Miscellaneous tools

Real-indexed vector

This is a simple implementation of a vector that can be accessed with real (floating point) sub-indices. It does simply a linear binning of a specified (semi-open) interval $[min,max)$ on the real line, and provides a convenient Vector-like syntax to access elements. The stored values can be of any type, but the interval and number of bins are fixed at construction.


julia> 	A = BinnedVector{String}(5,min=0.,max=1.)5-element BinnedVector{String}:
 #undef
 #undef
 #undef
 #undef
 #undef
julia> 	A[0.1]="hello""hello"
julia> 	A[0.2]="bye bye""bye bye"
julia> 	A5-element BinnedVector{String}:
    "hello"
    "bye bye"
 #undef
 #undef
 #undef

To initialise elements with a default value, give function with a signature like zeros:

B = BinnedVector{Rational{Int64}}(10,min=2.,max=8.,init=zeros)
B[2.1]=3//5
B[5.3]=4//1
B

10-element BinnedVector{Rational{Int64}}:
 3//5
 0//1
 0//1
 0//1
 0//1
 4//1
 0//1
 0//1
 0//1
 0//1

Alternatively, it is possible to construct specifying bin width and the interval. In this case, one of the values will need to be rounded to get an integer number of bins:

julia> 	C = BinnedVector{Int}(Δ=0.15,min=5.,max=10.,round_Δ=RoundUp); (C.Δ, interval(C))(0.15151515151515152, (5.0, 10.0))
julia> 	D = BinnedVector{Int}(Δ=0.15,min=5.,max=10.,round_max=RoundUp); (D.Δ, interval(D))(0.15, (5.0, 10.1))
julia> 	E = BinnedVector{Int}(Δ=0.15,min=5.,max=10.,round_min=RoundUp); (E.Δ, interval(E))(0.15, (5.05, 10.0))

RoundDown is also recognised.

Indexing with integers refers to bin numbers.

julia> 	A[1:2]2-element Vector{String}:
 "hello"
 "bye bye"
julia> 	B[1:5]5-element Vector{Rational{Int64}}:
 3//5
 0//1
 0//1
 0//1
 0//1

Outliers are mapped to bin 0 if below range, or -1 if above range.

julia> B[0.]=10//3 ; B[40.]=99//2;
julia> B[0]10//3
julia> B[-1]99//2

As an example of use, the Histogram type is implemented using BinnedVector.

Special treatment of zero

In some cases, like when computing space correlation functions, it is convenient to treat the case A[0.] separately from the bin that starts at 0. This is what the ZBinnedvector type does.

julia> Z = ZBinnedVector{Int}(Δ=0.2,max=0.5,round_max=RoundUp,init=zeros)4-element ZBinnedVector{Int64}:
 0
 0
 0
 0
julia> Z[0.] += 1010
julia> Z[0.1] += 1010
julia> Z[0.15] += 1020
julia> Z4-element ZBinnedVector{Int64}:
 10
 20
  0
  0

Note that there is no min argument in the construction of ZBinnedvector, since it is always zero. In other respects, ZBinnedvector behaves like BinnedVector, except that bin centres are not equally spaced: the first (pesudo-bin) is at 0, the next bin centre is delta(Z)/2, and the rest are delta(Z) units apart.

API

BioStatPhys.BinnedVector — Type

BinnedVector{T}

Simple real-indexed vector. Maps a real interval to an integer range 1:nbins then used to index a vector of arbitrary type. Can be used e.g. to build histograms. The real interval and number of bins nbins are fixed at the outset.

Example

Create with

A = BinnedVector{Int}(nbins,min=1.,max=10.,init=zeros)

for fixed number of bins, or

A = BinnedVector{Int}(;Δ=0.1,min=1.,max=10.init=zeros,round_Δ=RoundUp)
A = BinnedVector{Int}(;Δ=0.1,min=1.,max=10.init=zeros,round_min=RoundUp)
A = BinnedVector{Int}(;Δ=0.1,min=1.,max=10.init=zeros,round_max=RoundUp)

to get fixed (min, max), (Δ,max) or (min,Δ) respectively (rounding mode RoundDown is also recognised).

init is optional, defaults to leave elements undefined.

Access or write as a vector:

A[5.2] += 2

Numbers above and below range map to two special bins.

If indexed with integers, these are interpreted as bin numbers. A[0] and A[-1] are the outlier bins (below and above, respectively).

Miscellaneous tools

Real-indexed vector

Special treatment of zero

API

Distance binning

Regions