GroupNumbers

Installation

Install this package with Pkg.add("GroupNumbers")

Description

Index

Iterators delivering only grouped elements or indices

GroupNumbers.groupby2 — Function
groupby2(xs; keyfunc=identity, compare=isequal)

An iterator that yields a group of elements xg from the iterator xs, where the key is computed by applying keyfunc to each element of xs. Compare adjacent keys by compare function, then, delivers the vector xg of the grouped elements.

Examples

Example 1: Group characters

julia> collect(groupby2("A"))
1-element Vector{Vector{Char}}:
 ['A']

julia> collect(groupby2("AAAABBBCCD"))
4-element Vector{Vector{Char}}:
 ['A', 'A', 'A', 'A']
 ['B', 'B', 'B']
 ['C', 'C']
 ['D']

Example 2: Group integer numbers

julia> collect(groupby2([10,20,20,30]))
3-element Vector{Vector{Int64}}:
 [10]
 [20, 20]
 [30]

Example 3: Group floating point numbers

julia> collect(groupby2(
        [1+2e-10, -(1+2e-9), 1+2e-8, -(1+2e-7)];
        compare=isapprox, keyfunc=abs))
3-element Vector{Vector{Float64}}:
 [1.0000000002, -1.000000002]
 [1.00000002]
 [-1.0000002]

Example 4: Group noisy vectors with their norm

julia> using LinearAlgebra
julia> vs1=[ begin 
            v=(i1+(rand()-0.5)*1e-8,i2+(rand()-0.5)*1e-8);
            (v=v,n=norm(v))
        end for i1 in -2:2, i2 in -2:2] |> vec; 
julia> vs2=sort(vs1; by=x->x.n); 
julia> [ length(g) for g in groupby2(vs2; keyfunc=x->x.n, compare=isapprox) ]
6-element Vector{Int64}:
 1
 4
 4
 4
 8
 4
GroupNumbers.groupby2_indices — Function
groupby2_indices(xs; keyfunc=identity, compare=isequal)

An iterator that yields a group of indices ig from the iterator xs, where the key is computed by applying keyfunc to each element of xs. Compare adjacent keys by compare function, then, delivers the vector ig of the grouped indices.

Examples

Example 1: Group characters

julia> collect(groupby2_indices("A"))
1-element Vector{Vector{Int64}}:
 [1]
julia> collect(groupby2_indices("AAAABBBCCD"))
4-element Vector{Vector{Int64}}:
 [1, 2, 3, 4]
 [5, 6, 7]
 [8, 9]
 [10]

Example 2: Group integer numbers

julia> collect(groupby2_indices([10,20,20,30]))
3-element Vector{Vector{Int64}}:
 [1]
 [2, 3]
 [4]

Example 3: Group floating point numbers

julia> collect(groupby2_indices(
        [1+2e-10, -(1+2e-9), 1+2e-8, -(1+2e-7)];
        compare=isapprox, keyfunc=abs))
3-element Vector{Vector{Int64}}:
 [1, 2]
 [3]
 [4]

Example 4: Group noisy vectors with their norm

julia> using LinearAlgebra
julia> vs1=[ begin 
            v=(i1+(rand()-0.5)*1e-8,i2+(rand()-0.5)*1e-8);
            (v=v,n=norm(v))
        end for i1 in -2:2, i2 in -2:2] |> vec;
julia> vs2=sort(vs1; by=x->x.n);

julia> collect(groupby2_indices(vs2; keyfunc=x->x.n, compare=isapprox))
6-element Vector{Vector{Int64}}:
 [1]
 [2, 3, 4, 5]
 [6, 7, 8, 9]
 [10, 11, 12, 13]
 [14, 15, 16, 17, 18, 19, 20, 21]
 [22, 23, 24, 25]
GroupNumbers.groupby_numbers — Function
groupby_numbers(xs; keyfunc=identity, kwargs)

An iterator that yields a group of numbers xg from the iterator xs of presumably numbers, where the key is computed by applying keyfunc to each element of xs. Compare adjacent keys by isapprox function with supplied kwargs optional parameters, then, delivers the vector xg of the grouped numbers.

