Add doctest in all docstrings (#294)

Author: ytdHuang

src/linear_maps.jl

@@ -30,7 +30,7 @@ It is typically represented as a matrix with dimensions given by `size`, and thi
 
 As an example, we now define the linear map used in the [`eigsolve_al`](@ref) function for Arnoldi-Lindblad eigenvalue solver:
 
-```julia-repl
+```julia
 struct ArnoldiLindbladIntegratorMap{T,TS,TI} <: AbstractLinearMap{T,TS}
     elty::Type{T}
     size::TS

src/metrics.jl

@@ -19,7 +19,7 @@ matrix ``\hat{\rho}``.
 # Examples
 
 Pure state:
-```
+```jldoctest
 julia> ψ = fock(2,0)
 Quantum Object:   type=Ket   dims=[2]   size=(2,)
 2-element Vector{ComplexF64}:
@@ -37,7 +37,7 @@ julia> entropy_vn(ρ, base=2)
 ```
 
 Mixed state:
-```
+```jldoctest
 julia> ρ = maximally_mixed_dm(2)
 Quantum Object:   type=Operator   dims=[2]   size=(2, 2)   ishermitian=true
 2×2 Diagonal{ComplexF64, Vector{ComplexF64}}:

src/negativity.jl

@@ -17,7 +17,7 @@ and ``\Vert \hat{X} \Vert_1=\textrm{Tr}\sqrt{\hat{X}^\dagger \hat{X}}`` is the t
 
 # Examples
 
-```
+```jldoctest
 julia> Ψ = bell_state(0, 0)
 Quantum Object:   type=Ket   dims=[2, 2]   size=(4,)
 4-element Vector{ComplexF64}:
@@ -34,8 +34,8 @@ Quantum Object:   type=Operator   dims=[2, 2]   size=(4, 4)   ishermitian=true
  0.0+0.0im  0.0+0.0im  0.0+0.0im  0.0+0.0im
  0.5+0.0im  0.0+0.0im  0.0+0.0im  0.5+0.0im
 
-julia> negativity(ρ, 2)
-0.4999999999999998
+julia> round(negativity(ρ, 2), digits=2)
+0.5
 ```
 """
 function negativity(ρ::QuantumObject, subsys::Int; logarithmic::Bool = false)

src/qobj/arithmetic_and_attributes.jl

@@ -217,15 +217,15 @@ Note that this function only supports for [`Operator`](@ref) and [`SuperOperator
 
 # Examples
 
-```
+```jldoctest
 julia> a = destroy(20)
 Quantum Object:   type=Operator   dims=[20]   size=(20, 20)   ishermitian=false
 20×20 SparseMatrixCSC{ComplexF64, Int64} with 19 stored entries:
-⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
+⎡⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⎤
+⎢⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⎥
+⎢⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⎥
+⎢⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⎥
+⎣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⎦
 
 julia> tr(a' * a)
 190.0 + 0.0im
@@ -257,7 +257,7 @@ Return the standard vector `p`-norm or [Schatten](https://en.wikipedia.org/wiki/
 
 # Examples
 
-```
+```jldoctest
 julia> ψ = fock(10, 2)
 Quantum Object:   type=Ket   dims=[10]   size=(10,)
 10-element Vector{ComplexF64}:
@@ -474,8 +474,9 @@ proj(ψ::QuantumObject{<:AbstractArray{T},BraQuantumObject}) where {T} = ψ' * 
 Note that this function will always return [`Operator`](@ref). No matter the input [`QuantumObject`](@ref) is a [`Ket`](@ref), [`Bra`](@ref), or [`Operator`](@ref).
 
