### Import and Setup

Source: https://docs.pathsim.org/fmi/v0.1.1/examples/fmu-model-exchange-bouncing-ball

Imports necessary libraries and modules for the bouncing ball example.

```python
import numpy as np
import matplotlib.pyplot as plt
  

# Apply PathSim docs matplotlib style for consistent, theme-friendly figures
# plt.style.use removed for browser
  

from pathlib import Path
from pathsim import Simulation, Connection
from pathsim.blocks import Scope
from pathsim_fmi import ModelExchangeFMU
from pathsim.solvers import RKBS32
```

--------------------------------

### Import and Setup for Kalman Filter Example

Source: https://docs.pathsim.org/pathsim/v0.25.0/notebooks/kalman_filter.ipynb

Imports required libraries and PathSim blocks, and applies the PathSim docs matplotlib style.

```python
import numpy as np
import matplotlib.pyplot as plt

# Apply PathSim docs matplotlib style
plt.style.use('../pathsim_docs.mplstyle')

from pathsim import Simulation, Connection
from pathsim.blocks import (
    Constant,
    Integrator,
    Adder,
    WhiteNoise,
    KalmanFilter,
    Scope
)
```

--------------------------------

### Set up simulation parameters

Source: https://docs.pathsim.org/fmi/v0.1.1/notebooks/fmu_model_exchange_bouncing_ball.ipynb

Sets the start time, stop time, and step size for the simulation.

```python
start_time = 0.0
stop_time = 3.0
step_size = 0.01
```

--------------------------------

### Simulation Setup

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/fmu-model-exchange-vanderpol

Initializes a Simulation with the RKDP54 solver, dt=0.1, dt_max=0.1, and tolerances, then runs for 30 seconds.

```Python
# Initialize simulation
sim = Simulation(
    blocks,
    connections,
    dt=0.1,
    dt_max=0.1,
    Solver=RKDP54,
    tolerance_lte_rel=1e-6,
    tolerance_lte_abs=1e-9,
    log=True
)
  
# Run simulation
sim.run(30.0)
```

--------------------------------

### Import and Setup

Source: https://docs.pathsim.org/pathsim/v0.25.0/notebooks/dcmotor_control.ipynb

Imports the necessary PathSim classes and blocks, and applies the documentation matplotlib style.

```python
import numpy as np
import matplotlib.pyplot as plt

# Apply PathSim docs matplotlib style
plt.style.use('../pathsim_docs.mplstyle')

from pathsim import Simulation, Connection
from pathsim.blocks import StepSource, Integrator, Amplifier, Adder, Scope, AntiWindupPID, Clip
from pathsim.solvers import RKCK54
```

--------------------------------

### Import FastSim and print version

Source: https://docs.pathsim.org/fastsim/v0.28.3/examples/c-code-generation

Imports the FastSim library and its core components, then prints the library version. This is the initial setup for all subsequent examples on the page.

```Python
import fastsim as fs
from fastsim import Simulation, Connection
from fastsim.blocks import Source, Adder, Amplifier, Integrator, ODE, Scope
from fastsim.solvers import RK4

print(f"fastsim {fs.__version__}")
```

--------------------------------

### Setup System Blocks and Connections

Source: https://docs.pathsim.org/pathsim/v0.25.0/notebooks/chemical_reactor.ipynb

Initializes the ODE block for the reactor and defines the connections between system components and the scope.

```python
# Define system blocks
CSTR = ODE(reaction_rates, np.array([Ca_0, Cb_0, T_0]))
Sco = Scope(labels=['Ca', 'Cb', 'T'])

blocks = [CSTR, Src_Ca, Src_T, Sco]

connections = [
    Connection(CSTR, Sco),         # Ca output
    Connection(CSTR[1], Sco[1]),   # Cb output
    Connection(CSTR[2], Sco[2]),   # T output
    Connection(Src_Ca, CSTR[0]),   # Ca_in input
    Connection(Src_T, CSTR[1])     # T_in input
]
```

--------------------------------

### DC Motor Model Setup

Source: https://docs.pathsim.org/fastsim/v0.28.3/examples/one-script-two-engines

Initializes the environment and imports necessary libraries for the DC motor PI speed control model.

```python
import time
  

import numpy as np
import matplotlib.pyplot as plt
  

# Apply the FastSim docs matplotlib style
```

--------------------------------

### Import FastSim and dependencies for C code generation example

Source: https://docs.pathsim.org/fastsim/v0.28.3/notebooks/c_code_generation.ipynb

Imports numpy, matplotlib, and FastSim modules needed for the DC motor example. Applies the FastSim docs matplotlib style and prints the FastSim version.

```python
import numpy as np
import matplotlib.pyplot as plt

# Apply the FastSim docs matplotlib style
plt.style.use('../fastsim_docs.mplstyle')

import fastsim as fs
from fastsim import Simulation, Connection
from fastsim.blocks import Source, Adder, Amplifier, Integrator, ODE, Scope
from fastsim.solvers import RK4

print(f"fastsim {fs.__version__}")
```

--------------------------------

### Import and Setup

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/fmu-model-exchange-vanderpol

Imports numpy, matplotlib, Path, Simulation, Connection, ModelExchangeFMU, Scope, and solvers RKDP54 and ESDIRK43. The matplotlib style is removed for browser compatibility.

```Python
import numpy as np
import matplotlib.pyplot as plt
  
# Apply PathSim docs matplotlib style for consistent, theme-friendly figures
# plt.style.use removed for browser
  
from pathlib import Path
from pathsim import Simulation, Connection
from pathsim.blocks import ModelExchangeFMU, Scope
from pathsim.solvers import RKDP54, ESDIRK43
```

