Collections and Data Structures

    is translated into:

    1. next = iterate(iter)
    2. while next !== nothing
    3.     (i, state) = next
    4.     # body
    5.     next = iterate(iter, state)
    6. end

    The state object may be anything, and should be chosen appropriately for each iterable type. See the for more details about defining a custom iterable type.

    Base.iterate — Function

    1. iterate(iter [, state]) -> Union{Nothing, Tuple{Any, Any}}

    Advance the iterator to obtain the next element. If no elements remain, nothing should be returned. Otherwise, a 2-tuple of the next element and the new iteration state should be returned.

    Base.IteratorSize — Type

    1. IteratorSize(itertype::Type) -> IteratorSize

    Given the type of an iterator, return one of the following values:

    • SizeUnknown() if the length (number of elements) cannot be determined in advance.
    • HasLength() if there is a fixed, finite length.
    • HasShape{N}() if there is a known length plus a notion of multidimensional shape (as for an array). In this case N should give the number of dimensions, and the function is valid for the iterator.
    • IsInfinite() if the iterator yields values forever.

    The default value (for iterators that do not define this function) is HasLength(). This means that most iterators are assumed to implement length.

    This trait is generally used to select between algorithms that pre-allocate space for their result, and algorithms that resize their result incrementally.

    1. julia> Base.IteratorSize(1:5)
    2. Base.HasShape{1}()
    4. julia> Base.IteratorSize((2,3))
    5. Base.HasLength()

    Base.IteratorEltype — Type

    1. IteratorEltype(itertype::Type) -> IteratorEltype

    Given the type of an iterator, return one of the following values:

    • EltypeUnknown() if the type of elements yielded by the iterator is not known in advance.
    • HasEltype() if the element type is known, and would return a meaningful value.

    HasEltype() is the default, since iterators are assumed to implement eltype.

    This trait is generally used to select between algorithms that pre-allocate a specific type of result, and algorithms that pick a result type based on the types of yielded values.

    1. julia> Base.IteratorEltype(1:5)
    2. Base.HasEltype()

    Fully implemented by:

    Base.AbstractRange — Type

    1. AbstractRange{T}

    Supertype for ranges with elements of type T. and other types are subtypes of this.

    source

    — Type

    1. OrdinalRange{T, S} <: AbstractRange{T}

    Supertype for ordinal ranges with elements of type T with spacing(s) of type S. The steps should be always-exact multiples of oneunit, and T should be a “discrete” type, which cannot have values smaller than oneunit. For example, Integer or Date types would qualify, whereas Float64 would not (since this type can represent values smaller than oneunit(Float64). , StepRange, and other types are subtypes of this.

    Base.AbstractUnitRange — Type

    1. AbstractUnitRange{T} <: OrdinalRange{T, T}

    Supertype for ranges with a step size of with elements of type T. UnitRange and other types are subtypes of this.

    Base.StepRange — Type

    1. StepRange{T, S} <: OrdinalRange{T, S}

    Ranges with elements of type T with spacing of type S. The step between each element is constant, and the range is defined in terms of a start and stop of type T and a step of type S. Neither T nor S should be floating point types. The syntax a:b:c with b > 1 and a, b, and c all integers creates a StepRange.

    Examples

    1. julia> collect(StepRange(1, Int8(2), 10))
    2. 5-element Vector{Int64}:
    3.  1
    4.  3
    5.  5
    6.  7
    7.  9
    9. julia> typeof(StepRange(1, Int8(2), 10))
    10. StepRange{Int64, Int8}
    12. julia> typeof(1:3:6)
    13. StepRange{Int64, Int64}

    Base.UnitRange — Type

    1. UnitRange{T<:Real}

    A range parameterized by a start and stop of type T, filled with elements spaced by 1 from start until stop is exceeded. The syntax a:b with a and b both Integers creates a UnitRange.

    Examples

    1. julia> collect(UnitRange(2.3, 5.2))
    2. 3-element Vector{Float64}:
    3.  2.3
    4.  3.3
    5.  4.3
    7. julia> typeof(1:10)
    8. UnitRange{Int64}

    Base.LinRange — Type

    1. LinRange{T}

    A range with len linearly spaced elements between its start and stop. The size of the spacing is controlled by len, which must be an Int.

    Examples

    1. julia> LinRange(1.5, 5.5, 9)
    2. 9-element LinRange{Float64}:
    3.  1.5,2.0,2.5,3.0,3.5,4.0,4.5,5.0,5.5

    Compared to using , directly constructing a LinRange should have less overhead but won’t try to correct for floating point errors:

    1. julia> collect(range(-0.1, 0.3, length=5))
    2. 5-element Array{Float64,1}:
    3.  -0.1
    4.   0.0
    5.   0.1
    6.   0.2
    7.   0.3
    9. julia> collect(LinRange(-0.1, 0.3, 5))
    10. 5-element Array{Float64,1}:
    11.  -0.1
    12.  -1.3877787807814457e-17
    13.   0.09999999999999999
    14.   0.19999999999999998
    15.   0.3

    source

    General Collections

    — Function

    1. isempty(collection) -> Bool

    Determine whether a collection is empty (has no elements).

    Examples

    1. julia> isempty([])
    2. true
    4. julia> isempty([1 2 3])
    5. false

    source

    1. isempty(condition)

    Return true if no tasks are waiting on the condition, false otherwise.

    Base.empty! — Function

    1. empty!(collection) -> collection

    Remove all elements from a collection.

    Examples

    1. julia> A = Dict("a" => 1, "b" => 2)
    2. Dict{String, Int64} with 2 entries:
    3.   "b" => 2
    4.   "a" => 1
    6. julia> empty!(A);
    8. julia> A
    9. Dict{String, Int64}()

    Base.length — Function

    1. length(collection) -> Integer

    Return the number of elements in the collection.

    Use to get the last valid index of an indexable collection.

    Examples

    1. julia> length(1:5)
    2. 5
    4. julia> length([1, 2, 3, 4])
    5. 4
    7. julia> length([1 2; 3 4])
    8. 4

    source

    Fully implemented by:

    Base.in — Function

    1. in(item, collection) -> Bool
    2. ∈(item, collection) -> Bool

    Determine whether an item is in the given collection, in the sense that it is to one of the values generated by iterating over the collection. Returns a Bool value, except if item is missing or collection contains missing but not item, in which case missing is returned (, matching the behavior of any and ).

    Some collections follow a slightly different definition. For example, Sets check whether the item to one of the elements. Dicts look for key=>value pairs, and the key is compared using . To test for the presence of a key in a dictionary, use haskey or k in keys(dict). For these collections, the result is always a Bool and never missing.

    To determine whether an item is not in a given collection, see . You may also negate the in by doing !(a in b) which is logically similar to “not in”.

    When broadcasting with in.(items, collection) or items .∈ collection, both item and collection are broadcasted over, which is often not what is intended. For example, if both arguments are vectors (and the dimensions match), the result is a vector indicating whether each value in collection items is in the value at the corresponding position in collection. To get a vector indicating whether each value in items is in collection, wrap collection in a tuple or a Ref like this: in.(items, Ref(collection)) or items .∈ Ref(collection).

    Examples

    1. julia> a = 1:3:20
    2. 1:3:19
    4. julia> 4 in a
    5. true
    7. julia> 5 in a
    8. false
    10. julia> missing in [1, 2]
    11. missing
    13. julia> 1 in [2, missing]
    14. missing
    16. julia> 1 in [1, missing]
    17. true
    19. julia> missing in Set([1, 2])
    20. false
    22. julia> !(21 in a)
    23. true
    25. julia> !(19 in a)
    26. false
    28. julia> [1, 2] .∈ [2, 3]
    29. 2-element BitVector:
    30.  0
    31.  0
    33. julia> [1, 2] .∈ ([2, 3],)
    34. 2-element BitVector:
    35.  0
    36.  1

    source

    — Function

    1. ∉(item, collection) -> Bool
    2. ∌(collection, item) -> Bool

    Negation of ∈ and ∋, i.e. checks that item is not in collection.

    When broadcasting with items .∉ collection, both item and collection are broadcasted over, which is often not what is intended. For example, if both arguments are vectors (and the dimensions match), the result is a vector indicating whether each value in collection items is not in the value at the corresponding position in collection. To get a vector indicating whether each value in items is not in collection, wrap collection in a tuple or a Ref like this: items .∉ Ref(collection).

    Examples

    1. julia> 1 ∉ 2:4
    2. true
    4. julia> 1 ∉ 1:3
    5. false
    7. julia> [1, 2] .∉ [2, 3]
    8. 2-element BitVector:
    9.  1
    10.  1
    12. julia> [1, 2] .∉ ([2, 3],)
    13. 2-element BitVector:
    14.  1
    15.  0

    source

    — Function

    1. eltype(type)

    Determine the type of the elements generated by iterating a collection of the given type. For dictionary types, this will be a Pair{KeyType,ValType}. The definition eltype(x) = eltype(typeof(x)) is provided for convenience so that instances can be passed instead of types. However the form that accepts a type argument should be defined for new types.

    Examples

    1. julia> eltype(fill(1f0, (2,2)))
    2. Float32
    4. julia> eltype(fill(0x1, (2,2)))
    5. UInt8

    source

    — Function

    1. indexin(a, b)

    Return an array containing the first index in b for each value in a that is a member of b. The output array contains nothing wherever a is not a member of b.

    Examples

    1. julia> a = ['a', 'b', 'c', 'b', 'd', 'a'];
    3. julia> b = ['a', 'b', 'c'];
    5. julia> indexin(a, b)
    6. 6-element Vector{Union{Nothing, Int64}}:
    7.  1
    8.  2
    9.  3
    10.  2
    11.   nothing
    12.  1
    14. julia> indexin(b, a)
    15. 3-element Vector{Union{Nothing, Int64}}:
    16.  1
    17.  2
    18.  3

    source

    — Function

    1. unique(itr)

    Return an array containing only the unique elements of collection itr, as determined by isequal, in the order that the first of each set of equivalent elements originally appears. The element type of the input is preserved.

    Examples

    1. julia> unique([1, 2, 6, 2])
    2. 3-element Vector{Int64}:
    3.  1
    4.  2
    5.  6
    7. julia> unique(Real[1, 1.0, 2])
    8. 2-element Vector{Real}:
    9.  1
    10.  2

    1. unique(f, itr)

    Returns an array containing one value from itr for each unique value produced by f applied to elements of itr.

    Examples

    1. julia> unique(x -> x^2, [1, -1, 3, -3, 4])
    2. 3-element Vector{Int64}:
    3.  1
    4.  3
    5.  4

    source

    1. unique(A::AbstractArray; dims::Int)

    Return unique regions of A along dimension dims.

