Implement parametric types (#238)

* Start parametric typing for Ket/Bra

* Fix tensor vararg for StateVector

* Fix subspacebasis field parameters

* Fix semiclassical state for kets

* Update testing scripts

* Fix typo in appveyor

* Fix semiclassical_stochastic ket typing

* Fix travis 1.0 testing

* Parametric typing for CompositeBasis

* Rename Operator to AbstractOperator

* Proper parametric type for CompositeBasis

* Parametric typing for operators

* Parametrize basis dimensions

* Revert "Parametrize basis dimensions"

This reverts commit b451987.

* Update basis checks for states

* Update basis checks for dense operators

* Update basis checks for sparse operators

* Update LazyProduct implementation

* Update LazySum implementation

* Update LazyTensor implementation

* Add non-type parameters where needed to ensure correct basis dispatch

* Update basis checks for schroedinger

* Update basis checks for metrics

* Update basis checks for phasespace

* Update basis checks for master

* Update basis checks for mcwf

* Update basis checks for semiclassical

* Update superoperators and steadystate

* Update basis checks for stochastic solvers

* Update timecorrelations basis checks

src/QuantumOptics.jl

@@ -6,7 +6,7 @@ export bases, Basis, GenericBasis, CompositeBasis, basis,
         tensor, ⊗, permutesystems, @samebases,
         states, StateVector, Bra, Ket, basisstate, norm,
                 dagger, normalize, normalize!,
-        operators, Operator, expect, variance, identityoperator, ptrace, embed, dense, tr,
+        operators, AbstractOperator, expect, variance, identityoperator, ptrace, embed, dense, tr,
             sparse,
         operators_dense, DenseOperator, projector, dm,
         operators_sparse, SparseOperator, diagonaloperator,

src/bases.jl

@@ -71,14 +71,17 @@ Stores the subbases in a vector and creates the shape vector directly
 from the shape vectors of these subbases. Instead of creating a CompositeBasis
 directly `tensor(b1, b2...)` or `b1 ⊗ b2 ⊗ …` can be used.
 """
-mutable struct CompositeBasis <: Basis
+mutable struct CompositeBasis{B<:Tuple{Vararg{Basis}}} <: Basis
     shape::Vector{Int}
-    bases::Vector{Basis}
+    bases::B
 end
-CompositeBasis(bases::Vector{Basis}) = CompositeBasis(Int[prod(b.shape) for b in bases], bases)
-CompositeBasis(bases::Basis...) = CompositeBasis(Basis[bases...])
+CompositeBasis(bases::B) where B<:Tuple{Vararg{Basis}} = CompositeBasis{B}(Int[prod(b.shape) for b in bases], bases)
+CompositeBasis(shape::Vector{Int}, bases::Vector{B}) where B<:Basis = (tmp = (bases...,); CompositeBasis{typeof(tmp)}(shape, tmp))
+CompositeBasis(bases::Vector{B}) where B<:Basis = CompositeBasis((bases...,))
+CompositeBasis(bases::Basis...) = CompositeBasis((bases...,))
 
-==(b1::CompositeBasis, b2::CompositeBasis) = equal_shape(b1.shape, b2.shape) && equal_bases(b1.bases, b2.bases)
+==(b1::T, b2::T) where T<:CompositeBasis = equal_shape(b1.shape, b2.shape)
+==(b1::CompositeBasis, b2::CompositeBasis) = false
 
