User Manual 4.0 Numerical differentiation and integration - Historique des versions

Admin : /* Package Overview */

2018-02-21T08:36:52Z

Package Overview

← Version précédente		Version du 21 février 2018 à 08:36
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	Accuracy of integration method (all examples are based on sinus function):		Accuracy of integration method (all examples are based on sinus function):

	\|=~~(% colspan~~="3" %)Default setting~~\|=(% colspan~~="3" %)Value		{\| class="wikitable"
	\|~~(% colspan="3" %)~~Maximum absolute error\|~~(% colspan="6" %)~~1.0e-15		\|-
	\|~~(% colspan="3" %)~~Maximum relative error\|~~(% colspan="6" %)~~1.0e-6		! scope="col"\| Default setting
	\|~~(% colspan="3" %)~~Maximum number of iterations\|~~(% colspan="6" %)~~64		! scope="col"\| Value
	\|~~(% colspan="3" %)~~Minimum number of iterations\|~~(% colspan="6" %)~~3		\|-
			\|Maximum absolute error
			\|1.0e-15
			\|-
			\|Maximum relative error
			\|1.0e-6
			\|-
			\|Maximum number of iterations
			\|64
			\|-
			\|Minimum number of iterations
			\|3
			\|}

	Note : the accuracy of the results and the computing time are directly dependent on the value of maximum relative error.		Note : the accuracy of the results and the computing time are directly dependent on the value of maximum relative error.

Admin : /* Javadoc */

2018-02-21T08:35:35Z

Javadoc

← Version précédente		Version du 21 février 2018 à 08:35
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	\|-		\|-
	\|Patrius		\|Patrius
	\|[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/analysis/differentiation/package-summary.html Package fr.cnes.sirius.patrius.math.analysis.differentiation]		\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/analysis/differentiation/package-summary.html Package fr.cnes.sirius.patrius.math.analysis.differentiation]
	\|-		\|-
	\|Patrius		\|Patrius
	\|[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/analysis/integration/package-summary.html Package fr.cnes.sirius.patrius.math.analysis.integration]		\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/analysis/integration/package-summary.html Package fr.cnes.sirius.patrius.math.analysis.integration]
	\|}		\|}

Admin : /* Contents */

2018-02-21T08:35:00Z

Contents

← Version précédente		Version du 21 février 2018 à 08:35
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	== Contents ==		== Contents ==
	=== Interfaces ===		=== Interfaces ===
	\|=~~(% colspan~~="3" %)Interface~~\|=(% colspan~~="6" %)Summary~~\|=(% colspan~~="1" %)Javadoc		{\| class="wikitable"
	\|~~(% colspan="3" %)~~'''UnivariateFunctionDifferentiator'''\|~~(% colspan="6" %)~~This interface represents a generic numerical differentiator.\|[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/analysis/differentiation/UnivariateFunctionDifferentiator.html ...]		\|-
	\|~~(% colspan="3" %)~~UnivariateIntegrator\|~~(% colspan="6" %)~~Interface for univariate integration algorithms.\|[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/analysis/integration/UnivariateIntegrator.html ...]		! scope="col"\| Interface
			! scope="col"\| Summary
			! scope="col"\| Javadoc
			\|-
			\|'''UnivariateFunctionDifferentiator'''
			\|This interface represents a generic numerical differentiator.
			\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/analysis/differentiation/UnivariateFunctionDifferentiator.html ...]
			\|-
			\|UnivariateIntegrator
			\|Interface for univariate integration algorithms.
			\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/analysis/integration/UnivariateIntegrator.html ...]
			\|}

	=== Classes ===		=== Classes ===
	\|=~~(% colspan~~="3" %)Class~~\|=(% colspan~~="6" %)Summary~~\|=(% colspan~~="1" %)Javadoc		{\| class="wikitable"
	\|~~(% colspan="3" %)~~'''FiniteDifferencesDifferentiator'''\|~~(% colspan="6" %)~~Apply the finite difference method to differentiate a function.\|[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/analysis/differentiation/FiniteDifferencesDifferentiator.html ...]		\|-
	\|~~(% colspan="3" %)~~'''RiddersDifferentiator'''\|~~(% colspan="6" %)~~Apply the Ridders algorithm to differentiate a function.\|[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/analysis/differentiation/RiddersDifferentiator.html ...]		! scope="col"\| Class
	\|~~(% colspan="3" %)~~TrapezoidIntegrator\|~~(% colspan="6" %)~~The class implements the Trapezoidal rule\|~~(% colspan="1" %)~~[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/analysis/integration/TrapezoidIntegrator.html ...]		! scope="col"\| Summary
	\|~~(% colspan="3" %)~~SimpsonIntegrator\|~~(% colspan="6" %)~~The class implements the Simpson rule\|~~(% colspan="1" %)~~[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/analysis/integration/SimpsonIntegrator.html ...]		! scope="col"\| Javadoc
			\|-
			\|'''FiniteDifferencesDifferentiator'''
			\|Apply the finite difference method to differentiate a function.
			\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/analysis/differentiation/FiniteDifferencesDifferentiator.html ...]
			\|-
			\|'''RiddersDifferentiator'''
			\|Apply the Ridders algorithm to differentiate a function.
			\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/analysis/differentiation/RiddersDifferentiator.html ...]
			\|-
			\|TrapezoidIntegrator
			\|The class implements the Trapezoidal rule
			\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/analysis/integration/TrapezoidIntegrator.html ...]
			\|-
			\|SimpsonIntegrator
			\|The class implements the Simpson rule
			\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/analysis/integration/SimpsonIntegrator.html ...]
			\|}

	[[Category:User_Manual_4.0_Mathematics]]		[[Category:User_Manual_4.0_Mathematics]]

Admin : /* Javadoc */

2018-02-21T08:33:17Z

Javadoc

← Version précédente		Version du 21 février 2018 à 08:33
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	The numerical integrator objects are available in the package <code>fr.cnes.sirius.patrius.math.analysis.integration</code>.		The numerical integrator objects are available in the package <code>fr.cnes.sirius.patrius.math.analysis.integration</code>.

