### Install all recommended dependencies

Source: https://pybhpt.readthedocs.io/en/latest/_sources/installation.md

Install the package with all recommended software dependencies.

```bash
pip install '.[dev, testing, extended]'
```

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

### Install pybhpt with all recommended software

Source: https://pybhpt.readthedocs.io/en/latest/installation.html

Install pybhpt with all recommended software dependencies.

```bash
pip install '.[dev, testing, extended]'

```

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

### Install pybhpt from source

Source: https://pybhpt.readthedocs.io/en/latest/_sources/installation.md

Install the package from the source directory using pip.

```bash
pip install .
```

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

### Install basic development dependencies

Source: https://pybhpt.readthedocs.io/en/latest/_sources/installation.md

Install the package with basic development and testing dependencies.

```bash
pip install '.[dev, testing]'
```

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

### Example output of total fluxes

Source: https://pybhpt.readthedocs.io/en/latest/notebooks/fluxes.html

Example output showing the total fluxes for the circular Kerr example.

```text
Total fluxes (E, Lz, Q):  [0.00122957 0.01496423 0.        ]

```

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

### Install pybhpt with basic development dependencies

Source: https://pybhpt.readthedocs.io/en/latest/installation.html

Install pybhpt with the basic development and testing dependencies.

```bash
pip install '.[dev, testing]'

```

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

### Install compiler on Linux

Source: https://pybhpt.readthedocs.io/en/latest/_sources/installation.md

Install the necessary compiler for Linux using conda.

```bash
conda install gcc_linux-64 gxx_linux-64
```

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

### Install Jupyter dependencies

Source: https://pybhpt.readthedocs.io/en/latest/_sources/installation.md

Install ipykernel and matplotlib for running code in a Jupyter notebook.

```bash
pip install ipykernel matplotlib
```

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

### Example output of flux components

Source: https://pybhpt.readthedocs.io/en/latest/notebooks/fluxes.html

Example output showing horizon, infinity, and total fluxes for the mode.

```text
[-3.606222842872166e-36, -3.5075219557527026e-35, -1.979059439027494e-34]
[6.753687090778148e-25, 6.56884135710292e-24, 3.7063566971910574e-23]
[6.753687090742086e-25, 6.568841357067845e-24, 3.706356697171267e-23]

```

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

### Install compiler on macOS arm/silicon

Source: https://pybhpt.readthedocs.io/en/latest/_sources/installation.md

Install the necessary compiler for macOS arm/silicon using conda.

```bash
conda install clang_osx-arm64 clangxx_osx-arm64
```

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

### Install pybhpt with pip

Source: https://pybhpt.readthedocs.io/en/latest/_sources/index.md

Install the latest tagged release of pybhpt from PyPI using pip. This command is for macOS and 64-bit Linux wheel packages.

```bash
python3 -m pip install pybhpt
```

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

### Import pybhpt and matplotlib

Source: https://pybhpt.readthedocs.io/en/latest/_sources/notebooks/waveform.ipynb

Imports the pybhpt library and matplotlib for plotting. This is the initial setup for the notebook.

```python
import pybhpt
import matplotlib.pyplot as plt
import matplotlib as mpl
```

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

### Run unit tests with pytest

Source: https://pybhpt.readthedocs.io/en/latest/_sources/installation.md

Run the unit tests to ensure the package installed properly.

```bash
pytest .
```

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

### Run pybhpt unit tests with pytest

Source: https://pybhpt.readthedocs.io/en/latest/installation.html

Run the unit tests to ensure the package installed properly.

```bash
pytest .

```

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

### Import pybhpt.flux and dependencies

Source: https://pybhpt.readthedocs.io/en/latest/notebooks/fluxes.html

Imports TeukolskyMode, FluxMode, KerrGeodesic, numpy, and matplotlib for the flux tutorial.

```python
from pybhpt.teuk import TeukolskyMode
from pybhpt.flux import FluxMode
from pybhpt.geo import KerrGeodesic
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl

```

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

### KerrGeodesic.__init__

Source: https://pybhpt.readthedocs.io/en/latest/_modules/pybhpt/geo.html

Initializes a KerrGeodesic object with the given orbital parameters. Validates the black hole spin, sample count, and parametrization, then constructs the underlying Cython geodesic and computes various orbital quantities.

```APIDOC
## KerrGeodesic.__init__

### Description
Initializes a KerrGeodesic object with the given orbital parameters. Validates the black hole spin, sample count, and parametrization, then constructs the underlying Cython geodesic and computes various orbital quantities.

### Method
Constructor

### Signature
`KerrGeodesic(a, p, e, x, nsamples=256, parametrization="darwin")`

### Parameters
- **a** (float) - Required - The black hole spin parameter. Must be in the range [0, 1].
- **p** (float) - Required - The semilatus rectum of the orbit.
- **e** (float) - Required - The eccentricity of the orbit.
- **x** (float) - Required - The inclination of the orbit.
- **nsamples** (int) - Optional - The number of samples to use for the geodesic. Must be a power of two. Default is 256.
- **parametrization** (str) - Optional - The phase variable used to sample the geodesic and source. "mino" (default) samples uniformly in the Mino phases (q_r, q_theta); "darwin" (alias "psi") samples uniformly in the relativistic anomalies (psi radial, chi polar), which resolves high-eccentricity / near-separatrix orbits more efficiently. Both yield identical mode amplitudes. Default is "darwin".

### Attributes
- **blackholespin** (float) - The black hole spin parameter.
- **semilatusrectum** (float) - The semilatus rectum of the orbit.
- **eccentricity** (float) - The eccentricity of the orbit.
- **inclination** (float) - The inclination of the orbit.
- **orbitalenergy** (float) - The orbital energy En of the orbit.
- **orbitalangularmomentum** (float) - The z-component of the orbital angular momentum Lz of the orbit.
- **carterconstant** (float) - The Carter constant Qc of the orbit.
- **orbitalconstants** (numpy.ndarray) - The orbital constants (En, Lz, Qc) of the orbit.
- **radialroots** (numpy.ndarray) - The roots of the radial equation.
- **polarroots** (numpy.ndarray) - The roots of the polar equation.
- **minofrequencies** (numpy.ndarray) - The orbital frequencies with respect to Mino time.
- **timefrequencies** (numpy.ndarray) - The orbital frequencies with respect to the time coordinate.
- **frequencies** (numpy.ndarray) - The (coordinate time) frequencies of the orbit.
- **carterfrequencies** (numpy.ndarray) - The frequencies for computing Carter constant fluxes.
- **timeradialfourier** (numpy.ndarray) - The Fourier coefficients of coordinate time with respect to the radial Mino phase.
- **timepolarfourier** (numpy.ndarray) - The Fourier coefficients of coordinate time with respect to the polar Mino phase.
- **radialfourier** (numpy.ndarray) - The Fourier coefficients of radial position with respect to the radial Mino phase.
- **polarfourier** (numpy.ndarray) - The Fourier coefficients of polar position with respect to the polar Mino phase.
- **azimuthalradialfourier** (numpy.ndarray) - The Fourier coefficients of azimuthal position with respect to the radial Mino phase.
- **azimuthalpolarfourier** (numpy.ndarray) - The Fourier coefficients of azimuthal position with respect to the polar Mino phase.

### Exceptions
- **ValueError** - If `a` is not in the range [0, 1].
- **ValueError** - If `nsamples` is not a power of 2.
- **ValueError** - If the parametrization is unknown.
- **ValueError** - If the orbital parameters do not represent a valid bound non-plunging orbit.

### Example
```python
from pybhpt.geo import KerrGeodesic
geo = KerrGeodesic(a=0.5, p=10.0, e=0.2, x=0.8)
```
```

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

### Initialize boost submodule

Source: https://pybhpt.readthedocs.io/en/latest/_sources/installation.md

Initialize and update the boost submodule under extern/boost.

```bash
git submodule update --init --recursive extern/boost
```

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

### Install Jupyter dependencies for pybhpt

Source: https://pybhpt.readthedocs.io/en/latest/installation.html

Install ipykernel and matplotlib for running pybhpt in Jupyter notebooks.

```bash
pip install ipykernel matplotlib

```

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

### Build boost headers

Source: https://pybhpt.readthedocs.io/en/latest/_sources/installation.md

Build the Boost headers by running bootstrap.sh and b2 headers in the extern/boost directory.

```bash
cd extern/boost
chmod +x bootstrap.sh
./bootstrap.sh
./b2 headers
```

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

### Import pybhpt modules and dependencies

Source: https://pybhpt.readthedocs.io/en/latest/_sources/notebooks/waveform.ipynb

Loads TeukolskyMode, KerrGeodesic, SpinWeightedSpheroidalHarmonic, numpy, and matplotlib for the waveform computation.

```python
from pybhpt.teuk import TeukolskyMode
from pybhpt.geo import KerrGeodesic
from pybhpt.swsh import SpinWeightedSpheroidalHarmonic
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
```

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

### Install compiler on macOS Intel

Source: https://pybhpt.readthedocs.io/en/latest/_sources/installation.md

Install the necessary compiler for macOS Intel using conda.

```bash
conda install clang_osx-64 clangxx_osx-64
```

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

### Run all benchmarks

Source: https://pybhpt.readthedocs.io/en/latest/_sources/performance/index.md

Runs the full benchmark suite covering geodesic, swsh, radial, teuk, and flux computations. Use this command to reproduce the committed performance numbers on your own machine.

```bash
python -m benchmarks.run all          # geodesic, swsh, radial, teuk (+flux)
```

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

### Register Jupyter kernel

Source: https://pybhpt.readthedocs.io/en/latest/_sources/installation.md

Make the pybhpt-env environment accessible within Jupyter by installing a kernel.

```bash
python -m ipykernel install --user --name=pybhpt-env
```

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

### Import pybhpt.swsh and dependencies

Source: https://pybhpt.readthedocs.io/en/latest/_sources/notebooks/swsh.ipynb

Imports SpinWeightedSpheroidalHarmonic and swsh_eigenvalue from pybhpt.swsh, along with numpy and matplotlib for numerical and plotting support.

```python
from pybhpt.swsh import SpinWeightedSpheroidalHarmonic, swsh_eigenvalue
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
```