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devmotion committed May 19, 2024
1 parent 06da09e commit 0c65da9
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2 changes: 1 addition & 1 deletion docs/make.jl
Original file line number Diff line number Diff line change
Expand Up @@ -16,7 +16,7 @@ mathengine = MathJax3(Dict(:loader => Dict("load" => ["[tex]/require", "[tex]/ma
"ams",
"autoload",
"mathtools",
"require",
"require"
])))

makedocs(sitename = "ModelingToolkit.jl",
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5 changes: 3 additions & 2 deletions docs/pages.jl
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Expand Up @@ -10,7 +10,8 @@ pages = [
"tutorials/parameter_identifiability.md",
"tutorials/bifurcation_diagram_computation.md",
"tutorials/domain_connections.md"],
"Examples" => Any["Basic Examples" => Any["examples/higher_order.md",
"Examples" => Any[
"Basic Examples" => Any["examples/higher_order.md",
"examples/spring_mass.md",
"examples/modelingtoolkitize_index_reduction.md",
"examples/parsing.md"],
Expand All @@ -35,5 +36,5 @@ pages = [
"systems/DiscreteSystem.md",
"systems/PDESystem.md"],
"comparison.md",
"internals.md",
"internals.md"
]
35 changes: 22 additions & 13 deletions docs/src/basics/Composition.md
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Expand Up @@ -22,7 +22,7 @@ function decay(; name)
@variables x(t) f(t)
D = Differential(t)
ODESystem([
D(x) ~ -a * x + f,
D(x) ~ -a * x + f
];
name = name)
end
Expand All @@ -32,8 +32,9 @@ end
@parameters t
D = Differential(t)
connected = compose(ODESystem([decay2.f ~ decay1.x
D(decay1.f) ~ 0], t; name = :connected), decay1, decay2)
connected = compose(
ODESystem([decay2.f ~ decay1.x
D(decay1.f) ~ 0], t; name = :connected), decay1, decay2)
equations(connected)
Expand All @@ -52,10 +53,10 @@ Now we can solve the system:

```@example composition
x0 = [decay1.x => 1.0
decay1.f => 0.0
decay2.x => 1.0]
decay1.f => 0.0
decay2.x => 1.0]
p = [decay1.a => 0.1
decay2.a => 0.2]
decay2.a => 0.2]
using DifferentialEquations
prob = ODEProblem(simplified_sys, x0, (0.0, 100.0), p)
Expand Down Expand Up @@ -96,7 +97,7 @@ in their namespaced form. For example:

```julia
u0 = [x => 2.0
subsys.x => 2.0]
subsys.x => 2.0]
```

Note that any default values within the given subcomponent will be
Expand Down Expand Up @@ -210,19 +211,27 @@ N = S + I + R
@named ieqn = ODESystem([D(I) ~ β * S * I / N - γ * I])
@named reqn = ODESystem([D(R) ~ γ * I])
sir = compose(ODESystem([
sir = compose(
ODESystem(
[
S ~ ieqn.S,
I ~ seqn.I,
R ~ ieqn.R,
ieqn.S ~ seqn.S,
seqn.I ~ ieqn.I,
seqn.R ~ reqn.R,
ieqn.R ~ reqn.R,
reqn.I ~ ieqn.I], t, [S, I, R], [β, γ],
reqn.I ~ ieqn.I],
t,
[S, I, R],
[β, γ],
defaults = [seqn.β => β
ieqn.β => β
ieqn.γ => γ
reqn.γ => γ], name = :sir), seqn, ieqn, reqn)
ieqn.β => β
ieqn.γ => γ
reqn.γ => γ], name = :sir),
seqn,
ieqn,
reqn)
```

