##############
# Section 10
##############

set.seed(98)
mymat <- matrix(rnorm(16), nc=4)

mymat

max(mymat)

# Row-wise operation (and column-wise operations)

rowmaxes <- apply(mymat,1,max)

colmaxes <- apply(mymat,2,max)

rowmeans <- apply(mymat,1,mean)

# Some row-wise and column-wise operations have built-in shortcut functions:

simpmat = matrix(1:16,byrow=T,nrow=4,ncol=4)
simpmat
colSums(simpmat)
colMeans(simpmat)
rowSums(simpmat)
rowMeans(simpmat)

## can do more complicated row and column summing with an multidimensional array:

dim(UCBAdmissions)
print(UCBAdmissions)
rowSums(UCBAdmissions); rowSums(UCBAdmissions, dims = 2)
colSums(UCBAdmissions); colSums(UCBAdmissions, dims = 2)

# Using 'apply':

 apply(UCBAdmissions,1,sum)

 apply(UCBAdmissions,2,sum)

 apply(UCBAdmissions,3,sum)

 apply(UCBAdmissions,c(1,2),sum)

 apply(UCBAdmissions,c(1,3),sum)

 apply(UCBAdmissions,c(2,3),sum)


#Item by item comparison
a=c(1,5,7,8); b=c(4,7,2,11)
pmax(a,b)

# Row-wise operation with missing value

mymat <- cbind(mymat, c(0,1,2,NA))

mymat

rowmaxes <- apply(mymat,1,max)

rowmaxes <- apply(mymat,1,max,na.rm=T)


#Row-wise operation using a factor
tapply(state.x77[,"Murder"],state.region,mean)
by(state.x77[,"Murder"],state.region,mean)
tapply(state.x77[,"Illiteracy"],state.region,mean)
tapply(state.x77[,"Murder"],state.region,cummax)

# Can do medians by region too:
Income <-state.x77[,"Income"]
medinc.byreg <- tapply(Income,state.region,median)
medinc.byreg

# for and while loops:

mymat <- matrix(1:16, nc=4)

newmat<-matrix(0, nc=4, nr=4)

for (j in 1:ncol(mymat))
{
newmat[,j]<-(j+1)*mymat[,j]
}

newmat

j=1;
while (j <= ncol(mymat))
{
newmat[,j]<-(j+1)*mymat[,j]
j <- j+1
}

newmat


# Iteration

mymat <- matrix(rnorm(49), nc=7)

rowmaxes=NULL  # or rowmaxes=c()
rowabsmax=NULL
diffabsmax=NULL
for (j in 1:nrow(mymat)) {
rowmaxes[j]=max(mymat[j,])
rowabsmax[j]=max(abs(mymat[j,]))
diffabsmax[j]=rowabsmax[j]-rowmaxes[j]}
hist(diffabsmax)

#machine epsilon
x=.5
while(x!=0){y=x; x=x/2}
x
y

# "Outer products" of two vectors

myvec1 <- c(1,2,3)

myvec2 <- c(5,6,7)

outer(myvec1,myvec2,"*")

# Equivalently:
 
myvec1 %o% myvec2

# An "outer sum"

outer(myvec1,myvec2,"+")

# A table of selected powers

outer(myvec2, myvec1, "^")

month.abb

outer(month.abb, 2014:2018, FUN = "paste")