Introduction to Computingchitrabhanu/intro_to_computing/lecture4.pdf · Example - Determinant...

Introduction to Computing

Lecture 4

28 August 2019

Review of last lecture

Last time we discussed:

I Boolean datatype bool.I Boolean operators: and, or, not.I Relational operators: >, <, >=, <=, ==, !=.I Sequential and conditional control.I if, else and elif statements.I Indentation.

Program routines

I In order to manage the complexity of a large problem, it isoften broken down into smaller subproblems.

I Then, each subproblem can be focused on and solvedseparately.

I In programming, we do the same thing. Programs are dividedinto manageable pieces.

I In Python this is done using functions.

Program routines

Functions in PythonLet us start with an example:

def angle(s1, s2, s3):A = math.acos((s1**2 + s2**2 - s3**2)/(2*s1*s2))return 180*(A / math.pi)

This is a function with takes three side lengths of a triangle asarguments and returns the angle opposite to side 3.

Syntax

def <function name> (parameters...):.........

Syntax

Function Exampleangle.py

print("Enter the lengths of sides of a triangle.")a = float(input("side 1: "))b = float(input("side 2: "))c = float(input("side 3: "))

import mathA = angle(b, c, a)B = angle(c, a, b)C = angle(a, b, c)

print("The angles of the triangle in degrees are:",format(A, '.2f'), format(B, '.2f'), format(C, '.2f'))

Function terminologyI The variables listed inside brackets while defining a function are

called formal parameters or simply parameters.The parameters for angle are s1, s2, s3.

I Parameters can be of any of the datatypes, int, float,str, bool. We can define a function which does not have anyparameters whatsoever.

I Using a function inside the program is termed calling thefunction. A function can be called only after it has beendefined.

I While calling a function the exact same number of values haveto be passed as the number of parameters of the function.

I The values passed to a function when calling it are called theactual arguments or simply arguments.

Go back to the previous slide.

Mathematical functionsI Polynomial function f (x , y) = 3x2 + 4xy + 6y2:

def f(x, y):return 3*(x**2) + 4*x*y + 6*(y**2)

I Piecewise function

u(x) =

exp(−1/x) if x > 0− exp(1/x) if x < 00 if x = 0.

def u(x):if x == 0:

return 0else:

return (x/abs(x)) * math.exp(-1/abs(x))

Mathematical functionsI Polynomial function f (x , y) = 3x2 + 4xy + 6y2:

def f(x, y):return 3*(x**2) + 4*x*y + 6*(y**2)

I Piecewise function

u(x) =

exp(−1/x) if x > 0− exp(1/x) if x < 00 if x = 0.

def u(x):if x == 0:

return 0else:

return (x/abs(x)) * math.exp(-1/abs(x))

Function that returns a string:

def type_of_platonic_solid(num_sides):if num_sides == 4:

type = "Tetrahedron"elif num_sides == 6:

type = "Cube"elif num_sides == 8:

type = "Octahedron"elif num_sides == 12:

type = "Dodecahedron"elif num_sides == 20:

type = "Icosahedron"else:

type = "Not a platonic solid."

return type

Function that returns a boolean

def is_prime_less_than_25(n):if (n >= 25) or (n <= 1):

return Falseelif (n == 2) or (n == 3):

return Trueelif (n%2 == 0) or (n%3 == 0):

return Falseelse:

return True

Some built-in function

I abs(), bin(), hex(), oct(), len(), max(), min(). . .

I int(), float(), str(), chr(), bool(), ord() . . .

I input(), print(), format() . . .

I math.cos, math.sin, math.acos, math.asin . . .

I keyword.iskeyword()

Value-returning functions

So far we have mostly seen functions which always gives an output.Such functions are called value-returning functions.

This is achieved using the return keyword.

Syntax

return <value>

The returned value can be used elsewhere in the program.

Syntax

return <value>

Syntax

return <value>

Syntax

return <value>

Non-value-returning functions

Functions may also not return any value. For example the print()function.

I Such functions are called non-value-returning functions andthey do not have a return statement.

