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testJulia4.jl
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using DifferentialEquations
using Distances
using Distributions
using JLD2
using LinearAlgebra
using Phylo
## using PyCall
using Plots;
using PyPlot
# #using ApproxBayes
using KissABC
pyplot();
pygui(true);
#####################################################################################
#####################################################################################
function menura!(tree)
function diffusion(x0, tspan, p, mat, dt=0.001)
function drift(du, u, p, t)
alpha = p.alpha;
mu = p.mu;
## du .= alpha .* u would be BM with drift
du .= alpha .* (mu .- u); ## OU-like
end; # drift
function diff(du, u, p, t)
sigma = p.sigma;
du .= sigma; ## would be OU
## du .= sqrt.(u) .* sigma ## Cox-Ingersoll-Ross Gamma model
## du .= sqrt.(abs.(u .* (ones(length(sigma)) .- u))) .* sigma ## Beta model
end; # diff
cor1 = cor(mat);
noise = CorrelatedWienerProcess(cor1, tspan[1],
zeros(dim(cor1)),
zeros(dim(cor1)));
prob = SDEProblem(drift, diff, x0, tspan, p=p, noise=noise);
solve(prob, EM(), dt=dt, p=p, adaptive=false);
end; # diffusion
################################################################################
function Recurse!(tree, node, t0 = 0.0)
if ismissing(node.inbound) ## the root node, to get started
node.data["trace"]= [x0];
node.data["timebase"] = [t0];
else
ancestor = getancestors(tree, node)[1];
evol = diffusion(ancestor.data["trace"][end],
(getheight(tree, ancestor), getheight(tree, node)),
ancestor.data["parameters"], ancestor.data["matrix"]);
node.data["trace"] = evol.u;
node.data["timebase"] = evol.t;
end # else
if !isleaf(tree, node)
Recurse!(tree, node.other[1].inout[2]);
Recurse!(tree, node.other[2].inout[2]);
end
end # Recurse!
root = getroot(tree);
Recurse!(tree, root); # do the recursive simulations
tree;
end # menura!
###############################################################################
################################################################################
function menuramat!(tree) ## Only call after putp!
function Recurse!(tree, node)
if ismissing(node.inbound) ## if root
node.data["matrix"] = node.data["parameters"].mat; ## starting matrix
else
ancestor = getancestors(tree, node)[1];
node.data["matrix"] =
gen_cov_mat(ancestor.data["matrix"],
ancestor.data["parameters"],
(getheight(tree, ancestor),
getheight(tree, node)));
end;
if !isleaf(tree, node)
Recurse!(tree, node.other[1].inout[2]);
Recurse!(tree, node.other[2].inout[2]);
end;
end; # Recurse!
root = getroot(tree);
Recurse!(tree, root); # do the recursive simulations
tree;
end; # menuramat!
############################################################################33
#############################################################################
function predictTraitTree(tree)
#### get the last multivariate trait value in a branch
testtips = getleaves(tree);
res = Array{Vector{Float64}}(undef, length(testtips));
tipnames = Array{String}(undef, length(testtips));
tiptimes = Vector{Float64}();
for i in eachindex(testtips) ## could maybe use heightstoroot() for this computation
res[i] = testtips[i].data["trace"][end];
tipnames[i] = testtips[i].name;
push!(tiptimes, getheight(tree, testtips[i]));
end;
collect(Iterators.flatten(res))
end # predictTraitTree
##########################################################################33
###########################################################################3
function putp!(tree, p1, key)
for i in eachindex(tree.nodes)
tree.nodes[i].data[key] = p1;
end
tree;
end # putp!
