.. _section_ref_algorithm_FunctionTest_examples:
.. include:: snippets/Header2Algo09.rst
-.. include:: scripts/simple_FunctionTest.rst
+.. --------- ..
+.. include:: scripts/simple_FunctionTest1.rst
-.. literalinclude:: scripts/simple_FunctionTest.py
+.. literalinclude:: scripts/simple_FunctionTest1.py
.. include:: snippets/Header2Algo10.rst
-.. literalinclude:: scripts/simple_FunctionTest.res
+.. literalinclude:: scripts/simple_FunctionTest1.res
+ :language: none
+
+.. --------- ..
+.. include:: scripts/simple_FunctionTest2.rst
+
+.. literalinclude:: scripts/simple_FunctionTest2.py
+
+.. include:: snippets/Header2Algo10.rst
+
+.. literalinclude:: scripts/simple_FunctionTest2.res
+ :language: none
.. ------------------------------------ ..
.. include:: snippets/Header2Algo06.rst
+++ /dev/null
-# -*- coding: utf-8 -*-
-#
-from numpy import array, eye
-from adao import adaoBuilder
-case = adaoBuilder.New('')
-case.setCheckingPoint( Vector = array([0., 1., 2.]), Stored=True )
-case.setObservationOperator( Matrix = eye(3), )
-case.setAlgorithmParameters(
- Algorithm='FunctionTest',
- Parameters={
- 'NumberOfRepetition' : 5,
- 'NumberOfPrintedDigits' : 2,
- "ShowElementarySummary":False,
- },
- )
-case.execute()
+++ /dev/null
-
- FUNCTIONTEST
- ============
-
- This test allows to analyze the (repetition of) launch of some given
- operator. It shows simple statistics related to its successful execution,
- or related to the similarities of repetition of its execution.
-
-===> Information before launching:
- -----------------------------
- Characteristics of input vector X, internally converted:
- Type...............: <class 'numpy.ndarray'>
- Length of vector...: 3
- Minimum value......: 0.00e+00
- Maximum value......: 2.00e+00
- Mean of vector.....: 1.00e+00
- Standard error.....: 8.16e-01
- L2 norm of vector..: 2.24e+00
-
- ---------------------------------------------------------------------------
-
-===> Beginning of repeated evaluation, without activating debug
-
- ---------------------------------------------------------------------------
-
-===> End of repeated evaluation, without deactivating debug
-
- ---------------------------------------------------------------------------
-
-===> Launching statistical summary calculation for 5 states
-
- ---------------------------------------------------------------------------
-
-===> Statistical analysis of the outputs obtained through sequential repeated evaluations
-
- (Remark: numbers that are (about) under 2e-16 represent 0 to machine precision)
-
- Characteristics of the whole set of outputs Y:
- Number of evaluations.........................: 5
- Minimum value of the whole set of outputs.....: 0.00e+00
- Maximum value of the whole set of outputs.....: 2.00e+00
- Mean of vector of the whole set of outputs....: 1.00e+00
- Standard error of the whole set of outputs....: 8.16e-01
-
- Characteristics of the vector Ym, mean of the outputs Y:
- Size of the mean of the outputs...............: 3
- Minimum value of the mean of the outputs......: 0.00e+00
- Maximum value of the mean of the outputs......: 2.00e+00
- Mean of the mean of the outputs...............: 1.00e+00
- Standard error of the mean of the outputs.....: 8.16e-01
-
- Characteristics of the mean of the differences between the outputs Y and their mean Ym:
- Size of the mean of the differences...........: 3
- Minimum value of the mean of the differences..: 0.00e+00
- Maximum value of the mean of the differences..: 0.00e+00
- Mean of the mean of the differences...........: 0.00e+00
- Standard error of the mean of the differences.: 0.00e+00
-
- ---------------------------------------------------------------------------
-
+++ /dev/null
-.. index:: single: FunctionTest (example)
-
-This example describes the test of the correct operation of a given operator,
-and that its call proceeds in a way compatible with its common use in the ADAO
-algorithms. The required information are minimal, namely here an operator
-:math:`F` (described for the test by the observation command
-"*ObservationOperator*"), and a state :math:`\mathbf{x}^b` to test it on
-(described for the test by the command "*CheckingPoint*").