I These functions are used to perform a certain task within aprogram.

Example - Determinant

determinant.py

# Determinant of a small matrix

def det_2(a, b, c, d): # Determinant of 2X2 matrixreturn a*d - b*c

# Determinant of 3X3 matrix

def det_3(a11, a12, a13, a21, a22, a23, a31, a32, a33):determinant = 0determinant += a11 * det2(a22, a23, a32, a33)determinant += - a12 * det2(a21, a23, a31, a33)determinant += a13 * det2(a21, a22, a31, a32)return determinant

Example - Determinant continued

# Print matrices

def print_matrix2(a, b, c, d):print('[', format(a,'>5'), format(b, '>5'), ']')print('[', format(c,'<5'), format(d, '>5'), ']')

def print_matrix3(a11, a12, a13, a21, a22, a23, a31, a32, a33):print('[', format(a11,'<5'), format(a12, '^5'),

format(a13, '>5'), ']')print('[', format(a21,'<5'), format(a22, '^5'),

format(a23, '>5'), ']')print('[', format(a31,'<5'), format(a32, '^5'),

format(a33, '>5'), ']')

Example - Determinant continued

# Main

n = int(input("Enter the order of a sqaure matrix: "))

if n == 2:print("Enter a 2X2 matrix:\n")a = float(input("Entry (1,1): "))b = float(input("Entry (1,2): "))c = float(input("Entry (2,1): "))d = float(input("Entry (2,2): "))print("Determinant of")print_matrix2(a, b, c, d)print("is", det_2(a, b, c, d))

Example - Determinant continuedelif n == 3:

print("Enter a 3X3 matrix:\n")a11 = float(input("Entry (1,1): "))a12 = float(input("Entry (1,2): "))a13 = float(input("Entry (1,3): "))a21 = float(input("Entry (2,1): "))a22 = float(input("Entry (2,2): "))a23 = float(input("Entry (2,3): "))a31 = float(input("Entry (3,1): "))a32 = float(input("Entry (3,2): "))a33 = float(input("Entry (3,3): "))print("Determinant of")print_matrix3(a11, a12, a13, a21, a22, a23, a31, a32, a33)print("is",

det_3(a11, a12, a13, a21, a22, a23, a31, a32, a33))else:

print("Matrix too big for this program.")

Variables within a function

A variable which is assigned a value within a function is notavailable outside the function.

Consider the program: variable_scope.py

# Function to convert angles in radians to degrees

def angle360(angle_in_radians):n = angles_in_radians//(2*math.pi)angle_in_radians -= n * (2 * math.pi)angle_in_degrees = 180 * (angle_in_radians / math.pi)return angles_in_degrees

Variables within a function

# Main

A = float(input("Enter an angle in radians: "))B = angle360(A)print(A, "radians in degrees is", format(B, ".2f"))

input("Press enter to continue.")

print("What happens if we print angle_in_degrees",angle_in_degrees)

print("What happens if we print angle_in_radians",angle_in_radians)

print("What happens if we print n", n)

Variables outside a functionVariables outside a function are not changed if you assign a variablewith the same identifier inside a function. For instance spiderman.py

A = "Spiderman"

def Home():A = "Peter Parker"print("At home I am", A)

Home()print("But outside I am", A)

Produces the output

At home I am Peter ParkerBut outside I am Spiderman

Variables outside a functionVariables outside a function are not changed if you assign a variablewith the same identifier inside a function. For instance spiderman.py

A = "Spiderman"

def Home():A = "Peter Parker"print("At home I am", A)

Home()print("But outside I am", A)

Produces the output

At home I am Peter ParkerBut outside I am Spiderman

Salient features about functions to remember

I A function can be called only after it has been defines.

I Functions may or may not return a value.

I Variables passed on to functions as arguments do not changetheir values even if they get manipulated inside the function.

I Variables inside a function can not be accessed outside thefunction.

I Variables outside a function can be accessed inside the functiononly if there is no variable asigned in the function with thesame identifier.

Introduction to Computingchitrabhanu/intro_to_computing/lecture4.pdf · Example - Determinant...

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