    Examples

    1. julia> A = map(isodd, reshape(Vector(1:8), (2,2,2)))
    2. 2×2×2 Array{Bool, 3}:
    3. [:, :, 1] =
    4.  1  1
    5.  0  0
    7. [:, :, 2] =
    8.  1  1
    9.  0  0
    11. julia> unique(A)
    12. 2-element Vector{Bool}:
    13.  1
    14.  0
    16. julia> unique(A, dims=2)
    17. 2×1×2 Array{Bool, 3}:
    18. [:, :, 1] =
    19.  1
    20.  0
    22. [:, :, 2] =
    23.  1
    24.  0
    26. julia> unique(A, dims=3)
    27. 2×2×1 Array{Bool, 3}:
    28. [:, :, 1] =
    29.  1  1
    30.  0  0

    Base.unique! — Function

    1. unique!(f, A::AbstractVector)

    Selects one value from A for each unique value produced by f applied to elements of A, then return the modified A.

    Julia 1.1

    This method is available as of Julia 1.1.

    Examples

    1. julia> unique!(x -> x^2, [1, -1, 3, -3, 4])
    2. 3-element Vector{Int64}:
    3.  1
    4.  3
    5.  4
    7. julia> unique!(n -> n%3, [5, 1, 8, 9, 3, 4, 10, 7, 2, 6])
    8. 3-element Vector{Int64}:
    9.  5
    10.  1
    11.  9
    13. julia> unique!(iseven, [2, 3, 5, 7, 9])
    14. 2-element Vector{Int64}:
    15.  2
    16.  3

    1. unique!(A::AbstractVector)

    Remove duplicate items as determined by isequal, then return the modified A. unique! will return the elements of A in the order that they occur. If you do not care about the order of the returned data, then calling (sort!(A); unique!(A)) will be much more efficient as long as the elements of A can be sorted.

    Examples

    1. julia> unique!([1, 1, 1])
    2. 1-element Vector{Int64}:
    3.  1
    5. julia> A = [7, 3, 2, 3, 7, 5];
    7. julia> unique!(A)
    8. 4-element Vector{Int64}:
    9.  7
    10.  3
    11.  2
    12.  5
    14. julia> B = [7, 6, 42, 6, 7, 42];
    16. julia> sort!(B);  # unique! is able to process sorted data much more efficiently.
    18. julia> unique!(B)
    19. 3-element Vector{Int64}:
    20.   6
    21.   7
    22.  42

    Base.allunique — Function

    1. allunique(itr) -> Bool

    Return true if all values from itr are distinct when compared with .

    Examples

    1. julia> a = [1; 2; 3]
    2. 3-element Vector{Int64}:
    3.  1
    4.  2
    5.  3
    7. julia> allunique([a, a])
    8. false

    source

    — Method

    1. reduce(op, itr; [init])

    Reduce the given collection itr with the given binary operator op. If provided, the initial value init must be a neutral element for op that will be returned for empty collections. It is unspecified whether init is used for non-empty collections.

    For empty collections, providing init will be necessary, except for some special cases (e.g. when op is one of +, *, max, min, &, |) when Julia can determine the neutral element of op.

    Reductions for certain commonly-used operators may have special implementations, and should be used instead: maximum(itr), minimum(itr), sum(itr), prod(itr), any(itr), all(itr).

    The associativity of the reduction is implementation dependent. This means that you can’t use non-associative operations like - because it is undefined whether reduce(-,[1,2,3]) should be evaluated as (1-2)-3 or 1-(2-3). Use foldl or instead for guaranteed left or right associativity.

    Some operations accumulate error. Parallelism will be easier if the reduction can be executed in groups. Future versions of Julia might change the algorithm. Note that the elements are not reordered if you use an ordered collection.

    Examples

    1. julia> reduce(*, [2; 3; 4])
    2. 24
    4. julia> reduce(*, [2; 3; 4]; init=-1)
    5. -24

    source

    — Method

    1. foldl(op, itr; [init])

    Like reduce, but with guaranteed left associativity. If provided, the keyword argument init will be used exactly once. In general, it will be necessary to provide init to work with empty collections.

    Examples

    1. julia> foldl(=>, 1:4)
    2. ((1 => 2) => 3) => 4
    4. julia> foldl(=>, 1:4; init=0)
    5. (((0 => 1) => 2) => 3) => 4

    Base.foldr — Method

    1. foldr(op, itr; [init])

    Like , but with guaranteed right associativity. If provided, the keyword argument init will be used exactly once. In general, it will be necessary to provide init to work with empty collections.

    Examples

    1. julia> foldr(=>, 1:4)
    2. 1 => (2 => (3 => 4))
    4. julia> foldr(=>, 1:4; init=0)
    5. 1 => (2 => (3 => (4 => 0)))

    source

    — Function

    1. maximum(f, itr; [init])

    Returns the largest result of calling function f on each element of itr.

    The value returned for empty itr can be specified by init. It must be a neutral element for max (i.e. which is less than or equal to any other element) as it is unspecified whether init is used for non-empty collections.

    Julia 1.6

    Keyword argument init requires Julia 1.6 or later.

    Examples

    1. julia> maximum(length, ["Julion", "Julia", "Jule"])
    2. 6
    4. julia> maximum(length, []; init=-1)
    5. -1
    7. julia> maximum(sin, Real[]; init=-1.0)  # good, since output of sin is >= -1
    8. -1.0

    source

    1. maximum(itr; [init])

    Returns the largest element in a collection.

    The value returned for empty itr can be specified by init. It must be a neutral element for max (i.e. which is less than or equal to any other element) as it is unspecified whether init is used for non-empty collections.

    Julia 1.6

    Keyword argument init requires Julia 1.6 or later.

    Examples

    1. julia> maximum(-20.5:10)
    2. 9.5
    4. julia> maximum([1,2,3])
    5. 3
    7. julia> maximum(())
    8. ERROR: ArgumentError: reducing over an empty collection is not allowed
    9. Stacktrace:
    10. [...]
    12. julia> maximum((); init=-Inf)
    13. -Inf

    1. maximum(A::AbstractArray; dims)

    Compute the maximum value of an array over the given dimensions. See also the max(a,b) function to take the maximum of two or more arguments, which can be applied elementwise to arrays via max.(a,b).

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> maximum(A, dims=1)
    7. 1×2 Matrix{Int64}:
    8.  3  4
    10. julia> maximum(A, dims=2)
    11. 2×1 Matrix{Int64}:
    12.  2
    13.  4

    1. maximum(f, A::AbstractArray; dims)

    Compute the maximum value from of calling the function f on each element of an array over the given dimensions.

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> maximum(abs2, A, dims=1)
    7. 1×2 Matrix{Int64}:
    8.  9  16
    10. julia> maximum(abs2, A, dims=2)
    11. 2×1 Matrix{Int64}:
    12.   4
    13.  16

    source

    — Function

    1. maximum!(r, A)

    Compute the maximum value of A over the singleton dimensions of r, and write results to r.

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> maximum!([1; 1], A)
    7. 2-element Vector{Int64}:
    8.  2
    9.  4
    11. julia> maximum!([1 1], A)
    12. 1×2 Matrix{Int64}:
    13.  3  4

    source

    — Function

    1. minimum(f, itr; [init])

    Returns the smallest result of calling function f on each element of itr.

    The value returned for empty itr can be specified by init. It must be a neutral element for min (i.e. which is greater than or equal to any other element) as it is unspecified whether init is used for non-empty collections.

    Julia 1.6

    Keyword argument init requires Julia 1.6 or later.

    Examples

    1. julia> minimum(length, ["Julion", "Julia", "Jule"])
    2. 4
    4. julia> minimum(length, []; init=typemax(Int64))
    5. 9223372036854775807
    7. julia> minimum(sin, Real[]; init=1.0)  # good, since output of sin is <= 1
    8. 1.0

    source

    1. minimum(itr; [init])

    Returns the smallest element in a collection.

    The value returned for empty itr can be specified by init. It must be a neutral element for min (i.e. which is greater than or equal to any other element) as it is unspecified whether init is used for non-empty collections.

    Julia 1.6

    Keyword argument init requires Julia 1.6 or later.

    Examples

    1. julia> minimum(-20.5:10)
    2. -20.5
    4. julia> minimum([1,2,3])
    5. 1
    7. julia> minimum([])
    8. ERROR: ArgumentError: reducing over an empty collection is not allowed
    9. Stacktrace:
    10. [...]
    12. julia> minimum([]; init=Inf)
    13. Inf

    1. minimum(A::AbstractArray; dims)

    Compute the minimum value of an array over the given dimensions. See also the min(a,b) function to take the minimum of two or more arguments, which can be applied elementwise to arrays via min.(a,b).

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> minimum(A, dims=1)
    7. 1×2 Matrix{Int64}:
    8.  1  2
    10. julia> minimum(A, dims=2)
    11. 2×1 Matrix{Int64}:
    12.  1
    13.  3

    1. minimum(f, A::AbstractArray; dims)

    Compute the minimum value from of calling the function f on each element of an array over the given dimensions.

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> minimum(abs2, A, dims=1)
    7. 1×2 Matrix{Int64}:
    8.  1  4
    10. julia> minimum(abs2, A, dims=2)
    11. 2×1 Matrix{Int64}:
    12.  1
    13.  9

    source

    — Function

    1. minimum!(r, A)

    Compute the minimum value of A over the singleton dimensions of r, and write results to r.

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> minimum!([1; 1], A)
    7. 2-element Vector{Int64}:
    8.  1
    9.  3
    11. julia> minimum!([1 1], A)
    12. 1×2 Matrix{Int64}:
    13.  1  2

    source

    — Function

    1. extrema(itr) -> Tuple

    Compute both the minimum and maximum element in a single pass, and return them as a 2-tuple.

    Examples

    1. julia> extrema(2:10)
    2. (2, 10)
    4. julia> extrema([9,pi,4.5])
    5. (3.141592653589793, 9.0)

    source

    1. extrema(f, itr) -> Tuple

    Compute both the minimum and maximum of f applied to each element in itr and return them as a 2-tuple. Only one pass is made over itr.

    Julia 1.2

    This method requires Julia 1.2 or later.

    Examples

    1. julia> extrema(sin, 0:π)
    2. (0.0, 0.9092974268256817)

    1. extrema(A::AbstractArray; dims) -> Array{Tuple}

    Compute the minimum and maximum elements of an array over the given dimensions.

    Examples

    1. julia> A = reshape(Vector(1:2:16), (2,2,2))
    2. 2×2×2 Array{Int64, 3}:
    3. [:, :, 1] =
    4.  1  5
    5.  3  7
    7. [:, :, 2] =
    8.   9  13
    9.  11  15
    11. julia> extrema(A, dims = (1,2))
    12. 1×1×2 Array{Tuple{Int64, Int64}, 3}:
    13. [:, :, 1] =
    14.  (1, 7)
    16. [:, :, 2] =
    17.  (9, 15)

    source

    1. extrema(f, A::AbstractArray; dims) -> Array{Tuple}

    Compute the minimum and maximum of f applied to each element in the given dimensions of A.