Examples

Example 1: Group integer numbers

julia> collect(groupby_numbers([10,20,20,30]))
3-element Vector{Vector{Int64}}:
 [10]
 [20, 20]
 [30]
julia> collect(groupby_numbers([10,20,-20,30]; keyfunc=abs))
3-element Vector{Vector{Int64}}:
 [10]
 [20, -20]
 [30]

Example 2: Group floating point numbers

julia> collect(groupby_numbers([ 2e-5, 2e-4, 2e-3, 2e-2 ] .+ 1; rtol=1e-3))
3-element Vector{Vector{Float64}}:
 [1.00002, 1.0002]
 [1.002]
 [1.02]
julia> collect(groupby_numbers([ 1+2e-5, -(1+2e-4), 1+2e-3, -(1+2e-2) ]; keyfunc=abs, rtol=1e-3))
3-element Vector{Vector{Float64}}:
 [1.00002, -1.0002]
 [1.002]
 [-1.02]

Example 3: Group noisy vectors with their norm

julia> using LinearAlgebra

julia> vs1=[ begin 
            v=(i1+(rand()-0.5)*1e-8,i2+(rand()-0.5)*1e-8);
            (v=v,n=norm(v))
        end for i1 in -2:2, i2 in -2:2] |> vec;
julia> vs2=sort(vs1; by=x->x.n);
julia> map(length, groupby_numbers(vs2; keyfunc=x->x.n, rtol=1e-3))
6-element Vector{Int64}:
 1
 4
 4
 4
 8
 4
GroupNumbers.groupby_numbers_indices — Function
groupby_numbers_indices(xs; keyfunc=identity, kwargs)

An iterator that yields a group of indices ig from the iterator xs of presumably numbers, where the key is computed by applying keyfunc to each element of xs. Compare adjacent keys by isapprox function with supplied kwargs optional parameters, then, delivers the vector ig of the grouped indices.

Examples

Example 1: Group integer numbers

julia> collect(groupby_numbers_indices([10,20,20,30]))
3-element Vector{Vector{Int64}}:
 [1]
 [2, 3]
 [4]
julia> collect(groupby_numbers_indices([10,20,-20,30]; keyfunc=abs))
3-element Vector{Vector{Int64}}:
 [1]
 [2, 3]
 [4]

Example 2: Group floating point numbers

julia> collect(groupby_numbers_indices([ 2e-5, 2e-4, 2e-3, 2e-2 ] .+ 1; rtol=1e-3))
3-element Vector{Vector{Int64}}:
 [1, 2]
 [3]
 [4]
julia> collect(groupby_numbers_indices([ 1+2e-5, -(1+2e-4), 1+2e-3, -(1+2e-2) ]; 
        keyfunc=abs, rtol=1e-3))
3-element Vector{Vector{Int64}}:
 [1, 2]
 [3]
 [4]

Example 3: Group noisy vectors with their norm

 julia> using LinearAlgebra

julia> vs1=[ begin 
            v=(i1+(rand()-0.5)*1e-8,i2+(rand()-0.5)*1e-8);
            (v=v,n=norm(v))
        end for i1 in -2:2, i2 in -2:2] |> vec;
julia> vs2=sort(vs1; by=x->x.n);
julia> collect(groupby_numbers_indices(vs2; keyfunc=x->x.n, rtol=1e-3) )
6-element Vector{Vector{Int64}}:
 [1]
 [2, 3, 4, 5]
 [6, 7, 8, 9]
 [10, 11, 12, 13]
 [14, 15, 16, 17, 18, 19, 20, 21]
 [22, 23, 24, 25]

Iterators delivering keys and grouped elements or indices

GroupNumbers.groupby2_dict — Function
groupby2_dict(xs; keyfunc=identity, compare=isequal)

An iterator that yields a key-and-group pair (k,xg) from the iterator xs, where the key k is computed by applying keyfunc to each element of xs. Compare adjacent keys by compare function, then, delivers the key k and the vector xg of the grouped elements .

