Support dispatches on Number via union type

docs/src/examples.md

@@ -10,6 +10,7 @@ On your chemistry homework, you are faced with the following problem on the phot
 > The energy of the incident UV light is ``7.2 \cdot 10^{-19} \mathrm{J}`` per photon. Calculate the wavelength of the ejected electrons, in nanometers.
 
 Let's solve this problem with `DynamicQuantities.jl`!
+
 ```jldoctest examples
 julia> using DynamicQuantities
 
@@ -30,6 +31,356 @@ julia> λ = h / p # wavelength of ejected electrons
 julia> uconvert(us"nm", λ) # return answer in nanometers
 3.0294912478780556 nm
 ```
+
 Since units are automatically propagated, we can verify the dimension of our answer and all intermediates.
 Also, using `DynamicQuantities.Constants`, we were able to obtain the (dimensionful!) values of all necessary constants without typing them ourselves.
 
+## 2. Projectile motion
+
+Let's solve a simple projectile motion problem.
+First load the `DynamicQuantities` module:
+
+```julia
+using DynamicQuantities
+```
+
+Set up initial conditions as quantities:
+
+```julia
+y0 = 10u"km"
+v0 = 250u"m/s"
+θ = deg2rad(60)
+g = 9.81u"m/s^2"
+```
+
+Next, we use trig functions to calculate x and y components of initial velocity.
+`vx0` is the x component and
+`vy0` is the y component:
+
+```julia
+vx0 = v0 * cos(θ)
+vy0 = v0 * sin(θ)
+```
+
+Next, let's create a time vector from 0 seconds to 1.3 minutes.
+Note that these are the same dimension (time), so it's fine to treat
+them as dimensionally equivalent!
+
+```julia
+t = range(0u"s", 1.3u"min", length=100)
+```
+
+Next, use kinematic equations to calculate x and y as a function of time.
+`x(t)` is the x position at time t, and
+`y(t)` is the y position:
+
+```julia
+x(t) = vx0*t
+y(t) = vy0*t - 0.5*g*t^2 + y0
+```
+
+These are functions, so let's evaluate them:
+
+```julia
+x_si = x.(t)
+y_si = y.(t)
+```
+
+These are regular vectors of quantities
+with `Dimensions` for physical dimensions.
+
+Next, let's plot the trajectory.
+First convert to km and strip units:
+
+```julia
+x_km = ustrip.(uconvert(us"km").(x_si))
+y_km = ustrip.(uconvert(us"km").(y_si))
+```
+
+Now, we plot:
+
+```julia
+plot(x_km, y_km, label="Trajectory", xlabel="x [km]", ylabel="y [km]")
+```
+
+## 3. Various Simple Examples
+
+This section demonstrates miscellaneous examples of using `DynamicQuantities.jl`.
+
+### Conversion
+
+Convert a quantity to have a new type for the value:
+
+```julia
+quantity = 1.5u"m"
+
+convert_q = Quantity{Float32}(quantity)
+
+println("Converted Quantity to Float32: ", convert_q)
+```
+
+### Array basics
+
+Create a `QuantityArray` (an array of quantities with
+the same dimension) by passing an array and a single quantity:
+
+```julia
+x = QuantityArray(randn(32), u"km/s")
+```
+
+or, by passing an array of individual quantities:
+
+```julia
+y = randn(32)
+y_q = QuantityArray(y .* u"m * cd / s")
+```
+
+We can take advantage of this being `<:AbstractArray`:
+
+```julia
+println("Sum x: ", sum(x))
+```
+
+We can also do things like setting a particular element:
+
+```julia
+y_q[5] = Quantity(5, length=1, luminosity=1, time=-1)
+println("5th element of y_q: ", y_q[5])
+```
+
+We can get back the original array with `ustrip`:
+
+```julia
