2 Copyright (C) 2008-2015 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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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: StoreSupplementaryCalculations
51 The general required commands, available in the editing user interface, are the
55 *Required command*. This indicates the background or initial vector used,
56 previously noted as :math:`\mathbf{x}^b`. Its value is defined as a
57 "*Vector*" or a *VectorSerie*" type object.
60 *Required command*. This indicates the observation vector used for data
61 assimilation or optimization, previously noted as :math:`\mathbf{y}^o`. It
62 is defined as a "*Vector*" or a *VectorSerie* type object.
65 *Required command*. This indicates the observation operator, previously
66 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
67 results :math:`\mathbf{y}` to be compared to observations
68 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
69 a "*Matrix*" type one. In the case of "*Function*" type, different
70 functional forms can be used, as described in the section
71 :ref:`section_ref_operator_requirements`. If there is some control :math:`U`
72 included in the observation, the operator has to be applied to a pair
75 The general optional commands, available in the editing user interface, are
76 indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
77 of the command "*AlgorithmParameters*" allows to choose the specific options,
78 described hereafter, of the algorithm. See
79 :ref:`section_ref_options_Algorithm_Parameters` for the good use of this
82 The options of the algorithm are the following:
85 This key allows to define the real value of the desired quantile, between
86 0 and 1. The default is 0.5, corresponding to the median.
88 Example : ``{"Quantile":0.5}``
91 This key indicates the maximum number of iterations allowed for iterative
92 optimization. The default is 15000, which is very similar to no limit on
93 iterations. It is then recommended to adapt this parameter to the needs on
96 Example : ``{"MaximumNumberOfSteps":100}``
98 CostDecrementTolerance
99 This key indicates a limit value, leading to stop successfully the
100 iterative optimization process when the cost function or the surrogate
101 decreases less than this tolerance at the last step. The default is 1.e-6,
102 and it is recommended to adapt it to the needs on real problems.
104 Example : ``{"CostDecrementTolerance":1.e-7}``
106 StoreSupplementaryCalculations
107 This list indicates the names of the supplementary variables that can be
108 available at the end of the algorithm. It involves potentially costly
109 calculations or memory consumptions. The default is a void list, none of
110 these variables being calculated and stored by default. The possible names
111 are in the following list: ["BMA", "CostFunctionJ", "CurrentState", "OMA",
112 "OMB", "Innovation", "SimulatedObservationAtBackground",
113 "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum"].
115 Example : ``{"StoreSupplementaryCalculations":["BMA", "Innovation"]}``
117 *Tips for this algorithm:*
119 As the *"BackgroundError"* and *"ObservationError"* commands are required
120 for ALL the calculation algorithms in the interface, you have to provide a
121 value, even if these commands are not required for this algorithm, and will
122 not be used. The simplest way is to give "1" as a STRING for both.
124 Information and variables available at the end of the algorithm
125 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
127 At the output, after executing the algorithm, there are variables and
128 information originating from the calculation. The description of
129 :ref:`section_ref_output_variables` show the way to obtain them by the method
130 named ``get`` of the variable "*ADD*" of the post-processing. The input
131 variables, available to the user at the output in order to facilitate the
132 writing of post-processing procedures, are described in the
133 :ref:`subsection_r_o_v_Inventaire`.
135 The unconditional outputs of the algorithm are the following:
138 *List of vectors*. Each element is an optimal state :math:`\mathbf{x}*` in
139 optimization or an analysis :math:`\mathbf{x}^a` in data assimilation.
141 Example : ``Xa = ADD.get("Analysis")[-1]``
144 *List of values*. Each element is a value of the error function :math:`J`.
146 Example : ``J = ADD.get("CostFunctionJ")[:]``
149 *List of values*. Each element is a value of the error function :math:`J^b`,
150 that is of the background difference part.
152 Example : ``Jb = ADD.get("CostFunctionJb")[:]``
155 *List of values*. Each element is a value of the error function :math:`J^o`,
156 that is of the observation difference part.
158 Example : ``Jo = ADD.get("CostFunctionJo")[:]``
160 The conditional outputs of the algorithm are the following:
163 *List of vectors*. Each element is a vector of difference between the
164 background and the optimal state.
166 Example : ``bma = ADD.get("BMA")[-1]``
169 *List of vectors*. Each element is a usual state vector used during the
170 optimization algorithm procedure.
172 Example : ``Xs = ADD.get("CurrentState")[:]``
175 *List of vectors*. Each element is an innovation vector, which is in static
176 the difference between the optimal and the background, and in dynamic the
179 Example : ``d = ADD.get("Innovation")[-1]``
182 *List of vectors*. Each element is a vector of difference between the
183 observation and the optimal state in the observation space.
185 Example : ``oma = ADD.get("OMA")[-1]``
188 *List of vectors*. Each element is a vector of difference between the
189 observation and the background state in the observation space.
191 Example : ``omb = ADD.get("OMB")[-1]``
193 SimulatedObservationAtBackground
194 *List of vectors*. Each element is a vector of observation simulated from
195 the background :math:`\mathbf{x}^b`.
197 Example : ``hxb = ADD.get("SimulatedObservationAtBackground")[-1]``
199 SimulatedObservationAtCurrentState
200 *List of vectors*. Each element is an observed vector at the current state,
201 that is, in the observation space.
203 Example : ``Ys = ADD.get("SimulatedObservationAtCurrentState")[-1]``
205 SimulatedObservationAtOptimum
206 *List of vectors*. Each element is a vector of observation simulated from
207 the analysis or optimal state :math:`\mathbf{x}^a`.
209 Example : ``hxa = ADD.get("SimulatedObservationAtOptimum")[-1]``
214 Bibliographical references: