From 1009327a85f2af3fad5a84938f8998e57398ef65 Mon Sep 17 00:00:00 2001 From: Antoine GROSSE Date: Fri, 17 Apr 2026 17:11:38 +0200 Subject: [PATCH 1/9] DirectXUA initialized with a vector of trajectories --- src/DirectXUA.jl | 24 ++++++++++++++++++++---- 1 file changed, 20 insertions(+), 4 deletions(-) diff --git a/src/DirectXUA.jl b/src/DirectXUA.jl index c3f8ed5a..e1ae4e38 100644 --- a/src/DirectXUA.jl +++ b/src/DirectXUA.jl @@ -414,6 +414,10 @@ The solver does not yet support interior point methods. `initialstate` must be with zero time derivatives. It does not provide initial conditions for the problem, but an initial guess for the iterative solver. +- `initialtrajectory` an `AbstractVector` of Vector{`State`}: one initial trajectory for each experiment. + `initialtrajectory` elements are also initial guess for the iterative solver, representing a time-dependant trajectory. + its elements must then match the specific timerange respective to the experiment they refer to. + If not specified, initialstate is copied for each timestep to create the initial guess. - `time` an `AbstractVector` (of same length as `initialstate`) of `AbstractRange` of times at which to compute the steps. Example: 0:0.1:5. - `maxiter=50` maximum number of Newton-Raphson iterations. @@ -441,6 +445,7 @@ struct DirectXUA{OX,OU,IA} <: AbstractSolver end function solve(::Type{DirectXUA{OX,OU,IA}},pstate,verbose::𝕓,dbg; time::AbstractVector{AR}, initialstate::AbstractVector{STATE}, + initialtrajectory::Union{Nothing,AbstractVector}=nothing, maxiter::ℤ=50, maxΔλ::ℝ=1e-5,maxΔx::ℝ=1e-5,maxΔu::ℝ=1e-5,maxΔa::ℝ=1e-5, saveiter::𝔹=false, @@ -461,12 +466,23 @@ function solve(::Type{DirectXUA{OX,OU,IA}},pstate,verbose::𝕓,dbg; S = State{1,OX+1,OU+1,@NamedTuple{γ::Float64,iter::Int64}} state = [Vector{S}(undef,nstep[iexp]) for iexp=1:nexp] # state[iexp][istep] s = initialstate[1] - for (iexp,initialstateᵢ) ∈ enumerate(initialstate) - for (istep,timeᵢ) = enumerate(time[iexp]) - state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(initialstateᵢ.Λ),deepcopy(initialstateᵢ.X),deepcopy(initialstateᵢ.U),s.A,(γ=0.,iter=1),s.model,s.dis) # all state[iexp][istep].A are === + if isnothing(initialtrajectory) + for (iexp,initialstateᵢ) ∈ enumerate(initialstate) + for (istep,timeᵢ) = enumerate(time[iexp]) + state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(initialstateᵢ.Λ),deepcopy(initialstateᵢ.X),deepcopy(initialstateᵢ.U),s.A,(γ=0.,iter=1),s.model,s.dis) # all state[iexp][istep].A are === + end + end + else + length(initialtrajectory)== nexp || muscadeerror("initialtrajectory and time must be of the same length") + Ashared = initialtrajectory[1][1].A + for (iexp,trajexp) ∈ enumerate(initialtrajectory) + length(trajexp)== nstep[iexp] || muscadeerror("initialtrajectory must match the time grid") + for (istep,timeᵢ) = enumerate(time[iexp]) + trajstate = trajexp[istep] + state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(trajstate.Λ),deepcopy(trajstate.X),deepcopy(trajstate.U),Ashared,(γ=0.,iter=1),s.model,s.dis) + end end end - if saveiter stateiter = Vector{Vector{Vector{S}}}(undef,maxiter) # stateiter[iiter][iexp][istep] pstate[] = stateiter From 5452b295e036f1a73f7b9db671b13acc928d345c Mon Sep 17 00:00:00 2001 From: Antoine GROSSE Date: Thu, 9 Jul 2026 09:53:58 +0200 Subject: [PATCH 2/9] Minor modification from PR review --- src/DirectXUA.jl | 28 ++++++++++++++-------------- 1 file changed, 14 insertions(+), 14 deletions(-) diff --git a/src/DirectXUA.jl b/src/DirectXUA.jl index e1ae4e38..fabcc294 100644 --- a/src/DirectXUA.jl +++ b/src/DirectXUA.jl @@ -413,11 +413,11 @@ The solver does not yet support interior point methods. - `initialstate` an `AbstractVector` of `State`: one initial state for each experiment. `initialstate` must be with zero time derivatives. It does not provide initial conditions for the problem, but an initial guess - for the iterative solver. -- `initialtrajectory` an `AbstractVector` of Vector{`State`}: one initial trajectory for each experiment. + for the iterative solver. Omitted if `initialtrajectory` is provided. +- `initialtrajectory` an `AbstractVector` of `Vector{State}`: one initial trajectory for each experiment. `initialtrajectory` elements are also initial guess for the iterative solver, representing a time-dependant trajectory. its elements must then match the specific timerange respective to the experiment they refer to. - If not specified, initialstate is copied for each timestep to create the initial guess. + If not specified, `initialstate` is copied for each timestep to create the initial guess. - `time` an `AbstractVector` (of same length as `initialstate`) of `AbstractRange` of times at which to compute the steps. Example: 0:0.1:5. - `maxiter=50` maximum number of Newton-Raphson iterations. @@ -444,42 +444,44 @@ See also: [`solve`](@ref), [`initialize!`](@ref), [`SweepX`](@ref), [`FreqXU`](@ struct DirectXUA{OX,OU,IA} <: AbstractSolver end function solve(::Type{DirectXUA{OX,OU,IA}},pstate,verbose::𝕓,dbg; time::AbstractVector{AR}, - initialstate::AbstractVector{STATE}, - initialtrajectory::Union{Nothing,AbstractVector}=nothing, + initialstate::Union{Nothing,AbstractVector{STATE}}, + initialtrajectory::Union{Nothing,AbstractVector}, maxiter::ℤ=50, maxΔλ::ℝ=1e-5,maxΔx::ℝ=1e-5,maxΔu::ℝ=1e-5,maxΔa::ℝ=1e-5, saveiter::𝔹=false, kwargs...) where{OX,OU,IA,AR<:AbstractRange{𝕣},STATE<:State} + xor(isnothing(initialstate),isnothing(initialtrajectory)) || muscadeerror("initialstate XOR initialtrajectory should be provided") + # Mostly constants local LU nexp,nstep,Δt = length(time),length.(time),step.(time) - length(initialstate)== nexp || muscadeerror("initialstate and time must be of the same length=number of experiments") γ = 0. nder = (1,OX+1,OU+1,IA) model,dis = initialstate[1].model, initialstate[1].dis if IA==1 Δ², maxΔ² = 𝕣1(undef,4), [maxΔλ^2,maxΔx^2,maxΔu^2,maxΔa^2] else Δ², maxΔ² = 𝕣1(undef,3), [maxΔλ^2,maxΔx^2,maxΔu^2 ] end - + # State storage S = State{1,OX+1,OU+1,@NamedTuple{γ::Float64,iter::Int64}} state = [Vector{S}(undef,nstep[iexp]) for iexp=1:nexp] # state[iexp][istep] s = initialstate[1] if isnothing(initialtrajectory) + length(initialstate)== nexp || muscadeerror("initialstate length must be equal to the number of experiments") for (iexp,initialstateᵢ) ∈ enumerate(initialstate) for (istep,timeᵢ) = enumerate(time[iexp]) state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(initialstateᵢ.Λ),deepcopy(initialstateᵢ.X),deepcopy(initialstateᵢ.U),s.A,(γ=0.,iter=1),s.model,s.dis) # all state[iexp][istep].A are === end end else - length(initialtrajectory)== nexp || muscadeerror("initialtrajectory and time must be of the same length") - Ashared = initialtrajectory[1][1].A + length(initialtrajectory)== nexp || muscadeerror("initialtrajectory length must be equal to the number of experiments") + Ainit = initialtrajectory[1][1].A for (iexp,trajexp) ∈ enumerate(initialtrajectory) - length(trajexp)== nstep[iexp] || muscadeerror("initialtrajectory must match the time grid") + length(trajexp)== nstep[iexp] || muscadeerror("trajectories in `initialtrajectory` vector must match their associated time grid in `time` vector") for (istep,timeᵢ) = enumerate(time[iexp]) trajstate = trajexp[istep] - state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(trajstate.Λ),deepcopy(trajstate.X),deepcopy(trajstate.U),Ashared,(γ=0.,iter=1),s.model,s.dis) + state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(trajstate.Λ),deepcopy(trajstate.X),deepcopy(trajstate.U),Ainit,(γ=0.,iter=1),s.model,s.dis) end end end @@ -529,6 +531,4 @@ function solve(::Type{DirectXUA{OX,OU,IA}},pstate,verbose::𝕓,dbg; iter Date: Sun, 19 Jul 2026 10:26:00 +0200 Subject: [PATCH 3/9] Updating SweepXA2 test --- test/TestSweepXA2.jl | 66 ++++++++++++++++++++++++++++++-------------- 1 file changed, 45 insertions(+), 21 deletions(-) diff --git a/test/TestSweepXA2.jl b/test/TestSweepXA2.jl index b2c2e16e..ca1ddadf 100644 --- a/test/TestSweepXA2.jl +++ b/test/TestSweepXA2.jl @@ -1,4 +1,4 @@ -#module TestSweepXA2 +module TestSweepXA2 using Test using Muscade @@ -6,40 +6,64 @@ using Muscade include("SomeElements.jl") include("../examples/DryFriction.jl") +# Δt = 0.01 +# t = Δt:Δt:1000*Δt +Δt = 1. +t = Δt:Δt:10*Δt + +### Target K,C,M = 1.,.4,.3 -model = Model(:TestModel) +model = Model(:Target) +node = addnode!(model,𝕣[]) +osc = addelement!(model,AdjustableSdofOscillator,[node]; K,C,M) + +initialstate = initialize!(model;time=0.) +x,x′,x″ = 0.,1.,0. +initialstate = setdof!(initialstate,[x′];field=:tx1,nodID=[node],order=1) # initial speed + +state0 = solve(SweepX{ 2}; initialstate,time= t,verbose=false,catcherror=true) +xtarget = getdof(state0;field=:tx1,nodID=[node]) +target = Muscade.FunctionFromVector(t,xtarget) + +### Optimize + +K,C,M = 1.,.6,.3 + +model = Model(:Optim) node = addnode!(model,𝕣[]) osc = addelement!(model,AdjustableSdofOscillator,[node]; K,C,M) -@functor with(σ=2.) acost(a )=(a/σ)^2 -@functor with(σ=.1) xcost(x,t)=(x/σ)^2 -cK = addelement!(model,SingleAcost ,[node];field=:ΞK, cost=acost) +@functor with(σ=10. ) acost(a )=( a /σ)^2 +@functor with(σ=.0001,target) xcost(x,t)=((x-target(t))/σ)^2 +cK = addelement!(model,SingleAcost ,[node];field=:ΞC, cost=acost) cX = addelement!(model,SingleDofCost,[node];class=:X ,field=:tx1 ,cost=xcost) initialstate = initialize!(model;time=0.) x,x′,x″ = 0.,1.,0. initialstate = setdof!(initialstate,[x′];field=:tx1,nodID=[node],order=1) # initial speed +state = solve(SweepXA{2}; initialstate,time= t,verbose=false,catcherror=true,maxAiter=50,maxΔa=1e-10) +statewrong = solve(SweepX{ 2}; initialstate,time= t,verbose=false,catcherror=true) -Δt = 0.1 -t = Δt:Δt:100*Δt -state0 = solve(SweepX{2}; initialstate,time= t,verbose=true,catcherror=true) -state = solve(SweepXA{2}; initialstate,time= t,verbose=true,catcherror=true,maxAiter=20,maxΔa=1e-10) - -@show state[1].A[1] +A = getdof(state[1];class=:A,field=:ΞC,nodID=[node]) +xfitted = getdof(state;field=:tx1,nodID=[node]) +xwrong = getdof(statewrong;field=:tx1,nodID=[node]) -using GLMakie -fig = Figure(size = (1000,800)) -axeX = Axis(fig[1,1]) -x0 = [s.X[1][1] for s∈state0] -x = [s.X[1][1] for s∈state] -lines!(axeX,t,x,color=:black) -lines!(axeX,t,x0,color=:red) -display(fig) +# # Adjust the damping in the green model to match the red measurements +# using GLMakie +# fig = Figure(size = (1000,800)) +# axeX = Axis(fig[1,1]) +# scatter!(axeX,t[1:20:end],xtarget[1,1:20:end],color=:red) +# lines!( axeX,t,xfitted[1,:],color=:black) +# lines!( axeX,t,xwrong[1,:],color=:lightgreen) +# display(fig) +@testset "StaticX" begin + @test A ≈ [log10(0.4)-log10(0.6)] rtol= 1e-6 + @test xfitted≈xtarget rtol= 1e-5 +end -; -#end \ No newline at end of file +end \ No newline at end of file From 92dff2dacbef0c064bdfe91c36b7f2ef42db7db2 Mon Sep 17 00:00:00 2001 From: Antoine GROSSE Date: Sun, 19 Jul 2026 10:27:37 +0200 Subject: [PATCH 4/9] Updating PR on Trajectory DirectXUA and adding test for DirectXUA201 --- src/DirectXUA.jl | 364 +++++++++++++++++++++------------------ test/TestDirectXUA201.jl | 113 ++++++++++++ test/runtests.jl | 14 +- 3 files changed, 318 insertions(+), 173 deletions(-) create mode 100644 test/TestDirectXUA201.jl diff --git a/src/DirectXUA.jl b/src/DirectXUA.jl index e1ae4e38..0c3927c2 100644 --- a/src/DirectXUA.jl +++ b/src/DirectXUA.jl @@ -15,54 +15,82 @@ const nclass = length(ind) ## Assembly of sparse for a single time step arrnum(α ) = α arrnum(α,β) = nclass + β + nclass*(α-1) -mutable struct AssemblyDirect{OX,OU,IA} <:Assembly + + +mutable struct Wanted{NDΛ,NDX,NDU,NDA} + L1 :: Vector{Vector{𝕓}} # L1[α ][αder ] α∈ λ,x,u,a + L2 :: Matrix{Matrix{𝕓}} # L2[α,β][αder,βder] +end +function wantL1(vectors::Symbol,nder) + vectors==:all || muscadeerror("Invalid vector spec in Wanted") + return [ [true for i=1:nder[α]] for α∈λxua] +end +function wantL1(vectors::Tuple,nder) + L1 = [ [false for i=1:nder[α]] for α∈λxua] + for s ∈ vectors + L1[s[1]][s[2]] = true + end + return L1 +end +function wantL2(matrices::Symbol,nder) + matrices==:all || muscadeerror("Invalid matrix spec Wanted") + return [ [~(α==β==ind.Λ) for i=1:nder[α],j=1:nder[β]] for α∈λxua, β∈λxua] +end +function wantL2(matrices::Tuple,nder) + L2 = [ [false for i=1:nder[α],j=1:nder[β]] for α∈λxua, β∈λxua] + for s ∈ matrices + L2[s[1],s[2]][s[3],s[4]] = true + end + return L2 +end +function Wanted{NDΛ,NDX,NDU,NDA}(vectors::Union{Symbol,Tuple},matrices::Union{Symbol,Tuple}) where{NDΛ,NDX,NDU,NDA} + nder = (NDΛ,NDX,NDU,NDA) + return Wanted{NDΛ,NDX,NDU,NDA}(wantL1(vectors,nder),wantL2(matrices,nder)) +end +mutable struct AssemblyDirect{NDΛ,NDX,OU,NDA} <:Assembly L1 :: Vector{Vector{𝕣1 }} # L1[α ][αder ] α∈ λ,x,u,a L2 :: Matrix{Matrix{Sparse𝕣2}} # L2[α,β][αder,βder] end -function prepare(::Type{AssemblyDirect{OX,OU,IA}},model,dis;Xwhite=false,XUindep=false,UAindep=false,XAindep=false) where{OX,OU,IA} +function prepare(::Type{AssemblyDirect},model,dis,wanted::Wanted{NDΛ,NDX,NDU,NDA}) where{NDΛ,NDX,NDU,NDA} dofgr = (allΛdofs(model,dis),allXdofs(model,dis),allUdofs(model,dis),allAdofs(model,dis)) ndof = getndof.(dofgr) neletyp = getneletyp(model) asm = Matrix{𝕫2}(undef,nclass+nclass^2,neletyp) - nder = (1,OX+1,OU+1,IA) - L1 = Vector{Vector{Vector{𝕣}}}(undef,4) + nder = (NDΛ,NDX,NDU,NDA) + L1 = Vector{Vector{𝕣1}}(undef,4) for α∈λxua nα = nder[α] av = asmvec!(view(asm,arrnum(α),:),dofgr[α],dis) - L1[α] = Vector{Vector{𝕣}}(undef,nα) + L1[α] = Vector{𝕣1}(undef,nα) for αder = 1:nα - L1[α][αder] = copy(av) + if wanted.L1[α][αder] + L1[α][αder] = copy(av) + end end end L2 = Matrix{Matrix{Sparse𝕣2}}(undef,4,4) for α∈λxua, β∈λxua - am = asmmat!(view(asm,arrnum(α,β),:),view(asm,arrnum(α),:),view(asm,arrnum(β),:),ndof[α],ndof[β]) + am = asmmat!(view(asm,arrnum(α,β),:),view(asm,arrnum(α),:),view(asm,arrnum(β),:),ndof[α],ndof[β]) nα,nβ = nder[α], nder[β] - if α==β==ind.Λ nα,nβ=0,0 end # Lλλ is always zero - if Xwhite && α==β==ind.X nα,nβ=1,1 end # X-measurement error is white noise process - if XUindep && α==ind.X && β==ind.U nα,nβ=0,0 end # X-measurements indep of U - if XUindep && α==ind.U && β==ind.X nα,nβ=0,0 end # X-measurements indep of U - if XAindep && α==ind.X && β==ind.A nα,nβ=0,0 end # X-measurements indep of A - if XAindep && α==ind.A && β==ind.X nα,nβ=0,0 end # X-measurements indep of A - if UAindep && α==ind.U && β==ind.A nα,nβ=0,0 end # U-load indep of A - if UAindep && α==ind.A && β==ind.U nα,nβ=0,0 end # U-load indep of A L2[α,β] = Matrix{Sparse𝕣2}(undef,nα,nβ) for αder=1:nα,βder=1:nβ - L2[α,β][αder,βder] = copy(am) + if wanted.L2[α,β][αder,βder] + L2[α,β][αder,βder] = copy(am) + end end end - out = AssemblyDirect{OX,OU,IA}(L1,L2) + out = AssemblyDirect{NDΛ,NDX,NDU,NDA}(L1,L2) return out,asm,dofgr end -function zero!(out::AssemblyDirect) # who calls this??? +function zero!(out::AssemblyDirect) for L1∈out.L1 - for ℓ1∈L1 - zero!(ℓ1) + for i ∈ eachindex(L1) + isassigned(L1,i) && zero!(L1[i]) end end for L2∈out.L2 - for ℓ2∈L2 - zero!(ℓ2) + for i ∈ eachindex(L2) + isassigned(L2,i) && zero!(L2[i]) end end end @@ -71,151 +99,138 @@ function addin!{mission}(out::AssemblyDirect,asm,iele,scale,eleobj::Acost,A::SVe if mission==:matrices P=2 elseif mission==:vectors P=1 end - ∂A = revariate{P}(A) - ø = nothing - C,_ = lagrangian(eleobj,ø,ø,ø,∂A,ø,ø ,dbg) + _,_,∂A = variate{P}(A) +# ø = nothing +# C,_ = getlagrangian(eleobj,ø,ø,ø,∂A,ø,ø ,dbg) + C,_ = getlagrangian(eleobj,∂A,nothing,dbg) ∇ₐC = ∂{P,Na}(C) - add_value!(out.L1[ind.A][1],asm[arrnum(ind.A)],iele,∇ₐC) + isassigned(out.L1[ind.A],1) && add_value!(out.L1[ind.A][1],asm[arrnum(ind.A)],iele,∇ₐC) if mission==:matrices - add_∂!{1}(out.L2[ind.A,ind.A][1,1],asm[arrnum(ind.A,ind.A)],iele,∇ₐC) + isassigned(out.L2[ind.A,ind.A],1,1) && add_∂!{1}(out.L2[ind.A,ind.A][1,1],asm[arrnum(ind.A,ind.A)],iele,∇ₐC) end end -addin!{mission}(out::AssemblyDirect,asm,iele,scale,eleobj::Eleobj,Λ,X,U,A,t,Δt,SP,dbg) where{Eleobj,mission} = +function addin!{mission}(out::AssemblyDirect,asm,iele,scale,eleobj::Eleobj,Λ,X,U,A,t,Δt,SP,dbg) where{Eleobj,mission} addin!{mission}(out::AssemblyDirect,asm,iele,scale,eleobj,no_second_order(Eleobj),Λ,X,U,A,t,Δt,SP,dbg) -function addin!{mission}(out::AssemblyDirect{OX,OU,IA},asm,iele,scale,eleobj::Eleobj,no_second_order::Val{true}, - Λ::NTuple{1 ,SVector{Nx}}, - X::NTuple{NDX,SVector{Nx}}, - U::NTuple{NDU,SVector{Nu}}, - A:: SVector{Na} ,t,Δt,SP,dbg) where{mission,OX,OU,IA,NDX,NDU,Nx,Nu,Na,Eleobj} - @assert NDX==OX+1 @sprintf("got OX=%i and NDX=%i. Expected OX+1==NDX",OX,NDX) - @assert NDU==OU+1 @sprintf("got OU=%i and NDU=%i. Expected OU+1==NDU",OU,NDU) - ndof = (Nx, Nx, Nu, Na) - nder = (1,OX+1,OU+1,IA) +end +function addin!{mission}(out::AssemblyDirect{NDΛ,NDX,NDU,NDA},asm,iele,scale,eleobj::Eleobj,no_second_order::Val{true}, + Λ::NTuple{1 ,SVector{Nx}}, + X::NTuple{NDX_,SVector{Nx}}, + U::NTuple{NDU_,SVector{Nu}}, + A:: SVector{Na} ,t,Δt,SP,dbg) where{mission,NDΛ,NDX,NDU,NDA,NDX_,NDU_,Nx,Nu,Na,Eleobj} if mission==:matrices P=1 elseif mission==:vectors P=0 end - if IA == 1 - ∂X,∂U,∂A = revariate{1}((;X,U,A),(;X=scale.X,U=scale.U,A=scale.A)) - R,FB = residual(eleobj, ∂X,∂U,∂A,t,SP,dbg) + if NDA == 1 + _,_,(∂X,∂U,∂A) = variate{1}((X,U,A),scale=(AllElements(scale.X),AllElements(scale.U),scale.A)) + R,FB = getresidual(eleobj, ∂X,∂U,∂A,t,SP,dbg) else - ∂X,∂U = revariate{1}((;X,U ),(;X=scale.X,U=scale.U)) - R,FB = residual(eleobj, ∂X,∂U, A,t,SP,dbg) + _,_,(∂X,∂U) = variate{1}((X,U ),scale=(AllElements(scale.X),AllElements(scale.U))) + R,FB = getresidual(eleobj, ∂X,∂U, A,t,SP,dbg) end - iλ = 1:ndof[ind.Λ] - Lλ = out.L1[ind.Λ] - add_value!(Lλ[1] ,asm[arrnum(ind.Λ)],iele,R,iλ;Δt) + ndof = (Nx, Nx, Nu, Na) + nder = (NDΛ,NDX,NDU,NDA) + iλ = 1:ndof[ind.Λ] ### TODO CHECK + Lλ = out.L1[ind.Λ] + isassigned(Lλ,1) && add_value!(Lλ[1] ,asm[arrnum(ind.Λ)],iele,R,iλ;Δt) if mission==:matrices pβ = 0 - for β∈xua, j=1:nder[β] + for β∈xua, βder=1:nder[β] iβ = pβ.+(1:ndof[β]) pβ += ndof[β] Lλβ = out.L2[ind.Λ,β] Lβλ = out.L2[β,ind.Λ] - if j≤size(Lλβ,2) # ...but only add into existing matrices of L2, for better sparsity - add_∂!{1 }(Lλβ[1,j],asm[arrnum(ind.Λ,β)],iele,R,iλ,iβ;Δt) - add_∂!{1,:plus,:transpose}(Lβλ[j,1],asm[arrnum(β,ind.Λ)],iele,R,iλ,iβ;Δt) - end + isassigned(Lλβ,1,βder) && add_∂!{1 }(Lλβ[1,βder],asm[arrnum(ind.Λ,β)],iele,R,iλ,iβ;Δt) + isassigned(Lβλ,βder,1) && add_∂!{1,:plus,:transpose}(Lβλ[βder,1],asm[arrnum(β,ind.Λ)],iele,R,iλ,iβ;Δt) end end end -struct DirectXUA_lagrangian_addition!{mission,Nx,Nu,Na,OX,OU,IA} end -function DirectXUA_lagrangian_addition!{mission,Nx,Nu,Na,OX,OU,IA}(out,asm,L,iele,Δt) where{mission,Nx,Nu,Na,OX,OU,IA} +struct DirectXUA_lagrangian_addition!{mission,Nx,Nu,Na,NDΛ,NDX,NDU,NDA} end +function DirectXUA_lagrangian_addition!{mission,Nx,Nu,Na,NDΛ,NDX,NDU,NDA}(out,asm,L,iele,Δt) where{mission,Nx,Nu,Na,NDΛ,NDX,NDU,NDA} if mission==:matrices P=2 elseif mission==:vectors P=1 end ndof = (Nx, Nx, Nu, Na) - nder = (1,OX+1,OU+1,IA) - Np = Nx + Nx*(OX+1) + Nu*(OU+1) + Na*IA # number of partials + nder = (NDΛ,NDX,NDU,NDA) + Np = Nx + Nx*(NDX) + Nu*(NDU) + Na*NDA # number of partials λxua = 1:4 ∇L = ∂{P,Np}(L) pα = 0 # points into the partials, 1 entry before the start of relevant partial derivative in α,ider-loop - for α∈λxua, i=1:nder[α] # we must loop over all time derivatives to correctly point into the adiff-partials... + for α∈λxua, αder=1:nder[α] # we must loop over all time derivatives to correctly point into the adiff-partials... iα = pα.+(1:ndof[α]) pα += ndof[α] Lα = out.L1[α] - if i≤size(Lα,1) # ...but only add into existing vectors of L1, for speed - add_value!(Lα[i] ,asm[arrnum(α)],iele,∇L,iα;Δt) - end + isassigned(Lα,αder) && add_value!(Lα[αder] ,asm[arrnum(α)],iele,∇L,iα;Δt) if mission==:matrices pβ = 0 - for β∈λxua, j=1:nder[β] + for β∈λxua, βder=1:nder[β] iβ = pβ.+(1:ndof[β]) pβ += ndof[β] Lαβ = out.L2[α,β] - if i≤size(Lαβ,1) && j≤size(Lαβ,2) # ...but only add into existing matrices of L2, for better sparsity - add_∂!{1}(Lαβ[i,j],asm[arrnum(α,β)],iele,∇L,iα,iβ;Δt) - end + isassigned(Lαβ,αder,βder) && add_∂!{1}(Lαβ[αder,βder],asm[arrnum(α,β)],iele,∇L,iα,iβ;Δt) end end end end -function addin!{mission}(out::AssemblyDirect{OX,OU,IA},asm,iele,scale,eleobj::Eleobj,no_second_order::Val{false}, - Λ::NTuple{1 ,SVector{Nx}}, - X::NTuple{NDX,SVector{Nx}}, - U::NTuple{NDU,SVector{Nu}}, - A:: SVector{Na} ,t,Δt,SP,dbg) where{mission,OX,OU,IA,NDX,NDU,Nx,Nu,Na,Eleobj} - - @assert NDX==OX+1 @sprintf("got OX=%i and NDX=%i. Expected OX+1==NDX",OX,NDX) - @assert NDU==OU+1 @sprintf("got OU=%i and NDU=%i. Expected OU+1==NDU",OU,NDU) +function addin!{mission}(out::AssemblyDirect{NDΛ,NDX,NDU,NDA},asm,iele,scale,eleobj::Eleobj,no_second_order::Val{false}, + Λ::NTuple{1 ,SVector{Nx}}, + X::NTuple{NDX_,SVector{Nx}}, + U::NTuple{NDU_,SVector{Nu}}, + A:: SVector{Na} ,t,Δt,SP,dbg) where{mission,NDΛ,NDX,NDU,NDA,NDX_,NDU_,Nx,Nu,Na,Eleobj} if mission==:matrices P=2 elseif mission==:vectors P=1 end - if IA == 1 - ∂Λ,∂X,∂U,∂A = revariate{P}((;Λ=Λ[1],X,U,A),(;Λ=scale.Λ,X=scale.X,U=scale.U,A=scale.A)) + if NDA == 1 + _,_,(∂Λ,∂X,∂U,∂A) = variate{P}((Λ[1],X,U,A),scale=(scale.Λ,AllElements(scale.X),AllElements(scale.U),scale.A)) L,FB = getlagrangian(eleobj, ∂Λ,∂X,∂U,∂A,t,SP,dbg) else - ∂Λ,∂X,∂U = revariate{P}((;Λ=Λ[1],X,U),(;Λ=scale.Λ,X=scale.X,U=scale.U)) + _,_,(∂Λ,∂X,∂U) = variate{P}((Λ[1],X,U),scale=(scale.Λ,AllElements(scale.X),AllElements(scale.U))) L,FB = getlagrangian(eleobj, ∂Λ,∂X,∂U,A ,t,SP,dbg) end - DirectXUA_lagrangian_addition!{mission,Nx,Nu,Na,OX,OU,IA}(out,asm,L,iele,Δt) + DirectXUA_lagrangian_addition!{mission,Nx,Nu,Na,NDΛ,NDX,NDU,NDA}(out,asm,L,iele,Δt) end # Specialised to accelerate ElementCost and ElementConstraint -function addin!{mission}(out::AssemblyDirect{OX,OU,IA},asm,iele,scale,eleobj::ElementCost,no_second_order::Val{false}, - Λ::NTuple{1 ,SVector{Nx}}, - X::NTuple{NDX,SVector{Nx}}, - U::NTuple{NDU,SVector{Nu}}, - A:: SVector{Na} ,t,Δt,SP,dbg) where{mission,OX,OU,IA,NDX,NDU,Nx,Nu,Na} +function addin!{mission}(out::AssemblyDirect{NDΛ,NDX,NDU,NDA},asm,iele,scale,eleobj::ElementCost,no_second_order::Val{false}, # TODO can we compact this? + Λ::NTuple{1 ,SVector{Nx}}, + X::NTuple{NDX_,SVector{Nx}}, + U::NTuple{NDU_,SVector{Nu}}, + A:: SVector{Na} ,t,Δt,SP,dbg) where{mission,NDΛ,NDX,NDU,NDA,NDX_,NDU_,Nx,Nu,Na} addin!{mission}(out,asm,iele,scale,eleobj,Val(true),Λ,X,U,A,t,Δt,SP,dbg) end -function addin!{mission}(out::AssemblyDirect{OX,OU,IA},asm,iele,scale,eleobj::ElementCost,no_second_order::Val{true}, - Λ::NTuple{1 ,SVector{Nx}}, - X::NTuple{NDX,SVector{Nx}}, - U::NTuple{NDU,SVector{Nu}}, - A:: SVector{Na} ,t,Δt,SP,dbg) where{mission,OX,OU,IA,NDX,NDU,Nx,Nu,Na} - @assert NDX==OX+1 @sprintf("got OX=%i and NDX=%i. Expected OX+1==NDX",OX,NDX) - @assert NDU==OU+1 @sprintf("got OU=%i and NDU=%i. Expected OU+1==NDU",OU,NDU) +function addin!{mission}(out::AssemblyDirect{NDΛ,NDX,NDU,NDA},asm,iele,scale,eleobj::ElementCost,no_second_order::Val{true}, + Λ::NTuple{1 ,SVector{Nx}}, + X::NTuple{NDX_,SVector{Nx}}, + U::NTuple{NDU_,SVector{Nu}}, + A:: SVector{Na} ,t,Δt,SP,dbg) where{mission,NDΛ,NDX,NDU,NDA,NDX_,NDU_,Nx,Nu,Na} if mission==:matrices P=2 elseif mission==:vectors P=1 end - if IA == 1 # NB: compile-time condition - ∂X,∂U,∂A = revariate{P-1}((;X,U,A),(;X=scale.X,U=scale.U,A=scale.A)) - R,FB,eleres = residual(eleobj.eleobj, ∂X,∂U,∂A,t,SP,(dbg...,via=:ElementCostAccelerator),eleobj.req.eleres) - elseif IA == 0 - ∂X,∂U = revariate{P-1}((;X,U ),(;X=scale.X,U=scale.U)) - R,FB,eleres = residual(eleobj.eleobj, ∂X,∂U, A,t,SP,(dbg...,via=:ElementCostAccelerator),eleobj.req.eleres) + if NDA == 1 # NB: compile-time condition + _,_,(∂X,∂U,∂A) = variate{P-1}((X,U,A),scale=(AllElements(scale.X),Broacast(scale.U),scale.A)) + R,FB,eleres = getresidual(eleobj.eleobj, ∂X,∂U,∂A,t,SP,(dbg...,via=:ElementCostAccelerator),eleobj.req.eleres) + elseif NDA == 0 + _,_,(∂X,∂U) = variate{P-1}((X,U ),scale=(AllElements(scale.X),AllElements(scale.U))) + R,FB,eleres = getresidual(eleobj.eleobj, ∂X,∂U, A,t,SP,(dbg...,via=:ElementCostAccelerator),eleobj.req.eleres) end - Releres = revariate{P}(eleres) + _,_,Releres = variate{P}(eleres) Rcost = eleobj.cost(Releres,t,eleobj.costargs...) - cost = chainrule(Rcost,to_order{P}(eleres)) + cost = chainrule(Rcost,to_order{P,npartial(eleres)}(eleres)) L = Λ[1] ∘₁ R + cost - DirectXUA_lagrangian_addition!{mission,Nx,Nu,Na,OX,OU,IA}(out,asm,L,iele,Δt) + DirectXUA_lagrangian_addition!{mission,Nx,Nu,Na,NDΛ,NDX,NDU,NDA}(out,asm,L,iele,Δt) end -function addin!{mission}(out::AssemblyDirect{OX,OU,IA},asm,iele,scale,eleobj::ElementConstraint,no_second_order::Val{false}, - Λ::NTuple{1 ,SVector{Nx}}, - X::NTuple{NDX,SVector{Nx}}, - U::NTuple{NDU,SVector{Nu}}, - A:: SVector{Na} ,t,Δt,SP,dbg) where{mission,OX,OU,IA,NDX,NDU,Nx,Nu,Na} +function addin!{mission}(out::AssemblyDirect{NDΛ,NDX,NDU,NDA},asm,iele,scale,eleobj::ElementConstraint,no_second_order::Val{false}, + Λ::NTuple{1 ,SVector{Nx}}, + X::NTuple{NDX_,SVector{Nx}}, + U::NTuple{NDU_,SVector{Nu}}, + A:: SVector{Na} ,t,Δt,SP,dbg) where{mission,NDΛ,NDX,NDU,NDA,NDX_,NDU_,Nx,Nu,Na} addin!{mission}(out,asm,iele,scale,eleobj,Val(true),Λ,X,U,A,t,Δt,SP,dbg) end -function addin!{mission}(out::AssemblyDirect{OX,OU,IA},asm,iele,scale,eleobj::ElementConstraint,no_second_order::Val{true}, - Λ::NTuple{1 ,SVector{Nx}}, - X::NTuple{NDX,SVector{Nx}}, - U::NTuple{NDU,SVector{Nu}}, - A:: SVector{Na} ,t,Δt,SP,dbg) where{mission,OX,OU,IA,NDX,NDU,Nx,Nu,Na} +function addin!{mission}(out::AssemblyDirect{NDΛ,NDX,NDU,NDA},asm,iele,scale,eleobj::ElementConstraint,no_second_order::Val{true}, + Λ::NTuple{1 ,SVector{Nx}}, + X::NTuple{NDX_,SVector{Nx}}, + U::NTuple{NDU_,SVector{Nu}}, + A:: SVector{Na} ,t,Δt,SP,dbg) where{mission,NDΛ,NDX,NDU,NDA,NDX_,NDU_,Nx,Nu,Na} # TODO Specialised code to accelerate constraints in DirectXUA, but... it does not set FB, and DIrectXUA/solve has no line search... - @assert NDX==OX+1 @sprintf("got OX=%i and NDX=%i. Expected OX+1==NDX",OX,NDX) - @assert NDU==OU+1 @sprintf("got OU=%i and NDU=%i. Expected OU+1==NDU",OU,NDU) if mission==:matrices P=2 elseif mission==:vectors P=1 end @@ -223,26 +238,26 @@ function addin!{mission}(out::AssemblyDirect{OX,OU,IA},asm,iele,scale,eleobj::El λ = ∂0(U)[Nu] γ = default{:γ}(SP,0.) m = eleobj.mode(t) - if IA == 1 # NB: compile-time condition - ∂X,∂U,∂A = revariate{P-1}((X=X,U=U,A=A),(;X=scale.X,U=scale.U,A=scale.A)) - R,FB,eleres = residual(eleobj.eleobj, ∂X,∂U,∂A,t,SP,(dbg...,via=:ElementCoonstraintAccelerator),eleobj.req) - elseif IA == 0 - ∂X,∂U = revariate{P-1}((X=X,U=U ),(;X=scale.X,U=scale.U)) - R,FB,eleres = residual(eleobj.eleobj, ∂X,∂U, A,t,SP,(dbg...,via=:ElementConstraintAccelerator),eleobj.req) + if NDA == 1 # NB: compile-time condition + _,_,(∂X,∂U,∂A) = variate{P-1}((X,U,A),scale=(AllElements(scale.X),AllElements(scale.U),scale.A)) + R,FB,eleres = getresidual(eleobj.eleobj, ∂X,∂U,∂A,t,SP,(dbg...,via=:ElementCoonstraintAccelerator),eleobj.req) + elseif NDA == 0 + _,_,(∂X,∂U) = variate{P-1}((X,U ),scale=(AllElements(scale.X),AllElements(scale.U))) + R,FB,eleres = getresidual(eleobj.eleobj, ∂X,∂U, A,t,SP,(dbg...,via=:ElementConstraintAccelerator),eleobj.req) end - Releres = revariate{P}(eleres) + _,_,Releres = variate{P}(eleres) Rgap = eleobj.gap(eleres,t,eleobj.gargs...) - gap = chainrule(Rgap,to_order{P}(eleres)) + gap = chainrule(Rgap,to_order{P,npartial(eleres)}(eleres)) L = Λ[1] ∘₁ R + if m==:equal; -gap*λ elseif m==:positive; -KKT(λ,gap,γ) elseif m==:off; -0.5λ^2 end - DirectXUA_lagrangian_addition!{mission,Nx,Nu,Na,OX,OU,IA}(out,asm,L,iele,Δt) + DirectXUA_lagrangian_addition!{mission,Nx,Nu,Na,NDΛ,NDX,NDU,NDA}(out,asm,L,iele,Δt) end ## Assembly of bigsparse for all time steps at once -function makepattern(IA,nstep,out) +function makepattern(NDA,nstep,out) # Looking at all steps, class, order of fdiff and Δstep, for rows and columns: which blocks are actualy nz? # return a sparse matrix of sparse matrices maxblock = 1 + sum(nstep)*90 @@ -250,7 +265,7 @@ function makepattern(IA,nstep,out) βblk = 𝕫1(undef,maxblock) nz = Vector{Sparse𝕣2}(undef,maxblock) nblock = 0 - cumblk = 0 + cumblk = 0 for iexp = 1:length(nstep) for istep = 1:nstep[iexp] for α∈λxu @@ -258,12 +273,14 @@ function makepattern(IA,nstep,out) Lαβ = out.L2[α,β] for αder = 1:size(Lαβ,1) for βder = 1:size(Lαβ,2) - for iα ∈ finitediff(αder-1,nstep[iexp],istep) - for iβ ∈ finitediff(βder-1,nstep[iexp],istep) - nblock += 1 - αblk[nblock]=cumblk+3*(istep+iα.Δs-1)+α - βblk[nblock]=cumblk+3*(istep+iβ.Δs-1)+β - nz[ nblock]=Lαβ[1,1] + if isassigned(Lαβ,αder,βder) + for iα ∈ finitediff(αder-1,nstep[iexp],istep) + for iβ ∈ finitediff(βder-1,nstep[iexp],istep) + nblock += 1 + αblk[nblock]=cumblk+3*(istep+iα.Δs-1)+α + βblk[nblock]=cumblk+3*(istep+iβ.Δs-1)+β + nz[ nblock]=Lαβ[1,1] + end end end end @@ -274,7 +291,7 @@ function makepattern(IA,nstep,out) cumblk += 3*nstep[iexp] end - if IA==1 + if NDA==1 Ablk = 3*sum(nstep)+1 nblock +=1 αblk[nblock] = Ablk @@ -286,7 +303,8 @@ function makepattern(IA,nstep,out) for α∈λxu # loop over derivatives and finitediff is optimized out, as time derivatives will only # be added into superbloc already reached by non-derivatives. No, it's not a bug... - if size(out.L2[ind.A,α],1)>0 + Laα = out.L2[ind.A,α] + if size(Laα,1)>0 && isassigned(Laα,1) nblock += 1 αblk[nblock] = Ablk βblk[nblock] = cumblk+3*(istep-1)+α @@ -303,28 +321,29 @@ function makepattern(IA,nstep,out) end u = unique(i->(αblk[i],βblk[i]),1:nblock) - return sparse(αblk[u],βblk[u],nz[u]) + return sparse(αblk[u],βblk[u],nz[u]) end -function preparebig(IA,nstep,out) +function preparebig(NDA,nstep,out) # create an assembler and allocate for the big linear system - pattern = makepattern(IA,nstep,out) + pattern = makepattern(NDA,nstep,out) # Muscade.spypattern(pattern) Lvv,Lvvasm,Lvasm,Lvdis = prepare(pattern) Lv = 𝕣1(undef,size(Lvv,1)) return Lvv,Lv,Lvvasm,Lvasm,Lvdis end struct assemblebig!{mission} end -function assemblebig!{mission}(Lvv,Lv,Lvvasm,Lvasm,asm,model,dis,out::AssemblyDirect{OX,OU,IA},state,nstep,Δt,SP,dbg) where{mission,OX,OU,IA} +function assemblebig!{mission}(Lvv,Lv,Lvvasm,Lvasm,asm,model,dis,out::AssemblyDirect{NDΛ,NDX,NDU,NDA},state,nstep,Δt,SP,dbg) where{mission,NDΛ,NDX,NDU,NDA} zero!(Lvv) zero!(Lv ) cumblk = 0 - if IA==1 + if NDA==1 Ablk = 3sum(nstep)+1 assembleA!{mission}(out,asm,dis,model,state[1][1],(dbg...,asm=:assemblebig!)) - addin!(Lvasm ,Lv ,out.L1[ind.A ][1 ],Ablk ) - addin!(Lvvasm,Lvv,out.L2[ind.A,ind.A][1,1],Ablk,Ablk) + La, Laa = out.L1[ind.A], out.L2[ind.A,ind.A] + isassigned(La ,1 ) && addin!(Lvasm ,Lv ,out.L1[ind.A ][1 ],Ablk ) + isassigned(Laa,1,1) && addin!(Lvvasm,Lvv,out.L2[ind.A,ind.A][1,1],Ablk,Ablk) end - class = IA==1 ? λxua : λxu + class = NDA==1 ? λxua : λxu for iexp = 1:length(nstep) for istep = 1:nstep[iexp] state[iexp][istep].SP = SP @@ -332,21 +351,25 @@ function assemblebig!{mission}(Lvv,Lv,Lvvasm,Lvasm,asm,model,dis,out::AssemblyDi for β∈class Lβ = out.L1[β] for βder = 1:size(Lβ,1) - s = Δt[iexp]^(1-βder) - for iβ ∈ finitediff(βder-1,nstep[iexp],istep) # TODO transpose or not? Potential BUG to be revealed when cost on time derivative of X or U - βblk = β==ind.A ? Ablk : cumblk+3*(istep+iβ.Δs-1)+β - addin!(Lvasm,Lv ,Lβ[βder],βblk,iβ.w*s) + if isassigned(Lβ,βder) + s = Δt[iexp]^(1-βder) + for iβ ∈ finitediff(βder-1,nstep[iexp],istep) # TODO transpose or not? Potential BUG to be revealed when cost on time derivative of X or U + βblk = β==ind.A ? Ablk : cumblk+3*(istep+iβ.Δs-1)+β + addin!(Lvasm,Lv ,Lβ[βder],βblk,iβ.w*s) + end end end end for α∈class, β∈class Lαβ = out.L2[α,β] for αder=1:size(Lαβ,1), βder=1:size(Lαβ,2) - s = Δt[iexp]^(2-αder-βder) - for iα∈finitediff(αder-1,nstep[iexp],istep), iβ∈finitediff(βder-1,nstep[iexp],istep) # No transposition here, that's thoroughly checked against decay. - αblk = α==ind.A ? Ablk : cumblk+3*(istep+iα.Δs-1)+α - βblk = β==ind.A ? Ablk : cumblk+3*(istep+iβ.Δs-1)+β - addin!(Lvvasm,Lvv,Lαβ[αder,βder],αblk,βblk,iα.w*iβ.w*s) + if isassigned(Lαβ,αder,βder) + s = Δt[iexp]^(2-αder-βder) + for iα∈finitediff(αder-1,nstep[iexp],istep), iβ∈finitediff(βder-1,nstep[iexp],istep) # No transposition here, that's thoroughly checked against decay. + αblk = α==ind.A ? Ablk : cumblk+3*(istep+iα.Δs-1)+α + βblk = β==ind.A ? Ablk : cumblk+3*(istep+iβ.Δs-1)+β + addin!(Lvvasm,Lvv,Lαβ[αder,βder],αblk,βblk,iα.w*iβ.w*s) + end end end end @@ -375,7 +398,7 @@ function decrementbig!(state,Δ²,Lvasm,dofgr,Δv,nder,Δt,nstep) end cumblk += 3*nstep[iexp] end - if nder[4]==1 # IA==1 + if nder[4]==1 # NDA==1 Δa = disblock(Lvasm,Δv,3*sum(nstep)+1) Δ²[ind.A] = sum(Δa.^2) decrement!(state[1][1],1,Δa,dofgr[ind.A]) # all states share same A, so decrement only once @@ -409,15 +432,12 @@ The solver does not yet support interior point methods. # Named arguments - `dbg=(;)` a named tuple to trace the call tree (for debugging). - `verbose=true` set to false to suppress printed output (for testing). -- `silenterror=false` set to true to suppress print out of error (for testing) . -- `initialstate` an `AbstractVector` of `State`: one initial state for each experiment. - `initialstate` must be with zero time derivatives. It does not - provide initial conditions for the problem, but an initial guess - for the iterative solver. -- `initialtrajectory` an `AbstractVector` of Vector{`State`}: one initial trajectory for each experiment. - `initialtrajectory` elements are also initial guess for the iterative solver, representing a time-dependant trajectory. - its elements must then match the specific timerange respective to the experiment they refer to. - If not specified, initialstate is copied for each timestep to create the initial guess. +- `silenterror=false` set to true to suppress print out of error (for testing). +- `initialstate` an `AbstractVector` of `State` or an `AbstractVector` of `Vector{State}`: one primer for each experiment. + `initialstate` must be with zero time derivatives. It does not provide initial conditions for the problem, + but an initial guess for the iterative solver. The solver needs a time-dependant trajectory as input: `initialstate` + either directly provides it with a `Vector{State}`, or allows the creation of it by copying the same `State` for every time step. + By convention the Adofs for building this primer are taken from the first experiment, first state. - `time` an `AbstractVector` (of same length as `initialstate`) of `AbstractRange` of times at which to compute the steps. Example: 0:0.1:5. - `maxiter=50` maximum number of Newton-Raphson iterations. @@ -444,42 +464,48 @@ See also: [`solve`](@ref), [`initialize!`](@ref), [`SweepX`](@ref), [`FreqXU`](@ struct DirectXUA{OX,OU,IA} <: AbstractSolver end function solve(::Type{DirectXUA{OX,OU,IA}},pstate,verbose::𝕓,dbg; time::AbstractVector{AR}, - initialstate::AbstractVector{STATE}, - initialtrajectory::Union{Nothing,AbstractVector}=nothing, + # TODO HAVE A SIMPLER ONLY ONE VARIABLE + # TODO BY CONVENTION WE USE THE Ainit THAT IS THE FIRST EXP and FIRST STATE + initialstate::Union{Nothing,AbstractVector}, maxiter::ℤ=50, maxΔλ::ℝ=1e-5,maxΔx::ℝ=1e-5,maxΔu::ℝ=1e-5,maxΔa::ℝ=1e-5, saveiter::𝔹=false, - kwargs...) where{OX,OU,IA,AR<:AbstractRange{𝕣},STATE<:State} + wanted::Wanted=Wanted{1,OX+1,OU+1,IA}(:all,:all)) where{OX,OU,IA,AR<:AbstractRange{𝕣},STATE<:State} # Mostly constants local LU nexp,nstep,Δt = length(time),length.(time),step.(time) - length(initialstate)== nexp || muscadeerror("initialstate and time must be of the same length=number of experiments") γ = 0. nder = (1,OX+1,OU+1,IA) - model,dis = initialstate[1].model, initialstate[1].dis if IA==1 Δ², maxΔ² = 𝕣1(undef,4), [maxΔλ^2,maxΔx^2,maxΔu^2,maxΔa^2] else Δ², maxΔ² = 𝕣1(undef,3), [maxΔλ^2,maxΔx^2,maxΔu^2 ] end - + # State storage S = State{1,OX+1,OU+1,@NamedTuple{γ::Float64,iter::Int64}} state = [Vector{S}(undef,nstep[iexp]) for iexp=1:nexp] # state[iexp][istep] s = initialstate[1] - if isnothing(initialtrajectory) + + # Test input dimension compatibility + length(initialstate)== nexp || muscadeerror("initialstate length must be equal to the number of experiments") + + if isa(initialstate[1],Muscade.State) + model,dis = initialstate[1].model, initialstate[1].dis + # Case where initialstate is an AbstractVector of State. A primer trajectory of state is created from a repetition of this state. for (iexp,initialstateᵢ) ∈ enumerate(initialstate) for (istep,timeᵢ) = enumerate(time[iexp]) - state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(initialstateᵢ.Λ),deepcopy(initialstateᵢ.X),deepcopy(initialstateᵢ.U),s.A,(γ=0.,iter=1),s.model,s.dis) # all state[iexp][istep].A are === + state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(initialstateᵢ.Λ),deepcopy(initialstateᵢ.X),deepcopy(initialstateᵢ.U),s.A,(γ=0.,iter=1),model,dis) # all state[iexp][istep].A are === end end else - length(initialtrajectory)== nexp || muscadeerror("initialtrajectory and time must be of the same length") - Ashared = initialtrajectory[1][1].A - for (iexp,trajexp) ∈ enumerate(initialtrajectory) - length(trajexp)== nstep[iexp] || muscadeerror("initialtrajectory must match the time grid") + # Case where initialstate is already an AbstractVector of Vector{State}. + Ainit = initialstate[1][1].A + model,dis = initialstate[1][1].model, initialstate[1][1].dis + for (iexp,trajexp) ∈ enumerate(initialstate) + length(trajexp)== nstep[iexp] || muscadeerror("trajectories in `initialstate` vector must match their associated time grid in `time` vector") for (istep,timeᵢ) = enumerate(time[iexp]) trajstate = trajexp[istep] - state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(trajstate.Λ),deepcopy(trajstate.X),deepcopy(trajstate.U),Ashared,(γ=0.,iter=1),s.model,s.dis) + state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(trajstate.Λ),deepcopy(trajstate.X),deepcopy(trajstate.U),Ainit,(γ=0.,iter=1),model,dis) end end end @@ -492,7 +518,7 @@ function solve(::Type{DirectXUA{OX,OU,IA}},pstate,verbose::𝕓,dbg; # Prepare assembler verbose && @printf("\n Preparing assembler\n") - out,asm,dofgr = prepare(AssemblyDirect{OX,OU,IA},model,dis;kwargs...) # mem and assembler for system at any given step + out,asm,dofgr = prepare(AssemblyDirect,model,dis,wanted) # mem and assembler for system at any given step assemble!{:matrices}(out,asm,dis,model,state[1][1],idmult,(dbg...,solver=:DirectXUA,phase=:sparsity)) # create a sample "out" for preparebig Lvv,Lv,Lvvasm,Lvasm,Lvdis = preparebig(IA,nstep,out) # mem and assembler for big system cLvv = copy(Lvv) @@ -529,6 +555,4 @@ function solve(::Type{DirectXUA{OX,OU,IA}},pstate,verbose::𝕓,dbg; iter Date: Sun, 19 Jul 2026 10:44:44 +0200 Subject: [PATCH 5/9] Tests run for pre-merge --- .github/workflows/ci.yml | 2 +- Project.toml | 2 +- docs/make.jl | 2 +- docs/src/Adiff.md | 420 ++- docs/src/BeamElement.jl | 427 +++ docs/src/DecayAnalysis.md | 281 ++ docs/src/DryFriction.md | 89 + docs/src/DynamicBeamAnalysis.md | 246 ++ docs/src/Elements.md | 93 +- docs/src/LICENSE.md | 21 + docs/src/ModalBeamAnalysis.md | 106 + docs/src/Rotations.jl | 126 + docs/src/SCR.csv | 3001 +++++++++++++++++ docs/src/Solvers.md | 12 +- docs/src/StaticBeamAnalysis.md | 218 ++ docs/src/Theory.md | 2 +- docs/src/TuningFork.md | 256 ++ docs/src/assets/StaticBeamAnalysis1.png | Bin 229540 -> 153115 bytes docs/src/assets/StaticBeamAnalysis2.png | Bin 217287 -> 175354 bytes docs/src/assets/StaticBeamAnalysis3.png | Bin 116850 -> 93633 bytes docs/src/assets/TuningFork.png | Bin 0 -> 265154 bytes docs/src/assets/beamModes.png | Bin 864661 -> 550794 bytes docs/src/assets/decay.png | Bin 553286 -> 376987 bytes docs/src/assets/dynamicAnalysisSCR.png | Bin 275455 -> 327932 bytes docs/src/assets/staticEquilibriumSCR.png | Bin 175792 -> 240648 bytes docs/src/internals.md | 4 +- examples/DecayAnalysis.jl | 6 +- examples/DynamicBeamAnalysis.jl | 5 +- examples/ModalBeamAnalysis.jl | 10 +- examples/StaticBeamAnalysis1.png | Bin 0 -> 137371 bytes examples/StaticBeamAnalysis2.png | Bin 0 -> 167379 bytes examples/StaticBeamAnalysis3.png | Bin 0 -> 89253 bytes examples/TuningFork.jl | 165 + examples/TuningFork.png | Bin 0 -> 265154 bytes examples/beamModes.png | Bin 0 -> 550794 bytes examples/decay.png | Bin 0 -> 378365 bytes examples/dynamicAnalysisSCR.png | Bin 0 -> 327932 bytes examples/staticEquilibriumSCR.png | Bin 0 -> 240648 bytes {examples => inspect}/FollowerPointLoad.jl | 6 +- inspect/PerformanceEulerBeam3D.jl | 2 +- .../PerformanceEulerBeam3D_diffed_residual.jl | 26 +- inspect/Performance_McLaurin.jl | 39 + inspect/adiffs.jl | 60 + src/Adiff.jl | 372 +- src/Assemble.jl | 184 +- src/BasicElements.jl | 5 +- src/Diagnostic.jl | 8 +- src/Dialect.jl | 16 + src/Dots.jl | 2 + src/EigX.jl | 73 +- src/EigXU.jl | 56 +- src/Espy.jl | 1 + src/FreqXU.jl | 4 +- src/Functors.jl | 15 +- src/ModelDescription.jl | 8 + src/Muscade.jl | 8 +- src/SweepX.jl | 57 +- src/SweepXA.jl | 263 +- src/Taylor.jl | 443 ++- test/SomeElements.jl | 2 +- test/TestAdiff.jl | 41 +- test/TestBarElement.jl | 5 +- test/TestBeamElement.jl | 2 +- test/TestBeamElementStrainGauge.jl | 4 +- test/TestDirectXUA.jl | 17 +- test/TestDirectXUA001.jl | 5 +- test/TestDofConstraints.jl | 12 +- test/TestDrawBeamElement.jl | 10 +- test/TestEigX.jl | 32 +- test/TestEigXU.jl | 28 +- test/TestElementCost.jl | 4 +- test/TestFreqXU.jl | 2 +- test/TestNewmarkSweep.jl | 16 +- test/TestRigidBodyKinematics.jl | 56 + test/TestRotations.jl | 24 +- test/TestScale.jl | 8 +- test/TestSweepXA0.jl | 43 - test/TestTaylor.jl | 230 +- test/run_CI_tests.jl | 1 + toolbox/BarElement.jl | 41 +- toolbox/BeamElement.jl | 29 +- toolbox/PositionElement.jl | 5 +- toolbox/RigidBodyKinematics.jl | 6 +- toolbox/Rotations.jl | 120 +- 84 files changed, 6913 insertions(+), 972 deletions(-) create mode 100644 docs/src/BeamElement.jl create mode 100644 docs/src/DecayAnalysis.md create mode 100644 docs/src/DryFriction.md create mode 100644 docs/src/DynamicBeamAnalysis.md create mode 100644 docs/src/LICENSE.md create mode 100644 docs/src/ModalBeamAnalysis.md create mode 100644 docs/src/Rotations.jl create mode 100644 docs/src/SCR.csv create mode 100644 docs/src/StaticBeamAnalysis.md create mode 100644 docs/src/TuningFork.md create mode 100644 docs/src/assets/TuningFork.png create mode 100644 examples/StaticBeamAnalysis1.png create mode 100644 examples/StaticBeamAnalysis2.png create mode 100644 examples/StaticBeamAnalysis3.png create mode 100644 examples/TuningFork.jl create mode 100644 examples/TuningFork.png create mode 100644 examples/beamModes.png create mode 100644 examples/decay.png create mode 100644 examples/dynamicAnalysisSCR.png create mode 100644 examples/staticEquilibriumSCR.png rename {examples => inspect}/FollowerPointLoad.jl (97%) create mode 100644 inspect/Performance_McLaurin.jl create mode 100644 inspect/adiffs.jl create mode 100644 test/TestRigidBodyKinematics.jl delete mode 100644 test/TestSweepXA0.jl diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index 1a65eaf7..1aac0407 100644 --- a/.github/workflows/ci.yml +++ b/.github/workflows/ci.yml @@ -1,4 +1,4 @@ -name: Running tests on all platforms +name: Running tests on Linux on: push: branches: diff --git a/Project.toml b/Project.toml index e91342e2..4b6b3cf9 100644 --- a/Project.toml +++ b/Project.toml @@ -20,5 +20,5 @@ SparseArrays = "1" SpecialFunctions = "2" StaticArrays = "1" GLMakie = "0.13" -KrylovKit = "0.9" +KrylovKit = "0.10" julia = "1.11" diff --git a/docs/make.jl b/docs/make.jl index eec621a7..750266d9 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -4,7 +4,7 @@ docs = @__DIR__ muscade = normpath(joinpath(docs,"..")) docsrc = joinpath(docs,"src") examplesrc(ex) = normpath(joinpath(docs,"..","examples",ex)) -examples = ["StaticBeamAnalysis","ModalBeamAnalysis","DynamicBeamAnalysis","DecayAnalysis","DryFriction"] +examples = ["StaticBeamAnalysis","ModalBeamAnalysis","DynamicBeamAnalysis","DecayAnalysis","TuningFork","DryFriction"] requiredIncludeFiles = ["toolbox" "BeamElement.jl"; "toolbox" "Rotations.jl"; diff --git a/docs/src/Adiff.md b/docs/src/Adiff.md index 37379e63..fbc4c7a7 100644 --- a/docs/src/Adiff.md +++ b/docs/src/Adiff.md @@ -1,54 +1,404 @@ -# Automatic differentiation -## History +# [Automatic differentiation](@id adiff_appendix) -`Muscade` has its own implementation of forward automatic differentiation for historical reasons: Prototypes automatic differentiation of `Muscade` where developed in parallel with [`ForwardDiff.jl`](https://juliadiff.org/ForwardDiff.jl/stable/). While the inner workings of [`ForwardDiff.jl`](https://juliadiff.org/ForwardDiff.jl/stable/) and `Muscade`'s version are similar ( with `ForwardDiff.jl` probably having better performance), the API are quite different. +## Introduction +This section aims to provide an understanding of a variety of useful techniques in automatic differentiation. In `Muscade`, element-developers generaly need not concern themselves with automatic differentiation, except on two points: -`Muscade` evaluates second derivative of the Lagrangian, using nested *forward* differentiation, which is far from optimal. An ambition is to make use of reverse differentiation (using [`Zygote.jl`](https://fluxml.ai/Zygote.jl/latest/), [`Enzyme.jl`](https://docs.sciml.ai/Enzyme/stable/) or similar). +First, do not specify the type of inputs `Λ`, `X`, `U`, `A` and `t` to `Muscade.residual` and `Muscade.lagrangian`. For example -## Usage +```julia +@espy function Muscade.lagrangian(o::MyElement,Λ::Vector{𝕣},X,U,A,t,SP,dbg) +# |bad_idea| +``` + +(where `𝕣` is a `Muscade` alias for `Float64`) would cause a `MethodError`, because `Muscade` will attempt to call `lagrangian` with a `SVector{L,∂ℝ...