Note that the states are forwarded by an equality relationship, while
Expand All @@ -244,7 +253,7 @@ u0 = [seqn.S => 990.0,
reqn.R => 0.0]
p = [β => 0.5
γ => 0.25]
γ => 0.25]
tspan = (0.0, 40.0)
prob = ODEProblem(sireqn_simple, u0, tspan, p, jac = true)
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13 changes: 7 additions & 6 deletions docs/src/basics/Events.md
Original file line number Diff line number Diff line change
Expand Up @@ -69,7 +69,7 @@ function UnitMassWithFriction(k; name)
@variables t x(t)=0 v(t)=0
D = Differential(t)
eqs = [D(x) ~ v
D(v) ~ sin(t) - k * sign(v)]
D(v) ~ sin(t) - k * sign(v)]
ODESystem(eqs, t; continuous_events = [v ~ 0], name) # when v = 0 there is a discontinuity
end
@named m = UnitMassWithFriction(0.7)
Expand All @@ -94,7 +94,7 @@ root_eqs = [x ~ 0] # the event happens at the ground x(t) = 0
affect = [v ~ -v] # the effect is that the velocity changes sign
@named ball = ODESystem([D(x) ~ v
D(v) ~ -9.8], t; continuous_events = root_eqs => affect) # equation => affect
D(v) ~ -9.8], t; continuous_events = root_eqs => affect) # equation => affect
ball = structural_simplify(ball)
Expand All @@ -114,13 +114,14 @@ Multiple events? No problem! This example models a bouncing ball in 2D that is e
D = Differential(t)
continuous_events = [[x ~ 0] => [vx ~ -vx]
[y ~ -1.5, y ~ 1.5] => [vy ~ -vy]]
[y ~ -1.5, y ~ 1.5] => [vy ~ -vy]]
@named ball = ODESystem([
@named ball = ODESystem(
[
D(x) ~ vx,
D(y) ~ vy,
D(vx) ~ -9.8 - 0.1vx, # gravity + some small air resistance
D(vy) ~ -0.1vy,
D(vy) ~ -0.1vy
], t; continuous_events)
ball = structural_simplify(ball)
Expand Down Expand Up @@ -189,7 +190,7 @@ affect interface:
sts = @variables x(t), v(t)
par = @parameters g = 9.8
bb_eqs = [D(x) ~ v
D(v) ~ -g]
D(v) ~ -g]
function bb_affect!(integ, u, p, ctx)
integ.u[u.v] = -integ.u[u.v]
Expand Down
4 changes: 2 additions & 2 deletions docs/src/basics/Linearization.md
Original file line number Diff line number Diff line change
Expand Up @@ -26,8 +26,8 @@ using ModelingToolkit
D = Differential(t)
eqs = [u ~ kp * (r - y) # P controller
D(x) ~ -x + u # First-order plant
y ~ x] # Output equation
D(x) ~ -x + u # First-order plant
y ~ x] # Output equation
@named sys = ODESystem(eqs, t)
matrices, simplified_sys = linearize(sys, [r], [y]) # Linearize from r to y
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2 changes: 1 addition & 1 deletion docs/src/basics/Variable_metadata.md
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Expand Up @@ -142,7 +142,7 @@ Dₜ = Differential(t)
@parameters T [tunable = true, bounds = (0, Inf)]
@parameters k [tunable = true, bounds = (0, Inf)]
eqs = [Dₜ(x) ~ (-x + k * u) / T # A first-order system with time constant T and gain k
y ~ x]
y ~ x]
sys = ODESystem(eqs, t, name = :tunable_first_order)
```

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4 changes: 2 additions & 2 deletions docs/src/examples/parsing.md
Original file line number Diff line number Diff line change
Expand Up @@ -7,8 +7,8 @@ symbolic forms from that? For example, say we had the following system we wanted

```@example parsing
ex = [:(y ~ x)
:(y ~ -2x + 3 / z)
:(z ~ 2)]
:(y ~ -2x + 3 / z)
:(z ~ 2)]
```

We can use the function `parse_expr_to_symbolic` from Symbolics.jl to generate the symbolic
Expand Down
8 changes: 4 additions & 4 deletions docs/src/examples/spring_mass.md
Original file line number Diff line number Diff line change
Expand Up @@ -26,7 +26,7 @@ end
function connect_spring(spring, a, b)
[spring.x ~ norm(scalarize(a .- b))
scalarize(spring.dir .~ scalarize(a .- b))]
scalarize(spring.dir .~ scalarize(a .- b))]
end
function spring_force(spring)
Expand All @@ -43,7 +43,7 @@ g = [0.0, -9.81]
@named spring = Spring(k = k, l = l)
eqs = [connect_spring(spring, mass.pos, center)
scalarize(D.(mass.v) .~ spring_force(spring) / mass.m .+ g)]
scalarize(D.(mass.v) .~ spring_force(spring) / mass.m .+ g)]
@named _model = ODESystem(eqs, t, [spring.x; spring.dir; mass.pos], [])
@named model = compose(_model, mass, spring)
Expand Down Expand Up @@ -96,7 +96,7 @@ We now define functions that help construct the equations for a mass-spring syst
```@example component
function connect_spring(spring, a, b)
[spring.x ~ norm(scalarize(a .- b))
scalarize(spring.dir .~ scalarize(a .- b))]
scalarize(spring.dir .~ scalarize(a .- b))]
end
```

Expand Down Expand Up @@ -125,7 +125,7 @@ We can now create the equations describing this system, by connecting `spring` t

