Posted By: Anonymous
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?
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.
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.