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Merge pull request #14 from devmotion/history_params
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Add parameters to history function
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@ChrisRackauckas
ChrisRackauckas authored Mar 25, 2018
2 parents 83123f3 + 56740bd commit a346d45
Showing 1 changed file with 45 additions and 45 deletions.
90 changes: 45 additions & 45 deletions src/dde_premade_problems.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -5,7 +5,7 @@
### In-place function

function f_1delay(du, u, h, p, t)
du[1] = - h(t - oneunit(t))[1] / oneunit(t)
du[1] = - h(p, t - oneunit(t))[1] / oneunit(t)
end

function f_1delay(::Type{Val{:analytic}}, u₀, p, t)
Expand Down Expand Up @@ -47,7 +47,7 @@ function f_1delay(::Type{Val{:analytic}}, u₀, p, t)
end

build_prob_dde_1delay(u₀, ::T=u₀) where {T} =
DDEProblem(f_1delay, [u₀], t->[zero(u₀)], (zero(T), T(10)),
DDEProblem(f_1delay, [u₀], (p, t)->[zero(u₀)], (zero(T), T(10)),
constant_lags = [oneunit(T)])

"""
Expand Down Expand Up @@ -79,15 +79,15 @@ prob_dde_1delay = build_prob_dde_1delay(1.0)
### Not in-place function

function f_1delay_notinplace(u, h, p, t)
- h(t - oneunit(t)) ./ oneunit(t)
- h(p, t - oneunit(t)) ./ oneunit(t)
end

f_1delay_notinplace(::Type{Val{:analytic}}, u0, p, t) = f_1delay(Val{:analytic}, u0, p, t)

#### Vectorized history function

build_prob_dde_1delay_notinplace(u₀, ::T=u₀) where {T} =
DDEProblem(f_1delay_notinplace, [u₀], t->[zero(u₀)], (zero(T), T(10)),
DDEProblem(f_1delay_notinplace, [u₀], (p, t)->[zero(u₀)], (zero(T), T(10)),
constant_lags = [oneunit(T)])

"""
Expand All @@ -101,8 +101,8 @@ prob_dde_1delay_notinplace = build_prob_dde_1delay_notinplace(1.0)
#### Scalar history function

build_prob_dde_1delay_scalar_notinplace(u₀, ::T=u₀) where {T} =
DDEProblem(f_1delay_notinplace, u₀, t -> zero(u₀), (zero(T), T(10)),
constant_lags = [oneunit(T)])
DDEProblem(f_1delay_notinplace, u₀, (p, t) -> zero(u₀), (zero(T), T(10)),
constant_lags = [oneunit(T)])

"""
prob_dde_1delay_scalar_notinplace
Expand All @@ -117,7 +117,7 @@ prob_dde_1delay_scalar_notinplace = build_prob_dde_1delay_scalar_notinplace(1.0)
### In-place function

function f_2delays(du, u, h, p, t::T) where T
du[1] = (- h(t - T(1//3))[1] - h(t - T(1//5))[1]) / oneunit(t)
du[1] = (- h(p, t - T(1//3))[1] - h(p, t - T(1//5))[1]) / oneunit(t)
end

function f_2delays(::Type{Val{:analytic}}, u₀, p, t)
Expand Down Expand Up @@ -157,7 +157,7 @@ function f_2delays(::Type{Val{:analytic}}, u₀, p, t)
end

build_prob_dde_2delays(u₀, ::T=u₀) where {T} =
DDEProblem(f_2delays, [u₀], t -> [zero(u₀)], (zero(T), oneunit(T)),
DDEProblem(f_2delays, [u₀], (p, t) -> [zero(u₀)], (zero(T), oneunit(T)),
constant_lags = [T(1//3), T(1//5)])

