3 ================================================================================
4 Examples on using the ADAO module
5 ================================================================================
7 .. |eficas_new| image:: images/eficas_new.png
10 .. |eficas_save| image:: images/eficas_save.png
13 .. |eficas_yacs| image:: images/eficas_yacs.png
17 This section presents some examples on using the ADAO module in SALOME. The
18 first one shows how to build a simple data assimilation case defining
19 explicitly all the required data through the GUI. The second one shows, on the
20 same case, how to define data using external sources through scripts.
22 Building a simple estimation case with explicit data definition
23 ---------------------------------------------------------------
25 This simple example is a demonstration one, and describes how to set a BLUE
26 estimation framework in order to get *weighted least square estimated state* of
27 a system from an observation of the state and from an *a priori* knowledge (or
28 background) of this state. In other words, we look for the weighted middle
29 between the observation and the background vectors. All the numerical values of
30 this example are arbitrary.
35 We choose to operate in a 3-dimensional space. 3D is chosen in order to restrict
36 the size of numerical object to explicitly enter by the user, but the problem is
37 not dependant of the dimension and can be set in dimension 1000... The
38 observation :math:`\mathbf{y}^o` is of value 1 in each direction, so:
42 The background state :math:`\mathbf{x}^b`, which represent some *a priori*
43 knowledge or a regularization, is of value of 0 in each direction, which is:
47 Data assimilation requires information on errors covariances :math:`\mathbf{R}`
48 and :math:`\mathbf{B}` respectively for observation and background variables. We
49 choose here to have uncorrelated errors (that is, diagonal matrices) and to have
50 the same variance of 1 for all variables (that is, identity matrices). We get:
52 ``B = R = [1 0 0 ; 0 1 0 ; 0 0 1]``
54 Last, we need an observation operator :math:`\mathbf{H}` to convert the
55 background value in the space of observation value. Here, because the space
56 dimensions are the same, we can choose the identity as the observation
59 ``H = [1 0 0 ; 0 1 0 ; 0 0 1]``
61 With such choices, the Best Linear Unbiased Estimator (BLUE) will be the average
62 vector between :math:`\mathbf{y}^o` and :math:`\mathbf{x}^b`, named the
63 *analysis* and denoted by :math:`\mathbf{x}^a`:
65 ``Xa = [0.5 0.5 0.5]``
67 As en extension of this example, one can change the variances for
68 :math:`\mathbf{B}` or :math:`\mathbf{R}` independently, and the analysis will
69 move to :math:`\mathbf{y}^o` or to :math:`\mathbf{x}^b` in inverse proportion of
70 the variances in :math:`\mathbf{B}` and :math:`\mathbf{R}`. It is also
71 equivalent to search for the analysis thought a BLUE algorithm or a 3DVAR one.
73 Using the GUI to build the ADAO case
74 ++++++++++++++++++++++++++++++++++++
76 First, you have to activate the ADAO module by choosing the appropriate module
77 button or menu of SALOME, and you will see:
80 .. image:: images/adao_activate.png
84 **Activating the module ADAO in SALOME**
86 Choose the "*New*" button in this window. You will directly get the EFICAS
87 interface for variables definition, along with the "*Object browser*". You can
88 then click on the "*New*" button |eficas_new| to create a new ADAO case, and you
92 .. image:: images/adao_viewer.png
96 **The EFICAS viewer for cases definition in module ADAO**
98 Then fill in the variables to build the ADAO case by using the experimental set
99 up described above. All the technical information given above will be directly
100 inserted in the ADAO case definition, by using the *String* type for all the
101 variables. When the case definition is ready, save it to a "*JDC (\*.comm)*"
102 native file somewhere in your path. Remember that other files will be also
103 created near this first one, so it is better to make a specific directory for
104 your case, and to save the file inside. The name of the file will appear in the
105 "*Object browser*" window, under the "*ADAO*" menu. The final case definition
108 .. _adao_jdcexample01:
109 .. image:: images/adao_jdcexample01.png
113 **Definition of the experimental set up chosen for the ADAO case**
115 To go further, we need now to generate the YACS scheme from the ADAO case
116 definition. In order to do that, right click on the name of the file case in the
117 "*Object browser*" window, and choose the "*Export to YACS*" sub-menu (or the
118 "*Export to YACS*" button |eficas_yacs|) as below:
120 .. _adao_exporttoyacs:
121 .. image:: images/adao_exporttoyacs.png
125 **"Export to YACS" sub-menu to generate the YACS scheme from the ADAO case**
127 This command will generate the YACS scheme, activate YACS module in SALOME, and
128 open the new scheme in the GUI of the YACS module [#]_. After reordering the
129 nodes by using the "*arrange local node*" sub-menu of the YACS graphical view of
130 the scheme, you get the following representation of the generated ADAO scheme:
132 .. _yacs_generatedscheme:
133 .. image:: images/yacs_generatedscheme.png
137 **YACS generated scheme from the ADAO case**
139 After that point, all the modifications, executions and post-processing of the
140 data assimilation scheme will be done in YACS. In order to check the result in a
141 simple way, we create here a new YACS node by using the "*in-line script node*"
142 sub-menu of the YACS graphical view, and we name it "*PostProcessing*".
