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handling floating point errors #31

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handling floating point errors #31

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1fdf02a
handling floating point errors
EtiDg Sep 18, 2019
cc87014
handles floating point on dinic's algorithm
etiennedeg Nov 25, 2019
fe2aeff
wider tolerance for floating point
etiennedeg Nov 26, 2019
60f2f8a
Update src/push_relabel.jl
matbesancon Oct 12, 2020
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4 changes: 2 additions & 2 deletions src/dinic.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -21,7 +21,7 @@ function dinic_impl end

while true
augment = blocking_flow!(residual_graph, source, target, capacity_matrix, flow_matrix, P)
augment == 0 && break
is_zero(augment) && break
flow += augment
end
return flow, flow_matrix
Expand Down Expand Up @@ -80,7 +80,7 @@ function blocking_flow! end
end
end

flow == 0 && continue # Flow cannot be augmented along path
is_zero(flow) && continue # Flow cannot be augmented along path

v = target
u = bv
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16 changes: 16 additions & 0 deletions src/maximum_flow.jl
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Expand Up @@ -178,3 +178,19 @@ function maximum_flow(
end
return maximum_flow(flow_graph, source, target, capacity_matrix, algorithm)
end

"""
is_zero(value)
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You could replace iszero with isapprox directly, which handles both integers and abstract floats correctly

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We already discussed of that point, unfortunately eps is not defined for integers

The default isapprox is not well suited for our problem. If isapprox(0.2+0.1, 0.3) is returning true, isapprox(0.2+0.1-0.3, 0.0) is returning false. In fact, x ≈ 0 is equivalent to x == 0.
As we compare to 0, rtol is just useless, so we must define an atol.
If we want the tolerance to rely on the type, we must separate Float and Integer case (as the default rtol do), because eps is not defined for Integer types.
This is not an absurd way o do it as rtol is defined quite similarly:

# default tolerance arguments
rtoldefault(::Type{T}) where {T<:AbstractFloat} = sqrt(eps(T))
rtoldefault(::Type{<:Real}) = 0
function rtoldefault(x::Union{T,Type{T}}, y::Union{S,Type{S}}, atol::Real) where {T<:Number,S<:Number}
    rtol = max(rtoldefault(real(T)),rtoldefault(real(S)))
    return atol > 0 ? zero(rtol) : rtol
end

See Base.isapprox
and floatfuncs lines 285-291 for the definition of rtol


Test if the value is equal to zero. It handles floating point errors.
"""
function is_zero end
function is_zero(
value::T
) where {T}
if isa(value,AbstractFloat)
return isapprox(value, 0, atol = sqrt(eps(T)))
else
return value == 0
end
end
5 changes: 2 additions & 3 deletions src/push_relabel.jl
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Expand Up @@ -169,7 +169,6 @@ function relabel! end
nothing
end


"""
discharge!(residual_graph, v, capacity_matrix, flow_matrix, excess, height, active, count, Q)

Expand All @@ -189,11 +188,11 @@ function discharge! end
Q::AbstractVector # FIFO queue
)
for to in lg.outneighbors(residual_graph, v)
excess[v] == 0 && break
is_zero(excess[v]) && break
push_flow!(residual_graph, v, to, capacity_matrix, flow_matrix, excess, height, active, Q)
end

if excess[v] > 0
if excess[v] ≉ zero(excess[v])
if count[height[v] + 1] == 1
gap!(residual_graph, height[v], excess, height, active, count, Q)
else
Expand Down