"""
Expand Down Expand Up @@ -189,7 +189,7 @@ prob_dde_2delays = build_prob_dde_2delays(1.0)
### Not in-place function

function f_2delays_notinplace(u, h, p, t::T) where T
(- h(t - T(1//3)) .- h(t - T(1//5))) ./ oneunit(t)
(- h(p, t - T(1//3)) .- h(p, t - T(1//5))) ./ oneunit(t)
end

f_2delays_notinplace(::Type{Val{:analytic}}, u0, p, t) =
Expand All @@ -198,7 +198,7 @@ f_2delays_notinplace(::Type{Val{:analytic}}, u0, p, t) =
#### Vectorized history function

build_prob_dde_2delays_notinplace(u₀, ::T=u₀) where {T} =
DDEProblem(f_2delays_notinplace, [u₀], t -> [zero(u₀)], (zero(T), oneunit(T)),
DDEProblem(f_2delays_notinplace, [u₀], (p, t) -> [zero(u₀)], (zero(T), oneunit(T)),
constant_lags = [T(1//3), T(1//5)])

"""
Expand All @@ -212,7 +212,7 @@ prob_dde_2delays_notinplace = build_prob_dde_2delays_notinplace(1.0)
#### Scalar history function

build_prob_dde_2delays_scalar_notinplace(u₀, ::T=u₀) where {T} =
DDEProblem(f_2delays_notinplace, u₀, t -> zero(u₀), (zero(T), oneunit(T)),
DDEProblem(f_2delays_notinplace, u₀, (p, t) -> zero(u₀), (zero(T), oneunit(T)),
constant_lags = [T(1//3), T(1//5)])

"""
Expand All @@ -230,11 +230,11 @@ prob_dde_2delays_scalar_notinplace = build_prob_dde_2delays_scalar_notinplace(1.
### In-place function

function f_1delay_long(du, u, h, p, t::T) where T
du[1] = (- h(t - T(1//5))[1] + u[1]) / oneunit(t)
du[1] = (- h(p, t - T(1//5))[1] + u[1]) / oneunit(t)
end

build_prob_dde_1delay_long(u₀, ::T=u₀) where {T} =
DDEProblem(f_1delay_long, [u₀], t -> [zero(u₀)], (zero(T), T(100)),
DDEProblem(f_1delay_long, [u₀], (p, t) -> [zero(u₀)], (zero(T), T(100)),
constant_lags = [T(1//5)])

"""
Expand Down Expand Up @@ -264,11 +264,11 @@ prob_dde_1delay_long = build_prob_dde_1delay_long(1.0)
### Not in-place function

function f_1delay_long_notinplace(u, h, p, t::T) where T
(- h(t - T(1//5)) .+ u ) ./ oneunit(t)
(- h(p, t - T(1//5)) .+ u ) ./ oneunit(t)
end

build_prob_dde_1delay_long_notinplace(u₀, ::T=u₀) where {T} =
DDEProblem(f_1delay_long_notinplace, [u₀], t -> [zero(u₀)], (zero(T), T(100)),
DDEProblem(f_1delay_long_notinplace, [u₀], (p, t) -> [zero(u₀)], (zero(T), T(100)),
constant_lags = [T(1//5)])

"""
Expand All @@ -280,7 +280,7 @@ in-place function.
prob_dde_1delay_long_notinplace = build_prob_dde_1delay_long_notinplace(1.0)

build_prob_dde_1delay_long_scalar_notinplace(u₀, ::T=u₀) where {T} =
DDEProblem(f_1delay_long_notinplace, u₀, t -> zero(u₀), (zero(T), T(100)),
DDEProblem(f_1delay_long_notinplace, u₀, (p, t) -> zero(u₀), (zero(T), T(100)),
constant_lags = [T(1//5)])