 """
     tensor(x, y, z...)
@@ -98,7 +101,7 @@ Any given CompositeBasis is expanded so that the resulting CompositeBasis never
 contains another CompositeBasis.
 """
 tensor(b1::Basis, b2::Basis) = CompositeBasis(Int[prod(b1.shape); prod(b2.shape)], Basis[b1, b2])
-tensor(b1::CompositeBasis, b2::CompositeBasis) = CompositeBasis(Int[b1.shape; b2.shape], Basis[b1.bases; b2.bases])
+tensor(b1::CompositeBasis, b2::CompositeBasis) = CompositeBasis(Int[b1.shape; b2.shape], (b1.bases..., b2.bases...))
 function tensor(b1::CompositeBasis, b2::Basis)
     N = length(b1.bases)
     shape = Vector{Int}(undef, N+1)

src/manybody.jl

@@ -20,16 +20,18 @@ The basis has to know the associated one-body basis `b` and which occupation sta
 should be included. The occupations_hash is used to speed up checking if two
 many-body bases are equal.
 """
-mutable struct ManyBodyBasis <: Basis
+mutable struct ManyBodyBasis{B<:Basis,H} <: Basis
     shape::Vector{Int}
-    onebodybasis::Basis
+    onebodybasis::B
     occupations::Vector{Vector{Int}}
     occupations_hash::UInt
 
-    function ManyBodyBasis(onebodybasis::Basis, occupations::Vector{Vector{Int}})
+    function ManyBodyBasis{B,H}(onebodybasis::Basis, occupations::Vector{Vector{Int}}) where {B<:Basis,H}
+        @assert isa(H, UInt)
         new([length(occupations)], onebodybasis, occupations, hash(hash.(occupations)))
     end
 end
+ManyBodyBasis(onebodybasis::B, occupations::Vector{Vector{Int}}) where B<:Basis = ManyBodyBasis{B,hash(hash.(occupations))}(onebodybasis,occupations)
 
 """
     fermionstates(Nmodes, Nparticles)
@@ -228,7 +230,7 @@ where ``X`` is the N-particle operator, ``x`` is the one-body operator and
 ``|u⟩`` are the one-body states associated to the
 different modes of the N-particle basis.
 """
-function manybodyoperator(basis::ManyBodyBasis, op::T)::T where T<:Operator
+function manybodyoperator(basis::ManyBodyBasis, op::T) where T<:AbstractOperator
     @assert op.basis_l == op.basis_r
     if op.basis_l == basis.onebodybasis
         result =  manybodyoperator_1(basis, op)
@@ -321,7 +323,7 @@ end
 
 Expectation value of the one-body operator `op` in respect to the many-body `state`.
 """
-function onebodyexpect(op::Operator, state::Ket)
+function onebodyexpect(op::AbstractOperator, state::Ket)
     @assert isa(state.basis, ManyBodyBasis)
     @assert op.basis_l == op.basis_r
     if state.basis.onebodybasis == op.basis_l
@@ -335,7 +337,7 @@ function onebodyexpect(op::Operator, state::Ket)
     result
 end
 
-function onebodyexpect(op::Operator, state::Operator)
+function onebodyexpect(op::AbstractOperator, state::AbstractOperator)
     @assert op.basis_l == op.basis_r
     @assert state.basis_l == state.basis_r
     @assert isa(state.basis_l, ManyBodyBasis)
@@ -349,7 +351,7 @@ function onebodyexpect(op::Operator, state::Operator)
     end
     result
 end
-onebodyexpect(op::Operator, states::Vector) = [onebodyexpect(op, state) for state=states]
+onebodyexpect(op::AbstractOperator, states::Vector) = [onebodyexpect(op, state) for state=states]
 
 function onebodyexpect_1(op::DenseOperator, state::Ket)
     N = length(state.basis)

src/master.jl

@@ -17,14 +17,14 @@ Integrate the master equation with dmaster_h as derivative function.
 
