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Jul 31, 2025
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Apply JuliaFormatter to fix code formatting #42

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3 changes: 3 additions & 0 deletions .JuliaFormatter.toml
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Original file line number Diff line number Diff line change
@@ -0,0 +1,3 @@
style = "sciml"
format_markdown = true
format_docstrings = true
1 change: 0 additions & 1 deletion LICENSE.md
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Original file line number Diff line number Diff line change
Expand Up @@ -19,4 +19,3 @@ The MATLABDiffEq.jl package is licensed under the MIT "Expat" License:
> LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
> OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
> SOFTWARE.
>
274 changes: 131 additions & 143 deletions README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -37,24 +37,24 @@ but are not exported. Thus to use `ode45`, you would specify the algorithm as
using MATLABDiffEq, ParameterizedFunctions

f = @ode_def LotkaVolterra begin
dx = 1.5x - x*y
dy = -3y + x*y
dx = 1.5x - x*y
dy = -3y + x*y
end

tspan = (0.0,10.0)
u0 = [1.0,1.0]
prob = ODEProblem(f,u0,tspan)
sol = solve(prob,MATLABDiffEq.ode45())
tspan = (0.0, 10.0)
u0 = [1.0, 1.0]
prob = ODEProblem(f, u0, tspan)
sol = solve(prob, MATLABDiffEq.ode45())

function lorenz(du,u,p,t)
du[1] = 10.0(u[2]-u[1])
du[2] = u[1]*(28.0-u[3]) - u[2]
du[3] = u[1]*u[2] - (8/3)*u[3]
function lorenz(du, u, p, t)
du[1] = 10.0(u[2]-u[1])
du[2] = u[1]*(28.0-u[3]) - u[2]
du[3] = u[1]*u[2] - (8/3)*u[3]
end
u0 = [1.0;0.0;0.0]
tspan = (0.0,100.0)
prob = ODEProblem(lorenz,u0,tspan)
sol = solve(prob,MATLABDiffEq.ode45())
u0 = [1.0; 0.0; 0.0]
tspan = (0.0, 100.0)
prob = ODEProblem(lorenz, u0, tspan)
sol = solve(prob, MATLABDiffEq.ode45())
```

## Measuring Overhead
Expand Down Expand Up @@ -82,28 +82,28 @@ Generally, for long enough problems the overhead is minimal. Example:
```julia
using DiffEqBase, ParameterizedFunctions, MATLABDiffEq
f = @ode_def_bare RigidBodyBench begin
dy1 = -2*y2*y3
dy2 = 1.25*y1*y3
dy3 = -0.5*y1*y2 + 0.25*sin(t)^2
dy1 = -2*y2*y3
dy2 = 1.25*y1*y3
dy3 = -0.5*y1*y2 + 0.25*sin(t)^2
end
prob = ODEProblem(f,[1.0;0.0;0.9],(0.0,100.0))
prob = ODEProblem(f, [1.0; 0.0; 0.9], (0.0, 100.0))
alg = MATLABDiffEq.ode45()
algstr = string(typeof(alg).name.name)
```

For this, we get the following:

```julia
julia> @time sol = solve(prob,alg);
julia> @time sol = solve(prob, alg);
0.063918 seconds (38.84 k allocations: 1.556 MB)

julia> @time sol = solve(prob,alg);
julia> @time sol = solve(prob, alg);
0.062600 seconds (38.84 k allocations: 1.556 MB)

julia> @time sol = solve(prob,alg);
julia> @time sol = solve(prob, alg);
0.061438 seconds (38.84 k allocations: 1.556 MB)

julia> @time sol = solve(prob,alg);
julia> @time sol = solve(prob, alg);
0.065460 seconds (38.84 k allocations: 1.556 MB)

