API

RootSolvers

Contains functions for solving roots of non-linear equations. See find_zero.

Example

julia> using RootSolvers

julia> sol = find_zero(x -> x^2 - 100^2,
                       SecantMethod{Float64}(0.0, 1000.0),
                       CompactSolution());

julia> sol
RootSolvers.CompactSolutionResults{Float64}(99.99999999994358, true)

julia> sol.root
99.99999999994358

sol = find_zero(
        f::F,
        method::RootSolvingMethod{FT},
        soltype::SolutionType,
        tol::Union{Nothing, AbstractTolerance} = nothing,
        maxiters::Int = 10_000,
        )

Finds the nearest root of f. Returns a the value of the root x such that f(x) ≈ 0, and a Boolean value converged indicating convergence.

• f function of the equation to find the root
• method can be one of:
  • SecantMethod(): Secant method
  • RegulaFalsiMethod(): Regula Falsi method
  • NewtonsMethodAD(): Newton's method using Automatic Differentiation
  • NewtonsMethod(): Newton's method
• soltype is a solution type which may be one of: CompactSolution GPU-capable. Solution has converged and root only, see CompactSolutionResults VerboseSolution CPU-only. Solution has additional diagnostics, see VerboseSolutionResults
• tol is a tolerance type to determine when to stop iterations.
• maxiters is the maximum number of iterations.

NewtonsMethodAD

Fields

• x0 initial guess

NewtonsMethod

Fields

• x0 initial guess

RegulaFalsiMethod

Fields

• x0 lower bound
• x1 upper bound

SecantMethod

Fields

• x0 lower bound
• x1 upper bound

CompactSolution <: SolutionType

Used to return a CompactSolutionResults

VerboseSolution <: SolutionType

Used to return a VerboseSolutionResults

VerboseSolutionResults{FT} <: AbstractSolutionResults{FT}

Result returned from find_zero when VerboseSolution is passed as the soltype.

CompactSolutionResults{FT} <: AbstractSolutionResults{FT}

Result returned from find_zero when CompactSolution is passed as the soltype.

To extract the root, use

sol = RootSolvers.find_zero(...)
sol.root

ResidualTolerance

A tolerance type based on the residual of the equation $f(x) = 0$

SolutionTolerance

A tolerance type based on the solution $x$ of the equation $f(x) = 0$

RelativeSolutionTolerance

A tolerance type based on consecutive iterations of solution $x$ of the equation $f(x) = 0$

RelativeOrAbsoluteSolutionTolerance(rtol, atol)

A combined tolerance type based on relative and absolute tolerances.

See RelativeSolutionTolerance and SolutionTolerance

value_deriv(f, x)

Compute the value and derivative f(x) using ForwardDiff.jl.

method_args(method::RootSolvingMethod)

Return tuple of positional args for RootSolvingMethod.