--------------------------------

### Import PathSim classes

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/fmcw-radar

Initial setup to import the necessary libraries and PathSim components for the radar simulation.

```python
import numpy as np
import matplotlib.pyplot as plt
  

# Apply PathSim docs matplotlib style for consistent, theme-friendly figures
# plt.style.use removed for browser
  

from pathsim import Simulation, Connection
```

--------------------------------

### Prompt supercritical simulation setup

Source: https://docs.pathsim.org/chem/v0.2.8/notebooks/point_kinetics.ipynb

Sets up a simulation with a step reactivity of 0.008 (prompt supercritical) using the PointKinetics block, GEAR52A solver, and a relaxed tolerance. Runs for 0.5 seconds.

```python
reactor = PointKinetics(n0=1.0)

rho_prompt = 0.008
src_rho = Source(lambda t: rho_prompt if t > 0 else 0.0)
src_s = Source(lambda t: 0.0)
sco = Scope(labels=["n"])

sim = Simulation(
    [src_rho, src_s, reactor, sco],
    [
        Connection(src_rho, reactor),
        Connection(src_s, reactor[1]),
        Connection(reactor, sco),
    ],
    dt=0.001,
    Solver=GEAR52A,
    tolerance_fpi=1e-6,
    log=True,
)

sim.run(0.5)
```

--------------------------------

### Flash Distillation Simulation Setup and Execution

Source: https://docs.pathsim.org/chem/v0.2.8/examples/flash-distillation

Defines the feed sources, scope, and simulation parameters for a flash distillation process, followed by the execution of the simulation.

```python
# Feed: 10 mol/s, equimolar (z1 = 0.5), 1 atm
src_f = Source(lambda t: 10.0)
src_z = Source(lambda t: 0.5)
src_t = Source(lambda t: 340.0 + t * 0.5) # ramp 340 -> 400 K
src_p = Source(lambda t: 101325.0)
  

sco = Scope(labels=["V_rate", "L_rate", "y_1 (benzene)", "x_1 (benzene)"])
  

sim = Simulation(
[src_f, src_z, src_t, src_p, flash, sco],
[
Connection(src_f, flash), # F
Connection(src_z, flash[1]), # z_1
Connection(src_t, flash[2]), # T
Connection(src_p, flash[3]), # P
Connection(flash, sco), # V_rate
Connection(flash[1], sco[1]), # L_rate
Connection(flash[2], sco[2]), # y_1
Connection(flash[3], sco[3]), # x_1
],
dt=0.5,
log=True,
)
  

sim.run(120)
```

--------------------------------

### Connect blocks and initialize simulation with RKCK54

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/spectrum-analysis

Wire the blocks: the source feeds the filter, scope, and spectrum; the filtered output goes to the scope and spectrum second channels. Initializes the simulation with dt=1e-2, logging enabled, and the RKCK54 solver with tolerances 1e-5 (relative) and 1e-7 (absolute). The shown log output confirms setup with 4 blocks and 5 edges.

```python
# The connections between the blocks
connections = [
Connection(Src, FLT, Sco, Spc),
Connection(FLT, Sco[1], Spc[1])
]
```

```python
# Initialize simulation
Sim = Simulation(
blocks,
connections,
dt=1e-2,
log=True,
Solver=RKCK54,
tolerance_lte_rel=1e-5,
tolerance_lte_abs=1e-7
)
```

```text
18:38:08 - INFO - LOGGING (log: True)
18:38:08 - INFO - BLOCKS (total: 4, dynamic: 2, static: 2, eventful: 0)
18:38:08 - INFO - GRAPH (nodes: 4, edges: 5, alg. depth: 1, loop depth: 0, runtime: 0.072ms)


```

--------------------------------

### Initialize simulation with RKCK54 solver

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/transfer-function

Initializes the PathSim Simulation with the created blocks and connections, using the RKCK54 solver (Runge-Kutta-Cash-Karp 5(4) method) for accurate integration. The log output shows the simulation setup details.

```Python
# Initialize simulation
Sim = Simulation(blocks, connections, dt=dt, log=True, Solver=RKCK54)
```

```Log
18:38:16 - INFO - LOGGING (log: True)
18:38:16 - INFO - BLOCKS (total: 3, dynamic: 1, static: 2, eventful: 0)
18:38:16 - INFO - GRAPH (nodes: 3, edges: 3, alg. depth: 1, loop depth: 0, runtime: 0.056ms)
```

--------------------------------

### Set up sources, scope, and run simulation

Source: https://docs.pathsim.org/chem/v0.2.8/examples/heat-exchanger

Creates Source blocks for hot (370 K) and cold (290 K) inlets, a Scope to record outlet temperatures, and a Simulation with connections. Runs the simulation for 200 seconds with dt=0.02 and logging enabled.

```python
src_th = Source(lambda t: 370.0) # hot inlet [K]
src_tc = Source(lambda t: 290.0) # cold inlet [K]
  

sco = Scope(labels=["T_h_out [K]", "T_c_out [K]"])
  

sim = Simulation(
[src_th, src_tc, hx, sco],
[
Connection(src_th, hx), # T_h_in
Connection(src_tc, hx[1]), # T_c_in
Connection(hx, sco), # T_h_out
Connection(hx[1], sco[1]), # T_c_out
],
dt=0.02,
log=True,
)
  

sim.run(200)
```

```text
15:05:58 - INFO - LOGGING (log: True)
15:05:58 - INFO - BLOCKS (total: 4, dynamic: 1, static: 3, eventful: 0)
15:05:58 - INFO - GRAPH (nodes: 4, edges: 4, alg. depth: 1, loop depth: 0, runtime: 0.185ms)
15:05:58 - INFO - STARTING -> TRANSIENT (Duration: 200.00s)
15:05:58 - INFO - --------------------   1% | 0.1s<2.2s | 4479.6 it/s
15:05:58 - INFO - ####----------------  20% | 0.4s<1.0s | 8005.6 it/s
15:05:58 - INFO - ########------------  40% | 0.8s<1.1s | 5336.6 it/s
15:05:59 - INFO - ############--------  60% | 1.1s<0.8s | 5293.4 it/s
15:05:59 - INFO - ################----  80% | 1.5s<0.4s | 5531.5 it/s
15:05:59 - INFO - #################### 100% | 1.8s<--:-- | 6519.9 it/s
15:05:59 - INFO - FINISHED -> TRANSIENT (total steps: 10000, successful: 10000, runtime: 1765.92 ms)
```

