Minor source update for OM compatibility

[modules/adao.git] / doc / en / ref_algorithm_NonLinearLeastSquares.rst

..
   Copyright (C) 2008-2024 EDF R&D

   This file is part of SALOME ADAO module.

   This library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

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   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
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   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA

   See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com

   Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D

.. index:: single: NonLinearLeastSquares
.. _section_ref_algorithm_NonLinearLeastSquares:

Calculation algorithm "*NonLinearLeastSquares*"
-----------------------------------------------

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.. include:: snippets/Header2Algo01.rst

This algorithm realizes a state estimation by variational minimization of the
classical :math:`J` function of weighted "Least Squares":

.. math:: J(\mathbf{x})=(\mathbf{y}^o-\mathbf{H}.\mathbf{x})^T.\mathbf{R}^{-1}.(\mathbf{y}^o-\mathbf{H}.\mathbf{x})

It is similar to a :ref:`section_ref_algorithm_3DVAR`, without its background
part. The background, required in the interface, is only used as an initial
point for the variational minimization.

This mono-objective optimization algorithm is naturally written for a single
estimate, without any dynamic or iterative notion (there is no need in this
case for an incremental evolution operator, nor for an evolution error
covariance). In ADAO, it can also be used on a succession of observations,
placing the estimate in a recursive framework partly similar to a Kalman
Filter. A standard estimate is made at each observation step on the state
predicted by the incremental evolution model.

In all cases, it is recommended to prefer a :ref:`section_ref_algorithm_3DVAR`
for its stability as for its behavior during optimization.

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.. include:: snippets/Header2Algo12.rst

.. include:: snippets/FeaturePropLocalOptimization.rst

.. include:: snippets/FeaturePropDerivativeNeeded.rst

.. include:: snippets/FeaturePropParallelDerivativesOnly.rst

.. include:: snippets/FeaturePropConvergenceOnBoth.rst

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.. include:: snippets/Header2Algo02.rst

.. include:: snippets/Background.rst

.. include:: snippets/Observation.rst

.. include:: snippets/ObservationError.rst

.. include:: snippets/ObservationOperator.rst

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.. include:: snippets/Header2Algo03AdOp.rst

.. include:: snippets/BoundsWithNone.rst

.. include:: snippets/CostDecrementTolerance.rst

.. include:: snippets/EstimationOf_Parameters.rst

.. include:: snippets/GradientNormTolerance.rst

.. include:: snippets/InitializationPoint.rst

.. include:: snippets/MaximumNumberOfIterations.rst

.. include:: snippets/Minimizer_xDVAR.rst

.. include:: snippets/ProjectedGradientTolerance.rst


StoreSupplementaryCalculations
  .. index:: single: StoreSupplementaryCalculations

  *List of names*. This list indicates the names of the supplementary
  variables, that can be available during or at the end of the algorithm, if
  they are initially required by the user. Their availability involves,
  potentially, costly calculations or memory consumptions. The default is then
  a void list, none of these variables being calculated and stored by default
  (excepted the unconditional variables). The possible names are in the
  following list (the detailed description of each named variable is given in
  the following part of this specific algorithmic documentation, in the
  sub-section "*Information and variables available at the end of the
  algorithm*"): [
  "Analysis",
  "BMA",
  "CostFunctionJ",
  "CostFunctionJAtCurrentOptimum",
  "CostFunctionJb",
  "CostFunctionJbAtCurrentOptimum",
  "CostFunctionJo",
  "CostFunctionJoAtCurrentOptimum",
  "CurrentIterationNumber",
  "CurrentOptimum",
  "CurrentState",
  "CurrentStepNumber",
  "ForecastState",
  "IndexOfOptimum",
  "Innovation",
  "InnovationAtCurrentAnalysis",
  "InnovationAtCurrentState",
  "OMA",
  "OMB",
  "SimulatedObservationAtBackground",
  "SimulatedObservationAtCurrentOptimum",
  "SimulatedObservationAtCurrentState",
  "SimulatedObservationAtOptimum",
  ].

  Example :
  ``{"StoreSupplementaryCalculations":["CurrentState", "Residu"]}``

*Tips for this algorithm:*

    As the *"BackgroundError"* command is required for ALL the calculation
    algorithms in the graphical interface ADAO EFICAS, you have to provide a
    value, even if this command is not required for this algorithm, and will
    not be used. The simplest way is to give "1" as a STRING.

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.. include:: snippets/Header2Algo04.rst

.. include:: snippets/Analysis.rst

.. include:: snippets/CostFunctionJ.rst

.. include:: snippets/CostFunctionJb.rst

.. include:: snippets/CostFunctionJo.rst

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.. include:: snippets/Header2Algo05.rst

.. include:: snippets/Analysis.rst

.. include:: snippets/BMA.rst

.. include:: snippets/CostFunctionJ.rst

.. include:: snippets/CostFunctionJAtCurrentOptimum.rst

.. include:: snippets/CostFunctionJb.rst

.. include:: snippets/CostFunctionJbAtCurrentOptimum.rst

.. include:: snippets/CostFunctionJo.rst

.. include:: snippets/CostFunctionJoAtCurrentOptimum.rst

.. include:: snippets/CurrentIterationNumber.rst

.. include:: snippets/CurrentOptimum.rst

.. include:: snippets/CurrentState.rst

.. include:: snippets/CurrentStepNumber.rst

.. include:: snippets/ForecastState.rst

.. include:: snippets/IndexOfOptimum.rst

.. include:: snippets/Innovation.rst

.. include:: snippets/InnovationAtCurrentAnalysis.rst

.. include:: snippets/InnovationAtCurrentState.rst

.. include:: snippets/OMA.rst

.. include:: snippets/OMB.rst

.. include:: snippets/SimulatedObservationAtBackground.rst

.. include:: snippets/SimulatedObservationAtCurrentOptimum.rst

.. include:: snippets/SimulatedObservationAtCurrentState.rst

.. include:: snippets/SimulatedObservationAtOptimum.rst

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.. _section_ref_algorithm_NonLinearLeastSquares_examples:

.. include:: snippets/Header2Algo09.rst

.. include:: scripts/simple_NonLinearLeastSquares.rst

.. literalinclude:: scripts/simple_NonLinearLeastSquares.py

.. include:: snippets/Header2Algo10.rst

.. literalinclude:: scripts/simple_NonLinearLeastSquares.res

.. include:: snippets/Header2Algo11.rst

.. _simple_NonLinearLeastSquares:
.. image:: scripts/simple_NonLinearLeastSquares.png
  :align: center
  :width: 90%

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.. include:: snippets/Header2Algo06.rst

- :ref:`section_ref_algorithm_LinearLeastSquares`
- :ref:`section_ref_algorithm_3DVAR`
- :ref:`section_ref_algorithm_LinearityTest`

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.. include:: snippets/Header2Algo07.rst

- [Byrd95]_
- [Morales11]_
- [Zhu97]_