### F-distribution Explanation and Example

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.rad.html

Explains the F-statistic, its degrees of freedom, and provides an example of drawing samples from the F-distribution and interpreting the results.

```APIDOC
## F-distribution

### Description
The F statistic is used to compare in-group variances to between-group variances. Its distribution depends on the sampling and is a function of the respective degrees of freedom.

### Degrees of Freedom
- **dfnum**: The number of samples minus one (between-groups degrees of freedom).
- **dfden**: The sum of the number of samples in each group minus the number of groups (within-groups degrees of freedom).

### Example Calculation
An example from Glantz[1], pp 47-40, involving two groups (children of diabetics and controls) with fasting blood glucose measurements. The F statistic is calculated to test the null hypothesis that parental diabetic status does not affect children's blood glucose levels.

### Draw Samples from the Distribution
```python
import numpy as np

dfnum = 1. # between group degrees of freedom
dfden = 48. # within groups degrees of freedom
s = np.random.f(dfnum, dfden, 1000)
```

### Lower Bound for Top 1% of Samples
```python
# Assuming 's' is the array of samples from np.random.f
# The lower bound for the top 1% is the 990th element (index 989) if sorted
# Or more generally, the 10th element from the end
print(np.sort(s)[-10]) # Example output: 7.61988120985
```

### Interpretation
If the measured F statistic (e.g., 36.01) exceeds the lower bound for the top 1% of samples (e.g., 7.62), the null hypothesis is rejected at the 1% significance level.
```

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

### MethodTM Parameter Setup

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/index.rst.txt

Configures MethodTM to use specific transfer maps for different element types.

```python
class MethodTM:
    """The class creates a transfer map for elements that depend on user-defined parameters ("parameters").
    By default, the parameters = {"global": TransferMap}, which means that all elements will have linear transfer maps.
    You can also specify different transfer maps for any type of element.

    Example:
    --------
    # use linear matrices for all elements except Sextupole which will have nonlinear kick map (KickTM)
    method = MethodTM()
    method.global_method = TransferMap
    method.params[Sextupole] = KickTM

    # All elements are assigned matrices of the second order.
    # For elements for which there are no matrices of the second order are assigned default matrices, e.g. linear matrices.
    method2 = MethodTM()
    method2.global_method = SecondTM
    """
    def create_tm(self, element):
        pass

    def set_tm(self, element, method):
        pass
```

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

### MethodTM and SecondTM Initialization

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.cpbd.html

Demonstrates the initialization of MethodTM and SecondTM classes, setting global methods and default matrices.

```python
method2 = MethodTM()
method2.global_method = SecondTM
```

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

### Estimate CSR Start Index

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/cpbd/csr/index.rst.txt

This method estimates the starting index for CSR calculations to optimize performance by discarding trajectory regions that do not contribute to the effect. It tests a subset of points along the reference trajectory against a minimum threshold.

```python
def estimate_start_index(self, i, traj, w_min, beta, i_min=1000, n_test=10):
    """Estimates the index of the first trajectory point for CSR computation."""
    # Logic to test w <= w_min for n_test points
    if i < i_min:
        return 0
    # Implementation details for index estimation
    return estimated_index
```

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

### Execute Genesis 1.3 v4 Simulation

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/adaptors/genesis4/index.html

Demonstrates how to initialize a launcher and execute a Genesis 1.3 v4 simulation using the Ocelot adaptor.

```python
from ocelot.adaptors.genesis4 import get_genesis4_launcher, run_genesis4

# Initialize the launcher
launcher = get_genesis4_launcher(launcher_program='genesis4')

# Execute simulation with a GenesisInput object
# run_genesis4(inp_object, launcher)
```

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

### GET /distributions/zipf

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.adaptors.html

Draws samples from a Zipf distribution.

```APIDOC
## GET /distributions/zipf

### Description
Draws samples from a Zipf distribution (zeta distribution) where frequency is inversely proportional to rank.

### Method
GET

### Endpoint
/distributions/zipf

### Parameters
#### Query Parameters
- **a** (float) - Required - The distribution parameter (must be greater than 1).
- **size** (int/tuple) - Optional - The output shape of the samples.

### Response
#### Success Response (200)
- **samples** (ndarray) - An array of drawn samples from the Zipf distribution.
```

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

### POST /ocelot/simulation/prepare

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/genindex.html

Initializes simulation processes and configures physics processors for beam dynamics and radiation calculations.

```APIDOC
## POST /ocelot/simulation/prepare

### Description
Initializes the specified simulation component or physics processor, such as SpaceCharge, CSR, or Wake modules.

### Method
POST

### Endpoint
/ocelot/simulation/prepare

### Parameters
#### Request Body
- **component** (string) - Required - The simulation component to prepare (e.g., SpaceCharge, CSR, Wake)
- **config** (object) - Optional - Configuration parameters for the processor

### Request Example
{
  "component": "SpaceCharge",
  "config": { "method": "standard" }
}

### Response
#### Success Response (200)
- **status** (string) - Initialization status
- **processor_id** (string) - Unique identifier for the initialized processor

#### Response Example
{
  "status": "success",
  "processor_id": "sc_001"
}
```

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

### Generate Power Distribution Samples and Visualize

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.rad.html

Demonstrates generating samples from a power distribution using np.random.power and visualizing the histogram against the theoretical probability density function using Matplotlib.

