"""Created on Aug 03 21:12:13 2024"""
from typing import Dict
import numpy as np
from .backend import BaseDistribution, errorHandling as erH
from .utilities_d import laplace_cdf_, laplace_pdf_, laplace_log_pdf_, laplace_log_cdf_
from .. import md_scipy_like, OneDArray
[docs]
class LaplaceDistribution(BaseDistribution):
r"""
Class for Laplace distribution.
:param amplitude: The amplitude of the PDF. Defaults to 1.0. Ignored if **normalize** is ``True``.
:type amplitude: float, optional
:param mean: The mean parameter, :math:`\mu`. Defaults to 0.0.
:type mean: float, optional
:param diversity: The diversity parameter, :math:`b`. Defaults to 1.0.
:type diversity: float, optional
:param normalize: If ``True``, the distribution is normalized so that the total area under the PDF equals 1. Defaults to ``False``.
:type normalize: bool, optional
:raise NegativeAmplitudeError: If the provided value of amplitude is negative.
:raise NegativeScaleError: If the provided value of diversity is negative.
Examples
--------
Importing libraries:
.. literalinclude:: ../../../examples/basic/laplace.py
:language: python
:linenos:
:lineno-start: 3
:lines: 3-7
Generating a standard Laplace(:math:`\mu=0, b = 1`) distribution with ``pyMultiFit`` and ``scipy``:
.. literalinclude:: ../../../examples/basic/laplace.py
:language: python
:linenos:
:lineno-start: 9
:lines: 9-12
Plotting **PDF** and **CDF**:
.. literalinclude:: ../../../examples/basic/laplace.py
:language: python
:linenos:
:lineno-start: 14
:lines: 14-29
.. image:: ../../../images/laplace_example1.png
:alt: Laplace(0, 1)
:align: center
Generating a translated Laplace(:math:`\mu=3, b=2`) distribution:
.. literalinclude:: ../../../examples/basic/laplace.py
:language: python
:lineno-start: 32
:lines: 32
Plotting **PDF** and **CDF**:
.. literalinclude:: ../../../examples/basic/laplace.py
:language: python
:lineno-start: 34
:lines: 34-49
.. image:: ../../../images/laplace_example2.png
:alt: Laplace(3, 2)
:align: center
"""
def __init__(self, amplitude: float = 1.0, mean: float = 0, diversity: float = 1, normalize: bool = False):
if not normalize and amplitude <= 0:
raise erH.NegativeAmplitudeError()
if diversity <= 0:
raise erH.NegativeScaleError("diversity")
self.amplitude = 1.0 if normalize else amplitude
self.mu = mean
self.b = diversity
self.norm = normalize
[docs]
@classmethod
@md_scipy_like("1.0.7")
def scipy_like(cls, loc: float = 0.0, scale: float = 1.0) -> "LaplaceDistribution":
"""
Instantiate LaplaceDistribution with scipy parametrization.
Parameters
----------
loc: float, optional
The location parameter. Defaults to 0.0.
scale: float, optional
The scale parameter. Defaults to 1.0.
Returns
-------
LaplaceDistribution
An instance of normalized LaplaceDistribution.
"""
return cls(mean=loc, diversity=scale, normalize=True)
[docs]
@classmethod
def from_scipy_params(cls, loc: float = 0.0, scale: float = 1.0) -> "LaplaceDistribution":
"""
Instantiate LaplaceDistribution with scipy parametrization.
Parameters
----------
loc: float, optional
The location parameter. Defaults to 0.0.
scale: float, optional
The scale parameter. Defaults to 1.0.
Returns
-------
LaplaceDistribution
An instance of normalized LaplaceDistribution.
"""
return cls(mean=loc, diversity=scale, normalize=True)
[docs]
def pdf(self, x: OneDArray) -> OneDArray:
return laplace_pdf_(x, amplitude=self.amplitude, mean=self.mu, diversity=self.b, normalize=self.norm)
[docs]
def logpdf(self, x: OneDArray) -> OneDArray:
return laplace_log_pdf_(x, amplitude=self.amplitude, mean=self.mu, diversity=self.b, normalize=self.norm)
[docs]
def cdf(self, x: OneDArray) -> OneDArray:
return laplace_cdf_(x, amplitude=self.amplitude, mean=self.mu, diversity=self.b, normalize=self.norm)
[docs]
def logcdf(self, x: OneDArray) -> OneDArray:
return laplace_log_cdf_(x, amplitude=self.amplitude, mean=self.mu, diversity=self.b, normalize=self.norm)
[docs]
def stats(self) -> Dict[str, float]:
m, b = self.mu, self.b
variance_ = 2 * b**2
return {"mean": m, "median": m, "mode": m, "variance": variance_, "std": np.sqrt(variance_)}