RollingWindowArrays.jl provides a RollingWindowVector type that allows you to efficiently compute
rolling window operations on arrays. This is useful for tasks such as computing moving averages,
rolling standard deviations, or other rolling window operations.
The function rolling is used to create a RollingWindowVector of given window size from an array:
julia> using RollingWindowArrays
julia> x = rand(10)
10-element Vector{Float64}:
0.5641112488276627
0.22120012232070818
0.3679067902780746
0.5623875869261128
0.6440904700394701
0.247718935392934
0.24983687211882766
0.4477721985453925
0.5929269441970979
0.3541576787013937
julia> rolling(x, 3)
8-element RollingWindowArrays.RollingWindowVector{SubArray{Float64, 1, Vector{Float64}, Tuple{UnitRange{Int64}}, true}, 1, Vector{Float64}, Nothing}:
[0.5641112488276627, 0.22120012232070818, 0.3679067902780746]
[0.22120012232070818, 0.3679067902780746, 0.5623875869261128]
[0.3679067902780746, 0.5623875869261128, 0.6440904700394701]
[0.5623875869261128, 0.6440904700394701, 0.247718935392934]
[0.6440904700394701, 0.247718935392934, 0.24983687211882766]
[0.247718935392934, 0.24983687211882766, 0.4477721985453925]
[0.24983687211882766, 0.4477721985453925, 0.5929269441970979]
[0.4477721985453925, 0.5929269441970979, 0.3541576787013937]The center keyword argument can be used to specify whether the window should be centered around the
current element, affecting the axes of the resulting RollingWindowVector (notice how the indices
are now 2:9 instead of 1:8):
julia> rolling(x, 3; center=true)
8-element RollingWindowArrays.RollingWindowVector{SubArray{Float64, 1, Vector{Float64}, Tuple{UnitRange{Int64}}, true}, 1, Vector{Float64}, Int64} with indices 2:9:
[0.5641112488276627, 0.22120012232070818, 0.3679067902780746]
[0.22120012232070818, 0.3679067902780746, 0.5623875869261128]
[0.3679067902780746, 0.5623875869261128, 0.6440904700394701]
[0.5623875869261128, 0.6440904700394701, 0.247718935392934]
[0.6440904700394701, 0.247718935392934, 0.24983687211882766]
[0.247718935392934, 0.24983687211882766, 0.4477721985453925]
[0.24983687211882766, 0.4477721985453925, 0.5929269441970979]
[0.4477721985453925, 0.5929269441970979, 0.3541576787013937]This is especially useful for the DimensionalData.jl integration, where rolling has special
support for DimArrays:
julia> x = DimArray(rand(10), Ti(2015:2024))
╭────────────────────────────────╮
│ 10-element DimArray{Float64,1} │
├────────────────────────────────┴────────────────────────────────────────────────────────────────────────────────────────────────────────── dims ┐
↓ Ti Sampled{Int64} 2015:2024 ForwardOrdered Regular Points
└─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
2015 0.395081
2016 0.362025
2017 0.178012
2018 0.81853
2019 0.538458
2020 0.203418
2021 0.433708
2022 0.649627
2023 0.901228
2024 0.712791
julia> rolling(x, 3; center = true)
╭─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ 8-element DimArray{DimVector{Float64, Tuple{Ti{DimensionalData.Dimensions.Lookups.Sampled{Int64, UnitRange{Int64}, DimensionalData.Dimensions.Lookups.ForwardOrdered, DimensionalData.Dimensions.Lookups.Regular{Int64}, DimensionalData.Dimensions.Lookups.Points, DimensionalData.Dimensions.Lookups.NoMetadata}}}, Tuple{}, SubArray{Float64, 1, Vector{Float64}, Tuple{UnitRange{Int64}}, true}, DimensionalData.NoName, DimensionalData.Dimensions.Lookups.NoMetadata},1} │
├─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── dims ┤
↓ Ti Sampled{Int64} OffsetArrays.IdOffsetRange(values=2016:2023, indices=2:9) ForwardOrdered Regular Points
└─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
2016 [0.395081, 0.362025, 0.178012]
2017 [0.362025, 0.178012, 0.81853]
2018 [0.178012, 0.81853, 0.538458]
2019 [0.81853, 0.538458, 0.203418]
2020 [0.538458, 0.203418, 0.433708]
2021 [0.203418, 0.433708, 0.649627]
2022 [0.433708, 0.649627, 0.901228]
