List of functions

FunctionTabulations.create_tabulation_1DMethod
create_tabulation_1D(
    func::Function[,
    args...];
    xmin::T,
    xmax::T,
    npoints::Int[,
    x_scale::Symbol = :linear,
    f_scale = :linear,
    jld_base_path = nothing,
    custom_name = nothing,
    interpolation_type = :linear,
    extrapolation_bc = Throw,
    check_SHA = true,
    check_SHA_mode = :warn,
    metadata=nothing,
    metadata_validation_fn=nothing,
    kwargs...]
) where {T<:Union{Real,Quantity}}

Computes or loads the tabulation for a given function of the kind f(x).

Arguments

  • func::Function: the function which should be tabulated. Must be of the kind f(x)
  • xmin::Union{Real,Quantity}: the minimum x for the range which will be covered by the tabulation
  • xmax::Union{Real,Quantity}: the maximum x for the range which will be covered by the tabulation
  • npoints::Int: the number of points for which f(x) will be computed
  • x_scale::Symbol: the scale which will be used for tabulation. If :linear is choosen, the x points will be evenly spaced. If :log10 is chosen, the points will be logarithmically spaced. Defaults to :linear
  • f_scale::Symbol: the scale which will be used for tabulation. If :linear is choosen, the f(x) points will not be alterated. If :log10 is chosen, log10 will be applied to the f(x) points before interpolating. Defaults to :linear
  • jld_base_path::String: path to the folder where the tabulation should be saved. Defaults to the current folder
  • custom_name::String: custom name for the tabulation file, to which _data.jld2 will be appended. Defaults to the name of the function to be tabulated
  • interpolation_type::Symbol: Type of the spline to be used for interpolation. Can either be :linear (1st order spline) or :cubic (3rd order spline)
  • extrapolation_bc: behaviour of the tabulation outside of the boundaries defined by [xmin, xmax]. Possible behaviours are handled by Interpolations.jl and include Throw(throws and eror if a value out of bounds is acessed) orLine(extrapolate linearly). Defaults toThrow`
  • check_SHA::Bool: Whether to check the SHA of the tabulated function. If the SHA of the tabulated function does not match the SHA stored inside the tabulation file, it might be necessary to recompute the tabulation, since it's likely that the definition of the tabulated function has changed.
  • check_SHA_mode::Symbol: Describes the behaviour of this function if the SHA of the tabulated function does not match the SHA stored inside the tabulation file. Defaults to :warn (print a warning but load the tabulation all the same). Other options include :throw (throw an error to suggest manual deletion of the old tabulation) and :none (don't do anything).
  • metadata::Dict{String,Any}: an optional Dict{String, Any} which contains additional metadata to be stored in the tabulation achive.
  • metadata_validation_fn::Function: a function of the kind metadata_validation_fn(metadata1::Dict{String, Any}, metadata2::Dict{String, Any}) to chech whether two metadata dictionaries contain the same data.
  • args..., kwargs...: additional args and kwargs will be passed to the function which is to be tabulated

Examples

julia>  func_1d(x) = sin(x)

julia>  itp_1d_1 = create_tabulation_1D(
            func_1d,
            xmin = 0.0,
            xmax = 3.0,
            npoints = 100,
            x_scale = :linear,
            f_scale = :linear
        )

julia>  isapprox(itp_1d_1(2.0), func_1d(2.0), rtol = 1e-3)
true

Measurement units are supported too:

julia>  using Unitful

julia>  func_1d(x) = x^2

julia>  itp_1d_1 = create_tabulation_1D(
            func_1d,
            xmin = 0.0u"m",
            xmax = 3.0u"m",
            npoints = 100,
            x_scale = :linear,
            f_scale = :linear
        )

julia>  isapprox(itp_1d_1(2.0u"m"), func_1d(2.0u"m"), rtol = 1e-3)
true
FunctionTabulations.create_tabulation_1DMethod
create_tabulation_1D(
    func::Function,
    x::Vector{T},
    args...;
    jld_base_path = nothing,
    custom_name = nothing,
    x_scale::Symbol = :linear,
    f_scale = :linear,
    interpolation_type = :linear,
    extrapolation_bc = Throw,
    check_SHA = true,
    check_SHA_mode = :warn,
    metadata=nothing,
    metadata_validation_fn=nothing,
    kwargs...
    ) where {T<:Union{Real,Quantity}}

