Collections and Data Structures · The Julia Language

Collections and Data Structures

# Collections and Data Structures

## Iteration

Sequential iteration is implemented by the `iterate` function. The general `for` loop:

    for i in iter   # or  "for i = iter"
        # body
    end

is translated into:

    next = iterate(iter)
    while next !== nothing
        (i, state) = next
        # body
        next = iterate(iter, state)
    end

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

`Base.iterate` — Function.

    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.

source
`Base.IteratorSize` — Type.

    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 `axes` 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.

    julia> Base.IteratorSize(1:5)
    Base.HasShape{1}()

    julia> Base.IteratorSize((2,3))
    Base.HasLength()

source
`Base.IteratorEltype` — Type.

    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 `eltype` 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.

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

source

Fully implemented by:

- `AbstractRange`
- `UnitRange`
- `Tuple`
- `Number`
- `AbstractArray`
- `BitSet`
- `IdDict`
- `Dict`
- `WeakKeyDict`
- `EachLine`
- `AbstractString`
- `Set`
- `Pair`
- `NamedTuple`

## Constructors and Types

`Base.AbstractRange` — Type.

    AbstractRange{T}

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

source
`Base.OrdinalRange` — Type.

    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)`. `UnitRange`, `StepRange`, and other types are subtypes of this.

source
`Base.AbstractUnitRange` — Type.

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

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

source
`Base.StepRange` — Type.

    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

    julia> collect(StepRange(1, Int8(2), 10))
    5-element Array{Int64,1}:
     1
     3
     5
     7
     9

    julia> typeof(StepRange(1, Int8(2), 10))
    StepRange{Int64,Int8}

    julia> typeof(1:3:6)
    StepRange{Int64,Int64}

source
`Base.UnitRange` — Type.

    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 `Integer`s creates a `UnitRange`.

Examples

    julia> collect(UnitRange(2.3, 5.2))
    3-element Array{Float64,1}:
     2.3
     3.3
     4.3

    julia> typeof(1:10)
    UnitRange{Int64}

source
`Base.LinRange` — Type.

    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

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

source

## General Collections

`Base.isempty` — Function.

    isempty(collection) -> Bool

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

Examples

    julia> isempty([])
    true

    julia> isempty([1 2 3])
    false

source

    isempty(condition)

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

source
`Base.empty!` — Function.

    empty!(collection) -> collection

Remove all elements from a `collection`.

Examples

    julia> A = Dict("a" => 1, "b" => 2)
    Dict{String,Int64} with 2 entries:
      "b" => 2
      "a" => 1

    julia> empty!(A);

    julia> A
    Dict{String,Int64} with 0 entries

source
`Base.length` — Function.

    length(collection) -> Integer

Return the number of elements in the collection.

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

Examples

    julia> length(1:5)
    5

    julia> length([1, 2, 3, 4])
    4

    julia> length([1 2; 3 4])
    4

source

Fully implemented by:

- `AbstractRange`
- `UnitRange`
- `Tuple`
- `Number`
- `AbstractArray`
- `BitSet`
- `IdDict`
- `Dict`
- `WeakKeyDict`
- `AbstractString`
- `Set`
- `NamedTuple`

## Iterable Collections

`Base.in` — Function.

    in(item, collection) -> Bool
    ∈(item, collection) -> Bool
    ∋(collection, item) -> 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 (three-valued logic, matching the behavior of `any` and `==`).

Some collections follow a slightly different definition. For example, `Set`s check whether the item `isequal` to one of the elements. `Dict`s look for `key=>value` pairs, and the key is compared using `isequal`. 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`.

Examples

    julia> a = 1:3:20
    1:3:19

    julia> 4 in a
    true

    julia> 5 in a
    false

    julia> missing in [1, 2]
    missing

    julia> 1 in [2, missing]
    missing

    julia> 1 in [1, missing]
    true

    julia> missing in Set([1, 2])
    false

source
`Base.:∉` — Function.

    ∉(item, collection) -> Bool
    ∌(collection, item) -> Bool

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

Examples

    julia> 1 ∉ 2:4
    true

    julia> 1 ∉ 1:3
    false

source
`Base.eltype` — Function.

    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

    julia> eltype(fill(1f0, (2,2)))
    Float32

    julia> eltype(fill(0x1, (2,2)))
    UInt8

source
`Base.indexin` — Function.

    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

    julia> a = ['a', 'b', 'c', 'b', 'd', 'a'];

    julia> b = ['a', 'b', 'c'];

    julia> indexin(a, b)
    6-element Array{Union{Nothing, Int64},1}:
     1
     2
     3
     2
      nothing
     1

    julia> indexin(b, a)
    3-element Array{Union{Nothing, Int64},1}:
     1
     2
     3

source
`Base.unique` — Function.

    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

    julia> unique([1, 2, 6, 2])
    3-element Array{Int64,1}:
     1
     2
     6

    julia> unique(Real[1, 1.0, 2])
    2-element Array{Real,1}:
     1
     2

source

    unique(f, itr)

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

Examples

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

source

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

Return unique regions of `A` along dimension `dims`.