    Julia 1.2

    This method requires Julia 1.2 or later.

    Base.argmax — Function

    1. argmax(r::AbstractRange)

    Ranges can have multiple maximal elements. In that case argmax will return a maximal index, but not necessarily the first one.

    1. argmax(itr)

    Return the index or key of the maximum element in a collection. If there are multiple maximal elements, then the first one will be returned.

    The collection must not be empty.

    Examples

    1. julia> argmax([8,0.1,-9,pi])
    2. 1
    4. julia> argmax([1,7,7,6])
    5. 2
    7. julia> argmax([1,7,7,NaN])
    8. 4

    source

    1. argmax(A; dims) -> indices

    For an array input, return the indices of the maximum elements over the given dimensions. NaN is treated as greater than all other values.

    Examples

    1. julia> A = [1.0 2; 3 4]
    2. 2×2 Matrix{Float64}:
    3.  1.0  2.0
    4.  3.0  4.0
    6. julia> argmax(A, dims=1)
    7. 1×2 Matrix{CartesianIndex{2}}:
    8.  CartesianIndex(2, 1)  CartesianIndex(2, 2)
    10. julia> argmax(A, dims=2)
    11. 2×1 Matrix{CartesianIndex{2}}:
    12.  CartesianIndex(1, 2)
    13.  CartesianIndex(2, 2)

    Base.argmin — Function

    1. argmin(r::AbstractRange)

    Ranges can have multiple minimal elements. In that case argmin will return a minimal index, but not necessarily the first one.

    1. argmin(itr)

    Return the index or key of the minimum element in a collection. If there are multiple minimal elements, then the first one will be returned.

    The collection must not be empty.

    Examples

    1. julia> argmin([8,0.1,-9,pi])
    2. 3
    4. julia> argmin([7,1,1,6])
    5. 2
    7. julia> argmin([7,1,1,NaN])
    8. 4

    source

    1. argmin(A; dims) -> indices

    For an array input, return the indices of the minimum elements over the given dimensions. NaN is treated as less than all other values.

    Examples

    1. julia> A = [1.0 2; 3 4]
    2. 2×2 Matrix{Float64}:
    3.  1.0  2.0
    4.  3.0  4.0
    6. julia> argmin(A, dims=1)
    7. 1×2 Matrix{CartesianIndex{2}}:
    8.  CartesianIndex(1, 1)  CartesianIndex(1, 2)
    10. julia> argmin(A, dims=2)
    11. 2×1 Matrix{CartesianIndex{2}}:
    12.  CartesianIndex(1, 1)
    13.  CartesianIndex(2, 1)

    Base.findmax — Function

    1. findmax(itr) -> (x, index)

    Return the maximum element of the collection itr and its index or key. If there are multiple maximal elements, then the first one will be returned. If any data element is NaN, this element is returned. The result is in line with max.

    The collection must not be empty.

    Examples

    1. julia> findmax([8,0.1,-9,pi])
    2. (8.0, 1)
    4. julia> findmax([1,7,7,6])
    5. (7, 2)
    7. julia> findmax([1,7,7,NaN])
    8. (NaN, 4)

    1. findmax(A; dims) -> (maxval, index)

    For an array input, returns the value and index of the maximum over the given dimensions. NaN is treated as greater than all other values.

    Examples

    1. julia> A = [1.0 2; 3 4]
    2. 2×2 Matrix{Float64}:
    3.  1.0  2.0
    4.  3.0  4.0
    6. julia> findmax(A, dims=1)
    7. ([3.0 4.0], CartesianIndex{2}[CartesianIndex(2, 1) CartesianIndex(2, 2)])
    9. julia> findmax(A, dims=2)
    10. ([2.0; 4.0], CartesianIndex{2}[CartesianIndex(1, 2); CartesianIndex(2, 2)])

    source

    — Function

    1. findmin(itr) -> (x, index)

    Return the minimum element of the collection itr and its index or key. If there are multiple minimal elements, then the first one will be returned. If any data element is NaN, this element is returned. The result is in line with min.

    The collection must not be empty.

    Examples

    1. julia> findmin([8,0.1,-9,pi])
    2. (-9.0, 3)
    4. julia> findmin([7,1,1,6])
    5. (1, 2)
    7. julia> findmin([7,1,1,NaN])
    8. (NaN, 4)

    source

    1. findmin(A; dims) -> (minval, index)

    For an array input, returns the value and index of the minimum over the given dimensions. NaN is treated as less than all other values.

    Examples

    1. julia> A = [1.0 2; 3 4]
    2. 2×2 Matrix{Float64}:
    3.  1.0  2.0
    4.  3.0  4.0
    6. julia> findmin(A, dims=1)
    7. ([1.0 2.0], CartesianIndex{2}[CartesianIndex(1, 1) CartesianIndex(1, 2)])
    9. julia> findmin(A, dims=2)
    10. ([1.0; 3.0], CartesianIndex{2}[CartesianIndex(1, 1); CartesianIndex(2, 1)])

    Base.findmax! — Function

    1. findmax!(rval, rind, A) -> (maxval, index)

    Find the maximum of A and the corresponding linear index along singleton dimensions of rval and rind, and store the results in rval and rind. NaN is treated as greater than all other values.

    Base.findmin! — Function

    1. findmin!(rval, rind, A) -> (minval, index)

    Find the minimum of A and the corresponding linear index along singleton dimensions of rval and rind, and store the results in rval and rind. NaN is treated as less than all other values.

    Base.sum — Function

    1. sum(f, itr; [init])

    Sum the results of calling function f on each element of itr.

    The return type is Int for signed integers of less than system word size, and UInt for unsigned integers of less than system word size. For all other arguments, a common return type is found to which all arguments are promoted.

    The value returned for empty itr can be specified by init. It must be the additive identity (i.e. zero) as it is unspecified whether init is used for non-empty collections.

    Julia 1.6

    Keyword argument init requires Julia 1.6 or later.

    Examples

    1. julia> sum(abs2, [2; 3; 4])
    2. 29

    Note the important difference between sum(A) and reduce(+, A) for arrays with small integer eltype:

    1. julia> sum(Int8[100, 28])
    2. 128
    4. julia> reduce(+, Int8[100, 28])
    5. -128

    In the former case, the integers are widened to system word size and therefore the result is 128. In the latter case, no such widening happens and integer overflow results in -128.

    1. sum(itr; [init])

    Returns the sum of all elements in a collection.

    The return type is Int for signed integers of less than system word size, and UInt for unsigned integers of less than system word size. For all other arguments, a common return type is found to which all arguments are promoted.

    The value returned for empty itr can be specified by init. It must be the additive identity (i.e. zero) as it is unspecified whether init is used for non-empty collections.

    Julia 1.6

    Keyword argument init requires Julia 1.6 or later.

    Examples

    1. julia> sum(1:20)
    2. 210
    4. julia> sum(1:20; init = 0.0)
    5. 210.0

    source

    1. sum(A::AbstractArray; dims)

    Sum elements of an array over the given dimensions.

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> sum(A, dims=1)
    7. 1×2 Matrix{Int64}:
    8.  4  6
    9. julia> sum(A, dims=2)
    10. 2×1 Matrix{Int64}:
    11.  3
    12.  7

    Sum the results of calling function on each element of an array over the given dimensions.

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> sum(abs2, A, dims=1)
    7. 1×2 Matrix{Int64}:
    8.  10  20
    10. julia> sum(abs2, A, dims=2)
    11. 2×1 Matrix{Int64}:
    12.   5
    13.  25

    source

    — Function

    1. sum!(r, A)

    Sum elements of A over the singleton dimensions of r, and write results to r.

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> sum!([1; 1], A)
    7. 2-element Vector{Int64}:
    8.  3
    9.  7
    11. julia> sum!([1 1], A)
    12. 1×2 Matrix{Int64}:
    13.  4  6

    source

    — Function

    1. prod(f, itr; [init])

    Returns the product of f applied to each element of itr.

    The value returned for empty itr can be specified by init. It must be the multiplicative identity (i.e. one) as it is unspecified whether init is used for non-empty collections.

    Julia 1.6

    Keyword argument init requires Julia 1.6 or later.

    Examples

    1. julia> prod(abs2, [2; 3; 4])
    2. 576

    source

    1. prod(itr; [init])

    Returns the product of all elements of a collection.

    The return type is Int for signed integers of less than system word size, and UInt for unsigned integers of less than system word size. For all other arguments, a common return type is found to which all arguments are promoted.

    The value returned for empty itr can be specified by init. It must be the multiplicative identity (i.e. one) as it is unspecified whether init is used for non-empty collections.

    Julia 1.6

    Keyword argument init requires Julia 1.6 or later.

    Examples

    1. julia> prod(1:5)
    2. 120
    4. julia> prod(1:5; init = 1.0)
    5. 120.0

    1. prod(A::AbstractArray; dims)

    Multiply elements of an array over the given dimensions.

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> prod(A, dims=1)
    7. 1×2 Matrix{Int64}:
    8.  3  8
    10. julia> prod(A, dims=2)
    11. 2×1 Matrix{Int64}:
    12.   2
    13.  12

    source

    1. prod(f, A::AbstractArray; dims)

    Multiply the results of calling the function f on each element of an array over the given dimensions.

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> prod(abs2, A, dims=1)
    7. 1×2 Matrix{Int64}:
    8.  9  64
    10. julia> prod(abs2, A, dims=2)
    11. 2×1 Matrix{Int64}:
    12.    4
    13.  144

    Base.prod! — Function

    1. prod!(r, A)

    Multiply elements of A over the singleton dimensions of r, and write results to r.

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> prod!([1; 1], A)
    7. 2-element Vector{Int64}:
    8.   2
    9.  12
    11. julia> prod!([1 1], A)
    12. 1×2 Matrix{Int64}:
    13.  3  8

    Base.any — Method

    1. any(itr) -> Bool

    Test whether any elements of a boolean collection are true, returning true as soon as the first true value in itr is encountered (short-circuiting).

    If the input contains values, return missing if all non-missing values are false (or equivalently, if the input contains no true value), following three-valued logic.

    Examples

    1. julia> a = [true,false,false,true]
    2. 4-element Vector{Bool}:
    3.  1
    4.  0
    5.  0
    6.  1
    8. julia> any(a)
    9. true
    11. julia> any((println(i); v) for (i, v) in enumerate(a))
    12. 1
    13. true
    15. julia> any([missing, true])
    16. true
    18. julia> any([false, missing])
    19. missing

    Base.any — Method

    1. any(p, itr) -> Bool

    Determine whether predicate p returns true for any elements of itr, returning true as soon as the first item in itr for which p returns true is encountered (short-circuiting).

