version 1.0 (5.04 KB) by
Ioannis Filippidis

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

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

MATLAB 7.14 (R2012a)