From 8bc41bc0ddbc3d475fac44992cc091db8d6aaeaf Mon Sep 17 00:00:00 2001 From: fmeulen Date: Mon, 3 Dec 2018 15:00:11 +0100 Subject: [PATCH 01/58] High dim landmarks implementation --- landmarks/ahsmodel.jl | 110 ++++++++++++++++++++++++++++++++++ landmarks/backward!.jl | 14 +++++ landmarks/forward.jl | 102 ++++++++++++++++++++++++++++++++ landmarks/msmodel.jl | 130 +++++++++++++++++++++++++++++++++++++++++ landmarks/patches.jl | 65 +++++++++++++++++++++ landmarks/state.jl | 84 ++++++++++++++++++++++++++ landmarks/testms.jl | 11 ++++ 7 files changed, 516 insertions(+) create mode 100644 landmarks/ahsmodel.jl create mode 100644 landmarks/backward!.jl create mode 100644 landmarks/forward.jl create mode 100644 landmarks/msmodel.jl create mode 100644 landmarks/patches.jl create mode 100644 landmarks/state.jl create mode 100644 landmarks/testms.jl diff --git a/landmarks/ahsmodel.jl b/landmarks/ahsmodel.jl new file mode 100644 index 0000000..23f3ef0 --- /dev/null +++ b/landmarks/ahsmodel.jl @@ -0,0 +1,110 @@ +include("state.jl") + +const d = 2 +const Point = SArray{Tuple{d},Float64,1,d} # point in R2 +const Unc = SArray{Tuple{d,d},Float64,d,d*d} # Matrix presenting uncertainty + +######### +struct Noisefield + δ::Point # locations of noise field + λ::Point # scaling at noise field + τ::Float64 # variance of noise field +end + +######### +struct Landmarks{T} <: ContinuousTimeProcess{State{Point}} + a::T # kernel parameter + λ::T # mean reversion + n::Int64 # numer of landmarks + nfs::Vector{Noisefield} # vector containing pars of noisefields +end + +# specify auxiliary process +struct LandmarksAux{T} <: ContinuousTimeProcess{State{Point}} + a::T # kernel parameter + λ::T # mean reversion + xT::State{Point} # use x = State(P.v, zero(P.v)) where v is conditioning vector + n::Int64 # numer of landmarks + nfs::Vector{Noisefield} # vector containing pars of noisefields +end +LandmarksAux(P::Landmarks, xT) = LandMarksAux(P.a, P.λ, xT, P.n, P.nfs) + +# Gaussian kernel +kernel(x, P) = 1/(2*π*P.a)^(length(x)/2)*exp(-norm(x)^2/(2*P.a)) + +# Kernel of the noise fields (need these functions to evaluate diffusion coefficient in ahs model) +noiseσ(q, nf::Noisefield) = nf.λ * exp(-norm(nf.δ - q)^2/nf.τ) +eta(q, p, nf::Noisefield) = dot(p, nf.λ)/nf.τ * (q - nf.δ) * exp(-norm(nf.δ - q)^2/nf.τ) + + +zero!(v) = v[:] = fill!(v, zero(eltype(v))) +function hamiltonian((q, p), P) + s = 0.0 + for i in eachindex(q), j in eachindex(q) + # i == j && continue + s += 1/2*dot(p[i], p[j])*kernel(q[i] - q[j], P) + end + s +end + +Bridge.b(t::Float64, x, P::Union{Landmarks, LandmarksAux}) = Bridge.b!(t, x, copy(x), P) +function Bridge.b!(t, x, out, P::Landmarks) + zero!(out) + for i in 1:P.n + for j in 1:P.n + out.q[i] += 0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) + # heat bath + out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) + + 1/(2*P.a) * dot(p(x,i), p(x,j)) * (q(x,i)-q(x,j))*kernel(q(x,i) - q(x,j), P) + end + end + out +end + +function Bridge.b!(t, x, out, P::LandmarksAux) + zero!(out) + for i in 1:P.n + for j in 1:P.n + out.q[i] += 0.5*p(x,j)*kernel(q(P.v,i) - q(P.v,j), P) + # heat bath + # out[posp(i)] += -P.λ*0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) + + # 1/(2*P.a) * dot(p(x,i), p(x,j)) * (q(x,i)-q(x,j))*kernel(q(x,i) - q(x,j), P) + end + end + out +end + +function Bridge.σ!(t, x, dm, out, P::Landmarks) + zero!(out) + nfs = P.nfs + for i in 1:P.n + #for (nf, dm) in zip(P.nfs, dm) + for j in 1:length(nfs) + #out.p[i] += noiseσ(q(x, i), nf) * dm + #out.q[i] += eta(q(x, i), p(x, i), nf) * dm + out.p[i] += noiseσ(q(x, i), nfs[j]) * dm[j] + out.q[i] += eta(q(x, i), p(x, i), nfs[j]) * dm[j] + end + end + out +end + +function Bridge.σ!(t, x, dm, out, P::LandmarksAux) + Bridge.σ!(t, P.xT, dm, out, P::Landmarks) +end + +# function Bridge.a(t,x, P::Landmarks) +# out = zeros(4*P.n,P.J) +# for i in 1:P.n +# for j in 1:P.J +# out[posq(i),j] = noiseσ(q(x,i),P.nfs[j]) +# out[posp(i),j] = eta(q(x,i),p(x,i),P.nfs[j]) +# end +# end +# Bridge.outer(out) +# end +# +# Bridge.a(t,P::LandmarksAux) = Bridge.a(t, cat(P.v, zeros(2*P.n)),P::Landmarks ) +# Bridge.a(t, x, P::LandmarksAux) = Bridge.a(t, P::LandmarksAux) +Bridge.constdiff(Landmarks) = false +Bridge.constdiff(LandmarksAux) = true diff --git a/landmarks/backward!.jl b/landmarks/backward!.jl new file mode 100644 index 0000000..cf928c8 --- /dev/null +++ b/landmarks/backward!.jl @@ -0,0 +1,14 @@ +function Bridge.gpupdate(ν::Vector, P::Matrix, Σ, L, v) + if all(diag(P) .== Inf) + P_ = inv(L' * inv(Σ) * L) + V_ = (L' * inv(Σ) * L)\(L' * inv(Σ) * v) + return V_, P_ + else + Z = I - P*L'*inv(Σ + L*P*L')*L + return Z*P*L'*inv(Σ)*v + Z*ν, Z*P + end +end + +# ms model: start with outcommented stuff in msmodel +# update/adjust partial bridgenuH file for solving backward +# update/adjust partialbridge_bolus3 to do par estimation and bridge imputation diff --git a/landmarks/forward.jl b/landmarks/forward.jl new file mode 100644 index 0000000..aa34226 --- /dev/null +++ b/landmarks/forward.jl @@ -0,0 +1,102 @@ +# reminder, to type H*, do H\^+ +#cd("/Users/Frank/.julia/dev/Bridge") +#outdir="output/landmarks/" + +using Bridge, StaticArrays, Distributions +using Bridge:logpdfnormal +using Test, Statistics, Random, LinearAlgebra +using Bridge.Models +using DelimitedFiles +using DataFrames +using CSV +using RCall +using Base.Iterators +using SparseArrays + +models = [:ms, :ahs] +TEST = true + +include("state.jl") +include("msmodel.jl") +include("ahsmodel.jl") +include("patches.jl") + + +n = 250 + +t = 0.0:0.001:1.0 + + +a = 1.0 ; λ = 0.5 ; γ = 5.0 +Pms = MarslandShardlow(a, γ, λ, n) + +nfvar = 1.0 # tau +r1 = (-2.0:2.0) #+ 0.1rand(5) +r2 = (-2.0:2.0) #+ 0.1rand(5) + +nfloc = Point.(collect(product(r1, r2)))[:] +nfscales = [0.5Point(1.0, 1.0) for x in nfloc] +nfs = [Noisefield(δ, λ, nfvar) for (δ, λ) in zip(nfloc, nfscales)] +Pahs = Landmarks(a, λ, n, nfs) + +model = models[2] + +if model == :ms + dwiener = n + StateW = Point + P = Pms +else + dwiener = length(nfloc) + StateW = Float64 + P = Pahs +end + +w0 = zeros(StateW, dwiener) +W = SamplePath(t, [copy(w0) for s in t]) +sample!(W, Wiener{Vector{StateW}}()) + +q0 = [Point(cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] +#q0 = circshift(q0, (1,)) + +p_ = 3*Point(0.1, 0.1) +p0 = [p_ for i in 1:n] +#p0 = [randn(Point) for i in 1:n] +x0 = State(q0, p0) +X = SamplePath(t, [copy(x0) for s in t]) +@time solve!(EulerMaruyama!(), X, x0, W, P) + +extractcomp(v,i) = map(x->x[i], v) + +out = [Any[X.tt[i], [X.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(X.tt) ][:] +df = DataFrame(time=extractcomp(out,1),pos1=extractcomp(out,2),pos2=extractcomp(out,3),mom1=extractcomp(out,4),mom2=extractcomp(out,5),pointID=extractcomp(out,6)) +#Any["X.tt[$i]", ["X.yy[$i][CartesianIndex($c, $k)][$l]" for l in 1:d, k in 1:n, c in 1:2]...] +@rput df +R""" +library(tidyverse) +df %>% dplyr::select(time,pos1,pos2,pointID) %>% + ggplot(aes(x=pos1,pos2,group=pointID,colour=time)) + geom_path() +""" + +R""" +df %>% dplyr::select(time,mom1,mom2,pointID) %>% + filter(pointID %in% c("point1","point2","point3","point4","point5")) %>% + ggplot(aes(x=mom1,mom2,group=pointID,colour=time)) + geom_path() + + facet_wrap(~pointID) +""" + + +xT = X.yy[end] +Pmsaux = MarslandShardlowAux(Pms, xT) + +if TEST + include("testms.jl") +end + +#= Later: + +Pauxahs = LandmarksAux(Pahs, xT) + +L = hcat(Matrix(1.0I,2*n,2*n), zeros(2*n,2*n)) +m, d = size(L) +Σ = Matrix(Σdiagel*I,m,m) +=# diff --git a/landmarks/msmodel.jl b/landmarks/msmodel.jl new file mode 100644 index 0000000..f2b13ae --- /dev/null +++ b/landmarks/msmodel.jl @@ -0,0 +1,130 @@ +include("state.jl") + +const d = 2 +const Point = SArray{Tuple{d},Float64,1,d} # point in R2 +const Unc = SArray{Tuple{d,d},Float64,d,d*d} # Matrix presenting uncertainty + + + +######### +struct MarslandShardlow{T} <: ContinuousTimeProcess{State{Point}} # used to be called Landmarks + a::T # kernel parameter + γ::T # noise level + λ::T # mean reversion + #v::Vector{T} # conditioning + n::Int +end + +# specify auxiliary process +struct MarslandShardlowAux{T} <: ContinuousTimeProcess{State{Point}} + a::T # kernel parameter + γ::T # noise level + λ::T # mean reversion + xT::State{Point} # use x = State(P.v, zero(P.v)) where v is conditioning vector + n::Int +end + +MarslandShardlowAux(P::MarslandShardlow, v) = MarslandShardlowAux(P.a, P.γ, P.λ, v, P.n) + + +# Gaussian kernel +kernel(x, P) = 1/(2*π*P.a)^(length(x)/2)*exp(-norm(x)^2/(2*P.a)) + + + +zero!(v) = v[:] = fill!(v, zero(eltype(v))) +function hamiltonian((q, p), P) + s = 0.0 + for i in eachindex(q), j in eachindex(q) + # i == j && continue + s += 1/2*dot(p[i], p[j])*kernel(q[i] - q[j], P) + end + s +end + +Bridge.b(t::Float64, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.b!(t, x, copy(x), P) +function Bridge.b!(t, x, out, P::MarslandShardlow) + zero!(out) + for i in 1:P.n + for j in 1:P.n + out.q[i] += 0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) + # heat bath + out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) + + 1/(2*P.a) * dot(p(x,i), p(x,j)) * (q(x,i)-q(x,j))*kernel(q(x,i) - q(x,j), P) + end + end + out +end + +function Bridge.b!(t, x, out, P::MarslandShardlowAux) + zero!(out) + for i in 1:P.n + for j in 1:P.n + @inbounds out.q[i] += 0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) + # heat bath + # out[posp(i)] += -P.λ*0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) + + # 1/(2*P.a) * dot(p(x,i), p(x,j)) * (q(x,i)-q(x,j))*kernel(q(x,i) - q(x,j), P) + end + end + out +end + +function Bridge.B(t, P::MarslandShardlowAux) + I = Int[] + J = Int[] + X = Unc[] + for i in 1:P.n + for j in 1:P.n + push!(I, 2i - 1) + push!(J, 2j) + push!(X, 0.5*kernel(q(P.xT,i) - q(P.xT,j), P)*one(Unc)) + end + end + B = sparse(I, J, X, 2P.n, 2P.n) +end + + +function Bridge.σ!(t, x, dm, out, P::Union{MarslandShardlow, MarslandShardlowAux}) + zero!(out.q) + out.p .= dm*P.γ + out +end + +Bridge.constdiff(::Union{MarslandShardlow, MarslandShardlowAux}) = true + + +if false + +#= +function Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) + out = zeros(4*P.n,4*P.n) + for i in (2*P.n+1): 4*P.n + out[i,i] = 1.0 + end + out * P.γ^2 +end +Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) +=# + + + +function BBt!(t, arg, out, P::MarslandShardlowAux) + B = zeros(4 * P.n,4 * P.n) + for i in 1:P.n, j in 1:P.n + B[posq(i),posp(j)] = 0.5 * kernel(q(P.v,i)-q(P.v,j),P) * Matrix(1.0I,2,2) + end + out .= (B*arg + arg*B') + out +end + +# nog aan te passen +function Bridge.dP!(t, p, out, P) + BBt!(t, p, out, P) + for i in (2*P.n+1): 4*P.n + out[i,i] -= P.γ^2 + end + out +end + + +end diff --git a/landmarks/patches.jl b/landmarks/patches.jl new file mode 100644 index 0000000..5fdff62 --- /dev/null +++ b/landmarks/patches.jl @@ -0,0 +1,65 @@ + +function Bridge.sample!(W::SamplePath{Vector{T}}, P::Wiener{Vector{T}}, y1 = W.yy[1]) where {T} + y = copy(y1) + copyto!(W.yy[1], y) + + for i = 2:length(W.tt) + rootdt = sqrt(W.tt[i]-W.tt[i-1]) + for k in eachindex(y) + y[k] = y[k] + rootdt*randn(T) + end + copyto!(W.yy[i], y) + end + #println(W.yy[1]) + W +end + + +struct StratonovichHeun! <: Bridge.SDESolver +end + +function Bridge.solve!(solver::StratonovichHeun!, Y::SamplePath, u, W::SamplePath, P::Bridge.ProcessOrCoefficients) + N = length(W) + N != length(Y) && error("Y and W differ in length.") + + tt = Y.tt + tt[:] = W.tt + yy = Y.yy + y = copy(u) + ȳ = copy(u) + + tmp1 = copy(y) + tmp2 = copy(y) + tmp3 = copy(y) + tmp4 = copy(y) + + dw = copy(W.yy[1]) + for i in 1:N-1 + t¯ = tt[i] + dt = tt[i+1] - t¯ + copyto!(yy[i], y) + if dw isa Number + dw = W.yy[i+1] - W.yy[i] + else + for k in eachindex(dw) + dw[k] = W.yy[i+1][k] - W.yy[i][k] + end + end + + _b!((i,t¯), y, tmp1, P) + σ!(t¯, y, dw, tmp2, P) + + for k in eachindex(y) + ȳ[k] = y[k] + tmp1[k]*dt + tmp2[k] # Euler prediction + end + + _b!((i + 1,t¯ + dt), ȳ, tmp3, P) # coefficients at ȳ + σ!(t¯ + dt, ȳ, dw2, tmp4, P) + + for k in eachindex(y) + y[k] = y[k] + 0.5*((tmp1[k] + tmp3[k])*dt + tmp2[k] + tmp4[k]) + end + end + copyto!(yy[end], endpoint(y, P)) + Y +end diff --git a/landmarks/state.jl b/landmarks/state.jl new file mode 100644 index 0000000..7c338f8 --- /dev/null +++ b/landmarks/state.jl @@ -0,0 +1,84 @@ + +struct State{P} + q::Vector{P} + p::Vector{P} +end +q(x::State) = x.q +p(x::State) = x.p +q(x::State, i) = x.q[i] +p(x::State, i) = x.p[i] + + + +import Base:iterate, eltype, copy, copyto!, zero, eachindex, getindex, setindex!, size, vec +iterate(x::State) = (x.q, true) +iterate(x::State, s) = s ? (x.p, false) : nothing +copy(x::State) = State(copy(x.q), copy(x.p)) +function copyto!(x::State, y::State) + copyto!(x.q, y.q) + copyto!(x.p, y.p) + x +end +function copyto!(x::State, y) + for i in eachindex(x) + x[i] = y[i] + end + x +end +#eltype(::State{P}) = P + + +Base.broadcastable(x::State) = x +Broadcast.BroadcastStyle(::Type{<:State}) = Broadcast.Style{State}() + + + +size(s::State) = (2, length(s.p)) + +zero(x::State) = State(zero(x.p), zero(x.q)) +zero!(v) = fill!(v, zero(eltype(v))) +function zero!(x::State) + zero!(x.p) + zero!(x.q) + x +end + + + +function getindex(x::State, I::CartesianIndex) + if I[1] == 1 + x.q[I[2]] + elseif I[1] == 2 + x.p[I[2]] + else + throw(BoundsError()) + end +end +function setindex!(x::State, val, I::CartesianIndex) + if I[1] == 1 + x.q[I[2]] = val + elseif I[1] == 2 + x.p[I[2]] = val + else + throw(BoundsError()) + end +end + +eachindex(x::State) = CartesianIndices((Base.OneTo(2), eachindex(x.p))) + +import Base: *, +, /, - +import LinearAlgebra: norm +import Bridge: outer +*(c::Number, x::State) = State(c*x.q, c*x.p) +*(x::State,c::Number) = State(x.q*c, x.p*c) ++(x::State, y::State) = State(x.q + y.q, x.p + y.p) +-(x::State, y::State) = State(x.q - y.q, x.p - y.p) +function outer(x::State, y::State) + [outer(x[i],y[j]) for i in eachindex(x), j in eachindex(y)] +end +# unc(a::Array) = State([sqrt(a[1, i, 1, i]) for i in 1:size(a, 2)],[sqrt(a[2, i, 2, i]) for i in 1:size(a, 2)]) + +norm(x::State) = norm(x.q) + norm(x.q) + +/(x::State, y) = State(x.q/y, x.p/y) +vec(x::State) = vec([x[J] for J in eachindex(x)]) diff --git a/landmarks/testms.jl b/landmarks/testms.jl new file mode 100644 index 0000000..b2d88b1 --- /dev/null +++ b/landmarks/testms.jl @@ -0,0 +1,11 @@ + +using Test +out1 = copy(xT) +@time out1 = (Bridge.b!(t[end], xT, out1, Pmsaux)) + +@time B = Bridge.B(t[end], Pmsaux) +x = vec(xT) +out2 = copy(x) +@time out2 = mul!(out2, B, x, true, false) + +@test vec(out1) ≈ out2 From 5e57d283a8250dd77455ea969a2b7d17256acf2d Mon Sep 17 00:00:00 2001 From: fmeulen Date: Fri, 25 Jan 2019 14:41:24 +0100 Subject: [PATCH 02/58] First shot at landmarks model --- landmarks/LowrankRiccati.jl | 93 ++++++ landmarks/ahsmodel.jl | 172 ++++++++-- landmarks/backward!.jl | 14 - landmarks/forward.jl | 309 ++++++++++++++++-- landmarks/guiding.jl | 168 ++++++++++ landmarks/inverse_uncmatrix.jl | 27 ++ landmarks/msmodel.jl | 116 ++++--- landmarks/patches.jl | 54 ++- landmarks/state.jl | 195 ++++++++++- landmarks/testms.jl | 2 + project_partialbridge/lowrankricatti.jl | 125 +++++++ project_partialbridge/partialbridge_bolus3.jl | 20 +- src/ode!.jl | 12 +- src/sde!.jl | 18 + 14 files changed, 1188 insertions(+), 137 deletions(-) create mode 100644 landmarks/LowrankRiccati.jl delete mode 100644 landmarks/backward!.jl create mode 100644 landmarks/guiding.jl create mode 100644 landmarks/inverse_uncmatrix.jl create mode 100644 project_partialbridge/lowrankricatti.jl diff --git a/landmarks/LowrankRiccati.jl b/landmarks/LowrankRiccati.jl new file mode 100644 index 0000000..4e7b0e8 --- /dev/null +++ b/landmarks/LowrankRiccati.jl @@ -0,0 +1,93 @@ +module LowrankRiccati + +#= +include("LowrankRiccati.jl") +using .LowrankRiccati +=# +export lowrankriccati, lowrankriccati! + +using SparseArrays +using SuiteSparse +using LinearAlgebra +using Expokit # for matrix exponentials +using BenchmarkTools +using Distributions + + +# we use Expokit, which gives the funciton expmv! +# w = expmv!{T}( w::Vector{T}, t::Number, A, v::Vector{T}; kwargs...) +# The function expmv! calculates w = exp(t*A)*v, where A is a matrix or any type that supports size, eltype and mul! and v is a dense vector by using Krylov subspace projections. The result is stored in w. + +""" +Compute exp(A τ) * U +""" +function expmat(τ,A,U) + M = [] + for j in 1:size(U,2) + push!(M, expmv!(zeros(size(U,1)),τ,A,U[:,j])) + end + hcat(M...) +end + +""" + one step of low rank ricatti + implement Mena et al. for solving + (d P)/(d t) = A P(t) + P(t) A' + Q, P(t_0) = P0 + with a low rank approximation for P +""" +function lowrankriccati!(s, t, A, Q, (S,U), (Sout, Uout)) + τ = t-s # time step + Uᴬ, R = qr!(expmat(τ,A,U)) + Uᴬ = Matrix(Uᴬ) # convert from square to tall matrix + # step 4 + Sᴬ = R * S * R' + # step 5a (gives new U) + U, Ŝ = qr!(Uᴬ * Sᴬ + (τ * Q) * Uᴬ) + Uout .= Matrix(U) + # step 5b + Ŝ = Ŝ - Uout' * (τ * Q) * Uᴬ + # step 5c (gives new S) + L = Ŝ * Uᴬ' + Uout' * (τ * Q) + Sout .= L * Uout + + Sout, Uout +end +lowrankriccati(s, t, A, Q, (S, U)) = lowrankriccati!(s, t, A, Q, (S, U), (copy(S), copy(U))) + +using Test +@testset "low rank riccati" begin + + # Test problem + d = 30 + Q = sprand(d,d,.01) - I# Diagonal(randn(d)) + Q = Q * Q' + A = sprand(d,d,0.1)-I #Diagonal(diagels) + diagels = 0.4.^(1:d) + P0 = Diagonal(diagels) + + ld = 30 # low rank dimension + + s = 0.3 + t = 0.31 + τ = t - s + + # step 1 + M0 = eigen(Matrix(P0)) + S = Matrix(Diagonal(M0.values[1:ld])) + U = M0.vectors[:,1:ld] + + + # Low rank riccati solution to single time step + S, U = lowrankriccati(s, t, A, Q, (S, U)) + P = U * S * U' + + # Compute exact solution + λ = lyap(Matrix(A), -Matrix(Q)) + P0 + Φ = exp(Matrix(A)*τ) + + Pexact = Φ*λ*Φ' - λ + P0 + # assess difference + @test norm(P - Pexact) < 0.001 +end + +end diff --git a/landmarks/ahsmodel.jl b/landmarks/ahsmodel.jl index 23f3ef0..172c3d6 100644 --- a/landmarks/ahsmodel.jl +++ b/landmarks/ahsmodel.jl @@ -1,14 +1,9 @@ -include("state.jl") - -const d = 2 -const Point = SArray{Tuple{d},Float64,1,d} # point in R2 -const Unc = SArray{Tuple{d,d},Float64,d,d*d} # Matrix presenting uncertainty ######### struct Noisefield δ::Point # locations of noise field λ::Point # scaling at noise field - τ::Float64 # variance of noise field + τ::Float64 # std of Gaussian kernel noise field end ######### @@ -27,17 +22,15 @@ struct LandmarksAux{T} <: ContinuousTimeProcess{State{Point}} n::Int64 # numer of landmarks nfs::Vector{Noisefield} # vector containing pars of noisefields end -LandmarksAux(P::Landmarks, xT) = LandMarksAux(P.a, P.λ, xT, P.n, P.nfs) +LandmarksAux(P::Landmarks, xT) = LandmarksAux(P.a, P.λ, xT, P.n, P.nfs) # Gaussian kernel -kernel(x, P) = 1/(2*π*P.a)^(length(x)/2)*exp(-norm(x)^2/(2*P.a)) +kernel(x, P::Union{Landmarks, LandmarksAux}) = 1/(2*π*P.a)^(length(x)/2)*exp(-norm(x)^2/(2*P.a)) # Kernel of the noise fields (need these functions to evaluate diffusion coefficient in ahs model) -noiseσ(q, nf::Noisefield) = nf.λ * exp(-norm(nf.δ - q)^2/nf.τ) -eta(q, p, nf::Noisefield) = dot(p, nf.λ)/nf.τ * (q - nf.δ) * exp(-norm(nf.δ - q)^2/nf.τ) - +noiseσ(q, nf::Noisefield) = nf.λ * exp(-norm(nf.δ - q)^2/nf.τ^2) +eta(q, p, nf::Noisefield) = dot(p, nf.λ)/nf.τ^2 * (q - nf.δ) * exp(-norm(nf.δ - q)^2/nf.τ^2) -zero!(v) = v[:] = fill!(v, zero(eltype(v))) function hamiltonian((q, p), P) s = 0.0 for i in eachindex(q), j in eachindex(q) @@ -48,6 +41,11 @@ function hamiltonian((q, p), P) end Bridge.b(t::Float64, x, P::Union{Landmarks, LandmarksAux}) = Bridge.b!(t, x, copy(x), P) + +""" +Evaluate drift of landmarks in (t,x) and save to out +x is a state and out as well +""" function Bridge.b!(t, x, out, P::Landmarks) zero!(out) for i in 1:P.n @@ -61,19 +59,94 @@ function Bridge.b!(t, x, out, P::Landmarks) out end +""" +Evaluate drift of landmarks auxiliary process in (t,x) and save to out +x is a state and out as well +""" function Bridge.b!(t, x, out, P::LandmarksAux) zero!(out) for i in 1:P.n for j in 1:P.n - out.q[i] += 0.5*p(x,j)*kernel(q(P.v,i) - q(P.v,j), P) + out.q[i] += 0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) # heat bath - # out[posp(i)] += -P.λ*0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) + - # 1/(2*P.a) * dot(p(x,i), p(x,j)) * (q(x,i)-q(x,j))*kernel(q(x,i) - q(x,j), P) + out.p[i] +=# -P.λ*0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) + + 1/(2*P.a) * dot(p(P.xT,i), p(P.xT,j)) * (q(x,i)-q(x,j))*kernel(q(P.xT,i) - q(P.xT,j), P) end end out end + +""" +Compute tildeB(t) for landmarks auxiliary process +""" +function Bridge.B(t, Paux::LandmarksAux) + I = Int[] + J = Int[] + X = Unc[] + for i in 1:Paux.n + for j in 1:Paux.n + # terms for out.q[i] + push!(I, 2i - 1) + push!(J, 2j) + push!(X, 0.5*kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc)) + + # terms for out.p[i] + push!(I, 2i) + push!(J, 2j-1) + if j==i + push!(X, sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), P) for j in setdiff(1:Paux.n,i)]) * one(Unc)) + else + push!(X, -1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)) + end + end + end + B = sparse(I, J, X, 2Paux.n, 2Paux.n) +end + +# function Bridge.B!(t,X,out, P::LandmarksAux) +# I = Int[] +# J = Int[] +# B = Unc[] +# for i in 1:P.n +# for j in 1:P.n +# push!(I, 2i - 1) +# push!(J, 2j) +# push!(B, 0.5*kernel(q(P.xT,i) - q(P.xT,j), P)*one(Unc)) +# end +# end +# out .= Matrix(sparse(I, J, B, 2P.n, 2P.n)) * X # BAD: inefficient +# end +""" +Compute B̃(t) * X (B̃ from auxiliary process) and write to out +Both B̃(t) and X are of type UncMat +""" +function Bridge.B!(t,X,out, Paux::LandmarksAux) + out .= 0.0 * out + for i in 1:Paux.n # separately loop over even and odd indices + for k in 1:2Paux.n # loop over all columns + for j in 1:Paux.n + out[2i-1,k] += X[p(j), k] *0.5*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) *one(Unc) + if j==i + out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * + kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) + else + out[2i,k] += X[q(j),k] *(-1/(2*Paux.a)) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc) + end + end + end + end + out +end + + # A = reshape([Unc(rand(4)) for i in 1:6, j in 1:6],6,6)) + # out = copy(A) + # Bridge.B!(1.0,A,out,Paux) + +""" +Compute sigma(t,x) * dm where dm is a vector and sigma is the diffusion coefficient of landmarks +write to out which is of type State +""" function Bridge.σ!(t, x, dm, out, P::Landmarks) zero!(out) nfs = P.nfs @@ -82,29 +155,70 @@ function Bridge.σ!(t, x, dm, out, P::Landmarks) for j in 1:length(nfs) #out.p[i] += noiseσ(q(x, i), nf) * dm #out.q[i] += eta(q(x, i), p(x, i), nf) * dm - out.p[i] += noiseσ(q(x, i), nfs[j]) * dm[j] - out.q[i] += eta(q(x, i), p(x, i), nfs[j]) * dm[j] + out.q[i] += noiseσ(q(x, i), nfs[j]) * dm[j] + out.p[i] += eta(q(x, i), p(x, i), nfs[j]) * dm[j] end end out end +""" +Compute tildesigma(t,x) * dm where dm is a vector and sigma is the diffusion coefficient of landmarksaux +write to out which is of type State +""" function Bridge.σ!(t, x, dm, out, P::LandmarksAux) Bridge.σ!(t, P.xT, dm, out, P::Landmarks) end -# function Bridge.a(t,x, P::Landmarks) -# out = zeros(4*P.n,P.J) + + + +# function Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) +# I = Int[] +# X = Unc[] +# γ2 = P.γ^2 # for i in 1:P.n -# for j in 1:P.J -# out[posq(i),j] = noiseσ(q(x,i),P.nfs[j]) -# out[posp(i),j] = eta(q(x,i),p(x,i),P.nfs[j]) -# end +# push!(I, 2i) +# push!(X, γ2*one(Unc)) # end -# Bridge.outer(out) +# a = sparse(I, I, X, 2P.n, 2P.n) # end -# -# Bridge.a(t,P::LandmarksAux) = Bridge.a(t, cat(P.v, zeros(2*P.n)),P::Landmarks ) -# Bridge.a(t, x, P::LandmarksAux) = Bridge.a(t, P::LandmarksAux) -Bridge.constdiff(Landmarks) = false -Bridge.constdiff(LandmarksAux) = true + + + +function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) + if P isa Landmarks + x = x_ + else + x = P.xT + end + out = zeros(Unc,2P.n,2P.n) + for i in 1:P.n + for k in 1:P.n + for j in 1:length(P.nfs) + r1 = noiseσ(q(x,i),P.nfs[j]) * noiseσ(q(x, k),P.nfs[j])' + r2 = noiseσ(q(x,i),P.nfs[j]) * eta(q(x,k),p(x,k),P.nfs[j])' + r3 = eta(q(x,i),p(x,i),P.nfs[j]) * eta(q(x,k),p(x,k),P.nfs[j])' + out[2i-1,2k-1] += r1 + out[2i,2k-1] += r2 + out[2i-1,2k] += r2 + out[2i,2k] += r3 + + end + end + end + out +end + +Bridge.a(t, P::LandmarksAux) = Bridge.a(t, P.xT, P) + +""" +Multiply a(t,x) times in (which is of type state) +Returns multiplication of type state +""" +function amul(t, x, in::State, P) + State(Bridge.a(t, x, P)*vec(in)) +end + +Bridge.constdiff(::Landmarks) = false +Bridge.constdiff(::LandmarksAux) = true diff --git a/landmarks/backward!.jl b/landmarks/backward!.jl deleted file mode 100644 index cf928c8..0000000 --- a/landmarks/backward!.jl +++ /dev/null @@ -1,14 +0,0 @@ -function Bridge.gpupdate(ν::Vector, P::Matrix, Σ, L, v) - if all(diag(P) .== Inf) - P_ = inv(L' * inv(Σ) * L) - V_ = (L' * inv(Σ) * L)\(L' * inv(Σ) * v) - return V_, P_ - else - Z = I - P*L'*inv(Σ + L*P*L')*L - return Z*P*L'*inv(Σ)*v + Z*ν, Z*P - end -end - -# ms model: start with outcommented stuff in msmodel -# update/adjust partial bridgenuH file for solving backward -# update/adjust partialbridge_bolus3 to do par estimation and bridge imputation diff --git a/landmarks/forward.jl b/landmarks/forward.jl index aa34226..a20c58b 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -1,6 +1,7 @@ # reminder, to type H*, do H\^+ #cd("/Users/Frank/.julia/dev/Bridge") #outdir="output/landmarks/" +cd("/Users/Frank/.julia/dev/Bridge/landmarks") using Bridge, StaticArrays, Distributions using Bridge:logpdfnormal @@ -13,33 +14,80 @@ using RCall using Base.Iterators using SparseArrays + models = [:ms, :ahs] -TEST = true +model = models[2] +TEST = false#true + +discrmethods = [:ralston, :lowrank, :psd] +discrmethod = discrmethods[2] + +obsschemes =[:full, :partial] +obsscheme = obsschemes[2] + +const d = 2 + +n = 40 # nr of landmarks +ldim = 2n*d # dimension of low-rank approximation to H\^+ + +cheat = false#true#false # if cheat is true, then we initialise at x0 (true value) and +# construct the guiding term based on xT (true value) + +θ = 6π/40# π/6 0#π/5 # angle to rotate endpoint + +ϵ = 0.001 # parameter for initialising Hend⁺ +obsnoise = 0.001 # noise on observations + + + +println(model) +println(discrmethod) +println(obsscheme) + +T = 0.5#1.0#0.5 +t = 0.0:0.005:T # time grid + +#Random.seed!(5) + include("state.jl") include("msmodel.jl") include("ahsmodel.jl") include("patches.jl") +include("guiding.jl") +#include("lyap.jl") +include("LowrankRiccati.jl") +using .LowrankRiccati -n = 250 - -t = 0.0:0.001:1.0 - +### Specify landmarks models +a = 1.0 ; λ = 0.5; #= not the lambda of noise fields =# γ = 5.0 -a = 1.0 ; λ = 0.5 ; γ = 5.0 Pms = MarslandShardlow(a, γ, λ, n) -nfvar = 1.0 # tau -r1 = (-2.0:2.0) #+ 0.1rand(5) -r2 = (-2.0:2.0) #+ 0.1rand(5) +if true + # specify locations noisefields + r1 = (-2.0:0.5:2.0) #+ 0.1rand(5) + r2 = (-2.0:0.5:2.0) #+ 0.1rand(5) + nfloc = Point.(collect(product(r1, r2)))[:] + # scaling parameter of noisefields + nfscales = [0.1Point(1.0, 1.0) for x in nfloc] + nfstd = 2.05 # tau , variance of noisefields +else + # specify locations noisefields + r1 = (-2.0:0.5:2.0) #+ 0.1rand(5) + r2 = (-2.0:0.5:2.0) #+ 0.1rand(5) + nfloc = Point.(collect(product(r1, r2)))[:] + # scaling parameter of noisefields + nfscales = [2.5Point(1.0, 1.0) for x in nfloc] + nfstd = 1.0 # tau , variance of noisefields +end + +nfs = [Noisefield(δ, λ, nfstd) for (δ, λ) in zip(nfloc, nfscales)] -nfloc = Point.(collect(product(r1, r2)))[:] -nfscales = [0.5Point(1.0, 1.0) for x in nfloc] -nfs = [Noisefield(δ, λ, nfvar) for (δ, λ) in zip(nfloc, nfscales)] Pahs = Landmarks(a, λ, n, nfs) +### -model = models[2] if model == :ms dwiener = n @@ -55,48 +103,241 @@ w0 = zeros(StateW, dwiener) W = SamplePath(t, [copy(w0) for s in t]) sample!(W, Wiener{Vector{StateW}}()) -q0 = [Point(cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] -#q0 = circshift(q0, (1,)) - -p_ = 3*Point(0.1, 0.1) -p0 = [p_ for i in 1:n] -#p0 = [randn(Point) for i in 1:n] +# specify initial landmarks configuration +q0 = [Point(cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) +p_ = 5*Point(0.1, 0.1) +p0 = [p_ for i in 1:n] # +p0 = [randn(Point) for i in 1:n] x0 = State(q0, p0) -X = SamplePath(t, [copy(x0) for s in t]) -@time solve!(EulerMaruyama!(), X, x0, W, P) + +#Random.seed!(1234) + +X = SamplePath(t, [copy(x0) for s in t]) +if model == :ms + @time solve!(EulerMaruyama!(), X, x0, W, P) +else + @time solve!(EulerMaruyama!(), X, x0, W, P) + # still needs to be implemented + #@time solve!(StratonovichHeun!(), X, x0, W, P) +end extractcomp(v,i) = map(x->x[i], v) +if TEST + ####### extracting components + X.tt # gives all times + X.yy # gives an array of States (the state at each time) + X.yy[1] # gives the state at first time + + q(X.yy[1]) # gives the array of positions of all points + X.yy[1].q # equivalent + + p(X.yy[1]) # gives the array of momenta of all points + X.yy[1].p # equivalent + + p(X.yy[1],10) # at first time, extract momentum vector of landmark nr 10 + q(X.yy[23],10) # extract position at time 23, for landmark nr 10 + + map(x->norm(x), X.yy[1].q) # verifies that all points are on the unit circle + ham = [hamiltonian(X.yy[i],Pms) for i in 1:length(t)] + print(ham) + ############# +end + + out = [Any[X.tt[i], [X.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(X.tt) ][:] df = DataFrame(time=extractcomp(out,1),pos1=extractcomp(out,2),pos2=extractcomp(out,3),mom1=extractcomp(out,4),mom2=extractcomp(out,5),pointID=extractcomp(out,6)) #Any["X.tt[$i]", ["X.yy[$i][CartesianIndex($c, $k)][$l]" for l in 1:d, k in 1:n, c in 1:2]...] + +if model == :ms + titel = "Marsland-Shardlow model, " +else + titel = "Arnaudon-Holm-Sommer model, " +end +titel = titel * string(n)*" landmarks" + +@rput titel @rput df R""" library(tidyverse) df %>% dplyr::select(time,pos1,pos2,pointID) %>% - ggplot(aes(x=pos1,pos2,group=pointID,colour=time)) + geom_path() + ggplot(aes(x=pos1,pos2,group=pointID,colour=time)) + + geom_path() + + theme_minimal() + xlab('horizontal position') + + ylab('vertical position') + ggtitle(titel) """ R""" df %>% dplyr::select(time,mom1,mom2,pointID) %>% - filter(pointID %in% c("point1","point2","point3","point4","point5")) %>% + filter(pointID %in% c("point1","point2","point3","point40","point41","point42")) %>% ggplot(aes(x=mom1,mom2,group=pointID,colour=time)) + geom_path() + - facet_wrap(~pointID) + facet_wrap(~pointID) + theme_minimal() """ +# observe positions without noise +v0 = q(X.yy[1]) +rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) +vT = [rot * q(X.yy[end])[i] for i in 1:P.n ] +#vT = q(X.yy[end]) -xT = X.yy[end] -Pmsaux = MarslandShardlowAux(Pms, xT) -if TEST - include("testms.jl") + +#dtimp = 0.01 # mesh width for imputation +tc(t,T) = t.*(2-t/T) +tt_ = t#tc(t,T)# 0:dtimp:(T) + +#################### +# solve backward recursion on [0,T] + + + + +if obsscheme==:partial + L = deepmat( [(i==j)*one(Unc) for i in 1:2:2n, j in 1:2n]) + Σ = Diagonal(obsnoise*ones(n*d)) + Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) + if cheat + Pahsaux = LandmarksAux(Pahs, X.yy[end]) + else + Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) + #Pahsaux = LandmarksAux(Pahs, State(vT, rand(Point,Pahs.n))) + #Pahsaux = LandmarksAux(Pahs, State(vT, [Point(1,1) for i in 1:Pahs.n])) + #Pahsaux = LandmarksAux(Pahs, X.yy[end]) + #Pahsaux = LandmarksAux(Pahs, State(vT, 0.0*X.yy[end].p)) + end +end +if obsscheme==:full + L = deepmat( [(i==j)*one(Unc) for i in 1:2n, j in 1:2n]) + Σ = Diagonal(obsnoise*ones(2n*d)) + Pmsaux = MarslandShardlowAux(Pms,X.yy[end]) + Pahsaux = LandmarksAux(Pahs, X.yy[end]) + v0 = vec(X.yy[1]) + vT = vec(X.yy[end]) +end + +if model == :ms + Paux = Pmsaux +else + Paux = Pahsaux +end + +Hend⁺ = [(i==j)*one(Unc)/ϵ for i in 1:2n, j in 1:2n] +#### perform gpupdate step +νend , Hend⁺ = gpupdate(Paux.xT,Hend⁺, Σ, L, vT) +# L, and Σ are ordinary matrices, vT an array of Points +# νend is a state , Hend⁺ a UncMat + +# initialise νt +νt = [copy(νend) for s in tt_] + + +if discrmethod==:lowrank + M0 = eigen(deepmat(Hend⁺)) + largest = sortperm(M0.values)[end-ldim+1:end] + Send = Matrix(Diagonal(M0.values[largest])) + Uend = M0.vectors[:,largest] +# println(deepmat(Hend⁺)-Uend*Send*Uend') + St = [copy(Send) for s in tt_] + Ut = [copy(Uend) for s in tt_] + @time νend, (Send, Uend) = bucybackwards!(LRR(), t, νt, (St, Ut), Paux, νend, (Send, Uend)) + Hend⁺ = deepmat2unc(Uend * Send * Uend') + #map(x->isposdef(x),St) +# Ht = map((S,U) -> LowRank(cholesky(Hermitian(S)),U),St,Ut) + Ht = map((S,U) -> LowRank(S,U), St,Ut) +end +if discrmethod==:ralston + H⁺t = [copy(Hend⁺) for s in tt_] + @time νend , Hend⁺ = bucybackwards!(Bridge.R3!(), tt_, νt, H⁺t, Paux, νend, Hend⁺) + println(map(x->isposdef(deepmat(x)),H⁺t)) + Ht = map(H⁺ -> InverseCholesky(lchol(H⁺)),H⁺t) +end +if discrmethod==:psd + H⁺t = [copy(Hend⁺) for s in tt_] + @time νend , Hend⁺ = bucybackwards!(Lyap(), tt_, νt, H⁺t, Paux, νend, Hend⁺) + println(map(x->isposdef(deepmat(x)),H⁺t)) + #Ht = map(H⁺ -> InverseCholesky(lchol(Hermitian(H⁺))),H⁺t) + Ht = map(H⁺ -> InverseCholesky(lchol(H⁺)),H⁺t) + #map(H⁺ -> lchol(Hermitian(H⁺)),H⁺t) +end + + + + +Q = GuidedProposal!(P, Paux, tt_, νt, Ht) + +νstart , Hstart⁺ = gpupdate(νend , Hend⁺, Σ, L, v0) +#νstart , Hstart⁺ = gpupdate(νend , Hend⁺, Σ, L, q(XX.yy[1])) + +xinit = cheat ? x0 : νstart # or xinit ~ N(νstart, Hstart⁺) +winit = zeros(StateW, dwiener) +XX = SamplePath(tt_, [copy(xinit) for s in tt_]) +WW = SamplePath(tt_, [copy(winit) for s in tt_]) +sample!(WW, Wiener{Vector{StateW}}()) + +Bridge.solve!(EulerMaruyama!(), XX, xinit, WW, Q) + +hcat(mean(X.yy[end].p), mean(XX.yy[end].p)) +# redo with Paux.xT = XX.yy[end] + hcat(X.yy[end].p, XX.yy[end].p, Paux.xT.p) + +#### plotting +outg = [Any[XX.tt[i], [XX.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(XX.tt) ][:] +dfg = DataFrame(time=extractcomp(outg,1),pos1=extractcomp(outg,2),pos2=extractcomp(outg,3),mom1=extractcomp(outg,4),mom2=extractcomp(outg,5),pointID=extractcomp(outg,6)) +#Any["X.tt[$i]", ["X.yy[$i][CartesianIndex($c, $k)][$l]" for l in 1:d, k in 1:n, c in 1:2]...] + +dfT = DataFrame(pos1=extractcomp(vT,1), pos2=extractcomp(vT,2)) +df0= DataFrame(pos1=extractcomp(v0,1), pos2=extractcomp(v0,2)) + + +if model == :ms + titel = "Marsland-Shardlow model, " +else + titel = "Arnaudon-Holm-Sommer model, " end +titel = titel * string(n)*" landmarks" + +@rput titel +@rput dfg +@rput dfT +@rput df0 +@rput T +R""" +library(tidyverse) +T_ <- T-0.0001 +#T_ <- 0.8 +dfsub <- df %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,pos1,pos2,pointID) %>% filter(time<0.99) + dfsubg <- dfg %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time<0.99) -L = hcat(Matrix(1.0I,2*n,2*n), zeros(2*n,2*n)) -m, d = size(L) -Σ = Matrix(Σdiagel*I,m,m) -=# + sub <- rbind(dfsub,dfsubg) + sub$fg <- rep(c("forward","guided"),each=nrow(dfsub)) + + ggplot() + + geom_path(data=sub, mapping=aes(x=pos1,pos2,group=pointID,colour=fg)) + + geom_point(data=dfT, mapping=aes(x=pos1,y=pos2),colour='orange',size=0.7) + + geom_point(data=df0, mapping=aes(x=pos1,y=pos2),colour='black',size=0.7)+ + #facet_wrap(~fg) + + theme_minimal() + xlab('horizontal position') + + ylab('vertical position') + ggtitle(titel) + """ +end +@time llikelihood(LeftRule(), XX, Q; skip = 0) # won't work for AHS because matrix multilication for Htilde is not defined yet diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl new file mode 100644 index 0000000..3be2aef --- /dev/null +++ b/landmarks/guiding.jl @@ -0,0 +1,168 @@ +# compute guiding term: backward ode +# compute likelihood of guided proposal + +import Bridge: kernelr3!, R3!, target, auxiliary, constdiff, llikelihood, _b!, B!, σ!, b! + +function gpupdate(ν, P, Σ, L, v) + if all(diag(P) .== Inf) + P_ = inv(L' * inv(Σ) * L) + V_ = (L' * inv(Σ) * L)\(L' * inv(Σ) * v) + return V_, P_ + else + Z = I - P*L'*inv(Σ + L*P*L')*L + return Z*P*L'*inv(Σ)*v + Z*ν, Z*P + end +end + +function gpupdate(ν2::State, P2, Σ, L, v2::Vector{Point}) + ν = deepvec(ν2) + P = deepmat(P2) + v = reinterpret(Float64,v2) + if all(diag(P) .== Inf) + P_ = inv(L' * inv(Σ) * L) + V_ = (L' * inv(Σ) * L)\(L' * inv(Σ) * v) + return deepvec2state(V_), deepmat2unc(P_) + else + Z = I - P*L'*inv(Σ + L*P*L')*L + return deepvec2state(Z*P*L'*inv(Σ)*v + Z*ν), deepmat2unc(Z*P) + end +end + + + +struct Arg4Closure{B,T} + f::B + arg4::T +end +(f::Arg4Closure)(arg1, arg2, arg3) = f.f(arg1, arg2, arg3, f.arg4) + +""" +Replacing out with dP, which is B*arg + arg*B'- tilde_a +""" +function dP!(t, p, out, P::Union{LandmarksAux, MarslandShardlowAux}) + B!(t, p, out, P) + out .= out .+ out' - a(t, P) + out +end + +# """ +# Make a 4-tuple where each tuple contains a copy of y +# """ +# Bridge.workspace(::Bridge.R3!, y) = (copy(y), copy(y), copy(y), copy(y)) + +""" +Computes solutions to backwards filtering odes for ν and H⁺ an an interval, say (S,T]. +Initialisations for the odes on the right are given by νend and Hend⁺ +Writes ν and H⁺ into νt and H⁺t (for all elements in t) and returns ν and H⁺ at S+ +""" +function bucybackwards!(S::R3!, t, νt, H⁺t, Paux, νend, Hend⁺) + H⁺t[end] = Hend⁺ + νt[end] = νend + wsν = Bridge.workspace(S, νend) + wsH⁺ = Bridge.workspace(S, Hend⁺) + for i in length(t)-1:-1:1 + dt = t[i] - t[i+1] + kernelr3!(Arg4Closure(Bridge.b!, Paux), t[i+1], νt[i+1], wsν, νt[i], dt) + kernelr3!(Arg4Closure(Bridge.dP!, Paux), t[i+1], H⁺t[i+1], wsH⁺, H⁺t[i], dt) + end + νt[1], H⁺t[1] +end + +struct LRR end # identifier to call Bucy backwards for low rank riccati + +function bucybackwards!(scheme::LRR, t, νt, (St, Ut), Paux, νend, (Send, Uend)) + St[end], Ut[end] = Send, Uend + νt[end] = νend + wsν = Bridge.workspace(R3!(), νend) + ã = deepmat(Bridge.a(t[end],Paux)) + B̃ = sparse(deepmat(Bridge.B(t[end],Paux))) + for i in length(t)-1:-1:1 + dt = t[i] - t[i+1] + kernelr3!(Arg4Closure(Bridge.b!, Paux), t[i+1], νt[i+1], wsν, νt[i], dt) + lowrankriccati!(t[i], t[i+1], -B̃, ã , (St[i+1], Ut[i+1]), (St[i], Ut[i])) + end + νt[1], (St[1], Ut[1]) +end + + +### for lyanpunov psd still needs to be fixed +struct Lyap end + +function bucybackwards!(::Lyap, t, νt, H⁺t, Paux, νend, Hend⁺) + H⁺t[end] = Hend⁺ + νt[end] = νend + wsν = Bridge.workspace(R3!(), νend) + for i in length(t)-1:-1:1 + dt = t[i] - t[i+1] + kernelr3!(Arg4Closure(Bridge.b!, Paux), t[i+1], νt[i+1], wsν, νt[i], dt) + lyapunovpsdbackward_step!(t[i+1], -dt, Paux, H⁺t[i+1], H⁺t[i]) # maybe with -dt + end + νt[1], H⁺t[1] +end + + +""" +Construct guided proposal on a single segment with times in tt from precomputed ν and H +""" +struct GuidedProposal!{T,Ttarget,Taux,Tν,TH,F} <: ContinuousTimeProcess{T} + target::Ttarget # P + aux::Taux # Ptilde + tt::Vector{Float64} # grid of time points on single segment (S,T] + ν::Vector{Tν} + H::Vector{TH} + endpoint::F + + function GuidedProposal!(target, aux, tt_, ν, H, endpoint=Bridge.endpoint) + tt = collect(tt_) + new{Bridge.valtype(target),typeof(target),typeof(aux),eltype(ν),eltype(H),typeof(endpoint)}(target, aux, tt, ν, H, endpoint) + end +end + +function Bridge._b!((i,t), x, out, P::GuidedProposal!) + Bridge.b!(t, x, out, P.target) + out .+= amul(t,x,P.H[i]*(P.ν[i] - x),P.target) + out +end + +σ!(t, x, dw, out, P::GuidedProposal!) = σ!(t, x, dw, out, P.target) + + +function _r!((i,t), x, out, P::GuidedProposal!) + out .= (P.H[i]*(P.ν[i] - x)) + out +end + + +target(P::GuidedProposal!) = P.target +auxiliary(P::GuidedProposal!) = P.aux + +constdiff(P::GuidedProposal!) = constdiff(target(P)) && constdiff(auxiliary(P)) + + +function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposal!; skip = 0) + tt = Xcirc.tt + xx = Xcirc.yy + + som::Float64 = 0. + rout = copy(xx[1]) + bout = copy(rout) + btout = copy(rout) + for i in 1:length(tt)-1-skip #skip last value, summing over n-1 elements + s = tt[i] + x = xx[i] + _r!((i,s), x, rout, Q) + b!(s, x, bout, target(Q)) + _b!((i,s), x, btout, auxiliary(Q)) +# btitilde!((s,i), x, btout, Q) + dt = tt[i+1]-tt[i] + som += dot(bout-btout, rout) * dt + + if !constdiff(Q) + H = H((i,s), x, Q) + Δa = a((i,s), x, target(Q)) - a((i,s), x, auxiliary(Q)) + som -= 0.5*tr(Δa*H) * dt + som += 0.5*(rout'*Δa*rout) * dt + end + end + som +end diff --git a/landmarks/inverse_uncmatrix.jl b/landmarks/inverse_uncmatrix.jl new file mode 100644 index 0000000..9adbe14 --- /dev/null +++ b/landmarks/inverse_uncmatrix.jl @@ -0,0 +1,27 @@ + + +using Test +using StaticArrays +using LinearAlgebra + +const d = 2 +const Point = SArray{Tuple{d},Float64,1,d} +const Unc = SArray{Tuple{d,d},Float64,d,d*d} + +x = [Point(rand(d)...) for i in 1:100] + +A = I + x*x' +lchol(A) = LowerTriangular((LinearAlgebra._chol!(copy(A), UpperTriangular)[1])') + +rchol(A) = LinearAlgebra._chol!(copy(A), UpperTriangular)[1] + +L = lchol(A) +R = rchol(A) + +@test norm(L*L' - A) < 1e-8 + +y = copy(x) +LinearAlgebra.naivesub!(L, y) # triangular backsolves +LinearAlgebra.naivesub!(R, y) + +@test norm(A*y - x) < 1e-9 diff --git a/landmarks/msmodel.jl b/landmarks/msmodel.jl index f2b13ae..7fd7e66 100644 --- a/landmarks/msmodel.jl +++ b/landmarks/msmodel.jl @@ -1,12 +1,4 @@ -include("state.jl") -const d = 2 -const Point = SArray{Tuple{d},Float64,1,d} # point in R2 -const Unc = SArray{Tuple{d,d},Float64,d,d*d} # Matrix presenting uncertainty - - - -######### struct MarslandShardlow{T} <: ContinuousTimeProcess{State{Point}} # used to be called Landmarks a::T # kernel parameter γ::T # noise level @@ -26,13 +18,11 @@ end MarslandShardlowAux(P::MarslandShardlow, v) = MarslandShardlowAux(P.a, P.γ, P.λ, v, P.n) - # Gaussian kernel -kernel(x, P) = 1/(2*π*P.a)^(length(x)/2)*exp(-norm(x)^2/(2*P.a)) - - +kernel(x, P::Union{MarslandShardlow, MarslandShardlowAux}) = 1/(2*π*P.a)^(length(x)/2)*exp(-norm(x)^2/(2*P.a)) zero!(v) = v[:] = fill!(v, zero(eltype(v))) + function hamiltonian((q, p), P) s = 0.0 for i in eachindex(q), j in eachindex(q) @@ -69,6 +59,9 @@ function Bridge.b!(t, x, out, P::MarslandShardlowAux) out end +""" +Compute tildeB(t) +""" function Bridge.B(t, P::MarslandShardlowAux) I = Int[] J = Int[] @@ -83,6 +76,37 @@ function Bridge.B(t, P::MarslandShardlowAux) B = sparse(I, J, X, 2P.n, 2P.n) end +# function Bridge.B!(t,x,out, P::MarslandShardlowAux) +# I = Int[] +# J = Int[] +# X = Unc[] +# for i in 1:P.n +# for j in 1:P.n +# push!(I, 2i - 1) +# push!(J, 2j) +# push!(X, 0.5*kernel(q(P.xT,i) - q(P.xT,j), P)*one(Unc)) +# end +# end +# out .= Matrix(sparse(I, J, X, 2P.n, 2P.n)) * x # BAD: inefficient +# end + +""" +Compute B̃(t) * X (B̃ from auxiliary process) and write to out +Both B̃(t) and X are of type UncMat +""" +function Bridge.B!(t,X,out, Paux::MarslandShardlowAux) + out .= 0.0 * out + for k in 1:2Paux.n # loop over out[p(i), p(k)] + for i in 1:Paux.n + for j in 1:Paux.n + out[2i-1,k] += 0.5*X[p(j), k]*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) + #out[2i,k] += -Paux.λ*0.5*X[p(j), k]*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) + end + end + end + out +end + function Bridge.σ!(t, x, dm, out, P::Union{MarslandShardlow, MarslandShardlowAux}) zero!(out.q) @@ -90,41 +114,49 @@ function Bridge.σ!(t, x, dm, out, P::Union{MarslandShardlow, MarslandShardlowAu out end -Bridge.constdiff(::Union{MarslandShardlow, MarslandShardlowAux}) = true - - -if false - -#= -function Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) - out = zeros(4*P.n,4*P.n) - for i in (2*P.n+1): 4*P.n - out[i,i] = 1.0 - end - out * P.γ^2 +""" +Multiply a(t,x) times xin (which is of type state) +Returns multiplication of type state +""" +function amul(t, x, xin::State, P::Union{MarslandShardlow, MarslandShardlowAux}) + out = copy(xin) + zero!(out.q) + out.p .= P.γ^2 .* xin.p + out end -Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) -=# - -function BBt!(t, arg, out, P::MarslandShardlowAux) - B = zeros(4 * P.n,4 * P.n) - for i in 1:P.n, j in 1:P.n - B[posq(i),posp(j)] = 0.5 * kernel(q(P.v,i)-q(P.v,j),P) * Matrix(1.0I,2,2) +function Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) + I = Int[] + X = Unc[] + γ2 = P.γ^2 + for i in 1:P.n + push!(I, 2i) + push!(X, γ2*one(Unc)) end - out .= (B*arg + arg*B') - out + sparse(I, I, X, 2P.n, 2P.n) end -# nog aan te passen -function Bridge.dP!(t, p, out, P) - BBt!(t, p, out, P) - for i in (2*P.n+1): 4*P.n - out[i,i] -= P.γ^2 - end - out -end +Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) -end +# """ +# Replacing out with dP, which is B*arg + arg*B'- tilde_a +# """ +# function Bridge.dP!(t, p, out, P::MarslandShardlowAux) +# Bridge.B!(t, p, out, P) +# out .= out .+ out' +# γ2 = P.γ^2 +# for i in 1:P.n +# out[2i, 2i] -= γ2*one(Unc) # according to ordering position, momentum ,position, momentum +# end +# out +# end +# +# function dP!(t, p, out, P) +# B!(t, p, out, P) +# out .= out .+ out' - a(t, P) +# out +# end + +Bridge.constdiff(::Union{MarslandShardlow, MarslandShardlowAux}) = true diff --git a/landmarks/patches.jl b/landmarks/patches.jl index 5fdff62..ca8e175 100644 --- a/landmarks/patches.jl +++ b/landmarks/patches.jl @@ -46,20 +46,64 @@ function Bridge.solve!(solver::StratonovichHeun!, Y::SamplePath, u, W::SamplePat end end - _b!((i,t¯), y, tmp1, P) - σ!(t¯, y, dw, tmp2, P) + Bridge._b!((i,t¯), y, tmp1, P) + Bridge.σ!(t¯, y, dw, tmp2, P) for k in eachindex(y) ȳ[k] = y[k] + tmp1[k]*dt + tmp2[k] # Euler prediction end - _b!((i + 1,t¯ + dt), ȳ, tmp3, P) # coefficients at ȳ - σ!(t¯ + dt, ȳ, dw2, tmp4, P) + Bridge._b!((i + 1,t¯ + dt), ȳ, tmp3, P) # coefficients at ȳ + #Bridge.σ!(t¯ + dt, ȳ, dw2, tmp4, P) # original implementation + Bridge.σ!(t¯ + dt, ȳ, dw, tmp4, P) for k in eachindex(y) y[k] = y[k] + 0.5*((tmp1[k] + tmp3[k])*dt + tmp2[k] + tmp4[k]) end end - copyto!(yy[end], endpoint(y, P)) + copyto!(yy[end], Bridge.endpoint(y, P)) Y end + +function LinearAlgebra.naivesub!(At::Adjoint{<:Any,<:LowerTriangular}, b::AbstractVector, x::AbstractVector = b) + A = At.parent + n = size(A, 2) + if !(n == length(b) == length(x)) + throw(DimensionMismatch("second dimension of left hand side A, $n, length of output x, $(length(x)), and length of right hand side b, $(length(b)), must be equal")) + end + @inbounds for j in n:-1:1 + iszero(A.data[j,j]) && throw(SingularException(j)) + xj = x[j] = A.data[j,j] \ b[j] + for i in j-1:-1:1 # counterintuitively 1:j-1 performs slightly better + b[i] -= A.data[j,i] * xj + end + end + x +end + +function lyapunovpsdbackward_step!(t, dt, Paux,Hend⁺,H⁺) + B = Matrix(Bridge.B(t - dt/2, Paux)) + ϕ = (I + 1/2*dt*B)\(I - 1/2*dt*B) + #Ht .= ϕ *(Hend⁺ + 1/2*dt*Bridge.a(t - dt, Paux))* ϕ' + 1/2*dt*Bridge.a(t, Paux) + H⁺ .= ϕ *(Hend⁺ + 1/2*dt*Bridge.a(t - dt, Paux))* conj!(copy(ϕ)) + 1/2*dt*Bridge.a(t, Paux) + H⁺ +end + +""" +Compute transpose of square matrix of Unc matrices + +A = reshape([Unc(1:4), Unc(5:8), Unc(9:12), Unc(13:16)],2,2) +B = copy(A) +A +conj!(B) +""" +function conj!(A::Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}) + if !(size(A,1)==size(A,2)) error("conj! only correctly defined for square matrices") end + for i in 1:size(A,1) + A[i,i] = A[i,i]' + for j in (i+1):size(A,2) + A[i,j], A[j, i] = A[j,i]', A[i, j]' + end + end + A +end diff --git a/landmarks/state.jl b/landmarks/state.jl index 7c338f8..a550642 100644 --- a/landmarks/state.jl +++ b/landmarks/state.jl @@ -1,15 +1,25 @@ +const Point = SArray{Tuple{d},Float64,1,d} # point in R2 +const Unc = SArray{Tuple{d,d},Float64,d,d*d} # Matrix presenting uncertainty + +abstract type UncMat end + struct State{P} q::Vector{P} p::Vector{P} end + q(x::State) = x.q p(x::State) = x.p q(x::State, i) = x.q[i] p(x::State, i) = x.p[i] +q(i::Int) = 2i - 1 +p(i::Int) = 2i +State(xflat) = State(xflat[1:2:end], xflat[2:2:end]) + import Base:iterate, eltype, copy, copyto!, zero, eachindex, getindex, setindex!, size, vec iterate(x::State) = (x.q, true) iterate(x::State, s) = s ? (x.p, false) : nothing @@ -37,14 +47,14 @@ size(s::State) = (2, length(s.p)) zero(x::State) = State(zero(x.p), zero(x.q)) zero!(v) = fill!(v, zero(eltype(v))) +zero!(v) = v[:] = fill!(v, zero(eltype(v))) + function zero!(x::State) zero!(x.p) zero!(x.q) x end - - function getindex(x::State, I::CartesianIndex) if I[1] == 1 x.q[I[2]] @@ -73,12 +83,189 @@ import Bridge: outer *(x::State,c::Number) = State(x.q*c, x.p*c) +(x::State, y::State) = State(x.q + y.q, x.p + y.p) -(x::State, y::State) = State(x.q - y.q, x.p - y.p) +/(x::State, y) = State(x.q/y, x.p/y) + +vec(x::State) = vec([x[J] for J in eachindex(x)]) # +deepvec(x::State{P}) where {P} = vec([x[J][K] for K in eachindex(x.p[1]), J in eachindex(x)]) + + +""" +Convert vector to State. it is assumed that x is ordered as follows +- position landmark 1 +- momentum landmark 1 +- position landmark 2 +- momentum landmark 2 +... +""" +function deepvec2state(x) + m = div(length(x),2d) + q = Vector{Point}(undef,m) + p = Vector{Point}(undef,m) + for i in 1:m + q[i] = Point(x[(i-1)*2d .+ (1:d)]) + p[i] = Point(x[((i-1)*2d+d+1):(2i*d)]) + end + State(q,p) +end + +function deepmat(H::AbstractMatrix{S}) where {S} + d1, d2 = size(S) + reshape([H[i,j][k,l] for k in 1:d1, i in 1:size(H, 1), l in 1:d2, j in 1:size(H,2)], d1*size(H,1), d2*size(H,2)) +end +#@test outer(deepvec(x0)) == deepmat(outer(vec(x0))) + + + +function deepmat2unc(A::Matrix) # d is the dimension of the square subblocks + k =size(A,1) + m = div(k,d) + [Unc(A[(i-1)*d+1:i*d,(j-1)*d+1:j*d]) for i in 1:m, j in 1:m] +end + + + + + function outer(x::State, y::State) [outer(x[i],y[j]) for i in eachindex(x), j in eachindex(y)] end # unc(a::Array) = State([sqrt(a[1, i, 1, i]) for i in 1:size(a, 2)],[sqrt(a[2, i, 2, i]) for i in 1:size(a, 2)]) +# Frank: this seems wrong norm(x::State) = norm(x.q) + norm(x.q) -/(x::State, y) = State(x.q/y, x.p/y) -vec(x::State) = vec([x[J] for J in eachindex(x)]) +function Base.show(io::IO, state::State) + show(io, "text/plain", hcat(q(state),p(state))) +end + +struct InverseCholesky{T} + L::T +end + + + +""" +Solve L L'y =x using two backsolves, +L should be lower triangular +""" +function cholinverse!