Types

Quantity{T<:Number,D<:AbstractDimensions} <: AbstractQuantity{T,D} <: Number

Physical quantity with value value of type T and dimensions dimensions of type D. For example, the velocity of an object with mass 1 kg and velocity 2 m/s is Quantity(2, mass=1, length=1, time=-1). You should access these fields with ustrip(q), and dimension(q). You can access specific dimensions with ulength(q), umass(q), utime(q), ucurrent(q), utemperature(q), uluminosity(q), and uamount(q).

Severals operators in Base are extended to work with Quantity objects, including *, +, -, /, abs, ^, sqrt, and cbrt, which manipulate dimensions according to the operation.

Fields

• value::T: value of the quantity of some type T. Access with ustrip(::Quantity)
• dimensions::D: dimensions of the quantity. Access with dimension(::Quantity)

Constructors

• Quantity(x; kws...): Construct a quantity with value x and dimensions given by the keyword arguments. The value type is inferred from x. R is set to DEFAULT_DIM_TYPE.
• Quantity(x, ::Type{D}; kws...): Construct a quantity with value x with dimensions given by the keyword arguments, and the dimensions type set to D.
• Quantity(x, d::D): Construct a quantity with value x and dimensions d of type D.
• Quantity{T}(...): As above, but converting the value to type T. You may also pass a Quantity as input.
• Quantity{T,D}(...): As above, but converting the value to type T and dimensions to D. You may also pass a Quantity as input.

Dimensions{R<:Real} <: AbstractDimensions{R}

A type representing the dimensions of a quantity, with each field giving the power of the corresponding dimension. For example, the dimensions of velocity are Dimensions(length=1, time=-1). Each of the 7 dimensions are stored using the type R, which is by default a rational number.

Fields

• length: length dimension (i.e., meters^(length))
• mass: mass dimension (i.e., kg^(mass))
• time: time dimension (i.e., s^(time))
• current: current dimension (i.e., A^(current))
• temperature: temperature dimension (i.e., K^(temperature))
• luminosity: luminosity dimension (i.e., cd^(luminosity))
• amount: amount dimension (i.e., mol^(amount))

Constructors

• Dimensions(args...): Pass all the dimensions as arguments.
• Dimensions(; kws...): Pass a subset of dimensions as keyword arguments. R is set to DEFAULT_DIM_BASE_TYPE.
• Dimensions(::Type{R}; kws...) or Dimensions{R}(; kws...): Pass a subset of dimensions as keyword arguments, with the output type set to Dimensions{R}.
• Dimensions{R}(): Create a dimensionless object typed as Dimensions{R}.
• Dimensions{R}(d::Dimensions): Copy the dimensions from another Dimensions object, with the output type set to Dimensions{R}.

AbstractDimensions{R}

An abstract type for dimension types. R is the type of the exponents of the dimensions, and by default is set to DynamicQuantities.DEFAULT_DIM_BASE_TYPE. AbstractDimensions are used to store the dimensions of UnionAbstractQuantity objects. Together these enable many operators in Base to manipulate dimensions. This type has generic constructors for creating dimension objects, so user-defined dimension types can be created by simply subtyping AbstractDimensions, without the need to define many other functions.

The key function that one could wish to overload is DynamicQuantities.dimension_name(::AbstractDimensions, k::Symbol) for mapping from a field name to a base unit (e.g., length by default maps to m). You may also need to overload constructorof(::Type{T}) in case of non-standard construction.

AbstractQuantity{T,D} <: Number

An abstract type for quantities. T is the type of the value of the quantity, which should be <:Number. D is the type of the dimensions of the quantity. By default, D is set to DynamicQuantities.DEFAULT_DIM_TYPE. T is inferred from the value in a calculation, but in other cases is defaulted to DynamicQuantities.DEFAULT_VALUE_TYPE. It is assumed that the value is stored in the :value field, and the dimensions object is stored in the :dimensions field. These fields can be accessed with ustrip and dimension, respectively. Many operators in Base are defined on AbstractQuantity objects, including +, -, *, /, ^, sqrt, cbrt, abs.

See also AbstractGenericQuantity for creating quantities subtyped to Any.

Note: In general, you should probably specialize on UnionAbstractQuantity which is the union of both AbstractQuantity and AbstractGenericQuantity, as well as any other future abstract quantity types,

SymbolicDimensions{R} <: AbstractDimensions{R}

An AbstractDimensions with one dimension for every unit and constant symbol. This is to allow for lazily reducing to SI base units, whereas Dimensions is always in SI base units. Furthermore, SymbolicDimensions stores dimensions using a sparse vector for efficiency (since there are so many unit symbols).

You can convert a quantity using SymbolicDimensions as its dimensions to one which uses Dimensions as its dimensions (i.e., base SI units) with uexpand.