####################################################################33
######################################################################3
function gen_cov_mat(mat, p, tspan, u0=zeros(size(mat)), dt = 0.001)
function drift(du, u, p, t) ## drift function for the SDE
du .= p.a .* t .* p.A;
end # drift
function diffusion(du, u, p, t) ## diffusion function for the SDE
du .= p.b .* t .* p.B ;
end # diffusion
lowertri = LowerTriangular(mat);
uppertri = - UpperTriangular(mat);
skewsymm = lowertri + uppertri;
W = WienerProcess(0.0, 0.0, 0.0);
pp = (A=skewsymm, B=skewsymm, a=p.a, b=p.b); ## skew symmetric matrices not necessarily the same.
prob = SDEProblem(drift, diffusion, u0, tspan, p=pp, noise=W,
noise_rate_prototype=zeros(size(mat))); ## setup SDE problem
sol = solve(prob, EM(), p=pp, dt=dt);
Omega1 = exp(last(sol.u)); ## get the final matrix
Omega1 * mat * Omega1'; ## reconstruct P_1
end # gen_cov_mat
######################################################################3
##################################################################3n
a1=1.0;
b1= 1.0;
x0 = repeat([0.0], 8);
tree1 = Ultrametric(20);
tree = rand(tree1);
time_tot = 1.0;
tspan = (0.0, time_tot);
P0 = [0.329 0.094 -0.083 -0.089 0.293 0.079 0.208 0.268;
0.094 0.449 0.349 0.24 0.071 0.075 0.03 0.009;
-0.083 0.349 1.426 0.487 -0.371 -0.098 -0.053 -0.172;
-0.089 0.24 0.487 0.546 -0.168 0.017 -0.051 -0.081;
0.293 0.071 -0.371 -0.168 1.441 1.008 0.904 0.945;
0.079 0.075 -0.098 0.017 1.008 1.087 0.731 0.78;
0.208 0.03 -0.053 -0.051 0.904 0.731 0.809 0.783;
0.268 0.009 -0.172 -0.081 0.945 0.78 0.783 0.949];
alpha1 = repeat([1.0], 8);
mu1 = repeat([0.0], 8); ## randn(8); ## Start at the trait means
sigma1 = repeat([1.0], 8);
parms= (alpha=alpha1, sigma=sigma1)
####################################################
function simulate(parms = parms, mu=mu1, mat=P0, a=a1, b=b1, tree=tree)
alpha, sigma = parms
p1 = (alpha=alpha, sigma = sigma, mu=mu, mat = mat, a=a, b=b)
putp!(tree, p1, "parameters");
menuramat!(tree);
menura!(tree);
(tree, predictTraitTree(tree))[2];
end; # simulate
true_data = simulate(parms, mu1, P0, a1, b1, tree);
priordists = [Truncated(Normal(0,3), 0, Inf)]
priors = Factored(repeat(priordists, 16)...,)
#= priors = [Truncated(Normal(0,3), 0, Inf), Truncated(Normal(0,3), 0, Inf),
Truncated(Normal(0,3), 0, Inf), Truncated(Normal(0,3), 0, Inf),
Truncated(Normal(0,3), 0, Inf), Truncated(Normal(0,3), 0, Inf),
Truncated(Normal(0,3), 0, Inf), Truncated(Normal(0,3), 0, Inf),
Truncated(Normal(0,3), 0, Inf), Truncated(Normal(0,3), 0, Inf),
Truncated(Normal(0,3), 0, Inf), Truncated(Normal(0,3), 0, Inf),
Truncated(Normal(0,3), 0, Inf), Truncated(Normal(0,3), 0, Inf),
Truncated(Normal(0,3), 0, Inf), Truncated(Normal(0,3), 0, Inf)] =#
# setup = ABCRejection(simulate, #simulation function
# 16, # number of parameters
# 1.0, #target ϵ
# Prior(priors); # Prior for each of the parameters
# maxiterations = 10^6, #Maximum number of iterations before the algorithm terminates
# )
# # run ABC inference
# rejection = runabc(setup, true_data)
#################################3 END WORK REGION ##############################
function cost((alpha, sigma))
x=simulate((alpha=alpha, sigma=sigma))
y=true_data
euclidean(x, y)
end #cost
approx_density = ApproxKernelizedPosterior(priors,cost,0.005)
res = sample(approx_density, AIS(25), 1000, ntransitions=100, discard_initial = 10)
save_object("ABCResults.jld2", res)