(L, x) + LinearAlgebra.naivesub!(L, x) # triangular backsolves + LinearAlgebra.naivesub!(UpperTriangular(L'), x) + x +end + +""" +Compute y = H*x where Hinv = L*L' (Cholesky decomposition + +Input are L and x, output is y + +y=Hx is equivalent to LL'y=x, which can be solved +by first backsolving Lz=x for z and next +backsolving L'y=z + +L is a lower triangular matrix with element of type UncMat +x is a State or vector of points +Returns a State (Todo: split up again and return vector for vector input) +""" +function Base.:*(H::InverseCholesky, x::Union{State,Vector{Point}}) + y = copy(x) + if isa(x,State) + y = cholinverse!(H.L, vec(x)) # triangular backsolves + else + y = cholinverse!(H.L, x) # triangular backsolve + end + State(y[1:d:end], y[d:d:end]) +end + + +""" +Compute y = H*X where Hinv = L*L' (Cholesky decomposition + +Input are L and X, output is Y + +y=Hx is equivalent to LL'y=X, which can be solved +by first backsolving LZ=X for z and next +backsolving L'Y=Z + +L is a lower triangular matrix with element of type UncMat +X is a matrix with elements of type UncMat +Returns a matrix with elements of type UncMat +""" +function Base.:*(H::InverseCholesky, X) + cholinverse!(H.L, copy(X)) # triangular backsolves +end + + + +# """ +# Input: H = inverse(L L'), with L lower-triangular +# Output: H*v +# """ +# function Base.:*(H::InverseCholesky, v) +# # two backsolves +# y =copy(v) +# cholinverse!(H.L,y) +# y +# end + + + + +# L = LowerTriangular(rand(5,5)) +# H = InverseCholesky(L) +# v = rand(5) +# H*v - inv(L*L')*v +# + +lchol(A) = LowerTriangular(Matrix(LinearAlgebra._chol!(copy(A), UpperTriangular)[1])') + + +# di = 10 +# L_ = Matrix(LowerTriangular(rand(di,di))) +# L = LowerTriangular(deepmat2unc(L_)) +# H = InverseCholesky(L) +# v = reinterpret(Point, rand(di)) +# H*v - deepmat2unc(inv(L_*L_'))*v + +""" +Hdagger = U S U' with S = L L' (cholesky) +U has orthonormal columns, S is a small positive definite symmetric matrix given +in factorized form, e.g. `S <: Cholesky` + +Then H*x is defined as U inv(S) U' (that is the Moore Penrose inverse) +""" +struct LowRank{TS,TU} + S::TS + U::TU +end + +function Base.:*(H::LowRank, x::State) + #z = H.S\(H.U' * deepvec(x)) # e.g. uses two triangular backsolves if S is `Cholesky` + #deepvec2state(H.U*z) + deepvec2state(H.U * (inv(H.S) * (H.U' * deepvec(x)))) +end + +# function isposdef(A::Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}) +# LinearAlgebra.isposdef(deepmat(A)) +# end + +if TEST + A = reshape([Unc(1:4), Unc(5:8), Unc(9:12), Unc(13:16)],2,2) + B = reshape([-Unc(1:4), Unc(3:6), Unc(9:12), Unc(13:16)],2,2) + @test deepmat(A*B)==deepmat(A)*deepmat(B) + @test deepmat(A') == deepmat(A)' + @test deepmat(A*A')==deepmat(A)*deepmat(A') + Q = deepmat2unc(Matrix(qr(deepmat(A)).Q)) + C = Q * Q' + lchol(C) + @test deepmat(lchol(C))== cholesky(deepmat(C)).L + isposdef(deepmat(C)) + + # check cholinverse! + H = InverseCholesky(lchol(C)) + x = rand(4) + xstate = deepvec2state(x) + @test norm(deepvec(H*xstate) - inv(deepmat(C))*x)<10^(-10) + + LinearAlgebra.naivesub!(lchol(C), A) # triangular backsolves +end diff --git a/landmarks/testms.jl b/landmarks/testms.jl index b2d88b1..7e753cf 100644 --- a/landmarks/testms.jl +++ b/landmarks/testms.jl @@ -9,3 +9,5 @@ out2 = copy(x) @time out2 = mul!(out2, B, x, true, false) @test vec(out1) ≈ out2 + +Bridge.a(1.1,Pmsaux) diff --git a/project_partialbridge/lowrankricatti.jl b/project_partialbridge/lowrankricatti.jl new file mode 100644 index 0000000..7723e33 --- /dev/null +++ b/project_partialbridge/lowrankricatti.jl @@ -0,0 +1,125 @@ +# implement Mena et al. for solving +# (d P)/(d t) = A P(t) + P(t) A' + Q, P(t_0) = P0 +# with a low rank approximation for Q + +using SparseArrays +using SuiteSparse +using LinearAlgebra +using Expokit # for matrix exponentials +using BenchmarkTools + +# construct an example +d = 800 +Q = sprand(d,d,.01) - I# Diagonal(randn(d)) +diagels = 0.4.^(1:d) +A = sprand(d,d,0.1)#Diagonal(diagels) +P0 = Matrix(sprand(d,d,0.1))# Diagonal(diagels) + +# we use Expokit, which gives the funciton expmv! +# w = expmv!{T}( w::Vector{T}, t::Number, A, v::Vector{T}; kwargs...) +# The function expmv! calculates w = exp(t*A)*v, where A is a matrix or any type that supports size, eltype and mul! and v is a dense vector by using Krylov subspace projections. The result is stored in w. + +# It is much faster for large systems +v = rand(d) +@time a1=expmv!(zeros(d),1,Q,v) +@time a2=exp(Matrix(Q))*v +a1-a2 + +# Let's consider a few implementations +matexpvec1 = function(A,U,τ) + exp(Matrix(τ * A)) * U +end + +matexpvec2 = function(A,U,τ) + M = [] + for j in 1:size(U,2) + push!(M, expmv!(zeros(size(U,1)),τ,A,U[:,j])) + end + M = hcat(M...) +end + +# matexpvec3 = function(A,U) # is wrong for some reason +# τ = 1.0 +# for j in 1:size(U,2) +# expmv!(U[:,j],τ,A,U[:,j]) +# end +# U +# end + +matexpvec4 = function(A,U,τ) + hcat([ expmv!(U[:,j],τ,A,U[:,j]) for j in 1:size(U,2)]...) +end + +τ = 1.0 +R = A # or Q +M0 = svd(P0) +U = Matrix(M0.U[:,1:ld]) + +@benchmark matexpvec1(R,U,τ) +@benchmark matexpvec2(R,U,τ) +@benchmark matexpvec4(R,U,τ) + +maximum(matexpvec4(R,U,τ)-matexpvec1(R,U,τ)) + + +function lowrankricatti(P0, A, Q, t, ld) +# P0 is the value of P at time t[1]; t is an increasing sequence of times, +# ld is the dimension of the low rank approximation +# output: at each time t a low rank approximation of P(t), where the couple (U,S) is such that P = U*S*U' + + # step 1 + M0 = svd(P0) + global U = Matrix(M0.U[:,1:ld]) + global S = Diagonal(M0.S[1:ld]) + + Ulowrank = [U] + Slowrank = [S] + for i in 1:length(t)-1 + τ = t[i+1] - t[i] + if false + matexp = exp(Matrix(τ * A)) + # step 3 + M = matexp * U + else + M = matexpvec4(A,U,τ) + end + Uᴬcompact, R = qr(M) + Uᴬ = Matrix(Uᴬcompact) + # step 4 + Sᴬ = R * S * R' + # step 5 + K = Uᴬ * Sᴬ + (τ * Q) * Uᴬ + Ucompact, Ŝ = qr(K) + U = Matrix(Ucompact) + Ŝ = Ŝ - U' * (τ * Q) * Uᴬ + L = Ŝ * Uᴬ' + U' * (τ * Q) + S = L * U + + push!(Ulowrank,U) + push!(Slowrank,Diagonal(S)) + # ??? should S be diagonal or not: either convert it, or make Slowrank an array of full matrices + #push!(Slowrank,S) + end + + Ulowrank, Slowrank +end + + +# Example: +ld = 10 # low rank dimension +τ = 0.01; t0 =0.5; tend=0.8 +t = t0:τ:tend + +@time U,S = lowrankricatti(P0,A, Q, t,ld) +P = U[end]*S[end]*U[end]' + +# compute exact solution +λ = lyap(Matrix(Q), -Matrix(A)) + P0 +Φ = exp(Matrix(Q)*(tend- t0)) +Pexact = Φ*λ*Φ' - λ + P0 + +# assess difference +dif = P - Pexact + +print(maximum(abs.(dif))) +dif diff --git a/project_partialbridge/partialbridge_bolus3.jl b/project_partialbridge/partialbridge_bolus3.jl index 5f0be78..f40788e 100644 --- a/project_partialbridge/partialbridge_bolus3.jl +++ b/project_partialbridge/partialbridge_bolus3.jl @@ -22,8 +22,8 @@ obs_scheme =["full","firstcomponent"][2] Σdiagel = 10^(-4) # settings sampler -iterations = 25000 -skip_it = 1000# 1000 +iterations = 20000 +skip_it = 400# 1000 subsamples = 0:skip_it:iterations ρ = 0.0#95 @@ -85,7 +85,7 @@ if simlongpath # Random.seed!(2) x0 = ℝ{2}(0.0, 0.0) #x0 = ℝ{2}(-8.0, 1.0) - T_long = 8.0#10.0 + T_long = 12.0#10.0 dt = 0.0001 tt_long = 0.:dt:T_long W_long = sample(tt_long, Wiener{ℝ{dp}}()) @@ -102,7 +102,7 @@ if simlongpath # else # error("provide valid number of observations ") # end - obsnum = 10 + obsnum = 15 if obsnum > 2 obsind = 1:(lt÷obsnum):lt obsnum = length(obsind) @@ -232,7 +232,7 @@ accparams = 0 mhsteps = 0 mhstepsparams = 0 -Hzero⁺ = SMatrix{d,d}(0.01*I) +Hzero⁺ = SMatrix{d,d}(0.1*I) param(P) = [P.β P.σ1] logπ(P) = logpdf(Gamma(1,100),P.β) + logpdf(Gamma(1,100),P.σ1) @@ -333,7 +333,6 @@ for iter in 1:iterations end if updateparams # this term is still not correct diffll += (V.tt[end]-V.tt[1]) *(tr(Bridge.B(0.0, Ptᵒ)) - tr(Bridge.B(0.0,Pt))) + logπ(Pᵒ) - logπ(P) - #diffll += (V.tt[2]-V.tt[1]) *(tr(Bridge.B(0.0, Ptᵒ)) - tr(Bridge.B(0.0,Pt)))+ logπ(Pᵒ) - logπ(P) end println("ind: ",ind," updateparms= ",updateparams," diff_ll: ",round(diffll, digits=3)) @@ -375,6 +374,7 @@ println("Average acceptance percentage params: ",ave_acc_percparams,"\n") trueval = param(Ptrue) est = DataFrame(iteration = 1:length(C), beta= map(x->x[1],C), sigma1=map(x->x[2],C)) + @rput est #@rput P @rput trueval @@ -422,11 +422,15 @@ if write2csv writedlm(f,obs,",") close(f) +# CSV.write("parestimates.csv",est) fn = outdir*"parestimates.csv" f = open(fn,"w") - headl = "iterate, beta\n" + headl = "iterate, beta, sigma1 \n" write(f,headl) - writedlm(f,hcat(1:length(C), C),",") + truevals = [0 param(Ptrue)] + estim = hcat(1:length(C), first.(C),last.(C)) + writedlm(f,vcat(truevals,estim),",") + # iterate 0 corresponds to the true values close(f) end diff --git a/src/ode!.jl b/src/ode!.jl index d640f6b..c962ee3 100644 --- a/src/ode!.jl +++ b/src/ode!.jl @@ -7,7 +7,17 @@ to solve ``y(t + dt) - y(t) = \\int_t^{t+dt} F(s, y(s)) ds``. struct R3! <: ODESolver end -workspace(::Bridge.R3!, y) = (copy(y), copy(y), copy(y), copy(y)) +workspace(::Bridge.R3!, y) = (copy(y), copy(y), copy(y), copy(y)) + +""" +One step for inplace Ralston (1965) update (order 3 step of the Bogacki–Shampine 1989 method) +to solve ``y(t + dt) - y(t) = \\int_t^{t+dt} f(s, y(s)) ds``. +Starting point is specified by (t,y) + +f!(t,y,k) is a function that takes (t,y) and writes the result in k. +ws contains 4 copies of the type of y +the result is written into out which is of type y +""" function kernelr3!(f!, t, y, ws, out, dt) y2, k1, k2, k3 = ws f!(t, y, k1) diff --git a/src/sde!.jl b/src/sde!.jl index 350c5b4..18aaa79 100644 --- a/src/sde!.jl +++ b/src/sde!.jl @@ -1,5 +1,23 @@ +""" +Inplace sde solver. +Typical call is like +solve!(EulerMaruyama!(), X, x0, W, P) +or +solve!(StratonovichHeun!(), X, x0, W, P) + +Here +- x0 is the starting point, +- W the driving Wiener process, +- P the ContinuousTimeProcess + +Requires +- drift function _b!((i,t¯), y, tmp1, P) +- diffusion function σ!(t¯, y, dw, tmp2, P) + +The result is written into X +""" function solve!(solver::EulerMaruyama!, Y::VSamplePath, u::T, W, P::ProcessOrCoefficients) where {T} N = length(W) N != length(Y) && error("Y and W differ in length.") From 8e287acc8bad26eb19dca90f31e989fc6ecf88f3 Mon Sep 17 00:00:00 2001 From: fmeulen Date: Sat, 26 Jan 2019 20:34:01 +0100 Subject: [PATCH 03/58] added lu factorisation type, checked various functions in state.jl --- landmarks/ahsmodel.jl | 7 +- landmarks/state.jl | 168 ++++++++++++++++++++++++++---------------- 2 files changed, 110 insertions(+), 65 deletions(-) diff --git a/landmarks/ahsmodel.jl b/landmarks/ahsmodel.jl index 172c3d6..2a995a4 100644 --- a/landmarks/ahsmodel.jl +++ b/landmarks/ahsmodel.jl @@ -1,5 +1,8 @@ -######### +""" +Specify parameters for noisefield +λ * exp(-|δ - q|^2/τ^2) +""" struct Noisefield δ::Point # locations of noise field λ::Point # scaling at noise field @@ -217,7 +220,7 @@ Multiply a(t,x) times in (which is of type state) Returns multiplication of type state """ function amul(t, x, in::State, P) - State(Bridge.a(t, x, P)*vec(in)) + vecofpoints2state(Bridge.a(t, x, P)*vec(in)) end Bridge.constdiff(::Landmarks) = false diff --git a/landmarks/state.jl b/landmarks/state.jl index a550642..f9ffe81 100644 --- a/landmarks/state.jl +++ b/landmarks/state.jl @@ -1,3 +1,4 @@ +import Base:iterate, eltype, copy, copyto!, zero, eachindex, getindex, setindex!, size, vec const Point = SArray{Tuple{d},Float64,1,d} # point in R2 const Unc = SArray{Tuple{d,d},Float64,d,d*d} # Matrix presenting uncertainty @@ -17,10 +18,6 @@ p(x::State, i) = x.p[i] q(i::Int) = 2i - 1 p(i::Int) = 2i - -State(xflat) = State(xflat[1:2:end], xflat[2:2:end]) - -import Base:iterate, eltype, copy, copyto!, zero, eachindex, getindex, setindex!, size, vec iterate(x::State) = (x.q, true) iterate(x::State, s) = s ? (x.p, false) : nothing copy(x::State) = State(copy(x.q), copy(x.p)) @@ -89,6 +86,48 @@ vec(x::State) = vec([x[J] for J in eachindex(x)]) # deepvec(x::State{P}) where {P} = vec([x[J][K] for K in eachindex(x.p[1]), J in eachindex(x)]) + +# matrix multiplication of mat of Uncs +function Base.:*(A::Array{SArray{Tuple{2,2},Float64,2,4},2}, + B::Array{SArray{Tuple{2,2},Float64,2,4},2}) + C = zeros(Unc,size(A,1), size(B,2)) + for i in 1:size(A,1) + for j in 1:size(B,2) + for k in 1:size(A,2) + C[i,j] += A[i,k] * B[k,j] + end + end + end + C +end + +function Base.:*(A::Array{SArray{Tuple{2,2},Float64,2,4},2}, + B::Adjoint{Array{SArray{Tuple{2,2},Float64,2,4},2}}) + C = zeros(Unc,size(A,1), size(B,1)) + for i in 1:size(A,1) + for j in 1:size(B,1) + for k in 1:size(A,2) + C[i,j] += A[i,k] * B[j,k] + end + end + end + C +end + +if TEST + A = reshape(rand(Unc,6),3,2) + B = reshape(rand(Unc,8),2,4) + C = B' + @test norm(deepmat(A*B) - deepmat(A) * deepmat(B))<10^(-8) + @test norm(deepmat(A*C') - deepmat(A) * deepmat(C'))<10^(-8) + + # backsolving matrix equation A X = using lu + A1=reshape(rand(Unc,9),3,3) + B1=reshape(rand(Unc,9),3,3) + @test norm(deepmat(A1\B1) - deepmat(A1)\deepmat(B1))<10^(-10) +end + + """ Convert vector to State. it is assumed that x is ordered as follows - position landmark 1 @@ -108,42 +147,33 @@ function deepvec2state(x) State(q,p) end +vecofpoints2state(x::Vector{Point}) = State(x[1:d:end], x[d:d:end]) + function deepmat(H::AbstractMatrix{S}) where {S} d1, d2 = size(S) reshape([H[i,j][k,l] for k in 1:d1, i in 1:size(H, 1), l in 1:d2, j in 1:size(H,2)], d1*size(H,1), d2*size(H,2)) end #@test outer(deepvec(x0)) == deepmat(outer(vec(x0))) - - function deepmat2unc(A::Matrix) # d is the dimension of the square subblocks k =size(A,1) m = div(k,d) [Unc(A[(i-1)*d+1:i*d,(j-1)*d+1:j*d]) for i in 1:m, j in 1:m] end - - - - function outer(x::State, y::State) [outer(x[i],y[j]) for i in eachindex(x), j in eachindex(y)] end -# unc(a::Array) = State([sqrt(a[1, i, 1, i]) for i in 1:size(a, 2)],[sqrt(a[2, i, 2, i]) for i in 1:size(a, 2)]) -# Frank: this seems wrong -norm(x::State) = norm(x.q) + norm(x.q) +norm(x::State) = norm(vec(x)) +""" +Good display of variable of type State +""" function Base.show(io::IO, state::State) show(io, "text/plain", hcat(q(state),p(state))) end -struct InverseCholesky{T} - L::T -end - - - """ Solve L L'y =x using two backsolves, L should be lower triangular @@ -154,6 +184,13 @@ function cholinverse!(L, x) x end +lchol(A) = LowerTriangular(Matrix(LinearAlgebra._chol!(copy(A), UpperTriangular)[1])') + +############################ InverseCholesky ######################## +struct InverseCholesky{T} + L::T +end + """ Compute y = H*x where Hinv = L*L' (Cholesky decomposition @@ -167,23 +204,23 @@ L is a lower triangular matrix with element of type UncMat x is a State or vector of points Returns a State (Todo: split up again and return vector for vector input) """ -function Base.:*(H::InverseCholesky, x::Union{State,Vector{Point}}) - y = copy(x) - if isa(x,State) - y = cholinverse!(H.L, vec(x)) # triangular backsolves - else - y = cholinverse!(H.L, x) # triangular backsolve - end - State(y[1:d:end], y[d:d:end]) +function Base.:*(H::InverseCholesky, x::State) + y = copy(vec(x)) + cholinverse!(H.L, y) # triangular backsolve + vecofpoints2state(y) end +function Base.:*(H::InverseCholesky, x::Vector{Point}) + y = copy(x) + cholinverse!(H.L, y) # triangular backsolve +end """ Compute y = H*X where Hinv = L*L' (Cholesky decomposition Input are L and X, output is Y -y=Hx is equivalent to LL'y=X, which can be solved +y=HX is equivalent to LL'y=X, which can be solved by first backsolving LZ=X for z and next backsolving L'Y=Z @@ -197,36 +234,7 @@ end -# """ -# Input: H = inverse(L L'), with L lower-triangular -# Output: H*v -# """ -# function Base.:*(H::InverseCholesky, v) -# # two backsolves -# y =copy(v) -# cholinverse!(H.L,y) -# y -# end - - - - -# L = LowerTriangular(rand(5,5)) -# H = InverseCholesky(L) -# v = rand(5) -# H*v - inv(L*L')*v -# - -lchol(A) = LowerTriangular(Matrix(LinearAlgebra._chol!(copy(A), UpperTriangular)[1])') - - -# di = 10 -# L_ = Matrix(LowerTriangular(rand(di,di))) -# L = LowerTriangular(deepmat2unc(L_)) -# H = InverseCholesky(L) -# v = reinterpret(Point, rand(di)) -# H*v - deepmat2unc(inv(L_*L_'))*v - +############################ LowRank ######################## """ Hdagger = U S U' with S = L L' (cholesky) U has orthonormal columns, S is a small positive definite symmetric matrix given @@ -245,9 +253,33 @@ function Base.:*(H::LowRank, x::State) deepvec2state(H.U * (inv(H.S) * (H.U' * deepvec(x)))) end -# function isposdef(A::Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}) -# LinearAlgebra.isposdef(deepmat(A)) -# end +############################ InverseCholesky ######################## +struct InverseLu{TL,TU} + L::TL + U::TU +end + +""" +Compute y = H x where x is a state vector and +Hinv = LU (LU decomposition) + +From LU y =x, it follows that we +solve first z from Lz=x, and next y from Uy=z +""" +function Base.:*(H::InverseLu, x::Vector{Point}) + LinearAlgebra.naivesub!(LowerTriangular(H.L), x) + LinearAlgebra.naivesub!(UpperTriangular(H.U), x) + x +end + +function Base.:*(H::InverseLu, x::State) + y = vec(x) + LinearAlgebra.naivesub!(LowerTriangular(H.L), y) + LinearAlgebra.naivesub!(UpperTriangular(H.U), y) + vecofpoints2state(y) +end + + if TEST A = reshape([Unc(1:4), Unc(5:8), Unc(9:12), Unc(13:16)],2,2) @@ -262,10 +294,20 @@ if TEST isposdef(deepmat(C)) # check cholinverse! - H = InverseCholesky(lchol(C)) + HH = InverseCholesky(lchol(C)) x = rand(4) xstate = deepvec2state(x) - @test norm(deepvec(H*xstate) - inv(deepmat(C))*x)<10^(-10) + @test norm(deepvec(HH*xstate) - inv(deepmat(C))*x)<10^(-10) LinearAlgebra.naivesub!(lchol(C), A) # triangular backsolves + + A = reshape(rand(Unc,16),4,4) + L, U = lu(A) + W = InverseLu(L,U) + + xs= rand(Point,4) + xss = [xs[1]; xs[2];xs[3];xs[4]] + inv(deepmat(A)) * xss + W * xs + @test norm(deepvec2state(inv(deepmat(A)) * xss) - W * deepvec2state(xss))<10^(-10) end From 95be06c41231b977ce0d8b98bf6b9eb2f3abd162 Mon Sep 17 00:00:00 2001 From: fmeulen Date: Mon, 28 Jan 2019 12:53:26 +0100 Subject: [PATCH 04/58] extract common functions to ahs and ms model into bothmodels.jl --- landmarks/ahsmodel.jl | 171 +++++----------------------------------- landmarks/bothmodels.jl | 119 ++++++++++++++++++++++++++++ landmarks/forward.jl | 90 ++++++++++----------- landmarks/msmodel.jl | 121 ++-------------------------- 4 files changed, 189 insertions(+), 312 deletions(-) create mode 100644 landmarks/bothmodels.jl diff --git a/landmarks/ahsmodel.jl b/landmarks/ahsmodel.jl index 2a995a4..ec5a08b 100644 --- a/landmarks/ahsmodel.jl +++ b/landmarks/ahsmodel.jl @@ -1,7 +1,5 @@ - """ Specify parameters for noisefield -λ * exp(-|δ - q|^2/τ^2) """ struct Noisefield δ::Point # locations of noise field @@ -9,142 +7,30 @@ struct Noisefield τ::Float64 # std of Gaussian kernel noise field end -######### struct Landmarks{T} <: ContinuousTimeProcess{State{Point}} - a::T # kernel parameter + a::T # kernel std λ::T # mean reversion n::Int64 # numer of landmarks nfs::Vector{Noisefield} # vector containing pars of noisefields end -# specify auxiliary process struct LandmarksAux{T} <: ContinuousTimeProcess{State{Point}} - a::T # kernel parameter + a::T # kernel std λ::T # mean reversion xT::State{Point} # use x = State(P.v, zero(P.v)) where v is conditioning vector n::Int64 # numer of landmarks nfs::Vector{Noisefield} # vector containing pars of noisefields end -LandmarksAux(P::Landmarks, xT) = LandmarksAux(P.a, P.λ, xT, P.n, P.nfs) - -# Gaussian kernel -kernel(x, P::Union{Landmarks, LandmarksAux}) = 1/(2*π*P.a)^(length(x)/2)*exp(-norm(x)^2/(2*P.a)) - -# Kernel of the noise fields (need these functions to evaluate diffusion coefficient in ahs model) -noiseσ(q, nf::Noisefield) = nf.λ * exp(-norm(nf.δ - q)^2/nf.τ^2) -eta(q, p, nf::Noisefield) = dot(p, nf.λ)/nf.τ^2 * (q - nf.δ) * exp(-norm(nf.δ - q)^2/nf.τ^2) - -function hamiltonian((q, p), P) - s = 0.0 - for i in eachindex(q), j in eachindex(q) - # i == j && continue - s += 1/2*dot(p[i], p[j])*kernel(q[i] - q[j], P) - end - s -end - -Bridge.b(t::Float64, x, P::Union{Landmarks, LandmarksAux}) = Bridge.b!(t, x, copy(x), P) - -""" -Evaluate drift of landmarks in (t,x) and save to out -x is a state and out as well -""" -function Bridge.b!(t, x, out, P::Landmarks) - zero!(out) - for i in 1:P.n - for j in 1:P.n - out.q[i] += 0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) - # heat bath - out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) + - 1/(2*P.a) * dot(p(x,i), p(x,j)) * (q(x,i)-q(x,j))*kernel(q(x,i) - q(x,j), P) - end - end - out -end - -""" -Evaluate drift of landmarks auxiliary process in (t,x) and save to out -x is a state and out as well -""" -function Bridge.b!(t, x, out, P::LandmarksAux) - zero!(out) - for i in 1:P.n - for j in 1:P.n - out.q[i] += 0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) - # heat bath - out.p[i] +=# -P.λ*0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) + - 1/(2*P.a) * dot(p(P.xT,i), p(P.xT,j)) * (q(x,i)-q(x,j))*kernel(q(P.xT,i) - q(P.xT,j), P) - end - end - out -end - -""" -Compute tildeB(t) for landmarks auxiliary process -""" -function Bridge.B(t, Paux::LandmarksAux) - I = Int[] - J = Int[] - X = Unc[] - for i in 1:Paux.n - for j in 1:Paux.n - # terms for out.q[i] - push!(I, 2i - 1) - push!(J, 2j) - push!(X, 0.5*kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc)) - - # terms for out.p[i] - push!(I, 2i) - push!(J, 2j-1) - if j==i - push!(X, sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), P) for j in setdiff(1:Paux.n,i)]) * one(Unc)) - else - push!(X, -1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)) - end - end - end - B = sparse(I, J, X, 2Paux.n, 2Paux.n) -end - -# function Bridge.B!(t,X,out, P::LandmarksAux) -# I = Int[] -# J = Int[] -# B = Unc[] -# for i in 1:P.n -# for j in 1:P.n -# push!(I, 2i - 1) -# push!(J, 2j) -# push!(B, 0.5*kernel(q(P.xT,i) - q(P.xT,j), P)*one(Unc)) -# end -# end -# out .= Matrix(sparse(I, J, B, 2P.n, 2P.n)) * X # BAD: inefficient -# end -""" -Compute B̃(t) * X (B̃ from auxiliary process) and write to out -Both B̃(t) and X are of type UncMat -""" -function Bridge.B!(t,X,out, Paux::LandmarksAux) - out .= 0.0 * out - for i in 1:Paux.n # separately loop over even and odd indices - for k in 1:2Paux.n # loop over all columns - for j in 1:Paux.n - out[2i-1,k] += X[p(j), k] *0.5*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) *one(Unc) - if j==i - out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * - kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) - else - out[2i,k] += X[q(j),k] *(-1/(2*Paux.a)) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc) - end - end - end - end - out -end +LandmarksAux(P::Landmarks, xT) = LandmarksAux(P.a, P.λ, xT, P.n, P.nfs) - # A = reshape([Unc(rand(4)) for i in 1:6, j in 1:6],6,6)) - # out = copy(A) - # Bridge.B!(1.0,A,out,Paux) +# kernel for noisefields +K̄(x,τ) = (2*π*τ^2)^(-d/2)*exp(-norm(x)^2/(2*τ^2)) +# gradient of kernel for noisefields +∇K̄(x,τ) = -τ^(-2) * K̄(x,τ) * x +# function for specification of diffusivity of landmarks +σq(q, nf::Noisefield) = nf.λ * K̄(q - nf.δ,nf.τ) +σp(q, p, nf::Noisefield) = -dot(p, nf.λ) * ∇K̄(q - nf.δ,nf.τ) """ Compute sigma(t,x) * dm where dm is a vector and sigma is the diffusion coefficient of landmarks @@ -152,14 +38,10 @@ write to out which is of type State """ function Bridge.σ!(t, x, dm, out, P::Landmarks) zero!(out) - nfs = P.nfs for i in 1:P.n - #for (nf, dm) in zip(P.nfs, dm) - for j in 1:length(nfs) - #out.p[i] += noiseσ(q(x, i), nf) * dm - #out.q[i] += eta(q(x, i), p(x, i), nf) * dm - out.q[i] += noiseσ(q(x, i), nfs[j]) * dm[j] - out.p[i] += eta(q(x, i), p(x, i), nfs[j]) * dm[j] + for j in 1:length(P.nfs) + out.q[i] += σq(q(x, i), P.nfs[j]) * dm[j] + out.p[i] += σp(q(x, i), p(x, i), P.nfs[j]) * dm[j] end end out @@ -173,22 +55,6 @@ function Bridge.σ!(t, x, dm, out, P::LandmarksAux) Bridge.σ!(t, P.xT, dm, out, P::Landmarks) end - - - -# function Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) -# I = Int[] -# X = Unc[] -# γ2 = P.γ^2 -# for i in 1:P.n -# push!(I, 2i) -# push!(X, γ2*one(Unc)) -# end -# a = sparse(I, I, X, 2P.n, 2P.n) -# end - - - function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) if P isa Landmarks x = x_ @@ -199,9 +65,9 @@ function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) for i in 1:P.n for k in 1:P.n for j in 1:length(P.nfs) - r1 = noiseσ(q(x,i),P.nfs[j]) * noiseσ(q(x, k),P.nfs[j])' - r2 = noiseσ(q(x,i),P.nfs[j]) * eta(q(x,k),p(x,k),P.nfs[j])' - r3 = eta(q(x,i),p(x,i),P.nfs[j]) * eta(q(x,k),p(x,k),P.nfs[j])' + r1 = σq(q(x,i),P.nfs[j]) * σq(q(x, k),P.nfs[j])' + r2 = σq(q(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' + r3 = σp(q(x,i),p(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' out[2i-1,2k-1] += r1 out[2i,2k-1] += r2 out[2i-1,2k] += r2 @@ -213,15 +79,16 @@ function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) out end -Bridge.a(t, P::LandmarksAux) = Bridge.a(t, P.xT, P) +Bridge.a(t, P::Union{Landmarks,LandmarksAux}) = Bridge.a(t, P.xT, P::Union{Landmarks,LandmarksAux}) """ Multiply a(t,x) times in (which is of type state) Returns multiplication of type state """ -function amul(t, x, in::State, P) +function amul(t, x, in::State, P::Landmarks) vecofpoints2state(Bridge.a(t, x, P)*vec(in)) end + Bridge.constdiff(::Landmarks) = false Bridge.constdiff(::LandmarksAux) = true diff --git a/landmarks/bothmodels.jl b/landmarks/bothmodels.jl new file mode 100644 index 0000000..cad264c --- /dev/null +++ b/landmarks/bothmodels.jl @@ -0,0 +1,119 @@ +function hamiltonian((q, p), P) + s = 0.0 + for i in eachindex(q), j in eachindex(q) + s += 1/2*dot(p[i], p[j])*kernel(q[i] - q[j], P) + end + s +end + +""" +kernel in Hamiltonian +""" +kernel(x, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) = + (2*π*P.a^2)^(-d/2)*exp(-norm(x)^2/(2*P.a^2)) +∇kernel(x, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) = -P.a^(-2) * kernel(x,P) * x + +""" +Needed for b! in case P is auxiliary process +""" +∇kernel(x,xT, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) = -P.a^(-2) * kernel(xT,P) * x + +Bridge.b(t::Float64, x, P::Union{Landmarks,MarslandShardlow})= Bridge.b!(t, x, copy(x), P) + +Bridge.b(t::Float64, x, P::Union{LandmarksAux,MarslandShardlowAux})= Bridge.b!(t, x, copy(x), P) + + +""" +Evaluate drift of landmarks in (t,x) and save to out +x is a state and out as well +""" +function Bridge.b!(t, x, out, P::Union{Landmarks,MarslandShardlow}) + zero!(out) + for i in 1:P.n + for j in 1:P.n + out.q[i] += 0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) + # heat bath + out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) - + 0.5* dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) + end + end + out +end + +""" +Evaluate drift of landmarks auxiliary process in (t,x) and save to out +x is a state and out as well +""" +function Bridge.b!(t, x, out, P::Union{LandmarksAux,MarslandShardlowAux}) + zero!(out) + for i in 1:P.n + for j in 1:P.n + out.q[i] += 0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) + # heat bath + out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) + -0.5* dot(p(P.xT,i), p(P.xT,j)) * ∇kernel(q(x,i) - q(x,j),q(P.xT,i) - q(P.xT,j), P) + # 1/(2*P.a) * dot(p(P.xT,i), p(P.xT,j)) * (q(x,i)-q(x,j))*kernel(q(P.xT,i) - q(P.xT,j), P) + end + end + out +end + + +""" +Compute tildeB(t) for landmarks auxiliary process +""" +function Bridge.B(t, Paux::Union{LandmarksAux,MarslandShardlowAux}) + I = Int[] + J = Int[] + X = Unc[] + for i in 1:Paux.n + for j in 1:Paux.n + # terms for out.q[i] + push!(I, 2i - 1) + push!(J, 2j) + push!(X, 0.5*kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc)) + + # terms for out.p[i] + push!(I, 2i) + push!(J, 2j-1) + if j==i + push!(X, sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), P) for j in setdiff(1:Paux.n,i)]) * one(Unc)) + else + push!(X, -1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)) + end + end + end + B = sparse(I, J, X, 2Paux.n, 2Paux.n) +end + + +""" +Compute B̃(t) * X (B̃ from auxiliary process) and write to out +Both B̃(t) and X are of type UncMat +""" +function Bridge.B!(t,X,out, Paux::Union{LandmarksAux,MarslandShardlowAux}) + out .= 0.0 * out + for i in 1:Paux.n # separately loop over even and odd indices + for k in 1:2Paux.n # loop over all columns + for j in 1:Paux.n + out[2i-1,k] += X[p(j), k] *0.5*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) *one(Unc) + if j==i + out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * + kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) + else + out[2i,k] += X[q(j),k] *(-1/(2*Paux.a)) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc) + end + end + end + end + out +end + + +if TEST + Hend⁺ = [rand(Unc) for i in 1:2Paux.n, j in 1:2Paux.n] + BB = Matrix(Bridge.B(0,Paux)) * Hend⁺ + out = deepcopy(Hend⁺) + Bridge.B!(t,Hend⁺,out,Paux) + @test out==BB +end diff --git a/landmarks/forward.jl b/landmarks/forward.jl index a20c58b..104c7f2 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -1,5 +1,4 @@ # reminder, to type H*, do H\^+ -#cd("/Users/Frank/.julia/dev/Bridge") #outdir="output/landmarks/" cd("/Users/Frank/.julia/dev/Bridge/landmarks") @@ -14,30 +13,28 @@ using RCall using Base.Iterators using SparseArrays - models = [:ms, :ahs] model = models[2] TEST = false#true discrmethods = [:ralston, :lowrank, :psd] -discrmethod = discrmethods[2] +discrmethod = discrmethods[1] obsschemes =[:full, :partial] obsscheme = obsschemes[2] const d = 2 -n = 40 # nr of landmarks -ldim = 2n*d # dimension of low-rank approximation to H\^+ +n = 50 # nr of landmarks +ldim = 75#n*d # dimension of low-rank approximation to H\^+ cheat = false#true#false # if cheat is true, then we initialise at x0 (true value) and # construct the guiding term based on xT (true value) -θ = 6π/40# π/6 0#π/5 # angle to rotate endpoint - -ϵ = 0.001 # parameter for initialising Hend⁺ -obsnoise = 0.001 # noise on observations +θ = 2π/n# π/6 0#π/5 # angle to rotate endpoint +ϵ = 0.01 # parameter for initialising Hend⁺ +σobs = 0.001 # noise on observations println(model) @@ -45,7 +42,7 @@ println(discrmethod) println(obsscheme) T = 0.5#1.0#0.5 -t = 0.0:0.005:T # time grid +t = 0.0:0.01:T # time grid #Random.seed!(5) @@ -53,34 +50,37 @@ t = 0.0:0.005:T # time grid include("state.jl") include("msmodel.jl") include("ahsmodel.jl") +include("bothmodels.jl") include("patches.jl") include("guiding.jl") -#include("lyap.jl") include("LowrankRiccati.jl") using .LowrankRiccati ### Specify landmarks models -a = 1.0 ; λ = 0.5; #= not the lambda of noise fields =# γ = 5.0 + +a = 1.0 ; λ = 0.0; #= not the lambda of noise fields =# γ = 5.0 Pms = MarslandShardlow(a, γ, λ, n) if true + db = 2.0 # domainbound # specify locations noisefields - r1 = (-2.0:0.5:2.0) #+ 0.1rand(5) - r2 = (-2.0:0.5:2.0) #+ 0.1rand(5) + r1 = (-db:0.8:db) #+ 0.1rand(5) + r2 = (-db:0.8:db) #+ 0.1rand(5) nfloc = Point.(collect(product(r1, r2)))[:] # scaling parameter of noisefields nfscales = [0.1Point(1.0, 1.0) for x in nfloc] nfstd = 2.05 # tau , variance of noisefields else + db = 5.0 # domainbound # specify locations noisefields - r1 = (-2.0:0.5:2.0) #+ 0.1rand(5) - r2 = (-2.0:0.5:2.0) #+ 0.1rand(5) + r1 = (-db:0.5:db) #+ 0.1rand(5) + r2 = (-db:0.5:db) #+ 0.1rand(5) nfloc = Point.(collect(product(r1, r2)))[:] # scaling parameter of noisefields - nfscales = [2.5Point(1.0, 1.0) for x in nfloc] - nfstd = 1.0 # tau , variance of noisefields + nfscales = [.3Point(1.0, 1.0) for x in nfloc] + nfstd = 4.0 # tau , variance of noisefields end nfs = [Noisefield(δ, λ, nfstd) for (δ, λ) in zip(nfloc, nfscales)] @@ -88,7 +88,6 @@ nfs = [Noisefield(δ, λ, nfstd) for (δ, λ) in zip(nfloc, nfscales)] Pahs = Landmarks(a, λ, n, nfs) ### - if model == :ms dwiener = n StateW = Point @@ -107,7 +106,7 @@ sample!(W, Wiener{Vector{StateW}}()) q0 = [Point(cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) p_ = 5*Point(0.1, 0.1) p0 = [p_ for i in 1:n] # -p0 = [randn(Point) for i in 1:n] +#p0 = [randn(Point) for i in 1:n] x0 = State(q0, p0) @@ -145,6 +144,14 @@ if TEST end +# observe positions without noise +v0 = q(X.yy[1]) +rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) +vT = [rot * q(X.yy[end])[i] for i in 1:P.n ] +#vT = q(X.yy[end]) + + + out = [Any[X.tt[i], [X.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(X.tt) ][:] df = DataFrame(time=extractcomp(out,1),pos1=extractcomp(out,2),pos2=extractcomp(out,3),mom1=extractcomp(out,4),mom2=extractcomp(out,5),pointID=extractcomp(out,6)) #Any["X.tt[$i]", ["X.yy[$i][CartesianIndex($c, $k)][$l]" for l in 1:d, k in 1:n, c in 1:2]...] @@ -156,13 +163,20 @@ else end titel = titel * string(n)*" landmarks" +dfT = DataFrame(pos1=extractcomp(vT,1), pos2=extractcomp(vT,2)) +df0= DataFrame(pos1=extractcomp(v0,1), pos2=extractcomp(v0,2)) + @rput titel @rput df +@rput dfT +@rput df0 R""" library(tidyverse) -df %>% dplyr::select(time,pos1,pos2,pointID) %>% - ggplot(aes(x=pos1,pos2,group=pointID,colour=time)) + - geom_path() + +#df %>% dplyr::select(time,pos1,pos2,pointID) %>% + ggplot() + + geom_path(data=df,aes(x=pos1,pos2,group=pointID,colour=time)) + + geom_point(data=dfT, mapping=aes(x=pos1,y=pos2),colour='orange',size=0.7) + + geom_point(data=df0, mapping=aes(x=pos1,y=pos2),colour='black',size=0.7)+ theme_minimal() + xlab('horizontal position') + ylab('vertical position') + ggtitle(titel) """ @@ -174,11 +188,6 @@ df %>% dplyr::select(time,mom1,mom2,pointID) %>% facet_wrap(~pointID) + theme_minimal() """ -# observe positions without noise -v0 = q(X.yy[1]) -rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) -vT = [rot * q(X.yy[end])[i] for i in 1:P.n ] -#vT = q(X.yy[end]) @@ -186,6 +195,8 @@ vT = [rot * q(X.yy[end])[i] for i in 1:P.n ] tc(t,T) = t.*(2-t/T) tt_ = t#tc(t,T)# 0:dtimp:(T) +#tt_ = 0.0:0.001:T + #################### # solve backward recursion on [0,T] @@ -194,7 +205,7 @@ tt_ = t#tc(t,T)# 0:dtimp:(T) if obsscheme==:partial L = deepmat( [(i==j)*one(Unc) for i in 1:2:2n, j in 1:2n]) - Σ = Diagonal(obsnoise*ones(n*d)) + Σ = Diagonal(σobs^2*ones(n*d)) Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) if cheat Pahsaux = LandmarksAux(Pahs, X.yy[end]) @@ -208,7 +219,7 @@ if obsscheme==:partial end if obsscheme==:full L = deepmat( [(i==j)*one(Unc) for i in 1:2n, j in 1:2n]) - Σ = Diagonal(obsnoise*ones(2n*d)) + Σ = Diagonal(σobs^2*ones(2n*d)) Pmsaux = MarslandShardlowAux(Pms,X.yy[end]) Pahsaux = LandmarksAux(Pahs, X.yy[end]) v0 = vec(X.yy[1]) @@ -236,38 +247,27 @@ if discrmethod==:lowrank largest = sortperm(M0.values)[end-ldim+1:end] Send = Matrix(Diagonal(M0.values[largest])) Uend = M0.vectors[:,largest] -# println(deepmat(Hend⁺)-Uend*Send*Uend') St = [copy(Send) for s in tt_] Ut = [copy(Uend) for s in tt_] @time νend, (Send, Uend) = bucybackwards!(LRR(), t, νt, (St, Ut), Paux, νend, (Send, Uend)) Hend⁺ = deepmat2unc(Uend * Send * Uend') - #map(x->isposdef(x),St) -# Ht = map((S,U) -> LowRank(cholesky(Hermitian(S)),U),St,Ut) - Ht = map((S,U) -> LowRank(S,U), St,Ut) + Ht = map((S,U) -> LowRank(S,U), St,Ut) end if discrmethod==:ralston H⁺t = [copy(Hend⁺) for s in tt_] @time νend , Hend⁺ = bucybackwards!(Bridge.R3!(), tt_, νt, H⁺t, Paux, νend, Hend⁺) - println(map(x->isposdef(deepmat(x)),H⁺t)) Ht = map(H⁺ -> InverseCholesky(lchol(H⁺)),H⁺t) end if discrmethod==:psd H⁺t = [copy(Hend⁺) for s in tt_] @time νend , Hend⁺ = bucybackwards!(Lyap(), tt_, νt, H⁺t, Paux, νend, Hend⁺) - println(map(x->isposdef(deepmat(x)),H⁺t)) - #Ht = map(H⁺ -> InverseCholesky(lchol(Hermitian(H⁺))),H⁺t) +# println(map(x->isposdef(deepmat(x)),H⁺t)) Ht = map(H⁺ -> InverseCholesky(lchol(H⁺)),H⁺t) - #map(H⁺ -> lchol(Hermitian(H⁺)),H⁺t) end - - - Q = GuidedProposal!(P, Paux, tt_, νt, Ht) νstart , Hstart⁺ = gpupdate(νend , Hend⁺, Σ, L, v0) -#νstart , Hstart⁺ = gpupdate(νend , Hend⁺, Σ, L, q(XX.yy[1])) - xinit = cheat ? x0 : νstart # or xinit ~ N(νstart, Hstart⁺) winit = zeros(StateW, dwiener) XX = SamplePath(tt_, [copy(xinit) for s in tt_]) @@ -303,8 +303,8 @@ titel = titel * string(n)*" landmarks" @rput T R""" library(tidyverse) -T_ <- T-0.0001 -#T_ <- 0.8 +T_ <- T#-0.0001 +T_ <- T + 0.05 dfsub <- df %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,pos1,pos2,pointID) %>% filter(time Date: Sun, 10 Feb 2019 19:56:04 +0100 Subject: [PATCH 05/58] lmguiding and lmpar contain code for simulating bridges using lm parametrisation (as in hypo-elliptic paper). The Ito-Stratonovich correction term has been added for the landmarks model of AHS. There is still a bug in Bridge.a for auxiliary process, as the resulting matrix fails to be positive definite. --- landmarks/ahsmodel.jl | 67 ++++++++-- landmarks/bothmodels.jl | 175 +++++++++++++++++++++----- landmarks/forward.jl | 37 +++--- landmarks/guiding.jl | 27 ++-- landmarks/lmguiding.jl | 87 +++++++++++++ landmarks/lmpar.jl | 268 ++++++++++++++++++++++++++++++++++++++++ landmarks/msmodel.jl | 4 +- landmarks/patches.jl | 19 ++- landmarks/state.jl | 2 + 9 files changed, 613 insertions(+), 73 deletions(-) create mode 100644 landmarks/lmguiding.jl create mode 100644 landmarks/lmpar.jl diff --git a/landmarks/ahsmodel.jl b/landmarks/ahsmodel.jl index ec5a08b..9750afe 100644 --- a/landmarks/ahsmodel.jl +++ b/landmarks/ahsmodel.jl @@ -31,12 +31,29 @@ K̄(x,τ) = (2*π*τ^2)^(-d/2)*exp(-norm(x)^2/(2*τ^2)) # function for specification of diffusivity of landmarks σq(q, nf::Noisefield) = nf.λ * K̄(q - nf.δ,nf.τ) σp(q, p, nf::Noisefield) = -dot(p, nf.λ) * ∇K̄(q - nf.δ,nf.τ) +# ∇q_σq(q, nf::Noisefield) = nf.λ * ∇K̄(q - nf.δ,nf.τ) +# +# function Δσq(q,nf::Noisefield,α::Int64) +# out = Matrix{Float64}(undef,d,d) # would like to have Unc here +# for β in 1:d +# for γ in 1:d +# out[β, γ] = nf.τ^(-2) * nf.λ[β] * K̄(q,nf.τ) * +# (nf.τ^(-2)*q[α]*q[γ] - 2* q[α]*(α==γ) ) +# end +# end +# out +# end """ Compute sigma(t,x) * dm where dm is a vector and sigma is the diffusion coefficient of landmarks write to out which is of type State """ -function Bridge.σ!(t, x, dm, out, P::Landmarks) +function Bridge.σ!(t, x_, dm, out, P::Union{Landmarks,LandmarksAux}) + if P isa Landmarks + x = x_ + else + x = P.xT + end zero!(out) for i in 1:P.n for j in 1:length(P.nfs) @@ -47,13 +64,32 @@ function Bridge.σ!(t, x, dm, out, P::Landmarks) out end -""" -Compute tildesigma(t,x) * dm where dm is a vector and sigma is the diffusion coefficient of landmarksaux -write to out which is of type State -""" -function Bridge.σ!(t, x, dm, out, P::LandmarksAux) - Bridge.σ!(t, P.xT, dm, out, P::Landmarks) -end + +# function Bridge.σ(t, x_, P::Union{Landmarks,LandmarksAux}) +# if P isa Landmarks +# x = x_ +# else +# x = P.xT +# end +# #zero!(out) +# out = 0.0*Matrix{Unc}(undef,2P.n,length(P.nfs)) +# for i in 1:P.n +# for j in 1:length(P.nfs) +# out[2i-1,j] = σq(q(x, i), P.nfs[j]) +# out[2i,j] = σp(q(x, i), p(x, i), P.nfs[j]) +# end +# end +# out +# end + + +# """ +# Compute tildesigma(t,x) * dm where dm is a vector and sigma is the diffusion coefficient of landmarksaux +# write to out which is of type State +# """ +# function Bridge.σ!(t, x, dm, out, P::LandmarksAux) +# Bridge.σ!(t, P.xT, dm, out, P::Landmarks) +# end function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) if P isa Landmarks @@ -65,21 +101,29 @@ function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) for i in 1:P.n for k in 1:P.n for j in 1:length(P.nfs) + # r1 = σq(q(x,i),P.nfs[j]) * σq(q(x, k),P.nfs[j])' + # r2 = σq(q(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' + # r3 = σp(q(x,i),p(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' + # out[2i-1,2k-1] += r1 + # out[2i-1,2k] += r2 + # out[2i,2k-1] += r2' + # out[2i,2k] += r3 r1 = σq(q(x,i),P.nfs[j]) * σq(q(x, k),P.nfs[j])' r2 = σq(q(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' + r4 = σp(q(x,i),p(x,i),P.nfs[j]) * σq(q(x,k),P.nfs[j])' r3 = σp(q(x,i),p(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' out[2i-1,2k-1] += r1 - out[2i,2k-1] += r2 out[2i-1,2k] += r2 + out[2i,2k-1] += r4 out[2i,2k] += r3 - end end end out end -Bridge.a(t, P::Union{Landmarks,LandmarksAux}) = Bridge.a(t, P.xT, P::Union{Landmarks,LandmarksAux}) +Bridge.a(t, P::LandmarksAux) = Bridge.a(t, 0, P) +#Bridge.a(t, P::Union{Landmarks,LandmarksAux}) = Bridge.a(t, P.xT, P::Union{Landmarks,LandmarksAux}) """ Multiply a(t,x) times in (which is of type state) @@ -87,6 +131,7 @@ Returns multiplication of type state """ function amul(t, x, in::State, P::Landmarks) vecofpoints2state(Bridge.a(t, x, P)*vec(in)) + #Bridge.a(t, x, P)*in end diff --git a/landmarks/bothmodels.jl b/landmarks/bothmodels.jl index cad264c..cc4d27c 100644 --- a/landmarks/bothmodels.jl +++ b/landmarks/bothmodels.jl @@ -9,14 +9,14 @@ end """ kernel in Hamiltonian """ -kernel(x, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) = - (2*π*P.a^2)^(-d/2)*exp(-norm(x)^2/(2*P.a^2)) -∇kernel(x, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) = -P.a^(-2) * kernel(x,P) * x +kernel(q, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) = + (2*π*P.a^2)^(-d/2)*exp(-norm(q)^2/(2*P.a^2)) +∇kernel(q, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) = -P.a^(-2) * kernel(q,P) * q """ Needed for b! in case P is auxiliary process """ -∇kernel(x,xT, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) = -P.a^(-2) * kernel(xT,P) * x +∇kernel(q,qT, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) = -P.a^(-2) * kernel(qT,P) * q Bridge.b(t::Float64, x, P::Union{Landmarks,MarslandShardlow})= Bridge.b!(t, x, copy(x), P) @@ -27,32 +27,72 @@ Bridge.b(t::Float64, x, P::Union{LandmarksAux,MarslandShardlowAux})= Bridge.b!(t Evaluate drift of landmarks in (t,x) and save to out x is a state and out as well """ -function Bridge.b!(t, x, out, P::Union{Landmarks,MarslandShardlow}) +function Bridge.b!(t, x, out, P::MarslandShardlow) zero!(out) for i in 1:P.n for j in 1:P.n - out.q[i] += 0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) + out.q[i] += p(x,j)*kernel(q(x,i) - q(x,j), P) # heat bath - out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(x,i) - q(x,j), P) - - 0.5* dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) + out.p[i] += -P.λ*p(x,j)*kernel(q(x,i) - q(x,j), P) - + dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) end end out end """ -Evaluate drift of landmarks auxiliary process in (t,x) and save to out +Evaluate drift of landmarks in (t,x) and save to out x is a state and out as well """ -function Bridge.b!(t, x, out, P::Union{LandmarksAux,MarslandShardlowAux}) +function Bridge.b!(t, x, out, P::Landmarks) zero!(out) for i in 1:P.n for j in 1:P.n - out.q[i] += 0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) - # heat bath - out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) - -0.5* dot(p(P.xT,i), p(P.xT,j)) * ∇kernel(q(x,i) - q(x,j),q(P.xT,i) - q(P.xT,j), P) - # 1/(2*P.a) * dot(p(P.xT,i), p(P.xT,j)) * (q(x,i)-q(x,j))*kernel(q(P.xT,i) - q(P.xT,j), P) + out.q[i] += p(x,j)*kernel(q(x,i) - q(x,j), P) + out.p[i] += -dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) + end + for k in 1:length(P.nfs) + nf = P.nfs[k] + out.q[i] -= 0.5 * nf.τ^(-2) * dot(q(x,i),nf.λ) * K̄(q(x,i),nf.τ)^2 * nf.λ + out.p[i] += 0.5 * nf.τ^(-2) * dot(p(x,i),nf.λ) * K̄(q(x,i),nf.τ)^2 * nf.λ + end + end + out +end + + +""" +Evaluate drift of landmarks auxiliary process in (t,x) and save to out +x is a state and out as well +""" +function Bridge.b!(t, x, out, Paux::MarslandShardlowAux) + zero!(out) + for i in 1:Paux.n + for j in 1:Paux.n + out.q[i] += p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) + # out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) + # -0.5* dot(p(P.xT,i), p(P.xT,j)) * ∇kernel(q(x,i) - q(x,j),q(P.xT,i) - q(P.xT,j), P) + end + end + out +end + +""" +Evaluate drift of landmarks auxiliary process in (t,x) and save to out +x is a state and out as well +""" +function Bridge.b!(t, x, out, Paux::LandmarksAux) + zero!(out) + for i in 1:Paux.n + for j in 1:Paux.n + out.q[i] += p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) + end + # out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) + # -0.5* dot(p(P.xT,i), p(P.xT,j)) * ∇kernel(q(x,i) - q(x,j),q(P.xT,i) - q(P.xT,j), P) + for k in 1:length(Paux.nfs) + nf = P.nfs[k] + out.q[i] -= 0.5 * nf.τ^(-2) * dot(q(x,i),nf.λ) * K̄(q(Paux.xT,i),nf.τ)^2 * nf.λ + out.p[i] += 0.5 * nf.τ^(-2) * dot(p(x,i),nf.λ) * K̄(q(Paux.xT,i),nf.τ)^2 * nf.λ end end out @@ -62,7 +102,7 @@ end """ Compute tildeB(t) for landmarks auxiliary process """ -function Bridge.B(t, Paux::Union{LandmarksAux,MarslandShardlowAux}) +function Bridge.B(t, Paux::MarslandShardlowAux) I = Int[] J = Int[] X = Unc[] @@ -71,16 +111,57 @@ function Bridge.B(t, Paux::Union{LandmarksAux,MarslandShardlowAux}) # terms for out.q[i] push!(I, 2i - 1) push!(J, 2j) - push!(X, 0.5*kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc)) + push!(X, kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc)) # terms for out.p[i] - push!(I, 2i) - push!(J, 2j-1) - if j==i - push!(X, sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), P) for j in setdiff(1:Paux.n,i)]) * one(Unc)) - else - push!(X, -1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)) + # push!(I, 2i) + # push!(J, 2j-1) + # if j==i + # push!(X, sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), P) for j in setdiff(1:Paux.n,i)]) * one(Unc)) + # else + # push!(X, -1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)) + # end + end + end + B = sparse(I, J, X, 2Paux.n, 2Paux.n) +end + +""" +Compute tildeB(t) for landmarks auxiliary process +""" +function Bridge.B(t, Paux::LandmarksAux) + I = Int[] + J = Int[] + X = Unc[] + for i in 1:Paux.n + for j in 1:Paux.n + # terms for out.q[i] + push!(I, 2i - 1) + push!(J, 2j) + push!(X, kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc)) + + global out1 = zero(Unc) + #out2 = zero(Unc) + for k in 1:length(Paux.nfs) + nf = P.nfs[k] + out1 -= 0.5 * nf.τ^(-2) * K̄(q(Paux.xT,i)-nf.δ,nf.τ)^2 * nf.λ * nf.λ' + #out2 += 0.5 * nf.τ^(-2) * K̄(q(Paux.xT,i),nf.τ)^2 * nf.λ * nf.λ' end + push!(I, 2i - 1) + push!(J, 2j - 1) + push!(X, out1) + push!(I, 2i) + push!(J, 2j) + push!(X, -out1) + + # terms for out.p[i] + # push!(I, 2i) + # push!(J, 2j-1) + # if j==i + # push!(X, sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), P) for j in setdiff(1:Paux.n,i)]) * one(Unc)) + # else + # push!(X, -1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)) + # end end end B = sparse(I, J, X, 2Paux.n, 2Paux.n) @@ -91,17 +172,46 @@ end Compute B̃(t) * X (B̃ from auxiliary process) and write to out Both B̃(t) and X are of type UncMat """ -function Bridge.B!(t,X,out, Paux::Union{LandmarksAux,MarslandShardlowAux}) +function Bridge.B!(t,X,out, Paux::MarslandShardlowAux) out .= 0.0 * out for i in 1:Paux.n # separately loop over even and odd indices for k in 1:2Paux.n # loop over all columns for j in 1:Paux.n - out[2i-1,k] += X[p(j), k] *0.5*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) *one(Unc) - if j==i - out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * - kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) - else - out[2i,k] += X[q(j),k] *(-1/(2*Paux.a)) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc) + out[2i-1,k] += kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*X[p(j), k] #*one(Unc) + # if j==i + # out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * + # kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) + # else + # out[2i,k] += X[q(j),k] *(-1/(2*Paux.a)) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc) + # end + end + end + end + + out +end + +""" +Compute B̃(t) * X (B̃ from auxiliary process) and write to out +Both B̃(t) and X are of type UncMat +""" +function Bridge.B!(t,X,out, Paux::LandmarksAux) + + out .= 0.0 * out + quickway = true + if quickway + out = Matrix(Bridge.B(t,Paux)) * X + else + for i in 1:Paux.n # separately loop over even and odd indices + for k in 1:2Paux.n # loop over all columns + for j in 1:Paux.n + out[2i-1,k] += kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*X[p(j), k] #*one(Unc) + # if j==i + # out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * + # kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) + # else + # out[2i,k] += X[q(j),k] *(-1/(2*Paux.a)) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc) + # end end end end @@ -112,8 +222,9 @@ end if TEST Hend⁺ = [rand(Unc) for i in 1:2Paux.n, j in 1:2Paux.n] - BB = Matrix(Bridge.B(0,Paux)) * Hend⁺ + t0 = 2.0 + BB = Matrix(Bridge.B(t0,Paux)) * Hend⁺ out = deepcopy(Hend⁺) - Bridge.B!(t,Hend⁺,out,Paux) + Bridge.B!