Misc

Utils.invvech — Function

invvech(v, p; fillupper = true)

Construct a symmetric matrix from its diagonal and lower diagonal elements. Fills by columns.

v is a vector with the unique elements
p is the number of rows or columns of the returned symmetric matrix.

Examples

julia> invvech([11,21,31,22,32,33], 3)
3×3 Matrix{Int64}:
 11  21  31
 21  22  32
 31  32  33

source

Utils.invvech_byrow — Function

invvech_byrow(v, p; fillupper = true)

Construct a symmetric matrix from its diagonal and lower diagonal elements. Fills by row.

v is a vector with the unique elements
p is the number of rows or columns of the returned symmetric matrix.

Examples

julia> invvech_byrow([11,21,22,31,32,33], 3)
3×3 Matrix{Int64}:
 11  21  31
 21  22  32
 31  32  33

source

Utils.CovMatEquiCorr — Function

CovMatEquiCorr(σₓ, ρ, pBlock)

Set up a covariance matrix with equi-correlation within blocks of variables

σₓ is a p-vector with standard deviations
ρ[i] is the correlation within block i
pBlock[j] is the number of variables in block j

Examples

julia> σₓ = [1,2,3]; ρ = [0.5,0.8]; pBlock = [1,2];
julia> CovMatEquiCorr(σₓ, ρ, pBlock)
3×3 Matrix{Float64}:
 1.0  0.0  0.0
 0.0  4.0  4.8
 0.0  4.8  9.0

source

Utils.Cov2Corr — Function

ρ, σ = Cov2Corr(Σ)

Compute the correlation matrix ρ and vector standard deviations σ for the covariance matrix Σ.

Examples

julia> Σ = CovMatEquiCorr([1,2,3], [0.7], [3]) # Covariance matrix with all corr = 0.7
3×3 Matrix{Float64}:
 1.0  1.4  2.1
 1.4  4.0  4.2
 2.1  4.2  9.0

julia> ρ, σ = Cov2Corr(Σ); ρ
3×3 Matrix{Float64}:
 1.0  0.7  0.7
 0.7  1.0  0.7
 0.7  0.7  1.0

source