Base.log
— Function.log(b,x)
Compute the base b
logarithm of x
. Throws DomainError
for negative Real
arguments.
Examples
julia> log(4,8)
1.5
julia> log(4,2)
0.5
julia> log(-2, 3)
ERROR: DomainError with -2.0:
log will only return a complex result if called with a complex argument. Try log(Complex(x)).
Stacktrace:
[1] throw_complex_domainerror(::Symbol, ::Float64) at ./math.jl:31
[...]
julia> log(2, -3)
ERROR: DomainError with -3.0:
log will only return a complex result if called with a complex argument. Try log(Complex(x)).
Stacktrace:
[1] throw_complex_domainerror(::Symbol, ::Float64) at ./math.jl:31
[...]
log(x)
Compute the natural logarithm of x
. Throws DomainError
for negative Real
arguments. Use complex negative arguments to obtain complex results.
Examples
julia> log(2)
0.6931471805599453
julia> log(-3)
ERROR: DomainError with -3.0:
log will only return a complex result if called with a complex argument. Try log(Complex(x)).
Stacktrace:
[1] throw_complex_domainerror(::Symbol, ::Float64) at ./math.jl:31
[...]
log(A{T}::StridedMatrix{T})
If A
has no negative real eigenvalue, compute the principal matrix logarithm of A
, i.e. the unique matrix $X$ such that $e^X = A$ and $-\pi < Im(\lambda) < \pi$ for all the eigenvalues $\lambda$ of $X$. If A
has nonpositive eigenvalues, a nonprincipal matrix function is returned whenever possible.
If A
is symmetric or Hermitian, its eigendecomposition (eigen
) is used, if A
is triangular an improved version of the inverse scaling and squaring method is employed (see [AH12] and [AHR13]). For general matrices, the complex Schur form (schur
) is computed and the triangular algorithm is used on the triangular factor.
Awad H. Al-Mohy and Nicholas J. Higham, "Improved inverse scaling and squaring algorithms for the matrix logarithm", SIAM Journal on Scientific Computing, 34(4), 2012, C153-C169. doi:10.1137/110852553
Awad H. Al-Mohy, Nicholas J. Higham and Samuel D. Relton, "Computing the Fréchet derivative of the matrix logarithm and estimating the condition number", SIAM Journal on Scientific Computing, 35(4), 2013, C394-C410. doi:10.1137/120885991
Examples
julia> A = Matrix(2.7182818*I, 2, 2)
2×2 Array{Float64,2}:
2.71828 0.0
0.0 2.71828
julia> log(A)
2×2 Array{Float64,2}:
1.0 0.0
0.0 1.0
log(message::Union{String,Symbol,Number,Exception}, level::Union{String,Symbol} = :debug; showst = false) :: Nothing
Logs message
to all registered logger, taking into account the log level
.