-
-The test is repeated a configurable number of times, and a final statistic
-makes it possible to quickly verify the operator's good behavior. The simplest
-diagnostic consists in checking, at the very end of the display, the order of
-magnitude of the values indicated as the mean of the differences between the
-repeated outputs and their mean, under the part entitled "*Characteristics of
-the mean of the differences between the outputs Y and their mean Ym*". For a
-satisfactory operator, these values should be close to the numerical zero.
--- /dev/null
+# -*- coding: utf-8 -*-
+#
+from numpy import array, eye
+from adao import adaoBuilder
+case = adaoBuilder.New()
+case.setCheckingPoint( Vector = array([0., 1., 2.]), Stored=True )
+case.setObservationOperator( Matrix = eye(3) )
+case.setAlgorithmParameters(
+ Algorithm='FunctionTest',
+ Parameters={
+ 'NumberOfRepetition' : 5,
+ 'NumberOfPrintedDigits' : 2,
+ 'ShowElementarySummary':False,
+ },
+ )
+case.execute()
--- /dev/null
+
+ FUNCTIONTEST
+ ============
+
+ This test allows to analyze the (repetition of) launch of some given
+ operator. It shows simple statistics related to its successful execution,
+ or related to the similarities of repetition of its execution.
+
+===> Information before launching:
+ -----------------------------
+ Characteristics of input vector X, internally converted:
+ Type...............: <class 'numpy.ndarray'>
+ Length of vector...: 3
+ Minimum value......: 0.00e+00
+ Maximum value......: 2.00e+00
+ Mean of vector.....: 1.00e+00
+ Standard error.....: 8.16e-01
+ L2 norm of vector..: 2.24e+00
+
+ ---------------------------------------------------------------------------
+
+===> Beginning of repeated evaluation, without activating debug
+
+ ---------------------------------------------------------------------------
+
+===> End of repeated evaluation, without deactivating debug
+
+ ---------------------------------------------------------------------------
+
+===> Launching statistical summary calculation for 5 states
+
+ ---------------------------------------------------------------------------
+
+===> Statistical analysis of the outputs obtained through sequential repeated evaluations
+
+ (Remark: numbers that are (about) under 2e-16 represent 0 to machine precision)
+
+ Characteristics of the whole set of outputs Y:
+ Number of evaluations.........................: 5
+ Minimum value of the whole set of outputs.....: 0.00e+00
+ Maximum value of the whole set of outputs.....: 2.00e+00
+ Mean of vector of the whole set of outputs....: 1.00e+00
+ Standard error of the whole set of outputs....: 8.16e-01
+
+ Characteristics of the vector Ym, mean of the outputs Y:
+ Size of the mean of the outputs...............: 3
+ Minimum value of the mean of the outputs......: 0.00e+00
+ Maximum value of the mean of the outputs......: 2.00e+00
+ Mean of the mean of the outputs...............: 1.00e+00
+ Standard error of the mean of the outputs.....: 8.16e-01
+
+ Characteristics of the mean of the differences between the outputs Y and their mean Ym:
+ Size of the mean of the differences...........: 3
+ Minimum value of the mean of the differences..: 0.00e+00
+ Maximum value of the mean of the differences..: 0.00e+00
+ Mean of the mean of the differences...........: 0.00e+00
+ Standard error of the mean of the differences.: 0.00e+00
+
+ ---------------------------------------------------------------------------
+
--- /dev/null
+.. index:: single: FunctionTest (example)
+
+First example
+.............
+
+This example describes the test of the correct operation of a given operator,
+and that its call proceeds in a way compatible with its common use in the ADAO
+algorithms. The required information are minimal, namely here an operator
+:math:`F` (described for the test by the command "*ObservationOperator*"), and
+a particular state :math:`\mathbf{x}` to test it on (described for the test by
+the command "*CheckingPoint*").
+
+The test is repeated a configurable number of times, and a final statistic
+makes it possible to quickly verify the operator's good behavior. The simplest
+diagnostic consists in checking, at the very end of the display, the order of
+magnitude of the values indicated as the mean of the differences between the
+repeated outputs and their mean, under the part entitled "*Characteristics of
+the mean of the differences between the outputs Y and their mean Ym*". For a
+satisfactory operator, these values should be close to the numerical zero.