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

a = 5.
samples = 1000
s = np.random.power(a, samples)

count, bins, ignored = plt.hist(s, bins=30)
x = np.linspace(0, 1, 100)
y = a*x**(a-1.)
normed_y = samples*np.diff(bins)[0]*y
plt.plot(x, normed_y)
plt.show()
```

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

### GET /distributions/weibull

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.adaptors.html

Draws samples from a Weibull distribution.

```APIDOC
## GET /distributions/weibull

### Description
Draws samples from a 1-parameter Weibull distribution, used for modeling extreme value problems.

### Method
GET

### Endpoint
/distributions/weibull

### Parameters
#### Query Parameters
- **a** (float) - Required - The shape parameter of the distribution (must be non-negative).
- **size** (int/tuple) - Optional - The output shape of the samples.

### Response
#### Success Response (200)
- **samples** (ndarray) - An array of drawn samples from the Weibull distribution.
```

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

### GET /get_envelope

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/index.rst.txt

Calculates Twiss parameters from a ParticleArray.

```APIDOC
## GET /get_envelope

### Description
Computes Twiss parameters based on the distribution of a ParticleArray.

### Method
GET

### Endpoint
/get_envelope

### Parameters
#### Query Parameters
- **p_array** (ParticleArray) - Required - The particle array to analyze.
- **tws_i** (Twiss) - Optional - Design Twiss parameters.
- **bounds** (list) - Optional - Bounds in units of std(p_array.tau()).

### Response
#### Success Response (200)
- **twiss** (Twiss) - The calculated Twiss parameters.
```

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

### Apply SmoothBeam process to a lattice

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/index.rst.txt

Demonstrates how to initialize the SmoothBeam process, configure the number of particles per slice, and add it to a Navigator instance for a specific lattice element.

```python
navi = Navigator(lat)
smooth = SmoothBeam()
smooth.mslice = 10000
navi.add_physics_process(smooth, start=elem, stop=elem)
```

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

### Start Background Process in Python

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.common.html

Launches a given command as a background process. The command should ideally be provided as a string, preferably enclosed in triple quotes for clarity.

```python
from ocelot.common.py_func import background

command = "ls -l" # Example command
background(command)
```

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

### GET /ocelot/rad/bmrad/noncentral_chisquare

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.rad.html

Draws samples from a noncentral chi-square distribution.

```APIDOC
## GET /ocelot/rad/bmrad/noncentral_chisquare

### Description
Draws samples from a noncentral chi-square distribution, which is a generalization of the chi-square distribution.

### Method
GET

### Endpoint
/ocelot/rad/bmrad/noncentral_chisquare

### Parameters
#### Query Parameters
- **df** (float) - Required - Degrees of freedom, must be > 0.
- **nonc** (float) - Required - Non-centrality, must be non-negative.
- **size** (int/tuple) - Optional - Output shape.

### Request Example
GET /ocelot/rad/bmrad/noncentral_chisquare?df=3.0&nonc=1.5

### Response
#### Success Response (200)
- **out** (ndarray) - Drawn samples from the noncentral chi-square distribution.

#### Response Example
{
  "samples": [2.4, 3.1, 1.8]
}
```

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

### GET /ocelot.cpbd.high_order.verlet

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.cpbd.html

Performs a single step of Verlet integration.

```APIDOC
## GET ocelot.cpbd.high_order.verlet

### Description
Calculates the next state (q, p) using the Verlet integration method.

### Parameters
#### Query Parameters
- **vec_x** (array) - Required - Current state vector
- **step** (float) - Required - Step size
- **h** (float) - Required - Curvature
- **k1** (float) - Required - Quadrupole strength
- **k2** (float) - Required - Sextupole strength
- **beta** (float) - Optional - Beta parameter
- **g_inv** (float) - Optional - Inverse g parameter

### Response
#### Success Response (200)
- **state** (array) - Updated state vector
```

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

### Manage Physics Processes with Navigator

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/index.rst.txt

Shows how to use the Navigator class to add physics processes to a lattice. This allows for the simulation of effects like Wake fields or SpaceCharge between specific elements.

```python
from ocelot.cpbd.beam import Navigator

# Initialize navigator with a lattice
navi = Navigator(lattice)

# Add a physics process between two elements
navi.add_physics_proc(space_charge_proc, elem_start, elem_end)

# Retrieve all active processes
procs = navi.get_phys_procs()
```

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

### Initialize SectionLattice and Calculate Twiss Parameters

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.utils.html

Demonstrates the initialization of a SectionLattice object and the calculation of Twiss parameters for a given lattice sequence. This is essential for tracking particle beams through defined sections.

```python
from ocelot.utils.section_track import SectionLattice

# Initialize lattice with sequence and initial Twiss parameters
lattice = SectionLattice(sequence=my_sequence, tws0=initial_tws)

# Calculate Twiss parameters for the whole lattice
twiss_list = lattice.calculate_twiss(tws0=initial_tws)
```

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

### GET /optics/wave/dfldomain_check

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/optics/wave/index.html

Utility function to validate wave domains.

