GitHub

asinh

Compute the arc hyperbolic sine of x.

Base.asinh — Function
asinh(x)

Compute the inverse hyperbolic sine of x.

source
asinh(A::AbstractMatrix)

Compute the inverse hyperbolic matrix sine of a square matrix A. For the theory and logarithmic formulas used to compute this function, see [AH16_5].

Methods

julia> methods(asinh, (Any,), [Base, Base.Math, Base.MathConstants, Base.MPFR])# 7 methods for generic function "asinh" from Base:
 [1] asinh(a::Float16)
     @ Base.Math math.jl:1511
 [2] asinh(a::ComplexF16)
     @ Base.Math math.jl:1512
 [3] asinh(::Missing)
     @ Base.Math math.jl:1533
 [4] asinh(x::BigFloat)
     @ Base.MPFR mpfr.jl:860
 [5] asinh(x::T) where T<:Union{Float32, Float64}
     @ Base.Math special/hyperbolic.jl:165
 [6] asinh(x::Real)
     @ Base.Math math.jl:1528
 [7] asinh(z::Complex)
     @ complex.jl:1013

Examples

julia> using UnicodePlots
julia> lineplot(-4, 4, asinh, ylim=(-2, 2))           ┌────────────────────────────────────────┐
         2 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀│ asinh(x)
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
   f(x)    │⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⡯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
        -2 │⠀⢀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           └────────────────────────────────────────┘
           ⠀-4⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀4⠀
           ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Real Numbers

julia> asinh(0)
0.0

julia> asinh(1)
0.881373587019543

Complex

julia> asinh(0+0im)
0.0 - 0.0im

Tips

See Also

Extended Inputs

Matrix

With Array like input:

julia> methods(asinh, (Any,), [LinearAlgebra])# 5 methods for generic function "asinh" from Base:
 [1] asinh(J::UniformScaling)
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/uniformscaling.jl:173
 [2] asinh(A::Hermitian{var"#s5028", S} where {var"#s5028"<:Complex, S<:(AbstractMatrix{<:var"#s5028"})})
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/symmetric.jl:714
 [3] asinh(D::Diagonal)
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/diagonal.jl:802
 [4] asinh(A::Union{Hermitian{var"#s5029", S}, Symmetric{var"#s5029", S}} where {var"#s5029"<:Real, S})
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/symmetric.jl:710
 [5] asinh(A::AbstractMatrix)
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/dense.jl:1310

Tech Notes

  • asinh(::Real): by pure julia
  • asinh(::BigFloat): by MPFR

Version History

Introduced in Julia v1.0 (2018)