 Further information can be found at [`master`](@ref).
 """
-function master_h(tspan, rho0::DenseOperator, H::Operator, J::Vector;
+function master_h(tspan, rho0::T, H::AbstractOperator{B,B}, J::Vector;
                 rates::DecayRates=nothing,
                 Jdagger::Vector=dagger.(J),
                 fout::Union{Function,Nothing}=nothing,
-                kwargs...)
+                kwargs...) where {B<:Basis,T<:DenseOperator{B,B}}
     check_master(rho0, H, J, Jdagger, rates)
     tmp = copy(rho0)
-    dmaster_(t, rho::DenseOperator, drho::DenseOperator) = dmaster_h(rho, H, rates, J, Jdagger, drho, tmp)
+    dmaster_(t, rho::T, drho::T) = dmaster_h(rho, H, rates, J, Jdagger, drho, tmp)
     integrate_master(tspan, dmaster_, rho0, fout; kwargs...)
 end
 
@@ -39,15 +39,15 @@ H_{nh} = H - \\frac{i}{2} \\sum_k J^†_k J_k
 ```
 Further information can be found at [`master`](@ref).
 """
-function master_nh(tspan, rho0::DenseOperator, Hnh::Operator, J::Vector;
+function master_nh(tspan, rho0::T, Hnh::AbstractOperator{B,B}, J::Vector;
                 rates::DecayRates=nothing,
-                Hnhdagger::Operator=dagger(Hnh),
+                Hnhdagger::AbstractOperator=dagger(Hnh),
                 Jdagger::Vector=dagger.(J),
                 fout::Union{Function,Nothing}=nothing,
-                kwargs...)
+                kwargs...) where {B<:Basis,T<:DenseOperator{B,B}}
     check_master(rho0, Hnh, J, Jdagger, rates)
     tmp = copy(rho0)
-    dmaster_(t, rho::DenseOperator, drho::DenseOperator) = dmaster_nh(rho, Hnh, Hnhdagger, rates, J, Jdagger, drho, tmp)
+    dmaster_(t, rho::T, drho::T) = dmaster_nh(rho, Hnh, Hnhdagger, rates, J, Jdagger, drho, tmp)
     integrate_master(tspan, dmaster_, rho0, fout; kwargs...)
 end
 
@@ -83,15 +83,15 @@ non-hermitian Hamiltonian and then calls master_nh which is slightly faster.
         be changed.
 * `kwargs...`: Further arguments are passed on to the ode solver.
 """
-function master(tspan, rho0::DenseOperator, H::Operator, J::Vector;
+function master(tspan, rho0::T, H::AbstractOperator{B,B}, J::Vector;
                 rates::DecayRates=nothing,
                 Jdagger::Vector=dagger.(J),
                 fout::Union{Function,Nothing}=nothing,
-                kwargs...)
+                kwargs...) where {B<:Basis,T<:DenseOperator{B,B}}
     isreducible = check_master(rho0, H, J, Jdagger, rates)
     if !isreducible
         tmp = copy(rho0)
-        dmaster_h_(t, rho::DenseOperator, drho::DenseOperator) = dmaster_h(rho, H, rates, J, Jdagger, drho, tmp)
+        dmaster_h_(t, rho::T, drho::T) = dmaster_h(rho, H, rates, J, Jdagger, drho, tmp)
         return integrate_master(tspan, dmaster_h_, rho0, fout; kwargs...)
     else
         Hnh = copy(H)
@@ -110,7 +110,7 @@ function master(tspan, rho0::DenseOperator, H::Operator, J::Vector;
         end
         Hnhdagger = dagger(Hnh)
         tmp = copy(rho0)
-        dmaster_nh_(t, rho::DenseOperator, drho::DenseOperator) = dmaster_nh(rho, Hnh, Hnhdagger, rates, J, Jdagger, drho, tmp)
+        dmaster_nh_(t, rho::T, drho::T) = dmaster_nh(rho, Hnh, Hnhdagger, rates, J, Jdagger, drho, tmp)
         return integrate_master(tspan, dmaster_nh_, rho0, fout; kwargs...)
