From c0d4c04c6a2bc91a26d4b67a5f785ed9e3ba9f7c Mon Sep 17 00:00:00 2001
From: Philipp Arras <parras@mpa-garching.mpg.de>
Date: Thu, 28 Jan 2021 16:59:53 +0100
Subject: [PATCH] Add Laplace distribution
---
src/__init__.py | 3 ++-
src/library/special_distributions.py | 28 +++++++++++++++++++++++++++-
2 files changed, 29 insertions(+), 2 deletions(-)
diff --git a/src/__init__.py b/src/__init__.py
index d5e0b9b9e..787e158ab 100644
--- a/src/__init__.py
+++ b/src/__init__.py
@@ -77,7 +77,8 @@ from .sugar import *
from .plot import Plot
-from .library.special_distributions import InverseGammaOperator, UniformOperator
+from .library.special_distributions import (InverseGammaOperator, UniformOperator,
+ LaplaceOperator)
from .library.los_response import LOSResponse
from .library.dynamic_operator import (dynamic_operator,
dynamic_lightcone_operator)
diff --git a/src/library/special_distributions.py b/src/library/special_distributions.py
index a46f17c04..4913ce0f3 100644
--- a/src/library/special_distributions.py
+++ b/src/library/special_distributions.py
@@ -17,7 +17,7 @@
import numpy as np
from scipy.interpolate import CubicSpline
-from scipy.stats import invgamma, norm
+from scipy.stats import invgamma, norm, laplace
from .. import random
from ..domain_tuple import DomainTuple
@@ -158,3 +158,29 @@ class UniformOperator(Operator):
def inverse(self, field):
res = norm._ppf(field.val/self._scale - self._loc)
return Field(field.domain, res)
+
+
+def LaplaceOperator(domain, alpha, delta=1e-2):
+ """Transforms a Gaussian with unit covariance and zero mean into a
+ Laplacian distribution.
+
+ The pdf of the laplace distribution is defined as follows:
+
+ .. math::
+ \\frac{\\alpha}{2} \\exp \\left(-\\alpha |x| \\right)
+
+ This transformation is implemented as a spline interpolation which maps a
+ Gaussian onto a Laplace distribution.
+
+ Parameters
+ ----------
+ domain : Domain, tuple of Domain or DomainTuple
+ The domain on which the field shall be defined. This is at the same
+ time the domain and the target of the operator.
+ alpha : float
+ The alpha-parameter of the Laplace distribution.
+ delta : float
+ Distance between sampling points for spline interpolation.
+ """
+ return _InterpolationOperator(domain, lambda x: laplace.ppf(norm._cdf(x), float(alpha)),
+ -8.2, 8.2, delta)
--
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