Introduction

In this tutorial, we will try to understand some fundamental control structures used in statistical programming. In the beginning, we will separately analyze different control structures.

if and else: testing a condition and acting on it
for: execute a loop a fixed number of times
while: execute a loop while a condition is true

Part 1: If-Else Statements

General Construction:

if:

if (CONDITION) {
    ACTION
}

if else:

if (CONDITION) {
    ACTION 1
} else {
    ACTION 2
}

ifelse():

ifelse(CONDITION,ACTION1,ACTION2)

Chunk 1: Illustration of If

x = 3
if(x > 0){
  print(log(x))
}

x = -3
if(x > 0){
  print(log(x))
}

Chunk 2: Illustration of If-Else

x = 3
if(x > 0){
  print(log(x))
} else{
  message("Unable to Take Logarithm")
}

x = -3
if(x > 0){
  print(log(x))
} else {
  message("Unable to Take Logarithm")
}

Excercise 1

Write code that takes numbers a and b as input and prints ‘a is greater than b’ if a>b, otherwise prints ‘a is not greater than b’.

a = 10
b = 8
# write code here
if (a>b){
  print('a is greater than b')
} else {
  print('a is not greater than b')
}

## [1] "a is greater than b"

Chunk 3: Potential Problem of If-Else Statements

x = BLANK
if(x > 0){
  print(log(x))
}

if(x > 0){
  print(log(x))
} else{
  message("Unable to Take Logarithm")
}

Chunk 4: Fixing Potential Problem in Chunk 3

x=BLANK
if(is.numeric(x)){
  if(x > 0){
    print(log(x))
  } else{
    message("Unable to Take Logarithm")
  }
} else{
  message("Please Input Numbers")
}

Excercise 2

Redo Excercise 1 but check the data types before doing the comparison. Hint: && (and) and || (or) can be used to combine multiple logical expressions. Please don’t use & and | in an if statement: these are vectorized operations.

a = '10'
b = 8
# write code here
if (is.numeric(a) && is.numeric(b)){
  if (a>b){
    print('a is greater than b')
  } else {
    print('a is not greater than b')
  }
} else {
  message("Please Input Numbers")
}

## Please Input Numbers

Chunk 5: Vectorized Version with `ifelse()`

x=c(-1,3,200)
print(log(x))

y1 =  if(x > 0){
        log(x)
      } else{
        NA
      }
print(y1)

y2 = ifelse(x>0,log(x),NA)
print(y2)

Chunk 6: Nested `ifelse()` Statements

x=rnorm(1000,mean=0,sd=1)
y=ifelse(abs(x)<1,"Within 1 SD",ifelse(abs(x)>2,"Far Far Away","Between 1 and 2 SD"))
y.fct=factor(y,levels=c("Within 1 SD","Between 1 and 2 SD","Far Far Away"))
ggplot() +
  geom_bar(aes(x=y.fct),fill="lightskyblue1") +
  theme_minimal()

Excercise 3

Please use ifelse() function to create a new column WageLevel with lwage column of the Wages dataset from Ecdat.

If the lwage is greater than \(7.0\), the corresponding value in the final vector is High Wage.
If lwage is lower than \(6.4\), the value is Low Wage.
For all the other cases, the values are Normal.

New_Wages = Wages %>%
  mutate(WageLevel=ifelse(lwage>7.0,'High Wage',
                          ifelse(lwage<6.4, 'Low Wage', 'Normal')
                          )
         )
head(New_Wages,5)

##   exp wks bluecol ind south smsa married  sex union ed black   lwage WageLevel
## 1   3  32      no   0   yes   no     yes male    no  9    no 5.56068  Low Wage
## 2   4  43      no   0   yes   no     yes male    no  9    no 5.72031  Low Wage
## 3   5  40      no   0   yes   no     yes male    no  9    no 5.99645  Low Wage
## 4   6  39      no   0   yes   no     yes male    no  9    no 5.99645  Low Wage
## 5   7  42      no   1   yes   no     yes male    no  9    no 6.06146  Low Wage

Part 2: Loops

Chunk 1: Checking Geometric Series Proof with for loop

Geometric Series: \(a, ar, ar^2, ar^3,...\)

Formula of Sum: \(\sum_{k=0}^\infty ar^k=\frac{a}{1-r}\), for \(|r|<1\).

a=1 #Any Number
r=1/2 #Any Number Between -1 and 1: abs(r)<1

theoretical.limit=a/(1-r)

START=a

FINISH.1 = START + a*r^1

FINISH.2 = FINISH.1 + a*r^2

FINISH.3 = FINISH.2 + a*r^3

FINISH.10 = a 
for(k in 1:10){
  FINISH.10=FINISH.10+a*r^k
}

FINISH.100 = a 
for(k in 1:100){
  FINISH.100=FINISH.100+a*r^k
}

DATA = tibble(k=c(1,2,3,10,100,"Infinity"),
            SUMMATION=c(FINISH.1,FINISH.2,FINISH.3,
                        FINISH.10,FINISH.100,
                        theoretical.limit))
print(DATA)

ABSOLUTE.ERROR = abs(FINISH.100-theoretical.limit)
print(ABSOLUTE.ERROR)

Excercise 4

set.seed(4)
u = rnorm(100)

