From 0ecbed3bb670e69ab65556fb6e607983b656f473 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?K=C3=BChle=2C=20Laura=20Christine=20=28lakue103=29?=
<laura.kuehle@uni-duesseldorf.de>
Date: Tue, 21 Sep 2021 17:14:47 +0200
Subject: [PATCH] Added documentation to 'InitialCondition'.
---
Initial_Condition.py | 553 +++++++++++++++++++++++++++++++++++++++++++
1 file changed, 553 insertions(+)
diff --git a/Initial_Condition.py b/Initial_Condition.py
index 28ef065..2fb972e 100644
--- a/Initial_Condition.py
+++ b/Initial_Condition.py
@@ -2,33 +2,109 @@
"""
@author: Laura C. Kühle
+TODO: Add is_smooth() to DiscontinuousConstant class
+
"""
import numpy as np
class InitialCondition(object):
+ """Class for initial condition function.
+
+ Attributes
+ ----------
+ interval_len : float
+ Length of the interval between left and right boundary.
+
+ Methods
+ -------
+ get_name()
+ Returns string of class name.
+ is_smooth()
+ Returns flag whether function is smooth.
+ induce_adjustment(value)
+ Adjusts x-value of function.
+ randomize(config)
+ Sets all instance variables to random value if not determined otherwise.
+ calculate(x)
+ Evaluates function at given x-value.
+
+ """
def __init__(self, left_bound, right_bound, config):
+ """Initializes InitialCondition.
+
+ Parameters
+ ----------
+ left_bound : float
+ Left boundary of interval.
+ right_bound : float
+ Right boundary of interval.
+ config : dict
+ Additional parameters for initial condition.
+
+ """
self._left_bound = left_bound
self._right_bound = right_bound
self._reset(config)
def _reset(self, config):
+ """Resets instance variables.
+
+ Parameters
+ ----------
+ config : dict
+ Additional parameters for initial condition.
+
+ """
self._interval_len = self._right_bound-self._left_bound
def get_name(self):
+ """Returns string of class name."""
return self.__class__.__name__
def is_smooth(self):
+ """Returns flag that function is smooth."""
return True
def induce_adjustment(self, value):
+ """Adjusts x-value of function.
+
+ Parameters
+ ----------
+ value : float
+ Value of adjustment on x-axis in right direction.
+
+ """
pass
def randomize(self, config):
+ """Sets all instance variables to random value if not determined otherwise.
+
+ Parameters
+ ----------
+ config : dict
+ Fixed parameters for initial condition.
+
+ """
pass
def calculate(self, x):
+ """Evaluates function at given x-value.
+
+ Projects x-value into interval of the periodic function and evaluates the function.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
while x < self._left_bound:
x = x + self._interval_len
while x > self._right_bound:
@@ -36,27 +112,103 @@ class InitialCondition(object):
return self._get_point(x)
def _get_point(self, x):
+ """Evaluates function at given x-value.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
pass
class Sine(InitialCondition):
+ """Class for the sine wave.
+
+ Attributes
+ ----------
+ factor : float
+ Factor by which is the evaluation point is multiplied before applying sine.
+
+ Methods
+ -------
+ randomize(config)
+ Sets all instance variables to random value if not determined otherwise.
+
+ """
def _reset(self, config):
+ """Resets instance variables.
+
+ Parameters
+ ----------
+ config : dict
+ Additional parameters for initial condition.
+
+ """
super()._reset(config)
# Unpack necessary configurations
self._factor = config.pop('factor', 2)
def randomize(self, config):
+ """Sets all instance variables to random value if not determined otherwise.
+
+ Parameters
+ ----------
+ config : dict
+ Fixed parameters for initial condition.
+
+ """
factor = config.pop('factor', np.random.uniform(low=-100, high=100))
config = {'factor': factor}
self._reset(config)
def _get_point(self, x):
+ """Evaluates function at given x-value.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
return np.sin(self._factor * np.pi * x)
class Box(InitialCondition):
+ """Class for a continuous function with two jumps (forming a box).
+
+ Methods
+ -------
+ is_smooth()
+ Returns flag whether function is smooth.
+
+ """
def _get_point(self, x):
+ """Evaluates function at given x-value.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
if x < -1:
x = x + 2
if x > 1:
@@ -67,11 +219,44 @@ class Box(InitialCondition):
return 0
def is_smooth(self):
+ """Returns flag that function is not smooth."""
return False
class FourPeakWave(InitialCondition):
+ """Class for a function with four peaks.
+
+ The function is defined piece-by-piece and consists of a Gaussian function, a box function,
+ a symmetric absolute function, and an elliptic function.
+
+ Attributes
+ ----------
+ alpha : float
+ Factor used for the elliptic function..
+ delta : float
+ Value used to adjust z for the Gaussian function.
+ beta : float
+ Factor used for the Gaussian function.
+ a : float
+ Value for x-value adjustment for elliptic function.
+ z : float
+ Value for x-value adjustment for Gaussian function.
+
+ Methods
+ -------
+ is_smooth()
+ Returns flag whether function is smooth.