"""
Expand All @@ -296,12 +296,12 @@ prob_dde_1delay_long_scalar_notinplace = build_prob_dde_1delay_long_scalar_notin
### In-place function

function f_2delays_long(du, u, h, p, t::T) where T
du[1] = (- h(t - T(1//3))[1] - h(t - T(1//5))[1]) / oneunit(t)
du[1] = (- h(p, t - T(1//3))[1] - h(p, t - T(1//5))[1]) / oneunit(t)
end

build_prob_dde_2delays_long(u₀, ::T=u₀) where {T} =
DDEProblem(f_2delays_long, [u₀], t -> [zero(u₀)], (zero(T), T(100)),
constant_lags = [T(1//3), T(1//5)])
DDEProblem(f_2delays_long, [u₀], (p, t) -> [zero(u₀)], (zero(T), T(100)),
constant_lags = [T(1//3), T(1//5)])

"""
prob_dde_2delays_long
Expand Down Expand Up @@ -330,13 +330,13 @@ prob_dde_2delays_long = build_prob_dde_2delays_long(1.0)
### Not in-place function

function f_2delays_long_notinplace(u, h, p, t::T) where T
(- h(t - T(1//3)) .- h(t - T(1//5))) ./ oneunit(t)
(- h(p, t - T(1//3)) .- h(p, t - T(1//5))) ./ oneunit(t)
end

#### Vectorized history function

build_prob_dde_2delays_long_notinplace(u₀, ::T=u₀) where {T} =
DDEProblem(f_2delays_long_notinplace, [u₀], t -> [zero(u₀)], (zero(T), T(100)),
DDEProblem(f_2delays_long_notinplace, [u₀], (p, t) -> [zero(u₀)], (zero(T), T(100)),
constant_lags = [T(1//3), T(1//5)])

"""
Expand All @@ -350,7 +350,7 @@ prob_dde_2delays_long_notinplace = build_prob_dde_2delays_long_notinplace(1.0)
#### Scalar history function

build_prob_dde_2delays_long_scalar_notinplace(u₀, ::T=u₀) where {T} =
DDEProblem(f_2delays_long_notinplace, u₀, t -> zero(u₀), (zero(T), T(100)),
DDEProblem(f_2delays_long_notinplace, u₀, (p, t) -> zero(u₀), (zero(T), T(100)),
constant_lags = [T(1//3), T(1//5)])

"""
Expand All @@ -368,7 +368,7 @@ differential equations.
=#

function f_dde_mackey(du, u, h, p, t)
du[1] = 0.2*h(t-14)[1]/(1 + h(t-14)[1]^10) - 0.1*u[1]
du[1] = 0.2*h(p, t-14)[1]/(1 + h(p, t-14)[1]^10) - 0.1*u[1]
end

"""
Expand All @@ -377,11 +377,11 @@ end
Model of blood production with constant delay (M. C. Mackey and L. Glass, Oscillation and
chaos in physiological control systems, 1977).
"""
prob_dde_mackey = DDEProblem(f_dde_mackey, [0.5], t -> [0.5], (0.0, 500.0),
prob_dde_mackey = DDEProblem(f_dde_mackey, [0.5], (p, t) -> [0.5], (0.0, 500.0),
constant_lags = [14])

function f_dde_wheldon(du, u, h, p, t)
du[1] = 1.1/(1 + sqrt(10)*(h(t-20)[1])^(5/4)) - 10*u[1]/(1 + 40*u[2])
du[1] = 1.1/(1 + sqrt(10)*(h(p, t-20)[1])^(5/4)) - 10*u[1]/(1 + 40*u[2])
du[2] = 100*u[1]/(1 + 40*u[2]) - 2.43*u[2]
end
u0_wheldon = [1.05767027/3; 1.030713491/3]
Expand All @@ -392,11 +392,11 @@ u0_wheldon = [1.05767027/3; 1.030713491/3]
Model of chronic granulocytic leukemia with constant delay (T. Wheldon, J. Kirk and
H. Finlay, Cyclical granulopoiesis in chronic granulocytic leukemia: A simulation study, 1974).
"""
prob_dde_wheldon = DDEProblem(f_dde_wheldon, u0_wheldon, t -> u0_wheldon, (0., 100.),
prob_dde_wheldon = DDEProblem(f_dde_wheldon, u0_wheldon, (p, t) -> u0_wheldon, (0., 100.),
constant_lags = [20])

