# L-12 MCS 471 Mon 19 Sep 2022 : ourcholesky.jl
# Illustrates the formulas for the Cholesky factorization
# of a symmetric positive definite matrix.

"""
    ourCholesky(mat::Array{Float64,2})

Performs an inplace Cholesky factorization on mat.
"""
function ourCholesky(mat::Array{Float64,2})
    nbrows, nbcols = size(mat)
    for col=1:nbcols
        for idx in 1:col-1
            mat[col, col] = mat[col, col] - mat[col, idx]^2;
        end
        mat[col, col] = sqrt(mat[col, col])
        for row in col+1: nbrows
            for idx in 1:col-1
                mat[row, col] = mat[row, col] - mat[row, idx]*mat[col, idx]
            end
            mat[row, col] = mat[row, col]/mat[col, col]
        end
    end
end