```@example component
eqs = [connect_spring(spring, mass.pos, center)
scalarize(D.(mass.v) .~ spring_force(spring) / mass.m .+ g)]
scalarize(D.(mass.v) .~ spring_force(spring) / mass.m .+ g)]
```

Finally, we can build the model using these equations and components.
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27 changes: 14 additions & 13 deletions docs/src/examples/tearing_parallelism.md
Original file line number Diff line number Diff line change
Expand Up @@ -32,7 +32,7 @@ function ConstantVoltage(; name, V = 1.0)
@named n = Pin()
@parameters V = V
eqs = [V ~ p.v - n.v
0 ~ p.i + n.i]
0 ~ p.i + n.i]
compose(ODESystem(eqs, t, [], [V], name = name), p, n)
end
Expand All @@ -48,10 +48,10 @@ function HeatingResistor(; name, R = 1.0, TAmbient = 293.15, alpha = 1.0)
@variables v(t) RTherm(t)
@parameters R=R TAmbient=TAmbient alpha=alpha
eqs = [RTherm ~ R * (1 + alpha * (h.T - TAmbient))
v ~ p.i * RTherm
h.Q_flow ~ -v * p.i # -LossPower
v ~ p.v - n.v
0 ~ p.i + n.i]
v ~ p.i * RTherm
h.Q_flow ~ -v * p.i # -LossPower
v ~ p.v - n.v
0 ~ p.i + n.i]
compose(ODESystem(eqs, t, [v, RTherm], [R, TAmbient, alpha],
name = name), p, n, h)
end
Expand All @@ -61,7 +61,7 @@ function HeatCapacitor(; name, rho = 8050, V = 1, cp = 460, TAmbient = 293.15)
C = rho * V * cp
@named h = HeatPort()
eqs = [
D(h.T) ~ h.Q_flow / C,
D(h.T) ~ h.Q_flow / C
]
compose(ODESystem(eqs, t, [], [rho, V, cp],
name = name), h)
Expand All @@ -73,8 +73,8 @@ function Capacitor(; name, C = 1.0)
@variables v(t) = 0.0
@parameters C = C
eqs = [v ~ p.v - n.v
0 ~ p.i + n.i
D(v) ~ p.i / C]
0 ~ p.i + n.i
D(v) ~ p.i / C]
compose(ODESystem(eqs, t, [v], [C],
name = name), p, n)
end
Expand All @@ -85,9 +85,9 @@ function parallel_rc_model(i; name, source, ground, R, C)
heat_capacitor = HeatCapacitor(name = Symbol(:heat_capacitor, i))
rc_eqs = [connect(source.p, resistor.p)
connect(resistor.n, capacitor.p)
connect(capacitor.n, source.n, ground.g)
connect(resistor.h, heat_capacitor.h)]
connect(resistor.n, capacitor.p)
connect(capacitor.n, source.n, ground.g)
connect(resistor.h, heat_capacitor.h)]
compose(ODESystem(rc_eqs, t, name = Symbol(name, i)),
[resistor, capacitor, source, ground, heat_capacitor])
Expand All @@ -113,7 +113,7 @@ end;
@variables E(t) = 0.0
eqs = [
D(E) ~ sum(((i, sys),) -> getproperty(sys, Symbol(:resistor, i)).h.Q_flow,
enumerate(rc_systems)),
enumerate(rc_systems))
]
@named _big_rc = ODESystem(eqs, t, [E], [])
@named big_rc = compose(_big_rc, rc_systems)
Expand Down Expand Up @@ -155,7 +155,8 @@ ts = TearingState(expand_connections(big_rc))
inc_org = BipartiteGraphs.incidence_matrix(ts.structure.graph)
blt_org = StructuralTransformations.sorted_incidence_matrix(ts, only_algeqs = true,
only_algvars = true)
blt_reduced = StructuralTransformations.sorted_incidence_matrix(ModelingToolkit.get_tearing_state(sys),
blt_reduced = StructuralTransformations.sorted_incidence_matrix(
ModelingToolkit.get_tearing_state(sys),
only_algeqs = true,
only_algvars = true)
```
Expand Down
4 changes: 2 additions & 2 deletions docs/src/tutorials/acausal_components.md
Original file line number Diff line number Diff line change
Expand Up @@ -102,7 +102,7 @@ end
@mtkbuild rc_model = RCModel(resistor.R = 2.0)
u0 = [
rc_model.capacitor.v => 0.0,
rc_model.capacitor.v => 0.0
]
prob = ODEProblem(rc_model, u0, (0, 10.0))
sol = solve(prob)
Expand Down Expand Up @@ -316,7 +316,7 @@ This is done as follows:

```@example acausal
u0 = [rc_model.capacitor.v => 0.0
rc_model.capacitor.p.i => 0.0]
rc_model.capacitor.p.i => 0.0]
prob = ODEProblem(rc_model, u0, (0, 10.0))
sol = solve(prob)
Expand Down
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