Provides an interface for create_tabulation_1D where the tabulation points are defined by the Vector x. Only linear_interpolation is supported.`

FunctionTabulations.create_tabulation_2DMethod
create_tabulation_2D(
    func::Function[,
    args...];
    xmin::T,
    xmax::T,
    ymin::V,
    ymax::V,
    npoints_x::Int,
    npoints_y::Int[,
    x_scale::Symbol = :linear,
    y_scale::Symbol = :linear,
    f_scale = :linear,
    jld_base_path = nothing,
    custom_name = nothing,
    interpolation_type = :linear,
    extrapolation_bc = Throw,
    check_SHA = true,
    check_SHA_mode = :warn,
    metadata=nothing,
    metadata_validation_fn=nothing,
    kwargs...]
) where {T<:Union{Real,Quantity},V<:Union{Real,Quantity}}

Computes or loads the tabulation for a given function of the kind f(x, y).

Arguments

  • func::Function: the function which should be tabulated. Must be of the kind f(x, y)
  • xmin::Union{Real,Quantity}: the minimum x for the range which will be covered by the tabulation
  • xmax::Union{Real,Quantity}: the maximum x for the range which will be covered by the tabulation
  • ymin::Union{Real,Quantity}: the minimum y for the range which will be covered by the tabulation
  • ymax::Union{Real,Quantity}: the maximum y for the range which will be covered by the tabulation
  • npoints_x::Int: the number of points along the x axis for which f(x,y) will be computed
  • npoints_y::Int: the number of points along the y axis for which f(x,y) will be computed
  • x_scale::Symbol: the scale which will be used for tabulation. If :linear is choosen, the x points will be evenly spaced. If :log10 is chosen, the points will be logarithmically spaced. Defaults to :linear
  • y_scale::Symbol: the scale which will be used for tabulation. If :linear is choosen, the y points will be evenly spaced. If :log10 is chosen, the points will be logarithmically spaced. Defaults to :linear
  • f_scale::Symbol: the scale which will be used for tabulation. If :linear is choosen, the f(x) points will not be alterated. If :log10 is chosen, log10 will be applied to the f(x) points before interpolating. Defaults to :linear
  • jld_base_path: path to the folder where the tabulation should be saved. Defaults to the current folder
  • custom_name: custom name for the tabulation file, to which _data.jld2 will be appended. Defaults to the name of the function to be tabulated
  • interpolation_type: Type of the spline to be used for interpolation. Can either be :linear (1st order spline) or :cubic (3rd order spline)
  • extrapolation_bc: behaviour of the tabulation outside of the boundaries defined by [xmin, xmax]. Possible behaviours are handled by Interpolations.jl and include Throw(throws and eror if a value out of bounds is acessed) orLine(extrapolate linearly). Defaults toThrow`
  • check_SHA::Bool: Whether to check the SHA of the tabulated function. If the SHA of the tabulated function does not match the SHA stored inside the tabulation file, it might be necessary to recompute the tabulation, since it's likely that the definition of the tabulated function has changed.
  • check_SHA_mode::Symbol: Describes the behaviour of this function if the SHA of the tabulated function does not match the SHA stored inside the tabulation file. Defaults to :warn (print a warning but load the tabulation all the same). Other options include :throw (throw an error to suggest manual deletion of the old tabulation) and :none (don't do anything).
  • metadata::Dict{String,Any}: an optional Dict{String, Any} which contains additional metadata to be stored in the tabulation achive.
  • metadata_validation_fn::Function: a function of the kind metadata_validation_fn(metadata1::Dict{String, Any}, metadata2::Dict{String, Any}) to chech whether two metadata dictionaries contain the same data.
  • args..., kwargs...: additional args and kwargs will be passed to the function which is to be tabulated

