方法

函数 中说到,函数是从参数多元组映射到返回值的对象,若没有合适返回值则抛出异常。实际中常需要对不同类型的参数做同样的运算,例如对整数做加法、对浮点数做加法、对整数与浮点数做加法,它们都是加法。在 Julia 中,它们都属于同一对象: + 函数。

对同一概念做一系列实现时,可以逐个定义特定参数类型、个数所对应的特定函数行为。 方法 是对函数中某一特定的行为定义。函数中可以定义多个方法。对一个特定的参数多元组调用函数时,最匹配此参数多元组的方法被调用。

函数调用时,选取调用哪个方法,被称为 重载 。 Julia 依据参数个数、类型来进行重载。

定义方法

Julia 的所有标准函数和运算符,如前面提到的 + 函数,都有许多针对各种参数类型组合和不同参数个数而定义的方法。

定义函数时,可以像 复合类型 中介绍的那样,使用 :: 类型断言运算符,选择性地对参数类型进行限制:

julia> f(x::Float64, y::Float64) = 2x + y;

此函数中参数 xy 只能是 Float64 类型:

julia> f(2.0, 3.0)
7.0

如果参数是其它类型,会引发 “no method” 错误:

julia> f(2.0, 3)
ERROR: `f` has no method matching f(::Float64, ::Int64)

julia> f(float32(2.0), 3.0)
ERROR: `f` has no method matching f(::Float32, ::Float64)

julia> f(2.0, "3.0")
ERROR: `f` has no method matching f(::Float64, ::ASCIIString)

julia> f("2.0", "3.0")
ERROR: `f` has no method matching f(::ASCIIString, ::ASCIIString)

有时需要写一些通用方法,这时应声明参数为抽象类型:

julia> f(x::Number, y::Number) = 2x - y;

julia> f(2.0, 3)
1.0

要想给一个函数定义多个方法,只需要多次定义这个函数,每次定义的参数个数和类型需不同。函数调用时,最匹配的方法被重载:

julia> f(2.0, 3.0)
7.0

julia> f(2, 3.0)
1.0

julia> f(2.0, 3)
1.0

julia> f(2, 3)
1

对非数值的值,或参数个数少于 2 , f 是未定义的,调用它会返回 “no method” 错误:

julia> f("foo", 3)
ERROR: `f` has no method matching f(::ASCIIString, ::Int64)

julia> f()
ERROR: `f` has no method matching f()

在交互式会话中输入函数对象本身,可以看到函数所存在的方法:

julia> f
f (generic function with 2 methods)

This output tells us that f is a function object with two methods. To find out what the signatures of those methods are, use the methods function:

julia> methods(f)
# 2 methods for generic function "f":
f(x::Float64,y::Float64) at none:1
f(x::Number,y::Number) at none:1

which shows that f has two methods, one taking two Float64 arguments and one taking arguments of type Number. It also indicates the file and line number where the methods were defined: because these methods were defined at the REPL, we get the apparent line number none:1.

定义类型时如果没使用 :: ,则方法参数的类型默认为 Any 。对 f 定义一个总括匹配的方法:

julia> f(x,y) = println("Whoa there, Nelly.");

julia> f("foo", 1)
Whoa there, Nelly.

总括匹配的方法,是重载时的最后选择。

重载是 Julia 最强大最核心的特性。核心运算一般都有好几十种方法:

