hadamard: Hadamard Matrix

Description Usage Arguments Details Value Note See Also Examples

View source: R/hadamard.R

Description

Generate Hadamard matrix of a certain size.

Usage

1

Arguments

n

An integer of the form 2^e, 12*2^e, or 20*2^e

Details

An n-by-n Hadamard matrix with n>2 exists only if rem(n,4)=0. This function handles only the cases where n, n/12, or n/20 is a power of 2.

Value

Matrix of size n-by-n of orthogonal columns consisting of 1 and -1 only.

Note

Hadamard matrices have applications in combinatorics, signal processing, and numerical analysis.

See Also

hankel, Toeplitz

Examples

1
2
3
hadamard(4)
H <- hadamard(8)
t(H) 

Example output

     [,1] [,2] [,3] [,4]
[1,]    1    1    1    1
[2,]    1   -1    1   -1
[3,]    1    1   -1   -1
[4,]    1   -1   -1    1
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,]    1    1    1    1    1    1    1    1
[2,]    1   -1    1   -1    1   -1    1   -1
[3,]    1    1   -1   -1    1    1   -1   -1
[4,]    1   -1   -1    1    1   -1   -1    1
[5,]    1    1    1    1   -1   -1   -1   -1
[6,]    1   -1    1   -1   -1    1   -1    1
[7,]    1    1   -1   -1   -1   -1    1    1
[8,]    1   -1   -1    1   -1    1    1   -1

pracma documentation built on Dec. 11, 2021, 9:57 a.m.