--------------------------------

### Import libraries and PathSim components

Source: https://docs.pathsim.org/rf/v0.1.2/examples/rf-amplifier-compression

Imports numpy, matplotlib, PathSim simulation components, and the RFAmplifier block. This setup is required for the subsequent simulation examples.

```python
import numpy as np
import matplotlib.pyplot as plt
  

# Apply PathSim docs matplotlib style
# plt.style.use removed for browser
  

from pathsim import Simulation, Connection
from pathsim.blocks import Source, Scope
from pathsim.solvers import RKCK54
  

from pathsim_rf import RFAmplifier
```

--------------------------------

### Initialize and Run Simulation

Source: https://docs.pathsim.org/fmi/v0.1.1/examples/fmu-model-exchange-bouncing-ball

Sets up the simulation with the RKBS32 solver and runs it for 4 seconds.

```python
# Initialize simulation
sim = Simulation(
    blocks,
    connections,
    dt=0.01,
    dt_max=0.01,
    Solver=RKBS32,
    tolerance_lte_rel=1e-6,
    tolerance_lte_abs=1e-9,
    log=True
)
  

# Run simulation
sim.run(4.0)
```

--------------------------------

### Simulation setup with CellElectrothermal

Source: https://docs.pathsim.org/batt/v0.2.2/examples/01-spme-discharge

Imports required libraries and blocks for the simulation. The code is part of a Python example that requires external dependencies and cannot be run in the browser.

```python
import matplotlib.pyplot as plt
  

from pathsim import Simulation, Connection
from pathsim.blocks import Constant, Scope
from pathsim.solvers import ESDIRK43
  

from pathsim_batt import CellElectrothermal
```

--------------------------------

### Install PathSim FMI

Source: https://docs.pathsim.org/fmi

Install the required package via pip.

```bash
pip install pathsim-fmi==0.1.1
```

--------------------------------

### Initialize and run simulation with RKBS32 solver

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/bouncing-ball

Sets up the Simulation with blocks, connections, events, dt=0.01, dt_max=0.04, logging enabled, and RKBS32 solver with LTE tolerances. Runs for 10 seconds and prints progress logs.

```python
from pathsim.solvers import RKBS32
# Initialize simulation
Sim = Simulation(
blocks,
connections,
events,
dt=0.01,
dt_max=0.04,
log=True,
Solver=RKBS32,
tolerance_lte_rel=1e-5,
tolerance_lte_abs=1e-7
)
  

# Run the simulation
Sim.run(10)
```

--------------------------------

### Configure and Run Simulation

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/lorenz-attractor

Initializes the simulation with an adaptive RKBS32 solver and executes it for 50 seconds.

```python
Sim = Simulation(
blocks,
connections,
Solver=RKBS32,
tolerance_lte_rel=1e-4,
tolerance_lte_abs=1e-6,
tolerance_fpi=1e-6
)
  

# Run the simulation
Sim.run(50)
```

```text
18:37:48 - INFO - LOGGING (log: True)
18:37:48 - INFO - BLOCKS (total: 13, dynamic: 3, static: 10, eventful: 0)
18:37:48 - INFO - GRAPH (nodes: 13, edges: 20, alg. depth: 4, loop depth: 0, runtime: 0.145ms)
18:37:48 - INFO - STARTING -> TRANSIENT (Duration: 50.00s)
18:37:49 - INFO - --------------------   1% | 0.1s<6.5s | 896.1 it/s
18:37:49 - INFO - ####----------------  20% | 0.6s<2.1s | 1044.7 it/s
18:37:50 - INFO - ########------------  40% | 1.5s<1.8s | 1047.2 it/s
18:37:51 - INFO - ############--------  60% | 2.5s<2.3s | 1046.4 it/s
18:37:52 - INFO - ###############-----  78% | 3.5s<2.7s | 1064.5 it/s
18:37:52 - INFO - ################----  80% | 3.6s<0.8s | 1051.6 it/s
18:37:53 - INFO - #################### 100% | 4.5s<--:-- | 1054.1 it/s
18:37:53 - INFO - FINISHED -> TRANSIENT (total steps: 4669, successful: 4057, runtime: 4539.55 ms)
```

--------------------------------

### Install FMPy

Source: https://docs.pathsim.org/fmi/v0.1.1/examples/fmu-model-exchange-bouncing-ball

Install the FMPy package, required for using FMU blocks in PathSim.

```bash
pip install fmpy
```

--------------------------------

### Install PathSim via conda

Source: https://docs.pathsim.org/pathsim

Install the specific version 0.25.0 of the PathSim package from the conda-forge channel.

```bash
conda install -c conda-forge pathsim=0.25.0
```