function f_dde_neves1(du, u, h, p, t)
du[1] = 1 - h(exp(1-1/t))[1]
du[1] = 1 - h(p, exp(1-1/t))[1]
end
# only valid for specific history function
function f_dde_neves1(::Type{Val{:analytic}}, u₀, p, t )
Expand All @@ -410,11 +410,11 @@ end
DDE with vanishing time dependent delay at ``t = 1`` (K. W. Neves, Automatic integratorion
of functional differential equations: An approach, 1975).
"""
prob_dde_neves_1 = DDEProblem(f_dde_neves1, [log(0.1)], t -> [log(t)], (0.1, 10.),
prob_dde_neves_1 = DDEProblem(f_dde_neves1, [log(0.1)], (p, t) -> [log(t)], (0.1, 10.),
dependent_lags = [(u,p,t) -> t - exp(1 - 1/t)])

function f_dde_neves_thompson(du, u, h, p, t)
if h(t/2)[1] < 0
if h(p, t/2)[1] < 0
du[1] = 1 - u[1]
else
du[1] = -1 - u[1]
Expand Down Expand Up @@ -455,11 +455,11 @@ u(t) = 1
for ``t \\leq 0``.
"""
prob_dde_neves_thompson = DDEProblem(f_dde_neves_thompson, [1.], t -> [1.], (0., 2*log(66)),
prob_dde_neves_thompson = DDEProblem(f_dde_neves_thompson, [1.], (p, t) -> [1.], (0., 2*log(66)),
constant_lags = [(u,p,t) -> t/2])

function f_dde_paul1(du, u, h, p, t)
du[1] = - 2*h(t - 1 - abs(u[1]))[1]*(1 - u[1]^2)
du[1] = - 2*h(p, t - 1 - abs(u[1]))[1]*(1 - u[1]^2)
end

"""
Expand All @@ -480,11 +480,11 @@ u(t) = 1/2
for ``t \\leq 0``.
"""
prob_dde_paul1 = DDEProblem(f_dde_paul1, [0.5], t -> [0.5], (0., 30.),
prob_dde_paul1 = DDEProblem(f_dde_paul1, [0.5], (p, t) -> [0.5], (0., 30.),
dependent_lags = [(u,p,t) -> 1 + abs(u[1])])

function f_dde_paul2(du, u, h, p, t)
h1 = h(t - u[2])[1]
h1 = h(p, t - u[2])[1]
du[1] = -2*h1
du[2] = (abs(h1) - abs(u[1]))/(1 + abs(h1))
end
Expand All @@ -494,22 +494,22 @@ end
DDE with state dependent delay (C. A. H. Paul, A test set of functional differential equations, 1994).
"""
prob_dde_paul2 = DDEProblem(f_dde_paul2, [1; 0.5], t -> [1; 0.5], (0., 30.),
prob_dde_paul2 = DDEProblem(f_dde_paul2, [1; 0.5], (p, t) -> [1; 0.5], (0., 30.),
dependent_lags = [(u,p,t) -> u[2]])

function build_prob_dde_mahaffy(tspan, h, σ₀, T₁, γ, Q, k, a, K, r)
function f(du, u, h, p, t)
du[1] = σ₀*h(t-T₁)[2] - γ*u[1] - Q
du[1] = σ₀*h(p, t-T₁)[2] - γ*u[1] - Q
du[2] = a/(1 + K*u[1]^r) - k*u[2]
du[3] = 1 - Q*exp(γ*u[3])/(σ₀*h(t-T₁-u[3])[2])
du[3] = 1 - Q*exp(γ*u[3])/(σ₀*h(p, t-T₁-u[3])[2])
end

