2 Copyright (C) 2008-2018 EDF R&D
4 This file is part of SALOME ADAO module.
6 This library is free software; you can redistribute it and/or
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13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
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18 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
20 See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
22 Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
24 .. index:: single: QuantileRegression
25 .. _section_ref_algorithm_QuantileRegression:
27 Calculation algorithm "*QuantileRegression*"
28 --------------------------------------------
33 This algorithm allows to estimate the conditional quantiles of the state
34 parameters distribution, expressed with a model of the observed variables. These
35 are then the quantiles on the observed variables which will allow to determine
36 the model parameters that satisfy to the quantiles conditions.
38 Optional and required commands
39 ++++++++++++++++++++++++++++++
41 .. index:: single: AlgorithmParameters
42 .. index:: single: Background
43 .. index:: single: Observation
44 .. index:: single: ObservationOperator
45 .. index:: single: Quantile
46 .. index:: single: Minimizer
47 .. index:: single: MaximumNumberOfSteps
48 .. index:: single: CostDecrementTolerance
49 .. index:: single: Bounds
50 .. index:: single: StoreSupplementaryCalculations
52 The general required commands, available in the editing user interface, are the
56 *Required command*. This indicates the background or initial vector used,
57 previously noted as :math:`\mathbf{x}^b`. Its value is defined as a
58 "*Vector*" or a *VectorSerie*" type object.
61 *Required command*. This indicates the observation vector used for data
62 assimilation or optimization, previously noted as :math:`\mathbf{y}^o`. It
63 is defined as a "*Vector*" or a *VectorSerie* type object.
66 *Required command*. This indicates the observation operator, previously
67 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
68 results :math:`\mathbf{y}` to be compared to observations
69 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
70 a "*Matrix*" type one. In the case of "*Function*" type, different
71 functional forms can be used, as described in the section
72 :ref:`section_ref_operator_requirements`. If there is some control :math:`U`
73 included in the observation, the operator has to be applied to a pair
76 The general optional commands, available in the editing user interface, are
77 indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
78 of the command "*AlgorithmParameters*" allows to choose the specific options,
79 described hereafter, of the algorithm. See
80 :ref:`section_ref_options_Algorithm_Parameters` for the good use of this
83 The options of the algorithm are the following:
86 This key allows to define the real value of the desired quantile, between
87 0 and 1. The default is 0.5, corresponding to the median.
89 Example : ``{"Quantile":0.5}``
92 This key indicates the maximum number of iterations allowed for iterative
93 optimization. The default is 15000, which is very similar to no limit on
94 iterations. It is then recommended to adapt this parameter to the needs on
97 Example : ``{"MaximumNumberOfSteps":100}``
99 CostDecrementTolerance
100 This key indicates a limit value, leading to stop successfully the
101 iterative optimization process when the cost function or the surrogate
102 decreases less than this tolerance at the last step. The default is 1.e-6,
103 and it is recommended to adapt it to the needs on real problems.
105 Example : ``{"CostDecrementTolerance":1.e-7}``
108 This key allows to define upper and lower bounds for every state variable
109 being optimized. Bounds have to be given by a list of list of pairs of
110 lower/upper bounds for each variable, with possibly ``None`` every time
111 there is no bound. The bounds can always be specified, but they are taken
112 into account only by the constrained optimizers.
114 Example : ``{"Bounds":[[2.,5.],[1.e-2,10.],[-30.,None],[None,None]]}``
116 StoreSupplementaryCalculations
117 This list indicates the names of the supplementary variables that can be
118 available at the end of the algorithm. It involves potentially costly
119 calculations or memory consumptions. The default is a void list, none of
120 these variables being calculated and stored by default. The possible names
121 are in the following list: ["BMA", "CostFunctionJ", "CostFunctionJb",
122 "CostFunctionJo", "CurrentState", "OMA", "OMB", "Innovation",
123 "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentState",
124 "SimulatedObservationAtOptimum"].
126 Example : ``{"StoreSupplementaryCalculations":["BMA", "Innovation"]}``
128 *Tips for this algorithm:*
130 As the *"BackgroundError"* and *"ObservationError"* commands are required
131 for ALL the calculation algorithms in the interface, you have to provide a
132 value, even if these commands are not required for this algorithm, and will
133 not be used. The simplest way is to give "1" as a STRING for both.
135 Information and variables available at the end of the algorithm
136 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
138 At the output, after executing the algorithm, there are variables and
139 information originating from the calculation. The description of
140 :ref:`section_ref_output_variables` show the way to obtain them by the method
141 named ``get`` of the variable "*ADD*" of the post-processing. The input
142 variables, available to the user at the output in order to facilitate the
143 writing of post-processing procedures, are described in the
144 :ref:`subsection_r_o_v_Inventaire`.
146 The unconditional outputs of the algorithm are the following:
149 *List of vectors*. Each element is an optimal state :math:`\mathbf{x}*` in
150 optimization or an analysis :math:`\mathbf{x}^a` in data assimilation.
152 Example : ``Xa = ADD.get("Analysis")[-1]``
155 *List of values*. Each element is a value of the error function :math:`J`.
157 Example : ``J = ADD.get("CostFunctionJ")[:]``
160 *List of values*. Each element is a value of the error function :math:`J^b`,
161 that is of the background difference part.
163 Example : ``Jb = ADD.get("CostFunctionJb")[:]``
166 *List of values*. Each element is a value of the error function :math:`J^o`,
167 that is of the observation difference part.
169 Example : ``Jo = ADD.get("CostFunctionJo")[:]``
171 The conditional outputs of the algorithm are the following:
174 *List of vectors*. Each element is a vector of difference between the
175 background and the optimal state.
177 Example : ``bma = ADD.get("BMA")[-1]``
180 *List of vectors*. Each element is a usual state vector used during the
181 optimization algorithm procedure.
183 Example : ``Xs = ADD.get("CurrentState")[:]``
186 *List of vectors*. Each element is an innovation vector, which is in static
187 the difference between the optimal and the background, and in dynamic the
190 Example : ``d = ADD.get("Innovation")[-1]``
193 *List of vectors*. Each element is a vector of difference between the
194 observation and the optimal state in the observation space.
196 Example : ``oma = ADD.get("OMA")[-1]``
199 *List of vectors*. Each element is a vector of difference between the
200 observation and the background state in the observation space.
202 Example : ``omb = ADD.get("OMB")[-1]``
204 SimulatedObservationAtBackground
205 *List of vectors*. Each element is a vector of observation simulated from
206 the background :math:`\mathbf{x}^b`.
208 Example : ``hxb = ADD.get("SimulatedObservationAtBackground")[-1]``
210 SimulatedObservationAtCurrentState
211 *List of vectors*. Each element is an observed vector at the current state,
212 that is, in the observation space.
214 Example : ``Ys = ADD.get("SimulatedObservationAtCurrentState")[-1]``
216 SimulatedObservationAtOptimum
217 *List of vectors*. Each element is a vector of observation simulated from
218 the analysis or optimal state :math:`\mathbf{x}^a`.
220 Example : ``hxa = ADD.get("SimulatedObservationAtOptimum")[-1]``
225 Bibliographical references: