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tanh

Compute the hyperbolic tangent of x.

Base.tanh — Function
tanh(x)

Compute hyperbolic tangent of x.

See also tan, atanh.

Examples

julia> tanh.(-3:3f0)  # Here 3f0 isa Float32
7-element Vector{Float32}:
 -0.9950548
 -0.9640276
 -0.7615942
  0.0
  0.7615942
  0.9640276
  0.9950548

julia> tan.(im .* (1:3))
3-element Vector{ComplexF64}:
 0.0 + 0.7615941559557649im
 0.0 + 0.9640275800758169im
 0.0 + 0.9950547536867306im
source
tanh(A::AbstractMatrix)

Compute the matrix hyperbolic tangent of a square matrix A.

Methods

julia> methods(tanh, (Any,), [Base, Base.Math, Base.MathConstants, Base.MPFR])# 7 methods for generic function "tanh" from Base:
 [1] tanh(a::Float16)
     @ Base.Math math.jl:1511
 [2] tanh(a::ComplexF16)
     @ Base.Math math.jl:1512
 [3] tanh(::Missing)
     @ Base.Math math.jl:1533
 [4] tanh(x::BigFloat)
     @ Base.MPFR mpfr.jl:733
 [5] tanh(x::T) where T<:Union{Float32, Float64}
     @ Base.Math special/hyperbolic.jl:143
 [6] tanh(x::Real)
     @ Base.Math math.jl:1528
 [7] tanh(z::Complex{T}) where T
     @ complex.jl:991

Examples

julia> using UnicodePlots
julia> lineplot(-3, 3, tanh)           ┌────────────────────────────────────────┐
         1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠊⠉⠉⠉⠉⠉⠉│ tanh(x)
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
   f(x)    │⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
        -1 │⣀⣀⣀⣀⣀⣀⡠⠤⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           └────────────────────────────────────────┘
           ⠀-3⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀3⠀
           ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Real Numbers

julia> tanh(0)
0.0

julia> tanh(-0.0)
-0.0

julia> tanh(1.0)
0.7615941559557649

Complex

julia> tanh(0+0im)
0.0 + 0.0im

Tips

See Also

Extended Inputs

Matrix

With Array like input:

julia> methods(tanh, (Any,), [LinearAlgebra])# 5 methods for generic function "tanh" from Base:
 [1] tanh(J::UniformScaling)
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/uniformscaling.jl:173
 [2] tanh(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] tanh(D::Diagonal)
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/diagonal.jl:802
 [4] tanh(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] tanh(A::AbstractMatrix)
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/dense.jl:1176

Tech Notes

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

Version History

Introduced in Julia v1.0 (2018)