+println("Stripped y_q: ", ustrip(y_q))
+```
+
+This `QuantityArray` is useful for broadcasting:
+
+```julia
+f_square(v) = v^2 * 1.5 - v^2
+println("Applying function to y_q: ", sum(f_square.(y_q)))
+```
+
+### Fill
+
+We can also make `QuantityArray` using `fill`:
+
+```julia
+filled_q = fill(u"m/s", 10)
+println("Filled QuantityArray: ", filled_q)
+```
+
+`fill` works for 0 dimensional `QuantityArray`s as well:
+
+```julia
+empty_q = fill(u"m/s", ())
+println("0 dimensional QuantityArray: ", empty_q)
+```
+
+### Similar
+
+Likewise, we can create a `QuantityArray` with the same properties as another `QuantityArray`:
+
+```julia
+qa = QuantityArray(rand(3, 4), u"m")
+
+new_qa = similar(qa)
+
+println("Similar qa: ", new_qa)
+```
+
+### Promotion
+
+Promotion rules are defined for `QuantityArray`s:
+
+```julia
+qarr1 = QuantityArray(randn(32), convert(Dimensions{Rational{Int32}}, dimension(u"km/s")))
+qarr2 = QuantityArray(randn(Float16, 32), convert(Dimensions{Rational{Int64}}, dimension(u"km/s")))
+```
+
+See what type they promote to:
+
+```julia
+println("Promoted type: ", typeof(promote(qarr1, qarr2)))
+```
+
+### Array Concatenation
+
+Likewise, we can take advantage of array concatenation,
+which will ensure we have the same dimensions:
+
+```julia
+qarr1 = QuantityArray(randn(3) .* u"km/s")
+qarr2 = QuantityArray(randn(3) .* u"km/s")
+```
+
+Concatenate them:
+
+```julia
+concat_qarr = hcat(qarr1, qarr2)
+println("Concatenated QuantityArray: ", concat_qarr)
+```
+
+### Symbolic Units
+
+We can use arbitrary `AbstractQuantity` and `AbstractDimensions`
+in a `QuantityArray`, including `SymbolicDimensions`:
+
+```julia
+z_ar = randn(32)
+z = QuantityArray(z_ar, us"Constants.M_sun * km/s")
+```
+
+Expand to standard units:
+
+```julia
+z_expanded = uexpand(z)
+println("Expanded z: ", z_expanded)
+```
+
+
+### GenericQuantity Construction
+
+In addition to `Quantity`, we can also use `GenericQuantity`:
+
+
+```julia
+x = GenericQuantity(1.5)
+y = GenericQuantity(0.2u"km")
+println(y)
+```
+
+This `GenericQuantity` is subtyped to `Any`,
+rather than `Number`, and thus can also store
+custom non-scalar types.
+
+For example, we can work with `Coords`, and
+wrap it in a single `GenericQuantity` type:
+
+```julia
+struct Coords
+    x::Float64
+    y::Float64
+end
+
+# Define arithmetic operations on Coords
+Base.:+(a::Coords, b::Coords) = Coords(a.x + b.x, a.y + b.y)
+Base.:-(a::Coords, b::Coords) = Coords(a.x - b.x, a.y - b.y)
+Base.:*(a::Coords, b::Number) = Coords(a.x * b, a.y * b)
+Base.:*(a::Number, b::Coords) = Coords(a * b.x, a * b.y)
+Base.:/(a::Coords, b::Number) = Coords(a.x / b, a.y / b)
+```
+
+We can then build a `GenericQuantity` out of this:
+
+```julia
+coord1 = GenericQuantity(Coords(0.3, 0.9), length=1)
+coord2 = GenericQuantity(Coords(0.2, -0.1), length=1)
+```
+
+and perform operations on these:
+
+```julia
+coord1 + coord2 |> uconvert(us"cm")
+# (Coords(50.0, 80.0)) cm
+```
+
+The nice part about this is it only stores a single Dimensions
+(or `SymbolicDimensions`) for the entire struct!
+
+### GenericQuantity and Quantity Promotion
+
+When we combine a `GenericQuantity` and a `Quantity`,
+the result is another `GenericQuantity`:
+
+```julia