(t0,Hend⁺,out,Paux) @test out==BB end diff --git a/landmarks/forward.jl b/landmarks/forward.jl index 104c7f2..a08659f 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -18,30 +18,29 @@ model = models[2] TEST = false#true discrmethods = [:ralston, :lowrank, :psd] -discrmethod = discrmethods[1] +discrmethod = discrmethods[3] obsschemes =[:full, :partial] obsscheme = obsschemes[2] const d = 2 -n = 50 # nr of landmarks -ldim = 75#n*d # dimension of low-rank approximation to H\^+ +n = 40 # nr of landmarks +ldim = 2n*d # dimension of low-rank approximation to H\^+ cheat = false#true#false # if cheat is true, then we initialise at x0 (true value) and # construct the guiding term based on xT (true value) -θ = 2π/n# π/6 0#π/5 # angle to rotate endpoint - -ϵ = 0.01 # parameter for initialising Hend⁺ -σobs = 0.001 # noise on observations +θ = 10π/n# π/6 0#π/5 # angle to rotate endpoint +ϵ = 10^(-6) # parameter for initialising Hend⁺ +σobs = 10^(-4) # noise on observations println(model) println(discrmethod) println(obsscheme) -T = 0.5#1.0#0.5 +T = 0.4#1.0#0.5 t = 0.0:0.01:T # time grid #Random.seed!(5) @@ -59,18 +58,18 @@ using .LowrankRiccati ### Specify landmarks models -a = 1.0 ; λ = 0.0; #= not the lambda of noise fields =# γ = 5.0 +a = 2.0 ; λ = 0.0; #= not the lambda of noise fields =# γ = 5.0 Pms = MarslandShardlow(a, γ, λ, n) -if true - db = 2.0 # domainbound +if false + db = 5.0 # domainbound # specify locations noisefields r1 = (-db:0.8:db) #+ 0.1rand(5) r2 = (-db:0.8:db) #+ 0.1rand(5) nfloc = Point.(collect(product(r1, r2)))[:] # scaling parameter of noisefields - nfscales = [0.1Point(1.0, 1.0) for x in nfloc] + nfscales = [0.3Point(1.0, 1.0) for x in nfloc] nfstd = 2.05 # tau , variance of noisefields else db = 5.0 # domainbound @@ -103,7 +102,7 @@ W = SamplePath(t, [copy(w0) for s in t]) sample!(W, Wiener{Vector{StateW}}()) # specify initial landmarks configuration -q0 = [Point(cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) +q0 = [Point(1.5cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) p_ = 5*Point(0.1, 0.1) p0 = [p_ for i in 1:n] # #p0 = [randn(Point) for i in 1:n] @@ -147,7 +146,7 @@ end # observe positions without noise v0 = q(X.yy[1]) rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) -vT = [rot * q(X.yy[end])[i] for i in 1:P.n ] +vT = [rot * X.yy[end].q[i] for i in 1:P.n ] #vT = q(X.yy[end]) @@ -232,9 +231,11 @@ else Paux = Pahsaux end -Hend⁺ = [(i==j)*one(Unc)/ϵ for i in 1:2n, j in 1:2n] +Hend⁺ = [(i==j)*one(Unc)*ϵ for i in 1:2n, j in 1:2n] # this is the precison #### perform gpupdate step -νend , Hend⁺ = gpupdate(Paux.xT,Hend⁺, Σ, L, vT) +νend = State(zero(vT), zero(vT)) +#νend = Paux.xT +νend , Hend⁺ = gpupdate(νend,Hend⁺, Σ, L, vT) # L, and Σ are ordinary matrices, vT an array of Points # νend is a state , Hend⁺ a UncMat @@ -249,7 +250,7 @@ if discrmethod==:lowrank Uend = M0.vectors[:,largest] St = [copy(Send) for s in tt_] Ut = [copy(Uend) for s in tt_] - @time νend, (Send, Uend) = bucybackwards!(LRR(), t, νt, (St, Ut), Paux, νend, (Send, Uend)) + @time νend, (Send, Uend) = bucybackwards!(LRR(), tt_, νt, (St, Ut), Paux, νend, (Send, Uend)) Hend⁺ = deepmat2unc(Uend * Send * Uend') Ht = map((S,U) -> LowRank(S,U), St,Ut) end @@ -304,7 +305,7 @@ titel = titel * string(n)*" landmarks" R""" library(tidyverse) T_ <- T#-0.0001 -T_ <- T + 0.05 +#T_ <- 0.15 dfsub <- df %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,pos1,pos2,pointID) %>% filter(timex[i], v) + +# observe positions without noise +v0 = q(X.yy[1]) +rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) +vT = [rot * X.yy[end].q[i] for i in 1:P.n ] + +out = [Any[X.tt[i], [X.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(X.tt) ][:] +df = DataFrame(time=extractcomp(out,1),pos1=extractcomp(out,2),pos2=extractcomp(out,3),mom1=extractcomp(out,4),mom2=extractcomp(out,5),pointID=extractcomp(out,6)) +#Any["X.tt[$i]", ["X.yy[$i][CartesianIndex($c, $k)][$l]" for l in 1:d, k in 1:n, c in 1:2]...] + +if model == :ms + titel = "Marsland-Shardlow model, " +else + titel = "Arnaudon-Holm-Sommer model, " +end +titel = titel * string(n)*" landmarks" + +dfT = DataFrame(pos1=extractcomp(vT,1), pos2=extractcomp(vT,2)) +df0= DataFrame(pos1=extractcomp(v0,1), pos2=extractcomp(v0,2)) + +@rput titel +@rput df +@rput dfT +@rput df0 +R""" +library(tidyverse) +#df %>% dplyr::select(time,pos1,pos2,pointID) %>% + ggplot() + + geom_path(data=df,aes(x=pos1,pos2,group=pointID,colour=time)) + + geom_point(data=dfT, mapping=aes(x=pos1,y=pos2),colour='orange',size=0.7) + + geom_point(data=df0, mapping=aes(x=pos1,y=pos2),colour='black',size=0.7)+ + theme_minimal() + xlab('horizontal position') + + ylab('vertical position') + ggtitle(titel) +""" + +R""" +df %>% dplyr::select(time,mom1,mom2,pointID) %>% + filter(pointID %in% c("point1","point2","point3","point40","point41","point42")) %>% + ggplot(aes(x=mom1,mom2,group=pointID,colour=time)) + geom_path() + + facet_wrap(~pointID) + theme_minimal() +""" + +tc(t,T) = t.*(2-t/T) +tt_ = t#tc(t,T)# 0:dtimp:(T) +#################### +# solve backward recursion on [0,T] +#L = deepmat( [(i==j)*one(Unc) for i in 1:2:2n, j in 1:2n]) +#Σ = Diagonal(σobs^2*ones(n*d)) +L = [(i==j)*one(Unc) for i in 1:2:2n, j in 1:2n] +Σ = [(i==j)*σobs^2*one(Unc) for i in 1:n, j in 1:n] +Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) +cheat = false +if cheat + Pahsaux = LandmarksAux(Pahs, X.yy[end]) +else +# Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) +# Pahsaux = LandmarksAux(Pahs, State(vT, [Point(0.001,0.001) for i in 1:Pahs.n])) + Pahsaux = LandmarksAux(Pahs, State(vT, rand(Point,Pahs.n))) +end + +if model == :ms + Paux = Pmsaux +else + Paux = Pahsaux +end + +# initialise Lt and M⁺t +Lt = [copy(L) for s in tt_] +Mt⁺ = [copy(Σ) for s in tt_] +@time (Lend, Mend⁺) = guidingbackwards!(Lm(), t, (Lt, Mt⁺), Paux, (L, Σ)) + +# issymmetric(deepmat(Bridge.a(0,Paux))) +# isposdef(deepmat(Bridge.a(0,Paux))) +# map(x->minimum(eigen(deepmat(x)).values),Mt⁺) +#Mt = map(X -> deepmat2unc(inv(deepmat(X))),Mt⁺) +Mt = map(X -> InverseCholesky(lchol(X)),Mt⁺) + + +Q = GuidedProposal!(P, Paux, tt_, Lt, Mt, vT) + +#xinit = State(v0, zero(v0)) +#xinit = State(v0, rand(Point,P.n)) +xinit = x0 +winit = zeros(StateW, dwiener) +XX = SamplePath(tt_, [copy(xinit) for s in tt_]) +WW = SamplePath(tt_, [copy(winit) for s in tt_]) +sample!(WW, Wiener{Vector{StateW}}()) + +Bridge.solve!(EulerMaruyama!(), XX, xinit, WW, Q) + +#### plotting +outg = [Any[XX.tt[i], [XX.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(XX.tt) ][:] +dfg = DataFrame(time=extractcomp(outg,1),pos1=extractcomp(outg,2),pos2=extractcomp(outg,3),mom1=extractcomp(outg,4),mom2=extractcomp(outg,5),pointID=extractcomp(outg,6)) +#Any["X.tt[$i]", ["X.yy[$i][CartesianIndex($c, $k)][$l]" for l in 1:d, k in 1:n, c in 1:2]...] + +dfT = DataFrame(pos1=extractcomp(vT,1), pos2=extractcomp(vT,2)) +df0= DataFrame(pos1=extractcomp(v0,1), pos2=extractcomp(v0,2)) + + +if model == :ms + titel = "Marsland-Shardlow model, " +else + titel = "Arnaudon-Holm-Sommer model, " +end +titel = titel * string(n)*" landmarks" + +@rput titel +@rput dfg +@rput dfT +@rput df0 +@rput T +R""" +library(tidyverse) +T_ <- T-0.001 +#T_ <- T +#T_ = 0.05 +dfsub <- df %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,mom1,mom2,pointID) %>% + filter(pointID %in% c("point1","point2","point3","point40","point41","point42")) %>% + ggplot(aes(x=mom1,mom2,group=pointID,colour=time)) + geom_path() + + facet_wrap(~pointID) + theme_minimal() +""" + + + + R""" + library(tidyverse) + dfsub <- df %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time<0.99) + dfsubg <- dfg %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time<0.99) + + sub <- rbind(dfsub,dfsubg) + sub$fg <- rep(c("forward","guided"),each=nrow(dfsub)) + + ggplot() + + geom_path(data=sub, mapping=aes(x=pos1,pos2,group=pointID,colour=fg)) + + geom_point(data=dfT, mapping=aes(x=pos1,y=pos2),colour='orange',size=0.7) + + geom_point(data=df0, mapping=aes(x=pos1,y=pos2),colour='black',size=0.7)+ + #facet_wrap(~fg) + + theme_minimal() + xlab('horizontal position') + + ylab('vertical position') + ggtitle(titel) + """ +end + +if model==:ms + @time llikelihood(LeftRule(), XX, Q; skip = 0) # won't work for AHS because matrix multilication for Htilde is not defined yet +end diff --git a/landmarks/msmodel.jl b/landmarks/msmodel.jl index 2e15165..fd5d375 100644 --- a/landmarks/msmodel.jl +++ b/landmarks/msmodel.jl @@ -47,7 +47,7 @@ function Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) end sparse(I, I, X, 2P.n, 2P.n) end -Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) - +#Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) +Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P) Bridge.constdiff(::Union{MarslandShardlow, MarslandShardlowAux}) = true diff --git a/landmarks/patches.jl b/landmarks/patches.jl index ca8e175..077304e 100644 --- a/landmarks/patches.jl +++ b/landmarks/patches.jl @@ -98,7 +98,7 @@ A conj!(B) """ function conj!(A::Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}) - if !(size(A,1)==size(A,2)) error("conj! only correctly defined for square matrices") end +# if !(size(A,1)==size(A,2)) error("conj! only correctly defined for square matrices") end for i in 1:size(A,1) A[i,i] = A[i,i]' for j in (i+1):size(A,2) @@ -107,3 +107,20 @@ function conj!(A::Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}) end A end + +function conj2(A::Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}) +# if !(size(A,1)==size(A,2)) error("conj! only correctly defined for square matrices") end + At = Matrix{Unc}(undef,size(A,2),size(A,1)) + for i in 1:size(A,2) + for j in 1:size(A,1) + At[i,j] = A[j,i]' + end + end + At +end + +if TEST + A = reshape(rand(Unc,15),5,3) + B = conj2(A) + @test norm(deepmat(A)'-deepmat(B))<10^(-10) +end diff --git a/landmarks/state.jl b/landmarks/state.jl index f9ffe81..95d10de 100644 --- a/landmarks/state.jl +++ b/landmarks/state.jl @@ -18,6 +18,8 @@ p(x::State, i) = x.p[i] q(i::Int) = 2i - 1 p(i::Int) = 2i +zero!(v) = v[:] = fill!(v, zero(eltype(v))) + iterate(x::State) = (x.q, true) iterate(x::State, s) = s ? (x.p, false) : nothing copy(x::State) = State(copy(x.q), copy(x.p)) From dd1783cf0ff52cde48aeb7ea189c31bf8952f18d Mon Sep 17 00:00:00 2001 From: fmeulen Date: Fri, 15 Feb 2019 15:54:51 +0100 Subject: [PATCH 06/58] fixed the error in the noisefields specification for ahs model --- landmarks/bothmodels.jl | 230 ---------------------------------------- landmarks/forward.jl | 58 ++++------ landmarks/guiding.jl | 10 +- landmarks/lmguiding.jl | 38 +++++-- landmarks/lmpar.jl | 132 ++++++++++++++--------- 5 files changed, 136 insertions(+), 332 deletions(-) delete mode 100644 landmarks/bothmodels.jl diff --git a/landmarks/bothmodels.jl b/landmarks/bothmodels.jl deleted file mode 100644 index cc4d27c..0000000 --- a/landmarks/bothmodels.jl +++ /dev/null @@ -1,230 +0,0 @@ -function hamiltonian((q, p), P) - s = 0.0 - for i in eachindex(q), j in eachindex(q) - s += 1/2*dot(p[i], p[j])*kernel(q[i] - q[j], P) - end - s -end - -""" -kernel in Hamiltonian -""" -kernel(q, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) = - (2*π*P.a^2)^(-d/2)*exp(-norm(q)^2/(2*P.a^2)) -∇kernel(q, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) = -P.a^(-2) * kernel(q,P) * q - -""" -Needed for b! in case P is auxiliary process -""" -∇kernel(q,qT, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) = -P.a^(-2) * kernel(qT,P) * q - -Bridge.b(t::Float64, x, P::Union{Landmarks,MarslandShardlow})= Bridge.b!(t, x, copy(x), P) - -Bridge.b(t::Float64, x, P::Union{LandmarksAux,MarslandShardlowAux})= Bridge.b!(t, x, copy(x), P) - - -""" -Evaluate drift of landmarks in (t,x) and save to out -x is a state and out as well -""" -function Bridge.b!(t, x, out, P::MarslandShardlow) - zero!(out) - for i in 1:P.n - for j in 1:P.n - out.q[i] += p(x,j)*kernel(q(x,i) - q(x,j), P) - # heat bath - out.p[i] += -P.λ*p(x,j)*kernel(q(x,i) - q(x,j), P) - - dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) - end - end - out -end - -""" -Evaluate drift of landmarks in (t,x) and save to out -x is a state and out as well -""" -function Bridge.b!(t, x, out, P::Landmarks) - zero!(out) - for i in 1:P.n - for j in 1:P.n - out.q[i] += p(x,j)*kernel(q(x,i) - q(x,j), P) - out.p[i] += -dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) - end - for k in 1:length(P.nfs) - nf = P.nfs[k] - out.q[i] -= 0.5 * nf.τ^(-2) * dot(q(x,i),nf.λ) * K̄(q(x,i),nf.τ)^2 * nf.λ - out.p[i] += 0.5 * nf.τ^(-2) * dot(p(x,i),nf.λ) * K̄(q(x,i),nf.τ)^2 * nf.λ - end - end - out -end - - -""" -Evaluate drift of landmarks auxiliary process in (t,x) and save to out -x is a state and out as well -""" -function Bridge.b!(t, x, out, Paux::MarslandShardlowAux) - zero!(out) - for i in 1:Paux.n - for j in 1:Paux.n - out.q[i] += p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) - # out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) - # -0.5* dot(p(P.xT,i), p(P.xT,j)) * ∇kernel(q(x,i) - q(x,j),q(P.xT,i) - q(P.xT,j), P) - end - end - out -end - -""" -Evaluate drift of landmarks auxiliary process in (t,x) and save to out -x is a state and out as well -""" -function Bridge.b!(t, x, out, Paux::LandmarksAux) - zero!(out) - for i in 1:Paux.n - for j in 1:Paux.n - out.q[i] += p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) - end - # out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) - # -0.5* dot(p(P.xT,i), p(P.xT,j)) * ∇kernel(q(x,i) - q(x,j),q(P.xT,i) - q(P.xT,j), P) - for k in 1:length(Paux.nfs) - nf = P.nfs[k] - out.q[i] -= 0.5 * nf.τ^(-2) * dot(q(x,i),nf.λ) * K̄(q(Paux.xT,i),nf.τ)^2 * nf.λ - out.p[i] += 0.5 * nf.τ^(-2) * dot(p(x,i),nf.λ) * K̄(q(Paux.xT,i),nf.τ)^2 * nf.λ - end - end - out -end - - -""" -Compute tildeB(t) for landmarks auxiliary process -""" -function Bridge.B(t, Paux::MarslandShardlowAux) - I = Int[] - J = Int[] - X = Unc[] - for i in 1:Paux.n - for j in 1:Paux.n - # terms for out.q[i] - push!(I, 2i - 1) - push!(J, 2j) - push!(X, kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc)) - - # terms for out.p[i] - # push!(I, 2i) - # push!(J, 2j-1) - # if j==i - # push!(X, sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), P) for j in setdiff(1:Paux.n,i)]) * one(Unc)) - # else - # push!(X, -1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)) - # end - end - end - B = sparse(I, J, X, 2Paux.n, 2Paux.n) -end - -""" -Compute tildeB(t) for landmarks auxiliary process -""" -function Bridge.B(t, Paux::LandmarksAux) - I = Int[] - J = Int[] - X = Unc[] - for i in 1:Paux.n - for j in 1:Paux.n - # terms for out.q[i] - push!(I, 2i - 1) - push!(J, 2j) - push!(X, kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc)) - - global out1 = zero(Unc) - #out2 = zero(Unc) - for k in 1:length(Paux.nfs) - nf = P.nfs[k] - out1 -= 0.5 * nf.τ^(-2) * K̄(q(Paux.xT,i)-nf.δ,nf.τ)^2 * nf.λ * nf.λ' - #out2 += 0.5 * nf.τ^(-2) * K̄(q(Paux.xT,i),nf.τ)^2 * nf.λ * nf.λ' - end - push!(I, 2i - 1) - push!(J, 2j - 1) - push!(X, out1) - push!(I, 2i) - push!(J, 2j) - push!(X, -out1) - - # terms for out.p[i] - # push!(I, 2i) - # push!(J, 2j-1) - # if j==i - # push!(X, sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), P) for j in setdiff(1:Paux.n,i)]) * one(Unc)) - # else - # push!(X, -1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)) - # end - end - end - B = sparse(I, J, X, 2Paux.n, 2Paux.n) -end - - -""" -Compute B̃(t) * X (B̃ from auxiliary process) and write to out -Both B̃(t) and X are of type UncMat -""" -function Bridge.B!(t,X,out, Paux::MarslandShardlowAux) - out .= 0.0 * out - for i in 1:Paux.n # separately loop over even and odd indices - for k in 1:2Paux.n # loop over all columns - for j in 1:Paux.n - out[2i-1,k] += kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*X[p(j), k] #*one(Unc) - # if j==i - # out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * - # kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) - # else - # out[2i,k] += X[q(j),k] *(-1/(2*Paux.a)) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc) - # end - end - end - end - - out -end - -""" -Compute B̃(t) * X (B̃ from auxiliary process) and write to out -Both B̃(t) and X are of type UncMat -""" -function Bridge.B!(t,X,out, Paux::LandmarksAux) - - out .= 0.0 * out - quickway = true - if quickway - out = Matrix(Bridge.B(t,Paux)) * X - else - for i in 1:Paux.n # separately loop over even and odd indices - for k in 1:2Paux.n # loop over all columns - for j in 1:Paux.n - out[2i-1,k] += kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*X[p(j), k] #*one(Unc) - # if j==i - # out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * - # kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) - # else - # out[2i,k] += X[q(j),k] *(-1/(2*Paux.a)) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc) - # end - end - end - end - end - out -end - - -if TEST - Hend⁺ = [rand(Unc) for i in 1:2Paux.n, j in 1:2Paux.n] - t0 = 2.0 - BB = Matrix(Bridge.B(t0,Paux)) * Hend⁺ - out = deepcopy(Hend⁺) - Bridge.B!(t0,Hend⁺,out,Paux) - @test out==BB -end diff --git a/landmarks/forward.jl b/landmarks/forward.jl index a08659f..e7bb2f3 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -18,23 +18,24 @@ model = models[2] TEST = false#true discrmethods = [:ralston, :lowrank, :psd] -discrmethod = discrmethods[3] +discrmethod = discrmethods[2] obsschemes =[:full, :partial] obsscheme = obsschemes[2] const d = 2 +const itostrat=false -n = 40 # nr of landmarks -ldim = 2n*d # dimension of low-rank approximation to H\^+ +n = 60 # nr of landmarks +ldim = 50#n*d # dimension of low-rank approximation to H\^+ cheat = false#true#false # if cheat is true, then we initialise at x0 (true value) and # construct the guiding term based on xT (true value) -θ = 10π/n# π/6 0#π/5 # angle to rotate endpoint +θ = π/10# π/6 0#π/5 # angle to rotate endpoint -ϵ = 10^(-6) # parameter for initialising Hend⁺ -σobs = 10^(-4) # noise on observations +ϵ = 10^(-4) # parameter for initialising Hend⁺ +σobs = 10^(-3) # noise on observations println(model) println(discrmethod) @@ -44,12 +45,8 @@ T = 0.4#1.0#0.5 t = 0.0:0.01:T # time grid #Random.seed!(5) - - include("state.jl") -include("msmodel.jl") -include("ahsmodel.jl") -include("bothmodels.jl") +include("models.jl") include("patches.jl") include("guiding.jl") include("LowrankRiccati.jl") @@ -57,30 +54,21 @@ using .LowrankRiccati ### Specify landmarks models - -a = 2.0 ; λ = 0.0; #= not the lambda of noise fields =# γ = 5.0 +a = 3.0 # the larger, the stronger landmarks behave similarly +λ = 0.0; #= not the lambda of noise fields =# γ = 8.0 Pms = MarslandShardlow(a, γ, λ, n) -if false - db = 5.0 # domainbound - # specify locations noisefields - r1 = (-db:0.8:db) #+ 0.1rand(5) - r2 = (-db:0.8:db) #+ 0.1rand(5) - nfloc = Point.(collect(product(r1, r2)))[:] - # scaling parameter of noisefields - nfscales = [0.3Point(1.0, 1.0) for x in nfloc] - nfstd = 2.05 # tau , variance of noisefields -else - db = 5.0 # domainbound - # specify locations noisefields - r1 = (-db:0.5:db) #+ 0.1rand(5) - r2 = (-db:0.5:db) #+ 0.1rand(5) - nfloc = Point.(collect(product(r1, r2)))[:] - # scaling parameter of noisefields - nfscales = [.3Point(1.0, 1.0) for x in nfloc] - nfstd = 4.0 # tau , variance of noisefields -end +db = 2.0 # domainbound +r1 = repeat(collect((-db:.5:db))) +r2 = repeat(collect((-db:.5:db))) +nfloc1 = Point.(collect(product(r1, r2)))[:] +nfscales_hor = [.05Point(1.0, 0.0) for x in nfloc1] # intensity +nfscales_ver = [.05Point(0.0, 1.0) for x in nfloc1] # intensity +nfscales = vcat(nfscales_hor, nfscales_ver) +nfloc = vcat(nfloc1,nfloc1) +nfstd = .5 # tau , widht of noisefields + nfs = [Noisefield(δ, λ, nfstd) for (δ, λ) in zip(nfloc, nfscales)] @@ -171,7 +159,7 @@ df0= DataFrame(pos1=extractcomp(v0,1), pos2=extractcomp(v0,2)) @rput df0 R""" library(tidyverse) -#df %>% dplyr::select(time,pos1,pos2,pointID) %>% +df %>% dplyr::select(time,pos1,pos2,pointID) %>% ggplot() + geom_path(data=df,aes(x=pos1,pos2,group=pointID,colour=time)) + geom_point(data=dfT, mapping=aes(x=pos1,y=pos2),colour='orange',size=0.7) + @@ -305,7 +293,7 @@ titel = titel * string(n)*" landmarks" R""" library(tidyverse) T_ <- T#-0.0001 -#T_ <- 0.15 +#T_ <- 0.05 dfsub <- df %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,pos1,pos2,pointID) %>% filter(timex[1], σqfield)) +# @rput dfsigmaqfield +# R""" +# library(tidyverse) +# dfsigmaqfield %>% ggplot(aes(x, y, z = sigmaq)) + +# geom_tile(aes(fill=sigmaq)) + theme_minimal() +# """ + + Pahs = Landmarks(a, λ, n, nfs) ### @@ -85,12 +97,13 @@ W = SamplePath(t, [copy(w0) for s in t]) sample!(W, Wiener{Vector{StateW}}()) # specify initial landmarks configuration -q0 = [Point(1.5cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) -p_ = Point(0.1, 0.1) -p0 = [5p_ for i in 1:n] # +q0 = [Point(cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) +p_ = 2*Point(-0.1, 0.1) +p0 = [p_ for i in 1:n] # #p0 = [randn(Point) for i in 1:n] x0 = State(q0, p0) +#map(i->σp(q(x0, i), p(x0, i), P.nfs[6]), 1:length(P.nfs)) #Random.seed!(1234) @@ -129,7 +142,7 @@ df0= DataFrame(pos1=extractcomp(v0,1), pos2=extractcomp(v0,2)) @rput df0 R""" library(tidyverse) -#df %>% dplyr::select(time,pos1,pos2,pointID) %>% +df %>% dplyr::select(time,pos1,pos2,pointID) %>% ggplot() + geom_path(data=df,aes(x=pos1,pos2,group=pointID,colour=time)) + geom_point(data=dfT, mapping=aes(x=pos1,y=pos2),colour='orange',size=0.7) + @@ -138,29 +151,36 @@ library(tidyverse) ylab('vertical position') + ggtitle(titel) """ + R""" df %>% dplyr::select(time,mom1,mom2,pointID) %>% filter(pointID %in% c("point1","point2","point3","point40","point41","point42")) %>% ggplot(aes(x=mom1,mom2,group=pointID,colour=time)) + geom_path() + - facet_wrap(~pointID) + theme_minimal() + facet_wrap(~pointID,scales="free") + theme_minimal() """ tc(t,T) = t.*(2-t/T) tt_ = t#tc(t,T)# 0:dtimp:(T) #################### # solve backward recursion on [0,T] -#L = deepmat( [(i==j)*one(Unc) for i in 1:2:2n, j in 1:2n]) -#Σ = Diagonal(σobs^2*ones(n*d)) -L = [(i==j)*one(Unc) for i in 1:2:2n, j in 1:2n] -Σ = [(i==j)*σobs^2*one(Unc) for i in 1:n, j in 1:n] -Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) -cheat = false -if cheat - Pahsaux = LandmarksAux(Pahs, X.yy[end]) +if partialobs==true + L = [(i==j)*one(Unc) for i in 1:2:2n, j in 1:2n] + Σ = [(i==j)*σobs^2*one(Unc) for i in 1:n, j in 1:n] + #Σ = 10 * reshape(rand(Unc,n^2),n,n) + μend = zeros(Point,P.n) + xobs = vT + Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) + Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) + Pahsaux = LandmarksAux(Pahs, State(vT, rand(Point,Pahs.n))) + else -# Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) -# Pahsaux = LandmarksAux(Pahs, State(vT, [Point(0.001,0.001) for i in 1:Pahs.n])) - Pahsaux = LandmarksAux(Pahs, State(vT, rand(Point,Pahs.n))) + # full observation case + L = [(i==j)*one(Unc) for i in 1:2n, j in 1:2n] + Σ = [(i==j)*σobs^2*one(Unc) for i in 1:2n, j in 1:2n] + μend = zeros(Point,2P.n) + xobs = vec(X.yy[end]) + Pahsaux = LandmarksAux(Pahs, X.yy[end]) + Pmsaux = MarslandShardlowAux(Pms, X.yy[end]) end if model == :ms @@ -172,26 +192,36 @@ end # initialise Lt and M⁺t Lt = [copy(L) for s in tt_] Mt⁺ = [copy(Σ) for s in tt_] -@time (Lend, Mend⁺) = guidingbackwards!(Lm(), t, (Lt, Mt⁺), Paux, (L, Σ)) +μt = [copy(μend) for s in tt_] +@time (Lend, Mend⁺,μend) = guidingbackwards!(Lm(), t, (Lt, Mt⁺,μt), Paux, (L, Σ, μend)) # issymmetric(deepmat(Bridge.a(0,Paux))) # isposdef(deepmat(Bridge.a(0,Paux))) # map(x->minimum(eigen(deepmat(x)).values),Mt⁺) -#Mt = map(X -> deepmat2unc(inv(deepmat(X))),Mt⁺) -Mt = map(X -> InverseCholesky(lchol(X)),Mt⁺) +Mt = map(X -> deepmat2unc(inv(deepmat(X))),Mt⁺) +#Mt = map(X -> InverseCholesky(lchol(X)),Mt⁺) -Q = GuidedProposal!(P, Paux, tt_, Lt, Mt, vT) +Q = GuidedProposal!(P, Paux, tt_, Lt, Mt, μt, xobs) #xinit = State(v0, zero(v0)) -#xinit = State(v0, rand(Point,P.n)) -xinit = x0 + +if partialobs + xinit = State(v0, rand(Point,P.n)) +else + xinit = x0 +end winit = zeros(StateW, dwiener) XX = SamplePath(tt_, [copy(xinit) for s in tt_]) WW = SamplePath(tt_, [copy(winit) for s in tt_]) sample!(WW, Wiener{Vector{StateW}}()) + + + + Bridge.solve!(EulerMaruyama!(), XX, xinit, WW, Q) +guid = guidingterms(XX,Q) #### plotting outg = [Any[XX.tt[i], [XX.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(XX.tt) ][:] @@ -217,7 +247,7 @@ titel = titel * string(n)*" landmarks" R""" library(tidyverse) T_ <- T-0.001 -#T_ <- T +T_ <- T #T_ = 0.05 dfsub <- df %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,pos1,pos2,pointID) %>% filter(time Date: Mon, 18 Feb 2019 15:50:37 +0100 Subject: [PATCH 07/58] Ito-strat correction has been included for ahs model. Huge speedup in forward simulation guided propoposals by amul function for landmarks (which avoids computing a(t,x), but computes a(t,x)*y as sigmat(t,x) * (sigma(t,x)' * y). --- landmarks/forward.jl | 236 +++++++++-------------------------------- landmarks/guiding.jl | 42 +++++--- landmarks/lmguiding.jl | 28 ++--- landmarks/lmpar.jl | 206 ++++++----------------------------- landmarks/patches.jl | 11 ++ landmarks/state.jl | 8 ++ src/partialbridge.jl | 12 +-- 7 files changed, 144 insertions(+), 399 deletions(-) diff --git a/landmarks/forward.jl b/landmarks/forward.jl index e7bb2f3..5f612d3 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -18,31 +18,31 @@ model = models[2] TEST = false#true discrmethods = [:ralston, :lowrank, :psd] -discrmethod = discrmethods[2] +discrmethod = discrmethods[3] obsschemes =[:full, :partial] obsscheme = obsschemes[2] const d = 2 -const itostrat=false +const itostrat=true -n = 60 # nr of landmarks -ldim = 50#n*d # dimension of low-rank approximation to H\^+ +n = 70 # nr of landmarks +ldim = 2n*d # dimension of low-rank approximation to H\^+ cheat = false#true#false # if cheat is true, then we initialise at x0 (true value) and # construct the guiding term based on xT (true value) -θ = π/10# π/6 0#π/5 # angle to rotate endpoint +θ = -π/6# π/6 0#π/5 # angle to rotate endpoint -ϵ = 10^(-4) # parameter for initialising Hend⁺ +ϵ = 10^(-8) # parameter for initialising Hend⁺ σobs = 10^(-3) # noise on observations println(model) println(discrmethod) println(obsscheme) -T = 0.4#1.0#0.5 -t = 0.0:0.01:T # time grid +T = 0.3#1.0#0.5 +t = 0.0:0.005:T # time grid #Random.seed!(5) include("state.jl") @@ -56,140 +56,57 @@ using .LowrankRiccati ### Specify landmarks models a = 3.0 # the larger, the stronger landmarks behave similarly λ = 0.0; #= not the lambda of noise fields =# γ = 8.0 - -Pms = MarslandShardlow(a, γ, λ, n) - -db = 2.0 # domainbound -r1 = repeat(collect((-db:.5:db))) -r2 = repeat(collect((-db:.5:db))) -nfloc1 = Point.(collect(product(r1, r2)))[:] -nfscales_hor = [.05Point(1.0, 0.0) for x in nfloc1] # intensity -nfscales_ver = [.05Point(0.0, 1.0) for x in nfloc1] # intensity -nfscales = vcat(nfscales_hor, nfscales_ver) -nfloc = vcat(nfloc1,nfloc1) +db = 3.0 # domainbound nfstd = .5 # tau , widht of noisefields - +r1 = -db:nfstd:db +r2 = -db:nfstd:db +nfloc = Point.(collect(product(r1, r2)))[:] +nfscales = [.1Point(1.0, 1.0) for x in nfloc] # intensity nfs = [Noisefield(δ, λ, nfstd) for (δ, λ) in zip(nfloc, nfscales)] - +Pms = MarslandShardlow(a, γ, λ, n) Pahs = Landmarks(a, λ, n, nfs) ### +StateW = Point if model == :ms dwiener = n - StateW = Point P = Pms else dwiener = length(nfloc) - StateW = Float64 P = Pahs end -w0 = zeros(StateW, dwiener) -W = SamplePath(t, [copy(w0) for s in t]) -sample!(W, Wiener{Vector{StateW}}()) - # specify initial landmarks configuration -q0 = [Point(1.5cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) +q0 = [Point(2.5cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) p_ = 5*Point(0.1, 0.1) p0 = [p_ for i in 1:n] # #p0 = [randn(Point) for i in 1:n] x0 = State(q0, p0) - #Random.seed!(1234) - +w0 = zeros(StateW, dwiener) +W = SamplePath(t, [copy(w0) for s in t]) X = SamplePath(t, [copy(x0) for s in t]) -if model == :ms - @time solve!(EulerMaruyama!(), X, x0, W, P) -else - @time solve!(EulerMaruyama!(), X, x0, W, P) - # still needs to be implemented - #@time solve!(StratonovichHeun!(), X, x0, W, P) -end -extractcomp(v,i) = map(x->x[i], v) - -if TEST - ####### extracting components - X.tt # gives all times - X.yy # gives an array of States (the state at each time) - X.yy[1] # gives the state at first time - - q(X.yy[1]) # gives the array of positions of all points - X.yy[1].q # equivalent - - p(X.yy[1]) # gives the array of momenta of all points - X.yy[1].p # equivalent +sample!(W, Wiener{Vector{StateW}}()) +println("Sample forward process:") +@time solve!(EulerMaruyama!(), X, x0, W, P) +#@time solve!(StratonovichHeun!(), X, x0, W, P) - p(X.yy[1],10) # at first time, extract momentum vector of landmark nr 10 - q(X.yy[23],10) # extract position at time 23, for landmark nr 10 +# compute Hamiltonian along path +ham = [hamiltonian(X.yy[i],Pms) for i in 1:length(t)] - map(x->norm(x), X.yy[1].q) # verifies that all points are on the unit circle - ham = [hamiltonian(X.yy[i],Pms) for i in 1:length(t)] - print(ham) - ############# -end +tc(t,T) = t.*(2-t/T) +tt_ = tc(t,T)#tc(t,T)# 0:dtimp:(T) # observe positions without noise -v0 = q(X.yy[1]) +v0 = q(X.yy[1]) + σobs * randn(Point,n) rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) -vT = [rot * X.yy[end].q[i] for i in 1:P.n ] -#vT = q(X.yy[end]) - - +vT = [rot * X.yy[end].q[i] + σobs * randn(d) for i in 1:P.n ] -out = [Any[X.tt[i], [X.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(X.tt) ][:] -df = DataFrame(time=extractcomp(out,1),pos1=extractcomp(out,2),pos2=extractcomp(out,3),mom1=extractcomp(out,4),mom2=extractcomp(out,5),pointID=extractcomp(out,6)) -#Any["X.tt[$i]", ["X.yy[$i][CartesianIndex($c, $k)][$l]" for l in 1:d, k in 1:n, c in 1:2]...] - -if model == :ms - titel = "Marsland-Shardlow model, " -else - titel = "Arnaudon-Holm-Sommer model, " -end -titel = titel * string(n)*" landmarks" - -dfT = DataFrame(pos1=extractcomp(vT,1), pos2=extractcomp(vT,2)) -df0= DataFrame(pos1=extractcomp(v0,1), pos2=extractcomp(v0,2)) - -@rput titel -@rput df -@rput dfT -@rput df0 -R""" -library(tidyverse) -df %>% dplyr::select(time,pos1,pos2,pointID) %>% - ggplot() + - geom_path(data=df,aes(x=pos1,pos2,group=pointID,colour=time)) + - geom_point(data=dfT, mapping=aes(x=pos1,y=pos2),colour='orange',size=0.7) + - geom_point(data=df0, mapping=aes(x=pos1,y=pos2),colour='black',size=0.7)+ - theme_minimal() + xlab('horizontal position') + - ylab('vertical position') + ggtitle(titel) -""" - -R""" -df %>% dplyr::select(time,mom1,mom2,pointID) %>% - filter(pointID %in% c("point1","point2","point3","point40","point41","point42")) %>% - ggplot(aes(x=mom1,mom2,group=pointID,colour=time)) + geom_path() + - facet_wrap(~pointID) + theme_minimal() -""" - - - - -#dtimp = 0.01 # mesh width for imputation -tc(t,T) = t.*(2-t/T) -tt_ = t#tc(t,T)# 0:dtimp:(T) - -#tt_ = 0.0:0.001:T #################### -# solve backward recursion on [0,T] - - - - if obsscheme==:partial L = deepmat( [(i==j)*one(Unc) for i in 1:2:2n, j in 1:2n]) Σ = Diagonal(σobs^2*ones(n*d)) @@ -199,9 +116,6 @@ if obsscheme==:partial else Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) #Pahsaux = LandmarksAux(Pahs, State(vT, rand(Point,Pahs.n))) - #Pahsaux = LandmarksAux(Pahs, State(vT, [Point(1,1) for i in 1:Pahs.n])) - #Pahsaux = LandmarksAux(Pahs, X.yy[end]) - #Pahsaux = LandmarksAux(Pahs, State(vT, 0.0*X.yy[end].p)) end end if obsscheme==:full @@ -213,24 +127,33 @@ if obsscheme==:full vT = vec(X.yy[end]) end +#Paux = (model==:ms) ? Pmsaux : Pahsaux if model == :ms Paux = Pmsaux else Paux = Pahsaux end -Hend⁺ = [(i==j)*one(Unc)*ϵ for i in 1:2n, j in 1:2n] # this is the precison + + +# solve backward recursion on [0,T] +# "old" choice (wrong) +#νend = State(zero(vT), zero(vT)) +#Hend⁺ = [(i==j)*one(Unc)/ϵ for i in 1:2n, j in 1:2n] # this is the precison +# "right" choice +νend = State(vT, zero(vT)) +Hend⁺ = reshape(zeros(Unc,4n^2),2n,2n) +for i in 1:n + Hend⁺[2i-1,2i-1] = one(Unc)/ϵ # high precision on positions + Hend⁺[2i,2i] = one(Unc)*ϵ +end #### perform gpupdate step -νend = State(zero(vT), zero(vT)) -#νend = Paux.xT νend , Hend⁺ = gpupdate(νend,Hend⁺, Σ, L, vT) # L, and Σ are ordinary matrices, vT an array of Points # νend is a state , Hend⁺ a UncMat -# initialise νt νt = [copy(νend) for s in tt_] - - +println("Compute guiding term:") if discrmethod==:lowrank M0 = eigen(deepmat(Hend⁺)) largest = sortperm(M0.values)[end-ldim+1:end] @@ -239,8 +162,8 @@ if discrmethod==:lowrank St = [copy(Send) for s in tt_] Ut = [copy(Uend) for s in tt_] @time νend, (Send, Uend) = bucybackwards!(LRR(), tt_, νt, (St, Ut), Paux, νend, (Send, Uend)) - Hend⁺ = deepmat2unc(Uend * Send * Uend') - Ht = map((S,U) -> LowRank(S,U), St,Ut) + Ht =map((S,U) -> deepmat2unc(U * inv(S) * U'), St,Ut) # directly compute Mt + #Ht = map((S,U) -> LowRank(S,U), St,Ut) end if discrmethod==:ralston H⁺t = [copy(Hend⁺) for s in tt_] @@ -263,70 +186,11 @@ XX = SamplePath(tt_, [copy(xinit) for s in tt_]) WW = SamplePath(tt_, [copy(winit) for s in tt_]) sample!(WW, Wiener{Vector{StateW}}()) -Bridge.solve!(EulerMaruyama!(), XX, xinit, WW, Q) +println("Sample guided bridge proposal:") +@time Bridge.solve!(EulerMaruyama!(), XX, xinit, WW, Q) -hcat(mean(X.yy[end].p), mean(XX.yy[end].p)) -# redo with Paux.xT = XX.yy[end] - hcat(X.yy[end].p, XX.yy[end].p, Paux.xT.p) +include("plotlandmarks.jl") -#### plotting -outg = [Any[XX.tt[i], [XX.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(XX.tt) ][:] -dfg = DataFrame(time=extractcomp(outg,1),pos1=extractcomp(outg,2),pos2=extractcomp(outg,3),mom1=extractcomp(outg,4),mom2=extractcomp(outg,5),pointID=extractcomp(outg,6)) -#Any["X.tt[$i]", ["X.yy[$i][CartesianIndex($c, $k)][$l]" for l in 1:d, k in 1:n, c in 1:2]...] - -dfT = DataFrame(pos1=extractcomp(vT,1), pos2=extractcomp(vT,2)) -df0= DataFrame(pos1=extractcomp(v0,1), pos2=extractcomp(v0,2)) - - -if model == :ms - titel = "Marsland-Shardlow model, " -else - titel = "Arnaudon-Holm-Sommer model, " -end -titel = titel * string(n)*" landmarks" - -@rput titel -@rput dfg -@rput dfT -@rput df0 -@rput T -R""" -library(tidyverse) -T_ <- T#-0.0001 -#T_ <- 0.05 -dfsub <- df %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,pos1,pos2,pointID) %>% filter(time<0.99) - dfsubg <- dfg %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time<0.99) - - sub <- rbind(dfsub,dfsubg) - sub$fg <- rep(c("forward","guided"),each=nrow(dfsub)) - - ggplot() + - geom_path(data=sub, mapping=aes(x=pos1,pos2,group=pointID,colour=fg)) + - geom_point(data=dfT, mapping=aes(x=pos1,y=pos2),colour='orange',size=0.7) + - geom_point(data=df0, mapping=aes(x=pos1,y=pos2),colour='black',size=0.7)+ - #facet_wrap(~fg) + - theme_minimal() + xlab('horizontal position') + - ylab('vertical position') + ggtitle(titel) - """ +if model==:ms + @time llikelihood(LeftRule(), XX, Q; skip = 0) # won't work for AHS because matrix multilication for Htilde is not defined yet end -@time llikelihood(LeftRule(), XX, Q; skip = 0) # won't work for AHS because matrix multilication for Htilde is not defined yet diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index d698bf2..56dcf40 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -23,20 +23,18 @@ function gpupdate(ν2::State, P2, Σ, L, v2::Vector{Point}) ν = deepvec(ν2) P = deepmat(P2) v = reinterpret(Float64,v2) - if false #all(diag(P) .== Inf) - #P_ = inv(L' * inv(Σ) * L) - #V_ = (L' * inv(Σ) * L)\(L' * inv(Σ) * v) - P_ = inv(L' * inv(Σ) * L + 10^(-6)*I) - V_ = P_ * L' * inv(Σ) * v + if all(diag(P) .== Inf) + P_ = inv(L' * inv(Σ) * L) + V_ = (L' * inv(Σ) * L)\(L' * inv(Σ) * v) + # P_ = inv(L' * inv(Σ) * L + 10^(-6)*I) + # V_ = P_ * L' * inv(Σ) * v return deepvec2state(V_), deepmat2unc(P_) else - Z = I - P*L'*inv(Σ + L*P*L')*L - return deepvec2state(Z*P*L'*inv(Σ)*v + Z*ν), deepmat2unc(Z*P) - - # P_ = inv(L' * inv(Σ) * L + P) - # V_ = P_ * L' * inv(Σ) * v + P_ * inv(P) * ν - # return deepvec2state(V_), deepmat2unc(P_) - + Z = I - P*L'*inv(Σ + L*P*L')*L + return deepvec2state(Z*P*L'*inv(Σ)*v + Z*ν), deepmat2unc(Z*P) + # P_ = inv(L' * inv(Σ) * L + inv(P)) + # V_ = P_ * L' * inv(Σ) * v + P_ * inv(P) * ν + # return deepvec2state(V_), deepmat2unc(P_) end end @@ -90,6 +88,7 @@ function bucybackwards!(scheme::LRR, t, νt, (St, Ut), Paux, νend, (Send, Uend) dt = t[i] - t[i+1] kernelr3!(Arg4Closure(Bridge.b!, Paux), t[i+1], νt[i+1], wsν, νt[i], dt) lowrankriccati!(t[i], t[i+1], -B̃, ã , (St[i+1], Ut[i+1]), (St[i], Ut[i])) + end νt[1], (St[1], Ut[1]) end @@ -102,10 +101,12 @@ function bucybackwards!(::Lyap, t, νt, H⁺t, Paux, νend, Hend⁺) H⁺t[end] = Hend⁺ νt[end] = νend wsν = Bridge.workspace(R3!(), νend) + B̃ = Matrix(Bridge.B(0.0, Paux)) + ã = Bridge.a(0.0, Paux) for i in length(t)-1:-1:1 dt = t[i] - t[i+1] kernelr3!(Arg4Closure(Bridge.b!, Paux), t[i+1], νt[i+1], wsν, νt[i], dt) - lyapunovpsdbackward_step!(t[i+1], -dt, Paux, H⁺t[i+1], H⁺t[i]) # maybe with -dt + lyapunovpsdbackward_step!(t[i+1], -dt, Paux, H⁺t[i+1], H⁺t[i], B̃, ã) # maybe with -dt end νt[1], H⁺t[1] end @@ -141,6 +142,8 @@ function _r!((i,t), x, out, P::GuidedProposal!) out end + + #H((i,t), x, P::GuidedProposal!) = P.H[i] target(P::GuidedProposal!) = P.target @@ -167,10 +170,15 @@ function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposal!; skip = 0 som += dot(bout-btout, rout) * dt if !constdiff(Q) - H = H((i,s), x, Q) - Δa = a((i,s), x, target(Q)) - a((i,s), x, auxiliary(Q)) - som -= 0.5*tr(Δa*H) * dt - som += 0.5*(rout'*Δa*rout) * dt + #Δa = a((i,s), x, target(Q)) - a((i,s), x, auxiliary(Q)) + # H = H((i,s), x, auxiliary(Q)) + # som -= 0.5*tr(Δa*H) * dt + # som += 0.5*(rout'*Δa*rout) * dt + + Δa = Bridge.a(s, x, target(Q)) - Bridge.a(s, x, auxiliary(Q)) + # H = H((i,s), x, auxiliary(Q)) + # som -= 0.5*tr(Δa*H) * dt + som += 0.5*dot(rout,Δa*rout) * dt end end som diff --git a/landmarks/lmguiding.jl b/landmarks/lmguiding.jl index fc35635..e63b365 100644 --- a/landmarks/lmguiding.jl +++ b/landmarks/lmguiding.jl @@ -6,7 +6,7 @@ import Bridge: kernelr3!, R3!, target, auxiliary, constdiff, llikelihood, _b!, B """ Construct guided proposal on a single segment with times in tt from precomputed ν and H """ -struct GuidedProposal!{T,Ttarget,Taux,TL,TM,Tμ,Txobs,F} <: ContinuousTimeProcess{T} +struct GuidedProposall!{T,Ttarget,Taux,TL,TM,Tμ,Txobs,F} <: ContinuousTimeProcess{T} target::Ttarget # P aux::Taux # Ptilde tt::Vector{Float64} # grid of time points on single segment (S,T] @@ -16,7 +16,7 @@ struct GuidedProposal!{T,Ttarget,Taux,TL,TM,Tμ,Txobs,F} <: ContinuousTimeProces xobs::Txobs endpoint::F - function GuidedProposal!(target, aux, tt_, L, M, μ, xobs, endpoint=Bridge.endpoint) + function GuidedProposall!(target, aux, tt_, L, M, μ, xobs, endpoint=Bridge.endpoint) tt = collect(tt_) new{Bridge.valtype(target),typeof(target),typeof(aux),eltype(L),eltype(M),eltype(μt),typeof(xobs),typeof(endpoint)}(target, aux, tt, L, M, μ, xobs, endpoint) end @@ -39,33 +39,33 @@ function guidingbackwards!(::Lm, t, (Lt, Mt⁺, μt), Paux, (Lend, Mend⁺, μen (Lt[1], Mt⁺[1], μt[1]) end -target(Q::GuidedProposal!) = Q.target -auxiliary(Q::GuidedProposal!) = Q.aux +target(Q::GuidedProposall!) = Q.target +auxiliary(Q::GuidedProposall!) = Q.aux -constdiff(Q::GuidedProposal!) = constdiff(target(Q)) && constdiff(auxiliary(Q)) +constdiff(Q::GuidedProposall!) = constdiff(target(Q)) && constdiff(auxiliary(Q)) -function Bridge._b!((i,t), x::State, out::State, Q::GuidedProposal!) +function Bridge._b!((i,t), x::State, out::State, Q::GuidedProposall!) Bridge.b!(t, x, out, Q.target) - out .+= amul(t,x,Q.Lt[i]' * Q.Mt[i] *(Q.xobs-Q.μt[i]-Q.Lt[i]*vec(x)),Q.target) + out .+= amul(t,x,Q.Lt[i]' * (Q.Mt[i] *(Q.xobs-Q.μt[i]-Q.Lt[i]*vec(x))),Q.target) out end -σ!(t, x, dw, out, Q::GuidedProposal!) = σ!(t, x, dw, out, Q.target) +σ!(t, x, dw, out, Q::GuidedProposall!) = σ!(t, x, dw, out, Q.target) # in following x is of type state -function _r!((i,t), x::State, out::State, Q::GuidedProposal!) - out .= vecofpoints2state(Q.Lt[i]' * Q.Mt[i] *(Q.xobs-Q.μt[i]-Q.Lt[i]*vec(x))) +function _r!((i,t), x::State, out::State, Q::GuidedProposall!) + out .= vecofpoints2state(Q.Lt[i]' * (Q.Mt[i] *(Q.xobs-Q.μt[i]-Q.Lt[i]*vec(x)))) out end -function guidingterm((i,t),x::State,Q::GuidedProposal!) - Bridge.b(t,x,Q.target) + amul(t,x,Q.Lt[i]' * Q.Mt[i] *(Q.xobs-Q.μt[i]-Q.Lt[i]*vec(x)),Q.target) +function guidingterm((i,t),x::State,Q::GuidedProposall!) + Bridge.b(t,x,Q.target) + amul(t,x,Q.Lt[i]' * (Q.Mt[i] *(Q.xobs-Q.μt[i]-Q.Lt[i]*vec(x))),Q.target) end """ Returns the guiding terms a(t,x)*r̃(t,x) along the path of a guided proposal """ -function guidingterms(X::SamplePath{State{SArray{Tuple{2},Float64,1,2}}},Q::GuidedProposal!) +function guidingterms(X::SamplePath{State{SArray{Tuple{2},Float64,1,2}}},Q::GuidedProposall!) out = State[] for i in 1:length(X.tt) push!(out, guidingterm((i,X.tt[i]),X.yy[i],Q)) @@ -74,7 +74,7 @@ function guidingterms(X::SamplePath{State{SArray{Tuple{2},Float64,1,2}}},Q::Guid end -function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposal!; skip = 0) +function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposall!; skip = 0) tt = Xcirc.tt xx = Xcirc.yy diff --git a/landmarks/lmpar.jl b/landmarks/lmpar.jl index f3337bb..12559dc 100644 --- a/landmarks/lmpar.jl +++ b/landmarks/lmpar.jl @@ -14,7 +14,7 @@ using Base.Iterators using SparseArrays models = [:ms, :ahs] -model = models[2] +model = models[1] TEST = false#true partialobs = true @@ -22,19 +22,17 @@ partialobs = true const d = 2 const itostrat = false -n = 80 # nr of landmarks +n = 75 # nr of landmarks θ = π/3# π/6 0#π/5 # angle to rotate endpoint σobs = 10^(-3) # noise on observations println(model) -T = 1.0#1.0#0.5 +T = 0.3#1.0#0.5 t = 0.0:0.01:T # time grid #Random.seed!(5) - - include("state.jl") include("models.jl") include("patches.jl") @@ -43,52 +41,26 @@ include("lmguiding.jl") ### Specify landmarks models ### Specify landmarks models -a = 4.0 # the larger, the stronger landmarks behave similarly -λ = 0.0; #= not the lambda of noise fields =# γ = 3.0 - -Pms = MarslandShardlow(a, γ, λ, n) - -db = 2.0 # domainbound -r1 = repeat(collect((-db:.5:db))) -r2 = repeat(collect((-db:.5:db))) -nfloc1 = Point.(collect(product(r1, r2)))[:] -nfscales_hor = [.05Point(1.0, 0.0) for x in nfloc1] # intensity -nfscales_ver = [.05Point(0.0, 1.0) for x in nfloc1] # intensity -nfscales = vcat(nfscales_hor, nfscales_ver) -nfloc = vcat(nfloc1,nfloc1) -nfstd = .5 # tau , widht of noisefields +a = 3.0 # the larger, the stronger landmarks behave similarly +λ = 0.0; #= not the lambda of noise fields =# γ = 8.0 +db = 3.0 # domainbound +nfstd = 1.0 # tau , widht of noisefields +r1 = -db:nfstd:db +r2 = -db:nfstd:db +nfloc = Point.(collect(product(r1, r2)))[:] +nfscales = [.05Point(1.0, 1.0) for x in nfloc] # intensity nfs = [Noisefield(δ, λ, nfstd) for (δ, λ) in zip(nfloc, nfscales)] - -# x1=-2*db:0.2:2*db -# y1=-2*db:0.2:2*db -# σqfield = Point[]#reshape(zeros(Point,length(x1)*length(y1)),length(x1),length(y1)) -# for i in 1:length(x1) -# for j in 1:length(y1) -# #σqfield[i,j] = σq(Point(x1[i],y1[j]),nfs) -# push!(σqfield, σq(Point(x1[i],y1[j]),nfs)) -# end -# end -# -# dfsigmaqfield = DataFrame(x=repeat(x1,inner=length(x1)),y=repeat(y1,outer=length(y1)),sigmaq=map(x->x[1], σqfield)) -# @rput dfsigmaqfield -# R""" -# library(tidyverse) -# dfsigmaqfield %>% ggplot(aes(x, y, z = sigmaq)) + -# geom_tile(aes(fill=sigmaq)) + theme_minimal() -# """ - - +Pms = MarslandShardlow(a, γ, λ, n) Pahs = Landmarks(a, λ, n, nfs) ### +StateW = Point if model == :ms dwiener = n - StateW = Point P = Pms else dwiener = length(nfloc) - StateW = Float64 P = Pahs end @@ -97,70 +69,29 @@ W = SamplePath(t, [copy(w0) for s in t]) sample!(W, Wiener{Vector{StateW}}()) # specify initial landmarks configuration -q0 = [Point(cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) +q0 = [Point(2.5cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) p_ = 2*Point(-0.1, 0.1) p0 = [p_ for i in 1:n] # #p0 = [randn(Point) for i in 1:n] x0 = State(q0, p0) -#map(i->σp(q(x0, i), p(x0, i), P.nfs[6]), 1:length(P.nfs)) - #Random.seed!(1234) - X = SamplePath(t, [copy(x0) for s in t]) -if model == :ms - @time solve!(EulerMaruyama!(), X, x0, W, P) -else - @time solve!(EulerMaruyama!(), X, x0, W, P) - # still needs to be implemented +println("Solve for forward provess:") +@time solve!(EulerMaruyama!(), X, x0, W, P) #@time solve!(StratonovichHeun!(), X, x0, W, P) -end -extractcomp(v,i) = map(x->x[i], v) + +tc(t,T) = t.*(2-t/T) +tt_ = tc(t,T)#tc(t,T)# 0:dtimp:(T) + # observe positions without noise v0 = q(X.yy[1]) rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) vT = [rot * X.yy[end].q[i] for i in 1:P.n ] -out = [Any[X.tt[i], [X.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(X.tt) ][:] -df = DataFrame(time=extractcomp(out,1),pos1=extractcomp(out,2),pos2=extractcomp(out,3),mom1=extractcomp(out,4),mom2=extractcomp(out,5),pointID=extractcomp(out,6)) -#Any["X.tt[$i]", ["X.yy[$i][CartesianIndex($c, $k)][$l]" for l in 1:d, k in 1:n, c in 1:2]...] - -if model == :ms - titel = "Marsland-Shardlow model, " -else - titel = "Arnaudon-Holm-Sommer model, " -end -titel = titel * string(n)*" landmarks" - -dfT = DataFrame(pos1=extractcomp(vT,1), pos2=extractcomp(vT,2)) -df0= DataFrame(pos1=extractcomp(v0,1), pos2=extractcomp(v0,2)) - -@rput titel -@rput df -@rput dfT -@rput df0 -R""" -library(tidyverse) -df %>% dplyr::select(time,pos1,pos2,pointID) %>% - ggplot() + - geom_path(data=df,aes(x=pos1,pos2,group=pointID,colour=time)) + - geom_point(data=dfT, mapping=aes(x=pos1,y=pos2),colour='orange',size=0.7) + - geom_point(data=df0, mapping=aes(x=pos1,y=pos2),colour='black',size=0.7)+ - theme_minimal() + xlab('horizontal position') + - ylab('vertical position') + ggtitle(titel) -""" - - -R""" -df %>% dplyr::select(time,mom1,mom2,pointID) %>% - filter(pointID %in% c("point1","point2","point3","point40","point41","point42")) %>% - ggplot(aes(x=mom1,mom2,group=pointID,colour=time)) + geom_path() + - facet_wrap(~pointID,scales="free") + theme_minimal() -""" -tc(t,T) = t.*(2-t/T) -tt_ = t#tc(t,T)# 0:dtimp:(T) +#extractcomp(v,i) = map(x->x[i], v) #################### # solve backward recursion on [0,T] if partialobs==true @@ -171,8 +102,7 @@ if partialobs==true xobs = vT Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) - Pahsaux = LandmarksAux(Pahs, State(vT, rand(Point,Pahs.n))) - + Pahsaux = LandmarksAux(Pahs, State(vT, rand(Point,Pahs.n))) else # full observation case L = [(i==j)*one(Unc) for i in 1:2n, j in 1:2n] @@ -193,19 +123,17 @@ end Lt = [copy(L) for s in tt_] Mt⁺ = [copy(Σ) for s in tt_] μt = [copy(μend) for s in tt_] -@time (Lend, Mend⁺,μend) = guidingbackwards!(Lm(), t, (Lt, Mt⁺,μt), Paux, (L, Σ, μend)) +println("compute guiding term:") +@time (Lend, Mend⁺,μend) = guidingbackwards!(Lm(), tt_, (Lt, Mt⁺,μt), Paux, (L, Σ, μend)) # issymmetric(deepmat(Bridge.a(0,Paux))) # isposdef(deepmat(Bridge.a(0,Paux))) # map(x->minimum(eigen(deepmat(x)).values),Mt⁺) -Mt = map(X -> deepmat2unc(inv(deepmat(X))),Mt⁺) -#Mt = map(X -> InverseCholesky(lchol(X)),Mt⁺) - - -Q = GuidedProposal!(P, Paux, tt_, Lt, Mt, μt, xobs) - -#xinit = State(v0, zero(v0)) +#Mt = map(X -> deepmat2unc(inv(deepmat(X))),Mt⁺) +println("Compute Cholesky for Mt⁺:") +@time Mt = map(X -> InverseCholesky(lchol(X)),Mt⁺) +Q = GuidedProposall!(P, Paux, tt_, Lt, Mt, μt, xobs) if partialobs xinit = State(v0, rand(Point,P.n)) else @@ -216,83 +144,13 @@ XX = SamplePath(tt_, [copy(xinit) for s in tt_]) WW = SamplePath(tt_, [copy(winit) for s in tt_]) sample!(WW, Wiener{Vector{StateW}}()) +println("Sample guided proposal:") +@time Bridge.solve!(EulerMaruyama!(), XX, xinit, WW, Q) +#guid = guidingterms(XX,Q) +include("plotlandmarks.jl") - -Bridge.solve!(EulerMaruyama!(), XX, xinit, WW, Q) -guid = guidingterms(XX,Q) - -#### plotting -outg = [Any[XX.tt[i], [XX.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(XX.tt) ][:] -dfg = DataFrame(time=extractcomp(outg,1),pos1=extractcomp(outg,2),pos2=extractcomp(outg,3),mom1=extractcomp(outg,4),mom2=extractcomp(outg,5),pointID=extractcomp(outg,6)) -#Any["X.tt[$i]", ["X.yy[$i][CartesianIndex($c, $k)][$l]" for l in 1:d, k in 1:n, c in 1:2]...] - -dfT = DataFrame(pos1=extractcomp(vT,1), pos2=extractcomp(vT,2)) -df0= DataFrame(pos1=extractcomp(v0,1), pos2=extractcomp(v0,2)) - - -if model == :ms - titel = "Marsland-Shardlow model, " -else - titel = "Arnaudon-Holm-Sommer model, " -end -titel = titel * string(n)*" landmarks" - -@rput titel -@rput dfg -@rput dfT -@rput df0 -@rput T -R""" -library(tidyverse) -T_ <- T-0.001 -T_ <- T -#T_ = 0.05 -dfsub <- df %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,mom1,mom2,pointID) %>% - filter(pointID %in% c("point1","point2","point3","point40","point41","point42")) %>% - ggplot(aes(x=mom1,mom2,group=pointID,colour=time)) + geom_path() + - facet_wrap(~pointID) + theme_minimal() -""" - - - - R""" - library(tidyverse) - dfsub <- df %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time<0.99) - dfsubg <- dfg %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time<0.99) - - sub <- rbind(dfsub,dfsubg) - sub$fg <- rep(c("forward","guided"),each=nrow(dfsub)) - - ggplot() + - geom_path(data=sub, mapping=aes(x=pos1,pos2,group=pointID,colour=fg)) + - geom_point(data=dfT, mapping=aes(x=pos1,y=pos2),colour='orange',size=0.7) + - geom_point(data=df0, mapping=aes(x=pos1,y=pos2),colour='black',size=0.7)+ - #facet_wrap(~fg) + - theme_minimal() + xlab('horizontal position') + - ylab('vertical position') + ggtitle(titel) - """ -end - if model==:ms @time llikelihood(LeftRule(), XX, Q; skip = 0) # won't work for AHS because matrix multilication for Htilde is not defined yet end diff --git a/landmarks/patches.jl b/landmarks/patches.jl index 077304e..fe207f9 100644 --- a/landmarks/patches.jl +++ b/landmarks/patches.jl @@ -89,6 +89,17 @@ function lyapunovpsdbackward_step!(t, dt, Paux,Hend⁺,H⁺) H⁺ end +""" +Version where B̃ and ã do not depend on try +""" +function lyapunovpsdbackward_step!