```APIDOC
## GET /optics/wave/dfldomain_check

### Description
Checks the validity of the provided wave domains.

### Method
GET

### Endpoint
/optics/wave/dfldomain_check

### Parameters
#### Query Parameters
- **domains** (object) - Required - The domain configuration to check
- **both_req** (boolean) - Optional - Flag to require both domains

### Request Example
{
  "domains": "td",
  "both_req": false
}

### Response
#### Success Response (200)
- **status** (string) - Validation result
```

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

### Sample Binomial Distribution with NumPy

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.adaptors.html

Demonstrates how to draw samples from a binomial distribution using NumPy. Includes a basic coin flip simulation and a real-world probability estimation for oil exploration wells.

```python
import numpy as np

# Basic coin flip simulation: 10 trials, 0.5 probability, 1000 samples
n, p = 10, 0.5
s = np.random.binomial(n, p, 1000)

# Real-world example: Probability of 0 successes in 9 wells with 0.1 success rate
# Running 20,000 trials to estimate probability
prob_zero_success = sum(np.random.binomial(9, 0.1, 20000) == 0) / 20000.0
```

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

### GET /ocelot/get_current

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.html

Calculates the beam current from a given ParticleArray.

```APIDOC
## GET /ocelot/get_current

### Description
Calculates beam current from a particleArray object.

### Method
GET

### Parameters
#### Query Parameters
- **p_array** (ParticleArray) - Required - The particle array to analyze.
- **num_bins** (int) - Optional - Number of bins for calculation, default 200.

### Response
#### Success Response (200)
- **s** (np.array) - Beam positions in [m].
- **I** (np.array) - Beam currents in [A].
```

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

### Initialize Ocelot Beamline Elements

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.cpbd.html

Examples of initializing standard beamline elements such as SBend, Sextupole, and Undulator within the Ocelot framework.

```python
from ocelot.cpbd.elements import SBend, Sextupole, Undulator, TDCavity

# Initialize a sector bending magnet
bend = SBend(l=1.0, angle=0.1, k1=0.5)

# Initialize a sextupole
sext = Sextupole(l=0.2, k2=10.0)

# Initialize an undulator
und = Undulator(lperiod=0.02, nperiods=100, Kx=1.5)

# Initialize a transverse deflecting cavity
td_cav = TDCavity(l=0.5, freq=2.8e9, v=0.05, phi=90.0)
```

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

### GET /twiss

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/cpbd/optics/index.html

Calculates Twiss parameters for a given lattice.

```APIDOC
## GET /twiss

### Description
Calculates Twiss parameters for the provided lattice.

### Method
GET

### Endpoint
/twiss

### Parameters
#### Query Parameters
- **lattice** (object) - Required - The lattice structure
- **tws0** (object) - Optional - Initial Twiss parameters
- **nPoints** (int) - Optional - Number of points

### Response
#### Success Response (200)
- **twiss_params** (object) - Calculated Twiss parameters
```

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

### GET /beam/get_current

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/cpbd/beam/index.html

Calculates the beam current from a ParticleArray object.

```APIDOC
## GET /beam/get_current

### Description
Calculates beam current from particleArray by binning particles.

### Method
GET

### Endpoint
/beam/get_current

### Parameters
#### Query Parameters
- **p_array** (object) - Required - The ParticleArray instance.
- **num_bins** (int) - Optional - Number of bins for current calculation (default: 200).
- **charge** (float) - Optional - Charge of the macro-particle.

### Response
#### Success Response (200)
- **s** (array) - Beam positions [m].
- **I** (array) - Beam currents [A].
```

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

### Sample from Laplace Distribution with Python

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.adaptors.html

Demonstrates how to draw samples from a Laplace distribution and visualize the results against the probability density function and a Gaussian distribution for comparison.

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

loc, scale = 0., 1.
s = np.random.laplace(loc, scale, 1000)

# Histogram and PDF
count, bins, ignored = plt.hist(s, 30, density=True)
x = np.arange(-8., 8., .01)
pdf = np.exp(-abs(x-loc)/scale)/(2.*scale)
plt.plot(x, pdf)

# Gaussian comparison
g = (1/(scale * np.sqrt(2 * np.pi)) * np.exp(-(x - loc)**2 / (2 * scale**2)))
plt.plot(x, g)
```

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

### Implement Custom Physics Process

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/index.rst.txt

Demonstrates how to create a custom physics process by inheriting from PhysProc. Users must implement the prepare, apply, and finalize methods to define behavior during tracking.

```python
from ocelot.cpbd.physics_proc import PhysProc

class MyProcess(PhysProc):
    def prepare(self, lat):
        # Initialization logic
        pass

    def apply(self, p_array, dz):
        # Logic applied at every step
        pass

    def finalize(self, *args, **kwargs):
        # Cleanup logic
        pass
```

