Add test_bases from QuantumOpticsBase and reorganize a bit

Author: akirakyle

src/QuantumInterface.jl

@@ -1,14 +1,33 @@
 module QuantumInterface
 
-import Base: ==, +, -, *, /, ^, length, one, exp, conj, conj!, transpose, copy
-import LinearAlgebra: tr, ishermitian, norm, normalize, normalize!
-import Base: show, summary
-import SparseArrays: sparse, spzeros, AbstractSparseMatrix # TODO move to an extension
+##
+# Basis specific
+##
+
+"""
+    basis(a)
+
+Return the basis of an object.
+
+If it's ambiguous, e.g. if an operator has a different left and right basis,
+an [`IncompatibleBases`](@ref) error is thrown.
+"""
+function basis end
+
+##
+# Standard methods
+##
 
 function apply! end
 
 function dagger end
 
+"""
+    directsum(x, y, z...)
+
+Direct sum of the given objects. Alternatively, the unicode
+symbol ⊕ (\\oplus) can be used.
+"""
 function directsum end
 const ⊕ = directsum
 directsum() = GenericBasis(0)
@@ -86,8 +105,9 @@ function squeeze end
 function wigner end
 
 
-include("bases.jl")
 include("abstract_types.jl")
+include("bases.jl")
+include("show.jl")
 
 include("linalg.jl")
 include("tensor.jl")

src/abstract_types.jl

@@ -1,3 +1,18 @@
+"""
+Abstract base class for all specialized bases.
+
+The Basis class is meant to specify a basis of the Hilbert space of the
+studied system. Besides basis specific information all subclasses must
+implement a shape variable which indicates the dimension of the used
+Hilbert space. For a spin-1/2 Hilbert space this would be the
+vector `[2]`. A system composed of two spins would then have a
+shape vector `[2 2]`.
+
+Composite systems can be defined with help of the [`CompositeBasis`](@ref)
+class.
+"""
+abstract type Basis end
+
 """
 Abstract base class for `Bra` and `Ket` states.
 