+
+ """
def _reset(self, config):
+ """Resets instance variables.
+
+ Parameters
+ ----------
+ config : dict
+ Additional parameters for initial condition.
+
+ """
super()._reset(config)
# Set additional necessary parameter
@@ -82,9 +267,23 @@ class FourPeakWave(InitialCondition):
self._z = -0.7
def is_smooth(self):
+ """Returns flag that function is not smooth."""
return False
def _get_point(self, x):
+ """Evaluates function at given x-value.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
if (x >= -0.8) & (x <= -0.6):
return 1/6 * (self._gaussian_function(x, self._z-self._delta)
+ self._gaussian_function(x, self._z+self._delta)
@@ -100,49 +299,200 @@ class FourPeakWave(InitialCondition):
return 0
def _gaussian_function(self, x, z):
+ """Evaluates Gaussian function.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+ z : float
+ Value for x-value adjustment.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
return np.exp(-self._beta * (x-z)**2)
def _elliptic_function(self, x, a):
+ """Evaluates elliptic function.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+ a : float
+ Value for x-value adjustment.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
return np.sqrt(max(1 - self._alpha**2 * (x-a)**2, 0))
class Linear(InitialCondition):
+ """Class for the linear function.
+
+ Attributes
+ ----------
+ factor : float
+ Factor by which is the evaluation point is multiplied.
+
+ Methods
+ -------
+ randomize(config)
+ Sets all instance variables to random value if not determined otherwise.
+
+ """
def _reset(self, config):
+ """Resets instance variables.
+
+ Parameters
+ ----------
+ config : dict
+ Additional parameters for initial condition.
+
+ """
+ def _reset(self, config):
+ """Resets instance variables.
+
+ Parameters
+ ----------
+ config : dict
+ Additional parameters for initial condition.
+
+ """
super()._reset(config)
# Unpack necessary configurations
self._factor = config.pop('factor', 1)
def randomize(self, config):
+ """Sets all instance variables to random value if not determined otherwise.
+
+ Parameters
+ ----------
+ config : dict
+ Fixed parameters for initial condition.
+
+ """
factor = config.pop('factor', np.random.uniform(low=-100, high=100))
config = {'factor': factor}
self._reset(config)
def _get_point(self, x):
+ """Evaluates function at given x-value.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
return self._factor * x
class LinearAbsolut(InitialCondition):
+ """Class for the absolute values of the linear function.
+
+ Attributes
+ ----------
+ factor : float
+ Factor by which is the evaluation point is multiplied.
+
+ Methods
+ -------
+ is_smooth()
+ Returns flag whether function is smooth.
+ randomize(config)
+ Sets all instance variables to random value if not determined otherwise.
+
+ """
def _reset(self, config):
+ """Resets instance variables.
+
+ Parameters
+ ----------
+ config : dict
+ Additional parameters for initial condition.
+
+ """
super()._reset(config)
# Unpack necessary configurations
self._factor = config.pop('factor', 1)
def is_smooth(self):
+ """Returns flag that function is not smooth."""
return False
def randomize(self, config):
+ """Sets all instance variables to random value if not determined otherwise.
+
+ Parameters
+ ----------
+ config : dict
+ Fixed parameters for initial condition.
+
+ """
factor = config.pop('factor', np.random.uniform(low=-100, high=100))
config = {'factor': factor}
self._reset(config)
def _get_point(self, x):
+ """Evaluates function at given x-value.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
return self._factor * abs(x)
class DiscontinuousConstant(InitialCondition):
+ """Class for the otherwise continuous function with one jump.
+
+ Attributes
+ ----------
+ x0 : float
+ X-value where jump is induced.
+ left_factor : float
+ Factor by which is the evaluation point is multiplied before the jump.
+ right_factor : float
+ Factor by which is the evaluation point is multiplied after the jump.
+
+ Methods
+ -------
+ is_smooth()
+ Returns flag whether function is smooth.
+
+ """
def _reset(self, config):
+ """Resets instance variables.
+
+ Parameters
+ ----------
+ config : dict
+ Additional parameters for initial condition.
+
+ """
super()._reset(config)
# Unpack necessary configurations
@@ -151,11 +501,47 @@ class DiscontinuousConstant(InitialCondition):
self._right_factor = config.pop('right_factor', 0.5)
def _get_point(self, x):
+ """Evaluates function at given x-value.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
return self._left_factor * (x <= self._x0) + self._right_factor * (x > self._x0)
class Polynomial(InitialCondition):
+ """Class for the polynomial function.
+
+ Attributes
+ ----------
+ factor : float
+ Factor by which is the evaluation point is multiplied.
+ exponential : int
+ Degree of the polynomial.
+
+ Methods
+ -------
+ randomize(config)
+ Sets all instance variables to random value if not determined otherwise.
+
+ """
def _reset(self, config):
+ """Resets instance variables.
+
+ Parameters
+ ----------
+ config : dict
+ Additional parameters for initial condition.