    If the input contains values, return missing if all non-missing values are false (or equivalently, if the input contains no true value), following three-valued logic.

    Examples

    1. julia> any(i->(4<=i<=6), [3,5,7])
    2. true
    4. julia> any(i -> (println(i); i > 3), 1:10)
    5. 1
    6. 2
    7. 3
    8. 4
    9. true
    11. julia> any(i -> i > 0, [1, missing])
    12. true
    14. julia> any(i -> i > 0, [-1, missing])
    15. missing
    17. julia> any(i -> i > 0, [-1, 0])
    18. false

    Base.any! — Function

    1. any!(r, A)

    Test whether any values in A along the singleton dimensions of r are true, and write results to r.

    Examples

    1. julia> A = [true false; true false]
    2. 2×2 Matrix{Bool}:
    3.  1  0
    4.  1  0
    6. julia> any!([1; 1], A)
    7. 2-element Vector{Int64}:
    8.  1
    9.  1
    11. julia> any!([1 1], A)
    12. 1×2 Matrix{Int64}:
    13.  1  0

    Base.all — Method

    1. all(itr) -> Bool

    Test whether all elements of a boolean collection are true, returning false as soon as the first false value in itr is encountered (short-circuiting).

    If the input contains values, return missing if all non-missing values are true (or equivalently, if the input contains no false value), following three-valued logic.

    Examples

    1. julia> a = [true,false,false,true]
    2. 4-element Vector{Bool}:
    3.  1
    4.  0
    5.  0
    6.  1
    8. julia> all(a)
    9. false
    11. julia> all((println(i); v) for (i, v) in enumerate(a))
    12. 1
    13. 2
    14. false
    16. julia> all([missing, false])
    17. false
    19. julia> all([true, missing])
    20. missing

    Base.all — Method

    1. all(p, itr) -> Bool

    Determine whether predicate p returns true for all elements of itr, returning false as soon as the first item in itr for which p returns false is encountered (short-circuiting).

    If the input contains values, return missing if all non-missing values are true (or equivalently, if the input contains no false value), following three-valued logic.

    Examples

    1. julia> all(i->(4<=i<=6), [4,5,6])
    2. true
    4. julia> all(i -> (println(i); i < 3), 1:10)
    5. 1
    6. 2
    7. 3
    8. false
    10. julia> all(i -> i > 0, [1, missing])
    11. missing
    13. julia> all(i -> i > 0, [-1, missing])
    14. false
    16. julia> all(i -> i > 0, [1, 2])
    17. true

    Base.all! — Function

    1. all!(r, A)

    Test whether all values in A along the singleton dimensions of r are true, and write results to r.

    Examples

    1. julia> A = [true false; true false]
    2. 2×2 Matrix{Bool}:
    3.  1  0
    4.  1  0
    6. julia> all!([1; 1], A)
    7. 2-element Vector{Int64}:
    8.  0
    9.  0
    11. julia> all!([1 1], A)
    12. 1×2 Matrix{Int64}:
    13.  1  0

    Base.count — Function

    1. count([f=identity,] itr; init=0) -> Integer

    Count the number of elements in itr for which the function f returns true. If f is omitted, count the number of true elements in itr (which should be a collection of boolean values). init optionally specifies the value to start counting from and therefore also determines the output type.

    Julia 1.6

    init keyword was added in Julia 1.6.

    Examples

    1. julia> count(i->(4<=i<=6), [2,3,4,5,6])
    2. 3
    4. julia> count([true, false, true, true])
    5. 3
    7. julia> count(>(3), 1:7, init=0x03)
    8. 0x07

    1. count(
    2.     pattern::Union{AbstractString,AbstractPattern},
    3.     string::AbstractString;
    4.     overlap::Bool = false,
    5. )

    Return the number of matches for pattern in string. This is equivalent to calling length(findall(pattern, string)) but more efficient.

    If overlap=true, the matching sequences are allowed to overlap indices in the original string, otherwise they must be from disjoint character ranges.

    Julia 1.3

    This method requires at least Julia 1.3.

    source

    1. count([f=identity,] A::AbstractArray; dims=:)

    Count the number of elements in A for which f returns true over the given dimensions.

    Julia 1.5

    dims keyword was added in Julia 1.5.

    Julia 1.6

    init keyword was added in Julia 1.6.

    Examples

    1. julia> A = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> count(<=(2), A, dims=1)
    7. 1×2 Matrix{Int64}:
    8.  1  1
    10. julia> count(<=(2), A, dims=2)
    11. 2×1 Matrix{Int64}:
    12.  2
    13.  0

    Base.any — Method

    1. any(p, itr) -> Bool

    Determine whether predicate p returns true for any elements of itr, returning true as soon as the first item in itr for which p returns true is encountered (short-circuiting).

    If the input contains values, return missing if all non-missing values are false (or equivalently, if the input contains no true value), following three-valued logic.

    Examples

    1. julia> any(i->(4<=i<=6), [3,5,7])
    2. true
    4. julia> any(i -> (println(i); i > 3), 1:10)
    5. 1
    6. 2
    7. 3
    8. 4
    9. true
    11. julia> any(i -> i > 0, [1, missing])
    12. true
    14. julia> any(i -> i > 0, [-1, missing])
    15. missing
    17. julia> any(i -> i > 0, [-1, 0])
    18. false

    Base.all — Method

    1. all(p, itr) -> Bool

    Determine whether predicate p returns true for all elements of itr, returning false as soon as the first item in itr for which p returns false is encountered (short-circuiting).

    If the input contains values, return missing if all non-missing values are true (or equivalently, if the input contains no false value), following three-valued logic.

    Examples

    1. julia> all(i->(4<=i<=6), [4,5,6])
    2. true
    4. julia> all(i -> (println(i); i < 3), 1:10)
    5. 1
    6. 2
    7. 3
    8. false
    10. julia> all(i -> i > 0, [1, missing])
    11. missing
    13. julia> all(i -> i > 0, [-1, missing])
    14. false
    16. julia> all(i -> i > 0, [1, 2])
    17. true

    Base.foreach — Function

    1. foreach(f, c...) -> Nothing

    Call function f on each element of iterable c. For multiple iterable arguments, f is called elementwise. foreach should be used instead of map when the results of f are not needed, for example in foreach(println, array).

    Examples

    1. julia> a = 1:3:7;
    3. julia> foreach(x -> println(x^2), a)
    4. 1
    5. 16
    6. 49

    Base.map — Function

    1. map(f, c...) -> collection

    Transform collection c by applying f to each element. For multiple collection arguments, apply f elementwise.

    See also:

    Examples

    1. julia> map(x -> x * 2, [1, 2, 3])
    2. 3-element Vector{Int64}:
    3.  2
    4.  4
    5.  6
    7. julia> map(+, [1, 2, 3], [10, 20, 30])
    8. 3-element Vector{Int64}:
    9.  11
    10.  22
    11.  33

    source

    — Function

    1. map!(function, destination, collection...)

    Like map, but stores the result in destination rather than a new collection. destination must be at least as large as the first collection.

    Examples

    1. julia> a = zeros(3);
    3. julia> map!(x -> x * 2, a, [1, 2, 3]);
    5. julia> a
    6. 3-element Vector{Float64}:
    7.  2.0
    8.  4.0
    9.  6.0

    1. map!(f, values(dict::AbstractDict))

    Modifies dict by transforming each value from val to f(val). Note that the type of dict cannot be changed: if f(val) is not an instance of the value type of dict then it will be converted to the value type if possible and otherwise raise an error.

    Julia 1.2

    map!(f, values(dict::AbstractDict)) requires Julia 1.2 or later.

    Examples

    1. julia> d = Dict(:a => 1, :b => 2)
    2. Dict{Symbol, Int64} with 2 entries:
    3.   :a => 1
    4.   :b => 2
    6. julia> map!(v -> v-1, values(d))
    7. ValueIterator for a Dict{Symbol, Int64} with 2 entries. Values:
    8.   0
    9.   1

    source

    — Method

    1. mapreduce(f, op, itrs...; [init])

    Apply function f to each element(s) in itrs, and then reduce the result using the binary function op. If provided, init must be a neutral element for op that will be returned for empty collections. It is unspecified whether init is used for non-empty collections. In general, it will be necessary to provide init to work with empty collections.

    mapreduce is functionally equivalent to calling reduce(op, map(f, itr); init=init), but will in general execute faster since no intermediate collection needs to be created. See documentation for and map.

    Julia 1.2

    mapreduce with multiple iterators requires Julia 1.2 or later.

    Examples

    1. julia> mapreduce(x->x^2, +, [1:3;]) # == 1 + 4 + 9
    2. 14

    The associativity of the reduction is implementation-dependent. Additionally, some implementations may reuse the return value of f for elements that appear multiple times in itr. Use or mapfoldr instead for guaranteed left or right associativity and invocation of f for every value.

    Base.mapfoldl — Method

    1. mapfoldl(f, op, itr; [init])

    Like , but with guaranteed left associativity, as in foldl. If provided, the keyword argument init will be used exactly once. In general, it will be necessary to provide init to work with empty collections.

    Base.mapfoldr — Method

    1. mapfoldr(f, op, itr; [init])

    Like , but with guaranteed right associativity, as in foldr. If provided, the keyword argument init will be used exactly once. In general, it will be necessary to provide init to work with empty collections.

    Base.first — Function

    1. first(coll)

    Get the first element of an iterable collection. Return the start point of an even if it is empty.

    Examples

    1. julia> first(2:2:10)
    2. 2
    4. julia> first([1; 2; 3; 4])
    5. 1

    source

    1. first(itr, n::Integer)

    Get the first n elements of the iterable collection itr, or fewer elements if v is not long enough.

    Julia 1.6

    This method requires at least Julia 1.6.

    Examples

    1. julia> first(["foo", "bar", "qux"], 2)
    2. 2-element Vector{String}:
    3.  "foo"
    4.  "bar"
    6. julia> first(1:6, 10)
    7. 1:6
    9. julia> first(Bool[], 1)
    10. Bool[]

    1. first(s::AbstractString, n::Integer)

    Get a string consisting of the first n characters of s.

    Examples

    1. julia> first("∀ϵ≠0: ϵ²>0", 0)
    2. ""
    4. julia> first("∀ϵ≠0: ϵ²>0", 1)
    5. "∀"
    7. julia> first("∀ϵ≠0: ϵ²>0", 3)
    8. "∀ϵ≠"

    source

    — Function

    1. last(coll)

    Get the last element of an ordered collection, if it can be computed in O(1) time. This is accomplished by calling lastindex to get the last index. Return the end point of an even if it is empty.

