Conditional branching

• Run code-blocks according to a condition
  • An if code-block is executed when the condition is True
  • An else code-block is executed when the condition is False

if <condition>:
    <statement>
    ...

if <condition>:
    <statement>
    ...
else <condition>:
    <statement>
    ...

Conditional branching

• elif keyword acts as a else if
• multiple elif statements can follow an if, with an optional else

if <condition>:
    <statement>
    ...
elif <condition>:
    <statement>
    ...
elif <condition>:
    <statement>
    ...
else <condition>:
    <statement>
    ...

if <condition>:
    <statement>
    ...
elif <condition>:
    <statement>
    ...
elif <condition>:
    <statement>
    ...

Conditional branching

• Run code-blocks according to a condition
  • An if code-block is executed when the condition is True

age = 46
if age >= 16:
  print("You can drive a tractor")  # if code-block

You can drive a tractor

Conditional branching

• Run code-blocks according to a condition
  • if code-block is executed when the condition is True
• The indented code-block can contain multiple statements

speed_limit = 120
speed = 137
if speed > speed_limit:
  speed_diff = speed - speed_limit
  print(f"You drive {speed_diff} km/h too fast")

You drive 17 km/h too fast

Conditional branching

• Run code-blocks according to a condition
  • if code-block is executed when the condition is True
  • else code-block is executed when the condition is False

age = 11
if age > 18:
  print("You can drive a car")
else:
  print("You should take the bus")

You should take the bus

Conditional branching

• Run code-blocks according to a condition
  • if code-block is executed when the condition is True
  • else code-block is executed when the condition is False
  • elif keyword acts as a else if

age = 17
if age > 18:
  print("You can drive a car")
elif age > 16:
  print("You can drive a tractor")
else:
  print("You can ride a bicycle")

You can drive a tractor

Conditional branching

• Run code-blocks according to a condition
  • if code-block is executed when the condition is True
• The indented code-block can contain multiple statements
• indentation is the same within a code-block

age = 19
if age > 18:
    print("You can drive a car")    # This line is indented differently
  print("You can drive a bicycle")
  print("You can drive a tractor")

IndentationError: unindent does not match any outer indentation level (<string>, line 4)

The while loop

• Repeats code-block until the condition is False

• A while loop is used when:

  • we don’t know how many iterations we need, and
  • we have a stopping criterium/condition

  while <condition>:
    <statement>
    <statement>
    <statement>
    ...
    <statement>

The while loop

• Repeats code-block until the condition is False

• A while loop is used when:

  • we don’t know how many iterations we need, and
  • we have a stopping criterium/condition

  t = 0; t_max = 10
  while t < t_max:
    t = t + 3.86
    print(f"The elapsed time is: {t:5.3} s")
  print("End of the program")

  The elapsed time is:  3.86 s
  The elapsed time is:  7.72 s
  The elapsed time is:  11.6 s
  End of the program

The while loop

• Repeats code-block until the condition is False

• Can get in an infinite loop !

  • Stop the program with the stop button, in a terminal press key combination Ctrl + c
  • Adapt the stopping criterium/condition

  n = 0
  while n > -100:
  n = n + 1
  print(f"The current number is: {n}")

Lists of objects

• A list can contain several objects
• The object types can be different
• Lists are also objects

# A list with mixed object types
my_list_of_objects = ["It's Monday", False, 34, 23.4]

# Lists can be elements of a list
a_list_with_a_list = [5, 10.5, ["green", "red"], True]
print(a_list_with_a_list)

[5, 10.5, ['green', 'red'], True]

Lists of objects

• Length of the list is the number of elements applying the len() function: len(a_list)
• The object types can be different
• Lists are also objects

# A list with mixed object types
my_list_of_objects = ["It's Monday", False, 34, 23.4]

# Lists can be elements of a list
a_list_with_a_list = [5, 10.5, ["green", "red"], True]
print(a_list_with_a_list)

[5, 10.5, ['green', 'red'], True]

Appending an element to a list

• Append an element to the end of a list
• Length (number of elements) of the list increases with one

# Printing the first and then the second element
a_list = ["First", False, 34, 23.4]
print(a_list)
print(f"The length of the list = {len(a_list)}")
a_list.append("extra_element")
print(a_list)
print(f"The length of the adapted list = {len(a_list)}")

['First', False, 34, 23.4]
The length of the list = 4
['First', False, 34, 23.4, 'extra_element']
The length of the adapted list = 5

More methods of list

• We use the dot-notation: the_list.append(the_element)
• This notation is to call a method on an object
• We will see how to make our own methods (and classes) later in the chapter on object oriented programming
• There are more methods we can make use of, see https://docs.python.org/3/tutorial/datastructures.html#more-on-lists

a_list = ["First", False, 34, 5, 34]  # Define the list
a_list.remove(34)                     # Remove first 34
a_list.insert(3, "inserted_string")   # Insert str
print(a_list)                         # Print the list