julia> @time MATLABDiffEq.eval_string("[t,u] = $(algstr)(diffeqf,tspan,u0,options);")
Expand Down Expand Up @@ -131,14 +131,14 @@ MATLAB solvers do outperform that of Python and R.

```julia
f = @ode_def_bare LotkaVolterra begin
dx = a*x - b*x*y
dy = -c*y + d*x*y
dx = a*x - b*x*y
dy = -c*y + d*x*y
end a b c d
p = [1.5,1,3,1]
tspan = (0.0,10.0)
u0 = [1.0,1.0]
prob = ODEProblem(f,u0,tspan,p)
sol = solve(prob,Vern7(),abstol=1/10^14,reltol=1/10^14)
p = [1.5, 1, 3, 1]
tspan = (0.0, 10.0)
u0 = [1.0, 1.0]
prob = ODEProblem(f, u0, tspan, p)
sol = solve(prob, Vern7(), abstol = 1/10^14, reltol = 1/10^14)
test_sol = TestSolution(sol)

setups = [Dict(:alg=>DP5())
Expand All @@ -152,32 +152,29 @@ setups = [Dict(:alg=>DP5())
Dict(:alg=>SciPyDiffEq.odeint())
Dict(:alg=>deSolveDiffEq.lsoda())
Dict(:alg=>deSolveDiffEq.ode45())
Dict(:alg=>CVODE_Adams())
]

names = [
"Julia: DP5"
"Hairer: dopri5"
"Julia: Tsit5"
"Julia: Vern7"
"MATLAB: ode45"
"MATLAB: ode113"
"SciPy: RK45"
"SciPy: LSODA"
"SciPy: odeint"
"deSolve: lsoda"
"deSolve: ode45"
"Sundials: Adams"
]
Dict(:alg=>CVODE_Adams())]

names = ["Julia: DP5"
"Hairer: dopri5"
"Julia: Tsit5"
"Julia: Vern7"
"MATLAB: ode45"
"MATLAB: ode113"
"SciPy: RK45"
"SciPy: LSODA"
"SciPy: odeint"
"deSolve: lsoda"
"deSolve: ode45"
"Sundials: Adams"]

abstols = 1.0 ./ 10.0 .^ (6:13)
reltols = 1.0 ./ 10.0 .^ (3:10)
wp = WorkPrecisionSet(prob,abstols,reltols,setups;
names = names,
appxsol=test_sol,dense=false,
save_everystep=false,numruns=100,maxiters=10000000,
timeseries_errors=false,verbose=false)
plot(wp,title="Non-stiff 1: Lotka-Volterra")
wp = WorkPrecisionSet(prob, abstols, reltols, setups;
names = names,
appxsol = test_sol, dense = false,
save_everystep = false, numruns = 100, maxiters = 10000000,
timeseries_errors = false, verbose = false)
plot(wp, title = "Non-stiff 1: Lotka-Volterra")
```

![](https://user-images.githubusercontent.com/1814174/71537082-ef42ac00-28e4-11ea-9acc-67dfd9990221.png)
Expand All @@ -186,12 +183,12 @@ plot(wp,title="Non-stiff 1: Lotka-Volterra")

```julia
f = @ode_def_bare RigidBodyBench begin
dy1 = -2*y2*y3
dy2 = 1.25*y1*y3
dy3 = -0.5*y1*y2 + 0.25*sin(t)^2
dy1 = -2*y2*y3
dy2 = 1.25*y1*y3
dy3 = -0.5*y1*y2 + 0.25*sin(t)^2
end
prob = ODEProblem(f,[1.0;0.0;0.9],(0.0,100.0))
sol = solve(prob,Vern7(),abstol=1/10^14,reltol=1/10^14)
prob = ODEProblem(f, [1.0; 0.0; 0.9], (0.0, 100.0))
sol = solve(prob, Vern7(), abstol = 1/10^14, reltol = 1/10^14)
test_sol = TestSolution(sol)

setups = [Dict(:alg=>DP5())
Expand All @@ -205,32 +202,29 @@ setups = [Dict(:alg=>DP5())
Dict(:alg=>SciPyDiffEq.odeint())
Dict(:alg=>deSolveDiffEq.lsoda())
Dict(:alg=>deSolveDiffEq.ode45())
Dict(:alg=>CVODE_Adams())
]

names = [
"Julia: DP5"
"Hairer: dopri5"
"Julia: Tsit5"
"Julia: Vern7"
"MATLAB: ode45"
"MATLAB: ode113"
"SciPy: RK45"
"SciPy: LSODA"
"SciPy: odeint"
"deSolve: lsoda"
"deSolve: ode45"
"Sundials: Adams"
]
Dict(:alg=>CVODE_Adams())]

names = ["Julia: DP5"
"Hairer: dopri5"
"Julia: Tsit5"
"Julia: Vern7"
"MATLAB: ode45"
"MATLAB: ode113"
"SciPy: RK45"
"SciPy: LSODA"
"SciPy: odeint"
"deSolve: lsoda"
"deSolve: ode45"
"Sundials: Adams"]

abstols = 1.0 ./ 10.0 .^ (6:13)
reltols = 1.0 ./ 10.0 .^ (3:10)
wp = WorkPrecisionSet(prob,abstols,reltols,setups;
names = names,
appxsol=test_sol,dense=false,
save_everystep=false,numruns=100,maxiters=10000000,
timeseries_errors=false,verbose=false)
plot(wp,title="Non-stiff 2: Rigid-Body")
wp = WorkPrecisionSet(prob, abstols, reltols, setups;
names = names,
appxsol = test_sol, dense = false,
save_everystep = false, numruns = 100, maxiters = 10000000,
timeseries_errors = false, verbose = false)
plot(wp, title = "Non-stiff 2: Rigid-Body")
```