144 This script will retrieve the data assimilation analysis from the
145 "*algoResults*" output port of the computation bloc (which gives access to a
146 SALOME Python Object), and will print it on the standard output.
148 To obtain this, the in-line script node need to have an input port of type
149 "*pyobj*" named "*results*" for example, that have to be linked graphically to
150 the "*algoResults*" output port of the computation bloc. Then the code to fill
151 in the script node is::
153 Xa = results.ADD.get("Analysis").valueserie(-1)
156 print "Analysis =",Xa
159 The augmented YACS scheme can be saved (overwriting the generated scheme if the
160 simple "*Save*" command or button are used, or with a new name). Then,
161 classically in YACS, it have to be prepared for run, and then executed. After
162 completion, the printing on standard output is available in the "*YACS Container
163 Log*", obtained through the right click menu of the "*proc*" window in the YACS
164 scheme as shown below:
166 .. _yacs_containerlog:
167 .. image:: images/yacs_containerlog.png
171 **YACS menu for Container Log, and dialog window showing the log**
173 We verify that the result is correct by checking that the log dialog window
174 contains the following line::
176 Analysis = [0.5, 0.5, 0.5]
178 as shown in the image above.
180 As a simple extension of this example, one can notice that the same problem
181 solved with a 3DVAR algorithm gives the same result. This algorithm can be
182 chosen at the ADAO case building step, before entering in YACS step. The
183 ADAO 3DVAR case will look completely similar to the BLUE algorithmic case, as
184 shown by the following figure:
186 .. _adao_jdcexample02:
187 .. image:: images/adao_jdcexample02.png
191 **Defining an ADAO 3DVAR case looks completely similar to a BLUE case**
193 There is only one command changing, with "*3DVAR*" value instead of "*Blue*".
195 Building a simple estimation case with external data definition by scripts
196 --------------------------------------------------------------------------
198 It is useful to get parts or all of the data from external definition, using
199 Python script files to provide access to the data. As an example, we build here
200 an ADAO case representing the same experimental set up as in the above example
201 `Building a simple estimation case with explicit data definition`_, but using
202 data form a single one external Python script file.
204 First, we write the following script file, using conventional names for the
205 desired variables. Here, all the input variables are defined in the script, but
206 the user can choose to split the file in several ones, or to mix explicit data
207 definition in the ADAO GUI and implicit data definition by external files. The
208 present script looks like::
212 # Definition of the Background as a vector
213 # ----------------------------------------
214 Background = [0, 0, 0]
216 # Definition of the Observation as a vector
217 # -----------------------------------------
218 Observation = "1 1 1"
220 # Definition of the Background Error covariance as a matrix
221 # ---------------------------------------------------------
222 BackgroundError = numpy.array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]])
224 # Definition of the Observation Error covariance as a matrix
225 # ----------------------------------------------------------
226 ObservationError = numpy.matrix("1 0 0 ; 0 1 0 ; 0 0 1")
228 # Definition of the Observation Operator as a matrix
229 # --------------------------------------------------
230 ObservationOperator = numpy.identity(3)
232 The names of the Python variables above are mandatory, in order to define the
233 right variables, but the Python script can be bigger and define classes,
234 functions, etc. with other names. It shows different ways to define arrays and
235 matrices, using list, string (as in Numpy or Octave), Numpy array type or Numpy
236 matrix type, and Numpy special functions. All of these syntaxes are valid.