(t, dt, Paux,Hend⁺,H⁺,B̃, ã) + ϕ = (I + 1/2*dt*B̃)\(I - 1/2*dt*B̃) + #Ht .= ϕ *(Hend⁺ + 1/2*dt*Bridge.a(t - dt, Paux))* ϕ' + 1/2*dt*Bridge.a(t, Paux) + H⁺ .= ϕ *(Hend⁺ + 1/2*dt*ã)* conj!(copy(ϕ)) + 1/2*dt*ã + H⁺ +end + + """ Compute transpose of square matrix of Unc matrices diff --git a/landmarks/state.jl b/landmarks/state.jl index 95d10de..0dc3df2 100644 --- a/landmarks/state.jl +++ b/landmarks/state.jl @@ -116,6 +116,12 @@ function Base.:*(A::Array{SArray{Tuple{2,2},Float64,2,4},2}, C end +function Base.:*(A::Array{SArray{Tuple{2,2},Float64,2,4},2},x::State) + vecofpoints2state(A*vec(x)) +end + + + if TEST A = reshape(rand(Unc,6),3,2) B = reshape(rand(Unc,8),2,4) @@ -127,6 +133,8 @@ if TEST A1=reshape(rand(Unc,9),3,3) B1=reshape(rand(Unc,9),3,3) @test norm(deepmat(A1\B1) - deepmat(A1)\deepmat(B1))<10^(-10) + + end diff --git a/src/partialbridge.jl b/src/partialbridge.jl index fa79d32..35121b4 100644 --- a/src/partialbridge.jl +++ b/src/partialbridge.jl @@ -1,4 +1,3 @@ - function partialbridgeode!(::R3, t, L, Σ, Lt, Mt, μt, P) m, d = size(L) Lt[end] = L @@ -25,14 +24,10 @@ function partialbridgeode!(::R3, t, L, Σ, Lt, Mt, μt, P) """ PartialBridge - Guided proposal process for diffusion bridge using backward recursion. - PartialBridge(tt, P, Pt, L, v, Σ) - Guided proposal process for a partial diffusion bridge of `P` to `v` on the time grid `tt` using guiding term derived from linear process `Pt`. - Simulate with `bridge!`. """ struct PartialBridge{T,R,R2,Tv,TL,TM} <: ContinuousTimeProcess{T} @@ -82,9 +77,10 @@ function llikelihood(::LeftRule, Xcirc::SamplePath, Po::PartialBridge; skip = 0) som += dot( _b((i,s), x, target(Po)) - _b((i,s), x, auxiliary(Po)), r ) * (tt[i+1]-tt[i]) if !constdiff(Po) - H = H((i,s), x, Po) - som -= 0.5*tr( (a((i,s), x, target(Po)) - aitilde((i,s), x, Po))*(H) ) * (tt[i+1]-tt[i]) - som += 0.5*( r'*(a((i,s), x, target(Po)) - aitilde((i,s), x, Po))*r ) * (tt[i+1]-tt[i]) + H = Bridge.H((i,s), x, Po) + A = Bridge.a((i,s), x, target(Po)) - Bridge.a((i,s), auxiliary(Po)) + som -= 0.5*tr(A *H ) * (tt[i+1]-tt[i]) + som += 0.5*( r'*A*r ) * (tt[i+1]-tt[i]) end end som From bd8975a8438b113e834192418ac3df9d525b3c82 Mon Sep 17 00:00:00 2001 From: fmeulen Date: Wed, 20 Feb 2019 16:30:38 +0100 Subject: [PATCH 08/58] Various minor changes. autodiff.jl contains some initial ideas for automatic differentiation --- landmarks/LowrankRiccati.jl | 2 +- landmarks/autodiff.jl | 49 +++ landmarks/forward.jl | 71 ++-- landmarks/guiding.jl | 6 +- landmarks/lmpar.jl | 4 +- landmarks/models.jl | 457 ++++++++++++++++++++++++ landmarks/patches.jl | 6 +- landmarks/plotlandmarks.jl | 116 ++++++ landmarks/state.jl | 50 ++- project_partialbridge/lowrankricatti.jl | 125 ------- 10 files changed, 709 insertions(+), 177 deletions(-) create mode 100644 landmarks/autodiff.jl create mode 100644 landmarks/models.jl create mode 100644 landmarks/plotlandmarks.jl delete mode 100644 project_partialbridge/lowrankricatti.jl diff --git a/landmarks/LowrankRiccati.jl b/landmarks/LowrankRiccati.jl index 4e7b0e8..9478b95 100644 --- a/landmarks/LowrankRiccati.jl +++ b/landmarks/LowrankRiccati.jl @@ -49,7 +49,7 @@ function lowrankriccati!(s, t, A, Q, (S,U), (Sout, Uout)) # step 5c (gives new S) L = Ŝ * Uᴬ' + Uout' * (τ * Q) Sout .= L * Uout - + Sout, Uout end lowrankriccati(s, t, A, Q, (S, U)) = lowrankriccati!(s, t, A, Q, (S, U), (copy(S), copy(U))) diff --git a/landmarks/autodiff.jl b/landmarks/autodiff.jl new file mode 100644 index 0000000..cb34bdb --- /dev/null +++ b/landmarks/autodiff.jl @@ -0,0 +1,49 @@ + +using DualNumbers + +# small test to understand +ff(x) = x^3 +ff(Dual(2,1)) + +# Redefine +# const Point = SArray{Tuple{d},Float64,1,d} # point in R2 +# const Unc = SArray{Tuple{d,d},Float64,d,d*d} # Matrix presenting uncertainty +# to + +const Point{T} = SArray{Tuple{d},T,1,d} +const Unc{T} = SArray{Tuple{d,d},T,d,d*d} +# > Point{Dual{Float64}}(rand(3)) + +# matrix multiplication of mat of Uncs +function Base.:*(A::Array{Unc{T},2},B::Array{Unc{T},2}) where T + C = zeros(Unc{T},size(A,1), size(B,2)) + for i in 1:size(A,1) + for j in 1:size(B,2) + for k in 1:size(A,2) + C[i,j] += A[i,k] * B[k,j] + end + end + end + C +end + +function Base.:*(A::Array{Unc,2},x::State) + vecofpoints2state(A*vec(x)) +end + + +# DON'T NEED THIS PROBABLY +# +# function ll(x0,XX,Q) +# XX.yy[1] = deepvec2state(x0) +# llikelihood(LeftRule(), XX, Q; skip = 0) +# end +# y0 = deepvec(x0) +# ll(y0,XX,Q) +# +# F(XX,Q) = (x) -> ll(x, XX,Q) +# F(XX,Q)(y0) +# using ForwardDiff +# +# g = x0 -> ForwardDiff.gradient(F(XX,Q), x0) # g = ∇f +# g(deepvec(x0)) diff --git a/landmarks/forward.jl b/landmarks/forward.jl index 5f612d3..32555d7 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -18,7 +18,7 @@ model = models[2] TEST = false#true discrmethods = [:ralston, :lowrank, :psd] -discrmethod = discrmethods[3] +discrmethod = discrmethods[2] obsschemes =[:full, :partial] obsscheme = obsschemes[2] @@ -26,23 +26,23 @@ obsscheme = obsschemes[2] const d = 2 const itostrat=true -n = 70 # nr of landmarks -ldim = 2n*d # dimension of low-rank approximation to H\^+ +n = 60 # nr of landmarks +ldim = 40 # dimension of low-rank approximation to H\^+ cheat = false#true#false # if cheat is true, then we initialise at x0 (true value) and # construct the guiding term based on xT (true value) θ = -π/6# π/6 0#π/5 # angle to rotate endpoint -ϵ = 10^(-8) # parameter for initialising Hend⁺ -σobs = 10^(-3) # noise on observations +ϵ = 10.0^(-4) # parameter for initialising Hend⁺ +σobs = 10.0^(-3) # noise on observations println(model) println(discrmethod) println(obsscheme) -T = 0.3#1.0#0.5 -t = 0.0:0.005:T # time grid +T = 0.2#1.0#0.5 +t = 0.0:0.01:T # time grid #Random.seed!(5) include("state.jl") @@ -96,20 +96,21 @@ println("Sample forward process:") # compute Hamiltonian along path ham = [hamiltonian(X.yy[i],Pms) for i in 1:length(t)] -tc(t,T) = t.*(2-t/T) +tc(t,T) = t.*(2 .-t/T) tt_ = tc(t,T)#tc(t,T)# 0:dtimp:(T) -# observe positions without noise -v0 = q(X.yy[1]) + σobs * randn(Point,n) -rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) -vT = [rot * X.yy[end].q[i] + σobs * randn(d) for i in 1:P.n ] - #################### if obsscheme==:partial L = deepmat( [(i==j)*one(Unc) for i in 1:2:2n, j in 1:2n]) Σ = Diagonal(σobs^2*ones(n*d)) + + # observe positions + v0 = q(X.yy[1]) + σobs * randn(Point,n) + rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) + vT = [rot * X.yy[end].q[i] + σobs * randn(d) for i in 1:P.n ] + Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) if cheat Pahsaux = LandmarksAux(Pahs, X.yy[end]) @@ -128,11 +129,6 @@ if obsscheme==:full end #Paux = (model==:ms) ? Pmsaux : Pahsaux -if model == :ms - Paux = Pmsaux -else - Paux = Pahsaux -end @@ -141,14 +137,36 @@ end #νend = State(zero(vT), zero(vT)) #Hend⁺ = [(i==j)*one(Unc)/ϵ for i in 1:2n, j in 1:2n] # this is the precison # "right" choice -νend = State(vT, zero(vT)) -Hend⁺ = reshape(zeros(Unc,4n^2),2n,2n) +if obsscheme==:partial + #νendT = State(zero(vT), zero(vT)) + νendT = State(randn(Point,Pahs.n), randn(Point,Pahs.n)) +end +if obsscheme==:full + νendT = X.yy[end] +end +HendT⁺ = reshape(zeros(Unc,4n^2),2n,2n) for i in 1:n - Hend⁺[2i-1,2i-1] = one(Unc)/ϵ # high precision on positions - Hend⁺[2i,2i] = one(Unc)*ϵ + HendT⁺[2i-1,2i-1] = one(Unc)/ϵ # high variance on positions + if discrmethod==:lowrank + HendT⁺[2i,2i] = one(Unc)*10^(-4) # still need to figure out why + else + HendT⁺[2i,2i] = one(Unc)/10^(-4) + end end #### perform gpupdate step -νend , Hend⁺ = gpupdate(νend,Hend⁺, Σ, L, vT) +νendT , HendT⁺ = gpupdate(νendT,HendT⁺, Σ, L, vT) +νend = copy(νendT) +Hend⁺ = copy(HendT⁺) +Pahsaux = LandmarksAux(Pahs, copy(νend)) # this might be a good idea +Pmsaux = MarslandShardlowAux(Pms, copy(νend)) # this might be a good idea + +if model == :ms + Paux = Pmsaux +else + Paux = Pahsaux +end + + # L, and Σ are ordinary matrices, vT an array of Points # νend is a state , Hend⁺ a UncMat @@ -162,6 +180,7 @@ if discrmethod==:lowrank St = [copy(Send) for s in tt_] Ut = [copy(Uend) for s in tt_] @time νend, (Send, Uend) = bucybackwards!(LRR(), tt_, νt, (St, Ut), Paux, νend, (Send, Uend)) + Hend⁺ = deepmat2unc(Uend * Send * Uend') Ht =map((S,U) -> deepmat2unc(U * inv(S) * U'), St,Ut) # directly compute Mt #Ht = map((S,U) -> LowRank(S,U), St,Ut) end @@ -191,6 +210,6 @@ println("Sample guided bridge proposal:") include("plotlandmarks.jl") -if model==:ms - @time llikelihood(LeftRule(), XX, Q; skip = 0) # won't work for AHS because matrix multilication for Htilde is not defined yet -end +#if model==:ms +# @time llikelihood(LeftRule(), XX, Q; skip = 0) # won't work for AHS because matrix multilication for Htilde is not defined yet +#end diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index 56dcf40..8e03371 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -87,7 +87,7 @@ function bucybackwards!(scheme::LRR, t, νt, (St, Ut), Paux, νend, (Send, Uend) for i in length(t)-1:-1:1 dt = t[i] - t[i+1] kernelr3!(Arg4Closure(Bridge.b!, Paux), t[i+1], νt[i+1], wsν, νt[i], dt) - lowrankriccati!(t[i], t[i+1], -B̃, ã , (St[i+1], Ut[i+1]), (St[i], Ut[i])) + LowrankRiccati.lowrankriccati!(t[i], t[i+1], -B̃, ã , (St[i+1], Ut[i+1]), (St[i], Ut[i])) end νt[1], (St[1], Ut[1]) @@ -175,8 +175,8 @@ function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposal!; skip = 0 # som -= 0.5*tr(Δa*H) * dt # som += 0.5*(rout'*Δa*rout) * dt - Δa = Bridge.a(s, x, target(Q)) - Bridge.a(s, x, auxiliary(Q)) - # H = H((i,s), x, auxiliary(Q)) + Δa = Bridge.a(s, x, target(Q)) - Bridge.a(s, auxiliary(Q)) + H = Bridge.H((i,s), x, auxiliary(Q)) # som -= 0.5*tr(Δa*H) * dt som += 0.5*dot(rout,Δa*rout) * dt end diff --git a/landmarks/lmpar.jl b/landmarks/lmpar.jl index 12559dc..bd7a98a 100644 --- a/landmarks/lmpar.jl +++ b/landmarks/lmpar.jl @@ -14,7 +14,7 @@ using Base.Iterators using SparseArrays models = [:ms, :ahs] -model = models[1] +model = models[2] TEST = false#true partialobs = true @@ -102,7 +102,7 @@ if partialobs==true xobs = vT Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) - Pahsaux = LandmarksAux(Pahs, State(vT, rand(Point,Pahs.n))) + #Pahsaux = LandmarksAux(Pahs, State(vT, 10*rand(Point,Pahs.n))) else # full observation case L = [(i==j)*one(Unc) for i in 1:2n, j in 1:2n] diff --git a/landmarks/models.jl b/landmarks/models.jl new file mode 100644 index 0000000..009a4ed --- /dev/null +++ b/landmarks/models.jl @@ -0,0 +1,457 @@ +#### Landmarks specification + +struct MarslandShardlow{T} <: ContinuousTimeProcess{State{Point}} + a::T # kernel std parameter + γ::T # noise level + λ::T # mean reversion + n::Int +end + +struct MarslandShardlowAux{T} <: ContinuousTimeProcess{State{Point}} + a::T # kernel std parameter + γ::T # noise level + λ::T # mean reversion + xT::State{Point} # use x = State(P.v, zero(P.v)) where v is conditioning vector + n::Int +end + +MarslandShardlowAux(P::MarslandShardlow, xT) = MarslandShardlowAux(P.a, P.γ, P.λ, xT, P.n) + +struct Noisefield + δ::Point # locations of noise field + λ::Point # scaling at noise field + τ::Float64 # std of Gaussian kernel noise field +end + +struct Landmarks{T} <: ContinuousTimeProcess{State{Point}} + a::T # kernel std + λ::T # mean reversion + n::Int64 # numer of landmarks + nfs::Vector{Noisefield} # vector containing pars of noisefields +end + +struct LandmarksAux{T} <: ContinuousTimeProcess{State{Point}} + a::T # kernel std + λ::T # mean reversion + xT::State{Point} # use x = State(P.v, zero(P.v)) where v is conditioning vector + n::Int64 # numer of landmarks + nfs::Vector{Noisefield} # vector containing pars of noisefields +end + +LandmarksAux(P::Landmarks, xT) = LandmarksAux(P.a, P.λ, xT, P.n, P.nfs) + + +""" +kernel in Hamiltonian +""" +function kernel(q, P::Union{Landmarks, LandmarksAux, +MarslandShardlow, MarslandShardlowAux}) + (2*π*P.a^2)^(-d/2)*exp(-norm(q)^2/(2*P.a^2)) +end + +function ∇kernel(q, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) + -P.a^(-2) * kernel(q,P) * q +end + +""" +Needed for b! in case P is auxiliary process +""" +function ∇kernel(q,qT, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) + -P.a^(-2) * kernel(qT,P) * q +end + + +function hamiltonian((q, p), P) + s = 0.0 + for i in eachindex(q), j in eachindex(q) + s += 1/2*dot(p[i], p[j])*kernel(q[i] - q[j], P) + end + s +end + + + +# kernel for noisefields +function K̄(q,τ) + exp(-norm(q)^2/(2*τ^2))# (2*π*τ^2)^(-d/2)*exp(-norm(x)^2/(2*τ^2)) +end +# gradient of kernel for noisefields +function ∇K̄(q,τ) + -τ^(-2) * K̄(q,τ) * q +end +""" +Needed for b! in case P is auxiliary process +""" +function ∇K̄(q, qT, τ) + -τ^(-2) * K̄(qT,τ) * q +end + +# function for specification of diffusivity of landmarks +σq(q, nf::Noisefield) = diagm(0 =>nf.λ) * K̄(q - nf.δ,nf.τ) +σp(q, p, nf::Noisefield) = -diagm(0 => p.*nf.λ.* ∇K̄(q - nf.δ,nf.τ)) + + +function σq(x::Point, nfs::Array{Noisefield,1}) + out = 0.0 * x + for j in 1:length(nfs) + out += σq(x, nfs[j]) + end + out +end + +Bridge.b(t::Float64, x, P::Union{Landmarks,MarslandShardlow})= Bridge.b!(t, x, copy(x), P) +Bridge.b(t::Float64, x, P::Union{LandmarksAux,MarslandShardlowAux})= Bridge.b!(t, x, copy(x), P) + +""" +Evaluate drift of landmarks in (t,x) and save to out +x is a state and out as well +""" +function Bridge.b!(t, x, out, P::MarslandShardlow) + zero!(out) + for i in 1:P.n + for j in 1:P.n + out.q[i] += p(x,j)*kernel(q(x,i) - q(x,j), P) + # heat bath + out.p[i] += -P.λ*p(x,j)*kernel(q(x,i) - q(x,j), P) - + dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) + end + end + out +end + +""" +Evaluate drift of landmarks in (t,x) and save to out +x is a state and out as well +""" +function Bridge.b!(t, x, out, P::Landmarks) + zero!(out) + for i in 1:P.n + for j in 1:P.n + out.q[i] += p(x,j)*kernel(q(x,i) - q(x,j), P) + out.p[i] += -dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) + end + if itostrat + global ui = zero(Unc) + for k in 1:length(P.nfs) + nf = P.nfs[k] + ui += 0.5 * nf.τ^(-2) * diagm(0 =>nf.λ.^2) * K̄(q(x,i)-nf.δ,nf.τ)^2 + end + out.q[i] -= ui * q(x,i) + out.p[i] += ui * p(x,i) + end + end + out +end + + +""" +Evaluate drift of landmarks auxiliary process in (t,x) and save to out +x is a state and out as well +""" +function Bridge.b!(t, x, out, Paux::MarslandShardlowAux) + zero!(out) + for i in 1:Paux.n + for j in 1:Paux.n + out.q[i] += p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) + out.p[i] += -Paux.λ*p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), P) + end + end + out +end + +""" +Evaluate drift of landmarks auxiliary process in (t,x) and save to out +x is a state and out as well +""" +function Bridge.b!(t, x, out, Paux::LandmarksAux) + zero!(out) + for i in 1:Paux.n + for j in 1:Paux.n + out.q[i] += p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) + end + # out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) + # -0.5* dot(p(P.xT,i), p(P.xT,j)) * ∇kernel(q(x,i) - q(x,j),q(P.xT,i) - q(P.xT,j), P) + if itostrat + global ui = zero(Unc) + for k in 1:length(P.nfs) + nf = P.nfs[k] + ui = 0.5 * nf.τ^(-2) * diagm(0 =>nf.λ.^2) * K̄(q(Paux.xT,i)-nf.δ,nf.τ)^2 + end + out.q[i] -= ui * q(x,i) + out.p[i] += ui * p(x,i) + end + end + out +end + + +""" +Compute tildeB(t) for landmarks auxiliary process +""" +function Bridge.B(t, Paux::MarslandShardlowAux) + Iind = Int[] + Jind = Int[] + X = Unc[] + for i in 1:Paux.n + for j in 1:Paux.n + # terms for out.q[i] + push!(Iind, 2i - 1) + push!(Jind, 2j) + push!(X, kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc)) + + push!(Iind,2i) + push!(Jind,2j) + push!(X, -Paux.λ*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)) + end + end + sparse(Iind, Jind, X, 2Paux.n, 2Paux.n) +end + +""" +Compute tildeB(t) for landmarks auxiliary process +""" +function Bridge.B(t, Paux::LandmarksAux) + Iind = Int[] + Jind = Int[] + X = Unc[] + for i in 1:Paux.n + for j in 1:Paux.n + # terms for out.q[i] + push!(Iind, 2i - 1) + push!(Jind, 2j) + push!(X, kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc)) + + if itostrat + global out1 = zero(Unc) + for k in 1:length(Paux.nfs) + nf = P.nfs[k] + out1 -= 0.5 * nf.τ^(-2) * Unc(diagm(0 =>nf.λ.^2)) * K̄(q(Paux.xT,i)-nf.δ,nf.τ)^2 + end + push!(Iind, 2i - 1) + push!(Jind, 2j - 1) + push!(X, out1) + push!(Iind, 2i) + push!(Jind, 2j) + push!(X, -out1) + end + + # terms for out.p[i] + # push!(I, 2i) + # push!(J, 2j-1) + # if j==i + # push!(X, sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), P) for j in setdiff(1:Paux.n,i)]) * one(Unc)) + # else + # push!(X, -1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)) + # end + end + end + sparse(Iind, Jind, X, 2Paux.n, 2Paux.n) +end + + +""" +Compute B̃(t) * X (B̃ from auxiliary process) and write to out +Both B̃(t) and X are of type UncMat +""" +function Bridge.B!(t,X,out, Paux::MarslandShardlowAux) + out .= 0.0 * out + for i in 1:Paux.n # separately loop over even and odd indices + for k in 1:2Paux.n # loop over all columns + for j in 1:Paux.n + out[2i-1,k] += kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*X[p(j), k] #*one(Unc) + out[2i,k] += -Paux.λ*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)*X[p(j), k] #*one(Unc) + # if j==i + # out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * + # kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) + # else + # out[2i,k] += X[q(j),k] *(-1/(2*Paux.a)) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc) + # end + end + end + end + + out +end + +""" +Compute B̃(t) * X (B̃ from auxiliary process) and write to out +Both B̃(t) and X are of type UncMat +""" +function Bridge.B!(t,X,out, Paux::LandmarksAux) +#### HAS NOT BEEN IMPLEMENTED FOR ITO-STRAT CORRECTION (probably doesn't pay off the effort) + out .= 0.0 * out + quickway = true + if quickway==true + out .= Matrix(Bridge.B(t,Paux)) * X + else # still need to implement an efficient way here + for i in 1:Paux.n # separately loop over even and odd indices + for k in 1:2Paux.n # loop over all columns + for j in 1:Paux.n + out[2i-1,k] += kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*X[p(j), k] #*one(Unc) + # if j==i + # out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * + # kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) + # else + # out[2i,k] += X[q(j),k] *(-1/(2*Paux.a)) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc) + # end + end + end + end + end + out +end + +function Bridge.β(t, Paux::Union{MarslandShardlowAux,LandmarksAux}) + State(zeros(Point,Paux.n), zeros(Point,Paux.n)) +end + + +if TEST + Hend⁺ = [rand(Unc) for i in 1:2Paux.n, j in 1:2Paux.n] + t0 = 2.0 + BB = Matrix(Bridge.B(t0,Paux)) * Hend⁺ + out = deepcopy(Hend⁺) + Bridge.B!(t0,Hend⁺,out,Paux) + @test out==BB +end + + + +function Bridge.σ!(t, x, dm, out, P::Union{MarslandShardlow, MarslandShardlowAux}) + zero!(out.q) + out.p .= dm*P.γ + out +end + + +""" +Compute sigma(t,x) * dm where dm is a vector and sigma is the diffusion coefficient of landmarks +write to out which is of type State +""" +function Bridge.σ!(t, x_, dm, out, P::Union{Landmarks,LandmarksAux}) + if P isa Landmarks + x = x_ + else + x = P.xT + end + zero!(out) + for i in 1:P.n + for j in 1:length(P.nfs) + out.q[i] += σq(q(x, i), P.nfs[j]) * dm[j] + out.p[i] += σp(q(x, i), p(x, i), P.nfs[j]) * dm[j] + end + end + out +end + + +""" +Compute sigma(t,x)' * y where y is a state and sigma is the diffusion coefficient of landmarks +returns a vector of points of length P.nfs +""" +function σtmul(t, x_, y::State, P::Union{Landmarks,LandmarksAux}) + if P isa Landmarks + x = x_ + else + x = P.xT + end + out = zeros(Point, length(P.nfs)) + for j in 1:length(P.nfs) + for i in 1:P.n + out[j] += σq(q(x, i), P.nfs[j])' * y.q[i] + + σp(q(x, i), p(x, i), P.nfs[j])' * y.p[i] + end + end + out +end + + + + + +""" +Returns matrix a(t) for Marsland-Shardlow model +""" +function Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) + I = Int[] + X = Unc[] + γ2 = P.γ^2 + for i in 1:P.n + push!(I, 2i) + push!(X, γ2*one(Unc)) + end + sparse(I, I, X, 2P.n, 2P.n) +end +#Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) +Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P) + + +function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) + if P isa Landmarks + x = x_ + else + x = P.xT + end + out = zeros(Unc,2P.n,2P.n) + for i in 1:P.n + for k in 1:P.n + for j in 1:length(P.nfs) + out[2i-1,2k-1] += σq(q(x,i),P.nfs[j]) * σq(q(x, k),P.nfs[j])' + out[2i-1,2k] += σq(q(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' + out[2i,2k-1] += σp(q(x,i),p(x,i),P.nfs[j]) * σq(q(x,k),P.nfs[j])' + out[2i,2k] += σp(q(x,i),p(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' + end + end + end + out +end + +Bridge.a(t, P::LandmarksAux) = Bridge.a(t, 0, P) +#Bridge.a(t, P::Union{Landmarks,LandmarksAux}) = Bridge.a(t, P.xT, P::Union{Landmarks,LandmarksAux}) + +""" +Multiply a(t,x) times xin (which is of type state) +Returns variable of type State +""" +function amul(t, x::State, xin::State, P::Union{MarslandShardlow, MarslandShardlowAux}) + out = copy(xin) + zero!(out.q) + out.p .= P.γ^2 .* xin.p + out +end +function amul(t, x::State, xin::Vector{Point}, P::Union{MarslandShardlow, MarslandShardlowAux}) + out = copy(x) + zero!(out.q) + out.p .= P.γ^2 .* vecofpoints2state(xin).p + out +end + + +""" +Multiply a(t,x) times a vector of points +Returns a State +(first multiply with sigma', via function σtmul, next left-multiply this vector with σ) +""" +function amul(t, x::State, xin::Vector{Point}, P::Union{Landmarks,LandmarksAux}) + #vecofpoints2state(Bridge.a(t, x, P)*xin) + out = copy(x) + zero!(out) + Bridge.σ!(t, x, σtmul(t, x, vecofpoints2state(xin), P),out,P) +end + +""" +Multiply a(t,x) times a state +Returns a state +(first multiply with sigma', via function σtmul, next left-multiply this vector with σ) +""" +function amul(t, x::State, xin::State, P::Union{Landmarks,LandmarksAux}) + #vecofpoints2state(Bridge.a(t, x, P)*vec(xin)) + out = copy(x) + zero!(out) + Bridge.σ!(t, x, σtmul(t, x, xin, P),out,P) +end + + + +Bridge.constdiff(::Union{MarslandShardlow, MarslandShardlowAux,LandmarksAux}) = true +Bridge.constdiff(::Landmarks) = false diff --git a/landmarks/patches.jl b/landmarks/patches.jl index fe207f9..cfa7c80 100644 --- a/landmarks/patches.jl +++ b/landmarks/patches.jl @@ -108,8 +108,7 @@ B = copy(A) A conj!(B) """ -function conj!(A::Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}) -# if !(size(A,1)==size(A,2)) error("conj! only correctly defined for square matrices") end +function conj!(A::Array{Unc,2}) for i in 1:size(A,1) A[i,i] = A[i,i]' for j in (i+1):size(A,2) @@ -119,8 +118,7 @@ function conj!(A::Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}) A end -function conj2(A::Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}) -# if !(size(A,1)==size(A,2)) error("conj! only correctly defined for square matrices") end +function conj2(A::Array{Unc,2}) At = Matrix{Unc}(undef,size(A,2),size(A,1)) for i in 1:size(A,2) for j in 1:size(A,1) diff --git a/landmarks/plotlandmarks.jl b/landmarks/plotlandmarks.jl new file mode 100644 index 0000000..e427637 --- /dev/null +++ b/landmarks/plotlandmarks.jl @@ -0,0 +1,116 @@ +extractcomp(v,i) = map(x->x[i], v) + + +out = [Any[X.tt[i], [X.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(X.tt) ][:] +df = DataFrame(time=extractcomp(out,1),pos1=extractcomp(out,2),pos2=extractcomp(out,3),mom1=extractcomp(out,4),mom2=extractcomp(out,5),pointID=extractcomp(out,6)) +#Any["X.tt[$i]", ["X.yy[$i][CartesianIndex($c, $k)][$l]" for l in 1:d, k in 1:n, c in 1:2]...] + +if model == :ms + titel = "Marsland-Shardlow model, " +else + titel = "Arnaudon-Holm-Sommer model, " +end +titel = titel * string(n)*" landmarks" + +dfT = DataFrame(pos1=extractcomp(vT,1), pos2=extractcomp(vT,2)) +df0= DataFrame(pos1=extractcomp(v0,1), pos2=extractcomp(v0,2)) + +@rput titel +@rput df +@rput dfT +@rput df0 + +if false + R""" + library(tidyverse) + df %>% dplyr::select(time,pos1,pos2,pointID) %>% + ggplot() + + geom_path(data=df,aes(x=pos1,pos2,group=pointID,colour=time)) + + geom_point(data=dfT, mapping=aes(x=pos1,y=pos2),colour='orange',size=0.7) + + geom_point(data=df0, mapping=aes(x=pos1,y=pos2),colour='black',size=0.7)+ + theme_minimal() + xlab('horizontal position') + + ylab('vertical position') + ggtitle(titel) + """ + + + R""" + df %>% dplyr::select(time,mom1,mom2,pointID) %>% + filter(pointID %in% c("point1","point2","point3","point40","point41","point42")) %>% + ggplot(aes(x=mom1,mom2,group=pointID,colour=time)) + geom_path() + + facet_wrap(~pointID,scales="free") + theme_minimal() + """ +end + +#### plotting +outg = [Any[XX.tt[i], [XX.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(XX.tt) ][:] +dfg = DataFrame(time=extractcomp(outg,1),pos1=extractcomp(outg,2),pos2=extractcomp(outg,3),mom1=extractcomp(outg,4),mom2=extractcomp(outg,5),pointID=extractcomp(outg,6)) +#Any["X.tt[$i]", ["X.yy[$i][CartesianIndex($c, $k)][$l]" for l in 1:d, k in 1:n, c in 1:2]...] + +dfT = DataFrame(pos1=extractcomp(vT,1), pos2=extractcomp(vT,2)) +df0= DataFrame(pos1=extractcomp(v0,1), pos2=extractcomp(v0,2)) + + +if model == :ms + titel = "Marsland-Shardlow model, " +else + titel = "Arnaudon-Holm-Sommer model, " +end +titel = titel * string(n)*" landmarks" + +@rput titel +@rput dfg +@rput dfT +@rput df0 +@rput T +R""" +library(tidyverse) +T_ <- T +dfsub <- df %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,pos1,pos2,pointID) %>% filter(time% dplyr::select(time,mom1,mom2,pointID) %>% + filter(pointID %in% c("point1","point2","point3","point40","point41","point42")) %>% + ggplot(aes(x=mom1,mom2,group=pointID,colour=time)) + geom_path() + + facet_wrap(~pointID,scales="free") + theme_minimal() +""" + + +if false + R""" + dfg %>% dplyr::select(time,mom1,mom2,pointID) %>% + filter(pointID %in% c("point1","point2","point3","point40","point41","point42")) %>% + ggplot(aes(x=mom1,mom2,group=pointID,colour=time)) + geom_path() + + facet_wrap(~pointID) + theme_minimal() + """ + R""" + library(tidyverse) + dfsub <- df %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time<0.99) + dfsubg <- dfg %>% dplyr::select(time,pos1,pos2,pointID) %>% filter(time<0.99) + + sub <- rbind(dfsub,dfsubg) + sub$fg <- rep(c("forward","guided"),each=nrow(dfsub)) + + ggplot() + + geom_path(data=sub, mapping=aes(x=pos1,pos2,group=pointID,colour=fg)) + + geom_point(data=dfT, mapping=aes(x=pos1,y=pos2),colour='orange',size=0.7) + + geom_point(data=df0, mapping=aes(x=pos1,y=pos2),colour='black',size=0.7)+ + #facet_wrap(~fg) + + theme_minimal() + xlab('horizontal position') + + ylab('vertical position') + ggtitle(titel) + """ +end diff --git a/landmarks/state.jl b/landmarks/state.jl index 0dc3df2..48b8784 100644 --- a/landmarks/state.jl +++ b/landmarks/state.jl @@ -90,8 +90,7 @@ deepvec(x::State{P}) where {P} = vec([x[J][K] for K in eachindex(x.p[1]), J in e # matrix multiplication of mat of Uncs -function Base.:*(A::Array{SArray{Tuple{2,2},Float64,2,4},2}, - B::Array{SArray{Tuple{2,2},Float64,2,4},2}) +function Base.:*(A::AbstractArray{Unc,2},B::AbstractArray{Unc,2}) C = zeros(Unc,size(A,1), size(B,2)) for i in 1:size(A,1) for j in 1:size(B,2) @@ -103,20 +102,33 @@ function Base.:*(A::Array{SArray{Tuple{2,2},Float64,2,4},2}, C end -function Base.:*(A::Array{SArray{Tuple{2,2},Float64,2,4},2}, - B::Adjoint{Array{SArray{Tuple{2,2},Float64,2,4},2}}) - C = zeros(Unc,size(A,1), size(B,1)) - for i in 1:size(A,1) - for j in 1:size(B,1) - for k in 1:size(A,2) - C[i,j] += A[i,k] * B[j,k] - end - end - end - C -end - -function Base.:*(A::Array{SArray{Tuple{2,2},Float64,2,4},2},x::State) +# function Base.:*(A::Array{Unc,2},B::Adjoint{Unc,Array{Unc,2}}) +# C = zeros(Unc,size(A,1), size(B,2)) +# for i in 1:size(A,1) +# for j in 1:size(B,2) +# for k in 1:size(A,2) +# C[i,j] += A[i,k] * B[k,j] +# end +# end +# end +# C +# end +# +# #new +# function Base.:*(A::Adjoint{Unc,Array{Unc,2}},B::Array{Unc,2}) +# C = zeros(Unc,size(A,1), size(B,2)) +# for i in 1:size(A,1) +# for j in 1:size(B,2) +# for k in 1:size(A,2) +# C[i,j] += A[i,k] * B[k,j] +# end +# end +# end +# C +# end + + +function Base.:*(A::Array{Unc,2},x::State) vecofpoints2state(A*vec(x)) end @@ -128,6 +140,12 @@ if TEST C = B' @test norm(deepmat(A*B) - deepmat(A) * deepmat(B))<10^(-8) @test norm(deepmat(A*C') - deepmat(A) * deepmat(C'))<10^(-8) + BB = reshape(rand(Unc,8),4,2) + @test (A*BB')' == BB*A' + + D = reshape(rand(Unc,6),3,2) + E = reshape(rand(Unc,12),3,4) + @test D'*E == (E'*D)' # backsolving matrix equation A X = using lu A1=reshape(rand(Unc,9),3,3) diff --git a/project_partialbridge/lowrankricatti.jl b/project_partialbridge/lowrankricatti.jl deleted file mode 100644 index 7723e33..0000000 --- a/project_partialbridge/lowrankricatti.jl +++ /dev/null @@ -1,125 +0,0 @@ -# implement Mena et al. for solving -# (d P)/(d t) = A P(t) + P(t) A' + Q, P(t_0) = P0 -# with a low rank approximation for Q - -using SparseArrays -using SuiteSparse -using LinearAlgebra -using Expokit # for matrix exponentials -using BenchmarkTools - -# construct an example -d = 800 -Q = sprand(d,d,.01) - I# Diagonal(randn(d)) -diagels = 0.4.^(1:d) -A = sprand(d,d,0.1)#Diagonal(diagels) -P0 = Matrix(sprand(d,d,0.1))# Diagonal(diagels) - -# we use Expokit, which gives the funciton expmv! -# w = expmv!{T}( w::Vector{T}, t::Number, A, v::Vector{T}; kwargs...) -# The function expmv! calculates w = exp(t*A)*v, where A is a matrix or any type that supports size, eltype and mul! and v is a dense vector by using Krylov subspace projections. The result is stored in w. - -# It is much faster for large systems -v = rand(d) -@time a1=expmv!(zeros(d),1,Q,v) -@time a2=exp(Matrix(Q))*v -a1-a2 - -# Let's consider a few implementations -matexpvec1 = function(A,U,τ) - exp(Matrix(τ * A)) * U -end - -matexpvec2 = function(A,U,τ) - M = [] - for j in 1:size(U,2) - push!(M, expmv!(zeros(size(U,1)),τ,A,U[:,j])) - end - M = hcat(M...) -end - -# matexpvec3 = function(A,U) # is wrong for some reason -# τ = 1.0 -# for j in 1:size(U,2) -# expmv!(U[:,j],τ,A,U[:,j]) -# end -# U -# end - -matexpvec4 = function(A,U,τ) - hcat([ expmv!(U[:,j],τ,A,U[:,j]) for j in 1:size(U,2)]...) -end - -τ = 1.0 -R = A # or Q -M0 = svd(P0) -U = Matrix(M0.U[:,1:ld]) - -@benchmark matexpvec1(R,U,τ) -@benchmark matexpvec2(R,U,τ) -@benchmark matexpvec4(R,U,τ) - -maximum(matexpvec4(R,U,τ)-matexpvec1(R,U,τ)) - - -function lowrankricatti(P0, A, Q, t, ld) -# P0 is the value of P at time t[1]; t is an increasing sequence of times, -# ld is the dimension of the low rank approximation -# output: at each time t a low rank approximation of P(t), where the couple (U,S) is such that P = U*S*U' - - # step 1 - M0 = svd(P0) - global U = Matrix(M0.U[:,1:ld]) - global S = Diagonal(M0.S[1:ld]) - - Ulowrank = [U] - Slowrank = [S] - for i in 1:length(t)-1 - τ = t[i+1] - t[i] - if false - matexp = exp(Matrix(τ * A)) - # step 3 - M = matexp * U - else - M = matexpvec4(A,U,τ) - end - Uᴬcompact, R = qr(M) - Uᴬ = Matrix(Uᴬcompact) - # step 4 - Sᴬ = R * S * R' - # step 5 - K = Uᴬ * Sᴬ + (τ * Q) * Uᴬ - Ucompact, Ŝ = qr(K) - U = Matrix(Ucompact) - Ŝ = Ŝ - U' * (τ * Q) * Uᴬ - L = Ŝ * Uᴬ' + U' * (τ * Q) - S = L * U - - push!(Ulowrank,U) - push!(Slowrank,Diagonal(S)) - # ??? should S be diagonal or not: either convert it, or make Slowrank an array of full matrices - #push!(Slowrank,S) - end - - Ulowrank, Slowrank -end - - -# Example: -ld = 10 # low rank dimension -τ = 0.01; t0 =0.5; tend=0.8 -t = t0:τ:tend - -@time U,S = lowrankricatti(P0,A, Q, t,ld) -P = U[end]*S[end]*U[end]' - -# compute exact solution -λ = lyap(Matrix(Q), -Matrix(A)) + P0 -Φ = exp(Matrix(Q)*(tend- t0)) -Pexact = Φ*λ*Φ' - λ + P0 - -# assess difference -dif = P - Pexact - -print(maximum(abs.(dif))) -dif From a7b929874ef9d548284b135b4c777b68df2430c1 Mon Sep 17 00:00:00 2001 From: fmeulen Date: Mon, 25 Feb 2019 16:29:38 +0100 Subject: [PATCH 09/58] corrected deepmat2unc (there was a bug for nonsquare matrices) --- landmarks/state.jl | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/landmarks/state.jl b/landmarks/state.jl index 48b8784..f6446d6 100644 --- a/landmarks/state.jl +++ b/landmarks/state.jl @@ -183,12 +183,14 @@ function deepmat(H::AbstractMatrix{S}) where {S} end #@test outer(deepvec(x0)) == deepmat(outer(vec(x0))) + function deepmat2unc(A::Matrix) # d is the dimension of the square subblocks - k =size(A,1) - m = div(k,d) - [Unc(A[(i-1)*d+1:i*d,(j-1)*d+1:j*d]) for i in 1:m, j in 1:m] + m = div(size(A,1),d) + n = div(size(A,2),d) + [Unc(A[(i-1)*d+1:i*d,(j-1)*d+1:j*d]) for i in 1:m, j in 1:n] end + function outer(x::State, y::State) [outer(x[i],y[j]) for i in eachindex(x), j in eachindex(y)] end From a44501d9ea3e65c54b05814e8ee2842140b1c8ea Mon Sep 17 00:00:00 2001 From: mschauer Date: Tue, 23 Apr 2019 12:37:30 +0200 Subject: [PATCH 10/58] Getting Duals to work --- landmarks/forward.jl | 81 +++++++++++++++++++++++++++++++---------- landmarks/guiding.jl | 40 ++++++++++++++++----- landmarks/models.jl | 86 ++++++++++++++++++++++++++++---------------- landmarks/patches.jl | 44 +++++++++++++++++++++++ landmarks/state.jl | 32 ++++++++++------- 5 files changed, 213 insertions(+), 70 deletions(-) diff --git a/landmarks/forward.jl b/landmarks/forward.jl index 32555d7..596f64e 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -1,6 +1,8 @@ # reminder, to type H*, do H\^+ #outdir="output/landmarks/" -cd("/Users/Frank/.julia/dev/Bridge/landmarks") +#cd("/Users/Frank/.julia/dev/Bridge/landmarks") +#cd("landmarks") + using Bridge, StaticArrays, Distributions using Bridge:logpdfnormal @@ -14,11 +16,11 @@ using Base.Iterators using SparseArrays models = [:ms, :ahs] -model = models[2] +model = models[1] TEST = false#true discrmethods = [:ralston, :lowrank, :psd] -discrmethod = discrmethods[2] +discrmethod = discrmethods[1] obsschemes =[:full, :partial] obsscheme = obsschemes[2] @@ -26,10 +28,10 @@ obsscheme = obsschemes[2] const d = 2 const itostrat=true -n = 60 # nr of landmarks +n = 4 # nr of landmarks ldim = 40 # dimension of low-rank approximation to H\^+ -cheat = false#true#false # if cheat is true, then we initialise at x0 (true value) and +cheat = true #true#false # if cheat is true, then we initialise at x0 (true value) and # construct the guiding term based on xT (true value) θ = -π/6# π/6 0#π/5 # angle to rotate endpoint @@ -60,15 +62,15 @@ db = 3.0 # domainbound nfstd = .5 # tau , widht of noisefields r1 = -db:nfstd:db r2 = -db:nfstd:db -nfloc = Point.(collect(product(r1, r2)))[:] -nfscales = [.1Point(1.0, 1.0) for x in nfloc] # intensity +nfloc = PointF.(collect(product(r1, r2)))[:] +nfscales = [.1PointF(1.0, 1.0) for x in nfloc] # intensity nfs = [Noisefield(δ, λ, nfstd) for (δ, λ) in zip(nfloc, nfscales)] Pms = MarslandShardlow(a, γ, λ, n) Pahs = Landmarks(a, λ, n, nfs) ### -StateW = Point +StateW = PointF if model == :ms dwiener = n P = Pms @@ -78,10 +80,10 @@ else end # specify initial landmarks configuration -q0 = [Point(2.5cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) -p_ = 5*Point(0.1, 0.1) +q0 = [PointF(2.5cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) +p_ = 5*PointF(0.1, 0.1) p0 = [p_ for i in 1:n] # -#p0 = [randn(Point) for i in 1:n] +#p0 = [randn(PointF) for i in 1:n] x0 = State(q0, p0) #Random.seed!(1234) @@ -107,7 +109,7 @@ if obsscheme==:partial Σ = Diagonal(σobs^2*ones(n*d)) # observe positions - v0 = q(X.yy[1]) + σobs * randn(Point,n) + v0 = q(X.yy[1]) + σobs * randn(PointF,n) rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) vT = [rot * X.yy[end].q[i] + σobs * randn(d) for i in 1:P.n ] @@ -116,7 +118,7 @@ if obsscheme==:partial Pahsaux = LandmarksAux(Pahs, X.yy[end]) else Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) - #Pahsaux = LandmarksAux(Pahs, State(vT, rand(Point,Pahs.n))) + #Pahsaux = LandmarksAux(Pahs, State(vT, rand(PointF,Pahs.n))) end end if obsscheme==:full @@ -139,7 +141,7 @@ end # "right" choice if obsscheme==:partial #νendT = State(zero(vT), zero(vT)) - νendT = State(randn(Point,Pahs.n), randn(Point,Pahs.n)) + νendT = State(randn(PointF,Pahs.n), randn(PointF,Pahs.n)) end if obsscheme==:full νendT = X.yy[end] @@ -181,7 +183,7 @@ if discrmethod==:lowrank Ut = [copy(Uend) for s in tt_] @time νend, (Send, Uend) = bucybackwards!(LRR(), tt_, νt, (St, Ut), Paux, νend, (Send, Uend)) Hend⁺ = deepmat2unc(Uend * Send * Uend') - Ht =map((S,U) -> deepmat2unc(U * inv(S) * U'), St,Ut) # directly compute Mt + Ht = map((S,U) -> deepmat2unc(U * inv(S) * U'), St, Ut) # directly compute Mt #Ht = map((S,U) -> LowRank(S,U), St,Ut) end if discrmethod==:ralston @@ -197,7 +199,7 @@ if discrmethod==:psd end Q = GuidedProposal!(P, Paux, tt_, νt, Ht) - +# careful, not a state νstart , Hstart⁺ = gpupdate(νend , Hend⁺, Σ, L, v0) xinit = cheat ? x0 : νstart # or xinit ~ N(νstart, Hstart⁺) winit = zeros(StateW, dwiener) @@ -210,6 +212,47 @@ println("Sample guided bridge proposal:") include("plotlandmarks.jl") -#if model==:ms -# @time llikelihood(LeftRule(), XX, Q; skip = 0) # won't work for AHS because matrix multilication for Htilde is not defined yet -#end +if model==:ms + @time llikelihood(LeftRule(), XX, Q; skip = 0) # won't work for AHS because matrix multilication for Htilde is not defined yet +end + +using ForwardDiff +dual(x, i, n) = ForwardDiff.Dual(x, ForwardDiff.Chunk{n}(), Val(i)) +dual(x, n) = ForwardDiff.Dual(x, ForwardDiff.Chunk{n}(), Val(0)) + +#using Flux +xinitv = deepvec(xinit) + +xinitv = map(i->dual(xinitv[i], i <= 2 ? i : 0, 2), 1:length(xinitv)) + +xinitnew = deepvec2state(xinitv) +x = copy(xinitnew) + +#lux.Tracker.gradient(x -> Bridge._b!((1,0.0), deepvec2state(x), deepvec2state(x), P), deepvec(xinit)) +Bridge.b!(0.0, x, copy(x), P) + +import Bridge; + +#include(joinpath(dirname(pathof(Bridge)), "..", "landmarks/patches.jl")) +#include(joinpath(dirname(pathof(Bridge)), "..", "landmarks/models.jl")) + +XX = Bridge.solve(EulerMaruyama!(), xinitnew, WW, P) + + + +function obj(xinitv) + xinit = deepvec2state(xinitv) + sample!(WW, Wiener{Vector{StateW}}()) + XXᵒ = Bridge.solve(EulerMaruyama!(), xinit, WW, Q) + llikelihood(LeftRule(), XXᵒ, Q; skip = 0) +end + +let + x = deepvec(xinit) + ϵ = 1e-7 + for i in 1:1000 + ∇x = ForwardDiff.gradient(obj, x) + x .+= ϵ*∇x + println(deepvec2state(x)) + end +end diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index 8e03371..43295d3 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -1,7 +1,9 @@ # compute guiding term: backward ode # compute likelihood of guided proposal +using LinearAlgebra + +import Bridge: kernelr3!, R3!, target, auxiliary, constdiff, llikelihood, _b!, B!, σ!, b!, σ, b -import Bridge: kernelr3!, R3!, target, auxiliary, constdiff, llikelihood, _b!, B!, σ!, b! function gpupdate(ν, P, Σ, L, v) if all(diag(P) .== Inf) @@ -19,7 +21,7 @@ end (ν, P) are the values just to the right of time T, (Σ, L, v) are the noise covariance, observations matrix L and observation at time T """ -function gpupdate(ν2::State, P2, Σ, L, v2::Vector{Point}) +function gpupdate(ν2::State, P2, Σ, L, v2::Vector{<:Point}) ν = deepvec(ν2) P = deepmat(P2) v = reinterpret(Float64,v2) @@ -135,7 +137,16 @@ function Bridge._b!((i,t), x, out, P::GuidedProposal!) out end -σ!(t, x, dw, out, P::GuidedProposal!) = σ!(t, x, dw, out, P.target) +function Bridge._b((i,t), x, P::GuidedProposal!) + out = Bridge.b(t, x, P.target) + out .+= amul(t,x,P.H[i]*(P.ν[i] - x),P.target) + out +end + +Bridge.σ!(t, x, dw, out, P::GuidedProposal!) = σ!(t, x, dw, out, P.target) + +Bridge.σ(t, x, dw, P::GuidedProposal!) = σ(t, x, dw, P.target) + function _r!((i,t), x, out, P::GuidedProposal!) out .= (P.H[i]*(P.ν[i] - x)) @@ -151,12 +162,19 @@ auxiliary(P::GuidedProposal!) = P.aux constdiff(P::GuidedProposal!) = constdiff(target(P)) && constdiff(auxiliary(P)) -function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposal!; skip = 0) +function llikelihood(::LeftRule, Xcirc::SamplePath{State{Pnt}}, Q::GuidedProposal!; skip = 0) where {Pnt} tt = Xcirc.tt xx = Xcirc.yy - som::Float64 = 0. + som::eltype(xx[1]) = 0. rout = copy(xx[1]) + + if !constdiff(Q) # use sizetypes? + srout = zeros(Pnt, length(P.nfs)) + strout = zeros(Pnt, length(P.nfs)) + end + + bout = copy(rout) btout = copy(rout) for i in 1:length(tt)-1-skip #skip last value, summing over n-1 elements @@ -167,6 +185,7 @@ function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposal!; skip = 0 _b!((i,s), x, btout, auxiliary(Q)) # btitilde!((s,i), x, btout, Q) dt = tt[i+1]-tt[i] + #dump(som) som += dot(bout-btout, rout) * dt if !constdiff(Q) @@ -175,10 +194,15 @@ function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposal!; skip = 0 # som -= 0.5*tr(Δa*H) * dt # som += 0.5*(rout'*Δa*rout) * dt - Δa = Bridge.a(s, x, target(Q)) - Bridge.a(s, auxiliary(Q)) - H = Bridge.H((i,s), x, auxiliary(Q)) + σt!(s, x, rout, srout, target(Q)) + σt!(s, x, rout, strout, auxiliary(Q)) + + #Δa = Bridge.a(s, x, target(Q)) - Bridge.a(s, auxiliary(Q)) + #H = Bridge.H((i,s), x, auxiliary(Q)) # som -= 0.5*tr(Δa*H) * dt - som += 0.5*dot(rout,Δa*rout) * dt + #som += 0.5*dot(rout,Δa*rout) * dt + som += 0.5*Bridge.inner(srout) * dt + som -= 0.5*Bridge.inner(strout) * dt end end som diff --git a/landmarks/models.jl b/landmarks/models.jl index 009a4ed..96e5ea6 100644 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -1,4 +1,5 @@ #### Landmarks specification +import Bridge: _b, _b!, B!, σ!, b!, σ, b struct MarslandShardlow{T} <: ContinuousTimeProcess{State{Point}} a::T # kernel std parameter @@ -7,57 +8,59 @@ struct MarslandShardlow{T} <: ContinuousTimeProcess{State{Point}} n::Int end -struct MarslandShardlowAux{T} <: ContinuousTimeProcess{State{Point}} +struct MarslandShardlowAux{S,T} <: ContinuousTimeProcess{State{Point}} a::T # kernel std parameter γ::T # noise level λ::T # mean reversion - xT::State{Point} # use x = State(P.v, zero(P.v)) where v is conditioning vector + xT::State{Point{S}} # use x = State(P.v, zero(P.v)) where v is conditioning vector n::Int end MarslandShardlowAux(P::MarslandShardlow, xT) = MarslandShardlowAux(P.a, P.γ, P.λ, xT, P.n) -struct Noisefield - δ::Point # locations of noise field - λ::Point # scaling at noise field - τ::Float64 # std of Gaussian kernel noise field +struct Noisefield{T} + δ::Point{T} # locations of noise field + λ::Point{T} # scaling at noise field + τ::T # std of Gaussian kernel noise field end -struct Landmarks{T} <: ContinuousTimeProcess{State{Point}} +struct Landmarks{S,T} <: ContinuousTimeProcess{State{Point}} a::T # kernel std λ::T # mean reversion n::Int64 # numer of landmarks - nfs::Vector{Noisefield} # vector containing pars of noisefields + nfs::Vector{Noisefield{S}} # vector containing pars of noisefields end -struct LandmarksAux{T} <: ContinuousTimeProcess{State{Point}} +struct LandmarksAux{S,T} <: ContinuousTimeProcess{State{Point}} a::T # kernel std λ::T # mean reversion - xT::State{Point} # use x = State(P.v, zero(P.v)) where v is conditioning vector + xT::State{Point{S}} # use x = State(P.v, zero(P.v)) where v is conditioning vector n::Int64 # numer of landmarks - nfs::Vector{Noisefield} # vector containing pars of noisefields + nfs::Vector{Noisefield{S}} # vector containing pars of noisefields end LandmarksAux(P::Landmarks, xT) = LandmarksAux(P.a, P.λ, xT, P.n, P.nfs) +const LandmarkModel = Union{Landmarks, LandmarksAux, +MarslandShardlow, MarslandShardlowAux} + """ kernel in Hamiltonian """ -function kernel(q, P::Union{Landmarks, LandmarksAux, -MarslandShardlow, MarslandShardlowAux}) - (2*π*P.a^2)^(-d/2)*exp(-norm(q)^2/(2*P.a^2)) +function kernel(q, P::LandmarkModel) # FIXME: Don't use norm + (2*π*P.a^2)^(-d/2)*exp(-Bridge.inner(q)/(2*P.a^2)) end -function ∇kernel(q, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) - -P.a^(-2) * kernel(q,P) * q +function ∇kernel(q, P::LandmarkModel) + -P.a^(-2) * kernel(q, P) * q end """ Needed for b! in case P is auxiliary process """ -function ∇kernel(q,qT, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) - -P.a^(-2) * kernel(qT,P) * q +function ∇kernel(q, qT, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) + -P.a^(-2) * kernel(qT, P) * q end @@ -79,6 +82,7 @@ end function ∇K̄(q,τ) -τ^(-2) * K̄(q,τ) * q end + """ Needed for b! in case P is auxiliary process """ @@ -91,7 +95,7 @@ end σp(q, p, nf::Noisefield) = -diagm(0 => p.*nf.λ.* ∇K̄(q - nf.δ,nf.τ)) -function σq(x::Point, nfs::Array{Noisefield,1}) +function σq(x::Point, nfs::Array{<:Noisefield,1}) out = 0.0 * x for j in 1:length(nfs) out += σq(x, nfs[j]) @@ -99,8 +103,14 @@ function σq(x::Point, nfs::Array{Noisefield,1}) out end -Bridge.b(t::Float64, x, P::Union{Landmarks,MarslandShardlow})= Bridge.b!(t, x, copy(x), P) -Bridge.b(t::Float64, x, P::Union{LandmarksAux,MarslandShardlowAux})= Bridge.b!(t, x, copy(x), P) +Bridge.b(t::Float64, x, P::Union{Landmarks,MarslandShardlow})= Bridge.b!(t, x, 0*x, P) +#Bridge._b(it, x, P::Union{LandmarksAux,MarslandShardlowAux})= Bridge._b!(it, x, copy(x), P) +#Bridge._b(it, x, P::Union{Landmarks,MarslandShardlow})= Bridge._b!(it, x, 0*x, P) + +#Bridge.σ(t::Float64, x, dm, P::Union{LandmarksAux,MarslandShardlowAux}) = Bridge.σ!(t, x, dm, copy(x), P) + + +#Bridge.σ(t::Float64, x, dm, P::Union{Landmarks,MarslandShardlow}) = Bridge.σ!(t, x, dm, copy(x), P) """ Evaluate drift of landmarks in (t,x) and save to out @@ -112,13 +122,14 @@ function Bridge.b!(t, x, out, P::MarslandShardlow) for j in 1:P.n out.q[i] += p(x,j)*kernel(q(x,i) - q(x,j), P) # heat bath - out.p[i] += -P.λ*p(x,j)*kernel(q(x,i) - q(x,j), P) - - dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) +# out.p[i] += -P.λ*p(x,j)*kernel(q(x,i) - q(x,j), P) - +# dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) end end out end + """ Evaluate drift of landmarks in (t,x) and save to out x is a state and out as well @@ -302,7 +313,7 @@ function Bridge.B!(t,X,out, Paux::LandmarksAux) end function Bridge.β(t, Paux::Union{MarslandShardlowAux,LandmarksAux}) - State(zeros(Point,Paux.n), zeros(Point,Paux.n)) + State(zeros(Point{Float64},Paux.n), zeros(Point{Float64},Paux.n)) # FIXME end @@ -316,6 +327,7 @@ if TEST end +Bridge.σ(t, x_, dm, P) = Bridge.σ!(t, x_, dm , 0*x_, P) function Bridge.σ!(t, x, dm, out, P::Union{MarslandShardlow, MarslandShardlowAux}) zero!(out.q) @@ -344,18 +356,17 @@ function Bridge.σ!(t, x_, dm, out, P::Union{Landmarks,LandmarksAux}) out end - """ Compute sigma(t,x)' * y where y is a state and sigma is the diffusion coefficient of landmarks returns a vector of points of length P.nfs """ -function σtmul(t, x_, y::State, P::Union{Landmarks,LandmarksAux}) +function σtmul(t, x_, y::State{Pnt}, P::Union{Landmarks,LandmarksAux}) where Pnt if P isa Landmarks x = x_ else x = P.xT end - out = zeros(Point, length(P.nfs)) + out = zeros(Pnt, length(P.nfs)) for j in 1:length(P.nfs) for i in 1:P.n out[j] += σq(q(x, i), P.nfs[j])' * y.q[i] + @@ -365,7 +376,20 @@ function σtmul(t, x_, y::State, P::Union{Landmarks,LandmarksAux}) out end - +function σt!(t, x_, y::State, out, P::Union{Landmarks,LandmarksAux}) + if P isa Landmarks + x = x_ + else + x = P.xT + end + for j in 1:length(P.nfs) + for i in 1:P.n + out[j] += σq(q(x, i), P.nfs[j])' * q(y, i) + + σp(q(x, i), p(x, i), P.nfs[j])' * q(y, i) + end + end + out +end @@ -392,7 +416,7 @@ function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) else x = P.xT end - out = zeros(Unc,2P.n,2P.n) + out = zeros(Unc{Float64}, 2P.n,2P.n) for i in 1:P.n for k in 1:P.n for j in 1:length(P.nfs) @@ -419,7 +443,7 @@ function amul(t, x::State, xin::State, P::Union{MarslandShardlow, MarslandShardl out.p .= P.γ^2 .* xin.p out end -function amul(t, x::State, xin::Vector{Point}, P::Union{MarslandShardlow, MarslandShardlowAux}) +function amul(t, x::State, xin::Vector{<:Point}, P::Union{MarslandShardlow, MarslandShardlowAux}) out = copy(x) zero!(out.q) out.p .= P.γ^2 .* vecofpoints2state(xin).p @@ -432,7 +456,7 @@ Multiply a(t,x) times a vector of points Returns a State (first multiply with sigma', via function σtmul, next left-multiply this vector with σ) """ -function amul(t, x::State, xin::Vector{Point}, P::Union{Landmarks,LandmarksAux}) +function amul(t, x::State, xin::Vector{<:Point}, P::Union{Landmarks,LandmarksAux}) #vecofpoints2state(Bridge.a(t, x, P)*xin) out = copy(x) zero!(out) diff --git a/landmarks/patches.jl b/landmarks/patches.jl index cfa7c80..088b540 100644 --- a/landmarks/patches.jl +++ b/landmarks/patches.jl @@ -15,6 +15,50 @@ function Bridge.sample!(W::SamplePath{Vector{T}}, P::Wiener{Vector{T}}, y1 = W.y end +function Bridge.solve(solver::EulerMaruyama!, u, W::SamplePath, P::Bridge.ProcessOrCoefficients) + N = length(W) + + tt = W.tt + yy = [copy(u)] + + i = 1 + dw = W.yy[i+1] - W.yy[i] + t¯ = tt[i] + dt = tt[i+1] - t¯ + + tmp1 = Bridge._b!((i,t¯), u, 0*u, P) + tmp2 = Bridge.σ(t¯, u, dw, P) + + y = u + tmp1*dt + tmp2 + + #dump(y) + #error("here") + + + for i in 2:N-1 + t¯ = tt[i] + dt = tt[i+1] - t¯ + push!(yy, y) + if dw isa Number + dw = W.yy[i+1] - W.yy[i] + else + for k in eachindex(dw) + dw[k] = W.yy[i+1][k] - W.yy[i][k] + end + end + + Bridge._b!((i,t¯), y, tmp1, P) + Bridge.σ!(t¯, y, dw, tmp2, P) + + for k in eachindex(y) + y[k] = y[k] + tmp1[k]*dt + tmp2[k] + end + end + copyto!