![](https://user-images.githubusercontent.com/1814174/71537083-ef42ac00-28e4-11ea-8dc7-a5dca0518baf.png)
Expand All @@ -239,12 +233,12 @@ plot(wp,title="Non-stiff 2: Rigid-Body")

```julia
rober = @ode_def begin
dy₁ = -k₁*y₁+k₃*y₂*y₃
dy₂ = k₁*y₁-k₂*y₂^2-k₃*y₂*y₃
dy₃ = k₂*y₂^2
dy₁ = -k₁*y₁+k₃*y₂*y₃
dy₂ = k₁*y₁-k₂*y₂^2-k₃*y₂*y₃
dy₃ = k₂*y₂^2
end k₁ k₂ k₃
prob = ODEProblem(rober,[1.0,0.0,0.0],(0.0,1e5),[0.04,3e7,1e4])
sol = solve(prob,CVODE_BDF(),abstol=1/10^14,reltol=1/10^14)
prob = ODEProblem(rober, [1.0, 0.0, 0.0], (0.0, 1e5), [0.04, 3e7, 1e4])
sol = solve(prob, CVODE_BDF(), abstol = 1/10^14, reltol = 1/10^14)
test_sol = TestSolution(sol)

abstols = 1.0 ./ 10.0 .^ (7:8)
Expand All @@ -261,30 +255,27 @@ setups = [Dict(:alg=>Rosenbrock23())
Dict(:alg=>SciPyDiffEq.BDF())
Dict(:alg=>SciPyDiffEq.odeint())
Dict(:alg=>deSolveDiffEq.lsoda())
Dict(:alg=>CVODE_BDF())
]

names = [
"Julia: Rosenbrock23"
"Julia: TRBDF2"
"Julia: radau"
"Hairer: rodas"
"Hairer: radau"
"MATLAB: ode23s"
"MATLAB: ode15s"
"SciPy: LSODA"
"SciPy: BDF"
"SciPy: odeint"
"deSolve: lsoda"
"Sundials: CVODE"
]

wp = WorkPrecisionSet(prob,abstols,reltols,setups;
names = names,print_names = true,
dense=false,verbose = false,
save_everystep=false,appxsol=test_sol,
maxiters=Int(1e5))
plot(wp,title="Stiff 1: ROBER", legend=:topleft)
Dict(:alg=>CVODE_BDF())]

names = ["Julia: Rosenbrock23"
"Julia: TRBDF2"
"Julia: radau"
"Hairer: rodas"
"Hairer: radau"
"MATLAB: ode23s"
"MATLAB: ode15s"
"SciPy: LSODA"
"SciPy: BDF"
"SciPy: odeint"
"deSolve: lsoda"
"Sundials: CVODE"]

wp = WorkPrecisionSet(prob, abstols, reltols, setups;
names = names, print_names = true,
dense = false, verbose = false,
save_everystep = false, appxsol = test_sol,
maxiters = Int(1e5))
plot(wp, title = "Stiff 1: ROBER", legend = :topleft)
```