+x = GenericQuantity(1.5f0)
+y = Quantity(1.5, length=1)
+println("Promoted type of x and y: ", typeof(x * y))
+```
+
+### Custom Dimensions
+
+We can create custom dimensions by subtyping to
+`AbstractDimensions`:
+
+```julia
+struct MyDimensions{R} <: AbstractDimensions{R}
+    cookie::R
+    milk::R
+end
+```
+
+Many constructors and functions are defined on `AbstractDimensions`,
+so this can be used out-of-the-box.
+We can then use this in a `Quantity`, and all operations will work as expected:
+
+```julia
+x = Quantity(1.5, MyDimensions(cookie=1, milk=-1))
+y = Quantity(2.0, MyDimensions(milk=1))
+
+x * y
+```
+
+which gives us `3.0 cookie` computed from a rate of `1.5 cookie milk⁻¹` multiplied
+by `2.0 milk`. Likewise, we can use these in a `QuantityArray`:
+
+```julia
+x_qa = QuantityArray(randn(32), MyDimensions(cookie=1, milk=-1))
+
+x_qa .^ 2
+```
+
+### Custom Quantities
+
+We can also create custom dimensions by subtyping
+to either `AbstractQuantity` (for `<:Number`) or
+`AbstractGenericQuantity` (for `<:Any`):
+
+```julia
+struct MyQuantity{T,D} <: AbstractQuantity{T,D}
+    value::T
+    dimensions::D
+end
+```
+
+Since `AbstractQuantity <: Number`, this will also be a number.
+Keep in mind that you must call these fields `value` and `dimensions`
+for `ustrip(...)` and `dimension(...)` to work. Otherwise, simply
+redefine those.
+
+We can use this custom quantity just like we would use `Quantity`:
+
+```julia
+q1 = MyQuantity(1.2, Dimensions(length=-2))
+# prints as `1.2 m⁻²`
+
+q2 = MyQuantity(1.5, MyDimensions(cookie=1))
+# prints as `1.5 cookie`
+```
+
+Including mathematical operations:
+
+```julia
+q2 ^ 2
+# `2.25 cookie²`
+```
+
+The main reason you would use a custom quantity is if you want
+to change built-in behavior, or maybe have special methods for
+different types of quantities.
+
+Note that you can declare a method on `AbstractQuantity`, or
+`AbstractGenericQuantity` to allow their respective inputs.
+
+**Note**: In general, you should probably
+specialize on `UnionAbstractQuantity` which is
+the union of these two abstract quantities, _as well as any other future abstract quantity types_,
+such as the planned `AbstractRealQuantity`.
+
+```julia
+function my_func(x::UnionAbstractQuantity{T,D}) where {T,D}
+    # value has type T and dimensions has type D
+    return x / ustrip(x)
+end
+```

docs/src/types.md

@@ -30,3 +30,16 @@ SymbolicDimensions
 ```@docs
 QuantityArray
 ```
+
+## Generic quantities
+
+Whereas `Quantity` is subtyped to `Number`,
+a more general type of quantity is `GenericQuantity`,
+which is subtyped to `Any`.
+
+```@docs
+GenericQuantity
+AbstractGenericQuantity
+UnionAbstractQuantity
+DynamicQuantities.ABSTRACT_QUANTITY_TYPES
+```

ext/DynamicQuantitiesLinearAlgebraExt.jl

@@ -1,8 +1,8 @@
 module DynamicQuantitiesLinearAlgebraExt
 
 import LinearAlgebra: norm
-import DynamicQuantities: AbstractQuantity, ustrip, dimension, new_quantity
+import DynamicQuantities: UnionAbstractQuantity, ustrip, dimension, new_quantity
 
-norm(q::AbstractQuantity, p::Real=2) = new_quantity(typeof(q), norm(ustrip(q), p), dimension(q))
+norm(q::UnionAbstractQuantity, p::Real=2) = new_quantity(typeof(q), norm(ustrip(q), p), dimension(q))
 
 end