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handle unitful infinite arguments #65

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Jan 18, 2023
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handle unitful infinite arguments #65

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53 changes: 30 additions & 23 deletions src/adapt.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -20,7 +20,7 @@ function do_quadgk(f::F, s::NTuple{N,T}, n, atol, rtol, maxevals, nrm, segbuf) w
numevals = (2n+1) * (N-1)

# logic here is mainly to handle dimensionful quantities: we
# don't know the correct type of atol, in particular, until
# don't know the correct type of atol115, in particular, until
# this point where we have the type of E from f. Also, follow
# Base.isapprox in that if atol≠0 is supplied by the user, rtol
# defaults to zero.
Expand Down Expand Up @@ -84,30 +84,33 @@ function adapt(f::F, segs::Vector{T}, I, E, numevals, x,w,gw,n, atol, rtol, maxe
return (I, E)
end

realone(x) = false
realone(x::Number) = one(x) isa Real

# transform f and the endpoints s to handle infinite intervals, if any,
# and pass transformed data to workfunc(f, s, tfunc)
function handle_infinities(workfunc, f, s)
s1, s2 = s[1], s[end]
if s1 isa Real && s2 isa Real # check for infinite or semi-infinite intervals
if realone(s1) && realone(s2) # check for infinite or semi-infinite intervals
inf1, inf2 = isinf(s1), isinf(s2)
if inf1 || inf2
if inf1 && inf2 # x = t/(1-t^2) coordinate transformation
return workfunc(t -> begin t2 = t*t; den = 1 / (1 - t2);
f(t*den) * (1+t2)*den*den; end,
map(x -> isinf(x) ? copysign(one(x), x) : 2x / (1+hypot(1,2x)), s),
t -> t / (1 - t^2))
f(oneunit(s1)*t*den) * (1+t2)*den*den*oneunit(s1); end,
map(x -> isinf(x) ? (signbit(x) ? -one(x) : one(x)) : 2x / (oneunit(x)+hypot(oneunit(x),2x)), s),
t -> oneunit(s1) * t / (1 - t^2))
end
let (s0,si) = inf1 ? (s2,s1) : (s1,s2) # let is needed for JuliaLang/julia#15276
if si < 0 # x = s0 - t/(1-t)
if si < zero(si) # x = s0 - t/(1-t)
return workfunc(t -> begin den = 1 / (1 - t);
f(s0 - t*den) * den*den; end,
reverse(map(x -> 1 / (1 + 1 / (s0 - x)), s)),
t -> s0 - t/(1-t))
f(s0 - oneunit(s1)*t*den) * den*den*oneunit(s1); end,
reverse(map(x -> 1 / (1 + oneunit(x) / (s0 - x)), s)),
t -> s0 - oneunit(s1)*t/(1-t))
else # x = s0 + t/(1-t)
return workfunc(t -> begin den = 1 / (1 - t);
f(s0 + t*den) * den*den; end,
map(x -> 1 / (1 + 1 / (x - s0)), s),
t -> s0 + t/(1-t))
f(s0 + oneunit(s1)*t*den) * den*den*oneunit(s1); end,
map(x -> 1 / (1 + oneunit(x) / (x - s0)), s),
t -> s0 + oneunit(s1)*t/(1-t))
end
end
end
Expand All @@ -117,26 +120,27 @@ end

function handle_infinities(workfunc, f::InplaceIntegrand, s)
s1, s2 = s[1], s[end]
if s1 isa Real && s2 isa Real # check for infinite or semi-infinite intervals
if realone(s1) && realone(s2) # check for infinite or semi-infinite intervals
inf1, inf2 = isinf(s1), isinf(s2)
if inf1 || inf2
ftmp = f.fx # original integrand may have different units
if inf1 && inf2 # x = t/(1-t^2) coordinate transformation
return workfunc(InplaceIntegrand((v, t) -> begin t2 = t*t; den = 1 / (1 - t2);
f.f!(v, t*den); v .*= (1+t2)*den*den; end, f.I, f.fx),
map(x -> isinf(x) ? copysign(one(x), x) : 2x / (1+hypot(1,2x)), s),
t -> t / (1 - t^2))
f.f!(ftmp, oneunit(s1)*t*den); v .= ftmp .* ((1+t2)*den*den*oneunit(s1)); end, f.I, f.fx * oneunit(s1)),
map(x -> isinf(x) ? (signbit(x) ? -one(x) : one(x)) : 2x / (oneunit(x)+hypot(oneunit(x),2x)), s),
t -> oneunit(s1) * t / (1 - t^2))
end
let (s0,si) = inf1 ? (s2,s1) : (s1,s2) # let is needed for JuliaLang/julia#15276
if si < 0 # x = s0 - t/(1-t)
if si < zero(si) # x = s0 - t/(1-t)
return workfunc(InplaceIntegrand((v, t) -> begin den = 1 / (1 - t);
f.f!(v, s0 - t*den); v .*= den * den; end, f.I, f.fx),
reverse(map(x -> 1 / (1 + 1 / (s0 - x)), s)),
t -> s0 - t/(1-t))
f.f!(ftmp, s0 - oneunit(s1)*t*den); v .= ftmp .* (den * den * oneunit(s1)); end, f.I, f.fx * oneunit(s1)),
reverse(map(x -> 1 / (1 + oneunit(x) / (s0 - x)), s)),
t -> s0 - oneunit(s1)*t/(1-t))
else # x = s0 + t/(1-t)
return workfunc(InplaceIntegrand((v, t) -> begin den = 1 / (1 - t);
f.f!(v, s0 + t*den); v .*= den * den; end, f.I, f.fx),
map(x -> 1 / (1 + 1 / (x - s0)), s),
t -> s0 + t/(1-t))
f.f!(ftmp, s0 + oneunit(s1)*t*den); v .= ftmp .* (den * den * oneunit(s1)); end, f.I, f.fx * oneunit(s1)),
map(x -> 1 / (1 + oneunit(x) / (x - s0)), s),
t -> s0 + oneunit(s1)*t/(1-t))
end
end
end
Expand Down Expand Up @@ -250,6 +254,9 @@ For integrands whose values are *small* arrays whose length is known at compile-
it is usually more efficient to use `quadgk` and modify your integrand to return
an `SVector` from the [StaticArrays.jl package](https://github.com/JuliaArrays/StaticArrays.jl).
"""
quadgk!(f!, result, segs...; kws...) =
quadgk!(f!, result, promote(segs...)...; kws...)

function quadgk!(f!, result, a::T,b::T,c::T...; atol=nothing, rtol=nothing, maxevals=10^7, order=7, norm=norm, segbuf=nothing) where {T}
fx = result / oneunit(T) # pre-allocate array of correct type for integrand evaluations
f = InplaceIntegrand(f!, result, fx)
Expand Down
5 changes: 5 additions & 0 deletions test/runtests.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -93,6 +93,11 @@ end
r[2] = sin(30x)
end
@test quadgk(x -> [cos(100x), sin(30x)], 0, 1) ≅ (I′,E′) ≅ ([-0.005063656411097513, 0.028191618337080532], 4.2100180879009775e-10)
I″,E″= quadgk!(I, 0, 1.0) do r,x # check mixed-type argument promotion
r[1] = cos(100x)
r[2] = sin(30x)
end
@test (I″,E″) ≅ (I′,E′)
@test I === I′ # result is written in-place to I
end

Expand Down