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

### GET /distributions/wald

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.adaptors.html

Draws samples from a Wald (Inverse Gaussian) distribution.

```APIDOC
## GET /distributions/wald

### Description
Draws samples from the Wald distribution, often used to model Brownian motion and reliability.

### Method
GET

### Endpoint
/distributions/wald

### Parameters
#### Query Parameters
- **mean** (float) - Required - The mean of the distribution.
- **scale** (float) - Required - The scale parameter of the distribution.
- **size** (int/tuple) - Optional - The output shape of the samples.

### Response
#### Success Response (200)
- **samples** (ndarray) - An array of drawn samples from the Wald distribution.
```

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

### GET /random/pareto

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.rad.html

Draws samples from a Pareto II (Lomax) distribution.

```APIDOC
## GET /random/pareto

### Description
Draws samples from a Pareto II (Lomax) distribution with a specified shape parameter.

### Method
GET

### Endpoint
/random/pareto

### Parameters
#### Query Parameters
- **a** (float) - Required - Shape of the distribution (must be positive).
- **size** (int/tuple) - Optional - Output shape of the samples.

### Request Example
GET /random/pareto?a=3.0&size=10

### Response
#### Success Response (200)
- **samples** (array) - Drawn samples from the Pareto distribution.

#### Response Example
{
  "samples": [1.2, 0.5, 3.1, ...]
}
```

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

### Configure Navigator Physics Processes

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/index.rst.txt

Shows how to add a physics process to a Navigator instance to be applied between specific elements in a lattice.

```python
from ocelot.cpbd.elements import Navigator

# Assuming 'lattice' and 'physics_proc' are defined
navi = Navigator(lattice)
navi.add_physics_proc(physics_proc, elem1, elem2)
```

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

### Sample from Logistic Distribution with Python

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.adaptors.html

Demonstrates how to generate samples from a logistic distribution using specified location and scale parameters and visualize the distribution via a histogram.

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

loc, scale = 10, 1
s = np.random.logistic(loc, scale, 10000)
count, bins, ignored = plt.hist(s, bins=50)
```

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

### GET /random/normal

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.rad.html

Draws samples from a parameterized normal (Gaussian) distribution.

```APIDOC
## GET /random/normal

### Description
Draws samples from a normal (Gaussian) distribution defined by a mean (loc) and standard deviation (scale).

### Method
GET

### Endpoint
/random/normal

### Parameters
#### Query Parameters
- **loc** (float) - Required - Mean of the distribution.
- **scale** (float) - Required - Standard deviation of the distribution (must be non-negative).
- **size** (int/tuple) - Optional - Output shape of the samples.

### Request Example
GET /random/normal?loc=0&scale=0.1&size=1000

### Response
#### Success Response (200)
- **samples** (array) - Drawn samples from the normal distribution.

#### Response Example
{
  "samples": [0.01, -0.05, 0.02, ...]
}
```

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

### GET /ocelot.cpbd.high_order.t_nnn

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.cpbd.html

Calculates the second-order transport matrix for a beam element.

```APIDOC
## GET ocelot.cpbd.high_order.t_nnn

### Description
Returns a second-order matrix for beam tracking using variables: x, px/p0, y, py/p0, tau, dE/(p0c).

### Parameters
#### Query Parameters
- **L** (float) - Required - Length in [m]
- **h** (float) - Required - Curvature in [1/m]
- **k1** (float) - Required - Quadrupole strength in [1/m^2]
- **k2** (float) - Required - Sextupole strength in [1/m^3]
- **energy** (float) - Optional - Energy in [GeV]

### Response
#### Success Response (200)
- **matrix** (numpy.ndarray) - Second order matrix with shape (6, 6, 6)
```

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

### Moga Class Initialization and Parameter Setting (Python)

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/cpbd/moga/index.html

Initializes the Moga class with bounds and optional weights, and provides a method to set various genetic algorithm parameters like population size, number of generations, and logging options.

```python
class Moga:
    def __init__(self, bounds, weights=-1.0, -1.0):
        # ... initialization logic ...
        pass

    def set_params(self, n_pop=None, weights=None, elite=None, penalty=None, n_gen=None, seed=None, log_print=None, log_file=False, plt_file=False):
        # ... parameter setting logic ...
        pass
```

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

### Sample Hypergeometric Distribution

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.adaptors.html

Demonstrates how to draw samples from a hypergeometric distribution to simulate selecting items without replacement. The example shows how to configure the number of good and bad items along with the sample size.

```python
import numpy as np
from matplotlib.pyplot import hist

# Define parameters: 100 good, 2 bad, 10 samples
ngood, nbad, nsamp = 100, 2, 10

# Draw 1000 samples
s = np.random.hypergeometric(ngood, nbad, nsamp, 1000)

# Visualize the distribution
hist(s)
```

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

### GET /calc_wigner

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/optics/wave/index.html

Calculates the Wigner distribution for a given radiation field.

```APIDOC
## GET /calc_wigner

### Description
Calculates the Wigner distribution of a radiation field using multi-processing.

### Method
GET

### Endpoint
/calc_wigner

### Parameters
#### Query Parameters
- **field** (object) - Required - The radiation field
- **method** (string) - Optional - Calculation method (default: 'mp')

### Response
#### Success Response (200)
- **wigner** (object) - The calculated Wigner distribution.
```

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

### GET /ocelot/gui/genesis_plot/plot_gen_out_evo

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/gui/genesis_plot/index.html

Plots the evolution of specified parameters over the undulator length.

