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

version 1.0.0.0 (5.04 KB) by Ioannis Filippidis

### Ioannis Filippidis (view profile)

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

Updated 19 Apr 2012

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

### Cite As

Ioannis Filippidis (2020). Normalize N-D Vectors in Single Matrix or N Component Matrices (https://www.mathworks.com/matlabcentral/fileexchange/36248-normalize-n-d-vectors-in-single-matrix-or-n-component-matrices), MATLAB Central File Exchange. Retrieved .