hitchiker42/physical.jl

Units, physical constants, error propagation.

Physical provides simple support for units in Julia, as well a nice set of predefined units and constants. The keys are the types Quantity and Unit, but you should just use predefined unit constants for the most part. Since Physical is not yet an official package, install with Pkg.clone("https://github.com/ggggggggg/Physical.jl.git").

julia> using Physical
julia> f = 1*ElectronVolt/H_plank # H_plank is in units of h, so resulting expression have units with h
1.0 eV h⁻¹
julia> asbase(f)
2.4270444990211597e14 s⁻¹ # all Quantities can be reduced to base units
julia> f+1e9*(Mega*Hertz)
5.120237599283019 eV h⁻¹
julia> 1e9*(Mega*Hertz)+f # adding compatible Quantities casts to units of the first Quantity
1.242704449902116e9 MHz 

Using units is as simple as multiplying any number or array by the predefined unit constants. Using units it will keep you from doing stupid things like

julia> d = 17*(Milli*Meter)
17 mm 
julia> d+f
ERROR: incompatible base units s⁻¹ and m 

Say you want to call sin, but you want to be sure that the argument is in radians?

julia> theta = pi/2*Radian
1.5707963267948966 rad 
julia> sin(theta/Radian)
1.0
julia> sin(1*Meter/Radian)
ERROR: no method sin(Quantity{Float64},)

This works because any operation that leads to a unitless number, just returns a standard Julia datatype.

julia> R=[1,2,3,4]*Ohm
[1,2,3,4] Ω 
julia> R*17*Ampere/(14*Volt)
4-element Float64 Array:
 1.21429
 2.42857
 3.64286
 4.85714

Create new units with QUnit, unit symbols can be unicode, like that Ω above. Convert units to base units and other units using asbase and as. Warning, when you use as(from,to) it uses the unit of to but ignores the value of to.

julia> Foot = QUnit("ft", 0.3048*Meter)
julia> Pound = QUnit("lb", 4.44822162*Newton)
julia> asbase(12*Foot*Pound)
16.269815397312 m²kg s⁻²
julia> as(12*Foot*Pound, Newton*Meter)
16.269815397312 m N 
julia> as(12*Foot*Pound, 7000*Newton*Meter) # note the value of the second argument doesn't matter
16.269815397312 m N 

QUnit(x::String) creates a new base unit. QUnit(x::String, y::Quantity) creates a new derived unit. Both of these will overwrite existing units. I'm going to use this to switch my base mass unit to the slug. The unit system and constants are defined by a few files in .Julia/Physical/data. If you add a .jl file to the data folder it will be loaded in a fixed order automatically by Physical. This allows you to add or replace units and constants easily. For debugging purposes, Physical.loaded_files contains the file names in the order they were loaded.

julia> Slug = QUnit("slug")
1 slug 
julia> QUnit("kg", 0.0685217659*Slug)
1 kg 
julia> asbase(KiloGram)
0.0685217659 slug 

There is also a Type for uncertain numbers, with error propagation. It currently treats the covariance and correlation between numbers as 0. If you have a good idea of how to implement covariance and correlation, let me know, or do it yourself.

julia> a = Uncertain(100,1)
100.0 ± 1.0
julia> b = Uncertain(10,5)
10.0 ± 5.0
julia> a*b
1000.0 ± 500.09999000199946
julia> a-b
90.0 ± 5.0990195135927845
julia> a+b
110.0 ± 5.0990195135927845
julia> (a*b*Meter)^2
1.0e6 ± 1.0001999800039988e6 m²

Future features

• LaTex printing in iJulia
• Guesses at pretty unit reduction
• Maximally accurate fundamental units from CODATA
• Round properly when displaying Uncertain numbers

Feel free to start an issue if you have any problems or questions or just want to get in contact with me.