struct PadeApprox{Q <: Number}

PadeApprox type with fields:

• coeffs :: Vector{Q} : coefficients for continued fraction fit
• xdat :: Vector{Q} : evaluation nodes for data

struct PeriodicPulay{Q <: Number}

PeriodicPulay type with fields:

• x :: Vector{Q} : solution vector
• Fs :: Matrix{Q} : history for function evaluations
• Xs :: Matrix{Q} : history for intermediate solutions
• aerrs :: Vector{Float64} : absolute errors
• rerrs :: Vector{Float64} : relative errors

function coeffs(
    PA :: PadeApprox{Q}
    )  :: Vector{Q} where {Q <: Number}

Returns PA.coeffs

function xdat(
    PA :: PadeApprox{Q}
    )  :: Vector{Q} where {Q <: Number}

Returns PA.xdat

function solve!(
    f!      :: Function,
    P       :: PeriodicPulay{Q}
    ;
    p       :: Int64   = 3,
    iters   :: Int64   = 100,
    α       :: Float64 = 0.5,
    atol    :: Float64 = 1e-8,
    rtol    :: Float64 = 1e-8,
    verbose :: Bool    = false
    )       :: Nothing where {Q <: Number}

Runs the periodic Pulay solver. Here, f(x) = g(x) - x computes the residue for the fixed-point equation g(x) = x. f! should have the form (F, x) -> f!(F, x), such that the residue can be written into a pre-allocated array F. The following keyword arguments are supported:

• p : Pulay period (every p-th iteration Pulay mixing is used)
• iters : maximum number of iterations
• α : mixing factor
• atol : absolute error tolerance
• rtol : relative error tolerance
• verbose : show intermediate results?