Normalize a vector, Python Programming

Normalize a vector

Let's imagine we want  to normalize a vector  of three  variables;  that  is to compute a new  vector  of three values,  such that its size  is 1. Here is our ?rst attempt; it is a procedure that takes as input a list of three values, and gives a list of three numbers:

def normalize3(v):

 

return [v[0]/math.sqrt(v[0]**2+v[1]**2+v[2]**2), v[1]/math.sqrt(v[0]**2+v[1]**2+v[2]**2), v[2]/math.sqrt(v[0]**2+v[1]**2+v[2]**2)]

 

This is correct, but it looks pretty complicated. Let's start by giving that we're recalculating the denominator three times, and instead store the variable value.

 

def normalize3(v):

magv = math.sqrt(v[0]**2+v[1]**2+v[2]**2)

return [v[0]/magv,v[1]/magv,v[2]/magv]

 

Now,  we can see a repeated structure, of going through and dividing each component by magv.  Also, we seem that  the  computation of the  magnitude of a vector  is a useful  and  understandable operation in its own  right,  and  could probably be give  in its own method. That tends  to this procedure:

 

def mag(v):

return math.sqrt(sum([vi**2 for vi in v]))

 

def normalize3(v):

return [vi/mag(v) for vi in v]

 

This is especially nice, because  now,  in fact, it gives not just to vectors  of size  three.  So, it's both smaller and  more general than  what  we started with.  But, one of our real causes has snuck back in: we're recomputing mag(v) once for each element of the vector.  So, At last, here's a version that we're very happy with:9

 

def mag(v):

return math.sqrt(sum([vi**2 for vi in v]))

 

def normalize3(v):

magv = mag(v)

return [vi/magv for vi in v]

 

Posted Date: 8/9/2012 7:23:36 AM | Location : United States







Related Discussions:- Normalize a vector, Assignment Help, Ask Question on Normalize a vector, Get Answer, Expert's Help, Normalize a vector Discussions

Write discussion on Normalize a vector
Your posts are moderated
Related Questions
Tuples  and strings Python has two different more list-like data  types  that are very important to understand.A tuple  is a structure that  is like a list, but  is not  mutab

Synthetic models One  goal  of various  people in a variety of sub-disciplines of  electrical  engineering and  computer science is automatic synthesis of machine from  formal

Ask question #Minimum 100 worIn this project, create the pseudo code from the following request. The program must have some sort of menu that allows users to make selections to

Bank transfer What  if we  have  two  values,  representing bank  accounts, and  need  to transfer an  amount of money  amt between them?  Consider that a bank account is show

Write an algorithm for a program that receives, as input from the user, 2 string variables and 2 integer variables; then joins together and displays the combined strings; and final

Procedures in Firrst-class objects In Python, unlike  many  other  languages, methods are behave in much  the same way as num­ bers:  they  can be stored as values  of variabl

#ques Write the pseudocode (use a word processor please) and the Python 3.0 program for the following problem. A monkey is being fed some food. Read in the starting weight in lbs:o

Procedures as first-class objects In Python, unlike  many  other  languages, methods are behave in much  the same way as num­ bers:  they  can be stored as values  of variable

how to use re.sub to seperate distint words and phrases when translating text from English to Spanish or vis versa in python programming

python program of motion of a particle in viscus medium