2023 [0.649627, 0.901228, 0.712791]This can then be used to create a rolling 3-year mean for example, by simply using broadcasting:
julia> using Statistics
julia> mean.(rolling(x, 3; center = true))
╭───────────────────────────────╮
│ 8-element DimArray{Float64,1} │
├───────────────────────────────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── dims ┐
↓ Ti Sampled{Int64} OffsetArrays.IdOffsetRange(values=2016:2023, indices=2:9) ForwardOrdered Regular Points
└─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
2016 0.311706
2017 0.452856
2018 0.511667
2019 0.520135
2020 0.391861
2021 0.428917
2022 0.661521
2023 0.754549Creating rolling windows over mulidimensional arrays is also supported through the dims keyword:
julia> grid = DimArray(rand(3, 3, 10), (X(-1:1), Y(-1:1), Ti(2015:2024)))
╭────────────────────────────╮
│ 3×3×10 DimArray{Float64,3} │
├────────────────────────────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────── dims ┐
↓ X Sampled{Int64} -1:1 ForwardOrdered Regular Points,
→ Y Sampled{Int64} -1:1 ForwardOrdered Regular Points,
↗ Ti Sampled{Int64} 2015:2024 ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
[:, :, 1]
↓ → -1 0 1
-1 0.21157 0.645023 0.537563
0 0.596212 0.423664 0.451312
1 0.893659 0.0941666 0.0751371
julia> grid_3y_mean = dropdims.(mean.(rolling(grid, 3; center = true, dims = Ti); dims = Ti); dims = Ti)
╭─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ 8-element DimArray{DimMatrix{Float64, Tuple{X{DimensionalData.Dimensions.Lookups.Sampled{Int64, UnitRange{Int64}, DimensionalData.Dimensions.Lookups.ForwardOrdered, DimensionalData.Dimensions.Lookups.Regular{Int64}, DimensionalData.Dimensions.Lookups.Points, DimensionalData.Dimensions.Lookups.NoMetadata}}, Y{DimensionalData.Dimensions.Lookups.Sampled{Int64, UnitRange{Int64}, DimensionalData.Dimensions.Lookups.ForwardOrdered, DimensionalData.Dimensions.Lookups.Regular{Int64}, DimensionalData.Dimensions.Lookups.Points, DimensionalData.Dimensions.Lookups.NoMetadata}}}, Tuple{Ti{DimensionalData.Dimensions.Lookups.Sampled{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, DimensionalData.Dimensions.Lookups.ForwardOrdered, DimensionalData.Dimensions.Lookups.Regular{Float64}, DimensionalData.Dimensions.Lookups.Points, DimensionalData.Dimensions.Lookups.NoMetadata}}}, Matrix{Float64}, DimensionalData.NoName, DimensionalData.Dimensions.Lookups.NoMetadata},1} │
├─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── dims ┤
↓ Ti Sampled{Int64} OffsetArrays.IdOffsetRange(values=2016:2023, indices=2:9) ForwardOrdered Regular Points
└─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
2016 [0.612901 0.612267 0.685449; 0.474032 0.773932 0.450534; 0.310023 0.469109 0.342738]
2017 [0.834115 0.692197 0.506474; 0.525868 0.761104 0.603797; 0.132387 0.767909 0.458608]
2018 [0.815439 0.589489 0.562757; 0.479255 0.701758 0.345831; 0.210421 0.585885 0.64285]
2019 [0.632451 0.483513 0.485063; 0.350861 0.537574 0.369789; 0.41726 0.516414 0.535672]
2020 [0.389338 0.323465 0.541948; 0.270706 0.52332 0.173777; 0.505959 0.389705 0.716001]
2021 [0.176405 0.484392 0.471247; 0.217172 0.496473 0.40988; 0.545246 0.572485 0.55958]
2022 [0.389112 0.682227 0.321591; 0.490578 0.364561 0.629233; 0.383283 0.555528 0.56231]
2023 [0.672318 0.627305 0.416213; 0.343098 0.399091 0.679177; 0.443748 0.421359 0.504259]
julia> stack(grid_3y_mean)
╭───────────────────────────╮
│ 3×3×8 DimArray{Float64,3} │
├───────────────────────────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── dims ┐
↓ X Sampled{Int64} -1:1 ForwardOrdered Regular Points,
→ Y Sampled{Int64} -1:1 ForwardOrdered Regular Points,
↗ Ti Sampled{Int64} OffsetArrays.IdOffsetRange(values=2016:2023, indices=2:9) ForwardOrdered Regular Points
└─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
[:, :, 2]
↓ → -1 0 1
-1 0.612901 0.612267 0.685449
0 0.474032 0.773932 0.450534
1 0.310023 0.469109 0.342738