['First', False, 5, 'inserted_string', 34]

Selecting elements in a list

• Select an element of a list by its index
• syntax for indexing: a_list[element_index]
• index is zero-based
• negative index starts from the end of the list

# Printing the first and then the second element
a_list = ["First", False, 34, 23.4]
print(a_list[0])
print(a_list[1])

First
False

Selecting elements in a list

• Select an element of a list by its index
• syntax for indexing: a_list[element_index]
• index is zero-based
• negative index starts from the end of the list

# Using negative indexing
a_list = ["First", False, 34, 23.4]
print(a_list[-1])

23.4

Slicing a list

• Selecting multiple elements is called slicing
• syntax for slicing: a_list[start:stop_exclusive]

# A list with mixed object types
a_list = [23, 45, 65, 78, 92, 100, 102, 105 ]
print(a_list[2:5])

[65, 78, 92]

Slicing a list

• Selecting multiple elements is called slicing
• syntax for slicing: a_list[start:stop_exclusive]

# An empty start_index starts from the first index
a_list = [23, 45, 65, 78, 92, 100, 102, 105 ]
print(a_list[:5])

[23, 45, 65, 78, 92]

# An empty end_index end at the last index
a_list = [23, 45, 65, 78, 92, 100, 102, 105 ]
print(a_list[3:])

[78, 92, 100, 102, 105]

Slicing a list

• Selecting multiple elements is called slicing
• syntax for slicing: a_list[start:stop_exclusive]
• Additional step parameter: a_list[start:stop_exclusive:step]

# Take every second element by stepping
a_list = [23, 45, 65, 78, 92, 100, 102, 105 ]
print(a_list[1::2])

[45, 78, 100, 105]

The for loop

• To iterate: to repeat a process
• A for loop can be used when:
  • the number of iterations is known, or
  • we iterate over a list of elements

for <element> in <list>:
    <statement>
    <statement>
    ...
    <statement>

The for loop

• To iterate: to repeat a process
• A for loop can be used when:
  • the number of iterations is known, or
  • we iterate over a list of elements

# Print all elements of a list
days = ["Mon", "Tue", "Wed", "Thu", "Fri"]
for el in days:
  print(el)

Mon
Tue
Wed
Thu
Fri

Intermezzo: using range()

• A range is a sequence type (like list) for integer numbers
• Construct it using: range(start, stop_exclusive, step)
• It is convenient for for loop
• See also: https://docs.python.org/3/library/stdtypes.html#range

# A list with mixed object types
a_range = range(1, 10, 2)  # Construct a range
print(a_range)             # Lazy evaluated
print(list(a_range))       # Converted to a list

range(1, 10, 2)
[1, 3, 5, 7, 9]

The for loop

• To iterate: to repeat a process
• A for loop can be used when:
  • the number of iterations is known, or
  • we iterate over a list of elements

# Use the range function to get a sequence of numbers
for i in range(1,10,2):
  print(i)

1
3
5
7
9

The for loop

• To iterate: to repeat a process
• A for loop can be used when:
  • the number of iterations is known, or
  • we iterate over a list of elements

# Use the range function to get indices
days = ["Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"]
for i in range(0,len(days),2):
  print(days[i])

Mon
Wed
Fri
Sun

Numerical approx. of the trajectory of a ball

• Gravitation: \(g=9.81\) m/s\(^2\)
• Air resistance: ignore for a slow heavy ball
• horizontal velocity is constant

Trajectory of a ball

# Load library for sine and cosine
import math

# Algorithm parameters in MKS units
v0 = 6
angle_in_degrees = 37
g = 9.81
x = 0; y = 1.20; t = 0

# Calculate initial velocity in x 
#     and y directions
angle = angle_in_degrees * math.pi/180
vx = v0 * math.cos(angle)
vy = v0 * math.sin(angle)

# Initiate values at time t = 0
x_values = list([x])
y_values = list([y])
t_values = list([t])

dt = 0.1
while (y >= 0) and (t < 10):
  # update velocities (vx, vy), coords
  #     (x, y), and time t
  vy = vy - g*dt
  y = y + vy*dt
  x = x + vx*dt
  t = t + dt
  x_values.append(x)
  y_values.append(y)
  t_values.append(t)
  print(f't = {t:.2f}: ({x:.2f},{y:.2f})')

Numerical approximation errors

Comparison with exact trajectory obtained before

Summary

• Control flow exists of
  • Branching if/else
  • while/for loops
• Allows implementing complex algorithms
• Lists are versatile data structures
• The for loop: iterating over list elements
• More complex scientific algorithms:
  • Iterative methods
  • Stopping criteria