--- /dev/null
+# -*- coding: utf-8 -*-
+#
+from numpy import array, ravel
+def QuadFunction( coefficients ):
+ """
+ Quadratic simulation in x: y = a x^2 + b x + c
+ """
+ a, b, c = list(ravel(coefficients))
+ x_points = (-5, 0, 1, 3, 10)
+ y_points = []
+ for x in x_points:
+ y_points.append( a*x*x + b*x + c )
+ return array(y_points)
+#
+# (Re)naming statement for the simulation function
+DirectOperator = QuadFunction
+#
+from adao import adaoBuilder
+case = adaoBuilder.New()
+case.setCheckingPoint( Vector = array([1., 1., 1.]), Stored=True )
+case.setObservationOperator( OneFunction = DirectOperator )
+case.setAlgorithmParameters(
+ Algorithm='FunctionTest',
+ Parameters={
+ 'NumberOfRepetition' : 15,
+ 'NumberOfPrintedDigits' : 3,
+ 'ShowElementarySummary':False,
+ },
+ )
+case.execute()
--- /dev/null
+
+ FUNCTIONTEST
+ ============
+
+ This test allows to analyze the (repetition of) launch of some given
+ operator. It shows simple statistics related to its successful execution,
+ or related to the similarities of repetition of its execution.
+
+===> Information before launching:
+ -----------------------------
+ Characteristics of input vector X, internally converted:
+ Type...............: <class 'numpy.ndarray'>
+ Length of vector...: 3
+ Minimum value......: 1.000e+00
+ Maximum value......: 1.000e+00
+ Mean of vector.....: 1.000e+00
+ Standard error.....: 0.000e+00
+ L2 norm of vector..: 1.732e+00
+
+ ---------------------------------------------------------------------------
+
+===> Beginning of repeated evaluation, without activating debug
+
+ ---------------------------------------------------------------------------
+
+===> End of repeated evaluation, without deactivating debug
+
+ ---------------------------------------------------------------------------
+
+===> Launching statistical summary calculation for 15 states
+
+ ---------------------------------------------------------------------------
+
+===> Statistical analysis of the outputs obtained through sequential repeated evaluations
+
+ (Remark: numbers that are (about) under 2e-16 represent 0 to machine precision)
+
+ Characteristics of the whole set of outputs Y:
+ Number of evaluations.........................: 15
+ Minimum value of the whole set of outputs.....: 1.000e+00
+ Maximum value of the whole set of outputs.....: 1.110e+02
+ Mean of vector of the whole set of outputs....: 2.980e+01
+ Standard error of the whole set of outputs....: 4.123e+01
+
+ Characteristics of the vector Ym, mean of the outputs Y:
+ Size of the mean of the outputs...............: 5
+ Minimum value of the mean of the outputs......: 1.000e+00
+ Maximum value of the mean of the outputs......: 1.110e+02
+ Mean of the mean of the outputs...............: 2.980e+01
+ Standard error of the mean of the outputs.....: 4.123e+01
+
+ Characteristics of the mean of the differences between the outputs Y and their mean Ym:
+ Size of the mean of the differences...........: 5
+ Minimum value of the mean of the differences..: 0.000e+00
+ Maximum value of the mean of the differences..: 0.000e+00
+ Mean of the mean of the differences...........: 0.000e+00
+ Standard error of the mean of the differences.: 0.000e+00
+
+ ---------------------------------------------------------------------------
+
--- /dev/null
+Second example
+..............
+
+This new example describes the test of the correct operation of a given
+operator named ``QuadFunction``, available under its functional form. It is
+defined by the command "*ObservationOperator*" as
+:ref:`section_ref_operator_one`. Using the command "*CheckingPoint*", one add
+also a particular state :math:`\mathbf{x}` to test the operator on.
+
+The test is repeated here 15 times, and a final statistic makes it possible to
+quickly verify the operator's good behavior. The simplest diagnostic consists
+in checking, at the very end of the display, the order of magnitude of the
+values indicated as the mean of the differences between the repeated outputs
+and their mean, under the part entitled "*Characteristics of the mean of the
+differences between the outputs Y and their mean Ym*". For a satisfactory
+operator, these values should be close to the numerical zero.
.. _section_ref_algorithm_FunctionTest_examples:
.. include:: snippets/Header2Algo09.rst
-.. include:: scripts/simple_FunctionTest.rst
+.. --------- ..