--------------------------------

### Set up Simulation with RKCK54 solver

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/bouncing-pendulum

Initializes a Simulation instance with the blocks, connections, events, a time step of 0.1, logging enabled, and the RKCK54 solver with absolute and relative tolerances. The output shows the logging information about blocks, graph, and runtime.

```Python
# Simulation instance from the blocks and connections
Sim = Simulation(
blocks,
connections,
events,
dt=0.1,
log=True,
Solver=RKCK54,
tolerance_lte_abs=1e-8,
tolerance_lte_rel=1e-6
)
```

```Output
18:37:15 - INFO - LOGGING (log: True)
18:37:15 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
18:37:15 - INFO - GRAPH (nodes: 5, edges: 6, alg. depth: 3, loop depth: 0, runtime: 0.078ms)
```

--------------------------------

### Install PathSim via pip

Source: https://docs.pathsim.org/pathsim

Install the specific version 0.25.0 of the PathSim package using pip.

```bash
pip install pathsim==0.25.0
```

--------------------------------

### Reject unknown start value name

Source: https://docs.pathsim.org/fastsim/v0.28.3/examples/fmi-import

Attempts to create a ModelExchangeFMU with an unknown start value name and catches the resulting ValueError, printing the error message.

```python
try:
    ModelExchangeFMU(fmu("Dahlquist"), start_values={"not_a_variable": 1.0})
except ValueError as e:
    print(f"ValueError: {e}")
```

--------------------------------

### Initialize and run simulation with RKBS32 solver

Source: https://docs.pathsim.org/pathsim/v0.25.0/notebooks/bouncing_ball.ipynb

Sets up the Simulation with the blocks, connections, and events, using the RKBS32 adaptive solver. The simulation runs for 10 seconds with specified tolerances and logging enabled.

```python
from pathsim.solvers import RKBS32
             
# Initialize simulation
Sim = Simulation(
    blocks, 
    connections, 
    events, 
    dt=0.01, 
    dt_max=0.04,
    log=True, 
    Solver=RKBS32, 
    tolerance_lte_rel=1e-5, 
    tolerance_lte_abs=1e-7
)

# Run the simulation
Sim.run(10)
```

--------------------------------

### Import NumPy and Matplotlib for standalone JIT example

Source: https://docs.pathsim.org/fastsim/v0.28.3/examples/standalone-jit

Imports required for the standalone JIT example, which compiles a hand-written NumPy function to native Rust and computes its exact Jacobian.

```python
import numpy as np
import matplotlib.pyplot as plt
```

--------------------------------

### Simulate with RKBS32 Solver

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/delta-sigma-adc

Sets up the simulation with the blocks and connections, using the RKBS32 adaptive solver with a maximum timestep equal to 10% of the sampling period. Runs for 2 seconds and shows logging with throughput and step counts.

```python
# Simulation with adaptive solver
Sim = Simulation(
blocks,
connections,
dt_max=T_clk*0.1,
Solver=RKBS32
)
  

# Run simulation for 2 seconds
Sim.run(2)
```

--------------------------------

### Override start value for Dahlquist FMU

Source: https://docs.pathsim.org/fastsim/v0.28.3/examples/fmi-import

Creates a ModelExchangeFMU with a start value for the decay rate k set to 3.0, runs the simulation, and prints the worst error against exp(-3t).

```python
f3 = ModelExchangeFMU(fmu("Dahlquist"), start_values={"k": 3.0})
sco3 = Scope(labels=["x"], sampling_period=1e-2)
sim3 = Simulation([f3, sco3], [Connection(f3, sco3)], Solver=RKCK54, dt=1e-2, log=False)
sim3.run(5.0)

t3, [x3] = sco3.read()
print(f"k=3: worst |x - exp(-3t)| = {np.max(np.abs(x3 - np.exp(-3 * t3))):.3e}")
```

--------------------------------

### Initialize and Run Simulation

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/nested-subsystems

Configures the simulation with a stiff solver and executes it.

```python
# Initialize simulation
Sim = Simulation(
blocks,
connections,
dt=dt,
log=True,
Solver=ESDIRK43,
tolerance_lte_abs=1e-6,
tolerance_lte_rel=1e-4,
tolerance_fpi=1e-7
)
  

# Run simulation (note: 2*mu for long-term dynamics)
Sim.run(2*mu)
```

```text
18:37:49 - INFO - LOGGING (log: True)
18:37:49 - INFO - BLOCKS (total: 2, dynamic: 1, static: 1, eventful: 0)
18:37:49 - INFO - GRAPH (nodes: 2, edges: 1, alg. depth: 1, loop depth: 0, runtime: 0.024ms)
18:37:49 - INFO - STARTING -> TRANSIENT (Duration: 2000.00s)
18:37:49 - INFO - --------------------   1% | 0.8s<20.1s | 24.3 it/s
18:37:50 - INFO - #####---------------  27% | 1.2s<1.8s | 15.6 it/s
18:37:51 - INFO - ########------------  40% | 2.0s<8.5s | 28.4 it/s
18:37:53 - INFO - ########------------  41% | 4.8s<19.8s | 32.1 it/s
18:37:54 - INFO - #############-------  67% | 5.5s<1.0s | 14.1 it/s
18:37:55 - INFO - ################----  80% | 6.3s<3.4s | 15.9 it/s
18:37:57 - INFO - ################----  81% | 9.0s<9.7s | 47.2 it/s
18:37:58 - INFO - #################### 100% | 9.4s<--:-- | 18.6 it/s
18:37:58 - INFO - FINISHED -> TRANSIENT (total steps: 341, successful: 234, runtime: 9390.20 ms)
```