```APIDOC
## GET /ocelot/gui/genesis_plot/plot_gen_out_evo

### Description
Visualizes the evolution of electron beam and radiation parameters as a function of undulator length.

### Method
GET

### Endpoint
ocelot.gui.genesis_plot.plot_gen_out_evo

### Parameters
#### Path Parameters
- **g** (GenesisOutput) - Required - The Genesis output object.

#### Query Parameters
- **params** (list) - Optional - Parameters to track (e.g., 'el_energy', 'rad_pow_en_log').
- **figsize** (int) - Optional - Figure size.
- **legend** (bool) - Optional - Whether to show the legend.

### Request Example
plot_gen_out_evo(g=my_genesis_obj, params=['el_energy', 'rad_pow_en_log'])

### Response
#### Success Response (200)
- **figure** (matplotlib.figure) - The generated evolution plot.
```

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

### Initialize Ocelot Particle and Elements

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/index.html

Demonstrates how to instantiate common Ocelot objects such as a Particle, an Undulator, and different types of Bending Magnets.

```python
from ocelot import Particle, Undulator, Bend, RBend, SBend

# Initialize a particle
p = Particle(x=0.0, y=0.0, E=1.0)

# Initialize an undulator
und = Undulator(lperiod=0.025, nperiods=100, Kx=1.0, Ky=1.0)

# Initialize bending magnets
bend = Bend(l=1.0, angle=0.1)
rbend = RBend(l=1.0, angle=0.1)
sbend = SBend(l=1.0, angle=0.1)
```

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

### GET /ocelot/adaptors/genesis/read_out_file_stat

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.adaptors.html

Reads statistical information from Genesis simulation output files.

```APIDOC
## GET /ocelot/adaptors/genesis/read_out_file_stat

### Description
Reads statistical info of Genesis simulations from a standard project directory structure.

### Method
GET

### Endpoint
ocelot.adaptors.genesis.read_out_file_stat

### Parameters
#### Query Parameters
- **proj_dir** (str) - Required - Project directory path
- **stage** (str) - Required - Stage number
- **run_inp** (list) - Optional - List of genesis runs to process
- **param_inp** (list) - Optional - List of output parameters to process

### Response
#### Success Response (200)
- **output** (GenStatOutput) - Statistical output object
```

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

### LocalLauncher Class API

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/utils/launcher/index.rst.txt

Documentation for the LocalLauncher class, used for launching simulations locally.

```APIDOC
## LocalLauncher Class

### Description
Manages the preparation, launching, and collection of simulations executed on the local machine.

### Method

- **prepare(self)**
  Prepares the local environment for simulation.

- **outputfile(self, filename)**
  Returns the expected output file path for a given filename.

- **launch(self)**
  Launches the simulation locally.

- **collect(self, inputDir, outputDir, pattern='*')**
  Collects simulation output files from a directory.
```

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

### GET /ocelot/rad/bmrad/randint

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.rad.html

Returns random integers from low (inclusive) to high (exclusive).

```APIDOC
## GET /ocelot/rad/bmrad/randint

### Description
Return random integers from the discrete uniform distribution in the half-open interval [low, high).

### Method
GET

### Endpoint
/ocelot/rad/bmrad/randint

### Parameters
#### Query Parameters
- **low** (int) - Required - Lowest integer to be drawn.
- **high** (int) - Optional - One above the largest integer to be drawn.
- **size** (tuple) - Optional - Output shape.
- **dtype** (string) - Optional - Desired dtype of the result.

### Response
#### Success Response (200)
- **out** (ndarray) - Array of random integers.

### Response Example
{
  "result": [1, 0, 0, 0, 1]
}
```

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

### NewLauncher Class API

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/utils/launcher/index.rst.txt

Documentation for the NewLauncher class, potentially used for specific simulation types like MOGA.

```APIDOC
## NewLauncher Class

### Description
A launcher class, possibly for MOGA or temporary simulations.

### Methods

- **prepare(self)**
  Prepares the environment for the simulation.

- **launch(self)**
  Launches the simulation.

- **collect(self, inputDir, outputDir, pattern='*')**
  Collects simulation output files from a directory.
```

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

### GET /api/ocelot/current

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/index.rst.txt

Calculates the beam current profile for a specified particle array.

```APIDOC
## GET /api/ocelot/current

### Description
Computes the current profile of a particle array object within the Ocelot framework.

### Method
GET

### Endpoint
/api/ocelot/current

### Parameters
#### Query Parameters
- **particle_array_id** (string) - Required - The ID of the particle array to process.

### Request Example
{
  "particle_array_id": "pa_882"
}

### Response
#### Success Response (200)
- **current_profile** (array) - List of current values along the longitudinal coordinate.

