From 6f9fad9ddee0ebcd935ae1652ade66d34accdb65 Mon Sep 17 00:00:00 2001 From: Jean-Philippe ARGAUD Date: Tue, 28 Feb 2023 13:51:43 +0100 Subject: [PATCH] Documentation update et example improvement --- doc/en/ref_algorithm_3DVAR.rst | 64 +++++++++++-- doc/en/scripts/simple_3DVAR.png | Bin 39917 -> 0 bytes doc/en/scripts/simple_3DVAR.rst | 17 ---- doc/en/scripts/simple_3DVAR1.png | Bin 0 -> 40688 bytes .../{simple_3DVAR.py => simple_3DVAR1.py} | 10 +-- .../{simple_3DVAR.res => simple_3DVAR1.res} | 0 doc/en/scripts/simple_3DVAR1.rst | 25 ++++++ doc/en/scripts/simple_3DVAR1Plus.png | Bin 0 -> 42003 bytes doc/en/scripts/simple_3DVAR1Plus.rst | 14 +++ doc/en/scripts/simple_3DVAR2.py | 73 +++++++++++++++ doc/en/scripts/simple_3DVAR2.res | 8 ++ doc/en/scripts/simple_3DVAR2.rst | 24 +++++ doc/en/scripts/simple_3DVAR2_state.png | Bin 0 -> 33463 bytes doc/en/scripts/simple_3DVAR2_variance.png | Bin 0 -> 19503 bytes doc/en/scripts/simple_3DVAR3.py | 84 ++++++++++++++++++ doc/en/scripts/simple_3DVAR3.res | 8 ++ doc/en/scripts/simple_3DVAR3.rst | 31 +++++++ doc/en/scripts/simple_3DVAR3_state.png | Bin 0 -> 36301 bytes doc/en/scripts/simple_3DVAR3_variance.png | Bin 0 -> 26856 bytes doc/en/snippets/Header2Algo09.rst | 6 +- doc/en/snippets/ModuleCompatibility.rst | 2 +- doc/fr/ref_algorithm_3DVAR.rst | 63 +++++++++++-- doc/fr/scripts/simple_3DVAR.png | Bin 40236 -> 0 bytes doc/fr/scripts/simple_3DVAR.rst | 18 ---- doc/fr/scripts/simple_3DVAR1.png | Bin 0 -> 41028 bytes .../{simple_3DVAR.py => simple_3DVAR1.py} | 10 +-- .../{simple_3DVAR.res => simple_3DVAR1.res} | 0 doc/fr/scripts/simple_3DVAR1.rst | 25 ++++++ doc/fr/scripts/simple_3DVAR1Plus.png | Bin 0 -> 44279 bytes doc/fr/scripts/simple_3DVAR1Plus.rst | 15 ++++ doc/fr/scripts/simple_3DVAR2.py | 73 +++++++++++++++ doc/fr/scripts/simple_3DVAR2.res | 8 ++ doc/fr/scripts/simple_3DVAR2.rst | 25 ++++++ doc/fr/scripts/simple_3DVAR2_state.png | Bin 0 -> 32270 bytes doc/fr/scripts/simple_3DVAR2_variance.png | Bin 0 -> 19654 bytes doc/fr/scripts/simple_3DVAR3.py | 84 ++++++++++++++++++ doc/fr/scripts/simple_3DVAR3.res | 8 ++ doc/fr/scripts/simple_3DVAR3.rst | 32 +++++++ doc/fr/scripts/simple_3DVAR3_state.png | Bin 0 -> 35046 bytes doc/fr/scripts/simple_3DVAR3_variance.png | Bin 0 -> 27077 bytes doc/fr/snippets/Header2Algo09.rst | 7 +- doc/fr/snippets/ModuleCompatibility.rst | 2 +- 42 files changed, 673 insertions(+), 63 deletions(-) delete mode 100644 doc/en/scripts/simple_3DVAR.png delete mode 100644 doc/en/scripts/simple_3DVAR.rst create mode 100644 doc/en/scripts/simple_3DVAR1.png rename doc/en/scripts/{simple_3DVAR.py => simple_3DVAR1.py} (87%) rename doc/en/scripts/{simple_3DVAR.res => simple_3DVAR1.res} (100%) create mode 100644 doc/en/scripts/simple_3DVAR1.rst create mode 100644 doc/en/scripts/simple_3DVAR1Plus.png create mode 100644 doc/en/scripts/simple_3DVAR1Plus.rst create mode 100644 doc/en/scripts/simple_3DVAR2.py create mode 100644 doc/en/scripts/simple_3DVAR2.res create mode 100644 doc/en/scripts/simple_3DVAR2.rst create mode 100644 doc/en/scripts/simple_3DVAR2_state.png create mode 100644 doc/en/scripts/simple_3DVAR2_variance.png create mode 100644 doc/en/scripts/simple_3DVAR3.py create mode 100644 doc/en/scripts/simple_3DVAR3.res create mode 100644 doc/en/scripts/simple_3DVAR3.rst create mode 100644 doc/en/scripts/simple_3DVAR3_state.png create mode 100644 doc/en/scripts/simple_3DVAR3_variance.png delete mode 100644 doc/fr/scripts/simple_3DVAR.png delete mode 100644 doc/fr/scripts/simple_3DVAR.rst create mode 100644 doc/fr/scripts/simple_3DVAR1.png rename doc/fr/scripts/{simple_3DVAR.py => simple_3DVAR1.py} (87%) rename doc/fr/scripts/{simple_3DVAR.res => simple_3DVAR1.res} (100%) create mode 100644 doc/fr/scripts/simple_3DVAR1.rst create mode 100644 doc/fr/scripts/simple_3DVAR1Plus.png create mode 100644 doc/fr/scripts/simple_3DVAR1Plus.rst create mode 100644 doc/fr/scripts/simple_3DVAR2.py create mode 100644 doc/fr/scripts/simple_3DVAR2.res create mode 100644 doc/fr/scripts/simple_3DVAR2.rst create mode 100644 doc/fr/scripts/simple_3DVAR2_state.png create mode 100644 doc/fr/scripts/simple_3DVAR2_variance.png create mode 100644 doc/fr/scripts/simple_3DVAR3.py create mode 100644 doc/fr/scripts/simple_3DVAR3.res create mode 100644 doc/fr/scripts/simple_3DVAR3.rst create mode 100644 doc/fr/scripts/simple_3DVAR3_state.png create mode 100644 doc/fr/scripts/simple_3DVAR3_variance.png diff --git a/doc/en/ref_algorithm_3DVAR.rst b/doc/en/ref_algorithm_3DVAR.rst index 08c4b77..b2023f1 100644 --- a/doc/en/ref_algorithm_3DVAR.rst +++ b/doc/en/ref_algorithm_3DVAR.rst @@ -255,18 +255,71 @@ StoreSupplementaryCalculations .. include:: snippets/Header2Algo09.rst -.. include:: scripts/simple_3DVAR.rst +.. --------- .. +.. include:: scripts/simple_3DVAR1.rst -.. literalinclude:: scripts/simple_3DVAR.py +.. literalinclude:: scripts/simple_3DVAR1.py .. include:: snippets/Header2Algo10.rst -.. literalinclude:: scripts/simple_3DVAR.res +.. literalinclude:: scripts/simple_3DVAR1.res + :language: none .. include:: snippets/Header2Algo11.rst -.. _simple_3DVAR: -.. image:: scripts/simple_3DVAR.png +.. _simple_3DVAR1: +.. image:: scripts/simple_3DVAR1.png + :align: center + :width: 90% + +.. include:: scripts/simple_3DVAR1Plus.rst + +.. _simple_3DVAR1Plus: +.. image:: scripts/simple_3DVAR1Plus.png + :align: center + :width: 90% + +.. --------- .. +.. include:: scripts/simple_3DVAR2.rst + +.. literalinclude:: scripts/simple_3DVAR2.py + +.. include:: snippets/Header2Algo10.rst + +.. literalinclude:: scripts/simple_3DVAR2.res + :language: none + +.. include:: snippets/Header2Algo11.rst + +.. _simple_3DVAR2_state: +.. image:: scripts/simple_3DVAR2_state.png + :align: center + :width: 90% + +.. simple_3DVAR2_variance: +.. image:: scripts/simple_3DVAR2_variance.png + :align: center + :width: 90% + +.. --------- .. +.. include:: scripts/simple_3DVAR3.rst + +.. literalinclude:: scripts/simple_3DVAR3.py + +.. include:: snippets/Header2Algo10.rst + +.. literalinclude:: scripts/simple_3DVAR3.res + :language: none + +.. include:: snippets/Header2Algo11.rst + +.. _simple_3DVAR3_state: +.. image:: scripts/simple_3DVAR3_state.png + :align: center + :width: 90% + +.. _simple_3DVAR3_variance: +.. image:: scripts/simple_3DVAR3_variance.png :align: center :width: 90% @@ -275,6 +328,7 @@ StoreSupplementaryCalculations - :ref:`section_ref_algorithm_Blue` - :ref:`section_ref_algorithm_ExtendedBlue` +- :ref:`section_ref_algorithm_KalmanFilter` - :ref:`section_ref_algorithm_LinearityTest` .. ------------------------------------ .. diff --git a/doc/en/scripts/simple_3DVAR.png b/doc/en/scripts/simple_3DVAR.png deleted file mode 100644 index 6bb44ce487fe2314f09d1ceb25155c0cdc0bcbbd..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 39917 zcmdSBc~p*V8!y~|NF-^JiYU@Zlx7h^i9)4GrP4glBT)!RrP9P>2&GZwZq_^(r9tyt zn&-Lp@8Wsiz4rR{`o6WkzxM83&+|TVcXwasb)LuZn~v+@F+wGh@BI4hA;1#+DX)j|$*_e0y)(*;$DT3jWU*2w2(} 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This model is here represented as a -function named ``QuadFunction``. This function get as input the coefficients -vector :math:`\mathbf{x}`, and return as output the evaluation vector -:math:`\mathbf{y}` of the quadratic model at the predefined internal control -points. The calibration is done using an initial coefficient set (background -state specified by ``Xb`` in the code), and with the information -:math:`\mathbf{y}^o` (specified by ``Yobs`` in the code) of 5 measures obtained -in these same internal control points. We set twin experiments (see -:ref:`section_methodology_twin`) and the measurements are supposed to be -perfect. We choose to emphasize the observations versus the background by -setting a great variance for the background error, here of :math:`10^{6}`. - -The adjustment is carried out by displaying intermediate results during -iterative optimization. diff --git a/doc/en/scripts/simple_3DVAR1.png b/doc/en/scripts/simple_3DVAR1.png new file mode 100644 index 0000000000000000000000000000000000000000..987dcaa2a61525c198f1583cb6b575d1a72832c0 GIT binary patch literal 40688 zcmdSBby!vH+AoR%DvBTmp@f2n7<8urDk8Rm(jXw+odzg^BA|qnfuhpgA&sP>bhpyo zuzy2c-*@&o`&`%F=fA_c)>`k2(>dpO#`E0wukPV_`Qq8_Tla1yAtBi=cTVOi2?^;C z3CV`%TQ=c0k_zWF@qc8Nr{u10!H?6HJCE`26lUjcS(1=Ys6aY(7+XK+O8L%;HqPxtUpkRwB>c zy8R?vs#(RA-1!&!zrHlLu_@I`yqxdiOmd8N8?BdnS6A1t)Zoy!ch$XvHDSsR75($W z#BKQ;X6~NxVXn@y9)8jvDtsi~QNngi#d4W=-Dq`)uy8tys6}Lxc6DBQ{Rf50RPOvB z+>bRb4#&;=Sy|J4QVkowry43=jF2);Uagg0@56uZjJBjo%+#IM<#Xbn{r%JHxN=%w zrs+siVpXW<^oO#`j5cF!70RZ$I&s3L9c?aO+B}lRjW1t*zDVlx_;GplpWX4K_#Wxz 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This model :math:`H` is here represented +as a function named ``QuadFunction`` for the purpose of this example. This +function get as input the coefficients vector :math:`\mathbf{x}` of the +quadratic form, and return as output the evaluation vector :math:`\mathbf{y}` +of the quadratic model at the predefined internal control points, predefined in +a static way in the model. + +The calibration is done using an initial coefficient set (background state +specified by ``Xb`` in the example), and with the information +:math:`\mathbf{y}^o` (specified by ``Yobs`` in the example) of 5 measures +obtained in these same internal control points. We set twin experiments (see +:ref:`section_methodology_twin`) and the measurements are supposed to be +perfect. We choose to emphasize the observations, versus the background, by +setting artificially a great variance for the background error, here of +:math:`10^{6}`. + +The adjustment is carried out by displaying intermediate results using +"*observer*" (for reference, see :ref:`section_advanced_observer`) during +iterative optimization. diff --git a/doc/en/scripts/simple_3DVAR1Plus.png b/doc/en/scripts/simple_3DVAR1Plus.png new file mode 100644 index 0000000000000000000000000000000000000000..cb3ac043db74e9043cb8128aced9e3e4e014f40b GIT binary patch literal 42003 zcmdSBc|4VE+cvyJ5i*3R$WY0UF$!hYBvgh75mF(UlUYTXRi;KHl9@7=IYX#Ok<3G) zWGW$|Z#%lK`+5F(-{<{(-|ze9?Vhfi)mrO3&*RwlZQ76EBRc!n&~KopP$+8-9?;OG zP^d>K6sqfVtMC&=ZA}aO4~>i3L47*>@uoW!g#W+V@xXBx3WXWJW454rtek3tAIiJ# zHFDK+IPL0g;cQK@w{Uel=iqwI#**)XwX=(j!+Abwar|pL-&t2zM+FIq|9*kEgYy}Q zs|oKJC=@=*K@C;?i}$|uc$n%N{Gpv{&SmQ26S!RLzfnZsZ1E+A^BT5SZEVi_um5Uw zemJ&5-}JlG*17F*^lus8vCE3Rqr8rxsp0szLbi4#JImhoAB$ItnW=Y33ekNTS@L|% 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Naturally, the final simulation obtained with the +adjusted coefficients coincides with the observations at the 5 control points. + +To illustrate more clearly the recalibration performed, using the same +information, we can plot the continuous version of the quadratic curves +available for the background state of the coefficients, and for the optimal +state of the coefficients, together with the values obtained at the control +points. In addition, to improve readability, the lines joining the simulations +in the previous graph have been removed. diff --git