     end
 end
@@ -128,12 +128,12 @@ The given function can either be of the form `f(t, rho) -> (Hnh, Hnhdagger, J, J
 or `f(t, rho) -> (Hnh, Hnhdagger, J, Jdagger, rates)` For further information look
 at [`master_dynamic`](@ref).
 """
-function master_nh_dynamic(tspan, rho0::DenseOperator, f::Function;
+function master_nh_dynamic(tspan, rho0::T, f::Function;
                 rates::DecayRates=nothing,
                 fout::Union{Function,Nothing}=nothing,
-                kwargs...)
+                kwargs...) where {B<:Basis,T<:DenseOperator{B,B}}
     tmp = copy(rho0)
-    dmaster_(t, rho::DenseOperator, drho::DenseOperator) = dmaster_nh_dynamic(t, rho, f, rates, drho, tmp)
+    dmaster_(t, rho::T, drho::T) = dmaster_nh_dynamic(t, rho, f, rates, drho, tmp)
     integrate_master(tspan, dmaster_, rho0, fout; kwargs...)
 end
 
@@ -162,36 +162,36 @@ operators:
         be changed.
 * `kwargs...`: Further arguments are passed on to the ode solver.
 """
-function master_dynamic(tspan, rho0::DenseOperator, f::Function;
+function master_dynamic(tspan, rho0::T, f::Function;
                 rates::DecayRates=nothing,
                 fout::Union{Function,Nothing}=nothing,
-                kwargs...)
+                kwargs...) where {B<:Basis,T<:DenseOperator{B,B}}
     tmp = copy(rho0)
-    dmaster_(t, rho::DenseOperator, drho::DenseOperator) = dmaster_h_dynamic(t, rho, f, rates, drho, tmp)
+    dmaster_(t, rho::T, drho::T) = dmaster_h_dynamic(t, rho, f, rates, drho, tmp)
     integrate_master(tspan, dmaster_, rho0, fout; kwargs...)
 end
 
 
 # Automatically convert Ket states to density operators
-master(tspan, psi0::Ket, H::Operator, J::Vector; kwargs...) = master(tspan, dm(psi0), H, J; kwargs...)
-master_h(tspan, psi0::Ket, H::Operator, J::Vector; kwargs...) = master_h(tspan, dm(psi0), H, J; kwargs...)
-master_nh(tspan, psi0::Ket, Hnh::Operator, J::Vector; kwargs...) = master_nh(tspan, dm(psi0), Hnh, J; kwargs...)
-master_dynamic(tspan, psi0::Ket, f::Function; kwargs...) = master_dynamic(tspan, dm(psi0), f; kwargs...)
-master_nh_dynamic(tspan, psi0::Ket, f::Function; kwargs...) = master_nh_dynamic(tspan, dm(psi0), f; kwargs...)
+master(tspan, psi0::Ket{B}, H::AbstractOperator{B,B}, J::Vector; kwargs...) where B<:Basis = master(tspan, dm(psi0), H, J; kwargs...)
+master_h(tspan, psi0::Ket{B}, H::AbstractOperator{B,B}, J::Vector; kwargs...) where B<:Basis = master_h(tspan, dm(psi0), H, J; kwargs...)
+master_nh(tspan, psi0::Ket{B}, Hnh::AbstractOperator{B,B}, J::Vector; kwargs...) where B<:Basis = master_nh(tspan, dm(psi0), Hnh, J; kwargs...)
+master_dynamic(tspan, psi0::Ket{B}, f::Function; kwargs...) where B<:Basis = master_dynamic(tspan, dm(psi0), f; kwargs...)
+master_nh_dynamic(tspan, psi0::Ket{B}, f::Function; kwargs...) where B<:Basis = master_nh_dynamic(tspan, dm(psi0), f; kwargs...)
 
 
 # Recasting needed for the ODE solver is just providing the underlying data
-function recast!(x::Array{ComplexF64, 2}, rho::DenseOperator)
+function recast!(x::T, rho::DenseOperator{B,B,T}) where {B<:Basis,T<:Matrix{ComplexF64}}
     rho.data = x
 end
-recast!(rho::DenseOperator, x::Array{ComplexF64, 2}) = nothing
