fix docstrings for v0.7

Author: ChrisRackauckas

src/ode/brusselator_prob.jl

@@ -50,7 +50,7 @@ function init_brusselator_2d(xyd)
 end
 xyd_brusselator = linspace(0,1,32)
 
-"""
+doc"""
 2D Brusselator
 
 ```math
@@ -128,7 +128,7 @@ function init_brusselator_1d(N)
   u
 end
 
-"""
+doc"""
 1D Brusselator
 
 ```math

src/ode/pollution_prob.jl

@@ -1,47 +1,3 @@
-"""
-[Pollution Problem](http://nbviewer.jupyter.org/github/JuliaDiffEq/DiffEqBenchmarks.jl/blob/master/StiffODE/Pollution.ipynb) (Stiff)
-
-This IVP is a stiff system of 20 non-linear Ordinary Differential Equations. It is in the form of ``\\frac{dy}{dt}=f(y), \\quad y(0)=y0,`` with
-
-```math
-y \\in ℝ^20, \\quad 0 ≤ t ≤ 60
-```
-
-where ``f`` is defined by
-
-```math
-f(y) = \\begin{pmatrix}
--\\sum_{j∈\{1,10,14,23,24\}} r_j + \\sum_{j∈\{2,3,9,11,12,22,25\}} r_j \\\\
--r_2 - r_3 - r_9 - r_12 + r_1 + r_{21} \\\\
--r_{15} + r_1 + r_{17} + r_{19} + r_{22} \\\\
--r_2 - r_{16} - r_{17} - r_{23} + r_{15} \\\\
--r_3 + 2r_4 + r_6 + r_7 + r_{13} + r_{20} \\\\
--r_6 - r_8 - r_{14} - r_{20} + r_3 + 2r_{18} \\\\
--r_4 - r_5 - r_6 + r_{13} \\\\
-r_4 + r_5 + r_6 + r_7 \\\\
--r_7 - r_8 \\\\
--r_{12} + r_7 + r_9 \\\\
--r_9 - r_{10} + r_8 + r_{11} \\\\
-r_9 \\\\
--r_{11} + r_{10} \\\\
--r_{13} + r_{12} \\\\
-r_{14} \\\\
--r_{18} - r_{19} + r_{16} \\\\
--r_{20} \\\\
-r_{20} \\\\
--r{21} - r_{22} - r_{24} + r_{23} + r_{25} \\\\
--r_{25} + r_{24}
-\\end{pmatrix}
-```
-
-with the initial condition of
-
-```math
-y0 = (0, 0.2, 0, 0.04, 0, 0, 0.1, 0.3, 0.01, 0, 0, 0, 0 ,0, 0, 0, 0.007, 0, 0, 0)^T
-```
-
-https://archimede.dm.uniba.it/~testset/report/pollu.pdf
-"""
 const k1=.35e0
 const k2=.266e2
 const k3=.123e5
@@ -231,4 +187,49 @@ u0[7]  = 0.1
 u0[8]  = 0.3
 u0[9]  = 0.01
 u0[17] = 0.007
+
+doc"""
+[Pollution Problem](http://nbviewer.jupyter.org/github/JuliaDiffEq/DiffEqBenchmarks.jl/blob/master/StiffODE/Pollution.ipynb) (Stiff)
+
+This IVP is a stiff system of 20 non-linear Ordinary Differential Equations. It is in the form of ``\\frac{dy}{dt}=f(y), \\quad y(0)=y0,`` with
+
+```math
+y \\in ℝ^20, \\quad 0 ≤ t ≤ 60
+```
+
+where ``f`` is defined by
+
+```math
+f(y) = \\begin{pmatrix}
+-\\sum_{j∈\{1,10,14,23,24\}} r_j + \\sum_{j∈\{2,3,9,11,12,22,25\}} r_j \\\\
+-r_2 - r_3 - r_9 - r_12 + r_1 + r_{21} \\\\
+-r_{15} + r_1 + r_{17} + r_{19} + r_{22} \\\\
+-r_2 - r_{16} - r_{17} - r_{23} + r_{15} \\\\
+-r_3 + 2r_4 + r_6 + r_7 + r_{13} + r_{20} \\\\
+-r_6 - r_8 - r_{14} - r_{20} + r_3 + 2r_{18} \\\\
+-r_4 - r_5 - r_6 + r_{13} \\\\
+r_4 + r_5 + r_6 + r_7 \\\\
+-r_7 - r_8 \\\\
+-r_{12} + r_7 + r_9 \\\\
+-r_9 - r_{10} + r_8 + r_{11} \\\\
+r_9 \\\\
+-r_{11} + r_{10} \\\\
+-r_{13} + r_{12} \\\\
+r_{14} \\\\
+-r_{18} - r_{19} + r_{16} \\\\
+-r_{20} \\\\
+r_{20} \\\\
+-r{21} - r_{22} - r_{24} + r_{23} + r_{25} \\\\
+-r_{25} + r_{24}
+\\end{pmatrix}
+```
+
+with the initial condition of
+
+```math
+y0 = (0, 0.2, 0, 0.04, 0, 0, 0.1, 0.3, 0.01, 0, 0, 0, 0 ,0, 0, 0, 0.007, 0, 0, 0)^T
+```
+
+https://archimede.dm.uniba.it/~testset/report/pollu.pdf
+"""
 prob_ode_pollution = ODEProblem(pollution,u0,(0.0,60.0))