238 After saving this script somewhere in your path (named here "*script.py*" for
239 the example), we use the GUI to build the ADAO case. The procedure to fill in
240 the case is similar except that, instead of selecting the "*String*" option for
241 the "*FROM*" keyword, we select the "*Script*" one. This leads to a
242 "*SCRIPT_DATA/SCRIPT_FILE*" entry in the tree, allowing to choose a file as:
244 .. _adao_scriptentry01:
245 .. image:: images/adao_scriptentry01.png
249 **Defining an input value using an external script file**
251 Other steps and results are exactly the same as in the `Building a simple
252 estimation case with explicit data definition`_ previous example.
254 In fact, this script methodology allows to retrieve data from in-line or previous
255 calculations, from static files, from database or from stream, all of them
256 outside of SALOME. It allows also to modify easily some input data, for example
257 for debug purpose or for repetitive execution process, and it is the most
258 versatile method in order to parametrize the input data. **But be careful,
259 script methodology is not a "safe" procedure, in the sense that erroneous
260 data, or errors in calculations, can be directly injected into the YACS scheme
263 Adding parameters to control the data assimilation algorithm
264 ------------------------------------------------------------
266 One can add some optional parameters to control the data assimilation algorithm
267 calculation. This is done by using the "*AlgorithmParameters*" keyword in the
268 definition of the ADAO case, which is an keyword of the ASSIMILATION_STUDY. This
269 keyword requires a Python dictionary, containing some key/value pairs.
271 For example, with a 3DVAR algorithm, the possible keys are "*Minimizer*",
272 "*MaximumNumberOfSteps*", "*ProjectedGradientTolerance*",
273 "*GradientNormTolerance*" and "*Bounds*":
275 #. The "*Minimizer*" key allows to choose the optimization minimizer. The
276 default choice is "LBFGSB", and the possible ones are "LBFGSB" (nonlinear
277 constrained minimizer, see [Byrd95] and [Zhu97]), "TNC" (nonlinear
278 constrained minimizer), "CG" (nonlinear unconstrained minimizer), "BFGS"
279 (nonlinear unconstrained minimizer), "NCG" (Newton CG minimizer).
280 #. The "*MaximumNumberOfSteps*" key indicates the maximum number of iterations
281 allowed for iterative optimization. The default is 15000, which very
282 similar of no limit on iterations. It is then recommended to adapt this
283 parameter to the needs on real problems.
284 #. The "*ProjectedGradientTolerance*" key indicates a limit value, leading to
285 stop successfully the iterative optimization process when all the
286 components of the projected gradient are under this limit.
287 #. The "*GradientNormTolerance*" key indicates a limit value, leading to stop
288 successfully the iterative optimization process when the norm of the
289 gradient is under this limit.
290 #. The "*Bounds*" key allows to define upper and lower bounds for every
291 control variable being optimized. Bounds can be given by a list of list of
292 pairs of lower/upper bounds for each variable, with possibly ``None`` every
293 time there is no bound. The bounds can always be specified, but they are
294 taken into account only by the constrained minimizers.
296 If no bounds at all are required on the control variables, then one can choose
297 the "BFGS" or "CG" minimisation algorithm for the 3DVAR algorithm. For
298 constrained optimization, the minimizer "LBFGSB" is often more robust, but the
299 "TNC" is always more performant.