a/doc/en/scripts/simple_3DVAR2.py b/doc/en/scripts/simple_3DVAR2.py new file mode 100644 index 0000000..a7e8db0 --- /dev/null +++ b/doc/en/scripts/simple_3DVAR2.py @@ -0,0 +1,73 @@ +# -*- coding: utf-8 -*- +# +from numpy import array, random +random.seed(1234567) +Xtrue = -0.37727 +Yobs = [] +for i in range(51): + Yobs.append([random.normal(Xtrue, 0.1, size=(1,)),]) +# +print("Variational estimation of a time trajectory") +print("-------------------------------------------") +print(" Noisy measurements acquired on %i time steps"%(len(Yobs)-1,)) +print("") +from adao import adaoBuilder +case = adaoBuilder.New() +# +case.setBackground (Vector = [0.]) +case.setBackgroundError (ScalarSparseMatrix = 0.1**2) +# +case.setObservationOperator(Matrix = [1.]) +case.setObservation (VectorSerie = Yobs) +case.setObservationError (ScalarSparseMatrix = 0.3**2) +# +case.setEvolutionModel (Matrix = [1.]) +case.setEvolutionError (ScalarSparseMatrix = 1e-5) +# +case.setAlgorithmParameters( + Algorithm="3DVAR", + Parameters={ + "EstimationOf":"State", + "StoreSupplementaryCalculations":[ + "Analysis", + "APosterioriCovariance", + ], + }, + ) +# +case.execute() +Xa = case.get("Analysis") +Pa = case.get("APosterioriCovariance") +# +print(" Analyzed state at final observation:", Xa[-1]) +print("") +print(" Final a posteriori variance:", Pa[-1]) +print("") +# +#------------------------------------------------------------------------------- +# +Observations = array([yo[0] for yo in Yobs]) +Estimates = array([xa[0] for xa in case.get("Analysis")]) +Variances = array([pa[0,0] for pa in case.get("APosterioriCovariance")]) +# +import matplotlib.pyplot as plt +plt.rcParams['figure.figsize'] = (10, 4) +# +plt.figure() +plt.plot(Observations,'kx',label='Noisy measurements') +plt.plot(Estimates,'r-',label='Estimated state') +plt.axhline(Xtrue,color='b',label='Truth value') +plt.legend() +plt.title('Estimate of the state', fontweight='bold') +plt.xlabel('Observation step') +plt.ylabel('Voltage') +plt.savefig("simple_3DVAR2_state.png") +# +plt.figure() +iobs = range(1,len(Observations)) +plt.plot(iobs,Variances[iobs],label='A posteriori error variance') +plt.title('Estimate of the a posteriori error variance', fontweight='bold') +plt.xlabel('Observation step') +plt.ylabel('$(Voltage)^2$') +plt.setp(plt.gca(),'ylim',[0,.01]) +plt.savefig("simple_3DVAR2_variance.png") diff --git a/doc/en/scripts/simple_3DVAR2.res b/doc/en/scripts/simple_3DVAR2.res new file mode 100644 index 0000000..ec9bd02 --- /dev/null +++ b/doc/en/scripts/simple_3DVAR2.res @@ -0,0 +1,8 @@ +Variational estimation of a time trajectory +------------------------------------------- + Noisy measurements acquired on 50 time steps + + Analyzed state at final observation: [-0.37110687] + + Final a posteriori variance: [[0.009]] + diff --git a/doc/en/scripts/simple_3DVAR2.rst b/doc/en/scripts/simple_3DVAR2.rst new file mode 100644 index 0000000..56ce659 --- /dev/null +++ b/doc/en/scripts/simple_3DVAR2.rst @@ -0,0 +1,24 @@ +Second example +.............. + +The 3DVAR can also be used for a **time analysis of the observations of a given +dynamic model**. In this case, the analysis is performed iteratively, at the +arrival of each observation. For this example, we use the same simple dynamic +system [Welch06]_ that is analyzed in the Kalman Filter +:ref:`section_ref_algorithm_KalmanFilter_examples`. + +At each step, the classical 3DVAR analysis updates only the state of the +system. By modifying the *a priori* covariance values with respect to the +initial assumptions of the filtering, this 3DVAR reanalysis allows to converge +towards the true trajectory, as illustrated in the associated figure, in a +slightly slower speed than with a Kalman Filter. + +.. note:: + + Note about *a posteriori* covariances: classically, the 3DVAR iterative + analysis updates only the state and not its covariance. As the assumptions + of operators and *a priori* covariance remain unchanged here during the + evolution, the *a posteriori* covariance is constant. The following plot of + this *a posteriori* covariance allows us to insist on this property, which + is entirely expected from the 3DVAR analysis. 