Examples

    julia> A = map(isodd, reshape(Vector(1:8), (2,2,2)))
    2×2×2 Array{Bool,3}:
    [:, :, 1] =
     1  1
     0  0

    [:, :, 2] =
     1  1
     0  0

    julia> unique(A)
    2-element Array{Bool,1}:
     1
     0

    julia> unique(A, dims=2)
    2×1×2 Array{Bool,3}:
    [:, :, 1] =
     1
     0

    [:, :, 2] =
     1
     0

    julia> unique(A, dims=3)
    2×2×1 Array{Bool,3}:
    [:, :, 1] =
     1  1
     0  0

source
`Base.unique!` — Function.

    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

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

    julia> unique!(n -> n%3, [5, 1, 8, 9, 3, 4, 10, 7, 2, 6])
    3-element Array{Int64,1}:
     5
     1
     9

    julia> unique!(iseven, [2, 3, 5, 7, 9])
    2-element Array{Int64,1}:
     2
     3

source

    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

    julia> unique!([1, 1, 1])
    1-element Array{Int64,1}:
     1

    julia> A = [7, 3, 2, 3, 7, 5];

    julia> unique!(A)
    4-element Array{Int64,1}:
     7
     3
     2
     5

    julia> B = [7, 6, 42, 6, 7, 42];

    julia> sort!(B);  # unique! is able to process sorted data much more efficiently.

    julia> unique!(B)
    3-element Array{Int64,1}:
      6
      7
     42

source
`Base.allunique` — Function.

    allunique(itr) -> Bool

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

Examples

    julia> a = [1; 2; 3]
    3-element Array{Int64,1}:
     1
     2
     3

    julia> allunique([a, a])
    false

source
`Base.reduce` — Method.

    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 `foldr` 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

    julia> reduce(*, [2; 3; 4])
    24

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

source
`Base.foldl` — Method.

    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

    julia> foldl(=>, 1:4)
    ((1 => 2) => 3) => 4

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

source
`Base.foldr` — Method.

    foldr(op, itr; [init])

Like `reduce`, 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

    julia> foldr(=>, 1:4)
    1 => (2 => (3 => 4))

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

source
`Base.maximum` — Function.

    maximum(f, itr)

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

Examples

    julia> maximum(length, ["Julion", "Julia", "Jule"])
    6

source

    maximum(itr)

Returns the largest element in a collection.

Examples

    julia> maximum(-20.5:10)
    9.5

    julia> maximum([1,2,3])
    3

source

    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

    julia> A = [1 2; 3 4]
    2×2 Array{Int64,2}:
     1  2
     3  4

    julia> maximum(A, dims=1)
    1×2 Array{Int64,2}:
     3  4

    julia> maximum(A, dims=2)
    2×1 Array{Int64,2}:
     2
     4

source
`Base.maximum!` — Function.

    maximum!(r, A)

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

Examples

    julia> A = [1 2; 3 4]
    2×2 Array{Int64,2}:
     1  2
     3  4

    julia> maximum!([1; 1], A)
    2-element Array{Int64,1}:
     2
     4

    julia> maximum!([1 1], A)
    1×2 Array{Int64,2}:
     3  4

source
`Base.minimum` — Function.

    minimum(f, itr)

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

Examples

    julia> minimum(length, ["Julion", "Julia", "Jule"])
    4

source

    minimum(itr)

Returns the smallest element in a collection.

Examples

    julia> minimum(-20.5:10)
    -20.5

    julia> minimum([1,2,3])
    1

source

    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

    julia> A = [1 2; 3 4]
    2×2 Array{Int64,2}:
     1  2
     3  4

    julia> minimum(A, dims=1)
    1×2 Array{Int64,2}:
     1  2

    julia> minimum(A, dims=2)
    2×1 Array{Int64,2}:
     1
     3

source
`Base.minimum!` — Function.

    minimum!(r, A)

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

Examples

    julia> A = [1 2; 3 4]
    2×2 Array{Int64,2}:
     1  2
     3  4

    julia> minimum!([1; 1], A)
    2-element Array{Int64,1}:
     1
     3

    julia> minimum!([1 1], A)
    1×2 Array{Int64,2}:
     1  2

source
`Base.extrema` — Function.

    extrema(itr) -> Tuple

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

Examples

    julia> extrema(2:10)
    (2, 10)

    julia> extrema([9,pi,4.5])
    (3.141592653589793, 9.0)

source

    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

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

source

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

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

Examples

    julia> A = reshape(Vector(1:2:16), (2,2,2))
    2×2×2 Array{Int64,3}:
    [:, :, 1] =
     1  5
     3  7

    [:, :, 2] =
      9  13
     11  15

    julia> extrema(A, dims = (1,2))
    1×1×2 Array{Tuple{Int64,Int64},3}:
    [:, :, 1] =
     (1, 7)

    [:, :, 2] =
     (9, 15)

source

    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.

source
`Base.argmax` — Function.

    argmax(itr) -> Integer

Return the index 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

    julia> argmax([8,0.1,-9,pi])
    1

    julia> argmax([1,7,7,6])
    2

    julia> argmax([1,7,7,NaN])
    4

source

    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

    julia> A = [1.0 2; 3 4]
    2×2 Array{Float64,2}:
     1.0  2.0
     3.0  4.0

    julia> argmax(A, dims=1)
    1×2 Array{CartesianIndex{2},2}:
     CartesianIndex(2, 1)  CartesianIndex(2, 2)

    julia> argmax(A, dims=2)
    2×1 Array{CartesianIndex{2},2}:
     CartesianIndex(1, 2)
     CartesianIndex(2, 2)

source
`Base.argmin` — Function.

