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Improve computation of residuals #124

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Dec 21, 2018
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Improve computation of residuals #124

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88 changes: 88 additions & 0 deletions src/misc_utils.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -39,6 +39,94 @@ end
get_chunksize(x) = 0
get_chunksize(x::NLSOLVEJL_SETUP{CS,AD}) where {CS,AD} = CS

"""
calculate_residuals(ũ, u₀, u₁, α, ρ, scalarnorm)

Return element-wise residuals
```math
\\frac{ũ}{α+\\max{scalarnorm(u₀),scalarnorm(u₁)}*ρ}.
```
"""
@inline @muladd function calculate_residuals(ũ::Number, u₀::Number, u₁::Number, α::Real,
ρ::Real, scalarnorm)
ũ / (α + max(scalarnorm(u₀), scalarnorm(u₁)) * ρ)
end

"""
calculate_residuals(E₁, E₂, u₀, u₁, α, ρ, δ, scalarnorm)

Return element-wise residuals
```math
\\frac{δ E₁ + E₂}{α+\\max{scalarnorm(u₀),scalarnorm(u₁)}*ρ}.
```
"""
@inline @muladd function calculate_residuals(E₁::Number, E₂::Number, u₀::Number, u₁::Number,
α::Real, ρ::Real, δ::Number, scalarnorm)
(δ * E₁ + E₂) / (α + max(scalarnorm(u₀), scalarnorm(u₁)) * ρ)
end

"""
calculate_residuals!(out, ũ, u₀, u₁, α, ρ, scalarnorm)

Same as [`calculate_residuals`](@ref) but save result in `out`.
"""
@inline function calculate_residuals!(out, ũ, u₀, u₁, α, ρ, scalarnorm)
@. out = calculate_residuals(ũ, u₀, u₁, α, ρ, scalarnorm)
out
end

@inline function calculate_residuals!(out::Array{<:Number}, ũ::Array{<:Number},
u₀::Array{<:Number}, u₁::Array{<:Number}, α::Real,
ρ::Real, scalarnorm)
@tight_loop_macros @inbounds for i in eachindex(out)
out[i] = calculate_residuals(ũ[i], u₀[i], u₁[i], α, ρ, scalarnorm)
end
out
end

@inline function calculate_residuals(ũ, u₀, u₁, α, ρ, scalarnorm)
@. calculate_residuals(ũ, u₀, u₁, α, ρ, scalarnorm)
end

@inline function calculate_residuals(ũ::Array{<:Number}, u₀::Array{<:Number},
u₁::Array{<:Number}, α::Real, ρ::Real, scalarnorm)
out = similar(ũ)
calculate_residuals!(out, ũ, u₀, u₁, α, ρ, scalarnorm)
out
end

"""
calculate_residuals!(out, E₁, E₂, u₀, u₁, α, ρ, δ, scalarnorm)

Same as [`calculate_residuals`](@ref) but save result in `out`.
"""
@inline function calculate_residuals!(out, E₁, E₂, u₀, u₁, α, ρ, δ, scalarnorm)
@. out = calculate_residuals(E₁, E₂, u₀, u₁, α, ρ, δ, scalarnorm)
out
end

@inline function calculate_residuals!(out::Array{<:Number}, E₁::Array{<:Number},
E₂::Array{<:Number}, u₀::Array{<:Number},
u₁::Array{<:Number}, α::Real, ρ::Real, δ::Number,
scalarnorm)
@tight_loop_macros @inbounds for i in eachindex(out)
out[i] = calculate_residuals(E₁[i], E₂[i], u₀[i], u₁[i], α, ρ, δ, scalarnorm)
end
out
end

@inline function calculate_residuals(E₁, E₂, u₀, u₁, α, ρ, δ, scalarnorm)
@. calculate_residuals(E₁, E₂, u₀, u₁, α, ρ, δ, scalarnorm)
end

@inline function calculate_residuals(E₁::Array{<:Number}, E₂::Array{<:Number},
u₀::Array{<:Number}, u₁::Array{<:Number}, α::Real,
ρ::Real, δ::Number, scalarnorm)
out = similar(u₀)
calculate_residuals!(out, E₁, E₂, u₀, u₁, α, ρ, δ, scalarnorm)
out
end

macro cache(expr)
name = expr.args[2].args[1].args[1]
fields = expr.args[3].args[2:2:end]
Expand Down
18 changes: 9 additions & 9 deletions src/perform_step/implicit_split_step.jl
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Expand Up @@ -73,16 +73,17 @@
En = ggprime.*(integrator.W.dW.^2)./2
end

