# scalar

q <- 3
w <- 17
e <- q * w
e
e <- w / q
e

log(exp(sin(pi/4)^2) * exp(cos(pi/4)^2))

# vectors

qq <- c( 1:10 )
qq <- 1:10
ww <- runif( 10 )
ee <- qq * ww
ee
ee <- qq / ww
ee
qqq <- qq[2]
qqq
qqq <- qq[2:4]
qqq
qqq <- qq[c( 1:3, 7 )]

length(qqq)

# matrices

Q <- cbind( qq, ww )
Q
dim( Q )

Q <- rbind( qq, ww )
Q
dim( Q )

Q <- t( Q )
Q
dim( Q )

W <- cbind( ww, qq )
W
WW <- W[2, 1]
WW
WW <- W[, 1]
WW
WW <- W[2, ]
WW

WWW <- t( W )

# scalar multiplication
QQ = Q * 3
QQ

# element by element
E <- Q * W
E

# multiplication
Q %*% W
large <- Q %*% t( W )
large
small <- t( Q )%*% W
small

# inverse
small_i <- solve( small )
small_i

# Identity
small_i %*% small


# example
xvalues <- 1:200
yvalues <- 17 + 2 * xvalues + rnorm( 200, sd = 10 )

# plotting
plot( x = xvalues, y = yvalues, col = "blue", type = "p" )
lines( x = xvalues, y = 17 + 2 * xvalues, col = "green", lw = 5 )

# OLS
X <- cbind( rep( 1, 200 ), xvalues )
solve( ( t( X )%*% X ))%*% t( X )%*% yvalues

# check with internal formula
summary( lm( yvalues ~ xvalues ))

########################
# functions

# descriptive statistics
sd( ww )
mean( ww )
min( ww )
max( ww )

sd( WW )
mean( WW )
min( WW )
max( WW )

sd( W[1, ] )
mean( W[, 2] )
min( W[2:3, ] )
max( W[c( 1, 3 ), ] )

descr_stats <- function( INFRATRAIN )
{
 c( sd( INFRATRAIN ), mean( INFRATRAIN ), min( INFRATRAIN ), max( INFRATRAIN ) )
}
descr_stats( ww )

descr_stats <- function( INFRATRAIN )
{
 t1 <- c( sd( INFRATRAIN ), mean( INFRATRAIN ), min( INFRATRAIN ), max( INFRATRAIN ))
 t2 <- as.matrix( t1 )
 rownames( t2 )<- c( "sd", "mean", "min", "max" )
 t2
}
descr_stats( ww )


ww_descr <- descr_stats( ww )

# call the function from the other
descr_stats_row <- function( INFRATRAIN )
{
 t1 <- descr_stats( descr_stats( ww ))
 t( t1 )
}
descr_stats_row( ww )

# rounding
round( ww_descr, digits = 3 )


###################

# programming

rr <- rnorm( 1, mean = 10 )
rr

if ( rr >= 0 ){
 print( "My random number is greater or equal 0." )} else {
 print( "My random number is smaller than 0." )
}

# ifelse
ifelse( ww > 0.5, "larger", "smaller" )

# conditions
rrr <- rnorm( 1, mean = -10 )
rrr

rr > 0 & rrr > 0
rr > 0 | rrr > 0

## Repetitive Execution

countries <- c( "Austria", "Belgium", "Germany", "Netherlands", "United Kingdom", "United States", "Zimbabwe" )
for ( i in countries ){
 print( i )
}

for ( i in 1:5 ){
 print( countries[i] )
}

for ( i in 1:5 ){
 cat( " Country is: ", countries[i], "\n" )
}

# APPLY instead of for-loop
# apply( myobject, in.which.direction, which.function )

apply( Q, MARGIN = 1, mean )
apply( Q, MARGIN = 1, descr_stats )

apply( t( Q ), MARGIN = 2, mean )

# folder specification
setwd("~/research/data")
getwd()

# import / export
mm <- 17

x1 <- sample( mm )
x2 <- sample( mm )
x3 <- sample( mm )
x4 <- sample( mm )
x5 <- sample( mm )
write.table( cbind( x1, x2, x3, x4, x5 ), file = "x.dat", sep = ", ", row.names = F, col.names = T )

y <- rep( 1, mm )
y[sample( mm, 10 )] <- -1
write.table( y, file = "y.dat", sep = ", ", row.names = F, col.names = T )


q_data <- read.csv( "x.dat", header = F )

# paste
paste( "",getwd(),"/x.dat", sep = "" )


# read the data
dat <- read.csv( paste( "",getwd(),"/x.dat", sep = "" ), header = T, sep = "," )
dat

# sorting and other data manupulations
data1 = dat[order( dat$x1 ), ]
data1
n <- nrow( dat )

data2 <- matrix( c( dat$x2 ), nrow = n, ncol = 1 )
data2
data3 <- matrix( c( dat$x2, dat$x3, dat$x4 ), nrow = n, ncol = 3 )
data3