julia> methods(+)
# 125 methods for generic function "+":
+(x::Bool) at bool.jl:36
+(x::Bool,y::Bool) at bool.jl:39
+(y::FloatingPoint,x::Bool) at bool.jl:49
+(A::BitArray{N},B::BitArray{N}) at bitarray.jl:848
+(A::Union(DenseArray{Bool,N},SubArray{Bool,N,A<:DenseArray{T,N},I<:(Union(Range{Int64},Int64)...,)}),B::Union(DenseArray{Bool,N},SubArray{Bool,N,A<:DenseArray{T,N},I<:(Union(Range{Int64},Int64)...,)})) at array.jl:797
+{S,T}(A::Union(SubArray{S,N,A<:DenseArray{T,N},I<:(Union(Range{Int64},Int64)...,)},DenseArray{S,N}),B::Union(SubArray{T,N,A<:DenseArray{T,N},I<:(Union(Range{Int64},Int64)...,)},DenseArray{T,N})) at array.jl:719
+{T<:Union(Int16,Int32,Int8)}(x::T<:Union(Int16,Int32,Int8),y::T<:Union(Int16,Int32,Int8)) at int.jl:16
+{T<:Union(Uint32,Uint16,Uint8)}(x::T<:Union(Uint32,Uint16,Uint8),y::T<:Union(Uint32,Uint16,Uint8)) at int.jl:20
+(x::Int64,y::Int64) at int.jl:33
+(x::Uint64,y::Uint64) at int.jl:34
+(x::Int128,y::Int128) at int.jl:35
+(x::Uint128,y::Uint128) at int.jl:36
+(x::Float32,y::Float32) at float.jl:119
+(x::Float64,y::Float64) at float.jl:120
+(z::Complex{T<:Real},w::Complex{T<:Real}) at complex.jl:110
+(x::Real,z::Complex{T<:Real}) at complex.jl:120
+(z::Complex{T<:Real},x::Real) at complex.jl:121
+(x::Rational{T<:Integer},y::Rational{T<:Integer}) at rational.jl:113
+(x::Char,y::Char) at char.jl:23
+(x::Char,y::Integer) at char.jl:26
+(x::Integer,y::Char) at char.jl:27
+(a::Float16,b::Float16) at float16.jl:132
+(x::BigInt,y::BigInt) at gmp.jl:194
+(a::BigInt,b::BigInt,c::BigInt) at gmp.jl:217
+(a::BigInt,b::BigInt,c::BigInt,d::BigInt) at gmp.jl:223
+(a::BigInt,b::BigInt,c::BigInt,d::BigInt,e::BigInt) at gmp.jl:230
+(x::BigInt,c::Uint64) at gmp.jl:242
+(c::Uint64,x::BigInt) at gmp.jl:246
+(c::Union(Uint32,Uint16,Uint8,Uint64),x::BigInt) at gmp.jl:247
+(x::BigInt,c::Union(Uint32,Uint16,Uint8,Uint64)) at gmp.jl:248
+(x::BigInt,c::Union(Int64,Int16,Int32,Int8)) at gmp.jl:249
+(c::Union(Int64,Int16,Int32,Int8),x::BigInt) at gmp.jl:250
+(x::BigFloat,c::Uint64) at mpfr.jl:147
+(c::Uint64,x::BigFloat) at mpfr.jl:151
+(c::Union(Uint32,Uint16,Uint8,Uint64),x::BigFloat) at mpfr.jl:152
+(x::BigFloat,c::Union(Uint32,Uint16,Uint8,Uint64)) at mpfr.jl:153
+(x::BigFloat,c::Int64) at mpfr.jl:157
+(c::Int64,x::BigFloat) at mpfr.jl:161
+(x::BigFloat,c::Union(Int64,Int16,Int32,Int8)) at mpfr.jl:162
+(c::Union(Int64,Int16,Int32,Int8),x::BigFloat) at mpfr.jl:163
+(x::BigFloat,c::Float64) at mpfr.jl:167
+(c::Float64,x::BigFloat) at mpfr.jl:171
+(c::Float32,x::BigFloat) at mpfr.jl:172
+(x::BigFloat,c::Float32) at mpfr.jl:173
+(x::BigFloat,c::BigInt) at mpfr.jl:177
+(c::BigInt,x::BigFloat) at mpfr.jl:181
+(x::BigFloat,y::BigFloat) at mpfr.jl:328
+(a::BigFloat,b::BigFloat,c::BigFloat) at mpfr.jl:339