tmp = Ed+En
integrator.EEst = integrator.opts.internalnorm(tmp./(integrator.opts.abstol + max.(integrator.opts.internalnorm.(uprev),integrator.opts.internalnorm.(u))*integrator.opts.reltol))
resids = calculate_residuals(Ed, En, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.delta,
integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(resids)
end

integrator.u = u
end

@muladd function perform_step!(integrator,
cache::Union{ISSEMCache,
ISSEulerHeunCache},
@muladd function perform_step!(integrator, cache::Union{ISSEMCache,
ISSEulerHeunCache},
f=integrator.f)
@unpack t,dt,uprev,u,p = integrator
@unpack uf,du1,dz,z,k,J,W,jac_config,gtmp,gtmp2,tmp,tmp,dW_cache = cache
Expand Down Expand Up @@ -216,10 +217,9 @@ end

end

@tight_loop_macros for (i,atol,rtol,δ) in zip(eachindex(u),Iterators.cycle(integrator.opts.abstol),
Iterators.cycle(integrator.opts.reltol),Iterators.cycle(integrator.opts.delta))
@inbounds tmp[i] = (k[i]+dz[i])/(atol + max(integrator.opts.internalnorm(uprev[i]),integrator.opts.internalnorm(u[i]))*rtol)
end
calculate_residuals!(tmp, k, dz, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.delta,
integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(tmp)

end
Expand Down
12 changes: 7 additions & 5 deletions src/perform_step/kencarp.jl
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Expand Up @@ -128,7 +128,10 @@

E₁ = z₁ + z₂ + z₃ + z₄

integrator.EEst = integrator.opts.internalnorm((integrator.opts.delta*E₁+E₂)./(integrator.opts.abstol + max.(integrator.opts.internalnorm.(uprev),integrator.opts.internalnorm.(u))*integrator.opts.reltol))
resids = calculate_residuals(E₁, E₂, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.delta,
integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(resids)
end

integrator.u = u
Expand Down Expand Up @@ -340,10 +343,9 @@ end

@. E₁ = z₁ + z₂ + z₃ + z₄

@tight_loop_macros for (i,atol,rtol,δ) in zip(eachindex(u),Iterators.cycle(integrator.opts.abstol),
Iterators.cycle(integrator.opts.reltol),Iterators.cycle(integrator.opts.delta))
@inbounds tmp[i] = (δ*E₁[i]+E₂[i])/(atol + max(integrator.opts.internalnorm(uprev[i]),integrator.opts.internalnorm(u[i]))*rtol)
end
calculate_residuals!(tmp, E₁, E₂, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.delta,
integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(tmp)
end
end
26 changes: 14 additions & 12 deletions src/perform_step/lamba.jl
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Expand Up @@ -21,7 +21,10 @@
ggprime = (integrator.g(utilde,p,t).-L)./(integrator.sqdt)
En = ggprime.*(W.dW.^2 .- dt)./2

integrator.EEst = integrator.opts.internalnorm((Ed + En)/((integrator.opts.abstol + max.(integrator.opts.internalnorm(uprev),integrator.opts.internalnorm(u))*integrator.opts.reltol)))
resids = calculate_residuals(Ed, En, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.delta,
integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(resids)
end

integrator.u = u
Expand Down Expand Up @@ -72,12 +75,10 @@ end

# Ed
integrator.f(du2,K,p,t+dt)
@. tmp += integrator.opts.internalnorm(dt*(du2 - du1)/2)
@. tmp += integrator.opts.internalnorm(integrator.opts.delta * dt * (du2 - du1) / 2)


@tight_loop_macros for (i,atol,rtol) in zip(eachindex(u),Iterators.cycle(integrator.opts.abstol),Iterators.cycle(integrator.opts.reltol))
@inbounds tmp[i] = (tmp[i])/(atol + max(integrator.opts.internalnorm(uprev[i]),integrator.opts.internalnorm(u[i]))*rtol)
end
calculate_residuals!(tmp, tmp, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(tmp)
end
end
Expand Down Expand Up @@ -111,7 +112,10 @@ end
ggprime = (integrator.g(utilde,p,t).-L)./(integrator.sqdt)
En = ggprime.*(W.dW.^2)./2

integrator.EEst = integrator.opts.internalnorm((Ed + En)/((integrator.opts.abstol + max.(integrator.opts.internalnorm(uprev),integrator.opts.internalnorm(u))*integrator.opts.reltol)))
resids = calculate_residuals(Ed, En, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.delta,
integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(resids)
end

integrator.u = u
Expand Down Expand Up @@ -169,12 +173,10 @@ end

# Ed
integrator.f(du2,K,p,t+dt)
@. tmp += integrator.opts.internalnorm(dt*(du2 - du1)/2)
@. tmp += integrator.opts.internalnorm(integrator.opts.delta * dt * (du2 - du1) / 2)