    Examples

    1. julia> last(1:2:10)
    2. 9
    4. julia> last([1; 2; 3; 4])
    5. 4

    source

    1. last(itr, n::Integer)

    Get the last n elements of the iterable collection itr, or fewer elements if v is not long enough.

    Julia 1.6

    This method requires at least Julia 1.6.

    Examples

    1. julia> last(["foo", "bar", "qux"], 2)
    2. 2-element Vector{String}:
    3.  "bar"
    4.  "qux"
    6. julia> last(1:6, 10)
    7. 1:6
    9. julia> last(Float64[], 1)
    10. Float64[]

    1. last(s::AbstractString, n::Integer)

    Get a string consisting of the last n characters of s.

    Examples

    1. julia> last("∀ϵ≠0: ϵ²>0", 0)
    2. ""
    4. julia> last("∀ϵ≠0: ϵ²>0", 1)
    5. "0"
    7. julia> last("∀ϵ≠0: ϵ²>0", 3)
    8. "²>0"

    source

    — Function

    1. front(x::Tuple)::Tuple

    Return a Tuple consisting of all but the last component of x.

    Examples

    1. julia> Base.front((1,2,3))
    2. (1, 2)
    4. julia> Base.front(())
    5. ERROR: ArgumentError: Cannot call front on an empty tuple.

    source

    — Function

    1. tail(x::Tuple)::Tuple

    Return a Tuple consisting of all but the first component of x.

    Examples

    1. julia> Base.tail((1,2,3))
    2. (2, 3)
    4. julia> Base.tail(())
    5. ERROR: ArgumentError: Cannot call tail on an empty tuple.

    source

    — Function

    1. step(r)

    Get the step size of an AbstractRange object.

    Examples

    1. julia> step(1:10)
    2. 1
    4. julia> step(1:2:10)
    5. 2
    7. julia> step(2.5:0.3:10.9)
    8. 0.3
    10. julia> step(range(2.5, stop=10.9, length=85))
    11. 0.1

    Base.collect — Method

    1. collect(collection)

    Return an Array of all items in a collection or iterator. For dictionaries, returns Pair{KeyType, ValType}. If the argument is array-like or is an iterator with the trait, the result will have the same shape and number of dimensions as the argument.

    Examples

    1. julia> collect(1:2:13)
    2. 7-element Vector{Int64}:
    3.   1
    4.   3
    5.   5
    6.   7
    7.   9
    8.  11
    9.  13

    source

    — Method

    1. collect(element_type, collection)

    Return an Array with the given element type of all items in a collection or iterable. The result has the same shape and number of dimensions as collection.

    Examples

    1. julia> collect(Float64, 1:2:5)
    2. 3-element Vector{Float64}:
    3.  1.0
    4.  3.0
    5.  5.0

    source

    — Function

    1. filter(f, a)

    Return a copy of collection a, removing elements for which f is false. The function f is passed one argument.

    Julia 1.4

    Support for a as a tuple requires at least Julia 1.4.

    Examples

    1. julia> a = 1:10
    2. 1:10
    4. julia> filter(isodd, a)
    5. 5-element Vector{Int64}:
    6.  1
    7.  3
    8.  5
    9.  7
    10.  9

    source

    1. filter(f, d::AbstractDict)

    Return a copy of d, removing elements for which f is false. The function f is passed key=>value pairs.

    Examples

    1. julia> d = Dict(1=>"a", 2=>"b")
    2. Dict{Int64, String} with 2 entries:
    3.   2 => "b"
    4.   1 => "a"
    6. julia> filter(p->isodd(p.first), d)
    7. Dict{Int64, String} with 1 entry:
    8.   1 => "a"

    1. filter(f, itr::SkipMissing{<:AbstractArray})

    Return a vector similar to the array wrapped by the given SkipMissing iterator but with all missing elements and those for which f returns false removed.

    Julia 1.2

    This method requires Julia 1.2 or later.

    Examples

    1. julia> x = [1 2; missing 4]
    2. 2×2 Matrix{Union{Missing, Int64}}:
    3.  1         2
    4.   missing  4
    6. julia> filter(isodd, skipmissing(x))
    7. 1-element Vector{Int64}:
    8.  1

    source

    — Function

    1. filter!(f, a)

    Update collection a, removing elements for which f is false. The function f is passed one argument.

    Examples

    1. julia> filter!(isodd, Vector(1:10))
    2. 5-element Vector{Int64}:
    3.  1
    4.  3
    5.  5
    6.  7
    7.  9

    source

    1. filter!(f, d::AbstractDict)

    Update d, removing elements for which f is false. The function f is passed key=>value pairs.

    Example

    1. julia> d = Dict(1=>"a", 2=>"b", 3=>"c")
    2. Dict{Int64, String} with 3 entries:
    3.   2 => "b"
    4.   3 => "c"
    5.   1 => "a"
    7. julia> filter!(p->isodd(p.first), d)
    8. Dict{Int64, String} with 2 entries:
    9.   3 => "c"
    10.   1 => "a"

    Base.replace — Method

    1. replace(A, old_new::Pair...; [count::Integer])

    Return a copy of collection A where, for each pair old=>new in old_new, all occurrences of old are replaced by new. Equality is determined using . If count is specified, then replace at most count occurrences in total.

    The element type of the result is chosen using promotion (see promote_type) based on the element type of A and on the types of the new values in pairs. If count is omitted and the element type of A is a Union, the element type of the result will not include singleton types which are replaced with values of a different type: for example, Union{T,Missing} will become T if missing is replaced.

    See also .

    Examples

    1. julia> replace([1, 2, 1, 3], 1=>0, 2=>4, count=2)
    2. 4-element Vector{Int64}:
    3.  0
    4.  4
    5.  1
    6.  3
    8. julia> replace([1, missing], missing=>0)
    9. 2-element Vector{Int64}:
    10.  1
    11.  0

    source

    — Method

    1. replace(new::Function, A; [count::Integer])

    Return a copy of A where each value x in A is replaced by new(x). If count is specified, then replace at most count values in total (replacements being defined as new(x) !== x).

    Examples

    1. julia> replace(x -> isodd(x) ? 2x : x, [1, 2, 3, 4])
    2. 4-element Vector{Int64}:
    3.  2
    4.  2
    5.  6
    6.  4
    8. julia> replace(Dict(1=>2, 3=>4)) do kv
    9.            first(kv) < 3 ? first(kv)=>3 : kv
    10.        end
    11. Dict{Int64, Int64} with 2 entries:
    12.   3 => 4
    13.   1 => 3

    source

    — Function

    1. replace!(A, old_new::Pair...; [count::Integer])

    For each pair old=>new in old_new, replace all occurrences of old in collection A by new. Equality is determined using isequal. If count is specified, then replace at most count occurrences in total. See also .

    Examples

    1. julia> replace!([1, 2, 1, 3], 1=>0, 2=>4, count=2)
    2. 4-element Vector{Int64}:
    3.  0
    4.  4
    5.  1
    6.  3
    8. julia> replace!(Set([1, 2, 3]), 1=>0)
    9. Set{Int64} with 3 elements:
    10.   0
    11.   2
    12.   3

    source

    1. replace!(new::Function, A; [count::Integer])

    Replace each element x in collection A by new(x). If count is specified, then replace at most count values in total (replacements being defined as new(x) !== x).

    Examples

    1. julia> replace!(x -> isodd(x) ? 2x : x, [1, 2, 3, 4])
    2. 4-element Vector{Int64}:
    3.  2
    4.  2
    5.  6
    6.  4
    8. julia> replace!(Dict(1=>2, 3=>4)) do kv
    9.            first(kv) < 3 ? first(kv)=>3 : kv
    10.        end
    11. Dict{Int64, Int64} with 2 entries:
    12.   3 => 4
    13.   1 => 3
    15. julia> replace!(x->2x, Set([3, 6]))
    16. Set{Int64} with 2 elements:
    17.   6
    18.   12

    Base.rest — Function

    1. Base.rest(collection[, itr_state])

    Generic function for taking the tail of collection, starting from a specific iteration state itr_state. Return a Tuple, if collection itself is a Tuple, a subtype of AbstractVector, if collection is an AbstractArray, a subtype of AbstractString if collection is an AbstractString, and an arbitrary iterator, falling back to Iterators.rest(collection[, itr_state]), otherwise. Can be overloaded for user-defined collection types to customize the behavior of slurping in assignments, like a, b... = collection.

    Julia 1.6

    Base.rest requires at least Julia 1.6.

    Examples

    1. julia> a = [1 2; 3 4]
    2. 2×2 Matrix{Int64}:
    3.  1  2
    4.  3  4
    6. julia> first, state = iterate(a)
    7. (1, 2)
    9. julia> first, Base.rest(a, state)
    10. (1, [3, 2, 4])

    Base.getindex — Function

    1. getindex(collection, key...)

    Retrieve the value(s) stored at the given key or index within a collection. The syntax a[i,j,...] is converted by the compiler to getindex(a, i, j, ...).

    Examples

    1. julia> A = Dict("a" => 1, "b" => 2)
    2. Dict{String, Int64} with 2 entries:
    3.   "b" => 2
    4.   "a" => 1
    6. julia> getindex(A, "a")
    7. 1

    Base.setindex! — Function

    1. setindex!(collection, value, key...)

    Store the given value at the given key or index within a collection. The syntax a[i,j,...] = x is converted by the compiler to (setindex!(a, x, i, j, ...); x).

    Base.firstindex — Function

    1. firstindex(collection) -> Integer
    2. firstindex(collection, d) -> Integer

    Return the first index of collection. If d is given, return the first index of collection along dimension d.

    Examples

    1. julia> firstindex([1,2,4])
    2. 1
    4. julia> firstindex(rand(3,4,5), 2)
    5. 1

    Base.lastindex — Function

    1. lastindex(collection) -> Integer
    2. lastindex(collection, d) -> Integer

    Return the last index of collection. If d is given, return the last index of collection along dimension d.

    The syntaxes A[end] and A[end, end] lower to A[lastindex(A)] and A[lastindex(A, 1), lastindex(A, 2)], respectively.

    Examples

    1. julia> lastindex([1,2,4])
    2. 3
    4. julia> lastindex(rand(3,4,5), 2)
    5. 4

    Fully implemented by:

    Partially implemented by:

    Dictionaries

    is the standard dictionary. Its implementation uses hash as the hashing function for the key, and to determine equality. Define these two functions for custom types to override how they are stored in a hash table.

    IdDict is a special hash table where the keys are always object identities.

    is a hash table implementation where the keys are weak references to objects, and thus may be garbage collected even when referenced in a hash table. Like Dict it uses hash for hashing and isequal for equality, unlike Dict it does not convert keys on insertion.