src/sde_premade_problems.jl

@@ -3,7 +3,8 @@
 f = (u,p,t) -> 1.01u
 σ = (u,p,t) -> 0.87u
 (ff::typeof(f))(::Type{Val{:analytic}},u0,p,t,W) = u0.*exp.(0.63155t+0.87W)
-"""
+
+doc"""
 ```math
 du_t = βudt + αudW_t
 ```
@@ -32,7 +33,7 @@ end
   end
 end
 (ff::typeof(f))(::Type{Val{:analytic}},u0,p,t,W) = u0.*exp.(0.63155*t+0.87*W)
-"""
+doc"""
 8 linear SDEs (as a 4x2 matrix):
 
 ```math
@@ -62,7 +63,7 @@ prob_sde_2Dlinear_stratonovich = SDEProblem(f,σ,ones(4,2)/2,(0.0,1.0))
 f = (u,p,t) -> -.25*u*(1-u^2)
 σ = (u,p,t) -> .5*(1-u^2)
 (ff::typeof(f))(::Type{Val{:analytic}},u0,p,t,W) = ((1+u0).*exp.(W)+u0-1)./((1+u0).*exp.(W)+1-u0)
-"""
+doc"""
 ```math
 du_t = \\frac{1}{4}u(1-u^2)dt + \\frac{1}{2}(1-u^2)dW_t
 ```
@@ -78,7 +79,7 @@ prob_sde_cubic = SDEProblem(f,σ,1/2,(0.0,1.0))
 f = (u,p,t) -> -0.01*sin.(u).*cos.(u).^3
 σ = (u,p,t) -> 0.1*cos.(u).^2
 (ff::typeof(f))(::Type{Val{:analytic}},u0,p,t,W) = atan.(0.1*W + tan.(u0))
-"""
+doc"""
 ```math
 du_t = -\\frac{1}{100}\sin(u)\cos^3(u)dt + \\frac{1}{10}\cos^{2}(u_t) dW_t
 ```
@@ -96,7 +97,7 @@ f = (u,p,t) -> p[2]./sqrt.(1+t) - u./(2*(1+t))
 p = (0.1,0.05)
 (ff::typeof(f))(::Type{Val{:analytic}},u0,p,t,W) = u0./sqrt.(1+t) + p[2]*(t+p[1]*W)./sqrt.(1+t)
 
-"""
+doc"""
 Additive noise problem
 
 ```math
@@ -126,7 +127,7 @@ end
 end
 (ff::typeof(f))(::Type{Val{:analytic}},u0,p,t,W) = u0./sqrt(1+t) + sde_wave_βvec.*(t+sde_wave_αvec.*W)./sqrt(1+t)
 