}`, and the method only accepts a `Vector{𝕣}`. + +Second, beware of branches (`if` and `cond ? opt1 : opt2`). In the following code + +```julia +if x>0 + y=x # y is of type ∂ℝ +else + y=0. # y is of type 𝕣 +end +``` + +the type of `y` depends on the *value* of `x` and thus cannot be determined at compilation. This is [type instability](TypeStable.md) and results in *very* slow execution. + +However, for advanced element implementation, `residual` or `lagrangian` may themselves use automatic differentiation, and the following provides the necesary guidance. + +!!! warning + Read and understand the section on "perturbation confusion" before using any of the techniques described below. + +`Muscade` has its own implementation of forward automatic differentiation for historical reasons: `Muscade`'s developers started dabling in automatic differentiation while [`ForwardDiff.jl`](https://juliadiff.org/ForwardDiff.jl/stable/) was still very much in the works. + +The inner workings of [`ForwardDiff.jl`](https://juliadiff.org/ForwardDiff.jl/stable/) and `Muscade`'s version are very similar. The APIs, on the other hand, are quite different: [`ForwardDiff.jl`](https://juliadiff.org/ForwardDiff.jl/stable/) is designed for safety, `Muscade`'s automatic differentiation for flexibility. When using the techniques described in the following, it is possible to introduce some confusing bugs if one is not quite careful. `Muscade` also offers some innovative differentiation functionality (see the Section on chain rule). + +## Type definition + +`Muscade`'s data-type for automatic differentiation, `∂ℝ`, is defined as + +```julia +struct ∂ℝ{P,N,R} <:ℝ where{R<:ℝ} + x :: R # value + dx :: SVector{N,R} # partials +end +``` + +where `ℝ` is a `Muscade` alias for `Real`. The type parameters of `∂ℝ` is + +- `P` is the *precedence*, or order of differentiation (more on this later). +- `N` is the number of partial derivatives. +- `R` is the underlying datatype (either `𝕣`, or another `∂ℝ` when computing higher order derivatives). + +A variable `v` of precedence 1 is printed as `∂₁⟨v.x|v.dx⟩`, for example `∂₁⟨1.23|0,0.6,1.2⟩` (here with three partials). + +This structure is nested to represent higher derivatives, so `R` can itself be a `∂ℝ`. The rule is that in any `∂ℝ{P,N,R}`, we must have `P==1+predence(R)`, where the precedence of `𝕣` is 0. A variable `v` of precedence 2 is printed as `∂₂⟨∂₁⟨v.x.x|v.x.dx⟩|∂₁⟨x.dxᵢ.x|x.dxᵢ.dx⟩ ∀i⟩`. For example, + +```julia +v = SVector(2.,3.); +P,N,x2=variate{2}(v); +v2 +``` + +(`variate` will be discussed in the following) gives + +```julia +2-element SVector{2, Muscade.∂ℝ{2, 2, Muscade.∂ℝ{1, 2, Float64}}} with indices SOneTo(2): + ∂₂⟨∂₁⟨2|1,0⟩|∂₁⟨1|0,0⟩,∂₁⟨0|0,0⟩⟩ + ∂₂⟨∂₁⟨3|0,1⟩|∂₁⟨0|0,0⟩,∂₁⟨1|0,0⟩⟩ +``` + +In the following, the informal notations `∂₂⟨∂₁⟨v.x.x|v.x.dx⟩|∂₁⟨v.dx.x|v.dx.dx⟩⟩` or `∂₂⟨∂₁⟨v|vₓ⟩|∂₁⟨vₓ|vₓₓ⟩⟩` may be used. Both notations gloss over the fact that `dx` is a vector, but they provide a useful mental picture for when unpacking such variables. These notations are not executable: they can not be used to create a `∂ℝ` variable. + +## Gradient evaluation + +Gradient evaluation is the simplest form for automatic differentiation. + +```julia +using StaticArrays +using Muscade: variate,value,∂ + +f(x) = x.*x .+ sum(x) +x = SVector(1.,2.,3.) +P,N,x1 = variate(x) # P==1,N=length(x) +y1 = f(x1) +y = value{P}(y1) +yₓ = ∂{P,N}(y1) +``` + +[`Muscade.variate`](@ref) here builds a `SVector` of `∂ℝ{P,N,R}`, where `R == eltype(x) == 𝕣`, `P == Muscade.precedence(x)+1 == 1` (the precedence of an `𝕣` is 0) and `N == 3` is the length of `x`. +. `Muscade` developers speak of `x1` being the "variated" form of `x`". The partials are "seeded", so that `∂{P,N}(x1)[i]` is a `SVector{N}` of `zero(R)`, except for the `i`-th term that is `one(R)`. + +```julia +julia> x1 +3-element SVector{3, Muscade.∂ℝ{1, 3, Float64}} with indices SOneTo(3): + ∂₁⟨1|1,0,0⟩ + ∂₁⟨2|0,1,0⟩ + ∂₁⟨3|0,0,1⟩ +``` + +Here we can note the identify matrix that appears: the Jacobian of the vector `x` with respect to itself. + +```julia +julia> y1 +3-element SVector{3, Muscade.∂ℝ{1, 3, Float64}} with indices SOneTo(3): + ∂₁⟨ 7|3,1,1⟩ + ∂₁⟨10|1,5,1⟩ + ∂₁⟨15|1,1,7⟩ +``` + +[`value`](@ref)`{P}(y1)`, where `y1` is a `StaticArray{S,∂{P,N,R}}`, retrieves the value `y`, of type `StaticArray{S,R}`. + +[`∂`](@ref)`{P,N}(y1)`, where `y1` is a `StaticArray{S,∂{P,N,R}}`, retrieves the gradient `yₓ`, of type `StaticArray{Syₓ,R}`. `size(yₓ) = (size(y)...,N)` +where the last index refers to the partial derivatives with respect to the `SVector` `x`. + +```julia +julia> y +3-element SVector{3, Float64} with indices SOneTo(3): + 7.0 + 10.0 + 15.0 + +julia> yₓ +3×3 SMatrix{3, 3, Float64, 9} with indices SOneTo(3)×SOneTo(3): + 3.0 1.0 1.0 + 1.0 5.0 1.0 + 1.0 1.0 7.0 +``` + +## Joint derivatives + +Joint derivatives are partial derivatives with respect to several variables, computed at the same time. An example of the technique is + +```julia +using StaticArrays +using Muscade: variate,variate_indices,value,∂,δ + +res(x,u) = x.*x .+ sum(u) # SVector-valued +x = SVector(1.,2.) +u = SVector(3.,4.,5.) +P,N,(x1,u1) = variate((x,u)) # note the parentheses +(ix,iu) = variate_indices((x,u)) +r1 = res(x1,u1) +r = value{P}(r1) +rₓ = ∂{P,N}(r1)[:,ix] # the last index refers to +rᵤ = ∂{P,N}(r1)[:,iu] # the partial derivatives +``` + +yields + +```julia +julia> x1 +2-element SVector{2, Muscade.∂ℝ{1, 5, Float64}} with indices SOneTo(2): + ∂₁⟨1|1,0,0,0,0⟩ + ∂₁⟨2|0,1,0,0,0⟩ + +julia> u1 +3-element SVector{3, Muscade.∂ℝ{1, 5, Float64}} with indices SOneTo(3): + ∂₁⟨3|0,0,1,0,0⟩ + ∂₁⟨4|0,0,0,1,0⟩ + ∂₁⟨5|0,0,0,0,1⟩ + +julia> rₓ +2×2 SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2): + 2.0 0.0 + 0.0 4.0 + +julia> rᵤ +2×3 SMatrix{2, 3, Float64, 6} with indices SOneTo(2)×SOneTo(3): + 1.0 1.0 1.0 + 1.0 1.0 1.0 +``` + +## Directional derivatives + +Derivatives with respect to a given linear combination `dir` of the input to a function or expression, can be computed as follows + +```julia +using StaticArrays +using Muscade: value,∂,variate0 -`Muscade`s automatic differentiation is used as follows: +f(x) = x.*x .+ sum(x) +x = SVector(1.,2.,3.) +dir = SVector(1.,0.,2.) +P,N,δs = variate0(0.)[1] +x1 = x + dir*δs +y1 = f(x1) +y = value{P}(y1) +yₓ = ∂{P,N}(y1) +``` + +giving + +```julia +julia> δs + ∂₁⟨0|1⟩ + +julia> x1 +3-element SVector{3, Muscade.∂ℝ{1, 1, Float64}} with indices SOneTo(3): + ∂₁⟨1|1⟩ + ∂₁⟨2|0⟩ + ∂₁⟨3|2⟩ +``` + +## Higher order derivatives + +Higher order derivatives are obtained by using `variate{O}(...)` where `O` (defaulting to 1, as seen in previous examples) is the order of differentiation. + +```julia +using StaticArrays +using Muscade: variate,value,∂ + +lag(x,u) = x[1]*x[1]+u[2]*u[3]+x[2]*u[3] +x = SVector(1.,2.) +u = SVector(3.,4.,5.) +P,N,x2 = variate{2}(x) +ℓ2 = lag(x2,u) +ℓ = value{P-1}(value{P}(ℓ2)) +ℓₓ = ∂{P-1,N }(value{P}(ℓ2)) +ℓₓ = value{P-1}(∂{P,N }(ℓ2)) +ℓₓₓ = ∂{P-1,N }(∂{P,N }(ℓ2)) +``` + +produces + +```julia +julia> x2 +2-element SVector{2, Muscade.∂ℝ{2, 2, Muscade.∂ℝ{1, 2, Float64}}} with indices SOneTo(2): + ∂₂⟨∂₁⟨1|1,0⟩|∂₁⟨1|0,0⟩,∂₁⟨0|0,0⟩⟩ + ∂₂⟨∂₁⟨2|0,1⟩|∂₁⟨0|0,0⟩,∂₁⟨1|0,0⟩⟩ + +julia> ℓ2 +∂₂⟨∂₁⟨31|2,5⟩|∂₁⟨2|2,0⟩,∂₁⟨5|0,0⟩⟩ +``` + +As mentionned above `variate{2}` produces a nested structure, that can be loosely represented as `x2==∂₂⟨∂₁⟨x|xₓ⟩|∂₁⟨xₓ|xₓₓ⟩⟩`, and where `xₓ` is the Jacobian of `x` with respect to itself, and `xₓₓ` is, for each element of `x`, a matrix of zeros. `x2` has precedence `P==2`, as the variable name used here suggests. + +The computations result in `ℓ2=∂₂⟨∂₁⟨ℓ|ℓₓ⟩|∂₁⟨ℓₓ|ℓₓₓ⟩⟩`, of precedence 2 "inherited" from `x2`. + +To unpack this nested structure, we first use `value{2}(ℓ2) → ∂₁⟨ℓ|ℓₓ⟩` and `∂{2,N}(ℓ2) → ∂₁⟨ℓₓ|ℓₓₓ⟩`. On these, we then use: + +- `value{1}(∂₁⟨ℓ|ℓₓ⟩) → ℓ` +- `∂{1,N}(∂₁⟨ℓ|ℓₓ⟩) → ℓₓ` +- `value{1}(∂₁⟨ℓₓ|ℓₓₓ⟩) → ℓₓ` +- `∂{1,N}(∂₁⟨ℓₓ|ℓₓₓ⟩) → ℓₓₓ` + +`ℓₓ` is stored twice in `ℓ2` and so can be extracted by two different paths. + +A caution about performance: higher derivatives means that variated numbers carry a significant amount of information, and all operations on them become slower. Also, because the compiler rolls out all the loops in operations with variated numbers, compilation can become very heavy. + +## Nested derivatives + +Nested derivatives typicaly occur when a function like `Muscade.residual`, which is called by `Muscade` with automatic differentiation, itself uses automatic differentiation internaly. An example in `Muscade.Toolbox` is the implementation of `EulerBeam3D`. This beam element uses a co-rotated reference system, which poses the problem of transforming, for example, bending moments `mᵢ` at Gauss quadrature points, back into nodal loads `R`. Mathematicaly, their contribution to the residual is `mᵢ ∘₁ κ∂X₀`, where `κ∂X₀` is the Jacobian of the curvatures `κ` with respect to the 0-th order time derivative `X₀` of the element's `X`-dofs. + +Here is a simple (if contrived) example: + +```julia +using StaticArrays +using Muscade: variate,value,∂,𝕣 + +function f(x1) + a1 = x1.^2 + P,N,a2 = variate(a1) # P==2 + g2 = sum(a2)*sin(sum(a2)) + gₐ = ∂{P,N}(g2) + return x.*x + sum(u).*gₐ +end + +x = SVector(1.,2.,3.) +P,N,x1 = variate(x) # P==1 +y1 = f(x1) +y = value{P}(y1) +yₓ = ∂{P,N}(y1) +``` + +The function `f` calls `variate`, on `x1` which has itself been obtained by calling `variate`. `x`, `x1` and `a2` have precedence 0, 1 and 2, respectively. The unpacking of the variables is as for higher order derivatives, but here, each segment of code takes care to unpack what it has variated. + +`a2` has structure `a2==∂₂⟨∂₁⟨a|aₓ⟩|∂₁⟨aₐ|aₓₐ⟩⟩`. Note that `a2` now stores two distinct first order derivatives. + +## Understanding and avoiding perturbation confusion + +Nested differentiation in all its forms carries the danger of "perturbation confusion". + +Here is an example of how things go wrong. Variable names include the precedence. This is only done here to help readability. When implementing an element in `Muscade` the precedence of input variables is not known to the developer, because `residual` and `lagrangian` are called by various `Muscade`-solvers with input variables `Λ`, `X`, `U`, `A` and `t` that may or may not be variated, and that to different orders. + +```julia +using StaticArrays +using Muscade: variate,value,∂,𝕣 + +function residual(x1,u) + Pu,Nu,u1 = variate(u) # Pu==Px !!! + g1 = sum(x1)*sin(sum(u1)) # crash + gᵤ = ∂{Pu,Nu}(g1) + return sum(x1.*x1) + sum(u.*gᵤ) +end + +x = SVector(1.,2.,3.) +u = SVector(4.,5.) +Px,Nx,x1 = variate(x) # Px==1 +r1 = residual(x1,u) +r = value{Px}(r1) +rₓ = ∂{Px,Nx}(r1) +``` + +The above, *luckily*, crashes. In `residual`, we have `u1[1]==∂₁⟨4|1,0⟩` and `x1[1]==∂₁⟨1|1,0,0⟩`. The problem is that `u1` contains partial derivatives with respect to `u` while `x1` contains partial derivatives with respect to `x`. However `Muscade`'s implementation of automatic differentiation assumes that since both variables have the same precedence 1 (as marked by the subscript in `∂₁`), they both refer to partial derivatives with respect to the same variable. Mayhem follows when attempting to compute linear combinations of the two vectors of partial derivatives. A similar counter example, with `u` of length 3 leads to an even more undesirable situation, since the "perturbation confusion" then can go undetected. + +To avoid these problems, the call to `variate` in the definition of `residual` must be rewriten: + +```julia +using StaticArrays +using Muscade: variate,value,∂,𝕣 + +function residual(x1,u) + Pu,Nu,u2 = variate(u,context=x1) # Pu==Px+1 + g2 = sum(x1)*sin(sum(u2)) # (u1 renamed u2) + g1ᵤ = ∂{Pu,Nu}(g2) + return sum(x1.*x1) + sum(u.*g1ᵤ) +end + +x = SVector(1.,2.,3.) +u = SVector(4.,5.) +Px,Nx,x1 = variate(x) # P==1 +r1 = residual(x1,u) +r = value{Px}(r1) +rₓ = ∂{Px,Nx}(r1) +``` + +Thanks to the `context` input, `variate` can now detect that although `u` has precedence 0, `x1` already "occupies" precedence 1. Variate thus returns `u2`, of precedence `u==2`. `u2` has the structure `∂₂⟨∂₁⟨u|uₓ⟩|∂₁⟨uᵤ|uₓᵤ⟩⟩`, where `uₓ` and `uₓᵤ` are zero (`u` does not depend on `x`). `x1` and `u2` operate correctly with each other, in spite of the different precedences. + +When implementing an element, the safest is to set `context=(Λ,X,U,A,t)` (`lagrangian`) or `context=(X,U,A,t)` (`residual`). + +But if, for example, a solver was calling `residual` with only `A` variated, and a `∂ᵢ` issued by a call to `variate` within `residual` never touches `A` or any variable influenced by `A`, then omitting `A` from the `context` allows `variate` to issue a variable of lower precedence, enabling faster execution. _Be very deliberate about this_: + +!!! important + Never allow two `∂ᵢ` issuing from different calls to [`variate`](@ref), [`variate0`](@ref), [`revariate`](@ref) and [`motion`](@ref) to mix. + +Consider using `let` blocks to create a local scope to contain "dangerous variables": ```julia -using SVector -x = SVector(1.,2.,3.) -N = length(x) -x1 = variate{1,N}(x) -y1 = f(x1) -y = value{1}(y1) -yₓ = ∂{1,N}(y2) +function f(x) + gₓ = let P,N,x_ = variate(x) + g_ = sum(x_)*sin(sum(x_)) + ∂{P,N}(g_) + end + x.*x + sum(u).*gₓ +end ``` -`x` *must* be a `SVector`. In `yₓ`, the index over `x` is post-pended to the indices of `y`. +## Time derivatives + +Dynamic solvers call `Muscade.residual` and `Muscade.lagrangian` with `X` and `U` that are `NTuple`s of `SVector`s. The elements of the `NTuple`s represent the time derivatives of the element's degrees of freedom. - Where automatic differentiation is nested, the extractions must be carried out in reverse order: +Finite elements solve differential equations by introducing interpolations schemes to represent fields within the element as a function of the degrees of freedom. For example, this could be a relation of the type `ε₀ = kinematics(X₀)`, where `X₀` and `ε₀` are the nodal displacements and the strain at integration points. In some elements, `kinematics` can be non-linear and complicated to differentiate. [`Toolbox.EulerBeam3D`](@ref) provide a good example of this. In some material models, the time derivative of `ε₁` can be required. The function `motion` uses directional derivatives to transform the `NTuple` `X` into nested `∂ℝ` `X_`. `X_` is used to call `kinematics`, and `motion⁻¹` used to recover a tuple containing the time derivatives of `ε`. This works whether `X` is already variated or not. ```julia -x = SVector(1.,2.,3.) -N = length(x) -x1 = variate{1,N}(x) -x2 = variate{2,N}(x1) -y2 = f(x2) -y = value{1}(value{2}(y2)) -yₓ = ∂{1,N}(value{2}(y2)) -yₓ = value{1}(∂{2,N}(y2)) -yₓₓ = ∂{1,N}(∂{2,N}(y2)) +kinematics(X₀) = sum(X₀.*X₀) +X₀,X₁,X₂ = (SVector(1.),SVector(2.),SVector(3.)) +X = (X₀,X₁,X₂) # argument to residual +(P,ND,X_) = motion(X) +ε_ = kinematics(X_) +ε = motion⁻¹{P,ND}(ε_) +ε₀, ε₁ = ∂0(ε), ∂1(ε) ``` -The first type parameter given to [`variate`](@ref), [`value`](@ref) and [`∂`](@ref) is the *precedence* `P`. When automatic differentiation is nested, `variate` must be called with a value of `P` that is higher than the precedence of an variable that will influence the output. Inside a function, this precedence can vary depending on the type of arguments provided to the function. To this end, the function [`constants`](@ref) is provided: +Like `variate`, `motion` has an optional keyword argument `context` and the same rules of caution apply. On the other hand, the above example is quite typical: `kinematics` is a function of `X_` only, and there is no need to extend the context. + +If `x` (lower case) is the i-th degree of freedom, then `X_[i]` has the structure `∂₂⟨∂₁⟨x₀|x₁⟩|∂₁⟨x₁|x₂⟩⟩`, where `xᵢ` is the i-th time derivative. Hence the number of partials is 1 for both `∂₂` and `∂₁`: while higher order derivatives in general are expensive to compute, `motion` tends to be affordable. + +If `X₀`,`X₁`,`X₂` or `context` contains variables of precedence for example 1, then `motion` returns `∂₃⟨∂₂⟨x₀|x₁⟩|∂₂⟨x₁|x₂⟩⟩`. + +## Chain rule + +Applying the chain rule *can*, under the right circumstances accelerate computations. We are differentiating a function `f` with respect to a long vector `x`. Within `f`, a computationaly expensive subfunction `z=g(y)` is only function of a significantly shorter vector `y`. + +Instead of traversing the function `g` with a large number of partials with respect to `x`, one can instead evaluate the derivatives of `z` with respect to `y`, and, having the derivatives of `y` with respect to `x`, recover the derivatives of `z` with respect to `x`. + +When differentiating to the first order, this is the chain rule +``\frac{\partial z_i}{\partial x_k} = \sum_j \frac{\partial z_i}{\partial y_j}\cdot\frac{\partial y_j}{\partial x_i}``. When diffrentiating to an arbitrary order, the computation `z=g(y)` yields a variated number `z` that contains value and multiple derivatives. This data is used to evaluate a multi-dimensional Taylor expansion of `g`, with respect to `y-VALUE(y)`. ```julia -using SVector -... -N = length(x) -P = constants(x,a,b,c) -x1 = variate{P,N}(x) -y1 = f(x1,a,b,c) -y = value{P}(y1) -yₓ = ∂{P,N}(y2) +using StaticArrays +using Muscade: variate,apply + +g(y) = sin.(y).*y # computationaly expensive +x = SVector(1.,2.,3.) # long x +P,N,X = variate(x) # N is large +Y = 3. .+ X[1] .+ X[2]*X[3] # short y +# Z = g(Y) # too slow +Z = apply{:chainrule}(g,Y) # faster (well, sometimes) ``` -## Taylor expansions +Looking under the hood, the code of `apply` is + +```julia +function apply{:chainrule}(f,x) + x_ = revariate(x) # with the code above, N=1 + y_ = f(x_) # this is accelerated, as wanted + y = chainrule(y_,x) # evaluating the Taylor expansion can be slow + return y +end +apply{:direct}(f,x)=f(x) +``` -One way to accelerate automatic differentiation of complicated functions can be to chainrule the differentiation of simpler functions, in particular function with smaller inputs. Use [`apply`](@ref) for basic applications, and [`revariate`](@ref) and [`chainrule`](@ref) for advanced usage. +Try `apply{:chainrule}` vs. `apply{:direct}` to see which is faster. diff --git a/docs/src/BeamElement.jl b/docs/src/BeamElement.jl new file mode 100644 index 00000000..1b93e7c7 --- /dev/null +++ b/docs/src/BeamElement.jl @@ -0,0 +1,427 @@ +# # Euler beam element + +using StaticArrays, LinearAlgebra, Muscade +@functor with() g̃_default(t) = SVector(0.,0.,1.); + +""" + BeamCrossSection + +Data structure containing the cross section material properties, for example to a [`EulerBeam3D`](@ref) +# Arguments to the constructor +- `EA :: 𝕣` is the axial stiffness [N] +- `EI₂ :: 𝕣` is the bending stiffness [Nm/(1/m)] about second axis +- `EI₃ :: 𝕣` is the bending stiffness [Nm/(1/m)] about third axis +- `GJ :: 𝕣` is the torsional stiffness [Nm/(rad/m)] about longitudinal axis +- `μ :: 𝕣` is the mass per unit length [kg/m] +- `ι₁ :: 𝕣` is the (mass) moment of inertia about longitudial axis per unit length [kgm²/m] + +# Optional argument to the constructor (all set to zero by default) +- `w :: 𝕣` is the weight per unit length [N/m] +- `g̃ :: Functor` describes the gravity field divided by acceleration of gravity [-], function of time, set to SVector(0.,0.,1.) by default +- `Ca₁ :: 𝕣` is the tangential added mass per unit length [kg/m] +- `Cl₁ :: 𝕣` is the tangential linear damping coefficient per unit length [N/m/(m/s)] +- `Cq₁ :: 𝕣` is the tangential quadratic damping coefficient per unit length [N/m/(m/s)^2], for example from drag +- `Ca₂ :: 𝕣` is the transverse added mass per unit length [kg/m] for motions along second axis +- `Cl₂ :: 𝕣` is the transverse linear damping coefficient per unit length [N/m/(m/s)] for motions along second axis +- `Cq₂ :: 𝕣` is the transverse quadratic damping coefficient per unit length [N/m/(m/s)^2], for motions along second axis +- `Ca₃ :: 𝕣` is the transverse added mass per unit length [kg/am] for motions along third axis +- `Cl₃ :: 𝕣` is the transverse linear damping coefficient per unit length [N/m/(m/s)] for motions along third axis +- `Cq₃ :: 𝕣` is the transverse quadratic damping coefficient per unit length [N/m/(m/s)^2], for motions along third axis + +# Example +``` +EA = 10. +EI₂ = 1. +EI₃ = 1. +GJ = 1. +μ = 1. +ι₁ = 0.1 +mat = BeamCrossSection(EA=EA,EI₂=EI₂,EI₃=EI₃,GJ=GJ,μ=μ,ι₁=ι₁) +``` + +See also: [`EulerBeam3D`](@ref), [`AxisymmetricBarCrossSection`](@ref) +""" +struct BeamCrossSection{Tg̃} + EA :: 𝕣 + EI₂ :: 𝕣 + EI₃ :: 𝕣 + GJ :: 𝕣 + μ :: 𝕣 + ι₁ :: 𝕣 + w :: 𝕣 + g̃ :: Tg̃ # a Functor + Ca₁ :: 𝕣 + Cl₁ :: 𝕣 + Cq₁ :: 𝕣 + Ca₂ :: 𝕣 + Cl₂ :: 𝕣 + Cq₂ :: 𝕣 + Ca₃ :: 𝕣 + Cl₃ :: 𝕣 + Cq₃ :: 𝕣 +end +BeamCrossSection(;EA,EI₂=EI₂,EI₃=EI₃,GJ=GJ,μ=μ,ι₁=ι₁,w=0.,g̃=g̃_default,Ca₁=0.,Cl₁=0.,Cq₁=0.,Ca₂=0.,Cl₂=0.,Cq₂=0.,Ca₃=0.,Cl₃=0.,Cq₃=0.) = BeamCrossSection(EA,EI₂,EI₃,GJ,μ,ι₁,w,g̃,Ca₁,Cl₁,Cq₁,Ca₂,Cl₂,Cq₂,Ca₃,Cl₃,Cq₃); + +# Resultant function that computes the internal loads from the strains and curvatures, and external loads on the element. +@espy function resultants(o::BeamCrossSection,ε,κ,xᵧ,rₛₘ,vᵢ,t) + r₀ = ∂0(rₛₘ) # orientation of the element's local refsys + vᵢ₁ = ∂1(vᵢ) # intrinsic rotation rate of the element's local refsys + vᵢ₂ = ∂2(vᵢ) # intrinsic rotation acceleration of the element's local refsys + xᵧ₀,xᵧ₁,xᵧ₂ = ∂0(xᵧ),∂1(xᵧ),∂2(xᵧ) + xₗ₁ = xᵧ₁ ∘₁ r₀ + xₗ₂ = xᵧ₂ ∘₁ r₀ + ## Weight + fw = - o.w * o.g̃(t) + ## Compute translational inertia force + fi = o.μ * xᵧ₂ + ## Compute added mass force + faₗ = SVector(o.Ca₁ * xₗ₂[1], o.Ca₂ * xₗ₂[2], o.Ca₃ * xₗ₂[3]) + faᵧ = r₀ ∘₁ faₗ + ## Compute linear damping force + flₗ = SVector( o.Cl₁ * xₗ₁[1], o.Cl₂ * xₗ₁[2], o.Cl₃ * xₗ₁[3]) + flᵧ = r₀ ∘₁ flₗ + ## Compute quadratic damping force + fq1ₗ = o.Cq₁ * xₗ₁[1]^2; if xₗ₁[1] < 0; fq1ₗ = -fq1ₗ end + fq2ₗ = o.Cq₂ * xₗ₁[2]^2; if xₗ₁[2] < 0; fq2ₗ = -fq2ₗ end + fq3ₗ = o.Cq₃ * xₗ₁[3]^2; if xₗ₁[3] < 0; fq3ₗ = -fq3ₗ end + fqₗ = SVector(fq1ₗ,fq2ₗ,fq3ₗ) + fqᵧ = r₀ ∘₁ fqₗ + # Summing up forces + ☼fₑ = fi + faᵧ + flᵧ + fqᵧ + fw # external forces at Gauss point. + ## Compute roll inertia moment + m₁ₗ = o.ι₁*vᵢ₂[1] #local + mᵧ = ∂0(rₛₘ)[:,1] * m₁ₗ #global + ☼mₑ = mᵧ # external couples at Gauss point. + ## Compute internal loads + ☼fᵢ = o.EA*∂0(ε) + ## WARNING: curvatures are defined as rate of rotation along the element, not second derivatives of deflection. + ## Hence κ[3]>0 implies +2 direction is inside curve, + ## κ[2]>0 implies -3 direction is inside curve. + ☼mᵢ = SVector(o.GJ*∂0(κ)[1],o.EI₃*∂0(κ)[2],o.EI₂*∂0(κ)[3]) + return fᵢ,mᵢ,fₑ,mₑ +end; + +## Static Euler beam element, with two nodes, four Gauss points and 12 degrees of freedom. +const ngp = 4 +const ndim = 3 +const nXdof = 12 +const nUdof = 3 +const nXnod = 2; + +# Shape functions for a beam element with support ζ∈[-1/2,1/2]. Though the shape function matrices are sparse, do not "unroll" them. That would be applyer but considerably clutter the code +yₐ(ζ) = 2ζ # differential axial displacement or roll field +yᵤ(ζ) = -4ζ^3 +3ζ # deflection due to differential nodal transverse translation +yᵥ(ζ) = ζ^2 - 1/4 # deflection due to differenttial rotation (bending, not torsion) +κₐ(ζ) = 2 # torsion . κₐ = yₐ′ . Divide by L . +κᵤ(ζ) = -24ζ # curvature. κᵤ = yᵤ′′. Divide by L². +κᵥ(ζ) = 2; # curvature. κᵥ = yᵥ′′. Divide by L . + +# Data structure describing an EulerBeam3D element as meshed +""" + EulerBeam3D <: AbstractElement + +A three-dimensional Euler beam element, with two nodes, twelve X-dofs and three U-dofs. +# Arguments to the constructor +- `nod :: Vector{Node}` contains the element's nodes +- `mat :: Mat` contains the material properties ([`BeamCrossSection`](@ref), for example) + +# Optional argument to the constructor +- `orient2 :: SVector{3,𝕣}` defines the direction of the first bending axis in the global coordinate system. +Default is `SVector(0.,1.,0.)`. + +# Example +``` +EA = 10. +EI₂ = 3. +EI₃ = 3. +GJ = 4. +μ = 1. +ι₁ = 1.0 +L = 5 +model = Model(:TestModel) +node1 = addnode!(model,𝕣[0,0,0]) +node2 = addnode!(model,𝕣[L,0,0]) +mat = BeamCrossSection(EA=EA,EI₂=EI₂,EI₃=EI₃,GJ=GJ,μ=μ,ι₁=ι₁) +addelement!(model,EulerBeam3D,[node1 node2];mat) +``` + +See also: [`BeamCrossSection`](@ref), [`Bar3D`](@ref) +""" +struct EulerBeam3D{Mat,Uforce} <: AbstractElement + cₘ :: SVector{3,𝕣} # Position of the middle of the element, as meshed + rₘ :: Mat33{𝕣} # Orientation of the element, as meshed, represented by a rotation matrix + ζgp :: SVector{ngp,𝕣} # Location of the Gauss points for the normalized element with length 1 + ζnod :: SVector{nXnod,𝕣} # Location of the nodes for the normalized element with length 1 + tgₘ :: SVector{ndim,𝕣} # Vector connecting the nodes of the element in the global coordinate system + tgₑ :: SVector{ndim,𝕣} # Vector connecting the nodes of the element in the local coordinate system + yₐ :: SVector{ngp,𝕣} # Value at gp of shape function for differential axial displacement or roll field + yᵤ :: SVector{ngp,𝕣} # Value at gp of shape function for deflection due to differential nodal transverse translation + yᵥ :: SVector{ngp,𝕣} # Value at gp of shape function for deflection due to differenttial rotation (bending, not torsion). Multiplied by L . + κₐ :: SVector{ngp,𝕣} # Value at gp of shape function for torsion . κₐ = yₐ′ . Divided by L . + κᵤ :: SVector{ngp,𝕣} # Value at gp of shape function for curvature. κᵤ = yᵤ′′. Divided by L². + κᵥ :: SVector{ngp,𝕣} # Value at gp of shape function for curvature. κᵥ = yᵥ′′. Divided by L . + L :: 𝕣 # as meshed length of the element + dL :: SVector{ngp,𝕣} # weight associated to each Gauss point + mat :: Mat # used to store material properties (BeamCrossSection, for example) +end; + +# For performance, `residual` will only accept differentiation to first order +Muscade.no_second_order(::Type{<:EulerBeam3D}) = Val(true) + +# Define nodes, classes, and field names of dofs +Muscade.doflist( ::Type{EulerBeam3D{Mat,false}}) where{Mat} = + (inod = (1,1,1,1,1,1, 2,2,2,2,2,2), + #class= ntuple(i->:X,nXdof), # not typestable + class= (:X,:X,:X,:X,:X,:X,:X,:X,:X,:X,:X,:X), + field= (:t1,:t2,:t3,:r1,:r2,:r3, :t1,:t2,:t3,:r1,:r2,:r3) ) +Muscade.doflist( ::Type{EulerBeam3D{Mat,true}}) where{Mat} = + (inod = (1,1,1,1,1,1, 2,2,2,2,2,2, 3,3,3), + #class= (ntuple(i->:X,nXdof)...,ntuple(i->:U,nUdof)...), # not typestable + class= (:X,:X,:X,:X,:X,:X,:X,:X,:X,:X,:X,:X,:U,:U,:U), + field= (:t1,:t2,:t3,:r1,:r2,:r3, :t1,:t2,:t3,:r1,:r2,:r3, :t1,:t2,:t3) ) + +# ElementType for the EulerBeam3D element. Arguments: node list, material, and direction of the first bending axis in the global coordinate system. +EulerBeam3D(nod;kwargs...) = EulerBeam3D{false}(nod;kwargs...) # by default, EulerBeam3D does not have Udof. +function EulerBeam3D{Udof}(nod::Vector{Node};mat,orient2::SVector{ndim,𝕣}=SVector(0.,1.,0.)) where {Udof} + c = coord(nod) + ## Position of the middle of the element in the global coordinate system (as-meshed) + cₘ = SVector{ndim}((c[1]+c[2])/2) + ## Length and tangential vector to the element in the global coordinate system + tgₘ = SVector{ndim}( c[2]-c[1] ) + L = norm(tgₘ) + t = tgₘ/L + ## Create t, n, b which are the longitudinal and two transverse unit vectors to the element (as-meshed). + ## NB: orient2, provided by the user, will define the first bending axis. + orient2/= norm(orient2) + n = orient2 - t*dot(orient2,t) + nn = norm(n) + nn>1e-3 || muscadeerror("Provide a 'orient' input that is not nearly parallel to the element") + n /= nn + b = cross(t,n) + rₘ = SMatrix{ndim,ndim}(t...,n...,b...) + ## Tangential vector and node coordinates in the local coordinate system + tgₑ = SVector{ndim}(L,0,0) + ## Weight associated to each Gauss point + dL = SVector{ngp}(L/2*(18-sqrt(30))/36,L/2*(18+sqrt(30))/36 ,L/2*(18+sqrt(30))/36,L/2*(18-sqrt(30))/36 ) + ## Location ζgp of the Gauss points for a unit-length beam element, with nodes at ζnod=±1/2. + ζgp = SVector{ngp }(-1/2*sqrt(3/7+2/7*sqrt(6/5)),-1/2*sqrt(3/7-2/7*sqrt(6/5)), +1/2*sqrt(3/7-2/7*sqrt(6/5)),+1/2*sqrt(3/7+2/7*sqrt(6/5))) + ζnod = SVector{nXnod}(-1/2 ,1/2 ) + shapes = (yₐ.(ζgp), yᵤ.(ζgp), yᵥ.(ζgp)*L, κₐ.(ζgp)/L, κᵤ.(ζgp)/L^2, κᵥ.(ζgp)/L) + return EulerBeam3D{typeof(mat),Udof}(cₘ,rₘ,ζgp,ζnod,tgₘ,tgₑ,shapes...,L,dL,mat) +end; + +# Define now the residual function for the EulerBeam3D element. +@espy function Muscade.residual(o::EulerBeam3D{Mat,Udof}, X,U,A,t,SP,dbg) where{Mat,Udof} + ## Compute all quantities at Gauss point, their time derivatives, including intrinsic roll rate and acceleration + P,ND,X_ = motion(X) + gp_,ε_,vₛₘ_,rₛₘ_,vₗ₂_,_,_ = kinematics{:direct}(o,X_) + gpval,☼ε,☼rₛₘ = motion⁻¹{P,ND}(gp_,ε_,rₛₘ_) + vᵢ = intrinsicrotationrates(rₛₘ) + ## compute all Jacobians of the above quantities with respect to X₀ + X₀ = ∂0(X) + TX₀ = revariate{P+1}(X₀) + Tgp,Tε,Tvₛₘ,_,_,_,_ = kinematics{:direct}(o,TX₀) # the crux + gp∂X₀,ε∂X₀,vₛₘ∂X₀ = chainrule_Jacobian((Tgp,Tε,Tvₛₘ),X₀) + ## Quadrature loop: compute resultants + gp = ntuple(ngp) do igp + ☼x,☼κgp = gpval[igp].x, gpval[igp].κ + x∂X₀,κ∂X₀ = gp∂X₀[igp].x, gp∂X₀[igp].κ + fᵢ,mᵢ,fₑ,mₑ = ☼resultants(o.mat,ε,κgp,x,rₛₘ,vᵢ,t) # call the "resultant" function to compute loads (local coordinates) from strains/curvatures/etc. using material properties. Note that output is dual of input. + fₑ = Udof ? fₑ-∂0(U) : fₑ # U is per unit length + R_ = (fᵢ ∘₀ ε∂X₀ + mᵢ ∘₁ κ∂X₀ + fₑ ∘₁ x∂X₀ + mₑ ∘₁ vₛₘ∂X₀) * o.dL[igp] # Contribution to the local nodal load of this Gauss point [nXdof] = scalar*[nXdof] + [ndim]⋅[ndim,nXdof] + [ndim]⋅[ndim,nXdof] + @named(R_) + end + R = sum(gpᵢ.R_ for gpᵢ∈gp) + ♢κ = motion⁻¹{P,ND}(SVector(vₗ₂_[1],vₗ₂_[3],-vₗ₂_[2])).*(2/o.L) + return R,noFB +end; + +struct kinematics{Mode} end # Mode: +function kinematics{Mode}(o::EulerBeam3D,X₀) where{Mode} + cₘ,rₘ,tgₘ,tgₑ,ζnod,ζgp,L = o.cₘ,o.rₘ,o.tgₘ,o.tgₑ,o.ζnod,o.ζgp,o.L # As-meshed element coordinates and describing tangential vector + vₛₘ,rₛₘ,uₗ₂,vₗ₂,cₛₘ = corotated{Mode}(o,X₀) + ε = √((uₗ₂[1]+L/2)^2+uₗ₂[2]^2+uₗ₂[3]^2)*2/L - 1. + gp = ntuple(ngp) do igp # gp[igp].κ, gp[igp].x + yₐ,yᵤ,yᵥ,κₐ,κᵤ,κᵥ = o.yₐ[igp],o.yᵤ[igp],o.yᵥ[igp],o.κₐ[igp],o.κᵤ[igp],o.κᵥ[igp] + κ = SVector( κₐ*vₗ₂[1], κᵤ*uₗ₂[2]+κᵥ*vₗ₂[3], κᵤ*uₗ₂[3]-κᵥ*vₗ₂[2]) + y = SVector(yₐ*uₗ₂[1] , yᵤ*uₗ₂[2]+yᵥ*vₗ₂[3], yᵤ*uₗ₂[3]-yᵥ*vₗ₂[2]) + x = rₛₘ∘₁(tgₑ*ζgp[igp]+y)+cₛₘ + (κ=κ,x=x) + end + return gp,ε,vₛₘ,rₛₘ,vₗ₂,uₗ₂,cₛₘ +end + +struct corotated{Mode} end +function corotated{Mode}(o::EulerBeam3D,X₀) where{Mode} + cₘ,rₘ,tgₘ,tgₑ,ζnod,ζgp = o.cₘ,o.rₘ,o.tgₘ,o.tgₑ,o.ζnod,o.ζgp # As-meshed element coordinates and describing tangential vector + uᵧ₁,vᵧ₁,uᵧ₂,vᵧ₂ = vec3(X₀,1:3), vec3(X₀,4:6), vec3(X₀,7:9), vec3(X₀,10:12) + Δvᵧ,rₛₘ,vₛₘ = apply{Mode}((vᵧ₁=vᵧ₁,vᵧ₂=vᵧ₂)) do v + rₛ₁ = apply{Mode}(Rodrigues,v.vᵧ₁) + rₛ₂ = apply{Mode}(Rodrigues,v.vᵧ₂) + Δvᵧ_ = 0.5*Rodrigues⁻¹(rₛ₂ ∘₁ rₛ₁') + rₛₘ_ = apply{Mode}(Rodrigues,Δvᵧ_) ∘₁ rₛ₁ ∘₁ o.rₘ + vₛₘ_ = Rodrigues⁻¹(rₛₘ_) + return Δvᵧ_,rₛₘ_,vₛₘ_ + end + cₛ = 0.5*(uᵧ₁+uᵧ₂) + uₗ₂ = rₛₘ' ∘₁ (uᵧ₂+tgₘ*ζnod[2]-cₛ)-tgₑ*ζnod[2] #Local displacement of node 2 + vₗ₂ = rₛₘ' ∘₁ Δvᵧ + return vₛₘ,rₛₘ,uₗ₂,vₗ₂,cₛ+cₘ +end; + +# The following functions explain how the beam element should be drawn +using GLMakie +""" + +Drawing a `EulerBeam3D`. + + draw!(axis,state) + + draw!(axis,state;EulerBeam3D=(;style=:shape)) + + α = 2π*(0:19)/20 + circle = 0.1*[cos.(α) sin.(α)]' + draw!(axis,state;EulerBeam3D=(;style=:solid,section = circle)) + +`style=:shape` shows the deformed neutral axis of the element. It has optional arguments `frame=true` +(draws the element's corotated frame of reference) +and `nseg=10` (number of points to show the deflected shape of each element). + +`style=:solid` shows the deformed shape of the element. It requires the input `section=...` to be given +a matrix of size `(2,nsec)` describing `nsec` points around the cross section of the element (no need to close +the circumference by repeating the first point at the end). It has optional arguments `nseg=10` as above, `marking=true` +to draw a longitudinal marking and `solid_color=:yellow`. + +Other optional arguments (and their default values) are +- `Udof` (`true` iff element has Udofs) wether to draw U-forces. +- `draw_frame = false` wether to draw the local reference frame of each element +- `draw_marking = true` wether to draw "longitudinal marking" along the element. Will only draw if style=:solid. +- `nseg = 1` number of segments to display the shape of a deformed element +- `solid_color = :yellow` color of the surface if `style=:solid` +- `line_color = :black` color of the line if `style=:sshape` +- `Uscale = 1.` How many meter is a Newton per meter? +""" +function Muscade.allocate_drawing(axis,o::AbstractVector{EulerBeam3D{Tmat,Udof}};kwargs...) where{Tmat,Udof} + args = default{:EulerBeam3D }(kwargs,(;) ) + section = default{:section }(args,zeros(2,0)) + nsec = size(section,2) + opt = (default(args,(style=:shape,draw_frame=false,draw_marking=true,nseg=1, + solid_color=:yellow,line_color=:black,Uscale=1.,Udof=Udof))..., + nel = length(o) , + nsec = nsec , + section = section , + markrad = nsec==0 ? 0. : 1.01*maximum(section[1,:]) + ) + opt.style==:solid && nsec<2 && muscadeerror("An section description must be provided for 'solid' plot") + nel_shape = opt.style==:shape ? opt.nel : 0 + nel_shape_frame = opt.draw_frame ? nel_shape : 0 + nel_solid = opt.style==:solid ? opt.nel : 0 + nel_solid_marking = opt.draw_marking ? nel_solid : 0 + nel_udof = opt.Udof ? opt.nel : 0 + + mut=( + node = 𝕣2(undef,3,3*opt.nel) , + shape_x = 𝕣2(undef,3,(opt.nseg+2)*nel_shape) , + shape_frame = 𝕣2(undef,3,3*3*nel_shape_frame) , # idim, point-point-lift, ivec, iel + solid_vertex = 𝕣2(undef,3,opt.nsec*(opt.nseg+1)*nel_solid) , + solid_face = 𝕫2(undef,2*opt.nsec* opt.nseg *nel_solid,3), + solid_mark = 𝕣2(undef,3,(opt.nseg+2)*nel_solid_marking) , + ucrest = 𝕣2(undef,3,5*nel_udof) , # idim, 6point-lift,iel + ) + return mut,opt +end + +function Muscade.update_drawing(axis,o::AbstractVector{EulerBeam3D{Tmat,Udof}},oldmut,opt, Λ,X,U,A,t,SP,dbg) where{Tmat,Udof} + mut = oldmut + X₀ = ∂0(X) + U₀ = ∂0(U) + it1,ir1,it2,ir2 = SVector{3}(1:3),SVector{3}(4:6),SVector{3}(7:9),SVector{3}(10:12) + nsec = size(opt.section,2) + node = reshape(mut.node,(3,3,opt.nel)) + for (iel,oᵢ) = enumerate(o) + node[:,1,iel] = oᵢ.cₘ - oᵢ.tgₘ/2 + X₀[it1,iel] + node[:,2,iel] = oᵢ.cₘ + oᵢ.tgₘ/2 + X₀[it2,iel] + node[:,3,iel].= NaN + end + + if opt.style==:shape + ζ = range(-1/2,1/2,opt.nseg+1) + if opt.draw_frame shape_frame = reshape(mut.shape_frame ,(3,3,3 ,opt.nel)) end + if opt.Udof ucrest = reshape(mut.ucrest, (3,5 ,opt.nel)) end + shape_x = reshape(mut.shape_x ,(3,opt.nseg+2,opt.nel)) + for (iel,oᵢ) = enumerate(o) + cₘ,rₘ,tgₘ,tgₑ,ζnod,ζgp,L = oᵢ.cₘ,oᵢ.rₘ,oᵢ.tgₘ,oᵢ.tgₑ,oᵢ.ζnod,oᵢ.ζgp,oᵢ.L + X₀ₑ = view(X₀,:,iel) + vₛₘ,rₛₘ,uₗ₂,vₗ₂,cₛₘ = corotated{:direct}(oᵢ,X₀ₑ) + if opt.draw_frame + for ivec = 1:3 + shape_frame[:,1,ivec,iel] = cₛₘ + shape_frame[:,2,ivec,iel] = cₛₘ + oᵢ.L/3*rₛₘ[:,ivec] + shape_frame[:,3,ivec,iel].= NaN + end + end + if opt.Udof + ucrest[:,1,iel] = node[:,1,iel] + ucrest[:,2,iel] = node[:,1,iel] + rₛₘ ∘₁ view(U₀,:,iel) * opt.Uscale + ucrest[:,3,iel] = node[:,2,iel] + rₛₘ ∘₁ view(U₀,:,iel) * opt.Uscale + ucrest[:,4,iel] = node[:,2,iel] + ucrest[:,5,iel].= NaN + end + for (i,ζᵢ) ∈ enumerate(ζ) + y = SVector(yₐ(ζᵢ)*uₗ₂[1] , yᵤ(ζᵢ)*uₗ₂[2]+L*yᵥ(ζᵢ)*vₗ₂[3], yᵤ(ζᵢ)*uₗ₂[3]-L*yᵥ(ζᵢ)*vₗ₂[2]) + shape_x[:,i ,iel] = rₛₘ∘₁(tgₑ*ζᵢ+y)+cₛₘ + shape_x[:,opt.nseg+2,iel].= NaN + end + end + elseif opt.style==:solid + ζ = range(-1/2,1/2,opt.nseg+1) + idx(iel,iseg,isec) = Muscade.mod_onebased(isec,opt.nsec)+opt.nsec*(iseg-1+(opt.nseg+1)*(iel-1)) # 1st index into rvertex + if opt.Udof ucrest = reshape(mut.ucrest ,(3,5 ,opt.nel)) end + if opt.draw_marking solid_mark = reshape(mut.solid_mark ,(3,opt.nseg+2 ,opt.nel)) end + solid_face = reshape(mut.solid_face ,(2,opt.nsec, opt.nseg ,opt.nel,3)) + solid_vertex = reshape(mut.solid_vertex,(3,opt.nsec, opt.nseg+1 ,opt.nel)) + for (iel,oᵢ) = enumerate(o) + cₘ,rₘ,tgₘ,tgₑ,ζnod,ζgp,L = oᵢ.cₘ,oᵢ.rₘ,oᵢ.tgₘ,oᵢ.tgₑ,oᵢ.ζnod,oᵢ.ζgp,oᵢ.L + X₀ₑ = view(X₀,:,iel) + vₛₘ,rₛₘ,uₗ₂,vₗ₂,cₛₘ = corotated{:direct}(oᵢ,X₀ₑ) + vᵧ₁,vᵧ₂ = vec3(X₀ₑ,4:6), vec3(X₀ₑ,10:12) + rₛ₁ = Rodrigues(vᵧ₁) + rₛ₂ = Rodrigues(vᵧ₂) + if opt.Udof + ucrest[:,1,iel] = node[:,1,iel] + ucrest[:,2,iel] = node[:,1,iel] + rₛₘ ∘₁ view(U₀,:,iel) * opt.Uscale + ucrest[:,3,iel] = node[:,2,iel] + rₛₘ ∘₁ view(U₀,:,iel) * opt.Uscale + ucrest[:,4,iel] = node[:,2,iel] + ucrest[:,5,iel].= NaN + end + Δv = Rodrigues⁻¹(rₛ₂ ∘₁ rₛ₁')/opt.nseg + for (iseg,ζᵢ) ∈ enumerate(ζ) # actualy iterating over nseg+1 segment boundaries + y = SVector(yₐ(ζᵢ)*uₗ₂[1] , yᵤ(ζᵢ)*uₗ₂[2]+L*yᵥ(ζᵢ)*vₗ₂[3], yᵤ(ζᵢ)*uₗ₂[3]-L*yᵥ(ζᵢ)*vₗ₂[2]) # interpolate + xn = rₛₘ∘₁(tgₑ*ζᵢ+y)+cₛₘ # point on neutral axis + r = Rodrigues((iseg-1)*Δv) ∘₁ rₛ₁ ∘₁ rₘ + if opt.draw_marking + solid_mark[:, iseg ,iel] = xn .+ r[:,2]*opt.markrad + solid_mark[:,opt.nseg+2,iel].= NaN + end + for isec = 1:opt.nsec + solid_vertex[:,isec,iseg,iel] = xn .+ r[:,2]*opt.section[1,isec] + r[:,3]*opt.section[2,isec] + if iseg≤opt.nseg + i1,i2,i3,i4 = idx(iel,iseg,isec),idx(iel,iseg ,isec+1),idx(iel,iseg+1,isec ),idx(iel,iseg+1,isec+1) + solid_face[1,isec,iseg,iel,:] = SVector(i1,i2,i4) + solid_face[2,isec,iseg,iel,:] = SVector(i1,i4,i3) + end + end + end + end + end + return mut +end + +function Muscade.display_drawing!(axis,::Type{EulerBeam3D{Tmat,Udof}},obs,opt) where{Tmat,Udof} + scatter!( axis, obs.node ,color = opt.line_color , marker=:circle,markersize=3) + opt.style==:shape && lines!( axis, obs.shape_x ,color = opt.line_color ,linewidth=.5 ) + opt.style==:shape && opt.draw_frame && lines!( axis, obs.shape_frame ,color = :grey ,linewidth=.5 ) + opt.style==:solid && mesh!( axis, obs.solid_vertex, obs.solid_face ,color = opt.solid_color ) + opt.style==:solid && opt.draw_marking && lines!( axis, obs.solid_mark ,color = opt.line_color ) + opt.Udof && lines!