#### Response Example
{
  "current_profile": [0.5, 1.2, 5.0, 1.1],
  "unit": "Amperes"
}
```

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

### Configure MethodTM for Element Transfer Maps

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/index.rst.txt

Demonstrates how to initialize MethodTM to define global or element-specific transfer map strategies. This allows users to mix linear and non-linear (e.g., KickTM) maps within a single lattice simulation.

```python
method = MethodTM()
method.global_method = TransferMap
method.params[Sextupole] = KickTM

method2 = MethodTM()
method2.global_method = SecondTM
```

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

### GET /ocelot/rad/bmrad/chisquare

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.rad.html

Draws samples from a chi-square distribution based on degrees of freedom.

```APIDOC
## GET /ocelot/rad/bmrad/chisquare

### Description
Draws samples from a chi-square distribution. When df independent random variables, each with standard normal distributions, are squared and summed, the resulting distribution is chi-square.

### Method
GET

### Endpoint
ocelot.rad.bmrad.chisquare(df, size=None)

### Parameters
#### Query Parameters
- **df** (float) - Required - Number of degrees of freedom, must be > 0.
- **size** (int or tuple) - Optional - Output shape of the drawn samples.

### Response
#### Success Response (200)
- **out** (ndarray or scalar) - Drawn samples from the parameterized chi-square distribution.

### Response Example
{
  "samples": [1.89, 9.00, 3.13, 5.62]
}
```

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

### Configure Transfer Map Method

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.html

Demonstrates how to instantiate a MethodTM object and customize the tracking method for specific beamline elements, such as assigning a nonlinear KickTM to Sextupole elements while maintaining linear maps for others.

```python
from ocelot.cpbd.optics import MethodTM, TransferMap, KickTM
from ocelot.cpbd.elements import Sextupole

# Use linear matrices for all elements except Sextupole
method = MethodTM()
method.global_method = TransferMap
method.params[Sextupole] = KickTM
```

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

### GET /api/ocelot/envelope

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/index.rst.txt

Retrieves the beam envelope parameters for a given lattice configuration.

```APIDOC
## GET /api/ocelot/envelope

### Description
Calculates and retrieves the beam envelope based on the provided lattice and beam parameters.

### Method
GET

### Endpoint
/api/ocelot/envelope

### Parameters
#### Query Parameters
- **lattice_id** (string) - Required - The identifier of the magnetic lattice to analyze.
- **beam_id** (string) - Required - The identifier of the beam object.

### Request Example
{
  "lattice_id": "lattice_001",
  "beam_id": "beam_001"
}

### Response
#### Success Response (200)
- **envelope_data** (object) - The calculated envelope parameters including sigma_x, sigma_y, and beta functions.

#### Response Example
{
  "sigma_x": 0.001,
  "sigma_y": 0.001,
  "status": "success"
}
```

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

### Sample from Geometric Distribution using NumPy

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.adaptors.html

Demonstrates how to draw samples from a geometric distribution and calculate the frequency of success in the first trial.

```python
import numpy as np
z = np.random.geometric(p=0.35, size=10000)
success_rate = (z == 1).sum() / 10000.
```

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

### GET /spectrum

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.cpbd.html

Computes the frequency and Fourier transform of 1D sample data.

```APIDOC
## GET /spectrum

### Description
Computes the frequency and Fourier transform of input 1D sample data.

### Method
GET

### Endpoint
ocelot.cpbd.track.spectrum

### Parameters
#### Query Parameters
- **data1D** (array) - Required - 1D sample data.

### Response
#### Success Response (200)
- **result** (tuple) - Returns frequency and Fourier transform.
```

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

### Generate and Visualize Uniform Distribution Samples

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.adaptors.html

Demonstrates how to draw samples from a uniform distribution within a specified range and visualize the result using a histogram and the probability density function.

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

# Draw samples
s = np.random.uniform(-1, 0, 1000)

# Validate range
print(np.all(s >= -1))
print(np.all(s < 0))

# Visualize
count, bins, ignored = plt.hist(s, 15, density=True)
plt.plot(bins, np.ones_like(bins), linewidth=2, color='r')
plt.show()
```

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

### SshMpiLauncher Class API

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/utils/launcher/index.rst.txt

Documentation for the SshMpiLauncher class, used for launching MPI simulations over SSH.

```APIDOC
## SshMpiLauncher Class

### Description
Manages the launching of MPI simulations remotely via SSH.

### Methods

- **prepare(self)**
  Prepares the environment for the simulation over SSH.

- **launch(self)**
  Launches the MPI simulation via SSH.

- **collect(self, inputDir, outputDir, pattern='*')**
  Collects simulation output files from a remote directory.
```

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

### Get Lattice Map

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.cpbd.html

Retrieves a map for a given lattice and spatial discretization.

```APIDOC
## POST /api/lattice/get_map

### Description
Retrieves a map for a given lattice with specified spatial discretization.

### Method
POST

### Endpoint
/api/lattice/get_map

### Parameters
#### Request Body
- **lattice** (MagneticLattice) - Required - The magnetic lattice object.
- **dz** (float) - Required - The spatial step size for the map.
- **navi** (bool) - Required - Navigation flag (purpose may vary).

### Request Example
```json
{
  "lattice": "lattice_object_representation",
  "dz": 0.1,
  "navi": true
}
```

### Response
#### Success Response (200)
- **lattice_map** (object) - The generated map data for the lattice.

#### Response Example
```json
{
  "lattice_map": {"map_data": "..."}
}
```
```