@@ -38,20 +53,3 @@ A_{br_1,br_2} = B_{bl_1,bl_2} S_{(bl_1,bl_2) ↔ (br_1,br_2)}
 ```
 """
 abstract type AbstractSuperOperator{B1,B2} end
-
-function summary(stream::IO, x::AbstractOperator)
-    print(stream, "$(typeof(x).name.name)(dim=$(length(x.basis_l))x$(length(x.basis_r)))\n")
-    if samebases(x)
-        print(stream, "  basis: ")
-        show(stream, basis(x))
-    else
-        print(stream, "  basis left:  ")
-        show(stream, x.basis_l)
-        print(stream, "\n  basis right: ")
-        show(stream, x.basis_r)
-    end
-end
-
-show(stream::IO, x::AbstractOperator) = summary(stream, x)
-
-traceout!(s::StateVector, i) = ptrace(s,i)

src/bases.jl

@@ -1,35 +1,10 @@
-"""
-Abstract base class for all specialized bases.
-
-The Basis class is meant to specify a basis of the Hilbert space of the
-studied system. Besides basis specific information all subclasses must
-implement a shape variable which indicates the dimension of the used
-Hilbert space. For a spin-1/2 Hilbert space this would be the
-vector `[2]`. A system composed of two spins would then have a
-shape vector `[2 2]`.
-
-Composite systems can be defined with help of the [`CompositeBasis`](@ref)
-class.
-"""
-abstract type Basis end
-
 """
     length(b::Basis)
 
 Total dimension of the Hilbert space.
 """
 Base.length(b::Basis) = prod(b.shape)
 
-"""
-    basis(a)
-
-Return the basis of an object.
-
-If it's ambiguous, e.g. if an operator has a different left and right basis,
-an [`IncompatibleBases`](@ref) error is thrown.
-"""
-function basis end
-
 
 """
     GenericBasis(N)
@@ -366,9 +341,9 @@ SumBasis(shape, bases::Vector) = (tmp = (bases...,); SumBasis(shape, tmp))
 SumBasis(bases::Vector) = SumBasis((bases...,))
 SumBasis(bases::Basis...) = SumBasis((bases...,))
 
-==(b1::T, b2::T) where T<:SumBasis = equal_shape(b1.shape, b2.shape)
-==(b1::SumBasis, b2::SumBasis) = false
-length(b::SumBasis) = sum(b.shape)
+Base.:(==)(b1::T, b2::T) where T<:SumBasis = equal_shape(b1.shape, b2.shape)
+Base.:(==)(b1::SumBasis, b2::SumBasis) = false
+Base.length(b::SumBasis) = sum(b.shape)
 
 """
     directsum(b1::Basis, b2::Basis)
@@ -393,62 +368,3 @@ function directsum(b1::SumBasis, b2::SumBasis)
     bases = [b1.bases...;b2.bases...]
     return SumBasis(shape, (bases...,))
 end
-
-embed(b::SumBasis, indices, ops) = embed(b, b, indices, ops)
-
-##
-# show methods
-##
-
-function show(stream::IO, x::GenericBasis)
-    if length(x.shape) == 1
-        write(stream, "Basis(dim=$(x.shape[1]))")
-    else
-        s = replace(string(x.shape), " " => "")
-        write(stream, "Basis(shape=$s)")
-    end
-end
-
-function show(stream::IO, x::CompositeBasis)
-    write(stream, "[")
-    for i in 1:length(x.bases)
-        show(stream, x.bases[i])
-        if i != length(x.bases)
-            write(stream, " ⊗ ")
-        end
-    end
-    write(stream, "]")
-end
-
-function show(stream::IO, x::SpinBasis)
-    d = denominator(x.spinnumber)
-    n = numerator(x.spinnumber)
-    if d == 1
-        write(stream, "Spin($n)")
-    else
-        write(stream, "Spin($n/$d)")
-    end
-end
-
-function show(stream::IO, x::FockBasis)
-    if iszero(x.offset)
-        write(stream, "Fock(cutoff=$(x.N))")
-    else
-        write(stream, "Fock(cutoff=$(x.N), offset=$(x.offset))")
-    end
-end
-
-function show(stream::IO, x::NLevelBasis)
-    write(stream, "NLevel(N=$(x.N))")
-end
-
-function show(stream::IO, x::SumBasis)
-    write(stream, "[")
-    for i in 1:length(x.bases)
-        show(stream, x.bases[i])
-        if i != length(x.bases)
-            write(stream, " ⊕ ")
-        end
-    end
-    write(stream, "]")
-end

src/embed_permute.jl

@@ -67,8 +67,8 @@ function embed(basis_l::CompositeBasis, basis_r::CompositeBasis,
     ops_sb = [x[2] for x in idxop_sb]
 
     for (idxsb, opsb) in zip(indices_sb, ops_sb)
-        (opsb.basis_l == basis_l.bases[idxsb]) || throw(IncompatibleBases())
-        (opsb.basis_r == basis_r.bases[idxsb]) || throw(IncompatibleBases())