SymbolicDimensionsSingleton{R} <: AbstractSymbolicDimensions{R}

This special symbolic dimensions types stores a single unit or constant, and can be used for constructing symbolic units and constants without needing to allocate mutable storage.

AbstractSymbolicDimensions{R} <: AbstractDimensions{R}

Abstract type to allow for custom types of symbolic dimensions. In defining this abstract type we allow for units to declare themselves as a special type of symbolic dimensions which are immutable, whereas the regular SymbolicDimensions type has mutable storage.

QuantityArray{T,N,D<:AbstractDimensions,Q<:UnionAbstractQuantity,V<:AbstractArray}

An array of quantities with value value of type V and dimensions dimensions of type D (which are shared across all elements of the array). This is a subtype of AbstractArray{Q,N}, and so can be used in most places where a normal array would be used, including broadcasting operations.

Fields

• value: The underlying array of values. Access with ustrip(a).
• dimensions: The dimensions of the array. Access with dimension(a).

Constructors

You can create a QuantityArray by multiplying an array with a Quantity:

x = (0:0.1:10)u"km/s"

Alternatively, the following constructors are available:

• QuantityArray(v::AbstractArray, d::AbstractDimensions): Create a QuantityArray with value v and dimensions d, using Quantity if the eltype of v is numeric, and GenericQuantity otherwise.

• QuantityArray(v::AbstractArray{<:Number}, q::AbstractQuantity): Create a QuantityArray with value v and dimensions inferred with dimension(q). This is so that you can easily create an array with the units module, like so:

  A = QuantityArray(randn(32), 1u"m")

• QuantityArray(v::AbstractArray{<:Any}, q::AbstractGenericQuantity): Create a QuantityArray with value v and dimensions inferred with dimension(q). This is so that you can easily create quantity arrays of non-numeric eltypes, like so:

  A = QuantityArray([[1.0], [2.0, 3.0]], GenericQuantity(1u"m"))

• QuantityArray(v::AbstractArray{<:UnionAbstractQuantity}): Create a QuantityArray from an array of quantities. This means the following syntax works:

  A = QuantityArray(randn(32) .* 1u"km/s")

• QuantityArray(v::AbstractArray; kws...): Create a QuantityArray with dimensions inferred from the keyword arguments. For example:

  A = QuantityArray(randn(32); length=1)

  is equivalent to

  A = QuantityArray(randn(32), u"m")

  The keyword arguments are passed to DEFAULT_DIM_TYPE.

GenericQuantity{T<:Any,D<:AbstractDimensions} <: AbstractGenericQuantity{T,D} <: Any

This has the same behavior as Quantity but is subtyped to AbstractGenericQuantity <: Any rather than AbstractQuantity <: Number.

AbstractGenericQuantity{T,D} <: Any

This has the same behavior as AbstractQuantity but is subtyped to Any rather than Number.

Note: In general, you should probably specialize on UnionAbstractQuantity which is the union of both AbstractQuantity and AbstractGenericQuantity, as well as any other future abstract quantity types,

RealQuantity{T<:Real,D<:AbstractDimensions} <: AbstractRealQuantity{T,D} <: Real

This has the same behavior as Quantity but is subtyped to AbstractRealQuantity <: Real.

AbstractRealQuantity{T,D} <: Real

This has the same behavior as AbstractQuantity but is subtyped to Real rather than Number.

UnionAbstractQuantity{T,D}

This is a union of both AbstractQuantity{T,D} and AbstractGenericQuantity{T,D}. It is used throughout the library to declare methods which can take both types. You should generally specialize on this type, rather than its constituents, as it will also include future abstract quantity types.

ABSTRACT_QUANTITY_TYPES

A constant tuple of the existing abstract quantity types, each as a tuple with (1) the abstract type, (2) the base type, and (3) the default exported concrete type.

constructorof(::Type{<:AbstractDimensions})
constructorof(::Type{<:UnionAbstractQuantity})

Return the constructor of the given type. This is used to create new objects of the same type as the input. Overload a method for a new type, especially if you need custom behavior.

with_type_parameters(::Type{<:AbstractDimensions}, ::Type{R})
with_type_parameters(::Type{<:UnionAbstractQuantity}, ::Type{T}, ::Type{D})

Return the type with the given type parameters instead of the ones in the input type. This is used to get Dimensions{R} from input (Dimensions{R1}, R), for example. Overload a method for a new type, especially if you need custom behavior.

dimension_names(::Type{<:AbstractDimensions})

Return a tuple of symbols with the names of the dimensions of the given type. This should be static so that it can be hardcoded during compilation. The default is to use fieldnames, but you can overload this for custom behavior.