301 This dictionary has to be defined, for example, in an external Python script
302 file, using the mandatory variable name "*AlgorithmParameters*" for the
303 dictionary. All the keys inside the dictionary are optional, they all have
304 default values, and can exist without being used. For example::
306 AlgorithmParameters = {
307 "Minimizer" : "CG", # Possible choice : "LBFGSB", "TNC", "CG", "BFGS"
308 "MaximumNumberOfSteps" : 10,
311 Then the script can be added to the ADAO case, in a file entry describing the
312 "*AlgorithmParameters*" keyword, as follows:
314 .. _adao_scriptentry02:
315 .. image:: images/adao_scriptentry02.png
319 **Adding parameters to control the algorithm**
321 Other steps and results are exactly the same as in the `Building a simple
322 estimation case with explicit data definition`_ previous example. The dictionary
323 can also be directly given in the input field associated with the keyword.
325 Building a complex case with external data definition by scripts
326 ----------------------------------------------------------------
328 This more complex and complete example has to been considered as a framework for
329 user inputs, that need to be tailored for each real application. Nevertheless,
330 the file skeletons are sufficiently general to have been used for various
331 applications in neutronic, fluid mechanics... Here, we will not focus on the
332 results, but more on the user control of inputs and outputs in an ADAO case. As
333 previously, all the numerical values of this example are arbitrary.
335 The objective is to set up the input and output definitions of a physical case
336 by external python scripts, using a general non-linear operator, adding control
337 on parameters and so on... The complete framework scripts can be found in the
338 ADAO skeletons examples directory under the name
339 "*External_data_definition_by_scripts*".
344 We continue to operate in a 3-dimensional space, in order to restrict
345 the size of numerical object shown in the scripts, but the problem is
346 not dependant of the dimension.
348 We choose a twin experiment context, using a known true state
349 :math:`\mathbf{x}^t` of arbitrary values:
353 The background state :math:`\mathbf{x}^b`, which represent some *a priori*
354 knowledge of the true state, is build as a normal random perturbation of 20% the
355 true state :math:`\mathbf{x}^t` for each component, which is:
357 ``Xb = Xt + normal(0, 20%*Xt)``
359 To describe the background error covariances matrix :math:`\mathbf{B}`, we make
360 as previously the hypothesis of uncorrelated errors (that is, a diagonal matrix,
361 of size 3x3 because :math:`\mathbf{x}^b` is of lenght 3) and to have the same
362 variance of 0.1 for all variables. We get:
364 ``B = 0.1 * diagonal( lenght(Xb) )``
366 We suppose that there exist an observation operator :math:`\mathbf{H}`, which
367 can be non linear. In real calibration procedure or inverse problems, the
368 physical simulation codes are embedded in the observation operator. We need also
369 to know its gradient with respect to each calibrated variable, which is a rarely
370 known information with industrial codes. But we will see later how to obtain an
371 approximated gradient in this case.
373 Being in twin experiments, the observation :math:`\mathbf{y}^o` and its error
374 covariances matrix :math:`\mathbf{R}` are generated by using the true state
375 :math:`\mathbf{x}^t` and the observation operator :math:`\mathbf{H}`:
379 and, with an arbitrary standard deviation of 1% on each error component:
