Dimensions
Dimensions are kept in the sub-module Dimensions.
DimensionsSub-module for Dimensions wrappers, and operations on them used in DimensionalData.jl.
To load Dimensions types and methods into scope:
using DimensionalData
using DimensionalData.DimensionsDimensions have a type-hierarchy that organises plotting and dimension matching.
DimensionAbstract supertype of all dimension types.
Example concrete implementations are X, Y, Z, Ti (Time), and the custom Dim dimension.
Dimensions label the axes of an AbstractDimArray, or other dimensional objects, and are used to index into an array.
They may also wrap lookup values for each array axis. This may be any AbstractVector matching the array axis length, but will usually be converted to a Lookup when use in a constructed object.
A Lookup gives more details about the dimension, such as that it is Categorical or Sampled as Points or Intervals along some transect. DimensionalData will attempt to guess the lookup from the passed-in index value.
Example:
using DimensionalData, Dates
x = X(2:2:10)
y = Y(['a', 'b', 'c'])
ti = Ti(DateTime(2021, 1):Month(1):DateTime(2021, 12))
A = DimArray(zeros(3, 5, 12), (y, x, ti))
# output
╭────────────────────────────╮
│ 3×5×12 DimArray{Float64,3} │
├────────────────────────────┴─────────────────────────────────────────── dims ┐
↓ Y Categorical{Char} ['a', 'b', 'c'] ForwardOrdered,
→ X Sampled{Int64} 2:2:10 ForwardOrdered Regular Points,
↗ Ti Sampled{Dates.DateTime} Dates.DateTime("2021-01-01T00:00:00"):Dates.Month(1):Dates.DateTime("2021-12-01T00:00:00") ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
[:, :, 1]
↓ → 2 4 6 8 10
'a' 0.0 0.0 0.0 0.0 0.0
'b' 0.0 0.0 0.0 0.0 0.0
'c' 0.0 0.0 0.0 0.0 0.0For simplicity, the same Dimension types are also used as wrappers in getindex, like:
x = A[X(2), Y(3)]
# output
╭────────────────────────────────╮
│ 12-element DimArray{Float64,1} │
├────────────────────────────────┴─────────────────────────────────────── dims ┐
↓ Ti Sampled{Dates.DateTime} Dates.DateTime("2021-01-01T00:00:00"):Dates.Month(1):Dates.DateTime("2021-12-01T00:00:00") ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
2021-01-01T00:00:00 0.0
2021-02-01T00:00:00 0.0
2021-03-01T00:00:00 0.0
2021-04-01T00:00:00 0.0
2021-05-01T00:00:00 0.0
2021-06-01T00:00:00 0.0
2021-07-01T00:00:00 0.0
2021-08-01T00:00:00 0.0
2021-09-01T00:00:00 0.0
2021-10-01T00:00:00 0.0
2021-11-01T00:00:00 0.0
2021-12-01T00:00:00 0.0A Dimension can also wrap Selector.
x = A[X(Between(3, 4)), Y(At('b'))]
# output
╭──────────────────────────╮
│ 1×12 DimArray{Float64,2} │
├──────────────────────────┴───────────────────────────────────────────── dims ┐
↓ X Sampled{Int64} 4:2:4 ForwardOrdered Regular Points,
→ Ti Sampled{Dates.DateTime} Dates.DateTime("2021-01-01T00:00:00"):Dates.Month(1):Dates.DateTime("2021-12-01T00:00:00") ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
↓ → 2021-01-01T00:00:00 2021-02-01T00:00:00 … 2021-12-01T00:00:00
4 0.0 0.0 0.0DependentDim <: DimensionAbstract supertype for dependent dimensions. These will plot on the Y axis.
IndependentDim <: DimensionAbstract supertype for independent dimensions. These will plot on the X axis.
XDim <: IndependentDimAbstract supertype for all X dimensions.
YDim <: DependentDimAbstract supertype for all Y dimensions.
ZDim <: DependentDimAbstract supertype for all Z dimensions.
TimeDim <: IndependentDimAbstract supertype for all time dimensions.