( axis, obs.ucrest ,color = :red ,linewidth=.5 ) +end \ No newline at end of file diff --git a/docs/src/DecayAnalysis.md b/docs/src/DecayAnalysis.md new file mode 100644 index 00000000..b07854b4 --- /dev/null +++ b/docs/src/DecayAnalysis.md @@ -0,0 +1,281 @@ +```@meta +EditURL = "../../examples/DecayAnalysis.jl" +``` + +# Estimating model parameters + +We estimate the mass and damping matrices of a coupled linear oscillator (floater moving in the surge, sway and yaw) based on a decay tests +In the following, we define the necessary element and residual function describing the dynamic behaviour of the floater. + +NB: In two places in this script, `solve` is called with optional `verbose=false`, because this script is part of the generation +of `Muscade`'s online documentation. Setting `verbose=true` would be more relevant in other contexts. + +````@example DecayAnalysis +using Muscade,StaticArrays,Interpolations,GLMakie + +fold(x::SVector{6}) = SMatrix{3,3}( x[1],x[2],x[3], + x[2],x[4],x[5], + x[3],x[5],x[6]) + +const floatermotion = (:surge,:sway,:yaw) +const idx = (:11,:12,:16,:22,:26,:66) + +struct FloaterOnCalmWater <: AbstractElement + K :: SMatrix{3,3,𝕣} + C :: SMatrix{3,3,𝕣} + M :: SMatrix{3,3,𝕣} +end +FloaterOnCalmWater(nod::Vector{Node};K,C,M ) = FloaterOnCalmWater(K,C,M) + +Muscade.no_second_order(::Type{<:FloaterOnCalmWater}) = Val(true) + +Muscade.doflist(::Type{<:FloaterOnCalmWater}) = (inod = (ntuple(i-> 1,3)...,ntuple(i-> 1,3)...,ntuple(i-> 1,6)..., ntuple(i-> 1,6)... ), + class = (ntuple(i->:X,3)...,ntuple(i->:U,3)...,ntuple(i->:A,6)..., ntuple(i->:A,6)... ), + field = (floatermotion... ,floatermotion... ,ntuple(i->Symbol(:M,idx[i]),6)..., ntuple(i->Symbol(:C,idx[i]),6)...)) + +@espy function Muscade.residual(o::FloaterOnCalmWater, X,U,A,t,SP,dbg) + x,x′,x″ = ∂0(X),∂1(X),∂2(X) + ☼u = ∂0(U) + a = exp10.(A) + ☼r₂ = (o.M.*fold(a[@SVector [i for i∈1:6 ]]))∘₁x″ + ☼r₁ = (o.C.*fold(a[@SVector [i for i∈7:12]]))∘₁x′ + ☼r₀ = o.K∘₁x + return r₀+r₁+r₂-u, noFB +end +```` + +This is a tailor-made cost element where the cost is made dependent on the iteration number. In practice, this is used to first solve an XU problem (costs on A are prohibitive) before solving the actual XUA problem. + +````@example DecayAnalysis +struct SingleDecayAcost{Field,Tcost,Tcostargs} <: AbstractElement + cost :: Tcost + costargs :: Tcostargs + fac :: 𝕣1 +end + +SingleDecayAcost(nod::Vector{Node};field::Symbol,fac,cost::Functor ,costargs=()) = SingleDecayAcost{field,typeof(cost),typeof(costargs)}(cost,costargs,fac) +Muscade.doflist(::Type{<:SingleDecayAcost{Field,Tcost,Tcostargs}}) where{Field,Tcost,Tcostargs} = (inod=(1,),class=(:A,),field=(Field,)) +@espy function Muscade.lagrangian(o::SingleDecayAcost,Λ,X,U,A,t,SP,dbg) + iter = min(length(o.fac),default{:iter}(SP,length(o.fac))) + ☼cost = o.cost( A[1] ,o.costargs...) + return cost*o.fac[iter],noFB +end +```` + +Define stiffness, damping and mass matrix for the true system + +````@example DecayAnalysis +K = fold(SVector{6}([1.0, 0.0, 0.0, 1.0, 0.0, 1.0])) +C = fold(SVector{6}([0.25, -0.2, 0.1, 0.15, -0.15, 0.03])) +M = fold(SVector{6}([1.0, 0.1, 0.2, 0.5, 0.1, 0.1])); +nothing #hide +```` + +Solve direct problem + +````@example DecayAnalysis +model = Model(:MooredFloater) +n1 = addnode!(model,𝕣[0,0,0]) +e1 = addelement!(model,FloaterOnCalmWater,[n1]; K,C,M) +initialstate = initialize!(model;time=0.) +initialstate = setdof!(initialstate,[2.0]; field=:surge, nodID=[n1], order=0) +initialstate = setdof!(initialstate,[1.0]; field=:sway, nodID=[n1], order=0) +initialstate = setdof!(initialstate,[-5.0]; field=:yaw, nodID=[n1], order=0) +T = 0.1 *(1:250) +state = solve(SweepX{2}; initialstate,time= T,verbose=false); +surge = [s.X[1][1] for s∈state] +sway = [s.X[1][2] for s∈state] +yaw = [s.X[1][3] for s∈state]; +nothing #hide +```` + +Create fake measurements + +````@example DecayAnalysis +surgeMeas = surge + .05 * randn(length(T)) +swayMeas = sway + .05 * randn(length(T)) +yawMeas = yaw + .1 * randn(length(T)); +nothing #hide +```` + +Create intial guesses for M and C + +````@example DecayAnalysis +Cguess = fold(SVector{6}([0.1, -0.1, 0.1, 0.1, -0.1, 0.1])) +Mguess = fold(SVector{6}([1.0, 1.0, 1.0, 1.0, 1.0, 1.0])); +nothing #hide +```` + +Create XUA model + +````@example DecayAnalysis +modelXUA = Model(:MooredFloater) +n1 = addnode!(modelXUA,𝕣[0,0,0]) +e1 = addelement!(modelXUA,FloaterOnCalmWater,[n1]; K,C=Cguess,M=Mguess); +nothing #hide +```` + +Assign costs to unknown forces + +````@example DecayAnalysis +Quu = @SVector [0.05 ^-2 for i=1:3 ] +@functor with(Quu) cost1(u,t,i) = 0.5*Quu[i]*u^2 +e2 = [addelement!(modelXUA,SingleDofCost ,[n1]; class=:U,field=f , cost=cost1,costargs=(i,)) for (i,f)∈enumerate(floatermotion)]; +nothing #hide +```` + +Assign costs to variations of model parameters (wrt guess). + +````@example DecayAnalysis +fac = [256,128,64,32,16,8,4,2,1] +QCaa = @SVector [.1 ^-2 for i=1:6 ] +@functor with(QCaa,T) cost2(a,i) = 0.5*QCaa[i]/length(T)*a^2 +e3 = [addelement!(modelXUA,SingleDecayAcost ,[n1]; field=f,fac, cost=cost2,costargs=(i,)) for (i,f)∈enumerate((:C11,:C12,:C16,:C22,:C26,:C66))] +QMaa = @SVector [.1 ^-2 for i=1:6 ] +@functor with(QMaa,T) cost3(a,i) = 0.5*QMaa[i]/length(T)*a^2 +e4 = [addelement!(modelXUA,SingleDecayAcost ,[n1]; field=f,fac, cost=cost3,costargs=(i,)) for (i,f)∈enumerate((:M11,:M12,:M16,:M22,:M26,:M66))]; +nothing #hide +```` + +Assign costs to measurement errors + +````@example DecayAnalysis +surgeInt = linear_interpolation(T, surgeMeas) +swayInt = linear_interpolation(T, swayMeas) +yawInt = linear_interpolation(T, yawMeas) +@functor with(surgeInt) devSurge(surge,t) = 1e-1 ^-2 * (surge-surgeInt(t))^2 +@functor with(swayInt ) devSway(sway,t) = 1e-1 ^-2 * (sway-swayInt(t))^2 +@functor with(yawInt ) devYaw(yaw,t) = 1e-1 ^-2 * (yaw-yawInt(t))^2 +e5 = addelement!(modelXUA,SingleDofCost,[n1];class=:X,field=:surge, cost=devSurge) +e6 = addelement!(modelXUA,SingleDofCost,[n1];class=:X,field=:sway, cost=devSway) +e7 = addelement!(modelXUA,SingleDofCost,[n1];class=:X,field=:yaw, cost=devYaw); + + + + + +#Solve inverse problem +initialstateXUA = initialize!(modelXUA;time=0.) +stateXUA = solve(DirectXUA{2,0,1};initialstate=[initialstateXUA],time=[T], + maxiter=100,saveiter=true,verbose=false, + maxΔx=1e-5,maxΔλ=Inf,maxΔu=1e-5,maxΔa=1e-5); +nothing #hide +```` + +Fetch and display estimated model parameters + +````@example DecayAnalysis +lastIter = findlastassigned(stateXUA); niter = lastIter; iexp=1; +Mest = Mguess .* fold(exp10.(SVector{6}(stateXUA[niter][iexp][1].A[1:6 ]))) +Cest = Cguess .* fold(exp10.(SVector{6}(stateXUA[niter][iexp][1].A[7:12]))); +nothing #hide +```` + +Fetch response and loads + +````@example DecayAnalysis +surgeRec = [s.X[1][1] for s∈stateXUA[niter][iexp]] +swayRec = [s.X[1][2] for s∈stateXUA[niter][iexp]] +yawRec = [s.X[1][3] for s∈stateXUA[niter][iexp]] +surgeExtF = [s.U[1][1] for s∈stateXUA[niter][iexp]] +swayExtF = [s.U[1][2] for s∈stateXUA[niter][iexp]] +yawExtF = [s.U[1][3] for s∈stateXUA[niter][iexp]] +req = @request r₂,r₁,r₀ +loads = getresult(stateXUA[niter][iexp],req,[e1]) +inertiaLoads = [loads[i][:r₂] for i∈1:length(T)] +dampingLoads = [loads[i][:r₁] for i∈1:length(T)] +stiffnessLoads = [loads[i][:r₀] for i∈1:length(T)]; +nothing #hide +```` + +Create a figure with the results + +````@example DecayAnalysis +fig = Figure(size = (2000,1000)); +nothing #hide +```` + +Display response + +````@example DecayAnalysis +ax=Axis(fig[1,1], ylabel="Surge", yminorgridvisible = true,xminorgridvisible = true) +scatter!(fig[1,1],T,surgeMeas, color=RGBf(.8, .8, .8), label=L"\text{Measurements}") +lines!(fig[1,1],T,surge, color=:black, linestyle=:dash, label=L"\text{Exact direct solution } (M,C,K)") +lines!(fig[1,1],T,surgeRec, color=:black, label=L"\text{Inverse solution } (\hat{M},\hat{C},K)") +ylims!(ax,minimum(surgeMeas),maximum(surgeMeas)) +ax.title="Displacements [m,deg]" +axislegend() + +ax=Axis(fig[2,1], ylabel="Sway", yminorgridvisible = true,xminorgridvisible = true) +scatter!(fig[2,1],T,swayMeas, color=RGBf(.8, .8, .8)) +lines!(fig[2,1],T,sway, color=:black, linestyle=:dash) +ylims!(ax,-1,2) +lines!(fig[2,1],T,swayRec, color=:black) +ylims!(ax,minimum(swayMeas),maximum(swayMeas)) + +ax=Axis(fig[3,1], ylabel="Yaw", yminorgridvisible = true,xminorgridvisible = true,xlabel="Time [s]") +scatter!(fig[3,1],T,yawMeas, color=RGBf(.8, .8, .8)) +lines!(fig[3,1],T,yaw, color=:black, linestyle=:dash) +lines!(fig[3,1],T,yawRec, color=:black) +ylims!(ax,minimum(yawMeas),maximum(yawMeas)) +```` + +Display loads + +````@example DecayAnalysis +ax=Axis(fig[1,2], yminorgridvisible = true,xminorgridvisible = true) +lines!(fig[1,2],T,-[inertiaLoads[i][1] for i∈1:length(T)], color=:red, label=L"\text{Inertia } (\hat{M})") +lines!(fig[1,2],T,-[dampingLoads[i][1] for i∈1:length(T)], color=:blue, label=L"\text{Damping } (\hat{C})") +lines!(fig[1,2],T,-[stiffnessLoads[i][1] for i∈1:length(T)],color=:green, label=L"\text{Stiffness } (K)") +lines!(fig[1,2],T,surgeExtF, color=:black, label=L"\text{Unknown}") +ax.title="Loads [N, Nm]" +ylims!(ax,-2,2) +axislegend() + +ax=Axis(fig[2,2], yminorgridvisible = true,xminorgridvisible = true) +lines!(fig[2,2],T,-[inertiaLoads[i][2] for i∈1:length(T)], color=:red ) +lines!(fig[2,2],T,-[dampingLoads[i][2] for i∈1:length(T)], color=:blue ) +lines!(fig[2,2],T,-[stiffnessLoads[i][2] for i∈1:length(T)], color=:green) +lines!(fig[2,2],T,swayExtF, color=:black) +ylims!(ax,-2,3) + +ax=Axis(fig[3,2], yminorgridvisible = true,xminorgridvisible = true,xlabel="Time [s]") +lines!(fig[3,2],T,-[inertiaLoads[i][3] for i∈1:length(T)], color=:red ) +lines!(fig[3,2],T,-[dampingLoads[i][3] for i∈1:length(T)], color=:blue) +lines!(fig[3,2],T,-[stiffnessLoads[i][3] for i∈1:length(T)], color=:green) +lines!(fig[3,2],T,yawExtF, color=:black) +ylims!(ax,-4,4) + +ax=Axis(fig[1,3], limits=(nothing,nothing,0,2), + xticks = (1:6, [L"\hat{M}_{11}/M_{11}", L"\hat{M}_{12}/M_{12}", L"\hat{M}_{16}/M_{16}",L"\hat{C}_{11}/C_{11}", L"\hat{C}_{12}/C_{12}", L"\hat{C}_{16}/C_{16}"]), + yminorgridvisible = true,xminorgridvisible = true) +barplot!(ax,[1,2,3,4,5,6], [Mest[1,1]/M[1,1],Mest[1,2]/M[1,2],Mest[1,3]/M[1,3], Cest[1,1]/C[1,1],Cest[1,2]/C[1,2],Cest[1,3]/C[1,3]], + bar_labels = :y,color=:white,strokewidth=1,strokecolor=[:red,:red,:red,:blue,:blue,:blue]) +ax.title="Estimated model parameters compared to exact solution (iteration " * string(niter) * "/" * string(lastIter) * ")" + +ax=Axis(fig[2,3], limits=(nothing,nothing,0,2), + xticks = (1:6, [L"\hat{M}_{21}/M_{21}", L"\hat{M}_{22}/M_{22}", L"\hat{M}_{26}/M_{26}",L"\hat{C}_{21}/C_{21}", L"\hat{C}_{22}/C_{22}", L"\hat{C}_{26}/C_{26}"]), + yminorgridvisible = true,xminorgridvisible = true) +barplot!(ax,[1,2,3,4,5,6], [Mest[2,1]/M[2,1],Mest[2,2]/M[2,2],Mest[2,3]/M[2,3], Cest[2,1]/C[2,1],Cest[2,2]/C[2,2],Cest[2,3]/C[2,3]], + bar_labels = :y,color=:white,strokewidth=1,strokecolor=[:red,:red,:red,:blue,:blue,:blue]) + +ax=Axis(fig[3,3], limits=(nothing,nothing,0,2), + xticks = (1:6, [L"\hat{M}_{61}/M_{61}", L"\hat{M}_{62}/M_{62}", L"\hat{M}_{66}/M_{66}",L"\hat{C}_{61}/C_{61}", L"\hat{C}_{62}/C_{62}", L"\hat{C}_{66}/C_{66}"]), + yminorgridvisible = true,xminorgridvisible = true) +barplot!(ax,[1,2,3,4,5,6], [Mest[3,1]/M[3,1],Mest[3,2]/M[3,2],Mest[3,3]/M[3,3], Cest[3,1]/C[3,1],Cest[3,2]/C[3,2],Cest[3,3]/C[3,3]], + bar_labels = :y,color=:white,strokewidth=1,strokecolor=[:red,:red,:red,:blue,:blue,:blue]) + +currentDir = @__DIR__ +if occursin("build", currentDir) + save(normpath(joinpath(currentDir,"..","src","assets","decay.png")),fig) +elseif occursin("examples", currentDir) + save(normpath(joinpath(currentDir,"decay.png")),fig) +end +```` + +![Result](assets/decay.png) + +--- + +*This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).* + diff --git a/docs/src/DryFriction.md b/docs/src/DryFriction.md new file mode 100644 index 00000000..d49df55d --- /dev/null +++ b/docs/src/DryFriction.md @@ -0,0 +1,89 @@ +```@meta +EditURL = "../../examples/DryFriction.jl" +``` + +````@example DryFriction +using Muscade,StaticArrays +```` + +# DryFriction + +Besides providing a general example of how to implement an element in `Muscade`, this element illustrates how to implement hysteretic behaviour +(here: dry friction, but this would also apply to plasticity) without internal variables, since these make problems with `U`dofs intractable. +This is handled by making what would otherwise have been an internal variable into an additional `X`dof. In this case, the element's second degree +of freedom is the friction force. +## Type +The struct contains the values provided (indirectly) by the user. Note `Fx` and `Ff` which are type parameters: these will be `Symbol`s that +represent the field of the `X`dof on which to apply the friction, and a `X`dof to represent the friction force + +````@example DryFriction +struct DryFriction{Fx,Ff} <: AbstractElement + fric :: 𝕣 + x′scale :: 𝕣 + k⁻¹ :: 𝕣 # ∈ [0,∞[, so k ∈ ]0,∞] +end +```` + +## Constructor +We provide a constructor, which will be called by `AddElement!`. The keyword arguments can, or must be given by the user when calling `AddElement!`, and are passed on +to the constructor. Note that the constructor is type unstable: it gets `fields` and `fieldf` as values and uses them as type parameters. This is not deemed to be a problem for +the constructor (type instability in `residual` would be another matter) + +````@example DryFriction +DryFriction(nod::Vector{Node};fieldx::Symbol,fieldf::Symbol=:f, + friction::𝕣,Δx::𝕣=0.,x′scale::𝕣=1.) = + DryFriction{fieldx,fieldf}(friction,x′scale,Δx/friction) +```` + +## `residual` +The `residual` function is prepended by `@espy` to facilitate the extraction of element-results . +Variables `old` and `new` are prepended by `☼` (`\sun`), to tell `@espy` the values of these variables can +be requested using [`getresult`](@ref). + +The full name `Muscade.residual` must be used, because we are adding a method to a function defined in the `module` `Muscade`. + +````@example DryFriction +@espy function Muscade.residual(o::DryFriction, X,U,A, t,SP,dbg) + x,x′,f,f′ = ∂0(X)[1],∂1(X)[1], ∂0(X)[2], ∂1(X)[2] + stick = (x′-o.k⁻¹*f′)/o.x′scale + slip = abs(f)/o.fric -1 + ☼old = abs(slip)o.fric ☼new = :slip + elseif old==:slip && f*x′<0 ☼new = :stick + else ☼new = old + end + return (new==:slip ? SVector(f,slip) : SVector(f,stick)), noFB +end; +nothing #hide +```` + +In the above `f` (a force) uses the "nod-on-el" convention (force exterted by the element's node on the element), so the sign is unusual. + +If the element was in stick the previous iteration, the variable `stick = (x′-o.k⁻¹*f′)/o.x′scale` will be very close to zero. +Similarly, if the element was in slip the previous iteration, the variable `slip = abs(f)/o.fric -1` will be very close to zero. +`old` is then either `:stick` or `:slip` depending on which of the two above is smallest. + +The `if` construct can be read as follows: +- If we were in stick at previous iteration but `|f|` from previous iteration exceeds `o.fric`, we slip in this iteration. +- If we were in slip at previous iteration but force from previous iteration is in the wrong direction, we stick in this iteration. +- Otherwise, no change. + +The function returns a 2-vector of residuals (corresponding to the two `X`dofs). The first residual `f` is the friction force applied to the dof `fieldx`. + +The second residual corresponds to dof `fieldf`. Importantly, this later dof must not be shared with any other element, so the that solver will set +the second residual to zero in this iteration: depending on `new`, this will enforce `slip==0` or `stick==0`. The relevant condition will +be enforced exactly (to rounding errors) because both conditions are linear in `X`. + +## `doflist` +Another function that must be overloaded, in order to tell `Muscade` what dofs the element provides. Note that this is a function of the element *type*, not +of the element *variable*: elements of the same concrete type must have the same dofs. + +````@example DryFriction +Muscade.doflist( ::Type{DryFriction{Fx,Ff}}) where{Fx,Ff} = + (inod =(1 ,1 ), class=(:X,:X), field=(Fx,Ff)) +```` + +--- + +*This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).* + diff --git a/docs/src/DynamicBeamAnalysis.md b/docs/src/DynamicBeamAnalysis.md new file mode 100644 index 00000000..3214fe6f --- /dev/null +++ b/docs/src/DynamicBeamAnalysis.md @@ -0,0 +1,246 @@ +```@meta +EditURL = "../../examples/DynamicBeamAnalysis.jl" +``` + +# Dynamic analysis of a beam + +We perform the dynamic analysis of a steel catenary riser (SCR) subject to forced top motions. We compare the results against the corresponding SIMA/RIFLEX example case. The riser consists of three segments with two different cross-sections. + +NB: In two places in this script, `solve` is called with optional `verbose=false`, because this script is part of the generation +of `Muscade`'s online documentation. Setting `verbose=true` would be more relevant in other contexts. + +````@example DynamicBeamAnalysis +using Muscade, StaticArrays, GLMakie, Muscade.Toolbox, Interpolations, CSV, DataFrames +```` + +Read RIFLEX motions, tensions, bending moment and curvatures time series (verification data) + +````@example DynamicBeamAnalysis +file_path = "SCR.csv" +df = CSV.read(file_path, DataFrame; delim=' ') +dynMotionX = vcat(0,df[:,"Displacement in x - direction"].-df[1,"Displacement in x - direction"],df[end,"Displacement in x - direction"]-df[1,"Displacement in x - direction"]) +dynMotionZ = vcat(0,df[:,"Displacement in z - direction"].-df[1,"Displacement in z - direction"],df[end,"Displacement in z - direction"]-df[1,"Displacement in z - direction"]) +dynMotionT = vcat(-10.,df[:,"x"],df[end,"x"]+100) +xMotion = linear_interpolation(dynMotionT,-dynMotionX) +zMotion = linear_interpolation(dynMotionT,dynMotionZ); +nothing #hide +```` + +Some physical constants + +````@example DynamicBeamAnalysis +const g=9.81 +const ρ=1025.; +nothing #hide +```` + +Normalized gravity field, ramping up during static analysis + +````@example DynamicBeamAnalysis +@functor with() ramping_gravityField(t)= clutch(t,-9.,-5.,0.,1.,1) * SVector(0.,0.,-1.); +nothing #hide +```` + +Define parameters for cross-section 1 + +````@example DynamicBeamAnalysis +x1_D = 0.429 # Outer diameter [m] +x1_t = 0.022 # Thickness [m] +x1_steelArea = (x1_D-x1_t)*π*x1_t # Pipe wall area [m^2] +x1_innerArea = (x1_D-2*x1_t)^2*π/4 # Inner area [m^2] +x1_ρₛ = 7850. # Steel denstiy [kg/m^3] +x1_ρᵢ = 200. # Internal fluid density [kg/m^3] +x1_EA = 5.823e9 # Axial stiffness [N] +x1_EI₂ = 1.209e8 # Bending stiffness [Nm/(1/m)] +x1_EI₃ = 1.209e8 # Bending stiffness [Nm/(1/m)] +x1_GJ = 9.347e7 # Torsional stiffness [Nm/(rad/m)] +x1_μ = x1_steelArea*x1_ρₛ + x1_innerArea*x1_ρᵢ # Mass per unit length [m] +x1_ι₁ = 0.2053^2*x1_steelArea*x1_ρₛ # Moment of inertia about x-axis per unit length [kgm²/m] +x1_w = x1_μ*g - π*x1_D^2/4*ρ*g # Weight per unit length [N/m] +x1_Dh = 0.459 # Hydrodynamic outer diameter [m] +x1_Ca₂ = 1.0 * ρ * π*x1_Dh^2/4 # Transverse added mass coefficients [N/m/(m/s^2)] +x1_Ca₃ = 1.0 * ρ * π*x1_Dh^2/4 +x1_Cq₂ = 1.0 * 0.5 * ρ * x1_Dh # Transverse drag coefficients [N/m/(m/s)^2] +x1_Cq₃ = 1.0 * 0.5 * ρ * x1_Dh +x1_mat = BeamCrossSection(EA=x1_EA, EI₂=x1_EI₂, EI₃=x1_EI₃, GJ=x1_GJ, μ=x1_μ, ι₁=x1_ι₁, w=x1_w, g̃=ramping_gravityField, Ca₂=x1_Ca₂, Cq₂=x1_Cq₂, Ca₃=x1_Ca₃, Cq₃=x1_Cq₃) +```` + +Define parameters for cross-section 2 + +````@example DynamicBeamAnalysis +x2_D = 0.441 # Outer diameter [m] +x2_t = 0.028 # Thickness [m] +x2_steelArea = (x2_D-x2_t)*π*x2_t # Pipe wall area [m^2] +x2_innerArea = (x2_D-2*x2_t)^2*π/4 # Inner area [m^2] +x2_ρₛ = 7850. # Steel denstiy [kg/m^3] +x2_ρᵢ = 200. # Internal fluid density [kg/m^3] +x2_EA = 7.520e9 # Axial stiffness [N] +x2_EI₂ = 1.611e8 # Bending stiffness [Nm/(1/m)] +x2_EI₃ = 1.611e8 # Bending stiffness [Nm/(1/m)] +x2_GJ = 1.245e8 # Torsional stiffness [Nm/(rad/m)] +x2_μ = x2_steelArea*x2_ρₛ + x2_innerArea*x2_ρᵢ # Mass per unit length [m] +x2_ι₁ = 0.2084^2*x2_steelArea*x2_ρₛ # Moment of inertia about x-axis per unit length [kgm²/m] +x2_w = x2_μ*g - π*x2_D^2/4*ρ*g # Weight per unit length [N/m] +x2_Dh = 0.471 # Hydrodynamic outer diameter [m] +x2_Ca₂ = 1.0 * ρ * π*x2_Dh^2/4 # Transverse added mass coefficients [N/m/(m/s^2)] +x2_Ca₃ = 1.0 * ρ * π*x2_Dh^2/4 +x2_Cq₂ = 1.0 * 0.5 * ρ * x2_Dh # Transverse drag coefficients [N/m/(m/s)^2] +x2_Cq₃ = 1.0 * 0.5 * ρ * x2_Dh +x2_mat = BeamCrossSection(EA=x2_EA, EI₂=x2_EI₂, EI₃=x2_EI₃, GJ=x2_GJ, μ=x2_μ, ι₁=x2_ι₁, w=x2_w, g̃=ramping_gravityField, Ca₂=x2_Ca₂, Cq₂=x2_Cq₂, Ca₃=x2_Ca₃, Cq₃=x2_Cq₃) +```` + +Model SCR, starting from the extremity located on seabed + +````@example DynamicBeamAnalysis +nel = [60, 30, 10] # Number of elements per segment +segLength = [300., 300., 80.] # Segment lengths +xSection = [x1_mat, x2_mat, x1_mat]; # Cross-section type +nothing #hide +```` + +Create Muscade model + +````@example DynamicBeamAnalysis +model = Model(:CatenaryRiser); +nothing #hide +```` + +Create nodes, elements representing the SCR + +````@example DynamicBeamAnalysis +topNode = addnode!(model,[0,0,0]) +nodeList, elementList, nodeCoord = MeshLine!(model, topNode, π, EulerBeam3D, xSection, segLength, nel; orient2=SVector(0.,1,0)); +nothing #hide +```` + +Fix lower extremity + +````@example DynamicBeamAnalysis +[addelement!(model,Hold,[nodeList[1][1]] ;field) for field∈[:t1,:t2,:t3,:r1]]; +nothing #hide +```` + +Loading procedure for the static analysis is as follows +1) start by elongating the line to create geometric stiffness +2) apply the weight (can be done rapidly) +3) move the end of the line to the prescribed displacement +4) contact forces + +Define the prescribed end displacements of the top extremity + +````@example DynamicBeamAnalysis +@functor with(xMotion) horizMove(x,t)= SVector( x[1]-(1.0 - clutch(t,-10.,0,0.,1.,3)*181.0 + xMotion(t)) ) +@functor with(zMotion) vertMove(x,t) = SVector( x[1]-( clutch(t,-10.,0,0.,1.,3)*303.1 + zMotion(t)) ) +addelement!(model,DofConstraint,[nodeList[3][end]]; λclass=:X, xinod=(1,),xfield=(:t1,), λinod=(1,),λfield=(:λt1,), gap=horizMove, mode=Muscade.equal) +addelement!(model,DofConstraint,[nodeList[3][end]]; λclass=:X, xinod=(1,),xfield=(:t3,), λinod=(1,),λfield=(:λt3,), gap=vertMove , mode=Muscade.equal); +nothing #hide +```` + +Contact elements for the bottom segment + +````@example DynamicBeamAnalysis +[addelement!(model,SoilContact,[nodeList[1][idxNod]],z₀=0.,Kh=1.0e3,Kv=1.0e4,Ch=0.,Cv=0.) for idxNod = 1:length(nodeList[1])]; +nothing #hide +```` + +Run the static analysis + +````@example DynamicBeamAnalysis +initialstate = initialize!(model); +staticLoadSteps = (-10:.2:0)*1. +nStaticLoadSteps = length(staticLoadSteps) +staticStates = solve(SweepX{0};initialstate,time=staticLoadSteps,verbose=false,maxΔx=1e-6,maxiter=100); +nothing #hide +```` + +Plot the static analysis sequence + +````@example DynamicBeamAnalysis +fig = Figure(size = (1000,1000)) +ax = Axis3(fig[1,1]) +for stateIdx ∈ 1:nStaticLoadSteps + draw!(ax,staticStates[stateIdx],EulerBeam3D=(;style=:shape)) +end +currentDir = @__DIR__ +if occursin("build", currentDir) + save(normpath(joinpath(currentDir,"..","src","assets","staticEquilibriumSCR.png")),fig) +elseif occursin("examples", currentDir) + save(normpath(joinpath(currentDir,"staticEquilibriumSCR.png")),fig) +end +```` + +![Result](assets/staticEquilibriumSCR.png) + +Run the dynamic analysis + +````@example DynamicBeamAnalysis +dynamicLoadSteps = (0.1:0.3:300)*1.0 +nDynamicLoadSteps = length(dynamicLoadSteps) +dynamicStates = solve(SweepX{2}; + initialstate=staticStates[nStaticLoadSteps], + time=dynamicLoadSteps, + verbose=false, + maxΔx=1e-5); +nothing #hide +```` + +Retrieve axial force at top location + +````@example DynamicBeamAnalysis +req = @request gp(resultants(fᵢ)) +out = getresult(dynamicStates,req,[elementList[end]]) +Fgp1_ = [ out[idxEl].gp[1][:resultants][:fᵢ] for idxEl ∈ 1:size(out,2)]; +nothing #hide +```` + +Retrieve bending moments near touch down point + +````@example DynamicBeamAnalysis +req = @request gp(resultants(mᵢ)) +out = getresult(dynamicStates,req,[elementList[64]]) +Mgp1_ = [ out[idxEl].gp[1][:resultants][:mᵢ] for idxEl ∈ 1:size(out,2)]; +nothing #hide +```` + +Retrieve curvature near touch down point + +````@example DynamicBeamAnalysis +req = @request gp(κgp) +out = getresult(dynamicStates,req,[elementList[64]]) +κgp1_ = [ out[idxEl].gp[1].κgp[1] for idxEl ∈ 1:size(out,2)]; +nothing #hide +```` + +Plot comparison between Muscade and RIFLEX results. + +````@example DynamicBeamAnalysis +fig2 = Figure(size = (1000,1000)) +ax1 = Axis(fig2[1, 1],ylabel="Top horiz. disp. [m]") +lines!(ax1,dynamicLoadSteps,xMotion(dynamicLoadSteps)) +ax2 = Axis(fig2[2, 1],ylabel="Top vert. disp. [m]") +lines!(ax2,dynamicLoadSteps,zMotion(dynamicLoadSteps)) +ax3 = Axis(fig2[3, 1],ylabel="Axial force [N]") +lines!(ax3, dynamicLoadSteps, Fgp1_, label="Muscade") +lines!(ax3, df[:,"x"],df[:,"Axial force"], label="RIFLEX") +axislegend() +ax4 = Axis(fig2[4, 1],ylabel="Bending mom. [Nm]") +lines!(ax4, dynamicLoadSteps, getindex.(Mgp1_,3), label="Muscade") +lines!(ax4, df[:,"x"],df[:,"Mom. about local y-axis, end 1"], label="RIFLEX") +ax5 = Axis(fig2[5, 1],ylabel="Curvature [m^{-1}]") +lines!(ax5, dynamicLoadSteps, getindex.(κgp1_,3), label="Muscade") +lines!(ax5, df[:,"x"],df[:,"Curvature about local y-axis, end 1"], label="RIFLEX") +if occursin("build", currentDir) + save(normpath(joinpath(currentDir,"..","src","assets","dynamicAnalysisSCR.png")),fig2) +elseif occursin("examples", currentDir) + save(normpath(joinpath(currentDir,"dynamicAnalysisSCR.png")),fig2) +end +```` + +Minor discrepancies might be due to the fact that loads are extracted at Gauss points in Muscade, while they are extracted at nodes in RIFLEX. + +![Result](assets/dynamicAnalysisSCR.png) + +--- + +*This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).* + diff --git a/docs/src/Elements.md b/docs/src/Elements.md index dbf9cf6a..ed40ff00 100644 --- a/docs/src/Elements.md +++ b/docs/src/Elements.md @@ -226,18 +226,74 @@ See [`Muscade.residual`](@ref) for the list of arguments and outputs. Some solvers may prefer to evaluate 2nd order derivatives of `residual`. However, for elements with anything but a small number of degrees of freedom, this quickly leads to intractably high compilation and/or execution times. If this is the case, then the element should implement [`Muscade.no_second_order`](@ref) to limit differentiation to the first order only. + + + ### Automatic differentiation -The gradients and Hessians of `R` or `L` do not need to be implemented, because `Muscade` uses [automatic differentiation](Adiff.md). Because of this, it is important not to over-specify the inputs. For example, -implementing a function header with +While solvers usualy require the Jacobians of `R` with respect to `X`, `̇X`, `̈X`, `U` and `A`, and the gradient and Hessians of `L`, their evaluation does not need to be implemented in `Muscade.lagrangian` or `Muscade.residual`. This is because Muscade uses a form of automatic differentiation known as "forward automatic differentiation by operator overleading". In this technique, instead of passing an input `X` that is a `ntuple` of `SVector` of `Float64` (that can be noted `𝕣` "\Bbbr" in `Muscade`), all or some of the `SVector` in the `tuple` can have elements of type `∂ℝ`, while is a real number with partial differences, to the first or second order. As `∂ℝ` propagates through the function, operations like `*` and `sin` also update the partial derivatives, because they have been "overloaded" (specific methods have been added to these functions). Two simplified examples of differentiation to the first order: + +```julia +struct ∂ℝ{P,N,R} <:Real where{R<:Real} # P precedence, N number of partials, + # R type of the variable (∂ℝ can be nested) + x :: R # value + dx :: SVector{N,R} # N partial derivatives +end + +# value partial derivatives +Base.(:* )(a::∂ℝ{1,N,𝕣},b::∂ℝ{1,N,𝕣}) where{N} = ∂ℝ{1,N,𝕣}(a.x*b.x , a.x*b.dx+a.dx*b.dx) +Base.(sin)(a::∂ℝ{1,N,𝕣} ) where{N} = ∂ℝ{1,N,𝕣}(sin(a.x) , cos(a.x)*a.dx ) +Base.(:< )(a::∂ℝ{1,N,𝕣},b::∂ℝ{1,N,𝕣}) where{N} = a.x < b.x # not affected by derivatives +``` + +where `a.dx` and `b.dx` are vectors with `N` partial derivatives. These function definitions express if ``c = a \cdot b``, then ``\frac{\partial c}{\partial x} = a\cdot\frac{\partial b}{\partial x} + \frac{\partial a}{\partial x}⋅ b``, and if ``b = \sin(a)`` then ``\frac{\partial b}{\partial x} = \cos(a)\cdot\frac{\partial a}{\partial x}``. + +In general, the fact that `Muscade.lagrangian` or `Muscade.residual` can be differentiated in this way does generaly not affect how the function is to be written. See the `Muscade.residual` method of [`Muscade.Toolbox.Bar3D`](@ref) for a simple example. There are however two points to be aware of: + +First, do not specify the type of inputs `Λ`, `X`, `U`, `A` and `t`. For example ```julia @espy function Muscade.lagrangian(o::MyElement,Λ::Vector{Float64},X,U,A,t,SP,dbg) -# |___bad_idea___| +# |____bad_idea___| ``` -would cause a `MethodError`, because `Muscade` will attempt to call with a `SVector` instead of `Vector`, and a special -datatype supporting automatic differentiation instead of `Float64`. +would cause a `MethodError`, because `Muscade` will attempt to call `lagrangian` with a `SVector{L,∂ℝ...}`, and the method only accepts a`Vector{𝕣}`. + +Second, beware of branches (`if` and `cond ? opt1 : opt2`). In the following code + +```julia +if x>0 + y=x # y is of type ∂ℝ +else + y=0. # y is of type 𝕣 +end +``` + +the type of `y` depends on the *value* of `x` and can thus not be determined at compilation. This is [type instability](TypeStable.md) and results in *very* slow execution. + +When a number of type `∂ℝ` is printed, both value and partial derivatives are presented, but strongly truncated, to keep printouts compact + +```julia +@show x +x = 3.1+∂₁⟨1.3,0.6⟩ +``` + +When debugging an element which uses simple automatic differentiation, a good rule of thumb is to get the values computed correctly, then the derivatives will be correct too. When inserting debug printouts in the code, use [`VALUE`](@ref) to strip all the partials: + +```julia +@show VALUE(x) +VALUE(x) = 3.1458766 +``` + +Do not use `VALUE` for other purposes - unless you know what you are doing. + +The `Muscade.residual` method of [`Muscade.Toolbox.EulerBeam3D`](@ref) shows an *advanced* example where the code is written in order to + +1) accelerate automatic differentiation (where possible). +2) compute derivatives to handle the transformation from e.g. stress resultants into nodal forces, in the presence of a corotated reference system. + +See [automatic differentiation](Adiff.md) for a discussion of these and other advanced techniques. + ### [Extraction of element-results](@id espy) @@ -351,19 +407,23 @@ For a given element formulation, the performance of `Muscade.residual` and `Musc **Type stable code** allows the compiler to know the type of every variable in a function given the type of its parameters. Code that is type unstable is significantly slower. See the page on [type stability](TypeStable.md). -**Allocation**, and the corresponding deallocation of memory *on the heap* takes time. By contrast, allocation and deallocation *on the stack* is fast. In Julia, only immutable variables can be allocated on the stack. See the page on [memory management](Memory.md) +**Allocation** *on the heap* and the corresponding deallocation of memory by Julia's "garbage collector" takes time. By contrast, allocation and deallocation *on the stack* is fast. In Julia, only immutable variables of length known at compile time can be allocated on the stack. See the page on [memory management](Memory.md). One gotcha to be aware of is when extracting a subvector from a vector: the code -**Automatic differentiation** generaly does not affect how `Muscade.residual` and `Muscade.lagrangian` are written. There are two performance-related exceptions to this: +```julia +r = X0[4:6] # r is a Vector, heap allocated, slow +``` -1. If a complicated sub-function in `Muscade.residual` and `Muscade.lagrangian` (typicaly a material model or other closure) operates on an array (for example, the strain) that is smaller than the number of degrees of freedom of the system, computing time can be saved by computing the derivative of the output (in the example, the stress) with respect to the input to the subfunction, and then chainrule the derivatives. -2. Iterative precedures are sometimes used within `Muscade.residual` and `Muscade.lagrangian`, a typical example being in plastic material formulations. There is no need to propagate automatic differentiation through all the iterations - doing so with the result of the iteration provides the same result. -3. Elements with corotated reference system (e.g. [beam elements](StaticBeamAnalysis.md)) can use automatic differentiation to transform the residual back to the global reference system. +results in allocations. `r` is a `Vector`, because the length of a range like `4:6` is not part of its type and thus not known to the compiler, making it impossible to make `r` a SVector. Instead we need to write one of the lines below. -See the page on [automatic differentiation](Adiff.md). +```julia +r = X0[SVector(4,5,6) ] # The compiler can count 3 arguments +r = X0[SVector{3}(4:6)] # or read a type parameter + # r is a SVector, on the stack, fast +``` -## Method for graphics: `Muscade.allocate_drawing`, `Muscade.update_drawing` and `Muscade.display_drawing!` +## Method for graphics ### Template The element can provide methods of the form @@ -466,15 +526,6 @@ For those prefering to think in terms of Cartesian tensor algebra, rather than m Elements with a corotated reference system, can make use of [`toolbox/Rotations.jl`](StaticBeamAnalysis.md) that provides functionality to handle rotations in ℝ³. See [`toolbox/BeamElement.jl`](StaticBeamAnalysis.md) for an example. -## Automatic differentiation within element code - -Some advanced elements (in particular, elements with co-rotated element systems) can be implemented elegantly by using automatic differentiation within `residual` or `lagrangian`. These are advanced techniques, requiring a good understanding of [`automatic differentiation`](Adiff.md). Example of usage can be found in [`toolbox/BeamElement.jl`](StaticBeamAnalysis.md). - -Helper functions [`motion`](@ref) and [`motion⁻¹`](@ref) allow to transform a `tuple` of `SVectors`, like the input `X` given to `residual` and `lagrangian`, into a an automatic differentiation structure, so that functions of `∂0(X)` only can be differentiated with respect to time. - -It is sometimes possible to improve performance by identifying a part of `residual` or `lagrangian` which takes a single, `SVector` as an input: A vector shorter than the list of dofs differentiated by the solver allow to accelerate computations, by using [`apply`](@ref), or for more advanced usage, [`revariate`](@ref) in combination with [`chainrule`](@ref). - -In [`toolbox/BeamElement.jl`](StaticBeamAnalysis.md), in function `kinematics`, [`apply`](@ref) is applied to accelerate a process of differentiation to the 2nd order. In `residual`, [`revariate`](@ref) and [`chainrule`](@ref) in order to differentiate `kinematics` and accelerate computations by exploiting the fact that `kinematic` is a function of `∂0(X)` only. diff --git a/docs/src/LICENSE.md b/docs/src/LICENSE.md new file mode 100644 index 00000000..2dc17752 --- /dev/null +++ b/docs/src/LICENSE.md @@ -0,0 +1,21 @@ +# MIT License + +Copyright (c) 2022-2026 SINTEF Ocean + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/docs/src/ModalBeamAnalysis.md b/docs/src/ModalBeamAnalysis.md new file mode 100644 index 00000000..603d46ed --- /dev/null +++ b/docs/src/ModalBeamAnalysis.md @@ -0,0 +1,106 @@ +```@meta +EditURL = "../../examples/ModalBeamAnalysis.jl" +``` + +# Modal analysis of a beam + +Beam simply supported at both ends + +````@example ModalBeamAnalysis +using Muscade, StaticArrays, GLMakie +using Muscade.Toolbox + +L = 1.; # Beam length [m] +q = 0.0; # Uniform lateral load [N/m] +EI₂ = 1.; # Bending stiffness [Nm²] +EI₃ = 1.; # Bending stiffness [Nm²] +EA = 1e6; # Axial stiffness [N] +GJ = 1e6; # Torsional stiffness [Nm²] +μ = 1.; +ι₁= 1.; +nothing #hide +```` + +Create model + +````@example ModalBeamAnalysis +nel = 50 +Nnod = nel+1 +nodeCoord = hcat((0:L/nel:L),zeros(Float64,Nnod,2)) +mat = BeamCrossSection(EA=EA,EI₂=EI₂,EI₃=EI₃,GJ=GJ,μ=μ,ι₁=ι₁) +model = Model(:TestModel) +nodid = addnode!(model,nodeCoord) +mesh = hcat(nodid[1:Nnod-1],nodid[2:Nnod]) +eleid = addelement!(model,EulerBeam3D,mesh;mat=mat,orient2=SVector(0.,1.,0.)); +nothing #hide +```` + +Set boundary conditions and constraints + +````@example ModalBeamAnalysis +[addelement!(model,Hold,[nodid[1]] ;field) for field∈[:t1,:t2,:t3,:r1]] # Simply supported end 1 +[addelement!(model,Hold,[nodid[end]];field) for field∈[:t1,:t2,:t3,:r1]] # Simply supported end 2 +[addelement!(model,Hold,[nodid[nodeidx]];field=:t3) for nodeidx∈2:Nnod-1] # Enforce beam motions in one dimension to obtain planar modeshapes +@functor with(q,L,Nnod) val(t) = sin(t)*q*L/Nnod +[addelement!(model,DofLoad,[nodid[nodeidx]];field=:t2,value=val) for nodeidx=1:Nnod]; # Distributed vertical load q +nothing #hide +```` + +Static analysis + +````@example ModalBeamAnalysis +initialstate = initialize!(model); +state = solve(SweepX{0};initialstate,time=[0.]); +nothing #hide +```` + +Solve eigenvalue problem + +````@example ModalBeamAnalysis +nmod = 15 +res = solve(EigX{ℝ};state=state[1],nmod); +nothing #hide +```` + +Analytical solutions for the natural frequency of a simply supported beam +See e.g. https://roymech.org/Useful_Tables/Vibrations/Natural_Vibrations_derivation.html + +````@example ModalBeamAnalysis +fₙ(k) = √(EI₂/μ)*(k^2*π)/(2*L^2) +Φₙ(k,x) = sin.(k*π/L.*x); +nothing #hide +```` + +Display solution and comparison against analytical solution + +````@example ModalBeamAnalysis +fig = Figure(size = (2000,1000)) +axes = [Axis(fig[idxLine,1], yminorgridvisible = false,xminorgridvisible = false ) for idxLine=1:3] +axes[1].title = "Modeshapes of a simply supported beam. Muscade (" *string(nel)*" elements): markers. Analytical solution: lines. " +for idxMod=1:nmod + eigres = increment(state[1],res,[idxMod],[1]); + t2_eig = getdof(eigres;field=:t2,nodID=nodid[1:Nnod]) + δ = sign(Φₙ(idxMod,0:L/nel:L)'*t2_eig) * maximum(t2_eig) + selectAxis = axes[mod(idxMod-1,3)+1] + labelStr= "Mode "*string(idxMod)*", Muscade: "*string(round(res.ω[idxMod]/(2π),digits=3))*" Hz, Analytical: " *string(round(fₙ(idxMod),digits=3))* " Hz" + scatter!(selectAxis,(0:L/nel:L), t2_eig[:]/δ, label=labelStr ); + lines!( selectAxis,(0:L/nel:L), Φₙ(idxMod,0:L/nel:L) ); +end +for ax∈axes; + xlims!(ax,0,1); ylims!(ax, -2,2); axislegend(ax) +end + +currentDir = @__DIR__ +if occursin("build", currentDir) + save(normpath(joinpath(currentDir,"..","src","assets","beamModes.png")),fig) +elseif occursin("examples", currentDir) + save(normpath(joinpath(currentDir,"beamModes.png")),fig) +end +```` + +![Result](assets/beamModes.png) + +--- + +*This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).* + diff --git a/docs/src/Rotations.jl b/docs/src/Rotations.jl new file mode 100644 index 00000000..64c5e459 --- /dev/null +++ b/docs/src/Rotations.jl @@ -0,0 +1,126 @@ +# # 3D rotations +using LinearAlgebra, StaticArrays +using Muscade: sinc1 +""" + Toolbox.scac(x) + +`scac(x) = sinc1(acos(x)),` The function can be differentiated +to the fourth order over ]-1,1] . + +See also [`Toolbox.sinc1`](@ref) +""" +function scac(x) + dx = x-1 + if abs(dx)>1e-3 + sinc1(acos(x)) + else # deliberately a long Taylor series (5th order): this function will be adiffed at least to 2nd order, up to 4th order + evalpoly(dx,(1,1/3,-2/90,0.0052911879917544626,-0.0016229317117234072,0.0005625)) + end +end + +const Mat33{R} = SMatrix{3,3,R,9} +const Vec3{R} = SVector{3,R} + +""" + Toolbox.spin(v::SVector{3}) + +Transform a rotation vector `v` into the cross product matrix `M`, such that +`M ∘₁ a = v × a`. + +See also [`Toolbox.spin⁻¹`](@ref), [`Toolbox.Rodrigues`](@ref), [`Toolbox.Rodrigues⁻¹`](@ref). +""" +spin(v::Vec3) = SMatrix{3,3}(0,v[3],-v[2],-v[3],0,v[1],v[2],-v[1],0) +""" + toolbox.spin⁻¹(M::SMatrix{3,3}) + +Transform a cross product matrix `M` into the rotation vector `v`, such that +`v × a = M ∘₁ a`. + +See also [`Toolbox.spin`](@ref), [`Toolbox.Rodrigues`](@ref), [`Toolbox.Rodrigues⁻¹`](@ref). +""" +spin⁻¹(m::Mat33) = SVector{3}(m[3,2]-m[2,3],m[1,3]-m[3,1],m[2,1]-m[1,2])/2 +""" + trace(v::SMatrix{3,3}) + +Computes the trace of a matrix. +""" +trace(m::Mat33) = m[1,1]+m[2,2]+m[3,3] +""" + Toolbox.Rodrigues⁻¹(v::SVector{3}) + +Transform a rotation matrix `M` into the rotation vector `v`, such that +`|v| < π`. Undefined for rotations of angle `π` + +See also [`Toolbox.spin`](@ref), [`Toolbox.spin⁻¹`](@ref), [`Toolbox.Rodrigues`](@ref), [`Toolbox.adjust`](@ref). +""" +Rodrigues⁻¹(m) = spin⁻¹(m)/scac((trace(m)-1.)/2.) # NB: is necessarily singular for π turn +function LinearAlgebra.norm(v::Vec3) # executes faster, COMPILES MUCH FASTER , and adiffs poorly at origin + n = sqrt(v[1]*v[1]+v[2]*v[2]+v[3]*v[3]) + if n<1e-14 + n = zero(eltype(v)) + end + return n +end + +function spin²(S::Vec3) + ab = S[2,3]*S[3,1] + ca = S[1,2]*S[2,3] + bc = S[3,1]*S[1,2] + ma² = S[3,2]*S[2,3] + mb² = S[3,1]*S[1,3] + mc² = S[2,1]*S[1,2] + return SMatrix{3,3}(mc²+mb²,ab,ca, ab,ma²+mc²,bc, ca,bc,ma²+mb²) +end + +""" + Toolbox.Rodrigues(v::SVector{3}) + +Transform a rotation vector `v` into the rotation matrix `M`. + +See also [`Toolbox.spin`](@ref), [`Toolbox.spin⁻¹`](@ref), [`Toolbox.Rodrigues⁻¹`](@ref), [`Toolbox.adjust`](@ref). +""" +@inline function Rodrigues(v::Vec3{R}) where{R} + # I + spin(v)*sinc1(norm3(v)) + spin²(v)*sinc1(norm3(v)/2)/√2 + θ = norm(v) + s₁ = sinc1(θ ) + s₂ = sinc1(θ/2)*(1/√2) + a,b,c = s₁*v[1],s₁*v[2],s₁*v[3] + vs₂ = v*s₂ + ab ,ac ,bc = vs₂[1]*vs₂[2], vs₂[1]*vs₂[3], vs₂[2]*vs₂[3] + ma²,mb²,mc² = vs₂[1]*vs₂[1], vs₂[2]*vs₂[2], vs₂[3]*vs₂[3] + return Mat33{R}(1. -mc²-mb²,ab+c,ac-b, ab-c,1. -ma²-mc²,bc+a, ac+b,bc-a,1. -ma²-mb²) +end + +""" + Toolbox.adjust(u::SVector{3},v::SVector{3}) + +Compute the matrix of the rotation with smallest angle that transforms `u` into a vector colinear with v. +Fails if |u|=0, |v|=0 or if the angle of the rotation is π. + +See also [`Toolbox.spin`](@ref), [`Toolbox.spin⁻¹`](@ref), [`Toolbox.Rodrigues`](@ref), [`Toolbox.Rodrigues⁻¹`](@ref). +""" +function adjust(u::Vec3{R},v::Vec3{R}) where{R} + u,v = normalize.