Python: module methodsnm.intrule

methodsnm.intrule_1d

index
/builds/lehrenfeld/methodsnm/git-repo/jlcontent/src/methodsnm/intrule_1d.py

This module provides classes for 1D numerical integration rules.

Modules

numpy

scipy

Classes

methodsnm.intrule.IntRule(builtins.object)

IntRule1D

GaussJacobiRule
GaussLegendreRule
MidPointRule
NP_GaussLegendreRule
NewtonCotesRule
SP_GaussJacobiRule

class GaussJacobiRule(IntRule1D)

GaussJacobiRule(n, alpha, beta, interval=(0, 1))

Class for the Gauss-Jacobi rule for 1D numerical integration.

Method resolution order:: GaussJacobiRule; IntRule1D; methodsnm.intrule.IntRule; builtins.object

Methods defined here:

__init__(self, n, alpha, beta, interval=(0, 1)): Initializes the Gauss-Jacobi rule with the given interval and number of nodes.

Parameters:
n (int): The number of nodes to use for integration.
interval (tuple): The interval to integrate over.
alpha, beta (float): The parameters of the Jacobi polynomial.

Data and other attributes inherited from IntRule1D:

interval = None

Methods inherited from methodsnm.intrule.IntRule:

__str__(self): Return str(self).

integrate(self, f)

Data descriptors inherited from methodsnm.intrule.IntRule:

__dict__: dictionary for instance variables

__weakref__: list of weak references to the object

Data and other attributes inherited from methodsnm.intrule.IntRule:

exactness_degree = None

nodes = None

weights = None

class GaussLegendreRule(IntRule1D)

GaussLegendreRule(n, interval=(0, 1))

Class for the Gauss-Legendre rule for 1D numerical integration.

Method resolution order:: GaussLegendreRule; IntRule1D; methodsnm.intrule.IntRule; builtins.object

Methods defined here:

__init__(self, n, interval=(0, 1)): Initializes the Gauss-Legendre rule with the given interval and number of nodes.

Parameters:
n (int): The number of nodes to use for integration.
interval (tuple): The interval to integrate over.

Data and other attributes inherited from IntRule1D:

interval = None

Methods inherited from methodsnm.intrule.IntRule:

__str__(self): Return str(self).

integrate(self, f)

Data descriptors inherited from methodsnm.intrule.IntRule:

__dict__: dictionary for instance variables

__weakref__: list of weak references to the object

Data and other attributes inherited from methodsnm.intrule.IntRule:

exactness_degree = None

nodes = None

weights = None

class IntRule1D(methodsnm.intrule.IntRule)

IntRule1D(interval=(0, 1))

Abstract base class for 1D numerical integration rules.

Method resolution order:: IntRule1D; methodsnm.intrule.IntRule; builtins.object

Methods defined here:

__init__(self, interval=(0, 1)): Initializes the integration rule with the given interval.

Data and other attributes defined here:

interval = None

Methods inherited from methodsnm.intrule.IntRule:

__str__(self): Return str(self).

integrate(self, f)

Data descriptors inherited from methodsnm.intrule.IntRule:

__dict__: dictionary for instance variables

__weakref__: list of weak references to the object

Data and other attributes inherited from methodsnm.intrule.IntRule:

exactness_degree = None

nodes = None

weights = None

class MidPointRule(IntRule1D)

MidPointRule(interval=(0, 1))

Class for the midpoint rule for 1D numerical integration.

Method resolution order:: MidPointRule; IntRule1D; methodsnm.intrule.IntRule; builtins.object

Methods defined here:

__init__(self, interval=(0, 1)): Initializes the midpoint rule with the given interval.

Parameters:
interval (tuple): The interval to integrate over.

Data and other attributes inherited from IntRule1D:

interval = None

Methods inherited from methodsnm.intrule.IntRule:

__str__(self): Return str(self).

integrate(self, f)

Data descriptors inherited from methodsnm.intrule.IntRule:

__dict__: dictionary for instance variables

__weakref__: list of weak references to the object

Data and other attributes inherited from methodsnm.intrule.IntRule:

exactness_degree = None

nodes = None

weights = None

class NP_GaussLegendreRule(IntRule1D)

NP_GaussLegendreRule(n, interval=(0, 1))

Wrapper class for the Gauss-Legendre rule for 1D numerical integration of numpy.

Method resolution order:: NP_GaussLegendreRule; IntRule1D; methodsnm.intrule.IntRule; builtins.object

Methods defined here:

__init__(self, n, interval=(0, 1)): Initializes the Gauss-Legendre rule with the given interval and number of nodes.

Parameters:
n (int): The number of nodes to use for integration.
interval (tuple): The interval to integrate over.

Data and other attributes inherited from IntRule1D:

interval = None

Methods inherited from methodsnm.intrule.IntRule:

__str__(self): Return str(self).

integrate(self, f)

Data descriptors inherited from methodsnm.intrule.IntRule:

__dict__: dictionary for instance variables

__weakref__: list of weak references to the object

Data and other attributes inherited from methodsnm.intrule.IntRule:

exactness_degree = None

nodes = None

weights = None

class NewtonCotesRule(IntRule1D)

NewtonCotesRule(n=None, nodes=None, interval=(0, 1))

Class for the Newton-Cotes rule for 1D numerical integration.

Method resolution order:: NewtonCotesRule; IntRule1D; methodsnm.intrule.IntRule; builtins.object

Methods defined here:

__init__(self, n=None, nodes=None, interval=(0, 1)): Initializes the Newton-Cotes rule with the given interval and number of nodes.

Parameters:
n (int or list): The number of nodes or a list of nodes to use for integration.
nodes (list): A list of nodes to use for integration.
interval (tuple): The interval to integrate over.

Data and other attributes inherited from IntRule1D:

interval = None

Methods inherited from methodsnm.intrule.IntRule:

__str__(self): Return str(self).

integrate(self, f)

Data descriptors inherited from methodsnm.intrule.IntRule:

__dict__: dictionary for instance variables

__weakref__: list of weak references to the object

Data and other attributes inherited from methodsnm.intrule.IntRule:

exactness_degree = None

nodes = None

weights = None

class SP_GaussJacobiRule(IntRule1D)

SP_GaussJacobiRule(n, alpha, beta, interval=(0, 1))

Wrapper class for the Gauss-Jacobi rule for 1D numerical integration of numpy.

Method resolution order:: SP_GaussJacobiRule; IntRule1D; methodsnm.intrule.IntRule; builtins.object

Methods defined here:

__init__(self, n, alpha, beta, interval=(0, 1)): Initializes the Gauss-Legendre rule with the given interval and number of nodes.

Parameters:
n (int): The number of nodes to use for integration.
interval (tuple): The interval to integrate over.
alpha, beta (float): The parameters of the Jacobi polynomial.

Data and other attributes inherited from IntRule1D:

interval = None

Methods inherited from methodsnm.intrule.IntRule:

__str__(self): Return str(self).

integrate(self, f)

Data descriptors inherited from methodsnm.intrule.IntRule:

__dict__: dictionary for instance variables

__weakref__: list of weak references to the object

Data and other attributes inherited from methodsnm.intrule.IntRule:

exactness_degree = None

nodes = None

weights = None

Functions
		evaluate_exactness_degree(rule, max_order=None) Evaluates the exactness degree of the given integration rule. Parameters: rule (IntRule1D): The integration rule to evaluate. max_order (int or None): maximum order to check for exactness degree. If None, the exactness degree is checked until it is found. Returns: int: The exactness degree of the integration rule.