+recast!(rho::DenseOperator{B,B,T}, x::T) where {B<:Basis,T<:Matrix{ComplexF64}} = nothing
 
-function integrate_master(tspan, df::Function, rho0::DenseOperator,
-                        fout::Union{Nothing, Function}; kwargs...)
+function integrate_master(tspan, df::Function, rho0::T,
+                        fout::Union{Nothing, Function}; kwargs...) where {B<:Basis,T<:DenseOperator{B,B}}
     tspan_ = convert(Vector{Float64}, tspan)
     x0 = rho0.data
-    state = DenseOperator(rho0.basis_l, rho0.basis_r, rho0.data)
-    dstate = DenseOperator(rho0.basis_l, rho0.basis_r, rho0.data)
+    state = T(rho0.basis_l, rho0.basis_r, rho0.data)
+    dstate = T(rho0.basis_l, rho0.basis_r, rho0.data)
     integrate(tspan_, df, x0, state, dstate, fout; kwargs...)
 end
 
@@ -205,9 +205,9 @@ end
 # the type of the given decay rate object which can either be nothing, a vector
 # or a matrix.
 
-function dmaster_h(rho::DenseOperator, H::Operator,
+function dmaster_h(rho::T, H::AbstractOperator{B,B},
                     rates::Nothing, J::Vector, Jdagger::Vector,
-                    drho::DenseOperator, tmp::DenseOperator)
+                    drho::T, tmp::T) where {B<:Basis,T<:DenseOperator{B,B}}
     operators.gemm!(-1im, H, rho, 0, drho)
     operators.gemm!(1im, rho, H, 1, drho)
     for i=1:length(J)
@@ -222,9 +222,9 @@ function dmaster_h(rho::DenseOperator, H::Operator,
     return drho
 end
 
-function dmaster_h(rho::DenseOperator, H::Operator,
+function dmaster_h(rho::T, H::AbstractOperator{B,B},
                     rates::Vector{Float64}, J::Vector, Jdagger::Vector,
-                    drho::DenseOperator, tmp::DenseOperator)
+                    drho::T, tmp::T) where {B<:Basis,T<:DenseOperator{B,B}}
     operators.gemm!(-1im, H, rho, 0, drho)
     operators.gemm!(1im, rho, H, 1, drho)
     for i=1:length(J)
@@ -239,9 +239,9 @@ function dmaster_h(rho::DenseOperator, H::Operator,
     return drho
 end
 
-function dmaster_h(rho::DenseOperator, H::Operator,
+function dmaster_h(rho::T, H::AbstractOperator{B,B},
                     rates::Matrix{Float64}, J::Vector, Jdagger::Vector,
-                    drho::DenseOperator, tmp::DenseOperator)
+                    drho::T, tmp::T) where {B<:Basis,T<:DenseOperator{B,B}}
     operators.gemm!(-1im, H, rho, 0, drho)
     operators.gemm!(1im, rho, H, 1, drho)
     for j=1:length(J), i=1:length(J)
@@ -256,9 +256,9 @@ function dmaster_h(rho::DenseOperator, H::Operator,
     return drho
 end
 
-function dmaster_nh(rho::DenseOperator, Hnh::Operator, Hnh_dagger::Operator,
+function dmaster_nh(rho::T1, Hnh::T2, Hnh_dagger::T2,
                     rates::Nothing, J::Vector, Jdagger::Vector,
-                    drho::DenseOperator, tmp::DenseOperator)
+                    drho::T1, tmp::T1) where {B<:Basis,T1<:DenseOperator{B,B},T2<:AbstractOperator{B,B}}
     operators.gemm!(-1im, Hnh, rho, 0, drho)
     operators.gemm!(1im, rho, Hnh_dagger, 1, drho)
     for i=1:length(J)
@@ -268,9 +268,9 @@ function dmaster_nh(rho::DenseOperator, Hnh::Operator, Hnh_dagger::Operator,
     return drho
 end
 
-function dmaster_nh(rho::DenseOperator, Hnh::Operator, Hnh_dagger::Operator,
+function dmaster_nh(rho::T1, Hnh::T2, Hnh_dagger::T2,