    argmin(itr) -> Integer

Return the index 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

    julia> argmin([8,0.1,-9,pi])
    3

    julia> argmin([7,1,1,6])
    2

    julia> argmin([7,1,1,NaN])
    4

source

    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

    julia> A = [1.0 2; 3 4]
    2×2 Array{Float64,2}:
     1.0  2.0
     3.0  4.0

    julia> argmin(A, dims=1)
    1×2 Array{CartesianIndex{2},2}:
     CartesianIndex(1, 1)  CartesianIndex(1, 2)

    julia> argmin(A, dims=2)
    2×1 Array{CartesianIndex{2},2}:
     CartesianIndex(1, 1)
     CartesianIndex(2, 1)

source
`Base.findmax` — Function.

    findmax(itr) -> (x, index)

Return the maximum element of the collection `itr` and its index. 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

    julia> findmax([8,0.1,-9,pi])
    (8.0, 1)

    julia> findmax([1,7,7,6])
    (7, 2)

    julia> findmax([1,7,7,NaN])
    (NaN, 4)

source

    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

    julia> A = [1.0 2; 3 4]
    2×2 Array{Float64,2}:
     1.0  2.0
     3.0  4.0

    julia> findmax(A, dims=1)
    ([3.0 4.0], CartesianIndex{2}[CartesianIndex(2, 1) CartesianIndex(2, 2)])

    julia> findmax(A, dims=2)
    ([2.0; 4.0], CartesianIndex{2}[CartesianIndex(1, 2); CartesianIndex(2, 2)])

source
`Base.findmin` — Function.

    findmin(itr) -> (x, index)

Return the minimum element of the collection `itr` and its index. 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

    julia> findmin([8,0.1,-9,pi])
    (-9.0, 3)

    julia> findmin([7,1,1,6])
    (1, 2)

    julia> findmin([7,1,1,NaN])
    (NaN, 4)

source

    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

    julia> A = [1.0 2; 3 4]
    2×2 Array{Float64,2}:
     1.0  2.0
     3.0  4.0

    julia> findmin(A, dims=1)
    ([1.0 2.0], CartesianIndex{2}[CartesianIndex(1, 1) CartesianIndex(1, 2)])

    julia> findmin(A, dims=2)
    ([1.0; 3.0], CartesianIndex{2}[CartesianIndex(1, 1); CartesianIndex(2, 1)])

source
`Base.findmax!` — Function.

    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.

source
`Base.findmin!` — Function.

    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.

source
`Base.sum` — Function.

    sum(f, itr)

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.

Examples

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

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

    julia> sum(Int8[100, 28])
    128

    julia> reduce(+, Int8[100, 28])
    -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.

source

    sum(itr)

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.

Examples

    julia> sum(1:20)
    210

source

    sum(A::AbstractArray; dims)

Sum elements of an array over the given dimensions.

Examples

    julia> A = [1 2; 3 4]
    2×2 Array{Int64,2}:
     1  2
     3  4

    julia> sum(A, dims=1)
    1×2 Array{Int64,2}:
     4  6

    julia> sum(A, dims=2)
    2×1 Array{Int64,2}:
     3
     7

source
`Base.sum!` — Function.

    sum!(r, A)

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

Examples

    julia> A = [1 2; 3 4]
    2×2 Array{Int64,2}:
     1  2
     3  4

    julia> sum!([1; 1], A)
    2-element Array{Int64,1}:
     3
     7

    julia> sum!([1 1], A)
    1×2 Array{Int64,2}:
     4  6

source
`Base.prod` — Function.

    prod(f, itr)

Returns the product of `f` applied to 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.

Examples

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

source

    prod(itr)

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.

Examples

    julia> prod(1:20)
    2432902008176640000

source

    prod(A::AbstractArray; dims)

Multiply elements of an array over the given dimensions.

Examples

    julia> A = [1 2; 3 4]
    2×2 Array{Int64,2}:
     1  2
     3  4

    julia> prod(A, dims=1)
    1×2 Array{Int64,2}:
     3  8

    julia> prod(A, dims=2)
    2×1 Array{Int64,2}:
      2
     12

source
`Base.prod!` — Function.

    prod!(r, A)

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

Examples

    julia> A = [1 2; 3 4]
    2×2 Array{Int64,2}:
     1  2
     3  4

    julia> prod!([1; 1], A)
    2-element Array{Int64,1}:
      2
     12

    julia> prod!([1 1], A)
    1×2 Array{Int64,2}:
     3  8

source
`Base.any` — Method.

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

Examples

    julia> a = [true,false,false,true]
    4-element Array{Bool,1}:
     1
     0
     0
     1

    julia> any(a)
    true

    julia> any((println(i); v) for (i, v) in enumerate(a))
    1
    true

    julia> any([missing, true])
    true

    julia> any([false, missing])
    missing

source
`Base.any` — Method.

