sethaxen

sethaxen

Let $A$ be an $n \times m$ matrix, $Y$ be an $m \times k$ matrix, and $B$ be an $n \times k$ matrix such that $$Y = A \ B = A^+ \ B,$$ where $A^+$ is a Moore-Penrose pseudoinverse, given by $$ A^+ = \begin{cases} A^\top (AA^\top)^{-1} & n \le m\ (A^\top A)^{-1} A^\top & n \ge m\ \end{cases}. $$ Let $C = A^+$.

sethaxen

#!/bin/bash

# Adapted from https://github.com/JuliaLang/juliaup/issues/96#issuecomment-1480110471

# Set variables for directories and files
JULIA_DIR="$HOME/.julia/juliaup/julia-nightly"
TMP_FILE="/tmp/julia-nightly.tar.gz"
JULIA_NIGHTLY_URL="https://julialangnightlies-s3.julialang.org/bin/linux/x86_64/julia-latest-linux-x86_64.tar.gz"

# Download the nightly Julia build

sethaxen

using Bijectors, ChangesOfVariables, LinearAlgebra

"""
    QRReflectorBijector(n, k; special::Bool=false, fullR::Bool=false)

A bijector that maps parameters of elementary LAPACK-style reflectors to a QR factorization
with size `(n, k)`.

The `R` factor of the element has a positive real diagonal.
If `fullR=false`, then the `R` factor is diagonal, which reduces the number of

sethaxen

using Distributions, Bijectors, Random, FillArrays, LogExpFunctions

struct DistributionWithTransform{D<:ContinuousDistribution,B,V<:VariateForm} <: Distribution{V,Continuous}
    dist::D
    transform::B
    function DistributionWithTransform(d::ContinuousDistribution, b)
        F = Distributions.variate_form(typeof(d))
        return new{typeof(d),typeof(b),F}(d, b)
    end
end

sethaxen

using Bijectors, ChangesOfVariables, LinearAlgebra

struct VecCholeskyCorrBijectorWithZeros{Z<:AbstractVector{Tuple{Int,Int}}} <: Bijectors.Bijector
    zero_inds::Z
    function VecCholeskyCorrBijectorWithZeros(zero_inds::Z) where Z<:AbstractVector{Tuple{Int,Int}}
        new{Z}(unique!(sort(map(sort, zero_inds); by=reverse)))
    end
end

function Bijectors.output_size(b::VecCholeskyCorrBijectorWithZeros, sz::Tuple{Int,Int})

sethaxen

using Bijectors, Distributions, LinearAlgebra, PDMats

"""
    DirichletMvLogitNormal(α::AbstractVector, J::AbstractMatrix; check=false)

A distribution that contains `MvLogitNormal` and `Dirichlet` as special cases.[^Aitchison1985]

Let ``x \\sim \\mathrm{DirichletMvLogitNormal}(α, J)`` be a length ``N`` probability vector,
where ``α`` is a length ``N`` vector, and ``J`` is a size ``(N-1,N-1)`` positive
semi-definite matrix. Given ``z_i = \\log(x_i)``, the density function of the

sethaxen

sethaxen

using Distributions
using IrrationalConstants
using LogExpFunctions
using Random

abstract type WrappedNormalDensityMethod end
struct WrappedMethod <: WrappedNormalDensityMethod end
struct JacobiMethod <: WrappedNormalDensityMethod end

"""

sethaxen