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

Solution 1:

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.

Solution 2:

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