+
+ """
super()._reset(config)
# Unpack necessary configurations
@@ -163,52 +549,189 @@ class Polynomial(InitialCondition):
self._exponential = config.pop('exponential', 2)
def randomize(self, config):
+ """Sets all instance variables to random value if not determined otherwise.
+
+ Parameters
+ ----------
+ config : dict
+ Fixed parameters for initial condition.
+
+ """
factor = config.pop('factor', np.random.uniform(low=-100, high=100))
exponential = config.pop('exponential', np.random.randint(2, high=6))
config = {'factor': factor, 'exponential': exponential}
self._reset(config)
def _get_point(self, x):
+ """Evaluates function at given x-value.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
return self._factor * (x ** self._exponential)
class Continuous(InitialCondition):
+ """Class for the continuous function.
+
+ Attributes
+ ----------
+ factor : float
+ Factor by which is the evaluation point is multiplied.
+
+ Methods
+ -------
+ randomize(config)
+ Sets all instance variables to random value if not determined otherwise.
+
+ """
def _reset(self, config):
+ """Resets instance variables.
+
+ Parameters
+ ----------
+ config : dict
+ Additional parameters for initial condition.
+
+ """
super()._reset(config)
# Unpack necessary configurations
self._factor = config.pop('factor', 1)
def randomize(self, config):
+ """Sets all instance variables to random value if not determined otherwise.
+
+ Parameters
+ ----------
+ config : dict
+ Fixed parameters for initial condition.
+
+ """
factor = config.pop('factor', np.random.uniform(low=-100, high=100))
config = {'factor': factor}
self._reset(config)
def _get_point(self, x):
+ """Evaluates function at given x-value.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
return self._factor
class HeavisideOneSided(InitialCondition):
+ """Class for the one-sided heaviside function.
+
+ Attributes
+ ----------
+ factor : float
+ Factor by which is the evaluation point is multiplied.
+
+ Methods
+ -------
+ is_smooth()
+ Returns flag whether function is smooth.
+ randomize(config)
+ Sets all instance variables to random value if not determined otherwise.
+
+ """
def _reset(self, config):
+ """Resets instance variables.
+
+ Parameters
+ ----------
+ config : dict
+ Additional parameters for initial condition.
+
+ """
super()._reset(config)
# Unpack necessary configurations
self._factor = config.pop('factor', -1)
def is_smooth(self):
+ """Returns flag that function is not smooth."""
return False
def randomize(self, config):
+ """Sets all instance variables to random value if not determined otherwise.
+
+ Parameters
+ ----------
+ config : dict
+ Fixed parameters for initial condition.
+
+ """
factor = config.pop('factor', np.random.choice([-1, 1]))
config = {'factor': factor}
self._reset(config)
def _get_point(self, x):
+ """Evaluates function at given x-value.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
return self._factor - 2 * self._factor * np.heaviside(x, 0)
class HeavisideTwoSided(InitialCondition):
+ """Class for the two-sided heaviside function.
+
+ Attributes
+ ----------
+ left_factor : float
+ Factor by which is the evaluation point is multiplied before the jump.
+ right_factor : float
+ Factor by which is the evaluation point is multiplied after the jump.
+ adjustment : float
+ Extent of adjustment of evaluation point in x-direction.
+
+ Methods
+ -------
+ is_smooth()
+ Returns flag whether function is smooth.
+ induce_adjustment(value)
+ Adjusts x-value of function.
+ randomize(config)
+ Sets all instance variables to random value if not determined otherwise.
+
+ """
def _reset(self, config):
+ """Resets instance variables.
+
+ Parameters
+ ----------
+ config : dict
+ Additional parameters for initial condition.
+
+ """
super()._reset(config)
# Unpack necessary configurations
@@ -217,12 +740,29 @@ class HeavisideTwoSided(InitialCondition):
self._adjustment = config.pop('adjustment', 0)
def is_smooth(self):
+ """Returns flag that function is not smooth."""
return False
def induce_adjustment(self, value):
+ """Adjusts x-value of function.
+
+ Parameters
+ ----------
+ value : float
+ Value of adjustment on x-axis in right direction.
+
+ """
self._adjustment = value
def randomize(self, config):
+ """Sets all instance variables to random value if not determined otherwise.
+
+ Parameters
+ ----------
+ config : dict
+ Fixed parameters for initial condition.
+
+ """
left_factor = config.pop('left_factor', np.random.choice([-1, 1]))
right_factor = config.pop('right_factor', np.random.choice([-1, 1]))
adjustment = config.pop('adjustment', np.random.uniform(low=-1, high=1))
@@ -231,6 +771,19 @@ class HeavisideTwoSided(InitialCondition):
self._reset(config)
def _get_point(self, x):
+ """Evaluates function at given x-value.
+
+ Parameters
+ ----------
+ x : float
+ Evaluation point of function.
+
+ Returns
+ -------
+ float
+ Value of function evaluates at x-value.
+
+ """
return self._left_factor\
- self._left_factor * np.heaviside(x - self._adjustment, 0)\
- self._right_factor * np.heaviside(x + self._adjustment, 0)
--
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