+.. include:: scripts/simple_FunctionTest1.rst
-.. literalinclude:: scripts/simple_FunctionTest.py
+.. literalinclude:: scripts/simple_FunctionTest1.py
.. include:: snippets/Header2Algo10.rst
-.. literalinclude:: scripts/simple_FunctionTest.res
+.. literalinclude:: scripts/simple_FunctionTest1.res
+ :language: none
+
+.. --------- ..
+.. include:: scripts/simple_FunctionTest2.rst
+
+.. literalinclude:: scripts/simple_FunctionTest2.py
+
+.. include:: snippets/Header2Algo10.rst
+
+.. literalinclude:: scripts/simple_FunctionTest2.res
:language: none
.. ------------------------------------ ..
+++ /dev/null
-# -*- coding: utf-8 -*-
-#
-from numpy import array, eye
-from adao import adaoBuilder
-case = adaoBuilder.New('')
-case.setCheckingPoint( Vector = array([0., 1., 2.]), Stored=True )
-case.setObservationOperator( Matrix = eye(3), )
-case.setAlgorithmParameters(
- Algorithm='FunctionTest',
- Parameters={
- 'NumberOfRepetition' : 5,
- 'NumberOfPrintedDigits' : 2,
- 'ShowElementarySummary':False,
- },
- )
-case.execute()
+++ /dev/null
-
- FUNCTIONTEST
- ============
-
- This test allows to analyze the (repetition of) launch of some given
- operator. It shows simple statistics related to its successful execution,
- or related to the similarities of repetition of its execution.
-
-===> Information before launching:
- -----------------------------
- Characteristics of input vector X, internally converted:
- Type...............: <class 'numpy.ndarray'>
- Length of vector...: 3
- Minimum value......: 0.00e+00
- Maximum value......: 2.00e+00
- Mean of vector.....: 1.00e+00
- Standard error.....: 8.16e-01
- L2 norm of vector..: 2.24e+00
-
- ---------------------------------------------------------------------------
-
-===> Beginning of repeated evaluation, without activating debug
-
- ---------------------------------------------------------------------------
-
-===> End of repeated evaluation, without deactivating debug
-
- ---------------------------------------------------------------------------
-
-===> Launching statistical summary calculation for 5 states
-
- ---------------------------------------------------------------------------
-
-===> Statistical analysis of the outputs obtained through sequential repeated evaluations
-
- (Remark: numbers that are (about) under 2e-16 represent 0 to machine precision)
-
- Characteristics of the whole set of outputs Y:
- Number of evaluations.........................: 5
- Minimum value of the whole set of outputs.....: 0.00e+00
- Maximum value of the whole set of outputs.....: 2.00e+00
- Mean of vector of the whole set of outputs....: 1.00e+00
- Standard error of the whole set of outputs....: 8.16e-01
-
- Characteristics of the vector Ym, mean of the outputs Y:
- Size of the mean of the outputs...............: 3
- Minimum value of the mean of the outputs......: 0.00e+00
- Maximum value of the mean of the outputs......: 2.00e+00
- Mean of the mean of the outputs...............: 1.00e+00
- Standard error of the mean of the outputs.....: 8.16e-01
-
- Characteristics of the mean of the differences between the outputs Y and their mean Ym:
- Size of the mean of the differences...........: 3
- Minimum value of the mean of the differences..: 0.00e+00
- Maximum value of the mean of the differences..: 0.00e+00
- Mean of the mean of the differences...........: 0.00e+00
- Standard error of the mean of the differences.: 0.00e+00
-
- ---------------------------------------------------------------------------
-
+++ /dev/null
-.. index:: single: FunctionTest (exemple)
-
-Cet exemple décrit le test du bon fonctionnement d'un opérateur quelconque, et
-que son appel se déroule de manière compatible avec son usage courant dans les
-algorithmes d'ADAO. Les informations nécessaires sont minimales, à savoir ici
-un opérateur :math:`F` (décrit pour le test par la commande d'observation
-"*ObservationOperator*"), et un état :math:`\mathbf{x}^b` sur lequel le tester
-(décrit pour le test par la commande "*CheckingPoint*").
-
-Le test est répété un nombre paramétrable de fois, et une statistique finale
-permet de vérifier rapidement le bon comportement de l'opérateur. Le diagnostic
-le plus simple consiste à vérifier, à la toute fin de l'affichage, l'ordre de
-grandeur des valeurs indiquées comme la moyenne des différences entre les
-sorties répétées et leur moyenne, sous la partie titrée "*Characteristics of
-the mean of the differences between the outputs Y and their mean Ym*". Pour un
-opérateur satisfaisant, ces valeurs doivent être proches du zéro numérique.