--------------------------------

### Inspect generated C header interface

Source: https://docs.pathsim.org/fastsim/v0.28.3/examples/c-code-generation

Prints the beginning of the generated `motor.h` header file starting from the `typedef struct` definition, and lists all function declarations that start with `void motor_`, `double motor_`, or `int motor_`.

```Python
header = files["motor.h"]
start = header.index("typedef struct")
print(header[start:start + 900])
```

```Python
for line in files["motor.h"].splitlines():
    if line.startswith(("void motor_", "double motor_", "int motor_")):
        print(line)
```

--------------------------------

### Instantiate the simulation

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/thermostat

Configure the simulation using the defined blocks, connections, events, and an adaptive RKBS32 integrator.

```python
sim = Simulation(
    blocks=blocks,
    connections=connections,
    events=events,
    integrator=RKBS32(dt=0.01)
)

sim.run(t_end=10.0)
```

--------------------------------

### Run simulation with sources and scope

Source: https://docs.pathsim.org/chem/v0.2.8/notebooks/heat_exchanger.ipynb

Sets up the simulation with constant temperature sources for inlets and runs the transient analysis for 200 time steps.

```python
src_th = Source(lambda t: 370.0)   # hot inlet [K]
src_tc = Source(lambda t: 290.0)   # cold inlet [K]

sco = Scope(labels=["T_h_out [K]", "T_c_out [K]"])

sim = Simulation(
    [src_th, src_tc, hx, sco],
    [
        Connection(src_th, hx),        # T_h_in
        Connection(src_tc, hx[1]),     # T_c_in
        Connection(hx, sco),           # T_h_out
        Connection(hx[1], sco[1]),     # T_c_out
    ],
    dt=0.02,
    log=True,
)

sim.run(200)
```

--------------------------------

### Initialize and Run Simulation

Source: https://docs.pathsim.org/pathsim/v0.25.0/notebooks/nested_subsystems.ipynb

Configures the simulation using the ESDIRK43 stiff solver and executes it for the specified duration.

```python
# Initialize simulation
Sim = Simulation(
    blocks, 
    connections, 
    dt=dt, 
    log=True, 
    Solver=ESDIRK43, 
    tolerance_lte_abs=1e-6, 
    tolerance_lte_rel=1e-4,
    tolerance_fpi=1e-7
)

# Run simulation (note: 2*mu for long-term dynamics)
Sim.run(2*mu)
```

--------------------------------

### Set up simulation with temperature ramp

Source: https://docs.pathsim.org/chem/v0.2.8/notebooks/vapor_pressure_curves.ipynb

Creates a Source block generating a linear temperature ramp from 300 K to 500 K over 200 seconds, connects it to all three correlation blocks in parallel, and uses a Scope to record the three pressure outputs. Runs the simulation for 200 seconds.

```python
# Temperature ramp: 300 K to 500 K over 200 seconds
src_t = Source(lambda t: 300 + t)

# Scope to record all three vapor pressures
sco = Scope(labels=["Antoine", "Kirchhoff", "Wagner"])

sim = Simulation(
    [src_t, antoine, kirchhoff, wagner, sco],
    [
        Connection(src_t, antoine, kirchhoff, wagner),
        Connection(antoine, sco),
        Connection(kirchhoff, sco[1]),
        Connection(wagner, sco[2]),
    ],
    dt=1.0,
    log=True,
)

sim.run(200)
```

--------------------------------

### Verify Orbit Periodicity

Source: https://docs.pathsim.org/fastsim/v0.28.3/examples/periodic-steady-state

Checks the closure residual to verify that the state at the end of the period matches the start.

```python
start = np.array([x_lc[0], v_lc[0]])
end = np.array([x_lc[-1], v_lc[-1]])
print(f"x(0), v(0) = {start}")
print(f"x(T), v(T) = {end}")
print(f"closure residual ||x(T) - x(0)|| = {np.linalg.norm(end - start):.3e}")
```

--------------------------------

### Import required modules

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/cascade-controller

Imports numpy, matplotlib, and PathSim classes needed for the cascade controller example.

```python
import numpy as np
import matplotlib.pyplot as plt
  

# Apply PathSim docs matplotlib style
# plt.style.use removed for browser
  

from pathsim import Simulation, Connection, Subsystem, Interface
from pathsim.blocks import Source, TransferFunctionZPG, Adder, Scope, PID, WhiteNoise
from pathsim.solvers import RKCK54
```

--------------------------------

### Create simulation with connections and run

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/rf-network-oneport

Creates the PathSim simulation with the source, RF network, and spectrum blocks, and defines connections. Uses RKBS32 solver with tight tolerances due to super tiny states. Runs the simulation for 1e-9 seconds.

```python
# create the system connections and simulation setup
sim = Simulation(
blocks=[src, rfntwk, spc],
connections=[
Connection(src, rfntwk, spc[0]),
Connection(rfntwk, spc[1])
],
tolerance_lte_abs=1e-16, # this is due to the super tiny states
tolerance_lte_rel=1e-5, # so error control is dominated by the relative truncation error
Solver=RKBS32,
)
  

sim.run(1e-9)
```

