mschauer

using IterativeSolvers
using LinearAlgebra

A = rand(-10:10, 16, 16) + 5*LinearAlgebra.I
x = rand(-10:10, 16)
b = A*x


y = idrs(BigFloat.(A), BigFloat.(b), s=4, tol=1e-100, maxiter=100, verbose=true)

mschauer

using Distributions, Statistics, LinearAlgebra

## simulate sample trajectory

μ = [1.0, 0.0]
Σ = [0.5  0.0
     0.0  0.5]
x0 = rand(MultivariateNormal(μ, Σ))   #start point

β = [0.0, 0.0]

mschauer

# Fit a Brownian motion with drift to and scale to
# Georgia election data:
# fraction of total count of votes vs difference in votes

data = [0.9222672139181572 103896.10389610389
    0.9267802009311443 87662.33766233765
    0.9277217593727027 85714.28571428571
    0.9285683655966674 83116.88311688312
    0.9299797843665768 79220.77922077922
    0.9310169076206811 78571.42857142857

mschauer

#=
Newborn babies are more likely to be boys than girls.
A random sample found 13 173 boys were born among 25 468
newborn children. Population: All children born that time period. Alternatively,
the unknown p could be the unknown probability.
=#

b = 13173
n = 25486

mschauer

using GaussianDistributions
using GaussianDistributions: correct, ⊕
using LinearAlgebra
using Statistics


lchol(a) = cholesky(a).L
llikelihood(yres, S) = GaussianDistributions.logpdf(Gaussian(zero(yres), Symmetric(S)), yres)

mschauer

# Linear state space system forward filtering backward sampling with Zygote

using LinearAlgebra
using GaussianDistributions
using GaussianDistributions: ⊕, logpdf
using StaticArrays

using Statistics

using Zygote

mschauer

using ForwardDiff: derivative

partiali(f, x, i) = ForwardDiff.partials(f([Dual{}(x[j], 1.0*(i==j)) for j in eachindex(x)]))[]


struct ∂{k, F} <: Function
    f::F
    ∂{k}(f::F) where {k, F} = new{k, F}(f)
end
function (pd::∂{k})(args...) where {k}

mschauer

using Distributions
using Makie
using Random
g(x, α, β) = pdf(Gamma(α, 1/β), x)
lg(x, α, β) = logpdf(Gamma(α, 1/β), x)

Random.seed!(1)

T = 100

mschauer

# ] add https://github.com/mschauer/BridgeSPDE.jl

# will run in the parent directory
# of the script location and create output folder there
cd(joinpath(@__DIR__, ".."))


using SparseArrays
using BridgeSPDE
using FileIO

mschauer

# Zig zag and Boomerang reference implementation 

"""
    poisson_time(a,b,u)
obtaining waiting time for inhomogeneous Poisson Process
with rate of the form λ(t) = (a + b*t)^+, `a`,`b` ∈ R, `u` uniform random variable
"""
function poisson_time(a,b,u)
    if b > 0
        if a < 0