LogRange{T}(start, stop, len) <: AbstractVector{T}

A range whose elements are spaced logarithmically between start and stop, with spacing controlled by len. Returned by logrange.

Like LinRange, the first and last elements will be exactly those provided, but intermediate values may have small floating-point errors. These are calculated using the logs of the endpoints, which are stored on construction, often in higher precision than T.

Examples

julia> logrange(1, 4, length=5)
5-element Base.LogRange{Float64, Base.TwicePrecision{Float64}}:
 1.0, 1.41421, 2.0, 2.82843, 4.0

julia> Base.LogRange{Float16}(1, 4, 5)
5-element Base.LogRange{Float16, Float64}:
 1.0, 1.414, 2.0, 2.828, 4.0

julia> logrange(1e-310, 1e-300, 11)[1:2:end]
6-element Vector{Float64}:
 1.0e-310
 9.999999999999974e-309
 9.999999999999981e-307
 9.999999999999988e-305
 9.999999999999994e-303
 1.0e-300

julia> prevfloat(1e-308, 5) == ans[2]
true

Note that integer eltype T is not allowed. Use for instance round.(Int, xs), or explicit powers of some integer base:

julia> xs = logrange(1, 512, 4)
4-element Base.LogRange{Float64, Base.TwicePrecision{Float64}}:
 1.0, 8.0, 64.0, 512.0

julia> 2 .^ (0:3:9) |> println
[1, 8, 64, 512]

_valid_macro(expr)

Check if expr is a valid macro call with no arguments.

logrange(start, stop, length)
logrange(start, stop; length)

Construct a specialized array whose elements are spaced logarithmically between the given endpoints. That is, the ratio of successive elements is a constant, calculated from the length.

This is similar to geomspace in Python. Unlike PowerRange in Mathematica, you specify the number of elements not the ratio. Unlike logspace in Python and Matlab, the start and stop arguments are always the first and last elements of the result, not powers applied to some base.

Examples

julia> logrange(10, 4000, length=3)
3-element Base.LogRange{Float64, Base.TwicePrecision{Float64}}:
 10.0, 200.0, 4000.0

julia> ans[2] ≈ sqrt(10 * 4000)  # middle element is the geometric mean
true

julia> range(10, 40, length=3)[2] ≈ (10 + 40)/2  # arithmetic mean
true

julia> logrange(1f0, 32f0, 11)
11-element Base.LogRange{Float32, Float64}:
 1.0, 1.41421, 2.0, 2.82843, 4.0, 5.65685, 8.0, 11.3137, 16.0, 22.6274, 32.0

julia> logrange(1, 1000, length=4) ≈ 10 .^ (0:3)
true

See the Compat.LogRange type for further details.