--------------------------------

### Create and run Simulation with RKBS32 solver

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/stick-slip

Instantiate a Simulation with blocks, connections, events, and solver parameters (dt=0.01, dt_max=0.1, log=True, Solver=RKBS32, tolerance_lte_abs=1e-6, tolerance_lte_rel=1e-4), then run for 2*T. The log output shows transient progress with total steps and runtime.

```python
# Create a simulation instance from the blocks and connections
Sim = Simulation(
blocks,
connections,
events,
dt=0.01,
dt_max=0.1,
log=True,
Solver=RKBS32,
tolerance_lte_abs=1e-6,
tolerance_lte_rel=1e-4
)
  

# Run the simulation for some time
Sim.run(2*T)
```

```text
18:38:10 - INFO - LOGGING (log: True)
18:38:10 - INFO - BLOCKS (total: 11, dynamic: 2, static: 9, eventful: 0)
18:38:10 - INFO - GRAPH (nodes: 11, edges: 17, alg. depth: 5, loop depth: 0, runtime: 0.118ms)
18:38:10 - INFO - STARTING -> TRANSIENT (Duration: 100.00s)
18:38:10 - INFO - --------------------   1% | 0.0s<0.5s | 1981.6 it/s
18:38:11 - INFO - ####----------------  20% | 0.2s<0.5s | 1497.0 it/s
18:38:11 - INFO - ########------------  40% | 0.5s<0.5s | 1572.4 it/s
18:38:11 - INFO - ############--------  60% | 0.8s<0.3s | 1514.2 it/s
18:38:12 - INFO - ###############-----  75% | 1.8s<31:53:33 | 1478.4 it/s
18:38:13 - INFO - ###############-----  76% | 2.9s<0.1s | 1839.2 it/s
18:38:13 - INFO - ################----  80% | 2.9s<0.1s | 1828.5 it/s
18:38:13 - INFO - #################### 100% | 3.1s<--:-- | 1405.7 it/s
18:38:13 - INFO - FINISHED -> TRANSIENT (total steps: 5055, successful: 2409, runtime: 3116.29 ms)
```

--------------------------------

### Run Simulation

Source: https://docs.pathsim.org/pathsim/v0.25.0/notebooks/sar_adc.ipynb

Initialize the simulation using an adaptive solver.

```python
# Simulation with adaptive solver
Sim = Simulation(
    blocks,
    connections,
```

--------------------------------

### Run Model Exchange FMU in PathSim

Source: https://docs.pathsim.org/fmi

Example of integrating a Model Exchange FMU into a PathSim simulation with a Scope block.

```python
from pathsim import Simulation, Connection
from pathsim.blocks import Scope
from pathsim_fmi import ModelExchangeFMU
  

fmu = ModelExchangeFMU("VanDerPol.fmu")
sco = Scope(labels=["x0", "x1"], sampling_period=0.02)
  

sim = Simulation(
blocks=[fmu, sco],
connections=[
Connection(fmu[0], sco[0]),
Connection(fmu[1], sco[1]),
],
dt=0.01,
)
sim.run(5.0)
sco.plot()
```

--------------------------------

### Configure CSTR parameters

Source: https://docs.pathsim.org/chem/v0.2.8/examples/cstr-reaction

Initializes the CSTR reactor with specific physical and kinetic parameters, starting from an empty state at ambient temperature.

```python
reactor = CSTR(
V=1.0, # reactor volume [m³]
F=0.05, # volumetric flow rate [m³/s] -> tau = 20 s
k0=1e6, # pre-exponential factor [1/s]
Ea=40000.0, # activation energy [J/mol]
n=1.0, # first-order reaction
dH_rxn=-40000.0, # exothermic [J/mol]
rho=1000.0, # density [kg/m³]
Cp=4184.0, # heat capacity [J/(kg·K)]
UA=800.0, # cooling jacket [W/K]
C_A0=0.0, # start empty
T0=300.0, # initial temperature [K]
)
```

--------------------------------

### Initialize Kalman Filter and Simulation Blocks

Source: https://docs.pathsim.org/pathsim/v0.25.0/notebooks/kalman_filter.ipynb

Sets up the WhiteNoise, KalmanFilter, and Scope blocks required for the simulation.

```python
# Noisy measurement (spectral_density must be scaled by dt for discrete-time white noise)
noise = WhiteNoise(spectral_density=measurement_std**2 * dt)
measured_pos = Adder()

# Kalman filter
kf = KalmanFilter(F, H, Q, R, x0=x0_kf, P0=P0_kf)

# Scopes for recording
sc_true = Scope(labels=["true position", "true velocity"])
sc_meas = Scope(labels=["measured position"])
sc_est = Scope(labels=["estimated position", "estimated velocity"])

blocks = [vel, pos, noise, measured_pos, kf, sc_true, sc_meas, sc_est]
```

--------------------------------

### Import PathSim and plotting libraries

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/algebraic-loop

Imports numpy, matplotlib, and PathSim modules needed for the example. The matplotlib style is not applied in the browser.

```Python
import numpy as np
import matplotlib.pyplot as plt
  

# Apply PathSim docs matplotlib style for consistent, theme-friendly figures
# plt.style.use removed for browser
  

from pathsim import Simulation, Connection
from pathsim.blocks import Source, Amplifier, Adder, Scope
```

--------------------------------

### Instantiate system blocks

Source: https://docs.pathsim.org/pathsim/v0.25.0/notebooks/harmonic_oscillator.ipynb

Creates the required Integrator, Amplifier, Adder, and Scope blocks with specified parameters and collects them into a list.

```python
# Blocks that define the system
I1 = Integrator(v0)   # integrator for velocity
I2 = Integrator(x0)   # integrator for position
A1 = Amplifier(c)
A2 = Amplifier(k)
A3 = Amplifier(-1/m)
P1 = Adder()
Sc = Scope(labels=["velocity", "position"])

blocks = [I1, I2, A1, A2, A3, P1, Sc]
```

