View Source Demo
Mix.install([
{:measurements, path: "."},
{:vega_lite, "~> 0.1.6"},
{:kino_vega_lite, "~> 0.1.7"}
])
alias VegaLite, as: Vl
introduction
Introduction
measurements is a package helping with manipulation of real physics quantities.
usage
Usage
A measurement is just a struct that can be easily created like so:
Measurements.new(4, :kilometer)If desired, an associated error can be added onto that measurement
Measurements.new(300, :second) |> Measurements.add_error(4, :millisecond)A measurement can be converted to another unit of the same dimension
Measurements.new(300, :second, 5) |> Measurements.best_convert(:microsecond)The best unit is chosen to avoid loosing precision. If the target unit is not better than the current one, the conversion is simply ignored.
Measurements.new(300, :millisecond, 5) |> Measurements.best_convert(:second)This allows to operate on measurements without knowing their precision, but remaining confident no precision in lost in various computations.
arithmetic
Arithmetic
addition
Addition
Measurements support addition with automated conversion, provided the unit dimension matches.
m1 = Measurements.new(4, :millimeter)
m2 = Measurements.new(543, :micrometer, 2)
Measurements.sum(m1, m2)Otherwise an explicit error with clean measurement representation is displayed:
m1 = Measurements.new(4, :second) |> Measurements.add_error(5, :millisecond)
m2 = Measurements.new(543, :micrometer)
Measurements.sum(m1, m2)
scaling
Scaling
Scaling the Measurement by a constant is also supported. Note the scale also applies to the error.
m1 = Measurements.new(4, :second) |> Measurements.add_error(5, :millisecond)
Measurements.scale(m1, 60)
difference
Difference
Therefore difference of two measurements with unit of same dimension is also supported.
A more convenient delta/2 function is provided for this purpose.
m1 = Measurements.new(4, :millimeter)
m2 = Measurements.new(543, :micrometer, 2)
Measurements.delta(m1, m2)
ratio
Ratio
The ratio of two measurement is also supported.
The result will be a measurement, with its unit adjusted.
Therefore the nil Unit is just a constant, with potentially an error...
m1 = Measurements.new(4, :millimeter)
m2 = Measurements.new(543, :micrometer, 2)
Measurements.ratio(m1, m2)We can verify this result, and maybe get an exact match, even if the value is a float:
[
Measurements.ratio(m1, m2).value * 0.543 == 4,
# relative error recovery is a bit more involved.
# Refer to Error propagation theory when in doubt (TODO link?)
Measurements.ratio(m1, m2).error * 543 / 2 == Measurements.ratio(m1, m2).value
]
todo-product
TODO : Product
This will require more involved unit dimension manipulation...
discrete-calculus
Discrete Calculus
With the capabilities in Measurements so far, we can already implement some basic discrete calculus on physical quantities.
local-discrete-derivative
Local Discrete Derivative
TODO
local-discrete-integral
Local Discrete Integral
TODO