Halton's quasi-random numbers
Generating quasi-random numbers by Halton's radical inversion algorithm.
HS247(K,N,R,P=rep(0,K))
K |
Integer, number of random sequences |
N |
Integer, length of the random sequences |
R |
Integer 1..K, roots of inversion, should be prime |
P |
Integer 1..K, starting points of inversion |
A matrix of K columns containing the sequences.
Halton, J.H., Smith, G.G., 1961. Algorithm 247 Radical-inverse quasi-random point sequence Computes a sequence of N quasi-random points lying in the K-dimensional unit cube given by 0 < x_i < 1, i = 1,2,..,K. The i-th component of the m-th point is stored in Q[m,i]. The sequence is initiated by a zero-th point stored in P, and each component sequence is iteratively generated with parameter R[i]. E is a positive error-parameter. K, N, E, P[i], R[i], i=1..K, are to be given.
Christian W. Hoffmann, hoffmann@wsl.ch
J. H. Halton, 1964. Algorithm 247: Radical-inverse quasi-random point sequence, Communications of the ACM, Vol.7,12, pp. 701 - 702 .
http://en.wikipedia.org/wiki/Halton_sequences
par(mfrow=c(2,2))
n <- 400
q1 <- HS247(2,n,c(2,2),c(0,pi/10))
q2 <- HS247(2,n,c(2,3))
q3 <- HS247(2,n,c(2,5))
q4 <- HS247(2,n,c(17,19)) # prone to correlations
q5 <- HS247(2,n,c(2,3),c(pi/10,pi/10))
of <- 0.2
q6 <- HS247(2,n,c(2,3),c(pi/10+of,pi/10+of))
## Not run:
plot (q1,pch="+",col="blue",cex=0.5,xlab="roots = (2,2), +blue, green")
points(q2,pch=4, col="green",cex=0.5)
plot (q2,pch=4,col="green",cex=0.5,xlab="roots = (2,3),
:green, (2,5) :red, (17,19) magenta")
points(q3,pch=":",col="red")
points(q4,pch=4,col="magenta",cex=0.5)
plot (q2,pch=4,col="green",cex=0.5,xlab="roots = 2, 2, green, red")
points(q5,pch=5,cex=0.5,col="red")
plot (q5,pch=5,cex=0.5,col="red",xlab="roots = 2, 3, red")
points(q6,pch="-")
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.