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Refactor SDEProblem constructor #117

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Sep 22, 2023
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Refactor SDEProblem constructor #117

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25 changes: 11 additions & 14 deletions lib/SDEProblemLibrary/src/SDEProblemLibrary.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -33,13 +33,12 @@ u(u_0,p,t,W_t)=u_0\exp((α-\frac{β^2}{2})t+βW_t)

"""
prob_sde_linear = SDEProblem(SDEFunction(f_linear, σ_linear,
analytic = linear_analytic), σ_linear, 1 / 2,
analytic = linear_analytic), 1 / 2,
(0.0, 1.0))

linear_analytic_strat(u0, p, t, W) = @.(u0*exp(1.01t + 0.87W))
prob_sde_linear_stratonovich = SDEProblem(SDEFunction(f_linear, σ_linear,
analytic = linear_analytic_strat),
σ_linear, 1 / 2, (0.0, 1.0))
analytic = linear_analytic_strat), 1 / 2, (0.0, 1.0))
f_linear_iip(du, u, p, t) = @.(du=1.01 * u)
σ_linear_iip(du, u, p, t) = @.(du=0.87 * u)
@doc doc"""
Expand All @@ -55,11 +54,9 @@ u(u_0,p,t,W_t)=u_0\exp((α-\frac{β^2}{2})t+βW_t)
```
"""
prob_sde_2Dlinear = SDEProblem(SDEFunction(f_linear_iip, σ_linear_iip,
analytic = linear_analytic),
σ_linear_iip, ones(4, 2) / 2, (0.0, 1.0))
analytic = linear_analytic), ones(4, 2) / 2, (0.0, 1.0))
prob_sde_2Dlinear_stratonovich = SDEProblem(SDEFunction(f_linear_iip, σ_linear_iip,
analytic = linear_analytic_strat),
σ_linear_iip, ones(4, 2) / 2, (0.0, 1.0))
analytic = linear_analytic_strat), ones(4, 2) / 2, (0.0, 1.0))

f_cubic(u, p, t) = -0.25 * u * (1 - u^2)
σ_cubic(u, p, t) = 0.5 * (1 - u^2)
Expand All @@ -76,7 +73,7 @@ and initial condition ``u_0=\frac{1}{2}``, with solution
u(u0,p,t,W_t)=\frac{(1+u_0)\exp(W_t)+u)0-1}{(1+u_0)\exp(W_t)+1-u_0}
```
"""
prob_sde_cubic = SDEProblem(ff_cubic, σ_cubic, 1 / 2, (0.0, 1.0))
prob_sde_cubic = SDEProblem(ff_cubic, 1 / 2, (0.0, 1.0))

f_wave(u, p, t) = @. -0.01 * sin(u) * cos(u)^3
σ_wave(u, p, t) = @. 0.1 * cos(u)^2
Expand All @@ -93,7 +90,7 @@ and initial condition ``u_0=1`` with solution
u(u_0,p,t,W_t)=\arctan(\frac{W_t}{10} + \tan(u_0))
```
"""
prob_sde_wave = SDEProblem(ff_wave, σ_wave, 1.0, (0.0, 1.0))
prob_sde_wave = SDEProblem(ff_wave, 1.0, (0.0, 1.0))

f_additive(u, p, t) = @. p[2] / sqrt(1 + t) - u / (2 * (1 + t))
σ_additive(u, p, t) = @. p[1] * p[2] / sqrt(1 + t)
Expand All @@ -113,7 +110,7 @@ and initial condition ``u_0=1`` with ``α=0.1`` and ``β=0.05``, with solution
u(u_0,p,t,W_t)=\frac{u_0}{\sqrt{1+t}} + \frac{β(t+αW_t)}{\sqrt{1+t}}
```
"""
prob_sde_additive = SDEProblem(ff_additive, σ_additive, 1.0, (0.0, 1.0), p)
prob_sde_additive = SDEProblem(ff_additive, 1.0, (0.0, 1.0), p)

f_additive_iip(du, u, p, t) = @.(du=p[2] / sqrt(1 + t) - u / (2 * (1 + t)))
σ_additive_iip(du, u, p, t) = @.(du=p[1] * p[2] / sqrt(1 + t))
Expand All @@ -123,7 +120,7 @@ p = ([0.1; 0.1; 0.1; 0.1], [0.5; 0.25; 0.125; 0.1115])
A multiple dimension extension of `additiveSDEExample`

"""
prob_sde_additivesystem = SDEProblem(ff_additive_iip, σ_additive_iip, [1.0; 1.0; 1.0; 1.0],
prob_sde_additivesystem = SDEProblem(ff_additive_iip, [1.0; 1.0; 1.0; 1.0],
(0.0, 1.0), p)

function f_lorenz(du, u, p, t)
Expand Down Expand Up @@ -157,7 +154,7 @@ ff_nltest = SDEFunction(f_nltest, σ_nltest, analytic = analytic_nltest)
Runge–Kutta methods for numerical solution of stochastic differential equations
Tocino and Ardanuy
"""
prob_sde_nltest = SDEProblem(ff_nltest, σ_nltest, 1.0, (0.0, 10.0))
prob_sde_nltest = SDEProblem(ff_nltest, 1.0, (0.0, 10.0))

@doc doc"""
oval2ModelExample(;largeFluctuations=false,useBigs=false,noiseLevel=1)
Expand Down Expand Up @@ -404,7 +401,7 @@ Stiffness of Euler is determined by α+β²<1
Higher α or β is stiff, with α being deterministic stiffness and
β being noise stiffness (and grows by square).
"""
prob_sde_stiffquadito = SDEProblem(ff_stiff_quad_ito, stiff_quad_g, 0.5, (0.0, 3.0),
prob_sde_stiffquadito = SDEProblem(ff_stiff_quad_ito, 0.5, (0.0, 3.0),
(1.0, 1.0))

@doc doc"""
Expand All @@ -424,7 +421,7 @@ Stiffness of Euler is determined by α+β²<1
Higher α or β is stiff, with α being deterministic stiffness and
β being noise stiffness (and grows by square).
"""
prob_sde_stiffquadstrat = SDEProblem(ff_stiff_quad_strat, stiff_quad_g, 0.5, (0.0, 3.0),
prob_sde_stiffquadstrat = SDEProblem(ff_stiff_quad_strat, 0.5, (0.0, 3.0),
(1.0, 1.0))

@doc doc"""
Expand Down