--- /dev/null
+# -*- coding: utf-8 -*-
+#
+from numpy import array, eye
+from adao import adaoBuilder
+case = adaoBuilder.New()
+case.setCheckingPoint( Vector = array([0., 1., 2.]), Stored=True )
+case.setObservationOperator( Matrix = eye(3) )
+case.setAlgorithmParameters(
+ Algorithm='FunctionTest',
+ Parameters={
+ 'NumberOfRepetition' : 5,
+ 'NumberOfPrintedDigits' : 2,
+ 'ShowElementarySummary':False,
+ },
+ )
+case.execute()
--- /dev/null
+
+ FUNCTIONTEST
+ ============
+
+ This test allows to analyze the (repetition of) launch of some given
+ operator. It shows simple statistics related to its successful execution,
+ or related to the similarities of repetition of its execution.
+
+===> Information before launching:
+ -----------------------------
+ Characteristics of input vector X, internally converted:
+ Type...............: <class 'numpy.ndarray'>
+ Length of vector...: 3
+ Minimum value......: 0.00e+00
+ Maximum value......: 2.00e+00
+ Mean of vector.....: 1.00e+00
+ Standard error.....: 8.16e-01
+ L2 norm of vector..: 2.24e+00
+
+ ---------------------------------------------------------------------------
+
+===> Beginning of repeated evaluation, without activating debug
+
+ ---------------------------------------------------------------------------
+
+===> End of repeated evaluation, without deactivating debug
+
+ ---------------------------------------------------------------------------
+
+===> Launching statistical summary calculation for 5 states
+
+ ---------------------------------------------------------------------------
+
+===> Statistical analysis of the outputs obtained through sequential repeated evaluations
+
+ (Remark: numbers that are (about) under 2e-16 represent 0 to machine precision)
+
+ Characteristics of the whole set of outputs Y:
+ Number of evaluations.........................: 5
+ Minimum value of the whole set of outputs.....: 0.00e+00
+ Maximum value of the whole set of outputs.....: 2.00e+00
+ Mean of vector of the whole set of outputs....: 1.00e+00
+ Standard error of the whole set of outputs....: 8.16e-01
+
+ Characteristics of the vector Ym, mean of the outputs Y:
+ Size of the mean of the outputs...............: 3
+ Minimum value of the mean of the outputs......: 0.00e+00
+ Maximum value of the mean of the outputs......: 2.00e+00
+ Mean of the mean of the outputs...............: 1.00e+00
+ Standard error of the mean of the outputs.....: 8.16e-01
+
+ Characteristics of the mean of the differences between the outputs Y and their mean Ym:
+ Size of the mean of the differences...........: 3
+ Minimum value of the mean of the differences..: 0.00e+00
+ Maximum value of the mean of the differences..: 0.00e+00
+ Mean of the mean of the differences...........: 0.00e+00
+ Standard error of the mean of the differences.: 0.00e+00
+
+ ---------------------------------------------------------------------------
+
--- /dev/null
+.. index:: single: FunctionTest (exemple)
+
+Premier exemple
+...............
+
+Cet exemple décrit le test du bon fonctionnement d'un opérateur quelconque, et
+que son appel se déroule de manière compatible avec son usage courant dans les
+algorithmes d'ADAO. Les informations nécessaires sont minimales, à savoir ici
+un opérateur (décrit pour le test par la commande d'observation
+"*ObservationOperator*"), et un état particulier :math:`\mathbf{x}` sur lequel
+le tester (décrit pour le test par la commande "*CheckingPoint*").
+
+Le test est répété un nombre paramétrable de fois, et une statistique finale
+permet de vérifier rapidement le bon comportement de l'opérateur. Le diagnostic
+le plus simple consiste à vérifier, à la toute fin de l'affichage, l'ordre de
+grandeur des valeurs indiquées comme la moyenne des différences entre les
+sorties répétées et leur moyenne, sous la partie titrée "*Characteristics of
+the mean of the differences between the outputs Y and their mean Ym*". Pour un
+opérateur satisfaisant, ces valeurs doivent être proches du zéro numérique.