--------------------------------

### Set up PathSim simulation with temperature ramp and scope

Source: https://docs.pathsim.org/chem/v0.2.8/examples/vapor-pressure-curves

Creates a Source block generating a linear temperature ramp from 300 K to 500 K over 200 seconds, a Scope to record the three pressure outputs, and a Simulation connecting the source to all correlations in parallel. Runs the simulation for 200 seconds with a time step of 1.0 second.

```python
# Temperature ramp: 300 K to 500 K over 200 seconds
src_t = Source(lambda t: 300 + t)
  

# Scope to record all three vapor pressures
sco = Scope(labels=["Antoine", "Kirchhoff", "Wagner"])
  

sim = Simulation(
[src_t, antoine, kirchhoff, wagner, sco],
[
Connection(src_t, antoine, kirchhoff, wagner),
Connection(antoine, sco),
Connection(kirchhoff, sco[1]),
Connection(wagner, sco[2]),
],
dt=1.0,
log=True,
)
  

sim.run(200)
```

--------------------------------

### Importing dependencies for the Duffing oscillator simulation

Source: https://docs.pathsim.org/fastsim/v0.28.3/examples/periodic-steady-state

Initial imports required for the Duffing oscillator example, including time, numpy, and matplotlib.

```python
import time
  

import numpy as np
import matplotlib.pyplot as plt
  
```

--------------------------------

### Run Simulation

Source: https://docs.pathsim.org/pathsim/v0.25.0/notebooks/kalman_filter.ipynb

Initializes the simulation with the defined blocks and connections, then executes it for 20 seconds.

```python
# Initialize simulation
Sim = Simulation(
    blocks,
    connections,
    dt=dt,
)

# Run the simulation for 20 seconds
Sim.run(duration=20)
```

--------------------------------

### Import PathSim and RFNetwork libraries

Source: https://docs.pathsim.org/rf/v0.1.2/examples/rf-network-oneport

Import the required libraries for the RF network simulation. The RFNetwork block requires the scikit-rf package to be installed.

```python
import matplotlib.pyplot as plt
  

# Apply PathSim docs matplotlib style for consistent, theme-friendly figures
# plt.style.use removed for browser
  

from pathsim import Simulation, Connection
from pathsim.blocks import Spectrum, GaussianPulseSource
from pathsim.solvers import RKBS32
  

from pathsim_rf import RFNetwork # requires the scikit-rf package to be installed
```

--------------------------------

### Configure System Components and Connections

Source: https://docs.pathsim.org/pathsim/v0.25.0/notebooks/noisy_amplifier.ipynb

Initializes the sinusoidal source, scope, and spectrum analyzer, then defines the system blocks and connections.

```python
Src = SinusoidalSource(frequency=2e5, amplitude=1)
Sco = Scope(labels=["Src", "AMP"])
Spc = Spectrum(freq=np.logspace(4.1, 7, 250), labels=["Src", "AMP"])

blocks = [AMP, Src, Sco, Spc]

connections = [
    Connection(Src, AMP, Sco[0], Spc[0]),
    Connection(AMP, Sco[1], Spc[1])
    ]
```

--------------------------------

### Steady-state summary output

Source: https://docs.pathsim.org/chem/v0.2.8/examples/process-flowsheet

Example output from the steady-state summary print script, showing the unit flows and temperatures, plus the reactor concentration and conversion.

```text
Process Steady State
=============================================
Unit             Flow [m³/s]      T [K]
---------------------------------------------
Fresh feed              0.05      300.0
Second stream           0.05      310.0
Mixer outlet          0.1000     305.00
Heater outlet         0.1000     305.48
CSTR outlet                —     305.46

Reactor: C_A = 1.9452 mol/m³ (feed = 2.0 mol/m³)
Conversion = 2.7%
```

--------------------------------

### Instantiate and run the Simulation

Source: https://docs.pathsim.org/pathsim/v0.25.0/notebooks/stick_slip.ipynb

Creates a Simulation instance using the RKBS32 adaptive timestep ODE solver and runs it for a specified duration.

```python
# Create a simulation instance from the blocks and connections
Sim = Simulation(
    blocks, 
    connections, 
    events,
    dt=0.01, 
    dt_max=0.1, 
    log=True, 
    Solver=RKBS32, 
    tolerance_lte_abs=1e-6, 
    tolerance_lte_rel=1e-4
)

# Run the simulation for some time
Sim.run(2*T)
```

--------------------------------

### Create FMU Block and Scope

Source: https://docs.pathsim.org/fmi/v0.1.1/examples/fmu-model-exchange-bouncing-ball

Creates the ModelExchangeFMU block with start values and tolerance, and a Scope to record height and velocity. Connects FMU outputs to the scope.

```python
# Create the Model Exchange FMU block
fmu = ModelExchangeFMU(
    fmu_path=str(fmu_path),
    instance_name="bouncing_ball",
    start_values={"e": 0.7}, # coefficient of restitution
    tolerance=1e-10,
    verbose=False
)
  

# Scope to record height and velocity
sco = Scope(labels=["h [m]", "v [m/s]"])
  

blocks = [fmu, sco]
  

# Connect FMU outputs to scope
connections = [
    Connection(fmu[0], sco[0]), # height
    Connection(fmu[1], sco[1]), # velocity
]
```

--------------------------------

### Configure and run the stiff system simulation

Source: https://docs.pathsim.org/fmi/v0.1.1/notebooks/fmu_model_exchange_vanderpol.ipynb

Sets up a simulation for a stiff system using the ESDIRK43 solver with specific tolerance settings and runs it for 1500 seconds.

```python
    verbose=False
)

sco_stiff = Scope(labels=[r"$x_0$", r"$x_1$"])

sim_stiff = Simulation(
    [fmu_stiff, sco_stiff],
    [Connection(fmu_stiff[0], sco_stiff[0]), Connection(fmu_stiff[1], sco_stiff[1])],
    dt=0.1,
    Solver=ESDIRK43,          # implicit solver for stiff systems
    tolerance_lte_rel=1e-4,
    tolerance_lte_abs=1e-6,
    tolerance_fpi=1e-8,
    log=True
)

sim_stiff.run(1500.0)
```