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b/doc/en/scripts/simple_3DVAR3.py new file mode 100644 index 0000000..2d9ad44 --- /dev/null +++ b/doc/en/scripts/simple_3DVAR3.py @@ -0,0 +1,84 @@ +# -*- coding: utf-8 -*- +# +from numpy import array, random +random.seed(1234567) +Xtrue = -0.37727 +Yobs = [] +for i in range(51): + Yobs.append([random.normal(Xtrue, 0.1, size=(1,)),]) +# +print("Variational estimation of a time trajectory") +print("-------------------------------------------") +print(" Noisy measurements acquired on %i time steps"%(len(Yobs)-1,)) +print("") +from adao import adaoBuilder +case = adaoBuilder.New() +# +case.setBackground (Vector = [0.]) +# +case.setObservationOperator(Matrix = [1.]) +case.setObservationError (ScalarSparseMatrix = 0.3**2) +# +case.setEvolutionModel (Matrix = [1.]) +case.setEvolutionError (ScalarSparseMatrix = 1e-5) +# +case.setAlgorithmParameters( + Algorithm="3DVAR", + Parameters={ + "EstimationOf":"State", + "StoreSupplementaryCalculations":[ + "Analysis", + "APosterioriCovariance", + ], + }, + ) +# +# Loop to obtain an analysis at each observation arrival +# +Ca = 1. +for i in range(1,len(Yobs)): + case.setObservation(Vector = Yobs[i]) + case.setBackgroundError(ScalarSparseMatrix = Ca) # Update of the covariance + case.execute( nextStep = True ) + # + # Hypothesis of the a priori covariance decay of the background error + # + if float(Ca) <= 0.1**2: + Ca = 0.1**2 + else: + Ca = Ca * 0.9**2 +# +Xa = case.get("Analysis") +Pa = case.get("APosterioriCovariance") +# +print(" Analyzed state at final observation:", Xa[-1]) +print("") +print(" Final a posteriori variance:", Pa[-1]) +print("") +# +#------------------------------------------------------------------------------- +# +Observations = array([yo[0] for yo in Yobs]) +Estimates = array([xa[0] for xa in case.get("Analysis")]) +Variances = array([pa[0,0] for pa in case.get("APosterioriCovariance")]) +# +import matplotlib.pyplot as plt +plt.rcParams['figure.figsize'] = (10, 4) +# +plt.figure() +plt.plot(Observations,'kx',label='Noisy measurements') +plt.plot(Estimates,'r-',label='Estimated state') +plt.axhline(Xtrue,color='b',label='Truth value') +plt.legend() +plt.title('Estimate of the state', fontweight='bold') +plt.xlabel('Observation step') +plt.ylabel('Voltage') +plt.savefig("simple_3DVAR3_state.png") +# +plt.figure() +iobs = range(1,len(Observations)) +plt.plot(iobs,Variances[iobs],label='A posteriori error variance') +plt.title('Estimate of the a posteriori error variance', fontweight='bold') +plt.xlabel('Observation step') +plt.ylabel('$(Voltage)^2$') +plt.savefig("simple_3DVAR3_variance.png") diff --git a/doc/en/scripts/simple_3DVAR3.res b/doc/en/scripts/simple_3DVAR3.res new file mode 100644 index 0000000..21c9b65 --- /dev/null +++ b/doc/en/scripts/simple_3DVAR3.res @@ -0,0 +1,8 @@ +Variational estimation of a time trajectory +------------------------------------------- + Noisy measurements acquired on 50 time steps + + Analyzed state at final observation: [-0.37334336] + + Final a posteriori variance: [[0.009]] + diff --git a/doc/en/scripts/simple_3DVAR3.rst