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

Examples

    julia> any(i->(4<=i<=6), [3,5,7])
    true

    julia> any(i -> (println(i); i > 3), 1:10)
    1
    2
    3
    4
    true

    julia> any(i -> i > 0, [1, missing])
    true

    julia> any(i -> i > 0, [-1, missing])
    missing

    julia> any(i -> i > 0, [-1, 0])
    false

source
`Base.any!` — Function.

    any!(r, A)

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

Examples

    julia> A = [true false; true false]
    2×2 Array{Bool,2}:
     1  0
     1  0

    julia> any!([1; 1], A)
    2-element Array{Int64,1}:
     1
     1

    julia> any!([1 1], A)
    1×2 Array{Int64,2}:
     1  0

source
`Base.all` — Method.

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

Examples

    julia> a = [true,false,false,true]
    4-element Array{Bool,1}:
     1
     0
     0
     1

    julia> all(a)
    false

    julia> all((println(i); v) for (i, v) in enumerate(a))
    1
    2
    false

    julia> all([missing, false])
    false

    julia> all([true, missing])
    missing

source
`Base.all` — Method.

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

Examples

    julia> all(i->(4<=i<=6), [4,5,6])
    true

    julia> all(i -> (println(i); i < 3), 1:10)
    1
    2
    3
    false

    julia> all(i -> i > 0, [1, missing])
    missing

    julia> all(i -> i > 0, [-1, missing])
    false

    julia> all(i -> i > 0, [1, 2])
    true

source
`Base.all!` — Function.

    all!(r, A)

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

Examples

    julia> A = [true false; true false]
    2×2 Array{Bool,2}:
     1  0
     1  0

    julia> all!([1; 1], A)
    2-element Array{Int64,1}:
     0
     0

    julia> all!([1 1], A)
    1×2 Array{Int64,2}:
     1  0

source
`Base.count` — Function.

    count(p, itr) -> Integer
    count(itr) -> Integer

Count the number of elements in `itr` for which predicate `p` returns `true`. If `p` is omitted, counts the number of `true` elements in `itr` (which should be a collection of boolean values).

Examples

    julia> count(i->(4<=i<=6), [2,3,4,5,6])
    3

    julia> count([true, false, true, true])
    3

source

    count(
        pattern::Union{AbstractString,Regex},
        string::AbstractString;
        overlap::Bool = false,
    )

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.

source
`Base.any` — Method.

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

Examples

    julia> any(i->(4<=i<=6), [3,5,7])
    true

    julia> any(i -> (println(i); i > 3), 1:10)
    1
    2
    3
    4
    true

    julia> any(i -> i > 0, [1, missing])
    true

    julia> any(i -> i > 0, [-1, missing])
    missing

    julia> any(i -> i > 0, [-1, 0])
    false

source
`Base.all` — Method.

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

Examples

    julia> all(i->(4<=i<=6), [4,5,6])
    true

    julia> all(i -> (println(i); i < 3), 1:10)
    1
    2
    3
    false

    julia> all(i -> i > 0, [1, missing])
    missing

    julia> all(i -> i > 0, [-1, missing])
    false

    julia> all(i -> i > 0, [1, 2])
    true

source
`Base.foreach` — Function.

    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

    julia> a = 1:3:7;

    julia> foreach(x -> println(x^2), a)
    1
    16
    49

source
`Base.map` — Function.

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

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

See also: `mapslices`

Examples

    julia> map(x -> x * 2, [1, 2, 3])
    3-element Array{Int64,1}:
     2
     4
     6

    julia> map(+, [1, 2, 3], [10, 20, 30])
    3-element Array{Int64,1}:
     11
     22
     33

source
`Base.map!` — Function.

    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

    julia> a = zeros(3);

    julia> map!(x -> x * 2, a, [1, 2, 3]);

    julia> a
    3-element Array{Float64,1}:
     2.0
     4.0
     6.0

source

    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 key type of `dict` then it will be converted to the key type if possible and otherwise raise an error.

