Functions

haltonvalue(n, base[, T])

Return the nth element of the Halton sequence with prime base base (defaults to 2). If a <:Real type T is given, compute the value in that type.

Examples

julia> haltonvalue(4,3,Rational)
4//9

Halton(base=2; <keyword arguments>)
Halton{T<:Real}(base=2; <keyword arguments>)

Create a Vector-like object for a Halton sequence. Optionally, use a <:Real type T for the elements.

Arguments

• base::Integer: prime number base for the sequence
• start=1 (keyword): starting/offset index
• length=typemax(UInt32) (keyword): length of the sequence vector

Examples

julia> Halton(3,length=4)
4-element Halton{Float64}:
 0.3333333333333333
 0.6666666666666666
 0.1111111111111111
 0.4444444444444444

julia> Halton{Rational}(2,length=7)
7-element Halton{Rational}:
 1//2
 1//4
 3//4
 1//8
 5//8
 3//8
 7//8

julia> sum( Halton()[1:10000] )/10000
0.4998324768066406

See also: HaltonPoint, haltonvalue

HaltonPoint(ndim::Integer; <keyword arguments>)
HaltonPoint(base::Vector{<:Integer}; <keyword arguments>)
HaltonPoint{T<:Real}(base::Vector{<:Integer}; <keyword arguments>)

Create a Vector-like object for a sequence of ndim-dimensional vectors constructed from Halton sequences. If given, base should be a vector of primes and then ndim=length(base). If T is given, it is the element type for the vectors.

Keyword arguments

• start=1: starting/offset index
• length=typemax(UInt32): length of the sequence vector

Examples

julia> HaltonPoint(4,length=5)
5-element HaltonPoint{Float64}:
 [0.5, 0.333333, 0.2, 0.142857]
 [0.25, 0.666667, 0.4, 0.285714]
 [0.75, 0.111111, 0.6, 0.428571]
 [0.125, 0.444444, 0.8, 0.571429]
 [0.625, 0.777778, 0.04, 0.714286]

julia> h = HaltonPoint([5,11,17]);  sum(h[10001:20000])/10000
3-element Array{Float64,1}:
 0.49996162048000015
 0.5000650725546567
 0.49992980926952507

See also: Halton, haltonvalue