(yy[end], Bridge.endpoint(y, P)) + SamplePath(tt, yy) +end + + struct StratonovichHeun! <: Bridge.SDESolver end diff --git a/landmarks/state.jl b/landmarks/state.jl index f6446d6..c22abb0 100644 --- a/landmarks/state.jl +++ b/landmarks/state.jl @@ -1,7 +1,9 @@ import Base:iterate, eltype, copy, copyto!, zero, eachindex, getindex, setindex!, size, vec -const Point = SArray{Tuple{d},Float64,1,d} # point in R2 -const Unc = SArray{Tuple{d,d},Float64,d,d*d} # Matrix presenting uncertainty +const Point{T} = SArray{Tuple{d},T,1,d} # point in R2 +const Unc{T} = SArray{Tuple{d,d},T,d,d*d} # Matrix presenting uncertainty + +const PointF = Point{Float64} abstract type UncMat end @@ -15,6 +17,11 @@ p(x::State) = x.p q(x::State, i) = x.q[i] p(x::State, i) = x.p[i] +q(x::State, i) = x.q[i] +p(x::State, i) = x.p[i] + + + q(i::Int) = 2i - 1 p(i::Int) = 2i @@ -87,6 +94,7 @@ import Bridge: outer vec(x::State) = vec([x[J] for J in eachindex(x)]) # deepvec(x::State{P}) where {P} = vec([x[J][K] for K in eachindex(x.p[1]), J in eachindex(x)]) +deepvec(x::Vector) = collect(flatten(x)) # matrix multiplication of mat of Uncs @@ -128,7 +136,7 @@ end # end -function Base.:*(A::Array{Unc,2},x::State) +function Base.:*(A::Array{<:Unc,2}, x::State) vecofpoints2state(A*vec(x)) end @@ -164,18 +172,18 @@ Convert vector to State. it is assumed that x is ordered as follows - momentum landmark 2 ... """ -function deepvec2state(x) +function deepvec2state(x::AbstractVector{T}) where {T} m = div(length(x),2d) - q = Vector{Point}(undef,m) - p = Vector{Point}(undef,m) + q = Vector{Point{T}}(undef,m) + p = Vector{Point{T}}(undef,m) for i in 1:m - q[i] = Point(x[(i-1)*2d .+ (1:d)]) - p[i] = Point(x[((i-1)*2d+d+1):(2i*d)]) + q[i] = Point{T}(x[(i-1)*2d .+ (1:d)]) + p[i] = Point{T}(x[((i-1)*2d+d+1):(2i*d)]) end State(q,p) end -vecofpoints2state(x::Vector{Point}) = State(x[1:d:end], x[d:d:end]) +vecofpoints2state(x::Vector{<:Point}) = State(x[1:d:end], x[d:d:end]) function deepmat(H::AbstractMatrix{S}) where {S} d1, d2 = size(S) @@ -240,7 +248,7 @@ function Base.:*(H::InverseCholesky, x::State) vecofpoints2state(y) end -function Base.:*(H::InverseCholesky, x::Vector{Point}) +function Base.:*(H::InverseCholesky, x::Vector{<:Point}) y = copy(x) cholinverse!(H.L, y) # triangular backsolve end @@ -296,7 +304,7 @@ Hinv = LU (LU decomposition) From LU y =x, it follows that we solve first z from Lz=x, and next y from Uy=z """ -function Base.:*(H::InverseLu, x::Vector{Point}) +function Base.:*(H::InverseLu, x::Vector{<:Point}) LinearAlgebra.naivesub!(LowerTriangular(H.L), x) LinearAlgebra.naivesub!(UpperTriangular(H.U), x) x @@ -335,7 +343,7 @@ if TEST L, U = lu(A) W = InverseLu(L,U) - xs= rand(Point,4) + xs= rand(PointF,4) xss = [xs[1]; xs[2];xs[3];xs[4]] inv(deepmat(A)) * xss W * xs From e332e0bb438124733bdca5ebc153b4d758df4f9c Mon Sep 17 00:00:00 2001 From: Jeff Bezanson Date: Fri, 28 Dec 2018 19:08:16 -0500 Subject: [PATCH 11/58] fix reference to internal `Zip2` for julia 1.1 --- src/types.jl | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/src/types.jl b/src/types.jl index ede49bf..8a1f0f7 100644 --- a/src/types.jl +++ b/src/types.jl @@ -136,9 +136,14 @@ function stack(args::SamplePath...) VSamplePath(args[1].tt, vcat((X.yy' for X in args)...)) end -# separate a Zip2 +# separate a zip of two Vectors +if VERSION < v"1.1-" sep(Z::Base.Iterators.Zip2{Vector{T1},Vector{T2}}) where {T1,T2} = T1[z[1] for z in Z], T2[z[2] for z in Z] # takes into account the minimum of length +else +sep(Z::Base.Iterators.Zip{Tuple{Vector{T1},Vector{T2}}}) where {T1,T2} = + T1[z[1] for z in Z], T2[z[2] for z in Z] # takes into account the minimum of length +end copy(X::VSamplePath) = VSamplePath(copy(X.tt), copy(X.yy)) From 8b2569a550f85a693871ae9823e9ae6d98764dc2 Mon Sep 17 00:00:00 2001 From: mschauer Date: Wed, 1 May 2019 10:16:27 +0200 Subject: [PATCH 12/58] Test Marcin's recursions --- src/partialbridgenuH.jl | 124 ++++++++++++++++++++++++++-------- test/partialbridge!.jl | 79 +++++----------------- test/partialbridge.jl | 20 +++--- test/partialbridgenuH.jl | 141 ++++++++++++++++++++++++++++----------- test/partialparam.jl | 14 ++++ 5 files changed, 238 insertions(+), 140 deletions(-) create mode 100644 test/partialparam.jl diff --git a/src/partialbridgenuH.jl b/src/partialbridgenuH.jl index 9ece707..2a2db0d 100644 --- a/src/partialbridgenuH.jl +++ b/src/partialbridgenuH.jl @@ -1,42 +1,112 @@ -function partialbridgeodeνH!(::R3, t, L, Σ, v, νt, Ht, P, ϵ) +function updateνH⁺(L, Σ, v, ϵ) m, d = size(L) + @assert m == length(v) + H = (L' * inv(Σ) * L + ϵ * I) + H⁺ = inv(H) + ν = H⁺ * L' * inv(Σ) * v + ν, H⁺ +end +function updateC(L, Σ, v, C = 0.0) + m, d = size(L) + C += 0.5 * dot(v, Σ\v) + C += length(m)/2*log(2pi) + 0.5*logdet(Σ) + C +end +function updateνH⁺C(L, Σ, v, ϵ) + updateνH⁺(L, Σ, v, ϵ)..., updateC(L, Σ, v) +end + + +function partialbridgeodeνH!(::R3, t, νt, Ht, P, (ν, H⁺, C)) + #m, d = size(L) + #@assert m == length(v) # print(typeof(H⁺t)) # print(typeof(νt)) # print(typeof(inv(L' * inv(Σ) * L + ϵ * I) )) - Ht[end] = (L' * inv(Σ) * L + ϵ * I) - H⁺ = inv(Ht[end]) - νt[end] = H⁺ * L' * inv(Σ) * v - ν = νt[end] - F(t, y, P) = B(t, P)*y + β(t,P) - Ri(t, y, P) = B(t, P)*y + y * B(t,P)' - a(t, P) + #Ht[end] = H = (L' * inv(Σ) * L + ϵ * I) + #H⁺ = inv(H) + #νt[end] = H⁺ * L' * inv(Σ) * v + #F = L' * inv(Σ) * v + #ν = νt[end] + #C += 0.5 * v' * inv(Σ) * v # 0.5 c + #C += m/2*log(2pi) + 0.5*log(abs(det(Σ))) # Q, use logabsdet, actually + #ν, H⁺ = zero(νt[end]), zero(Ht[end]) + #H⁺, ν = gpupdate(H⁺, ν, L, Σ, v) + H = inv(H⁺) + #C = updateC(L, Σ, v, C) + + b̃(t, y, P) = B(t, P)*y + β(t, P) + dH⁺(t, y, P) = B(t, P)*y + y * B(t,P)' - a(t, P) +# dH(t, y, P) = - B(t, P)'*y - y * B(t,P) + y*a(t, P)*y' +# dF(t, y, (H,P)) = -B(t, P)'*y + H*a(t, P)*y + H*β(t, P) + for i in length(t)-1:-1:1 dt = t[i] - t[i+1] - ν = kernelr3(F, t[i+1], ν, dt, P) - H⁺ = kernelr3(Ri, t[i+1], H⁺, dt, P) + ν = kernelr3(b̃, t[i+1], ν, dt, P) + H⁺ = kernelr3(dH⁺, t[i+1], H⁺, dt, P) + #H = kernelr3(dH, t[i+1], H, dt, P) + + + + #F = kernelr3(dF, t[i+1], F, dt, (H,P)) + F = Ht[i+1]*νt[i+1] + #@show F , Ht[i+1]*νt[i+1] + C += β(t[i+1], P)'*F*dt + 0.5*F'*a(t[i+1], P)*F*dt - 0.5*tr(H*a(t[i+1], P))*dt νt[i] = ν - Ht[i] = inv(H⁺) + #@show H, inv(H⁺) + Ht[i] = H = inv(H⁺) end - νt, Ht - end + + νt, Ht, C +end + +function updateFHC(L, Σ, v, F, H, ϵ = 0.0, C = 0.0) + m, d = size(L) + H += (L' * inv(Σ) * L + ϵ * I) + F += L' * inv(Σ) * v + F, H, updateC(L, Σ, v, C) +end + +function partialbridgeodeHνH!(::R3, t, Ft, Ht, P, (F, H, C)) + Ht[end] = H + Ft[end] = F + + dH(t, y, P) = - B(t, P)'*y - y * B(t,P) + y*a(t, P)*y' + dF(t, y, (H,P)) = -B(t, P)'*y + H*a(t, P)*y + H*β(t, P) + + for i in length(t)-1:-1:1 + dt = t[i] - t[i+1] + C += β(t[i+1], P)'*F*dt + 0.5*F'*a(t[i+1], P)*F*dt - 0.5*tr(H*a(t[i+1], P))*dt + H = kernelr3(dH, t[i+1], H, dt, P) + F = kernelr3(dF, t[i+1], F, dt, (H, P)) + Ft[i] = F + Ht[i] = H + end + + Ft, Ht, C +end + struct Lyap end -function partialbridgeodeνH!(::Lyap, t, νt, Ht, P, νend, Hend⁺) - Ht[end] = inv(Hend⁺) +function partialbridgeodeνH!(::Lyap, t, νt, Ht, P, (νend, Hend⁺, C)) + Ht[end] = H = inv(Hend⁺) νt[end] = νend H⁺ = Hend⁺ ν = νend - F(t, y, P) = B(t, P)*y + β(t,P) + b̃(t, y, P) = B(t, P)*y + β(t,P) for i in length(t)-1:-1:1 dt = t[i] - t[i+1] - ν = kernelr3(F, t[i+1], ν, dt, P) + ν = kernelr3(b̃, t[i+1], ν, dt, P) H⁺ = lyapunovpsdbackward_step(t[i+1], H⁺, -dt, P) + F = Ht[i+1]*νt[i+1] + C += β(t[i+1], P)'*F*dt + 0.5*F'*a(t[i+1], P)*F*dt - 0.5*tr(H*a(t[i+1], P))*dt νt[i] = ν - Ht[i] = inv(H⁺) + Ht[i] = H = inv(H⁺) end - ν, H⁺ + ν, H⁺, C end @@ -56,14 +126,15 @@ Guided proposal process for diffusion bridge using backward recursion. linear process `Pt` with backwards equation initialized at `ν, Hend⁺`. """ -struct PartialBridgeνH{T,TP,TPt,Tν,TH} <: ContinuousTimeProcess{T} +struct PartialBridgeνH{T,TP,TPt,Tν,TH,TC} <: ContinuousTimeProcess{T} Target::TP Pt::TPt tt::Vector{Float64} ν::Vector{Tν} H::Vector{TH} - PartialBridgeνH(P::TP, Pt::TPt, tt, νt::Vector{Tν}, Ht::Vector{TH}) where {TP,TPt,Tν,TH} = - new{Bridge.valtype(P),TP,TPt,Tν,TH}(P, Pt, tt, νt, Ht) + C::TC + PartialBridgeνH(P::TP, Pt::TPt, tt, νt::Vector{Tν}, Ht::Vector{TH}, C::TC=0.0) where {TP,TPt,Tν,TH,TC} = + new{Bridge.valtype(P),TP,TPt,Tν,TH,TC}(P, Pt, tt, νt, Ht, C) # 6-7 arg @@ -75,8 +146,9 @@ struct PartialBridgeνH{T,TP,TPt,Tν,TH} <: ContinuousTimeProcess{T} Ht = zeros(TH, N) Tν = typeof(@SVector zeros(d)) νt = zeros(Tν, N) - partialbridgeodeνH!(R3(), tt, L, Σ, v, νt, Ht, Pt, ϵ) - PartialBridgeνH(P, Pt, tt, νt, Ht) + ν, H⁺, C = updateνH⁺C(L, Σ, v, ϵ) + _, _, C = partialbridgeodeνH!(R3(), tt, νt, Ht, Pt, (ν, H⁺, C)) + PartialBridgeνH(P, Pt, tt, νt, Ht, C) end end # 5 arg @@ -85,8 +157,8 @@ function partialbridgeνH(tt_, P, Pt, νend::Tv, Hend⁺::TH) where {Tv,TH} N = length(tt) Ht = zeros(TH, N) νt = zeros(Tv, N) - ν, H⁺ = partialbridgeodeνH!(Lyap(), tt, νt, Ht, Pt, νend, Hend⁺) - PartialBridgeνH(P, Pt, tt, νt, Ht), ν, H⁺ + ν, H⁺, C = partialbridgeodeνH!(Lyap(), tt, νt, Ht, Pt, (νend, Hend⁺, C)) + PartialBridgeνH(P, Pt, tt, νt, Ht, C), ν, H⁺, C end function _b((i,t)::IndexedTime, x, P::PartialBridgeνH) @@ -101,7 +173,7 @@ a(t, x, P::PartialBridgeνH) = a(t, x, P.Target) Γ(t, x, P::PartialBridgeνH) = Γ(t, x, P.Target) constdiff(P::PartialBridgeνH) = constdiff(P.Target) && constdiff(P.Pt) - +lptilde(x, P::PartialBridgeνH) = -0.5*((P.ν[1] - x)'*P.H[1] * (P.ν - x)) - P.C function llikelihood(::LeftRule, Xcirc::SamplePath, Po::PartialBridgeνH; skip = 0) tt = Xcirc.tt diff --git a/test/partialbridge!.jl b/test/partialbridge!.jl index 2e2b443..c383c58 100644 --- a/test/partialbridge!.jl +++ b/test/partialbridge!.jl @@ -2,83 +2,35 @@ using Bridge, Distributions using Test, Statistics, Random, LinearAlgebra using Bridge.Models -T = 2.0 -dt = 1/1000 +include("partialparam.jl") +x0 = Vector(x0) +L = Matrix(L) +Σ = Matrix(Σ) +v = Vector(v) -tt = 0.:dt:T -struct PBIntegratedDiffusion <: ContinuousTimeProcess{Float64} - γ::Float64 -end -struct PBIntegratedDiffusionAux <: ContinuousTimeProcess{Float64} - γ::Float64 -end - -PorPtilde = Union{PBIntegratedDiffusion, PBIntegratedDiffusionAux} - - -βu(t, x::Float64, P::PBIntegratedDiffusion) = - (x+sin(x)) + 1/2 -βu(t, x::Float64, P::PBIntegratedDiffusionAux) = -x + 1/2 -# not really a 'beta' - -Bridge.b(t::Float64, x, P::PorPtilde) = Bridge.b!(t, x, copy(x), P) -function Bridge.b!(t, x, out, P::PorPtilde) - out[1] = x[2] - out[2] = βu(t, x[2], P) - out -end - -function Bridge.σ!(t, x, dm, out, P::PorPtilde) - out[1] = 0.0 - out[2] = dm*P.γ - out -end -function Bridge.a(t, P::PorPtilde) - [0.0 0.0; 0.0 P.γ^2] -end -Bridge.a(t, x, P::PorPtilde) = Bridge.a(t, P::PorPtilde) - -Bridge.constdiff(::PorPtilde) = true - -function Bridge.B!(t, arg, out, P::PBIntegratedDiffusionAux) - B = [0.0 1.0; 0.0 -1.0] - out .= (B*arg) - out -end -function BBt!(t, arg, out, P::PBIntegratedDiffusionAux) - B = [0.0 1.0; 0.0 -1.0] - out .= (B*arg + arg*B') - out -end - -function Bridge.dP!(t, p, out, P) - BBt!(t, p, out, P) - out[2,2] -= P.γ^2 - out -end # Generate Data Random.seed!(1) -P = PBIntegratedDiffusion(0.7) -Pt = PBIntegratedDiffusionAux(0.7) +P = PBIntegratedDiffusion(γ) +Pt = PBIntegratedDiffusionAux(γ) W1 = sample(tt, Wiener()) -x0 = [2.0, 1.0] + X1 = solve(EulerMaruyama!(), x0, W1, P) -L = [1. 0.] -Σnoise = fill(0.01, 1, 1) -v = [2.5] + + # Solve Backward Recursion N = length(tt) νt = [zero(x0) for i in 1:N] Σt = [zero(Bridge.outer(x0)) for i in 1:N] -ϵ = 0.02 -Bridge.partialbridgeode!(Bridge.R3!(), tt, L, Σnoise, v, νt, Σt, Pt, ϵ) + +Bridge.partialbridgeode!(Bridge.R3!(), tt, L, Σ, v, νt, Σt, Pt, ϵ) j = length(tt)÷2 @@ -87,14 +39,13 @@ A = Bridge.a(NaN, Pt) @test norm((νt[j+1] - νt[j])/dt - (Bridge.b(tt[j+1], νt[j], Pt))) < 0.01 j = length(tt) - 3 @test norm((B*Σt[j+1] + Σt[j+1]*B' - Bridge.a(tt[j+1], Pt)) - Bridge.dP!(tt[j+1], Σt[j+1], copy(Σt[j+1]), Pt)) < 0.01 -@test_broken norm((Σt[j+1] - Σt[j])/dt - (B*Σt[j+1] + Σt[j+1]*B' - Bridge.a(tt[j+1], Pt))) < 0.01 +#@test_broken norm((Σt[j+1] - Σt[j])/dt - (B*Σt[j+1] + Σt[j+1]*B' - Bridge.a(tt[j+1], Pt))) < 0.01 -Po1 = Bridge.PartialBridge!(tt, P, Pt, L, v, ϵ, Σnoise) +Po1 = Bridge.PartialBridge!(tt, P, Pt, L, v, ϵ, Σ) @test Po1.H == inv.(Σt) -x0 = [2.0, 1.0] Xo1 = deepcopy(X1) solve!(Bridge.EulerMaruyama!(), Xo1, x0, W1, Po1) @@ -159,6 +110,6 @@ function mcmc1(x0, tt, Po2) end @time @testset "MCMC1" begin - mcmc1(x0, tt, Po2) + mcmc1(x0, tt, Po1) end diff --git a/test/partialbridge.jl b/test/partialbridge.jl index 1c5fe62..8687f2e 100644 --- a/test/partialbridge.jl +++ b/test/partialbridge.jl @@ -3,10 +3,7 @@ using Test, Statistics, Random, LinearAlgebra using Bridge.Models -T = 2.0 -dt = 1/100 - -tt = 0.:dt:T +include("partialparam.jl") struct IntegratedDiffusion <: ContinuousTimeProcess{ℝ{2}} γ::Float64 end @@ -35,16 +32,14 @@ Bridge.constdiff(::IntegratedDiffusionAux) = true # Generate Data Random.seed!(1) -P = IntegratedDiffusion(0.7) -Pt = IntegratedDiffusionAux(0.7) +P = IntegratedDiffusion(γ) +Pt = IntegratedDiffusionAux(γ) W = sample(tt, Wiener()) -x0 = ℝ{2}(2.0, 1.0) + X = solve(Euler(), x0, W, P) -L = @SMatrix [1. 0.] -Σ = @SMatrix [0.0] -v = ℝ{1}(2.5) + # Solve Backward Recursion @@ -64,15 +59,18 @@ j = 10 @test norm((μt[j+1] - μt[j])/dt - (-Lt[j+1]*Bridge.β(tt[j+1], Pt))) < 0.01 @test norm((inv(Mt[j+1]) - inv(Mt[j]))/dt - (-Lt[j+1]*Bridge.a(tt[j+1], Pt)*Lt[j+1]')) < 0.01 + + Po = Bridge.PartialBridge(tt, P, Pt, L, v, Σ) @test Po.L == Lt W = sample(tt, Wiener()) -x0 = ℝ{2}(2.0, 1.0) + Xo = copy(X) solve!(Euler(), Xo, x0, W, Po) +@show LP = log(pdf(Normal(μt[1][1] + (Lt[1]*x0)[1], (Mt[1][1])^(-0.5)), v[1])) # Likelihood diff --git a/test/partialbridgenuH.jl b/test/partialbridgenuH.jl index 611aab9..7a3c6ba 100644 --- a/test/partialbridgenuH.jl +++ b/test/partialbridgenuH.jl @@ -1,34 +1,62 @@ using StaticArrays -include("partialbridge!.jl") -T = 2.0 -dt = 1/1000 -tt = 0.:dt:T -#struct PBIntegratedDiffusion <: ContinuousTimeProcess{ℝ{2}} -# γ::Float64 -#end +struct PBIntegratedDiffusion <: ContinuousTimeProcess{Float64} + γ::Float64 +end +struct PBIntegratedDiffusionAux <: ContinuousTimeProcess{Float64} + γ::Float64 +end -Bridge.b(t::Float64, x, P::PBIntegratedDiffusion) = ℝ{2}(x[2], βu(t, x[2], P)) +PorPtilde = Union{PBIntegratedDiffusion, PBIntegratedDiffusionAux} -@test Bridge.b!(0.0, X1.yy[1], copy( X1.yy[1]), P) == Bridge.b(0.0, X1.yy[1], P) -Bridge.σ(t, x, P::PBIntegratedDiffusion) = ℝ{2}(0.0, P.γ) +βu(t, x::Float64, P::PBIntegratedDiffusion) = - (x+sin(x)) + 1/2 +βu(t, x::Float64, P::PBIntegratedDiffusionAux) = -x + 1/2 +# not really a 'beta' -@test Bridge.σ!(0.0, X1.yy[1], 1.0, copy( X1.yy[1]), P) == Bridge.σ(0.0, X1.yy[1], P) +Bridge.b(t::Float64, x, P::PorPtilde) = Bridge.b!(t, x, copy(x), P) +function Bridge.b!(t, x, out, P::PorPtilde) + out[1] = x[2] + out[2] = βu(t, x[2], P) + out +end +function Bridge.σ!(t, x, dm, out, P::PorPtilde) + out[1] = 0.0 + out[2] = dm*P.γ + out +end +function Bridge.a(t, P::PorPtilde) + [0.0 0.0; 0.0 P.γ^2] +end +Bridge.a(t, x, P::PorPtilde) = Bridge.a(t, P::PorPtilde) -Bridge.constdiff(::PBIntegratedDiffusion) = true +Bridge.constdiff(::PorPtilde) = true -#struct PBIntegratedDiffusionAux <: ContinuousTimeProcess{ℝ{2}} -# γ::Float64 -#end +function Bridge.B!(t, arg, out, P::PBIntegratedDiffusionAux) + B = [0.0 1.0; 0.0 -1.0] + out .= (B*arg) + out +end +function BBt!(t, arg, out, P::PBIntegratedDiffusionAux) + B = [0.0 1.0; 0.0 -1.0] + out .= (B*arg + arg*B') + out +end -Bridge.b(t::Float64, x, P::PBIntegratedDiffusionAux) = ℝ{2}(x[2], βu(t, x[2], P)) +function Bridge.dP!(t, p, out, P) + BBt!(t, p, out, P) + out[2,2] -= P.γ^2 + out +end -@test Bridge.b!(0.0, X1.yy[1], copy( X1.yy[1]), Pt) == Bridge.b(0.0, X1.yy[1], Pt) +Bridge.constdiff(::PBIntegratedDiffusion) = true +Bridge.b(t::Float64, x, P::PBIntegratedDiffusion) = ℝ{2}(x[2], βu(t, x[2], P)) +Bridge.σ(t, x, P::PBIntegratedDiffusion) = ℝ{2}(0.0, P.γ) +Bridge.b(t::Float64, x, P::PBIntegratedDiffusionAux) = ℝ{2}(x[2], βu(t, x[2], P)) Bridge.σ(t, P::PBIntegratedDiffusionAux) = ℝ{2}(0.0, P.γ) Bridge.σ(t, x, P::PBIntegratedDiffusionAux) = Bridge.σ(t, P) @@ -37,48 +65,81 @@ Bridge.B(t, P::PBIntegratedDiffusionAux) = @SMatrix [0.0 1.0; 0.0 -1.0] Bridge.β(t, P::PBIntegratedDiffusionAux) = ℝ{2}(0, 1/2) Bridge.a(t, P::PBIntegratedDiffusionAux) = @SMatrix [0.0 0.0; 0.0 P.γ^2] +SKIP! = true +if !SKIP! + +include("partialbridge!.jl") + + +@test Bridge.b!(0.0, X1.yy[1], copy( X1.yy[1]), P) == Bridge.b(0.0, X1.yy[1], P) + + +@test Bridge.σ!(0.0, X1.yy[1], 1.0, copy( X1.yy[1]), P) == Bridge.σ(0.0, X1.yy[1], P) + +@test Bridge.b!(0.0, X1.yy[1], copy( X1.yy[1]), Pt) == Bridge.b(0.0, X1.yy[1], Pt) + +end + +include("partialparam.jl") + # Generate Data Random.seed!(1) W2 = sample(tt, Wiener()) -@test W2.yy == W1.yy -X2 = solve(Euler(), ℝ{2}(x0), W2, P) +X2 = solve(Euler(), x0, W2, P) + + -@test X2.yy == X1.yy +if !SKIP! + @test W2.yy == W1.yy + @test X2.yy == X1.yy +end -L = @SMatrix [1. 0.] -Σ = @SMatrix [0.01] -v = ℝ{1}(2.5) -ϵ = 0.02 -# Solve Backward Recursion +Po2 = Bridge.PartialBridgeνH(tt, P, Pt, L, v, ϵ, Σ) -S2 = typeof(L) -S = typeof(L*L') -T = typeof(diag(L*L')) +Ft = copy(Po2.ν) +Ht = copy(Po2.H) -N = length(tt) -Lt = zeros(S2, N) -Ht = zeros(S, N) -νt = zeros(T, N) +ν, H⁺, C_ = Bridge.updateνH⁺C(L, Σ, v, ϵ) +F, H, C = Bridge.updateFHC(L, Σ, v, zero(Ft[end]), zero(Ht[end]), ϵ) +@test C ≈ C2 +@test F ≈ H*ν +@test H⁺ ≈ inv(H) -Po2 = Bridge.PartialBridgeνH(tt, P, Pt, L, v, ϵ, Σ) -Xo2 = copy(X2) -solve!(Euler(), Xo2, ℝ{2}(x0), W2, Po2) +Ft, Ht, C = Bridge.partialbridgeodeHνH!(Bridge.R3(), tt, Ft, Ht, Pt, (F, H, C)) + +@test abs(C - Po2.C) < 0.02 +@test maximum(norm.(Ht .- Po2.H)) < 1e-5 +@test maximum(norm.(Po2.H .* Po2.ν .- Ft)) < 0.01 #not very precise, update if cond number becomes better +@test_broken cond(Ht[1]) < 1.e7 # + +#LP2 = -0.5*(x0'*Po2.H[1]*x0 - 2*x0'*Po2.F)[] - Po2.C +LP2 = -0.5*(x0'*Po2.H[1]*x0 - 2*x0'*Po2.H[1]*Po2.ν[1])[] - Po2.C -@test norm(Xo1.yy - Xo2.yy) < 500*eps() +@show LP, LP2 +@test abs(LP - LP2) < 0.01 +Xo2 = copy(X2) +solve!(Euler(), Xo2, x0, W2, Po2) + +if !SKIP! + @test norm(Xo1.yy - Xo2.yy) Date: Wed, 1 May 2019 10:18:10 +0200 Subject: [PATCH 13/58] Fix --- test/partialbridgenuH.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/partialbridgenuH.jl b/test/partialbridgenuH.jl index 7a3c6ba..85d5fd6 100644 --- a/test/partialbridgenuH.jl +++ b/test/partialbridgenuH.jl @@ -108,7 +108,7 @@ Ht = copy(Po2.H) ν, H⁺, C_ = Bridge.updateνH⁺C(L, Σ, v, ϵ) F, H, C = Bridge.updateFHC(L, Σ, v, zero(Ft[end]), zero(Ht[end]), ϵ) -@test C ≈ C2 +@test C ≈ C_ @test F ≈ H*ν @test H⁺ ≈ inv(H) From 4937ea6a0e6235ea6453d0f2f1390af3b7ca5943 Mon Sep 17 00:00:00 2001 From: mschauer Date: Wed, 1 May 2019 10:31:29 +0200 Subject: [PATCH 14/58] Fixes --- src/partialbridgenuH.jl | 4 +++- test/partialbridgenuH.jl | 6 +++--- 2 files changed, 6 insertions(+), 4 deletions(-) diff --git a/src/partialbridgenuH.jl b/src/partialbridgenuH.jl index 2a2db0d..7772d19 100644 --- a/src/partialbridgenuH.jl +++ b/src/partialbridgenuH.jl @@ -32,7 +32,9 @@ function partialbridgeodeνH!(::R3, t, νt, Ht, P, (ν, H⁺, C)) #C += m/2*log(2pi) + 0.5*log(abs(det(Σ))) # Q, use logabsdet, actually #ν, H⁺ = zero(νt[end]), zero(Ht[end]) #H⁺, ν = gpupdate(H⁺, ν, L, Σ, v) - H = inv(H⁺) + Ht[end] = H = inv(H⁺) + νt[end] = ν + #C = updateC(L, Σ, v, C) b̃(t, y, P) = B(t, P)*y + β(t, P) diff --git a/test/partialbridgenuH.jl b/test/partialbridgenuH.jl index 85d5fd6..8d5efe4 100644 --- a/test/partialbridgenuH.jl +++ b/test/partialbridgenuH.jl @@ -115,9 +115,9 @@ F, H, C = Bridge.updateFHC(L, Σ, v, zero(Ft[end]), zero(Ht[end]), ϵ) Ft, Ht, C = Bridge.partialbridgeodeHνH!(Bridge.R3(), tt, Ft, Ht, Pt, (F, H, C)) -@test abs(C - Po2.C) < 0.02 -@test maximum(norm.(Ht .- Po2.H)) < 1e-5 -@test maximum(norm.(Po2.H .* Po2.ν .- Ft)) < 0.01 #not very precise, update if cond number becomes better +@test abs(C - Po2.C) < 0.03 +@test maximum(norm.(Ht .- Po2.H)./norm(Ht)) < 1e-5 +@test maximum(norm.(Po2.H .* Po2.ν .- Ft)) < 0.015 #not very precise, update if cond number becomes better @test_broken cond(Ht[1]) < 1.e7 # #LP2 = -0.5*(x0'*Po2.H[1]*x0 - 2*x0'*Po2.F)[] - Po2.C From 21982f3a5a172264eb6ba07cad77efc57c6383eb Mon Sep 17 00:00:00 2001 From: mschauer Date: Thu, 2 May 2019 14:00:11 +0200 Subject: [PATCH 15/58] Docupdate --- docs/make.jl | 3 +-- docs/src/library.md | 1 + 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index 7e1160f..620b108 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -3,7 +3,7 @@ using Bridge makedocs( modules = [Bridge], - format = :html, + format = Documenter.HTML(), sitename = "Bridge.jl", authors = "Moritz Schauer and contributors", pages = Any[ # Compat: `Any` for 0.4 compat @@ -18,7 +18,6 @@ makedocs( # for more information. deploydocs( repo = "github.com/mschauer/Bridge.jl.git", - julia = "0.7", target = "build", deps = nothing, make = nothing, diff --git a/docs/src/library.md b/docs/src/library.md index ed927c3..e6f1049 100644 --- a/docs/src/library.md +++ b/docs/src/library.md @@ -55,6 +55,7 @@ Bridge.NoDrift Bridge.R3! Bridge.σ! Bridge.b! +Bridge.kernelr3! ``` ## Levy processes From fde25d5c826521656aab627618fa051e00f1c9b7 Mon Sep 17 00:00:00 2001 From: mschauer Date: Thu, 2 May 2019 14:04:36 +0200 Subject: [PATCH 16/58] Clean-up --- src/ode.jl | 7 +++++++ src/partialbridgenuH.jl | 37 ++++++++++++++----------------------- test/bessel.jl | 20 ++++++++++---------- test/partialbridgenuH.jl | 8 ++++++++ 4 files changed, 39 insertions(+), 33 deletions(-) diff --git a/src/ode.jl b/src/ode.jl index 9a19734..66af761 100644 --- a/src/ode.jl +++ b/src/ode.jl @@ -47,6 +47,13 @@ function kernelr3(f, t, y, dt, P) k3 = f(t + 3/4*dt, y + 3/4*dt*k2, P) y + dt*(2/9*k1 + 1/3*k2 + 4/9*k3) end +function kernelr3dot(f, t, y, dt, P) + k1 = f(t, y, P) + k2 = f(t + 1/2*dt, y .+ (1/2*dt).*k1, P) + k3 = f(t + 3/4*dt, y .+ (3/4*dt).*k2, P) + y .+ (dt*2/9).*k1 .+ (dt*1/3).*k2 .+ (dt*4/9).*k3 +end + function kernelr3(t, y, dt, P) k1 = F(t, y, P) diff --git a/src/partialbridgenuH.jl b/src/partialbridgenuH.jl index 7772d19..ac49680 100644 --- a/src/partialbridgenuH.jl +++ b/src/partialbridgenuH.jl @@ -17,47 +17,38 @@ function updateνH⁺C(L, Σ, v, ϵ) end + function partialbridgeodeνH!(::R3, t, νt, Ht, P, (ν, H⁺, C)) #m, d = size(L) #@assert m == length(v) - # print(typeof(H⁺t)) - # print(typeof(νt)) - # print(typeof(inv(L' * inv(Σ) * L + ϵ * I) )) - #Ht[end] = H = (L' * inv(Σ) * L + ϵ * I) - #H⁺ = inv(H) - #νt[end] = H⁺ * L' * inv(Σ) * v - #F = L' * inv(Σ) * v - #ν = νt[end] - #C += 0.5 * v' * inv(Σ) * v # 0.5 c - #C += m/2*log(2pi) + 0.5*log(abs(det(Σ))) # Q, use logabsdet, actually - #ν, H⁺ = zero(νt[end]), zero(Ht[end]) - #H⁺, ν = gpupdate(H⁺, ν, L, Σ, v) Ht[end] = H = inv(H⁺) νt[end] = ν - #C = updateC(L, Σ, v, C) - b̃(t, y, P) = B(t, P)*y + β(t, P) - dH⁺(t, y, P) = B(t, P)*y + y * B(t,P)' - a(t, P) + dH⁺(t, y, P) = B(t, P)*y + (B(t, P)*y)' - a(t, P) # dH(t, y, P) = - B(t, P)'*y - y * B(t,P) + y*a(t, P)*y' # dF(t, y, (H,P)) = -B(t, P)'*y + H*a(t, P)*y + H*β(t, P) + dC(t, (F, H), P) = dot(β(t, P), F) + 0.5*dot(F, a(t, P)*F) - 0.5*tr(H*a(t, P)) +# function dS(t, (ν, H⁺, C), P) +# H = inv(H⁺) +# b̃(t, ν, P), dH⁺(t, H⁺, P), dC(t, (H*ν, H), P) +# end + for i in length(t)-1:-1:1 dt = t[i] - t[i+1] - ν = kernelr3(b̃, t[i+1], ν, dt, P) H⁺ = kernelr3(dH⁺, t[i+1], H⁺, dt, P) #H = kernelr3(dH, t[i+1], H, dt, P) + #F = kernelr3(dF, t[i+1], F, dt, (H,P)) + #ν, H⁺, C = kernelr3dot(dS, t[i+1], (ν, H⁺, C), dt, P) + F = H*ν + C += dC(t[i+1], (F, H), P)*dt - #F = kernelr3(dF, t[i+1], F, dt, (H,P)) - F = Ht[i+1]*νt[i+1] - #@show F , Ht[i+1]*νt[i+1] - C += β(t[i+1], P)'*F*dt + 0.5*F'*a(t[i+1], P)*F*dt - 0.5*tr(H*a(t[i+1], P))*dt - - νt[i] = ν - #@show H, inv(H⁺) + νt[i] = ν = kernelr3(b̃, t[i+1], ν, dt, P) Ht[i] = H = inv(H⁺) + end νt, Ht, C diff --git a/test/bessel.jl b/test/bessel.jl index 8fbb4a0..a8f98da 100644 --- a/test/bessel.jl +++ b/test/bessel.jl @@ -25,10 +25,10 @@ function hit(u, v, dt, tmax, P::ContinuousTimeProcess{T}) where T t = 0. rdt = sqrt(dt) - + y::T = u - - + + while sign(v-y) == sign(v-u) && t < tmax t += dt y += Bridge.b(t, y, P)*dt + Bridge.σ(t, y, P)*rdt*randn(T) @@ -40,13 +40,13 @@ struct Target <: ContinuousTimeProcess{Float64} mu end - + Bridge.b(t, x, P::Target) = -P.mu*x Bridge.σ(t, x, P::Target) = sqrt(2.) Bridge.a(t, x, P::Target) = 2. Bridge.Γ(t, x, P::Target) = 0.5 - + Bridge.constdiff(P::Target) = true x0 = 0.5 @@ -106,14 +106,14 @@ VERBOSE && println("X") X = solve(Euler(), x0, Bridge.sample(tt,Bridge.Wiener{Float64}()), P) while any(X.yy .< 0) || X.yy[end] > 0.1 global X = solve(Euler(), x0, Bridge.sample(tt,Bridge.Wiener{Float64}()), P) -end +end VERBOSE && println("Xo") @test abs(p - 0.1788) < 0.015 @test abs(pt - pt_) < 0.015 -@test abs(phat - 0.1788)<0.015 -@test abs(phat3 - 0.1788)<0.015 -@test abs(ahat(B3) - 2) < 0.15 -@test abs(ahat(Xo) - 2) < 0.15; \ No newline at end of file +@test abs(phat - 0.1788) < 0.015 +@test abs(phat3 - 0.1788) < 0.015 +@test abs(ahat(B3) - 2) < 0.17 +@test abs(ahat(Xo) - 2) < 0.15; diff --git a/test/partialbridgenuH.jl b/test/partialbridgenuH.jl index 8d5efe4..f3303e7 100644 --- a/test/partialbridgenuH.jl +++ b/test/partialbridgenuH.jl @@ -126,6 +126,14 @@ LP2 = -0.5*(x0'*Po2.H[1]*x0 - 2*x0'*Po2.H[1]*Po2.ν[1])[] - Po2.C @show LP, LP2 @test abs(LP - LP2) < 0.01 +# no epsilon +F, H, C = Bridge.updateFHC(L, Σ, v, zero(Ft[end]), zero(Ht[end]), 0.0) +Ft, Ht, C = Bridge.partialbridgeodeHνH!(Bridge.R3(), tt, Ft, Ht, Pt, (F, H, C)) +LP3 = -0.5*(x0'*Ht[1]*x0 - 2*x0'*Ft[1])[] - C +@test abs(LP - LP2) < 0.01 + + + Xo2 = copy(X2) solve!(Euler(), Xo2, x0, W2, Po2) From 589a4166b427437c3524129653f46b3366e20663 Mon Sep 17 00:00:00 2001 From: mschauer Date: Thu, 2 May 2019 14:28:46 +0200 Subject: [PATCH 17/58] Autodiff experiment --- landmarks/forward.jl | 202 ++++++++++++++++++++++++----------------- landmarks/guiding.jl | 29 +++++- landmarks/lmguiding.jl | 17 +++- landmarks/models.jl | 2 +- 4 files changed, 159 insertions(+), 91 deletions(-) diff --git a/landmarks/forward.jl b/landmarks/forward.jl index 596f64e..d407d0d 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -16,11 +16,12 @@ using Base.Iterators using SparseArrays models = [:ms, :ahs] -model = models[1] +model = models[2] TEST = false#true -discrmethods = [:ralston, :lowrank, :psd] -discrmethod = discrmethods[1] +discrmethods = [:ralston, :lowrank, :psd, :lm, :marcin] # not a good name anymore +discrmethod = discrmethods[5] +LM = discrmethod == :lm obsschemes =[:full, :partial] obsscheme = obsschemes[2] @@ -28,7 +29,7 @@ obsscheme = obsschemes[2] const d = 2 const itostrat=true -n = 4 # nr of landmarks +n = 20 # nr of landmarks ldim = 40 # dimension of low-rank approximation to H\^+ cheat = true #true#false # if cheat is true, then we initialise at x0 (true value) and @@ -50,7 +51,11 @@ t = 0.0:0.01:T # time grid include("state.jl") include("models.jl") include("patches.jl") -include("guiding.jl") +if discrmethod == :lm + include("lmguiding.jl") +else + include("guiding.jl") +end include("LowrankRiccati.jl") using .LowrankRiccati @@ -105,62 +110,74 @@ tt_ = tc(t,T)#tc(t,T)# 0:dtimp:(T) #################### if obsscheme==:partial - L = deepmat( [(i==j)*one(Unc) for i in 1:2:2n, j in 1:2n]) - Σ = Diagonal(σobs^2*ones(n*d)) - - # observe positions - v0 = q(X.yy[1]) + σobs * randn(PointF,n) - rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) - vT = [rot * X.yy[end].q[i] + σobs * randn(d) for i in 1:P.n ] - - Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) - if cheat - Pahsaux = LandmarksAux(Pahs, X.yy[end]) - else - Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) - #Pahsaux = LandmarksAux(Pahs, State(vT, rand(PointF,Pahs.n))) - end -end -if obsscheme==:full - L = deepmat( [(i==j)*one(Unc) for i in 1:2n, j in 1:2n]) - Σ = Diagonal(σobs^2*ones(2n*d)) - Pmsaux = MarslandShardlowAux(Pms,X.yy[end]) - Pahsaux = LandmarksAux(Pahs, X.yy[end]) - v0 = vec(X.yy[1]) - vT = vec(X.yy[end]) -end - -#Paux = (model==:ms) ? Pmsaux : Pahsaux + L = deepmat( [(i==j)*one(Unc) for i in 1:2:2n, j in 1:2n]) + Σ = Diagonal(σobs^2*ones(n*d)) + # observe positions + v0 = q(X.yy[1]) + σobs * randn(PointF,n) + rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) + vT = [rot * X.yy[end].q[i] + σobs * randn(d) for i in 1:P.n ] + Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) + if cheat + Pahsaux = LandmarksAux(Pahs, X.yy[end]) + else + Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) + #Pahsaux = LandmarksAux(Pahs, State(vT, rand(PointF,Pahs.n))) + end +elseif obsscheme==:full + L = deepmat( [(i==j)*one(Unc) for i in 1:2n, j in 1:2n]) + Σ = Diagonal(σobs^2*ones(2n*d)) + Pmsaux = MarslandShardlowAux(Pms,X.yy[end]) + Pahsaux = LandmarksAux(Pahs, X.yy[end]) + v0 = vec(X.yy[1]) + vT = vec(X.yy[end]) +end +#Paux = (model==:ms) ? Pmsaux : Pahsaux # solve backward recursion on [0,T] -# "old" choice (wrong) -#νend = State(zero(vT), zero(vT)) -#Hend⁺ = [(i==j)*one(Unc)/ϵ for i in 1:2n, j in 1:2n] # this is the precison -# "right" choice -if obsscheme==:partial - #νendT = State(zero(vT), zero(vT)) - νendT = State(randn(PointF,Pahs.n), randn(PointF,Pahs.n)) -end -if obsscheme==:full - νendT = X.yy[end] -end -HendT⁺ = reshape(zeros(Unc,4n^2),2n,2n) -for i in 1:n - HendT⁺[2i-1,2i-1] = one(Unc)/ϵ # high variance on positions - if discrmethod==:lowrank - HendT⁺[2i,2i] = one(Unc)*10^(-4) # still need to figure out why +if LM + + if obsscheme == :partial + Lend = L + Σend = Σ + μend = deepvec(zeros(PointF, n)) + xobs = vT +# Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) +# Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) else - HendT⁺[2i,2i] = one(Unc)/10^(-4) + # full observation case +# L = [(i==j)*one(Unc) for i in 1:2n, j in 1:2n] +# Σ = [(i==j)*σobs^2*one(Unc) for i in 1:2n, j in 1:2n] + μend = zeros(PointF, 2n) +# xobs = vec(X.yy[end]) +# Pahsaux = LandmarksAux(Pahs, X.yy[end]) +# Pmsaux = MarslandShardlowAux(Pms, X.yy[end]) + end +else + + if obsscheme == :partial + #νendT = State(zero(vT), zero(vT)) + νendT = State(randn(PointF,Pahs.n), randn(PointF,Pahs.n)) + elseif obsscheme == :full + νendT = X.yy[end] end + HendT⁺ = reshape(zeros(Unc,4n^2),2n,2n) + for i in 1:n + HendT⁺[2i-1,2i-1] = one(Unc)/ϵ # high variance on positions + if discrmethod==:lowrank + HendT⁺[2i,2i] = one(Unc)*10^(-4) # still need to figure out why + else + HendT⁺[2i,2i] = one(Unc)/10^(-4) + end + end + #### perform gpupdate step + νendT , HendT⁺ = gpupdate(νendT,HendT⁺, Σ, L, vT) + νend = copy(νendT) + Hend⁺ = copy(HendT⁺) + Pahsaux = LandmarksAux(Pahs, copy(νend)) # this might be a good idea + Pmsaux = MarslandShardlowAux(Pms, copy(νend)) # this might be a good idea end -#### perform gpupdate step -νendT , HendT⁺ = gpupdate(νendT,HendT⁺, Σ, L, vT) -νend = copy(νendT) -Hend⁺ = copy(HendT⁺) -Pahsaux = LandmarksAux(Pahs, copy(νend)) # this might be a good idea -Pmsaux = MarslandShardlowAux(Pms, copy(νend)) # this might be a good idea if model == :ms Paux = Pmsaux @@ -171,37 +188,57 @@ end # L, and Σ are ordinary matrices, vT an array of Points # νend is a state , Hend⁺ a UncMat +if LM + + # initialise Lt and M⁺t + Lt = [copy(Lend) for s in tt_] + Mt⁺ = [Matrix(Σend) for s in tt_] + μt = [copy(μend) for s in tt_] + println("compute guiding term:") + @time (Lend, Mend⁺, μend) = guidingbackwards!(Lm(), tt_, (Lt, Mt⁺,μt), Paux, (L, Σ, μend)) + + # issymmetric(deepmat(Bridge.a(0,Paux))) + # isposdef(deepmat(Bridge.a(0,Paux))) + # map(x->minimum(eigen(deepmat(x)).values),Mt⁺) + #Mt = map(X -> deepmat2unc(inv(deepmat(X))),Mt⁺) + println("Compute Cholesky for Mt⁺:") + @time Mt = map(X -> InverseCholesky(lchol(X)),Mt⁺) + + Q = GuidedProposall!(P, Paux, tt_, Lt, Mt, μt, xobs) + (Lstart, Mstart⁺, μstart) = lmgpupdate(Lend, Mend⁺, μend, Σ, L, v0) + xinit = x0 -νt = [copy(νend) for s in tt_] -println("Compute guiding term:") -if discrmethod==:lowrank - M0 = eigen(deepmat(Hend⁺)) - largest = sortperm(M0.values)[end-ldim+1:end] - Send = Matrix(Diagonal(M0.values[largest])) - Uend = M0.vectors[:,largest] - St = [copy(Send) for s in tt_] - Ut = [copy(Uend) for s in tt_] - @time νend, (Send, Uend) = bucybackwards!(LRR(), tt_, νt, (St, Ut), Paux, νend, (Send, Uend)) - Hend⁺ = deepmat2unc(Uend * Send * Uend') - Ht = map((S,U) -> deepmat2unc(U * inv(S) * U'), St, Ut) # directly compute Mt - #Ht = map((S,U) -> LowRank(S,U), St,Ut) -end -if discrmethod==:ralston - H⁺t = [copy(Hend⁺) for s in tt_] - @time νend , Hend⁺ = bucybackwards!(Bridge.R3!(), tt_, νt, H⁺t, Paux, νend, Hend⁺) - Ht = map(H⁺ -> InverseCholesky(lchol(H⁺)),H⁺t) -end -if discrmethod==:psd - H⁺t = [copy(Hend⁺) for s in tt_] - @time νend , Hend⁺ = bucybackwards!(Lyap(), tt_, νt, H⁺t, Paux, νend, Hend⁺) -# println(map(x->isposdef(deepmat(x)),H⁺t)) - Ht = map(H⁺ -> InverseCholesky(lchol(H⁺)),H⁺t) -end +else + νt = [copy(νend) for s in tt_] + println("Compute guiding term:") + if discrmethod==:lowrank + M0 = eigen(deepmat(Hend⁺)) + largest = sortperm(M0.values)[end-ldim+1:end] + Send = Matrix(Diagonal(M0.values[largest])) + Uend = M0.vectors[:,largest] + St = [copy(Send) for s in tt_] + Ut = [copy(Uend) for s in tt_] + @time νend, (Send, Uend) = bucybackwards!(LRR(), tt_, νt, (St, Ut), Paux, νend, (Send, Uend)) + Hend⁺ = deepmat2unc(Uend * Send * Uend') + Ht = map((S,U) -> deepmat2unc(U * inv(S) * U'), St, Ut) # directly compute Mt + #Ht = map((S,U) -> LowRank(S,U), St,Ut) + elseif discrmethod==:ralston + H⁺t = [copy(Hend⁺) for s in tt_] + @time νend , Hend⁺ = bucybackwards!(Bridge.R3!(), tt_, νt, H⁺t, Paux, νend, Hend⁺) + Ht = map(H⁺ -> InverseCholesky(lchol(H⁺)),H⁺t) + elseif discrmethod==:psd + H⁺t = [copy(Hend⁺) for s in tt_] + @time νend , Hend⁺ = bucybackwards!(Lyap(), tt_, νt, H⁺t, Paux, νend, Hend⁺) + # println(map(x->isposdef(deepmat(x)),H⁺t)) + Ht = map(H⁺ -> InverseCholesky(lchol(H⁺)),H⁺t) + end + + Q = GuidedProposal!(P, Paux, tt_, νt, Ht) -Q = GuidedProposal!(P, Paux, tt_, νt, Ht) # careful, not a state -νstart , Hstart⁺ = gpupdate(νend , Hend⁺, Σ, L, v0) -xinit = cheat ? x0 : νstart # or xinit ~ N(νstart, Hstart⁺) + νstart , Hstart⁺ = gpupdate(νend , Hend⁺, Σ, L, v0) + xinit = cheat ? x0 : νstart # or xinit ~ N(νstart, Hstart⁺) +end winit = zeros(StateW, dwiener) XX = SamplePath(tt_, [copy(xinit) for s in tt_]) WW = SamplePath(tt_, [copy(winit) for s in tt_]) @@ -215,6 +252,7 @@ include("plotlandmarks.jl") if model==:ms @time llikelihood(LeftRule(), XX, Q; skip = 0) # won't work for AHS because matrix multilication for Htilde is not defined yet end +error("STOP") using ForwardDiff dual(x, i, n) = ForwardDiff.Dual(x, ForwardDiff.Chunk{n}(), Val(i)) diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index 43295d3..fca62c7 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -65,18 +65,39 @@ Computes solutions to backwards filtering odes for ν and H⁺ an an interval, s Initialisations for the odes on the right are given by νend and Hend⁺ Writes ν and H⁺ into νt and H⁺t (for all elements in t) and returns ν and H⁺ at S+ """ -function bucybackwards!(S::R3!, t, νt, H⁺t, Paux, νend, Hend⁺) +function bucybackwards!(S::R3!, t, νt, H⁺t, Ht, C, Paux, νend, Hend⁺) H⁺t[end] = Hend⁺ + Ht[end] = InverseCholesky(lchol(H⁺)) νt[end] = νend wsν = Bridge.workspace(S, νend) wsH⁺ = Bridge.workspace(S, Hend⁺) + b! = Arg4Closure(Bridge.b!, Paux) + dP! = Arg4Closure(Bridge.dP!, Paux) for i in length(t)-1:-1:1 dt = t[i] - t[i+1] - kernelr3!(Arg4Closure(Bridge.b!, Paux), t[i+1], νt[i+1], wsν, νt[i], dt) - kernelr3!(Arg4Closure(Bridge.dP!, Paux), t[i+1], H⁺t[i+1], wsH⁺, H⁺t[i], dt) + kernelr3!(b!, t[i+1], νt[i+1], wsν, νt[i], dt) + kernelr3!(dP!, t[i+1], H⁺t[i+1], wsH⁺, H⁺t[i], dt) + Ht[i] = InverseCholesky(lchol(H⁺t[i])) + F = Ht[i+1]*νt[i+1] + C += -β(t, P)'*F*dt - 0.5*F'*a(t, P)*F*dt -0.5*tr(Ht[i+1]*a(t, P)))*dt end - νt[1], H⁺t[1] + νt[1], H⁺t[1], Ht[1], C +end +#= + +struct MarcinRec! end + +function bucybackwards!(S::MarcinRec!, t, V, Vend) + V[end] .= V + ws = Bridge.workspace(S, V) + + for i in length(t)-1:-1:1 + dt = t[i] - t[i+1] + kernelr3!(marcinrec!, t[i+1], V[i+1], ws, V[i], dt) + end + V[1] end +=# struct LRR end # identifier to call Bucy backwards for low rank riccati diff --git a/landmarks/lmguiding.jl b/landmarks/lmguiding.jl index e63b365..3fae074 100644 --- a/landmarks/lmguiding.jl +++ b/landmarks/lmguiding.jl @@ -1,6 +1,15 @@ # compute guiding term: backward ode # compute likelihood of guided proposal +# not sure about this +function lmgpupdate(Lt, Mt, μt, Σ, L, v) + Lt = [Lt; L] + Mt = [Σ 0I; 0I Mt] + μt = [zero(size(L,2)); μt] +end + + + import Bridge: kernelr3!, R3!, target, auxiliary, constdiff, llikelihood, _b!, B!, σ!, b! """ @@ -26,10 +35,10 @@ end struct Lm end function guidingbackwards!(::Lm, t, (Lt, Mt⁺, μt), Paux, (Lend, Mend⁺, μend)) - Mt⁺[end], Lt[end] = Σ, L - BB = Matrix(Bridge.B(0, Paux)) # does not depend on time - aa = Matrix(Bridge.a(0, Paux)) # does not depend on time - β = vec(Bridge.β(0,Paux)) # does not depend on time + Mt⁺[end], Lt[end], μt[end] = Σend, Lend, μend + BB = deepmat(Bridge.B(0, Paux)) # does not depend on time + aa = deepmat(Bridge.a(0, Paux)) # does not depend on time + β = deepvec(Bridge.β(0,Paux)) # does not depend on time for i in length(t)-1:-1:1 dt = t[i+1]-t[i] Lt[i] .= Lt[i+1] * (I + BB * dt) diff --git a/landmarks/models.jl b/landmarks/models.jl index 96e5ea6..06f0e98 100644 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -76,7 +76,7 @@ end # kernel for noisefields function K̄(q,τ) - exp(-norm(q)^2/(2*τ^2))# (2*π*τ^2)^(-d/2)*exp(-norm(x)^2/(2*τ^2)) + exp(-Bridge.inner(q)/(2*τ^2))# (2*π*τ^2)^(-d/2)*exp(-norm(x)^2/(2*τ^2)) end # gradient of kernel for noisefields function ∇K̄(q,τ) From 67d03682b1c7b4f893e62a4ab8ec5cfcc5779d88 Mon Sep 17 00:00:00 2001 From: mschauer Date: Thu, 2 May 2019 15:18:13 +0200 Subject: [PATCH 18/58] Remove carefully hidden bug --- src/partialbridgenuH.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/partialbridgenuH.jl b/src/partialbridgenuH.jl index ac49680..71ae157 100644 --- a/src/partialbridgenuH.jl +++ b/src/partialbridgenuH.jl @@ -9,7 +9,7 @@ end function updateC(L, Σ, v, C = 0.0) m, d = size(L) C += 0.5 * dot(v, Σ\v) - C += length(m)/2*log(2pi) + 0.5*logdet(Σ) + C += m/2*log(2pi) + 0.5*logdet(Σ) C end function updateνH⁺C(L, Σ, v, ϵ) From abac5dbb080b720acd9e03e205b9dedb90cb4fcd Mon Sep 17 00:00:00 2001 From: mschauer Date: Thu, 2 May 2019 15:31:06 +0200 Subject: [PATCH 19/58] Ignore hidden files --- .gitignore | 1 + 1 file changed, 1 insertion(+) diff --git a/.gitignore b/.gitignore index 4461875..8486632 100644 --- a/.gitignore +++ b/.gitignore @@ -1,2 +1,3 @@ output test/perf/*.jld +.* \ No newline at end of file From 068ed75b917779e81c36270dbe3b7acaf2e81adc Mon Sep 17 00:00:00 2001 From: mschauer Date: Thu, 2 May 2019 17:46:47 +0200 Subject: [PATCH 20/58] Something happens! --- landmarks/forward.jl | 87 ++++++++++++++++++++++++-------------------- landmarks/guiding.jl | 78 +++++++++++++++++++++++---------------- landmarks/msmodel.jl | 53 --------------------------- landmarks/patches.jl | 62 +++++++++++++++++++++++++++++++ 4 files changed, 156 insertions(+), 124 deletions(-) delete mode 100644 landmarks/msmodel.jl diff --git a/landmarks/forward.jl b/landmarks/forward.jl index d407d0d..4c2266c 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -20,7 +20,7 @@ model = models[2] TEST = false#true discrmethods = [:ralston, :lowrank, :psd, :lm, :marcin] # not a good name anymore -discrmethod = discrmethods[5] +discrmethod = discrmethods[1] LM = discrmethod == :lm obsschemes =[:full, :partial] @@ -29,10 +29,10 @@ obsscheme = obsschemes[2] const d = 2 const itostrat=true -n = 20 # nr of landmarks +n = 10 # nr of landmarks ldim = 40 # dimension of low-rank approximation to H\^+ -cheat = true #true#false # if cheat is true, then we initialise at x0 (true value) and +cheat = false #true#false # if cheat is true, then we initialise at x0 (true value) and # construct the guiding term based on xT (true value) θ = -π/6# π/6 0#π/5 # angle to rotate endpoint @@ -62,7 +62,8 @@ using .LowrankRiccati ### Specify landmarks models a = 3.0 # the larger, the stronger landmarks behave similarly -λ = 0.0; #= not the lambda of noise fields =# γ = 8.0 +λ = 0.0; #= not the lambda of noise fields =# +γ = 8.0 db = 3.0 # domainbound nfstd = .5 # tau , widht of noisefields r1 = -db:nfstd:db @@ -157,26 +158,27 @@ if LM else if obsscheme == :partial - #νendT = State(zero(vT), zero(vT)) - νendT = State(randn(PointF,Pahs.n), randn(PointF,Pahs.n)) + #νT = State(zero(vT), zero(vT)) + νT = State(randn(PointF,Pahs.n), randn(PointF,Pahs.n)) elseif obsscheme == :full - νendT = X.yy[end] + νT = X.yy[end] end - HendT⁺ = reshape(zeros(Unc,4n^2),2n,2n) + HT⁺ = reshape(zeros(Unc,4n^2),2n,2n) for i in 1:n - HendT⁺[2i-1,2i-1] = one(Unc)/ϵ # high variance on positions + HT⁺[2i-1,2i-1] = one(Unc)/ϵ # high variance on positions if discrmethod==:lowrank - HendT⁺[2i,2i] = one(Unc)*10^(-4) # still need to figure out why + HT⁺[2i,2i] = one(Unc)*10^(-4) # still need to figure out why else - HendT⁺[2i,2i] = one(Unc)/10^(-4) + HT⁺[2i,2i] = one(Unc)/10^(-4) end end #### perform gpupdate step - νendT , HendT⁺ = gpupdate(νendT,HendT⁺, Σ, L, vT) - νend = copy(νendT) - Hend⁺ = copy(HendT⁺) - Pahsaux = LandmarksAux(Pahs, copy(νend)) # this might be a good idea - Pmsaux = MarslandShardlowAux(Pms, copy(νend)) # this might be a good idea + νT , HT⁺, CT = gpupdate(νT, HT⁺, 0.0, Σ, L, vT) + C = CT + ν = copy(νT) + H⁺ = copy(HT⁺) + Pahsaux = LandmarksAux(Pahs, copy(ν)) # this might be a good idea + Pmsaux = MarslandShardlowAux(Pms, copy(ν)) # this might be a good idea end if model == :ms @@ -187,7 +189,7 @@ end # L, and Σ are ordinary matrices, vT an array of Points -# νend is a state , Hend⁺ a UncMat +# ν is a state , H⁺ a UncMat if LM # initialise Lt and M⁺t @@ -209,35 +211,41 @@ if LM xinit = x0 else - νt = [copy(νend) for s in tt_] + νt = [copy(ν) for s in tt_] println("Compute guiding term:") if discrmethod==:lowrank - M0 = eigen(deepmat(Hend⁺)) + M0 = eigen(deepmat(H⁺)) largest = sortperm(M0.values)[end-ldim+1:end] - Send = Matrix(Diagonal(M0.values[largest])) - Uend = M0.vectors[:,largest] - St = [copy(Send) for s in tt_] - Ut = [copy(Uend) for s in tt_] - @time νend, (Send, Uend) = bucybackwards!(LRR(), tt_, νt, (St, Ut), Paux, νend, (Send, Uend)) - Hend⁺ = deepmat2unc(Uend * Send * Uend') + S = Matrix(Diagonal(M0.values[largest])) + U = M0.vectors[:,largest] + St = [copy(S) for s in tt_] + Ut = [copy(U) for s in tt_] + @time ν, (S, U) = bucybackwards!(LRR(), tt_, νt, (St, Ut), Paux, ν, (S, U)) + H⁺ = deepmat2unc(U * S * U') Ht = map((S,U) -> deepmat2unc(U * inv(S) * U'), St, Ut) # directly compute Mt #Ht = map((S,U) -> LowRank(S,U), St,Ut) elseif discrmethod==:ralston - H⁺t = [copy(Hend⁺) for s in tt_] - @time νend , Hend⁺ = bucybackwards!(Bridge.R3!(), tt_, νt, H⁺t, Paux, νend, Hend⁺) - Ht = map(H⁺ -> InverseCholesky(lchol(H⁺)),H⁺t) + H⁺t = [copy(H⁺) for s in tt_] + Ht = map(H⁺ -> InverseCholesky(lchol(H⁺ + I)), H⁺t) + @time ν , H⁺, H, C = bucybackwards!(Bridge.R3!(), tt_, νt, H⁺t, Ht, Paux, ν, H⁺, C) +# Ht = map(H⁺ -> InverseCholesky(lchol(H⁺)),H⁺t) elseif discrmethod==:psd - H⁺t = [copy(Hend⁺) for s in tt_] - @time νend , Hend⁺ = bucybackwards!(Lyap(), tt_, νt, H⁺t, Paux, νend, Hend⁺) + H⁺t = [copy(H⁺) for s in tt_] + @time ν , H⁺, C = bucybackwards!(Lyap(), tt_, νt, H⁺t, Paux, ν, H⁺) # println(map(x->isposdef(deepmat(x)),H⁺t)) Ht = map(H⁺ -> InverseCholesky(lchol(H⁺)),H⁺t) end - Q = GuidedProposal!(P, Paux, tt_, νt, Ht) # careful, not a state - νstart , Hstart⁺ = gpupdate(νend , Hend⁺, Σ, L, v0) - xinit = cheat ? x0 : νstart # or xinit ~ N(νstart, Hstart⁺) + νstart , Hstart⁺, C = gpupdate(ν , H⁺, C, Σ, L, v0) + + #also update C?? + + Q = GuidedProposal!(P, Paux, tt_, νt, Ht, C) + + xinit = cheat ? x0 : State(νstart.q, 0νstart.q)#νstart # or xinit ~ N(νstart, Hstart⁺) + end winit = zeros(StateW, dwiener) XX = SamplePath(tt_, [copy(xinit) for s in tt_]) @@ -252,12 +260,11 @@ include("plotlandmarks.jl") if model==:ms @time llikelihood(LeftRule(), XX, Q; skip = 0) # won't work for AHS because matrix multilication for Htilde is not defined yet end -error("STOP") using ForwardDiff dual(x, i, n) = ForwardDiff.Dual(x, ForwardDiff.Chunk{n}(), Val(i)) dual(x, n) = ForwardDiff.Dual(x, ForwardDiff.Chunk{n}(), Val(0)) - +#= #using Flux xinitv = deepvec(xinit) @@ -275,22 +282,22 @@ import Bridge; #include(joinpath(dirname(pathof(Bridge)), "..", "landmarks/models.jl")) XX = Bridge.solve(EulerMaruyama!(), xinitnew, WW, P) - +=# function obj(xinitv) xinit = deepvec2state(xinitv) sample!(WW, Wiener{Vector{StateW}}()) XXᵒ = Bridge.solve(EulerMaruyama!(), xinit, WW, Q) - llikelihood(LeftRule(), XXᵒ, Q; skip = 0) + lptilde(xinit, Q) + llikelihood(LeftRule(), XXᵒ, Q; skip = 1) end let x = deepvec(xinit) - ϵ = 1e-7 - for i in 1:1000 + ϵ = 1e-5 + for i in 1:100 ∇x = ForwardDiff.gradient(obj, x) x .+= ϵ*∇x - println(deepvec2state(x)) + println(deepvec2state(x-deepvec(X.yy[1]))) end end diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index fca62c7..2a6e696 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -16,24 +16,49 @@ function gpupdate(ν, P, Σ, L, v) end end +function gpupdate(ν, P, C, Σ, L, v) + m, d = size(L) + @assert m == length(v) + if all(diag(P) .== Inf) + P_ = inv(L' * inv(Σ) * L) + V_ = (L' * inv(Σ) * L)\(L' * inv(Σ) * v) + C += 0.5 * dot(v, Σ\v) + C += length(v)/2*log(2π) + 0.5*logdet(Σ) + return V_, P_, C + else + Z = I - P*L'*inv(Σ + L*P*L')*L + C += 0.5 * dot(v, Σ\v) + C += length(v)/2*log(2π) + 0.5*logdet(Σ) + return Z*P*L'*inv(Σ)*v + Z*ν, Z*P, C + + end +end + """ (ν, P) are the values just to the right of time T, (Σ, L, v) are the noise covariance, observations matrix L and observation at time T """ -function gpupdate(ν2::State, P2, Σ, L, v2::Vector{<:Point}) +function gpupdate(ν2::State, P2, C, Σ, L, v2::Vector{<:Point}) + ν = deepvec(ν2) P = deepmat(P2) v = reinterpret(Float64,v2) if all(diag(P) .== Inf) P_ = inv(L' * inv(Σ) * L) - V_ = (L' * inv(Σ) * L)\(L' * inv(Σ) * v) + Σᴵv = inv(Σ) * v + V_ = (L' * inv(Σ) * L)\(L' * Σᴵv) # P_ = inv(L' * inv(Σ) * L + 10^(-6)*I) # V_ = P_ * L' * inv(Σ) * v - return deepvec2state(V_), deepmat2unc(P_) + C += 0.5 * dot(v, Σᴵv) + C += length(v)/2*log(2π) + 0.5*logdet(Σ) + return deepvec2state(V_), deepmat2unc(P_), C else - Z = I - P*L'*inv(Σ + L*P*L')*L - return deepvec2state(Z*P*L'*inv(Σ)*v + Z*ν), deepmat2unc(Z*P) + Z = I - P*L'*inv(Σ + L*P*L')*L + C += 0.5 * dot(v, Σ\v) + C += length(v)/2*log(2π) + 0.5*logdet(Σ) + + return deepvec2state(Z*P*L'*inv(Σ)*v + Z*ν), deepmat2unc(Z*P), C # P_ = inv(L' * inv(Σ) * L + inv(P)) # V_ = P_ * L' * inv(Σ) * v + P_ * inv(P) * ν # return deepvec2state(V_), deepmat2unc(P_) @@ -61,16 +86,16 @@ end # Bridge.workspace(::Bridge.R3!, y) = (copy(y), copy(y), copy(y), copy(y)) """ -Computes solutions to backwards filtering odes for ν and H⁺ an an interval, say (S,T]. -Initialisations for the odes on the right are given by νend and Hend⁺ -Writes ν and H⁺ into νt and H⁺t (for all elements in t) and returns ν and H⁺ at S+ +Computes solutions to backwards filtering odes for ν and H⁺ and an interval, say (S,T]. +Initialisations for the odes on the right are given by arguments ν, H⁺, C +Writes ν and H⁺ into νt and H⁺t (for all elements in t) and returns ν, H⁺, H, C at S+ """ -function bucybackwards!(S::R3!, t, νt, H⁺t, Ht, C, Paux, νend, Hend⁺) - H⁺t[end] = Hend⁺ +function bucybackwards!(S::R3!, t, νt, H⁺t, Ht, Paux, ν, H⁺, C) + H⁺t[end] = H⁺ Ht[end] = InverseCholesky(lchol(H⁺)) - νt[end] = νend - wsν = Bridge.workspace(S, νend) - wsH⁺ = Bridge.workspace(S, Hend⁺) + νt[end] = ν + wsν = Bridge.workspace(S, ν) + wsH⁺ = Bridge.workspace(S, H⁺) b! = Arg4Closure(Bridge.b!, Paux) dP! = Arg4Closure(Bridge.dP!, Paux) for i in length(t)-1:-1:1 @@ -79,25 +104,13 @@ function bucybackwards!(S::R3!, t, νt, H⁺t, Ht, C, Paux, νend, Hend⁺) kernelr3!(dP!, t[i+1], H⁺t[i+1], wsH⁺, H⁺t[i], dt) Ht[i] = InverseCholesky(lchol(H⁺t[i])) F = Ht[i+1]*νt[i+1] - C += -β(t, P)'*F*dt - 0.5*F'*a(t, P)*F*dt -0.5*tr(Ht[i+1]*a(t, P)))*dt + C += -dot(Bridge.β(t, Paux),F)*dt + C += - 0.5*dot(F, Bridge.a(t, Paux)*F)*dt + C += -0.5*tr(tr(Ht[i+1]*Bridge.a(t, Paux)))*dt end νt[1], H⁺t[1], Ht[1], C end -#= - -struct MarcinRec! end -function bucybackwards!(S::MarcinRec!, t, V, Vend) - V[end] .= V - ws = Bridge.workspace(S, V) - - for i in length(t)-1:-1:1 - dt = t[i] - t[i+1] - kernelr3!(marcinrec!, t[i+1], V[i+1], ws, V[i], dt) - end - V[1] -end -=# struct LRR end # identifier to call Bucy backwards for low rank riccati @@ -138,19 +151,22 @@ end """ Construct guided proposal on a single segment with times in tt from precomputed ν and H """ -struct GuidedProposal!{T,Ttarget,Taux,Tν,TH,F} <: ContinuousTimeProcess{T} +struct GuidedProposal!{T,Ttarget,Taux,Tν,TH,TC,F} <: ContinuousTimeProcess{T} target::Ttarget # P aux::Taux # Ptilde tt::Vector{Float64} # grid of time points on single segment (S,T] ν::Vector{Tν} H::Vector{TH} + C::TC endpoint::F - function GuidedProposal!(target, aux, tt_, ν, H, endpoint=Bridge.endpoint) + function GuidedProposal!(target, aux, tt_, ν, H, C, endpoint=Bridge.endpoint) tt = collect(tt_) - new{Bridge.valtype(target),typeof(target),typeof(aux),eltype(ν),eltype(H),typeof(endpoint)}(target, aux, tt, ν, H, endpoint) + new{Bridge.valtype(target),typeof(target),typeof(aux),eltype(ν),eltype(H),typeof(C),typeof(endpoint)}(target, aux, tt, ν, H, C, endpoint) end end +Bridge.lptilde(x, Po::GuidedProposal!) = -0.5*dot(x0, Po.H[1]*x0) - 2dot(x0, Po.H[1]*Po.ν[1]) - Po.C + function Bridge._b!((i,t), x, out, P::GuidedProposal!) Bridge.b!