381 ``R = 0.0001 * diagonal( lenght(Yo) )``
383 All the required data assimilation informations are then defined.
385 Skeletons of the scripts describing the setup
386 +++++++++++++++++++++++++++++++++++++++++++++
388 We give here the essential parts of each script used afterwards to build the ADAO
389 case. Remember that using these scripts in real Python files requires to
390 correctly define the path to imported modules or codes (even if the module is in
391 the same directory that the importing Python file ; we indicate the path
392 adjustment using the mention ``"# INSERT PHYSICAL SCRIPT PATH"``), the encoding
393 if necessary, etc. The indicated file names for the following scripts are
394 arbitrary. Examples of complete file scripts are available in the ADAO examples
397 We first define the true state :math:`\mathbf{x}^t` and some convenient matrix
398 building function, in a Python script file named
399 ``Physical_data_and_covariance_matrices.py``::
405 Arbitrary values and names, as a tuple of two series of same length
407 return (numpy.array([1, 2, 3]), ['Para1', 'Para2', 'Para3'])
409 def Simple_Matrix( size, diagonal=None ):
411 Diagonal matrix, with either 1 or a given vector on the diagonal
413 if diagonal is not None:
414 S = numpy.diag( diagonal )
416 S = numpy.matrix(numpy.identity(int(size)))
419 We can then define the background state :math:`\mathbf{x}^b` as a random
420 perturbation of the true state, adding at the end of the script the definition
421 of a *required ADAO variable* in order to export the defined value. It is done
422 in a Python script file named ``Script_Background_xb.py``::
424 from Physical_data_and_covariance_matrices import True_state
427 xt, names = True_state()
429 Standard_deviation = 0.2*xt # 20% for each variable
431 xb = xt + abs(numpy.random.normal(0.,Standard_deviation,size=(len(xt),)))
433 # Creating the required ADAO variable
434 # -----------------------------------
435 Background = list(xb)
437 In the same way, we define the background error covariance matrix
438 :math:`\mathbf{B}` as a diagonal matrix of the same diagonal length as the
439 background of the true state, using the convenient function already defined. It
440 is done in a Python script file named ``Script_BackgroundError_B.py``::
442 from Physical_data_and_covariance_matrices import True_state, Simple_Matrix
444 xt, names = True_state()
446 B = 0.1 * Simple_Matrix( size = len(xt) )
448 # Creating the required ADAO variable
449 # -----------------------------------
452 To continue, we need the observation operator :math:`\mathbf{H}` as a function
453 of the state. It is here defined in an external file named
454 ``"Physical_simulation_functions.py"``, which should contain functions
455 conveniently named here ``"FunctionH"`` and ``"AdjointH"``. These functions are
456 user ones, representing as programming functions the :math:`\mathbf{H}` operator
457 and its adjoint. We suppose these functions are given by the user. A simple
458 skeleton is given in the Python script file ``Physical_simulation_functions.py``
459 of the ADAO examples standard directory. It can be used in the case only the
460 non-linear direct physical simulation exists. The script is partly reproduced
461 here for convenience::
464 """ Direct non-linear simulation operator """
466 # --------------------------------------> EXAMPLE TO BE REMOVED
467 if type(XX) is type(numpy.matrix([])): # EXAMPLE TO BE REMOVED
468 HX = XX.A1.tolist() # EXAMPLE TO BE REMOVED
469 elif type(XX) is type(numpy.array([])): # EXAMPLE TO BE REMOVED
470 HX = numpy.matrix(XX).A1.tolist() # EXAMPLE TO BE REMOVED
471 else: # EXAMPLE TO BE REMOVED
472 HX = XX # EXAMPLE TO BE REMOVED
473 # --------------------------------------> EXAMPLE TO BE REMOVED
475 return numpy.array( HX )
477 def TangentH( X, increment = 0.01, centeredDF = False ):
478 """ Tangent operator (Jacobian) calculated by finite differences """
480 dX = increment * X.A1
485 for i in range( len(dX) ):
487 X_plus_dXi[i] = X[i] + dX[i]
489 X_moins_dXi[i] = X[i] - dX[i]
491 HX_plus_dXi = FunctionH( X_plus_dXi )
492 HX_moins_dXi = FunctionH( X_moins_dXi )
494 HX_Diff = ( HX_plus_dXi - HX_moins_dXi ) / (2.*dX[i])
496 Jacobian.append( HX_Diff )
501 for i in range( len(dX) ):
503 X_plus_dXi[i] = X[i] + dX[i]
505 HX_plus_dXi = FunctionH( X_plus_dXi )
507 HX_plus_dX.append( HX_plus_dXi )
512 for i in range( len(dX) ):
513 Jacobian.append( ( HX_plus_dX[i] - HX ) / dX[i] )
515 Jacobian = numpy.matrix( Jacobian )
519 def AdjointH( (X, Y) ):
520 """ Ajoint operator """
522 Jacobian = TangentH( X, centeredDF = False )
524 Y = numpy.asmatrix(Y).flatten().T
525 HtY = numpy.dot(Jacobian, Y)
529 We insist on the fact that these non-linear operator ``"FunctionH"``, tangent
530 operator ``"TangentH"`` and adjoint operator ``"AdjointH"`` come from the
531 physical knowledge, include the reference physical simulation code and its
532 eventual adjoint, and have to be carefully set up by the data assimilation user.