 # Examples
+
 Two qubits in the state ``\ket{\psi} = \ket{e,g}``:
-```
+```jldoctest
 julia> ψ = kron(fock(2,0), fock(2,1))
 Quantum Object:   type=Ket   dims=[2, 2]   size=(4,)
 4-element Vector{ComplexF64}:
@@ -492,7 +493,7 @@ Quantum Object:   type=Operator   dims=[2]   size=(2, 2)   ishermitian=true
 ```
 
 or in an entangled state ``\ket{\psi} = \frac{1}{\sqrt{2}} \left( \ket{e,e} + \ket{g,g} \right)``:
-```
+```jldoctest
 julia> ψ = 1 / √2 * (kron(fock(2,0), fock(2,0)) + kron(fock(2,1), fock(2,1)))
 Quantum Object:   type=Ket   dims=[2, 2]   size=(4,)
 4-element Vector{ComplexF64}:
@@ -693,12 +694,16 @@ Note that this method currently works for [`Ket`](@ref), [`Bra`](@ref), and [`Op
 
 If `order = [2, 1, 3]`, the Hilbert space structure will be re-arranged: ``\mathcal{H}_1 \otimes \mathcal{H}_2 \otimes \mathcal{H}_3 \rightarrow \mathcal{H}_2 \otimes \mathcal{H}_1 \otimes \mathcal{H}_3``.
 
-```
-julia> ψ1 = fock(2, 0)
-julia> ψ2 = fock(3, 1)
-julia> ψ3 = fock(4, 2)
-julia> ψ_123 = tensor(ψ1, ψ2, ψ3)
-julia> permute(ψ_123, [2, 1, 3]) ≈ tensor(ψ2, ψ1, ψ3)
+```jldoctest
+julia> ψ1 = fock(2, 0);
+
+julia> ψ2 = fock(3, 1);
+
+julia> ψ3 = fock(4, 2);
+
+julia> ψ_123 = tensor(ψ1, ψ2, ψ3);
+
+julia> permute(ψ_123, (2, 1, 3)) ≈ tensor(ψ2, ψ1, ψ3)
 true
 ```
 

src/qobj/eigsolve.jl

@@ -30,22 +30,37 @@ A struct containing the eigenvalues, the eigenvectors, and some information from
 
 # Examples
 One can obtain the eigenvalues and the corresponding [`QuantumObject`](@ref)-type eigenvectors by:
-```
-julia> result = eigenstates(sigmax());
+```jldoctest
+julia> result = eigenstates(sigmax())
+EigsolveResult:   type=Operator   dims=[2]
+values:
+2-element Vector{ComplexF64}:
+ -1.0 + 0.0im
+  1.0 + 0.0im
+vectors:
+2×2 Matrix{ComplexF64}:
+ -0.707107+0.0im  0.707107+0.0im
+  0.707107+0.0im  0.707107+0.0im
 
-julia> λ, ψ, T = result;
+julia> λ, ψ, U = result;
 
 julia> λ
 2-element Vector{ComplexF64}:
  -1.0 + 0.0im
   1.0 + 0.0im
 
 julia> ψ
-2-element Vector{QuantumObject{Vector{ComplexF64}, KetQuantumObject}}:
- QuantumObject{Vector{ComplexF64}, KetQuantumObject}(ComplexF64[-0.7071067811865475 + 0.0im, 0.7071067811865475 + 0.0im], KetQuantumObject(), [2])
- QuantumObject{Vector{ComplexF64}, KetQuantumObject}(ComplexF64[0.7071067811865475 + 0.0im, 0.7071067811865475 + 0.0im], KetQuantumObject(), [2])
+2-element Vector{QuantumObject{Vector{ComplexF64}, KetQuantumObject, 1}}:
+ Quantum Object:   type=Ket   dims=[2]   size=(2,)
+2-element Vector{ComplexF64}:
+ -0.7071067811865475 + 0.0im
+  0.7071067811865475 + 0.0im
+ Quantum Object:   type=Ket   dims=[2]   size=(2,)
+2-element Vector{ComplexF64}:
+ 0.7071067811865475 + 0.0im
+ 0.7071067811865475 + 0.0im
 
-julia> T
+julia> U
 2×2 Matrix{ComplexF64}:
  -0.707107+0.0im  0.707107+0.0im
   0.707107+0.0im  0.707107+0.0im
@@ -411,27 +426,20 @@ end
 Calculates the eigenvalues and eigenvectors of the [`QuantumObject`](@ref) `A` using
 the Julia [LinearAlgebra](https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/) package.
 
-```
+```jldoctest
 julia> a = destroy(5);
 
-julia> H = a + a'
-Quantum Object:   type=Operator   dims=[5]   size=(5, 5)   ishermitian=true
-5×5 SparseMatrixCSC{ComplexF64, Int64} with 8 stored entries:
-     ⋅          1.0+0.0im          ⋅              ⋅          ⋅
- 1.0+0.0im          ⋅      1.41421+0.0im          ⋅          ⋅
-     ⋅      1.41421+0.0im          ⋅      1.73205+0.0im      ⋅
-     ⋅              ⋅      1.73205+0.0im          ⋅      2.0+0.0im
-     ⋅              ⋅              ⋅          2.0+0.0im      ⋅
+julia> H = a + a';
 