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

### Initialize Navigator with SmoothBeam Physics Process

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.html

This snippet demonstrates how to initialize a Navigator object with a SmoothBeam physics process. The SmoothBeam process is configured with a specified mslice and then added to the navigator for a given lattice element.

```python
from ocelot.cpbd.navigator import Navigator
from ocelot.cpbd.physics_proc import SmoothBeam

lat = MagneticLattice()
avi = Navigator(lat)
smooth = SmoothBeam()
smooth.mslice = 10000
avi.add_physics_process(smooth, start=elem, stop=elem) # elem is the lattice element where you want to apply smoothing
```

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

### GET /ocelot.cpbd.high_order.scipy_track_in_field

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.cpbd.html

Tracks a particle through a magnetic field using scipy integration.

```APIDOC
## GET ocelot.cpbd.high_order.scipy_track_in_field

### Description
Tracks a particle through a magnetic field and returns the trajectory coordinates and field values.

### Parameters
#### Path Parameters
- **y0** (array) - Required - Initial state vector
- **l** (float) - Required - Length of tracking
- **N** (int) - Required - Number of steps
- **energy** (float) - Required - Energy of particle in [GeV]
- **mag_field** (function) - Required - Function returning Bx, By, Bz given X, Y, Z

### Response
#### Success Response (200)
- **result** (array) - Array of length N*9 containing coordinates and magnetic fields [x, x', y, y', z, dE/pc, Bx, By, Bz, ...]
```

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

### GET /ocelot/rad/transfer_function/get_transfer_function

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/rad/transfer_function/index.html

Retrieves the transfer function associated with a specific radiation element.

```APIDOC
## GET /ocelot/rad/transfer_function/get_transfer_function

### Description
Retrieves the transfer function for a given radiation element.

### Method
GET

### Endpoint
/ocelot/rad/transfer_function/get_transfer_function

### Parameters
#### Query Parameters
- **element** (object) - Required - The radiation element object for which to retrieve the transfer function.

### Request Example
{
  "element": "<radiation_element_object>"
}

### Response
#### Success Response (200)
- **transfer_function** (object) - The calculated transfer function for the element.

#### Response Example
{
  "transfer_function": "<transfer_function_data>"
}
```

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

### Generate and Verify Normal Distribution Samples

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.rad.html

Demonstrates how to draw random samples from a normal distribution using NumPy, verify the statistical properties (mean and standard deviation), and visualize the results with Matplotlib.

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

# Draw samples
mu, sigma = 0, 0.1
s = np.random.normal(mu, sigma, 1000)

# Verify mean and std
print(abs(mu - np.mean(s)))
print(abs(sigma - np.std(s, ddof=1)))

# Plot histogram and PDF
count, bins, ignored = plt.hist(s, 30, density=True)
plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) ), linewidth=2, color='r')
plt.show()
```

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

### Prepare Physics Process (Python)

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.html

Method called when a physics process is added to the Navigator class.

```python
def prepare(_lat_):
    """method is called at the moment of Physics Process addition to Navigator class.

    Parameters
      lat – 

    Returns
     
    """
    pass
```

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

### GET /genesis/output/spectrum

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/adaptors/genesis/index.html

Calculates and retrieves the on-axis spectrum from Genesis output files.

```APIDOC
## GET /genesis/output/spectrum

### Description
Calculates the on-axis spectrum at every position along the undulator using the GenesisOutput object.

### Method
GET

### Endpoint
/genesis/output/spectrum

### Parameters
#### Query Parameters
- **mode** (string) - Optional - 'mid' for on-axis power or 'int' for transversely integrated power.
- **npad** (integer) - Optional - Padding factor for resolution improvement.

### Response
#### Success Response (200)
- **spec** (array) - Calculated spectrum data.

#### Response Example
{
  "spec": [0.001, 0.005, 0.012]
}
```

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

### GET /response-matrix/measure

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/cpbd/orbit_correction/index.html

Measures the response matrix for a given orbit and lattice configuration.

```APIDOC
## GET /response-matrix/measure

### Description
Computes the response matrix by measuring the effect of correctors on the beam orbit.

### Method
GET

### Endpoint
/response-matrix/measure

### Parameters
#### Query Parameters
- **orbit** (object) - Required - The current orbit object.
- **lattice** (object) - Required - The magnetic lattice configuration.

### Request Example
GET /response-matrix/measure?orbit=current_orbit&lattice=main_lattice

### Response
#### Success Response (200)
- **matrix** (array) - The calculated response matrix.

#### Response Example
{
  "matrix": [[0.1, 0.0], [0.0, 0.1]]
}
```

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

### Track List Creation (Python)

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.html

Creates a list of Pxy (particle coordinates and momenta) from given arrays.

```python
def create_track_list(_x_array_, _y_array_, _p_array_, _energy=0.0):
    """the function create list of Pxy"""
    pass
```

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

### OCELOT Launcher Methods

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/genindex.html

Methods for launching simulation jobs.