533 The errors in or missuses of the operators can not be detected or corrected by
534 the data assimilation framework alone.
536 To operates in the module ADAO, it is required to define for ADAO these
537 different types of operators: the (potentially non-linear) standard observation
538 operator, named ``"Direct"``, its linearised approximation, named ``"Tangent"``,
539 and the adjoint operator named ``"Adjoint"``. The Python script have to retrieve
540 an input parameter, found under the key "value", in a variable named
541 ``"specificParameters"`` of the SALOME input data and parameters
542 ``"computation"`` dictionary variable. If the operator is already linear, the
543 ``"Direct"`` and ``"Tangent"`` functions are the same, as it is supposed here.
544 The following example Python script file named
545 ``Script_ObservationOperator_H.py``, illustrates the case::
547 import Physical_simulation_functions
548 import numpy, logging
550 # -----------------------------------------------------------------------
551 # SALOME input data and parameters: all information are the required input
552 # variable "computation", containing for example:
553 # {'inputValues': [[[[0.0, 0.0, 0.0]]]],
554 # 'inputVarList': ['adao_default'],
555 # 'outputVarList': ['adao_default'],
556 # 'specificParameters': [{'name': 'method', 'value': 'Direct'}]}
557 # -----------------------------------------------------------------------
559 # Recovering the type of computation: "Direct", "Tangent" or "Adjoint"
560 # --------------------------------------------------------------------
562 for param in computation["specificParameters"]:
563 if param["name"] == "method":
564 method = param["value"]
565 logging.info("ComputationFunctionNode: Found method is \'%s\'"%method)
567 # Loading the H operator functions from external definitions
568 # ----------------------------------------------------------
569 logging.info("ComputationFunctionNode: Loading operator functions")
570 FunctionH = Physical_simulation_functions.FunctionH
571 AdjointH = Physical_simulation_functions.AdjointH
573 # Executing the possible computations
574 # -----------------------------------
575 if method == "Direct":
576 logging.info("ComputationFunctionNode: Direct computation")
577 Xcurrent = computation["inputValues"][0][0][0]
578 data = FunctionH(numpy.matrix( Xcurrent ).T)
580 if method == "Tangent":
581 logging.info("ComputationFunctionNode: Tangent computation")
582 Xcurrent = computation["inputValues"][0][0][0]
583 data = FunctionH(numpy.matrix( Xcurrent ).T)
585 if method == "Adjoint":
586 logging.info("ComputationFunctionNode: Adjoint computation")
587 Xcurrent = computation["inputValues"][0][0][0]
588 Ycurrent = computation["inputValues"][0][0][1]
589 data = AdjointH((numpy.matrix( Xcurrent ).T, numpy.matrix( Ycurrent ).T))
591 # Formatting the output
592 # ---------------------
593 logging.info("ComputationFunctionNode: Formatting the output")
595 outputValues = [[[[]]]]
597 outputValues[0][0][0].append(val)
599 # Creating the required ADAO variable
600 # -----------------------------------
602 result["outputValues"] = outputValues
603 result["specificOutputInfos"] = []
604 result["returnCode"] = 0
605 result["errorMessage"] = ""
607 As output, this script has to define a nested list variable, as shown above with
608 the ``"outputValues"`` variable, where the nested levels describe the different
609 variables included in the state, then the different possible states at the same
610 time, then the different time steps. In this case, because there is only one
611 time step and one state, and all the variables are stored together, we only set
612 the most inner level of the lists.
