"""Created on Dec 04 03:57:18 2024"""
from typing import Dict
import numpy as np
from .backend import errorHandling as erH, BaseDistribution
from .utilities_d import half_normal_pdf_, half_normal_cdf_, half_normal_log_pdf_, half_normal_log_cdf_
from .. import md_scipy_like, OneDArray
[docs]
class HalfNormalDistribution(BaseDistribution):
r"""
Class for halfnormal distribution.
:param amplitude: The amplitude of the PDF. Defaults to 1.0. Ignored if **normalize** is ``True``.
:type amplitude: float, optional
:param scale: The standard deviation parameter, :math:`\sigma`. Defaults to 1.0.
:type scale: float, optional
:param loc: The location parameter, for shifting. Defaults to 0.0.
:type loc: 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 NegativeStandardDeviationError: If the provided value of standard deviation is negative.
Examples
--------
Importing libraries:
.. literalinclude:: ../../../examples/basic/halfnorm.py
:language: python
:linenos:
:lineno-start: 3
:lines: 3-7
Generating a standard Half Normal(:math:`\sigma = 1`) distribution with ``pyMultiFit`` and ``scipy``:
.. literalinclude:: ../../../examples/basic/halfnorm.py
:language: python
:linenos:
:lineno-start: 9
:lines: 9-12
Plotting **PDF** and **CDF**:
.. literalinclude:: ../../../examples/basic/halfnorm.py
:language: python
:linenos:
:lineno-start: 14
:lines: 14-29
.. image:: ../../../images/half_normal_example1.png
:alt: HN(1)
:align: center
Generating a translated Gaussian(:math:`\sigma=3`) distribution with :math:`\text{loc}=3`:
.. literalinclude:: ../../../examples/basic/halfnorm.py
:language: python
:lineno-start: 32
:lines: 32
Plotting **PDF** and **CDF**:
.. literalinclude:: ../../../examples/basic/halfnorm.py
:language: python
:lineno-start: 34
:lines: 34-49
.. image:: ../../../images/half_normal_example2.png
:alt: HN(2, 3)
:align: center
"""
def __init__(self, amplitude: float = 1.0, scale: float = 1.0, loc: float = 0.0, normalize: bool = False):
if not normalize and amplitude <= 0:
raise erH.NegativeAmplitudeError()
if scale < 0:
raise erH.NegativeScaleError()
self.amplitude = 1 if normalize else amplitude
self.scale = scale
self.loc = loc
self.norm = normalize
[docs]
@classmethod
@md_scipy_like("1.0.7")
def scipy_like(cls, loc: float = 0.0, scale: float = 1.0) -> "HalfNormalDistribution":
"""
Instantiate HalfNormalDistribution 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
-------
HalfNormalDistribution
An instance of normalized HalfNormalDistribution.
"""
return cls(loc=loc, scale=scale, normalize=True)
[docs]
@classmethod
def from_scipy_params(cls, loc: float = 0.0, scale: float = 1.0) -> "HalfNormalDistribution":
"""
Instantiate HalfNormalDistribution 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
-------
HalfNormalDistribution
An instance of normalized HalfNormalDistribution.
"""
return cls(loc=loc, scale=scale, normalize=True)
[docs]
def pdf(self, x: OneDArray) -> OneDArray:
return half_normal_pdf_(x, amplitude=self.amplitude, sigma=self.scale, loc=self.loc, normalize=self.norm)
[docs]
def logpdf(self, x: OneDArray) -> OneDArray:
return half_normal_log_pdf_(x, amplitude=self.amplitude, sigma=self.scale, loc=self.loc, normalize=self.norm)
[docs]
def cdf(self, x: OneDArray) -> OneDArray:
return half_normal_cdf_(x, amplitude=self.amplitude, sigma=self.scale, loc=self.loc, normalize=self.norm)
[docs]
def logcdf(self, x: OneDArray) -> OneDArray:
return half_normal_log_cdf_(x, amplitude=self.amplitude, sigma=self.scale, loc=self.loc, normalize=self.norm)
[docs]
def stats(self) -> Dict[str, float]:
s_, l_ = self.scale, self.loc
mean_ = np.sqrt(2 / np.pi)
mode_ = 0
variance_ = 1 - (2 / np.pi)
variance_ *= s_**2
return {"mean": (s_ * mean_) + l_, "mode": mode_, "variance": variance_, "std": np.sqrt(variance_)}