Examples

Example 1: Group characters

julia> collect(groupby2_dict("A"))
1-element Vector{Tuple{Any, Vector{Char}}}:
 ('A', ['A'])

julia> collect(groupby2_dict("AAAABBBCCD"))
4-element Vector{Tuple{Any, Vector{Char}}}:
 ('A', ['A', 'A', 'A', 'A'])
 ('B', ['B', 'B', 'B'])
 ('C', ['C', 'C'])
 ('D', ['D'])

Example 2: Group integer numbers

julia> collect(groupby2_dict([10,20,20,30]))
3-element Vector{Tuple{Any, Vector{Int64}}}:
 (10, [10])
 (20, [20, 20])
 (30, [30])

Example 3: Group floating point numbers

julia> collect(groupby2_dict(
        [1+2e-10, -(1+2e-9), 1+2e-8, -(1+2e-7)];
        compare=isapprox, keyfunc=abs))
3-element Vector{Tuple{Any, Vector{Float64}}}:
 (1.0000000002, [1.0000000002, -1.000000002])
 (1.00000002, [1.00000002])
 (1.0000002, [-1.0000002])

Example 4: Group noisy vectors with their norm

julia> using LinearAlgebra
julia> vs1=[ begin 
            v=(i1+(rand()-0.5)*1e-8,i2+(rand()-0.5)*1e-8);
            (v=v,n=norm(v))
        end for i1 in -2:2, i2 in -2:2] |> vec;
julia> vs2=sort(vs1; by=x->x.n);
julia> [ (k,length(g)) for (k,g) in groupby2_dict(vs2; keyfunc=x->x.n, compare=isapprox) ]
6-element Vector{Tuple{Float64, Int64}}:
 (4.16311498666887e-11, 1)
 (0.999999999984808, 4)
 (1.4142135623388605, 4)
 (1.9999999999726468, 4)
 (2.236067977467306, 8)
 (2.828427124726703, 4)
GroupNumbers.groupby2_dict_indices — Function
groupby2_dict_indices(xs; keyfunc=identity, compare=isequal)

An iterator that yields a key-and-group pair (k,ig) from the iterator xs, where the key k is computed by applying keyfunc to each element of xs. Compare adjacent keys by compare function, then, delivers the key k and the vector ig of the grouped indices.

Examples

Example 1: Group characters

julia> collect(groupby2_dict_indices("A"))
1-element Vector{Tuple{Any, Vector{Int64}}}:
 ('A', [1])
julia> collect(groupby2_dict_indices("AAAABBBCCD"))
4-element Vector{Tuple{Any, Vector{Int64}}}:
 ('A', [1, 2, 3, 4])
 ('B', [5, 6, 7])
 ('C', [8, 9])
 ('D', [10])

Example 2: Group integer numbers

julia> collect(groupby2_dict_indices([10,20,20,30]))
3-element Vector{Tuple{Any, Vector{Int64}}}:
 (10, [1])
 (20, [2, 3])
 (30, [4])

Example 3: Group floating point numbers

julia> collect(groupby2_dict_indices(
        [1+2e-10, -(1+2e-9), 1+2e-8, -(1+2e-7)];
        compare=isapprox, keyfunc=abs))
3-element Vector{Tuple{Any, Vector{Int64}}}:
 (1.0000000002, [1, 2])
 (1.00000002, [3])
 (1.0000002, [4])

Example 4: Group noisy vectors with their norm

julia> using LinearAlgebra
julia> vs1=[ begin 
            v=(i1+(rand()-0.5)*1e-8,i2+(rand()-0.5)*1e-8);
            (v=v,n=norm(v))
        end for i1 in -2:2, i2 in -2:2] |> vec;
julia> vs2=sort(vs1; by=x->x.n);
julia> collect(groupby2_dict_indices(vs2; keyfunc=x->x.n, compare=isapprox))
6-element Vector{Tuple{Any, Vector{Int64}}}:
 (3.444788576260325e-11, [1])
 (0.9999999999517916, [2, 3, 4, 5])
 (1.4142135623328898, [6, 7, 8, 9])
 (1.9999999999690443, [10, 11, 12, 13])
 (2.236067977456823, [14, 15, 16, 17, 18, 19, 20, 21])
 (2.828427124691792, [22, 23, 24, 25])
GroupNumbers.groupby_numbers_dict — Function
groupby_numbers_dict(xs; keyfunc=identity, kwargs)

An iterator that yields a key-and-group pair (k,xg) from the iterator xs of presumably numbers, where the key k is computed by applying keyfunc to each element of xs. Compare adjacent keys by isapprox function with supplied kwargs optional parameters, then, delivers the key k and the vector xg of grouped elements.