                     rates::Vector{Float64}, J::Vector, Jdagger::Vector,
-                    drho::DenseOperator, tmp::DenseOperator)
+                    drho::T1, tmp::T1) where {B<:Basis,T1<:DenseOperator{B,B},T2<:AbstractOperator{B,B}}
     operators.gemm!(-1im, Hnh, rho, 0, drho)
     operators.gemm!(1im, rho, Hnh_dagger, 1, drho)
     for i=1:length(J)
@@ -280,9 +280,9 @@ function dmaster_nh(rho::DenseOperator, Hnh::Operator, Hnh_dagger::Operator,
     return drho
 end
 
-function dmaster_nh(rho::DenseOperator, Hnh::Operator, Hnh_dagger::Operator,
+function dmaster_nh(rho::T1, Hnh::T2, Hnh_dagger::T2,
                     rates::Matrix{Float64}, J::Vector, Jdagger::Vector,
-                    drho::DenseOperator, tmp::DenseOperator)
+                    drho::T1, tmp::T1) where {B<:Basis,T1<:DenseOperator{B,B},T2<:AbstractOperator{B,B}}
     operators.gemm!(-1im, Hnh, rho, 0, drho)
     operators.gemm!(1im, rho, Hnh_dagger, 1, drho)
     for j=1:length(J), i=1:length(J)
@@ -292,9 +292,9 @@ function dmaster_nh(rho::DenseOperator, Hnh::Operator, Hnh_dagger::Operator,
     return drho
 end
 
-function dmaster_h_dynamic(t::Float64, rho::DenseOperator, f::Function,
+function dmaster_h_dynamic(t::Float64, rho::T, f::Function,
                     rates::DecayRates,
-                    drho::DenseOperator, tmp::DenseOperator)
+                    drho::T, tmp::T) where {B<:Basis,T<:DenseOperator{B,B}}
     result = f(t, rho)
     QO_CHECKS[] && @assert 3 <= length(result) <= 4
     if length(result) == 3
@@ -307,9 +307,9 @@ function dmaster_h_dynamic(t::Float64, rho::DenseOperator, f::Function,
     dmaster_h(rho, H, rates_, J, Jdagger, drho, tmp)
 end
 
-function dmaster_nh_dynamic(t::Float64, rho::DenseOperator, f::Function,
+function dmaster_nh_dynamic(t::Float64, rho::T, f::Function,
                     rates::DecayRates,
-                    drho::DenseOperator, tmp::DenseOperator)
+                    drho::T, tmp::T) where {B<:Basis,T<:DenseOperator{B,B}}
     result = f(t, rho)
     QO_CHECKS[] && @assert 4 <= length(result) <= 5
     if length(result) == 4
@@ -323,21 +323,21 @@ function dmaster_nh_dynamic(t::Float64, rho::DenseOperator, f::Function,
 end
 
 
-function check_master(rho0::DenseOperator, H::Operator, J::Vector, Jdagger::Vector, rates::DecayRates)
+function check_master(rho0::DenseOperator{B,B}, H::AbstractOperator{B,B}, J::Vector, Jdagger::Vector, rates::DecayRates) where B<:Basis
+    # TODO: clean up type checks by dispatch; make type of J known
     isreducible = true # test if all operators are sparse or dense
-    check_samebases(rho0, H)
     if !(isa(H, DenseOperator) || isa(H, SparseOperator))
         isreducible = false
     end
     for j=J
-        @assert isa(j, Operator)
+        @assert isa(j, AbstractOperator{B,B})
         if !(isa(j, DenseOperator) || isa(j, SparseOperator))
             isreducible = false
         end
         check_samebases(rho0, j)
     end
     for j=Jdagger
-        @assert isa(j, Operator)
+        @assert isa(j, AbstractOperator{B,B})
         if !(isa(j, DenseOperator) || isa(j, SparseOperator))
             isreducible = false
         end