Examples

```jldoctest julia> d = Dict(:a => 1, :b => 2) Dict{Symbol,Int64} with 2 entries: :a => 1 :b => 2

julia> map!(v -> v-1, values(d)) Dict{Symbol,Int64} with 2 entries: :a => 0 :b => 1 ```

source
`Base.mapreduce` — Method.

    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 `reduce` and `map`.

Julia 1.2

`mapreduce` with multiple iterators requires Julia 1.2 or later.

Examples

    julia> mapreduce(x->x^2, +, [1:3;]) # == 1 + 4 + 9
    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 `mapfoldl` or `mapfoldr` instead for guaranteed left or right associativity and invocation of `f` for every value.

source
`Base.mapfoldl` — Method.

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

Like `mapreduce`, 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.

source
`Base.mapfoldr` — Method.

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

Like `mapreduce`, 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.

source
`Base.first` — Function.

    first(coll)

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

Examples

    julia> first(2:2:10)
    2

    julia> first([1; 2; 3; 4])
    1

source

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

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

    julia> first("∀ϵ≠0: ϵ²>0", 0)
    ""

    julia> first("∀ϵ≠0: ϵ²>0", 1)
    "∀"

    julia> first("∀ϵ≠0: ϵ²>0", 3)
    "∀ϵ≠"

source
`Base.last` — Function.

    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 `AbstractRange` even if it is empty.

Examples

    julia> last(1:2:10)
    9

    julia> last([1; 2; 3; 4])
    4

source

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

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

    julia> last("∀ϵ≠0: ϵ²>0", 0)
    ""

    julia> last("∀ϵ≠0: ϵ²>0", 1)
    "0"

    julia> last("∀ϵ≠0: ϵ²>0", 3)
    "²>0"

source
`Base.front` — Function.

    front(x::Tuple)::Tuple

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

Examples

    julia> Base.front((1,2,3))
    (1, 2)

    julia> Base.front(())
    ERROR: ArgumentError: Cannot call front on an empty tuple.

source
`Base.tail` — Function.

    tail(x::Tuple)::Tuple

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

Examples

    julia> Base.tail((1,2,3))
    (2, 3)

    julia> Base.tail(())
    ERROR: ArgumentError: Cannot call tail on an empty tuple.

source
`Base.step` — Function.

    step(r)

Get the step size of an `AbstractRange` object.

Examples

    julia> step(1:10)
    1

    julia> step(1:2:10)
    2

    julia> step(2.5:0.3:10.9)
    0.3

    julia> step(range(2.5, stop=10.9, length=85))
    0.1

source
`Base.collect` — Method.

    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 `HasShape` trait, the result will have the same shape and number of dimensions as the argument.

Examples

    julia> collect(1:2:13)
    7-element Array{Int64,1}:
      1
      3
      5
      7
      9
     11
     13

source
`Base.collect` — Method.

    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

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

source
`Base.filter` — Function.

    filter(f, a::AbstractArray)

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

Examples

    julia> a = 1:10
    1:10

    julia> filter(isodd, a)
    5-element Array{Int64,1}:
     1
     3
     5
     7
     9

source

    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

    julia> d = Dict(1=>"a", 2=>"b")
    Dict{Int64,String} with 2 entries:
      2 => "b"
      1 => "a"

    julia> filter(p->isodd(p.first), d)
    Dict{Int64,String} with 1 entry:
      1 => "a"

source

    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

    julia> x = [1 2; missing 4]
    2×2 Array{Union{Missing, Int64},2}:
     1         2
      missing  4

    julia> filter(isodd, skipmissing(x))
    1-element Array{Int64,1}:
     1

source
`Base.filter!` — Function.

    filter!(f, a::AbstractVector)

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

Examples

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

source

    filter!(f, d::AbstractDict)

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

Example

    julia> d = Dict(1=>"a", 2=>"b", 3=>"c")
    Dict{Int64,String} with 3 entries:
      2 => "b"
      3 => "c"
      1 => "a"

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

source
`Base.replace` — Method.

    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 `isequal`. 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 `replace!`.

Examples

    julia> replace([1, 2, 1, 3], 1=>0, 2=>4, count=2)
    4-element Array{Int64,1}:
     0
     4
     1
     3

    julia> replace([1, missing], missing=>0)
    2-element Array{Int64,1}:
     1
     0

source
`Base.replace` — Method.

    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

    julia> replace(x -> isodd(x) ? 2x : x, [1, 2, 3, 4])
    4-element Array{Int64,1}:
     2
     2
     6
     4

    julia> replace(Dict(1=>2, 3=>4)) do kv
               first(kv) < 3 ? first(kv)=>3 : kv
           end
    Dict{Int64,Int64} with 2 entries:
      3 => 4
      1 => 3

source
`Base.replace!` — Function.

    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 `replace`.

Examples

    julia> replace!([1, 2, 1, 3], 1=>0, 2=>4, count=2)
    4-element Array{Int64,1}:
     0
     4
     1
     3

    julia> replace!(Set([1, 2, 3]), 1=>0)
    Set([0, 2, 3])

source

    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

    julia> replace!(x -> isodd(x) ? 2x : x, [1, 2, 3, 4])
    4-element Array{Int64,1}:
     2
     2
     6
     4

    julia> replace!(Dict(1=>2, 3=>4)) do kv
               first(kv) < 3 ? first(kv)=>3 : kv
           end
    Dict{Int64,Int64} with 2 entries:
      3 => 4
      1 => 3

    julia> replace!(x->2x, Set([3, 6]))
    Set([6, 12])

source

## Indexable Collections

`Base.getindex` — Function.

    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

    julia> A = Dict("a" => 1, "b" => 2)
    Dict{String,Int64} with 2 entries:
      "b" => 2
      "a" => 1

    julia> getindex(A, "a")
    1

source
`Base.setindex!` — Function.

    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)`.

source
`Base.firstindex` — Function.