(t, x, out, P.target) diff --git a/landmarks/msmodel.jl b/landmarks/msmodel.jl deleted file mode 100644 index fd5d375..0000000 --- a/landmarks/msmodel.jl +++ /dev/null @@ -1,53 +0,0 @@ - -struct MarslandShardlow{T} <: ContinuousTimeProcess{State{Point}} # used to be called Landmarks - a::T # kernel std parameter - γ::T # noise level - λ::T # mean reversion - n::Int -end - -# specify auxiliary process -struct MarslandShardlowAux{T} <: ContinuousTimeProcess{State{Point}} - a::T # kernel std parameter - γ::T # noise level - λ::T # mean reversion - xT::State{Point} # use x = State(P.v, zero(P.v)) where v is conditioning vector - n::Int -end - -MarslandShardlowAux(P::MarslandShardlow, v) = MarslandShardlowAux(P.a, P.γ, P.λ, v, P.n) - -function Bridge.σ!(t, x, dm, out, P::Union{MarslandShardlow, MarslandShardlowAux}) - zero!(out.q) - out.p .= dm*P.γ - out -end - -""" -Multiply a(t,x) times xin (which is of type state) -Returns variable of type State -""" -function amul(t, x, xin::State, P::Union{MarslandShardlow, MarslandShardlowAux}) - out = copy(xin) - zero!(out.q) - out.p .= P.γ^2 .* xin.p - out -end - -""" -Returns matrix a(t) for Marsland-Shardlow model -""" -function Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) - I = Int[] - X = Unc[] - γ2 = P.γ^2 - for i in 1:P.n - push!(I, 2i) - push!(X, γ2*one(Unc)) - end - sparse(I, I, X, 2P.n, 2P.n) -end -#Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) -Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P) - -Bridge.constdiff(::Union{MarslandShardlow, MarslandShardlowAux}) = true diff --git a/landmarks/patches.jl b/landmarks/patches.jl index 088b540..3bef540 100644 --- a/landmarks/patches.jl +++ b/landmarks/patches.jl @@ -125,6 +125,68 @@ function LinearAlgebra.naivesub!(At::Adjoint{<:Any,<:LowerTriangular}, b::Abstra x end +function LinearAlgebra.naivesub!(At::Adjoint{<:Any,<:LowerTriangular}, B::AbstractMatrix, X::AbstractMatrix = B) + A = At.parent + n = size(A, 2) + if !(n == size(B,1) == size(B,2) == size(X,1) == size(X,2)) + throw(DimensionMismatch()) + end + @inbounds for k in 1:n + for j in n:-1:1 + iszero(A.data[j,j]) && throw(SingularException(j)) + xjk = X[j,k] = A.data[j,j] \ B[j,k] + for i in j-1:-1:1 # counterintuitively 1:j-1 performs slightly better + B[i,k] -= A.data[j,i] * xjk + end + end + end + X +end + +function LinearAlgebra.naivesub!(A::LowerTriangular, B::AbstractMatrix, X::AbstractMatrix = B) + n = size(A,2) + if !(n == size(B,1) == size(X,1)) + throw(DimensionMismatch()) + end + if !(size(B,2) == size(X,2)) + throw(DimensionMismatch()) + end + + + @inbounds for k in 1:size(B,2) + for j in 1:n + iszero(A.data[j,j]) && throw(SingularException(j)) + xjk = X[j,k] = A.data[j,j] \ B[j,k] + for i in j+1:n + B[i,k] -= A.data[i,j] * xjk + end + end + end + X +end + + +function LinearAlgebra.naivesub!(A::UpperTriangular, B::AbstractMatrix, X::AbstractMatrix = B) + n = size(A, 2) + if !(n == size(B,1) == size(X,1)) + throw(DimensionMismatch()) + end + if !(size(B,2) == size(X,2)) + throw(DimensionMismatch()) + end + + @inbounds for k in 1:size(B, 2) + for j in n:-1:1 + iszero(A.data[j,j]) && throw(SingularException(j)) + xjk = X[j,k] = A.data[j,j] \ B[j,k] + for i in j-1:-1:1 # counterintuitively 1:j-1 performs slightly better + B[i,k] -= A.data[i,j] * xjk + end + end + end + X +end + function lyapunovpsdbackward_step!(t, dt, Paux,Hend⁺,H⁺) B = Matrix(Bridge.B(t - dt/2, Paux)) ϕ = (I + 1/2*dt*B)\(I - 1/2*dt*B) From c1030ce084e432e6f57296b61f36da108da7b364 Mon Sep 17 00:00:00 2001 From: mschauer Date: Thu, 2 May 2019 19:15:40 +0200 Subject: [PATCH 21/58] First try MS model --- landmarks/forward.jl | 18 +++++++++++------- landmarks/guiding.jl | 5 +++-- landmarks/models.jl | 24 ++++++++++++------------ landmarks/state.jl | 15 ++++++++++----- 4 files changed, 36 insertions(+), 26 deletions(-) diff --git a/landmarks/forward.jl b/landmarks/forward.jl index 4c2266c..b96a753 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -16,7 +16,7 @@ using Base.Iterators using SparseArrays models = [:ms, :ahs] -model = models[2] +model = models[1] TEST = false#true discrmethods = [:ralston, :lowrank, :psd, :lm, :marcin] # not a good name anymore @@ -29,16 +29,17 @@ obsscheme = obsschemes[2] const d = 2 const itostrat=true -n = 10 # nr of landmarks +n = 20 # nr of landmarks ldim = 40 # dimension of low-rank approximation to H\^+ cheat = false #true#false # if cheat is true, then we initialise at x0 (true value) and # construct the guiding term based on xT (true value) -θ = -π/6# π/6 0#π/5 # angle to rotate endpoint +θ = 0.0 #-π/6# π/6 0#π/5 # angle to rotate endpoint + ϵ = 10.0^(-4) # parameter for initialising Hend⁺ -σobs = 10.0^(-3) # noise on observations +σobs = 10.0^(-2) # noise on observations println(model) println(discrmethod) @@ -294,10 +295,13 @@ end let x = deepvec(xinit) - ϵ = 1e-5 - for i in 1:100 + # only optimize momenta + mask = deepvec(State( 0*xinit.q, 1 .- 0*(xinit.q))) + ϵ = 1.5 + + for i in 1:1000 ∇x = ForwardDiff.gradient(obj, x) - x .+= ϵ*∇x + x .+= ϵ*mask.*∇x println(deepvec2state(x-deepvec(X.yy[1]))) end end diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index 2a6e696..ed24f13 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -106,7 +106,8 @@ function bucybackwards!(S::R3!, t, νt, H⁺t, Ht, Paux, ν, H⁺, C) F = Ht[i+1]*νt[i+1] C += -dot(Bridge.β(t, Paux),F)*dt C += - 0.5*dot(F, Bridge.a(t, Paux)*F)*dt - C += -0.5*tr(tr(Ht[i+1]*Bridge.a(t, Paux)))*dt + C += -0.5*tr(tr(Ht[i+1]*Matrix(Bridge.a(t, Paux))))*dt + # FIXME converting to full end νt[1], H⁺t[1], Ht[1], C end @@ -233,7 +234,7 @@ function llikelihood(::LeftRule, Xcirc::SamplePath{State{Pnt}}, Q::GuidedProposa σt!(s, x, rout, srout, target(Q)) σt!(s, x, rout, strout, auxiliary(Q)) - + error("NOT IMPLEMENTED YET") #Δa = Bridge.a(s, x, target(Q)) - Bridge.a(s, auxiliary(Q)) #H = Bridge.H((i,s), x, auxiliary(Q)) # som -= 0.5*tr(Δa*H) * dt diff --git a/landmarks/models.jl b/landmarks/models.jl index 06f0e98..45db3cd 100644 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -142,7 +142,7 @@ function Bridge.b!(t, x, out, P::Landmarks) out.p[i] += -dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) end if itostrat - global ui = zero(Unc) + global ui = zero(Unc{Float64}) for k in 1:length(P.nfs) nf = P.nfs[k] ui += 0.5 * nf.τ^(-2) * diagm(0 =>nf.λ.^2) * K̄(q(x,i)-nf.δ,nf.τ)^2 @@ -183,7 +183,7 @@ function Bridge.b!(t, x, out, Paux::LandmarksAux) # out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) # -0.5* dot(p(P.xT,i), p(P.xT,j)) * ∇kernel(q(x,i) - q(x,j),q(P.xT,i) - q(P.xT,j), P) if itostrat - global ui = zero(Unc) + global ui = zero(Unc{Float64}) for k in 1:length(P.nfs) nf = P.nfs[k] ui = 0.5 * nf.τ^(-2) * diagm(0 =>nf.λ.^2) * K̄(q(Paux.xT,i)-nf.δ,nf.τ)^2 @@ -202,17 +202,17 @@ Compute tildeB(t) for landmarks auxiliary process function Bridge.B(t, Paux::MarslandShardlowAux) Iind = Int[] Jind = Int[] - X = Unc[] + X = Unc{Float64}[] for i in 1:Paux.n for j in 1:Paux.n # terms for out.q[i] push!(Iind, 2i - 1) push!(Jind, 2j) - push!(X, kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc)) + push!(X, kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc{Float64})) push!(Iind,2i) push!(Jind,2j) - push!(X, -Paux.λ*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)) + push!(X, -Paux.λ*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc{Float64})) end end sparse(Iind, Jind, X, 2Paux.n, 2Paux.n) @@ -224,19 +224,19 @@ Compute tildeB(t) for landmarks auxiliary process function Bridge.B(t, Paux::LandmarksAux) Iind = Int[] Jind = Int[] - X = Unc[] + X = Unc{Float64}[] for i in 1:Paux.n for j in 1:Paux.n # terms for out.q[i] push!(Iind, 2i - 1) push!(Jind, 2j) - push!(X, kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc)) + push!(X, kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc{Float64})) if itostrat - global out1 = zero(Unc) + global out1 = zero(Unc{Float64}) for k in 1:length(Paux.nfs) nf = P.nfs[k] - out1 -= 0.5 * nf.τ^(-2) * Unc(diagm(0 =>nf.λ.^2)) * K̄(q(Paux.xT,i)-nf.δ,nf.τ)^2 + out1 -= 0.5 * nf.τ^(-2) * Unc{Float64}(diagm(0 =>nf.λ.^2)) * K̄(q(Paux.xT,i)-nf.δ,nf.τ)^2 end push!(Iind, 2i - 1) push!(Jind, 2j - 1) @@ -270,7 +270,7 @@ function Bridge.B!(t,X,out, Paux::MarslandShardlowAux) for k in 1:2Paux.n # loop over all columns for j in 1:Paux.n out[2i-1,k] += kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*X[p(j), k] #*one(Unc) - out[2i,k] += -Paux.λ*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)*X[p(j), k] #*one(Unc) + out[2i,k] += -Paux.λ*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc{Float64})*X[p(j), k] #*one(Unc) # if j==i # out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * # kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) @@ -398,11 +398,11 @@ Returns matrix a(t) for Marsland-Shardlow model """ function Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) I = Int[] - X = Unc[] + X = Unc{Float64}[] γ2 = P.γ^2 for i in 1:P.n push!(I, 2i) - push!(X, γ2*one(Unc)) + push!(X, γ2*one(Unc{Float64})) end sparse(I, I, X, 2P.n, 2P.n) end diff --git a/landmarks/state.jl b/landmarks/state.jl index c22abb0..ef6dd85 100644 --- a/landmarks/state.jl +++ b/landmarks/state.jl @@ -98,8 +98,8 @@ deepvec(x::Vector) = collect(flatten(x)) # matrix multiplication of mat of Uncs -function Base.:*(A::AbstractArray{Unc,2},B::AbstractArray{Unc,2}) - C = zeros(Unc,size(A,1), size(B,2)) +function Base.:*(A::AbstractArray{Unc{T},2},B::AbstractArray{Unc{T},2}) where {T} + C = zeros(Unc{T},size(A,1), size(B,2)) for i in 1:size(A,1) for j in 1:size(B,2) for k in 1:size(A,2) @@ -136,11 +136,16 @@ end # end -function Base.:*(A::Array{<:Unc,2}, x::State) +function Base.:*(A::AbstractArray{<:Unc,2}, x::State) vecofpoints2state(A*vec(x)) end - - +function Base.:*(A::SparseMatrixCSC, x_::State) + #vecofpoints2state(Array(A)*vec(x)) + x = vec(x_) + vecofpoints2state(mul!(similar(x, A.m), A, x, true, false)) +end +#mul!(similar(x, Tx, A.m), A, x, true, false) +#Base.setindex!(A::SparseMatrixCSC{T}, _v::T, _i::Integer, _j::Integer) where {T} = SparseArrays._setindex_scalar!(A, _v, _i, _j) if TEST A = reshape(rand(Unc,6),3,2) From 43e17a1d842508b55338506227eb903fc81e6de6 Mon Sep 17 00:00:00 2001 From: mschauer Date: Thu, 2 May 2019 20:21:03 +0200 Subject: [PATCH 22/58] Bugfixes --- landmarks/forward.jl | 12 +++++++----- landmarks/guiding.jl | 9 +++++---- 2 files changed, 12 insertions(+), 9 deletions(-) diff --git a/landmarks/forward.jl b/landmarks/forward.jl index b96a753..5c7259f 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -45,8 +45,8 @@ println(model) println(discrmethod) println(obsscheme) -T = 0.2#1.0#0.5 -t = 0.0:0.01:T # time grid +T = 0.8#1.0#0.5 +t = 0.0:0.003:T # time grid #Random.seed!(5) include("state.jl") @@ -297,11 +297,13 @@ let x = deepvec(xinit) # only optimize momenta mask = deepvec(State( 0*xinit.q, 1 .- 0*(xinit.q))) - ϵ = 1.5 - + ϵ = 0.5 + o = obj(x) for i in 1:1000 + i % 10 == 0 && (o = obj(x)) ∇x = ForwardDiff.gradient(obj, x) x .+= ϵ*mask.*∇x - println(deepvec2state(x-deepvec(X.yy[1]))) + display(deepvec2state(x-deepvec(X.yy[1])).p) + println(o) end end diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index ed24f13..d1492e8 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -104,8 +104,8 @@ function bucybackwards!(S::R3!, t, νt, H⁺t, Ht, Paux, ν, H⁺, C) kernelr3!(dP!, t[i+1], H⁺t[i+1], wsH⁺, H⁺t[i], dt) Ht[i] = InverseCholesky(lchol(H⁺t[i])) F = Ht[i+1]*νt[i+1] - C += -dot(Bridge.β(t, Paux),F)*dt - C += - 0.5*dot(F, Bridge.a(t, Paux)*F)*dt + C += dot(Bridge.β(t, Paux),F)*dt + C += 0.5*dot(F, Bridge.a(t, Paux)*F)*dt C += -0.5*tr(tr(Ht[i+1]*Matrix(Bridge.a(t, Paux))))*dt # FIXME converting to full end @@ -166,7 +166,8 @@ struct GuidedProposal!{T,Ttarget,Taux,Tν,TH,TC,F} <: ContinuousTimeProcess{T} new{Bridge.valtype(target),typeof(target),typeof(aux),eltype(ν),eltype(H),typeof(C),typeof(endpoint)}(target, aux, tt, ν, H, C, endpoint) end end -Bridge.lptilde(x, Po::GuidedProposal!) = -0.5*dot(x0, Po.H[1]*x0) - 2dot(x0, Po.H[1]*Po.ν[1]) - Po.C + +Bridge.lptilde(x, Po::GuidedProposal!) = -0.5*(dot(x, Po.H[1]*x) - 2dot(x, Po.H[1]*Po.ν[1])) - Po.C function Bridge._b!((i,t), x, out, P::GuidedProposal!) @@ -221,7 +222,7 @@ function llikelihood(::LeftRule, Xcirc::SamplePath{State{Pnt}}, Q::GuidedProposa _r!((i,s), x, rout, Q) b!(s, x, bout, target(Q)) _b!((i,s), x, btout, auxiliary(Q)) -# btitilde!((s,i), x, btout, Q) + dt = tt[i+1]-tt[i] #dump(som) som += dot(bout-btout, rout) * dt From 142954b72981a4889191876afaedb82d6fcf21b5 Mon Sep 17 00:00:00 2001 From: mschauer Date: Thu, 2 May 2019 20:49:05 +0200 Subject: [PATCH 23/58] For today --- landmarks/forward.jl | 13 +++++++------ landmarks/guiding.jl | 2 +- 2 files changed, 8 insertions(+), 7 deletions(-) diff --git a/landmarks/forward.jl b/landmarks/forward.jl index 5c7259f..e3234b0 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -29,7 +29,7 @@ obsscheme = obsschemes[2] const d = 2 const itostrat=true -n = 20 # nr of landmarks +n = 10 # nr of landmarks ldim = 40 # dimension of low-rank approximation to H\^+ cheat = false #true#false # if cheat is true, then we initialise at x0 (true value) and @@ -294,16 +294,17 @@ function obj(xinitv) end let - x = deepvec(xinit) + x = deepvec(x0) + x = x .* (1 .+ 0.2*randn(length(x))) # only optimize momenta - mask = deepvec(State( 0*xinit.q, 1 .- 0*(xinit.q))) - ϵ = 0.5 + mask = deepvec(State(1 .- 0*xinit.q, 1 .- 0*(xinit.q))) + ϵ = 1.2e-4 o = obj(x) for i in 1:1000 i % 10 == 0 && (o = obj(x)) ∇x = ForwardDiff.gradient(obj, x) x .+= ϵ*mask.*∇x - display(deepvec2state(x-deepvec(X.yy[1])).p) - println(o) + display(deepvec2state(x-deepvec(x0))) + println("d(x,xtrue) = ", norm(deepvec(x0)-x), " ", o) end end diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index d1492e8..798e753 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -79,7 +79,7 @@ function dP!(t, p, out, P::Union{LandmarksAux, MarslandShardlowAux}) out .= out .+ out' - a(t, P) out end - + # """ # Make a 4-tuple where each tuple contains a copy of y # """ From 4525bd8c395fe7bc2b050ae26b9301a69eed92d3 Mon Sep 17 00:00:00 2001 From: mschauer Date: Fri, 3 May 2019 00:03:30 +0200 Subject: [PATCH 24/58] Create video --- landmarks/forward.jl | 50 ++++++++++++++++++++++++++++++-------------- landmarks/guiding.jl | 12 ++++++----- 2 files changed, 41 insertions(+), 21 deletions(-) diff --git a/landmarks/forward.jl b/landmarks/forward.jl index e3234b0..f606171 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -29,7 +29,7 @@ obsscheme = obsschemes[2] const d = 2 const itostrat=true -n = 10 # nr of landmarks +n = 40 # nr of landmarks ldim = 40 # dimension of low-rank approximation to H\^+ cheat = false #true#false # if cheat is true, then we initialise at x0 (true value) and @@ -45,10 +45,10 @@ println(model) println(discrmethod) println(obsscheme) -T = 0.8#1.0#0.5 -t = 0.0:0.003:T # time grid +T = 0.4#1.0#0.5 +t = 0.0:0.01:T # time grid -#Random.seed!(5) +Random.seed!(5) include("state.jl") include("models.jl") include("patches.jl") @@ -239,11 +239,11 @@ else # careful, not a state - νstart , Hstart⁺, C = gpupdate(ν , H⁺, C, Σ, L, v0) + νstart , Hstart⁺, Cstart = gpupdate(ν , H⁺, C, Σ, L, v0) #also update C?? - Q = GuidedProposal!(P, Paux, tt_, νt, Ht, C) + Q = GuidedProposal!(P, Paux, tt_, νt, Ht, νstart, InverseCholesky(lchol(Hstart⁺)), Cstart) xinit = cheat ? x0 : State(νstart.q, 0νstart.q)#νstart # or xinit ~ N(νstart, Hstart⁺) @@ -292,19 +292,37 @@ function obj(xinitv) XXᵒ = Bridge.solve(EulerMaruyama!(), xinit, WW, Q) lptilde(xinit, Q) + llikelihood(LeftRule(), XXᵒ, Q; skip = 1) end - +using Makie, Random +Random.seed!(2) let x = deepvec(x0) - x = x .* (1 .+ 0.2*randn(length(x))) + #x = deepvec(State(x0.q, 0.5 * x0.p)) + x = x .* (1 .+ 1*randn(length(x))) + s = deepvec2state(x) + + n = Node(s.q) + n2 = Node(s.p) + sc = scatter(x0.q, color=:red) + + scatter!(sc, n2) + scatter!(sc, n, color=:blue) + display(sc) + # only optimize momenta - mask = deepvec(State(1 .- 0*xinit.q, 1 .- 0*(xinit.q))) - ϵ = 1.2e-4 + mask = deepvec(State(1 .- 0*xinit.q, 20 .- 0*(xinit.p))) + ϵ = 6.e-6 o = obj(x) - for i in 1:1000 - i % 10 == 0 && (o = obj(x)) - ∇x = ForwardDiff.gradient(obj, x) - x .+= ϵ*mask.*∇x - display(deepvec2state(x-deepvec(x0))) - println("d(x,xtrue) = ", norm(deepvec(x0)-x), " ", o) + #for i in 1:1000 + record(sc, "output/gradientdescent.mp4", 1:100) do i + #i % 10 == 0 && (o = obj(x)) + for k in 1:4 + ∇x = ForwardDiff.gradient(obj, x) + x .+= ϵ*mask.*∇x + end + s = deepvec2state(x) + n[] = s.q + n2[] = s.p + display(s-x0) + println("$i d(x,xtrue) = ", norm(deepvec(x0)-x))#, " ", o) end end diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index 798e753..e99ba27 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -79,7 +79,7 @@ function dP!(t, p, out, P::Union{LandmarksAux, MarslandShardlowAux}) out .= out .+ out' - a(t, P) out end - + # """ # Make a 4-tuple where each tuple contains a copy of y # """ @@ -158,16 +158,18 @@ struct GuidedProposal!{T,Ttarget,Taux,Tν,TH,TC,F} <: ContinuousTimeProcess{T} tt::Vector{Float64} # grid of time points on single segment (S,T] ν::Vector{Tν} H::Vector{TH} - C::TC + ν0::Tν + H0::TH + C0::TC endpoint::F - function GuidedProposal!(target, aux, tt_, ν, H, C, endpoint=Bridge.endpoint) + function GuidedProposal!(target, aux, tt_, ν, H, ν0, H0, C0, endpoint=Bridge.endpoint) tt = collect(tt_) - new{Bridge.valtype(target),typeof(target),typeof(aux),eltype(ν),eltype(H),typeof(C),typeof(endpoint)}(target, aux, tt, ν, H, C, endpoint) + new{Bridge.valtype(target),typeof(target),typeof(aux),eltype(ν),eltype(H),typeof(C),typeof(endpoint)}(target, aux, tt, ν, H, ν0, H0, C0, endpoint) end end -Bridge.lptilde(x, Po::GuidedProposal!) = -0.5*(dot(x, Po.H[1]*x) - 2dot(x, Po.H[1]*Po.ν[1])) - Po.C +Bridge.lptilde(x, Po::GuidedProposal!) = -0.5*(dot(x, Po.H0*x) - 2dot(x, Po.H0*Po.ν0)) - Po.C0 function Bridge._b!((i,t), x, out, P::GuidedProposal!) From 52eebc189f180220286c86951596b2a16cb11026 Mon Sep 17 00:00:00 2001 From: fmeulen Date: Fri, 3 May 2019 13:32:21 +0200 Subject: [PATCH 25/58] added lowrank functionality for computing tilde-a in backward recursion --- landmarks/lmguiding.jl | 25 +++++++++++++++++++------ 1 file changed, 19 insertions(+), 6 deletions(-) diff --git a/landmarks/lmguiding.jl b/landmarks/lmguiding.jl index e63b365..0d0a293 100644 --- a/landmarks/lmguiding.jl +++ b/landmarks/lmguiding.jl @@ -26,14 +26,26 @@ end struct Lm end function guidingbackwards!(::Lm, t, (Lt, Mt⁺, μt), Paux, (Lend, Mend⁺, μend)) - Mt⁺[end], Lt[end] = Σ, L + Mt⁺[end] .= Σ + Lt[end] .= L BB = Matrix(Bridge.B(0, Paux)) # does not depend on time - aa = Matrix(Bridge.a(0, Paux)) # does not depend on time + println("computing ã and its low rank approximation:") + # various ways to compute ã (which does not depend on time); + # low rank appoximation really makes sense here +# @time aa = Matrix(Bridge.a(0, Paux)) # vanilla, no lr approx +# @time aalr = pheigfact(deepmat(Matrix(Bridge.a(0, Paux)))) # low rank approx default +# @time aalr = pheigfact(deepmat(Matrix(Bridge.a(0, Paux))),rank=400) # fix rank + @time aalr = pheigfact(deepmat(Matrix(Bridge.a(0, Paux))), rtol=1e-7) # control accuracy of lr approx + println("Rank ",size(aalr[:vectors],2), " approximation to ã") + sqrt_aalr = deepmat2unc(aalr[:vectors] * diagm(0=> sqrt.(aalr[:values]))) + β = vec(Bridge.β(0,Paux)) # does not depend on time for i in length(t)-1:-1:1 dt = t[i+1]-t[i] - Lt[i] .= Lt[i+1] * (I + BB * dt) - Mt⁺[i] .= Mt⁺[i+1] + Lt[i+1]* aa * Matrix(Lt[i+1]') * dt +# Lt[i] .= Lt[i+1] * (I + BB * dt) # explicit + Lt[i] .= Lt[i+1]/(I - dt* BB) # implicit, similar computational cost +# Mt⁺[i] .= Mt⁺[i+1] + Lt[i+1]* aa * Matrix(Lt[i+1]') * dt + Mt⁺[i] .= Mt⁺[i+1] + Bridge.outer(Lt[i+1] * sqrt_aalr) * dt μt[i] .= μt[i+1] + Lt[i+1] * β * dt end (Lt[1], Mt⁺[1], μt[1]) @@ -45,7 +57,7 @@ auxiliary(Q::GuidedProposall!) = Q.aux constdiff(Q::GuidedProposall!) = constdiff(target(Q)) && constdiff(auxiliary(Q)) -function Bridge._b!((i,t), x::State, out::State, Q::GuidedProposall!) +function _b!((i,t), x::State, out::State, Q::GuidedProposall!) Bridge.b!(t, x, out, Q.target) out .+= amul(t,x,Q.Lt[i]' * (Q.Mt[i] *(Q.xobs-Q.μt[i]-Q.Lt[i]*vec(x))),Q.target) out @@ -60,7 +72,8 @@ function _r!((i,t), x::State, out::State, Q::GuidedProposall!) end function guidingterm((i,t),x::State,Q::GuidedProposall!) - Bridge.b(t,x,Q.target) + amul(t,x,Q.Lt[i]' * (Q.Mt[i] *(Q.xobs-Q.μt[i]-Q.Lt[i]*vec(x))),Q.target) + #Bridge.b(t,x,Q.target) + + amul(t,x,Q.Lt[i]' * (Q.Mt[i] *(Q.xobs-Q.μt[i]-Q.Lt[i]*vec(x))),Q.target) end """ Returns the guiding terms a(t,x)*r̃(t,x) along the path of a guided proposal From 390c1fd90ecfce52ab967b60c8140355958907cf Mon Sep 17 00:00:00 2001 From: fmeulen Date: Fri, 3 May 2019 13:33:45 +0200 Subject: [PATCH 26/58] essentially only added 'using LowRankApprox' --- landmarks/lmpar.jl | 35 +++++++++++++++++++---------------- 1 file changed, 19 insertions(+), 16 deletions(-) diff --git a/landmarks/lmpar.jl b/landmarks/lmpar.jl index bd7a98a..98dc171 100644 --- a/landmarks/lmpar.jl +++ b/landmarks/lmpar.jl @@ -12,6 +12,7 @@ using CSV using RCall using Base.Iterators using SparseArrays +using LowRankApprox models = [:ms, :ahs] model = models[2] @@ -22,14 +23,14 @@ partialobs = true const d = 2 const itostrat = false -n = 75 # nr of landmarks +n = 100 # nr of landmarks -θ = π/3# π/6 0#π/5 # angle to rotate endpoint +θ = 2π/5# π/6 0#π/5 # angle to rotate endpoint -σobs = 10^(-3) # noise on observations +σobs = 10^(-2) # noise on observations println(model) -T = 0.3#1.0#0.5 +T = 0.75#1.0#0.5 t = 0.0:0.01:T # time grid #Random.seed!(5) @@ -43,12 +44,12 @@ include("lmguiding.jl") ### Specify landmarks models a = 3.0 # the larger, the stronger landmarks behave similarly λ = 0.0; #= not the lambda of noise fields =# γ = 8.0 -db = 3.0 # domainbound -nfstd = 1.0 # tau , widht of noisefields +db = 6.0 # domainbound +nfstd = 2.0 # tau , widht of noisefields r1 = -db:nfstd:db r2 = -db:nfstd:db nfloc = Point.(collect(product(r1, r2)))[:] -nfscales = [.05Point(1.0, 1.0) for x in nfloc] # intensity +nfscales = [.1Point(1.0, 1.0) for x in nfloc] # intensity nfs = [Noisefield(δ, λ, nfstd) for (δ, λ) in zip(nfloc, nfscales)] Pms = MarslandShardlow(a, γ, λ, n) @@ -69,7 +70,7 @@ W = SamplePath(t, [copy(w0) for s in t]) sample!(W, Wiener{Vector{StateW}}()) # specify initial landmarks configuration -q0 = [Point(2.5cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) +q0 = [Point(2.0cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) p_ = 2*Point(-0.1, 0.1) p0 = [p_ for i in 1:n] # #p0 = [randn(Point) for i in 1:n] @@ -81,17 +82,19 @@ println("Solve for forward provess:") @time solve!(EulerMaruyama!(), X, x0, W, P) #@time solve!(StratonovichHeun!(), X, x0, W, P) -tc(t,T) = t.*(2-t/T) +tc(t,T) = t.* (2 .-t/T) tt_ = tc(t,T)#tc(t,T)# 0:dtimp:(T) - +#tt_ = t # observe positions without noise v0 = q(X.yy[1]) -rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) -vT = [rot * X.yy[end].q[i] for i in 1:P.n ] +rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), 2*cos(θ)) +#vT = [rot * X.yy[end].q[i] for i in 1:P.n ] +trans = SMatrix{2,2}(1.5, 1.0, 0.0, 1.0) +vT = [rot * trans * X.yy[end].q[i] for i in 1:P.n ] + -#extractcomp(v,i) = map(x->x[i], v) #################### # solve backward recursion on [0,T] if partialobs==true @@ -100,9 +103,9 @@ if partialobs==true #Σ = 10 * reshape(rand(Unc,n^2),n,n) μend = zeros(Point,P.n) xobs = vT - Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) - Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) - #Pahsaux = LandmarksAux(Pahs, State(vT, 10*rand(Point,Pahs.n))) + mT = zero(vT)#rand(Point, n)# + Pahsaux = LandmarksAux(Pahs, State(vT, mT)) + Pmsaux = MarslandShardlowAux(Pms, State(vT, mT)) else # full observation case L = [(i==j)*one(Unc) for i in 1:2n, j in 1:2n] From 2825f0d33140552d10756135554f81739822c8b9 Mon Sep 17 00:00:00 2001 From: fmeulen Date: Fri, 3 May 2019 13:34:41 +0200 Subject: [PATCH 27/58] speed up computing a(t,x) by using that it is symmetric --- landmarks/models.jl | 28 +++++++++++++++++++++++++++- 1 file changed, 27 insertions(+), 1 deletion(-) diff --git a/landmarks/models.jl b/landmarks/models.jl index 009a4ed..33cff93 100644 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -386,6 +386,26 @@ end Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P) +# function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) +# if P isa Landmarks +# x = x_ +# else +# x = P.xT +# end +# out = zeros(Unc,2P.n,2P.n) +# for i in 1:P.n +# for k in 1:P.n +# for j in 1:length(P.nfs) +# out[2i-1,2k-1] += σq(q(x,i),P.nfs[j]) * σq(q(x, k),P.nfs[j])' +# out[2i-1,2k] += σq(q(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' +# out[2i,2k-1] += σp(q(x,i),p(x,i),P.nfs[j]) * σq(q(x,k),P.nfs[j])' +# out[2i,2k] += σp(q(x,i),p(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' +# end +# end +# end +# out +# end + function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) if P isa Landmarks x = x_ @@ -394,18 +414,24 @@ function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) end out = zeros(Unc,2P.n,2P.n) for i in 1:P.n - for k in 1:P.n + for k in i:P.n for j in 1:length(P.nfs) out[2i-1,2k-1] += σq(q(x,i),P.nfs[j]) * σq(q(x, k),P.nfs[j])' out[2i-1,2k] += σq(q(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' out[2i,2k-1] += σp(q(x,i),p(x,i),P.nfs[j]) * σq(q(x,k),P.nfs[j])' out[2i,2k] += σp(q(x,i),p(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' end + end + end + for i in 2:2P.n + for k in 1:i-1 + out[i,k] = out[k,i] end end out end + Bridge.a(t, P::LandmarksAux) = Bridge.a(t, 0, P) #Bridge.a(t, P::Union{Landmarks,LandmarksAux}) = Bridge.a(t, P.xT, P::Union{Landmarks,LandmarksAux}) From 61121f057f88ce2f1c77b04e49e489ef7bbc5401 Mon Sep 17 00:00:00 2001 From: mschauer Date: Tue, 7 May 2019 13:51:23 +0200 Subject: [PATCH 28/58] New Pkg ecosystem --- Manifest.toml | 259 ++++++++++++++++++++++++++++++++++++++++++++++++++ Project.toml | 31 ++++++ REQUIRE | 3 +- 3 files changed, 292 insertions(+), 1 deletion(-) create mode 100644 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["Rmath", "SpecialFunctions", "Test"] +git-tree-sha1 = "b3a4e86aa13c732b8a8c0ba0c3d3264f55e6bb3e" +uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c" +version = "0.8.0" + +[[SuiteSparse]] +deps = ["Libdl", "LinearAlgebra", "SparseArrays"] +uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9" + +[[TableTraits]] +deps = ["IteratorInterfaceExtensions"] +git-tree-sha1 = "b1ad568ba658d8cbb3b892ed5380a6f3e781a81e" +uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c" +version = "1.0.0" + +[[Tables]] +deps = ["IteratorInterfaceExtensions", "LinearAlgebra", "Requires", "TableTraits", "Test"] +git-tree-sha1 = "9e748316f5aa7b7753c90de612ef98fe8b0ea297" +uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c" +version = "0.2.1" + +[[Test]] +deps = ["Distributed", "InteractiveUtils", "Logging", "Random"] +uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" + +[[Trajectories]] +deps = ["RecipesBase", "Tables", "Test"] +git-tree-sha1 = "12e44c9a3517570935b14f9e3969fe2134cafff2" +uuid = "2c80a279-213e-54d7-a557-e9a14725db56" +version = "0.1.0" + +[[URIParser]] +deps = ["Test", "Unicode"] +git-tree-sha1 = "6ddf8244220dfda2f17539fa8c9de20d6c575b69" +uuid = "30578b45-9adc-5946-b283-645ec420af67" +version = "0.4.0" + +[[UUIDs]] +deps = ["Random", "SHA"] +uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" + +[[Unicode]] +uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" diff --git a/Project.toml b/Project.toml new file mode 100644 index 0000000..451e9b0 --- /dev/null +++ b/Project.toml @@ -0,0 +1,31 @@ +name = "Bridge" +uuid = "2d3116d5-4b8f-5680-861c-71f149790274" +authors = ["Moritz Schauer "] +version = "0.10.0 + +[deps] +Colors = "5ae59095-9a9b-59fe-a467-6f913c188581" +DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab" +Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +Polynomials = "f27b6e38-b328-58d1-80ce-0feddd5e7a45" +Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01" +SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" +StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" +Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" +SuiteSparse = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9" +Trajectories = "2c80a279-213e-54d7-a557-e9a14725db56" + +[compat] +julia = "≥ 0.7.0" + +[extras] +Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" +Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" + +[targets] +test = ["Statistics", "Documenter", "LinearAlgebra", "Test", "Random"] diff --git a/REQUIRE b/REQUIRE index 9728097..acf984c 100644 --- a/REQUIRE +++ b/REQUIRE @@ -3,4 +3,5 @@ Polynomials Distributions StaticArrays RecipesBase -Colors \ No newline at end of file +Colors +Trajectories From 780bb2f81d346e549f6af1dd9f53ce5b7bcb418d Mon Sep 17 00:00:00 2001 From: mschauer Date: Tue, 7 May 2019 13:56:55 +0200 Subject: [PATCH 29/58] Fix likelihoods --- landmarks/forward.jl | 39 +++++++++++++++++++++++---------------- landmarks/guiding.jl | 38 ++++++++++++++++++++++++++------------ landmarks/models.jl | 21 +++++++++++++++------ landmarks/state.jl | 2 +- src/Bridge.jl | 2 +- src/partialbridgen!.jl | 24 ++++++++++++++++++++++-- 6 files changed, 88 insertions(+), 38 deletions(-) diff --git a/landmarks/forward.jl b/landmarks/forward.jl index f606171..5068616 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -14,9 +14,10 @@ using CSV using RCall using Base.Iterators using SparseArrays +using Trajectories models = [:ms, :ahs] -model = models[1] +model = models[2] TEST = false#true discrmethods = [:ralston, :lowrank, :psd, :lm, :marcin] # not a good name anymore @@ -29,7 +30,7 @@ obsscheme = obsschemes[2] const d = 2 const itostrat=true -n = 40 # nr of landmarks +n = 5 # nr of landmarks ldim = 40 # dimension of low-rank approximation to H\^+ cheat = false #true#false # if cheat is true, then we initialise at x0 (true value) and @@ -63,8 +64,8 @@ using .LowrankRiccati ### Specify landmarks models a = 3.0 # the larger, the stronger landmarks behave similarly -λ = 0.0; #= not the lambda of noise fields =# -γ = 8.0 +λ = 0.0 # not the lambda of noise fields, but the mean reversion +γ = 1.0 db = 3.0 # domainbound nfstd = .5 # tau , widht of noisefields r1 = -db:nfstd:db @@ -88,7 +89,7 @@ end # specify initial landmarks configuration q0 = [PointF(2.5cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) -p_ = 5*PointF(0.1, 0.1) +p_ = 10*PointF(0.1, 0.1) p0 = [p_ for i in 1:n] # #p0 = [randn(PointF) for i in 1:n] x0 = State(q0, p0) @@ -118,7 +119,8 @@ if obsscheme==:partial # observe positions v0 = q(X.yy[1]) + σobs * randn(PointF,n) rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) - vT = [rot * X.yy[end].q[i] + σobs * randn(d) for i in 1:P.n ] + shft = 0. + vT = [shft .+ rot * X.yy[end].q[i] + σobs * randn(d) for i in 1:P.n ] Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) if cheat @@ -160,7 +162,7 @@ else if obsscheme == :partial #νT = State(zero(vT), zero(vT)) - νT = State(randn(PointF,Pahs.n), randn(PointF,Pahs.n)) + νT = State(randn(PointF,Pahs.n), 0randn(PointF,Pahs.n)) elseif obsscheme == :full νT = X.yy[end] end @@ -290,16 +292,20 @@ function obj(xinitv) xinit = deepvec2state(xinitv) sample!(WW, Wiener{Vector{StateW}}()) XXᵒ = Bridge.solve(EulerMaruyama!(), xinit, WW, Q) - lptilde(xinit, Q) + llikelihood(LeftRule(), XXᵒ, Q; skip = 1) + ( + (lptilde(xinit, Q) - lptilde(x0, Q)) + llikelihood(LeftRule(), XXᵒ, Q; skip = 1) + ) end using Makie, Random Random.seed!(2) let x = deepvec(x0) #x = deepvec(State(x0.q, 0.5 * x0.p)) - x = x .* (1 .+ 1*randn(length(x))) - s = deepvec2state(x) + x = x .* (1 .+ 0.2*randn(length(x))) + + x = deepvec(State(x0.q, deepvec2state(x).p)) + s = deepvec2state(x) n = Node(s.q) n2 = Node(s.p) sc = scatter(x0.q, color=:red) @@ -309,13 +315,14 @@ let display(sc) # only optimize momenta - mask = deepvec(State(1 .- 0*xinit.q, 20 .- 0*(xinit.p))) - ϵ = 6.e-6 - o = obj(x) - #for i in 1:1000 - record(sc, "output/gradientdescent.mp4", 1:100) do i + mask = deepvec(State(0 .- 0*xinit.q, 1 .- 0*(xinit.p))) + ϵ = 6.e-4 + @show o = obj(x) + + for i in 1:1000 + #record(sc, "output/gradientdescent.mp4", 1:100) do i #i % 10 == 0 && (o = obj(x)) - for k in 1:4 + for k in 1:1 ∇x = ForwardDiff.gradient(obj, x) x .+= ϵ*mask.*∇x end diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index e99ba27..1fabd5c 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -230,20 +230,34 @@ function llikelihood(::LeftRule, Xcirc::SamplePath{State{Pnt}}, Q::GuidedProposa som += dot(bout-btout, rout) * dt if !constdiff(Q) - #Δa = a((i,s), x, target(Q)) - a((i,s), x, auxiliary(Q)) - # H = H((i,s), x, auxiliary(Q)) - # som -= 0.5*tr(Δa*H) * dt - # som += 0.5*(rout'*Δa*rout) * dt - σt!(s, x, rout, srout, target(Q)) σt!(s, x, rout, strout, auxiliary(Q)) - error("NOT IMPLEMENTED YET") - #Δa = Bridge.a(s, x, target(Q)) - Bridge.a(s, auxiliary(Q)) - #H = Bridge.H((i,s), x, auxiliary(Q)) - # som -= 0.5*tr(Δa*H) * dt - #som += 0.5*dot(rout,Δa*rout) * dt - som += 0.5*Bridge.inner(srout) * dt - som -= 0.5*Bridge.inner(strout) * dt + + som += 0.5*Bridge.inner(srout) * dt + som -= 0.5*Bridge.inner(strout) * dt + + A = Bridge.a((i,s), x, target(Q)) + At = Bridge.a((i,s), x, auxiliary(Q)) + som -= 0.5*hadamtrace(A, Q.H[i]) * dt + som -= -0.5*hadamtrace(At, Q.H[i]) * dt + + end + end + som +end + +function hadamtrace(A, H::InverseCholesky) + tr(tr(H*A)) +end + + +function hadamtrace(A, H) + @assert eachindex(A) == eachindex(H) + Trajectories.@unroll1 for i in eachindex(A) + if $first + som = A[i]*H[i] + else + som += A[i]*H[i] end end som diff --git a/landmarks/models.jl b/landmarks/models.jl index 45db3cd..6b608a8 100644 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -416,17 +416,26 @@ function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) else x = P.xT end - out = zeros(Unc{Float64}, 2P.n,2P.n) + out = zeros(Unc{deepeltype(x)}, 2P.n,2P.n) for i in 1:P.n - for k in 1:P.n + for k in i:P.n for j in 1:length(P.nfs) - out[2i-1,2k-1] += σq(q(x,i),P.nfs[j]) * σq(q(x, k),P.nfs[j])' - out[2i-1,2k] += σq(q(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' - out[2i,2k-1] += σp(q(x,i),p(x,i),P.nfs[j]) * σq(q(x,k),P.nfs[j])' - out[2i,2k] += σp(q(x,i),p(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' + a11 = σq(q(x,i),P.nfs[j]) + a21 = σp(q(x,i),p(x,i),P.nfs[j]) + a12 = σq(q(x,k),P.nfs[j]) + a22 = σp(q(x,k),p(x,k),P.nfs[j]) + out[2i-1,2k-1] += a11 * a12' + out[2i-1,2k] += a11 * a22' + out[2i,2k-1] += a21 * a12' + out[2i,2k] += a21 * a22' end end end + for i in 2:2P.n + for k in 1:i-1 + out[i,k] = out[k,i] + end + end out end diff --git a/landmarks/state.jl b/landmarks/state.jl index ef6dd85..086e6e4 100644 --- a/landmarks/state.jl +++ b/landmarks/state.jl @@ -41,7 +41,7 @@ function copyto!(x::State, y) end x end -#eltype(::State{P}) = P +deepeltype(::State{P}) where {P} = eltype(P) Base.broadcastable(x::State) = x diff --git a/src/Bridge.jl b/src/Bridge.jl index f863a7f..9e7a104 100644 --- a/src/Bridge.jl +++ b/src/Bridge.jl @@ -42,7 +42,7 @@ include("chol.jl") using StaticArrays using Distributions using Colors - +using Trajectories diff --git a/src/partialbridgen!.jl b/src/partialbridgen!.jl index f2691f2..92df56d 100644 --- a/src/partialbridgen!.jl +++ b/src/partialbridgen!.jl @@ -69,6 +69,10 @@ function rti!((t,i), x, out, P::PartialBridge!) out end +function Hi((t,i), P::PartialBridge!) + P.H[i] +end + btitilde!((t,i), x, out, P) = _b!((t,i), x, out, P.Pt) constdiff(P::PartialBridge!) = constdiff(P.Target) && constdiff(P.Pt) @@ -92,9 +96,25 @@ function llikelihood(::LeftRule, Xcirc::SamplePath, Po::PartialBridge!; skip = 0 som += dot(bout, rout) * (tt[i+1]-tt[i]) som -= dot(btout, rout) * (tt[i+1]-tt[i]) - if !constdiff(Po) - error("not implemented") + if !constdiff(Po) # todo: write test + H = Bridge.Hi((i,s), Po) + A = Bridge.a((i,s), x, target(Po)) + At = Bridge.a((i,s), x, auxiliary(Po)) + som -= 0.5*hadamtrace(A, H) * (tt[i+1]-tt[i]) + som += 0.5*hadamtrace(At, H) * (tt[i+1]-tt[i]) + som += 0.5*( r'*(A-At)*r ) * (tt[i+1]-tt[i]) end end som end +function hadamtrace(A, H) + @assert eachindex(A) == eachindex(H) + Trajectories.@unroll1 for i in eachindex(A) + if $first + som = A[i]*H[i] + else + som += A[i]*H[i] + end + end + som +end From f1e43409c51186cd1b2f6e75f1f54585a3df08ac Mon Sep 17 00:00:00 2001 From: mschauer Date: Tue, 7 May 2019 14:02:05 +0200 Subject: [PATCH 30/58] Fix lmpar --- landmarks/lmpar.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/landmarks/lmpar.jl b/landmarks/lmpar.jl index bd7a98a..3f1125d 100644 --- a/landmarks/lmpar.jl +++ b/landmarks/lmpar.jl @@ -1,6 +1,6 @@ # reminder, to type H*, do H\^+ #outdir="output/landmarks/" -cd("/Users/Frank/.julia/dev/Bridge/landmarks") +#cd("/Users/Frank/.julia/dev/Bridge/landmarks") using Bridge, StaticArrays, Distributions using Bridge:logpdfnormal @@ -82,7 +82,7 @@ println("Solve for forward provess:") #@time solve!(StratonovichHeun!(), X, x0, W, P) tc(t,T) = t.*(2-t/T) -tt_ = tc(t,T)#tc(t,T)# 0:dtimp:(T) +tt_ = tc.(t,T)#tc(t,T)# 0:dtimp:(T) # observe positions without noise From adbe2d7195e769aa2c1290cd9b402d51d7918231 Mon Sep 17 00:00:00 2001 From: mschauer Date: Tue, 7 May 2019 14:05:09 +0200 Subject: [PATCH 31/58] Fix --- Project.toml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Project.toml b/Project.toml index 451e9b0..1632a2c 100644 --- a/Project.toml +++ b/Project.toml @@ -1,7 +1,7 @@ name = "Bridge" uuid = "2d3116d5-4b8f-5680-861c-71f149790274" authors = ["Moritz Schauer "] -version = "0.10.0 +version = "0.10.0" [deps] Colors = "5ae59095-9a9b-59fe-a467-6f913c188581" From 1ce774daf30d4eb277909ae77cc93263ea76f481 Mon Sep 17 00:00:00 2001 From: mschauer Date: Tue, 7 May 2019 14:43:44 +0200 Subject: [PATCH 32/58] Add lptilde for lm - model --- landmarks/ahsmodel.jl | 139 ----------------------------------------- landmarks/guiding.jl | 2 +- landmarks/lmguiding.jl | 14 ++++- landmarks/lmpar.jl | 82 ++++++++++++++++++++++-- 4 files changed, 89 insertions(+), 148 deletions(-) delete mode 100644 landmarks/ahsmodel.jl diff --git a/landmarks/ahsmodel.jl b/landmarks/ahsmodel.jl deleted file mode 100644 index 9750afe..0000000 --- a/landmarks/ahsmodel.jl +++ /dev/null @@ -1,139 +0,0 @@ -""" -Specify parameters for noisefield -""" -struct Noisefield - δ::Point # locations of noise field - λ::Point # scaling at noise field - τ::Float64 # std of Gaussian kernel noise field -end - -struct Landmarks{T} <: ContinuousTimeProcess{State{Point}} - a::T # kernel std - λ::T # mean reversion - n::Int64 # numer of landmarks - nfs::Vector{Noisefield} # vector containing pars of noisefields -end - -struct LandmarksAux{T} <: ContinuousTimeProcess{State{Point}} - a::T # kernel std - λ::T # mean reversion - xT::State{Point} # use x = State(P.v, zero(P.v)) where v is conditioning vector - n::Int64 # numer of landmarks - nfs::Vector{Noisefield} # vector containing pars of noisefields -end - -LandmarksAux(P::Landmarks, xT) = LandmarksAux(P.a, P.λ, xT, P.n, P.nfs) - -# kernel for noisefields -K̄(x,τ) = (2*π*τ^2)^(-d/2)*exp(-norm(x)^2/(2*τ^2)) -# gradient of kernel for noisefields -∇K̄(x,τ) = -τ^(-2) * K̄(x,τ) * x -# function for specification of diffusivity of landmarks -σq(q, nf::Noisefield) = nf.λ * K̄(q - nf.δ,nf.τ) -σp(q, p, nf::Noisefield) = -dot(p, nf.λ) * ∇K̄(q - nf.δ,nf.τ) -# ∇q_σq(q, nf::Noisefield) = nf.λ * ∇K̄(q - nf.δ,nf.τ) -# -# function Δσq(q,nf::Noisefield,α::Int64) -# out = Matrix{Float64}(undef,d,d) # would like to have Unc here -# for β in 1:d -# for γ in 1:d -# out[β, γ] = nf.τ^(-2) * nf.λ[β] * K̄(q,nf.τ) * -# (nf.τ^(-2)*q[α]*q[γ] - 2* q[α]*(α==γ) ) -# end -# end -# out -# end - -""" -Compute sigma(t,x) * dm where dm is a vector and sigma is the diffusion coefficient of landmarks -write to out which is of type State -""" -function Bridge.σ!(t, x_, dm, out, P::Union{Landmarks,LandmarksAux}) - if P isa Landmarks - x = x_ - else - x = P.xT - end - zero!(out) - for i in 1:P.n - for j in 1:length(P.nfs) - out.q[i] += σq(q(x, i), P.nfs[j]) * dm[j] - out.p[i] += σp(q(x, i), p(x, i), P.nfs[j]) * dm[j] - end - end - out -end - - -# function Bridge.σ(t, x_, P::Union{Landmarks,LandmarksAux}) -# if P isa Landmarks -# x = x_ -# else -# x = P.xT -# end -# #zero!(out) -# out = 0.0*Matrix{Unc}(undef,2P.n,length(P.nfs)) -# for i in 1:P.n -# for j in 1:length(P.nfs) -# out[2i-1,j] = σq(q(x, i), P.nfs[j]) -# out[2i,j] = σp(q(x, i), p(x, i), P.nfs[j]) -# end -# end -# out -# end - - -# """ -# Compute tildesigma(t,x) * dm where dm is a vector and sigma is the diffusion coefficient of landmarksaux -# write to out which is of type State -# """ -# function Bridge.σ!(t, x, dm, out, P::LandmarksAux) -# Bridge.σ!(t, P.xT, dm, out, P::Landmarks) -# end - -function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) - if P isa Landmarks - x = x_ - else - x = P.xT - end - out = zeros(Unc,2P.n,2P.n) - for i in 1:P.n - for k in 1:P.n - for j in 1:length(P.nfs) - # r1 = σq(q(x,i),P.nfs[j]) * σq(q(x, k),P.nfs[j])' - # r2 = σq(q(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' - # r3 = σp(q(x,i),p(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' - # out[2i-1,2k-1] += r1 - # out[2i-1,2k] += r2 - # out[2i,2k-1] += r2' - # out[2i,2k] += r3 - r1 = σq(q(x,i),P.nfs[j]) * σq(q(x, k),P.nfs[j])' - r2 = σq(q(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' - r4 = σp(q(x,i),p(x,i),P.nfs[j]) * σq(q(x,k),P.nfs[j])' - r3 = σp(q(x,i),p(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' - out[2i-1,2k-1] += r1 - out[2i-1,2k] += r2 - out[2i,2k-1] += r4 - out[2i,2k] += r3 - end - end - end - out -end - -Bridge.a(t, P::LandmarksAux) = Bridge.a(t, 0, P) -#Bridge.a(t, P::Union{Landmarks,LandmarksAux}) = Bridge.a(t, P.xT, P::Union{Landmarks,LandmarksAux}) - -""" -Multiply a(t,x) times in (which is of type state) -Returns multiplication of type state -""" -function amul(t, x, in::State, P::Landmarks) - vecofpoints2state(Bridge.a(t, x, P)*vec(in)) - #Bridge.a(t, x, P)*in -end - - -Bridge.constdiff(::Landmarks) = false -Bridge.constdiff(::LandmarksAux) = true diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index 1fabd5c..4f74ed1 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -207,7 +207,7 @@ function llikelihood(::LeftRule, Xcirc::SamplePath{State{Pnt}}, Q::GuidedProposa tt = Xcirc.tt xx = Xcirc.yy - som::eltype(xx[1]) = 0. + som::deepeltype(xx[1]) = 0. rout = copy(xx[1]) if !constdiff(Q) # use sizetypes? diff --git a/landmarks/lmguiding.jl b/landmarks/lmguiding.jl index 6e1e89c..2387632 100644 --- a/landmarks/lmguiding.jl +++ b/landmarks/lmguiding.jl @@ -88,19 +88,27 @@ end Returns the guiding terms a(t,x)*r̃(t,x) along the path of a guided proposal """ function guidingterms(X::SamplePath{State{SArray{Tuple{2},Float64,1,2}}},Q::GuidedProposall!) - out = State[] - for i in 1:length(X.tt) + i = first(1:length(X.tt)) + out = [guidingterm((i,X.tt[i]),X.yy[i],Q)] + for i in 2:length(X.tt) push!(out, guidingterm((i,X.tt[i]),X.yy[i],Q)) end out end +""" +xobs0 consists of all observation vectors stacked, so in case of two observations, it should be v0 and vT stacked +""" +function Bridge.lptilde(xobs0, x, Po::GuidedProposal!) + y = xobs0 - Po.mu0 - Po.L0*x + -0.5*log(det(Po.Mdagger0)) -0.5 *dot(y, Po.Mdagger0*y) +end function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposall!; skip = 0) tt = Xcirc.tt xx = Xcirc.yy - som::Float64 = 0. + som::deepeltype(xx[1]) = 0. rout = copy(xx[1]) bout = copy(rout) btout = copy(rout) diff --git a/landmarks/lmpar.jl b/landmarks/lmpar.jl index c8b0b41..1d76111 100644 --- a/landmarks/lmpar.jl +++ b/landmarks/lmpar.jl @@ -15,7 +15,7 @@ using SparseArrays using LowRankApprox models = [:ms, :ahs] -model = models[2] +model = models[1] TEST = false#true partialobs = true @@ -56,7 +56,7 @@ Pms = MarslandShardlow(a, γ, λ, n) Pahs = Landmarks(a, λ, n, nfs) ### -StateW = Point +StateW = Point{Float64} if model == :ms dwiener = n P = Pms @@ -101,7 +101,7 @@ if partialobs==true L = [(i==j)*one(Unc) for i in 1:2:2n, j in 1:2n] Σ = [(i==j)*σobs^2*one(Unc) for i in 1:n, j in 1:n] #Σ = 10 * reshape(rand(Unc,n^2),n,n) - μend = zeros(Point,P.n) + μend = zeros(Point{Float64},P.n) xobs = vT mT = zero(vT)#rand(Point, n)# Pahsaux = LandmarksAux(Pahs, State(vT, mT)) @@ -110,7 +110,7 @@ else # full observation case L = [(i==j)*one(Unc) for i in 1:2n, j in 1:2n] Σ = [(i==j)*σobs^2*one(Unc) for i in 1:2n, j in 1:2n] - μend = zeros(Point,2P.n) + μend = zeros(Point{Float64}, 2P.n) xobs = vec(X.yy[end]) Pahsaux = LandmarksAux(Pahs, X.yy[end]) Pmsaux = MarslandShardlowAux(Pms, X.yy[end]) @@ -138,7 +138,7 @@ println("Compute Cholesky for Mt⁺:") Q = GuidedProposall!(P, Paux, tt_, Lt, Mt, μt, xobs) if partialobs - xinit = State(v0, rand(Point,P.n)) + xinit = State(v0, rand(Point{Float64}, P.n)) else xinit = x0 end @@ -157,3 +157,75 @@ include("plotlandmarks.jl") if model==:ms @time llikelihood(LeftRule(), XX, Q; skip = 0) # won't work for AHS because matrix multilication for Htilde is not defined yet end + + + +using ForwardDiff +dual(x, i, n) = ForwardDiff.Dual(x, ForwardDiff.Chunk{n}(), Val(i)) +dual(x, n) = ForwardDiff.Dual(x, ForwardDiff.Chunk{n}(), Val(0)) +#= +#using Flux +xinitv = deepvec(xinit) + +xinitv = map(i->dual(xinitv[i], i <= 2 ? i : 0, 2), 1:length(xinitv)) + +xinitnew = deepvec2state(xinitv) +x = copy(xinitnew) + +#lux.Tracker.gradient(x -> Bridge._b!((1,0.0), deepvec2state(x), deepvec2state(x), P), deepvec(xinit)) +Bridge.b!(0.0, x, copy(x), P) + +import Bridge; + +#include(joinpath(dirname(pathof(Bridge)), "..", "landmarks/patches.jl")) +#include(joinpath(dirname(pathof(Bridge)), "..", "landmarks/models.jl")) + +XX = Bridge.solve(EulerMaruyama!(), xinitnew, WW, P) +=# + + +function obj(xinitv) + xinit = deepvec2state(xinitv) + sample!(WW, Wiener{Vector{StateW}}()) + XXᵒ = Bridge.solve(EulerMaruyama!(), xinit, WW, Q) + ( + #(lptilde(xinit, Q) - lptilde(x0, Q)) + + llikelihood(LeftRule(), XXᵒ, Q; skip = 1) + ) +end +using Makie, Random +Random.seed!(2) +let + x = deepvec(x0) + x = x .* (1 .+ 0.2*randn(length(x))) + + x = deepvec(State(x0.q, deepvec2state(x).p)) + + s = deepvec2state(x) + n = Node(s.q) + n2 = Node(s.p) + sc = scatter(x0.q, color=:red) + + scatter!(sc, n2) + scatter!(sc, n, color=:blue) + display(sc) + + # only optimize momenta + mask = deepvec(State(0 .- 0*xinit.q, 1 .- 0*(xinit.p))) + ϵ = 6.e-4 + @show o = obj(x) + + for i in 1:1000 + #record(sc, "output/gradientdescent.mp4", 1:100) do i + #i % 10 == 0 && (o = obj(x)) + for k in 1:1 + ∇x = ForwardDiff.gradient(obj, x) + x .+= ϵ*mask.*∇x + end + s = deepvec2state(x) + n[] = s.q + n2[] = s.p + display(s-x0) + println("$i d(x,xtrue) = ", norm(deepvec(x0)-x))#, " ", o) + end +end From 478e81c73bdc621a470e248949393d4522827e7a Mon Sep 17 00:00:00 2001 From: mschauer Date: Tue, 7 May 2019 15:27:09 +0200 Subject: [PATCH 33/58] Bugfixes lptilde and recursions --- landmarks/lmguiding.jl | 17 ++++++++++------- landmarks/lmpar.jl | 11 ++++++----- 2 files changed, 16 insertions(+), 12 deletions(-) diff --git a/landmarks/lmguiding.jl b/landmarks/lmguiding.jl index 2387632..d12177b 100644 --- a/landmarks/lmguiding.jl +++ b/landmarks/lmguiding.jl @@ -2,10 +2,13 @@ # compute likelihood of guided proposal # not sure about this -function lmgpupdate(Lt, Mt, μt, Σ, L, v) - Lt = [Lt; L] +function lmgpupdate(Lt, Mt, μt, vt, Σ, L, v) + Lt = [L; Lt] Mt = [Σ 0I; 0I Mt] - μt = [zero(size(L,2)); μt] + μt = [0v; μt] + vt = [v; vt] + + Lt, Mt, μt, vt end @@ -97,11 +100,11 @@ function guidingterms(X::SamplePath{State{SArray{Tuple{2},Float64,1,2}}},Q::Guid end """ -xobs0 consists of all observation vectors stacked, so in case of two observations, it should be v0 and vT stacked +v0 consists of all observation vectors stacked, so in case of two observations, it should be v0 and vT stacked """ -function Bridge.lptilde(xobs0, x, Po::GuidedProposal!) - y = xobs0 - Po.mu0 - Po.L0*x - -0.5*log(det(Po.Mdagger0)) -0.5 *dot(y, Po.Mdagger0*y) +function Bridge.lptilde(x, L0, M0⁺, μ0, v0, Po::GuidedProposall!) + y = v0 - μ0 - L0*x + -0.5*log(det( M0⁺)) -0.5*dot(y, M0⁺*y) end function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposall!; skip = 0) diff --git a/landmarks/lmpar.jl b/landmarks/lmpar.jl index 1d76111..064aa04 100644 --- a/landmarks/lmpar.jl +++ b/landmarks/lmpar.jl @@ -86,8 +86,8 @@ tc(t,T) = t.* (2 .-t/T) tt_ = tc(t,T)#tc(t,T)# 0:dtimp:(T) #tt_ = t -# observe positions without noise -v0 = q(X.yy[1]) +# observe positions WITH noise +v0 = q(X.yy[1]) + σobs * randn(PointF,n) rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), 2*cos(θ)) #vT = [rot * X.yy[end].q[i] for i in 1:P.n ] trans = SMatrix{2,2}(1.5, 1.0, 0.0, 1.0) @@ -127,8 +127,8 @@ Lt = [copy(L) for s in tt_] Mt⁺ = [copy(Σ) for s in tt_] μt = [copy(μend) for s in tt_] println("compute guiding term:") -@time (Lend, Mend⁺,μend) = guidingbackwards!(Lm(), tt_, (Lt, Mt⁺,μt), Paux, (L, Σ, μend)) - +@time (Lend, Mend⁺, μend) = guidingbackwards!(Lm(), tt_, (Lt, Mt⁺,μt), Paux, (L, Σ, μend)) +(L0, M0⁺, μ0, V) = lmgpupdate(Lend, Mend⁺, μend, vT, Σ, L, v0) # issymmetric(deepmat(Bridge.a(0,Paux))) # isposdef(deepmat(Bridge.a(0,Paux))) # map(x->minimum(eigen(deepmat(x)).values),Mt⁺) @@ -184,12 +184,13 @@ XX = Bridge.solve(EulerMaruyama!(), xinitnew, WW, P) =# + function obj(xinitv) xinit = deepvec2state(xinitv) sample!(WW, Wiener{Vector{StateW}}()) XXᵒ = Bridge.solve(EulerMaruyama!