    Dicts can be created by passing pair objects constructed with => to a constructor: Dict("A"=>1, "B"=>2). This call will attempt to infer type information from the keys and values (i.e. this example creates a Dict{String, Int64}). To explicitly specify types use the syntax Dict{KeyType,ValueType}(...). For example, Dict{String,Int32}("A"=>1, "B"=>2).

    Dictionaries may also be created with generators. For example, Dict(i => f(i) for i = 1:10).

    Given a dictionary D, the syntax D[x] returns the value of key x (if it exists) or throws an error, and D[x] = y stores the key-value pair x => y in D (replacing any existing value for the key x). Multiple arguments to D[...] are converted to tuples; for example, the syntax D[x,y] is equivalent to D[(x,y)], i.e. it refers to the value keyed by the tuple (x,y).

    Base.AbstractDict — Type

    1. AbstractDict{K, V}

    Supertype for dictionary-like types with keys of type K and values of type V. , IdDict and other types are subtypes of this. An should be an iterator of Pair{K, V}.

    Base.Dict — Type

    1. Dict([itr])

    Dict{K,V}() constructs a hash table with keys of type K and values of type V. Keys are compared with and hashed with hash.

    Given a single iterable argument, constructs a whose key-value pairs are taken from 2-tuples (key,value) generated by the argument.

    Examples

    1. julia> Dict([("A", 1), ("B", 2)])
    2. Dict{String, Int64} with 2 entries:
    3.   "B" => 2
    4.   "A" => 1

    Alternatively, a sequence of pair arguments may be passed.

    1. julia> Dict("A"=>1, "B"=>2)
    2. Dict{String, Int64} with 2 entries:
    3.   "B" => 2
    4.   "A" => 1

    source

    — Type

    1. IdDict([itr])

    IdDict{K,V}() constructs a hash table using object-id as hash and === as equality with keys of type K and values of type V.

    See Dict for further help.

    Base.WeakKeyDict — Type

    1. WeakKeyDict([itr])

    WeakKeyDict() constructs a hash table where the keys are weak references to objects which may be garbage collected even when referenced in a hash table.

    See for further help. Note, unlike Dict, WeakKeyDict does not convert keys on insertion, as this would imply the key object was unreferenced anywhere before insertion.

    Base.ImmutableDict — Type

    1. ImmutableDict

    ImmutableDict is a dictionary implemented as an immutable linked list, which is optimal for small dictionaries that are constructed over many individual insertions. Note that it is not possible to remove a value, although it can be partially overridden and hidden by inserting a new value with the same key.

    1. ImmutableDict(KV::Pair)

    Create a new entry in the ImmutableDict for a key => value pair

    • use (key => value) in dict to see if this particular combination is in the properties set
    • use get(dict, key, default) to retrieve the most recent value for a particular key

    Base.haskey — Function

    Determine whether a collection has a mapping for a given key.

    Examples

    1. julia> D = Dict('a'=>2, 'b'=>3)
    2. Dict{Char, Int64} with 2 entries:
    3.   'a' => 2
    4.   'b' => 3
    6. julia> haskey(D, 'a')
    7. true
    9. julia> haskey(D, 'c')
    10. false

    — Method

    1. get(collection, key, default)

    Return the value stored for the given key, or the given default value if no mapping for the key is present.

    Examples

    1. julia> d = Dict("a"=>1, "b"=>2);
    3. julia> get(d, "a", 3)
    4. 1
    6. julia> get(d, "c", 3)
    7. 3

    source

    — Function

    1. get(collection, key, default)

    Return the value stored for the given key, or the given default value if no mapping for the key is present.

    Examples

    1. julia> d = Dict("a"=>1, "b"=>2);
    3. julia> get(d, "a", 3)
    4. 1
    6. julia> get(d, "c", 3)
    7. 3

    source

    1. get(f::Function, collection, key)

    Return the value stored for the given key, or if no mapping for the key is present, return f(). Use to also store the default value in the dictionary.

    This is intended to be called using do block syntax

    1. get(dict, key) do
    2.     # default value calculated here
    3.     time()
    4. end

    source

    — Method

    1. get!(collection, key, default)

    Return the value stored for the given key, or if no mapping for the key is present, store key => default, and return default.

    Examples

    1. julia> d = Dict("a"=>1, "b"=>2, "c"=>3);
    3. julia> get!(d, "a", 5)
    4. 1
    6. 4
    8. julia> d
    9. Dict{String, Int64} with 4 entries:
    10.   "c" => 3
    11.   "b" => 2
    12.   "a" => 1
    13.   "d" => 4

    source

    — Method

    1. get!(f::Function, collection, key)

    Return the value stored for the given key, or if no mapping for the key is present, store key => f(), and return f().

    This is intended to be called using do block syntax.

    Examples

    1. julia> squares = Dict{Int, Int}();
    3. julia> function get_square!(d, i)
    4.            get!(d, i) do
    5.                i^2
    6.            end
    7.        end
    8. get_square! (generic function with 1 method)
    10. julia> get_square!(squares, 2)
    11. 4
    13. julia> squares
    14. Dict{Int64, Int64} with 1 entry:
    15.   2 => 4

    source

    — Function

    1. getkey(collection, key, default)

    Return the key matching argument key if one exists in collection, otherwise return default.

    Examples

    1. julia> D = Dict('a'=>2, 'b'=>3)
    2. Dict{Char, Int64} with 2 entries:
    3.   'a' => 2
    4.   'b' => 3
    6. julia> getkey(D, 'a', 1)
    7. 'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)
    9. julia> getkey(D, 'd', 'a')
    10. 'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)

    source

    — Function

    1. delete!(collection, key)

    Delete the mapping for the given key in a collection, if any, and return the collection.

    Examples

    1. julia> d = Dict("a"=>1, "b"=>2)
    2. Dict{String, Int64} with 2 entries:
    3.   "b" => 2
    4.   "a" => 1
    6. julia> delete!(d, "b")
    7. Dict{String, Int64} with 1 entry:
    8.   "a" => 1
    10. julia> delete!(d, "b") # d is left unchanged
    11. Dict{String, Int64} with 1 entry:
    12.   "a" => 1

    source

    — Method

    1. pop!(collection, key[, default])

    Delete and return the mapping for key if it exists in collection, otherwise return default, or throw an error if default is not specified.

    Examples

    1. julia> d = Dict("a"=>1, "b"=>2, "c"=>3);
    3. julia> pop!(d, "a")
    4. 1
    6. julia> pop!(d, "d")
    7. ERROR: KeyError: key "d" not found
    8. Stacktrace:
    9. [...]
    11. julia> pop!(d, "e", 4)
    12. 4

    source

    — Function

    1. keys(iterator)

    For an iterator or collection that has keys and values (e.g. arrays and dictionaries), return an iterator over the keys.

    source

    — Function

    1. values(iterator)

    For an iterator or collection that has keys and values, return an iterator over the values. This function simply returns its argument by default, since the elements of a general iterator are normally considered its “values”.

    Examples

    1. julia> d = Dict("a"=>1, "b"=>2);
    3. julia> values(d)
    4. ValueIterator for a Dict{String, Int64} with 2 entries. Values:
    5.   2
    6.   1
    8. julia> values([2])
    9. 1-element Vector{Int64}:
    10.  2

    source

    1. values(a::AbstractDict)

    Return an iterator over all values in a collection. collect(values(a)) returns an array of values. When the values are stored internally in a hash table, as is the case for Dict, the order in which they are returned may vary. But keys(a) and values(a) both iterate a and return the elements in the same order.

    Examples

    1. julia> D = Dict('a'=>2, 'b'=>3)
    2. Dict{Char, Int64} with 2 entries:
    3.   'a' => 2
    4.   'b' => 3
    6. julia> collect(values(D))
    7. 2-element Vector{Int64}:
    8.  2
    9.  3

    Base.pairs — Function

    1. pairs(IndexLinear(), A)
    2. pairs(IndexCartesian(), A)
    3. pairs(IndexStyle(A), A)

    An iterator that accesses each element of the array A, returning i => x, where i is the index for the element and x = A[i]. Identical to pairs(A), except that the style of index can be selected. Also similar to enumerate(A), except i will be a valid index for A, while enumerate always counts from 1 regardless of the indices of A.

    Specifying ensures that i will be an integer; specifying IndexCartesian() ensures that i will be a ; specifying IndexStyle(A) chooses whichever has been defined as the native indexing style for array A.

    Mutation of the bounds of the underlying array will invalidate this iterator.

    Examples

    1. julia> A = ["a" "d"; "b" "e"; "c" "f"];
    3. julia> for (index, value) in pairs(IndexStyle(A), A)
    4.            println("$index $value")
    5.        end
    6. 1 a
    7. 2 b
    8. 3 c
    9. 4 d
    10. 5 e
    11. 6 f
    13. julia> S = view(A, 1:2, :);
    15. julia> for (index, value) in pairs(IndexStyle(S), S)
    16.            println("$index $value")
    17.        end
    18. CartesianIndex(1, 1) a
    19. CartesianIndex(2, 1) b
    20. CartesianIndex(1, 2) d
    21. CartesianIndex(2, 2) e

    See also: IndexStyle, .

    source

    1. pairs(collection)

    Return an iterator over key => value pairs for any collection that maps a set of keys to a set of values. This includes arrays, where the keys are the array indices.

    Base.merge — Function

    1. merge(d::AbstractDict, others::AbstractDict...)

    Construct a merged collection from the given collections. If necessary, the types of the resulting collection will be promoted to accommodate the types of the merged collections. If the same key is present in another collection, the value for that key will be the value it has in the last collection listed. See also for custom handling of values with the same key.

    Examples

    1. julia> a = Dict("foo" => 0.0, "bar" => 42.0)
    2. Dict{String, Float64} with 2 entries:
    3.   "bar" => 42.0
    4.   "foo" => 0.0
    6. julia> b = Dict("baz" => 17, "bar" => 4711)
    7. Dict{String, Int64} with 2 entries:
    8.   "bar" => 4711
    9.   "baz" => 17
    11. julia> merge(a, b)
    12. Dict{String, Float64} with 3 entries:
    13.   "bar" => 4711.0
    14.   "baz" => 17.0
    15.   "foo" => 0.0
    17. julia> merge(b, a)
    18. Dict{String, Float64} with 3 entries:
    19.   "bar" => 42.0
    20.   "baz" => 17.0
    21.   "foo" => 0.0

    source

    1. merge(a::NamedTuple, bs::NamedTuple...)

    Construct a new named tuple by merging two or more existing ones, in a left-associative manner. Merging proceeds left-to-right, between pairs of named tuples, and so the order of fields present in both the leftmost and rightmost named tuples take the same position as they are found in the leftmost named tuple. However, values are taken from matching fields in the rightmost named tuple that contains that field. Fields present in only the rightmost named tuple of a pair are appended at the end. A fallback is implemented for when only a single named tuple is supplied, with signature merge(a::NamedTuple).