    firstindex(collection) -> Integer
    firstindex(collection, d) -> Integer

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

Examples

    julia> firstindex([1,2,4])
    1

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

source
`Base.lastindex` — Function.

    lastindex(collection) -> Integer
    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

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

    julia> lastindex(rand(3,4,5), 2)
    4

source

Fully implemented by:

- `Array`
- `BitArray`
- `AbstractArray`
- `SubArray`

Partially implemented by:

- `AbstractRange`
- `UnitRange`
- `Tuple`
- `AbstractString`
- `Dict`
- `IdDict`
- `WeakKeyDict`
- `NamedTuple`

## Dictionaries

`Dict` is the standard dictionary. Its implementation uses `hash` as the hashing function for the key, and `isequal` 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.

`WeakKeyDict` 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.

`Dict`s can be created by passing pair objects constructed with `=>` to a `Dict` 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.

    AbstractDict{K, V}

Supertype for dictionary-like types with keys of type `K` and values of type `V`. `Dict`, `IdDict` and other types are subtypes of this.

source
`Base.Dict` — Type.

    Dict([itr])

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

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

Examples

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

Alternatively, a sequence of pair arguments may be passed.

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

source
`Base.IdDict` — Type.

    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.

source
`Base.WeakKeyDict` — Type.

    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 `Dict` for further help. Note, unlike `Dict`, `WeakKeyDict` does not convert keys on insertion.

source
`Base.ImmutableDict` — Type.

    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

    ImmutableDict(KV::Pair)

Create a new entry in the Immutable Dictionary for the 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

source
`Base.haskey` — Function.

    haskey(collection, key) -> Bool

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

Examples

    julia> D = Dict('a'=>2, 'b'=>3)
    Dict{Char,Int64} with 2 entries:
      'a' => 2
      'b' => 3

    julia> haskey(D, 'a')
    true

    julia> haskey(D, 'c')
    false

source
`Base.get` — Method.

    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

    julia> d = Dict("a"=>1, "b"=>2);

    julia> get(d, "a", 3)
    1

    julia> get(d, "c", 3)
    3

source
`Base.get` — Function.

    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

    julia> d = Dict("a"=>1, "b"=>2);

    julia> get(d, "a", 3)
    1

    julia> get(d, "c", 3)
    3

source

    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 `get!` to also store the default value in the dictionary.

This is intended to be called using `do` block syntax

    get(dict, key) do
        # default value calculated here
        time()
    end

source
`Base.get!` — Method.

    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

    julia> d = Dict("a"=>1, "b"=>2, "c"=>3);

    julia> get!(d, "a", 5)
    1

    julia> get!(d, "d", 4)
    4

    julia> d
    Dict{String,Int64} with 4 entries:
      "c" => 3
      "b" => 2
      "a" => 1
      "d" => 4

source
`Base.get!` — Method.

    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:

    get!(dict, key) do
        # default value calculated here
        time()
    end

source
`Base.getkey` — Function.

    getkey(collection, key, default)

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

Examples

    julia> D = Dict('a'=>2, 'b'=>3)
    Dict{Char,Int64} with 2 entries:
      'a' => 2
      'b' => 3

    julia> getkey(D, 'a', 1)
    'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)

    julia> getkey(D, 'd', 'a')
    'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)

source
`Base.delete!` — Function.

    delete!(collection, key)

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

Examples

    julia> d = Dict("a"=>1, "b"=>2)
    Dict{String,Int64} with 2 entries:
      "b" => 2
      "a" => 1

    julia> delete!(d, "b")
    Dict{String,Int64} with 1 entry:
      "a" => 1

source
`Base.pop!` — Method.

    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

    julia> d = Dict("a"=>1, "b"=>2, "c"=>3);

    julia> pop!(d, "a")
    1

    julia> pop!(d, "d")
    ERROR: KeyError: key "d" not found
    Stacktrace:
    [...]

    julia> pop!(d, "e", 4)
    4

source
`Base.keys` — Function.

    keys(iterator)

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

source
`Base.values` — Function.

    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

    julia> d = Dict("a"=>1, "b"=>2);

    julia> values(d)
    Base.ValueIterator for a Dict{String,Int64} with 2 entries. Values:
      2
      1

    julia> values([2])
    1-element Array{Int64,1}:
     2

source

    values(a::AbstractDict)

Return an iterator over all values in a collection. `collect(values(a))` returns an array of values. Since the values are stored internally in a hash table, 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

    julia> D = Dict('a'=>2, 'b'=>3)
    Dict{Char,Int64} with 2 entries:
      'a' => 2
      'b' => 3

    julia> collect(values(D))
    2-element Array{Int64,1}:
     2
     3

source
`Base.pairs` — Function.

    pairs(IndexLinear(), A)
    pairs(IndexCartesian(), A)
    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 `IndexLinear()` ensures that `i` will be an integer; specifying `IndexCartesian()` ensures that `i` will be a `CartesianIndex`; 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

    julia> A = ["a" "d"; "b" "e"; "c" "f"];

    julia> for (index, value) in pairs(IndexStyle(A), A)
               println("$index $value")
           end
    1 a
    2 b
    3 c
    4 d
    5 e
    6 f

    julia> S = view(A, 1:2, :);

    julia> for (index, value) in pairs(IndexStyle(S), S)
               println("$index $value")
           end
    CartesianIndex(1, 1) a
    CartesianIndex(2, 1) b
