How to normalize a vector in MATLAB efficiently Any related built-in function

Question

I normalize a vector V in MATLAB as following   normalized V   V norm V     however  is it the most elegant  efficient  way to normalize a vector in MATLAB

User · Accepted Answer

The original code you suggest is the best way.

Matlab is extremely good at vectorized operations such as this, at least for large vectors.

The built-in norm function is very fast. Here are some timing results:

V = rand(10000000,1);
% Run once
tic; V1=V/norm(V); toc           % result:  0.228273s
tic; V2=V/sqrt(sum(V.*V)); toc   % result:  0.325161s
tic; V1=V/norm(V); toc           % result:  0.218892s

V1 is calculated a second time here just to make sure there are no important cache penalties on the first call.

Timing information here was produced with R2008a x64 on Windows.

EDIT:

Revised answer based on gnovice's suggestions (see comments). Matrix math (barely) wins:

clc; clear all;
V = rand(1024*1024*32,1);
N = 10;
tic; for i=1:N, V1 = V/norm(V);         end; toc % 6.3 s
tic; for i=1:N, V2 = V/sqrt(sum(V.*V)); end; toc % 9.3 s
tic; for i=1:N, V3 = V/sqrt(V'*V);      end; toc % 6.2 s ***
tic; for i=1:N, V4 = V/sqrt(sum(V.^2)); end; toc % 9.2 s
tic; for i=1:N, V1=V/norm(V);           end; toc % 6.4 s

IMHO, the difference between "norm(V)" and "sqrt(V'*V)" is small enough that for most programs, it's best to go with the one that's more clear. To me, "norm(V)" is clearer and easier to read, but "sqrt(V'*V)" is still idiomatic in Matlab.

User · Answer

The only problem you would run into is if the norm of V is zero  or very close to it   This could give you Inf or NaN when you divide  along with a divide-by-zero warning  If you don t care about getting an Inf or NaN  you can just turn the warning on and off using WARNING   oldState   warning  off   MATLAB divideByZero       Return previous state then                                                       turn off DBZ warning uV   V norm V   warning oldState      Restore previous state   If you don t want any Inf or NaN values  you have to check the size of the norm first   normV   norm V   if normV  gt  0     Or some other threshold  like EPS   uV   V normV  else    uV   V     Do nothing since it s basically 0 end   If I need it in a program  I usually put the above code in my own function  usually called unit  since it basically turns a vector into a unit vector pointing in the same direction

User · Answer

By the rational of making everything multiplication I add the entry at the end of the list      clc  clear all      V   rand 1024 1024 32 1       N   10      tic  for i 1 N  V1   V norm V           end  toc   4 5 s     tic  for i 1 N  V2   V sqrt sum V  V    end  toc   7 5 s     tic  for i 1 N  V3   V sqrt V  V        end  toc   4 9 s     tic  for i 1 N  V4   V sqrt sum V  2    end  toc   6 8 s     tic  for i 1 N  V1   V norm V           end  toc   4 7 s     tic  for i 1 N  d   1 norm V   V1   V d end  toc   4 9 s     tic  for i 1 N  d   norm V  -1  V1   V d end toc   4 4 s

User · Answer

Fastest by far  time is in comparison to Jacobs    clc  clear all  V   rand 1024 1024 32 1   N   10  tic   for i 1 N       d   1 sqrt V 1  V 1  V 2  V 2  V 3  V 3         V1   V d  end   toc   1 5s

User · Answer

I don t know any MATLAB and I ve never used it  but it seems to me you are dividing   Why   Something like this will be much faster   d   1 norm V  V1   V   d

User · Answer

I took Mr  Fooz s code and also added Arlen s solution too and here are the timings that I ve gotten for Octave   clc  clear all  V   rand 1024 1024 32 1   N   10  tic  for i 1 N  V1   V norm V           end  toc   7 0 s tic  for i 1 N  V2   V sqrt sum V  V    end  toc   6 4 s tic  for i 1 N  V3   V sqrt V  V        end  toc   5 5 s tic  for i 1 N  V4   V sqrt sum V  2    end  toc   6 6 s tic  for i 1 N  V1   V norm V           end  toc   7 1 s tic  for i 1 N  d   1 norm V   V1   V d end  toc   4 7 s   Then  because of something I m currently looking at  I tested out this code for ensuring that each row sums to 1   clc  clear all  m   2048  V   rand m   N   100  tic  for i 1 N  V1   V     sum V 2  ones 1 m                   end  toc   8 2 s tic  for i 1 N  V2   bsxfun  rdivide  V  sum V 2               end  toc   5 8 s tic  for i 1 N  V3   bsxfun  rdivide  V  V ones m 1            end  toc   5 7 s tic  for i 1 N  V4   V     V ones m m                          end  toc   77 5 s tic  for i 1 N  d   1  sum V 2  V5   bsxfun  times  V  d       end  toc   2 83 s tic  for i 1 N  d   1   V ones m 1   V6   bsxfun  times  V  d  end  toc   2 75 s tic  for i 1 N  V1   V     sum V 2  ones 1 m                   end  toc   8 2 s

[matlab] How to normalize a vector in MATLAB efficiently? Any related built-in function?

Examples related to matlab

Examples related to vector

Examples related to performance