+        (opsb.basis_l == basis_l.bases[idxsb]) || throw(IncompatibleBases()) # FIXME issue #12
+        (opsb.basis_r == basis_r.bases[idxsb]) || throw(IncompatibleBases()) # FIXME issue #12
     end
 
     S = length(operators) > 0 ? mapreduce(eltype, promote_type, operators) : Any
@@ -83,6 +83,8 @@ function embed(basis_l::CompositeBasis, basis_r::CompositeBasis,
     return embed_op
 end
 
+embed(b::SumBasis, indices, ops) = embed(b, b, indices, ops)
+
 permutesystems(a::AbstractOperator, perm) = arithmetic_unary_error("Permutations of subsystems", a)
 
 nsubsystems(s::AbstractKet) = nsubsystems(basis(s))

src/identityoperator.jl

@@ -1,4 +1,4 @@
-one(x::Union{<:Basis,<:AbstractOperator}) = identityoperator(x)
+Base.one(x::Union{<:Basis,<:AbstractOperator}) = identityoperator(x)
 
 """
     identityoperator(a::Basis[, b::Basis])
@@ -22,4 +22,4 @@ identityoperator(::Type{T}, ::Type{Any}, b1::Basis, b2::Basis) where T<:Abstract
 identityoperator(b1::Basis, b2::Basis) = identityoperator(ComplexF64, b1, b2)
 
 """Prepare the identity superoperator over a given space."""
-function identitysuperoperator end
+function identitysuperoperator end

src/julia_base.jl

@@ -1,3 +1,5 @@
+import Base: +, -, *, /, ^, length, exp, conj, conj!, adjoint, transpose, copy
+
 # Common error messages
 arithmetic_unary_error(funcname, x::AbstractOperator) = throw(ArgumentError("$funcname is not defined for this type of operator: $(typeof(x)).\nTry to convert to another operator type first with e.g. dense() or sparse()."))
 arithmetic_binary_error(funcname, a::AbstractOperator, b::AbstractOperator) = throw(ArgumentError("$funcname is not defined for this combination of types of operators: $(typeof(a)), $(typeof(b)).\nTry to convert to a common operator type first with e.g. dense() or sparse()."))
@@ -8,33 +10,33 @@ addnumbererror() = throw(ArgumentError("Can't add or subtract a number and an op
 # States
 ##
 
--(a::T) where {T<:StateVector} = T(a.basis, -a.data)
+-(a::T) where {T<:StateVector} = T(a.basis, -a.data) # FIXME issue #12
 *(a::StateVector, b::Number) = b*a
-copy(a::T) where {T<:StateVector} = T(a.basis, copy(a.data))
-length(a::StateVector) = length(a.basis)::Int
-basis(a::StateVector) = a.basis
+copy(a::T) where {T<:StateVector} = T(a.basis, copy(a.data)) # FIXME issue #12
+length(a::StateVector) = length(a.basis)::Int # FIXME issue #12
+basis(a::StateVector) = a.basis # FIXME issue #12
 directsum(x::StateVector...) = reduce(directsum, x)
+adjoint(a::StateVector) = dagger(a)
+
+
 
 # Array-like functions
-Base.size(x::StateVector) = size(x.data)
-@inline Base.axes(x::StateVector) = axes(x.data)
+Base.size(x::StateVector) = size(x.data) # FIXME issue #12
+@inline Base.axes(x::StateVector) = axes(x.data) # FIXME issue #12
 Base.ndims(x::StateVector) = 1
 Base.ndims(::Type{<:StateVector}) = 1
-Base.eltype(x::StateVector) = eltype(x.data)
+Base.eltype(x::StateVector) = eltype(x.data) # FIXME issue #12
 
 # Broadcasting
 Base.broadcastable(x::StateVector) = x
 
-Base.adjoint(a::StateVector) = dagger(a)
-
-
 ##
 # Operators
 ##
 
-length(a::AbstractOperator) = length(a.basis_l)::Int*length(a.basis_r)::Int
-basis(a::AbstractOperator) = (check_samebases(a); a.basis_l)
-basis(a::AbstractSuperOperator) = (check_samebases(a); a.basis_l[1])
+length(a::AbstractOperator) = length(a.basis_l)::Int*length(a.basis_r)::Int  # FIXME issue #12
+basis(a::AbstractOperator) = (check_samebases(a); a.basis_l) # FIXME issue #12
+basis(a::AbstractSuperOperator) = (check_samebases(a); a.basis_l[1]) # FIXME issue #12
 
 # Ensure scalar broadcasting
 Base.broadcastable(x::AbstractOperator) = Ref(x)
@@ -60,14 +62,17 @@ Operator exponential.
 """
 exp(op::AbstractOperator) = throw(ArgumentError("exp() is not defined for this type of operator: $(typeof(op)).\nTry to convert to dense operator first with dense()."))
 
-Base.size(op::AbstractOperator) = (length(op.basis_l),length(op.basis_r))
