function EstimateFunctionDiagonal(A::Matrix{Float64},fmat,f,Algorithm::Symbol, StoppingCriterion::Symbol, distribution::Symbol, MatFuncApprox::Symbol, deg::Int64, normalizationParam::Bool=true;maxqueries::Int,int::Tuple=(0.0,1.0),q=4,O=nothing)

Main function to compute a randomized estimate of the diagonal of a matrix function

Input:

• A: Matrix as input for the function
• f: Function to approximate diagonal of
• Algorithm: Choose which diagonal estimator is used, options are
  • :GirardHutchinson
  • :funDiagPP
  • :funNys
• MatFuncApprox: How to approximate f(A)b
  • Chebshev: Using Chebyshev polynomials
    • requires interval int and degree deg
  • Remez: Using Remez polynomials
    • requires interval int and degree deg
  • Krylov: Using the Arnoldi approximation
    • requires maximum potency of A in the Krylov subspace denoted by deg
  • CG: Use conjugate gradient method to approximate diagonal of the inverse, Attention: f is neglected
    • requires maximum potency of A in the Krylov subspace denoted by deg
• StoppingCriterion: How to terminate, possible options
  • queries: terminate when the maximum number of queries to A is reacher
    • maxqueries: maximum number of queries to A
• distribution: Select the distribution from which the random vectors are drawn, inbuilt options are
  • :Rademacher
  • :Gaussion
  • :custom, in this case provide a matrix with the test vectors as columns
    • O: matrix with the test vectors as columns
• deg: degree of polynomial or maximum potency of A in the Krylov subspace, depending on MatFuncApprox