    Julia 1.1

    Merging 3 or more NamedTuple requires at least Julia 1.1.

    Examples

    1. julia> merge((a=1, b=2, c=3), (b=4, d=5))
    2. (a = 1, b = 4, c = 3, d = 5)
    1. julia> merge((a=1, b=2), (b=3, c=(d=1,)), (c=(d=2,),))
    2. (a = 1, b = 3, c = (d = 2,))

    1. merge(a::NamedTuple, iterable)

    Interpret an iterable of key-value pairs as a named tuple, and perform a merge.

    1. julia> merge((a=1, b=2, c=3), [:b=>4, :d=>5])
    2. (a = 1, b = 4, c = 3, d = 5)

    source

    — Function

    1. mergewith(combine, d::AbstractDict, others::AbstractDict...)
    2. mergewith(combine)
    3. merge(combine, d::AbstractDict, others::AbstractDict...)

    Construct a merged collection from the given collections. If necessary, the types of the resulting collection will be promoted to accommodate the types of the merged collections. Values with the same key will be combined using the combiner function. The curried form mergewith(combine) returns the function (args...) -> mergewith(combine, args...).

    Method merge(combine::Union{Function,Type}, args...) as an alias of mergewith(combine, args...) is still available for backward compatibility.

    Julia 1.5

    mergewith requires Julia 1.5 or later.

    Examples

    1. julia> a = Dict("foo" => 0.0, "bar" => 42.0)
    2. Dict{String, Float64} with 2 entries:
    3.   "bar" => 42.0
    4.   "foo" => 0.0
    6. julia> b = Dict("baz" => 17, "bar" => 4711)
    7. Dict{String, Int64} with 2 entries:
    8.   "bar" => 4711
    9.   "baz" => 17
    11. julia> mergewith(+, a, b)
    12. Dict{String, Float64} with 3 entries:
    13.   "bar" => 4753.0
    14.   "baz" => 17.0
    15.   "foo" => 0.0
    17. julia> ans == mergewith(+)(a, b)
    18. true

    source

    — Function

    1. merge!(d::AbstractDict, others::AbstractDict...)

    Update collection with pairs from the other collections. See also merge.

    Examples

    1. julia> d1 = Dict(1 => 2, 3 => 4);
    3. julia> d2 = Dict(1 => 4, 4 => 5);
    5. julia> merge!(d1, d2);
    7. julia> d1
    8. Dict{Int64, Int64} with 3 entries:
    9.   4 => 5
    10.   3 => 4
    11.   1 => 4

    Base.mergewith! — Function

    1. mergewith!(combine, d::AbstractDict, others::AbstractDict...) -> d
    2. mergewith!(combine)
    3. merge!(combine, d::AbstractDict, others::AbstractDict...) -> d

    Update collection with pairs from the other collections. Values with the same key will be combined using the combiner function. The curried form mergewith!(combine) returns the function (args...) -> mergewith!(combine, args...).

    Method merge!(combine::Union{Function,Type}, args...) as an alias of mergewith!(combine, args...) is still available for backward compatibility.

    Julia 1.5

    mergewith! requires Julia 1.5 or later.

    Examples

    1. julia> d1 = Dict(1 => 2, 3 => 4);
    3. julia> d2 = Dict(1 => 4, 4 => 5);
    5. julia> mergewith!(+, d1, d2);
    7. julia> d1
    8. Dict{Int64, Int64} with 3 entries:
    9.   4 => 5
    10.   3 => 4
    11.   1 => 6
    13. julia> mergewith!(-, d1, d1);
    15. julia> d1
    16. Dict{Int64, Int64} with 3 entries:
    17.   4 => 0
    18.   3 => 0
    19.   1 => 0
    21. julia> foldl(mergewith!(+), [d1, d2]; init=Dict{Int64, Int64}())
    22. Dict{Int64, Int64} with 3 entries:
    23.   4 => 5
    24.   3 => 0
    25.   1 => 4

    Base.sizehint! — Function

    1. sizehint!(s, n)

    Suggest that collection s reserve capacity for at least n elements. This can improve performance.

    Notes on the performance model

    For types that support sizehint!,

    1. push! and append! methods generally may (but are not required to) preallocate extra

    storage. For types implemented in Base, they typically do, using a heuristic optimized for a general use case.

    1. sizehint! may control this preallocation. Again, it typically does this for types in

    Base.

    1. empty! is nearly costless (and O(1)) for types that support this kind of preallocation.

    Base.keytype — Function

    1. keytype(T::Type{<:AbstractArray})
    2. keytype(A::AbstractArray)

    Return the key type of an array. This is equal to the eltype of the result of keys(...), and is provided mainly for compatibility with the dictionary interface.

    Examples

    1. julia> keytype([1, 2, 3]) == Int
    2. true
    4. julia> keytype([1 2; 3 4])
    5. CartesianIndex{2}

    Julia 1.2

    For arrays, this function requires at least Julia 1.2.

    1. keytype(type)

    Get the key type of an dictionary type. Behaves similarly to eltype.

    Examples

    1. julia> keytype(Dict(Int32(1) => "foo"))
    2. Int32

    Base.valtype — Function

    1. valtype(T::Type{<:AbstractArray})
    2. valtype(A::AbstractArray)

    Return the value type of an array. This is identical to eltype and is provided mainly for compatibility with the dictionary interface.

    Examples

    1. julia> valtype(["one", "two", "three"])
    2. String

    Julia 1.2

    For arrays, this function requires at least Julia 1.2.

    1. valtype(type)

    Get the value type of an dictionary type. Behaves similarly to eltype.

    Examples

    1. julia> valtype(Dict(Int32(1) => "foo"))
    2. String

    Fully implemented by:

    Partially implemented by:

    Base.AbstractSet — Type

    1. AbstractSet{T}

    Supertype for set-like types whose elements are of type T. , BitSet and other types are subtypes of this.

    Base.Set — Type

    1. Set([itr])

    Construct a of the values generated by the given iterable object, or an empty set. Should be used instead of BitSet for sparse integer sets, or for sets of arbitrary objects.

    Base.BitSet — Type

    1. BitSet([itr])

    Construct a sorted set of Ints generated by the given iterable object, or an empty set. Implemented as a bit string, and therefore designed for dense integer sets. If the set will be sparse (for example, holding a few very large integers), use instead.

    source

    — Function

    1. union(s, itrs...)
    2. ∪(s, itrs...)

    Construct the union of sets. Maintain order with arrays.

    Examples

    1. julia> union([1, 2], [3, 4])
    2. 4-element Vector{Int64}:
    3.  1
    4.  2
    5.  3
    6.  4
    8. julia> union([1, 2], [2, 4])
    9. 3-element Vector{Int64}:
    10.  1
    11.  2
    12.  4
    14. julia> union([4, 2], 1:2)
    15. 3-element Vector{Int64}:
    16.  4
    17.  2
    18.  1
    20. julia> union(Set([1, 2]), 2:3)
    21. Set{Int64} with 3 elements:
    22.   2
    23.   3
    24.   1

    source

    — Function

    1. union!(s::Union{AbstractSet,AbstractVector}, itrs...)

    Construct the union of passed in sets and overwrite s with the result. Maintain order with arrays.

    Examples

    1. julia> a = Set([1, 3, 4, 5]);
    3. julia> union!(a, 1:2:8);
    5. julia> a
    6. Set{Int64} with 5 elements:
    7.   5
    8.   4
    9.   7
    10.   3
    11.   1

    source

    — Function

    1. intersect(s, itrs...)
    2. ∩(s, itrs...)

    Construct the intersection of sets. Maintain order with arrays.

    Examples

    1. julia> intersect([1, 2, 3], [3, 4, 5])
    2. 1-element Vector{Int64}:
    3.  3
    5. julia> intersect([1, 4, 4, 5, 6], [4, 6, 6, 7, 8])
    6. 2-element Vector{Int64}:
    7.  4
    8.  6
    10. julia> intersect(Set([1, 2]), BitSet([2, 3]))
    11. Set{Int64} with 1 element:
    12.   2

    source

    — Function

    1. setdiff(s, itrs...)

    Construct the set of elements in s but not in any of the iterables in itrs. Maintain order with arrays.

    Examples

    1. julia> setdiff([1,2,3], [3,4,5])
    2. 2-element Vector{Int64}:
    3.  1
    4.  2

    source

    — Function

    1. setdiff!(s, itrs...)

    Remove from set s (in-place) each element of each iterable from itrs. Maintain order with arrays.

    Examples

    1. julia> a = Set([1, 3, 4, 5]);
    3. julia> setdiff!(a, 1:2:6);
    5. julia> a
    6. Set{Int64} with 1 element:
    7.   4

    source

    — Function

    1. symdiff(s, itrs...)

    Construct the symmetric difference of elements in the passed in sets. When s is not an AbstractSet, the order is maintained. Note that in this case the multiplicity of elements matters.

    Examples

    1. julia> symdiff([1,2,3], [3,4,5], [4,5,6])
    2. 3-element Vector{Int64}:
    3.  1
    4.  2
    5.  6
    7. julia> symdiff([1,2,1], [2, 1, 2])
    8. 2-element Vector{Int64}:
    9.  1
    10.  2
    12. julia> symdiff(unique([1,2,1]), unique([2, 1, 2]))
    13. Int64[]

    source

    — Function

    1. symdiff!(s::Union{AbstractSet,AbstractVector}, itrs...)

    Construct the symmetric difference of the passed in sets, and overwrite s with the result. When s is an array, the order is maintained. Note that in this case the multiplicity of elements matters.

    source

    — Function

    1. intersect!(s::Union{AbstractSet,AbstractVector}, itrs...)

    Intersect all passed in sets and overwrite s with the result. Maintain order with arrays.

    source

    — Function

    1. issubset(a, b) -> Bool
    2. ⊆(a, b) -> Bool
    3. ⊇(b, a) -> Bool

    Determine whether every element of a is also in b, using in.

    Examples

    1. julia> issubset([1, 2], [1, 2, 3])
    2. true
    4. julia> [1, 2, 3] ⊆ [1, 2]
    5. false
    7. julia> [1, 2, 3] ⊇ [1, 2]
    8. true

    Base.:⊈ — Function

    1. ⊈(a, b) -> Bool
    2. ⊉(b, a) -> Bool

    Negation of ⊆ and ⊇, i.e. checks that a is not a subset of b.

    Examples

    1. julia> (1, 2) ⊈ (2, 3)
    2. true
    4. julia> (1, 2) ⊈ (1, 2, 3)
    5. false

    Base.:⊊ — Function

    1. ⊊(a, b) -> Bool
    2. ⊋(b, a) -> Bool

    Determines if a is a subset of, but not equal to, b.