In a TimeDime with Interval sampling the locus will automatically be set to Start(). Dates and times generally refer to the start of a month, hour, second etc., not the central point as is more common with spatial data. `
X <: XDim
X(val=:)X Dimension. X <: XDim <: IndependentDim
Examples
xdim = X(2:2:10)val = A[X(1)]mean(A; dims=X)Y <: YDim
Y(val=:)Y Dimension. Y <: YDim <: DependentDim
Examples
ydim = Y(['a', 'b', 'c'])val = A[Y(1)]mean(A; dims=Y)Z <: ZDim
Z(val=:)Z Dimension. Z <: ZDim <: Dimension
Example:
zdim = Z(10:10:100)val = A[Z(1)]mean(A; dims=Z)m Ti <: TimeDim
Ti(val=:)Time Dimension. Ti <: TimeDim <: IndependentDim
Time is already used by Dates, and T is a common type parameter, We use Ti to avoid clashes.
Example:
timedim = Ti(DateTime(2021, 1):Month(1):DateTime(2021, 12))val = A[Ti(1)]mean(A; dims=Ti)Dim{S}(val=:)A generic dimension. For use when custom dims are required when loading data from a file. Can be used as keyword arguments for indexing.
Dimension types take precedence over same named Dim types when indexing with symbols, or e.g. creating Tables.jl keys.
julia> dim = Dim{:custom}(['a', 'b', 'c'])
custom ['a', 'b', 'c']AnonDim <: Dimension
AnonDim()Anonymous dimension. Used when extra dimensions are created, such as during transpose of a vector.
@dim typ [supertype=Dimension] [label::String=string(typ)]Macro to easily define new dimensions.
The supertype will be inserted into the type of the dim. The default is simply YourDim <: Dimension.
Making a Dimension inherit from XDim, YDim, ZDim or TimeDim will affect automatic plot layout and other methods that dispatch on these types. <: YDim are plotted on the Y axis, <: XDim on the X axis, etc.
label is used in plots and similar, if the dimension is short for a longer word.
Example:
using DimensionalData
using DimensionalData: @dim, YDim, XDim
@dim Lat YDim "Latitude"
@dim Lon XDim "Longitude"
# outputExported methods
These are widely useful methods for working with dimensions.
dims(x, [dims::Tuple]) => Tuple{Vararg{Dimension}}
dims(x, dim) => DimensionReturn a tuple of Dimensions for an object, in the order that matches the axes or columns of the underlying data.
dims can be Dimension, Dimension types, or Symbols for Dim{Symbol}.
The default is to return nothing.
dims(x, query) => Tuple{Vararg{Dimension}}
dims(x, query...) => Tuple{Vararg{Dimension}}Get the dimension(s) matching the type(s) of the query dimension.
Lookup can be an Int or an Dimension, or a tuple containing any combination of either.
Arguments
x: any object with adimsmethod, or aTupleofDimension.query: Tuple or a singleDimensionorDimensionType.
Example
julia> using DimensionalData
julia> A = DimArray(ones(2, 3, 2), (X, Y, Z))
╭───────────────────────────╮
│ 2×3×2 DimArray{Float64,3} │
├───────────────────── dims ┤
↓ X, → Y, ↗ Z
└───────────────────────────┘
[:, :, 1]
1.0 1.0 1.0
1.0 1.0 1.0
julia> dims(A, (X, Y))
↓ X, → Yotherdims(x, query) => Tuple{Vararg{Dimension,N}}Get the dimensions of an object not in query.
Arguments
x: any object with adimsmethod, aTupleofDimension.query: Tuple or singleDimensionor dimensionType.f:<:by default, but can be>:to match abstract types to concrete types.
A tuple holding the unmatched dimensions is always returned.
Example
julia> using DimensionalData, DimensionalData.Dimensions
julia> A = DimArray(ones(10, 10, 10), (X, Y, Z));
julia> otherdims(A, X)
↓ Y, → Z
julia> otherdims(A, (Y, Z))
↓ Xdimnum(x, query::Tuple) => NTuple{Int}
dimnum(x, query) => IntGet the number(s) of Dimension(s) as ordered in the dimensions of an object.
Arguments
x: any object with adimsmethod, aTupleofDimensionor a singleDimension.query: Tuple, Array or singleDimensionor dimensionType.
The return type will be a Tuple of Int or a single Int, depending on whether query is a Tuple or single Dimension.
