Algebra common utilities

diageye

ReactiveMP.diageye — Function

diageye(::Type{T}, n::Int)

An alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.

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diageye(n::Int)

An alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.

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ReactiveMP.CompanionMatrix — Type

CompanionMatrix

Represents a matrix of the following structure:

θ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0

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ReactiveMP.PermutationMatrix — Type

PermutationMatrix(ind::Array{T}) creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind).

A permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:

\[ A_{ij} = \{0, 1\}\\ ∑_{i} A_{ij} = 1\\ ∑_{j} A_{ij} = 1\]

An example is the 3-dimensional permutation matrix

\[A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix}\]

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ReactiveMP.StandardBasisVector — Type

StandardBasisVector{T, len, ind}(scale::T)

StandardBasisVector creates a standard Cartesian basis vector of zeros of length len with a single element scale at index ind.

An example is the 3-dimensional standard basis vector for the first dimension

\[e = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}\]

Which can be constructed by calling e = StandardBasisVector(3, 1, 1)

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ReactiveMP.GammaShapeLikelihood — Type

ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))

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ReactiveMP.ImportanceSamplingApproximation — Type

ImportanceSamplingApproximation

This structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations

Fields