((u,v)) + c,w = dot(u,v), cross(u,v) + s = norm(w) + θ = atan(s,c) + return w/sinc1(θ) +end +""" + Toolbox.intrinsicrotationrates(rₑ::NTuple{ND,SMatrix{3,3}}) where{ND} + +Transform a `NTuple` containing a rotation matrix and its extrinsic time derivatives, +into a `NTuple` containing a (zero) rotation vector and its intrinsic time derivatives. + +See also [`Toolbox.spin`](@ref), [`Toolbox.spin⁻¹`](@ref), [`Toolbox.Rodrigues`](@ref), [`Toolbox.Rodrigues⁻¹`](@ref). +""" +function intrinsicrotationrates(rₑ::NTuple{ND,SMatrix{3,3}}) where{ND} + vᵢ₀ = (SVector{3,𝕣}(0,0,0), ) + vᵢ₁ = ND<2 ? vᵢ₀ : (vᵢ₀... , spin⁻¹(∂0(rₑ)' ∘₁ ∂1(rₑ)) ) + vᵢ = ND<3 ? vᵢ₁ : (vᵢ₁... , spin⁻¹(∂1(rₑ)' ∘₁ ∂1(rₑ) + ∂0(rₑ)' ∘₁ ∂2(rₑ))) + return vᵢ +end + + + +; \ No newline at end of file diff --git a/docs/src/SCR.csv b/docs/src/SCR.csv new file mode 100644 index 00000000..511c9f19 --- /dev/null +++ b/docs/src/SCR.csv @@ -0,0 +1,3001 @@ +"x" "Curvature about local y-axis, end 1" "Mom. about local y-axis, end 1" "Axial force" "Displacement in x - direction" "Displacement in z - direction" +0.10000000149011612 0.006851674057543278 1103638.0615234375 543760.3759765625 35.35993576049805 3.0999464988708496 +0.20000000298023224 0.006851695012301207 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4.849627494812012 +300.00000447034836 0.006735431496053934 1084914.1845703125 431996.9482421875 31.949846267700195 4.7335686683654785 diff --git a/docs/src/Solvers.md b/docs/src/Solvers.md index 2415b902..963ead4d 100644 --- a/docs/src/Solvers.md +++ b/docs/src/Solvers.md @@ -14,12 +14,22 @@ See the reference manual [`EigX`](@ref). `SweepX{2}` is a Newmark-β solver for differential equations of order `2` in time. A typical application is in structural dynamics. -`SweepX` solves forward FEM problems (not optimisation-FEM) (see [Theory](@ref)). However, `SweepX` can be applied to models that have ``U``- and ``A``-dofs. This is handled as follows: One input to `SweepX` is a `State`, which can come from [`initialize!`](@ref) or from the output of another solver. `SweepX` will keep the ``U``- and ``A``-dofs to the value in the input `State`. `initialize!` sets all dofs to zero, so when `SweepX` is given a `State` produced by `initialize!` the analysis starts with ``X``-dofs equal to zero, and ``U``- and ``A``-dofs are kept zero throughout the analysis. +`SweepX` solves forward FEM problems (not optimisation-FEM) (see [Theory](Theory.md)). However, `SweepX` can be applied to models that have ``U``- and ``A``-dofs. This is handled as follows: One input to `SweepX` is a `State`, which can come from [`initialize!`](@ref) or from the output of another solver. `SweepX` will keep the ``U``- and ``A``-dofs to the value in the input `State`. `initialize!` sets all dofs to zero, so when `SweepX` is given a `State` produced by `initialize!` the analysis starts with ``X``-dofs equal to zero, and ``U``- and ``A``-dofs are kept zero throughout the analysis. `SweepX` handles inequality constraints (for example defined with the built-in [`DofConstraint`](@ref) element) using a simplified interior point method. See the reference manual [`SweepX`](@ref). +## `SweepXA`: design optimisation + +Finds the design parameters `A` for which the response of the model, for given initial conditions, has minimum cost. The model will typicaly have costs contributions associated to the design parameters `A` ("expensive build"), and to the response parameters `X` ("this response of the system exceeds allowables stresses, leading to an expensive failure"). + +For a given value of `A`, `SweepXA{OX}` does the same computations as `SweepX{OX}`. + +As for `SweepX`, `SweepXA` can be applied to models that have ``U``-dofs. + +See the reference manual [`SweepXA`](@ref). + ## `DirectXUA`: non-linear inverse solver `DirectXUA` is a solver for non-linear, static (`OX=0`), first order (`OX=1`) or dynamic (`OX=2`), optimisation-FEM problems. The same remarks on "state" variables and the choice of `OX` as for `SweepX` apply here. diff --git a/docs/src/StaticBeamAnalysis.md b/docs/src/StaticBeamAnalysis.md new file mode 100644 index 00000000..381a7322 --- /dev/null +++ b/docs/src/StaticBeamAnalysis.md @@ -0,0 +1,218 @@ +```@meta +EditURL = "../../examples/StaticBeamAnalysis.jl" +``` + +# Static analysis of a beam + +Cantilever bend, with out-of-plane load leading to a three-dimensional response mobilizing axial force, bending moment and torque. +Comparison to solutions by Longva (2015) and Crisfield (1990) + +````@example StaticBeamAnalysis +using Muscade, StaticArrays, GLMakie +using Muscade.Toolbox + +R = 100.0; # Radius of the bend [m] +EI₂ = 833.33e3; # Bending stiffness [Nm²] +EI₃ = 833.33e3; # Bending stiffness [Nm²] +EA = 1e9; # Axial stiffness [N] +GJ = 705e3; # Torsional stiffness [Nm²] +nothing #hide +```` + +Create the model + +````@example StaticBeamAnalysis +nel = 8 +nnodes = nel+1 +nodeCoord = hcat( 0 .+ R*cos.(3π/2 .+ ((1:nnodes).-1)/(nnodes-1)*π/4), + 0 .+ zeros(Float64,nnodes,1), + R .+ R*sin.(3π/2 .+ ((1:nnodes).-1)/(nnodes-1)*π/4)) +mat = BeamCrossSection(EA=EA,EI₂=EI₂,EI₃=EI₃,GJ=GJ,μ=1.,ι₁=1.) +model = Model(:TestModel) +nodid = addnode!(model,nodeCoord) +mesh = hcat(nodid[1:nnodes-1],nodid[2:nnodes]) +eleid = addelement!(model,EulerBeam3D,mesh;mat=mat,orient2=SVector(0.,1.,0.)) +[addelement!(model,Hold,[nodid[1]] ;field) for field∈[:t1,:t2,:t3,:r1,:r2,:r3]]; # Clamp at one end +nothing #hide +```` + +Define the loading procedure. First 300 N then 450 and 600 N + +````@example StaticBeamAnalysis +@functor with() function load(t) + t<=1. ? load=t*300. : + t>1. && t<=2. ? load=300. +(t-1)*150. : + load=450. +(t-2)*150. +end +addelement!(model,DofLoad,[nodid[nnodes]];field=:t2,value=load); # Force along axis2 at other +nothing #hide +```` + +Run the static analysis + +````@example StaticBeamAnalysis +initialstate = initialize!(model); +loadSteps = [0.,1.,2.,3.]; +nLoadSteps = length(loadSteps) +state = solve(SweepX{0};initialstate,time=loadSteps,verbose=true,maxΔx=1e-9); +nothing #hide +```` + +Fetch and show beam profile for all load cases + +````@example StaticBeamAnalysis +x_ = [getdof(state[idxLoad];field=:t1,nodID=nodid[1:nnodes]) for idxLoad ∈ 1:nLoadSteps] +y_ = [getdof(state[idxLoad];field=:t2,nodID=nodid[1:nnodes]) for idxLoad ∈ 1:nLoadSteps] +z_ = [getdof(state[idxLoad];field=:t3,nodID=nodid[1:nnodes]) for idxLoad ∈ 1:nLoadSteps] + +fig = Figure(size = (1000,1000)) +ax = Axis3(fig[1,1],xlabel="x [m]", ylabel="y [m]", zlabel="z [m]",aspect=:equal) +clr = [:black,:blue,:green,:red] +for idxLoad ∈ 1:nLoadSteps + draw!(ax,state[idxLoad];EulerBeam3D=(;nseg=10,line_color=clr[idxLoad])) +end +xlims!(ax, 0,70); ylims!(ax, 0,60); zlims!(ax, 0,40); +currentDir = @__DIR__ +if occursin("build", currentDir) + save(normpath(joinpath(currentDir,"..","src","assets","StaticBeamAnalysis1.png")),fig) +elseif occursin("examples", currentDir) + save(normpath(joinpath(currentDir,"StaticBeamAnalysis1.png")),fig) +end +```` + +![Result](assets/StaticBeamAnalysis1.png) + +Fetch and display results at the Gauss points for the last load case + +````@example StaticBeamAnalysis +idxLoad = 4; +nothing #hide +```` + +Location of the 4 Gauss points + +````@example StaticBeamAnalysis +xgp1 = (1. /nel)*( (0.5-1/2*sqrt(3/7+2/7*sqrt(6/5))) :1:nel) +xgp2 = (1. /nel)*( (0.5-1/2*sqrt(3/7-2/7*sqrt(6/5))) :1:nel) +xgp3 = (1. /nel)*( (0.5+1/2*sqrt(3/7-2/7*sqrt(6/5))) :1:nel) +xgp4 = (1. /nel)*( (0.5+1/2*sqrt(3/7+2/7*sqrt(6/5))) :1:nel) +xgps = [xgp1;xgp2;xgp3;xgp4]; +nothing #hide +```` + +Axial force + +````@example StaticBeamAnalysis +req = @request gp(resultants(fᵢ)) +out = getresult(state[idxLoad],req,eleid) +Fgp1_ = [ out[idxEl].gp[1][:resultants][:fᵢ] for idxEl ∈ 1:nel] +Fgp2_ = [ out[idxEl].gp[2][:resultants][:fᵢ] for idxEl ∈ 1:nel] +Fgp3_ = [ out[idxEl].gp[3][:resultants][:fᵢ] for idxEl ∈ 1:nel] +Fgp4_ = [ out[idxEl].gp[4][:resultants][:fᵢ] for idxEl ∈ 1:nel]; +nothing #hide +```` + +Bending moments + +````@example StaticBeamAnalysis +req = @request gp(resultants(mᵢ)) +out = getresult(state[idxLoad],req,eleid) +Mgp1_ = [ out[idxEl].gp[1][:resultants][:mᵢ] for idxEl ∈ 1:nel] +Mgp2_ = [ out[idxEl].gp[2][:resultants][:mᵢ] for idxEl ∈ 1:nel] +Mgp3_ = [ out[idxEl].gp[3][:resultants][:mᵢ] for idxEl ∈ 1:nel] +Mgp4_ = [ out[idxEl].gp[4][:resultants][:mᵢ] for idxEl ∈ 1:nel]; +nothing #hide +```` + +Strains + +````@example StaticBeamAnalysis +req = @request ε +out = getresult(state[idxLoad],req,eleid) +εgp1_ = [ out[idxEl].ε[1] for idxEl ∈ 1:nel] +εgp2_ = [ out[idxEl].ε[1] for idxEl ∈ 1:nel]; +εgp3_ = [ out[idxEl].ε[1] for idxEl ∈ 1:nel]; +εgp4_ = [ out[idxEl].ε[1] for idxEl ∈ 1:nel]; +nothing #hide +```` + +Curvatures + +````@example StaticBeamAnalysis +req = @request gp(κgp) +out = getresult(state[idxLoad],req,eleid) +κgp1_ = [ out[idxEl].gp[1].κgp[1] for idxEl ∈ 1:nel] +κgp2_ = [ out[idxEl].gp[2].κgp[1] for idxEl ∈ 1:nel] +κgp3_ = [ out[idxEl].gp[3].κgp[1] for idxEl ∈ 1:nel] +κgp4_ = [ out[idxEl].gp[4].κgp[1] for idxEl ∈ 1:nel]; +nothing #hide +```` + +Plot strains, etc. at Gauss points + +````@example StaticBeamAnalysis +fig = Figure(size = (1000,1000)) +ax=Axis(fig[1,1], ylabel="Forces F [N]", yminorgridvisible = true,xminorgridvisible = true,xticks = (0:1. /nel:1)) +scatter!(ax,xgps, [[Fgp1_[iel][1] for iel=1:nel] ; [Fgp2_[iel][1] for iel=1:nel] ; [Fgp3_[iel][1] for iel=1:nel] ; [Fgp4_[iel][1] for iel=1:nel]], label="F₁"); +ax.title = "Internal loads, elongation and curvature at last load step" +axislegend(); +ax=Axis(fig[2,1], ylabel="Strain [-]", yminorgridvisible = true,xminorgridvisible = true,xticks = (0:1. /nel:1)) +scatter!(ax,xgps, [[εgp1_[iel][1] for iel=1:nel] ; [εgp2_[iel][1] for iel=1:nel] ; [εgp3_[iel][1] for iel=1:nel] ; [εgp4_[iel][1] for iel=1:nel]], label="ε"); +ax=Axis(fig[3,1], ylabel="Moments M [Nm]", yminorgridvisible = true,xminorgridvisible = true,xticks = (0:1. /nel:1)) +scatter!(ax,xgps, [[Mgp1_[iel][1] for iel=1:nel] ; [Mgp2_[iel][1] for iel=1:nel] ; [Mgp3_[iel][1] for iel=1:nel] ; [Mgp4_[iel][1] for iel=1:nel]], label="M₁"); +scatter!(ax,xgps, [[Mgp1_[iel][2] for iel=1:nel] ; [Mgp2_[iel][2] for iel=1:nel] ; [Mgp3_[iel][2] for iel=1:nel] ; [Mgp4_[iel][2] for iel=1:nel]], label="M₂"); +scatter!(ax,xgps, [[Mgp1_[iel][3] for iel=1:nel] ; [Mgp2_[iel][3] for iel=1:nel] ; [Mgp3_[iel][3] for iel=1:nel] ; [Mgp4_[iel][3] for iel=1:nel]], label="M₃"); +axislegend() +ax=Axis(fig[4,1], ylabel="Curvature κ [m⁻¹]", yminorgridvisible = true,xminorgridvisible = true,xticks = (0:1. /nel:1),xlabel="Position along beam / beam length [-]") +scatter!(ax,xgps, [[κgp1_[iel][1] for iel=1:nel] ; [κgp2_[iel][1] for iel=1:nel] ; [κgp3_[iel][1] for iel=1:nel] ; [κgp4_[iel][1] for iel=1:nel]], label="κ₁"); +scatter!(ax,xgps, [[κgp1_[iel][2] for iel=1:nel] ; [κgp2_[iel][2] for iel=1:nel] ; [κgp3_[iel][2] for iel=1:nel] ; [κgp4_[iel][2] for iel=1:nel]], label="κ₂"); +scatter!(ax,xgps, [[κgp1_[iel][3] for iel=1:nel] ; [κgp2_[iel][3] for iel=1:nel] ; [κgp3_[iel][3] for iel=1:nel] ; [κgp4_[iel][3] for iel=1:nel]], label="κ₃"); +axislegend() +if occursin("build", currentDir) + save(normpath(joinpath(currentDir,"..","src","assets","StaticBeamAnalysis2.png")),fig) +elseif occursin("examples", currentDir) + save(normpath(joinpath(currentDir,"StaticBeamAnalysis2.png")),fig) +end +```` + +![Result](assets/StaticBeamAnalysis2.png) + +Show comparison with solutions by Longva (2015) and Crisfield (1990) + +````@example StaticBeamAnalysis +# Load 300 N 450 N 600 N +# x,y,z x,y,z x,y,z +# Disp Longva 58.56, 40.47, 22.18 51.99, 48.72, 18.45 46.91, 53.64, 15.65 +# Disp Crisfield 58.53, 40.53, 22.16 51.93, 48.79, 18.43 46.84, 53.71, 15.61 +height = [ nodeCoord[end,1]+x_[2][end], 58.56, 58.53, nodeCoord[end,1]+x_[3][end], 51.99, 51.93, nodeCoord[end,1]+x_[4][end], 46.91, 46.84, + nodeCoord[end,2]+y_[2][end], 40.47, 40.53, nodeCoord[end,2]+y_[3][end], 48.72, 48.79, nodeCoord[end,2]+y_[4][end], 53.64, 53.71, + nodeCoord[end,3]+z_[2][end], 22.18, 22.16, nodeCoord[end,3]+z_[3][end], 18.45, 18.43, nodeCoord[end,3]+z_[4][end], 15.65, 15.61] +colors = [:red, :blue, :green] +tbl = (cat = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9],height, + grp = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) +fig = Figure(size = (2000, 400)) +ax = Axis(fig[1,1], xticks = (1:9, ["x @ 300 N", "x @ 450 N", "x @ 600 N", "y @ 300 N", "y @ 450 N", "y @ 600 N", "z @ 300 N", "z @ 450 N", "z @ 600 N"]), + ylabel = "End node coordinate [m]") +barplot!(ax, tbl.cat, tbl.height, + dodge = tbl.grp, + color = colors[tbl.grp], + bar_labels = :y + ) +ylims!(ax, 0,70); +labels = ["Muscade", "Longva (2015)", "Crisfield (1990)"] +elements = [PolyElement(polycolor = colors[i]) for i in 1:length(labels)] +title = "Method" +Legend(fig[1,2], elements, labels, title) +if occursin("build", currentDir) + save(normpath(joinpath(currentDir,"..","src","assets","StaticBeamAnalysis3.png")),fig) +elseif occursin("examples", currentDir) + save(normpath(joinpath(currentDir,"StaticBeamAnalysis3.png")),fig) +end +```` + +![Result](assets/StaticBeamAnalysis3.png) + +--- + +*This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).* + diff --git a/docs/src/Theory.md b/docs/src/Theory.md index 1ef65f07..2974fad8 100644 --- a/docs/src/Theory.md +++ b/docs/src/Theory.md @@ -1,4 +1,4 @@ -# Theory +# [Theory](@id theory) ## Introduction diff --git a/docs/src/TuningFork.md b/docs/src/TuningFork.md new file mode 100644 index 00000000..95888922 --- /dev/null +++ b/docs/src/TuningFork.md @@ -0,0 +1,256 @@ +```@meta +EditURL = "../../examples/TuningFork.jl" +``` + +# Tuning vibrations of a tuning fork + +Tuning forks should resonate at a desired frequency when subjected to an impulsive load. Achieving the right frequency cab be done by adding material or filing material off the prongs. +We start from a target solution establihed using SweepX. A sprious mass is then introduced, parametrized by an A-dof. We use the SweepXA and DirectXUA solvers to estimate how much mass should be removed. In SweepXA, the excitation is assume to be known, while it is estimated by DirectXUA. + +NB: In several places in this script, `solve` is called with optional `verbose=false`, because this script is part of the generation +of `Muscade`'s online documentation. Setting `verbose=true` would be more relevant in other contexts. + +````@example TuningFork +using Muscade, StaticArrays, GLMakie, Muscade.Toolbox +```` + +Dimensions of the tuning fork and number of elements + +````@example TuningFork +l₀=2.5e-2; n₀=1 # base - length and number of elements +l₁=1e-2; n₁=1 # fork - length and number of elements per side +l₂=9.5e-2; n₂=5 # prong - length and number of elements per side +b = 5e-3; # thickness of the cross-section +E = 210e9; # Young modulus +G = 79.3e9; # shear modulus +μ = 7850. *b^2; # mass per unit length, assumes steel +beamCrossSection = BeamCrossSection(EA=E*b^2, EI₂=1/12*E*b^4, EI₃=1/12*E*b^4, GJ=1/3*G*b^4, μ=μ, ι₁=1/6*μ*b^2,Cl₂=10.,Cl₃=10.); +nothing #hide +```` + +Define an A-parametrized point mass element (inducing an inertia force) + +````@example TuningFork +struct LumpedMass <: AbstractElement; m :: 𝕣; end +LumpedMass(nod::Vector{Node};m::𝕣) = LumpedMass(m) +@espy function Muscade.residual(o::LumpedMass, X,U,A, t,SP,dbg); return (o.m+A[1]).*∂2(X),noFB; end +Muscade.doflist( ::Type{LumpedMass}) = (inod =(1,1,1,2), class=(:X,:X,:X,:A), field=(:t1,:t2,:t3,:mass)); +nothing #hide +```` + +Time step and simulation length settings + +````@example TuningFork +Δt = 3e-4; +nDynamicLoadSteps = 200; +timeVec = Δt:Δt:nDynamicLoadSteps*Δt; +nothing #hide +```` + +Coordinates of the nodes. + +````@example TuningFork +XnodeCoord = vcat( + hcat((0:n₀) * l₀/n₀ , zeros(n₀+1,1) , zeros(n₀+1,1) ), # base nodes + hcat(ones(n₁,1)*l₀ , (1:n₁)*l₁/n₁ , zeros(n₁,1) ), # upper fork + hcat(ones(n₁,1)*l₀ , -(1:n₁)*l₁/n₁ , zeros(n₁,1) ), # lower fork + hcat(l₀ .+ (1:n₂)*l₂/n₂ , ones(n₂,1)*l₁ , zeros(n₂,1) ), # upper prong + hcat(l₀ .+ (1:n₂)*l₂/n₂ , -ones(n₂,1)*l₁, zeros(n₂,1) ) # lower prong +) +```` + +External excitation load at the end of the upper prong + +````@example TuningFork +@functor with() pling(t) = Muscade.FunctionFromVector([-10, 0, 10e-3, 12e-3, 10],[0,0,10,0,0])(t) +plingNode = n₀+2n₁+n₂+1; # where do we hit the tuning fork +nothing #hide +```` + +# Building the model + +````@example TuningFork +model = Model(:TuningFork); +nothing #hide +```` + +Add the nodes describing the beam model, the node that will contain the parameter to optimize + +````@example TuningFork +Xnod = addnode!(model,XnodeCoord) +Anod = addnode!(model,𝕣[]) +```` + +List of nodes that will be used to create the beam elements + +````@example TuningFork +nel = n₀+2n₁+2n₂ +mesh = vcat( + hcat(Xnod[1:n₀],Xnod[2:n₀+1]), # base + hcat(Xnod[n₀+1:n₀+n₁],Xnod[n₀+2:n₀+n₁+1]), # upper fork + [Xnod[n₀+1] Xnod[n₀+n₁+2]], hcat(Xnod[n₀+n₁+2:n₀+2n₁],Xnod[n₀+n₁+3:n₀+2n₁+1]) , # lower fork + [Xnod[n₀+n₁+1] Xnod[n₀+2n₁+2]], hcat(Xnod[n₀+2n₁+2:n₀+2n₁+n₂],Xnod[n₀+2n₁+3:n₀+2n₁+n₂+1]) , # upper prong + [Xnod[n₀+2n₁+1] Xnod[n₀+2n₁+n₂+2]], hcat(Xnod[n₀+2n₁+n₂+2:n₀+2n₁+2n₂],Xnod[n₀+2n₁+n₂+3:n₀+2n₁+2n₂+1]) # lower prong +) +```` + +In the XUA analysis we estimate the distributed load on the element close to the node where the load was applied + +````@example TuningFork +plingElement = n₀+2n₁+n₂; +nothing #hide +```` + +Add beam elements to the model, enabling Udof only for the element that is hit. + +````@example TuningFork +addelement!(model,EulerBeam3D{false}, mesh; mat=beamCrossSection,orient2=SVector(0.,0,1)) +[addelement!(model,Hold,[Xnod[1]] ;field) for field∈[:t1,:t2,:t3,:r1,:r2,:r3]]; +nothing #hide +```` + +# Create variations of the model + +````@example TuningFork +XAmodel = deepcopy(model) +XUAmodel = deepcopy(model); +nothing #hide +```` + +Add parasitic lump mass on both XA and XUA models + +````@example TuningFork +spuriousMass = 4e-3; +spuriousMassLocation = plingNode-1 +addelement!(XAmodel, LumpedMass, [Xnod[spuriousMassLocation] Anod]; m=spuriousMass) +addelement!(XUAmodel, LumpedMass, [Xnod[spuriousMassLocation] Anod]; m=spuriousMass); +nothing #hide +```` + +Add known external force to X and XA models, and an unknown force to XUA model + +````@example TuningFork +addelement!(model, DofLoad,[Xnod[plingNode]];field=:t2,value=pling) +addelement!(XAmodel, DofLoad,[Xnod[plingNode]];field=:t2,value=pling); +@functor with(σᵤₚ=0.1) UcostPling(u,t) = 0.5*(u/σᵤₚ)^2 * clutch(t,0.02,0.04,1.,100.,1) +addelement!(XUAmodel, SingleUdof,[Xnod[plingNode]];Xfield=:t2,Ufield=:t2,cost=UcostPling) +```` + +Establish target response + +````@example TuningFork +initialState = initialize!(model;time=0.); +dynamicStates = solve(SweepX{2};initialstate=initialState, time=timeVec, verbose=false) +vibTarget = getdof(dynamicStates;field=:t2,nodID=[Xnod[plingNode]]) +target = Muscade.FunctionFromVector(timeVec,vibTarget); +nothing #hide +```` + +Add costs on the deviation to target measurements, in the XA and XUA models + +````@example TuningFork +@functor with(σᵥ=1e-6,target) Xcost(x,t)=((x-target(t))/σᵥ)^2 +addelement!(XUAmodel,SingleDofCost,[Xnod[plingNode]]; class=:X, field=:t2, cost=Xcost); +addelement!(XAmodel, SingleDofCost,[Xnod[plingNode]]; class=:X, field=:t2, cost=Xcost) +```` + +Add costs on the correcting mass, in the XA and XUA models + +````@example TuningFork +@functor with(σₘ=5e-3,timeVec) Acost_(a) = 0.5*(a/σₘ)^2/length(timeVec) +addelement!(XUAmodel, SingleAcost,[Anod]; field=:mass, cost=Acost_) +addelement!(XAmodel, SingleAcost,[Anod]; field=:mass, cost=Acost_); +nothing #hide +```` + +# Run analyses + +XA model (before estimating the mass) + +````@example TuningFork +XAinitialState = initialize!(XAmodel;time=0.); +XAdynamicStates = solve(SweepX{2};initialstate=XAinitialState, time=timeVec,verbose=false); +nothing #hide +```` + +XA model (after having estimated the mass) + +````@example TuningFork +optimXAstate = solve(SweepXA{2}; initialstate=XAinitialState, time=timeVec, + maxAiter=20,maxΔa=1e-10,verbose=false); +nothing #hide +```` + +DirectXUA (slack convergence criteria and number of iterations) + +````@example TuningFork +XUAinitialState = initialize!(XUAmodel;time=0.); +optimXUAstate = solve(DirectXUA{2,0,1};initialstate=[XUAinitialState], time=[timeVec], + maxiter=15, maxΔx=5e-2,maxΔλ=Inf,maxΔu=5e-2,maxΔa=1e-4,verbose=false); +nothing #hide +```` + + Gather results for comparison + +````@example TuningFork +analysisResults = (dynamicStates, XAdynamicStates,optimXAstate,optimXUAstate[end]); +t1 = Matrix{Float64}(undef,length(analysisResults),length(timeVec)) +t2 = Matrix{Float64}(undef,length(analysisResults),length(timeVec)) +t3 = Matrix{Float64}(undef,length(analysisResults),length(timeVec)) +transmittedForce = Matrix{Float64}(undef,length(analysisResults),length(timeVec)) +req = @request gp(resultants(fᵢ)) +for idx ∈ 1:length(analysisResults) + t1[idx,:] = getdof(analysisResults[idx];field=:t1,nodID=[Xnod[plingNode]])[:] + t2[idx,:] = getdof(analysisResults[idx];field=:t2,nodID=[Xnod[plingNode]])[:] + t3[idx,:] = getdof(analysisResults[idx];field=:t3,nodID=[Xnod[plingNode]])[:] + end +excEstt2 = getdof(optimXUAstate[end];class=:U,field=:t2,nodID=[Xnod[plingNode]])[:]; +nothing #hide +```` + +Text output + +````@example TuningFork +println("Mass to remove in grams:") +print("- Estimated from DirectXUA analysis (unknown loading) : ") +println(-getdof(optimXUAstate[end];class=:A,field=:mass,nodID=[Anod])[1]*1e3) +print("- Estimated by SweepXA analysis (known loading) : ") +println(-getdof(optimXAstate[end];class=:A,field=:mass,nodID=[Anod])[1]*1e3) +print("- Expected : ") +println(spuriousMass*1e3) +```` + +Plot the axial and lateral displacement of the control node, and the estimated force. + +````@example TuningFork +fig = Figure(size = (1000,1000)) +ax1 = Axis(fig[1,1],ylabel="Axial disp. [mm]") +lines!(ax1,timeVec,t1[1,:]*1e3, label="Target", color=:black, linestyle=:dash) +lines!(ax1,timeVec,t1[2,:]*1e3, label="Detuned config.",color=:black, linestyle=:solid) +scatter!(ax1,timeVec,t1[3,:]*1e3, label="Tuned (XA)", color=:green, markersize = 10) +scatter!(ax1,timeVec,t1[4,:]*1e3, label="Tuned (XUA)", color=:red, markersize = 5) +axislegend(ax1) +ax2 = Axis(fig[2,1],ylabel="Lateral disp. [mm]") +lines!(ax2,timeVec,t2[1,:]*1e3, label="Target", color=:black, linestyle=:dash) +lines!(ax2,timeVec,t2[2,:]*1e3, label="Detuned config.",color=:black, linestyle=:solid) +scatter!(ax2,timeVec,t2[3,:]*1e3, label="Tuned (XA)", color=:green, markersize = 10) +scatter!(ax2,timeVec,t2[4,:]*1e3, label="Tuned (XUA)", color=:red, markersize = 5) +ax3 = Axis(fig[3,1],ylabel="Excitation [N]") +lines!(ax3,timeVec,pling.(timeVec), label="Actual",color=:black, linestyle=:dash) +lines!(ax3,timeVec,excEstt2, label="Estimated (XUA)",color=:red, linestyle=:solid) +axislegend(ax3) + +currentDir = @__DIR__ +if occursin("build", currentDir) + save(normpath(joinpath(currentDir,"..","src","assets","TuningFork.png")),fig) +elseif occursin("examples", currentDir) + save(normpath(joinpath(currentDir,"TuningFork.png")),fig) +end +```` + +![Result](assets/TuningFork.png) + +--- + +*This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).* + diff --git 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These are neither intended to be used by developers of `Muscade`-based applications - nor by users such applications. + nor by users such of applications. Interface changes can occur at any time. ## Muscade diff --git a/examples/DecayAnalysis.jl b/examples/DecayAnalysis.jl index 18c57185..78802b92 100644 --- a/examples/DecayAnalysis.jl +++ b/examples/DecayAnalysis.jl @@ -2,6 +2,10 @@ # # We estimate the mass and damping matrices of a coupled linear oscillator (floater moving in the surge, sway and yaw) based on a decay tests # In the following, we define the necessary element and residual function describing the dynamic behaviour of the floater. +# +# NB: In two places in this script, `solve` is called with optional `verbose=false`, because this script is part of the generation +# of `Muscade`'s online documentation. Setting `verbose=true` would be more relevant in other contexts. + using Muscade,StaticArrays,Interpolations,GLMakie fold(x::SVector{6}) = SMatrix{3,3}( x[1],x[2],x[3], @@ -125,7 +129,7 @@ e7 = addelement!(modelXUA,SingleDofCost,[n1];class=:X,field=:yaw, #Solve inverse problem initialstateXUA = initialize!(modelXUA;time=0.) stateXUA = solve(DirectXUA{2,0,1};initialstate=[initialstateXUA],time=[T], - maxiter=100,saveiter=true, + maxiter=100,saveiter=true,verbose=false, maxΔx=1e-5,maxΔλ=Inf,maxΔu=1e-5,maxΔa=1e-5); # Fetch and display estimated model parameters diff --git a/examples/DynamicBeamAnalysis.jl b/examples/DynamicBeamAnalysis.jl index 0729e64c..2a50efd7 100644 --- a/examples/DynamicBeamAnalysis.jl +++ b/examples/DynamicBeamAnalysis.jl @@ -1,6 +1,9 @@ # # Dynamic analysis of a beam # # We perform the dynamic analysis of a steel catenary riser (SCR) subject to forced top motions. We compare the results against the corresponding SIMA/RIFLEX example case. The riser consists of three segments with two different cross-sections. +# +# NB: In two places in this script, `solve` is called with optional `verbose=false`, because this script is part of the generation +# of `Muscade`'s online documentation. Setting `verbose=true` would be more relevant in other contexts. using Muscade, StaticArrays, GLMakie, Muscade.Toolbox, Interpolations, CSV, DataFrames # Read RIFLEX motions, tensions, bending moment and curvatures time series (verification data) @@ -95,7 +98,7 @@ addelement!(model,DofConstraint,[nodeList[3][end]]; λclass=:X, xinod=(1,),xfiel initialstate = initialize!(model); staticLoadSteps = (-10:.2:0)*1. nStaticLoadSteps = length(staticLoadSteps) -staticStates = solve(SweepX{0};initialstate,time=staticLoadSteps,verbose=true,maxΔx=1e-6,maxiter=100); +staticStates = solve(SweepX{0};initialstate,time=staticLoadSteps,verbose=false,maxΔx=1e-6,maxiter=100); # Plot the static analysis sequence fig = Figure(size = (1000,1000)) diff --git a/examples/ModalBeamAnalysis.jl b/examples/ModalBeamAnalysis.jl index 2c6f1540..a04d41e3 100644 --- a/examples/ModalBeamAnalysis.jl +++ b/examples/ModalBeamAnalysis.jl @@ -5,14 +5,14 @@ using Muscade, StaticArrays, GLMakie using Muscade.Toolbox -L = 1; # Beam length [m] +L = 1.; # Beam length [m] q = 0.0; # Uniform lateral load [N/m] -EI₂ = 1; # Bending stiffness [Nm²] -EI₃ = 1; # Bending stiffness [Nm²] +EI₂ = 1.; # Bending stiffness [Nm²] +EI₃ = 1.; # Bending stiffness [Nm²] EA = 1e6; # Axial stiffness [N] GJ = 1e6; # Torsional stiffness [Nm²] -μ = 1; -ι₁= 1; +μ = 1.; +ι₁= 1.; # Create model nel = 50 diff --git a/examples/StaticBeamAnalysis1.png b/examples/StaticBeamAnalysis1.png new file mode 100644 index 0000000000000000000000000000000000000000..afc03905b5c50360d22f1d84d13b3fc0225b7a04 GIT binary patch literal 137371 zcmeEvcRZH+|Nq5Nk%lN~aa5G-k|Lv{C^8PEaz{u+W+8i=_D~u|b`gq<%#cw^r>vrk z%!Uvmd;2}#_pMH6eE$9Y_3iOEAE!?DbzkrI`!$~9bzPqeziaN8JA3JDilXMK?%b|J zQ7j+GKdj97lbfIF7T^byz0M9LDzR*NJAT7*!^M>DdZyAYx#iewk@lN3Bg%x$`%>1{{^dC06x^AULwX&&!e(~{Ko$V}+ zqElh2hYB6{?K{!PFVBBk(|lcIqS3a6iYibl)H;@1Gk0WhSzHxDJ4hBsrrk5fjny&J18~oZJyz;_@ z3+?Ug(jlV!{EzGE4p5Z27y$*RvW~aBytZn`x^?UDk!;8K{CuxNhdzuBbVNl(DUNlf 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zy?e5gpS4t7yerMH67)die)@e*Ortk@XjM2gr7XdsY#EL?yv;S1?j_A7!DniMm$h-k<* z_V@6aFH&fj!C`s@SNY>VBOwcqW?4FfJmrcg6au2+`mn8DO#6&167b!ZpH?Ndieg7K zwY$_?cgATJ?E;|IFY>S7NPAVk^4iJWd?;eB;%i3IWKZVU9S06A9b~%t0ww=XtEsUX z!NSSUtJnfX$WYu6$eW&aL=yhB7i<}zi30sV)7p<<4yGFU+&$D*7Ts4_bZNuuJ?+`w zu5aIS;H1}=J3a^?vyKKg6ciQRA>9A{EaMaLp+dZCAmbh?g(+!+0pK8C2_f#cSpAGF z3yI-g_r$3pW(TK)$fYNEvk3Bm`>pJ+k;N=XpeQNXI0zC22U`N23dkiG?-hr|%tgz9w;I1;K-EnXlp|2w_d>jo3)-OSPs{;L69<&Q7CCME)U2 ztr=diwd5v`W&C4x%0o>X{m-W>e>bJRL>2jUNJo~Z{PL>s|6J_yWB>o-{_oE&|66&_ X3FoKXPKxu8$7SEksb`YiuVMcOdzLES literal 0 HcmV?d00001 diff --git a/examples/FollowerPointLoad.jl b/inspect/FollowerPointLoad.jl similarity index 97% rename from examples/FollowerPointLoad.jl rename to inspect/FollowerPointLoad.jl index bdbaba65..2007041a 100644 --- a/examples/FollowerPointLoad.jl +++ b/inspect/FollowerPointLoad.jl @@ -10,12 +10,12 @@ Muscade.no_second_order(::Type{<:FollowerPointLoad}) = Val(true) Muscade.doflist(::Type{<:FollowerPointLoad}) = (inod = (1,1,1,1,1,1),class= ntuple(i->:X,ndof),field= (:t1,:t2,:t3,:r1,:r2,:r3) ) FollowerPointLoad(nod::Vector{Node};f,m) = FollowerPointLoad(f,m) @espy function Muscade.residual(o::FollowerPointLoad, X,U,A,t,SP,dbg) - i = SVector(4,5,6) + i = SVector(4,5,6) + P,ND = precedence(X),length(X) + X_ = motion{P}(X) V_ = X_[i] - - P,ND = constants(X),length(X) X₀ = ∂0(X) TX₀ = revariate{1}(X₀) Tgp,Tε,Tvₛₘ,Trₛₘ,Tvₗ₂ = kinematics(o,TX₀) diff --git a/inspect/PerformanceEulerBeam3D.jl b/inspect/PerformanceEulerBeam3D.jl index 3aa063c8..69c3cc31 100644 --- a/inspect/PerformanceEulerBeam3D.jl +++ b/inspect/PerformanceEulerBeam3D.jl @@ -21,7 +21,7 @@ const t = 0. const SP = (;) const dbg = (status=:testing,) const x = SVector(1.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.) -const xv = variate{1,12}(x) +const xv = Muscade.variate_{1,12}(x) const X = (xv,) const U = (SVector{0,𝕣}(),) const A = SVector{0,𝕣}() diff --git a/inspect/PerformanceEulerBeam3D_diffed_residual.jl b/inspect/PerformanceEulerBeam3D_diffed_residual.jl index 37073572..e287cbfa 100644 --- a/inspect/PerformanceEulerBeam3D_diffed_residual.jl +++ b/inspect/PerformanceEulerBeam3D_diffed_residual.jl @@ -4,9 +4,7 @@ using Profile,ProfileView using BenchmarkTools using Muscade using StaticArrays - -include("../toolbox/BeamElement.jl") -#include("../examples/StrainGaugeOnBeamElement.jl") +using Muscade.Toolbox model = Model(:TestModel) @@ -24,20 +22,24 @@ const displacement = SVector(0.,0.,0.,0.,0.,0., 0.,0.,0.,0.,0.,0.); const velocity = SVector(0.,0.,0.,0.,0.,0., 0.,0.,0.,0.,0.,0.); const acceleration = SVector(0.,0.,0.,0.,0.,0., 0.,0.,0.,0.,0.,0.); const X = (displacement,)#,velocity,acceleration) -const U = (SVector{0,𝕣}(),) -const A = SVector{0,𝕣}() +const U = (SVector{0,𝕣}(),) +const A = SVector{0,𝕣}() -mission = :report -if mission == :report - out = diffed_residual(beam; X,U,A,t,SP) +mission = :time +if mission == :eval + out = Muscade.diffed_residual(beam; X,U,A,t,SP) elseif mission == :time - out = diffed_residual(beam; X,U,A,t,SP) - @btime diffed_residual(beam; X,U,A,t,SP) + # 121.500 μs baseline + # 104.400 μs if ...∂X₀ are computed with kinematics{:direct} + # 101.800 μs with improvements in Adiff.jl + # 87.300 μs with improvements in Rotation.jl + out = Muscade.diffed_residual(beam; X,U,A,t,SP) + @btime Muscade.diffed_residual(beam; X,U,A,t,SP) elseif mission == :profile - diffed_residual(beam; X,U,A,t,SP) + Muscade.diffed_residual(beam; X,U,A,t,SP) Profile.clear() Profile.@profile for i=1:250000 - local out = diffed_residual(beam; X,U,A,t,SP) + local out = Muscade.diffed_residual(beam; X,U,A,t,SP) end ProfileView.view(fontsize=30); # After clicking on a bar in the flame diagram, you can type warntype_last() and see the result of diff --git a/inspect/Performance_McLaurin.jl b/inspect/Performance_McLaurin.jl new file mode 100644 index 00000000..524f8d68 --- /dev/null +++ b/inspect/Performance_McLaurin.jl @@ -0,0 +1,39 @@ +#module Performance + +using Profile,ProfileView +using BenchmarkTools +using Muscade +using StaticArrays +using Muscade.Toolbox + +N = 12 +x = SVector{N,𝕣}(1:N) +X = revariate{2}(x) +i = SVector(1,2,3) +v = X[i] + +apply = Muscade.apply{:chainrule} +#apply = Muscade.apply{:direct} + +mission = :time +if mission == :eval + out = apply(Toolbox.Rodrigues,v) +elseif mission == :time + out = apply(Toolbox.Rodrigues,v); + @btime apply($Toolbox.Rodrigues,$v) +# @btime Toolbox.Rodrigues($v) +elseif mission == :profile + apply(Toolbox.Rodrigues,v) + Profile.clear() + Profile.@profile for i=1:250000 + local out = apply(Toolbox.Rodrigues,v) + end + ProfileView.view(fontsize=30); + # After clicking on a bar in the flame diagram, you can type warntype_last() and see the result of + # code_warntype for the call represented by that bar. +end +; + +#end # module + + diff --git a/inspect/adiffs.jl b/inspect/adiffs.jl new file mode 100644 index 00000000..6ba442f5 --- /dev/null +++ b/inspect/adiffs.jl @@ -0,0 +1,60 @@ +using Muscade, StaticArrays + +#Create two functions +f(ξ) = SVector(ξ[1]^ξ[2],ξ[1]^2) +g(ξ) = SVector(log(ξ[1]),log(ξ[2])) + +# Point at which we evaluate the functions and gradients +x = SVector(3.,2.) +@show typeof(x) +# returns typeof(x) = SVector{2, Float64} + +# Create an adiff xₐ at that point x +N = length(x) +xₐ = Muscade.variate_{1,N}(x) +@show typeof(xₐ) +# returns typeof(xₐ) = SVector{2, ∂ℝ{1, 2, Float64}} + +# Compute the gradient of f at x +fxₐ = f(xₐ) +@show value{1}(fxₐ) +# returns value{1}(fxₐ) = [9.0, 9.0] +@show ∂{1,N}(fxₐ) +# returns ∂{1, N}(fxₐ) = [6.0 9.887510598012987; 6.0 0.0] + +# Cmpute the gradient of g at x +gxₐ = g(xₐ) +@show value{1}(gxₐ) +# returns value{1}(gxₐ) = [1.0986122886681098, 0.6931471805599453] +@show ∂{1,N}(gxₐ) +# returns ∂{1, N}(gxₐ) = [0.3333333333333333 0.0; 0.0 0.5] + +# Cmpute the gradient of h=g∘f at x +hxₐ = g(f(xₐ)) +@show value{1}(hxₐ) +# returns value{1}(hxₐ) = [2.1972245773362196, 2.1972245773362196] +@show ∂{1,N}(hxₐ) +# returns ∂{1, N}(hxₐ) = [0.6666666666666666 1.0986122886681098; 0.6666666666666666 0.0] + + +# Compute the gradient of g, for a variable y depends on x +# Create an adiff yₐ at point xₐ +yₐ = Muscade.variate_{2,N}(fxₐ) +# Note: The level of preceedence (here, 2) can be obtained using constants(fxₐ) +@show typeof(yₐ) +# returns typeof(yₐ) = SVector{2, ∂ℝ{2, 2, ∂ℝ{1, 2, Float64}}} + +gyₐ = g(yₐ) + +# The result is an adiff contains nested partial derivatives (g wrt y and y wrt x) +@show gyₐ_value = value{2}(gyₐ) +# returns gyₐ_value = value{2}(gyₐ) = ∂ℝ{1, 2, Float64}[2.2+∂₁⟨0.667,1.1⟩ , 2.2+∂₁⟨0.667,0⟩ ] +# The gradient of g at yₐ also contains information about the gradient of y wrt x +@show ∂{2,N}(gyₐ); +# returns ∂{2, N}(gyₐ) = ∂ℝ{1, 2, Float64}[0.111+∂₁⟨-0.0741,-0.122⟩ 0+∂₁⟨0,0⟩ ; 0+∂₁⟨0,0⟩ 0.111+∂₁⟨-0.0741,0⟩ ] + +# Continue to unfold (decreasing the preceedence to 1) to get the the derivative of g wrt x +@show value{1}(gyₐ_value) +# returns value{1}(gyₐ_value) = [2.1972245773362196, 2.1972245773362196] +@show ∂{1,N}(gyₐ_value); +# returns ∂{1, N}(gyₐ_value) = [0.6666666666666666 1.0986122886681098; 0.6666666666666666 0.0] diff --git a/src/Adiff.jl b/src/Adiff.jl index 66d02de0..cf7b9c0d 100644 --- a/src/Adiff.jl +++ b/src/Adiff.jl @@ -1,11 +1,8 @@ -# TODO -# implement sincos -# differentiate x^0 at x=0 - ## Type and construction const SV = SVector const SA = SArray const SM = SMatrix +const Jℝ = Union{AbstractIrrational, AbstractFloat, Integer, Rational } # Types # P precedence. Newer, derivatives, outest in the adiff datastructure have higher numbers # N number of partials @@ -13,7 +10,24 @@ const SM = SMatrix struct ∂ℝ{P,N,R} <:ℝ where{R<:ℝ} # P for precedence, N number of partials, R type of the variable (∂ℝ can be nested) x :: R dx :: SV{N,R} -end +end +const Jℝ∂ = Union{AbstractIrrational, AbstractFloat, Integer, Rational,∂ℝ} + +struct T𝟘 <: Real end # Bbbzero +const 𝟘 = T𝟘() +@inline Base.:(+)(a::Jℝ∂, ::T𝟘 ) = a +@inline Base.:(+)( ::T𝟘 ,b::Jℝ∂) = b +@inline Base.:(+)( ::T𝟘 , ::T𝟘 ) = 𝟘 +@inline Base.:(-)(a::Jℝ∂, ::T𝟘 ) = a +@inline Base.:(-)( ::T𝟘 ,b::Jℝ∂) = -b +@inline Base.:(-)( ::T𝟘 , ::T𝟘 ) = 𝟘 +@inline Base.:(*)(a::Jℝ∂, ::T𝟘 ) = 𝟘 +@inline Base.:(*)( ::T𝟘 ,b::Jℝ∂) = 𝟘 +@inline Base.:(*)( ::T𝟘 , ::T𝟘 ) = 𝟘 +@inline Base.:(/)(a , ::T𝟘 ) = error("division by 𝟘") +@inline Base.:(/)( ::T𝟘 ,b ) = 𝟘 +Base.show(io::IO, ::T𝟘) = print(io,"𝟘") + # Constructors ∂ℝ{P,N }(x::R ,dx::SV{N,R}) where{P,N,R<:ℝ} = ∂ℝ{P,N,R}( x ,SV{N,R}(dx )) @@ -63,16 +77,15 @@ end # Pack and unpack """ - Muscade.precedence(a::∂ℝ{P,N,R}) → P - Muscade.precedence(typeof(a)) → P + precedence(a::∂ℝ{P,N,R}) → P + precedence(typeof(a)) → P Also handles static arrays and tuples. See also: [`npartial`](@ref) -""" -precedence( ::Type{Union{}}) = 0 -precedence( ::Type{<:∂ℝ{P,N,R}}) where{P,N,R<:ℝ} = P +""" +precedence """ Muscade.npartial(a::∂ℝ{P,N,R}) → N Muscade.npartial(typeof(a)) → N @@ -81,80 +94,83 @@ Also handle static arrays and tuples. See also: [`precedence`](@ref) -""" +""" +npartial + +precedence( ::Type{<:∂ℝ{P,N,R}}) where{P,N,R<:ℝ} = P npartial( ::Type{<:∂ℝ{P,N,R}}) where{P,N,R<:ℝ} = N +partialtype(::Type{<:∂ℝ{P,N,R}}) where{P,N,R<:ℝ} = R +precedence( ::Type{Union{}}) = 0 precedence( ::Type{<:ℝ}) = 0 npartial( ::Type{<:ℝ}) = 0 -precedence(a::SA) = precedence(eltype(a)) -npartial( a::SA) = npartial(eltype(a)) +partialtype(::Type{<:ℝ}) = Union{} + precedence(a::ℝ) = precedence(typeof(a)) npartial( a::ℝ) = npartial(typeof(a)) precedence( a,args...) = max(precedence(a),precedence(args...)) +precedence(a::SA) = precedence(eltype(a)) +npartial( a::SA) = npartial(eltype(a)) -""" - P = constants(a,b,c) - -Generate a precedence `P` that is higher than the precedence of the arguments. +function ∂ℝ_promote_type(::Ra,::Rb) where{Ra<:ℝ,Rb<:ℝ} + Pa,Na = Muscade.precedence(Ra),Muscade.npartial( Ra) + Pb,Nb = Muscade.precedence(Rb),Muscade.npartial( Rb) + P = Pa≥Pb ? Pa : Pb + N = Pa≥Pb ? Na : Nb + R = promote_type(partialtype(Ra),partialtype(Rb)) + return P,N,R +end -See also: [`variate`](@ref), [`δ`](@ref), [`value`](@ref), [`∂`](@ref), [`VALUE`](@ref), [`value_∂`](@ref) +# Muscade.variate_ +struct δ_{P,N,R} end # need dum, because syntax δ_{P,N,R}() collides with default constructor +struct variate_{P,N} end """ -constants(tup::Tuple) = constants(tup...) -constants( a,args...) = max(constants(a),constants(args...)) -constants( a) = 1+precedence(a) -constants(tup::Tuple{}) = 1 -constants( ::Nothing) = 1 - -# variate -struct δ{P,N,R} end # need dum, because syntax δ{P,N,R}() collides with default constructor -struct variate{P,N} end -struct directional{P,N} end -struct ∂²ℝ{P,N} end -""" - X = δ{P,N,R}() + X = δ_{P,N,R}() create a `SVector` of automatic differentiation objects of precedence `P` and value `zero`. - X = δ{P}() + X = δ_{P}() Create automatic differentiation object of precedence `P` and value `zero`. -See also: [`constants`](@ref), [`variate`](@ref), [`value`](@ref), [`∂`](@ref), [`VALUE`](@ref), [`value_∂`](@ref) +!!! Warning + Improper use may cause perturbation confusion + +See also: [`precedence`](@ref), [`Muscade.variate_`](@ref), [`value`](@ref), [`∂`](@ref), [`VALUE`](@ref), [`value_∂`](@ref) """ -δ{P,N,R}( ) where{P,N,R<:ℝ} = SV{N,∂ℝ{P,N,R}}(∂ℝ{P,N }(zero(R),i ) for i=1:N) -δ{P,N,R}( δa::SV{N,𝕣}) where{P,N,R<:ℝ} = SV{N,∂ℝ{P,N,R}}(∂ℝ{P,N,R}(zero(R),SV{N,R}(i==j ? δa[i] : zero(R) for i=1:N)) for j=1:N) -δ{P }( ) where{P } = ∂ℝ{P,1,𝕣}(0. ,SV{1,𝕣}(1. )) +@inline δ_{P,N,R}( ) where{P,N,R<:ℝ} = SV{N,∂ℝ{P,N,R}}(∂ℝ{P,N }(zero(R),i ) for i=1:N) +@inline δ_{P,N,R}( δa::SV{N,𝕣}) where{P,N,R<:ℝ} = SV{N,∂ℝ{P,N,R}}(∂ℝ{P,N,R}(zero(R),SV{N,R}(i==j ? δa[i] : zero(R) for i=1:N)) for j=1:N) +@inline δ_{P }( ) where{P } = ∂ℝ{P,1,𝕣}(0. ,SV{1,𝕣}(1. )) """ - X = variate{P,N}(x) + X = variate_{P,N}(x) where `typeof(x)<:SVector{N}`, create a `SVector` of automatic differentiation objects of precedence `P`. - X = variate{P}(x) + X = variate_{P}(x) where `typeof(x)<:Real`, create an object of precedence `P`. -See also: [`constants`](@ref), [`δ`](@ref), [`value`](@ref), [`∂`](@ref), [`VALUE`](@ref), [`value_∂`](@ref) +!!! Warning + Improper use may cause perturbation confusion. + Assumes, without testing, that precedence(x)=P-1 + +See also: [`precedence`](@ref), [`δ_`](@ref), [`value`](@ref), [`∂`](@ref), [`VALUE`](@ref), [`value_∂`](@ref) """ -variate{ P,N}(a::SV{N,R} ) where{P,N,R<:ℝ} = SV{N,∂ℝ{P,N,R}}(∂ℝ{P,N }(a[i],i) for i=1:N) -variate{ P,N}(a::SV{N,R},δa::SV{N,𝕣}) where{P,N,R<:ℝ} = SV{N,∂ℝ{P,N,R}}(∂ℝ{P,N,R}(a[j] ,SV{N,R}(i==j ? R(δa[i]) : zero(R) for i=1:N)) for j=1:N) -variate{ P }(a::R ) where{P, R<:ℝ} = ∂ℝ{P,1 }(a,SV{1,R}(one(R))) -directional{P }(a::SV{N,R},δa::SV{N,R}) where{P,N,R<:ℝ} = SV{N,∂ℝ{P,1,R}}(∂ℝ{P,1}(a[i],SV{1,R}(δa[i])) for i=1:N) -function ∂²ℝ{P,N}(x::R,i,s=one(R)) where{P,N,R<:ℝ} - R1 = ∂ℝ{P,N,R} - return ∂ℝ{P+1,N,R1}( ∂ℝ{P,N}(x,i,s) , SV{N,R1}(j==i ? R1(s) : zero(R1) for j=1:N )) -end +@inline variate_{ P,N}(a::SV{N,R} ) where{P,N,R<:ℝ} = SV{N,∂ℝ{P,N,R}}(∂ℝ{P,N }(a[i],i) for i=1:N) +@inline variate_{ P,N}(a::SV{N,R},δa::SV{N,𝕣}) where{P,N,R<:ℝ} = SV{N,∂ℝ{P,N,R}}(∂ℝ{P,N,R}(a[j] ,SV{N,R}(i==j ? R(δa[i]) : zero(R) for i=1:N)) for j=1:N) +@inline variate_{ P }(a::R ) where{P, R<:ℝ} = ∂ℝ{P,1 }(a,SV{1,R}(one(R))) # Analyse """ - @show VALUE(Y) + VALUE(Y) Completely strip `Y` of partial derivatives. Use only for debugging purpose. -See also: [`constants`](@ref), [`variate`](@ref), [`δ`](@ref), [`value`](@ref), [`∂`](@ref), [`value_∂`](@ref) +See also: [`precedence`](@ref), [`Muscade.variate_`](@ref), [`δ_`](@ref), [`value`](@ref), [`∂`](@ref), [`value_∂`](@ref) """ -VALUE(a::Nothing ) = nothing -VALUE(a::ℝ ) = a -VALUE(a::∂ℝ) = VALUE( a.x) -VALUE(a::SA) = VALUE.(a) +@inline VALUE(a::Nothing ) = nothing +@inline VALUE(a::ℝ ) = a +@inline VALUE(a::∂ℝ) = VALUE( a.x) +@inline VALUE(a::SA) = VALUE.(a) struct ∂{P,N} end struct value{P,N} end @@ -165,12 +181,13 @@ struct value_∂{P,N} end Extract the value of an automatic differentiation object, or `SArray` of such objects. -See also: [`constants`](@ref), [`variate`](@ref), [`δ`](@ref), [`∂`](@ref), [`VALUE`](@ref), [`value_∂`](@ref) +See also: [`precedence`](@ref), [`Muscade.variate_`](@ref), [`δ_`](@ref), [`∂`](@ref), [`VALUE`](@ref), [`value_∂`](@ref) """ -value{P}(a::∂ℝ{P,N,R}) where{P,N,R } = a.x -value{P}(a::R ) where{P ,R<:ℝ} = a -value{P}(a::SA ) where{P } = value{P}.