--------------------------------

### Import numpy and matplotlib for chemical reactor simulation

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/chemical-reactor

Initializes the Python environment for the chemical reactor example by importing numpy for numerical operations and matplotlib.pyplot for plotting.

```python
import numpy as np
import matplotlib.pyplot as plt
  
```

--------------------------------

### Import and Setup for PID Controller Simulation

Source: https://docs.pathsim.org/pathsim/v0.25.0/notebooks/pid_controller.ipynb

Imports required libraries and PathSim classes for the PID controller simulation. Applies the PathSim documentation matplotlib style.

```python
import numpy as np
import matplotlib.pyplot as plt

# Apply PathSim docs matplotlib style
plt.style.use('../pathsim_docs.mplstyle')

from pathsim import Simulation, Connection
from pathsim.blocks import Source, Integrator, Amplifier, Adder, Scope, PID
from pathsim.solvers import RKCK54
```

--------------------------------

### Configure and run the flash drum simulation

Source: https://docs.pathsim.org/chem/v0.2.8/notebooks/multicomponent_flash.ipynb

Sets up the MultiComponentFlash block with BTX defaults, defines feed sources, connects the simulation components, and runs the simulation for 80 steps.

```python
# Create the flash drum (3 components, BTX defaults)
flash = MultiComponentFlash(N_comp=3, holdup=100.0)

# Feed sources
src_f = Source(lambda t: 10.0)          # 10 mol/s
src_z1 = Source(lambda t: 0.5)          # 50% benzene
src_z2 = Source(lambda t: 0.1)          # 10% toluene (p-xylene = 40% inferred)
src_t = Source(lambda t: 340.0 + t)     # ramp 340 -> 420 K
src_p = Source(lambda t: 101325.0)      # 1 atm

# Record all outputs: V_rate, L_rate, y_benzene, y_toluene, x_benzene, x_toluene
sco = Scope(labels=["V_rate", "L_rate", "y_benz", "y_tol", "x_benz", "x_tol"])

sim = Simulation(
    [src_f, src_z1, src_z2, src_t, src_p, flash, sco],
    [
        Connection(src_f, flash),            # F
        Connection(src_z1, flash[1]),        # z_1 (benzene)
        Connection(src_z2, flash[2]),        # z_2 (toluene)
        Connection(src_t, flash[3]),         # T
        Connection(src_p, flash[4]),         # P
        Connection(flash, sco),              # V_rate
        Connection(flash[1], sco[1]),        # L_rate
        Connection(flash[2], sco[2]),        # y_benzene
        Connection(flash[3], sco[3]),        # y_toluene
        Connection(flash[4], sco[4]),        # x_benzene
        Connection(flash[5], sco[5]),        # x_toluene
    ],
    dt=0.5,
    log=True,
)

sim.run(80)
```

--------------------------------

### Create Simulation Instance with RKBS32 Solver

Source: https://docs.pathsim.org/pathsim/v0.25.0/examples/elastic-pendulum

Initializes a Simulation object with the provided blocks and connections, using the RKBS32 solver. The log output shows 5 blocks (2 dynamic, 3 static, 1 eventful) and a graph with 5 nodes and 9 edges.

```Python
# Simulation instance
sim = Simulation(
blocks,
connections,
Solver=RKBS32
)
```

```Output
18:37:34 - INFO - LOGGING (log: True)
18:37:34 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 1)
18:37:34 - INFO - GRAPH (nodes: 5, edges: 9, alg. depth: 2, loop depth: 0, runtime: 0.072ms)
```

--------------------------------

### Set up feed, coolant, and simulation

Source: https://docs.pathsim.org/chem/v0.2.8/notebooks/cstr_reaction.ipynb

Defines constant feed and coolant conditions, creates a Scope to record outlet concentration and temperature, and runs the simulation for 200 seconds with a time step of 0.1.

```python
# Constant feed and coolant conditions
src_c = Source(lambda t: 1000.0)   # feed concentration [mol/m³]
src_t = Source(lambda t: 320.0)    # feed temperature [K]
src_tc = Source(lambda t: 290.0)   # coolant temperature [K]

sco = Scope(labels=["C_A [mol/m³]", "T [K]"])

sim = Simulation(
    [src_c, src_t, src_tc, reactor, sco],
    [
        Connection(src_c, reactor),        # C_in
        Connection(src_t, reactor[1]),     # T_in
        Connection(src_tc, reactor[2]),    # T_c
        Connection(reactor, sco),          # C_out
        Connection(reactor[1], sco[1]),    # T_out
    ],
    dt=0.1,
    log=True,
)

sim.run(200)
```

--------------------------------

### Configure CSTR reactor parameters

Source: https://docs.pathsim.org/chem/v0.2.8/notebooks/cstr_reaction.ipynb

Creates a CSTR block with parameters for an exothermic liquid-phase reaction. The reactor starts empty at ambient temperature and is fed with a concentrated stream.

```python
reactor = CSTR(
    V=1.0,            # reactor volume [m³]
    F=0.05,           # volumetric flow rate [m³/s] -> tau = 20 s
    k0=1e6,           # pre-exponential factor [1/s]
    Ea=40000.0,       # activation energy [J/mol]
    n=1.0,            # first-order reaction
    dH_rxn=-40000.0,  # exothermic [J/mol]
    rho=1000.0,       # density [kg/m³]
    Cp=4184.0,        # heat capacity [J/(kg·K)]
    UA=800.0,         # cooling jacket [W/K]
    C_A0=0.0,         # start empty
    T0=300.0,         # initial temperature [K]
)
```