![](https://user-images.githubusercontent.com/1814174/71537080-ef42ac00-28e4-11ea-9abd-37631cd18ad9.png)
Expand All @@ -293,23 +284,23 @@ plot(wp,title="Stiff 1: ROBER", legend=:topleft)

```julia
f = @ode_def Hires begin
dy1 = -1.71*y1 + 0.43*y2 + 8.32*y3 + 0.0007
dy2 = 1.71*y1 - 8.75*y2
dy3 = -10.03*y3 + 0.43*y4 + 0.035*y5
dy4 = 8.32*y2 + 1.71*y3 - 1.12*y4
dy5 = -1.745*y5 + 0.43*y6 + 0.43*y7
dy6 = -280.0*y6*y8 + 0.69*y4 + 1.71*y5 -
0.43*y6 + 0.69*y7
dy7 = 280.0*y6*y8 - 1.81*y7
dy8 = -280.0*y6*y8 + 1.81*y7
dy1 = -1.71*y1 + 0.43*y2 + 8.32*y3 + 0.0007
dy2 = 1.71*y1 - 8.75*y2
dy3 = -10.03*y3 + 0.43*y4 + 0.035*y5
dy4 = 8.32*y2 + 1.71*y3 - 1.12*y4
dy5 = -1.745*y5 + 0.43*y6 + 0.43*y7
dy6 = -280.0*y6*y8 + 0.69*y4 + 1.71*y5 -
0.43*y6 + 0.69*y7
dy7 = 280.0*y6*y8 - 1.81*y7
dy8 = -280.0*y6*y8 + 1.81*y7
end

u0 = zeros(8)
u0[1] = 1
u0[8] = 0.0057
prob = ODEProblem(f,u0,(0.0,321.8122))
prob = ODEProblem(f, u0, (0.0, 321.8122))

sol = solve(prob,Rodas5(),abstol=1/10^14,reltol=1/10^14)
sol = solve(prob, Rodas5(), abstol = 1/10^14, reltol = 1/10^14)
test_sol = TestSolution(sol)

abstols = 1.0 ./ 10.0 .^ (5:8)
Expand All @@ -326,29 +317,26 @@ setups = [Dict(:alg=>Rosenbrock23())
Dict(:alg=>SciPyDiffEq.BDF())
Dict(:alg=>SciPyDiffEq.odeint())
Dict(:alg=>deSolveDiffEq.lsoda())
Dict(:alg=>CVODE_BDF())
]

names = [
"Julia: Rosenbrock23"
"Julia: TRBDF2"
"Julia: radau"
"Hairer: rodas"
"Hairer: radau"
"MATLAB: ode23s"
"MATLAB: ode15s"
"SciPy: LSODA"
"SciPy: BDF"
"SciPy: odeint"
"deSolve: lsoda"
"Sundials: CVODE"
]

wp = WorkPrecisionSet(prob,abstols,reltols,setups;
names = names,print_names = true,
save_everystep=false,appxsol=test_sol,
maxiters=Int(1e5),numruns=100)
plot(wp,title="Stiff 2: Hires",legend=:topleft)
Dict(:alg=>CVODE_BDF())]

names = ["Julia: Rosenbrock23"
"Julia: TRBDF2"
"Julia: radau"
"Hairer: rodas"
"Hairer: radau"
"MATLAB: ode23s"
"MATLAB: ode15s"
"SciPy: LSODA"
"SciPy: BDF"
"SciPy: odeint"
"deSolve: lsoda"
"Sundials: CVODE"]

wp = WorkPrecisionSet(prob, abstols, reltols, setups;
names = names, print_names = true,
save_everystep = false, appxsol = test_sol,
maxiters = Int(1e5), numruns = 100)
plot(wp, title = "Stiff 2: Hires", legend = :topleft)
```

![](https://user-images.githubusercontent.com/1814174/71537081-ef42ac00-28e4-11ea-950f-59c762ce9a69.png)
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