DDEProblem(f, h(0), h, tspan,
DDEProblem(f, h(nothing, 0), h, tspan,
constant_lags = [T₁],
dependent_lags = [(u,p,t) -> T₁ + u[3]])
end

function h_mahaffy1(t)
function h_mahaffy1(p, t)
if t < -6
return [3.325; 9.5; 120]
else
Expand All @@ -519,7 +519,7 @@ end
prob_dde_mahaffy1 = build_prob_dde_mahaffy((0., 300.), h_mahaffy1, 0.0031, 6, 0.001, 0.0275,
2.8, 6570, 0.0382, 6.96)

prob_dde_mahaffy2 = build_prob_dde_mahaffy((0., 100.), t -> [3.5; 10; 50], 0.00372, 3, 0.1,
prob_dde_mahaffy2 = build_prob_dde_mahaffy((0., 100.), (p, t) -> [3.5; 10; 50], 0.00372, 3, 0.1,
0.00178, 6.65, 15600, 0.0382, 6.96)

"""
Expand All @@ -531,7 +531,7 @@ prob_dde_mahaffy1, prob_dde_mahaffy2
function f_dde_neves2(du, u, h, p, t)
t2 = exp(1 - u[2])
du[1] = u[2]
du[2] = -h(t2)[2]*u[2]^2*t2
du[2] = -h(p, t2)[2]*u[2]^2*t2
end
# only valid for specific history function
function f_dde_neves2(::Type{Val{:analytic}}, u₀, p, t )
Expand All @@ -545,15 +545,15 @@ end
DDE with vanishing state dependent delay at ``t = 1`` (K. W. Neves, Automatic integration
of functional differential equations: An approach, 1975).
"""
prob_dde_neves2 = DDEProblem(f_dde_neves2, [log(0.1); 10], t -> [log(t); 1/t], (0.1, 5.),
prob_dde_neves2 = DDEProblem(f_dde_neves2, [log(0.1); 10], (p, t) -> [log(t); 1/t], (0.1, 5.),
dependent_lags = [(u,p,t) -> t - exp(1 - u[2])])

function build_f_dde_gatica(r₁, r₂, α, δ)
function f_dde_gatica(du, u, h, p, t)
u₁u₂ = u[1]*u[2]
r₁u₁u₂ = r₁*u₁u₂
r₂u₃ = r₂*u[3]
uₕ = h(t - u[4])
uₕ = h(p, t - u[4])
uₕ₁₂ = uₕ[1]*uₕ[2]

du[1] = -r₁u₁u₂ + r₂u₃
Expand All @@ -570,7 +570,7 @@ Model of antigen antibody dynamics with fading memory, with vanishing state depe
at ``t = 0`` (J. Gatica and P. Waltman, A threshold model of antigen antibody dynamics with fading memory, 1982).
"""
prob_dde_gatica = DDEProblem(build_f_dde_gatica(0.02, 0.005, 3, 0.01),
[5; 0.1; 0; 0], t -> [5; 0.1; 0; 0],
[5; 0.1; 0; 0], (p, t) -> [5; 0.1; 0; 0],
(0., 40.), dependent_lags = [(u,p,t) -> u[4]])

#=
Expand Down Expand Up @@ -614,7 +614,7 @@ function build_prob_dde_qs(u₀, tspan, τ, D, γₛ, Kₘ, nₛ, a, αₐ, β
du[4] = αC * (R - u[4]) * u[3] - γ₃ * u[4]
end

Cₜ = h(t - τ)[4]
Cₜ = h(p, t - τ)[4]
if Cₜ < 0
# eq. 5 not defined for Cₜ < 0
du[5] = 0
Expand All @@ -623,7 +623,7 @@ function build_prob_dde_qs(u₀, tspan, τ, D, γₛ, Kₘ, nₛ, a, αₐ, β
end
end

DDEProblem(f_dde_qs, u₀, t -> u₀, tspan, constant_lags = [τ])
DDEProblem(f_dde_qs, u₀, (p, t) -> u₀, tspan, constant_lags = [τ])
end

"""
Expand Down

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