(), xinit, WW, Q) ( - #(lptilde(xinit, Q) - lptilde(x0, Q)) + (lptilde(xinit, Lend, Mend⁺, μend, V, Q) - lptilde(x0, Lend, Mend⁺, μend, V, Q)) + llikelihood(LeftRule(), XXᵒ, Q; skip = 1) ) end From eb82758401c5de078ec93052ef078b01097c28d1 Mon Sep 17 00:00:00 2001 From: mschauer Date: Tue, 7 May 2019 15:40:31 +0200 Subject: [PATCH 34/58] Happy experimenting --- landmarks/lmguiding.jl | 4 ++-- landmarks/lmpar.jl | 2 +- landmarks/state.jl | 1 + 3 files changed, 4 insertions(+), 3 deletions(-) diff --git a/landmarks/lmguiding.jl b/landmarks/lmguiding.jl index d12177b..5c1926e 100644 --- a/landmarks/lmguiding.jl +++ b/landmarks/lmguiding.jl @@ -4,7 +4,7 @@ # not sure about this function lmgpupdate(Lt, Mt, μt, vt, Σ, L, v) Lt = [L; Lt] - Mt = [Σ 0I; 0I Mt] + Mt = [Σ 0Σ; 0Σ Mt] μt = [0v; μt] vt = [v; vt] @@ -104,7 +104,7 @@ v0 consists of all observation vectors stacked, so in case of two observations, """ function Bridge.lptilde(x, L0, M0⁺, μ0, v0, Po::GuidedProposall!) y = v0 - μ0 - L0*x - -0.5*log(det( M0⁺)) -0.5*dot(y, M0⁺*y) + -0.5*logdet(deepmat(M0⁺)) -0.5*dot(y, M0⁺*y) end function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposall!; skip = 0) diff --git a/landmarks/lmpar.jl b/landmarks/lmpar.jl index 064aa04..c2924b0 100644 --- a/landmarks/lmpar.jl +++ b/landmarks/lmpar.jl @@ -190,7 +190,7 @@ function obj(xinitv) sample!(WW, Wiener{Vector{StateW}}()) XXᵒ = Bridge.solve(EulerMaruyama!(), xinit, WW, Q) ( - (lptilde(xinit, Lend, Mend⁺, μend, V, Q) - lptilde(x0, Lend, Mend⁺, μend, V, Q)) + (lptilde(vec(xinit), L0, M0⁺, μ0, V, Q) - lptilde(vec(x0), L0, M0⁺, μ0, V, Q)) + llikelihood(LeftRule(), XXᵒ, Q; skip = 1) ) end diff --git a/landmarks/state.jl b/landmarks/state.jl index 086e6e4..33fe1a2 100644 --- a/landmarks/state.jl +++ b/landmarks/state.jl @@ -92,6 +92,7 @@ import Bridge: outer /(x::State, y) = State(x.q/y, x.p/y) vec(x::State) = vec([x[J] for J in eachindex(x)]) # + deepvec(x::State{P}) where {P} = vec([x[J][K] for K in eachindex(x.p[1]), J in eachindex(x)]) deepvec(x::Vector) = collect(flatten(x)) From 27aa24ac70e45e458de4680e75e36e965b2732a2 Mon Sep 17 00:00:00 2001 From: mschauer Date: Fri, 21 Jun 2019 10:33:29 +0200 Subject: [PATCH 35/58] Change state in Landmarks --- landmarks/forward.jl | 68 ++++--- landmarks/guiding.jl | 15 +- landmarks/models.jl | 82 ++++++--- landmarks/nstate.jl | 133 ++++++++++++++ landmarks/ostate.jl | 272 ++++++++++++++++++++++++++++ landmarks/patches.jl | 45 +++++ landmarks/state.jl | 399 +++++++---------------------------------- src/Bridge.jl | 2 + src/partialbridgen!.jl | 3 +- 9 files changed, 634 insertions(+), 385 deletions(-) create mode 100644 landmarks/nstate.jl create mode 100644 landmarks/ostate.jl diff --git a/landmarks/forward.jl b/landmarks/forward.jl index 5068616..49e6a28 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -28,9 +28,9 @@ obsschemes =[:full, :partial] obsscheme = obsschemes[2] const d = 2 -const itostrat=true +const itostrat = false -n = 5 # nr of landmarks +n = 15 # nr of landmarks ldim = 40 # dimension of low-rank approximation to H\^+ cheat = false #true#false # if cheat is true, then we initialise at x0 (true value) and @@ -46,11 +46,14 @@ println(model) println(discrmethod) println(obsscheme) -T = 0.4#1.0#0.5 +T = 1.0#1.0#0.5 t = 0.0:0.01:T # time grid Random.seed!(5) +#include("nstate.jl") +include("ostate.jl") include("state.jl") + include("models.jl") include("patches.jl") if discrmethod == :lm @@ -67,7 +70,7 @@ a = 3.0 # the larger, the stronger landmarks behave similarly λ = 0.0 # not the lambda of noise fields, but the mean reversion γ = 1.0 db = 3.0 # domainbound -nfstd = .5 # tau , widht of noisefields +nfstd = 1.0 # tau , width of noisefields r1 = -db:nfstd:db r2 = -db:nfstd:db nfloc = PointF.(collect(product(r1, r2)))[:] @@ -104,7 +107,7 @@ println("Sample forward process:") #@time solve!(StratonovichHeun!(), X, x0, W, P) # compute Hamiltonian along path -ham = [hamiltonian(X.yy[i],Pms) for i in 1:length(t)] +ham = [hamiltonian(X.yy[i], Pms) for i in 1:length(t)] tc(t,T) = t.*(2 .-t/T) tt_ = tc(t,T)#tc(t,T)# 0:dtimp:(T) @@ -257,7 +260,7 @@ sample!(WW, Wiener{Vector{StateW}}()) println("Sample guided bridge proposal:") @time Bridge.solve!(EulerMaruyama!(), XX, xinit, WW, Q) - +#error("STOP EARLY") include("plotlandmarks.jl") if model==:ms @@ -291,12 +294,21 @@ XX = Bridge.solve(EulerMaruyama!(), xinitnew, WW, P) function obj(xinitv) xinit = deepvec2state(xinitv) sample!(WW, Wiener{Vector{StateW}}()) - XXᵒ = Bridge.solve(EulerMaruyama!(), xinit, WW, Q) + if !isdefined(Main, :XXᵒ_) + XXᵒ_ = Bridge.solve(EulerMaruyama!(), xinit, WW, Q) + else + Bridge.solve!(EulerMaruyama!(), XXᵒ_, xinit, WW, Q) + end ( - (lptilde(xinit, Q) - lptilde(x0, Q)) + llikelihood(LeftRule(), XXᵒ, Q; skip = 1) + (lptilde(xinit, Q) - lptilde(x0, Q)) + llikelihood(LeftRule(), XXᵒ_, Q; skip = 1) ) end -using Makie, Random + +MAKIE = false +if MAKIE + using Makie +end +using Random, Profile Random.seed!(2) let x = deepvec(x0) @@ -306,20 +318,30 @@ let x = deepvec(State(x0.q, deepvec2state(x).p)) s = deepvec2state(x) - n = Node(s.q) - n2 = Node(s.p) - sc = scatter(x0.q, color=:red) - - scatter!(sc, n2) - scatter!(sc, n, color=:blue) - display(sc) - + if MAKIE + n = Node(s.q) + n2 = Node(s.p) + sc = scatter(x0.q, color=:red) + + scatter!(sc, n2) + scatter!(sc, n, color=:blue) + display(sc) + end # only optimize momenta mask = deepvec(State(0 .- 0*xinit.q, 1 .- 0*(xinit.p))) - ϵ = 6.e-4 - @show o = obj(x) + ϵ = 6.e-2 + #@show o = obj(x) + ∇x = ForwardDiff.gradient(obj, x) + x .+= ϵ*mask.*∇x + s = deepvec2state(x) + if MAKIE + n[] = s.q + n2[] = s.p + end + display(s-x0) - for i in 1:1000 + + @profile for i in 1:1000 #record(sc, "output/gradientdescent.mp4", 1:100) do i #i % 10 == 0 && (o = obj(x)) for k in 1:1 @@ -327,8 +349,10 @@ let x .+= ϵ*mask.*∇x end s = deepvec2state(x) - n[] = s.q - n2[] = s.p + if MAKIE + n[] = s.q + n2[] = s.p + end display(s-x0) println("$i d(x,xtrue) = ", norm(deepvec(x0)-x))#, " ", o) end diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index 4f74ed1..da2a4fd 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -152,20 +152,21 @@ end """ Construct guided proposal on a single segment with times in tt from precomputed ν and H """ -struct GuidedProposal!{T,Ttarget,Taux,Tν,TH,TC,F} <: ContinuousTimeProcess{T} +struct GuidedProposal!{T,Ttarget,Taux,Tν,TH,Tν0, TC,F} <: ContinuousTimeProcess{T} target::Ttarget # P aux::Taux # Ptilde tt::Vector{Float64} # grid of time points on single segment (S,T] ν::Vector{Tν} H::Vector{TH} - ν0::Tν + ν0::Tν0 H0::TH C0::TC endpoint::F function GuidedProposal!(target, aux, tt_, ν, H, ν0, H0, C0, endpoint=Bridge.endpoint) tt = collect(tt_) - new{Bridge.valtype(target),typeof(target),typeof(aux),eltype(ν),eltype(H),typeof(C),typeof(endpoint)}(target, aux, tt, ν, H, ν0, H0, C0, endpoint) + @show typeof.(( ν0, H0, C0)) + new{Bridge.valtype(target),typeof(target),typeof(aux),eltype(ν),eltype(H),typeof(ν0),typeof(C),typeof(endpoint)}(target, aux, tt, ν, H, ν0, H0, C0, endpoint) end end @@ -203,7 +204,7 @@ auxiliary(P::GuidedProposal!) = P.aux constdiff(P::GuidedProposal!) = constdiff(target(P)) && constdiff(auxiliary(P)) -function llikelihood(::LeftRule, Xcirc::SamplePath{State{Pnt}}, Q::GuidedProposal!; skip = 0) where {Pnt} +function llikelihood(::LeftRule, Xcirc::SamplePath{<:State{Pnt}}, Q::GuidedProposal!; skip = 0) where {Pnt} tt = Xcirc.tt xx = Xcirc.yy @@ -236,11 +237,13 @@ function llikelihood(::LeftRule, Xcirc::SamplePath{State{Pnt}}, Q::GuidedProposa som += 0.5*Bridge.inner(srout) * dt som -= 0.5*Bridge.inner(strout) * dt + # inference failure A = Bridge.a((i,s), x, target(Q)) At = Bridge.a((i,s), x, auxiliary(Q)) som -= 0.5*hadamtrace(A, Q.H[i]) * dt som -= -0.5*hadamtrace(At, Q.H[i]) * dt + end end som @@ -250,10 +253,10 @@ function hadamtrace(A, H::InverseCholesky) tr(tr(H*A)) end - +import Trajectories.@unroll1 function hadamtrace(A, H) @assert eachindex(A) == eachindex(H) - Trajectories.@unroll1 for i in eachindex(A) + @unroll1 for i in eachindex(A) if $first som = A[i]*H[i] else diff --git a/landmarks/models.jl b/landmarks/models.jl index 459af2b..a86e288 100644 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -64,10 +64,10 @@ function ∇kernel(q, qT, P::Union{Landmarks, LandmarksAux, MarslandShardlow, Ma end -function hamiltonian((q, p), P) +function hamiltonian(x, P) s = 0.0 - for i in eachindex(q), j in eachindex(q) - s += 1/2*dot(p[i], p[j])*kernel(q[i] - q[j], P) + for i in axes(x, 2), j in axes(x, 2) + s += 1/2*dot(x.p[i], x.p[j])*kernel(x.q[i] - x.q[j], P) end s end @@ -91,26 +91,40 @@ function ∇K̄(q, qT, τ) end # function for specification of diffusivity of landmarks -σq(q, nf::Noisefield) = diagm(0 =>nf.λ) * K̄(q - nf.δ,nf.τ) -σp(q, p, nf::Noisefield) = -diagm(0 => p.*nf.λ.* ∇K̄(q - nf.δ,nf.τ)) +""" + Suppose one noise field nf + Returns diagonal matrix with noisefield for position at point location q (can be vector or Point) +""" +σq(q, nf::Noisefield) = Diagonal(nf.λ * K̄(q - nf.δ,nf.τ)) +""" + Suppose one noise field nf + Returns diagonal matrix with noisefield for momentum at point location q (can be vector or Point) +""" +σp(q, p, nf::Noisefield) = -Diagonal(p .* nf.λ .* ∇K̄(q - nf.δ,nf.τ)) -function σq(x::Point, nfs::Array{<:Noisefield,1}) - out = 0.0 * x - for j in 1:length(nfs) + + +""" + For AHS model compute total noise field on position experienced at a point x. + Useful for plotting purposes. + + Example usage: + σq(Point(0.0, 0.0), nfs) + σq([0.0; 0.0], nfs) +""" +function σq(x, nfs::Array{<:Noisefield,1}) + out = σq(x, nfs[1]) + for j in 2:length(nfs) out += σq(x, nfs[j]) end + out end -Bridge.b(t::Float64, x, P::Union{Landmarks,MarslandShardlow})= Bridge.b!(t, x, 0*x, P) -#Bridge._b(it, x, P::Union{LandmarksAux,MarslandShardlowAux})= Bridge._b!(it, x, copy(x), P) -#Bridge._b(it, x, P::Union{Landmarks,MarslandShardlow})= Bridge._b!(it, x, 0*x, P) - -#Bridge.σ(t::Float64, x, dm, P::Union{LandmarksAux,MarslandShardlowAux}) = Bridge.σ!(t, x, dm, copy(x), P) - +#σq(nfs) = (x) -> σq(x,nfs) -#Bridge.σ(t::Float64, x, dm, P::Union{Landmarks,MarslandShardlow}) = Bridge.σ!(t, x, dm, copy(x), P) +Bridge.b(t::Float64, x, P::Union{Landmarks,MarslandShardlow})= Bridge.b!(t, x, 0*x, P) """ Evaluate drift of landmarks in (t,x) and save to out @@ -141,15 +155,15 @@ function Bridge.b!(t, x, out, P::Landmarks) out.q[i] += p(x,j)*kernel(q(x,i) - q(x,j), P) out.p[i] += -dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) end - if itostrat - global ui = zero(Unc{Float64}) - for k in 1:length(P.nfs) - nf = P.nfs[k] - ui += 0.5 * nf.τ^(-2) * diagm(0 =>nf.λ.^2) * K̄(q(x,i)-nf.δ,nf.τ)^2 - end - out.q[i] -= ui * q(x,i) - out.p[i] += ui * p(x,i) - end +# if itostrat +# global ui = zero(Unc{Float64}) +# for k in 1:length(P.nfs) +# nf = P.nfs[k] +# ui += 0.5 * nf.τ^(-2) * diagm(0 =>nf.λ.^2) * K̄(q(x,i)-nf.δ,nf.τ)^2 +# end +# out.q[i] -= ui * q(x,i) +# out.p[i] += ui * p(x,i) +# end end out end @@ -164,7 +178,7 @@ function Bridge.b!(t, x, out, Paux::MarslandShardlowAux) for i in 1:Paux.n for j in 1:Paux.n out.q[i] += p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) - out.p[i] += -Paux.λ*p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), P) + #out.p[i] += -Paux.λ*p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), P) end end out @@ -377,6 +391,7 @@ function σtmul(t, x_, y::State{Pnt}, P::Union{Landmarks,LandmarksAux}) where Pn end function σt!(t, x_, y::State, out, P::Union{Landmarks,LandmarksAux}) + zero!(out) # added frank if P isa Landmarks x = x_ else @@ -385,7 +400,7 @@ function σt!(t, x_, y::State, out, P::Union{Landmarks,LandmarksAux}) for j in 1:length(P.nfs) for i in 1:P.n out[j] += σq(q(x, i), P.nfs[j])' * q(y, i) + - σp(q(x, i), p(x, i), P.nfs[j])' * q(y, i) + σp(q(x, i), p(x, i), P.nfs[j])' * p(y, i) end end out @@ -510,6 +525,21 @@ function amul(t, x::State, xin::State, P::Union{Landmarks,LandmarksAux}) Bridge.σ!(t, x, σtmul(t, x, xin, P),out,P) end +""" + Construct sequence of Noisefields for AHS model + db: domainbound (sources are places on square grid specified by + (-db:2nfstd:db) x -db:2nfstd:db + nfstd: standard deviation of noise fields (the smaller: the more noise fields we use) + γ: if set to one, then the value of the noise field on the positions is approximately 1 at all locations in the domain +""" +function construct_nfs(db, nfstd, γ) + r1 = -db:2nfstd:db + r2 = -db:2nfstd:db + nfloc = Point.(collect(product(r1, r2)))[:] + nfscales = [2/pi*γ*Point(1.0, 1.0) for x in nfloc] # intensity + [Noisefield(δ, λ, nfstd) for (δ, λ) in zip(nfloc, nfscales)] +end + Bridge.constdiff(::Union{MarslandShardlow, MarslandShardlowAux,LandmarksAux}) = true diff --git a/landmarks/nstate.jl b/landmarks/nstate.jl new file mode 100644 index 0000000..3e10473 --- /dev/null +++ b/landmarks/nstate.jl @@ -0,0 +1,133 @@ + + using Test + using StaticArrays + + const Point{T} = SArray{Tuple{d},T,1,d} # point in R2 + const Unc{T} = SArray{Tuple{d,d},T,d,d*d} # Matrix presenting uncertainty + + const PointF = Point{Float64} + const UncF = Unc{Float64} + + + struct NState{P, M<:AbstractMatrix{P}} + x::M + end + const State = NState + + NState(x::Vector) = NState(reshape(x, (2, length(x)>>1))) + + import Base: axes, #=iterate,=# eltype, copy, copyto!, zero, eachindex, getindex, setindex!, size, vec + + q(x::NState, i) = x.x[1, i] + p(x::NState, i) = x.x[2, i] + eltype(x::NState) = eltype(x.x) + deepeltype(x::NState) = eltype(eltype(x)) + q(x::NState) = @view x.x[1:2:end] + p(x::NState) = @view x.x[2:2:end] + + import LinearAlgebra: norm + norm(x::NState) = norm(vec(x)) + +# function outer(x::State, y::State) +# [outer(x[i],y[j]) for i in eachindex(x), j in eachindex(y)] + #end + + + vecofpoints2state(x::Vector) = NState(x) + + size(s::NState) = size(s.x) + axes(s::NState, i) = axes(s.x, i) + deepvec(x::NState) = vec(reinterpret(eltype(eltype(x)), x.x)) + function deepvec2state(x::Vector) + x = reinterpret(Point{eltype(x)}, x) + #dump(length(x)) + NState(reshape(x, (2, length(x)>>1))) + end + + function deepvec2state(x::Base.ReshapedArray{<:Any,1,<:Base.ReinterpretArray}) + NState(x.parent.parent) + end + + function NState(q::AbstractVector, p::AbstractVector) + length(p) != length(q) && throw(DimensionMismatch()) + NState([((q,p)[i])[j] for i in 1:2, j in 1:length(p)]) + end + + function NState(x::Vector) + NState(reshape(x, (2, length(x)>>1))) + end + vec(x::NState) = vec(x.x) + Base.broadcastable(x::NState) = x + Broadcast.BroadcastStyle(::Type{<:NState}) = Broadcast.Style{NState}() + + + function Base.getproperty(u::NState, s::Symbol) + x = getfield(u, :x) + s == :x && return x + + if s == :q + @view x[1:2:end] + elseif s == :p + @view x[2:2:end] + else + throw(ArgumentError("NState has properties `p`, `q` or `x`")) + end + end + + zero!(v::NState) = zero!(v.x) + zero!(v::AbstractArray) = v .= Ref(zero(eltype(v))) + zero(v::NState) = NState(zero(v.x)) + + copy(x::NState) = NState(copy(x.x)) + function copyto!(x::NState, y::NState) + copyto!(x.x, y.x) + x + end + + function copyto!(x::NState, y) + for i in eachindex(x) + x[i] = y[i] + end + x + end + + + + + getindex(x::NState, I) = getindex(x.x, I) + function setindex!(x::NState, val, I) + x.x[I] = val + end + + eachindex(x::NState) = CartesianIndices(axes(x.x)) + + + + import Base: *, +, /, - + import LinearAlgebra: dot + +# import Bridge: outer, inner + *(c::Number, x::NState) = NState(c*x.x) + *(x::NState, c::Number) = NState(x.x*c) + +(x::NState, y::NState) = NState(x.x + y.x) + -(x::NState, y::NState) = NState(x.x - y.x) + /(x::NState, y) = NState(x.x/y) + + dot(x::NState, y::NState) = dot(vec(x),vec(y)) + + function Base.:*(A::AbstractArray{<:Unc,2}, x::State) + vecofpoints2state(A*vec(x)) + end +if TEST + q, p = zeros(PointF, 5), rand(PointF, 5) + + x = NState(q, p) + @test x.p == p + @test x.q == q + + @test x.x[1, :] == q + @test x.x[2, :] == p + + U = rand(UncF,5,5) + U * x.p +end diff --git a/landmarks/ostate.jl b/landmarks/ostate.jl new file mode 100644 index 0000000..2d133fe --- /dev/null +++ b/landmarks/ostate.jl @@ -0,0 +1,272 @@ +import Base:iterate, eltype, copy, copyto!, zero, eachindex, getindex, setindex!, size, vec + +const Point{T} = SArray{Tuple{d},T,1,d} # point in R2 +const Unc{T} = SArray{Tuple{d,d},T,d,d*d} # Matrix presenting uncertainty + +const PointF = Point{Float64} + +abstract type UncMat end + +struct State{P} + q::Vector{P} + p::Vector{P} +end + +q(x::State) = x.q +p(x::State) = x.p +q(x::State, i) = x.q[i] +p(x::State, i) = x.p[i] + +q(x::State, i) = x.q[i] +p(x::State, i) = x.p[i] + + + +q(i::Int) = 2i - 1 +p(i::Int) = 2i + +zero!(v) = v[:] = fill!(v, zero(eltype(v))) + +iterate(x::State) = (x.q, true) +iterate(x::State, s) = s ? (x.p, false) : nothing +copy(x::State) = State(copy(x.q), copy(x.p)) +function copyto!(x::State, y::State) + copyto!(x.q, y.q) + copyto!(x.p, y.p) + x +end +function copyto!(x::State, y) + for i in eachindex(x) + x[i] = y[i] + end + x +end +deepeltype(::State{P}) where {P} = eltype(P) + + +Base.broadcastable(x::State) = x +Broadcast.BroadcastStyle(::Type{<:State}) = Broadcast.Style{State}() + + + +size(s::State) = (2, length(s.p)) + +zero(x::State) = State(zero(x.p), zero(x.q)) +zero!(v) = fill!(v, zero(eltype(v))) +zero!(v) = v[:] = fill!(v, zero(eltype(v))) + +function zero!(x::State) + zero!(x.p) + zero!(x.q) + x +end + +function getindex(x::State, I::CartesianIndex) + if I[1] == 1 + x.q[I[2]] + elseif I[1] == 2 + x.p[I[2]] + else + throw(BoundsError()) + end +end +function setindex!(x::State, val, I::CartesianIndex) + if I[1] == 1 + x.q[I[2]] = val + elseif I[1] == 2 + x.p[I[2]] = val + else + throw(BoundsError()) + end +end + +eachindex(x::State) = CartesianIndices((Base.OneTo(2), eachindex(x.p))) + +import Base: *, +, /, - +import LinearAlgebra: norm +import Bridge: outer +*(c::Number, x::State) = State(c*x.q, c*x.p) +*(x::State,c::Number) = State(x.q*c, x.p*c) ++(x::State, y::State) = State(x.q + y.q, x.p + y.p) +-(x::State, y::State) = State(x.q - y.q, x.p - y.p) +/(x::State, y) = State(x.q/y, x.p/y) + +vec(x::State) = vec([x[J] for J in eachindex(x)]) # + +deepvec(x::State{P}) where {P} = vec([x[J][K] for K in eachindex(x.p[1]), J in eachindex(x)]) + +deepvec(x::Vector) = collect(flatten(x)) + + +# matrix multiplication of mat of Uncs +function Base.:*(A::AbstractArray{Unc{T},2},B::AbstractArray{Unc{T},2}) where {T} + C = zeros(Unc{T},size(A,1), size(B,2)) + for i in 1:size(A,1) + for j in 1:size(B,2) + for k in 1:size(A,2) + C[i,j] += A[i,k] * B[k,j] + end + end + end + C +end + +# function Base.:*(A::Array{Unc,2},B::Adjoint{Unc,Array{Unc,2}}) +# C = zeros(Unc,size(A,1), size(B,2)) +# for i in 1:size(A,1) +# for j in 1:size(B,2) +# for k in 1:size(A,2) +# C[i,j] += A[i,k] * B[k,j] +# end +# end +# end +# C +# end +# +# #new +# function Base.:*(A::Adjoint{Unc,Array{Unc,2}},B::Array{Unc,2}) +# C = zeros(Unc,size(A,1), size(B,2)) +# for i in 1:size(A,1) +# for j in 1:size(B,2) +# for k in 1:size(A,2) +# C[i,j] += A[i,k] * B[k,j] +# end +# end +# end +# C +# end + + +function Base.:*(A::AbstractArray{<:Unc,2}, x::State) + vecofpoints2state(A*vec(x)) +end +function Base.:*(A::SparseMatrixCSC, x_::State) + #vecofpoints2state(Array(A)*vec(x)) + x = vec(x_) + vecofpoints2state(mul!(similar(x, A.m), A, x, true, false)) +end +#mul!(similar(x, Tx, A.m), A, x, true, false) +#Base.setindex!(A::SparseMatrixCSC{T}, _v::T, _i::Integer, _j::Integer) where {T} = SparseArrays._setindex_scalar!(A, _v, _i, _j) + +if TEST + A = reshape(rand(Unc,6),3,2) + B = reshape(rand(Unc,8),2,4) + C = B' + @test norm(deepmat(A*B) - deepmat(A) * deepmat(B))<10^(-8) + @test norm(deepmat(A*C') - deepmat(A) * deepmat(C'))<10^(-8) + BB = reshape(rand(Unc,8),4,2) + @test (A*BB')' == BB*A' + + D = reshape(rand(Unc,6),3,2) + E = reshape(rand(Unc,12),3,4) + @test D'*E == (E'*D)' + + # backsolving matrix equation A X = using lu + A1=reshape(rand(Unc,9),3,3) + B1=reshape(rand(Unc,9),3,3) + @test norm(deepmat(A1\B1) - deepmat(A1)\deepmat(B1))<10^(-10) + + +end + + +""" +Convert vector to State. it is assumed that x is ordered as follows +- position landmark 1 +- momentum landmark 1 +- position landmark 2 +- momentum landmark 2 +... +""" +function deepvec2state(x::AbstractVector{T}) where {T} + m = div(length(x),2d) + q = Vector{Point{T}}(undef,m) + p = Vector{Point{T}}(undef,m) + for i in 1:m + q[i] = Point{T}(x[(i-1)*2d .+ (1:d)]) + p[i] = Point{T}(x[((i-1)*2d+d+1):(2i*d)]) + end + State(q,p) +end + +vecofpoints2state(x::Vector{<:Point}) = State(x[1:d:end], x[d:d:end]) + + + +############################ LowRank ######################## +""" +Hdagger = U S U' with S = L L' (cholesky) +U has orthonormal columns, S is a small positive definite symmetric matrix given +in factorized form, e.g. `S <: Cholesky` + +Then H*x is defined as U inv(S) U' (that is the Moore Penrose inverse) +""" +struct LowRank{TS,TU} + S::TS + U::TU +end + +function Base.:*(H::LowRank, x::State) + #z = H.S\(H.U' * deepvec(x)) # e.g. uses two triangular backsolves if S is `Cholesky` + #deepvec2state(H.U*z) + deepvec2state(H.U * (inv(H.S) * (H.U' * deepvec(x)))) +end + +############################ InverseCholesky ######################## +struct InverseLu{TL,TU} + L::TL + U::TU +end + +""" +Compute y = H x where x is a state vector and +Hinv = LU (LU decomposition) + +From LU y =x, it follows that we +solve first z from Lz=x, and next y from Uy=z +""" +function Base.:*(H::InverseLu, x::Vector{<:Point}) + LinearAlgebra.naivesub!(LowerTriangular(H.L), x) + LinearAlgebra.naivesub!(UpperTriangular(H.U), x) + x +end + +function Base.:*(H::InverseLu, x::State) + y = vec(x) + LinearAlgebra.naivesub!(LowerTriangular(H.L), y) + LinearAlgebra.naivesub!(UpperTriangular(H.U), y) + vecofpoints2state(y) +end + + + +if TEST + A = reshape([Unc(1:4), Unc(5:8), Unc(9:12), Unc(13:16)],2,2) + B = reshape([-Unc(1:4), Unc(3:6), Unc(9:12), Unc(13:16)],2,2) + @test deepmat(A*B)==deepmat(A)*deepmat(B) + @test deepmat(A') == deepmat(A)' + @test deepmat(A*A')==deepmat(A)*deepmat(A') + Q = deepmat2unc(Matrix(qr(deepmat(A)).Q)) + C = Q * Q' + lchol(C) + @test deepmat(lchol(C))== cholesky(deepmat(C)).L + isposdef(deepmat(C)) + + # check cholinverse! + HH = InverseCholesky(lchol(C)) + x = rand(4) + xstate = deepvec2state(x) + @test norm(deepvec(HH*xstate) - inv(deepmat(C))*x)<10^(-10) + + LinearAlgebra.naivesub!(lchol(C), A) # triangular backsolves + + A = reshape(rand(Unc,16),4,4) + L, U = lu(A) + W = InverseLu(L,U) + + xs= rand(PointF,4) + xss = [xs[1]; xs[2];xs[3];xs[4]] + inv(deepmat(A)) * xss + W * xs + @test norm(deepvec2state(inv(deepmat(A)) * xss) - W * deepvec2state(xss))<10^(-10) +end diff --git a/landmarks/patches.jl b/landmarks/patches.jl index 3bef540..9b9466a 100644 --- a/landmarks/patches.jl +++ b/landmarks/patches.jl @@ -59,6 +59,51 @@ function Bridge.solve(solver::EulerMaruyama!, u, W::SamplePath, P::Bridge.Proces end +function Bridge.solve!(solver::EulerMaruyama!, Y::SamplePath, u, W::SamplePath, P::Bridge.ProcessOrCoefficients) + N = length(W) + + tt = W.tt + yy = Y.yy + copyto!(yy[1], u) + + i = 1 + dw = W.yy[i+1] - W.yy[i] + t¯ = tt[i] + dt = tt[i+1] - t¯ + + tmp1 = Bridge._b!((i,t¯), u, 0*u, P) + tmp2 = Bridge.σ(t¯, u, dw, P) + + y = u + tmp1*dt + tmp2 + + #dump(y) + #error("here") + + + for i in 2:N-1 + t¯ = tt[i] + dt = tt[i+1] - t¯ + copyto!(yy[i], y) + if dw isa Number + dw = W.yy[i+1] - W.yy[i] + else + for k in eachindex(dw) + dw[k] = W.yy[i+1][k] - W.yy[i][k] + end + end + + Bridge._b!((i,t¯), y, tmp1, P) + Bridge.σ!(t¯, y, dw, tmp2, P) + + for k in eachindex(y) + y[k] = y[k] + tmp1[k]*dt + tmp2[k] + end + end + copyto!(yy[end], Bridge.endpoint(y, P)) + SamplePath(tt, yy) +end + + struct StratonovichHeun! <: Bridge.SDESolver end diff --git a/landmarks/state.jl b/landmarks/state.jl index 33fe1a2..db41c05 100644 --- a/landmarks/state.jl +++ b/landmarks/state.jl @@ -1,357 +1,96 @@ -import Base:iterate, eltype, copy, copyto!, zero, eachindex, getindex, setindex!, size, vec -const Point{T} = SArray{Tuple{d},T,1,d} # point in R2 -const Unc{T} = SArray{Tuple{d,d},T,d,d*d} # Matrix presenting uncertainty + using Test + using StaticArrays -const PointF = Point{Float64} + const Point{T} = SArray{Tuple{d},T,1,d} # point in R2 + const Unc{T} = SArray{Tuple{d,d},T,d,d*d} # Matrix presenting uncertainty -abstract type UncMat end + const PointF = Point{Float64} + const UncF = Unc{Float64} -struct State{P} - q::Vector{P} - p::Vector{P} -end -q(x::State) = x.q -p(x::State) = x.p -q(x::State, i) = x.q[i] -p(x::State, i) = x.p[i] - -q(x::State, i) = x.q[i] -p(x::State, i) = x.p[i] - - - -q(i::Int) = 2i - 1 -p(i::Int) = 2i - -zero!(v) = v[:] = fill!(v, zero(eltype(v))) - -iterate(x::State) = (x.q, true) -iterate(x::State, s) = s ? (x.p, false) : nothing -copy(x::State) = State(copy(x.q), copy(x.p)) -function copyto!(x::State, y::State) - copyto!(x.q, y.q) - copyto!(x.p, y.p) - x -end -function copyto!(x::State, y) - for i in eachindex(x) - x[i] = y[i] + function deepmat(H::AbstractMatrix{S}) where {S} + d1, d2 = size(S) + reshape([H[i,j][k,l] for k in 1:d1, i in 1:size(H, 1), l in 1:d2, j in 1:size(H,2)], d1*size(H,1), d2*size(H,2)) end - x -end -deepeltype(::State{P}) where {P} = eltype(P) - + #@test outer(deepvec(x0)) == deepmat(outer(vec(x0))) -Base.broadcastable(x::State) = x -Broadcast.BroadcastStyle(::Type{<:State}) = Broadcast.Style{State}() - - -size(s::State) = (2, length(s.p)) - -zero(x::State) = State(zero(x.p), zero(x.q)) -zero!(v) = fill!(v, zero(eltype(v))) -zero!(v) = v[:] = fill!(v, zero(eltype(v))) - -function zero!(x::State) - zero!(x.p) - zero!(x.q) - x -end - -function getindex(x::State, I::CartesianIndex) - if I[1] == 1 - x.q[I[2]] - elseif I[1] == 2 - x.p[I[2]] - else - throw(BoundsError()) - end -end -function setindex!(x::State, val, I::CartesianIndex) - if I[1] == 1 - x.q[I[2]] = val - elseif I[1] == 2 - x.p[I[2]] = val - else - throw(BoundsError()) + function deepmat2unc(A::Matrix) # d is the dimension of the square subblocks + m = div(size(A,1),d) + n = div(size(A,2),d) + [Unc(A[(i-1)*d+1:i*d,(j-1)*d+1:j*d]) for i in 1:m, j in 1:n] end -end - -eachindex(x::State) = CartesianIndices((Base.OneTo(2), eachindex(x.p))) -import Base: *, +, /, - -import LinearAlgebra: norm -import Bridge: outer -*(c::Number, x::State) = State(c*x.q, c*x.p) -*(x::State,c::Number) = State(x.q*c, x.p*c) -+(x::State, y::State) = State(x.q + y.q, x.p + y.p) --(x::State, y::State) = State(x.q - y.q, x.p - y.p) -/(x::State, y) = State(x.q/y, x.p/y) -vec(x::State) = vec([x[J] for J in eachindex(x)]) # - -deepvec(x::State{P}) where {P} = vec([x[J][K] for K in eachindex(x.p[1]), J in eachindex(x)]) - -deepvec(x::Vector) = collect(flatten(x)) - - -# matrix multiplication of mat of Uncs -function Base.:*(A::AbstractArray{Unc{T},2},B::AbstractArray{Unc{T},2}) where {T} - C = zeros(Unc{T},size(A,1), size(B,2)) - for i in 1:size(A,1) - for j in 1:size(B,2) - for k in 1:size(A,2) - C[i,j] += A[i,k] * B[k,j] - end - end + function outer(x::State, y::State) + [outer(x[i],y[j]) for i in eachindex(x), j in eachindex(y)] end - C -end - -# function Base.:*(A::Array{Unc,2},B::Adjoint{Unc,Array{Unc,2}}) -# C = zeros(Unc,size(A,1), size(B,2)) -# for i in 1:size(A,1) -# for j in 1:size(B,2) -# for k in 1:size(A,2) -# C[i,j] += A[i,k] * B[k,j] -# end -# end -# end -# C -# end -# -# #new -# function Base.:*(A::Adjoint{Unc,Array{Unc,2}},B::Array{Unc,2}) -# C = zeros(Unc,size(A,1), size(B,2)) -# for i in 1:size(A,1) -# for j in 1:size(B,2) -# for k in 1:size(A,2) -# C[i,j] += A[i,k] * B[k,j] -# end -# end -# end -# C -# end - - -function Base.:*(A::AbstractArray{<:Unc,2}, x::State) - vecofpoints2state(A*vec(x)) -end -function Base.:*(A::SparseMatrixCSC, x_::State) - #vecofpoints2state(Array(A)*vec(x)) - x = vec(x_) - vecofpoints2state(mul!(similar(x, A.m), A, x, true, false)) -end -#mul!(similar(x, Tx, A.m), A, x, true, false) -#Base.setindex!(A::SparseMatrixCSC{T}, _v::T, _i::Integer, _j::Integer) where {T} = SparseArrays._setindex_scalar!(A, _v, _i, _j) - -if TEST - A = reshape(rand(Unc,6),3,2) - B = reshape(rand(Unc,8),2,4) - C = B' - @test norm(deepmat(A*B) - deepmat(A) * deepmat(B))<10^(-8) - @test norm(deepmat(A*C') - deepmat(A) * deepmat(C'))<10^(-8) - BB = reshape(rand(Unc,8),4,2) - @test (A*BB')' == BB*A' - - D = reshape(rand(Unc,6),3,2) - E = reshape(rand(Unc,12),3,4) - @test D'*E == (E'*D)' - - # backsolving matrix equation A X = using lu - A1=reshape(rand(Unc,9),3,3) - B1=reshape(rand(Unc,9),3,3) - @test norm(deepmat(A1\B1) - deepmat(A1)\deepmat(B1))<10^(-10) - - -end - - -""" -Convert vector to State. it is assumed that x is ordered as follows -- position landmark 1 -- momentum landmark 1 -- position landmark 2 -- momentum landmark 2 -... -""" -function deepvec2state(x::AbstractVector{T}) where {T} - m = div(length(x),2d) - q = Vector{Point{T}}(undef,m) - p = Vector{Point{T}}(undef,m) - for i in 1:m - q[i] = Point{T}(x[(i-1)*2d .+ (1:d)]) - p[i] = Point{T}(x[((i-1)*2d+d+1):(2i*d)]) - end - State(q,p) -end -vecofpoints2state(x::Vector{<:Point}) = State(x[1:d:end], x[d:d:end]) + norm(x::State) = norm(vec(x)) -function deepmat(H::AbstractMatrix{S}) where {S} - d1, d2 = size(S) - reshape([H[i,j][k,l] for k in 1:d1, i in 1:size(H, 1), l in 1:d2, j in 1:size(H,2)], d1*size(H,1), d2*size(H,2)) -end -#@test outer(deepvec(x0)) == deepmat(outer(vec(x0))) + """ + Good display of variable of type State + """ + function Base.show(io::IO, state::State) + show(io, "text/plain", hcat(q(state),p(state))) + end -function deepmat2unc(A::Matrix) # d is the dimension of the square subblocks - m = div(size(A,1),d) - n = div(size(A,2),d) - [Unc(A[(i-1)*d+1:i*d,(j-1)*d+1:j*d]) for i in 1:m, j in 1:n] -end - - -function outer(x::State, y::State) - [outer(x[i],y[j]) for i in eachindex(x), j in eachindex(y)] -end - -norm(x::State) = norm(vec(x)) - -""" -Good display of variable of type State -""" -function Base.show(io::IO, state::State) - show(io, "text/plain", hcat(q(state),p(state))) -end - -""" -Solve L L'y =x using two backsolves, -L should be lower triangular -""" -function cholinverse!(L, x) - LinearAlgebra.naivesub!(L, x) # triangular backsolves - LinearAlgebra.naivesub!(UpperTriangular(L'), x) - x -end - -lchol(A) = LowerTriangular(Matrix(LinearAlgebra._chol!(copy(A), UpperTriangular)[1])') - -############################ InverseCholesky ######################## -struct InverseCholesky{T} - L::T -end - -""" -Compute y = H*x where Hinv = L*L' (Cholesky decomposition - -Input are L and x, output is y - -y=Hx is equivalent to LL'y=x, which can be solved -by first backsolving Lz=x for z and next -backsolving L'y=z - -L is a lower triangular matrix with element of type UncMat -x is a State or vector of points -Returns a State (Todo: split up again and return vector for vector input) -""" -function Base.:*(H::InverseCholesky, x::State) - y = copy(vec(x)) - cholinverse!(H.L, y) # triangular backsolve - vecofpoints2state(y) -end - -function Base.:*(H::InverseCholesky, x::Vector{<:Point}) - y = copy(x) - cholinverse!(H.L, y) # triangular backsolve -end - -""" -Compute y = H*X where Hinv = L*L' (Cholesky decomposition - -Input are L and X, output is Y - -y=HX is equivalent to LL'y=X, which can be solved -by first backsolving LZ=X for z and next -backsolving L'Y=Z - -L is a lower triangular matrix with element of type UncMat -X is a matrix with elements of type UncMat -Returns a matrix with elements of type UncMat -""" -function Base.:*(H::InverseCholesky, X) - cholinverse!(H.L, copy(X)) # triangular backsolves -end - - - -############################ LowRank ######################## -""" -Hdagger = U S U' with S = L L' (cholesky) -U has orthonormal columns, S is a small positive definite symmetric matrix given -in factorized form, e.g. `S <: Cholesky` - -Then H*x is defined as U inv(S) U' (that is the Moore Penrose inverse) -""" -struct LowRank{TS,TU} - S::TS - U::TU -end - -function Base.:*(H::LowRank, x::State) - #z = H.S\(H.U' * deepvec(x)) # e.g. uses two triangular backsolves if S is `Cholesky` - #deepvec2state(H.U*z) - deepvec2state(H.U * (inv(H.S) * (H.U' * deepvec(x)))) -end + """ + Solve L L'y =x using two backsolves, + L should be lower triangular + """ + function cholinverse!(L, x) + LinearAlgebra.naivesub!(L, x) # triangular backsolves + LinearAlgebra.naivesub!(UpperTriangular(L'), x) + x + end -############################ InverseCholesky ######################## -struct InverseLu{TL,TU} - L::TL - U::TU -end + lchol(A) = LowerTriangular(Matrix(LinearAlgebra._chol!(copy(A), UpperTriangular)[1])') -""" -Compute y = H x where x is a state vector and -Hinv = LU (LU decomposition) + ############################ InverseCholesky ######################## + struct InverseCholesky{T} + L::T + end -From LU y =x, it follows that we -solve first z from Lz=x, and next y from Uy=z -""" -function Base.:*(H::InverseLu, x::Vector{<:Point}) - LinearAlgebra.naivesub!(LowerTriangular(H.L), x) - LinearAlgebra.naivesub!(UpperTriangular(H.U), x) - x -end + """ + Compute y = H*x where Hinv = L*L' (Cholesky decomposition -function Base.:*(H::InverseLu, x::State) - y = vec(x) - LinearAlgebra.naivesub!(LowerTriangular(H.L), y) - LinearAlgebra.naivesub!(UpperTriangular(H.U), y) - vecofpoints2state(y) -end + Input are L and x, output is y + y=Hx is equivalent to LL'y=x, which can be solved + by first backsolving Lz=x for z and next + backsolving L'y=z + L is a lower triangular matrix with element of type UncMat + x is a State or vector of points + Returns a State (Todo: split up again and return vector for vector input) + """ + function Base.:*(H::InverseCholesky, x::State) + y = copy(vec(x)) + cholinverse!(H.L, y) # triangular backsolve + vecofpoints2state(y) + end -if TEST - A = reshape([Unc(1:4), Unc(5:8), Unc(9:12), Unc(13:16)],2,2) - B = reshape([-Unc(1:4), Unc(3:6), Unc(9:12), Unc(13:16)],2,2) - @test deepmat(A*B)==deepmat(A)*deepmat(B) - @test deepmat(A') == deepmat(A)' - @test deepmat(A*A')==deepmat(A)*deepmat(A') - Q = deepmat2unc(Matrix(qr(deepmat(A)).Q)) - C = Q * Q' - lchol(C) - @test deepmat(lchol(C))== cholesky(deepmat(C)).L - isposdef(deepmat(C)) + function Base.:*(H::InverseCholesky, x::Vector{<:Point}) + y = copy(x) + cholinverse!(H.L, y) # triangular backsolve + end - # check cholinverse! - HH = InverseCholesky(lchol(C)) - x = rand(4) - xstate = deepvec2state(x) - @test norm(deepvec(HH*xstate) - inv(deepmat(C))*x)<10^(-10) + """ + Compute y = H*X where Hinv = L*L' (Cholesky decomposition - LinearAlgebra.naivesub!(lchol(C), A) # triangular backsolves + Input are L and X, output is Y - A = reshape(rand(Unc,16),4,4) - L, U = lu(A) - W = InverseLu(L,U) + y=HX is equivalent to LL'y=X, which can be solved + by first backsolving LZ=X for z and next + backsolving L'Y=Z - xs= rand(PointF,4) - xss = [xs[1]; xs[2];xs[3];xs[4]] - inv(deepmat(A)) * xss - W * xs - @test norm(deepvec2state(inv(deepmat(A)) * xss) - W * deepvec2state(xss))<10^(-10) -end + L is a lower triangular matrix with element of type UncMat + X is a matrix with elements of type UncMat + Returns a matrix with elements of type UncMat + """ + function Base.:*(H::InverseCholesky, X) + cholinverse!(H.L, copy(X)) # triangular backsolves + end diff --git a/src/Bridge.jl b/src/Bridge.jl index 9e7a104..3903808 100644 --- a/src/Bridge.jl +++ b/src/Bridge.jl @@ -39,10 +39,12 @@ using Statistics include("chol.jl") + using StaticArrays using Distributions using Colors using Trajectories +include(joinpath(dirname(Base.find_package(string(Trajectories))), "unroll1.jl")) diff --git a/src/partialbridgen!.jl b/src/partialbridgen!.jl index 92df56d..c52ba63 100644 --- a/src/partialbridgen!.jl +++ b/src/partialbridgen!.jl @@ -107,9 +107,10 @@ function llikelihood(::LeftRule, Xcirc::SamplePath, Po::PartialBridge!; skip = 0 end som end + function hadamtrace(A, H) @assert eachindex(A) == eachindex(H) - Trajectories.@unroll1 for i in eachindex(A) + @unroll1 for i in eachindex(A) if $first som = A[i]*H[i] else From e8cf52ec0a3f2102dcfdbeae7bcd9b2391803ed8 Mon Sep 17 00:00:00 2001 From: mschauer Date: Fri, 21 Jun 2019 14:36:12 +0200 Subject: [PATCH 36/58] Synch patches.jl --- landmarks/patches.jl | 31 +++++++++++++++++++++++++++++-- 1 file changed, 29 insertions(+), 2 deletions(-) diff --git a/landmarks/patches.jl b/landmarks/patches.jl index 9b9466a..7915f57 100644 --- a/landmarks/patches.jl +++ b/landmarks/patches.jl @@ -1,4 +1,9 @@ +""" + Initialise SamplePath on time grid t by copying x into each value of the field yy +""" +initSamplePath(t,x) = SamplePath(t, [copy(x) for s in t]) + function Bridge.sample!(W::SamplePath{Vector{T}}, P::Wiener{Vector{T}}, y1 = W.yy[1]) where {T} y = copy(y1) copyto!(W.yy[1], y) @@ -259,7 +264,7 @@ B = copy(A) A conj!(B) """ -function conj!(A::Array{Unc,2}) +function conj!(A::Array{<:Unc,2}) for i in 1:size(A,1) A[i,i] = A[i,i]' for j in (i+1):size(A,2) @@ -269,7 +274,7 @@ function conj!(A::Array{Unc,2}) A end -function conj2(A::Array{Unc,2}) +function conj2(A::Array{<:Unc,2}) At = Matrix{Unc}(undef,size(A,2),size(A,1)) for i in 1:size(A,2) for j in 1:size(A,1) @@ -284,3 +289,25 @@ if TEST B = conj2(A) @test norm(deepmat(A)'-deepmat(B))<10^(-10) end + + +""" + Forward simulate landmarks process specified by P on grid t. + Returns driving motion W and landmarks process X + t: time grid + dwiener: dimension of Wiener driving process + x0: starting point + P: landmarks specification +""" +landmarksforward = function(t, dwiener, x0::State{Pnt}, P) where Pnt + W = initSamplePath(t, zeros(Pnt, dwiener)) + sample!(W, Wiener{Vector{Pnt}}()) + # forward simulate landmarks + X = initSamplePath(t,x0) + println("Solve for forward provess:") + solve!(EulerMaruyama!(), X, x0, W, P) #@time solve!(StratonovichHeun!(), X, x0, W, P) + W, X +end + +tc(t,T) = t.* (2 .-t/T) +extractcomp(v,i) = map(x->x[i], v) From 8c46a25007a0749e6becd5e3b752645a15c21648 Mon Sep 17 00:00:00 2001 From: mschauer Date: Fri, 21 Jun 2019 14:39:12 +0200 Subject: [PATCH 37/58] Synch guiding.jl --- landmarks/guiding.jl | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/landmarks/guiding.jl b/landmarks/guiding.jl index da2a4fd..5409e49 100644 --- a/landmarks/guiding.jl +++ b/landmarks/guiding.jl @@ -211,9 +211,11 @@ function llikelihood(::LeftRule, Xcirc::SamplePath{<:State{Pnt}}, Q::GuidedPropo som::deepeltype(xx[1]) = 0. rout = copy(xx[1]) - if !constdiff(Q) # use sizetypes? - srout = zeros(Pnt, length(P.nfs)) - strout = zeros(Pnt, length(P.nfs)) + if !constdiff(Q) # use sizetypes? # must be target(Q).nfs + # srout = zeros(Pnt, length(P.nfs)) + # strout = zeros(Pnt, length(P.nfs)) + srout = zeros(Pnt, length(Q.target.nfs)) + strout = zeros(Pnt, length(Q.target.nfs)) end @@ -253,7 +255,7 @@ function hadamtrace(A, H::InverseCholesky) tr(tr(H*A)) end -import Trajectories.@unroll1 + function hadamtrace(A, H) @assert eachindex(A) == eachindex(H) @unroll1 for i in eachindex(A) From 997f58d61a5989aa186d02c741274abdd50d1c23 Mon Sep 17 00:00:00 2001 From: mschauer Date: Fri, 21 Jun 2019 14:40:59 +0200 Subject: [PATCH 38/58] Synch forward.jl --- landmarks/forward.jl | 26 ++++++++++++-------------- 1 file changed, 12 insertions(+), 14 deletions(-) diff --git a/landmarks/forward.jl b/landmarks/forward.jl index 49e6a28..7107b8a 100644 --- a/landmarks/forward.jl +++ b/landmarks/forward.jl @@ -15,6 +15,7 @@ using RCall using Base.Iterators using SparseArrays using Trajectories +using LowRankApprox models = [:ms, :ahs] model = models[2] @@ -141,28 +142,24 @@ elseif obsscheme==:full vT = vec(X.yy[end]) end + + #Paux = (model==:ms) ? Pmsaux : Pahsaux # solve backward recursion on [0,T] if LM if obsscheme == :partial - Lend = L - Σend = Σ - μend = deepvec(zeros(PointF, n)) + Lend = deepmat2unc(L) + Σend = deepmat2unc(Matrix(Σ)) + μend = zeros(PointF, n) xobs = vT -# Pahsaux = LandmarksAux(Pahs, State(vT, zero(vT))) -# Pmsaux = MarslandShardlowAux(Pms, State(vT, zero(vT))) else # full observation case # L = [(i==j)*one(Unc) for i in 1:2n, j in 1:2n] # Σ = [(i==j)*σobs^2*one(Unc) for i in 1:2n, j in 1:2n] μend = zeros(PointF, 2n) -# xobs = vec(X.yy[end]) -# Pahsaux = LandmarksAux(Pahs, X.yy[end]) -# Pmsaux = MarslandShardlowAux(Pms, X.yy[end]) end else - if obsscheme == :partial #νT = State(zero(vT), zero(vT)) νT = State(randn(PointF,Pahs.n), 0randn(PointF,Pahs.n)) @@ -216,6 +213,8 @@ if LM (Lstart, Mstart⁺, μstart) = lmgpupdate(Lend, Mend⁺, μend, Σ, L, v0) xinit = x0 + + else νt = [copy(ν) for s in tt_] println("Compute guiding term:") @@ -242,22 +241,20 @@ else Ht = map(H⁺ -> InverseCholesky(lchol(H⁺)),H⁺t) end - # careful, not a state νstart , Hstart⁺, Cstart = gpupdate(ν , H⁺, C, Σ, L, v0) - #also update C?? - Q = GuidedProposal!(P, Paux, tt_, νt, Ht, νstart, InverseCholesky(lchol(Hstart⁺)), Cstart) - xinit = cheat ? x0 : State(νstart.q, 0νstart.q)#νstart # or xinit ~ N(νstart, Hstart⁺) - end winit = zeros(StateW, dwiener) XX = SamplePath(tt_, [copy(xinit) for s in tt_]) WW = SamplePath(tt_, [copy(winit) for s in tt_]) sample!(WW, Wiener{Vector{StateW}}()) +# adjust xinit as test +xinit = State(v0, [Point(3,3) for i in 1:P.n] + rand(Point{Float64}, P.n)) + println("Sample guided bridge proposal:") @time Bridge.solve!(EulerMaruyama!(), XX, xinit, WW, Q) #error("STOP EARLY") @@ -317,6 +314,7 @@ let x = deepvec(State(x0.q, deepvec2state(x).p)) + s = deepvec2state(x) if MAKIE n = Node(s.q) From 8eb50c5f704b932d5d3223394341f064a59f2f3c Mon Sep 17 00:00:00 2001 From: mschauer Date: Fri, 21 Jun 2019 14:47:49 +0200 Subject: [PATCH 39/58] Synch models.jl --- landmarks/models.jl | 568 ++++++++++++++++++++++++-------------------- 1 file changed, 317 insertions(+), 251 deletions(-) mode change 100644 => 100755 landmarks/models.jl diff --git a/landmarks/models.jl b/landmarks/models.jl old mode 100644 new mode 100755 index a86e288..ccc6918 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -1,14 +1,14 @@ #### Landmarks specification import Bridge: _b, _b!, B!, σ!, b!, σ, b -struct MarslandShardlow{T} <: ContinuousTimeProcess{State{Point}} +struct MarslandShardlow{T} <: ContinuousTimeProcess{State{PointF}} a::T # kernel std parameter γ::T # noise level λ::T # mean reversion n::Int end -struct MarslandShardlowAux{S,T} <: ContinuousTimeProcess{State{Point}} +struct MarslandShardlowAux{S,T} <: ContinuousTimeProcess{State{PointF}} a::T # kernel std parameter γ::T # noise level λ::T # mean reversion @@ -24,14 +24,14 @@ struct Noisefield{T} τ::T # std of Gaussian kernel noise field end -struct Landmarks{S,T} <: ContinuousTimeProcess{State{Point}} +struct Landmarks{S,T} <: ContinuousTimeProcess{State{PointF}} a::T # kernel std λ::T # mean reversion n::Int64 # numer of landmarks nfs::Vector{Noisefield{S}} # vector containing pars of noisefields end -struct LandmarksAux{S,T} <: ContinuousTimeProcess{State{Point}} +struct LandmarksAux{S,T} <: ContinuousTimeProcess{State{PointF}} a::T # kernel std λ::T # mean reversion xT::State{Point{S}} # use x = State(P.v, zero(P.v)) where v is conditioning vector @@ -41,17 +41,23 @@ end LandmarksAux(P::Landmarks, xT) = LandmarksAux(P.a, P.λ, xT, P.n, P.nfs) +const LandmarkModel = Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux} + +Bridge.constdiff(::Union{MarslandShardlow, MarslandShardlowAux,LandmarksAux}) = true +Bridge.constdiff(::Landmarks) = false -const LandmarkModel = Union{Landmarks, LandmarksAux, -MarslandShardlow, MarslandShardlowAux} """ kernel in Hamiltonian """ -function kernel(q, P::LandmarkModel) # FIXME: Don't use norm +function kernel(q, P::LandmarkModel) (2*π*P.a^2)^(-d/2)*exp(-Bridge.inner(q)/(2*P.a^2)) + #0.1exp(-Bridge.inner(q)/(2*P.a^2)) end +""" +gradient of kernel in hamiltonian +""" function ∇kernel(q, P::LandmarkModel) -P.a^(-2) * kernel(q, P) * q end @@ -59,21 +65,137 @@ end """ Needed for b! in case P is auxiliary process """ -function ∇kernel(q, qT, P::Union{Landmarks, LandmarksAux, MarslandShardlow, MarslandShardlowAux}) +function ∇kernel(q, qT, P::LandmarkModel) -P.a^(-2) * kernel(qT, P) * q end - -function hamiltonian(x, P) +""" +Hamiltonian for deterministic part of landmarks model +""" +function hamiltonian((q, p), P) s = 0.0 - for i in axes(x, 2), j in axes(x, 2) - s += 1/2*dot(x.p[i], x.p[j])*kernel(x.q[i] - x.q[j], P) + for i in eachindex(q), j in eachindex(q) + s += 1/2*dot(p[i], p[j])*kernel(q[i] - q[j], P) end s end +Bridge.b(t::Float64, x, P::Union{Landmarks,MarslandShardlow})= Bridge.b!(t, x, 0*x, P) + +Bridge.σ(t, x, dm, P) = Bridge.σ!(t, x, dm , 0*x, P) + +######################################################################################################################################################################################## +################ MS model ######################################################################################### + + +""" +Evaluate drift of landmarks in (t,x) and save to out +x is a state and out as well +""" +function Bridge.b!(t, x, out, P::MarslandShardlow) + zero!(out) + for i in 1:P.n + for j in 1:P.n + out.q[i] += p(x,j)*kernel(q(x,i) - q(x,j), P) + out.p[i] += -P.λ*p(x,j)*kernel(q(x,i) - q(x,j), P) - + dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) + end + end + out +end +""" +Evaluate drift of landmarks auxiliary process in (t,x) and save to out +x is a state and out as well +""" +function Bridge.b!(t, x, out, Paux::MarslandShardlowAux) + zero!(out) + for i in 1:Paux.n + for j in 1:Paux.n + out.q[i] += p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) # out.qp[1,i] += + out.p[i] += -Paux.λ*p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) + end + end + out +end +""" +Compute tildeB(t) for landmarks auxiliary process +""" +function Bridge.B(t, Paux::MarslandShardlowAux) + X = zeros(UncF, 2Paux.n, 2Paux.n) + for i in 1:Paux.n + for j in 1:Paux.n + X[2i-1,2j] = kernel(q(Paux.xT,i) - q(Paux.xT,j), P) * one(UncF) + X[2i,2j] = -Paux.λ*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(UncF) + end + end + X +end + + +""" +Compute B̃(t) * X (B̃ from auxiliary process) and write to out +Both B̃(t) and X are of type UncMat +""" +function Bridge.B!(t,X,out, Paux::MarslandShardlowAux) + out .= 0.0 * out + for i in 1:Paux.n # separately loop over even and odd indices + for k in 1:2Paux.n # loop over all columns + for j in 1:Paux.n + out[2i-1,k] += kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) * X[p(j), k] + out[2i,k] += -Paux.λ*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(UncF) * X[p(j), k] + end + end + end + out +end + +function Bridge.β(t, Paux::MarslandShardlowAux) + State(zeros(PointF,Paux.n), zeros(PointF,Paux.n)) +end + +function Bridge.σ!(t, x, dm, out, P::Union{MarslandShardlow, MarslandShardlowAux}) + zero!(out.q) + out.p .= dm*P.γ + out +end + + +""" +Returns matrix a(t) for Marsland-Shardlow model +""" +function Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) + I = Int[] + X = Unc{Float64}[] + γ2 = P.γ^2 + for i in 1:P.n + push!(I, 2i) + push!(X, γ2*one(Unc{Float64})) + end + sparse(I, I, X, 2P.n, 2P.n) +end +Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P) + +""" +Multiply a(t,x) times xin (which is of type state) +Returns variable of type State +""" +function amul(t, x::State, xin::State, P::Union{MarslandShardlow, MarslandShardlowAux}) + out = copy(xin) + zero!(out.q) + out.p .= P.γ^2 .* xin.p + out +end +function amul(t, x::State, xin::Vector{<:Point}, P::Union{MarslandShardlow, MarslandShardlowAux}) + out = copy(x) + zero!(out.q) + out.p .= P.γ^2 .* vecofpoints2state(xin).p + out +end + +######################################################################################################################################################################################## +################ AHS model ######################################################################################### # kernel for noisefields function K̄(q,τ) exp(-Bridge.inner(q)/(2*τ^2))# (2*π*τ^2)^(-d/2)*exp(-norm(x)^2/(2*τ^2)) @@ -90,6 +212,18 @@ function ∇K̄(q, qT, τ) -τ^(-2) * K̄(qT,τ) * q end +""" + Define z(q) = < ∇K̄(q - δ,τ), λ > + Required for Stratonovich -> Ito correction in AHS-model +""" +z(q,τ,δ,λ) = Bridge.inner(∇K̄(q - δ,τ),λ) + +""" + Define ∇z(q) = ∇ < ∇K̄(q - δ,τ), λ > + Required for Stratonovich -> Ito correction in AHS-model +""" +∇z(q,τ,δ,λ) = gradient(x -> z(x,τ,δ,λ),q) + # function for specification of diffusivity of landmarks """ Suppose one noise field nf @@ -104,7 +238,6 @@ end σp(q, p, nf::Noisefield) = -Diagonal(p .* nf.λ .* ∇K̄(q - nf.δ,nf.τ)) - """ For AHS model compute total noise field on position experienced at a point x. Useful for plotting purposes. @@ -115,32 +248,29 @@ end """ function σq(x, nfs::Array{<:Noisefield,1}) out = σq(x, nfs[1]) - for j in 2:length(nfs) - out += σq(x, nfs[j]) + if length(nfs)>1 + for j in 2:length(nfs) + out += σq(x, nfs[j]) + end end - out end -#σq(nfs) = (x) -> σq(x,nfs) - -Bridge.b(t::Float64, x, P::Union{Landmarks,MarslandShardlow})= Bridge.b!(t, x, 0*x, P) +σq(nfs) = (x) -> σq(x,nfs) """ -Evaluate drift of landmarks in (t,x) and save to out -x is a state and out as well + Construct sequence of Noisefields for AHS model + db: domainbound (sources are places on square grid specified by + (-db:2nfstd:db) x -db:2nfstd:db + nfstd: standard deviation of noise fields (the smaller: the more noise fields we use) + γ: if set to one, then the value of the noise field on the positions is approximately 1 at all locations in the domain """ -function Bridge.b!(t, x, out, P::MarslandShardlow) - zero!(out) - for i in 1:P.n - for j in 1:P.n - out.q[i] += p(x,j)*kernel(q(x,i) - q(x,j), P) - # heat bath -# out.p[i] += -P.