(a) -value{P}(a::Tuple ) where{P } = Tuple(value{P}(aᵢ) for aᵢ∈a) +@inline value{P}(a::∂ℝ{P ,N,R}) where{P ,N,R } = a.x +@inline value{P}(a::∂ℝ{Pa,N,R}) where{Pa,P,N,R } = P>Pa ? a : error("extracting value with invalid precedence") +@inline value{P}(a::R ) where{P ,R<:ℝ} = a +@inline value{P}(a::SA ) where{P } = value{P}.(a) +@inline value{P}(a::Tuple ) where{P } = Tuple(value{P}(aᵢ) for aᵢ∈a) # ∂{P}(a) is handled as ∂{P,1}(a) and returns a scalar """ @@ -182,48 +199,106 @@ the index of the partial derivative is appended to the indices of `Y`. y′ = ∂{P}(Y) Extract the derivative of an automatic differentiation object (or `SArray` of such), where the variation -was created by the syntax `variate{P}`. +was created by the syntax `Muscade.variate_{P}`. -See also: [`constants`](@ref), [`variate`](@ref), [`δ`](@ref), [`value`](@ref), [`VALUE`](@ref), [`value_∂`](@ref) +See also: [`precedence`](@ref), [`Muscade.variate_`](@ref), [`δ_`](@ref), [`value`](@ref), [`VALUE`](@ref), [`value_∂`](@ref) """ -∂{P,N}(a:: ∂ℝ{P,N,R} ) where{ P,N,R } = a.dx -∂{P,N}(a:: R ) where{ P,N,R<:ℝ} = SV{ N,R}(zero(R) for i=1:N ) -∂{P,N}(a::SV{M,∂ℝ{P,N,R}}) where{M,P,N,R } = SM{M,N,R}(a[i].dx[j] for i=1:M,j∈1:N) # ∂(a,x)[i,j] = ∂a[i]/∂x[j] -∂{P,N}(a::SV{M, R }) where{M,P,N,R } = SM{M,N,R}(zero(R) for i=1:M,j=1:N) -∂{P }(a:: R ) where{ P, R<:ℝ} = zero(R) -∂{P }(a:: ∂ℝ{P,1,R} ) where{ P, R } = a.dx[1] -∂{P }(a::SV{N,∂ℝ{P,1,R}}) where{ P,N,R } = SV{ N,R}(a[i].dx[1] for i=1:N ) # ∂(a,x)[i] = ∂a[i]/∂x - -∂{P,N}(a::SM{ M1,M2 ,∂ℝ{P,N,R}}) where{M1,M2 ,P,N,R} = SA{Tuple{M1,M2,N },R}(a[i].dx[j] for i∈eachindex(a),j∈1:N) # ∂(a,x)[i,...,j] = ∂a[i,...]/∂x[j] -∂{P,N}(a::SM{ M1,M2 , R }) where{M1,M2 ,P,N,R} = SA{Tuple{M1,M2,N },R}(zero(R) for i∈eachindex(a),j∈1:N) -∂{P,N}(a::SA{Tuple{M1,M2,M3 },∂ℝ{P,N,R}}) where{M1,M2,M3 ,P,N,R} = SA{Tuple{M1,M2,M3 ,N},R}(a[i].dx[j] for i∈eachindex(a),j∈1:N) # ∂(a,x)[i,...,j] = ∂a[i,...]/∂x[j] -∂{P,N}(a::SA{Tuple{M1,M2,M3 }, R }) where{M1,M2,M3 ,P,N,R} = SA{Tuple{M1,M2,M3 ,N},R}(zero(R) for i∈eachindex(a),j∈1:N) -∂{P,N}(a::SA{Tuple{M1,M2,M3,M4},∂ℝ{P,N,R}}) where{M1,M2,M3,M4,P,N,R} = SA{Tuple{M1,M2,M3,M4 ,N},R}(a[i].dx[j] for i∈eachindex(a),j∈1:N) # ∂(a,x)[i,...,j] = ∂a[i,...]/∂x[j] -∂{P,N}(a::SA{Tuple{M1,M2,M3,M4}, R }) where{M1,M2,M3,M4,P,N,R} = SA{Tuple{M1,M2,M3,M4 ,N},R}(zero(R) for i∈eachindex(a),j∈1:N) -∂{P,N}(a::Tuple ) where{ P,N } = Tuple(∂{P,N}(aᵢ) for aᵢ∈a) +@inline ∂{P,N}(a:: ∂ℝ{P ,N,R} ) where{ P,N,R } = a.dx +@inline ∂{P,N}(a:: ∂ℝ{Pa,N,R} ) where{ Pa,P,N,R } = P>Pa ? SV{ N,R}(zero(R) for i=1:N ) : error("extracting ∂ with invalid precedence") +@inline ∂{P,N}(a:: R ) where{ P,N,R<:ℝ} = SV{ N,R}(zero(R) for i=1:N ) +@inline ∂{P,N}(a::SV{M,∂ℝ{P ,N,R}}) where{M, P,N,R } = SM{M,N,R}(a[i].dx[j] for i=1:M,j∈1:N) # ∂(a,x)[i,j] = ∂a[i]/∂x[j] +@inline ∂{P,N}(a::SV{M,∂ℝ{Pa,N,R}}) where{M,Pa,P,N,R } = P>Pa ? SM{M,N,R}(a[i].dx[j] for i=1:M,j∈1:N) : error("extracting ∂ with invalid precedence")# ∂(a,x)[i,j] = ∂a[i]/∂x[j] +@inline ∂{P,N}(a::SV{M, R }) where{M, P,N,R } = SM{M,N,R}(zero(R) for i=1:M,j=1:N) +@inline ∂{P }(a:: R ) where{ P, R<:ℝ} = zero(R) +@inline ∂{P }(a:: ∂ℝ{P,1,R} ) where{ P, R } = a.dx[1] +@inline ∂{P }(a::SV{N,∂ℝ{P,1,R}}) where{ P,N,R } = SV{ N,R}(a[i].dx[1] for i=1:N ) # ∂(a,x)[i] = ∂a[i]/∂x + +@inline ∂{P,N}(a::SM{ M1,M2 ,∂ℝ{P, N,R}}) where{M1,M2, P,N,R} = SA{Tuple{M1,M2,N },R}(a[i].dx[j] for i∈eachindex(a),j∈1:N) # ∂(a,x)[i,...,j] = ∂a[i,...]/∂x[j] +@inline ∂{P,N}(a::SM{ M1,M2 ,∂ℝ{Pa,N,R}}) where{M1,M2, Pa,P,N,R} = P>Pa ? SA{Tuple{M1,M2,N },R}(a[i].dx[j] for i∈eachindex(a),j∈1:N) : error("extracting ∂ with invalid precedence")# ∂(a,x)[i,...,j] = ∂a[i,...]/∂x[j] +@inline ∂{P,N}(a::SM{ M1,M2 , R }) where{M1,M2, P,N,R} = SA{Tuple{M1,M2,N },R}(zero(R) for i∈eachindex(a),j∈1:N) +@inline ∂{P,N}(a::SA{Tuple{M1,M2,M3 },∂ℝ{P, N,R}}) where{M1,M2,M3, P,N,R} = SA{Tuple{M1,M2,M3 ,N},R}(a[i].dx[j] for i∈eachindex(a),j∈1:N) # ∂(a,x)[i,...,j] = ∂a[i,...]/∂x[j] +@inline ∂{P,N}(a::SA{Tuple{M1,M2,M3 },∂ℝ{Pa,N,R}}) where{M1,M2,M3, Pa,P,N,R} = P>Pa ? SA{Tuple{M1,M2,M3 ,N},R}(a[i].dx[j] for i∈eachindex(a),j∈1:N) : error("extracting ∂ with invalid precedence")# ∂(a,x)[i,...,j] = ∂a[i,...]/∂x[j] +@inline ∂{P,N}(a::SA{Tuple{M1,M2,M3 }, R }) where{M1,M2,M3, P,N,R} = SA{Tuple{M1,M2,M3 ,N},R}(zero(R) for i∈eachindex(a),j∈1:N) +@inline ∂{P,N}(a::SA{Tuple{M1,M2,M3,M4},∂ℝ{P, N,R}}) where{M1,M2,M3,M4, P,N,R} = SA{Tuple{M1,M2,M3,M4 ,N},R}(a[i].dx[j] for i∈eachindex(a),j∈1:N) # ∂(a,x)[i,...,j] = ∂a[i,...]/∂x[j] +@inline ∂{P,N}(a::SA{Tuple{M1,M2,M3,M4},∂ℝ{Pa,N,R}}) where{M1,M2,M3,M4,Pa,P,N,R} = P>Pa ? SA{Tuple{M1,M2,M3,M4 ,N},R}(a[i].dx[j] for i∈eachindex(a),j∈1:N) : error("extracting ∂ with invalid precedence")# ∂(a,x)[i,...,j] = ∂a[i,...]/∂x[j] +@inline ∂{P,N}(a::SA{Tuple{M1,M2,M3,M4}, R }) where{M1,M2,M3,M4, P,N,R} = SA{Tuple{M1,M2,M3,M4 ,N},R}(zero(R) for i∈eachindex(a),j∈1:N) +@inline ∂{P,N}(a::Tuple ) where{ P,N } = Tuple(∂{P,N}(aᵢ) for aᵢ∈a) """ y,yₓ = value_∂{P,N}(Y) y,y′ = value_∂{P }(Y) Get value and derivative in one operation. -See also: [`constants`](@ref), [`variate`](@ref), [`δ`](@ref), [`value`](@ref), [`∂`](@ref), [`VALUE`](@ref) +See also: [`precedence`](@ref), [`Muscade.variate_`](@ref), [`Muscade.δ_`](@ref), [`value`](@ref), [`∂`](@ref), [`VALUE`](@ref) """ -value_∂{P,N}(a) where{ P,N}= value{P}(a),∂{P,N}(a) -value_∂{P }(a) where{ P }= value{P}(a),∂{P }(a) +@inline value_∂{P,N}(a) where{ P,N}= value{P}(a),∂{P,N}(a) +@inline value_∂{P }(a) where{ P }= value{P}(a),∂{P }(a) + +# +struct ∂𝟘{P} end +@inline ∂𝟘{P}(a::∂ℝ{P}) where{P} = a.dx +@inline ∂𝟘{P}(a:: ℝ ) where{P} = 𝟘 +struct value_∂𝟘{P} end +@inline value_∂𝟘{P}(a::ℝ) where{P}= value{P}(a), ∂𝟘{P}(a) + + ## Binary operations + +# optimised implementations + +@inline Base.:(/)(a::Jℝ,b::∂ℝ) = Base.:(/)(a,b,inv(VALUE(b))) +@inline Base.:(/)(a::∂ℝ,b::Jℝ) = Base.:(/)(a,b,inv(VALUE(b))) +@inline Base.:(/)(a::∂ℝ,b::∂ℝ) = Base.:(/)(a,b,inv(VALUE(b))) +@inline Base.:(/)(a::Jℝ,b::Jℝ,b⁻¹::Jℝ) = a*b⁻¹ +@inline function Base.:(/)(a::Ra,b::Rb,b⁻¹::Jℝ) where{Ra<:ℝ,Rb<:ℝ} + if Ra <: ∂ℝ || Rb <: ∂ℝ + P,N,R = ∂ℝ_promote_type(a,b) + va,∂a = value_∂𝟘{P}(a) + vb,∂b = value_∂𝟘{P}(b) + return ∂ℝ{P,N}( convert(R,/(va,vb,b⁻¹)) , convert.(R,∂a*inv(vb) .- /(va,vb*vb,b⁻¹^2)*∂b) ) + else + return a*b⁻¹ + end +end + +@inline function Base.:(^)(a::∂ℝ{P,N,R},b::ℤ) where{P,N,R} + if b<0 # 'if' resolved at compile time thanks to inlining if b is a compile time constant in caller function + inv(a) + elseif b<-1 + inv(a)^(-b) + elseif b==0 + one(a) + elseif b==1 + a + elseif b==2 + a*a + else + va,∂a = value_∂𝟘{P}(a) + x = va^(b-1) + ∂ℝ{P,N,R}(va*x ,∂a*(b*x) ) + end +end +@inline Base.:(^)(a::∂ℝ,b::Jℝ) = exp(b*log(a)) +@inline Base.:(^)(a::Jℝ,b::∂ℝ) = exp(b*log(a)) +@inline Base.:(^)(a::∂ℝ,b::∂ℝ) = exp(b*log(a)) + +# straightforward implementations + for OP∈(:(>),:(<),:(==),:(>=),:(<=),:(!=)) - @eval Base.$OP(a::∂ℝ,b::∂ℝ) = $OP(VALUE(a),VALUE(b)) - @eval Base.$OP(a:: ℝ,b::∂ℝ) = $OP( a ,VALUE(b)) - @eval Base.$OP(a::∂ℝ,b:: ℝ) = $OP(VALUE(a), b ) + @eval @inline Base.$OP(a::∂ℝ,b::∂ℝ) = $OP(VALUE(a),VALUE(b)) + @eval @inline Base.$OP(a:: ℝ,b::∂ℝ) = $OP( a ,VALUE(b)) + @eval @inline Base.$OP(a::∂ℝ,b:: ℝ) = $OP(VALUE(a), b ) end +@inline Base.isapprox(a::∂ℝ,b::∂ℝ;kwargs...) = isapprox(VALUE(a),VALUE(b);kwargs...) +@inline Base.isapprox(a:: ℝ,b::∂ℝ;kwargs...) = isapprox( a ,VALUE(b);kwargs...) +@inline Base.isapprox(a::∂ℝ,b:: ℝ;kwargs...) = isapprox(VALUE(a), b ;kwargs...) macro DiffRule2(OP,AB,A,B) return esc(quote @inline $OP(a::∂ℝ{P,N,R},b::∂ℝ{P,N,R}) where{P,N,R<:ℝ} = ∂ℝ{P,N,R}($OP(a.x,b.x),$AB) - @inline $OP(a::∂ℝ{P,N,R},b::ℝ ) where{P,N,R<:ℝ} = ∂ℝ{P,N,R}($OP(a.x,b ),$A ) - @inline $OP(a::ℝ ,b::∂ℝ{P,N,R}) where{P,N,R<:ℝ} = ∂ℝ{P,N,R}($OP(a ,b.x),$B ) + @inline $OP(a::∂ℝ{P,N,R},b::Jℝ ) where{P,N,R<:ℝ} = ∂ℝ{P,N,R}($OP(a.x,b ),$A ) + @inline $OP(a::Jℝ ,b::∂ℝ{P,N,R}) where{P,N,R<:ℝ} = ∂ℝ{P,N,R}($OP(a ,b.x),$B ) @inline function $OP(a::∂ℝ{Pa,Na,Ra},b::∂ℝ{Pb,Nb,Rb}) where{Pa,Pb,Na,Nb,Ra<:ℝ,Rb<:ℝ} if Pa==Pb R = promote_type(Ra,Rb) @@ -243,32 +318,63 @@ end @DiffRule2(Base.:(+), a.dx+b.dx, a.dx, b.dx ) @DiffRule2(Base.:(-), a.dx-b.dx, a.dx, -b.dx ) @DiffRule2(Base.:(*), a.dx*b.x+a.x*b.dx, a.dx*b, a*b.dx ) -@DiffRule2(Base.:(/), a.dx/b.x-a.x/b.x^2*b.dx, a.dx/b, -a/b.x^2*b.dx ) -@DiffRule2(Base.:(^), a.dx*b.x*a.x^(b.x-1)+log(a.x)*a.x^b.x*b.dx, a.dx*b*a.x^(b -1), log(a)*a ^b.x*b.dx ) # for exponents ∈ ℝ -@inline Base.:(^)(a::∂ℝ{P,N,R},b::ℤ) where{P,N,R<:ℝ} = b==0 ? zero(a) : ∂ℝ{P,N,R}(a.x^b ,a.dx*b*a.x^(b-1) ) # for exponents ∈ ℤ + ## Functions + +# optimised implementations + +@inline Base.sqrt(a::∂ℝ) = Base.sqrt(a,Base.sqrt(VALUE(a))) +@inline Base.sqrt(a::Jℝ,sq::Jℝ) = sq +@inline function Base.sqrt(a::∂ℝ{P,N},sq::Jℝ) where{P,N} + SQ = Base.sqrt(a.x,sq) + ∂ℝ{P,N}(SQ, a.dx * inv(2*SQ)) +end +@inline function Base.inv(a::∂ℝ{P,N}) where{P,N} + x⁻¹ = inv(a.x) # minimal gain from computing x⁻¹ once, not twice + ∂ℝ{P,N}(x⁻¹,a.dx.*(-abs2(x⁻¹))) +end +@inline Base.exp(a::∂ℝ) = exp(a,exp(VALUE(a))) +@inline Base.exp(a::Jℝ,eˣ::Jℝ) = eˣ +@inline function Base.exp(a::∂ℝ{P,N},eˣ::Jℝ) where{P,N} + E = exp(a.x,eˣ) + ∂ℝ{P,N}(E,a.dx.*E) +end +@inline Base.sin(a::∂ℝ) = sin(a,sincos(VALUE(a))...) +@inline function Base.sin(a::∂ℝ{P,N},s::Jℝ,c::Jℝ) where{P,N} + S,C = sincos(a.x,s,c) + ∂ℝ{P,N}(S, a.dx.*C) +end +@inline Base.cos(a::∂ℝ) = cos(a,sincos(VALUE(a))...) +@inline function Base.cos(a::∂ℝ{P,N},s::Jℝ,c::Jℝ) where{P,N} + S,C = sincos(a.x,s,c) + ∂ℝ{P,N}(C, -a.dx.*S) +end +@inline Base.sincos(a::∂ℝ) = sincos(a,sincos(VALUE(a))...) +@inline Base.sincos(a::Jℝ,s::Jℝ,c::Jℝ) = s,c +@inline function Base.sincos(a::∂ℝ{P,N},s::Jℝ,c::Jℝ) where{P,N} + S,C = sincos(a.x,s,c) + ∂ℝ{P,N}(S, a.dx.*C), ∂ℝ{P,N}(C, -a.dx.*S) +end + +# straightforward implementations + macro DiffRule1(OP,A) return esc(:(@inline $OP(a::∂ℝ{P,N}) where{P,N} = ∂ℝ{P,N}($OP(a.x),$A))) end -@DiffRule1(Base.:(+), a.dx ) -@DiffRule1(Base.:(-), -a.dx ) -@DiffRule1(Base.abs ,a.x==0.0 ? zero(a.dx) : (a.x>0.0 ? a.dx : -a.dx) ) -@DiffRule1(Base.conj , a.dx ) -@DiffRule1(Base.sqrt, a.dx / 2. / sqrt(a.x) ) -@DiffRule1(Base.cbrt, a.dx / 3. / cbrt(a.x)^2 ) -@DiffRule1(Base.abs2, a.dx*2. * a.x ) -@DiffRule1(Base.inv, -a.dx * abs2(inv(a.x)) ) -@DiffRule1(Base.log, a.dx / a.x ) -@DiffRule1(Base.log10, a.dx / a.x / log(10.) ) -@DiffRule1(Base.log2, a.dx / a.x / log(2.) ) -@DiffRule1(Base.log1p, a.dx / (a.x + 1.) ) -@DiffRule1(Base.exp, exp(a.x) * a.dx ) +@DiffRule1(Base.:(+), a.dx ) +@DiffRule1(Base.:(-), -a.dx ) +@DiffRule1(Base.abs, a.x==0.0 ? zero(a.dx) : (a.x>0.0 ? a.dx : -a.dx) ) +@DiffRule1(Base.conj , a.dx ) +@DiffRule1(Base.log, a.dx / a.x ) +@DiffRule1(Base.log10, a.dx / a.x / log(10.) ) +@DiffRule1(Base.log2, a.dx / a.x / log(2.) ) +@DiffRule1(Base.log1p, a.dx / (a.x + 1.) ) +@DiffRule1(Base.cbrt, a.dx / 3. / cbrt(a.x)^2 ) +@DiffRule1(Base.abs2, a.dx*2. * a.x ) @DiffRule1(Base.exp2, log(2. ) * exp2( a.x) * a.dx ) @DiffRule1(Base.exp10, log(10.) * exp10(a.x) * a.dx ) @DiffRule1(Base.expm1, exp(a.x) * a.dx ) -@DiffRule1(Base.sin, cos(a.x) * a.dx ) -@DiffRule1(Base.cos, -sin(a.x) * a.dx ) @DiffRule1(Base.tan, (1. + tan(a.x)^2) * a.dx ) @DiffRule1(Base.sinpi, π*cos(a.x) * a.dx ) @DiffRule1(Base.cospi, -π*sin(a.x) * a.dx ) @@ -282,7 +388,7 @@ end @DiffRule1(Base.cscd, -π / 180. * cscd(a.x) * cotd(a.x) * a.dx ) @DiffRule1(Base.cotd, -π / 180. * (1. + cotd(a.x)^2) * a.dx ) @DiffRule1(Base.asin, a.dx / sqrt(1. - a.x^2) ) -@DiffRule1(Base.acos, -a.dx / sqrt(1. - a.x^2) ) +@DiffRule1(Base.acos, a.dx.*(-inv(sqrt(1-a.x^2))) ) @DiffRule1(Base.atan, a.dx / (1. + a.x^2) ) @DiffRule1(Base.asec, a.dx / abs(a.x) / sqrt(a.x^2 - 1.) ) @DiffRule1(Base.acsc, -a.dx / abs(a.x) / sqrt(a.x^2 - 1.) ) @@ -321,17 +427,38 @@ end @DiffRule1(SpecialFunctions.bessely0, -bessely1(a.x) * a.dx ) @DiffRule1(SpecialFunctions.bessely1, (bessely0(a.x) - bessely(2., a.x))/2. * a.dx ) +""" + Muscade.sinc1(x) + +`sinc1(x) = sin(x)/x` - but `sinc1(0.) = 1.`. The function can be differentiated +to the fourth order. + +This differs from Julia's `sinc(x) = sin(π*x)/(π*x)`. +""" +@inline sinc1( x::R ) where{R<:Jℝ} = abs(x)>1e-2 ? sin(x)/x : evalpoly(x*x,(1, -1/6, 1/120)) +@inline sinc1( x::R,s::R,c::R,x⁻¹::R,x²::R) where{R<:Jℝ} = abs(x)>1e-2 ? s*x⁻¹ : evalpoly(x² ,(1, -1/6, 1/120)) +@inline sinc1′(x::R,s::R,c::R,x⁻¹::R,x²::R) where{R<:Jℝ} = abs(x)>1e-3 ? x⁻¹*evalpoly(x⁻¹,(c,-s)) : x*evalpoly(x² ,(-1/3,1/30)) +@inline sinc1″(x::R,s::R,c::R,x⁻¹::R,x²::R) where{R<:Jℝ} = abs(x)>1e-1 ? x⁻¹*evalpoly(x⁻¹,(-s,-2c,2s)) : evalpoly(x² ,(-1/3,1/10,-1/168,1/6480)) +@inline sinc1‴(x::R,s::R,c::R,x⁻¹::R,x²::R) where{R<:Jℝ} = abs(x)>0.4 ? x⁻¹*evalpoly(x⁻¹,(-c,3s,6c,-6s)) : x*evalpoly(x² ,(1/5,-1/42,1/1080,-1/55440,1/4717440)) +@inline sinc1⁗(x::R,s::R,c::R,x⁻¹::R,x²::R) where{R<:Jℝ} = evalpoly(x² ,(1/5,-1/14,1/216,-1/7920,1/524160,-1/54432000,1/54432000,-1/8143027200,1/1656387532800)) + +@inline sinc1( x::R ) where{R<:∂ℝ} = sinc1(x,sincos(x)...,inv(x),x*x) +@inline sinc1( x::R,s::R,c::R,x⁻¹::R,x²::R) where{R<:∂ℝ} = R(sinc1( x.x,s.x,c.x,x⁻¹.x,x².x), x.dx*sinc1′(x.x,s.x,c.x,x⁻¹.x,x².x)) +@inline sinc1′(x::R,s::R,c::R,x⁻¹::R,x²::R) where{R<:∂ℝ} = R(sinc1′(x.x,s.x,c.x,x⁻¹.x,x².x), x.dx*sinc1″(x.x,s.x,c.x,x⁻¹.x,x².x)) +@inline sinc1″(x::R,s::R,c::R,x⁻¹::R,x²::R) where{R<:∂ℝ} = R(sinc1″(x.x,s.x,c.x,x⁻¹.x,x².x), x.dx*sinc1‴(x.x,s.x,c.x,x⁻¹.x,x².x)) +@inline sinc1‴(x::R,s::R,c::R,x⁻¹::R,x²::R) where{R<:∂ℝ} = R(sinc1‴(x.x,s.x,c.x,x⁻¹.x,x².x), x.dx*sinc1⁗(x.x,s.x,c.x,x⁻¹.x,x².x)) +@inline sinc1⁗(x::R ) where{R<:∂ℝ} = error("attempted to compute 5th derivative of sinc1") ## Find NaN in derivatives -hasnan(a::ℝ ) = isnan(a) -hasnan(a::∂ℝ ) = hasnan(a.x) || hasnan(a.dx) -hasnan(a::Tuple) = any(hasnan.(a)) -hasnan(a::NamedTuple) = any(hasnan.(values(a))) -hasnan(a...;) = any(hasnan.(a)) -hasnan(a) = false +@inline hasnan(a::ℝ ) = isnan(a) +@inline hasnan(a::∂ℝ ) = hasnan(a.x) || hasnan(a.dx) +@inline hasnan(a::Tuple) = any(hasnan.(a)) +@inline hasnan(a::NamedTuple) = any(hasnan.(values(a))) +@inline hasnan(a...;) = any(hasnan.(a)) +@inline hasnan(a) = false #hasnan(a::AbstractArray) = any(hasnan.(a)) # slow -function hasnan(a::AbstractArray) +@inline function hasnan(a::AbstractArray) for aᵢ ∈ a if hasnan(aᵢ) return true @@ -342,14 +469,33 @@ end # Print addifs const subscripts = ('₁','₂','₃','₄','₅','₆','₇','₈','₉') -string_(a::Float64) = strip(@sprintf("%4.3g",a)) +#string_(a::Float64) = strip(@sprintf("%18.16g",a)) +string_(a::Float64) = strip(replace(@sprintf("%5.3g",a),"e+0"=>"e","e+"=>"e","e-0"=>"e-")) function string_(a::∂ℝ{P,N,R}) where{P,N,R} p = subscripts[P] x = string_(a.x) dx = N==0 ? "" : @sprintf("%s",string_(a.dx[1])) for i = 2:N - dx = @sprintf("%s, %s",dx,string_(a.dx[i])) + dx = @sprintf("%s,%s",dx,string_(a.dx[i])) end - return @sprintf("%s + ∂%s⟨%s⟩",x,p,dx) # \partial \langle \rangle mathematicaly-explicit +# return @sprintf("%s+∂%s⟨%s⟩",x,p,dx) # \partial \langle \rangle mathematicaly-explicit + return @sprintf("∂%s⟨%s|%s⟩",p,x,dx) # \partial \langle \rangle mathematicaly-explicit end -Base.show(io::IO,x::∂ℝ) = print(io,string_(x)) +Base.show(io::IO,a::∂ℝ) = print(io,string_(a)) + +""" + Muscade.isapprox_dbg(a,b;kwargs...) + +Compare two `∂ℝ` of the same type (or two conformant `AbstractArrays` of same `eltype`). +The comparison applies to the value and the partial derivatives. + +This differs from + + isapprox(a,b;kwargs...) + +which only compares values, in keeping with the principle that `∂ℝ` must behave as `ℝ`. + +""" +isapprox_dbg(a::R,b::R;kwargs...) where{R<:∂ℝ} = isapprox_dbg(a.x,b.x;kwargs...) && all(isapprox_dbg.(a.dx,b.dx;kwargs...)) +isapprox_dbg(a::𝕣,b::𝕣;kwargs...) = isapprox( a, b ;kwargs...) +isapprox_dbg(a::AbstractArray{R},b::AbstractArray{R};kwargs...) where{R<:∂ℝ} = all(isapprox_dbg.(a,b;kwargs...)) diff --git a/src/Assemble.jl b/src/Assemble.jl index 1892040d..a064233e 100644 --- a/src/Assemble.jl +++ b/src/Assemble.jl @@ -155,9 +155,33 @@ function State{nΛder,nXder,nUder}(state;time=state.time,Λ=state.Λ,X=state.X,U state.dis = dis return state end -# A deep copy - except for SP,model and dis +""" + s2 = copy(s1::State) + +Copy a state so that `s1` and `s2` do not share memory. + +(Actualy the `State`s will stil share the same `Model`, but no operations are provided to mutate it). + + s2 = copy(s1;[time=t]) + +create a copied `State` with time `t`. + +See also: [`initialize!`](@ref), [`setdof!`](@ref) +""" Base.copy(s::State;time=s.time,SP=s.SP) = State(time,deepcopy(s.Λ),deepcopy(s.X),deepcopy(s.U),deepcopy(s.A),SP,s.model,s.dis) +function Base.show(io::IO,o::State{nΛder,nXder,nUder,TSP}) where{nΛder,nXder,nUder,TSP} + print(io,"State{",nΛder,",",nXder,",",nUder,",",TSP,"}(model=:",o.model.ID,", time=",o.time,", ...)") +end +function Base.show(io::IO,o::Vector{State{nΛder,nXder,nUder,TSP}}) where{nΛder,nXder,nUder,TSP} + println(io,length(o),"-element Vector{State{",nΛder,",",nXder,",",nUder,",",TSP,"}}:") + for (i,oᵢ) ∈ enumerate(o) + println(io," ",i,": model=:",oᵢ.model.ID,", time=",oᵢ.time) + end +end + + + #### DofGroup @@ -165,7 +189,7 @@ Base.copy(s::State;time=s.time,SP=s.SP) = State(time,deepcopy(s.Λ),deepcopy(s.X # of the dofs of the model. struct DofGroup - nX :: 𝕫 # of the _model + nX :: 𝕫 # of the _model_ nU :: 𝕫 nA :: 𝕫 @@ -216,20 +240,20 @@ function increment!(s::State,ider::𝕫,y::AbstractVector{𝕣},gr::DofGroup) if ider==1 for i ∈ eachindex(gr.iA); s.A[ gr.iA[i]] += y[gr.jA[i]] * gr.scaleA[i]; end end end function set!(s::State,ider::𝕫,y::AbstractVector{𝕣},gr::DofGroup) - s.Λ[ider+1] .= 0 - s.X[ider+1] .= 0 - s.U[ider+1] .= 0 - s.A .= 0 - for i ∈ eachindex(gr.iΛ); s.Λ[ider+1][gr.iΛ[i]] = y[gr.jΛ[i]] * gr.scaleΛ[i]; end - for i ∈ eachindex(gr.iX); s.X[ider+1][gr.iX[i]] = y[gr.jX[i]] * gr.scaleX[i]; end - for i ∈ eachindex(gr.iU); s.U[ider+1][gr.iU[i]] = y[gr.jU[i]] * gr.scaleU[i]; end - for i ∈ eachindex(gr.iA); s.A[ gr.iA[i]] = y[gr.jA[i]] * gr.scaleA[i]; end -end -function getdof!(s::State,ider::𝕫,y::AbstractVector{𝕣},gr::DofGroup) - for i ∈ eachindex(gr.iΛ); y[gr.jΛ[i]] = s.Λ[ider+1][gr.iΛ[i]] / gr.scaleΛ[i]; end - for i ∈ eachindex(gr.iX); y[gr.jX[i]] = s.X[ider+1][gr.iX[i]] / gr.scaleX[i]; end - for i ∈ eachindex(gr.iU); y[gr.jU[i]] = s.U[ider+1][gr.iU[i]] / gr.scaleU[i]; end - for i ∈ eachindex(gr.iA); y[gr.jA[i]] = s.A[ gr.iA[i]] / gr.scaleA[i]; end + if ider≤length(s.Λ) s.Λ[ider] .= 0 end + if ider≤length(s.X) s.X[ider] .= 0 end + if ider≤length(s.U) s.U[ider] .= 0 end + if ider==1 s.A .= 0 end + if ider≤length(s.Λ) for i ∈ eachindex(gr.iΛ); s.Λ[ider][gr.iΛ[i]] = y[gr.jΛ[i]] * gr.scaleΛ[i]; end end + if ider≤length(s.X) for i ∈ eachindex(gr.iX); s.X[ider][gr.iX[i]] = y[gr.jX[i]] * gr.scaleX[i]; end end + if ider≤length(s.U) for i ∈ eachindex(gr.iU); s.U[ider][gr.iU[i]] = y[gr.jU[i]] * gr.scaleU[i]; end end + if ider==1 for i ∈ eachindex(gr.iA); s.A[ gr.iA[i]] = y[gr.jA[i]] * gr.scaleA[i]; end end +end +function get!(s::State,ider::𝕫,y::AbstractVector{𝕣},gr::DofGroup) + if ider≤length(s.Λ)for i ∈ eachindex(gr.iΛ); y[gr.jΛ[i]] = s.Λ[ider][gr.iΛ[i]] / gr.scaleΛ[i]; end end + if ider≤length(s.X)for i ∈ eachindex(gr.iX); y[gr.jX[i]] = s.X[ider][gr.iX[i]] / gr.scaleX[i]; end end + if ider≤length(s.U)for i ∈ eachindex(gr.iU); y[gr.jU[i]] = s.U[ider][gr.iU[i]] / gr.scaleU[i]; end end + if ider==1 for i ∈ eachindex(gr.iA); y[gr.jA[i]] = s.A[ gr.iA[i]] / gr.scaleA[i]; end end end # create a tuple (Λ,X,U,A) of indices into the dofgroup - with zeros for modeldofs not in dofgroup # so the model's iλ-th Λdof is found in y[Λ[iλ]] @@ -467,6 +491,9 @@ struct assemble_!{mission} end struct assembleA!{mission} end struct assembleA_!{mission} end struct addin!{mission} end + +# standard assembler, everything except time-independant A-cost +# Assemble a state using the values of variables in the state. function assemble!{mission}(out::Assembly,asm,dis,model,state,Δt,dbg) where{mission} zero!(out) for ieletyp = 1:lastindex(model.eleobj) @@ -474,36 +501,41 @@ function assemble!{mission}(out::Assembly,asm,dis,model,state,Δt,dbg) where{mis assemble_!{mission}(out,view(asm,:,ieletyp),dis.dis[ieletyp],eleobj,state,state.time,Δt,state.SP,(dbg...,ieletyp=ieletyp)) end end -assemble_!{mission}(out::Assembly,asm,dis,eleobj::Acost,state,t,Δt,SP,dbg) where{mission} = nothing -function assemble_!{mission}(out::Assembly,asm,dis,eleobj,state::State{nΛder,nXder,nUder},t,Δt,SP,dbg) where{mission,nΛder,nXder,nUder} +assemble_!{ mission}(out::Assembly,asm,dis,eleobj::Vector{<:Acost},state::State{nΛder,nXder,nUder},t,Δt,SP,dbg) where{mission,nΛder,nXder,nUder} = nothing +function assemble_!{mission}(out::Assembly,asm,dis,eleobj ,state::State{nΛder,nXder,nUder},t,Δt,SP,dbg) where{mission,nΛder,nXder,nUder} for iele = 1:lastindex(eleobj) index = dis.index[iele] Λe = NTuple{nΛder}(λ[index.X] for λ∈state.Λ) Xe = NTuple{nXder}(x[index.X] for x∈state.X) Ue = NTuple{nUder}(u[index.U] for u∈state.U) - Ae = state.A[index.A] - addin!{mission}(out,asm,iele,dis.scale,eleobj[iele],Λe,Xe,Ue,Ae, t,Δt,SP,(dbg...,iele=iele)) # defined by solver. Called for each element. But the asm that is passed - end # is of the form asm[iarray][i,iele], because addin! will add to all arrays in one pass -end -function assemble!{mission}(out::Assembly,asm,dis,model,Λ,X,U,A,t,Δt,dbg) where{mission} - zero!(out) - for ieletyp = 1:lastindex(model.eleobj) - eleobj = model.eleobj[ieletyp] - assemble_!{mission}(out,view(asm,:,ieletyp),dis.dis[ieletyp],eleobj,Λ,X,U,A,t,Δt,nothing,(dbg...,ieletyp=ieletyp)) - end -end -assemble_!{mission}(out::Assembly,asm,dis,eleobj::Acost,Λ,X,U,A,t,Δt,SP,dbg) where{mission} = nothing -function assemble_!{mission}(out::Assembly,asm,dis,eleobj,Λ::NTuple{nΛder},X::NTuple{nXder},U::NTuple{nUder},A,t,Δt,SP,dbg) where{mission,nΛder,nXder,nUder} - for iele = 1:lastindex(eleobj) - index = dis.index[iele] - Λe = NTuple{nΛder}(λ[index.X] for λ∈Λ) - Xe = NTuple{nXder}(x[index.X] for x∈X) - Ue = NTuple{nUder}(u[index.U] for u∈U) - Ae = A[index.A] + Ae = state.A[index.A] addin!{mission}(out,asm,iele,dis.scale,eleobj[iele],Λe,Xe,Ue,Ae, t,Δt,SP,(dbg...,iele=iele)) # defined by solver. Called for each element. But the asm that is passed end # is of the form asm[iarray][i,iele], because addin! will add to all arrays in one pass end +# TODO stateless assembler. Who uses this??? +# if we keep this: make standard assemble! above call the assemble_! below +# +# function assemble!{mission}(out::Assembly,asm,dis,model,Λ,X,U,A,t,Δt,dbg) where{mission} +# zero!(out) +# for ieletyp = 1:lastindex(model.eleobj) +# eleobj = model.eleobj[ieletyp] +# assemble_!{mission}(out,view(asm,:,ieletyp),dis.dis[ieletyp],eleobj,Λ,X,U,A,t,Δt,nothing,(dbg...,ieletyp=ieletyp)) +# end +# end +# assemble_!{mission}(out::Assembly,asm,dis,eleobj::Acost,Λ,X,U,A,t,Δt,SP,dbg) where{mission} = nothing +# function assemble_!{mission}(out::Assembly,asm,dis,eleobj,Λ::NTuple{nΛder},X::NTuple{nXder},U::NTuple{nUder},A,t,Δt,SP,dbg) where{mission,nΛder,nXder,nUder} +# for iele = 1:lastindex(eleobj) +# index = dis.index[iele] +# Λe = NTuple{nΛder}(λ[index.X] for λ∈Λ) +# Xe = NTuple{nXder}(x[index.X] for x∈X) +# Ue = NTuple{nUder}(u[index.U] for u∈U) +# Ae = A[index.A] +# addin!{mission}(out,asm,iele,dis.scale,eleobj[iele],Λe,Xe,Ue,Ae, t,Δt,SP,(dbg...,iele=iele)) # defined by solver. Called for each element. But the asm that is passed +# end # is of the form asm[iarray][i,iele], because addin! will add to all arrays in one pass +# end + +# assemble the time-independant A-cost function assembleA!{mission}(out::Assembly,asm,dis,model,state,dbg) where{mission} zero!(out) for ieletyp = 1:lastindex(model.eleobj) @@ -544,6 +576,11 @@ function zero!(out::AbstractSparseArray) out.nzval[i] = 0 end end +function zero!(out::Tuple) + for oᵢ ∈ out + zero!(oᵢ) + end +end #### extract value or derivatives from a SVector 'a' of adiffs, and add it directly into vector, full matrix or nzval of sparse matrix 'out'. # given a vector a @@ -553,10 +590,10 @@ end # idasm: where in the second dim of out to put data (if transpose: first) # # out[asm[: ,iele]] += a -# out[asm[iasm,iele]] += a # pick: 'a' is only a part of the element vector (FreqXU) +# out[asm[iasm,iele]] += a # build: 'a' is only a part of the element vector (FreqXU) # out[asm[:, iele]] += a[ia] # split: parts of 'a' are assembled (DirectXUA) # out[asm[iasm,iele]] += a[ia] # not used -function add_value!(out::𝕣1,asm,iele,a::SVector{Na,<:ℝ},ia=1:Na;iasm=idvec,Δt=idmult) where{Na} +function add_value!(out::𝕣1,asm,iele,a::SVector{Na,<:ℝ},ia=1:Na ; iasm=idvec,Δt=idmult) where{Na} for (i,iaᵢ) ∈ enumerate(ia) iout = asm[iasm[i],iele] if iout≠0 @@ -564,12 +601,19 @@ function add_value!(out::𝕣1,asm,iele,a::SVector{Na,<:ℝ},ia=1:Na;iasm=idvec, end end end -function add_value!(out::𝕣0,a,ia::𝕫;Δt=idmult) # # Lr, scalar in Newmakr-β context - out[] += VALUE(a[ia])*Δt -end struct add_∂!{P,S,T} end # to allow syntax with type-parameter P: precedence, S: :plus|:minus, T: :transpose|:notranspose -function add_∂!{P,S,T}(out::Array,asm,iele,a::SVector{Na,∂ℝ{P,Nda,R}},ia=1:Na,ida=1:Nda;iasm=idvec,idasm=idvec,Δt=idmult) where{P,Nda,R,Na,S,T} +#### derivatives from a SVector 'a' of adiffs, and add it directly into full matrix or nzval of sparse matrix 'out'. +# given a vector a +# ia: where in the vector to pick data +# ida: where in the partials to pick data +# iasm: where in first dim of out to put data (if transpose: second) +# idasm: where in the second dim of out to put data (if transpose: first) +# +# ∀ i,j out[asm[iasm[i]+length(ia)*idasm[j]-1,iele]] += a[ia[i]].dx[ida[j]] +# +# out::Array is deliberately vague, encompassing 𝕣2 and sparse.nzval +function add_∂!{P,S,T}(out::Array,asm,iele,a::SVector{Na,∂ℝ{P,Nda,R}},ia=1:Na,ida=1:Nda ; iasm=idvec,idasm=idvec,Δt=idmult) where{P,Nda,R,Na,S,T} for (i,iaᵢ) ∈ enumerate(ia), (j,idaⱼ) ∈ enumerate(ida) k = if T==:transpose idasm[j]+length(ida)*( iasm[i]-1) elseif T==:notranspose iasm[ i]+length( ia)*(idasm[j]-1) @@ -585,11 +629,11 @@ function add_∂!{P,S,T}(out::Array,asm,iele,a::SVector{Na,∂ℝ{P,Nda,R}},ia=1 end end add_∂!{P }( args...;kwargs...) where{P } = add_∂!{P,:plus }(args...;kwargs...) -add_∂!{P ,S}( args...;kwargs...) where{P,S } = add_∂!{P,S ,:notranspose}(args...;kwargs...) +add_∂!{P,S }( args...;kwargs...) where{P,S } = add_∂!{P,S ,:notranspose}(args...;kwargs...) add_∂!{P,S,T}(out::SparseMatrixCSC, args...;kwargs...) where{P,S,T } = add_∂!{P,S ,T }(out.nzval, args...;kwargs...) add_∂!{P,S,T}(out::Array,asm,iele,a::SVector{Na,R},args...;kwargs...) where{P,S,T,Na,R} = nothing # if P does not match -function add_∂!{P,S,T}(out::Vector,asm, iele, a::SVector{Na,∂ℝ{P,Nda,R}},ia,ida::𝕫,Δt=idmult) where{P,S,T,Nda,R,Na} # Lλr::Vector in Newmark-β context +function add_∂!{P,S}(out::Vector,asm, iele, a::SVector{Na,∂ℝ{P,Nda,R}},ia,ida::𝕫 ; Δt=idmult) where{P,S,Nda,R,Na} # Lλr::Vector in Newmark-β context for (i,iaᵢ) ∈ enumerate(ia) iout = asm[i,iele] if iout≠0 @@ -644,34 +688,34 @@ end # has residual with no second order function getresidual(eleobj::Eleobj,hasres::Val{true},haslag,nso::Val{true}, X::NTuple{Ndx,SVector{Nx}}, U::NTuple{Ndu,SVector{Nu}}, A::SVector{Na} ,t::ℝ,SP,dbg,req) where{Eleobj<:AbstractElement,Ndx,Nx,Ndu,Nu,Na} - P = constants(X,U,A,t)-1 - X1,U1,A1,t1 = to_order{max(1,P)}((X,U,A,t)) + P,N = precedence((X,U,A,t)),npartial((X,U,A,t)) + X1,U1,A1,t1 = to_order{min(1,P),N}((X,U,A,t)) R,FB,eleres = residual( eleobj, X1,U1,A1,t1,SP,dbg,req) - return to_order{P}(R),FB,to_order{P}(eleres) + return to_order{P,N}(R),FB,to_order{P,N}(eleres) end function getresidual(eleobj::Eleobj,hasres::Val{true},haslag,nso::Val{true}, X::NTuple{Ndx,SVector{Nx}}, U::NTuple{Ndu,SVector{Nu}}, A::SVector{Na} ,t::ℝ,SP,dbg ) where{Eleobj<:AbstractElement,Ndx,Nx,Ndu,Nu,Na} - P = constants(X,U,A,t)-1 - X1,U1,A1,t1 = to_order{max(1,P)}((X,U,A,t)) + P,N = precedence((X,U,A,t)),npartial((X,U,A,t)) + X1,U1,A1,t1 = to_order{min(1,P),N}((X,U,A,t)) R,FB = residual( eleobj, X1,U1,A1,t1,SP,dbg ) - return to_order{P}(R),FB + return to_order{P,N}(R),FB end # has lagrangian function getresidual(eleobj::Eleobj,hasres::Val{false},haslag::Val{true},nso, X::NTuple{Ndx,SVector{Nx}}, U::NTuple{Ndu,SVector{Nu}}, A::SVector{Na} ,t::ℝ,SP,dbg,req) where{Eleobj<:AbstractElement,Ndx,Nx,Ndu,Nu,Na} - P = constants(∂0(X),∂0(U),A,t) - Λ = δ{P,Nx,𝕣}() + P = precedence(∂0(X),∂0(U),A,t) + Λ = δ_{P+1,Nx,𝕣}() # legal only because lagrangian is linear in Λ L,FB,eleres = lagrangian(eleobj,Λ,X,U,A,t,SP,dbg,req) - R = ∂{P,Nx}(L) + R = ∂{P+1,Nx}(L) return R,FB,eleres end function getresidual(eleobj::Eleobj,hasres::Val{false},haslag::Val{true},nso, X::NTuple{Ndx,SVector{Nx}}, U::NTuple{Ndu,SVector{Nu}}, A::SVector{Na} ,t::ℝ,SP,dbg ) where{Eleobj<:AbstractElement,Ndx,Nx,Ndu,Nu,Na} - P = constants(∂0(X),∂0(U),A,t) - Λ = δ{P,Nx,𝕣}() + P = precedence(∂0(X),∂0(U),A,t) + Λ = δ_{P+1,Nx,𝕣}() # legal only because lagrangian is linear in Λ L,FB = lagrangian(eleobj,Λ,X,U,A,t,SP,dbg ) - R = ∂{P,Nx}(L) + R = ∂{P+1,Nx}(L) return R,FB end @@ -679,6 +723,18 @@ end getresidual(eleobj::Eleobj,hasres::Val{false},haslag::Val{false},nso, X,U,A,t,SP,dbg,req...) where{Eleobj} = muscadeerror((dbg...,t=t,SP=SP),@sprintf("Element %s must have method 'Muscade.lagrangian' or/and 'Muscade.residual' with correct interface",Eleobj)) +# Acost +function getlagrangian(eleobj::Acost, A::SVector, SP, dbg,req) + L,FB,eleres = lagrangian(eleobj,A,SP,dbg,req) + hasnan(L,FB) && muscadeerror((dbg...,t=t,SP=SP),"lagrangian(Acost,...) returned NaN in L, FB or derivatives") + return L,FB,eleres +end +function getlagrangian(eleobj::Acost, A::SVector, SP, dbg) + L,FB = lagrangian(eleobj,A,SP,dbg) + hasnan(L,FB) && muscadeerror((dbg...,t=t,SP=SP),@sprintf("lagrangian(Acost,...) returned NaN in L, FB or derivatives",Eleobj)) + return L,FB +end + # dispatcher function getlagrangian(eleobj::Eleobj, Λ::SVector{Nx}, X::NTuple{Ndx,SVector{Nx}}, U::NTuple{Ndu,SVector{Nu}}, A::SVector{Na}, t::ℝ,SP,dbg,req) where{Eleobj<:AbstractElement,Ndx,Nx,Ndu,Nu,Na} @@ -720,18 +776,18 @@ end # has residual with no second order function getlagrangian(eleobj::Eleobj,hasres::Val{true},haslag::Val{false},nso::Val{true}, Λ::SVector{Nx}, X::NTuple{Ndx,SVector{Nx}}, U::NTuple{Ndu,SVector{Nu}}, A::SVector{Na}, t::ℝ,SP,dbg,req) where{Eleobj<:AbstractElement,Ndx,Nx,Ndu,Nu,Na} - P = constants(X,U,A,t)-1 - X1,U1,A1,t1 = to_order{max(1,P)}((X,U,A,t)) + P,N = precedence((X,U,A,t)),npartial((X,U,A,t)) + X1,U1,A1,t1 = to_order{min(1,P),N}((X,U,A,t)) R,FB,eleres = residual( eleobj, X1,U1,A1,t1,SP,dbg,req) - L = Λ ∘₁ to_order{P}(R) # to avoid loosing symmetry of Hessian... - return L,FB,to_order{P}(eleres) + L = Λ ∘₁ to_order{P,N}(R) # to avoid loosing symmetry of Hessian... + return L,FB,to_order{P,N}(eleres) end function getlagrangian(eleobj::Eleobj,hasres::Val{true},haslag::Val{false},nso::Val{true}, Λ::SVector{Nx}, X::NTuple{Ndx,SVector{Nx}}, U::NTuple{Ndu,SVector{Nu}}, A::SVector{Na}, t::ℝ,SP,dbg ) where{Eleobj<:AbstractElement,Ndx,Nx,Ndu,Nu,Na} - P = constants(X,U,A,t)-1 - X1,U1,A1,t1 = to_order{max(1,P)}((X,U,A,t)) + P,N = precedence((X,U,A,t)),npartial((X,U,A,t)) + X1,U1,A1,t1 = to_order{min(1,P),N}((X,U,A,t)) R,FB = residual( eleobj, X1,U1,A1,t1,SP,dbg ) - L = Λ ∘₁ to_order{P}(R) # to avoid loosing symmetry of Hessian... + L = Λ ∘₁ to_order{P,N}(R) # to avoid loosing symmetry of Hessian... return L,FB end diff --git a/src/BasicElements.jl b/src/BasicElements.jl index 4715cfc9..b75fa8a9 100644 --- a/src/BasicElements.jl +++ b/src/BasicElements.jl @@ -85,7 +85,7 @@ struct Acost{Na,inod,field,Tcost,Tcostargs} <: AbstractElement end Acost(nod::Vector{Node};inod::NTuple{Na,𝕫}=(),field::NTuple{Na,Symbol}=(),cost::Tcost,costargs::Tcostargs=()) where{Na,Tcost<:Functor,Tcostargs} = Acost{Na,inod,field,Tcost,Tcostargs}(cost,costargs) doflist(::Type{<:Acost{Na,inod,field}}) where{Na,inod,field} = (inod =inod,class=ntuple(i->:A,Na),field=field) -@espy function lagrangian(o::Acost,Λ,X,U,A,t,SP,dbg) +@espy function lagrangian(o::Acost,A,SP,dbg) ☼cost = o.cost( A ,o.costargs...) return cost,noFB end @@ -475,10 +475,9 @@ doflist(::Type{<:DofConstraint{λclass,Nλ,Nx,Nu,Na,λinod,λfield,xinod,xfield, iλ = SVector{Nλ}(1:Nλ) ix = SVector{Nx}(Nλ+1:Nλ+Nx) γ = default{:γ}(SP,0.) # γ=SP.γ - default 0 - P = constants(∂0(X),t) m = o.mode(t) ☼λ,x = ∂0(X)[iλ], ∂0(X)[ix] - x∂ = variate{P,Nx}(x) + P,_,x∂ = variate(x,context=(X,U,A,t)) ☼gap,g∂x = value_∂{P,Nx}(o.gap(x∂,t,o.gargs...)) R = if m==:equal; SVector{Nλ+Nx}(-gap... ,( -λ∘₁g∂x)...) # - sign: λ interpreted as an external force on generalised dof g∂x elseif m==:positive; SVector{Nλ+Nx}(-S(λ,gap,γ)...,( -λ∘₁g∂x)...) diff --git a/src/Diagnostic.jl b/src/Diagnostic.jl index df5eb5cd..2a51d7c2 100644 --- a/src/Diagnostic.jl +++ b/src/Diagnostic.jl @@ -313,7 +313,7 @@ function addin!{mission}(out::Assemblystudy_scale,asm,iele,scale,eleobj::E,Λ,X: U::NTuple{Nuder,<:SVector{Nu}},A::SVector{Na},t,Δt,SP,dbg) where{mission,E,Nxder,Nx,Nuder,Nu,Na} # TODO make Nx,Nu,Na types Nz = 2Nx+Nu+Na # Z =[Λ;X;U;A] scaleZ = SVector(scale.Λ...,scale.X...,scale.U...,scale.A...) - ΔZ = variate{2,Nz}(δ{1,Nz,𝕣}(scaleZ),scaleZ) + ΔZ = Muscade.variate_{2,Nz}(δ_{1,Nz,𝕣}(scaleZ),scaleZ) iλ,ix,iu,ia = gradientpartition(Nx,Nx,Nu,Na) # index into element vectors ΔZ and Lz ΔΛ,ΔX,ΔU,ΔA = view(ΔZ,iλ),view(ΔZ,ix),view(ΔZ,iu),view(ΔZ,ia) L,FB = getlagrangian(eleobj, ∂0(Λ)+ΔΛ, (∂0(X)+ΔX,),(∂0(U)+ΔU,),A+ΔA,t,SP,dbg) @@ -386,7 +386,7 @@ function study_scale(state::State;SP=nothing,verbose::𝕓=true,dbg=(;)) assemble!{:ok}(out,asm,dis,model,state,idmult,(dbg...,solver=:study_scale)) state.SP = tmp Z = zeros(getndof(dofgr)) - getdof!(state,0,Z,dofgr) + get!(state,1,Z,dofgr) type,types = listdoftypes(dis) matfrob = ∞norm(out.Lzz,type,types) vecfrob = ∞norm(out.Lz ,type,types) @@ -525,7 +525,7 @@ function addin!{mission}(out::Assemblystudy_singular,asm,iele,scale,eleobj::E,Λ Nz = 2Nx+Nu+Na scaleZ = SVector(scale.Λ...,scale.X...,scale.U...,scale.A...) - ΔZ = variate{2,Nz}(δ{1,Nz,𝕣}(scaleZ),scaleZ) + ΔZ = Muscade.variate_{2,Nz}(δ_{1,Nz,𝕣}(scaleZ),scaleZ) iλ,ix,iu,ia = gradientpartition(Nx,Nx,Nu,Na) # index into element vectors ΔZ and Lz ΔΛ,ΔX,ΔU,ΔA = view(ΔZ,iλ),view(ΔZ,ix),view(ΔZ,iu),view(ΔZ,ia) L,FB = getlagrangian(eleobj, ∂0(Λ)+ΔΛ, (∂0(X)+ΔX,),(∂0(U)+ΔU,),A+ΔA,t,nothing,SP,dbg) @@ -559,7 +559,7 @@ function study_singular(state::State;SP,iclasses=(Λ,:X,:U,:A),jclasses=iclasses end for iker = 1:nker @printf("\n\nBase vector #%i of the null-space:\n\n",iker) - set!(mech[iker],0,view(kernel,:,iker),jdofgr) + set!(mech[iker],1,view(kernel,:,iker),jdofgr) describe(mech[iker]) end return out.Lij diff --git a/src/Dialect.jl b/src/Dialect.jl index 03a7c640..bf3548fa 100644 --- a/src/Dialect.jl +++ b/src/Dialect.jl @@ -286,3 +286,19 @@ function colnormalize(a::SMatrix{ndim,nvec,R}) where{ndim,nvec,R<:ℝ} n = SVector{ nvec,R}(norm(a[:,ivec]) for ivec=1:nvec) out = SMatrix{ndim,nvec,R}(a[idim,ivec]/n[ivec] for idim=1:ndim,ivec=1:nvec) end + +""" + sA = symmetric!(A) + +Compute the symmetric part of a square `Matrix`. Mutates the input argument. +""" +function symmetric!(A::Matrix) + n,m = size(A) + @assert n==m + for i = 1:n + for j = 1:i-1 + A[j,i] = A[i,j] = 0.5 * (A[i,j]+A[j,i]) + end + end + return A +end \ No newline at end of file diff --git a/src/Dots.jl b/src/Dots.jl index 5c709d54..7d892e46 100644 --- a/src/Dots.jl +++ b/src/Dots.jl @@ -82,11 +82,13 @@ dots(a::Vector{Ta},b::Vector{Tb},::Val{0}) where {Ta<:Number,Tb<:Number } = ha,ta,hb,tb = sa[1:end-ndots], sa[end-ndots+1:end], sb[1:ndots], sb[ndots+1:end] lha,lta,ltb = prod(ha), prod(ta), prod(tb) so = Tuple{ha...,tb...} + zlo = ntuple(i->0,lha*ltb) @assert length(sa)≥ndots @assert length(sb)≥ndots @assert ta==hb return if ndots==0 quote SArray{$so}(SVector{$lha}(a)*SVector{$ltb}(b)') end # external product elseif length(sa)==ndots && length(sb)==ndots quote transpose(SVector{$lta}(a))*SVector{$lta}(b) end # scalar product + elseif lta==0 quote SArray{$so}($(zlo...)) end # sum over zero terms else quote SArray{$so}(SMatrix{$lha,$lta}(a)*SMatrix{$lta,$ltb}(b)) end # general product with summation and array output end end diff --git a/src/EigX.jl b/src/EigX.jl index 004b2429..066ec3a9 100644 --- a/src/EigX.jl +++ b/src/EigX.jl @@ -1,6 +1,11 @@ """ - eiginc = solve(EigX{ℝ};state=initialstate,nmod) - eiginc = solve(EigX{ℂ};state=initialstate,nmod) + eiginc = solve(EigX{ℝ };state=initialstate,nmod) + eiginc = solve(EigX{:fullℝ};state=initialstate,nmod) + eiginc = solve(EigX{ℂ };state=initialstate,nmod) + +!!! warning + `EigX` is currently not working well due to problems with the sparse eigenvalue solver. `EigX{:fullℝ}` works well, + but because it operates on a full matrix, it can only be applied to smaller problems. Given an initial (typicaly static) state `initialstate`, computes the lowest `nmod` eigenmodes of a system. `EigX{ℝ}` computes real eigenmodes not accounting for damping. `EigX{ℝ}` computes complex eigenmodes accounting for damping. @@ -32,9 +37,11 @@ function solve(::Type{EigX{ℝ}},pstate,verbose,dbg; model,dis = state.model,state.dis verbose && @printf("\n Assembling\n") - out,asm,dofgr = prepare(AssemblyDirect{OX,OU,IA},model,dis) + wantK,wantM = (ind.Λ,ind.X,1,1),(ind.Λ,ind.X,1,3) + wanted = Wanted{1,OX+1,OU+1,IA}(:all,(wantK,wantM)) + out,asm,dofgr = prepare(AssemblyDirect,model,dis,wanted) nXdof = getndof.(dofgr)[ind.X] - state₀ = State{1,OX+1,OU+1}(copy(state)) + state₀ = State{1,OX+1,OU+1}(copy(state)) assemble!{:matrices}(out,asm,dis,model,state₀,idmult,(dbg...,solver=:EigXℝ)) K = out.L2[ind.Λ,ind.X][1,1] M = out.L2[ind.Λ,ind.X][1,3] @@ -49,6 +56,35 @@ function solve(::Type{EigX{ℝ}},pstate,verbose,dbg; verbose && @printf("\n") return end +# Normalize a vector by setting its maxabs component to 1 +function maxto1(v::AbstractVector{𝕣}) + lo,hi = extrema(v) + maxabs = abs(lo)>abs(hi) ? lo : hi + return v./maxabs +end +function solve(::Type{EigX{:fullℝ}},pstate,verbose,dbg; state::State) + OX,OU,IA = 2,0,0 + model,dis = state.model,state.dis + + verbose && @printf("\n Assembling\n") + wantK,wantM = (ind.Λ,ind.X,1,1),(ind.Λ,ind.X,1,3) + wanted = Wanted{1,OX+1,OU+1,IA}(:all,(wantK,wantM)) + out,asm,dofgr = prepare(AssemblyDirect,model,dis,wanted) + nXdof = getndof.(dofgr)[ind.X] + state₀ = State{1,OX+1,OU+1}(copy(state)) + assemble!{:matrices}(out,asm,dis,model,state₀,idmult,(dbg...,solver=:EigXfullℝ)) + K = Matrix(out.L2[ind.Λ,ind.X][1,1]) + M = Matrix(out.L2[ind.Λ,ind.X][1,3]) + + verbose && @printf(" Solving Eigenvalues\n\n") + E = eigen(K,M) + ω² = E.values + Δx = [maxto1(view(E.vectors,:,i)) for i = 1:nXdof] + + pstate[] = EigXℝincrement(dofgr[ind.X],sqrt.(ω²),Δx) + verbose && @printf("\n") + return +end """ state = increment{OX}(initialstate,eiginc,imod,A) @@ -104,7 +140,9 @@ function solve(::Type{EigX{ℂ}},pstate,verbose,dbg; model,dis = state.model,state.dis verbose && @printf("\n Assembing\n") - out,asm,dofgr = prepare(AssemblyDirect{OX,OU,IA},model,dis) + wantK,wantC,wantM= (ind.Λ,ind.X,1,1),(ind.Λ,ind.X,1,2),(ind.Λ,ind.X,1,3) + wanted = Wanted{1,OX+1,OU+1,IA}(:all,(wantK,wantC,wantM)) + out,asm,dofgr = prepare(AssemblyDirect,model,dis,wanted) nXdof = getndof.(dofgr)[ind.X] state₀ = State{1,OX+1,OU+1}(copy(state)) assemble!{:matrices}(out,asm,dis,model,state₀,idmult,(dbg...,solver=:EigXℂ)) @@ -126,6 +164,31 @@ function solve(::Type{EigX{ℂ}},pstate,verbose,dbg; pstate[] = EigXℂincrement(dofgr[ind.X],p,Δx) return end +function solve(::Type{EigX{:fullℂ}},pstate,verbose,dbg; state::State) + OX,OU,IA = 2,0,0 + model,dis = state.model,state.dis + + verbose && @printf("\n Assembing\n") + wantK,wantC,wantM= (ind.Λ,ind.X,1,1),(ind.Λ,ind.X,1,2),(ind.Λ,ind.X,1,3) + wanted = Wanted{1,OX+1,OU+1,IA}(:all,(wantK,wantC,wantM)) + out,asm,dofgr = prepare(AssemblyDirect,model,dis,wanted) + nXdof = getndof.(dofgr)[ind.X] + state₀ = State{1,OX+1,OU+1}(copy(state)) + assemble!{:matrices}(out,asm,dis,model,state₀,idmult,(dbg...,solver=:EigXfullℂ)) + K = out.L2[ind.Λ,ind.X][1,1] + C = out.L2[ind.Λ,ind.X][1,2] + M = out.L2[ind.Λ,ind.X][1,3] + I = spdiagm(ones(nXdof)) + A,_ ,_ = blkasm([1,2 ],[1,2 ],[ I,K ]) + B,_ ,_ = blkasm([2,1,2],[1,2,2],[-I,M,C]) + + verbose && @printf(" Solving Eigenvalues\n\n") + E = eigen(Matrix(A),Matrix(B)) + p = E.values + Δx = [view(E.vectors,nXdof+1:2nXdof,i) for i = 1:nXdof] + pstate[] = EigXℂincrement(dofgr[ind.X],p,Δx) + return +end function increment{OX}(initialstate,eiginc::EigXℂincrement,imod::AbstractVector{𝕫},A::AbstractVector) where{OX} state = State{1,OX+1,1}(copy(initialstate)) maximum(imod)≤length(eiginc.p)|| muscadeerror(@sprintf("eiginc only has %n modes.",length(ω))) diff --git a/src/EigXU.jl b/src/EigXU.jl index 4e2147da..94b84f01 100644 --- a/src/EigXU.jl +++ b/src/EigXU.jl @@ -16,8 +16,7 @@ function make_λxu_sparsepattern(out) β = [1,1,2,2,2,3,3,3] # [. . .] return sparse(α,β,L2.(α,β)) # = [. . .] end - -function assemblebigmat!(L2::Vector{Sparse𝕣2},L2bigasm::SparseMatrixCSC,asm,model,dis,out::AssemblyDirect{OX,OU,0},dbg) where{OX,OU} +function assemblebigmat!(L2::Vector{Sparse𝕣2},L2bigasm::SparseMatrixCSC,asm,model,dis,out::AssemblyDirect,dbg) # does not call assemble!: solve has previously called assemble! to prepare bigasm, so out.L2 is already set, for L2ᵢ∈L2 zero!(L2ᵢ) @@ -28,14 +27,16 @@ function assemblebigmat!(L2::Vector{Sparse𝕣2},L2bigasm::SparseMatrixCSC,asm,m for αder = 1:size(Lαβ,1) for βder = 1:size(Lαβ,2) ider = αder+βder-1 - sgn = isodd(αder) ? +1 : -1 # TODO Antisymmetry for odd derivatives? conjugation? Check theory. See also DirectXUA - addin!(L2bigasm,L2[ider],Lαβ[αder,βder],α,β,sgn) + if isassigned(Lαβ,αder,βder) + sgn = isodd(αder) ? +1 : -1 # TODO Antisymmetry for odd derivatives? conjugation? Check theory. See also DirectXUA + addin!(L2bigasm,L2[ider],Lαβ[αder,βder],α,β,sgn) + end end end end end end -function assemblebigvec!(L1,L1bigasm::𝕫1,asm,model,dis,out::AssemblyDirect{OX,OU,0},state,Δt,dbg) where{OX,OU} +function assemblebigvec!(L1,L1bigasm::𝕫1,asm,model,dis,out::AssemblyDirect,state,Δt,dbg) zero!.(L1) assemble!{:vectors}(out,asm,dis,model,state,Δt,(dbg...,asm=:assemblebigvec!)) # first assemble model vectors for β ∈ λxu # then collate them into @@ -45,7 +46,6 @@ function assemblebigvec!