#. "Innovation" (automatic): the difference between the observations and the
control state transformed by the observation operator, noted as
:math:`\mathbf{y}^o - \mathbf{H}\mathbf{x}^b`.
+#. "APosterioriCovariance" (optional): the covariance matrix of the *a
+ posteriori* analysis errors, noted as :math:`\mathbf{A}`.
#. "OMB" (optional): the difference between the observations and the
background, similar to the innovation.
#. "BMA" (optional): the difference between the background and the analysis,
noted as :math:`\mathbf{x}^b - \mathbf{x}^a`.
#. "OMA" (optional): the difference between the observations and the analysis,
noted as :math:`\mathbf{y}^o - \mathbf{H}\mathbf{x}^a`.
+#. "CostFunctionJ" (optional): the minimisation function, noted as :math:`J`.
+#. "CostFunctionJo" (optional): the observation part of the minimisation
+ function, noted as :math:`J^o`.
+#. "CostFunctionJb" (optional): the background part of the minimisation
+ function, noted as :math:`J^b`.
Input variables are also available as output in order to gather all the
information at the end of the procedure.
The different commands are the following:
-:ASSIM_STUDY:
+:ASSIMILATION_STUDY:
*Required command*. This is the general command describing an ADAO case. It
hierarchicaly contains all the other commands.
:Debug:
*Required command*. This let choose the level of trace and intermediary
- debug informations.The choices are limited between 0 (for False) and 1 (for
+ debug informations. The choices are limited between 0 (for False) and 1 (for
True) and available through the GUI.
:InputVariables:
to results :math:`\mathbf{y}` to be compared to observations
:math:`\mathbf{y}^o`.
+:Observers:
+ *Optional command*. This command allows to set internal observers, that are
+ functions linked with a particular variable, which will be executed each
+ time this variable is modified. It is a convenient way to monitor interest
+ variables during the data assimilation process, by printing or plotting it,
+ etc.
+
:OutputVariables:
*Optional command*. This command allows to indicates the name and size of
physical variables that are bundled together in the output observation
unused.
:"Blue":
- no option
+
+ :CalculateAPosterioriCovariance:
+ This boolean key allows to enable the calculation and the storage of the
+ covariance matrix of a posteriori anlysis errors. Be careful, this is a
+ numericaly costly step. The default is "False".
:"LinearLeastSquares":
no option
real problems. For some algorithms, the effective stopping step can be
slightly different due to algorihtm internal control requirements.
+ :CalculateAPosterioriCovariance:
+ This boolean key allows to enable the calculation and the storage of the
+ covariance matrix of a posteriori anlysis errors. Be careful, this is a
+ numericaly costly step. The default is "False".
+
+ :CostDecrementTolerance:
+ This key indicates a limit value, leading to stop successfully the
+ iterative optimization process when the cost function decreases less than
+ this tolerance at the last step. The default is 10e-7, and it is
+ recommended to adapt it the needs on real problems.
+
:ProjectedGradientTolerance:
This key indicates a limit value, leading to stop successfully the
iterative optimization process when all the components of the projected
gradient are under this limit. It is only used for constrained algorithms.
+ The default is -1, that is the internal default of each algorithm, and it
+ is not recommended to change it.
:GradientNormTolerance:
This key indicates a limit value, leading to stop successfully the
iterative optimization process when the norm of the gradient is under this
- limit. It is only used for non-constrained algorithms.
+ limit. It is only used for non-constrained algorithms. The default is
+ 10e-5 and it is not recommended to change it.
:"NonLinearLeastSquares":
real problems. For some algorithms, the effective stopping step can be
slightly different due to algorihtm internal control requirements.
+ :CostDecrementTolerance:
+ This key indicates a limit value, leading to stop successfully the
+ iterative optimization process when the cost function decreases less than
+ this tolerance at the last step. The default is 10e-7, and it is
+ recommended to adapt it the needs on real problems.
+
:ProjectedGradientTolerance:
This key indicates a limit value, leading to stop successfully the
iterative optimization process when all the components of the projected
gradient are under this limit. It is only used for constrained algorithms.
+ The default is -1, that is the internal default of each algorithm, and it
+ is not recommended to change it.
:GradientNormTolerance:
This key indicates a limit value, leading to stop successfully the
iterative optimization process when the norm of the gradient is under this
- limit. It is only used for non-constrained algorithms.
+ limit. It is only used for non-constrained algorithms. The default is
+ 10e-5 and it is not recommended to change it.
:"EnsembleBlue":
no option
:"KalmanFilter":
- no option
+
+ :CalculateAPosterioriCovariance:
+ This boolean key allows to enable the calculation and the storage of the
+ covariance matrix of a posteriori anlysis errors. Be careful, this is a
+ numericaly costly step. The default is "False".
Examples of using these commands are available in the section
:ref:`section_examples` and in example files installed with ADAO module.
