Functions

Built-in Functions

Some functions are built into the Python language, whereas others needed to be imported. All of the following operations are actually built in and the syntax made compatible with what we typically use on paper. Typically, a function is called by using the round brackets () as follows 

range(10)


Python has a math module that provides most of the familiar mathematical functions. A module is a file that contains a collection of related functions grouped together. You need to import a module before you can use it. 

import math
print math.pi
print math.sqrt(2)
print math.sin(math.pi/2)
pi = math.pi
angleDegrees = 17
angleRadians = angleDegrees*2*pi/360
print math.sin(angleRadians)

Function Construction 

#def NAME (LIST OF PARAMETERS):
#	STATEMENTS
 
def sinDegrees(angleIn):
    angleRad = angleIn*2*pi/360
    return math.sin(angleRad)
 
#statements inside the function are not executed until the function is called
print sinDegrees(10)
 
#notice all variables assigned within the body of the function are not 'seen' outside;  
#they are local
#print angleRad
 
#another function that prints anything that is input twice.  This can take any type
def printTwice(whateverIn):
	print whateverIn, whateverIn
 
printTwice(7)
printTwice('Hi Joy')

Encapsulation and generalization

Encapsulation is the process of wrapping a piece of code in a function, allowing you to take advantage of all the things functions are good for. Generalization means taking something specific, such as printing the multiples of 2, and making it more general, such as printing the multiples of any integer.

Let's revisit some of the examples that we did in Intro_2 and wrap these into functions. As good coding practice, remember that variables within the body of a function are local so let's just use different names to highlight that and (hopefully) lessen any confusion 

def printEvenOdd(numberIn):
	if numberIn%2 == 0:
		print numberIn, "is even"
	else:
		print numberIn, "is odd"
 
printEvenOdd(8)
printEvenOdd(29)
#if-elif-else
def compare(xIn, yIn):
	if (xIn < yIn):
		print xIn, "is smaller than", yIn
	elif (xIn > yIn):
		print xIn, "is larger than", yIn
	else:
		print xIn, "is equal to", yIn
 
compare(20, 15)
compare(15, 20)

Composition 

# This is the very useful ability to call on another function from within a function
 
#ex
printTwice(sinDegrees(17))
 
# ex. let's take two points in 2D given by (xC, yC) and (xP, yP) which
# represents the center of a circle and a point on the perimeter of the circle and
# write a function that returns the area of this circle.
xC = 0
yC = 0
xP = 2
yP = 5
 
#Let's do this one step at a time for these specific points and then organize the resulting
#statements into functions.  
# Step 1:  calculate the distance bween (xC,yC) and (xP, yP) to get the radius of the circle
 
r = math.sqrt((xC-xP)**2 + (yC-yP)**2)
print r
# Step 2:  calculate the area of the circle
areaCircle = math.pi*r**2
print areaCircle
 
#it makes sense to write one function that calculates the distance betwen two points 
#given in 2D
def distance2D(x1, y1, x2, y2):
	return math.sqrt((x1-x2)**2 + (y1-y2)**2)
 
#which is called within another function that calculates the area of a circle based on 
#two points given in 2D
def areaCircleTwoPoints2D(x1, y1, x2, y2):
	radius = distance2D(x1, y1, x2, y2)
	return math.pi*radius**2
 
#check that this gives the same answer as before	
print areaCircleTwoPoints2D(xC, yC, xP, yP)
#it is now just a 1-liner to to calculate this for any other pair of points
print areaCircleTwoPoints2D(5, 3, 2, 1)
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