(L1,L1bigasm::𝕫1,asm,model,dis,out::AssemblyDirect{OX end end end - struct EigXUincrement{Tω} nmod :: 𝕫 dofgr :: DofGroup @@ -56,11 +56,13 @@ struct EigXUincrement{Tω} ΔΛXU :: Vector{𝕣11} # [iω][imod][idof] end - - """ EigXU{OX,OU} +!!! warning + `EigXU` is currently not working well due to problems with the sparse eigenvalue solver. + In addition, the solver is still experimental + Study the combinations of load and response that are least detected by sensor systems. An analysis is carried out by a call with the following syntax: @@ -71,7 +73,7 @@ eiginc = solve(EigXU{OX,OU};Δω, p, nmod,initialstate) ``` The solver linearises the problem (computes the Hessian of the Lagrangian) at `initialstate` and solves -the ΛXU-eigenvalue problem at frequencies ωᵢ = Δω*i with i∈{0,...,2ᵖ-1}. +the ΛXU-eigenvalue problem at frequencies ``ωᵢ = Δω*i`` with ``i∈{0,...,2ᵖ-1}``. # Parameters @@ -103,11 +105,12 @@ function solve(::Type{EigXU{OX,OU}},pstate,verbose::𝕓,dbg; initialstate::State, droptol::𝕣=1e-10, nmod::𝕫=5, + full::𝕓=false, σₓᵤ, kwargs...) where{OX,OU} # Mostly constants - local LU + local ◺A model,dis = initialstate.model, initialstate.dis nω = 2^p IA = 0 @@ -117,7 +120,8 @@ function solve(::Type{EigXU{OX,OU}},pstate,verbose::𝕓,dbg; state₀ = State{1,OX+1,OU+1}(copy(initialstate)) verbose && @printf(" Preparing assembler\n") - out,asm,dofgr = prepare(AssemblyDirect{OX,OU,IA},model,dis) # model assembler for all arrays + wanted = Wanted{1,OX+1,OU+1,IA}(:all,:all) # TODO refine + out,asm,dofgr = prepare(AssemblyDirect,model,dis,wanted) # model assembler for all arrays verbose && @printf(" Computing matrices\n") assemble!{:matrices}(out,asm,dis,model,state₀,idmult,(dbg...,solver=:EigXU,phase=:matrices)) # assemble all model matrices - in class-blocks @@ -155,25 +159,25 @@ function solve(::Type{EigXU{OX,OU}},pstate,verbose::𝕓,dbg; B.nzval .= N[1] + ωᵢ^2*N[2] + ωᵢ^4*N[3] A.nzval .= L2[1].nzval + ωᵢ^2*L2[3].nzval + ωᵢ^4*L2[5].nzval # complex if exponents 1 and 3 included try - if iω==1 LU = lu(A) - else lu!(LU ,A) + if iω==1 ◺A = lu(A) + else lu!(◺A,A) end - λ⁻¹, ΔΛXU[iω], ncv[iω] = geneig{:symmetric}(A,B,nmod;normalize=false,kwargs...) - nor[iω] = 𝕣1(undef,ncv[iω]) - λ[iω] = 1 ./λ⁻¹ - for imod = 1:ncv[iω] - Δ = ΔΛXU[iω][imod] - wrk[ixu] .= view(Δ,ixu) # this copy can be optimised by viewing the classes in Δ, operating on out.L2[α,β][αder,βder], and combining over derivatives. Is it worth the effort? - Anorm = √(ℜ(dot(wrk,A,wrk))/2) # ΔΛXU is real, A is complex Hermitian, so square norm is real: (imag part is zero to machine precision) - if iω>1 && imod≤nmod && sum(Δ[idof]*ΔΛXU[iω-1][imod][idof] for idof∈λxu_dofgr.jX)<0 - Anorm = -Anorm - end - Δ .*= 2.575829303549/Anorm # corresponds to a probability of exceedance of 0.01 - nor[iω][imod] = √(ℜ(dot(Δ,B,Δ))/2) - end catch muscadewarning(@sprintf("Factorization of matrix A failed for ω=%f",ωᵢ)); end + λ⁻¹, ΔΛXU[iω], ncv[iω] = geneig{:symmetric}(◺A,B,nmod;normalize=false,kwargs...) + nor[iω] = 𝕣1(undef,ncv[iω]) + λ[iω] = 1 ./λ⁻¹ + for imod = 1:ncv[iω] + Δ = ΔΛXU[iω][imod] + wrk[ixu] .= view(Δ,ixu) # this copy can be optimised by viewing the classes in Δ, operating on out.L2[α,β][αder,βder], and combining over derivatives. Is it worth the effort? + Anorm = √(ℜ(dot(wrk,A,wrk))/2) # ΔΛXU is real, A is complex Hermitian, so square norm is real: (imag part is zero to machine precision) + if iω>1 && imod≤nmod && sum(Δ[idof]*ΔΛXU[iω-1][imod][idof] for idof∈λxu_dofgr.jX)<0 + Anorm = -Anorm + end + Δ .*= 2.575829303549/Anorm # corresponds to a probability of exceedance of 0.01 + nor[iω][imod] = √(ℜ(dot(Δ,B,Δ))/2) + end end any(ncv.i≤x,f.x) + if i==length(f.x) + i -=1 + end + di = (x-f.x[i])/(f.x[i+1]-f.x[i]) + return f.y[i]*(1-di)+f.y[i+1]*di +end """ diff --git a/src/ModelDescription.jl b/src/ModelDescription.jl index 7e9a77b7..aae601a8 100644 --- a/src/ModelDescription.jl +++ b/src/ModelDescription.jl @@ -76,6 +76,14 @@ mutable struct Model locked :: 𝕓 end +function Base.show(io::IO,o::Model) + printstyled(io,":",o.ID;color=:green,bold=false) + lock = o.locked ? " (locked): " : " (unlocked): " + print(io,lock) + print(io,length(o.nod)," nodes, ",sum(length.(o.ele))," elements of ",length(o.ele)," types, ") + print(io,getndof(o,:X)," X-dofs, ",getndof(o,:U)," U-dofs, ",getndof(o,:A)," A-dofs") +end + # Model construction - private firstindex(x) = any(x) ? findfirst(x) : 0 diff --git a/src/Muscade.jl b/src/Muscade.jl index 1029698e..4e19689a 100644 --- a/src/Muscade.jl +++ b/src/Muscade.jl @@ -21,15 +21,13 @@ module Muscade include("OffsetVector.jl") include("Adiff.jl") - export ∂ℝ #\partial \bbR - export variate,δ,directional # \delta + export ∂ℝ #\partial\BbbR export value,VALUE,∂,value_∂ # \partial, \nabla - export constants public precedence,npartial #,norm include("Taylor.jl") - export motion,motion⁻¹,revariate,chainrule,apply - export composevalue,composeJacobian + export motion,motion⁻¹,variate,variate0,revariate,chainrule,apply,AllElements + export chainrule_Jacobian public Taylor,McLaurin include("Functors.jl") diff --git a/src/SweepX.jl b/src/SweepX.jl index 25b2067f..092e961a 100644 --- a/src/SweepX.jl +++ b/src/SweepX.jl @@ -44,64 +44,69 @@ addin!{:step}(out::AssemblySweepX{2},asm,iele,scale,eleobj,Λ,X::NTuple{Nxder,<: addin!{:iter}(out::AssemblySweepX{2},asm,iele,scale,eleobj,Λ,X::NTuple{Nxder,<:SVector{0}},U,A,t,Δt,SP,dbg) where{Nxder} = return function addin!{:step}(out::AssemblySweepX{2},asm,iele,scale,eleobj,Λ,X::NTuple{Nxder,<:SVector{Nx}},U,A,t,Δt,SP,dbg) where{Nxder,Nx} a₁,a₂,a₃,b₁,b₂,b₃ = out.c.a₁,out.c.a₂,out.c.a₃,out.c.b₁,out.c.b₂,out.c.b₃ - x,x′,x″ = ∂0(X),∂1(X),∂2(X) - δX,δr = reδ{1}((;X=x,r=0.),(;X=scale.X,r=1.)) + x,x′,x″ = X + _,_,(δX,δr)= variate0((x=x,r=0.),scale=(x=scale.X,r=1.)) + iX,ir = variate_indices((x,0.)) a = a₂*x′ + a₃*x″ b = b₂*x′ + b₃*x″ vx = x + δX - vx′ = x′ + a₁*δX + a*δr - vx″ = x″ + b₁*δX + b*δr + vx′ = x′ + a₁*δX - a*δr + vx″ = x″ + b₁*δX - b*δr Lλ,FB = getresidual(eleobj,(vx,vx′,vx″),U,A,t,SP,dbg) Lλ = Lλ .* scale.X - add_value!( out.Lλ ,asm[1],iele,Lλ ) # rhs = R - add_∂!{1,:minus}( out.Lλ ,asm[1],iele,Lλ,1:Nx,(Nx+1,)) # rhs += -C⋅a -M⋅b - add_∂!{1 }( out.Lλx,asm[2],iele,Lλ,1:Nx,1:Nx ) # Mat = K + a₁C + b₁M + add_value!(out.Lλ ,asm[1],iele,Lλ ) # rhs = R + add_∂!{1}( out.Lλ ,asm[1],iele,Lλ,iX,(ir,)) # rhs += -C⋅a -M⋅b + add_∂!{1}( out.Lλx,asm[2],iele,Lλ,iX,iX ) # Mat = K + a₁C + b₁M end function addin!{:iter}(out::AssemblySweepX{2},asm,iele,scale,eleobj,Λ,X::NTuple{Nxder,<:SVector{Nx}},U,A,t,Δt,SP,dbg) where{Nxder,Nx} a₁,b₁ = out.c.a₁,out.c.b₁ - δX = δ{1,Nx,𝕣}(scale.X) - Lλ,FB = getresidual(eleobj,(∂0(X)+δX, ∂1(X)+a₁*δX, ∂2(X)+b₁*δX),U,A,t,SP,dbg) + x,x′,x″ = X + δX = δ_{1,Nx,𝕣}(scale.X) + Lλ,FB = getresidual(eleobj,(x+δX, x′+a₁*δX, x″+b₁*δX),U,A,t,SP,dbg) Lλ = Lλ .* scale.X add_value!(out.Lλ ,asm[1],iele,Lλ ) add_∂!{1}( out.Lλx,asm[2],iele,Lλ,1:Nx,1:Nx) end function addin!{:step}(out::AssemblySweepX{1},asm,iele,scale,eleobj,Λ,X::NTuple{Nxder,<:SVector{Nx}},U,A,t,Δt,SP,dbg) where{Nxder,Nx} a₁,a₂ = out.c.a₁,out.c.a₂ - x,x′ = ∂0(X),∂1(X) - δX,δr = reδ{1}((;X=x,r=0.),(;X=scale.X,r=1.)) + x,x′ = X + _,_,(δX,δr)= variate0((;X=x,r=0.),scale=(;X=scale.X,r=1.)) a = a₂*x′ vx = x + δX - vx′ = x′ + a₁*δX + a*δr + vx′ = x′ + a₁*δX - a*δr Lλ,FB = getresidual(eleobj,(vx,vx′),U,A,t,SP,dbg) Lλ = Lλ .* scale.X - add_value!(out.Lλ ,asm[1],iele,Lλ ) # rhs = R - add_∂!{1,:minus}( out.Lλ ,asm[1],iele,Lλ,1:Nx,(Nx+1,)) # rhs += -C⋅a - add_∂!{1}( out.Lλx,asm[2],iele,Lλ,1:Nx,1:Nx ) # Mat = K + C/Δt + add_value!(out.Lλ ,asm[1],iele,Lλ ) # rhs = R + add_∂!{1}( out.Lλ ,asm[1],iele,Lλ,1:Nx,(Nx+1,)) # rhs += -C⋅a + add_∂!{1}( out.Lλx,asm[2],iele,Lλ,1:Nx,1:Nx ) # Mat = K + C/Δt end function addin!{:iter}(out::AssemblySweepX{1},asm,iele,scale,eleobj,Λ,X::NTuple{Nxder,<:SVector{Nx}},U,A,t,Δt,SP,dbg) where{Nxder,Nx} a₁ = out.c.a₁ - δX = δ{1,Nx,𝕣}(scale.X) - Lλ,FB = getresidual(eleobj,(∂0(X)+δX, ∂1(X)+a₁*δX),U,A,t,SP,dbg) + x,x′ = X + δX = δ_{1,Nx,𝕣}(scale.X) + Lλ,FB = getresidual(eleobj,(x+δX, x′+a₁*δX),U,A,t,SP,dbg) Lλ = Lλ .* scale.X add_value!(out.Lλ ,asm[1],iele,Lλ ) # rhs = R add_∂!{1}( out.Lλx,asm[2],iele,Lλ,1:Nx,1:Nx ) # Mat = K + C/Δt end function addin!{Both}(out::AssemblySweepX{0},asm,iele,scale,eleobj,Λ,X::NTuple{Nxder,<:SVector{Nx}},U,A,t,Δt,SP,dbg) where{Both,Nxder,Nx} - δX = δ{1,Nx,𝕣}(scale.X) - Lλ,FB = getresidual(eleobj,(∂0(X)+δX,),U,A,t,SP,dbg) + x, = X + δX = δ_{1,Nx,𝕣}(scale.X) + Lλ,FB = getresidual(eleobj,(x+δX,),U,A,t,SP,dbg) Lλ = Lλ .* scale.X add_value!(out.Lλ ,asm[1],iele,Lλ) add_∂!{1}( out.Lλx,asm[2],iele,Lλ) end struct Newmarkβdecrement!{OX} end -function Newmarkβdecrement!{2}(state,Δx ,Xdofgr,c,firstiter, a,b,x′,x″,Δx′,Δx″,args...) # x′, x″ are just mutable memory, neither input nor output. + +function Newmarkβdecrement!{2}(state::State,Δx ,Xdofgr,c,firstiter, a,b,x′,x″,Δx′,Δx″,args...) # x′, x″ are just mutable memory, neither input nor output. a₁,a₂,a₃,b₁,b₂,b₃ = c.a₁,c.a₂,c.a₃,c.b₁,c.b₂,c.b₃ if firstiter - getdof!(state,1,x′,Xdofgr) - getdof!(state,2,x″,Xdofgr) + get!(state,2,x′,Xdofgr) + get!(state,3,x″,Xdofgr) a .= a₂*x′.+ a₃*x″ b .= b₂*x′.+ b₃*x″ Δx′ .= a₁*Δx .+ a @@ -114,11 +119,11 @@ function Newmarkβdecrement!{2}(state,Δx ,Xdofgr,c,firstiter, a,b,x′,x″,Δx decrement!(state,2,Δx′,Xdofgr) decrement!(state,3,Δx″,Xdofgr) end -function Newmarkβdecrement!{1}(state,Δx ,Xdofgr,c,firstiter, a,x′,Δx′,args...) +function Newmarkβdecrement!{1}(state::State,Δx ,Xdofgr,c,firstiter, a,x′,Δx′,args...) a₁,a₂ = c.a₁,c.a₂ if firstiter - getdof!(state,1,x′,Xdofgr) + get!(state,2,x′,Xdofgr) a .= a₂*x′ Δx′ .= a₁*Δx .+ a else @@ -127,7 +132,7 @@ function Newmarkβdecrement!{1}(state,Δx ,Xdofgr,c,firstiter, a,x′,Δx′,arg decrement!(state,1,Δx ,Xdofgr) decrement!(state,2,Δx′,Xdofgr) end -function Newmarkβdecrement!{0}(state,Δx ,Xdofgr,args...) +function Newmarkβdecrement!{0}(state::State,Δx ,Xdofgr,args...) decrement!(state,1,Δx ,Xdofgr) end @@ -188,7 +193,7 @@ function solve(SX::Type{SweepX{OX}},pstate,verbose,dbg; model,dis = initialstate.model,initialstate.dis out,asm,Xdofgr = prepare(AssemblySweepX{OX},model,dis) nXdof = getndof(Xdofgr) - buffer = ntuple(i->𝕣1(undef,nXdof), 6) + buffer = NTuple{6}(𝕣1(undef,nXdof) for i=1:6) citer = 0 cΔx²,cLλ² = maxΔx^2,maxLλ^2 state = State{1,OX+1,1}(copy(initialstate)) diff --git a/src/SweepXA.jl b/src/SweepXA.jl index 23ab78f1..bb52922c 100644 --- a/src/SweepXA.jl +++ b/src/SweepXA.jl @@ -1,89 +1,34 @@ -### Assembler - -mutable struct AssemblySweepXA{OX,NDX} <: Assembly - # up - Lx :: 𝕣1 - La :: 𝕣1 - Lλa :: 𝕣2 - Lxx :: Sparse𝕣2 - Lax :: 𝕣2 - Laa :: 𝕣2 - # down - c :: Newmarkβcoefficients{OX} -end - -function prepare(::Type{AssemblySweepXA{OX}},model,dis) where{OX} - Xdofgr = allXdofs(model,dis) - Adofgr = allAdofs(model,dis) - nXdof = nΛdof = getndof(Xdofgr) - nAdof = getndof(Adofgr) - narray,neletyp = 6,getneletyp(model) - asm = Matrix{𝕫2}(undef,narray,neletyp) # asm[iarray,ieletyp][ieledof,iele] - Lx = asmvec!(view(asm, 1,:),Xdofgr,dis) - La = asmvec!(view(asm, 2,:),Adofgr,dis) - Lλa = asmfullmat!(view(asm, 3,:),view(asm,1,:),view(asm,2,:),nΛdof,nAdof) - Lxx = asmmat!(view(asm, 4,:),view(asm,1,:),view(asm,1,:),nXdof,nXdof) - Lax = asmfullmat!(view(asm, 5,:),view(asm,2,:),view(asm,1,:),nAdof,nXdof) - Laa = asmfullmat!(view(asm, 6,:),view(asm,2,:),view(asm,2,:),nAdof,nAdof) - - out = AssemblySweepXA{OX,OX+1}(Lx,La,Lλa,Lxx,Lax,Laa, Newmarkβcoefficients{OX}()) - return out,asm,Xdofgr,Adofgr -end -function zero!(out::AssemblySweepXA) # TODO - zero!(out.Lx ) - zero!(out.La ) - zero!(out.Lλa) - zero!(out.Lxx) - zero!(out.Lax) - zero!(out.Laa) -end - -#= TODO -solver -write specific adiff for ElementCost -SweepXA for order 0 and 1 -Multi load cases -=# - - -function addin!{:sensitivity}(out::AssemblySweepXA{2},asm,iele,scale,eleobj,Λ,X::NTuple{Nxder,<:SVector{Nx}},U,A::SVector{Na},t,Δt,SP,dbg) where{Nxder,Nx,Na} - a₁,a₂,a₃,b₁,b₂,b₃ = out.c.a₁,out.c.a₂,out.c.a₃,out.c.b₁,out.c.b₂,out.c.b₃ - x,x′,x″,λ = ∂0(X),∂1(X),∂2(X),∂0(Λ) - δΛ,δX,δA = reδ{2}((;Λ=λ,X=x,A),(;Λ=scale.Λ,X=scale.X,A=scale.A)) - iΛ,iX,iA,Nz = revariate_indices(λ,x,A) - vx = x + δX - vx′ = x′ + a₁*δX - vx″ = x″ + b₁*δX - L,FB = getlagrangian(eleobj,λ+δΛ,(vx,vx′,vx″),U,A+δA,t,SP,dbg) # TODO jump over elements with residual - ∇L = ∂{2,Nz}(L) - add_value!(out.Lx , asm[1], iele, ∇L, iX ;Δt) - add_value!(out.La , asm[2], iele, ∇L, iA ;Δt) - add_∂!{1 }(out.Lλa, asm[3], iele, ∇L, iΛ, iA;Δt) - add_∂!{1 }(out.Lxx, asm[4], iele, ∇L, iX, iX;Δt) - add_∂!{1 }(out.Lax, asm[5], iele, ∇L, iA, iX;Δt) - add_∂!{1 }(out.Laa, asm[6], iele, ∇L, iA, iA;Δt) -end -function addin!{:Acost}(out::AssemblySweepXA,asm,iele,scale,eleobj::Acost,A::SVector{Na},dbg) where{Na} - d = revariate{2}((;A),(;A=scale.A)) # careful: revariate returns a NamedTuple - ø = nothing - C,_ = lagrangian(eleobj,ø,ø,ø,d.A,ø,ø ,dbg) - ∇ₐC = ∂{2,Na}(C) - add_value!(out.La ,asm[2],iele,∇ₐC) - add_∂!{1 }(out.Laa,asm[6],iele,∇ₐC) +### add and decrement + +function Newmarkβdecrement!{OX}(Xₐ::NTuple{NDX,𝕣2},ΔXₐ,Xgr,Agr,c) where{OX,NDX} + # xₐ -= Δxₐ + # xₐ′ -= a₁*Δxₐ + # xₐ″ -= b₁*Δxₐ + f = (1.,c.a₁,c.b₁) + nA = size(Xₐ[1],2) + for ider = 1:OX+1 + for igA ∈ eachindex(Agr.iA) + iA,jA,sA = Agr.iA[igA], Agr.jA[igA], 1 / Agr.scaleA[igA] # inverse scaleA, because Xₐ is dX / dA + for igX ∈ eachindex(Xgr.iX) + iX,jX,sX = Xgr.iX[igX], Xgr.jX[igX], Xgr.scaleX[igX] + Xₐ[ider][iX,iA] -= f[ider] .* ΔXₐ[jX,jA] * sX * sA + end + end + end end - +### The solver """ SweepXA{OX} A non-linear, time domain solver, that solves the problem time-step by time-step. -Only the `X`-dofs of the model are solved for, while `U`-dofs and `A`-dofs are unchangeδ +Only the `X`-dofs of the model are solved for, while `U`-dofs and `A`-dofs are unchanged. -- `SweepXA{0}` is Newton-Raphson, with feasibility line-search, to handle inequality constraints. -- `SweepXA{1}` is implicit Euler, with feasibility line-search. -- `SweepXA{2}` is Newmark-β, with Newton-Raphson iterations and feasibility line search +- `SweepXA{0}` is Newton-Raphson. +- `SweepXA{1}` is implicit Euler. +- `SweepXA{2}` is Newmark-β, with Newton-Raphson iterations. IMPORTANT NOTE: Muscade does not allow elements to have state variables, for example, plastic strain, or shear-free position for dry friction. Where the element implements such physics, this @@ -94,7 +39,7 @@ An analysis is carried out by a call with the following syntax: ``` initialstate = initialize!(model) -setdof!(initialstate,1.;class=:U,field=:λcsr) +setdof!(initialstate,1.;class=:X,field=:tx1,order=1) states = solve(SweepXA{2};initialstate=initialstate,time=0:10) ``` # Named arguments to `solve`: @@ -104,19 +49,12 @@ states = solve(SweepXA{2};initialstate=initialstate,time=0:10) - `initialstate` a `State`, obtain from `ìnitialize!` or `SweepXA`. - `time` maximum number of Newton-Raphson iterations - `β=1/4`,`γ=1/2` parameters to the Newmark-β algorithm. Dummy if `OX<2` -- `maxXiter=50` maximum number of equilibrium iterations at each step. +- `maxXiter=50` maximum number of equilibrium iterations at each step. - `maxΔx=1e-5` convergence criteria: norm of `X`. - `maxLλ=∞` convergence criteria: norm of the residual. -- `maxLineIter=50` Maximum number of iteration in the feasibility line search. - set to 0 to skip the line search (not recommended for models - with inequality constraints). -- `sfac=0.5` Parameter in the line search for a feasible point. If a - tentative result is not feasible, backtrack by a factor `sfac`. - If still not feasible, backtrack what is left by a factor `sfac`, - and so forth, up to `maxLineIter` times. -- `γfac=0.5` Parameter for feasibility. For an inequality constraint `g(X)` - with reaction force `λ`, require `g(X)*λ==γ`, and multiply - `γ *= γfac` at each iteration. +- `maxAiter=50` maximum number of A-iterations +- `maxΔa=1e-5` convergence criteria: norm of `A`. +- `maxLa=∞` convergence criteria: norm of the residual. # Output @@ -124,89 +62,138 @@ A vector of length equal to that of the named input argument `time` containing t See also: [`solve`](@ref), [`initialize!`](@ref), [`findlastassigned`](@ref), [`study_singular`](@ref), [`DirectXUA`](@ref), [`FreqXU`](@ref) """ -struct SweepXA{OX} <: AbstractSolver end -function solve(SX::Type{SweepXA{OX}},pstate,verbose,dbg; - time::AbstractVector{𝕣}, - initialstate::State, - β::𝕣=1/4,γ::𝕣=1/2, - maxXiter::ℤ=50,maxΔx::ℝ=1e-5,maxLλ::ℝ=∞, - maxAiter::ℤ=50,maxΔa::ℝ=1e-5,maxLa::ℝ=∞) where{OX} +struct SweepXA{OX} <: AbstractSolver end +function solve(::Type{SweepXA{OX}},pstate,verbose,dbg; + time::AbstractVector{𝕣}, + initialstate::State, + β::𝕣=1/4,γ::𝕣=1/2, + maxXiter::ℤ=50,maxΔx::ℝ=1e-5,maxLλ::ℝ=∞, + maxAiter::ℤ=50,maxΔa::ℝ=1e-5,maxLa::ℝ=∞) where{OX} model,dis = initialstate.model,initialstate.dis - outX ,asmX ,Xdofgr = prepare(AssemblySweepX{ OX},model,dis) - outXA,asmXA,Xdofgr,Adofgr = prepare(AssemblySweepXA{OX},model,dis) + outX,asmX, Xdofgr = prepare(AssemblySweepX{OX},model,dis ) # assembler for std forward analysis + outA,asmA,(Λdofgr,Xdofgr,Udofgr,Adofgr) = prepare(AssemblyDirect ,model,dis,Wanted{1,OX+1,1,1}(:all,:all)) # assembler for A-update nXdof = getndof(Xdofgr) nAdof = getndof(Adofgr) - buffer = ntuple(i->𝕣1(undef,nXdof), 6) + buffer = NTuple{6}(𝕣1(undef,nXdof) for i=1:6) # TODO 6? cΔX²,cLλ² = maxΔx^2,maxLλ^2 cΔA²,cLa² = maxΔa^2,maxLa^2 cXiter = 0 + cAiter = 0 state = State{1,OX+1,1}(copy(initialstate)) state.Λ[1] .= 0. states = allocate(pstate,Vector{typeof(state)}(undef,length(time))) - La♯ = 𝕣1(undef,nAdof ) - Laa♯ = 𝕣2(undef,nAdof,nAdof) - local Lλx,ΔX # declare Lλx to scope the function, without having to actualy initialize the variable + Qa = 𝕣1(undef,nAdof ) + Qaa = 𝕣2(undef,nAdof,nAdof) + Xₐ = NTuple{OX+1}(𝕣2(undef,nXdof,nAdof) for idx=1:OX+1) + local ◺Lλx, ◺K♯, ΔA, cAiter # declare variables to be local to the present scope, i.e. scope the function. + # This way we can initialise within a loop, but have a variable that exists at next iter/step or even after the loop # main part - for iAiter = 1:maxAiter - - assembleA!{:Acost}(outXA,asmXA,dis,model,state,(dbg...,solver=:SweepXA,phase=:Acost,iAiter=iAiter)) - La♯ .= outXA.La - Laa♯ .= outXA.Laa - - # forward sweep - for (step,t) ∈ enumerate(time) + for iAiter ∈ 1:maxAiter + verbose && @printf " A-iteration %3d\n" iAiter + firstAiter = iAiter==1 + # time-independent Acost + assembleA!{:matrices}(outA,asmA,dis,model,state,(dbg...,solver=:SweepXA,phase=:fixedAcost,iAiter=iAiter)) + Qa .= outA.L1[ind.A][1] + Qaa .= outA.L2[ind.A,ind.A][1,1] + zero!(Xₐ) + + for (istep,t) ∈ enumerate(time) + #verbose && @printf " step %3d\n" istep oldt = state.time state.time = t Δt = t-oldt - Δt ≤ 0 && OX>0 && muscadeerror(@sprintf("Time step length not strictly positive at step=%3d",step)) - outX.c = Newmarkβcoefficients{OX}(Δt,β,γ) - for iXiter = 1:maxXiter + Δt ≤ 0 && OX>0 && muscadeerror(@sprintf("Time step length not strictly positive at step=%3d",istep)) + outX.c = c = Newmarkβcoefficients{OX}(Δt,β,γ) + + # step and iterations + + #verbose && @printf " Equilibrium iterations\n" + for iXiter ∈ 1:maxXiter cXiter += 1 - firstiter = iXiter==1 - if firstiter assemble!{:step}(outX,asmX,dis,model,state,Δt,(dbg...,solver=:SweepXA,step=step,iXiter=iXiter)) - else assemble!{:iter}(outX,asmX,dis,model,state,Δt,(dbg...,solver=:SweepXA,step=step,iXiter=iXiter)) + firstXiter = iXiter==1 + if firstXiter assemble!{:step}(outX,asmX,dis,model,state,Δt,(dbg...,solver=:SweepXA,mission=:step,iAiter=iAiter,istep=istep,iXiter=iXiter)) + else assemble!{:iter}(outX,asmX,dis,model,state,Δt,(dbg...,solver=:SweepXA,mission=:iter,iAiter=iAiter,istep=istep,iXiter=iXiter)) end - try if step==1 && firstiter Lλx = lu(outX.Lλx) # here we do not write "local Lλx", so we refer to the variable defined outside the loops (we do not shadow Lλx) - else lu!(Lλx, outX.Lλx) - end catch; muscadeerror(@sprintf("matrix factorization failed at step=%i, iXiter=%i",step,iXiter)) end - ΔX = Lλx\outX.Lλ - ΔX²,Lλ² = sum(ΔX.^2),sum(outX.Lλ.^2) - Newmarkβdecrement!{OX}(state,ΔX ,Xdofgr,outX.c,firstiter,buffer...) + try if istep==1 && firstXiter && firstAiter + ◺Lλx = lu( outX.Lλx) + else lu!(◺Lλx, outX.Lλx) + end catch; muscadeerror(@sprintf("matrix factorization failed at Newmark-β, iAiter=%i, step=%i, iXiter=%i",iAiter,istep,iXiter)) end + ΔX = ◺Lλx\outX.Lλ + Newmarkβdecrement!{OX}(state,ΔX ,Xdofgr,outX.c,firstXiter,buffer...) + ΔX²,Lλ² = sum(ΔX.^2),sum(outX.Lλ.^2) if ΔX²≤cΔX² && Lλ²≤cLλ² - #verbose && @printf " step %3d converged in %3d iterations. |Δx|=%7.1e |Lλ|=%7.1e\n" step iXiter √(ΔX²) √(Lλ²) - states[step] = State(state.time,state.Λ,deepcopy(state.X),state.U,state.A,state.SP,model,dis) + verbose && @printf " step %3d converged in %3d iterations. |Δx|=%7.1e |Lλ|=%7.1e\n" istep iXiter √(ΔX²) √(Lλ²) + states[istep] = State(state.time,state.Λ,deepcopy(state.X),state.U,state.A,state.SP,model,dis) break#out of the iXiter loop end - iXiter==maxXiter && muscadeerror(@sprintf("no convergence of step %3d after %3d iterations |Δx|=%g / %g, |Lλ|=%g / %g",step,iXiter,√(ΔX²),maxΔx,√(Lλ²)^2,maxLλ)) + iXiter==maxXiter && muscadeerror(@sprintf("no convergence of step %3d for iAiter %3d after %3d iterations |Δx|=%g / %g, |Lλ|=%g / %g",istep,iAiter,iXiter,√(ΔX²),maxΔx,√(Lλ²)^2,maxLλ)) end - assemble!{:sensitivity}(outXA,asmXA,dis,model,state,Δt,(dbg...,solver=:SweepXA,step=step,iAiter=iAiter)) - ΔXₐ = Lλx\outXA.Lλa - LaxΔXₐ = outXA.Lax ∘₁ ΔXₐ # aa - ΔXₐ′Lxx = ΔXₐ' ∘₁ outXA.Lxx # ax - La♯ .+= outXA.La .+ ΔXₐ′Lxx ∘₁ ΔX .- outXA.Lax ∘₁ ΔX .- outXA.Lx ∘₁ ΔXₐ - Laa♯ .+= outXA.Laa .+ ΔXₐ′Lxx ∘₁ ΔXₐ .- LaxΔXₐ .- LaxΔXₐ' + #verbose && @printf " Assembling matrices for optimisation phase\n" + assemble!{:matrices}(outA,asmA,dis,model,state,Δt,(dbg...,solver=:SweepXA,phase=:Asensitivity,iAiter=iAiter,istep=istep)) + Lx,La,Lxx,Lax,Laa = outA.L1[ind.X], outA.L1[ind.A], outA.L2[ind.X,ind.X], outA.L2[ind.A,ind.X], outA.L2[ind.A,ind.A] + Lλx,Lλa = outA.L2[ind.Λ,ind.X],outA.L2[ind.Λ,ind.A] + + # sensitivity of X to A + + #verbose && @printf " Evaluate sensitivity of X to A\n" + a₁,a₂,a₃,b₁,b₂,b₃ = c.a₁,c.a₂,c.a₃,c.b₁,c.b₂,c.b₃ + if OX≥2 b₂♯,b₃♯ = b₂/(1-a₂), a₃/(1-a₂)+b₃ end + if OX≥1 Xₐ[2] .= (1-a₂) .* Xₐ[2] .- a₃ .* Xₐ[3] end # xₐ′-= aₐ + if OX≥2 Xₐ[3] .= -b₂♯ .* Xₐ[2] .+ (1-b₃♯) .* Xₐ[3] end # same as xₐ″-= bₐ but in place + + Rₐ = Matrix(Lλa[1,1]) + Rₐ .+= Lλx[1,1]*Xₐ[1] + OX≥1 && Rₐ .+= Lλx[1,2]*Xₐ[2] + OX≥2 && Rₐ .+= Lλx[1,3]*Xₐ[3] + K♯ = Lλx[1,1] + OX≥1 && K♯.nzval .+= Lλx[1,2].nzval*c.a₁ # operate on nzval directly, lest Sparse resize it + OX≥2 && K♯.nzval .+= Lλx[1,3].nzval*c.b₁ + + try if istep==1 && firstAiter + ◺K♯ = lu( K♯) + else lu!(◺K♯, K♯) + end catch; muscadeerror(@sprintf("matrix factorization failed at Xₐ evaluation, iAiter=%i, step=%i",iAiter,istep)) end + ΔXₐ = ◺K♯\Rₐ + Newmarkβdecrement!{OX}(Xₐ,ΔXₐ ,Xdofgr,Adofgr,c) # increments without a or b + + # time-integrate total gradient and Hessian of L wrt A + + #verbose && @printf " Time-integrate total gradient and Hessian of L wrt A\n" + Qa .+= La[1] # this is gradient of cost over time Δt + Qaa .+= Laa[1,1] + for idx ∈ 1:OX+1 + Qa .+= Lx[ idx] ∘₁ Xₐ[idx] + Qaa .+= Lax[1 ,idx] ∘₁ Xₐ[idx] + Qaa .+= Xₐ[idx]' ∘₁ Lax[1 ,idx]' + for jdx ∈ 1:OX+1 + Qaa.+= Xₐ[idx]' ∘₁ Lxx[idx,jdx] ∘₁ Xₐ[jdx] + end + end end # istep # update A - ΔA = Laa♯\La♯ - ΔA²,La² = sum(ΔA.^2),sum(La♯.^2) + # verbose && @printf " Increment total cost given A\n" + try ΔA = Qaa\Qa + catch; muscadeerror(@sprintf("matrix factorization failed at A-update, iAiter=%i",iAiter)) end decrement!(state,1,ΔA,Adofgr) - verbose && @printf " In A-iteration %3d, |ΔA|=%7.1e |La♯|=%7.1e\n" iAiter √(ΔA²) √(La²) # Aiter convergence + ΔA²,La² = sum(ΔA.^2),sum(Qa.^2) + verbose && @printf " In A-iteration %3d, |ΔA|=%7.1e |Qa|=%7.1e\n" iAiter √(ΔA²) √(La²) if ΔA²≤cΔA² && La²≤cLa² verbose && @printf " SweepXA converged in %3d A-iterations. |ΔA|=%7.1e / %g |La|=%7.1e / %g\n" iAiter √(ΔA²) maxΔa √(La²) maxLa break#out of the iAiter loop end iAiter==maxAiter && muscadeerror(@sprintf("no convergence of SweepXA after %3d A-iterations |ΔA|=%g / %g, |La|=%g / %g",iAiter,√(ΔA²),maxΔa,√(La²)^2,maxLa)) + cAiter = iAiter - # reset state to initial conditions + # reset state to initial conditions for a new step-sweep state.time = initialstate.time for i=1:min(OX+1,length(initialstate.X)) state.X[i] .= initialstate.X[i] @@ -214,8 +201,8 @@ function solve(SX::Type{SweepXA{OX}},pstate,verbose,dbg; for i= length(initialstate.X)+1:OX+1 state.X[i] .= 0. end - end - verbose && @printf "\n nel=%d, nXdof=%d, nstep=%d, ΣnXiter=%d, mean(nXiter)=%d\n" getnele(model) getndof(Xdofgr) length(time) cXiter cXiter/length(time) + end # iAiter + verbose && @printf "\n nel=%d, nXdof=%d, nAdof=%d, nstep=%d, ΣnXiter=%d, mean(nXiter)=%d\n" getnele(model) getndof(Xdofgr) getndof(Adofgr) length(time) cXiter cXiter/length(time)/cAiter return -end \ No newline at end of file +end # solve \ No newline at end of file diff --git a/src/Taylor.jl b/src/Taylor.jl index e062dc06..33afbd92 100644 --- a/src/Taylor.jl +++ b/src/Taylor.jl @@ -1,59 +1,76 @@ -struct motion{P} end struct motion_{P,Q} end struct motion⁻¹{P,ND,OD} end """ - P = constant(X) - X_ = motion{P}(X) - -Transform a `NTuple` of `SVector`s, for example the vector `X` provided as an input to -`residual` or `Lagrangian` into a `SVector` of `∂ℝ`. This can be used by an element to -compute time derivatives, for example Euler, Coriolis and centrifugal accelerations, -or strain rates. - -Some principles of safe automatic differentiation must be adhered to: -- the function that uses `motion` must also 'unpack' : no variable that is touched by - the output of `motion` must be returned by the function without having been unpacked - by `motion⁻¹`. Touched variables can for example be marked with an underscore. -- The precendence `P` must be calculated using `constants` with all variables that are input to - the function and may be differentiated. -- If other levels of automatic differentiation are introduced within the function, unpack in reverse - order of packing. - -See [`motion⁻¹`](@ref) + P,ND,X_ = motion(X [;context]) + +Input variables `X` and `U` provided to`residual` or `Lagrangian` are `NTuples` which can +have a form like `(X₀,X₁,X₂)`, with the zeroth, first and second time derivative. `motion` +transform such a `NTuple` into a `SVector` of `∂ℝ`, containing derivatives with respect to time. + +Using a scalar instead of `SVector` to provide an idea, (`motion` actually only operates on `NTuple` of `SVector`s) +this transforms `(x₀,x₁,x₂)` into `x₀+∂₁⟨x₁⟩+∂₂⟨x₁+∂₁⟨x₂⟩⟩`. + +This enables an element to use automatic differentiation to use time derivatives of various results, such +as Coriolis and centrifugal accelerations, or strain rates. + +If the third output from `motion` (or variables computed from this 3rd ouput), are combined in computation +with variables obtained by `variate` or `revariate` (including the inputs `Λ`, `X`, `U`, `A` and `t`) to +`lagrangian` and `residual` (or variables computed from these), then the variables obtained by `variate` or `revariate` +must be included in `context`. `context` can be a variable or a ``tuple` of variables. To prevent bugs, mark variables "touched" +directly or indirectly by `motion`'s 3rd output with e.g. an underscore to keep track of the separation. + + P,ND,X_ = motion(X ,context=(A,t)]) + b = f(A) # b is "touched by A", which may be an addifed input to `residual` + Y_ = g(X_,b,t) # Y_ is touched by t, and indirectly by A. This is OK, they where + # declared in the context of X_ + +See [`toolbox.EulerBeam3D`] for an example of usage. + +!!! Warning + Use `∂0`, `∂1` and `∂2` to extract time derivatives from `X` and `U`, do not use + indexing `X[1]` as the `NTuple` may be truncated in e.g. static analyses. + +See [`motion⁻¹`](@ref), [`variate`](@ref) """ -motion{ P }(a::NTuple{ND,SV{N,R}}) where{ND,P,N,R } = SV{N}(motion_{P-1,P+ND-2}(let a=a - ntuple(j->a[j][i],Val(ND)) - end) for i=1:N) -#motion{ P }(a::NTuple{ND,SV{N,R}}) where{ND,P,N,R } = SV{N}(motion_{P-1,P+ND-2}(ntuple(j->a[j][i],Val(ND))) for i=1:N) +function motion(a::NTuple{ND,SV{N,R}};context=0) where{ND,N,R} + P,_,a_ = variate{0}(a;context) + A = SV{N}(motion_{P,P+ND-1}(let a=a + ntuple(j->a_[j][i],Val(ND)) + end) for i=1:N) + return P,ND,A +end motion_{P,Q }(a::NTuple{D, R }) where{D ,P ,R<:Real,Q} = ∂ℝ{Q,1}(motion_{P,Q-1}(a),SV(motion_{P,Q-1}(a[2:D]))) motion_{P,P }(a::NTuple{D, R }) where{D ,P ,R<:Real } = a[1] """ - P = constants(X,U,A,t) - ND = length(X) - X_ = motion{P,ND}(X) - Y_ = f(Y_) - Y₀ = motion⁻¹{P,ND,0}(Y_) - Y₁ = motion⁻¹{P,ND,1}(Y_) - Y₂ = motion⁻¹{P,ND,2}(Y_) - Y = motion⁻¹{P,ND }(Y) - -Extract the value and time derivatives from a variable that is a function of the output of `motion`. -In the above `Y` is a tuple of length `ND`. One can use `∂0`,`∂1` and `∂2` to unpack `Y`. + P,ND,X_ = motion(X) + Y_ = f(Y_) + Y = motion⁻¹{P,ND}(Y_) + +`motion⁻¹` transforms `Y_` into a `NTuple` `Y`. The values `P` and ``ND` +must be as returned by `motion`. Time derivatives can be accessed as + + Y₀ = ∂0(Y) + Y₁ = ∂1(Y) + Y₂ = ∂2(Y) + +One can also obtain the i-th time derivative directly as + + Yᵢ = motion⁻¹{P,ND,i}(Y_) See also [`motion`](@ref) """ motion⁻¹{P,1,0}(a::ℝ) where{P} = a -motion⁻¹{P,2,0}(a::ℝ) where{P} = value{P }(a) -motion⁻¹{P,3,0}(a::ℝ) where{P} = value{P}(value{P+1 }(a)) +motion⁻¹{P,2,0}(a::ℝ) where{P} = value{P+1 }(a) +motion⁻¹{P,3,0}(a::ℝ) where{P} = value{P+1}(value{P+2 }(a)) # velocities motion⁻¹{P,1,1}(a::ℝ) where{P} = 0. -motion⁻¹{P,2,1}(a::ℝ) where{P} = ∂{ P ,1}(a)[1] # [1]: only partial is wrt time -motion⁻¹{P,3,1}(a::ℝ) where{P} = value{P}(∂{ P+1,1}(a)[1]) +motion⁻¹{P,2,1}(a::ℝ) where{P} = ∂{ P+1,1}(a)[1] # [1]: only partial is wrt time +motion⁻¹{P,3,1}(a::ℝ) where{P} = value{P+1}(∂{ P+2,1}(a)[1]) # accelerations motion⁻¹{P,1,2}(a::ℝ) where{P} = 0. motion⁻¹{P,2,2}(a::ℝ) where{P} = 0. -motion⁻¹{P,3,2}(a::ℝ) where{P} = ∂{ P,1}(∂{ P+1,1}(a)[1])[1] +motion⁻¹{P,3,2}(a::ℝ) where{P} = ∂{ P+1,1}(∂{ P+2,1}(a)[1])[1] motion⁻¹{P,ND,OD}(a::SArray{S,R}) where{S,P,ND,OD,R<:ℝ} = SArray{S}(motion⁻¹{P,ND,OD}(aᵢ) for aᵢ∈a) motion⁻¹{P,1 }(a::Union{ℝ,SArray}) where{P } = (motion⁻¹{P,1,0}(a),) @@ -79,12 +96,28 @@ flat_eltype(a::SArray{S,T} ) where{S,T} = T flat_eltype(a::R ) where{R<:ℝ} = R precedence(a::NamedTuple ) = precedence(values(a)) -precedence(a::Tuple ) = max(precedence(first(a)),precedence(Base.tail(a))) precedence(a::Tuple{X} ) where{X} = precedence(a[1]) +function precedence(a::Tuple ) + pa1 = precedence(first(a)) + pat = precedence(Base.tail(a)) + pa1==0 && return pat + pat==0 && return pa1 + pa1==pat && return pat + error("precedence of a tuple with components of various precedence") +end + npartial( a::NamedTuple ) = npartial(values(a)) -npartial( a::Tuple ) = max(npartial(first(a)),npartial(Base.tail(a))) npartial( a::Tuple{X} ) where{X} = npartial(a[1]) +function npartial(a::Tuple ) + na1 = npartial(first(a)) + nat = npartial(Base.tail(a)) + na1==0 && return nat + nat==0 && return na1 + na1==nat && return nat + error("npartial of a tuple with components of various npartial") +end + struct flatten{T} end flatten(a) = flatten{flat_eltype(a)}(a) @@ -94,101 +127,212 @@ flatten{T}(a::Tuple{} ) where{T} = () flatten{T}(a::SArray ) where{T} = SVector{length(a),T}(a) flatten{T}(a::ℝ ) where{T} = T(a) -struct type_multivariate_𝕣{P,N} - dummy::𝕫 +@inline longuestfirst(a,b) = length(a)>length(b) ? (a,b) : (b,a) + +@inline function npartials(a::Tuple) + long,short = longuestfirst(npartials(first(a)),npartials(Base.tail(a))) + Δ = length(long)-length(short) + for i = 1:length(short) + @assert long[Δ+i] == short[i] "Perturbation collision" + end + return long # Core.Const end -type_multivariate_𝕣{0,N}() where{ N} = 𝕣 -type_multivariate_𝕣{P,N}() where{P,N} = ∂ℝ{P,N,type_multivariate_𝕣{P-1,N}()} # this causes (slight) type instability - because if Ra isnot ℝ, then return type is different. +@inline npartials(a::Tuple{} ) = () +@inline npartials(a::NamedTuple ) = npartials(values(a)) +@inline npartials(a::SArray ) = length(a)==0 ? () : npartials(first(a)) # edgecase empty array. Is that OK? +@inline npartials(a::∂ℝ{P,N,R}) where{P,N,R} = (N,npartials(a.x)...) +@inline npartials(a::ℝ ) = () + +struct front{P} end +@inline front{P}(tup) where{P} = Base.front(front{P-1}(tup)) +@inline front{0}(tup) = tup -struct multivariate_𝕣{P,N} end -multivariate_𝕣{P,N}(a ,i ) where{P,N} = ∂ℝ{P,N }(multivariate_𝕣{P-1,N}(a,i ),i) -multivariate_𝕣{0,N}(a::𝕣,i ) where{ N} = a +@inline zerovalue(v::∂ℝ{P,N,R}) where{P,N,R<:ℝ} = ∂ℝ{P,N,R}(zerovalue(v.x),v.dx) +@inline zerovalue(v:: R ) where{ R<:ℝ} = zero(R) -multivariate_𝕣{P,N}(a::R,i,scale) where{P,N,R} = ∂ℝ{P,N }(multivariate_𝕣{P-1,N}(a,i,scale),SV{N,R}(i==j ? scale : zero(R) for j=1:N)) -multivariate_𝕣{0,N}(a::𝕣,i,scale) where{ N} = a +struct AllElements{S} # apply a scaling to a whole Tuple or SArray + s::S +end +# type for static parametrization """ - TX = revariate{P}(V) + V = variate{O}(v[;context,scale]) + +variate `v` to the `O`-th order. + + V = variate(v[;context,scale]) + +variates `v` to the first order. -The variable `V` is a nested structure `NamedTuple`s, `Tuple`s and `SArrays` of +The variable `v` is a nested structure of `NamedTuple`s, `Tuple`s and `SArrays` of +`Real`s (possibly: `∂ℝ`s). `V` has the same structure as `v`. + +The output of `variate` must not be combined in computation +with variables obtained by `motion`, `revariate` or a separate call to `variate` (including the inputs `Λ`, `X`, `U`, `A` and `t`) to +`lagrangian` and `residual` (or variables computed from these). + +If output from `variate` (or variables computed from this ouput), are combined in computation +with variables obtained by `revariate`, `motion` or a separate call to `variate` (including the inputs `Λ`, `X`, `U`, `A` and `t`) to +`lagrangian` and `residual` (or variables computed from these), then the later variables +must be included in `context`. `context` can be a variable or a ``tuple` of variables. + + V = variate(∂1{X};context=(Λ,X,U,t)) # A left out + W = V*t+∂0(X) # safe + Y = V*A[1] # not safe!!! + +Not for use within elements: `scale` has the same structure as `v` except that `SArray`s and `NTuple`s can be replaced +by `AllElement(scaling)` to apply `scaling to all elements in the `SArray` or `NTuple` in `v`. + +See also: [`motion`](@ref), [`revariate`](@ref), [`chainrule`](@ref), [`variate_indices`](@ref) +""" +struct variate{O} end +""" + V = variate0{O}(v[;context,scale]) + +The same as [`variate`](@ref), but while all derivatives are as from [`variate`](@ref), all +values are set to 0. +""" +struct variate0{O} end # former δ: returns outputs with VALUE=0 +""" + V_ = revariate{P}(V) + +The variable `V` is a nested structure of `NamedTuple`s, `Tuple`s and `SArrays` of `Real`s (possibly: `∂ℝ`s). -`V` is stripped of its partials, an revariated to -order `P`. +`V` is stripped of its partials, an revariated to order `P`. - TV = revariate(VX) + V_ = revariate(V) -revariates to the order `precedence(V)`. +revariates to the order `precedence(V)`. `TV` has the same structure as `V`. One typical usage is with a `Tuple`: + + a_,b_,c_ = revariate((a,b,c)) `revariate`, in conjunction with `chainrule` can be used to improve performance when the length of `V` is smaller than the length of its partials. -Be extremely careful never to mix any variable that is a function of `V` with any other variables -containing `∂ℝ`s but not produced by the same `revariate`. +The output(s) of `revariate` must not be combined in computation +with variables obtained by `variate` or `revariate` (including the inputs `Λ`, `X`, `U`, `A` and `t`) to +`lagrangian` and `residual` (or variables computed from these). To prevent bugs, mark variables "touched" +directly or indirectly by `revariate`'s output with e.g. an underscore to keep track of the separation. + +See [`toolbox.EulerBeam3D`] for an example of usage. + +See also: [`chainrule`](@ref), [`variate_indices`](@ref), [`variate`](@ref) +""" +struct revariate{P} end +struct variate_work{A,B,C} end +struct revariate_work{A} end +struct variate_nested{A,B,C,D,E} end + +# API +@inline variate( v;kwargs...) = variate_work{1,identity ,:variate}(v;kwargs...) +@inline variate{O}( v;kwargs...) where{O} = variate_work{O,identity ,:variate}(v;kwargs...) +@inline variate0( v;kwargs...) = variate_work{1,zerovalue,:variate}(v;kwargs...) +@inline variate0{O}( v;kwargs...) where{O} = variate_work{O,zerovalue,:variate}(v;kwargs...) +@inline revariate( v;kwargs...) = revariate_work{precedence(v)}(v;kwargs...) +@inline revariate{P}(v;kwargs...) where{P} = revariate_work{P }(v;kwargs...) + +# workhorses +@inline function variate_work{O,VZ,:variate}(v;context=0,scale=nothing) where{O,VZ} + Nv = flat_length(v) # 𝕫 + Nc = npartials((v,context)) # ntuple(𝕫,Pvc) + P = O+length(Nc) # precedence of outputs + return if scale==nothing P,Nv,variate_nested{:variate,O,Nv,Nc,VZ}(v,1 ) + else P,Nv,variate_nested{:variate,O,Nv,Nc,VZ}(v,1,scale) + end +end +@inline function revariate_work{P}(v;scale=nothing) where{P} + N = flat_length(v) + return variate_nested{:revariate,P,N,Nothing,Nothing}(v,1) +end + +# nested types,recursion +@inline variate_nested{A,B,C,D,E}(v::NamedTuple,i ) where{A,B,C,D,E } = NamedTuple{keys(v)}(variate_nested{A,B,C,D,E}(values(v),i )) +@inline variate_nested{A,B,C,D,E}(v::NamedTuple,i,s::NamedTuple ) where{A,B,C,D,E } = NamedTuple{keys(v)}(variate_nested{A,B,C,D,E}(values(v),i,values(s))) +@inline variate_nested{A,B,C,D,E}(v::NamedTuple,i,s::AllElements) where{A,B,C,D,E } = NamedTuple{keys(v)}(variate_nested{A,B,C,D,E}(values(v),i,s )) +@inline variate_nested{A,B,C,D,E}(v::Tuple ,i ) where{A,B,C,D,E } = (variate_nested{A,B,C,D,E}(first(v),i ),variate_nested{A,B,C,D,E}(Base.tail(v),i+flat_length(first(v)) )...) +@inline variate_nested{A,B,C,D,E}(v::Tuple ,i,s::Tuple ) where{A,B,C,D,E } = (variate_nested{A,B,C,D,E}(first(v),i,first(s)),variate_nested{A,B,C,D,E}(Base.tail(v),i+flat_length(first(v)),Base.tail(s))...) +@inline variate_nested{A,B,C,D,E}(v::Tuple ,i,s::AllElements) where{A,B,C,D,E } = (variate_nested{A,B,C,D,E}(first(v),i,s.s ),variate_nested{A,B,C,D,E}(Base.tail(v),i+flat_length(first(v)),s )...) +@inline variate_nested{A,B,C,D,E}(v::Tuple{} ,i ) where{A,B,C,D,E } = () +@inline variate_nested{A,B,C,D,E}(v::Tuple{} ,i,s::Tuple{} ) where{A,B,C,D,E } = () +@inline variate_nested{A,B,C,D,E}(v::Tuple{} ,i,s::AllElements) where{A,B,C,D,E } = () +@inline variate_nested{A,B,C,D,E}(v::SArray{S} ,i ) where{A,B,C,D,E,S} = variate_nested{A,B,C,D,E}.(v,SArray{S,𝕫}(i-1+j for j∈eachindex(v)) ) +@inline variate_nested{A,B,C,D,E}(v::SArray{S} ,i,s::SArray{S} ) where{A,B,C,D,E,S} = variate_nested{A,B,C,D,E}.(v,SArray{S,𝕫}(i-1+j for j∈eachindex(v)),s ) +@inline variate_nested{A,B,C,D,E}(v::SArray{S} ,i,s::AllElements) where{A,B,C,D,E,S} = variate_nested{A,B,C,D,E}.(v,SArray{S,𝕫}(i-1+j for j∈eachindex(v)),SArray{S,typeof(s.s)}(s.s for j∈eachindex(v))) +@inline variate_nested{A,B,C,D,E}(v::ℝ ,i ) where{A,B,C,D,E } = variate_nested{A,B,C,D,E}(v,i,1.) + + +# add O variations on the outside +@inline function variate_nested{:variate,O ,Nv,Nc,VZ}(v::ℝ,i,s) where{O,Nv,Nc,VZ} + x = variate_nested{:variate,O-1,Nv,Nc,VZ}(v ,i,s) + R = typeof(x) + dx = SVector{Nv,R}(i==j ? R(s) : zero(R) for j=1:Nv) + return ∂ℝ{O+length(Nc),Nv,R}(x,dx) +end +# transition to getting v up to Nc +@inline function variate_nested{:variate, 0 ,Nv ,Nc,VZ}(v::ℝ,i,s) where{Nv,Nc,VZ} + Nc_ = front{precedence(v)}(Nc) # cut the tail of Nc if v is not 𝕣 + return variate_nested{:variate,-1 ,Nothing,Nc_,VZ}(v,i,s) +end +# get v up to Nc +@inline variate_nested{:variate,-1,Nothing,() ,VZ}(v::ℝ,i,s) where{VZ} = VZ(v) +@inline function variate_nested{:variate,-1,Nothing, Nc ,VZ}(v::ℝ,i,s) where{Nc,VZ} + x = variate_nested{:variate,-1,Nothing,Base.tail(Nc),VZ}(v ,i,s) + P,N,R = precedence(v)+length(Nc),first(Nc),typeof(x) + dx = SVector{N,R}(zero(R) for j=1:N) + return ∂ℝ{P,N,R}(x,dx) +end + +# revariate +@inline variate_nested{ :revariate,0 ,N,D,E}(v::ℝ,i,s) where{ N,D,E} = VALUE(v) +@inline function variate_nested{:revariate,P ,N,D,E}(v::ℝ,i,s) where{P,N,D,E} + x = variate_nested{:revariate,P-1,N,D,E}(v ,i,s) + R = typeof(x) + dx = SVector{N,R}(i==j ? R(s) : zero(R) for j=1:N) + return ∂ℝ{P,N,R}(x,dx) +end -A special version of `revariate` - V = (;X,U,A) - S = (X=scale.X,U=scale.U,A=scale.A) - TV = revariate{P}(V,S) +""" + iV = variate_indices(V) + +For use in conjunction with + + TV = revariate(V) -allows to introduce scaling in automatic differentiation. For this method, `S` and `V` -have the same structure, with the important exception that `Tuple`s in `V` must be -`ntuple`s (have elements of identical type `T`), and, to a `Tuple` in `V` corresponds -a variable of type `T` in `V`. Put simply: the same scale `scale.X` will be applied -to `∂0[X]`, `∂1[X]` and `∂2[X]`. +`iV` has the same structure as `V` and `TV` but contains integers: the indices into the partials of `TV` + +See also: [`revariate`](@ref) -See also: [`chainrule`](@ref) """ -struct revariate{P,N,Z} end -revariate(a) = revariate{precedence(a)}(a) -revariate{P }(a ) where{P} = revariate{P,flat_length(a),:variate}(a,1) -revariate{P,N,Z }(a::NamedTuple ,i) where{P,N,Z} = NamedTuple{keys(a)}(revariate{P,N,Z}(values(a),i)) -revariate{P,N,Z }(a::Tuple ,i) where{P,N,Z} = (revariate{P,N,Z}(first(a),i),revariate{P,N,Z}(Base.tail(a),i+flat_length(first(a)))...) -revariate{P,N,Z }(a::Tuple{} ,i) where{P,N,Z} = () -revariate{P,N,Z }(a::SArray{S} ,i) where{P,N,Z,S} = SArray{S,type_multivariate_𝕣{P,N}()}(revariate{P,N,Z}(aⱼ,i-1+j) for (j,aⱼ)∈enumerate(a)) -revariate{P,N,:δ }(a::ℝ ,i) where{P,N } = multivariate_𝕣{P,N}(zero( a),i) -revariate{P,N,:variate}(a::ℝ ,i) where{P,N } = multivariate_𝕣{P,N}(VALUE(a),i) - -# Specialised to adiff dofs, with scaling -# s for scale -# IMPORTANT: in a Tuple (but not NamedTuple), all a[i] share the same s -struct revariatevalues{P,N,Z} end -revariate(a,s) = revariate{precedence(a)}(a,s) -revariate{P }(a ,s ) where{P} = revariate{P,flat_length(a),:variate}(a,1,s) -revariate{P,N,Z }(a::NamedTuple ,i,s ) where{P,N,Z} = NamedTuple{keys(a)}(revariatevalues{P,N,Z}(values(a),i,values(s))) -revariatevalues{P,N,Z }(a::Tuple ,i,s ) where{P,N,Z} = (revariate{P,N,Z}(first(a),i,first(s)),revariatevalues{P,N,Z}(Base.tail(a),i+flat_length(first(a)),Base.tail(s))...) -revariatevalues{P,N,Z }(a::Tuple{} ,i,s ) where{P,N,Z} = () -revariate{P,N,Z }(a::Tuple ,i,s ) where{P,N,Z} = (revariate{P,N,Z}(first(a),i, s ),revariate{ P,N,Z}(Base.tail(a),i+flat_length(first(a)), s )...) -revariate{P,N,Z }(a::Tuple{} ,i,s ) where{P,N,Z} = () -revariate{P,N,Z }(a::SArray{S} ,i,s::SArray{S,𝕣}) where{P,N,Z,S} = SArray{S,type_multivariate_𝕣{P,N}()}(revariate{P,N,Z}(a[j],i-1+j,s[j]) for j∈eachindex(a)) -revariate{P,N,:δ }(a::ℝ ,i,s::𝕣 ) where{P,N } = multivariate_𝕣{P,N}(zero( a),i,s) -revariate{P,N,:variate}(a::ℝ ,i,s::𝕣 ) where{P,N } = multivariate_𝕣{P,N}(VALUE(a),i,s) - -struct reδ{P} end -reδ{P}(a ) where{P} = revariate{P,flat_length(a),:δ}(a,1 ) -reδ{P}(a,s) where{P} = revariate{P,flat_length(a),:δ}(a,1,s) - -# works with revariate{P}(a,s) and returns a structure of indices into the partials -revariate_indices( args...) = (revariate_indices_(args,0)...,flat_length(args)) -revariate_indices_(a::Tuple ,i) = (revariate_indices_(first(a),i),revariate_indices_(Base.tail(a),i+flat_length(first(a)))...) -revariate_indices_(a::Tuple{},i) = () -revariate_indices_(a::SArray ,i) = i+1:i+flat_length(a) -revariate_indices_(a::𝕣,i) = i+1 +variate_indices( a ) = revariate_indices_(a,0) +revariate_indices_(a::Tuple ,i) = (revariate_indices_(first(a),i),revariate_indices_(Base.tail(a),i+flat_length(first(a)))...) +revariate_indices_(a::Tuple{} ,i) = () +revariate_indices_(a::NamedTuple,i) = NamedTuple{keys(a)}(revariate_indices_(values(a),i)) +#revariate_indices_(a::SArray ,i) = i+1:i+flat_length(a) +revariate_indices_(a::SArray ,i) = SVector{flat_length(a),𝕫}(i+iₐ for iₐ∈1:flat_length(a)) +revariate_indices_(a::𝕣 ,i) = i+1 """ - to_order{P}(V) + to_order{P,N}(V) Decrease (lossy) or increase (pad partials with zeros) the order of differentiation of `V`. `V` is a nested structure of `NamedTuple`, `Tuple`, `SArray`, and the components -of `V` must be of type `∂ℝ` (otherwise, the number of partials would be undefined). +of `V` must be of type `∂ℝ` or `𝕣`. + +IMPORTANT: +1) assumes all the nested differentiations are with respect to the same variable. +2) to_order{P,N}(V::𝕣) = V """ struct to_order{P,N} end -to_order{P,N}(a::NamedTuple ) where{P,N} = NamedTuple{keys(a)}(to_order{P,N}(values(a))) -to_order{P,N}(a::Tuple ) where{P,N} = (to_order{P,N}(first(a)),to_order{P,N}(Base.tail(a))...) -to_order{P,N}(a::Tuple{} ) where{P,N} = () -to_order{P,N}(a::AbstractArray) where{P,N} = to_order{P,N}.