Examples

Example 1: Group integer numbers

julia> collect(groupby_numbers_dict([10,20,20,30]))
3-element Vector{Tuple{Any, Vector{Int64}}}:
 (10, [10])
 (20, [20, 20])
 (30, [30])
julia> collect(groupby_numbers_dict([10,20,-20,30]; keyfunc=abs))
3-element Vector{Tuple{Any, Vector{Int64}}}:
 (10, [10])
 (20, [20, -20])
 (30, [30])

Example 2: Group floating point numbers

julia> collect(groupby_numbers_dict([ 2e-5, 2e-4, 2e-3, 2e-2 ] .+ 1; rtol=1e-3))
3-element Vector{Tuple{Any, Vector{Float64}}}:
 (1.00002, [1.00002, 1.0002])
 (1.002, [1.002])
 (1.02, [1.02])
julia> collect(groupby_numbers_dict([ 1+2e-5, -(1+2e-4), 1+2e-3, -(1+2e-2) ];
        keyfunc=abs, rtol=1e-3))
3-element Vector{Tuple{Any, Vector{Float64}}}:
 (1.00002, [1.00002, -1.0002])
 (1.002, [1.002])
 (1.02, [-1.02])

Example 3: Group noisy vectors with their norm

julia> using LinearAlgebra
julia> vs1=[ begin 
            v=(i1+(rand()-0.5)*1e-8,i2+(rand()-0.5)*1e-8);
            (v=v,n=norm(v))
        end for i1 in -2:2, i2 in -2:2] |> vec;
julia> vs2=sort(vs1; by=x->x.n);
julia> [ (k,length(xg)) for (k,xg) in 
            groupby_numbers_dict(vs2; keyfunc=x->x.n, rtol=1e-3) ]
    end
6-element Vector{Tuple{Float64, Int64}}:
 (3.2527338422665044e-11, 1)
 (0.999999999995845, 4)
 (1.4142135623542986, 4)
 (2.000000000002051, 4)
 (2.236067977452884, 8)
 (2.8284271246921855, 4)
GroupNumbers.groupby_numbers_dict_indices — Function
groupby_numbers_dict(xs; keyfunc=identity, kwargs)

An iterator that yields a key-and-group pair (k,ig) from the iterator xs of presumably numbers, where the key k is computed by applying keyfunc to each element of xs. Compare adjacent keys by isapprox function with supplied kwargs optional parameters, then, delivers the key k and the vector ig of the grouped indices.

Examples

Example 1: Group integer numbers

julia> collect(groupby_numbers_dict([10,20,20,30]))
3-element Vector{Tuple{Any, Vector{Int64}}}:
 (10, [10])
 (20, [20, 20])
 (30, [30])
julia> collect(groupby_numbers_dict([10,20,-20,30]; keyfunc=abs))
3-element Vector{Tuple{Any, Vector{Int64}}}:
 (10, [10])
 (20, [20, -20])
 (30, [30])

Example 2: Group floating point numbers

julia> collect(groupby_numbers_dict([ 2e-5, 2e-4, 2e-3, 2e-2 ] .+ 1; rtol=1e-3))
3-element Vector{Tuple{Any, Vector{Float64}}}:
 (1.00002, [1.00002, 1.0002])
 (1.002, [1.002])
 (1.02, [1.02])
julia> collect(groupby_numbers_dict(
            [ 1+2e-5, -(1+2e-4), 1+2e-3, -(1+2e-2) ];  
            keyfunc=abs, rtol=1e-3))
3-element Vector{Tuple{Any, Vector{Float64}}}:
 (1.00002, [1.00002, -1.0002])
 (1.002, [1.002])
 (1.02, [-1.02])

Example 3: Group noisy vectors with their norm

julia> using LinearAlgebra
julia> vs1=[ begin 
            v=(i1+(rand()-0.5)*1e-8,i2+(rand()-0.5)*1e-8);
            (v=v,n=norm(v))
        end for i1 in -2:2, i2 in -2:2] |> vec;
julia> vs2=sort(vs1; by=x->x.n);
julia> [ (k,length(xg)) for (k,xg) in 
            groupby_numbers_dict(vs2; keyfunc=x->x.n, rtol=1e-3) ]
6-element Vector{Tuple{Float64, Int64}}:
 (4.641593797139748e-11, 1)
 (0.9999999999691114, 4)
 (1.4142135623658871, 4)
 (1.99999999995389, 4)
 (2.236067977448624, 8)
 (2.828427124697913, 4)

See also