had_kronecker {HadamardR}

had_kronecker

Description

had_kronecker performs the construction of an Hadamard matrix by kronecker product.

Usage

had_kronecker(n, exponent = NULL)

Arguments

n

an integer (Expected to be Hadamard Number)

exponent

an integer

Details

This function only applicable when n is the power of 2 and multiple of 4.

If n<-2, returns Hadamard matrix of order 2; if n is not Hadamard number, return NULL.

By default exponent=FALSE; when exponent is unknown it is computed.

If exponent is given use the same

Value

Hadamard Matrix of order n, if n is power of 2, otherwise NULL.

References

Hedayat, A. and Wallis, W.D. (1978). Hadamard Matrices and Their Application.Ann. Stat., 6, 1184-1238.

Sylvester, J.J. (1968). Problem 2511. Math. Questions and solutions, 10, 74.

Examples

had_kronecker(4)
#      [,1] [,2] [,3] [,4]
#[1,]    1    1    1    1
#[2,]    1   -1    1   -1
#[3,]    1    1   -1   -1
#[4,]    1   -1   -1    1
had_kronecker(8,3)
#     [,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
had_kronecker(9)
 # NULL