	\|=~~(% colspan~~="3" %)Library~~\|=(% colspan~~="6" %)Javadoc		{\| class="wikitable"
	\|~~(% colspan="3" %)~~Patrius\|~~(% colspan="6" %)~~[{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/analysis/differentiation/package-summary.html Package fr.cnes.sirius.patrius.math.analysis.differentiation]		\|-
	\|~~(% colspan="3" %)~~Patrius\|~~(% colspan="6" %)~~[{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/analysis/integration/package-summary.html Package fr.cnes.sirius.patrius.math.analysis.integration]		! scope="col"\| Library
			! scope="col"\| Javadoc
			\|-
			\|Patrius
			\|[{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/analysis/differentiation/package-summary.html Package fr.cnes.sirius.patrius.math.analysis.differentiation]
			\|-
			\|Patrius
			\|[{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/analysis/integration/package-summary.html Package fr.cnes.sirius.patrius.math.analysis.integration]
			\|}

	=== Links ===		=== Links ===

Admin le 20 février 2018 à 16:45

2018-02-20T16:45:47Z

← Version précédente		Version du 20 février 2018 à 16:45
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			__NOTOC__

	== Introduction ==		== Introduction ==
	=== Scope ===		=== Scope ===

Admin le 19 février 2018 à 09:14

2018-02-19T09:14:23Z

← Version précédente		Version du 19 février 2018 à 09:14
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	\|(% colspan="3" %)TrapezoidIntegrator\|(% colspan="6" %)The class implements the Trapezoidal rule\|(% colspan="1" %)[{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/analysis/integration/TrapezoidIntegrator.html ...]		\|(% colspan="3" %)TrapezoidIntegrator\|(% colspan="6" %)The class implements the Trapezoidal rule\|(% colspan="1" %)[{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/analysis/integration/TrapezoidIntegrator.html ...]
	\|(% colspan="3" %)SimpsonIntegrator\|(% colspan="6" %)The class implements the Simpson rule\|(% colspan="1" %)[{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/analysis/integration/SimpsonIntegrator.html ...]		\|(% colspan="3" %)SimpsonIntegrator\|(% colspan="6" %)The class implements the Simpson rule\|(% colspan="1" %)[{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/analysis/integration/SimpsonIntegrator.html ...]

			[[Category:User_Manual_4.0_Mathematics]]

Admin le 19 février 2018 à 09:13

2018-02-19T09:13:58Z

← Version précédente		Version du 19 février 2018 à 09:13
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	The numerical differentiation conception is described hereafter :		The numerical differentiation conception is described hereafter :

	[[File:differentiators.~~bmp~~\|center]]		[[File:differentiators.png\|center]]

	Accuracy of integration method (all examples are based on sinus function):		Accuracy of integration method (all examples are based on sinus function):

Admin : /* Ridders algorithm */

2018-02-19T09:13:25Z

Ridders algorithm

← Version précédente		Version du 19 février 2018 à 09:13
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	==== Ridders algorithm ====		==== Ridders algorithm ====
	~~{{specialInclusion prefix=$theme_sub section="~~Ridders ~~algorithm"/}}~~		The derivative of a function at a point x is computed using the Ridders method of polynomial extrapolation.

	=== Numerical Integration ===		=== Numerical Integration ===

Admin : /* Finite difference */

2018-02-19T09:12:54Z

Finite difference

← Version précédente		Version du 19 février 2018 à 09:12
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	==== Finite difference ====		==== Finite difference ====
	~~{{specialInclusion prefix=$theme_sub section="~~Finite difference~~"/}}~~		Finite difference is the discrete analog of the derivative. The user can choose the number of points to use and the step size (the gap between each point).

	==== Ridders algorithm ====		==== Ridders algorithm ====

Admin : Admin a déplacé la page Numerical differentiation and integration vers User Manual 4.0 Numerical differentiation and integration sans laisser de redirection

2018-02-19T09:11:32Z

Admin a déplacé la page Numerical differentiation and integration vers User Manual 4.0 Numerical differentiation and integration sans laisser de redirection

← Version précédente	Version du 19 février 2018 à 09:11
(Aucune différence)

User Manual 4.0 Numerical differentiation and integration - Historique des versions

Admin : /* Package Overview */

Admin : /* Javadoc */

Admin : /* Contents */

Admin : /* Javadoc */

Admin le 20 février 2018 à 16:45

Admin le 19 février 2018 à 09:14

Admin le 19 février 2018 à 09:13

Admin : /* Ridders algorithm */

Admin : /* Finite difference */

Admin : Admin a déplacé la page Numerical differentiation and integration vers User Manual 4.0 Numerical differentiation and integration sans laisser de redirection

Admin : /* Package Overview */

Admin : /* Javadoc */

Admin : /* Contents */

Admin : /* Javadoc */

Admin : /* Ridders algorithm */

Admin : /* Finite difference */

Admin : Admin a déplacé la page Numerical differentiation and integration vers User Manual 4.0 Numerical differentiation and integration sans laisser de redirection