-"""
+doc"""
 A multiple dimension extension of `additiveSDEExample`
 
 """
@@ -143,7 +144,7 @@ end σ ρ β
     du[i] = 3.0 #Additive
   end
 end
-"""
+doc"""
 Lorenz Attractor with additive noise
 
 ```math
@@ -162,7 +163,7 @@ prob_sde_lorenz = SDEProblem(f,σ,ones(3),(0.0,10.0),(10.0,28.0,2.66))
 f = (u,p,t) -> (1/3)*u^(1/3) + 6*u^(2/3)
 σ = (u,p,t) -> u^(2/3)
 (ff::typeof(f))(::Type{Val{:analytic}},u0,p,t,W) = (2t + 1 + W/3)^3
-"""
+doc"""
 Runge–Kutta methods for numerical solution of stochastic differential equations
 Tocino and Ardanuy
 """
@@ -316,8 +317,26 @@ function oval2ModelExample(;largeFluctuations=false,useBigs=false,noiseLevel=1)
   SDEProblem(f,σ,u0,(0.0,500.0))
 end
 
+stiff_quad_f_ito(u,p,t) = -(p[1]+(p[2]^2)*u)*(1-u^2)
+stiff_quad_f_strat(u,p,t) = -p[1]*(1-u^2)
+stiff_quad_g(u,p,t) = p[2]*(1-u^2)
 
-"""
+function stiff_quad_f_ito(::Type{Val{:analytic}},u0,p,t,W)
+    α = p[1]
+    β = p[2]
+    exp_tmp = exp(-2*α*t+2*β*W)
+    tmp = 1 + u0
+    (tmp*exp_tmp + u0 - 1)/(tmp*exp_tmp - u0 + 1)
+end
+function stiff_quad_f_strat(::Type{Val{:analytic}},u0,p,t,W)
+    α = p[1]
+    β = p[2]
+    exp_tmp = exp(-2*α*t+2*β*W)
+    tmp = 1 + u0
+    (tmp*exp_tmp + u0 - 1)/(tmp*exp_tmp - u0 + 1)
+end
+
+doc"""
 The composite Euler method for stiff stochastic
 differential equations
 
@@ -334,31 +353,28 @@ 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).
 """
-function generate_stiff_quad(α,β;ito=true)
-    if ito
-        f = function (u,p,t)
-            -(α+(β^2)*u)*(1-u^2)
-        end
-    else
-        f = function (u,p,t)
-            -α*(1-u^2)
-        end
-    end
+prob_sde_stiffquadito = SDEProblem(stiff_quad_f_ito,stiff_quad_g,0.5,(0.0,3.0),(1.0,1.0))
 
-    function g(u,p,t)
-        β*(1-u^2)
-    end
+doc"""
+The composite Euler method for stiff stochastic
+differential equations
 
-    function (::typeof(f))(::Type{Val{:analytic}},u0,p,t,W)
-        exp_tmp = exp(-2*α*t+2*β*W)
-        tmp = 1 + u0
-        (tmp*exp_tmp + u0 - 1)/(tmp*exp_tmp - u0 + 1)
-    end
+Kevin Burrage, Tianhai Tian
 
-    SDEProblem(f,g,0.5,(0.0,3.0))
-end
+And
+
+S-ROCK: CHEBYSHEV METHODS FOR STIFF STOCHASTIC
+DIFFERENTIAL EQUATIONS
 
+ASSYR ABDULLE AND STEPHANE CIRILLI
+
+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(stiff_quad_f_strat,stiff_quad_g,0.5,(0.0,3.0),(1.0,1.0))
+
+doc"""
 Stochastic Heat Equation with scalar multiplicative noise
 
 S-ROCK: CHEBYSHEV METHODS FOR STIFF STOCHASTIC
@@ -432,6 +448,7 @@ network = @reaction_network rnType  begin
     p10, SP2 --> 0
 end p1 p2 p3 p4 p5 p6 p7 p8 p9 p10
 p = (0.01,3.0,3.0,4.5,2.,15.,20.0,0.005,0.01,0.05)
+
 """
 An oscillatory chemical reaction system
 """