+(a::BigFloat,b::BigFloat,c::BigFloat,d::BigFloat) at mpfr.jl:345
+(a::BigFloat,b::BigFloat,c::BigFloat,d::BigFloat,e::BigFloat) at mpfr.jl:352
+(x::MathConst{sym},y::MathConst{sym}) at constants.jl:23
+{T<:Number}(x::T<:Number,y::T<:Number) at promotion.jl:188
+{T<:FloatingPoint}(x::Bool,y::T<:FloatingPoint) at bool.jl:46
+(x::Number,y::Number) at promotion.jl:158
+(x::Integer,y::Ptr{T}) at pointer.jl:68
+(x::Bool,A::AbstractArray{Bool,N}) at array.jl:767
+(x::Number) at operators.jl:71
+(r1::OrdinalRange{T,S},r2::OrdinalRange{T,S}) at operators.jl:325
+{T<:FloatingPoint}(r1::FloatRange{T<:FloatingPoint},r2::FloatRange{T<:FloatingPoint}) at operators.jl:331
+(r1::FloatRange{T<:FloatingPoint},r2::FloatRange{T<:FloatingPoint}) at operators.jl:348
+(r1::FloatRange{T<:FloatingPoint},r2::OrdinalRange{T,S}) at operators.jl:349
+(r1::OrdinalRange{T,S},r2::FloatRange{T<:FloatingPoint}) at operators.jl:350
+(x::Ptr{T},y::Integer) at pointer.jl:66
+{S,T<:Real}(A::Union(SubArray{S,N,A<:DenseArray{T,N},I<:(Union(Range{Int64},Int64)...,)},DenseArray{S,N}),B::Range{T<:Real}) at array.jl:727
+{S<:Real,T}(A::Range{S<:Real},B::Union(SubArray{T,N,A<:DenseArray{T,N},I<:(Union(Range{Int64},Int64)...,)},DenseArray{T,N})) at array.jl:736
+(A::AbstractArray{Bool,N},x::Bool) at array.jl:766
+{Tv,Ti}(A::SparseMatrixCSC{Tv,Ti},B::SparseMatrixCSC{Tv,Ti}) at sparse/sparsematrix.jl:530
+{TvA,TiA,TvB,TiB}(A::SparseMatrixCSC{TvA,TiA},B::SparseMatrixCSC{TvB,TiB}) at sparse/sparsematrix.jl:522
+(A::SparseMatrixCSC{Tv,Ti<:Integer},B::Array{T,N}) at sparse/sparsematrix.jl:621
+(A::Array{T,N},B::SparseMatrixCSC{Tv,Ti<:Integer}) at sparse/sparsematrix.jl:623
+(A::SymTridiagonal{T},B::SymTridiagonal{T}) at linalg/tridiag.jl:45
+(A::Tridiagonal{T},B::Tridiagonal{T}) at linalg/tridiag.jl:207
+(A::Tridiagonal{T},B::SymTridiagonal{T}) at linalg/special.jl:99
+(A::SymTridiagonal{T},B::Tridiagonal{T}) at linalg/special.jl:98
+{T,MT,uplo}(A::Triangular{T,MT,uplo,IsUnit},B::Triangular{T,MT,uplo,IsUnit}) at linalg/triangular.jl:10
+{T,MT,uplo1,uplo2}(A::Triangular{T,MT,uplo1,IsUnit},B::Triangular{T,MT,uplo2,IsUnit}) at linalg/triangular.jl:11
+(Da::Diagonal{T},Db::Diagonal{T}) at linalg/diagonal.jl:44
+(A::Bidiagonal{T},B::Bidiagonal{T}) at linalg/bidiag.jl:92
+{T}(B::BitArray{2},J::UniformScaling{T}) at linalg/uniformscaling.jl:26
+(A::Diagonal{T},B::Bidiagonal{T}) at linalg/special.jl:89
+(A::Bidiagonal{T},B::Diagonal{T}) at linalg/special.jl:90
+(A::Diagonal{T},B::Tridiagonal{T}) at linalg/special.jl:89
+(A::Tridiagonal{T},B::Diagonal{T}) at linalg/special.jl:90
+(A::Diagonal{T},B::Triangular{T,S<:AbstractArray{T,2},UpLo,IsUnit}) at linalg/special.jl:89
+(A::Triangular{T,S<:AbstractArray{T,2},UpLo,IsUnit},B::Diagonal{T}) at linalg/special.jl:90
+(A::Diagonal{T},B::Array{T,2}) at linalg/special.jl:89
