myCholesky.jl

# Cholesky!.jl

# The MIT License (MIT)
# Copyright (c) 2020 Sota Yoshida

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## A "destructive" implementation of cholesky decomposition to reduce memory usage.
## Sigma: PSD matrix
## ln: Dim. of the matrix
## cLL: pre-allocated lower triangular matrix to store cholesly factor 

function Cholesky!(Sigma::Array{Float64,2},
                     ln::Int64,cLL::LowerTriangular{Float64,Array{Float64,2}})
    l11 = sqrt(Sigma[1,1]) 
    cLL[1,1] = l11
    cLL[2,1] = Sigma[2,1]/l11; cLL[2,2] = sqrt( Sigma[2,2]-cLL[2,1]^2)
    for i=3:ln
        for j=1:i-1
            cLL[i,j] = Sigma[i,j]
            @simd for k = 1:j-1
                cLL[i,j] += - cLL[i,k]*cLL[j,k]                
            end
            cLL[i,j] = cLL[i,j] / cLL[j,j]            
        end
        cLL[i,i] = Sigma[i,i]
        @simd for j=1:i-1
            cLL[i,i] += -cLL[i,j]^2
        end
        cLL[i,i] = sqrt(cLL[i,i])             
    end
    nothing
end