Collections and Data Structures

Iteration

Sequential iteration is implemented by the methods start, done, and next. The general for loop:

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

is translated into:

state = start(I)
while !done(I, state)
    (i, state) = next(I, state)
    # body
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.start — Function.

start(iter) -> state

Get initial iteration state for an iterable object.

Examples

julia> start(1:5)
1

julia> start([1;2;3])
1

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

source

Base.done — Function.

done(iter, state) -> Bool

Test whether we are done iterating.

Examples

julia> done(1:5, 3)
false

julia> done(1:5, 5)
false

julia> done(1:5, 6)
true

source

Base.next — Function.

next(iter, state) -> item, state

For a given iterable object and iteration state, return the current item and the next iteration state.

Examples

julia> next(1:5, 3)
(3, 4)

julia> next(1:5, 5)
(5, 6)

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

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

Base.empty! — Function.

empty!(collection) -> collection

Remove all elements from a collection.

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

length(s::AbstractString) -> Int
length(s::AbstractString, i::Integer, j::Integer) -> Int

The number of characters in string s from indices i through j. This is computed as the number of code unit indices from i to j which are valid character indices. Without only a single string argument, this computes the number of characters in the entire string. With i and j arguments it computes the number of indices between i and j inclusive that are valid indices in the string s. In addition to in-bounds values, i may take the out-of-bounds value ncodeunits(s) + 1 and j may take the out-of-bounds value 0.

Examples

julia> length("jμΛIα")
5

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
∉(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, Sets check whether the item isequal to one of the elements. Dicts 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.

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.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, dim::Int)

Return unique regions of A along dimension dim.

Examples

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

[:, :, 2] =
  true   true
 false  false

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

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

[:, :, 2] =
  true
 false

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

source

Base.unique! — Function.

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, v0, itr)

Reduce the given collection itr with the given binary operator op. v0 must be a neutral element for op that will be returned for empty collections. It is unspecified whether v0 is used for non-empty collections.

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(*, 1, [2; 3; 4])
24

source

Base.reduce — Method.

reduce(op, itr)

Like reduce(op, v0, itr). This cannot be used with empty collections, except for some special cases (e.g. when op is one of +, *, max, min, &, |) when Julia can determine the neutral element of op.

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

source

Base.foldl — Method.

foldl(op, v0, itr)

Like reduce, but with guaranteed left associativity. v0 will be used exactly once.

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

source

Base.foldl — Method.

foldl(op, itr)

Like foldl(op, v0, itr), but using the first element of itr as v0. In general, this cannot be used with empty collections (see reduce(op, itr)).

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

source

Base.foldr — Method.

foldr(op, v0, itr)

Like reduce, but with guaranteed right associativity. v0 will be used exactly once.

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

source

Base.foldr — Method.

foldr(op, itr)

Like foldr(op, v0, itr), but using the last element of itr as v0. In general, this cannot be used with empty collections (see reduce(op, itr)).

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

source

Base.maximum — Function.

maximum(itr)

Returns the largest element in a collection.

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).

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(itr)

Returns the smallest element in a collection.

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 — Method.

extrema(itr) -> Tuple

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

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

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

source

Base.extrema — Method.

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

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

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

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

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.

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.

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.

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

source

prod(itr)

Returns the product of all elements of a collection.

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.

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

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.

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}:
 true  false
 true  false

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.

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

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.

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}:
 true  false
 true  false

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).

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

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

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.

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.

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.

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:

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.

Dicts 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.Dict — Type.

Dict([itr])

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

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

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, and thus may be garbage collected even when referenced in a hash table.

See Dict for further help.

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.

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.

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(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

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

Set-Like Collections

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 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 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)
⊆(a,b) -> Bool
⊈(a,b) -> Bool
⊊(a,b) -> Bool

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

Examples

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

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

source

Fully implemented by:

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> 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 is of the preceding example is equivalent to push!([1, 2, 3], 4, 5, 6).

source

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

source

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.