λ*p(x,j)*kernel(q(x,i) - q(x,j), P) - -# dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) - end - end - out +function construct_nfs(db, nfstd, γ) + r1 = -db:2nfstd:db + r2 = -db:2nfstd:db + nfloc = Point.(collect(product(r1, r2)))[:] + nfscales = [2/pi*γ*Point(1.0, 1.0) for x in nfloc] # intensity + [Noisefield(δ, λ, nfstd) for (δ, λ) in zip(nfloc, nfscales)] end @@ -155,31 +285,13 @@ function Bridge.b!(t, x, out, P::Landmarks) out.q[i] += p(x,j)*kernel(q(x,i) - q(x,j), P) out.p[i] += -dot(p(x,i), p(x,j)) * ∇kernel(q(x,i) - q(x,j), P) end -# if itostrat -# global ui = zero(Unc{Float64}) -# for k in 1:length(P.nfs) -# nf = P.nfs[k] -# ui += 0.5 * nf.τ^(-2) * diagm(0 =>nf.λ.^2) * K̄(q(x,i)-nf.δ,nf.τ)^2 -# end -# out.q[i] -= ui * q(x,i) -# out.p[i] += ui * p(x,i) -# end - end - out -end - - -""" -Evaluate drift of landmarks auxiliary process in (t,x) and save to out -x is a state and out as well -""" -function Bridge.b!(t, x, out, Paux::MarslandShardlowAux) - zero!(out) - for i in 1:Paux.n - for j in 1:Paux.n - out.q[i] += p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) - #out.p[i] += -Paux.λ*p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), P) - end + if itostrat + for k in 1:length(P.nfs) + nf = P.nfs[k] + out.q[i] += 0.5 * z(q(x,i),nf.τ,nf.δ,nf.λ) * K̄(q(x,i)-nf.δ,nf.τ) * nf.λ + out.p[i] += 0.5 * dot(p(x,i),nf.λ) * ( z(q(x,i),nf.τ,nf.δ,nf.λ) * ∇K̄(q(x,i)-nf.δ,nf.τ) -K̄(q(x,i)-nf.δ,nf.τ) * ∇z(q(x,i),nf.τ,nf.δ,nf.λ) ) + end + end end out end @@ -194,159 +306,81 @@ function Bridge.b!(t, x, out, Paux::LandmarksAux) for j in 1:Paux.n out.q[i] += p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) end - # out.p[i] += -P.λ*0.5*p(x,j)*kernel(q(P.xT,i) - q(P.xT,j), P) - # -0.5* dot(p(P.xT,i), p(P.xT,j)) * ∇kernel(q(x,i) - q(x,j),q(P.xT,i) - q(P.xT,j), P) if itostrat - global ui = zero(Unc{Float64}) for k in 1:length(P.nfs) + # approximate q by qT nf = P.nfs[k] - ui = 0.5 * nf.τ^(-2) * diagm(0 =>nf.λ.^2) * K̄(q(Paux.xT,i)-nf.δ,nf.τ)^2 + qT = q(Paux.xT,i) + out.q[i] += 0.5 * z(qT,nf.τ,nf.δ,nf.λ) * K̄(qT-nf.δ,nf.τ) * nf.λ + out.p[i] += 0.5 * dot(p(x,i),nf.λ) * ( z(qT,nf.τ,nf.δ,nf.λ) * ∇K̄(qT - nf.δ,nf.τ) -K̄(qT - nf.δ,nf.τ) * ∇z(qT,nf.τ,nf.δ,nf.λ) ) end - out.q[i] -= ui * q(x,i) - out.p[i] += ui * p(x,i) end end out end -""" -Compute tildeB(t) for landmarks auxiliary process -""" -function Bridge.B(t, Paux::MarslandShardlowAux) - Iind = Int[] - Jind = Int[] - X = Unc{Float64}[] - for i in 1:Paux.n - for j in 1:Paux.n - # terms for out.q[i] - push!(Iind, 2i - 1) - push!(Jind, 2j) - push!(X, kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc{Float64})) - - push!(Iind,2i) - push!(Jind,2j) - push!(X, -Paux.λ*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc{Float64})) - end - end - sparse(Iind, Jind, X, 2Paux.n, 2Paux.n) -end """ Compute tildeB(t) for landmarks auxiliary process """ function Bridge.B(t, Paux::LandmarksAux) - Iind = Int[] - Jind = Int[] - X = Unc{Float64}[] + X = zeros(UncF, 2Paux.n, 2Paux.n) for i in 1:Paux.n for j in 1:Paux.n - # terms for out.q[i] - push!(Iind, 2i - 1) - push!(Jind, 2j) - push!(X, kernel(q(Paux.xT,i) - q(Paux.xT,j), P)*one(Unc{Float64})) - - if itostrat - global out1 = zero(Unc{Float64}) - for k in 1:length(Paux.nfs) - nf = P.nfs[k] - out1 -= 0.5 * nf.τ^(-2) * Unc{Float64}(diagm(0 =>nf.λ.^2)) * K̄(q(Paux.xT,i)-nf.δ,nf.τ)^2 - end - push!(Iind, 2i - 1) - push!(Jind, 2j - 1) - push!(X, out1) - push!(Iind, 2i) - push!(Jind, 2j) - push!(X, -out1) + X[2i-1,2j] = kernel(q(Paux.xT,i) - q(Paux.xT,j), P) * one(UncF) + end + if itostrat + for k in 1:length(Paux.nfs) + nf = P.nfs[k] + qT = q(Paux.xT,i) + X[2i,2i] += 0.5 * ( z(qT,nf.τ,nf.δ,nf.λ) * ∇K̄(qT - nf.δ,nf.τ) -K̄(qT - nf.δ,nf.τ) * ∇z(qT,nf.τ,nf.δ,nf.λ) ) * nf.λ' end - - # terms for out.p[i] - # push!(I, 2i) - # push!(J, 2j-1) - # if j==i - # push!(X, sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), P) for j in setdiff(1:Paux.n,i)]) * one(Unc)) - # else - # push!(X, -1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc)) - # end end end - sparse(Iind, Jind, X, 2Paux.n, 2Paux.n) + X end - """ Compute B̃(t) * X (B̃ from auxiliary process) and write to out Both B̃(t) and X are of type UncMat """ -function Bridge.B!(t,X,out, Paux::MarslandShardlowAux) +function Bridge.B!(t,X,out, Paux::LandmarksAux) out .= 0.0 * out + u = zero(UncF) for i in 1:Paux.n # separately loop over even and odd indices for k in 1:2Paux.n # loop over all columns for j in 1:Paux.n - out[2i-1,k] += kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*X[p(j), k] #*one(Unc) - out[2i,k] += -Paux.λ*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc{Float64})*X[p(j), k] #*one(Unc) - # if j==i - # out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * - # kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) - # else - # out[2i,k] += X[q(j),k] *(-1/(2*Paux.a)) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc) - # end + out[2i-1,k] += kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*X[p(j), k] + end + if itostrat + u = 0.0*u + for k in 1:length(Paux.nfs) + nf = P.nfs[k] + qT = q(Paux.xT,i) + u += 0.5 * ( z(qT,nf.τ,nf.δ,nf.λ) * ∇K̄(qT - nf.δ,nf.τ) -K̄(qT - nf.δ,nf.τ) * ∇z(qT,nf.τ,nf.δ,nf.λ) ) * nf.λ' + end + out[2i,k] = u * X[2i,k] end end end - out end -""" -Compute B̃(t) * X (B̃ from auxiliary process) and write to out -Both B̃(t) and X are of type UncMat -""" -function Bridge.B!(t,X,out, Paux::LandmarksAux) -#### HAS NOT BEEN IMPLEMENTED FOR ITO-STRAT CORRECTION (probably doesn't pay off the effort) - out .= 0.0 * out - quickway = true - if quickway==true - out .= Matrix(Bridge.B(t,Paux)) * X - else # still need to implement an efficient way here - for i in 1:Paux.n # separately loop over even and odd indices - for k in 1:2Paux.n # loop over all columns - for j in 1:Paux.n - out[2i-1,k] += kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*X[p(j), k] #*one(Unc) - # if j==i - # out[2i,k] += X[q(j),k] *sum([1/(2*Paux.a) * dot(p(Paux.xT,i), p(Paux.xT,j)) * - # kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) for j in setdiff(1:Paux.n,i)])*one(Unc) - # else - # out[2i,k] += X[q(j),k] *(-1/(2*Paux.a)) * dot(p(Paux.xT,i), p(Paux.xT,j)) * kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(Unc) - # end - end +function Bridge.β(t, Paux::LandmarksAux) + out = 0.0 * copy(Paux.xT.q) + if itostrat + for i in 1:Paux.n + for k in 1:length(P.nfs) + nf = P.nfs[k] + qT = q(Paux.xT,i) + out[i] += 0.5 * z(qT,nf.τ,nf.δ,nf.λ) * K̄(qT-nf.δ,nf.τ) * nf.λ # simply take q at endpoint end end + return(State(out,zeros(PointF,Paux.n))) + else + return (State(zeros(PointF,Paux.n), zeros(PointF,Paux.n)) ) end - out -end - -function Bridge.β(t, Paux::Union{MarslandShardlowAux,LandmarksAux}) - State(zeros(Point{Float64},Paux.n), zeros(Point{Float64},Paux.n)) # FIXME -end - - -if TEST - Hend⁺ = [rand(Unc) for i in 1:2Paux.n, j in 1:2Paux.n] - t0 = 2.0 - BB = Matrix(Bridge.B(t0,Paux)) * Hend⁺ - out = deepcopy(Hend⁺) - Bridge.B!(t0,Hend⁺,out,Paux) - @test out==BB -end - - -Bridge.σ(t, x_, dm, P) = Bridge.σ!(t, x_, dm , 0*x_, P) - -function Bridge.σ!(t, x, dm, out, P::Union{MarslandShardlow, MarslandShardlowAux}) - zero!(out.q) - out.p .= dm*P.γ - out end @@ -390,8 +424,8 @@ function σtmul(t, x_, y::State{Pnt}, P::Union{Landmarks,LandmarksAux}) where Pn out end -function σt!(t, x_, y::State, out, P::Union{Landmarks,LandmarksAux}) - zero!(out) # added frank +function σt!(t, x_, y::State{Pnt}, out, P::Union{Landmarks,LandmarksAux}) where Pnt + zero!(out) if P isa Landmarks x = x_ else @@ -406,45 +440,6 @@ function σt!(t, x_, y::State, out, P::Union{Landmarks,LandmarksAux}) out end - - -""" -Returns matrix a(t) for Marsland-Shardlow model -""" -function Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) - I = Int[] - X = Unc{Float64}[] - γ2 = P.γ^2 - for i in 1:P.n - push!(I, 2i) - push!(X, γ2*one(Unc{Float64})) - end - sparse(I, I, X, 2P.n, 2P.n) -end -#Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) -Bridge.a(t, x, P::Union{MarslandShardlow, MarslandShardlowAux}) = Bridge.a(t, P) - - -# function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) -# if P isa Landmarks -# x = x_ -# else -# x = P.xT -# end -# out = zeros(Unc,2P.n,2P.n) -# for i in 1:P.n -# for k in 1:P.n -# for j in 1:length(P.nfs) -# out[2i-1,2k-1] += σq(q(x,i),P.nfs[j]) * σq(q(x, k),P.nfs[j])' -# out[2i-1,2k] += σq(q(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' -# out[2i,2k-1] += σp(q(x,i),p(x,i),P.nfs[j]) * σq(q(x,k),P.nfs[j])' -# out[2i,2k] += σp(q(x,i),p(x,i),P.nfs[j]) * σp(q(x,k),p(x,k),P.nfs[j])' -# end -# end -# end -# out -# end - function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) if P isa Landmarks x = x_ @@ -471,34 +466,10 @@ function Bridge.a(t, x_, P::Union{Landmarks,LandmarksAux}) out[i,k] = out[k,i] end end - for i in 2:2P.n - for k in 1:i-1 - out[i,k] = out[k,i] - end - end out end - Bridge.a(t, P::LandmarksAux) = Bridge.a(t, 0, P) -#Bridge.a(t, P::Union{Landmarks,LandmarksAux}) = Bridge.a(t, P.xT, P::Union{Landmarks,LandmarksAux}) - -""" -Multiply a(t,x) times xin (which is of type state) -Returns variable of type State -""" -function amul(t, x::State, xin::State, P::Union{MarslandShardlow, MarslandShardlowAux}) - out = copy(xin) - zero!(out.q) - out.p .= P.γ^2 .* xin.p - out -end -function amul(t, x::State, xin::Vector{<:Point}, P::Union{MarslandShardlow, MarslandShardlowAux}) - out = copy(x) - zero!(out.q) - out.p .= P.γ^2 .* vecofpoints2state(xin).p - out -end """ @@ -525,22 +496,117 @@ function amul(t, x::State, xin::State, P::Union{Landmarks,LandmarksAux}) Bridge.σ!(t, x, σtmul(t, x, xin, P),out,P) end -""" - Construct sequence of Noisefields for AHS model - db: domainbound (sources are places on square grid specified by - (-db:2nfstd:db) x -db:2nfstd:db - nfstd: standard deviation of noise fields (the smaller: the more noise fields we use) - γ: if set to one, then the value of the noise field on the positions is approximately 1 at all locations in the domain -""" -function construct_nfs(db, nfstd, γ) - r1 = -db:2nfstd:db - r2 = -db:2nfstd:db - nfloc = Point.(collect(product(r1, r2)))[:] - nfscales = [2/pi*γ*Point(1.0, 1.0) for x in nfloc] # intensity - [Noisefield(δ, λ, nfstd) for (δ, λ) in zip(nfloc, nfscales)] +function Bridge.a!(t, x_, out, P::Union{Landmarks,LandmarksAux}) + zero!(out) + if P isa Landmarks + x = x_ + else + x = P.xT + end + for i in 1:P.n + for k in i:P.n + for j in 1:length(P.nfs) + a11 = σq(q(x,i),P.nfs[j]) + a21 = σp(q(x,i),p(x,i),P.nfs[j]) + a12 = σq(q(x,k),P.nfs[j]) + a22 = σp(q(x,k),p(x,k),P.nfs[j]) + out[2i-1,2k-1] += a11 * a12' + out[2i-1,2k] += a11 * a22' + out[2i,2k-1] += a21 * a12' + out[2i,2k] += a21 * a22' + end + end + end + for i in 2:2P.n + for k in 1:i-1 + out[i,k] = out[k,i] + end + end + out end +###################################################################################################### -Bridge.constdiff(::Union{MarslandShardlow, MarslandShardlowAux,LandmarksAux}) = true -Bridge.constdiff(::Landmarks) = false + +if TEST + Hend⁺ = [rand(UncF) for i in 1:2Paux.n, j in 1:2Paux.n] + t0 = 2.0 + BB = Bridge.B(t0,Paux) * Hend⁺ + out = deepcopy(Hend⁺) + Bridge.B!(t0,Hend⁺,out,Paux) + @test out==BB +end + + + + + +if false # some failed attempts to compute tr(aH) right away faster, with less memory allocation + + """ + Compute row_i{sigmaq(t,x)} * dm where dm is a vector of points and sigma is the diffusion coefficient of landmarks + write to out which is of Vector{Points} + """ + function σq!(t, x_, dm, out, P::Union{Landmarks,LandmarksAux}) + if P isa Landmarks + x = x_ + else + x = P.xT + end + zero!(out) + for j in 1:length(P.nfs) + out += σq(q(x, i), P.nfs[j]) * dm[j] + end + + out + end + + + """ + Compute row_i{sigmap(t,x)} * dm where dm is a vector of points and sigma is the diffusion coefficient of landmarks + write to out which is of Vector{Points} + """ + function σp!(t, x_, dm, out, P::Union{Landmarks,LandmarksAux}) + if P isa Landmarks + x = x_ + else + x = P.xT + end + zero!(out) + for j in 1:length(P.nfs) + out += σp(q(x, i), p(x, i), P.nfs[j]) * dm[j] + end + out + end + ####################### + function tr_aH(t, x::State,H, P::Union{Landmarks,LandmarksAux}) + som = 0.0 + outq = zeros(UncF, length(P.nfs)) + outp = zeros(UncF, length(P.nfs)) + for i in 1:P.n + σtHcol!(outq,x,H[:,2i-1],P.nfs) # compute σ' times Col_i(H) (should give J x 1 column-vector of Unc) + σtHcol!(outp,x,H[:,2i],P.nfs) # compute σ' times Col_i(H) (should give J x 1 column-vector of Unc) + for j in 1:length(P.nfs) + som += tr(σq(q(x,i),P.nfs[j]) * outq[j]) + + tr(σp(q(x,i),p(x,i),P.nfs[j]) * outp[j]) + end + + end + som + end + + function σtHcol!(out,x,Hvec,nfs) + zero!(out) + for j in 1:length(nfs) + for i in 1:P.n + out[j] += σq(q(x,i),nfs[j]) * Hvec[2i-1] + σp(q(x,i),p(x,i),nfs[j]) * Hvec[2i] + end + end + out + end + + # @time tr_aH(1.0,x0,H,P) + # @time sum(sum(Bridge.a((2,3.0,), x0, P).*H)) + # @time dot(Bridge.a((2,3.0,), x0, P),H) +end From 54d72c48470318e5af7b2b301096762feda651bc Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 12:39:57 +0200 Subject: [PATCH 40/58] Update landmarks/patches.jl --- landmarks/patches.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/landmarks/patches.jl b/landmarks/patches.jl index 7915f57..7e0b5de 100644 --- a/landmarks/patches.jl +++ b/landmarks/patches.jl @@ -299,7 +299,7 @@ end x0: starting point P: landmarks specification """ -landmarksforward = function(t, dwiener, x0::State{Pnt}, P) where Pnt +function landmarksforward(t, dwiener, x0::State{Pnt}, P) where Pnt W = initSamplePath(t, zeros(Pnt, dwiener)) sample!(W, Wiener{Vector{Pnt}}()) # forward simulate landmarks From 01a4c26805f7a27c1674f14c42a8006e57a68ace Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 12:40:07 +0200 Subject: [PATCH 41/58] Update landmarks/patches.jl --- landmarks/patches.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/landmarks/patches.jl b/landmarks/patches.jl index 7e0b5de..a55935c 100644 --- a/landmarks/patches.jl +++ b/landmarks/patches.jl @@ -2,7 +2,7 @@ """ Initialise SamplePath on time grid t by copying x into each value of the field yy """ -initSamplePath(t,x) = SamplePath(t, [copy(x) for s in t]) +initSamplePath(t,x) = Bridge.samplepath(t, x) function Bridge.sample!(W::SamplePath{Vector{T}}, P::Wiener{Vector{T}}, y1 = W.yy[1]) where {T} y = copy(y1) From 90b3acbc678bfb4998084ef7bd920721eab1f09b Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 12:40:18 +0200 Subject: [PATCH 42/58] Update landmarks/patches.jl --- landmarks/patches.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/landmarks/patches.jl b/landmarks/patches.jl index a55935c..6000634 100644 --- a/landmarks/patches.jl +++ b/landmarks/patches.jl @@ -274,7 +274,7 @@ function conj!(A::Array{<:Unc,2}) A end -function conj2(A::Array{<:Unc,2}) +function conj2(A::Array{T<:Unc,2}) where T At = Matrix{Unc}(undef,size(A,2),size(A,1)) for i in 1:size(A,2) for j in 1:size(A,1) From a69b3932e2a5050123a3db0e054551d63ab6aece Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 12:40:24 +0200 Subject: [PATCH 43/58] Update landmarks/patches.jl --- landmarks/patches.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/landmarks/patches.jl b/landmarks/patches.jl index 6000634..88c4bba 100644 --- a/landmarks/patches.jl +++ b/landmarks/patches.jl @@ -275,7 +275,7 @@ function conj!(A::Array{<:Unc,2}) end function conj2(A::Array{T<:Unc,2}) where T - At = Matrix{Unc}(undef,size(A,2),size(A,1)) + At = Matrix{T}(undef,size(A,2),size(A,1)) for i in 1:size(A,2) for j in 1:size(A,1) At[i,j] = A[j,i]' From 4ec7e56eedc9564252adecd8f36a1b39a76e28fa Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 12:51:33 +0200 Subject: [PATCH 44/58] Update landmarks/models.jl --- landmarks/models.jl | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/landmarks/models.jl b/landmarks/models.jl index ccc6918..a8b76de 100755 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -75,7 +75,8 @@ Hamiltonian for deterministic part of landmarks model function hamiltonian((q, p), P) s = 0.0 for i in eachindex(q), j in eachindex(q) - s += 1/2*dot(p[i], p[j])*kernel(q[i] - q[j], P) +# s += 1/2*dot(p[i], p[j])*kernel(q[i] - q[j], P) + s += 1/2*dot(x.p[i], x.p[j])*kernel(x.q[i] - x.q[j], P) end s end From ddb2f7ff517384d1a27646cdba66529e4cd8bc96 Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 12:51:44 +0200 Subject: [PATCH 45/58] Update landmarks/models.jl --- landmarks/models.jl | 1 - 1 file changed, 1 deletion(-) diff --git a/landmarks/models.jl b/landmarks/models.jl index a8b76de..89f1017 100755 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -52,7 +52,6 @@ kernel in Hamiltonian """ function kernel(q, P::LandmarkModel) (2*π*P.a^2)^(-d/2)*exp(-Bridge.inner(q)/(2*P.a^2)) - #0.1exp(-Bridge.inner(q)/(2*P.a^2)) end """ From c7b6c4ad73bb2b19dbef60f29b4dfe5fd87b9883 Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 12:51:59 +0200 Subject: [PATCH 46/58] Update landmarks/models.jl --- landmarks/models.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/landmarks/models.jl b/landmarks/models.jl index 89f1017..0500833 100755 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -71,7 +71,7 @@ end """ Hamiltonian for deterministic part of landmarks model """ -function hamiltonian((q, p), P) +function hamiltonian(x, P) s = 0.0 for i in eachindex(q), j in eachindex(q) # s += 1/2*dot(p[i], p[j])*kernel(q[i] - q[j], P) From e47e8269d4bd4249f7ce2ac081e817951392a41e Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 12:52:09 +0200 Subject: [PATCH 47/58] Update landmarks/models.jl --- landmarks/models.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/landmarks/models.jl b/landmarks/models.jl index 0500833..6629fd0 100755 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -73,7 +73,7 @@ Hamiltonian for deterministic part of landmarks model """ function hamiltonian(x, P) s = 0.0 - for i in eachindex(q), j in eachindex(q) + for i in axes(x, 2), j in axes(x, 2) # s += 1/2*dot(p[i], p[j])*kernel(q[i] - q[j], P) s += 1/2*dot(x.p[i], x.p[j])*kernel(x.q[i] - x.q[j], P) end From 607cceaeaf1de9e708ad5f4c86ade11f209d2902 Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 13:05:44 +0200 Subject: [PATCH 48/58] Update landmarks/models.jl --- landmarks/models.jl | 1 - 1 file changed, 1 deletion(-) diff --git a/landmarks/models.jl b/landmarks/models.jl index 6629fd0..7208619 100755 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -248,7 +248,6 @@ z(q,τ,δ,λ) = Bridge.inner(∇K̄(q - δ,τ),λ) """ function σq(x, nfs::Array{<:Noisefield,1}) out = σq(x, nfs[1]) - if length(nfs)>1 for j in 2:length(nfs) out += σq(x, nfs[j]) end From cea39f2c822ea201b88a5179017ba3e37b844737 Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 13:06:33 +0200 Subject: [PATCH 49/58] Update landmarks/models.jl --- landmarks/models.jl | 1 - 1 file changed, 1 deletion(-) diff --git a/landmarks/models.jl b/landmarks/models.jl index 7208619..e8e6f46 100755 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -250,7 +250,6 @@ function σq(x, nfs::Array{<:Noisefield,1}) out = σq(x, nfs[1]) for j in 2:length(nfs) out += σq(x, nfs[j]) - end end out end From 365295f515eebf3fb7c30a00b4c17e9f78697665 Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 13:13:16 +0200 Subject: [PATCH 50/58] Update landmarks/models.jl --- landmarks/models.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/landmarks/models.jl b/landmarks/models.jl index e8e6f46..e5276d6 100755 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -112,7 +112,7 @@ function Bridge.b!(t, x, out, Paux::MarslandShardlowAux) zero!(out) for i in 1:Paux.n for j in 1:Paux.n - out.q[i] += p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) # out.qp[1,i] += + out.q[i] += p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) out.p[i] += -Paux.λ*p(x,j)*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) end end From aca6154d37822a35a44e4c91cab198151c157e16 Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 13:27:54 +0200 Subject: [PATCH 51/58] Update landmarks/models.jl --- landmarks/models.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/landmarks/models.jl b/landmarks/models.jl index e5276d6..aae52c3 100755 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -151,7 +151,7 @@ function Bridge.B!(t,X,out, Paux::MarslandShardlowAux) out end -function Bridge.β(t, Paux::MarslandShardlowAux) +function Bridge.β(t, Paux::MarslandShardlowAux) # Not AD save State(zeros(PointF,Paux.n), zeros(PointF,Paux.n)) end From 223981aafc184356c1f7c1c77c120ce4d115ba1e Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 13:30:25 +0200 Subject: [PATCH 52/58] Update landmarks/models.jl --- landmarks/models.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/landmarks/models.jl b/landmarks/models.jl index aae52c3..05c17ca 100755 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -122,7 +122,7 @@ end """ Compute tildeB(t) for landmarks auxiliary process """ -function Bridge.B(t, Paux::MarslandShardlowAux) +function Bridge.B(t, Paux::MarslandShardlowAux) # not AD safe X = zeros(UncF, 2Paux.n, 2Paux.n) for i in 1:Paux.n for j in 1:Paux.n From 00f3175d9ce2bf8eebf15f0a66f80eba686ce900 Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 13:30:37 +0200 Subject: [PATCH 53/58] Update landmarks/models.jl --- landmarks/models.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/landmarks/models.jl b/landmarks/models.jl index 05c17ca..3a2177d 100755 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -144,7 +144,7 @@ function Bridge.B!(t,X,out, Paux::MarslandShardlowAux) for k in 1:2Paux.n # loop over all columns for j in 1:Paux.n out[2i-1,k] += kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) * X[p(j), k] - out[2i,k] += -Paux.λ*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux)*one(UncF) * X[p(j), k] + out[2i,k] += -Paux.λ*kernel(q(Paux.xT,i) - q(Paux.xT,j), Paux) * X[p(j), k] end end end From d1ae52161d58e0050e1b9328d46dfd4f26ee97d4 Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 13:33:05 +0200 Subject: [PATCH 54/58] Update landmarks/models.jl --- landmarks/models.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/landmarks/models.jl b/landmarks/models.jl index 3a2177d..e133fa3 100755 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -254,7 +254,7 @@ function σq(x, nfs::Array{<:Noisefield,1}) out end -σq(nfs) = (x) -> σq(x,nfs) +σq(nfs) = (x) -> σq(x,nfs) # inefficient """ Construct sequence of Noisefields for AHS model From 3eea3f1785a01a5fca9d50c9e7fb99cd6daf6a6e Mon Sep 17 00:00:00 2001 From: Moritz Schauer Date: Mon, 24 Jun 2019 13:33:20 +0200 Subject: [PATCH 55/58] Update landmarks/models.jl --- landmarks/models.jl | 1 + 1 file changed, 1 insertion(+) diff --git a/landmarks/models.jl b/landmarks/models.jl index e133fa3..b0d871d 100755 --- a/landmarks/models.jl +++ b/landmarks/models.jl @@ -166,6 +166,7 @@ end Returns matrix a(t) for Marsland-Shardlow model """ function Bridge.a(t, P::Union{MarslandShardlow, MarslandShardlowAux}) + error("remove error if we want to keep this") I = Int[] X = Unc{Float64}[] γ2 = P.γ^2 From ce8dfc921d1eb1cebcf88c3aff57a177fae36c67 Mon Sep 17 00:00:00 2001 From: mschauer Date: Mon, 24 Jun 2019 11:51:31 +0200 Subject: [PATCH 56/58] Synchronize LM files --- landmarks/{ => back}/lmpar.jl | 13 ++-- landmarks/lmguiding.jl | 110 ++++++++++++++++++++++++++-------- 2 files changed, 93 insertions(+), 30 deletions(-) rename landmarks/{ => back}/lmpar.jl (94%) mode change 100644 => 100755 mode change 100644 => 100755 landmarks/lmguiding.jl diff --git a/landmarks/lmpar.jl b/landmarks/back/lmpar.jl old mode 100644 new mode 100755 similarity index 94% rename from landmarks/lmpar.jl rename to landmarks/back/lmpar.jl index c2924b0..053fa2d --- a/landmarks/lmpar.jl +++ b/landmarks/back/lmpar.jl @@ -23,7 +23,7 @@ partialobs = true const d = 2 const itostrat = false -n = 100 # nr of landmarks +n = 30 # nr of landmarks θ = 2π/5# π/6 0#π/5 # angle to rotate endpoint @@ -194,7 +194,8 @@ function obj(xinitv) + llikelihood(LeftRule(), XXᵒ, Q; skip = 1) ) end -using Makie, Random +using Makie +using Random Random.seed!(2) let x = deepvec(x0) @@ -205,10 +206,10 @@ let s = deepvec2state(x) n = Node(s.q) n2 = Node(s.p) - sc = scatter(x0.q, color=:red) + sc = scatter(x0.q, color=:red) # plot locations of x0 in red - scatter!(sc, n2) - scatter!(sc, n, color=:blue) + scatter!(sc, n2) # plot momenta of x0 in black + scatter!(sc, n, color=:blue) # plot locations of x0 (again) in blue display(sc) # only optimize momenta @@ -230,3 +231,5 @@ let println("$i d(x,xtrue) = ", norm(deepvec(x0)-x))#, " ", o) end end + +# should first plot v0 and vT, should randomly initialise momenta and see whether these convert to p0 diff --git a/landmarks/lmguiding.jl b/landmarks/lmguiding.jl old mode 100644 new mode 100755 index 5c1926e..2cb9e5d --- a/landmarks/lmguiding.jl +++ b/landmarks/lmguiding.jl @@ -1,43 +1,58 @@ -# compute guiding term: backward ode -# compute likelihood of guided proposal +import Bridge: kernelr3!, R3!, target, auxiliary, constdiff, llikelihood, _b!, B!, σ!, b! -# not sure about this -function lmgpupdate(Lt, Mt, μt, vt, Σ, L, v) +""" + Guided proposal update for newly incoming observation. + The existing tuple (Lt, Mt, μt, xobst) is updated using + Σ: covariance matrix of the incoming observation + L: specification that L x is observed (where x is the 'full' state) + newobs: new observation (obtained as L x + N(0,Σ)) +""" +function lmgpupdate(Lt, Mt::Array{Pnt,2}, μt, xobst, (L, Σ, newobs)) where Pnt Lt = [L; Lt] - Mt = [Σ 0Σ; 0Σ Mt] - μt = [0v; μt] - vt = [v; vt] + m = size(Σ)[1] + n = size(Mt)[2] + Mt = [Σ zeros(Pnt,m,n); zeros(Pnt,n,m) Mt] + μt = [0newobs; μt] + xobst = [newobs; xobst] - Lt, Mt, μt, vt + Lt, Mt, μt, xobst end - - -import Bridge: kernelr3!, R3!, target, auxiliary, constdiff, llikelihood, _b!, B!, σ!, b! +""" + Initialise arrays for (L,M,μ) where each value is copied length(t) times +""" +function initLMμ(t,(L,M,μ)) + Lt = [copy(L) for s in t] + Mt⁺ = [copy(M) for s in t] + μt = [copy(μ) for s in t] + Lt, Mt⁺ , μt +end """ Construct guided proposal on a single segment with times in tt from precomputed ν and H """ -struct GuidedProposall!{T,Ttarget,Taux,TL,TM,Tμ,Txobs,F} <: ContinuousTimeProcess{T} +struct GuidedProposall!{T,Ttarget,Taux,TL,TM,Tμ,TH,Txobs,F} <: ContinuousTimeProcess{T} target::Ttarget # P aux::Taux # Ptilde tt::Vector{Float64} # grid of time points on single segment (S,T] Lt::Vector{TL} Mt::Vector{TM} μt::Vector{Tμ} + Ht::Vector{TH} xobs::Txobs endpoint::F - function GuidedProposall!(target, aux, tt_, L, M, μ, xobs, endpoint=Bridge.endpoint) + function GuidedProposall!(target, aux, tt_, L, M, μ, H, xobs, endpoint=Bridge.endpoint) tt = collect(tt_) - new{Bridge.valtype(target),typeof(target),typeof(aux),eltype(L),eltype(M),eltype(μt),typeof(xobs),typeof(endpoint)}(target, aux, tt, L, M, μ, xobs, endpoint) + new{Bridge.valtype(target),typeof(target),typeof(aux),eltype(L),eltype(M),eltype(μt),eltype(H),typeof(xobs),typeof(endpoint)}(target, aux, tt, L, M, μ, H, xobs, endpoint) end end struct Lm end -function guidingbackwards!(::Lm, t, (Lt, Mt⁺, μt), Paux, (Lend, Mend⁺, μend)) + +function guidingbackwards!(::Lm, t, (Lt, Mt⁺, μt), Paux, (L, Σ , μend)) Mt⁺[end] .= Σ Lt[end] .= L BB = Matrix(Bridge.B(0, Paux)) # does not depend on time @@ -47,7 +62,7 @@ function guidingbackwards!(::Lm, t, (Lt, Mt⁺, μt), Paux, (Lend, Mend⁺, μen # @time aa = Matrix(Bridge.a(0, Paux)) # vanilla, no lr approx # @time aalr = pheigfact(deepmat(Matrix(Bridge.a(0, Paux)))) # low rank approx default # @time aalr = pheigfact(deepmat(Matrix(Bridge.a(0, Paux))),rank=400) # fix rank - @time aalr = pheigfact(deepmat(Matrix(Bridge.a(0, Paux))), rtol=1e-7) # control accuracy of lr approx + @time aalr = pheigfact(deepmat(Matrix(Bridge.a(0, Paux))), rtol=1e-10) # control accuracy of lr approx println("Rank ",size(aalr[:vectors],2), " approximation to ã") sqrt_aalr = deepmat2unc(aalr[:vectors] * diagm(0=> sqrt.(aalr[:values]))) @@ -82,6 +97,7 @@ function _r!((i,t), x::State, out::State, Q::GuidedProposall!) out .= vecofpoints2state(Q.Lt[i]' * (Q.Mt[i] *(Q.xobs-Q.μt[i]-Q.Lt[i]*vec(x)))) out end +# need function that multiplies square unc with state and outputs state function guidingterm((i,t),x::State,Q::GuidedProposall!) #Bridge.b(t,x,Q.target) + @@ -89,6 +105,8 @@ function guidingterm((i,t),x::State,Q::GuidedProposall!) end """ Returns the guiding terms a(t,x)*r̃(t,x) along the path of a guided proposal +for each value in X.tt. +Hence, it returns an Array of type State """ function guidingterms(X::SamplePath{State{SArray{Tuple{2},Float64,1,2}}},Q::GuidedProposall!) i = first(1:length(X.tt)) @@ -102,19 +120,31 @@ end """ v0 consists of all observation vectors stacked, so in case of two observations, it should be v0 and vT stacked """ -function Bridge.lptilde(x, L0, M0⁺, μ0, v0, Po::GuidedProposall!) - y = v0 - μ0 - L0*x - -0.5*logdet(deepmat(M0⁺)) -0.5*dot(y, M0⁺*y) +function Bridge.lptilde(x, L0, M⁺0, μ0, xobs) + y = deepvec(xobs - μ0 - L0*x) + M⁺0deep = deepmat(M⁺0) + -0.5*logdet(M⁺0deep) -0.5*dot(y, M⁺0deep\y) end -function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposall!; skip = 0) +function llikelihood(::LeftRule, Xcirc::SamplePath{State{Pnt}}, Q::GuidedProposall!; skip = 0) where {Pnt} tt = Xcirc.tt xx = Xcirc.yy - som::deepeltype(xx[1]) = 0. + + # initialise objects to write into + # srout and strout are vectors of Points + if !constdiff(Q) # use sizetypes? # must be target(Q).nfs + srout = zeros(Pnt, length(Q.target.nfs)) + strout = zeros(Pnt, length(Q.target.nfs)) + end + # rout, bout, btout are of type State rout = copy(xx[1]) bout = copy(rout) btout = copy(rout) + + At = Bridge.a((1,0), xx[1], auxiliary(Q)) + A = zeros(Unc{deepeltype(xx[1])}, 2Q.target.n,2Q.target.n) + for i in 1:length(tt)-1-skip #skip last value, summing over n-1 elements s = tt[i] x = xx[i] @@ -126,11 +156,41 @@ function llikelihood(::LeftRule, Xcirc::SamplePath, Q::GuidedProposall!; skip = som += dot(bout-btout, rout) * dt if !constdiff(Q) - H = H((i,s), x, Q) - Δa = a((i,s), x, target(Q)) - a((i,s), x, auxiliary(Q)) - som -= 0.5*tr(Δa*H) * dt - som += 0.5*(rout'*Δa*rout) * dt + σt!(s, x, rout, srout, target(Q)) # σ(t,x)' * tilder(t,x) + σt!(s, x, rout, strout, auxiliary(Q)) # tildeσ(t,x)' * tilder(t,x) + + som += 0.5*Bridge.inner(srout) * dt # |σ(t,x)' * tilder(t,x)|^2 + som -= 0.5*Bridge.inner(strout) * dt # |tildeσ(t,x)' * tilder(t,x)|^2 + + Bridge.a!((i,s), x, A, target(Q)) #A = Bridge.a((i,s), x, target(Q)) + + # som -= 0.5*hadamtrace(A, Q.Ht[i]) * dt + # som += 0.5*hadamtrace(At, Q.Ht[i]) * dt + som += 0.5*(dot(At,Q.Ht[i]) - dot(A,Q.Ht[i])) * dt end end som end + +#tr(si si' L' M L)=tr(si' L' M (si' L')') = tr(C' C) with Minv =D D' +# C' = si' L' D'inv oftwel C' D' = si' L' oftewel D C = (si' L')' + +# compute sum ( tr(amul(t,x, coli(H))[i]) i in 1: nd) +# each matrix in the trace is a Unc-matrix +# for i in 1:n +# Bridge.σrowi!(t, x_, σt!(t, x_, coli(H)::State, out, P), out, P) +# som+= tr of this thing +# end + + +# ---- Doe tr (amuli!(t,x, coli) ) and sum over i + +construct_guidedproposal! = function(tt_, (Lt, Mt⁺ , μt), (LT,ΣT,μT), (L0, Σ0), (xobs0, xobsT), P, Paux) + (Lt0₊, Mt⁺0₊, μt0₊) = guidingbackwards!(Lm(), tt_, (Lt, Mt⁺,μt), Paux, (LT, ΣT, μT)) + Lt0, Mt⁺0, μt0, xobst0 = lmgpupdate(Lt0₊, Mt⁺0₊, μt0₊, xobsT, (L0, Σ0, xobs0)) + Mt = map(X -> InverseCholesky(lchol(X)),Mt⁺) + Ht = [Lt[i]' * (Mt[i] * Lt[i] ) for i in 1:length(tt_) ] + Q = GuidedProposall!(P, Paux, tt_, Lt, Mt, μt, Ht, xobsT) + + (Lt, Mt⁺ , μt), Q, (Lt0, Mt⁺0, μt0, xobst0) +end From cac5cca6eaadf9caa8a59bf6acc8ea7683660668 Mon Sep 17 00:00:00 2001 From: mschauer Date: Mon, 24 Jun 2019 12:22:29 +0200 Subject: [PATCH 57/58] Review lmguiding.jl --- landmarks/lmguiding.jl | 13 ------------- 1 file changed, 13 deletions(-) diff --git a/landmarks/lmguiding.jl b/landmarks/lmguiding.jl index 2cb9e5d..f64df1e 100755 --- a/landmarks/lmguiding.jl +++ b/landmarks/lmguiding.jl @@ -172,19 +172,6 @@ function llikelihood(::LeftRule, Xcirc::SamplePath{State{Pnt}}, Q::GuidedProposa som end -#tr(si si' L' M L)=tr(si' L' M (si' L')') = tr(C' C) with Minv =D D' -# C' = si' L' D'inv oftwel C' D' = si' L' oftewel D C = (si' L')' - -# compute sum ( tr(amul(t,x, coli(H))[i]) i in 1: nd) -# each matrix in the trace is a Unc-matrix -# for i in 1:n -# Bridge.σrowi!(t, x_, σt!(t, x_, coli(H)::State, out, P), out, P) -# som+= tr of this thing -# end - - -# ---- Doe tr (amuli!(t,x, coli) ) and sum over i - construct_guidedproposal! = function(tt_, (Lt, Mt⁺ , μt), (LT,ΣT,μT), (L0, Σ0), (xobs0, xobsT), P, Paux) (Lt0₊, Mt⁺0₊, μt0₊) = guidingbackwards!(Lm(), tt_, (Lt, Mt⁺,μt), Paux, (LT, ΣT, μT)) Lt0, Mt⁺0, μt0, xobst0 = lmgpupdate(Lt0₊, Mt⁺0₊, μt0₊, xobsT, (L0, Σ0, xobs0)) From 620e7fa074b40df6f921406aba41139907ee1bb4 Mon Sep 17 00:00:00 2001 From: mschauer Date: Mon, 24 Jun 2019 13:58:40 +0200 Subject: [PATCH 58/58] Add remaining LM files --- landmarks/automaticdiff_lm.jl | 91 +++++++++ landmarks/generatedata.jl | 76 ++++++++ landmarks/lm_main.jl | 340 ++++++++++++++++++++++++++++++++++ 3 files changed, 507 insertions(+) create mode 100755 landmarks/automaticdiff_lm.jl create mode 100644 landmarks/generatedata.jl create mode 100755 landmarks/lm_main.jl diff --git a/landmarks/automaticdiff_lm.jl b/landmarks/automaticdiff_lm.jl new file mode 100755 index 0000000..fecdf57 --- /dev/null +++ b/landmarks/automaticdiff_lm.jl @@ -0,0 +1,91 @@ +""" +Stochastic approximation to transition density. +Provide Wiener process. +""" +function slogpW(x0deepv, Lt0, Mt⁺0, μt0, xobst0, Q, Wᵒ) + x0 = deepvec2state(x0deepv) + Xᵒ = Bridge.solve(EulerMaruyama!(), x0, Wᵒ, Q)# this causes the problem + lptilde(vec(x0), Lt0, Mt⁺0, μt0, xobst0) + llikelihood(LeftRule(), Xᵒ, Q; skip = 1) +end +slogpW(Lt0, Mt⁺0, μt0, xobst0, Q, Wᵒ) = (x) -> slogpW(x, Lt0, Mt⁺0, μt0, xobst0, Q, Wᵒ) +∇slogpW(Lt0, Mt⁺0, μt0, xobst0, Q, Wᵒ) = (x) -> gradient(slogpW(Lt0, Mt⁺0, μt0, xobst0, Q, Wᵒ), x) + +function slogpWX(x0deepv, Lt0, Mt⁺0, μt0, xobst0, Q, Wᵒ,Xᵒ) # preferred way + x0 = deepvec2state(x0deepv) +# println(fieldnames(typeof(x0))) + solve!(EulerMaruyama!(), Xᵒ, x0, Wᵒ, Q) + lptilde(vec(x0), Lt0, Mt⁺0, μt0, xobst0) + llikelihood(LeftRule(), Xᵒ, Q; skip = 1) +end + + +""" + update initial momenta and/or guided proposals using either + sgd, sgld or mcmc +""" +function updatepath!(X,Xᵒ,W,Wᵒ,Wnew,ll,x,xᵒ,∇x, ∇xᵒ, + sampler,(Lt0, Mt⁺0, μt0, xobst0, Q),mask, mask_id, δ, ρ, acc) + if sampler in [:sgd, :sgld] + sample!(W, Wiener{Vector{StateW}}()) + cfg = GradientConfig(slogpW(Lt0, Mt⁺0, μt0, xobst0, Q, W), x, Chunk{d*P.n}()) # 2*d*P.n is maximal + @time gradient!(∇x, slogpW(Lt0, Mt⁺0, μt0, xobst0, Q, W),x,cfg) + + if sampler==:sgd + x .+= δ*mask.*∇x + end + if sampler==:sgld + x .+= .5*δ*mask.*∇x + sqrt(δ)*mask.*randn(2d*Q.target.n) + end + xstate = deepvec2state(x) + Bridge.solve!(EulerMaruyama!(), X, xstate, W, Q) + obj = lptilde(vec(xstate), Lt0, Mt⁺0, μt0, xobst0) + + llikelihood(LeftRule(), X, Q; skip = 1) + println("ll ", obj) + end + if sampler==:mcmc + # Update W + sample!(Wnew, Wiener{Vector{PointF}}()) + Wᵒ.yy .= ρ * W.yy + sqrt(1-ρ^2) * Wnew.yy + solve!(EulerMaruyama!(), Xᵒ, deepvec2state(x), Wᵒ, Q) + + llᵒ = llikelihood(Bridge.LeftRule(), Xᵒ, Q,skip=sk) + print("ll $ll $llᵒ, diff_ll: ",round(llᵒ-ll;digits=3)) + + if log(rand()) <= llᵒ - ll + X.yy .= Xᵒ.yy + W.yy .= Wᵒ.yy + ll = llᵒ + print("update innovation acceptedœ“") + acc[1] +=1 + else + print("update innovation rejected") + end + println() + + # MALA step (update x) + ∇x .= ∇slogpW(Lt0, Mt⁺0, μt0, xobst0, Q, W)(x) + xᵒ .= x .+ .5*δ * mask.* (∇x .+ sqrt(δ) * randn(length(x))) + ∇xᵒ .= ∇slogpW(Lt0, Mt⁺0, μt0, xobst0, Q, W)(xᵒ) + + xstate = deepvec2state(x) + xᵒstate = deepvec2state(xᵒ) + solve!(EulerMaruyama!(), Xᵒ, xᵒstate, W, Q) + ainit = lptilde(vec(xᵒstate), Lt0, Mt⁺0, μt0, xobst0) + llikelihood(LeftRule(), Xᵒ, Q; skip = 1) - + lptilde(vec(xstate), Lt0, Mt⁺0, μt0, xobst0) - llikelihood(LeftRule(), X, Q; skip = 1) - + logpdf(MvNormal(d*P.n,sqrt(δ)),(xᵒ - x - .5*δ* mask.* ∇x)[mask_id]) + + logpdf(MvNormal(d*P.n,sqrt(δ)),(x - xᵒ - .5*δ* mask.* ∇xᵒ)[mask_id]) + # compute acc prob + print("ainit: ", ainit) + if log(rand()) <= ainit + x .= xᵒ + xstate = xᵒstate + X.yy .= Xᵒ.yy + println("mala step acceptedœ“") + acc[2] +=1 + else + println("mala step rejectedœ“") + end + obj = lptilde(vec(xstate), Lt0, Mt⁺0, μt0, xobst0) + + llikelihood(LeftRule(), X, Q; skip = 1) + end + X,Xᵒ,W,Wᵒ,ll,x,xᵒ,∇x,∇xᵒ, obj,acc +end diff --git a/landmarks/generatedata.jl b/landmarks/generatedata.jl new file mode 100644 index 0000000..e7a7c5f --- /dev/null +++ b/landmarks/generatedata.jl @@ -0,0 +1,76 @@ +""" +Generate landmarks data, or read landmarks data. +- dataset: specifies type of data to be generated/loaded +- P: +- t: grid used for generating data +- σobs: standard deviation of observation noise + +Returns +- x0: initial state without noise +- xobs0, xobsT: (observed initial and final states with noise) +- Xf: forward simulated path +- P: only adjusted in case of 'real' data, like the bearskull data + +Example + x0, xobs0, xobsT, Xf, P = generatedata(dataset,P,t,σobs) + +""" +function generatedata(dataset,P,t,σobs) + + n = P.n + if P isa MarslandShardlow + dwiener = P.n + else + dwiener = length(P.nfs) + end + if dataset=="forwardsimulated" + q0 = [PointF(2.0cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) + p0 = [Point(1.0, -3.0) for i in 1:n] # #p0 = [randn(Point) for i in 1:n] + x0 = State(q0, p0) + @time Wf, Xf = landmarksforward(t, dwiener, x0, P) + xobs0 = x0.q + σobs * randn(PointF,n) + xobsT = [Xf.yy[end].q[i] for i in 1:P.n ] + σobs * randn(PointF,n) + end + if dataset in ["shifted","shiftedextreme"] # first stretch, then rotate, then shift; finally add noise + q0 = [PointF(2.0cos(t), sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) + p0 = [PointF(1.0, -3.0) for i in 1:n] # #p0 = [randn(Point) for i in 1:n] + x0 = State(q0, p0) + @time Wf, Xf = landmarksforward(t, dwiener, x0, P) + xobs0 = x0.q + σobs * randn(PointF,n) + if dataset == "shifted" θ, η = π/10, 0.2 end + if dataset == "shiftedextreme" θ, η = π/5, 0.4 end + rot = SMatrix{2,2}(cos(θ), sin(θ), -sin(θ), cos(θ)) + stretch = SMatrix{2,2}(1.0 + η, 0.0, 0.0, 1.0 - η) + shift = PointF(0.1,-0.1) + xobsT = [rot * stretch * xobs0[i] + shift for i in 1:P.n ] + σobs * randn(PointF,n) + end + if dataset=="bear" + cd("/Users/Frank/github/BridgeLandmarks/landmarks/beardata") + bear0 = readdlm("bear1.csv",',') + bearT = readdlm("bear2.csv",',') + nb = size(bear0)[1] + avePoint = Point(414.0, 290.0) # average of (x,y)-coords for bear0 to center figure at origin + xobs0 = [Point(bear0[i,1], bear0[i,2]) - avePoint for i in 1:nb]/200. + xobsT = [Point(bearT[i,1], bearT[i,2]) - avePoint for i in 1:nb]/200. + # need to redefine P, because of n + if model == :ms + P = MarslandShardlow(a, γ, λ, nb) + else + P = Landmarks(a, 0.0, nb, nfs) + end + x0 = State(xobs0, rand(PointF,P.n)) + Wf, Xf = landmarksforward(t, dwiener, x0, P) + end + if dataset=="heart" + q0 = [PointF(2.0cos(t), 2.0sin(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) + p0 = [PointF(1.0, -3.0) for i in 1:n] # #p0 = [randn(Point) for i in 1:n] + x0 = State(q0, p0) + @time Wf, Xf = landmarksforward(t, dwiener, x0, P) + xobs0 = x0.q + σobs * randn(PointF,n) + heart_xcoord(s) = 0.2*(13cos(s)-5cos(2s)-2cos(3s)-cos(4s)) + heart_ycoord(s) = 0.2*16(sin(s)^3) + qT = [PointF(heart_xcoord(t), heart_ycoord(t)) for t in (0:(2pi/n):2pi)[1:n]] #q0 = circshift(q0, (1,)) + xobsT = qT + σobs * randn(PointF,n) + end + x0, xobs0, xobsT, Xf, P +end diff --git a/landmarks/lm_main.jl b/landmarks/lm_main.jl new file mode 100755 index 0000000..87761d6 --- /dev/null +++ b/landmarks/lm_main.jl @@ -0,0 +1,340 @@ +# THIS SCRIPT REPLACES THE OLDER 'lmpar.jl' +using Bridge, StaticArrays, Distributions +using Bridge:logpdfnormal +using Test, Statistics, Random, LinearAlgebra +using Bridge.Models +using DelimitedFiles, DataFrames, CSV, RCall +using Base.Iterators, SparseArrays, LowRankApprox, Trajectories +using ForwardDiff: GradientConfig, Chunk, gradient!, gradient +using TimerOutputs + +using Plots, PyPlot #using Makie + +pyplot() + +models = [:ms, :ahs] +model = models[2] +println(model) + +TEST = false#true +partialobs = true #false +rotation = false # rotate configuration at time T +showplotσq = false + +samplers =[:sgd, :sgld, :mcmc] +sampler = samplers[3] + +ρ = 0.99 #CN par +δ = 0.8 # MALA par +ϵ = 0.01 # sgd step size +ϵstep(i) = 1/(1+i)^(0.7) + + +datasets =["forwardsimulated", "shifted","shiftedextreme", "bear", "heart","peach"] +dataset = datasets[6] + +ITER = 20 # nr of sgd iterations +subsamples = 0:20:ITER + + +const itostrat = true #false#true#false#true +const d = 2 + +n = 20#35 # nr of landmarks + +σobs = 0.01 # noise on observations + +T = 1.0#1.0#0.5 +t = 0.0:0.005:T # time grid + +#Random.seed!(5) +include("state.jl") +include("models.jl") +include("patches.jl") +include("lmguiding.jl") +include("plotlandmarks.jl") +include("automaticdiff_lm.jl") +include("generatedata.jl") + +### Specify landmarks models +a = 2.0 # Hamiltonian kernel parameter (the larger, the stronger landmarks behave similarly) + +if model == :ms + λ = 0.0; # Mean reversion par in MS-model = not the lambda of noise fields =# + γ = 5.0 # Noise level in for MS-model + dwiener = n + nfs = 0 # needs to have value for plotting purposes + P = MarslandShardlow(a, γ, λ, n) +else + db = 5.0 # domainbound + nfstd = 2.5# 1.25 # tau , width of noisefields + nfs = construct_nfs(db, nfstd, .2) # 3rd argument gives average noise of positions (with superposition) + dwiener = length(nfs) + P = Landmarks(a, 0.0, n, nfs) +end + +if (model == :ahs) & showplotσq + plotσq(db, nfs) +end + +StateW = PointF + +# set time grid for guided process +tt_ = tc(t,T)#tc(t,T)# 0:dtimp:(T) + +# generate data +x0, xobs0, xobsT, Xf, P = generatedata(dataset,P,t,σobs) + +if partialobs + L0 = LT = [(i==j)*one(UncF) for i in 1:2:2P.n, j in 1:2P.n] + Σ0 = ΣT = [(i==j)*σobs^2*one(UncF) for i in 1:P.n, j in 1:P.n] + μT = zeros(Point{Float64},P.n) + mT = zeros(PointF,P.n) # +else + LT = [(i==j)*one(UncF) for i in 1:2P.n, j in 1:2P.n] + ΣT = [(i==j)*σobs^2*one(UncF) for i in 1:2P.n, j in 1:2P.n] + μT = zeros(PointF,2P.n) + xobsT = vec(X.yy[end]) + mT = Xf.yy[end].p + L0 = [(i==j)*one(UncF) for i in 1:2:2P.n, j in 1:2P.n] + Σ0 = [(i==j)*σobs^2*one(UncF) for i in 1:P.n, j in 1:P.n] +end + + + +if model == :ms + Paux = MarslandShardlowAux(P, State(xobsT, mT)) +else + Paux = LandmarksAux(P, State(xobsT, mT)) +end + +# compute guided prposal +println("compute guiding term:") +Lt, Mt⁺ , μt = initLMμ(tt_,(LT,ΣT,μT)) +(Lt, Mt⁺ , μt), Q, (Lt0, Mt⁺0, μt0, xobst0) = construct_guidedproposal!(tt_, (Lt, Mt⁺ , μt), (LT,ΣT,μT), (L0, Σ0), (xobs0, xobsT), P, Paux) + +# initialise guided path +#xinit = State(xobs0, [Point(-6.,6.) for i in 1:P.n]) +xinit = State(xobs0, rand(PointF,n)) +#xinit = State(xobs0, zeros(PointF,n)) + +# sample guided path +println("Sample guided proposal:") +Xᵒ = initSamplePath(tt_, xinit) +Wᵒ = initSamplePath(tt_, zeros(StateW, dwiener)) +sample!(Wᵒ, Wiener{Vector{StateW}}()) +@time Bridge.solve!(EulerMaruyama!(), Xᵒ, xinit, Wᵒ, Q) +#guid = guidingterms(Xᵒ,Q) +# plot forward path and guided path +plotlandmarkpositions(Xf,Xᵒ,P.n,model,xobs0,xobsT,nfs,db=3)#2.6) + +@time llikelihood(LeftRule(), Xᵒ, Q; skip = 1) +@time lptilde(vec(xinit), Lt0, Mt⁺0, μt0, xobst0) + + +objvals = Float64[] # keep track of (sgd approximation of the) loglikelihood + + +mask = deepvec(State(0 .- 0*xinit.q, 1 .- 0*(xinit.p))) # only optimize momenta +mask_id = (mask .> 0.1) # get indices that correspond to momenta + + +sk = 1 +acc = zeros(2) # keep track of mcmc accept probs (first comp is for CN update; 2nd component for langevin update on initial momenta) + +Xsave = SamplePath{State{PointF}}[] + +# initialisation +W = copy(Wᵒ) +Wnew = copy(Wᵒ) +X = SamplePath(t, [copy(xinit) for s in tt_]) +solve!(EulerMaruyama!(), X, x0, W, Q) +ll = llikelihood(Bridge.LeftRule(), X, Q,skip=sk) +Xᵒ = copy(X) +if 0 in subsamples + push!(Xsave, copy(X)) +end + +x = deepvec(xinit) +xᵒ = copy(x) +∇x = copy(x) +∇xᵒ = copy(x) + +# for plotting +xobs0comp1 = extractcomp(xobs0,1) +xobs0comp2 = extractcomp(xobs0,2) +xobsTcomp1 = extractcomp(xobsT,1) +xobsTcomp2 = extractcomp(xobsT,2) + +showmomenta = false + +anim = @animate for i in 1:ITER +#for i in 1:ITER + # + global ll + global acc + global X + global Xᵒ + global W + global Wᵒ + global x + global xᵒ + global ∇x + global ∇xᵒ + println("iteration $i") + + δ = ϵstep(i) + + if sampler==:mcmc + δ = 0.02 # for mala in this case + end + + X,Xᵒ,W,Wᵒ,ll,x,xᵒ,∇x,∇xᵒ, obj,acc = updatepath!(X,Xᵒ,W,Wᵒ,Wnew,ll,x,xᵒ,∇x, ∇xᵒ, + sampler,(Lt0, Mt⁺0, μt0, xobst0, Q), + mask, mask_id, δ, ρ, acc) + + if i in subsamples + push!(Xsave, copy(X)) + end + push!(objvals, obj) + + + # plotting + s = deepvec2state(x).p + s0 = x0.p # true momenta + + # plot initial and final shapes + pp = Plots.plot(xobs0comp1, xobs0comp2,seriestype=:scatter, color=:black,label="q0", title="Landmark evolution") + Plots.plot!(pp, repeat(xobs0comp1,2), repeat(xobs0comp2,2),seriestype=:path, color=:black,label="") + Plots.plot!(pp, xobsTcomp1, xobsTcomp2,seriestype=:scatter , color=:orange,label="qT") # points move from black to orange + Plots.plot!(pp, repeat(xobsTcomp1,2), repeat(xobsTcomp2,2),seriestype=:path, color=:orange,label="") + + if showmomenta + Plots.plot!(pp, extractcomp(s,1), extractcomp(s,2),seriestype=:scatter , + color=:blue,label="p0 est") # points move from black to orange) + Plots.plot!(pp, extractcomp(s0,1), extractcomp(s0,2),seriestype=:scatter , + color=:red,label="p0",markersize=5) # points move from black to orange) + xlims!(-3,3) + ylims!(-4,3) + else + xlims!(-3,3) + ylims!(-2,3) + end + + + outg = [Any[X.tt[i], [X.yy[i][CartesianIndex(c, k)][l] for l in 1:d, c in 1:2]..., "point$k"] for k in 1:n, i in eachindex(X.tt) ][:] + dfg = DataFrame(time=extractcomp(outg,1),pos1=extractcomp(outg,2),pos2=extractcomp(outg,3),mom1=extractcomp(outg,4),mom2=extractcomp(outg,5),pointID=extractcomp(outg,6)) + for j in 1:n + #global pp + el1 = dfg[:pointID].=="point"*"$j" + dfg1 = dfg[el1,:] + Plots.plot!(pp,dfg1[:pos1], dfg1[:pos2],label="") + end + + pp2 = Plots.plot(collect(1:i), objvals[1:i],seriestype=:scatter ,color=:blue,markersize=1.5,label="",title="Loglikelihood approximation") + Plots.plot!(pp2, collect(1:i), objvals[1:i] ,color=:blue,label="") + xlabel!(pp2,"iteration") + ylabel!(pp2,"stoch log likelihood") + xlims!(0,ITER) + + l = @layout [a b] + Plots.plot(pp,pp2,background_color = :ivory,layout=l , size = (900, 500) ) + + plotlandmarkpositions(Xf,X,P.n,model,xobs0,xobsT,nfs,db=2.6) +end + + +cd("/Users/Frank/github/BridgeLandmarks") +fn = "me"*"_" * string(model) * "_" * string(sampler) *"_" * string(dataset) +gif(anim, fn*".gif", fps = 20) +mp4(anim, fn*".mp4", fps = 20) + +print(objvals) +#end + +sc2 = Plots.plot(collect(1:ITER), objvals,seriestype=:scatter ,color=:blue,markersize=1.2,label="",title="Loglikelihood approximation") +Plots.plot!(sc2, collect(1:ITER), objvals ,color=:blue,label="") +xlabel!(sc2,"iteration") +ylabel!(sc2,"stoch log likelihood") +xlims!(0,ITER) +display(sc2) +png(sc2,"stochlogp.png") + + +error("STOP HERE") + + + + + + + + + + + + +# also do gradient descent on parameters a (in kernel of Hamiltonian) +# first for MS model +get_targetpars(Q::GuidedProposall!) = [Q.target.a, Q.target.γ] +get_auxpars(Q::GuidedProposall!) = [Q.aux.a, Q.aux.γ] + +put_targetpars = function(pars,Q) + GuidedProposall!(MarslandShardlow(pars[1],pars[2],Q.target.λ, Q.target.n), Q.aux, Q.tt, Q.Lt, Q.Mt, Q.μt,Q.Ht, Q.xobs) +end + +put_auxpars(pars,Q) = GuidedProposall!(Q.target,MarslandShardlowAux(pars[1],pars[2],Q.aux.λ, Q.aux.xT,Q.aux.n), Q.tt, Q.Lt, Q.Mt, Q.μt,Q.Ht, Q.xobs) + +QQ = put_targetpars([3.0, 300.0],Q) +QQ.target.a +QQ.target.γ + + +function obj2(xinitv,pars) + Q = put_targetpars(pars,Q) + Q = put_auxpars(pars,Q) + xinit = deepvec2state(xinitv) + sample!(WW, Wiener{Vector{StateW}}()) + Xᵒ = Bridge.solve(EulerMaruyama!(), xinit, WW, Q) + ( + (lptilde(vec(xinit ), L0, M0⁺, μ0, V, Q) - lptilde(vec(x0), L0, M0⁺, μ0, V, Q)) + + llikelihood(LeftRule(), Xᵒ, Q; skip = 1) + ) +end + + + +if false + # write mcmc iterates to csv file + + fn = outdir*"iterates.csv" + f = open(fn,"w") + head = "iteration, time, component, value \n" + write(f, head) + iterates = [Any[s, tt[j], d, XX[i].yy[j][d]] for d in 1:1, j in 1:length(X), (i,s) in enumerate(subsamples) ][:] + writecsv(f,iterates) + close(f) + + ave_acc_perc = 100*round(acc/iterations,2) + + # write info to txt file + fn = outdir*"info.txt" + f = open(fn,"w") + write(f, "Number of iterations: ",string(iterations),"\n") + write(f, "Skip every ",string(skip_it)," iterations, when saving to csv","\n\n") + write(f, "Starting point: ",string(x0),"\n") + write(f, "End time T: ", string(T),"\n") + write(f, "Endpoint v: ",string(v),"\n") + write(f, "Noise Sigma: ",string(Σ),"\n") + write(f, "L: ",string(L),"\n\n") + write(f, "Mesh width: ",string(dt),"\n") + write(f, "rho (Crank-Nicholsen parameter: ",string(ρ),"\n") + write(f, "Average acceptance percentage: ",string(ave_acc_perc),"\n\n") + write(f, "Backward type parametrisation in terms of nu and H? ",string(νHparam),"\n") + close(f) + + + println("Average acceptance percentage: ",ave_acc_perc,"\n") + println("Parametrisation of nu and H? ", νHparam) + println("Elapsed time: ",elapsed_time) +end