survey (version 3.1)

hadamard: Hadamard matrices

Description

Returns a Hadamard matrix of dimension larger than the argument. Matrices of dimension every multiple of 4 are thought to exist, but this function doesn't know about all of them, so it will sometimes return matrices that are larger than necessary.

Usage

hadamard(n)

Arguments

n

lower bound for size

Value

• A Hadamard matrix

References

Sloane NJA. A Library of Hadamard Matrices http://www.research.att.com/~njas/hadamard/

See Also

brrweights

Examples

par(mfrow=c(2,2))
## Sylvester-type
image(hadamard(63),main="Sylvester: 64")
## Paley-type
image(hadamard(57),main="Paley: 60")
## hybrid
image(hadamard(23),main="Stored: 24")
image(hadamard(90),main="Constructed: 96=4x24")

par(mfrow=c(1,1))
plot(2:150,sapply(2:150,function(i) ncol(hadamard(i))),type="S",
     ylab="Matrix size",xlab="n",xlim=c(1,150),ylim=c(1,150))
abline(0,1,lty=3)
lines(2:150, 2:150-(2:150 %% 4)+4,col="purple",type="S",lty=2)
legend(c(x=10,y=140),legend=c("Actual size","Minimum possible size"),
     col=c("black","purple"),bty="n",lty=c(1,2))