```APIDOC
## OCELOT Launcher Methods

### Description
Methods for launching simulation jobs, particularly for local execution.

### Method
- **outputfile()**: Specifies the output file for a simulation job.
  - **Class**: `LocalLauncher`
  - **Module**: `ocelot.utils.launcher`
```

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

### estimate_start_index Method

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.cpbd.html

Estimates the starting index for CSR effect computation to optimize performance.

```APIDOC
## Method estimate_start_index

### Description
Estimates the index of the first trajectory point from which CSR effects should be computed, optimizing computation time by discarding regions where w <= wmin.

### Parameters
- **i** (int): Iteration index.
- **traj** (ndarray): Reference trajectory along which CSR forces are calculated.
- **w_min** (float): Leftmost edge of the longitudinal bunch binning.
- **beta** (float): Relativistic factor.
- **i_min** (int, optional): Minimum iteration index. Defaults to 1000.
- **n_test** (int, optional): Number of points along the trajectory to test. Defaults to 10.

### Returns
- **estimated_start_index** (int): The estimated start index, which is always less than or equal to the real one.
```

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

### prepare Function

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/cpbd/csr/index.html

Prepares the trajectory in rectangular coordinates and calculates the CSR start position.

```APIDOC
## prepare Function

### Description
Calculates the trajectory in rectangular coordinates and determines the `z_csr_start`.

### Method
N/A (Function definition)

### Endpoint
N/A (Internal function)

### Parameters
#### Path Parameters
N/A

#### Query Parameters
N/A

#### Request Body
N/A

### Request Example
N/A

### Response
#### Success Response (200)
N/A

#### Response Example
N/A

### Parameters
* **lat** (Magnetic Lattice) - The magnetic lattice object used for calculations.
```

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

### Class: SimInfo

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/autoapi/ocelot/utils/sim_info/index.html

Represents the general simulation configuration settings.

```APIDOC
## CLASS SimInfo

### Description
Manages simulation settings and parameters.

### Parameters
- **n** (int) - Optional - Number of particles or steps, defaults to 10.

### Usage Example
```python
from ocelot.utils.sim_info import SimInfo
sim = SimInfo(n=100)
```
```

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

### Draw and Visualize Gamma Distribution Samples

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.rad.html

Shows how to generate samples from a Gamma distribution and visualize the results using Matplotlib and SciPy.

```python
import matplotlib.pyplot as plt
import scipy.special as sps

shape, scale = 2., 2.  # mean=4, std=2*sqrt(2)
s = np.random.gamma(shape, scale, 1000)

count, bins, ignored = plt.hist(s, 50, density=True)
y = bins**(shape-1)*(np.exp(-bins/scale) / (sps.gamma(shape)*scale**shape))
plt.plot(bins, y, linewidth=2, color='r')
plt.show()
```

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

### GET /ocelot/adaptors/madx/exponential

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/ocelot.adaptors.html

Draws samples from an exponential distribution based on a provided scale parameter.

```APIDOC
## GET /ocelot/adaptors/madx/exponential

### Description
Draws samples from an exponential distribution with a specified scale parameter. The exponential distribution is a continuous analogue of the geometric distribution.

### Method
GET

### Endpoint
ocelot.adaptors.madx.exponential

### Parameters
#### Query Parameters
- **scale** (float) - Optional - The scale parameter (beta), must be non-negative. Default is 1.0.
- **size** (int or tuple) - Optional - Output shape of the drawn samples.

### Request Example
{ "scale": 1.0, "size": [2, 2] }

### Response
#### Success Response (200)
- **out** (ndarray) - Drawn samples from the parameterized exponential distribution.

#### Response Example
{ "samples": [0.5, 1.2, 0.8, 2.1] }
```

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

### Database Creation

Source: https://ocelot-collab-docu.readthedocs.io/en/latest/_sources/autoapi/ocelot/utils/db/index.rst.txt

Provides functions for creating and testing new database instances.

```APIDOC
## create_db

### Description
Creates a new database file with the specified name.

### Method
Function

### Endpoint
N/A (Python function)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Request Example
```python
create_db(dbname='my_database.db')
```

### Response
#### Success Response (200)
None (operation is performed in place)

#### Response Example
None

## test_new_tunings

### Description
Tests the functionality of creating new tunings in the database.

### Method
Function

### Endpoint
N/A (Python function)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Request Example
```python
test_new_tunings(dbname='my_database.db')
```

### Response
#### Success Response (200)
None (operation is performed in place)

#### Response Example
None

## test_new_action

### Description
Tests the functionality of creating new actions in the database.

### Method
Function

### Endpoint
N/A (Python function)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Request Example
```python
test_new_action(dbname='my_database.db')
```

### Response
#### Success Response (200)
None (operation is performed in place)

#### Response Example
None

## test_add_action_parameters

### Description
Tests the functionality of adding parameters to actions in the database.

### Method
Function

### Endpoint
N/A (Python function)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Request Example
```python
test_add_action_parameters(dbname='my_database.db')
```

### Response
#### Success Response (200)
None (operation is performed in place)

#### Response Example
None
```