Example
julia> using DimensionalData
julia> A = DimArray(ones(10, 10, 10), (X, Y, Z));
julia> dimnum(A, (Z, X, Y))
(3, 1, 2)
julia> dimnum(A, Y)
2hasdim([f], x, query::Tuple) => NTuple{Bool}
hasdim([f], x, query...) => NTuple{Bool}
hasdim([f], x, query) => BoolCheck if an object x has dimensions that match or inherit from the query dimensions.
Arguments
x: any object with adimsmethod, aTupleofDimensionor a singleDimension.query: Tuple or singleDimensionor dimensionType.f:<:by default, but can be>:to match abstract types to concrete types.
Check if an object or tuple contains an Dimension, or a tuple of dimensions.
Example
julia> using DimensionalData
julia> A = DimArray(ones(10, 10, 10), (X, Y, Z));
julia> hasdim(A, X)
true
julia> hasdim(A, (Z, X, Y))
(true, true, true)
julia> hasdim(A, Ti)
falseNon-exported methods
lookup(x::Dimension) => Lookup
lookup(x, [dims::Tuple]) => Tuple{Vararg{Lookup}}
lookup(x::Tuple) => Tuple{Vararg{Lookup}}
lookup(x, dim) => LookupReturns the Lookup of a dimension. This dictates properties of the dimension such as array axis and lookup order, and sampling properties.
dims can be a Dimension, a dimension type, or a tuple of either.
This is separate from val in that it will only work when dimensions actually contain an AbstractArray lookup, and can be used on a DimArray or DimStack to retrieve all lookups, as there is no ambiguity of meaning as there is with val.
label(x) => String
label(x, dims::Tuple) => NTuple{N,String}
label(x, dim) => String
label(xs::Tuple) => NTuple{N,String}Get a plot label for data or a dimension. This will include the name and units if they exist, and anything else that should be shown on a plot.
Second argument dims can be Dimensions, Dimension types, or Symbols for Dim{Symbol}.
format(dims, x) => Tuple{Vararg{Dimension,N}}Format the passed-in dimension(s) dims to match the object x.
Errors are thrown if dims don't match the array dims or size, and any fields holding Auto- objects are filled with guessed objects.
If a Lookup hasn't been specified, a lookup is chosen based on the type and element type of the values.
dims2indices(dim::Dimension, I) => NTuple{Union{Colon,AbstractArray,Int}}Convert a Dimension or Selector I to indices of Int, AbstractArray or Colon.
selectindices(lookups, selectors)Converts Selector to regular indices.
Primitive methods
These low-level methods are really for internal use, but can be useful for writing dimensional algorithms.
They are not guaranteed to keep their interface, but usually will.
commondims([f], x, query) => Tuple{Vararg{Dimension}}This is basically dims(x, query) where the order of the original is kept, unlike dims where the query tuple determines the order
Also unlike dims,commondims always returns a Tuple, no matter the input. No errors are thrown if dims are absent from either x or query.
f is <: by default, but can be >: to sort abstract types by concrete types.
julia> using DimensionalData, .Dimensions
julia> A = DimArray(ones(10, 10, 10), (X, Y, Z));
julia> commondims(A, X)
↓ X
julia> commondims(A, (X, Z))
↓ X, → Z
julia> commondims(A, Ti)
()name2dim(s::Symbol) => Dimension
name2dim(dims...) => Tuple{Dimension,Vararg}
name2dim(dims::Tuple) => Tuple{Dimension,Vararg}Convert a symbol to a dimension object. :X, :Y, :Ti etc will be converted to X(), Y(), Ti(), as with any other dims generated with the @dim macro.
All other Symbols S will generate Dim{S}() dimensions.
reducedims(x, dimstoreduce) => Tuple{Vararg{Dimension}}Replace the specified dimensions with an index of length 1. This is usually to match a new array size where an axis has been reduced with a method like mean or reduce to a length of 1, but the number of dimensions has not changed.
Lookup traits are also updated to correspond to the change in cell step, sampling type and order.
swapdims(x::T, newdims) => T
swapdims(dims::Tuple, newdims) => Tuple{Vararg{Dimension}}Swap dimensions for the passed in dimensions, in the order passed.
