PosdefMatrix

PortfolioOptimisers.Posdef — Type
struct Posdef{T1} <: AbstractPosdefEstimator
    alg::T1
end

A concrete estimator type for projecting a matrix to the nearest positive definite (PD) matrix, typically used for covariance or correlation matrices.

Fields

  • alg: The algorithm used for the nearest correlation matrix projection.

Constructor

Posdef(; alg::Any = NearestCorrelationMatrix.Newton)

Keyword arguments correspond to the fields above.

Examples

julia> using LinearAlgebra

julia> est = Posdef()
Posdef
  alg | UnionAll: NearestCorrelationMatrix.Newton

Related

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PortfolioOptimisers.posdef! — Function
posdef!(pdm::Posdef, X::AbstractMatrix)
posdef!(::Nothing, args...)

In-place projection of a matrix to the nearest positive definite (PD) matrix using the specified estimator.

For covariance matrices, the function internally converts to a correlation matrix, applies the algorithm, and then rescales back to covariance.

Arguments

  • pdm: The estimator specifying the positive definite projection algorithm.

    • pdm::Posdef: The algorithm specified in pdm.alg is used to project X to the nearest PD matrix. If X is already positive definite, it is left unchanged.
    • pdm::Nothing: No-op.

  • X: The matrix to be projected in-place.

Returns

  • nothing. The input matrix X is modified in-place.

Validation

  • If the matrix cannot be made positive definite, a warning is emitted.

Examples

julia> using LinearAlgebra

julia> est = Posdef()
Posdef
  alg | UnionAll: NearestCorrelationMatrix.Newton

julia> X = [1.0 0.9; 0.9 1.0];

julia> X[1, 2] = 2.0;  # Not PD

julia> posdef!(est, X)

julia> X
2×2 Matrix{Float64}:
 1.0  1.0
 1.0  1.0

julia> isposdef(X)
true

Related

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PortfolioOptimisers.AbstractPosdefEstimator — Type
abstract type AbstractPosdefEstimator <: AbstractEstimator end

Abstract supertype for all positive definite matrix estimator types in PortfolioOptimisers.jl.

All concrete types that implement positive definite matrix projection or estimation (e.g., for covariance or correlation matrices) should subtype AbstractPosdefEstimator. This enables a consistent interface for positive definite matrix estimation routines throughout the package.

Related

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