    CartesianIndex(1, 2) d
    CartesianIndex(2, 2) e

See also: `IndexStyle`, `axes`.

source

    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.

source
`Base.merge` — Function.

    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.

Examples

    julia> a = Dict("foo" => 0.0, "bar" => 42.0)
    Dict{String,Float64} with 2 entries:
      "bar" => 42.0
      "foo" => 0.0

    julia> b = Dict("baz" => 17, "bar" => 4711)
    Dict{String,Int64} with 2 entries:
      "bar" => 4711
      "baz" => 17

    julia> merge(a, b)
    Dict{String,Float64} with 3 entries:
      "bar" => 4711.0
      "baz" => 17.0
      "foo" => 0.0

    julia> merge(b, a)
    Dict{String,Float64} with 3 entries:
      "bar" => 42.0
      "baz" => 17.0
      "foo" => 0.0

source

    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.

Examples

    julia> a = Dict("foo" => 0.0, "bar" => 42.0)
    Dict{String,Float64} with 2 entries:
      "bar" => 42.0
      "foo" => 0.0

    julia> b = Dict("baz" => 17, "bar" => 4711)
    Dict{String,Int64} with 2 entries:
      "bar" => 4711
      "baz" => 17

    julia> merge(+, a, b)
    Dict{String,Float64} with 3 entries:
      "bar" => 4753.0
      "baz" => 17.0
      "foo" => 0.0

source

    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

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

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

source

    merge(a::NamedTuple, iterable)

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

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

source
`Base.merge!` — Method.

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

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

Examples

    julia> d1 = Dict(1 => 2, 3 => 4);

    julia> d2 = Dict(1 => 4, 4 => 5);

    julia> merge!(d1, d2);

    julia> d1
    Dict{Int64,Int64} with 3 entries:
      4 => 5
      3 => 4
      1 => 4

source
`Base.merge!` — Method.

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

Update collection with pairs from the other collections. Values with the same key will be combined using the combiner function.

Examples

    julia> d1 = Dict(1 => 2, 3 => 4);

    julia> d2 = Dict(1 => 4, 4 => 5);

    julia> merge!(+, d1, d2);

    julia> d1
    Dict{Int64,Int64} with 3 entries:
      4 => 5
      3 => 4
      1 => 6

    julia> merge!(-, d1, d1);

    julia> d1
    Dict{Int64,Int64} with 3 entries:
      4 => 0
      3 => 0
      1 => 0

source
`Base.sizehint!` — Function.

    sizehint!(s, n)

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

source
`Base.keytype` — Function.

    keytype(T::Type{<:AbstractArray})
    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

    julia> keytype([1, 2, 3]) == Int
    true

    julia> keytype([1 2; 3 4])
    CartesianIndex{2}

Julia 1.2

For arrays, this function requires at least Julia 1.2.

source

    keytype(type)

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

Examples

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

source
`Base.valtype` — Function.

    valtype(T::Type{<:AbstractArray})
    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

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

Julia 1.2

For arrays, this function requires at least Julia 1.2.

source

    valtype(type)

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

Examples

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

source

Fully implemented by:

- `IdDict`
- `Dict`
- `WeakKeyDict`

Partially implemented by:

- `BitSet`
- `Set`
- `EnvDict`
- `Array`
- `BitArray`
- `ImmutableDict`
- `Iterators.Pairs`

## Set-Like Collections

`Base.AbstractSet` — Type.

    AbstractSet{T}

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

source
`Base.Set` — Type.

    Set([itr])

Construct a `Set` 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.

source
`Base.BitSet` — Type.

    BitSet([itr])

Construct a sorted set of `Int`s 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 `Set` instead.

source
`Base.union` — Function.

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

Construct the union of sets. Maintain order with arrays.

Examples

    julia> union([1, 2], [3, 4])
    4-element Array{Int64,1}:
     1
     2
     3
     4

    julia> union([1, 2], [2, 4])
    3-element Array{Int64,1}:
     1
     2
     4

    julia> union([4, 2], 1:2)
    3-element Array{Int64,1}:
     4
     2
     1

    julia> union(Set([1, 2]), 2:3)
    Set([2, 3, 1])

source
`Base.union!` — Function.

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

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

Examples

    julia> a = Set([1, 3, 4, 5]);

    julia> union!(a, 1:2:8);

    julia> a
    Set([7, 4, 3, 5, 1])

source
`Base.intersect` — Function.

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

Construct the intersection of sets. Maintain order with arrays.

Examples

    julia> intersect([1, 2, 3], [3, 4, 5])
    1-element Array{Int64,1}:
     3

    julia> intersect([1, 4, 4, 5, 6], [4, 6, 6, 7, 8])
    2-element Array{Int64,1}:
     4
     6

    julia> intersect(Set([1, 2]), BitSet([2, 3]))
    Set([2])

source
`Base.setdiff` — Function.

    setdiff(s, itrs...)

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

Examples

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

source
`Base.setdiff!` — Function.

    setdiff!(s, itrs...)

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

Examples

    julia> a = Set([1, 3, 4, 5]);

    julia> setdiff!(a, 1:2:6);

    julia> a
    Set([4])

source
`Base.symdiff` — Function.

    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

    julia> symdiff([1,2,3], [3,4,5], [4,5,6])
    3-element Array{Int64,1}:
     1
     2
     6

    julia> symdiff([1,2,1], [2, 1, 2])
    2-element Array{Int64,1}:
     1
     2

    julia> symdiff(unique([1,2,1]), unique([2, 1, 2]))
    0-element Array{Int64,1}

source
`Base.symdiff!` — Function.

    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
`Base.intersect!` — Function.

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

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

source
`Base.issubset` — Function.

