Code covered by the BSD License

### Highlights from Normalize N-D Vectors in Single Matrix or N Component Matrices

Be the first to rate this file! 13 Downloads (last 30 days) File Size: 5.04 KB File ID: #36248 Version: 1.0

# Normalize N-D Vectors in Single Matrix or N Component Matrices

### Ioannis Filippidis (view profile)

Normalizes N-D vectors provided either in one matrix, or as multiple component matrices.

File Information
Description

NORMVEC normalize vector(s).
NORMVEC computes the unit vectors in the direction of the vectors
provided. It can process two types of arguments:

1) single matrix of vectors
2) multiple matrices of vector components
(as those returned by MESHGRID and NDGRID)

In both cases, the p-norm to be used can be specified.
The default is the 2-norm (Euclidean).

Only in the first case, the matrix dimension along which the vectors
are defined can be defined. The default is the first non-singleton
This behavior is derived from VNORM (FEX id=#10708, by Winston Smith),
which is called by this function.

Zero vectors are normalized to 0 and NOT to NaN.

usage

Case A: matrix of N-dimensional column vectors
[v] = NORMVEC(v)
[v] = NORMVEC(v, 'p', n)
[v] = NORMVEC(v, 'p', n, 'dim', d)

v = matrix of column vectors
= [#dimensions x #vectors]
n = p-norm selected (e.g. 2 is the Euclidean norm ||.||_2)
d = norm for vectors defined along dimension d of matrix v
>= 1
or [] (vectors along first non-singleton dimension)

Case B: 2 component matrices of 2-dimensional vectors
[px, py] = NORMVEC(px, py)
[px, py] = NORMVEC(px, py, 'p', n)

px = matrix [M x N] of x vector components
py = matrix [M x N] of y vector components
n = 'p' norm selected

Case C: 3 component matrices of 3-dimensional vectors
[px, py, pz] = NORMVEC(px, py, pz)
[px, py, pz] = NORMVEC(px, py, pz, 'p', n)

px = matrix [M x N x L] of x vector components
py = matrix [M x N x L] of y vector components
pz = matrix [M x N x L] of z vector components
n = 'p' norm selected

Case D: N component matrices of N-dimensional vectors
[px1, px2, ..., pxN] = NORMVEC(px1, px2, ..., pxN)
[px1, px2, ..., pxN] = NORMVEC(px1, px2, ..., pxN, 'p', n)

pxi = matrix [M1 x M2 x ... x MN] of xi vector components
n = 'p' norm selected

dependency (included)
vnorm, File Exchange ID = 10708, (c) 2006 by Winston Smith
http://www.mathworks.com/matlabcentral/fileexchange/10708-vector-norm

Acknowledgements
Required Products MATLAB
MATLAB release MATLAB 7.14 (R2012a)