--- /dev/null
+# -*- coding: utf-8 -*-
+#
+from numpy import array, ravel
+def QuadFunction( coefficients ):
+ """
+ Simulation quadratique aux points x : y = a x^2 + b x + c
+ """
+ a, b, c = list(ravel(coefficients))
+ x_points = (-5, 0, 1, 3, 10)
+ y_points = []
+ for x in x_points:
+ y_points.append( a*x*x + b*x + c )
+ return array(y_points)
+#
+# Déclaration de (re)nommage de la fonction de simulation
+DirectOperator = QuadFunction
+#
+from adao import adaoBuilder
+case = adaoBuilder.New()
+case.setCheckingPoint( Vector = array([1., 1., 1.]), Stored=True )
+case.setObservationOperator( OneFunction = DirectOperator )
+case.setAlgorithmParameters(
+ Algorithm='FunctionTest',
+ Parameters={
+ 'NumberOfRepetition' : 15,
+ 'NumberOfPrintedDigits' : 3,
+ 'ShowElementarySummary':False,
+ },
+ )
+case.execute()
--- /dev/null
+
+ FUNCTIONTEST
+ ============
+
+ This test allows to analyze the (repetition of) launch of some given
+ operator. It shows simple statistics related to its successful execution,
+ or related to the similarities of repetition of its execution.
+
+===> Information before launching:
+ -----------------------------
+ Characteristics of input vector X, internally converted:
+ Type...............: <class 'numpy.ndarray'>
+ Length of vector...: 3
+ Minimum value......: 1.000e+00
+ Maximum value......: 1.000e+00
+ Mean of vector.....: 1.000e+00
+ Standard error.....: 0.000e+00
+ L2 norm of vector..: 1.732e+00
+
+ ---------------------------------------------------------------------------
+
+===> Beginning of repeated evaluation, without activating debug
+
+ ---------------------------------------------------------------------------
+
+===> End of repeated evaluation, without deactivating debug
+
+ ---------------------------------------------------------------------------
+
+===> Launching statistical summary calculation for 15 states
+
+ ---------------------------------------------------------------------------
+
+===> Statistical analysis of the outputs obtained through sequential repeated evaluations
+
+ (Remark: numbers that are (about) under 2e-16 represent 0 to machine precision)
+
+ Characteristics of the whole set of outputs Y:
+ Number of evaluations.........................: 15
+ Minimum value of the whole set of outputs.....: 1.000e+00
+ Maximum value of the whole set of outputs.....: 1.110e+02
+ Mean of vector of the whole set of outputs....: 2.980e+01
+ Standard error of the whole set of outputs....: 4.123e+01
+
+ Characteristics of the vector Ym, mean of the outputs Y:
+ Size of the mean of the outputs...............: 5
+ Minimum value of the mean of the outputs......: 1.000e+00
+ Maximum value of the mean of the outputs......: 1.110e+02
+ Mean of the mean of the outputs...............: 2.980e+01
+ Standard error of the mean of the outputs.....: 4.123e+01
+
+ Characteristics of the mean of the differences between the outputs Y and their mean Ym:
+ Size of the mean of the differences...........: 5
+ Minimum value of the mean of the differences..: 0.000e+00
+ Maximum value of the mean of the differences..: 0.000e+00
+ Mean of the mean of the differences...........: 0.000e+00
+ Standard error of the mean of the differences.: 0.000e+00
+
+ ---------------------------------------------------------------------------
+
--- /dev/null
+Deuxième exemple
+................
+
+Ce nouvel exemple décrit le test du bon fonctionnement d'un opérateur
+quelconque nommé ``QuadFunction``, disponible sous forme fonctionnelle. Il est
+définit par la commande "*ObservationOperator*" selon la
+:ref:`section_ref_operator_one`. Par la commande "*CheckingPoint*", on ajoute
+aussi un état particulier :math:`\mathbf{x}` sur lequel tester l'opérateur.
+
+Ce test est répété ici 15 fois, et une statistique finale permet de vérifier
+rapidement le bon comportement de l'opérateur. Le diagnostic le plus simple
+consiste à vérifier, à la toute fin de l'affichage, l'ordre de grandeur des
+valeurs indiquées comme la moyenne des différences entre les sorties répétées
+et leur moyenne, sous la partie titrée "*Characteristics of the mean of the
+differences between the outputs Y and their mean Ym*". Pour qu'un opérateur
+soit satisfaisant, ces valeurs doivent être proches du zéro numérique.