    Examples

    1. julia> (1, 2) ⊊ (1, 2, 3)
    2. true
    4. julia> (1, 2) ⊊ (1, 2)
    5. false

    Base.issetequal — Function

    1. issetequal(a, b) -> Bool

    Determine whether a and b have the same elements. Equivalent to a ⊆ b && b ⊆ a but more efficient when possible.

    Examples

    1. julia> issetequal([1, 2], [1, 2, 3])
    2. false
    4. julia> issetequal([1, 2], [2, 1])
    5. true

    Base.isdisjoint — Function

    1. isdisjoint(v1, v2) -> Bool

    Return whether the collections v1 and v2 are disjoint, i.e. whether their intersection is empty.

    Julia 1.5

    This function requires at least Julia 1.5.

    Fully implemented by:

    Partially implemented by:

    Dequeues

    — Function

    1. push!(collection, items...) -> collection

    Insert one or more items in collection. If collection is an ordered container, the items are inserted at the end (in the given order).

    Examples

    1. julia> push!([1, 2, 3], 4, 5, 6)
    2. 6-element Vector{Int64}:
    3.  1
    4.  2
    5.  3
    6.  4
    7.  5
    8.  6

    If collection is ordered, use append! to add all the elements of another collection to it. The result of the preceding example is equivalent to append!([1, 2, 3], [4, 5, 6]). For AbstractSet objects, can be used instead.

    See sizehint! for notes about the performance model.

    Base.pop! — Function

    1. pop!(collection) -> item

    Remove an item in collection and return it. If collection is an ordered container, the last item is returned; for unordered containers, an arbitrary element is returned.

    Examples

    1. julia> A=[1, 2, 3]
    2. 3-element Vector{Int64}:
    3.  1
    4.  2
    5.  3
    7. julia> pop!(A)
    8. 3
    10. julia> A
    11. 2-element Vector{Int64}:
    12.  1
    13.  2
    15. julia> S = Set([1, 2])
    16. Set{Int64} with 2 elements:
    17.   2
    18.   1
    20. julia> pop!(S)
    21. 2
    23. julia> S
    24. Set{Int64} with 1 element:
    25.   1
    27. julia> pop!(Dict(1=>2))
    28. 1 => 2

    1. pop!(collection, key[, default])

    Delete and return the mapping for key if it exists in collection, otherwise return default, or throw an error if default is not specified.

    Examples

    1. julia> d = Dict("a"=>1, "b"=>2, "c"=>3);
    3. julia> pop!(d, "a")
    4. 1
    6. julia> pop!(d, "d")
    7. ERROR: KeyError: key "d" not found
    8. Stacktrace:
    9. [...]
    11. julia> pop!(d, "e", 4)
    12. 4

    source

    — Function

    1. popat!(a::Vector, i::Integer, [default])

    Remove the item at the given i and return it. Subsequent items are shifted to fill the resulting gap. When i is not a valid index for a, return default, or throw an error if default is not specified. See also deleteat! and .

    Julia 1.5

    This function is available as of Julia 1.5.

    Examples

    1. julia> a = [4, 3, 2, 1]; popat!(a, 2)
    2. 3
    4. julia> a
    5. 3-element Vector{Int64}:
    6.  4
    7.  2
    8.  1
    10. julia> popat!(a, 4, missing)
    11. missing
    13. julia> popat!(a, 4)
    14. ERROR: BoundsError: attempt to access 3-element Vector{Int64} at index [4]
    15. [...]

    source

    — Function

    1. pushfirst!(collection, items...) -> collection

    Insert one or more items at the beginning of collection.

    Examples

    1. julia> pushfirst!([1, 2, 3, 4], 5, 6)
    2. 6-element Vector{Int64}:
    3.  5
    4.  6
    5.  1
    6.  2
    7.  3
    8.  4

    source

    — Function

    1. popfirst!(collection) -> item

    Remove the first item from collection.

    Examples

    1. julia> A = [1, 2, 3, 4, 5, 6]
    2. 6-element Vector{Int64}:
    3.  1
    4.  2
    5.  3
    6.  4
    7.  5
    8.  6
    10. julia> popfirst!(A)
    11. 1
    13. julia> A
    14. 5-element Vector{Int64}:
    15.  2
    16.  3
    17.  4
    18.  5
    19.  6

    source

    — Function

    1. insert!(a::Vector, index::Integer, item)

    Insert an item into a at the given index. index is the index of item in the resulting a.

    Examples

    1. julia> insert!([6, 5, 4, 2, 1], 4, 3)
    2. 6-element Vector{Int64}:
    3.  6
    4.  5
    5.  4
    6.  3
    7.  2
    8.  1

    source

    — Function

    1. deleteat!(a::Vector, i::Integer)

    Remove the item at the given i and return the modified a. Subsequent items are shifted to fill the resulting gap.

    Examples

    1. julia> deleteat!([6, 5, 4, 3, 2, 1], 2)
    2. 5-element Vector{Int64}:
    3.  6
    4.  4
    5.  3
    6.  2
    7.  1

    source

    1. deleteat!(a::Vector, inds)

    Remove the items at the indices given by inds, and return the modified a. Subsequent items are shifted to fill the resulting gap.

    inds can be either an iterator or a collection of sorted and unique integer indices, or a boolean vector of the same length as a with true indicating entries to delete.

    Examples

    1. julia> deleteat!([6, 5, 4, 3, 2, 1], 1:2:5)
    2. 3-element Vector{Int64}:
    3.  5
    4.  3
    5.  1
    7. julia> deleteat!([6, 5, 4, 3, 2, 1], [true, false, true, false, true, false])
    8. 3-element Vector{Int64}:
    9.  5
    10.  3
    11.  1
    13. julia> deleteat!([6, 5, 4, 3, 2, 1], (2, 2))
    14. ERROR: ArgumentError: indices must be unique and sorted
    15. Stacktrace:
    16. [...]

    Base.splice! — Function

    1. splice!(a::Vector, index::Integer, [replacement]) -> item

    Remove the item at the given index, and return the removed item. Subsequent items are shifted left to fill the resulting gap. If specified, replacement values from an ordered collection will be spliced in place of the removed item.

    Examples

    1. julia> A = [6, 5, 4, 3, 2, 1]; splice!(A, 5)
    2. 2
    4. julia> A
    5. 5-element Vector{Int64}:
    6.  6
    7.  5
    8.  4
    9.  3
    10.  1
    12. julia> splice!(A, 5, -1)
    13. 1
    15. julia> A
    16. 5-element Vector{Int64}:
    17.   6
    18.   5
    19.   4
    20.   3
    21.  -1
    23. julia> splice!(A, 1, [-1, -2, -3])
    24. 6
    26. julia> A
    27. 7-element Vector{Int64}:
    28.  -1
    29.  -2
    30.  -3
    31.   5
    32.   4
    33.   3
    34.  -1

    To insert replacement before an index n without removing any items, use splice!(collection, n:n-1, replacement).

    1. splice!(a::Vector, indices, [replacement]) -> items

    Remove items at specified indices, and return a collection containing the removed items. Subsequent items are shifted left to fill the resulting gaps. If specified, replacement values from an ordered collection will be spliced in place of the removed items; in this case, indices must be a UnitRange.

    To insert replacement before an index n without removing any items, use splice!(collection, n:n-1, replacement).

    Julia 1.5

    Prior to Julia 1.5, indices must always be a UnitRange.

    Examples

    1. julia> A = [-1, -2, -3, 5, 4, 3, -1]; splice!(A, 4:3, 2)
    2. Int64[]
    4. julia> A
    5. 8-element Vector{Int64}:
    6.  -1
    7.  -2
    8.  -3
    9.   2
    10.   5
    11.   4
    12.   3
    13.  -1

    source

    — Function

    1. resize!(a::Vector, n::Integer) -> Vector

    Resize a to contain n elements. If n is smaller than the current collection length, the first n elements will be retained. If n is larger, the new elements are not guaranteed to be initialized.

    Examples

    1. julia> resize!([6, 5, 4, 3, 2, 1], 3)
    2. 3-element Vector{Int64}:
    3.  6
    4.  5
    5.  4
    7. julia> a = resize!([6, 5, 4, 3, 2, 1], 8);
    9. julia> length(a)
    10. 8
    12. julia> a[1:6]
    13. 6-element Vector{Int64}:
    14.  6
    15.  5
    16.  4
    17.  3
    18.  2
    19.  1

    source

    — Function

    1. append!(collection, collections...) -> collection.

    For an ordered container collection, add the elements of each collections to the end of it.

    Julia 1.6

    Specifying multiple collections to be appended requires at least Julia 1.6.

    Examples

    1. julia> append!([1], [2, 3])
    2. 3-element Vector{Int64}:
    3.  1
    4.  2
    5.  3
    7. julia> append!([1, 2, 3], [4, 5], [6])
    8. 6-element Vector{Int64}:
    9.  1
    10.  2
    11.  3
    12.  4
    13.  5
    14.  6

    Use push! to add individual items to collection which are not already themselves in another collection. The result of the preceding example is equivalent to push!([1, 2, 3], 4, 5, 6).

    See for notes about the performance model.

    source

    — Function

    1. prepend!(a::Vector, collections...) -> collection

    Insert the elements of each collections to the beginning of a.

    When collections specifies multiple collections, order is maintained: elements of collections[1] will appear leftmost in a, and so on.

    Julia 1.6

    Specifying multiple collections to be prepended requires at least Julia 1.6.

    Examples

    1. julia> prepend!([3], [1, 2])
    2. 3-element Vector{Int64}:
    3.  1
    4.  2
    5.  3
    7. julia> prepend!([6], [1, 2], [3, 4, 5])
    8. 6-element Vector{Int64}:
    9.  1
    10.  2
    11.  3
    12.  4
    13.  5
    14.  6

    source

    Fully implemented by:

    • Vector (a.k.a. 1-dimensional )
    • BitVector (a.k.a. 1-dimensional BitArray)

    Utility Collections

    — Type

    1. Pair(x, y)
    2. x => y

    Construct a Pair object with type Pair{typeof(x), typeof(y)}. The elements are stored in the fields first and second. They can also be accessed via iteration (but a Pair is treated as a single “scalar” for broadcasting operations).

    See also: Dict

    Examples

    1. julia> p = "foo" => 7
    2. "foo" => 7
    4. julia> typeof(p)
    5. Pair{String, Int64}
    7. julia> p.first
    8. "foo"
    10. julia> for x in p
    11.            println(x)
    12.        end
    13. 7

    Base.Iterators.Pairs — Type

    Transforms an indexable container into an Dictionary-view of the same data. Modifying the key-space of the underlying data may invalidate this object.