Passing in the Dimension types rewraps the dimension index, keeping the index values and metadata, while constructed Dimension objects replace the original dimension. nothing leaves the original dimension as-is.
Arguments
x: any object with adimsmethod or aTupleofDimension.newdim: Tuple ofDimensionor dimensionType.
Example
using DimensionalData
A = ones(X(2), Y(4), Z(2))
Dimensions.swapdims(A, (Dim{:a}, Dim{:b}, Dim{:c}))
# output
╭───────────────────────────╮
│ 2×4×2 DimArray{Float64,3} │
├───────────────────── dims ┤
↓ a, → b, ↗ c
└───────────────────────────┘
[:, :, 1]
1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0slicedims(x, I) => Tuple{Tuple,Tuple}
slicedims(f, x, I) => Tuple{Tuple,Tuple}Slice the dimensions to match the axis values of the new array.
All methods return a tuple containing two tuples: the new dimensions, and the reference dimensions. The ref dimensions are no longer used in the new struct but are useful to give context to plots.
Called at the array level the returned tuple will also include the previous reference dims attached to the array.
Arguments
f: a functiongetindex,viewordotview. This will be used for slicinggetindexis the default iffis not included.x: AnAbstractDimArray,TupleofDimension, orDimensionI: A tuple ofInteger,ColonorAbstractArray
comparedims(A::AbstractDimArray...; kw...)
comparedims(A::Tuple...; kw...)
comparedims(A::Dimension...; kw...)
comparedims(::Type{Bool}, args...; kw...)Check that dimensions or tuples of dimensions passed as each argument are the same, and return the first valid dimension. If AbstractDimArrays are passed as arguments their dimensions are compared.
Empty tuples and nothing dimension values are ignored, returning the Dimension value if it exists.
Passing Bool as the first argument means true/false will be returned, rather than throwing an error.
Keywords
These are all Bool flags:
type: compare dimension type,trueby default.valtype: compare wrapped value type,falseby default.val: compare wrapped values,falseby default.order: compare order,falseby default.length: compare lengths,trueby default.ignore_length_one: ignore length1in comparisons, and return whichever dimension is not length 1, if any. This is useful in e.g. broadcasting comparisons.falseby default.warn: aStringornothing. Used only forBoolmethods, to give a warning forfalsevalues and includewarnin the warning text.
combinedims(xs; check=true)Combine the dimensions of each object in xs, in the order they are found.
sortdims([f], tosort, order) => TupleSort dimensions tosort by order. Dimensions in order but missing from tosort are replaced with nothing.
tosort and order can be Tuples or Vectors or Dimension or dimension type. Abstract supertypes like TimeDim can be used in order.
f is <: by default, but can be >: to sort abstract types by concrete types.
basetypeof(x) => TypeGet the "base" type of an object - the minimum required to define the object without it's fields. By default this is the full UnionAll for the type. But custom basetypeof methods can be defined for types with free type parameters.
In DimensionalData this is primarily used for comparing Dimensions, where Dim{:x} is different from Dim{:y}.
basedims(ds::Tuple)
basedims(d::Union{Dimension,Symbol,Type})Returns basetypeof(d)() or a Tuple of called on a Tuple.
See basetypeof
setdims(X, newdims) => AbstractArray
setdims(::Tuple, newdims) => Tuple{Vararg{Dimension,N}}Replaces the first dim matching <: basetypeof(newdim) with newdim, and returns a new object or tuple with the dimension updated.
Arguments
x: any object with adimsmethod, aTupleofDimensionor a singleDimension.newdim: Tuple or singleDimension,TypeorSymbol.
Example
using DimensionalData, DimensionalData.Dimensions, DimensionalData.Lookups
A = ones(X(10), Y(10:10:100))
B = setdims(A, Y(Categorical('a':'j'; order=ForwardOrdered())))
lookup(B, Y)
# output
Categorical{Char} ForwardOrdered
wrapping: 'a':1:'j'dimsmatch([f], dim, query) => Bool
dimsmatch([f], dims::Tuple, query::Tuple) => BoolCompare 2 dimensions or Tuple of Dimension are of the same base type, or are at least rotations/transformations of the same type.
f is <: by default, but can be >: to match abstract types to concrete types.