b/doc/en/scripts/simple_3DVAR3.rst new file mode 100644 index 0000000..0d6e9a5 --- /dev/null +++ b/doc/en/scripts/simple_3DVAR3.rst @@ -0,0 +1,31 @@ +Third example +............. + +From the preceding example, if one wants to adapt the time convergence of the +3DVAR, one can change, for example, the *a priori* covariance assumptions of +the background errors during the iterations. This update is an **assumption** +of the user, and there are multiple alternatives that will depend on the +physics of the case. We illustrate one of them here. + +We choose, in an arbitrary way, to make the *a priori* covariance of the +background errors to decrease by a constant factor :math:`0.9^2=0.81` as long +as it remains above a limit value of :math:`0.1^2=0.01` (which is the fixed +value of *a priori* covariance of the background errors of the previous +example), knowing that it starts at the value `1` (which is the fixed value of +*a priori* covariance of the background errors used for the first step of +Kalman filtering). This value is updated at each step, by reinjecting it as the +*a priori* covariance of the state which is used as a background in the next +step of analysis, in an explicit loop. + +We notice in this case that the state estimation converges faster to the true +value, and that the assimilation then behaves similarly to the examples for the +Kalman Filter, or to the previous example with the manually adapted *a priori* +covariances. Moreover, the *a posteriori* covariance decreases as long as we +force the decrease of the *a priori* covariance. + +.. note:: + + We insist on the fact that the *a priori* covariance variations, which + determine the *a posteriori* covariance variations, are a **user + assumption** and not an obligation. 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+++++++++++++++++++++++++ -Here is a very simple use of the given algorithm and its parameters, written in -:ref:`section_tui`, and from which input information allow to define an -equivalent case in graphical user interface. +Here is one or more very simple examples of the proposed algorithm and its +parameters, written in :ref:`section_tui`. Moreover, the information given as +input also allows to define an equivalent case in :ref:`section_gui_in_salome`. diff --git a/doc/en/snippets/ModuleCompatibility.rst b/doc/en/snippets/ModuleCompatibility.rst index 1138bf9..e5a5fcd 100644 --- a/doc/en/snippets/ModuleCompatibility.rst +++ b/doc/en/snippets/ModuleCompatibility.rst @@ -14,7 +14,7 @@ guarantee). Python, 3.6.5, 3.10.9 Numpy, 1.14.3, 1.24.2 - Scipy, 1.1.0, 1.10.0 + Scipy, 0.19.1, 1.10.1 MatplotLib, 2.2.2, 3.7.0 GnuplotPy, 1.8, 1.8 NLopt, 2.4.2, 2.7.1 diff --git a/doc/fr/ref_algorithm_3DVAR.rst b/doc/fr/ref_algorithm_3DVAR.rst index d3c10b4..c8cf19d 100644 --- a/doc/fr/ref_algorithm_3DVAR.rst +++ b/doc/fr/ref_algorithm_3DVAR.rst @@ -260,19 +260,71 @@ StoreSupplementaryCalculations .. include:: snippets/Header2Algo09.rst -.. include:: scripts/simple_3DVAR.rst +.. --------- .. +.. include:: scripts/simple_3DVAR1.rst -.. literalinclude:: scripts/simple_3DVAR.py +.. literalinclude:: scripts/simple_3DVAR1.py .. include:: snippets/Header2Algo10.rst -.. literalinclude:: scripts/simple_3DVAR.res +.. literalinclude:: scripts/simple_3DVAR1.res :language: none .. include:: snippets/Header2Algo11.rst -.. _simple_3DVAR: -.. image:: scripts/simple_3DVAR.png +.. _simple_3DVAR1: +.. image:: scripts/simple_3DVAR1.png + :align: center + :width: 90% + +.. include:: scripts/simple_3DVAR1Plus.rst + +.. _simple_3DVAR1Plus: +.. image:: scripts/simple_3DVAR1Plus.png + :align: center + :width: 90% + +.. --------- .. +.. include:: scripts/simple_3DVAR2.rst + +.. literalinclude:: scripts/simple_3DVAR2.py + +.. include:: snippets/Header2Algo10.rst + +.. literalinclude:: scripts/simple_3DVAR2.res + :language: none + +.. include:: snippets/Header2Algo11.rst + +.. _simple_3DVAR2_state: +.. image:: scripts/simple_3DVAR2_state.png + :align: center + :width: 90% + +.. simple_3DVAR2_variance: +.. image:: scripts/simple_3DVAR2_variance.png + :align: center + :width: 90% + +.. --------- .. +.. include:: scripts/simple_3DVAR3.rst + +.. literalinclude:: scripts/simple_3DVAR3.py + +.. include:: snippets/Header2Algo10.rst + +.. literalinclude:: scripts/simple_3DVAR3.res + :language: none + +.. include:: snippets/Header2Algo11.rst + +.. _simple_3DVAR3_state: +.. image:: scripts/simple_3DVAR3_state.png + :align: center + :width: 90% + +.. _simple_3DVAR3_variance: +.. image:: scripts/simple_3DVAR3_variance.png :align: center :width: 90% @@ -281,6 +333,7 @@ StoreSupplementaryCalculations - :ref:`section_ref_algorithm_Blue` - :ref:`section_ref_algorithm_ExtendedBlue` +- :ref:`section_ref_algorithm_KalmanFilter` - :ref:`section_ref_algorithm_LinearityTest` .. ------------------------------------ .. diff --git a/doc/fr/scripts/simple_3DVAR.png b/doc/fr/scripts/simple_3DVAR.png deleted file mode 100644 index 00388bac2e1c14fed8f93b5e5dc244af3cac17fd..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 40236 zcmdRWX*ibc+V+iP%2bI6Q7M$El39reB~vMLLX=tNqC%3Pl2GQzm^nk4GZck1m}i9u zAv1mZ)$^?NZr`@OKfgbpwVt(}(0yOmbspz&?9+MQJ#$)_o|c`KL?Y3jR8iC-ktjw< zB(nR|8}S|4Q>v!;zYR_bCv~XtjS2^!QA~E7;jHYC%@+nsMrlhlyp0l={ zg|n-vqdCdO)Y<;3o%2upkNZqV zBJCudR6M5R7Cq79YM}d#n`*k*+-QFDv8`1v_F3OblQ^Tz+<14FvdNQOg32LcN@o;n z6+~X{h)Rvx<>XhPs^xI$N#d|iG~2#@5}BrW^HeCu-Yk1&mg1o1mETg?ZL%XWBktuR z2Ky>xhTi%zkt_c5m2{T<2ZK+*KVOmYTbTcT>C&pV-2LZ!0%Uxn|Nd?`X^S)O->*bf 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Ce modèle est représenté ici comme une -fonction nommée ``QuadFunction``. Cette fonction accepte en entrée le vecteur -de coefficients :math:`\mathbf{x}`, et fournit en sortie le vecteur -:math:`\mathbf{y}` d'évaluation du modèle quadratique aux points de contrôle -internes prédéfinis dans le modèle. Le calage s'effectue sur la base d'un jeu -initial de coefficients (état d'ébauche désigné par ``Xb`` dans l'exemple), et -avec l'information :math:`\mathbf{y}^o` (désignée par ``Yobs`` dans l'exemple) -de 5 mesures obtenues à ces mêmes points de contrôle internes. On se place en -expériences jumelles (voir :ref:`section_methodology_twin`) et les mesures sont -parfaites. 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zN_GQO#;vME!~N*VlTF^<>nujSID1j;FTmLQ5KdcsUY>pX&L$w{j2_u)w-EMAgP_rc z;n?79C=mPl`o!w0;EenTSsHilkP`p^`bSiKfpdn=WC-Jx$EAU?>mHh(LD!OHPRz)o z9lh6P@KmK;t7U;b8UyiqXorK~@~c^W6mdC-fFlm~=VI3EMAi`i2(eDN!-pABJrETK zHvOJ~Hl!Bq8SgHjLd{N8+_>)dl9R0yO)MK<7NVTXVpYogc~9~$ZiV%v_3EE+g8zeY d{TB|KT-Wr9OKuSzTqDDelA?-2iu~m}{|`^t!~g&Q literal 0 HcmV?d00001 diff --git a/doc/fr/scripts/simple_3DVAR.py b/doc/fr/scripts/simple_3DVAR1.py similarity index 87% rename from doc/fr/scripts/simple_3DVAR.py rename to doc/fr/scripts/simple_3DVAR1.py index 88c307c..12da2a8 100644 --- a/doc/fr/scripts/simple_3DVAR.py +++ b/doc/fr/scripts/simple_3DVAR1.py @@ -5,7 +5,7 @@ def QuadFunction( coefficients ): """ Simulation quadratique aux points x : y = a x^2 + b x + c """ - a, b, c = list(ravel(coefficients)) + a, b, c = list(ravel(coefficients)) x_points = (-5, 0, 1, 3, 10) y_points = [] for x in x_points: @@ -64,11 +64,11 @@ import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = (10, 4) # plt.figure() -plt.plot((-5,0,1,3,10),QuadFunction(Xb),'b-',label="Simulation à l'ébauche") -plt.plot((-5,0,1,3,10),Yobs, 