    issubset(a, b) -> Bool
    ⊆(a, b) -> Bool
    ⊇(b, a) -> Bool

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

Examples

    julia> issubset([1, 2], [1, 2, 3])
    true

    julia> [1, 2, 3] ⊆ [1, 2]
    false

    julia> [1, 2, 3] ⊇ [1, 2]
    true

source
`Base.:⊈` — Function.

    ⊈(a, b) -> Bool
    ⊉(b, a) -> Bool

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

Examples

    julia> (1, 2) ⊈ (2, 3)
    true

    julia> (1, 2) ⊈ (1, 2, 3)
    false

source
`Base.:⊊` — Function.

    ⊊(a, b) -> Bool
    ⊋(b, a) -> Bool

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

Examples

    julia> (1, 2) ⊊ (1, 2, 3)
    true

    julia> (1, 2) ⊊ (1, 2)
    false

source
`Base.issetequal` — Function.

    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

    julia> issetequal([1, 2], [1, 2, 3])
    false

    julia> issetequal([1, 2], [2, 1])
    true

source

Fully implemented by:

- `BitSet`
- `Set`

Partially implemented by:

- `Array`

## Dequeues

`Base.push!` — Function.

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

Insert one or more `items` at the end of `collection`.

Examples

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

Use `append!` to add all the elements of another collection to `collection`. The result of the preceding example is equivalent to `append!([1, 2, 3], [4, 5, 6])`.

source
`Base.pop!` — Function.

    pop!(collection) -> item

Remove an item in `collection` and return it. If `collection` is an ordered container, the last item is returned.

Examples

    julia> A=[1, 2, 3]
    3-element Array{Int64,1}:
     1
     2
     3

    julia> pop!(A)
    3

    julia> A
    2-element Array{Int64,1}:
     1
     2

    julia> S = Set([1, 2])
    Set([2, 1])

    julia> pop!(S)
    2

    julia> S
    Set([1])

    julia> pop!(Dict(1=>2))
    1 => 2

source

    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

    julia> d = Dict("a"=>1, "b"=>2, "c"=>3);

    julia> pop!(d, "a")
    1

    julia> pop!(d, "d")
    ERROR: KeyError: key "d" not found
    Stacktrace:
    [...]

    julia> pop!(d, "e", 4)
    4

source
`Base.pushfirst!` — Function.

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

Insert one or more `items` at the beginning of `collection`.

Examples

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

source
`Base.popfirst!` — Function.

    popfirst!(collection) -> item

Remove the first `item` from `collection`.

Examples

    julia> A = [1, 2, 3, 4, 5, 6]
    6-element Array{Int64,1}:
     1
     2
     3
     4
     5
     6

    julia> popfirst!(A)
    1

    julia> A
    5-element Array{Int64,1}:
     2
     3
     4
     5
     6

source
`Base.insert!` — Function.

    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

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

source
`Base.deleteat!` — Function.

    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

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

source

    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

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

    julia> deleteat!([6, 5, 4, 3, 2, 1], [true, false, true, false, true, false])
    3-element Array{Int64,1}:
     5
     3
     1

    julia> deleteat!([6, 5, 4, 3, 2, 1], (2, 2))
    ERROR: ArgumentError: indices must be unique and sorted
    Stacktrace:
    [...]

source
`Base.splice!` — Function.

    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

    julia> A = [6, 5, 4, 3, 2, 1]; splice!(A, 5)
    2

    julia> A
    5-element Array{Int64,1}:
     6
     5
     4
     3
     1

    julia> splice!(A, 5, -1)
    1

    julia> A
    5-element Array{Int64,1}:
      6
      5
      4
      3
     -1

    julia> splice!(A, 1, [-1, -2, -3])
    6

    julia> A
    7-element Array{Int64,1}:
     -1
     -2
     -3
      5
      4
      3
     -1

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

source

    splice!(a::Vector, range, [replacement]) -> items

Remove items in the specified index range, and return a collection containing the removed items. 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 items.

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

Examples

    julia> A = [-1, -2, -3, 5, 4, 3, -1]; splice!(A, 4:3, 2)
    0-element Array{Int64,1}

    julia> A
    8-element Array{Int64,1}:
     -1
     -2
     -3
      2
      5
      4
      3
     -1

source
`Base.resize!` — Function.

    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

    julia> resize!([6, 5, 4, 3, 2, 1], 3)
    3-element Array{Int64,1}:
     6
     5
     4

    julia> a = resize!([6, 5, 4, 3, 2, 1], 8);

    julia> length(a)
    8

    julia> a[1:6]
    6-element Array{Int64,1}:
     6
     5
     4
     3
     2
     1

source
`Base.append!` — Function.

    append!(collection, collection2) -> collection.

Add the elements of `collection2` to the end of `collection`.

Examples

    julia> append!([1],[2,3])
    3-element Array{Int64,1}:
     1
     2
     3

    julia> append!([1, 2, 3], [4, 5, 6])
    6-element Array{Int64,1}:
     1
     2
     3
     4
     5
     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)`.

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`Base.prepend!` — Function.

    prepend!(a::Vector, items) -> collection

Insert the elements of `items` to the beginning of `a`.

Examples

    julia> prepend!([3],[1,2])
    3-element Array{Int64,1}:
     1
     2
     3

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Fully implemented by:

- `Vector` (a.k.a. 1-dimensional `Array`)
- `BitVector` (a.k.a. 1-dimensional `BitArray`)

## Utility Collections

`Base.Pair` — Type.

    Pair(x, y)
    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

    julia> p = "foo" => 7
    "foo" => 7

    julia> typeof(p)
    Pair{String,Int64}

    julia> p.first
    "foo"

    julia> for x in p
               println(x)
           end
    foo
    7

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`Base.Iterators.Pairs` — Type.

    Iterators.Pairs(values, keys) <: AbstractDict{eltype(keys), eltype(values)}

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

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