anirudhjayaraman

# Add a second variable loss_percent to the dataset: m1
m1 <- mutate(hflights, loss = ArrDelay - DepDelay, loss_percent = ((ArrDelay - DepDelay)/DepDelay)*100)

# mutate() allows you to use a new variable while creating a next variable in the same call
# Copy and adapt the previous command to reduce redendancy: m2
m2 <- mutate(hflights, loss = ArrDelay - DepDelay, loss_percent = (loss/DepDelay) * 100 )

# Add the three variables as described in the third instruction: m3
m3 <- mutate(hflights, TotalTaxi = TaxiIn + TaxiOut, ActualGroundTime = ActualElapsedTime - AirTime, Diff = TotalTaxi - ActualGroundTime)

anirudhjayaraman

# Add the new variable ActualGroundTime to a copy of hflights and save the result as g1.
g1 <- mutate(hflights, ActualGroundTime = ActualElapsedTime - AirTime)

# Add the new variable GroundTime to a g1. Save the result as g2.
g2 <- mutate(g1, GroundTime = TaxiIn + TaxiOut)

# Add the new variable AverageSpeed to g2. Save the result as g3.
g3 <- mutate(g2, AverageSpeed = Distance / AirTime * 60)

# Print out g3

anirudhjayaraman

# Some comparisons to basic R
# both hflights and dplyr are available

ex1r <- hflights[c("TaxiIn","TaxiOut","Distance")]
ex1d <- select(hflights, TaxiIn, TaxiOut, Distance) 

ex2r <- hflights[c("Year","Month","DayOfWeek","DepTime","ArrTime")]
ex2d <- select(hflights, Year:ArrTime, -DayofMonth)

ex3r <- hflights[c("TailNum","TaxiIn","TaxiOut")]

anirudhjayaraman

# Helper functions used with dplyr

# Print out a tbl containing just ArrDelay and DepDelay
select(hflights, ArrDelay, DepDelay)
# Use a combination of helper functions and variable names to print out 
# only the UniqueCarrier, FlightNum, TailNum, Cancelled, and CancellationCode 
# columns of hflights
select(hflights, UniqueCarrier, FlightNum, contains("Tail"), contains("Cancel"))

# Find the most concise way to return the following columns with select and its 

anirudhjayaraman

hflights[c('ActualElapsedTime','ArrDelay','DepDelay')]
# Equivalently, using dplyr:
select(hflights, ActualElapsedTime, ArrDelay, DepDelay)

# Print out a tbl with the four columns of hflights related to delay
select(hflights, ActualElapsedTime, AirTime, ArrDelay, DepDelay)

# Print out hflights, nothing has changed!
hflights

anirudhjayaraman

# INTRODUCTION TO dplyr AND tbls
# Load the dplyr package
library(dplyr)

# Load the hflights package
library(hflights)

# Call both head() and summary() on hflights
head(hflights)
summary(hflights)

anirudhjayaraman

% Solution for part (a)
p = permMatrices(3);
n = size(p,3); % number of permutation matrices 
v = zeros(n,1); % vector of zeros with dimension equalling number of permutation matrices
% check for permutation matrices other than identity matrix with 3rd power equalling identity matrix
for i = 1:n
  if p(:,:,i)^3 == eye(3)   
    v(i,1) = 1;
  end
end  

anirudhjayaraman

ans(:,:,1) =

   0   1   0
   0   0   1
   1   0   0

ans(:,:,2) =

   0   0   1
   1   0   0

anirudhjayaraman

m =

ans(:,:,1) =

   0   1   0   0
   0   0   1   0
   1   0   0   0
   0   0   0   1

ans(:,:,2) =

anirudhjayaraman

% function to generate permutation matrices given the size of the desired permutation matrices
function x = permMatrices(n)
x = zeros(n,n,factorial(n));
permutations = perms(1:n);
for i = 1:size(x,3)
  x(:,:,i) = eye(n)(permutations(i,:),:);
end
endfunction