(a) -function to_order{P,N}(a::Ra) where{Ra<:∂ℝ{Pa,N},P} where{Pa,N} +to_order{P,N}(a::NamedTuple ) where{P ,N} = NamedTuple{keys(a)}(to_order{P,N}(values(a))) +to_order{P,N}(a::Tuple ) where{P ,N} = (to_order{P,N}(first(a)),to_order{P,N}(Base.tail(a))...) +to_order{P,N}(a::Tuple{} ) where{P ,N} = () +to_order{P,N}(a::AbstractArray) where{P ,N} = to_order{P,N}.(a) +to_order{0,N}(a::𝕣 ) where{ N} = a +to_order{P,N}(a::𝕣 ) where{P, N} = a # deliberate! +to_order{0,N}(a::∂ℝ{Pa,N} ) where{Pa,N} = VALUE(a) +function to_order{P,N}(a::∂ℝ{Pa,N}) where{P,N,Pa} if Pa==P a elseif Pa> P @@ -198,22 +342,20 @@ function to_order{P,N}(a::Ra) where{Ra<:∂ℝ{Pa,N},P} where{Pa,N} ∂ℝ{P,N}(ap, SVector{N}(∂ℝ{P-1,N}(ap.dx[i]) for i=1:N) ) end end -function to_order{P,N}(a::𝕣) where{P,N} - P==0 ? a : ∂ℝ{P,N}(to_order{P-1,N}(a)) -end -to_order{Pa}(a) where{Pa}= to_order{Pa,npartial(a)}(a) - ######################### +struct McLaurin{d} end """ - McLaurin(Ty,Δx) + v=McLaurin(Ty,Δx) `Ty::∂ℝ` has partials to arbitrary order with respect to a variable `x`. These partials define a McLaurin expansion, which `McLaurin` evaluates at value `Δx`. +Thus the elements in `v` have the same type as `Δx` + `McLaurin` handles nested structures of `Tuple`s and `SVector`s of `∂ℝ`, applying the expansion to each element. @@ -223,23 +365,20 @@ See also: [`chainrule`](@ref), [`Taylor`](@ref), [`revariate`](@ref), [`apply`]( """ McLaurin(y::Tuple,Δx) = tuple(McLaurin(first(y),Δx),McLaurin(Base.tail(y),Δx)...) McLaurin( ::Tuple{},Δx) = tuple() -McLaurin(y::SArray{Sy,Ty,Dy,Ly},Δx::SVector{Sx,Tx}) where{Sy,Ty,Dy,Ly,Sx,Tx} = SArray{Sy,Tx,Dy,Ly}(McLaurin(yᵢ,Δx) for yᵢ∈y) -McLaurin(y::SArray{Sy,𝕣 ,Dy,Ly},Δx::SVector{Sx,Tx}) where{Sy, Dy,Ly,Sx,Tx} = y -McLaurin(y::∂ℝ,Δx) = McLaurin(y.x,Δx) .+ McLaurin_right(y,Δx) -McLaurin(y::𝕣 ,Δx) = y -function McLaurin_right(y::∂ℝ{P,N,R},Δx::SVector{N}) where{P,N,R} - if N==0 - return zero(y) # hum!!!! - else - s = McLaurin_right(y.dx[1],Δx)*Δx[1] - for i ∈ 2:N - s += McLaurin_right(y.dx[i],Δx)*Δx[i] - end - s /= P +McLaurin(y::SArray{Sy,Ty,Dy,Ly},Δx::SVector{Sx,Tx}) where{Sy,Ty<:∂ℝ,Dy,Ly,Sx,Tx} = SArray{Sy,Tx,Dy,Ly}(McLaurin(yᵢ,Δx) for yᵢ∈y) +McLaurin(y::SArray{Sy,Ty,Dy,Ly},Δx::SVector{Sx,Tx}) where{Sy,Ty<: ℝ,Dy,Ly,Sx,Tx} = SArray{Sy,Ty,Dy,Ly}(McLaurin(yᵢ,Δx) for yᵢ∈y) +McLaurin(y::ℝ,Δx) = McLaurin{1}(y::ℝ,Δx) +McLaurin{D}(y::𝕣 ,Δx::SVector{N}) where{N,D} = y +function McLaurin{D}(y::∂ℝ{P,N,R},Δx::SVector{N}) where{P,N,R,D} # Horner's algorithm + @assert N>0 # if this edge case is relevant, create specialised method that converts VALUE(y) to eltype(Δx) + o = McLaurin{D+1}(y.dx[1],Δx)*Δx[1] + for i ∈ 2:N + o += McLaurin{D+1}(y.dx[i],Δx)*Δx[i] end - return s + D>1 && (o *= inv(D)) + return VALUE(y)+o end -McLaurin_right(y::𝕣 ,Δx ) = y + """ Taylor(Ty,x₀,x) @@ -285,41 +424,37 @@ the length of its partials. Also works where `x` is a nested structure of `Tuple`s and `NamedTuple`s where the leaves are `ℝ` or `SArray{S,R} where {S,R<:ℝ}`. -Be extremely careful if `f` is a closure, making sure that `f` does not capture variables of type `∂ℝ`. +!!! warning + If `f` is a closure, make sure that `f` does not capture variables of type `∂ℝ`. + +!!! warning + See [`chainrule`](@ref) about when it is advisable to use chainrule, and when not. Wrapper function of [`revariate`](@ref) and [`chainrule`](@ref) """ struct apply{Mode} end -apply{:chainrule}(f,x) = chainrule(f(revariate(x)),x) +function apply{:chainrule}(f,x) + x_ = revariate(x) + y_ = f(x_) + y = chainrule(y_,x) + return y +end apply{:direct }(f,x) = f(x) """ - composevalue{P,ND}(Ty,X_) - -Given `Ty` obtained using `revariate`, and `X_`, obtained using `motion{P}(X)` where `X` is a tuple -of length `ND` and `P=constants(X)`, compute `y`, a tuple of length `ND` of `AbstractArrays` of same `eltype` as vectors in `X. - -See also [`revariate`](@ref), [`motion`](@ref), [`motion⁻¹`](@ref), [`composeJacobian`](@ref) -""" -struct composevalue{P,ND} end -composevalue{P,ND}(Ty ,X_) where{P,ND} = motion⁻¹{P,ND}(chainrule(value{P}(Ty),X_)) -composevalue{P,ND}(Ty::NamedTuple,X_) where{P,ND} = NamedTuple{keys(Ty)}(composevalue{P,ND}(values(Ty),X_)) -composevalue{P,ND}(Ty::Tuple ,X_) where{P,ND} = (composevalue{P,ND}(first(Ty),X_),composevalue{P,ND}(Base.tail(Ty),X_)...) -composevalue{P,ND}(Ty::Tuple{} ,X_) where{P,ND} = () -""" - composeJacobian{P}(Ty,X_) + chainrule_Jacobian{P}(Ty,X_) Given `Ty` obtained using `revariate`, and `X_`, obtained using `motion{P}(X)` where `X` is a tuple -of `SVectors` and `P=constants(X)`, compute `y`, a tuple of length `ND` of `AbstractArrays` of same `eltype` as vectors in `X, +of `SVectors` and `P=precedence(X)`, compute `y`, a tuple of length `ND` of `AbstractArrays` of same `eltype` as vectors in `X, and `y∂X₀`, the Jacobian of `∂0(y)` with respect to `∂0(X)`. -See also [`revariate`](@ref), [`motion`](@ref), [`motion⁻¹`](@ref), [`composevalue`](@ref) +See also [`revariate`](@ref), [`motion`](@ref), [`motion⁻¹`](@ref) """ -struct composeJacobian{P} end -composeJacobian{P}(Ty ,X₀) where{P} = chainrule(∂{P,npartial(Ty)}(Ty),X₀) # y∂X₀ -composeJacobian{P}(Ty::NamedTuple,X₀) where{P} = NamedTuple{keys(Ty)}(composeJacobian{P}(values(Ty),X₀)) -composeJacobian{P}(Ty::Tuple ,X₀) where{P} = (composeJacobian{P}(first(Ty),X₀),composeJacobian{P}(Base.tail(Ty),X₀)...) -composeJacobian{P}(Ty::Tuple{} ,X₀) where{P} = () +struct chainrule_Jacobian{P} end +chainrule_Jacobian(Ty ,X₀) = chainrule(∂{precedence(Ty),npartial(Ty)}(Ty),X₀) # y∂X₀ +chainrule_Jacobian(Ty::NamedTuple,X₀) = NamedTuple{keys(Ty)}(chainrule_Jacobian(values(Ty),X₀)) +chainrule_Jacobian(Ty::Tuple ,X₀) = (chainrule_Jacobian(first(Ty),X₀),chainrule_Jacobian(Base.tail(Ty),X₀)...) +chainrule_Jacobian(Ty::Tuple{} ,X₀) = () diff --git a/test/SomeElements.jl b/test/SomeElements.jl index 868f3cb9..c5ccca38 100644 --- a/test/SomeElements.jl +++ b/test/SomeElements.jl @@ -223,4 +223,4 @@ AdjustableSdofOscillator(nod::Vector{Node};K=1.::𝕣,C=0.::𝕣,M=0.::𝕣) = A return R,noFB end #Muscade.doflist( ::Type{AdjustableSdofOscillator}) = (inod =(1 ,1, 1, 1), class=(:X,:U,:A,:A), field=(:tx1,:tu1,:ΞK,:ΞC)) -Muscade.doflist( ::Type{AdjustableSdofOscillator}) = (inod =(1 ,1, 1), class=(:X,:U,:A), field=(:tx1,:tu1,:ΞK)) +Muscade.doflist( ::Type{AdjustableSdofOscillator}) = (inod =(1 ,1, 1), class=(:X,:U,:A), field=(:tx1,:tu1,:ΞC)) diff --git a/test/TestAdiff.jl b/test/TestAdiff.jl index 15f6fbbd..217107d9 100644 --- a/test/TestAdiff.jl +++ b/test/TestAdiff.jl @@ -20,11 +20,11 @@ t2 = promote_rule(typeof(dx1),typeof(x)) (g,h)=promote(dx1,x) ## Extraction -dscaled=δ{1,3,𝕣}(SVector(1.,2.,3.)) -vscaled=variate{1,3}(SVector(4.,4.,4.),SVector(1.,2.,3.)) -Δ = δ{1,2,𝕣}() -C1 = variate{constants(Δ),2}(SVector(3.,4.)) -C = variate{constants(C1),2}(C1) +dscaled=Muscade.δ_{1,3,𝕣}(SVector(1.,2.,3.)) +vscaled=Muscade.variate_{1,3}(SVector(4.,4.,4.),SVector(1.,2.,3.)) +Δ = Muscade.δ_{1,2,𝕣}() +C1 = Muscade.variate_{Muscade.precedence(Δ)+1,2}(SVector(3.,4.)) +C = Muscade.variate_{Muscade.precedence(C1)+1,2}(C1) PC = Muscade.precedence(C) PC1 = Muscade.precedence(C1) vC = value{PC}(C) @@ -36,9 +36,9 @@ v∂C = value{PC1}(∂C) dX1 = Muscade.toggle(false,dx1,3.) ## Operations -oa = variate{1}(1.) -ob = variate{constants(oa )}(2.) -oc = variate{constants(oa,ob)}(3.) +oa = Muscade.variate_{1}(1.) +ob = Muscade.variate_{Muscade.precedence(oa )+1}(2.) +oc = Muscade.variate_{Muscade.precedence(oa,ob)+1}(3.) od = oa+oc oe = od+ob oj = od^2 @@ -46,7 +46,7 @@ og = 2^od oh = oa^oc ok = oc*oa/oc ox = SVector(1.,2.,3.) -oX = variate{1,3}(ox) +oX = Muscade.variate_{1,3}(ox) ## norm @@ -55,7 +55,7 @@ nrm = norm(oX) ## atan(s,c) -x3 = variate{1}(1.6455) +x3 = Muscade.variate_{1}(1.6455) s3,c3=sin(x3),cos(x3) y3 = atan(s3,c3) @@ -76,13 +76,11 @@ y3 = atan(s3,c3) @test typeof(g) == ∂ℝ{2,2,∂𝕣12} @test g === ∂ℝ{2,2,∂𝕣12}(∂𝕣12(3.0, SVector(0.0, 0.0)), SVector(∂𝕣12(0.1, SVector(0.0, 0.0)), ∂𝕣12(0.2, SVector(0.0, 0.0)))) @test h === x - @test Muscade.∂²ℝ{1,2}(7.,2) === ∂ℝ{2, 2, ∂ℝ{1, 2, Float64}}(∂ℝ{1, 2, Float64}(7.0, [0.0, 1.0]), ∂ℝ{1, 2, Float64}[∂ℝ{1, 2, Float64}(0.0, [0.0, 0.0]), ∂ℝ{1, 2, Float64}(1.0, [0.0, 0.0])]) - @test Muscade.∂²ℝ{1,2}(7.,2,1.5) === ∂ℝ{2, 2, ∂ℝ{1, 2, Float64}}(∂ℝ{1, 2, Float64}(7.0, [0.0, 1.5]), ∂ℝ{1, 2, Float64}[∂ℝ{1, 2, Float64}(0.0, [0.0, 0.0]), ∂ℝ{1, 2, Float64}(1.5, [0.0, 0.0])]) end @testset "Adiff extraction" begin @test Δ === SVector(∂𝕣12(0.0, SVector(1.0, 0.0)),∂𝕣12(0.0, SVector(0.0, 1.0))) - @test constants(Δ) == 2 + @test Muscade.precedence(Δ) == 1 @test typeof(C) == SVector{2, ∂ℝ{3, 2, ∂ℝ{2, 2, Float64}}}#Array{∂ℝ{3,2,∂𝕣22},1} @test C[1] === ∂ℝ{3,2,∂𝕣22}(∂𝕣22(3.0, SVector(1.0, 0.0)), SVector(∂𝕣22(1.0, SVector(0.0, 0.0)), ∂𝕣22(0.0, SVector(0.0, 0.0)))) @test vC[1] === ∂𝕣22(3.0, SVector(1.0, 0.0)) @@ -101,12 +99,12 @@ y3 = atan(s3,c3) @test od === ∂ℝ{3,1,∂𝕣11}(∂𝕣11(4.0, SVector(1.0)), SVector(∂𝕣11(1.0, SVector(0.0)))) @test oe === ∂ℝ{3,1,∂ℝ{2,1,∂𝕣11}}(∂ℝ{2,1,∂𝕣11}(∂𝕣11(6.0, SVector(1.0)), SVector(∂𝕣11(1.0, SVector(0.0)))), SVector( ∂ℝ{2,1,∂𝕣11}(∂𝕣11(1.0, SVector(0.0)), SVector(∂𝕣11(0.0, SVector(0.0)))))) @test od === ∂ℝ{3,1,∂𝕣11}(∂𝕣11(4.0, SVector(1.0)), SVector(∂𝕣11(1.0, SVector(0.0)))) - @test og === ∂ℝ{3,1,∂𝕣11}(∂𝕣11(16.0, SVector(11.090354888959125)), SVector(∂𝕣11(11.090354888959125, SVector(7.687248222691222)))) + @test og === ∂ℝ{3,1,∂𝕣11}(∂𝕣11(15.999999999999998, SVector(11.090354888959123)), SVector(∂𝕣11(11.090354888959123, SVector(7.687248222691221)))) @test oj === od*od - @test og === ∂ℝ{3,1,∂𝕣11}(∂𝕣11(16.0, SVector(11.090354888959125)), SVector(∂𝕣11(11.090354888959125, SVector(7.687248222691222)))) @test ok === ∂ℝ{3,1,∂𝕣11}(∂𝕣11(1.0, SVector(1.0)), SVector(∂𝕣11(0.0, SVector(0.0)))) @test value{1}(2*oX)==2*ox - @test variate{1}(0.)^0 === ∂ℝ{1,1,𝕣}(0., SVector(0.)) + @test Muscade.variate_{1}(1.)^0 === ∂ℝ{1,1,𝕣}(1. , SVector(0.)) + @test Muscade.variate_{1}(0.)^0 === ∂ℝ{1,1,𝕣}(1. , SVector(0.)) # this can of course be discussed... end @@ -118,6 +116,17 @@ y3 = atan(s3,c3) y3 === ∂ℝ{1, 1, 𝕣}(1.6455, [1.0]) end + θ = [0,1e-8,1e-6,1e-2,.1,1,π] + @testset "sinc1" begin + @test Muscade.sinc1.( θ,sin.(θ),cos.(θ),inv.(θ),θ.*θ)≈[1.0,1.0,0.9999999999998334,0.9999833334166666,0.9983341664682817,0.8414709848078965,0.0] + @test Muscade.sinc1′.(θ,sin.(θ),cos.(θ),inv.(θ),θ.*θ)≈[ 0.0,-3.3333333333333334e-9,-3.3333333333329995e-7,-0.003333300000107897,-0.03330001190255594,-0.30116867893975674,-0.3183098861837907] + @test Muscade.sinc1″.(θ,sin.(θ),cos.(θ),inv.(θ),θ.*θ)≈[-0.3333333333333333, -0.3333333333333333, -0.33333333333323334, -0.33332333339285697, -0.33233392841710757, -0.23913362692838303, 0.20264236728467552] + @test Muscade.sinc1‴.(θ,sin.(θ),cos.(θ),inv.(θ),θ.*θ)≈[0.0, 2.0e-9, 1.999999999999762e-7, 0.001999976190568783, 0.019976199733646196, 0.1770985749170091, 0.12480067958459377] + @test Muscade.sinc1⁗.(θ,sin.(θ),cos.(θ),inv.(θ),θ.*θ)≈[0.2,0.2,0.1999999999999286,0.19999285718915333,0.19928617712243368,0.13307670326700266,-0.14309499132952147] + end + + + end # testset Adiff end diff --git a/test/TestBarElement.jl b/test/TestBarElement.jl index eb8d2849..66b71940 100644 --- a/test/TestBarElement.jl +++ b/test/TestBarElement.jl @@ -102,12 +102,13 @@ end ; # Testing weight -w = 10 +w = 10. +@functor with() g̃(t) = SVector(0.,0.,-1.) model = Model(:TestModel) node1 = addnode!(model,𝕣[0,0,0]) node2 = addnode!(model,𝕣[L₀,0,0]) elnod = [model.nod[n.inod] for n∈[node1,node2]] -mat = AxisymmetricBarCrossSection(EA=EA,μ=μ,w=w) +mat = AxisymmetricBarCrossSection(EA=EA,μ=μ,w=w,g̃=g̃) bar = Bar3D(elnod;mat) x = SVector(0., 0., 0., 0., 0., 0.); X = (x,) R,FB=Muscade.residual(bar, X,U,A,t,SP,dbg) diff --git a/test/TestBeamElement.jl b/test/TestBeamElement.jl index 23f4af51..81426416 100644 --- a/test/TestBeamElement.jl +++ b/test/TestBeamElement.jl @@ -241,7 +241,7 @@ end ## Testing weight ## Beam bent upwards with uniform weight (along negative t3) -w = 10 +w = 10. @functor with() g̃(t) = SVector(0.,0.,-1.) model = Model(:TestModel) node1 = addnode!(model,𝕣[0,0,0]) diff --git a/test/TestBeamElementStrainGauge.jl b/test/TestBeamElementStrainGauge.jl index 34344a7b..6e521989 100644 --- a/test/TestBeamElementStrainGauge.jl +++ b/test/TestBeamElementStrainGauge.jl @@ -6,7 +6,7 @@ model = Model(:TestModel) node1 = addnode!(model,𝕣[0,0,0]) node2 = addnode!(model,𝕣[4,0,0]) elnod = [model.nod[n.inod] for n∈[node1,node2]] -mat = BeamCrossSection(EA=10.,EI₂=3.,EI₃=3.,GJ=4.,μ=1.,ι₁=1.0) +mat = BeamCrossSection(EA=10.,EI₂=3.,EI₃=3.,GJ=4.,μ=1.,ι₁=1.0,w=10.) P = SMatrix{3,5}(0.,.5,0., 0.,0,.5, 0.,-.5,0., 0.,0,-.5, 0.,.5,0. ) D = SMatrix{3,5}(1.,0.,0., 1.,0.,0., 1.,0.,0., 1.,0.,0., 1/√2,0,1/√2) L = 0.1 @@ -23,7 +23,7 @@ instrumentedbeam = EulerBeam3DwithStrainGauge(elnod;P,D,elementkwargs=(mat=mat,o @test instrumentedbeam.K1 ≈ SVector(0.,0.,0.,0.,.25) @test instrumentedbeam.K2 ≈ SVector(-0.5, 0, 0.5, 0,-.25) @test instrumentedbeam.K3 ≈ SVector(0, -0.5, 0, 0.5,0) - @test typeof(instrumentedbeam) == EulerBeam3DwithStrainGauge{5, EulerBeam3D{BeamCrossSection, false}, @NamedTuple{strain::@NamedTuple{ε::Nothing, κ::Nothing}}} + @test typeof(instrumentedbeam) == EulerBeam3DwithStrainGauge{5, EulerBeam3D{BeamCrossSection{Functor{:g̃_default, @NamedTuple{}}}, false}, @NamedTuple{strain::@NamedTuple{ε::Nothing, κ::Nothing}}} end Λ = SVector(0,0,0, 0,.1,0, 0,0,0, 0,-.1,0) diff --git a/test/TestDirectXUA.jl b/test/TestDirectXUA.jl index c9393d91..0fb7548e 100644 --- a/test/TestDirectXUA.jl +++ b/test/TestDirectXUA.jl @@ -55,8 +55,9 @@ FAST = true Δt = 1. dis = state0.dis +wanted = Muscade.Wanted{1,OX+1,OU+1,IA}(:all,:all) -out,asm,dofgr = Muscade.prepare(Muscade.AssemblyDirect{OX,OU,IA},model,dis)#;Uwhite=true,Xwhite=true,XUindep=true,UAindep=true,XAindep=true) +out,asm,dofgr = Muscade.prepare(Muscade.AssemblyDirect,model,dis,wanted)#;Uwhite=true,Xwhite=true,XUindep=true,UAindep=true,XAindep=true) Muscade.zero!(out) state = [Muscade.State{1,OX+1,OU+1}(copy(state0,SP=(γ=0.,iter=1))) for i = 1:nstep] for i=1:nstep @@ -64,14 +65,16 @@ for i=1:nstep end Muscade.assembleA!{:matrices}(out,asm,dis,model,state[1],(;)) + @testset "prepareA_out" begin + @test typeof(out) == Muscade.AssemblyDirect{1, OX+1,OU+1,IA} @test all(all(v.==0) for v∈out.L1[1]) @test all(all(v.==0) for v∈out.L1[2]) @test all(all(v.==0) for v∈out.L1[3]) @test all(all(v.==0) for v∈out.L1[4]) - @test all(all(m.==0) for m∈out.L2[1]) - @test all(all(m.==0) for m∈out.L2[2]) - @test all(all(m.==0) for m∈out.L2[3]) + @test all(out.L2[1,2][1,1].==0.) + @test all(out.L2[2,2][1,1].==0.) + @test all(out.L2[3,3][1,1].==0.) @test out.L2[4,4][1,1] ≈ sparse([1, 2, 1, 2, 3, 4, 3, 4, 5, 6, 5, 6], [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6], [2.0e-14, 0.0, 0.0, 2.0e-14, 2.0e-14, 0.0, 0.0, 2.0e-14, 2.0e-14, 0.0, 0.0, 2.0e-14], 6, 6) end #Muscade.assemble!(out,asm,dis,model,state[1],(;)) @@ -88,14 +91,14 @@ Muscade.assemblebig!{:matrices}(Lvv,Lv,Lvvasm,Lvasm,asm,model,dis,out,[state],[n # fig = Muscade.spy(Lvv,title="bigsparse Lvv sparsity",size=500) # save("C:\\Users\\philippem\\.julia\\dev\\Muscade\\spy.jpg",fig) -stateXUA = solve(DirectXUA{OX,OU,IA};initialstate=[state0,state0],time=[0:1.:5, 6:1.:12],maxiter=100,verbose=false) +#stateXUA = solve(DirectXUA{OX,OU,IA};initialstate=[state0,state0],time=[0:1.:5, 6:1.:12],maxiter=100,verbose=false) @testset "prepare_out" begin @test out.L1[1] ≈ [[0.0, 0.0]] @test out.L1[2] ≈ [[0.055883099639785175, -0.1920340573300732], [0.0, 0.0], [0.0, 0.0]] @test out.L1[3] ≈ [[0.0, 0.0, 0.0, 0.0]] @test out.L1[4] ≈ [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]] - @test size(out.L2[1,1]) == (0,0) + @test size(out.L2[1,1]) == (1,1) @test out.L2[2,2][1,1] ≈ sparse([1, 2, 1, 2], [1, 1, 2, 2], [2.0, 0.0, 0.0, 2.0], 2, 2) @test out.L2[2,2][1,2] ≈ sparse([1, 2, 1, 2], [1, 1, 2, 2], [0.0, 0.0, 0.0, 0.0], 2, 2) @test out.L2[2,2][1,3] ≈ sparse([1, 2, 1, 2], [1, 1, 2, 2], [0.0, 0.0, 0.0, 0.0], 2, 2) @@ -104,7 +107,7 @@ stateXUA = solve(DirectXUA{OX,OU,IA};initialstate=[state0,state0],time=[ @test out.L2[2,1][3,1] ≈ sparse([1, 2, 1, 2], [1, 1, 2, 2], [1.0, 0.0, 0.0, 1.0], 2, 2) @test out.L2[3,3][1,1] ≈ sparse([1, 2, 3, 4], [1, 2, 3, 4], [0.0, 0.0, 2.0, 2.0], 4, 4) @test out.L2[3,4][1,1] ≈ sparse([1, 1, 2, 2], [1, 2, 3, 4], [0.0, 0.0, 0.0, 0.0], 4, 6) - @test out.L2[4,4][1,1] ≈ sparse([1, 2, 1, 2, 3, 4, 3, 4, 5, 6, 5, 6], [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6], [2.0e-14, 0.0, 0.0, 2.0e-14, 2.0e-14, 0.0, 0.0, 2.0e-14, 2.0e-14, 0.0, 0.0, 2.0e-14], 6, 6) + @test out.L2[4,4][1,1] ≈ sparse([1, 2, 1, 2, 3, 4, 3, 4, 5, 6, 5, 6], [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 6, 6) end @testset "prepare_asm" begin @test asm[1,1] ≈ [1 2] # asm[iarray,ieletyp][ieledof,iele] -> idof|inz diff --git a/test/TestDirectXUA001.jl b/test/TestDirectXUA001.jl index 1bb4b85c..93f712e8 100644 --- a/test/TestDirectXUA001.jl +++ b/test/TestDirectXUA001.jl @@ -21,6 +21,7 @@ e6 = addelement!(model,Hold ,[n3], field=:tx1) e7 = addelement!(model,Hold ,[n3], field=:tx2) @functor with() positionMeas(x,t) = 0.5*((x-0.12t)/0.01)^2 @functor with() acost(a) = 0.5*(a/.1)^2 +#@functor with() acost(a) = 0.5*(a)^2 e8 = addelement!(model,SingleDofCost ,class=:X, field=:tx1,[n1] ,cost=positionMeas) e9 = addelement!(model,SingleDofCost ,class=:X, field=:tx2,[n1] ,cost=positionMeas) @@ -31,8 +32,8 @@ stateX = solve(SweepX{0}; initialstate,time=[0.],verbose=false) stateXUA = solve(DirectXUA{0,0,1};initialstate=[stateX[1]],time = [0:.1:1],verbose=false,maxiter=50) iexp = 1 @testset "solution" begin - @test stateXUA[iexp][2].X[1]' ≈ [0.0154897 0.0154897 0.0 0.0 0.0 0.0 -0.0100155 1.55379e-5 1.55379e-5 -0.0100155] rtol=1e-4 - @test stateXUA[iexp][2].A' ≈ [ -0.000195471 -0.0400374] rtol=1e-4 + @test stateXUA[iexp][2].X[1]' ≈ [0.0125777 0.0125777 0.0 0.0 0.0 0.0 -0.0100126 1.26094e-5 1.26094e-5 -0.0100126] rtol=1e-4 + @test stateXUA[iexp][2].A' ≈ [ -3.83011e-5 -0.0672263] rtol=1e-4 @test stateXUA[iexp][2].A ≡ stateXUA[iexp][1].A end stateXUAcv = solve(DirectXUA{0,0,1};initialstate=[stateX[1]],time = [0:.1:1],saveiter=true,verbose=false) diff --git a/test/TestDofConstraints.jl b/test/TestDofConstraints.jl index b4d27a5b..ce25915f 100644 --- a/test/TestDofConstraints.jl +++ b/test/TestDofConstraints.jl @@ -14,8 +14,8 @@ SP0 = (γ=0.,) #--------------------------------------------------------- @functor with() g(x,t) = SVector(.3x[1] + .4x[2]) -Xctc = Muscade.variate{1,3}(SVector{3}(10.,4,-3)) # contact -Xgap = Muscade.variate{1,3}(SVector{3}(10.,4,3)) # gap +Xctc = Muscade.Muscade.variate_{1,3}(SVector{3}(10.,4,-3)) # contact +Xgap = Muscade.Muscade.variate_{1,3}(SVector{3}(10.,4,3)) # gap U = SVector{0,𝕣}() A = SVector{0,𝕣}() C = Muscade.DofConstraint{:X, 1 ,2 ,0 ,0 ,(1,) ,(:λ,) ,(1,1),(:t1,:t2),() ,() ,() ,() } @@ -82,8 +82,8 @@ end # Multiple X constraints @functor with() g(x,t) = x -Xctc = Muscade.variate{1,4}(SVector{4}(10.,3.,0,0)) # contact -Xgap = Muscade.variate{1,4}(SVector{4}( 0.,0.,2,1)) # gap +Xctc = Muscade.Muscade.variate_{1,4}(SVector{4}(10.,3.,0,0)) # contact +Xgap = Muscade.Muscade.variate_{1,4}(SVector{4}( 0.,0.,2,1)) # gap U = SVector{0,𝕣}() A = SVector{0,𝕣}() C = Muscade.DofConstraint{:X, 2 ,2 ,0 ,0 ,(1,1) ,(:λ1,:λ2) ,(1,1),(:t1,:t2),() ,() ,() ,() } @@ -140,8 +140,8 @@ end #--------------------------------------------------------- @functor with() g(x,u,a,t) = SVector(.3u[1] + .4u[2]) -Uctc = Muscade.variate{2,3}(Muscade.variate{1,3}(SVector{3}(10.,4,-3))) # contact -Ugap = Muscade.variate{2,3}(Muscade.variate{1,3}(SVector{3}(10.,4, 3))) # gap +Uctc = Muscade.Muscade.variate_{2,3}(Muscade.Muscade.variate_{1,3}(SVector{3}(10.,4,-3))) # contact +Ugap = Muscade.Muscade.variate_{2,3}(Muscade.Muscade.variate_{1,3}(SVector{3}(10.,4, 3))) # gap Λ = SVector{0,𝕣}() X = SVector{0,𝕣}() A = SVector{0,𝕣}() diff --git a/test/TestDrawBeamElement.jl b/test/TestDrawBeamElement.jl index e4c7ceb7..5bd403ae 100644 --- a/test/TestDrawBeamElement.jl +++ b/test/TestDrawBeamElement.jl @@ -4,14 +4,14 @@ using Printf using Muscade.Toolbox # Beam simply supported at both ends -L = 1; # Beam length [m] +L = 1.; # Beam length [m] q = 0.0; # Uniform lateral load [N/m] -EI₂ = 1; # Bending stiffness [Nm²] -EI₃ = 1; # Bending stiffness [Nm²] +EI₂ = 1.; # Bending stiffness [Nm²] +EI₃ = 1.; # Bending stiffness [Nm²] EA = 1e6; # Axial stiffness [N] GJ = 1e6; # Torsional stiffness [Nm²] -μ = 1; -ι₁ = 1; +μ = 1.; +ι₁ = 1.; # Create model nel = 3 diff --git a/test/TestEigX.jl b/test/TestEigX.jl index 84908b83..57a2ae7c 100644 --- a/test/TestEigX.jl +++ b/test/TestEigX.jl @@ -1,4 +1,4 @@ -module TestEigX +#module TestEigX using Muscade, StaticArrays,Test,Random include("SomeElements.jl") @@ -37,6 +37,20 @@ state = increment(initialstate,eiginc,imod,A) @test state.X[3][1:2:end] ≈ [-0.2937262712953869, -0.6962620392508903, -0.6613336756803813, -0.2137967604399907, 0.36006958839215825, 0.694478296097603] end +eiginc = solve(EigX{:fullℝ};state=initialstate,verbose=false) +imod = [1, 2] +A = [1,4+5im] +state = increment(initialstate,eiginc,imod,A) + +@testset "EigXfullR" begin + @test eiginc.ω[1:nmod] ≈ [ 0.143146493914704, 0.42677293340604844, 0.7024494006334382, 0.9650405646123343, 1.209654848799371] + @test state.X[1][1:2:end] ≈ [1.7338129265935287, 4.177182755457795, 4.192402275285353, 1.9005876862087123, -1.1387295193620908, -2.9254875682906434] + @test state.X[2][1:2:end] ≈ [-0.8521204984886861, -2.015355547777684, -1.8990540291889357, -0.5770550457522317, 1.1113125586121952, 2.0941148057104684] + @test state.X[3][1:2:end] ≈ [-0.2937262712953869, -0.6962620392508903, -0.6613336756803813, -0.2137967604399907, 0.36006958839215825, 0.694478296097603] +end + + + eiginc = solve(EigX{ℂ};state=initialstate,nmod,verbose=false) imod = [1, 2] A = [1,4+5im] @@ -49,4 +63,18 @@ state = increment(initialstate,eiginc,imod,A) @test state.X[3][1:2:end] ≈ [0.02223145453650511, 0.06504555832867998, 0.10303553062324605, 0.13338382896767445, 0.15383965890798573, 0.1628859051167022] atol=1e-6 end -end \ No newline at end of file +eiginc = solve(EigX{:fullℂ};state=initialstate,verbose=false) +imod = [1, 2] # modes not in same order as in EigX{ℂ} +A = [1,4+5im] +state = increment(initialstate,eiginc,imod,A) + +@testset "EigXfullC" begin + @test abs.(eiginc.p[1:nmod]) ≈ [0.10517722364770998, 2.078080371921441, 2.0780803719214407, 1.627145730632568, 1.627145730632568] + @test state.X[1][1:2:end] ≈ [-0.5204803125167823, -1.380280640445008, -1.7515434548282411, -1.475561386659547, -0.5922598565042344, 0.6684291616961805] atol=1e-6 + @test state.X[2][1:2:end] ≈ [0.36685998329180775, 0.9968795551054147, 1.3457604481290728, 1.3172451101745886, 0.9238884000674046, 0.2830867264304562] atol=1e-6 + @test state.X[3][1:2:end] ≈ [2.944311399320866, 7.9759926110463315, 10.686332896448118, 10.28674621116262, 6.894023935357853, 1.4962965862803947] atol=1e-6 +end + + + +#end \ No newline at end of file diff --git a/test/TestEigXU.jl b/test/TestEigXU.jl index 5521fec1..744e6f25 100644 --- a/test/TestEigXU.jl +++ b/test/TestEigXU.jl @@ -20,14 +20,14 @@ xn = 1. λn = 1e3 un = 1e3 -L = 1; # Beam length [m] +L = 1.; # Beam length [m] q = 0.0; # Uniform lateral load [N/m] -EI₂ = 1; # Bending stiffness [Nm²] -EI₃ = 10; # Bending stiffness [Nm²] +EI₂ = 1.; # Bending stiffness [Nm²] +EI₃ = 10.; # Bending stiffness [Nm²] EA = 1e6; # Axial stiffness [N] GJ = 1e6; # Torsional stiffness [Nm²] -μ = 1; -ι₁ = 1; +μ = 1.; +ι₁ = 1.; hasU = true σε = 100e-6*100 # precision of strain measurements σx = 1e-1 @@ -41,7 +41,7 @@ mat = BeamCrossSection(;EA,EI₂,EI₃,GJ,μ,ι₁) model = Model(:TestModel) Xnod = addnode!(model,XnodeCoord) Unod = addnode!(model,UnodeCoord) -mesh = hcat(Xnod,Xnod[mod_onebased.(iels.+1,nel)],Unod) +mesh = hcat(Xnod,Xnod[Muscade.mod_onebased.(iels.+1,nel)],Unod) nakedmesh = mesh[inaked,:] strainmesh = mesh[istrain,:] accmesh = reshape(Xnod[iacc],(length(iacc),1)) @@ -93,8 +93,10 @@ OX,OU = 2,0 # @show N ## EigXU analysis -Δω = 2^-6 -p = 2#11 +# Δω = 2^-6 +# p = 11 +Δω = 16^-6 +p = 8 nmod = 5 @@ -143,11 +145,11 @@ eigincXU = solve(EigXU{OX,OU};Δω, p, nmod,initialstate,verbose=true,v nα = 32 α = 2π*(1:nα)/nα circle = 0.05*[cos.(α) sin.(α)]' -GUI(initialstate,eigincXU;shadow = (;EulerBeam3D = (;style=:shape,line_color=:grey,Udof=false), - EulerBeam3DwithStrainGauge = (;gauge_color=:transparent) ), - model = (;EulerBeam3D = (;style=:solid,section=circle), - EulerBeam3DwithStrainGauge = (;L=0.03), - Position3D = (;L=.03)) ) +Muscade.GUI(initialstate,eigincXU;shadow = (;EulerBeam3D = (;style=:shape,line_color=:grey,Udof=false), + EulerBeam3DwithStrainGauge = (;gauge_color=:transparent) ), + model = (;EulerBeam3D = (;style=:solid,section=circle), + EulerBeam3DwithStrainGauge = (;L=0.03), + Position3D = (;L=.03)) ) # using SnoopCompileCore, SnoopCompile, AbstractTrees, ProfileView diff --git a/test/TestElementCost.jl b/test/TestElementCost.jl index a92860e9..b8396c37 100644 --- a/test/TestElementCost.jl +++ b/test/TestElementCost.jl @@ -15,7 +15,7 @@ d = Muscade.doflist(typeof(el)) Nx,Nu,Na = 3,0,2 Nz = 2Nx+Nu+Na iλ,ix,iu,ia = Muscade.gradientpartition(Nx,Nx,Nu,Na) -ΔZ = δ{1,Nz,𝕣}() +ΔZ = Muscade.δ_{1,Nz,𝕣}() ΔΛ,ΔX,ΔU,ΔA = view(ΔZ,iλ),view(ΔZ,ix),view(ΔZ,iu),view(ΔZ,ia) Λ = SVector{Nx}(0. for i=1:Nx) X = (SVector{Nx}(1. for i=1:Nx),) @@ -69,7 +69,7 @@ d = Muscade.doflist(typeof(el)) Nx,Nu,Na = 3,0+1,2 Nz = 2Nx+Nu+Na iλ,ix,iu,ia = Muscade.gradientpartition(Nx,Nx,Nu,Na) -ΔZ = δ{1,Nz,𝕣}() +ΔZ = Muscade.δ_{1,Nz,𝕣}() ΔΛ,ΔX,ΔU,ΔA = view(ΔZ,iλ),view(ΔZ,ix),view(ΔZ,iu),view(ΔZ,ia) Λ = SVector{Nx}(0. for i=1:Nx) X = (SVector{Nx}(1. for i=1:Nx),) diff --git a/test/TestFreqXU.jl b/test/TestFreqXU.jl index c91d89d2..b936c775 100644 --- a/test/TestFreqXU.jl +++ b/test/TestFreqXU.jl @@ -55,7 +55,7 @@ dof = getdof(state,field=:tx1) # end @testset "output" begin - @test dof[1,1:100:end] ≈ [-0.0008522224876621403, 0.09549942165460336, -0.05008960568585242, -0.06878034794799491, 0.08677879820843742, 0.02249032282693445, -0.09877571024378282, 0.030199161274387067, 0.08266670708994063, -0.07429569207304236, -0.043035489287326145] rtol=1e-10 + @test dof[1,1:100:end] ≈ [-0.0008522224876621403, 0.09549942165460336, -0.05008960568585242, -0.06878034794799491, 0.08677879820843742, 0.02249032282693445, -0.09877571024378282, 0.030199161274387067, 0.08266670708994063, -0.07429569207304236, -0.043035489287326145] rtol=1e-10 @test dof[2,1:100:end] ≈ [ 0.09808063976613206, -0.026980709523268566, -0.08368844089497145, 0.07162225920301411, 0.045483300397735474, -0.09588421213929227, 0.005663784838222031, 0.09286300479539936, -0.05519928099099323, -0.06341829990791986, 0.0890282202766159] rtol=1e-10 end diff --git a/test/TestNewmarkSweep.jl b/test/TestNewmarkSweep.jl index b0714616..098934f3 100644 --- a/test/TestNewmarkSweep.jl +++ b/test/TestNewmarkSweep.jl @@ -1,4 +1,4 @@ -#module TestNewmarkSweep +module TestNewmarkSweep using Muscade,Test,StaticArrays K = 1. @@ -79,14 +79,14 @@ end @test x″ ≈ y″ end -using GLMakie -fig = Figure(size = (1000,750)) -axe = Axis(fig[1,1],title="Test",xlabel="time",ylabel="x") -display(fig) -lines!( axe,Δt*(1:n),x , linewidth = 1,color=:black) -lines!( axe,Δt*(1:n),y , linewidth = 1,color=:red ) +# using GLMakie +# fig = Figure(size = (1000,750)) +# axe = Axis(fig[1,1],title="Test",xlabel="time",ylabel="x") +# display(fig) +# lines!( axe,Δt*(1:n),x , linewidth = 1,color=:black) +# lines!( axe,Δt*(1:n),y , linewidth = 1,color=:red ) -#end +end diff --git a/test/TestRigidBodyKinematics.jl b/test/TestRigidBodyKinematics.jl new file mode 100644 index 00000000..7f57873b --- /dev/null +++ b/test/TestRigidBodyKinematics.jl @@ -0,0 +1,56 @@ +module TestRigidBodyKinematics + +using Test, Muscade, Muscade.Toolbox, StaticArrays, LinearAlgebra + + model = Model(:TestModel) + master_node = addnode!(model, 𝕣[0., 0., 0.]) + emissary_node = addnode!(model, 𝕣[1/√2, 1/√2, 0.]) + ERCelement = ExcentricRigidConnection(model.nod) + +@testset "constructor" begin + dofs = Muscade.doflist(typeof(ERCelement)) + @test dofs.inod == (2, 2, 1, 1, 1, 2, 2) + @test dofs.class == (:X, :X, :X, :X, :X, :X, :X) + @test dofs.field == (:λt1, :λt2, :t1, :t2, :r3, :t1, :t2) + @test ERCelement.gargs[1] ≈ π/4 + @test ERCelement.gargs[2] ≈ 1.0 +end + +U = SVector{0,𝕣}() +A = SVector{0,𝕣}() +t,SP,dbg = 0.,(;),(status=:testing,) +δt1m, δt2m, δr3m = 0., 1., π/4; +δt1e, δt2e = -1/√2, 2-1/√2; +x0 = SVector(0.,0.,δt1m, δt2m, δr3m, δt1e, δt2e) +R,FB = Muscade.residual(ERCelement, (x0,),(U,),A, t,SP,dbg) +@testset "residual" begin + @test R ≈ [0., 0., 0., 0., 0., 0., 0.] atol=10*eps() +end + + +zsv7 = SVector(0.,0., 0.,0.,0., 0.,0.) +X = ntuple(i->zsv7, 7) +U = (SVector{0,𝕣}(),) +A = SVector{0,Float64}() +out = Muscade.diffed_residual(ERCelement; X,U,A) +K = out.∇R[2][1] +# Muscade.print_element_array(ERCelement,:X,K) +@testset "diffed residual" begin + @test K[1,3] ≈ 1. + @test K[1,4] ≈ 0. + @test K[1,5] ≈ -√2/2 + @test K[1,6] ≈ -1. + @test K[1,7] ≈ 0. + + @test K[2,3] ≈ 0. + @test K[2,4] ≈ 1. + @test K[2,5] ≈ √2/2 + @test K[2,6] ≈ 0. + @test K[2,7] ≈ -1. + + @test norm(K[1:2,1:2]) ≈ 0. + @test norm(K[3:7,3:7]) ≈ 0. +end + + +end \ No newline at end of file diff --git a/test/TestRotations.jl b/test/TestRotations.jl index 25f33f7a..60d122ba 100644 --- a/test/TestRotations.jl +++ b/test/TestRotations.jl @@ -3,14 +3,6 @@ module TestRotations using Test, StaticArrays, LinearAlgebra using Muscade, Muscade.Toolbox -θ = [0,1e-8,1e-6,1e-2,.1,1,π] -@testset "sinc1" begin - @test Toolbox.sinc1.( θ)≈[1.0,1.0,0.9999999999998334,0.9999833334166666,0.9983341664682817,0.8414709848078965,0.0] - @test Toolbox.sinc1′.(θ)≈[ 0.0,-3.3333333333333334e-9,-3.3333333333329995e-7,-0.003333300000107897,-0.03330001190255594,-0.30116867893975674,-0.3183098861837907] - @test Toolbox.sinc1″.(θ)≈[-0.3333333333333333, -0.3333333333333333, -0.33333333333323334, -0.33332333339285697, -0.33233392841710757, -0.23913362692838303, 0.20264236728467552] - @test Toolbox.sinc1‴.(θ)≈[0.0, 2.0e-9, 1.999999999999762e-7, 0.001999976190568783, 0.019976199733646196, 0.1770985749170091, 0.12480067958459377] - @test Toolbox.sinc1⁗.(θ)≈[0.2,0.2,0.1999999999999286,0.19999285718915333,0.19928617712243368,0.13307670326700266,-0.14309499132952147] -end # using GLMakie # fig = Figure(size = (1200,1000)) # display(fig) # open interactive window (gets closed down by "save") @@ -29,27 +21,27 @@ end # end function scac1(x) - X = variate{1}(x) + X = Muscade.variate_{1}(x) Y = Toolbox.scac(X) return ∂{1}(Y) end function scac2(x) - X = variate{2}(variate{1}(x)) + X = Muscade.variate_{2}(Muscade.variate_{1}(x)) Y = Toolbox.scac(X) return ∂{1}(∂{2}(Y)) end function scac3(x) - X = variate{3}(variate{2}(variate{1}(x))) + X = Muscade.variate_{3}(Muscade.variate_{2}(Muscade.variate_{1}(x))) Y = Toolbox.scac(X) return ∂{1}(∂{2}(∂{3}(Y))) end function scac4(x) - X = variate{4}(variate{3}(variate{2}(variate{1}(x)))) + X = Muscade.variate_{4}(Muscade.variate_{3}(Muscade.variate_{2}(Muscade.variate_{1}(x)))) Y = Toolbox.scac(X) return ∂{1}(∂{2}(∂{3}(∂{4}(Y)))) end function scac5(x) - X = variate{5}(variate{4}(variate{3}(variate{2}(variate{1}(x))))) + X = Muscade.variate_{5}(Muscade.variate_{4}(Muscade.variate_{3}(Muscade.variate_{2}(Muscade.variate_{1}(x))))) Y = Toolbox.scac(X) return ∂{1}(∂{2}(∂{3}(∂{4}(∂{5}(Y))))) end @@ -86,15 +78,15 @@ r = Toolbox.adjust(a,b) R = Toolbox.Rodrigues(r) u = R*a -v1 = variate{1,3}(SA[.1,.2,.3]) +v1 = Muscade.variate_{1,3}(SA[.1,.2,.3]) M1 = Toolbox.Rodrigues(v1) w1,w∂v1 = value_∂{1,3}(Toolbox.Rodrigues⁻¹(M1)) -v2 = variate{1,3}(SA[1e-7,2e-7,1e-8]) +v2 = Muscade.variate_{1,3}(SA[1e-7,2e-7,1e-8]) M2 = Toolbox.Rodrigues(v2) w2,w∂v2 = value_∂{1,3}(Toolbox.Rodrigues⁻¹(M2)) -v3 = variate{1,3}(SA[0.,0.,0.]) +v3 = Muscade.variate_{1,3}(SA[0.,0.,0.]) M3 = Toolbox.Rodrigues(v3) w3,w∂v3 = value_∂{1,3}(Toolbox.Rodrigues⁻¹(M3)) diff --git a/test/TestScale.jl b/test/TestScale.jl index a5f5f6f0..bc1081b8 100644 --- a/test/TestScale.jl +++ b/test/TestScale.jl @@ -49,10 +49,10 @@ end scale=Muscade.study_scale(stateX1[end],verbose=false) # scaling suggestions from looking at a state @testset "study_scale" begin - @test scale.Λ.tx1 ≈ 1900.0 - @test scale.Λ.tx2 ≈ 1900.0 - @test scale.X.λtx2 ≈ 0.00052 + @test scale.Λ.tx1 ≈ 81000.0 + @test scale.Λ.tx2 ≈ 81000.0 + @test scale.X.λtx2 ≈ 1.2e-5 @test scale.U == (;) - @test scale.A.ΞL₀ ≈ 8.3e-5 + @test scale.A.ΞL₀ ≈ 6.3e-7 end end diff --git a/test/TestSweepXA0.jl b/test/TestSweepXA0.jl deleted file mode 100644 index 78849d4b..00000000 --- a/test/TestSweepXA0.jl +++ /dev/null @@ -1,43 +0,0 @@ -#module TestSweepXA0 -using Test -using Muscade - - -include("SomeElements.jl") -#include("../examples/DryFriction.jl") - - -K,C,M = 1.,.3,0. - -model = Model(:TestModel) -node = addnode!(model,𝕣[]) -osc = addelement!(model,AdjustableSdofOscillator,[node]; K,C,M) - -@functor with( ) acost(a,σ)=(a/σ)^2 -@functor with(σ=.1) xcost(x,t)=(x/σ)^2 -@functor with( ) xload( t)= .5cos(3t) -# cK = addelement!(model,SingleAcost ,[node]; field=:ΞK,costargs=(.2,),cost =acost) -#cX = addelement!(model,SingleDofCost,[node];class=:X ,field=:tx1, cost =xcost) -#cF = addelement!(model,DofLoad ,[node]; field=:tx1, value=xload) - -initialstate = initialize!(model;time=0.) -x,x′,x″ = 0.3,1.,0. -initialstate = setdof!(initialstate,[x′];field=:tx1,nodID=[node],order=1) # initial speed - -t = .1:.1:4π -state = solve(SweepX{2}; initialstate,time=t) -#state = solve(SweepXA{1}; initialstate,time= t,verbose=true,catcherror=true,maxAiter=100) - -x = [state[i].X[1][1] for i = 1:length(t)] -#λ = [state[i].Λ[1][1] for i = 1:length(t)] - - -using GLMakie - -fig = Figure(size = (600,450)) -display(fig) # open interactive window (gets closed down by "save") -axe = Axis(fig[1,1],title="Test",xlabel="t") -ox = lines!( axe,t,x ,color = :black, linewidth = 1.) -#oλ = lines!( axe,t,λ/100,color = :red, linewidth = 1.) -#@show state[1].A[1] -;#end diff --git a/test/TestTaylor.jl b/test/TestTaylor.jl index 4100aaef..7de7812f 100644 --- a/test/TestTaylor.jl +++ b/test/TestTaylor.jl @@ -5,65 +5,79 @@ using Test,StaticArrays const X1 = (SVector{3,𝕣}(1,2,3),) const X2 = (SVector{3,𝕣}(1,2,3),SVector{3,𝕣}(4,5,6)) const X3 = (SVector{3,𝕣}(1,2,3),SVector{3,𝕣}(4,5,6),SVector{3,𝕣}(7,8,9)) -const X4 = (variate{1,3}(SVector{3,𝕣}(1,2,3)),) -const X5 = (variate{1,3}(SVector{3,𝕣}(1,2,3)),variate{1,3}(SVector{3,𝕣}(4,5,6))) -const X6 = (variate{1,3}(SVector{3,𝕣}(1,2,3)),variate{1,3}(SVector{3,𝕣}(4,5,6)),variate{1,3}(SVector{3,𝕣}(7,8,9))) - -Y1=motion{2}(X1) -Y2=motion{2}(X2) -Y3=motion{2}(X3) -Y4=motion{3}(X4) -Y5=motion{3}(X5) -Y6=motion{3}(X6) +const X4 = (Muscade.variate_{1,3}(SVector{3,𝕣}(1,2,3)),) +const X5 = (Muscade.variate_{1,3}(SVector{3,𝕣}(1,2,3)),Muscade.variate_{1,3}(SVector{3,𝕣}(4,5,6))) +const X6 = (Muscade.variate_{1,3}(SVector{3,𝕣}(1,2,3)),Muscade.variate_{1,3}(SVector{3,𝕣}(4,5,6)),Muscade.variate_{1,3}(SVector{3,𝕣}(7,8,9))) + +P1,ND1,Y1 = motion(X1) +P2,ND2,Y2 = motion(X2) +P3,ND3,Y3 = motion(X3) +P4,ND4,Y4 = motion(X4) +P5,ND5,Y5 = motion(X5) +P6,ND6,Y6 = motion(X6) + +Z1 = motion⁻¹{P1,ND1}(Y1) +Z2 = motion⁻¹{P2,ND2}(Y2) +Z3 = motion⁻¹{P3,ND3}(Y3) +Z4 = motion⁻¹{P4,ND4}(Y4) +Z5 = motion⁻¹{P5,ND5}(Y5) +Z6 = motion⁻¹{P6,ND6}(Y6) @testset "motion" begin @test typeof(X1) == Tuple{SVector{3, 𝕣}} @test typeof(Y1) == SVector{3, 𝕣} @test typeof(X2) == Tuple{SVector{3, 𝕣}, SVector{3, 𝕣}} - @test typeof(Y2) == SVector{3, ∂ℝ{2, 1, 𝕣}} + @test typeof(Y2) == SVector{3, ∂ℝ{1, 1, 𝕣}} @test typeof(X3) == Tuple{SVector{3, 𝕣}, SVector{3, 𝕣}, SVector{3, 𝕣}} - @test typeof(Y3) == SVector{3, ∂ℝ{3, 1, ∂ℝ{2, 1, 𝕣}}} + @test typeof(Y3) == SVector{3, ∂ℝ{2, 1, ∂ℝ{1, 1, 𝕣}}} @test typeof(X4) == Tuple{SVector{3, ∂ℝ{1, 3, 𝕣}}} @test typeof(Y4) == SVector{3, ∂ℝ{1, 3, 𝕣}} @test typeof(X5) == Tuple{SVector{3, ∂ℝ{1, 3, 𝕣}}, SVector{3, ∂ℝ{1, 3, 𝕣}}} - @test typeof(Y5) == SVector{3, ∂ℝ{3, 1, ∂ℝ{1, 3, 𝕣}}} + @test typeof(Y5) == SVector{3, ∂ℝ{2, 1, ∂ℝ{1, 3, 𝕣}}} @test typeof(X6) == Tuple{SVector{3, ∂ℝ{1, 3, 𝕣}}, SVector{3, ∂ℝ{1, 3, 𝕣}}, SVector{3, ∂ℝ{1, 3, 𝕣}}} - @test typeof(Y6) == SVector{3, ∂ℝ{4, 1, ∂ℝ{3, 1, ∂ℝ{1, 3, 𝕣}}}} + @test typeof(Y6) == SVector{3, ∂ℝ{3, 1, ∂ℝ{2, 1, ∂ℝ{1, 3, 𝕣}}}} end @testset "motion⁻¹" begin - @test motion⁻¹{2,1,0}(Y1) === SVector{3,𝕣}(1,2,3) - @test motion⁻¹{2,1,1}(Y1) === SVector{3,𝕣}(0,0,0) - @test motion⁻¹{2,1,2}(Y1) === SVector{3,𝕣}(0,0,0) - - @test motion⁻¹{2,2,0}(Y2) === SVector{3,𝕣}(1,2,3) - @test motion⁻¹{2,2,1}(Y2) === SVector{3,𝕣}(4,5,6) - @test motion⁻¹{2,2,2}(Y2) === SVector{3,𝕣}(0,0,0) - - @test motion⁻¹{2,3,0}(Y3) === SVector{3,𝕣}(1,2,3) - @test motion⁻¹{2,3,1}(Y3) === SVector{3,𝕣}(4,5,6) - @test motion⁻¹{2,3,2}(Y3) === SVector{3,𝕣}(7,8,9) - - @test motion⁻¹{3,1,0}(Y4) === variate{1,3}(SVector{3,𝕣}(1,2,3)) - @test motion⁻¹{3,1,1}(Y4) === SVector{3,𝕣}(0,0,0) - @test motion⁻¹{3,1,2}(Y4) === SVector{3,𝕣}(0,0,0) - - @test motion⁻¹{3,2,0}(Y5) === variate{1,3}(SVector{3,𝕣}(1,2,3)) - @test motion⁻¹{3,2,1}(Y5) === variate{1,3}(SVector{3,𝕣}(4,5,6)) - @test motion⁻¹{3,2,2}(Y5) === SVector{3,𝕣}(0,0,0) - - @test motion⁻¹{3,3,0}(Y6) === variate{1,3}(SVector{3,𝕣}(1,2,3)) - @test motion⁻¹{3,3,1}(Y6) === variate{1,3}(SVector{3,𝕣}(4,5,6)) - @test motion⁻¹{3,3,2}(Y6) === variate{1,3}(SVector{3,𝕣}(7,8,9)) - - @test motion⁻¹{2,1}(Y1) === (SVector{3,𝕣}(1,2,3),) - @test motion⁻¹{2,2}(Y2) === (SVector{3,𝕣}(1,2,3),SVector{3,𝕣}(4,5,6)) - @test motion⁻¹{2,3}(Y3) === (SVector{3,𝕣}(1,2,3),SVector{3,𝕣}(4,5,6),SVector{3,𝕣}(7,8,9)) + @test Z1===X1 + @test Z2===X2 + @test Z3===X3 + @test Z4===X4 + @test Z5===X5 + @test Z6===X6 + + @test motion⁻¹{P1,ND1,0}(Y1) === SVector{3,𝕣}(1,2,3) + @test motion⁻¹{P1,ND1,1}(Y1) === SVector{3,𝕣}(0,0,0) + @test motion⁻¹{P1,ND1,2}(Y1) === SVector{3,𝕣}(0,0,0) + + @test motion⁻¹{P2,ND2,0}(Y2) === SVector{3,𝕣}(1,2,3) + @test motion⁻¹{P2,ND2,1}(Y2) === SVector{3,𝕣}(4,5,6) + @test motion⁻¹{P2,ND2,2}(Y2) === SVector{3,𝕣}(0,0,0) + + @test motion⁻¹{P3,ND3,0}(Y3) === SVector{3,𝕣}(1,2,3) + @test motion⁻¹{P3,ND3,1}(Y3) === SVector{3,𝕣}(4,5,6) + @test motion⁻¹{P3,ND3,2}(Y3) === SVector{3,𝕣}(7,8,9) + + @test motion⁻¹{P4,ND4,0}(Y4) === Muscade.variate_{1,3}(SVector{3,𝕣}(1,2,3)) + @test motion⁻¹{P4,ND4,1}(Y4) === SVector{3,𝕣}(0,0,0) + @test motion⁻¹{P4,ND4,2}(Y4) === SVector{3,𝕣}(0,0,0) + + @test motion⁻¹{P5,ND5,0}(Y5) === Muscade.variate_{1,3}(SVector{3,𝕣}(1,2,3)) + @test motion⁻¹{P5,ND5,1}(Y5) === Muscade.variate_{1,3}(SVector{3,𝕣}(4,5,6)) + @test motion⁻¹{P5,ND5,2}(Y5) === SVector{3,𝕣}(0,0,0) + + @test motion⁻¹{P6,ND6,0}(Y6) === Muscade.variate_{1,3}(SVector{3,𝕣}(1,2,3)) + @test motion⁻¹{P6,ND6,1}(Y6) === Muscade.variate_{1,3}(SVector{3,𝕣}(4,5,6)) + @test motion⁻¹{P6,ND6,2}(Y6) === Muscade.variate_{1,3}(SVector{3,𝕣}(7,8,9)) + + @test motion⁻¹{P1,ND1}(Y1) === (SVector{3,𝕣}(1,2,3),) + @test motion⁻¹{P2,ND2}(Y2) === (SVector{3,𝕣}(1,2,3),SVector{3,𝕣}(4,5,6)) + @test motion⁻¹{P3,ND3}(Y3) === (SVector{3,𝕣}(1,2,3),SVector{3,𝕣}(4,5,6),SVector{3,𝕣}(7,8,9)) end a = SVector(3.,4.) @@ -80,20 +94,21 @@ h(X) = SVector(3.,4.) k(X) = 5. w(X) = (f(X),g(X),h(X),k(X)) X₀ = SVector(0.,0.,1.) -vX₀ = variate{1,3}(X₀) - +vX₀ = Muscade.variate_{1,3}(X₀) +wX₀ = Muscade.variate_{2,3}(vX₀) @testset "Muscade.fast" begin @test Muscade.apply{:chainrule}(w, X₀) === w( X₀) @test Muscade.apply{:chainrule}(w,vX₀) === w(vX₀) + @test Muscade.apply{:chainrule}(w,wX₀) === w(wX₀) end -yy = Muscade.to_order{1}((revariate{1}(SVector(4.,5.,6.)),revariate{2}(SVector(7.,8.,9.)) )) +yy = Muscade.to_order{1,3}((revariate{1}(SVector(4.,5.,6.)),revariate{2}(SVector(7.,8.,9.)) )) @testset "firstorderonly" begin @test yy[1] === revariate{1}(SVector(4.,5.,6.)) @test yy[2] === revariate{1}(SVector(7.,8.,9.)) - @test Muscade.to_order{0}(3.) == 3.0 - @test Muscade.to_order{1}(3.) == ∂ℝ{1, 0, Float64}(3.0, Float64[]) - @test Muscade.to_order{2}(3.) == ∂ℝ{2, 0, ∂ℝ{1, 0, Float64}}(∂ℝ{1, 0, Float64}(3.0, Float64[]), ∂ℝ{1, 0, Float64}[]) + @test Muscade.to_order{0,0}(3.) == 3.0 + @test Muscade.to_order{1,0}(3.) == ∂ℝ{1, 0, 𝕣}(3.0, 𝕣[]) + @test Muscade.to_order{2,0}(3.) == ∂ℝ{2, 0, ∂ℝ{1, 0, 𝕣}}(∂ℝ{1, 0, 𝕣}(3.0, 𝕣[]), ∂ℝ{1, 0, 𝕣}[]) end @@ -101,7 +116,7 @@ end #### chainrule with NamedTuple x = SVector(1.,2.,2.5,3.) -X = variate{1,4}(x) +X = Muscade.variate_{1,4}(x) ε = SMatrix{2,2}((X.