 julia> E, ψ, U = eigen(H)
 EigsolveResult:   type=Operator   dims=[5]
 values:
-5-element Vector{Float64}:
- -2.8569700138728
- -1.3556261799742608
-  1.3322676295501878e-15
-  1.3556261799742677
-  2.8569700138728056
+5-element Vector{ComplexF64}:
+       -2.8569700138728 + 0.0im
+    -1.3556261799742608 + 0.0im
+ 1.3322676295501878e-15 + 0.0im
+     1.3556261799742677 + 0.0im
+     2.8569700138728056 + 0.0im
 vectors:
 5×5 Matrix{ComplexF64}:
   0.106101+0.0im  -0.471249-0.0im  …   0.471249-0.0im  0.106101-0.0im

src/qobj/functions.jl

@@ -31,7 +31,7 @@ Note that `ψ` can also be given as a list of [`QuantumObject`](@ref), it return
 
 # Examples
 
-```
+```jldoctest
 julia> ψ = 1 / √2 * (fock(10,2) + fock(10,4));
 
 julia> a = destroy(10);
@@ -153,40 +153,23 @@ Returns the [Kronecker product](https://en.wikipedia.org/wiki/Kronecker_product)
 
 # Examples
 
-```
+```jldoctest
 julia> a = destroy(20)
 Quantum Object:   type=Operator   dims=[20]   size=(20, 20)   ishermitian=false
 20×20 SparseMatrixCSC{ComplexF64, Int64} with 19 stored entries:
-⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
-
-julia> kron(a, a)
-Quantum Object:   type=Operator   dims=[20, 20]   size=(400, 400)   ishermitian=false
-400×400 SparseMatrixCSC{ComplexF64, Int64} with 361 stored entries:
-⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀
-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦
+⎡⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⎤
+⎢⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⎥
+⎢⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⎥
+⎢⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⎥
+⎣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⎦
+
+julia> O = kron(a, a);
+
+julia> size(a), size(O)
+((20, 20), (400, 400))
+
+julia> a.dims, O.dims
+([20], [20, 20])
 ```
 """
 function LinearAlgebra.kron(

src/qobj/operators.jl

@@ -88,7 +88,7 @@ This operator acts on a fock state as ``\hat{a} \ket{n} = \sqrt{n} \ket{n-1}``.
 
 # Examples
 
-```
+```jldoctest
 julia> a = destroy(20)
 Quantum Object:   type=Operator   dims=[20]   size=(20, 20)   ishermitian=false
 20×20 SparseMatrixCSC{ComplexF64, Int64} with 19 stored entries:
@@ -113,7 +113,7 @@ This operator acts on a fock state as ``\hat{a}^\dagger \ket{n} = \sqrt{n+1} \ke
 
 # Examples
 
-```
+```jldoctest
 julia> a_d = create(20)
 Quantum Object:   type=Operator   dims=[20]   size=(20, 20)   ishermitian=false
 20×20 SparseMatrixCSC{ComplexF64, Int64} with 19 stored entries:
@@ -242,14 +242,14 @@ The parameter `which` specifies which of the following operator to return.
 Note that if the parameter `which` is not specified, returns a set of Spin-`j` operators: ``(\hat{S}_x, \hat{S}_y, \hat{S}_z)``
 
 # Examples
-```
+```jldoctest
 julia> jmat(0.5, :x)
 Quantum Object:   type=Operator   dims=[2]   size=(2, 2)   ishermitian=true
 2×2 SparseMatrixCSC{ComplexF64, Int64} with 2 stored entries:
      ⋅      0.5+0.0im
  0.5+0.0im      ⋅
 
-julia> jmat(0.5, :-)
+julia> jmat(0.5, Val(:-))
 Quantum Object:   type=Operator   dims=[2]   size=(2, 2)   ishermitian=false
 2×2 SparseMatrixCSC{ComplexF64, Int64} with 1 stored entry:
      ⋅          ⋅    

src/qobj/quantum_object.jl

@@ -19,7 +19,7 @@ Julia struct representing any quantum objects.
 
 # Examples
 
-```
+```jldoctest
 julia> a = destroy(20)
 Quantum Object:   type=Operator   dims=[20]   size=(20, 20)   ishermitian=false
 20×20 SparseMatrixCSC{ComplexF64, Int64} with 19 stored entries:

src/qobj/quantum_object_base.jl

@@ -19,7 +19,7 @@ export Bra, Ket, Operator, OperatorBra, OperatorKet, SuperOperator
 Abstract type for all quantum objects like [`QuantumObject`](@ref) and [`QuantumObjectEvolution`](@ref).
 
 # Example
-```
+```jldoctest
 julia> sigmax() isa AbstractQuantumObject
 true
 ```