'kX',label='Observation',markersize=10) -plt.plot((-5,0,1,3,10),QuadFunction(Xa),'r-',label="Simulation à l'optimum") +plt.plot((-5,0,1,3,10),QuadFunction(Xb),'b--',label="Simulation à l'ébauche") +plt.plot((-5,0,1,3,10),Yobs, 'kX', label='Observation',markersize=10) +plt.plot((-5,0,1,3,10),QuadFunction(Xa),'r-', label="Simulation à l'optimum") plt.legend() plt.title('Calage de coefficients', fontweight='bold') plt.xlabel('Coordonnée arbitraire') plt.ylabel('Observations') -plt.savefig("simple_3DVAR.png") +plt.savefig("simple_3DVAR1.png") diff --git a/doc/fr/scripts/simple_3DVAR.res b/doc/fr/scripts/simple_3DVAR1.res similarity index 100% rename from doc/fr/scripts/simple_3DVAR.res rename to doc/fr/scripts/simple_3DVAR1.res diff --git a/doc/fr/scripts/simple_3DVAR1.rst b/doc/fr/scripts/simple_3DVAR1.rst new file mode 100644 index 0000000..c1295d7 --- /dev/null +++ b/doc/fr/scripts/simple_3DVAR1.rst @@ -0,0 +1,25 @@ +.. index:: single: 3DVAR (exemple) + +Premier exemple +............... + +Cet exemple décrit le **recalage des paramètres** :math:`\mathbf{x}` d'un +modèle d'observation :math:`H` quadratique. Ce modèle :math:`H` est représenté +ici comme une fonction nommée ``QuadFunction`` pour les besoins de l'exemple. +Cette fonction accepte en entrée le vecteur de coefficients :math:`\mathbf{x}` +de la forme quadratique, et fournit en sortie le vecteur :math:`\mathbf{y}` +d'évaluation du modèle quadratique aux points de contrôle internes, prédéfinis +de manière statique dans le modèle. + +Le recalage s'effectue sur la base d'un jeu initial de coefficients (état +d'ébauche désigné par ``Xb`` dans l'exemple), et avec l'information +:math:`\mathbf{y}^o` (désignée par ``Yobs`` dans l'exemple) de 5 mesures +obtenues à aux points de contrôle internes. On se place ici en expériences +jumelles (voir :ref:`section_methodology_twin`), et les mesures sont +considérées comme parfaites. On choisit de privilégier les observations, au +détriment de l'ébauche, par l'indication artificielle d'une très importante +variance d'erreur d'ébauche, ici de :math:`10^{6}`. + +L'ajustement s'effectue en affichant des résultats intermédiaires lors de +l'optimisation itérative grâce à des "*observer*" (pour mémoire, voir +:ref:`section_advanced_observer`). diff --git a/doc/fr/scripts/simple_3DVAR1Plus.png b/doc/fr/scripts/simple_3DVAR1Plus.png new file mode 100644 index 0000000000000000000000000000000000000000..78b62f023320efa26d27ec75c4542897bcb449db GIT binary patch literal 44279 zcmeFZc{rA9`!;+lm7zikDTGLfh!QfT5}M3pmPFzU_U#|KDwUTdh?K_kCa2c^&6*?8mpyV>~s_gW!+H~ zWeo~t&MM|j&gS64@AQPKbT0TBmh zE77Zo4fGVsHp)?DMXihXhC4hBBW9P^j5l}uEFCM7QCpL8`hM_MmIpa4XLoJcZ)= z6T`v{ClcknNB3%KXl&aMjNi4Hr(fJ*C|V!G8EGhzJ#^CMkhwX}pP3PQ7Z;av=gui? z-(c4JCYa)9^*O<;y};>Qdx6;VygY8aFyHPpMRcFY<;$1Lmy(l{B`-=0R#sKQ?I-VdKe0k-X-q-$XRNEZ7O2gY;IP`sccVnP6FXMVx 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interface graphique. +Voici un ou des exemples très simple d'usage de l'algorithme proposé et de ses +paramètres, écrit en :ref:`section_tui`. De plus, les informations indiquées en +entrée permettent aussi de définir un cas équivalent en interface graphique +:ref:`section_gui_in_salome`. diff --git a/doc/fr/snippets/ModuleCompatibility.rst b/doc/fr/snippets/ModuleCompatibility.rst index b9adf27..2474ca6 100644 --- a/doc/fr/snippets/ModuleCompatibility.rst +++ b/doc/fr/snippets/ModuleCompatibility.rst @@ -14,7 +14,7 @@ la version atteinte (mais cela reste sans garantie). Python, 3.6.5, 3.10.9 Numpy, 1.14.3, 1.24.2 - Scipy, 1.1.0, 1.10.0 + Scipy, 0.19.1, 1.10.1 MatplotLib, 2.2.2, 3.7.0 GnuplotPy, 1.8, 1.8 NLopt, 2.4.2, 2.7.1 -- 2.39.2