+Base.size(op::AbstractOperator) = (length(op.basis_l),length(op.basis_r)) # FIXME issue #12
 function Base.size(op::AbstractOperator, i::Int)
     i < 1 && throw(ErrorException("dimension index is < 1"))
     i > 2 && return 1
-    i==1 ? length(op.basis_l) : length(op.basis_r)
+    i==1 ? length(op.basis_l) : length(op.basis_r) # FIXME issue #12
 end
 
-Base.adjoint(a::AbstractOperator) = dagger(a)
+adjoint(a::AbstractOperator) = dagger(a)
+
+transpose(a::AbstractOperator) = arithmetic_unary_error("Transpose", a)
+
 
 conj(a::AbstractOperator) = arithmetic_unary_error("Complex conjugate", a)
 conj!(a::AbstractOperator) = conj(a::AbstractOperator)

src/julia_linalg.jl

@@ -1,3 +1,5 @@
+import LinearAlgebra: tr, ishermitian, norm, normalize, normalize!
+
 """
     ishermitian(op::AbstractOperator)
 

src/linalg.jl

@@ -1,10 +1,10 @@
-samebases(a::AbstractOperator) = samebases(a.basis_l, a.basis_r)::Bool
-samebases(a::AbstractOperator, b::AbstractOperator) = samebases(a.basis_l, b.basis_l)::Bool && samebases(a.basis_r, b.basis_r)::Bool
-check_samebases(a::Union{AbstractOperator, AbstractSuperOperator}) = check_samebases(a.basis_l, a.basis_r)
-multiplicable(a::AbstractOperator, b::AbstractOperator) = multiplicable(a.basis_r, b.basis_l)
+samebases(a::AbstractOperator) = samebases(a.basis_l, a.basis_r)::Bool # FIXME issue #12
+samebases(a::AbstractOperator, b::AbstractOperator) = samebases(a.basis_l, b.basis_l)::Bool && samebases(a.basis_r, b.basis_r)::Bool # FIXME issue #12
+check_samebases(a::Union{AbstractOperator, AbstractSuperOperator}) = check_samebases(a.basis_l, a.basis_r) # FIXME issue #12
+multiplicable(a::AbstractOperator, b::AbstractOperator) = multiplicable(a.basis_r, b.basis_l) # FIXME issue #12
 dagger(a::AbstractOperator) = arithmetic_unary_error("Hermitian conjugate", a)
-transpose(a::AbstractOperator) = arithmetic_unary_error("Transpose", a)
 directsum(a::AbstractOperator...) = reduce(directsum, a)
 ptrace(a::AbstractOperator, index) = arithmetic_unary_error("Partial trace", a)
 _index_complement(b::CompositeBasis, indices) = complement(length(b.bases), indices)
 reduced(a, indices) = ptrace(a, _index_complement(basis(a), indices))
+traceout!(s::StateVector, i) = ptrace(s,i)

src/show.jl

@@ -0,0 +1,69 @@
+import Base: show, summary
+
+function summary(stream::IO, x::AbstractOperator)
+    print(stream, "$(typeof(x).name.name)(dim=$(length(x.basis_l))x$(length(x.basis_r)))\n")
+    if samebases(x)
+        print(stream, "  basis: ")
+        show(stream, basis(x))
+    else
+        print(stream, "  basis left:  ")
+        show(stream, x.basis_l)
+        print(stream, "\n  basis right: ")
+        show(stream, x.basis_r)
+    end
+end
+
+show(stream::IO, x::AbstractOperator) = summary(stream, x)
+
+function show(stream::IO, x::GenericBasis)
+    if length(x.shape) == 1
+        write(stream, "Basis(dim=$(x.shape[1]))")
+    else
+        s = replace(string(x.shape), " " => "")
+        write(stream, "Basis(shape=$s)")
+    end
+end
+
+function show(stream::IO, x::CompositeBasis)
+    write(stream, "[")
+    for i in 1:length(x.bases)
+        show(stream, x.bases[i])
+        if i != length(x.bases)
+            write(stream, " ⊗ ")
+        end
+    end
+    write(stream, "]")
+end
+
+function show(stream::IO, x::SpinBasis)
+    d = denominator(x.spinnumber)
+    n = numerator(x.spinnumber)
+    if d == 1
+        write(stream, "Spin($n)")
+    else
+        write(stream, "Spin($n/$d)")
+    end
+end
+
+function show(stream::IO, x::FockBasis)
+    if iszero(x.offset)
+        write(stream, "Fock(cutoff=$(x.N))")
+    else
+        write(stream, "Fock(cutoff=$(x.N), offset=$(x.offset))")
+    end
+end
+
+function show(stream::IO, x::NLevelBasis)
+    write(stream, "NLevel(N=$(x.N))")
+end
+
+function show(stream::IO, x::SumBasis)
+    write(stream, "[")
+    for i in 1:length(x.bases)
+        show(stream, x.bases[i])
+        if i != length(x.bases)
+            write(stream, " ⊕ ")
+        end
+    end
+    write(stream, "]")
+end