@tight_loop_macros for (i,atol,rtol) in zip(eachindex(u),Iterators.cycle(integrator.opts.abstol),Iterators.cycle(integrator.opts.reltol))
@inbounds tmp[i] = (tmp[i])/(atol + max(integrator.opts.internalnorm(uprev[i]),integrator.opts.internalnorm(u[i]))*rtol)
end
calculate_residuals!(tmp, tmp, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(tmp)
end
end
21 changes: 12 additions & 9 deletions src/perform_step/low_order.jl
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Expand Up @@ -125,7 +125,11 @@ end
du2 = integrator.f(K,p,t+dt)
Ed = dt*(du2 - du1)/2
En = W.dW.^3 .* ((du2-L)/(integrator.sqdt)).^2 / 6
integrator.EEst = integrator.opts.internalnorm((Ed + En)/((integrator.opts.abstol .+ max.(integrator.opts.internalnorm.(uprev),integrator.opts.internalnorm.(u))*integrator.opts.reltol)))

resids = calculate_residuals(Ed, En, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.delta,
integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(resids)
end
integrator.u = u
end
Expand Down Expand Up @@ -174,10 +178,10 @@ end
@. tmp = integrator.opts.internalnorm(W.dW^3)*
integrator.opts.internalnorm((du2-L)/(integrator.sqdt))^2 / 6
integrator.f(du2,K,p,t+dt)
@. tmp += integrator.opts.internalnorm(dt*(du2 - du1)/2)
@tight_loop_macros for (i,atol,rtol) in zip(eachindex(u),Iterators.cycle(integrator.opts.abstol),Iterators.cycle(integrator.opts.reltol))
@inbounds tmp[i] = (tmp[i])/(atol + max(integrator.opts.internalnorm(uprev[i]),integrator.opts.internalnorm(u[i]))*rtol)
end
@. tmp += integrator.opts.internalnorm(integrator.opts.delta * dt * (du2 - du1)/2)

calculate_residuals!(tmp, tmp, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(tmp)
end
end
Expand Down Expand Up @@ -219,11 +223,10 @@ end
if integrator.opts.adaptive
En = integrator.opts.internalnorm(W.dW)^3*ggprime_norm^2 / 6
integrator.f(du2,K,p,t+dt)
@. tmp = integrator.opts.internalnorm(dt*(du2 - du1)/2) + En
@. tmp = integrator.opts.internalnorm(integrator.opts.delta * dt * (du2 - du1) / 2) + En

@tight_loop_macros for (i,atol,rtol) in zip(eachindex(u),Iterators.cycle(integrator.opts.abstol),Iterators.cycle(integrator.opts.reltol))
@inbounds tmp[i] = (tmp[i])/(atol + max(integrator.opts.internalnorm(uprev[i]),integrator.opts.internalnorm(u[i]))*rtol)
end
calculate_residuals!(tmp, tmp, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(tmp)

end
Expand Down
13 changes: 7 additions & 6 deletions src/perform_step/sdirk.jl
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Expand Up @@ -84,8 +84,10 @@
integrator.opts.internalnorm.(ggprime).^2 ./ 6
end

tmp = Ed+En
integrator.EEst = integrator.opts.internalnorm(tmp./(integrator.opts.abstol + max.(integrator.opts.internalnorm.(uprev),integrator.opts.internalnorm.(u))*integrator.opts.reltol))
resids = calculate_residuals(Ed, En, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.delta,
integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(resids)
end

integrator.u = u
Expand Down Expand Up @@ -244,10 +246,9 @@ end
@. dz = integrator.opts.internalnorm(dW^3)*integrator.opts.internalnorm(gtmp3)^2 / 6
end

@tight_loop_macros for (i,atol,rtol,δ) in zip(eachindex(u),Iterators.cycle(integrator.opts.abstol),
Iterators.cycle(integrator.opts.reltol),Iterators.cycle(integrator.opts.delta))
@inbounds tmp[i] = (k[i]+dz[i])/(atol + max(integrator.opts.internalnorm(uprev[i]),integrator.opts.internalnorm(u[i]))*rtol)
end
calculate_residuals!(tmp, k, dz, uprev, u, integrator.opts.abstol,
integrator.opts.reltol, integrator.opts.delta,
integrator.opts.internalnorm)
integrator.EEst = integrator.opts.internalnorm(tmp)

end
Expand Down
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