Examples

julia>  func_2d(x, y) = sin(x) * sin(y)

julia>  itp_2d_1 = create_tabulation_2D(
            func_2d,
            xmin = 0.0,
            xmax = 1.0,
            ymin = 0.0,
            ymax = 2.0,
            npoints_x = 100,
            npoints_y = 100,
        )

julia>  isapprox(itp_2d_1(1.0, 1.3), func_2d(1.0, 1.3), rtol = 1e-3)
true

Measurement units are supported too:

julia>  using Unitful

julia>  func_2d(x, y) = x^2 + y

julia>  itp_2d_1 = create_tabulation_2D(
            func_2d,
            xmin = 0.0u"m",
            xmax = 1.0u"m",
            ymin = 0.0u"m^2",
            ymax = 2.0u"m^2",
            npoints_x = 100,
            npoints_y = 100,
        )

julia>  isapprox(itp_2d_1(1.0u"m", 1.3u"m^2"), func_2d(1.0u"m", 1.3u"m^2"), rtol = 1e-3)
true
FunctionTabulations.create_tabulation_2DMethod
function create_tabulation_2D(
    func::Function,
    x::Vector{T},
    y::Vector{V},
    args...;
    jld_base_path = nothing,
    custom_name = nothing,
    x_scale::Symbol = :linear,
    y_scale::Symbol = :linear,
    f_scale = :linear,
    interpolation_type = :linear,
    extrapolation_bc = Throw,
    check_SHA = true,
    check_SHA_mode = :warn,
    metadata=nothing,
    metadata_validation_fn=nothing,
    kwargs...
) where {T<:Union{Real,Quantity},V<:Union{Real,Quantity}}

Provides an interface for create_tabulation_2D where the tabulation points are defined by the Vectors x and y. Only linear_interpolation is supported.`

FunctionTabulations.create_tabulation_3DMethod
create_tabulation_3D(
    func::Function[,
    args...];
    xmin::T,
    xmax::T,
    ymin::V,
    ymax::V,
    zmin::W,
    zmax::W,
    npoints_x::Int,
    npoints_y::Int,
    npoints_z::Int[,
    x_scale::Symbol = :linear,
    y_scale::Symbol = :linear,
    z_scale::Symbol = :linear,
    f_scale = :linear,
    jld_base_path = nothing,
    custom_name = nothing,
    interpolation_type = :linear,
    extrapolation_bc = Throw,
    check_SHA = true,
    check_SHA_mode = :warn,
    metadata=nothing,
    metadata_validation_fn=nothing,
    kwargs...]
) where {T<:Union{Real,Quantity},V<:Union{Real,Quantity},W<:Union{Real,Quantity}}

Computes or loads the tabulation for a given function of the kind f(x, y, z).

