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Refactor var/varm #17

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Refactor var/varm #17

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4c9036d
Refactor var/varm
yuehhua Dec 12, 2019
1fd4d7a
Fix
yuehhua Dec 12, 2019
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86 changes: 48 additions & 38 deletions src/Statistics.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -174,46 +174,52 @@ realXcY(x::Complex, y::Complex) = real(x)*real(y) + imag(x)*imag(y)

var(iterable; corrected::Bool=true, mean=nothing) = _var(iterable, corrected, mean)

function _var(iterable, corrected::Bool, mean)
function _var(iterable, corrected::Bool, ::Nothing)
y = iterate(iterable)
if y === nothing
T = eltype(iterable)
return oftype((abs2(zero(T)) + abs2(zero(T)))/2, NaN)
end
# Use Welford algorithm as seen in (among other places)
# Knuth's TAOCP, Vol 2, page 232, 3rd edition.
count = 1
value, state = y
y = iterate(iterable, state)
if mean === nothing
# Use Welford algorithm as seen in (among other places)
# Knuth's TAOCP, Vol 2, page 232, 3rd edition.
M = value / 1
S = real(zero(M))
while y !== nothing
value, state = y
y = iterate(iterable, state)
count += 1
new_M = M + (value - M) / count
S = S + realXcY(value - M, value - new_M)
M = new_M
end
return S / (count - Int(corrected))
elseif isa(mean, Number) # mean provided
# Cannot use a compensated version, e.g. the one from
# "Updating Formulae and a Pairwise Algorithm for Computing Sample Variances."
# by Chan, Golub, and LeVeque, Technical Report STAN-CS-79-773,
# Department of Computer Science, Stanford University,
# because user can provide mean value that is different to mean(iterable)
sum2 = abs2(value - mean::Number)
while y !== nothing
value, state = y
y = iterate(iterable, state)
count += 1
sum2 += abs2(value - mean)
end
return sum2 / (count - Int(corrected))
else
throw(ArgumentError("invalid value of mean, $(mean)::$(typeof(mean))"))
M = value / 1
S = real(zero(M))
while y !== nothing
value, state = y
y = iterate(iterable, state)
count += 1
new_M = M + (value - M) / count
S = S + realXcY(value - M, value - new_M)
M = new_M
end
return S / (count - Int(corrected))
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end

function _var(iterable, corrected::Bool, mean::Number)
y = iterate(iterable)
if y === nothing
T = eltype(iterable)
return oftype((abs2(zero(T)) + abs2(zero(T)))/2, NaN)
end
# Cannot use a compensated version, e.g. the one from
# "Updating Formulae and a Pairwise Algorithm for Computing Sample Variances."
# by Chan, Golub, and LeVeque, Technical Report STAN-CS-79-773,
# Department of Computer Science, Stanford University,
# because user can provide mean value that is different to mean(iterable)
count = 1
value, state = y
y = iterate(iterable, state)
sum2 = abs2(value - mean::Number)
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while y !== nothing
value, state = y
y = iterate(iterable, state)
count += 1
sum2 += abs2(value - mean)
end
return sum2 / (count - Int(corrected))
end

centralizedabs2fun(m) = x -> abs2.(x - m)
Expand Down Expand Up @@ -296,11 +302,13 @@ over dimensions, and `m` may contain means for each dimension of `itr`.
"""
varm(A::AbstractArray, m::AbstractArray; corrected::Bool=true, dims=:) = _varm(A, m, corrected, dims)

varm(A::AbstractArray, m; corrected::Bool=true) = _varm(A, m, corrected, :)

varm(iterable, m; corrected::Bool=true) = _var(iterable, corrected, m)

_varm(A::AbstractArray{T}, m, corrected::Bool, region) where {T} =
varm!(Base.reducedim_init(t -> abs2(t)/2, +, A, region), A, m; corrected=corrected)

varm(A::AbstractArray, m; corrected::Bool=true) = _varm(A, m, corrected, :)

function _varm(A::AbstractArray{T}, m, corrected::Bool, ::Colon) where T
n = length(A)
n == 0 && return oftype((abs2(zero(T)) + abs2(zero(T)))/2, NaN)
Expand Down Expand Up @@ -334,13 +342,15 @@ over dimensions, and `mean` may contain means for each dimension of `itr`.
"""
var(A::AbstractArray; corrected::Bool=true, mean=nothing, dims=:) = _var(A, corrected, mean, dims)

_var(A::AbstractArray, corrected::Bool, mean, dims) =
varm(A, something(mean, Statistics.mean(A, dims=dims)); corrected=corrected, dims=dims)
_var(A::AbstractArray, corrected::Bool, mean, dims) = _varm(A, mean, corrected, dims)

_var(A::AbstractArray, corrected::Bool, mean, ::Colon) =
real(varm(A, something(mean, Statistics.mean(A)); corrected=corrected))
_var(A::AbstractArray, corrected::Bool, mean, ::Colon) = real(_var(A, corrected, mean))

varm(iterable, m; corrected::Bool=true) = _var(iterable, corrected, m)
_var(A::AbstractArray, corrected::Bool, ::Nothing, dims) =
_varm(A, Statistics.mean(A, dims=dims), corrected, dims)

_var(A::AbstractArray, corrected::Bool, ::Nothing, ::Colon) =
real(_var(A, corrected, Statistics.mean(A)))

## variances over ranges

Expand Down