unitlengthfast

 function [v,len] = unitlengthfast(v,dim)

 <v> is a vector (row or column) or a 2D matrix
 <dim> (optional) is dimension along which vectors are oriented.
   if not supplied, assume that <v> is a row or column vector.

 unit-length normalize <v>.  aside from input flexibility,
 the difference between this function and unitlength.m is that
 we do not deal with NaNs (i.e. we assume <v> does not have NaNs),
 and if a vector has 0 length, it becomes all NaNs.

 we also return <len> which is the original vector length of <v>.
 when <dim> is not supplied, <len> is a scalar.  when <dim> is
 supplied, <len> is the same dimensions as <v> except collapsed
 along <dim>.

 note some weird cases:
   unitlengthfast([]) is [].
   unitlengthfast([0 0]) is [NaN NaN].

 example:
 a = [3 0];
 isequalwithequalnans(unitlengthfast(a),[1 0])

0001 function [v,len] = unitlengthfast(v,dim)
0002 
0003 % function [v,len] = unitlengthfast(v,dim)
0004 %
0005 % <v> is a vector (row or column) or a 2D matrix
0006 % <dim> (optional) is dimension along which vectors are oriented.
0007 %   if not supplied, assume that <v> is a row or column vector.
0008 %
0009 % unit-length normalize <v>.  aside from input flexibility,
0010 % the difference between this function and unitlength.m is that
0011 % we do not deal with NaNs (i.e. we assume <v> does not have NaNs),
0012 % and if a vector has 0 length, it becomes all NaNs.
0013 %
0014 % we also return <len> which is the original vector length of <v>.
0015 % when <dim> is not supplied, <len> is a scalar.  when <dim> is
0016 % supplied, <len> is the same dimensions as <v> except collapsed
0017 % along <dim>.
0018 %
0019 % note some weird cases:
0020 %   unitlengthfast([]) is [].
0021 %   unitlengthfast([0 0]) is [NaN NaN].
0022 %
0023 % example:
0024 % a = [3 0];
0025 % isequalwithequalnans(unitlengthfast(a),[1 0])
0026 
0027 if nargin==1
0028   len = sqrt(v(:).'*v(:));
0029   v = v / len;
0030 else
0031   if dim==1
0032     len = sqrt(sum(v.^2,1));
0033     v = v ./ repmat(len,[size(v,1) 1]);  % like this for speed.  maybe use the indexing trick to speed up even more??
0034   else
0035     len = sqrt(sum(v.^2,2));
0036     v = v ./ repmat(len,[1 size(v,2)]);
0037   end
0038 end