Arguments

  • func::Function: the function which should be tabulated. Must be of the kind f(x, y)
  • xmin::Union{Real,Quantity}: the minimum x for the range which will be covered by the tabulation
  • xmax::Union{Real,Quantity}: the maximum x for the range which will be covered by the tabulation
  • ymin::Union{Real,Quantity}: the minimum y for the range which will be covered by the tabulation
  • ymax::Union{Real,Quantity}: the maximum y for the range which will be covered by the tabulation
  • zmin::Union{Real,Quantity}: the minimum z for the range which will be covered by the tabulation
  • zmax::Union{Real,Quantity}: the maximum z for the range which will be covered by the tabulation
  • npoints_x::Int: the number of points along the x axis for which f(x,y,z) will be computed
  • npoints_y::Int: the number of points along the y axis for which f(x,y,z) will be computed
  • npoints_z::Int: the number of points along the z axis for which f(x,y,z) will be computed
  • x_scale::Symbol: the scale which will be used for tabulation. If :linear is choosen, the x points will be evenly spaced. If :log10 is chosen, the points will be logarithmically spaced. Defaults to :linear
  • y_scale::Symbol: the scale which will be used for tabulation. If :linear is choosen, the y points will be evenly spaced. If :log10 is chosen, the points will be logarithmically spaced. Defaults to :linear
  • z_scale::Symbol: the scale which will be used for tabulation. If :linear is choosen, the z points will be evenly spaced. If :log10 is chosen, the points will be logarithmically spaced. Defaults to :linear
  • f_scale::Symbol: the scale which will be used for tabulation. If :linear is choosen, the f(x) points will not be alterated. If :log10 is chosen, log10 will be applied to the f(x) points before interpolating. Defaults to :linear
  • jld_base_path: path to the folder where the tabulation should be saved. Defaults to the current folder
  • custom_name: custom name for the tabulation file, to which _data.jld2 will be appended. Defaults to the name of the function to be tabulated
  • interpolation_type: Type of the spline to be used for interpolation. Can either be :linear (1st order spline) or :cubic (3rd order spline)
  • extrapolation_bc: behaviour of the tabulation outside of the boundaries defined by [xmin, xmax]. Possible behaviours are handled by Interpolations.jl and include Throw(throws and eror if a value out of bounds is acessed) orLine(extrapolate linearly). Defaults toThrow`
  • check_SHA::Bool: Whether to check the SHA of the tabulated function. If the SHA of the tabulated function does not match the SHA stored inside the tabulation file, it might be necessary to recompute the tabulation, since it's likely that the definition of the tabulated function has changed.
  • check_SHA_mode::Symbol: Describes the behaviour of this function if the SHA of the tabulated function does not match the SHA stored inside the tabulation file. Defaults to :warn (print a warning but load the tabulation all the same). Other options include :throw (throw an error to suggest manual deletion of the old tabulation) and :none (don't do anything).
  • metadata::Dict{String,Any}: an optional Dict{String, Any} which contains additional metadata to be stored in the tabulation achive.
  • metadata_validation_fn::Function: a function of the kind metadata_validation_fn(metadata1::Dict{String, Any}, metadata2::Dict{String, Any}) to chech whether two metadata dictionaries contain the same data.
  • args..., kwargs...: additional args and kwargs will be passed to the function which is to be tabulated

Examples

julia>  func_3d(x, y, z) = x * y + z

julia>  itp_3d_1 = create_tabulation_3D(
            func_3d,
            xmin = 0.0,
            xmax = 1.0,
            ymin = 0.0,
            ymax = 2.0,
            zmin = 0.0,
            zmax = 3.0,
            npoints_x = 100,
            npoints_y = 100,
            npoints_z = 100,
        )

julia>  isapprox(itp_3d_1(1.0, 1.3, 2.5), func_3d(1.0, 1.3, 2.5), rtol = 1e-3)
true

Measurement units are supported too:

julia>  using Unitful

julia>  func_3d(x, y, z) = x * y + z

julia>  itp_3d_1 = create_tabulation_3D(
            func_3d,
            xmin = 0.0u"m",
            xmax = 1.0u"m",
            ymin = 0.0"s^-1",
            ymax = 2.0"s^-1",
            zmin = 0.0u"m/s",
            zmax = 3.0u"m/s",
            npoints_x = 100,
            npoints_y = 100,
            npoints_z = 100,
        )

julia>  isapprox(itp_3d_1(1.0u"m", 1.3u"s^-1", 2.5u"m/s"), func_3d(1.0u"m", 1.3u"s^-1", 2.5u"m/s"), rtol = 1e-3)
true
FunctionTabulations.create_tabulation_3DMethod
function create_tabulation_3D(
    func::Function,
    x::Vector{T},
    y::Vector{V},
    z::Vector{W},
    args...;
    jld_base_path = nothing,
    custom_name = nothing,
    x_scale::Symbol = :linear,
    y_scale::Symbol = :linear,
    z_scale::Symbol = :linear,
    f_scale = :linear,
    interpolation_type = :linear,
    extrapolation_bc = Throw,
    check_SHA = true,
    check_SHA_mode = :warn,
    metadata=nothing,
    metadata_validation_fn=nothing,
    kwargs...
) where {T<:Union{Real,Quantity},V<:Union{Real,Quantity},W<:Union{Real,Quantity}}

Provides an interface for create_tabulation_3D where the tabulation points are defined by the Vectors x, y and z. Only linear_interpolation is supported.`

FunctionTabulations.scalerMethod

scaler(x::Real, scale::Symbol)

Utility function to scale a variable, accepts :linear and :log10 scale

FunctionTabulations.un_scalerMethod

un_scaler(x::Real, scale::Symbol)

Utility function to un_scale a variable, accepts :linear and :log10 scale