^2)...) eleres = (part=(ε = ε, x = X), y = 2x[2],z = 3.) @@ -126,43 +141,118 @@ end # 10: Neleres Releres = Muscade.revariate{2}(eleres) Rq = cost(Releres) -q = Muscade.chainrule(Rq,Muscade.to_order{2}(eleres)) # TODO this hangs. verify the output of to_order{2}(eleres) carefully. There are empty partials. -q2 = cost(Muscade.to_order{2}(eleres)) +q = Muscade.chainrule(Rq,Muscade.to_order{2,4}(eleres)) +q2 = cost(Muscade.to_order{2,4}(eleres)) @testset "chainrule NamedTuple" begin @test Muscade.flat_eltype(Muscade.revariate{2}(eleres)) == ∂ℝ{2, 10, ∂ℝ{1, 10, 𝕣}} @test Muscade.flat_eltype(Rq) == ∂ℝ{2, 10, ∂ℝ{1, 10, 𝕣}} @test Muscade.flat_eltype(q) == ∂ℝ{2, 4 , ∂ℝ{1, 4 , 𝕣}} - @test Muscade.flat_eltype(Muscade.to_order{2}(eleres)) == ∂ℝ{2, 4 , ∂ℝ{1, 4 , 𝕣}} + @test Muscade.flat_eltype(Muscade.to_order{2,4}(eleres)) == ∂ℝ{2, 4 , ∂ℝ{1, 4 , 𝕣}} @test Muscade.flat_eltype(q2) == ∂ℝ{2, 4 , ∂ℝ{1, 4 , 𝕣}} @test q == q2 end @testset "inferred" begin - @inferred Muscade.revariate{2}(eleres) - @inferred Muscade.to_order{2}(Muscade.flatten(eleres)) - @inferred Muscade.chainrule(Rq,Muscade.to_order{2}(Muscade.flatten(eleres))) + @inferred revariate{2}(eleres) + @inferred Muscade.to_order{2,4}(Muscade.flatten(eleres)) + @inferred Muscade.chainrule(Rq,Muscade.to_order{2,4}(Muscade.flatten(eleres))) end -X = (SVector(1.,2.),SVector(3.,4.)) -U = SVector(5.,6.,7.) -scale = (X=SVector(10.,10.),U=SVector(2.,2.,2.)) -d = Muscade.revariate{2}((;X,U),scale) - -@testset "scaled revariate" begin - @test typeof(d) == @NamedTuple{X::Tuple{SVector{2,∂ℝ{2,7,∂ℝ{1,7,𝕣}}}, SVector{2,∂ℝ{2,7,∂ℝ{1,7,𝕣}}}}, U::SVector{3,∂ℝ{2,7,∂ℝ{1,7,𝕣}}}} - @test d.X[2][2] === ∂ℝ{2,7,∂ℝ{1,7,𝕣}}(∂ℝ{1,7,𝕣}(4.0,[0.0,0.0,0.0,10.,0.0,0.0,0.0]), - ∂ℝ{1,7,𝕣}[∂ℝ{1,7,𝕣}(0.0,[0.0,0.0,0.0,0.0,0.0,0.0,0.0]), - ∂ℝ{1,7,𝕣}(0.0,[0.0,0.0,0.0,0.0,0.0,0.0,0.0]), - ∂ℝ{1,7,𝕣}(0.0,[0.0,0.0,0.0,0.0,0.0,0.0,0.0]), - ∂ℝ{1,7,𝕣}(10.,[0.0,0.0,0.0,0.0,0.0,0.0,0.0]), - ∂ℝ{1,7,𝕣}(0.0,[0.0,0.0,0.0,0.0,0.0,0.0,0.0]), - ∂ℝ{1,7,𝕣}(0.0,[0.0,0.0,0.0,0.0,0.0,0.0,0.0]), - ∂ℝ{1,7,𝕣}(0.0,[0.0,0.0,0.0,0.0,0.0,0.0,0.0])]) +@testset "multiple derivative" begin + a = SVector(1.,2.,3.) + b = SVector(3.,4.) + Pa,Na,A = variate{2}(a) + Pb,Nb,B = variate(b) # A and B not compatible + _ ,_ ,C = variate{2}(a,scale=AllElements(2.)) + _ ,_ ,D = variate{2}(a,scale=SVector(2.,2.,2.)) + A0 = Muscade.zerovalue(A[1]) + + @test Muscade.npartials((a=A,b=b)) == (3,3) + @test_throws AssertionError Muscade.npartials((a=A,b=B)) + + @test Pa==2 + @test Na==3 + @test A0 ===∂ℝ{2,3,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(0,[1,0,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(1,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0])]) + @test A[1]===∂ℝ{2,3,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(1,[1,0,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(1,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0])]) + @test A[2]===∂ℝ{2,3,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(2,[0,1,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(1,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0])]) + @test A[3]===∂ℝ{2,3,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(3,[0,0,1]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(1,[0,0,0])]) + @test Pb==1 + @test Nb==2 + @test B[1]===∂ℝ{1,2,𝕣}(3,[1,0]) + @test B[2]===∂ℝ{1,2,𝕣}(4,[0,1]) + @test C[1]===∂ℝ{2,3,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(1,[2,0,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(2,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0])]) + @test C[2]===∂ℝ{2,3,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(2,[0,2,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(2,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0])]) + @test C[3]===∂ℝ{2,3,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(3,[0,0,2]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(2,[0,0,0])]) + @test D[1]===∂ℝ{2,3,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(1,[2,0,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(2,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0])]) + @test D[2]===∂ℝ{2,3,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(2,[0,2,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(2,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0])]) + @test D[3]===∂ℝ{2,3,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(3,[0,0,2]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(2,[0,0,0])]) end +@testset "joint derivative" begin + a = SVector(1.,2.,3.) + b = SVector(3.,4.) + P,N,(A,B) = variate((a,b)) - + @test P==1 + @test N==5 + @test A[1]===∂ℝ{1,5,𝕣}(1,[1,0,0,0,0]) + @test A[2]===∂ℝ{1,5,𝕣}(2,[0,1,0,0,0]) + @test A[3]===∂ℝ{1,5,𝕣}(3,[0,0,1,0,0]) + @test B[1]===∂ℝ{1,5,𝕣}(3,[0,0,0,1,0]) + @test B[2]===∂ℝ{1,5,𝕣}(4,[0,0,0,0,1]) +end + +@testset "nested derivative" begin + a = SVector(1.,2.,3.) + b = SVector(3.,4.) + Pa,Na,A = variate{1}(a) + Pb,Nb,B = variate{1}(b,context=(A,0.)) + _ ,_ ,Bs = variate{1}(b,context=A,scale=AllElements(2.)) + + Pb0,Nb0,B0 = variate0{1}(b,context=A) + @test Pb==2 + @test Nb==2 + @test B[1]===∂ℝ{2,2,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(3,[0,0,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(1,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0])]) + @test B[2]===∂ℝ{2,2,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(4,[0,0,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(1,[0,0,0])]) + @test Muscade.npartials(B)==(2,3) + + @test Pb0==2 + @test Nb0==2 + @test B0[1]===∂ℝ{2,2,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(1,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0])]) + @test B0[2]===∂ℝ{2,2,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(1,[0,0,0])]) + + @test Bs[1]===∂ℝ{2,2,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(3,[0,0,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(2,[0,0,0]),∂ℝ{1,3,𝕣}(0,[0,0,0])]) + @test Bs[2]===∂ℝ{2,2,∂ℝ{1,3,𝕣}}(∂ℝ{1,3,𝕣}(4,[0,0,0]),∂ℝ{1,3,𝕣}[∂ℝ{1,3,𝕣}(0,[0,0,0]),∂ℝ{1,3,𝕣}(2,[0,0,0])]) +end + +@testset "revariate" begin + a = SVector(1.,2.,3.) + b = SVector(3.,4.) + P,N,(A,B) = variate{2}((a,b),scale=AllElements(AllElements(2.))) + B_ = revariate(B) + Bm1 = revariate{1}(B) + A2,B2 = revariate((A,B)) + @test B_[1]===∂ℝ{2,2,∂ℝ{1,2,𝕣}}(∂ℝ{1,2,𝕣}(3,[1,0]),∂ℝ{1,2,𝕣}[∂ℝ{1,2,𝕣}(1,[0,0]),∂ℝ{1,2,𝕣}(0,[0,0])]) + @test B_[2]===∂ℝ{2,2,∂ℝ{1,2,𝕣}}(∂ℝ{1,2,𝕣}(4,[0,1]),∂ℝ{1,2,𝕣}[∂ℝ{1,2,𝕣}(0,[0,0]),∂ℝ{1,2,𝕣}(1,[0,0])]) + @test B2[1]==∂ℝ{2,5,∂ℝ{1,5,𝕣}}(∂ℝ{1,5,𝕣}(3,[0,0,0,1,0]),∂ℝ{1,5,𝕣}[∂ℝ{1,5,𝕣}(0,[0,0,0,0,0]),∂ℝ{1,5,𝕣}(0,[0,0,0,0,0]),∂ℝ{1,5,𝕣}(0,[0,0,0,0,0]),∂ℝ{1,5,𝕣}(1,[0,0,0,0,0]),∂ℝ{1,5,𝕣}(0,[0,0,0,0,0])]) + @test Bm1[1]===∂ℝ{1,2,𝕣}(3,[1,0]) +end + +@testset "chainrule_Jacobian" begin + x = SVector(1.,2.,3.) + u = SVector(4.,5.) + P,N,(X,U) = variate{2}((x,u)) + TX1 = revariate{1}(X) + TY1 = TX1.^2 + Y∂X1 = chainrule_Jacobian(TY1,X) + TX2 = revariate(X) # revariate{2}, implicit + TY2 = TX2.^2 + Y∂X2 = chainrule_Jacobian(TY2,X) + + @test Y∂X1 === SMatrix{3,3,𝕣}(2,0,0, 0,4,0, 0,0,6) + @test Y∂X2[1,1] === ∂ℝ{2,5,∂ℝ{1,5,𝕣}}(∂ℝ{1,5,𝕣}(2,[2,0,0,0,0]),∂ℝ{1,5,𝕣}[∂ℝ{1,5,𝕣}(2,[0,0,0,0,0]),∂ℝ{1,5,𝕣}(0,[0,0,0,0,0]),∂ℝ{1,5,𝕣}(0,[0,0,0,0,0]),∂ℝ{1,5,𝕣}(0,[0,0,0,0,0]),∂ℝ{1,5,𝕣}(0,[0,0,0,0,0])]) +end end # module diff --git a/test/run_CI_tests.jl b/test/run_CI_tests.jl index 7a8c31e9..f0dad3d1 100644 --- a/test/run_CI_tests.jl +++ b/test/run_CI_tests.jl @@ -29,6 +29,7 @@ include(joinpath(workingDir,"ModalBeamAnalysis.jl")) include(joinpath(workingDir,"DynamicBeamAnalysis.jl")) include(joinpath(workingDir,"DecayAnalysis.jl")) include(joinpath(workingDir,"DryFriction.jl")) +include(joinpath(workingDir,"TuningFork.jl")) # generate documentation workingDir = joinpath(muscadeDir,"docs") diff --git a/toolbox/BarElement.jl b/toolbox/BarElement.jl index 290aad8d..b65bbc57 100644 --- a/toolbox/BarElement.jl +++ b/toolbox/BarElement.jl @@ -1,6 +1,7 @@ # # Bar element using StaticArrays, LinearAlgebra, Muscade +@functor with() g̃_default(t) = SVector(0.,0.,1.); """ AxisymmetricBarCrossSection @@ -11,6 +12,8 @@ Data structure containing the cross section material properties, for example to - `μ :: 𝕣` is the mass per unit length [kg/m] # Optional argument to the constructor (all set to zero by default) +- `w :: 𝕣` is the weight per unit length [N/m] +- `g̃ :: Functor` describes the gravity field divided by acceleration of gravity [-], function of time, set to SVector(0.,0.,1.) by default - `Caₜ :: 𝕣` is the tangential added mass per unit length [kg/m] - `Clₜ :: 𝕣` is the tangential linear damping coefficient per unit length [N/m/(m/s)] - `Cqₜ :: 𝕣` is the tangential quadratic damping coefficient per unit length [N/m/(m/s)^2], for example from drag @@ -31,19 +34,19 @@ mat = AxisymmetricBarCrossSection(EA=EA,μ=μ) See also: [`Bar3D`](@ref), [`EulerBeam3D`](@ref) """ -struct AxisymmetricBarCrossSection - EA :: 𝕣 # Axial stiffness [N] - μ :: 𝕣 # Mass per unit length [kg/m] - w :: 𝕣 # Weight per unit length [N/m] - Caₜ :: 𝕣 # Tangential added mass per unit length [kg/m] - Clₜ :: 𝕣 # Tangential linear damping coefficient per unit length [N/m/(m/s)] - Cqₜ :: 𝕣 # Tangential quadratic damping coefficient per unit length [N/m/(m/s)^2], for example from drag - Caₙ :: 𝕣 # Normal added mass per unit length [kg/m] - Clₙ :: 𝕣 # Normal linear damping coefficient per unit length [N/m/(m/s)] - Cqₙ :: 𝕣 # Normal quadratic damping coefficient per unit length [N/m/(m/s)^2], - # TODO: add gravity field to bar properties (time dependent), and use it to compute the weight. This to enable static analyses. +struct AxisymmetricBarCrossSection{Tg̃} + EA :: 𝕣 + μ :: 𝕣 + w :: 𝕣 + g̃ :: Tg̃ # a functor + Caₜ :: 𝕣 + Clₜ :: 𝕣 + Cqₜ :: 𝕣 + Caₙ :: 𝕣 + Clₙ :: 𝕣 + Cqₙ :: 𝕣 end -AxisymmetricBarCrossSection(;EA,μ,w=0.,Caₜ=0.,Clₜ=0.,Cqₜ=0.,Caₙ=0.,Clₙ=0.,Cqₙ=0.) = AxisymmetricBarCrossSection(EA,μ,w,Caₜ,Clₜ,Cqₜ,Caₙ,Clₙ,Cqₙ); +AxisymmetricBarCrossSection(;EA,μ,w=0.,g̃=g̃_default,Caₜ=0.,Clₜ=0.,Cqₜ=0.,Caₙ=0.,Clₙ=0.,Cqₙ=0.) = AxisymmetricBarCrossSection(EA,μ,w,g̃,Caₜ,Clₜ,Cqₜ,Caₙ,Clₙ,Cqₙ); const ngp = 4 # Number of Gauss points const ndim = 3 # Number of dimensions @@ -137,8 +140,8 @@ end; v,a = ∂1(x),∂2(x) # Inertia force fi = o.μ * a - # Weight (applied progressively from t=-10 to t=-5) - fw = SVector(0,0,(min(t,-5.)+10)/5 * o.w) + # Weight + fw = - o.w * o.g̃(t) # Added mass aₜ = a ∘₁ δ # Tangential acceleration (scalar) aₙ = a - aₜ * δ # Normal acceleration (vector) @@ -160,19 +163,19 @@ end; # Define now the residual function for the Bar3D element. @espy function Muscade.residual(o::Bar3D{Mat,Udof}, X,U,A,t,SP,dbg) where{Mat,Udof} # Obtain motions (i.e. including velocity and accelerations) from X - P,ND = constants(X),length(X) - x_ = motion{P}(X) + P,ND,x_ = motion(X) # Motions of the nodes, center of the element uᵧ₁,uᵧ₂ = vec3(x_,1:3), vec3(x_,4:6) c = o.cₘ + 0.5*(uᵧ₁+uᵧ₂) # Element direction and length tg = o.tgₘ + uᵧ₂ - uᵧ₁ - L = √(tg[1]^2+tg[2]^2+tg[3]^2) - δ_ = tg/L + L = norm(tg) + δ = tg/L + # Strains ε_ = L/o.Lₛ - 1 # Compute how strains vary with nodal displacements (will be used in the Princple of Virtual Work, PVW) - ε,δ = motion⁻¹{P,ND}(ε_,δ_); δ₀ = ∂0(δ) + ε,δ = motion⁻¹{P,ND}(ε_,δ); δ₀ = ∂0(δ) ε∂X₀ = 1/o.L₀*SVector{6}(-δ₀[1],-δ₀[2],-δ₀[3],δ₀[1],δ₀[2],δ₀[3]) # Compute Gauss point kinematics gp = ntuple(ngp) do igp; diff --git a/toolbox/BeamElement.jl b/toolbox/BeamElement.jl index 74e37fd7..1b93e7c7 100644 --- a/toolbox/BeamElement.jl +++ b/toolbox/BeamElement.jl @@ -17,7 +17,7 @@ Data structure containing the cross section material properties, for example to # Optional argument to the constructor (all set to zero by default) - `w :: 𝕣` is the weight per unit length [N/m] -- `g̃ :: Functor` describes the gravity field divided by acceleration of gravity [-], function of time +- `g̃ :: Functor` describes the gravity field divided by acceleration of gravity [-], function of time, set to SVector(0.,0.,1.) by default - `Ca₁ :: 𝕣` is the tangential added mass per unit length [kg/m] - `Cl₁ :: 𝕣` is the tangential linear damping coefficient per unit length [N/m/(m/s)] - `Cq₁ :: 𝕣` is the tangential quadratic damping coefficient per unit length [N/m/(m/s)^2], for example from drag @@ -41,7 +41,7 @@ mat = BeamCrossSection(EA=EA,EI₂=EI₂,EI₃=EI₃,GJ=GJ,μ=μ,ι See also: [`EulerBeam3D`](@ref), [`AxisymmetricBarCrossSection`](@ref) """ -struct BeamCrossSection +struct BeamCrossSection{Tg̃} EA :: 𝕣 EI₂ :: 𝕣 EI₃ :: 𝕣 @@ -49,7 +49,7 @@ struct BeamCrossSection μ :: 𝕣 ι₁ :: 𝕣 w :: 𝕣 - g̃ :: Functor + g̃ :: Tg̃ # a Functor Ca₁ :: 𝕣 Cl₁ :: 𝕣 Cq₁ :: 𝕣 @@ -149,7 +149,7 @@ See also: [`BeamCrossSection`](@ref), [`Bar3D`](@ref) """ struct EulerBeam3D{Mat,Uforce} <: AbstractElement cₘ :: SVector{3,𝕣} # Position of the middle of the element, as meshed - rₘ :: Mat33{𝕣} # Orientation of the element, as meshed, represented by a rotation matrix (from global to local) + rₘ :: Mat33{𝕣} # Orientation of the element, as meshed, represented by a rotation matrix ζgp :: SVector{ngp,𝕣} # Location of the Gauss points for the normalized element with length 1 ζnod :: SVector{nXnod,𝕣} # Location of the nodes for the normalized element with length 1 tgₘ :: SVector{ndim,𝕣} # Vector connecting the nodes of the element in the global coordinate system @@ -212,19 +212,19 @@ end; # Define now the residual function for the EulerBeam3D element. @espy function Muscade.residual(o::EulerBeam3D{Mat,Udof}, X,U,A,t,SP,dbg) where{Mat,Udof} - P,ND = constants(X),length(X) ## Compute all quantities at Gauss point, their time derivatives, including intrinsic roll rate and acceleration - gp_,ε_,vₛₘ_,rₛₘ_,vₗ₂_,_,_ = kinematics{:direct}(o,motion{P}(X)) + P,ND,X_ = motion(X) + gp_,ε_,vₛₘ_,rₛₘ_,vₗ₂_,_,_ = kinematics{:direct}(o,X_) gpval,☼ε,☼rₛₘ = motion⁻¹{P,ND}(gp_,ε_,rₛₘ_) vᵢ = intrinsicrotationrates(rₛₘ) ## compute all Jacobians of the above quantities with respect to X₀ - X₀ = ∂0(X) # returns concrete type - TX₀ = revariate{P}(X₀) # returns ::Any - Tgp,Tε,Tvₛₘ,_,_,_,_ = kinematics{:chainrule}(o,TX₀) # the crux - gp∂X₀,ε∂X₀,vₛₘ∂X₀ = composeJacobian{P}((Tgp,Tε,Tvₛₘ),X₀) + X₀ = ∂0(X) + TX₀ = revariate{P+1}(X₀) + Tgp,Tε,Tvₛₘ,_,_,_,_ = kinematics{:direct}(o,TX₀) # the crux + gp∂X₀,ε∂X₀,vₛₘ∂X₀ = chainrule_Jacobian((Tgp,Tε,Tvₛₘ),X₀) ## Quadrature loop: compute resultants gp = ntuple(ngp) do igp - ☼x,☼κgp = gpval[igp].x, gpval[igp].κ + ☼x,☼κgp = gpval[igp].x, gpval[igp].κ x∂X₀,κ∂X₀ = gp∂X₀[igp].x, gp∂X₀[igp].κ fᵢ,mᵢ,fₑ,mₑ = ☼resultants(o.mat,ε,κgp,x,rₛₘ,vᵢ,t) # call the "resultant" function to compute loads (local coordinates) from strains/curvatures/etc. using material properties. Note that output is dual of input. fₑ = Udof ? fₑ-∂0(U) : fₑ # U is per unit length @@ -253,7 +253,7 @@ end struct corotated{Mode} end function corotated{Mode}(o::EulerBeam3D,X₀) where{Mode} - cₘ,rₘ,tgₘ,tgₑ,ζnod,ζgp,L = o.cₘ,o.rₘ,o.tgₘ,o.tgₑ,o.ζnod,o.ζgp,o.L # As-meshed element coordinates and describing tangential vector + cₘ,rₘ,tgₘ,tgₑ,ζnod,ζgp = o.cₘ,o.rₘ,o.tgₘ,o.tgₑ,o.ζnod,o.ζgp # As-meshed element coordinates and describing tangential vector uᵧ₁,vᵧ₁,uᵧ₂,vᵧ₂ = vec3(X₀,1:3), vec3(X₀,4:6), vec3(X₀,7:9), vec3(X₀,10:12) Δvᵧ,rₛₘ,vₛₘ = apply{Mode}((vᵧ₁=vᵧ₁,vᵧ₂=vᵧ₂)) do v rₛ₁ = apply{Mode}(Rodrigues,v.vᵧ₁) @@ -424,7 +424,4 @@ function Muscade.display_drawing!(axis,::Type{EulerBeam3D{Tmat,Udof}},obs,opt) w opt.style==:solid && mesh!( axis, obs.solid_vertex, obs.solid_face ,color = opt.solid_color ) opt.style==:solid && opt.draw_marking && lines!( axis, obs.solid_mark ,color = opt.line_color ) opt.Udof && lines!( axis, obs.ucrest ,color = :red ,linewidth=.5 ) -end - - - +end \ No newline at end of file diff --git a/toolbox/PositionElement.jl b/toolbox/PositionElement.jl index 4f50f570..82990bc0 100644 --- a/toolbox/PositionElement.jl +++ b/toolbox/PositionElement.jl @@ -24,7 +24,7 @@ an `ElementCost`. # Requestables: -- `a` `a[isensor]` is the +- `a` `a[isensor]` is the XXXXXXXXXXXX TODO - `x` `x[oder+1][:,isensor]` contains the position, velocity and acceleration (oder=0,1,2) of the sensor which position was described in the `isensor`-th column of `P`. - `rᵢ` `rₑ[oder+1]` is a vector containing a zero vector, the intrinsic rotation rate vector and its time derivative (oder=0,1,2), for the element's node. @@ -58,8 +58,7 @@ Muscade.doflist(::Type{<:Position3D}) = (inod = (1 ,1 ,1 ,1 ,1 ,1 ), Muscade.no_second_order(::Type{<:Position3D}) = Val(true) @espy function Muscade.residual(o::Position3D{Nsensor}, X,U,A,t,SP,dbg) where{Nsensor} - P,ND = constants(X),length(X) - X_ = motion{P}(X) + P,ND,X_ = motion(X) Δx_ = X_[SVector(1,2,3)] r_ = X_[SVector(4,5,6)] R_ = Rodrigues(r_) diff --git a/toolbox/RigidBodyKinematics.jl b/toolbox/RigidBodyKinematics.jl index 7582b808..c9a6d29f 100644 --- a/toolbox/RigidBodyKinematics.jl +++ b/toolbox/RigidBodyKinematics.jl @@ -1,5 +1,3 @@ -@functor with() gap(v,t,θ₀,r₀)= SVector( v[4] - (v[1] + r₀*(cos(θ₀+v[3])-cos(θ₀))), - v[5] - (v[2] + r₀*(sin(θ₀+v[3])-sin(θ₀)))) """ ExcentricRigidConnection <: AbstractElement @@ -17,6 +15,8 @@ e = addelement!(model,ExcentricRigidConnection,[MasterNode EmissaryNode]) See also: [`Hold`](@ref), [`DofConstraint`](@ref) """ struct ExcentricRigidConnection <: AbstractElement end +@functor with() compatibility(v,t,θ₀,r₀)= SVector( v[4] - (v[1] + r₀*(cos(θ₀+v[3])-cos(θ₀))), + v[5] - (v[2] + r₀*(sin(θ₀+v[3])-sin(θ₀)))) function ExcentricRigidConnection(nod::Vector{Node}) c = coord(nod) xₘ = SVector{3}(c[1]) # coordinates of the master node @@ -28,5 +28,5 @@ function ExcentricRigidConnection(nod::Vector{Node}) (1,1,1,2,2),(:t1,:t2,:r3,:t1,:t2), (), (), (), (), - typeof(gap),typeof((r₀,θ₀)),typeof(equal)}(gap,(r₀,θ₀),equal) + typeof(compatibility),typeof((θ₀,r₀)),typeof(Muscade.equal)}(compatibility,(θ₀,r₀),Muscade.equal) end \ No newline at end of file diff --git a/toolbox/Rotations.jl b/toolbox/Rotations.jl index a61dd3ee..64c5e459 100644 --- a/toolbox/Rotations.jl +++ b/toolbox/Rotations.jl @@ -1,77 +1,8 @@ # # 3D rotations using LinearAlgebra, StaticArrays +using Muscade: sinc1 """ - Muscade.sinc1(x) - -`sinc1(x) = sin(x)/x` - but `sinc1(0.) = 1.`. The function can be differentiated -to the fourth order. - -This differs from Julia's `sinc(x) = sin(π*x)/(π*x)`. - -See also [`Toolbox.scac`](@ref) -""" -sinc1(x) = sinc(x/π) -""" - Toolbox.sinc1′(x) - -first derivative of [`Toolbox.sinc1(x)`](@ref). -""" -function sinc1′(x) - if abs(x)>1e-3 - s,c=sincos(x) - c/x -s/x^2 - else - x² = x*x - x*(-1/3 +x²/30) - end -end -""" - Toolbox.sinc1″(x) - -second derivative of [`Toolbox.sinc1(x)`](@ref). -""" -function sinc1″(x) - if abs(x)>1e-1 - s,c=sincos(x) - -s/x -2c/x^2 +2s/x^3 - else - x² = x*x - -1/3 +x²*(1/10 +x²*(-1/168 +x²*(1/6480))) - end -end -""" - Toolbox.sinc1‴(x) - -third derivative of [`Toolbox.sinc1(x)`](@ref). -""" -function sinc1‴(x) - if abs(x)>0.4 - s,c=sincos(x) - -c/x +3s/x^2 +6c/x^3 -6s/x^4 - else - x² = x*x - x*(1/5 +x²*(-1/42 +x²*(1/1080 +x²*(-1/55440 +x²*(1/4717440))))) - end -end -""" - Toolbox.sinc1⁗(x) - -fourth derivative of [`Toolbox.sinc1(x)`](@ref). -""" -function sinc1⁗(x) - x² = x*x - 1/5 +x²*(-1/14 +x²*(1/216 +x²*(-1/7920 +x²*(1/524160 +x²*(-1/54432000 +x²*(1/54432000 +x²*(-1/8143027200 +x²*(1/1656387532800)))))))) -end -sinc1⁗′(x) = x*NaN -using Muscade -Muscade.@DiffRule1(sinc1, sinc1′( a.x) * a.dx ) -Muscade.@DiffRule1(sinc1′, sinc1″( a.x) * a.dx ) -Muscade.@DiffRule1(sinc1″, sinc1‴( a.x) * a.dx ) -Muscade.@DiffRule1(sinc1‴, sinc1⁗( a.x) * a.dx ) -Muscade.@DiffRule1(sinc1⁗, sinc1⁗′(a.x) * a.dx ) - -""" - Toolboxscac(x) + Toolbox.scac(x) `scac(x) = sinc1(acos(x)),` The function can be differentiated to the fourth order over ]-1,1] . @@ -83,7 +14,7 @@ function scac(x) if abs(dx)>1e-3 sinc1(acos(x)) else # deliberately a long Taylor series (5th order): this function will be adiffed at least to 2nd order, up to 4th order - y = 1 + dx*(1/3 + dx*(-2/90 + dx*(0.0052911879917544626 + dx*(-0.0016229317117234072 + dx*(0.0005625))))) + evalpoly(dx,(1,1/3,-2/90,0.0052911879917544626,-0.0016229317117234072,0.0005625)) end end @@ -98,7 +29,7 @@ Transform a rotation vector `v` into the cross product matrix `M`, such that See also [`Toolbox.spin⁻¹`](@ref), [`Toolbox.Rodrigues`](@ref), [`Toolbox.Rodrigues⁻¹`](@ref). """ -spin( v::Vec3 ) = SMatrix{3,3}(0,v[3],-v[2],-v[3],0,v[1],v[2],-v[1],0) +spin(v::Vec3) = SMatrix{3,3}(0,v[3],-v[2],-v[3],0,v[1],v[2],-v[1],0) """ toolbox.spin⁻¹(M::SMatrix{3,3}) @@ -113,7 +44,7 @@ spin⁻¹(m::Mat33) = SVector{3}(m[3,2]-m[2,3],m[1,3]-m[3,1],m[2,1]-m[1,2])/2 Computes the trace of a matrix. """ -trace( m::Mat33) = m[1,1]+m[2,2]+m[3,3] +trace(m::Mat33) = m[1,1]+m[2,2]+m[3,3] """ Toolbox.Rodrigues⁻¹(v::SVector{3}) @@ -122,8 +53,8 @@ Transform a rotation matrix `M` into the rotation vector `v`, such that See also [`Toolbox.spin`](@ref), [`Toolbox.spin⁻¹`](@ref), [`Toolbox.Rodrigues`](@ref), [`Toolbox.adjust`](@ref). """ -Rodrigues⁻¹(m) = spin⁻¹(m)/scac((trace(m)-1)/2) # NB: is necessarily singular for π turn -function norm3(v::SVector{3}) # executes faster, COMPILES MUCH FASTER , and adiffs poorly at origin +Rodrigues⁻¹(m) = spin⁻¹(m)/scac((trace(m)-1.)/2.) # NB: is necessarily singular for π turn +function LinearAlgebra.norm(v::Vec3) # executes faster, COMPILES MUCH FASTER , and adiffs poorly at origin n = sqrt(v[1]*v[1]+v[2]*v[2]+v[3]*v[3]) if n<1e-14 n = zero(eltype(v)) @@ -131,7 +62,7 @@ function norm3(v::SVector{3}) # executes faster, COMPILES MUCH FASTER , and adi return n end -function spin²(S) +function spin²(S::Vec3) ab = S[2,3]*S[3,1] ca = S[1,2]*S[2,3] bc = S[3,1]*S[1,2] @@ -148,29 +79,18 @@ Transform a rotation vector `v` into the rotation matrix `M`. See also [`Toolbox.spin`](@ref), [`Toolbox.spin⁻¹`](@ref), [`Toolbox.Rodrigues⁻¹`](@ref), [`Toolbox.adjust`](@ref). """ -function Rodrigues(v::Vec3) - S = spin(v) - θ = norm3(v) - return LinearAlgebra.I + sinc1(θ).*S + (sinc1(θ/2)^2/2).*spin²(S) +@inline function Rodrigues(v::Vec3{R}) where{R} + # I + spin(v)*sinc1(norm3(v)) + spin²(v)*sinc1(norm3(v)/2)/√2 + θ = norm(v) + s₁ = sinc1(θ ) + s₂ = sinc1(θ/2)*(1/√2) + a,b,c = s₁*v[1],s₁*v[2],s₁*v[3] + vs₂ = v*s₂ + ab ,ac ,bc = vs₂[1]*vs₂[2], vs₂[1]*vs₂[3], vs₂[2]*vs₂[3] + ma²,mb²,mc² = vs₂[1]*vs₂[1], vs₂[2]*vs₂[2], vs₂[3]*vs₂[3] + return Mat33{R}(1. -mc²-mb²,ab+c,ac-b, ab-c,1. -ma²-mc²,bc+a, ac+b,bc-a,1. -ma²-mb²) end -# function Rodrigues(v::Vec3) # no substantial gain from this implementation -# a,b,c = v[1],v[2],v[3] -# ab = a*b -# ca = c*a -# bc = b*c -# a² = a*a -# b² = b*b -# c² = c*c -# θ = sqrt(a²+b²+c²) -# if θ<1e-14 -# θ = zero(eltype(v)) -# end -# A = sinc1(θ) -# B = sinc1(θ/2)^2/2 -# return SMatrix{3,3}(1-B*(b²+c²), -A*c+B*ab, A*b+B*ca, # SMatrix constructor: the code is the transposed of the matrix! -# A*c+B*ab, 1-B*(a²+c²), -A*a+B*bc, -# -A*b+B*ca, A*a*B*bc, 1-B*(a²+b²)) -# end + """ Toolbox.adjust(u::SVector{3},v::SVector{3}) @@ -182,7 +102,7 @@ See also [`Toolbox.spin`](@ref), [`Toolbox.spin⁻¹`](@ref), [`Toolbox.Rodrigue function adjust(u::Vec3{R},v::Vec3{R}) where{R} u,v = normalize.((u,v)) c,w = dot(u,v), cross(u,v) - s = norm3(w) + s = norm(w) θ = atan(s,c) return w/sinc1(θ) end From 8eefc02892bf09ed5706ae1ab4da2d3fef7adabb Mon Sep 17 00:00:00 2001 From: Antoine GROSSE Date: Sun, 2 Aug 2026 09:31:43 +0200 Subject: [PATCH 6/9] Changed ``initialstate" into ``primerstate" --- examples/DecayAnalysis.jl | 4 ++-- examples/TuningFork.jl | 2 +- src/DirectXUA.jl | 38 ++++++++++++++++++-------------------- test/TestDirectXUA001.jl | 6 +++--- test/TestDirectXUA201.jl | 4 ++-- 5 files changed, 26 insertions(+), 28 deletions(-) diff --git a/examples/DecayAnalysis.jl b/examples/DecayAnalysis.jl index 78802b92..d1f59b24 100644 --- a/examples/DecayAnalysis.jl +++ b/examples/DecayAnalysis.jl @@ -11,7 +11,7 @@ using Muscade,StaticArrays,Interpolations,GLMakie fold(x::SVector{6}) = SMatrix{3,3}( x[1],x[2],x[3], x[2],x[4],x[5], x[3],x[5],x[6]) - +solve const floatermotion = (:surge,:sway,:yaw) const idx = (:11,:12,:16,:22,:26,:66) @@ -128,7 +128,7 @@ e7 = addelement!(modelXUA,SingleDofCost,[n1];class=:X,field=:yaw, #Solve inverse problem initialstateXUA = initialize!(modelXUA;time=0.) -stateXUA = solve(DirectXUA{2,0,1};initialstate=[initialstateXUA],time=[T], +stateXUA = solve(DirectXUA{2,0,1};primerstate=[initialstateXUA],time=[T], maxiter=100,saveiter=true,verbose=false, maxΔx=1e-5,maxΔλ=Inf,maxΔu=1e-5,maxΔa=1e-5); diff --git a/examples/TuningFork.jl b/examples/TuningFork.jl index 21479721..d3faad56 100644 --- a/examples/TuningFork.jl +++ b/examples/TuningFork.jl @@ -111,7 +111,7 @@ optimXAstate = solve(SweepXA{2}; initialstate=XAinitialState, time=timeVec, # DirectXUA (slack convergence criteria and number of iterations) XUAinitialState = initialize!(XUAmodel;time=0.); -optimXUAstate = solve(DirectXUA{2,0,1};initialstate=[XUAinitialState], time=[timeVec], +optimXUAstate = solve(DirectXUA{2,0,1};primerstate=[XUAinitialState], time=[timeVec], maxiter=15, maxΔx=5e-2,maxΔλ=Inf,maxΔu=5e-2,maxΔa=1e-4,verbose=false); # Gather results for comparison diff --git a/src/DirectXUA.jl b/src/DirectXUA.jl index 0c3927c2..cd07f450 100644 --- a/src/DirectXUA.jl +++ b/src/DirectXUA.jl @@ -415,7 +415,7 @@ A non-linear direct solver for optimisation FEM. An analysis is carried out by a call with the following syntax: ``` -initialstate = initialize!(model) +primerstate = initialize!(model) ``` The solver does not yet support interior point methods. @@ -433,12 +433,12 @@ The solver does not yet support interior point methods. - `dbg=(;)` a named tuple to trace the call tree (for debugging). - `verbose=true` set to false to suppress printed output (for testing). - `silenterror=false` set to true to suppress print out of error (for testing). -- `initialstate` an `AbstractVector` of `State` or an `AbstractVector` of `Vector{State}`: one primer for each experiment. - `initialstate` must be with zero time derivatives. It does not provide initial conditions for the problem, - but an initial guess for the iterative solver. The solver needs a time-dependant trajectory as input: `initialstate` +- `primerstate` an `AbstractVector` of `State` or an `AbstractVector` of `Vector{State}`: one primer for each experiment. + `primerstate` must be with zero time derivatives. It does not provide initial conditions for the problem, + but an initial guess for the iterative solver. The solver needs a time-dependant trajectory as input: `primerstate` either directly provides it with a `Vector{State}`, or allows the creation of it by copying the same `State` for every time step. By convention the Adofs for building this primer are taken from the first experiment, first state. -- `time` an `AbstractVector` (of same length as `initialstate`) of `AbstractRange` +- `time` an `AbstractVector` (of same length as `primerstate`) of `AbstractRange` of times at which to compute the steps. Example: 0:0.1:5. - `maxiter=50` maximum number of Newton-Raphson iterations. - `maxΔλ=1e-5` convergence criteria: a norm of the scaled `Λ` increment. @@ -464,9 +464,7 @@ See also: [`solve`](@ref), [`initialize!`](@ref), [`SweepX`](@ref), [`FreqXU`](@ struct DirectXUA{OX,OU,IA} <: AbstractSolver end function solve(::Type{DirectXUA{OX,OU,IA}},pstate,verbose::𝕓,dbg; time::AbstractVector{AR}, - # TODO HAVE A SIMPLER ONLY ONE VARIABLE - # TODO BY CONVENTION WE USE THE Ainit THAT IS THE FIRST EXP and FIRST STATE - initialstate::Union{Nothing,AbstractVector}, + primerstate::Union{Nothing,AbstractVector}, maxiter::ℤ=50, maxΔλ::ℝ=1e-5,maxΔx::ℝ=1e-5,maxΔu::ℝ=1e-5,maxΔa::ℝ=1e-5, saveiter::𝔹=false, @@ -484,25 +482,25 @@ function solve(::Type{DirectXUA{OX,OU,IA}},pstate,verbose::𝕓,dbg; # State storage S = State{1,OX+1,OU+1,@NamedTuple{γ::Float64,iter::Int64}} state = [Vector{S}(undef,nstep[iexp]) for iexp=1:nexp] # state[iexp][istep] - s = initialstate[1] + s = primerstate[1] # Test input dimension compatibility - length(initialstate)== nexp || muscadeerror("initialstate length must be equal to the number of experiments") + length(primerstate)== nexp || muscadeerror("primerstate length must be equal to the number of experiments") - if isa(initialstate[1],Muscade.State) - model,dis = initialstate[1].model, initialstate[1].dis - # Case where initialstate is an AbstractVector of State. A primer trajectory of state is created from a repetition of this state. - for (iexp,initialstateᵢ) ∈ enumerate(initialstate) + if isa(primerstate[1],Muscade.State) + model,dis = primerstate[1].model, primerstate[1].dis + # Case where primerstate is an AbstractVector of State. A primer trajectory of state is created from a repetition of this state. + for (iexp,primerstateᵢ) ∈ enumerate(primerstate) for (istep,timeᵢ) = enumerate(time[iexp]) - state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(initialstateᵢ.Λ),deepcopy(initialstateᵢ.X),deepcopy(initialstateᵢ.U),s.A,(γ=0.,iter=1),model,dis) # all state[iexp][istep].A are === + state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(primerstateᵢ.Λ),deepcopy(primerstateᵢ.X),deepcopy(primerstateᵢ.U),s.A,(γ=0.,iter=1),model,dis) # all state[iexp][istep].A are === end end else - # Case where initialstate is already an AbstractVector of Vector{State}. - Ainit = initialstate[1][1].A - model,dis = initialstate[1][1].model, initialstate[1][1].dis - for (iexp,trajexp) ∈ enumerate(initialstate) - length(trajexp)== nstep[iexp] || muscadeerror("trajectories in `initialstate` vector must match their associated time grid in `time` vector") + # Case where primerstate is already an AbstractVector of Vector{State}. + Ainit = primerstate[1][1].A + model,dis = primerstate[1][1].model, primerstate[1][1].dis + for (iexp,trajexp) ∈ enumerate(primerstate) + length(trajexp)== nstep[iexp] || muscadeerror("trajectories in `primerstate` vector must match their associated time grid in `time` vector") for (istep,timeᵢ) = enumerate(time[iexp]) trajstate = trajexp[istep] state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(trajstate.Λ),deepcopy(trajstate.X),deepcopy(trajstate.U),Ainit,(γ=0.,iter=1),model,dis) diff --git a/test/TestDirectXUA001.jl b/test/TestDirectXUA001.jl index 93f712e8..da50f836 100644 --- a/test/TestDirectXUA001.jl +++ b/test/TestDirectXUA001.jl @@ -29,14 +29,14 @@ e10 = addelement!(model,SingleAcost , field=:ΞL₀,[n4] e11 = addelement!(model,SingleAcost , field=:ΞEI,[n4] ,cost=acost) initialstate = initialize!(model) stateX = solve(SweepX{0}; initialstate,time=[0.],verbose=false) -stateXUA = solve(DirectXUA{0,0,1};initialstate=[stateX[1]],time = [0:.1:1],verbose=false,maxiter=50) +stateXUA = solve(DirectXUA{0,0,1};primerstate=[stateX[1]],time = [0:.1:1],verbose=false,maxiter=50) iexp = 1 @testset "solution" begin @test stateXUA[iexp][2].X[1]' ≈ [0.0125777 0.0125777 0.0 0.0 0.0 0.0 -0.0100126 1.26094e-5 1.26094e-5 -0.0100126] rtol=1e-4 @test stateXUA[iexp][2].A' ≈ [ -3.83011e-5 -0.0672263] rtol=1e-4 @test stateXUA[iexp][2].A ≡ stateXUA[iexp][1].A end -stateXUAcv = solve(DirectXUA{0,0,1};initialstate=[stateX[1]],time = [0:.1:1],saveiter=true,verbose=false) +stateXUAcv = solve(DirectXUA{0,0,1};primerstate=[stateX[1]],time = [0:.1:1],saveiter=true,verbose=false) jiter = findlastassigned(stateXUAcv) @testset "saveiter" begin @test stateXUAcv[jiter][iexp][2].X[1] ≈ stateXUA[iexp][2].X[1] @@ -46,7 +46,7 @@ jiter = findlastassigned(stateXUAcv) @test !(stateXUAcv[jiter][iexp][1].A == stateXUAcv[1][iexp][1].A) end -stateXUAmult = solve(DirectXUA{0,0,1};initialstate=[stateX[1],stateX[1]],time = [0:.1:1,.1:.1:1],verbose=false,maxiter=50) +stateXUAmult = solve(DirectXUA{0,0,1};primerstate=[stateX[1],stateX[1]],time = [0:.1:1,.1:.1:1],verbose=false,maxiter=50) @testset "multiple" begin @test stateXUAmult[1][2].A === stateXUAmult[2][3].A end diff --git a/test/TestDirectXUA201.jl b/test/TestDirectXUA201.jl index e8ce7a53..c64f1f2a 100644 --- a/test/TestDirectXUA201.jl +++ b/test/TestDirectXUA201.jl @@ -48,7 +48,7 @@ x,x′,x″ = 0.,1.,0. initialstate2 = setdof!(initialstate,[x′];field=:tx1,nodID=[node],order=1) # initial speed statewrong = solve(SweepX{2}; initialstate=initialstate2,time= t,verbose=false,catcherror=true) -state = solve(DirectXUA{2,0,1}; initialstate=[initialstate],time= [t],verbose=false,catcherror=true,maxiter=50,maxΔa=1e-5,maxΔx=1e-5,maxΔu=1e-5,maxΔλ=Muscade.∞) +state = solve(DirectXUA{2,0,1}; primerstate=[initialstate],time= [t],verbose=false,catcherror=true,maxiter=50,maxΔa=1e-5,maxΔx=1e-5,maxΔu=1e-5,maxΔλ=Muscade.∞) A = getdof(state[1][1];class=:A,field=:ΞC,nodID=[node]) xfitted = getdof(state[1];field=:tx1,nodID=[node]) @@ -97,7 +97,7 @@ let primer = initialstate end end -statetraj = solve(DirectXUA{2,0,1}; initialstate=[traj],time= [t],verbose=false,catcherror=true,maxiter=20,maxΔa=1e-5,maxΔx=1e-5,maxΔu=1e-5,maxΔλ=Muscade.∞) +statetraj = solve(DirectXUA{2,0,1}; primerstate=[traj],time= [t],verbose=false,catcherror=true,maxiter=20,maxΔa=1e-5,maxΔx=1e-5,maxΔu=1e-5,maxΔλ=Muscade.∞) A = getdof(statetraj[1][1];class=:A,field=:ΞC,nodID=[node]) xfittedtraj = getdof(statetraj[1];field=:tx1,nodID=[node]) xtraj = getdof(traj;field=:tx1,nodID=[node]) From a4665f95dd7585cbf76c8108203587a72faeffbe Mon Sep 17 00:00:00 2001 From: Antoine GROSSE Date: Sun, 2 Aug 2026 09:54:32 +0200 Subject: [PATCH 7/9] Clearer docstring --- src/DirectXUA.jl | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/src/DirectXUA.jl b/src/DirectXUA.jl index cd07f450..3130f180 100644 --- a/src/DirectXUA.jl +++ b/src/DirectXUA.jl @@ -433,13 +433,14 @@ The solver does not yet support interior point methods. - `dbg=(;)` a named tuple to trace the call tree (for debugging). - `verbose=true` set to false to suppress printed output (for testing). - `silenterror=false` set to true to suppress print out of error (for testing). -- `primerstate` an `AbstractVector` of `State` or an `AbstractVector` of `Vector{State}`: one primer for each experiment. - `primerstate` must be with zero time derivatives. It does not provide initial conditions for the problem, - but an initial guess for the iterative solver. The solver needs a time-dependant trajectory as input: `primerstate` - either directly provides it with a `Vector{State}`, or allows the creation of it by copying the same `State` for every time step. +- `primerstate` an `AbstractVector` of `State` (1) or an `AbstractVector` of `Vector{State}` (2). `primerstate` must be with zero time derivatives. + It does not provide initial conditions for the problem, but an initial guess for the iterative solver. + As DirectXUA solves multiple experiments at once, the i-th element of `primerstate` is an initial guess for the i-th experiment. + If provided with (1), the i-th initial guess is constructed internally with replicating the i-th input `State` for each timestep of the i-th timerange (see `time`). + If provided with (2), the i-th initial guess is the input `Vector{State}`, if the length corresponds to the i-th timerange (see `time`). By convention the Adofs for building this primer are taken from the first experiment, first state. - `time` an `AbstractVector` (of same length as `primerstate`) of `AbstractRange` - of times at which to compute the steps. Example: 0:0.1:5. + of times at which to compute the steps, one for each experiment. Example: 0:0.1:5. - `maxiter=50` maximum number of Newton-Raphson iterations. - `maxΔλ=1e-5` convergence criteria: a norm of the scaled `Λ` increment. - `maxΔx=1e-5` convergence criteria: a norm of the scaled `X` increment. From f66c1640afe174698b122a90785199d1c7845167 Mon Sep 17 00:00:00 2001 From: Antoine GROSSE Date: Sun, 2 Aug 2026 10:14:14 +0200 Subject: [PATCH 8/9] More compact code --- src/DirectXUA.jl | 31 +++++++++++++------------------ 1 file changed, 13 insertions(+), 18 deletions(-) diff --git a/src/DirectXUA.jl b/src/DirectXUA.jl index 3130f180..97b7c1c5 100644 --- a/src/DirectXUA.jl +++ b/src/DirectXUA.jl @@ -483,31 +483,26 @@ function solve(::Type{DirectXUA{OX,OU,IA}},pstate,verbose::𝕓,dbg; # State storage S = State{1,OX+1,OU+1,@NamedTuple{γ::Float64,iter::Int64}} state = [Vector{S}(undef,nstep[iexp]) for iexp=1:nexp] # state[iexp][istep] - s = primerstate[1] # Test input dimension compatibility length(primerstate)== nexp || muscadeerror("primerstate length must be equal to the number of experiments") - if isa(primerstate[1],Muscade.State) - model,dis = primerstate[1].model, primerstate[1].dis - # Case where primerstate is an AbstractVector of State. A primer trajectory of state is created from a repetition of this state. - for (iexp,primerstateᵢ) ∈ enumerate(primerstate) - for (istep,timeᵢ) = enumerate(time[iexp]) - state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(primerstateᵢ.Λ),deepcopy(primerstateᵢ.X),deepcopy(primerstateᵢ.U),s.A,(γ=0.,iter=1),model,dis) # all state[iexp][istep].A are === - end - end - else - # Case where primerstate is already an AbstractVector of Vector{State}. - Ainit = primerstate[1][1].A - model,dis = primerstate[1][1].model, primerstate[1][1].dis - for (iexp,trajexp) ∈ enumerate(primerstate) - length(trajexp)== nstep[iexp] || muscadeerror("trajectories in `primerstate` vector must match their associated time grid in `time` vector") - for (istep,timeᵢ) = enumerate(time[iexp]) - trajstate = trajexp[istep] - state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(trajstate.Λ),deepcopy(trajstate.X),deepcopy(trajstate.U),Ainit,(γ=0.,iter=1),model,dis) + for (iexp,primerstateᵢ) ∈ enumerate(primerstate) + for (istep,timeᵢ) = enumerate(time[iexp]) + if eltype(primerstate) <: Muscade.State + # Case where primerstate is an AbstractVector of State. A primer trajectory of state is created from a repetition of this state. + model,dis,Ainit = primerstate[1].model, primerstate[1].dis, primerstate[1].A + primer = primerstateᵢ + else + # Case where primerstate is already an AbstractVector of Vector{State}. + length(primerstateᵢ)== nstep[iexp] || muscadeerror("trajectories in `primerstate` vector must match their associated time grid in `time` vector") + model,dis,Ainit = primerstate[1][1].model, primerstate[1][1].dis, primerstate[1][1].A + primer = primerstateᵢ[istep] end + state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(primer.Λ),deepcopy(primer.X),deepcopy(primer.U),Ainit,(γ=0.,iter=1),model,dis) end end + if saveiter stateiter = Vector{Vector{Vector{S}}}(undef,maxiter) # stateiter[iiter][iexp][istep] pstate[] = stateiter From 18fe9caed727d2a713e41e681ca12ac6aea03bfd Mon Sep 17 00:00:00 2001 From: Antoine GROSSE Date: Mon, 3 Aug 2026 10:34:27 +0200 Subject: [PATCH 9/9] Adjustement due to merging with dev --- src/DirectXUA.jl | 11 +++++++---- test/TestScale.jl | 4 ++-- 2 files changed, 9 insertions(+), 6 deletions(-) diff --git a/src/DirectXUA.jl b/src/DirectXUA.jl index 56350b32..05221503 100644 --- a/src/DirectXUA.jl +++ b/src/DirectXUA.jl @@ -496,20 +496,23 @@ function solve(::Type{DirectXUA{OX,OU,IA}},pstate,verbose::𝕓,dbg; # State storage S = State{1,OX+1,OU+1,@NamedTuple{γ::Float64,iter::Int64}} state = [Vector{S}(undef,nstep[iexp]) for iexp=1:nexp] # state[iexp][istep] - + if eltype(primerstate) <: Muscade.State + model,dis,Ainit = primerstate[1].model, primerstate[1].dis, primerstate[1].A + else + model,dis,Ainit = primerstate[1][1].model, primerstate[1][1].dis, primerstate[1][1].A + end + # Test input dimension compatibility length(primerstate)== nexp || muscadeerror("primerstate length must be equal to the number of experiments") - + for (iexp,primerstateᵢ) ∈ enumerate(primerstate) for (istep,timeᵢ) = enumerate(time[iexp]) if eltype(primerstate) <: Muscade.State # Case where primerstate is an AbstractVector of State. A primer trajectory of state is created from a repetition of this state. - model,dis,Ainit = primerstate[1].model, primerstate[1].dis, primerstate[1].A primer = primerstateᵢ else # Case where primerstate is already an AbstractVector of Vector{State}. length(primerstateᵢ)== nstep[iexp] || muscadeerror("trajectories in `primerstate` vector must match their associated time grid in `time` vector") - model,dis,Ainit = primerstate[1][1].model, primerstate[1][1].dis, primerstate[1][1].A primer = primerstateᵢ[istep] end state[iexp][istep] = State{1,OX+1,OU+1}(timeᵢ,deepcopy(primer.Λ),deepcopy(primer.X),deepcopy(primer.U),Ainit,(γ=0.,iter=1),model,dis) diff --git a/test/TestScale.jl b/test/TestScale.jl index bc1081b8..e551fb6b 100644 --- a/test/TestScale.jl +++ b/test/TestScale.jl @@ -30,12 +30,12 @@ model2 = deepcopy(model1) initialstate1 = initialize!(model1) stateX1 = solve(SweepX{0}; initialstate=initialstate1,time=[0.,1.],verbose=false) -stateXUA1 = solve(DirectXUA{0,0,1};initialstate=[stateX1[1]],time = [0:.1:1],maxΔλ=.5,maxΔa=1e-4,maxΔx=1e-4,verbose=false) +stateXUA1 = solve(DirectXUA{0,0,1};primerstate=[stateX1[1]],time = [0:.1:1],maxΔλ=.5,maxΔa=1e-4,maxΔx=1e-4,verbose=false) setscale!(model2;scale=(X=(tx1=1.,tx2=10.,rx3=2.),A=(Δseadrag=3.,Δskydrag=4.,ΔL=5)),Λscale=2) initialstate2 = initialize!(model2) stateX2 = solve(SweepX{0}; initialstate=initialstate2,time=[0.],verbose=false) -stateXUA2 = solve(DirectXUA{0,0,1};initialstate=[stateX2[1]],time = [0:.1:1],maxΔλ=.5,maxΔa=1e-4,maxΔx=1e-4,verbose=false) +stateXUA2 = solve(DirectXUA{0,0,1};primerstate=[stateX2[1]],time = [0:.1:1],maxΔλ=.5,maxΔa=1e-4,maxΔx=1e-4,verbose=false) step = 1 iexp = 1

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