+(A::Array{T,2},B::Diagonal{T}) at linalg/special.jl:90
+(A::Bidiagonal{T},B::Tridiagonal{T}) at linalg/special.jl:89
+(A::Tridiagonal{T},B::Bidiagonal{T}) at linalg/special.jl:90
+(A::Bidiagonal{T},B::Triangular{T,S<:AbstractArray{T,2},UpLo,IsUnit}) at linalg/special.jl:89
+(A::Triangular{T,S<:AbstractArray{T,2},UpLo,IsUnit},B::Bidiagonal{T}) at linalg/special.jl:90
+(A::Bidiagonal{T},B::Array{T,2}) at linalg/special.jl:89
+(A::Array{T,2},B::Bidiagonal{T}) at linalg/special.jl:90
+(A::Tridiagonal{T},B::Triangular{T,S<:AbstractArray{T,2},UpLo,IsUnit}) at linalg/special.jl:89
+(A::Triangular{T,S<:AbstractArray{T,2},UpLo,IsUnit},B::Tridiagonal{T}) at linalg/special.jl:90
+(A::Tridiagonal{T},B::Array{T,2}) at linalg/special.jl:89
+(A::Array{T,2},B::Tridiagonal{T}) at linalg/special.jl:90
+(A::Triangular{T,S<:AbstractArray{T,2},UpLo,IsUnit},B::Array{T,2}) at linalg/special.jl:89
+(A::Array{T,2},B::Triangular{T,S<:AbstractArray{T,2},UpLo,IsUnit}) at linalg/special.jl:90
+(A::SymTridiagonal{T},B::Triangular{T,S<:AbstractArray{T,2},UpLo,IsUnit}) at linalg/special.jl:98
+(A::Triangular{T,S<:AbstractArray{T,2},UpLo,IsUnit},B::SymTridiagonal{T}) at linalg/special.jl:99
+(A::SymTridiagonal{T},B::Array{T,2}) at linalg/special.jl:98
+(A::Array{T,2},B::SymTridiagonal{T}) at linalg/special.jl:99
+(A::Diagonal{T},B::SymTridiagonal{T}) at linalg/special.jl:107
+(A::SymTridiagonal{T},B::Diagonal{T}) at linalg/special.jl:108
+(A::Bidiagonal{T},B::SymTridiagonal{T}) at linalg/special.jl:107
+(A::SymTridiagonal{T},B::Bidiagonal{T}) at linalg/special.jl:108
+{T<:Number}(x::AbstractArray{T<:Number,N}) at abstractarray.jl:358
+(A::AbstractArray{T,N},x::Number) at array.jl:770
+(x::Number,A::AbstractArray{T,N}) at array.jl:771
+(J1::UniformScaling{T<:Number},J2::UniformScaling{T<:Number}) at linalg/uniformscaling.jl:25
+(J::UniformScaling{T<:Number},B::BitArray{2}) at linalg/uniformscaling.jl:27
+(J::UniformScaling{T<:Number},A::AbstractArray{T,2}) at linalg/uniformscaling.jl:28
+(J::UniformScaling{T<:Number},x::Number) at linalg/uniformscaling.jl:29
+(x::Number,J::UniformScaling{T<:Number}) at linalg/uniformscaling.jl:30
+{TA,TJ}(A::AbstractArray{TA,2},J::UniformScaling{TJ}) at linalg/uniformscaling.jl:33
+{T}(a::HierarchicalValue{T},b::HierarchicalValue{T}) at pkg/resolve/versionweight.jl:19
+(a::VWPreBuildItem,b::VWPreBuildItem) at pkg/resolve/versionweight.jl:82
+(a::VWPreBuild,b::VWPreBuild) at pkg/resolve/versionweight.jl:120
+(a::VersionWeight,b::VersionWeight) at pkg/resolve/versionweight.jl:164
+(a::FieldValue,b::FieldValue) at pkg/resolve/fieldvalue.jl:41
+(a::Vec2,b::Vec2) at graphics.jl:60
+(bb1::BoundingBox,bb2::BoundingBox) at graphics.jl:123
+(a,b,c) at operators.jl:82
+(a,b,c,xs...) at operators.jl:83

