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 = NearestCorrelationMatrix.Newton)

Creates a new Posdef with the specified algorithm.

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

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

  • If method is nothing, this is a no-op and returns nothing.
  • If method is a Posdef, the algorithm specified in method.alg is used to project X to the nearest PD matrix. If X is already positive definite, it is left unchanged.

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

Arguments

  • method::Posdef: The estimator specifying the projection algorithm.
  • X::AbstractMatrix: The matrix to be projected in-place.

ReturnsResult

  • 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

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

Same as posdef!, but returns a new matrix instead of modifying X in-place.

  • If method is nothing, this is a no-op and returns nothing.

Examples

julia> using LinearAlgebra

julia> est = Posdef();

julia> X = [1.0 2.0; 0.9 1.0];  # Not PD

julia> X_pd = posdef(est, X);

julia> isposdef(X_pd)
true

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

Related

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PortfolioOptimisers.AbstractPosdefEstimator — Type
AbstractPosdefEstimator <: AbstractEstimator

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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