Use for loop to calculate sum of the squares of the first 10 elements of vector u.

sum10 = 0
for(i in 1:10){
  sum10 = sum10 + u[i]^2
}
print(sum10)

## [1] 13.08209

Use for loop and if statement to calculate the sum of squares of the elements with even indices of vector u.

sum_even = 0
for(i in 1:100){
  if(i%%2==0){
    sum_even = sum_even + u[i]
  }
}
print(sum_even)

## [1] -1.567888

sum_odd = 0
for(i in 1:100){
  if(i%%2!=0){
    sum_odd = sum_odd + u[i]
  }
}
print(sum_odd)

## [1] 11.22039

sum_even = 0
for(i in seq(2,100,2)){
  sum_even = sum_even + u[i]
}
print(sum_even)

## [1] -1.567888

Chunk 2: Checking Geometric Series Proof with while loop

a=1
r=1/2

FINISH=a
k=0
while(abs(FINISH-a/(1-r)) > 1e-10) {
  k=k+1
  FINISH = FINISH + a*r^k
  #if(k>100) break
}
print(c(k,FINISH))

Chunk 3: Saving Steps in Geometric Series for Figure

a=10
r=-0.75
theoretical.limit=a/(1-r)

K=10 #How Many Steps Do You Want to Save?

summation=rep(NA,(K+1))
summation[1]=a
for (k in 1:K) {
  summation[k+1]=summation[k] + a*r^k
}

ggplot() +
  geom_line(aes(x=1:(K+1),y=summation)) +
  geom_hline(yintercept=theoretical.limit,
             linetype="dashed")

Excercise 5

Write for loops to generate 100 random samples from normal distributions with means of 0 to 99 and save the random samples to a vector a.

The kth component of a is generated from \(N(k-1,1)\).
Hint: Function for generating random samples from normal distribution rnorm.

set.seed(100)
a = rep(NA,100)
for (k in 1:100){
  a[k] = rnorm(1,k-1,1)
}
print(a)

##   [1] -0.5021924  1.1315312  1.9210829  3.8867848  4.1169713  5.3186301
##   [7]  5.4182093  7.7145327  7.1747406  8.6401379 10.0898861 11.0962745
##  [13] 11.7983660 13.7398405 14.1233795 14.9706833 15.6111458 17.5108563
##  [19] 17.0861858 21.3102968 19.5619100 21.7640606 22.2619613 23.7734046
##  [25] 23.1856209 24.5615494 25.2797784 27.2309445 26.8422705 29.2470760
##  [31] 29.9088864 32.7573756 31.8620704 32.8888065 33.3099857 34.7782058
##  [37] 36.1829077 37.4173233 39.0654023 39.9702020 39.8983708 42.4032035
##  [43] 40.2232244 43.6228674 43.4777166 46.3222310 45.6365597 48.3190657
##  [49] 48.0437791 47.1213441 49.5529378 49.2614021 52.1788648 54.8974657
##  [55] 51.7280745 55.9804641 54.6011744 58.8248724 59.3812987 58.1611481
##  [61] 59.7380042 60.9311560 61.6211164 65.5819589 64.1298341 64.2869750
##  [67] 66.6379942 67.2016916 67.9300831 68.9075101 70.4489033 69.9356443
##  [73] 70.8375807 74.6485217 71.9379040 75.0127497 74.9124717 77.2705395
##  [79] 79.0084519 76.9255952 80.8968223 80.9500042 80.6546507 81.0687885
##  [85] 84.7095816 84.8420950 86.2163679 87.8173621 89.7271758 88.8962297
##  [91] 89.4428777 92.4283014 91.1070426 91.8424288 93.4697035 97.4456828
##  [97] 95.1675042 97.4135198 96.8213169 97.8259652

STOR 320 Tutorial on Programming 1

March 15, 2021

Introduction

Part 1: If-Else Statements

Chunk 1: Illustration of If

Chunk 2: Illustration of If-Else

Excercise 1

Chunk 3: Potential Problem of If-Else Statements

Chunk 4: Fixing Potential Problem in Chunk 3

Excercise 2

Chunk 5: Vectorized Version with `ifelse()`

Chunk 6: Nested `ifelse()` Statements

Excercise 3

Part 2: Loops

Chunk 1: Checking Geometric Series Proof with for loop

Excercise 4

Chunk 2: Checking Geometric Series Proof with while loop

Chunk 3: Saving Steps in Geometric Series for Figure

Excercise 5

STOR 320 Tutorial on Programming 1

March 15, 2021

Introduction

Part 1: If-Else Statements

Chunk 1: Illustration of If

Chunk 2: Illustration of If-Else

Excercise 1

Chunk 3: Potential Problem of If-Else Statements

Chunk 4: Fixing Potential Problem in Chunk 3

Excercise 2

Chunk 5: Vectorized Version with ifelse()

Chunk 6: Nested ifelse() Statements

Excercise 3

Part 2: Loops

Chunk 1: Checking Geometric Series Proof with for loop

Excercise 4

Chunk 2: Checking Geometric Series Proof with while loop

Chunk 3: Saving Steps in Geometric Series for Figure

Excercise 5

Chunk 5: Vectorized Version with `ifelse()`

Chunk 6: Nested `ifelse()` Statements