重载和灵活的参数化类型系统一起,使得 Julia 可以抽象表达高级算法,不需关注实现的具体细节,生成有效率、运行时专用的代码。

方法歧义

函数方法的适用范围可能会重叠:

julia> g(x::Float64, y) = 2x + y;

julia> g(x, y::Float64) = x + 2y;
Warning: New definition
    g(Any,Float64) at none:1
is ambiguous with:
    g(Float64,Any) at none:1.
To fix, define
    g(Float64,Float64)
before the new definition.

julia> g(2.0, 3)
7.0

julia> g(2, 3.0)
8.0

julia> g(2.0, 3.0)
7.0

此处 g(2.0, 3.0) 既可以调用 g(Float64, Any) ,也可以调用 g(Any, Float64) ,两种方法没有优先级。遇到这种情况,Julia会警告定义含糊,但仍会任选一个方法来继续执行。应避免含糊的方法:

julia> g(x::Float64, y::Float64) = 2x + 2y;

julia> g(x::Float64, y) = 2x + y;

julia> g(x, y::Float64) = x + 2y;

julia> g(2.0, 3)
7.0

julia> g(2, 3.0)
8.0

julia> g(2.0, 3.0)
10.0

要消除 Julia 的警告,应先定义清晰的方法。

参数化方法

构造参数化方法,应在方法名与参数多元组之间,添加类型参数:

julia> same_type{T}(x::T, y::T) = true;

julia> same_type(x,y) = false;

这两个方法定义了一个布尔函数,它检查两个参数是否为同一类型:

julia> same_type(1, 2)
true

julia> same_type(1, 2.0)
false

julia> same_type(1.0, 2.0)
true

julia> same_type("foo", 2.0)
false

julia> same_type("foo", "bar")
true

julia> same_type(int32(1), int64(2))
false

类型参数可用于函数定义或函数体的任何地方:

julia> myappend{T}(v::Vector{T}, x::T) = [v..., x]
myappend (generic function with 1 method)

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

julia> myappend([1,2,3],2.5)
ERROR: `myappend` has no method matching myappend(::Array{Int64,1}, ::Float64)

julia> myappend([1.0,2.0,3.0],4.0)
4-element Array{Float64,1}:
 1.0
 2.0
 3.0
 4.0

julia> myappend([1.0,2.0,3.0],4)
ERROR: `myappend` has no method matching myappend(::Array{Float64,1}, ::Int64)

下例中,方法类型参数 T 被用作返回值:

julia> mytypeof{T}(x::T) = T
mytypeof (generic function with 1 method)

julia> mytypeof(1)
Int64

julia> mytypeof(1.0)
Float64

方法的类型参数也可以被限制范围:

same_type_numeric{T<:Number}(x::T, y::T) = true
same_type_numeric(x::Number, y::Number) = false

julia> same_type_numeric(1, 2)
true

julia> same_type_numeric(1, 2.0)
false

julia> same_type_numeric(1.0, 2.0)
true

julia> same_type_numeric("foo", 2.0)
no method same_type_numeric(ASCIIString,Float64)

julia> same_type_numeric("foo", "bar")
no method same_type_numeric(ASCIIString,ASCIIString)

julia> same_type_numeric(int32(1), int64(2))
false

same_type_numeric 函数与 same_type 大致相同,但只应用于数对儿。

关于可选参数和关键字参数

函数 中曾简略提到,可选参数是可由多方法定义语法的实现。例如:

f(a=1,b=2) = a+2b

可以翻译为下面三个方法:

f(a,b) = a+2b
f(a) = f(a,2)
f() = f(1,2)

关键字参数则与普通的与位置有关的参数不同。它们不用于方法重载。方法重载仅基于位置参数,选取了匹配的方法后,才处理关键字参数。