| had_williamson {HadamardR} | R Documentation |
had_williamson
Description
had_williamson performs the construction Hadamard matrix from Williamson method by using the williamson sequences.
Usage
had_williamson(x)
Arguments
x |
integer (order of the matrix) |
Details
This function construct Hadamard matrix of given order using williamson sequences. If Williamson sequences of length n,n,n,n are available, Hadamard matrix of order 4n can be constructed. If for given order of Matrix Williamson sequences are not available it retuns NULL.
The Williamson sequences are stored in internal dataset, available for length of seq(1,63, 2) except 15, 35, 47, 53, 59 in the internal table.
Value
Hadamard matrix
Source
The williamson sequences are available in London(2013) and Christos Koukouvinos
References
Williamson, J. (1944). Hadamard determinant theorem and the sum of four squares. Duke. Math. J., 11, 65-81.
Williamson, J. (1947). Note on Hadamard's determnant theorem. Bull. Amer. Math. Soc., 53, 608-613.
London, S. 2013. Constructing New Turyn Type Sequences, T-Sequences and Hadamard Matrices. PhD Thesis, University of Illinois at Chicago, Chicago.
Examples
had_williamson(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_williamson(8)
# NULL