1 2 9 5 4 6 3 6 4c = y[-4] # removing specific elements from a vector
c## [1] 8 5 3 1 0 4 2 7 6trim.mean = function(y) mean(sort(y)[-c(1,length(y))]) # defining a new function to produce a trimmed mean for y. Here, we are removing the first and last values to trim the vector, then sorting it and finding its mean.
trim.mean(y)## [1] 4.5LOGICAL ARITHEMATIC IN R:
m = c(8,3,5,7,6,6,8,9,2,3,9,4,10,4,11)
m## [1] 8 3 5 7 6 6 8 9 2 3 9 4 10 4 11# find the total number of instances when m is either very low or high. For definition, low=mean(y)-2, high=mean(y)+2
sum(m<mean(m)-2 | m>mean(m)+2)## [1] 9# now find the sum of instances discovered through above command
sum(m[m<mean(m)-2 | m>mean(m)+2])## [1] 55# replace values in m using for() and if()
#for(i in 1:length(m)) {if(m[i]<(mean(m)-2)) (m[i] = 0)}
#m
# performing above operation using in-built function
m[m<(mean(m)-2)] = 0
m## [1] 8 0 5 7 6 6 8 9 0 0 9 0 10 0 11PLOTTING MATHEMATICAL FUNCTIONS IN R:
# PLOTTING OVERLAYED FUNCTIONS - when the assumed values of constants change in the equation (from 3 to 2 and from 0.1 to 0.05, in this example)
x = 0:50
y1 = 3*(1-exp(-0.1*x))
plot(x,y1,type="l")
y2 = 2*(1-exp(-0.05*x)) # defining a new variable y2 to be added to the above plot
lines(x,y2,lty=2) # adding a new graph to an existing plot
y3 = 1*(1-exp(-0.025*x))
lines(x,y3,lty=3)
MATRICES IN R:
g = matrix(c(8,3,5,7,6,6,8,9,2,3,9,4,10,4,11),nrow=5)
h = matrix(c(25,37,13),ncol=1)
g## [,1] [,2] [,3]
## [1,] 8 6 9
## [2,] 3 8 4
## [3,] 5 9 10
## [4,] 7 2 4
## [5,] 6 3 11h## [,1]
## [1,] 25
## [2,] 37
## [3,] 13g %*% h # matrix multiplication. IMPORTANT - ncol(g) should be = nrow(h)## [,1]
## [1,] 539
## [2,] 423
## [3,] 588
## [4,] 301
## [5,] 404