614 In this twin experiments framework, the observation :math:`\mathbf{y}^o` and its
615 error covariances matrix :math:`\mathbf{R}` can be generated. It is done in two
616 Python script files, the first one being named ``Script_Observation_yo.py``::
618 from Physical_data_and_covariance_matrices import True_state
619 from Physical_simulation_functions import FunctionH
621 xt, noms = True_state()
625 # Creating the required ADAO variable
626 # -----------------------------------
627 Observation = list(yo)
629 and the second one named ``Script_ObservationError_R.py``::
631 from Physical_data_and_covariance_matrices import True_state, Simple_Matrix
632 from Physical_simulation_functions import FunctionH
634 xt, names = True_state()
638 R = 0.0001 * Simple_Matrix( size = len(yo) )
640 # Creating the required ADAO variable
641 # -----------------------------------
644 As in previous examples, it can be useful to define some parameters for the data
645 assimilation algorithm. For example, if we use the standard 3DVAR algorithm, the
646 following parameters can be defined in a Python script file named
647 ``Script_AlgorithmParameters.py``::
649 # Creating the required ADAO variable
650 # -----------------------------------
651 AlgorithmParameters = {
652 "Minimizer" : "TNC", # Possible : "LBFGSB", "TNC", "CG", "BFGS"
653 "MaximumNumberOfSteps" : 15, # Number of global iterative steps
655 [ None, None ], # Bound on the first parameter
656 [ 0., 4. ], # Bound on the second parameter
657 [ 0., None ], # Bound on the third parameter
661 Finally, it is common to post-process the results, retrieving them after the
662 data assimilation phase in order to analyse, print or show them. It requires to
663 use a intermediary Python script file in order to extract these results. The
664 following example Python script file named ``Script_UserPostAnalysis.py``,
665 illustrates the fact::
667 from Physical_data_and_covariance_matrices import True_state
670 xt, names = True_state()
671 xa = ADD.get("Analysis").valueserie(-1)
672 x_series = ADD.get("CurrentState").valueserie()
673 J = ADD.get("CostFunctionJ").valueserie()
675 # Verifying the results by printing
676 # ---------------------------------
679 print "xa = %s"%numpy.array(xa)
681 for i in range( len(x_series) ):
682 print "Step %2i : J = %.5e et X = %s"%(i, J[i], x_series[i])
685 At the end, we get a description of the whole case setup through a set of files
688 #. ``Physical_data_and_covariance_matrices.py``
689 #. ``Physical_simulation_functions.py``
690 #. ``Script_AlgorithmParameters.py``
691 #. ``Script_BackgroundError_B.py``
692 #. ``Script_Background_xb.py``
693 #. ``Script_ObservationError_R.py``
694 #. ``Script_ObservationOperator_H.py``
695 #. ``Script_Observation_yo.py``
696 #. ``Script_UserPostAnalysis.py``
698 We insist here that all these scripts are written by the user and can not be
699 automatically tested. So the user is required to verify the scripts (and in
700 particular their input/output) in order to limit the difficulty of debug. We
701 recall: **script methodology is not a "safe" procedure, in the sense that
702 erroneous data, or errors in calculations, can be directly injected into the
703 YACS scheme execution.**
705 Building the case with external data definition by scripts
706 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
708 All these scripts can then be used to define the ADAO case with external data
709 definition by Python script files. It is entirely similar to the method
710 described in the `Building a simple estimation case with external data
711 definition by scripts`_ previous section. For each variable to be defined, we
712 select the "*Script*" option of the "*FROM*" keyword, which leads to a
713 "*SCRIPT_DATA/SCRIPT_FILE*" entry in the tree.
715 The other steps to build the ADAO case are exactly the same as in the `Building
716 a simple estimation case with explicit data definition`_ previous section.
718 Using the simple linear operator :math:`\mathbf{H}` from the Python script file
719 ``Physical_simulation_functions.py`` in the ADAO examples standard directory,
720 the results will look like::
723 xa = [ 1.000014 2.000458 3.000390]
725 Step 0 : J = 1.81750e+03 et X = [1.014011, 2.459175, 3.390462]
726 Step 1 : J = 1.81750e+03 et X = [1.014011, 2.459175, 3.390462]
727 Step 2 : J = 1.79734e+01 et X = [1.010771, 2.040342, 2.961378]
728 Step 3 : J = 1.79734e+01 et X = [1.010771, 2.040342, 2.961378]
729 Step 4 : J = 1.81909e+00 et X = [1.000826, 2.000352, 3.000487]
730 Step 5 : J = 1.81909e+00 et X = [1.000826, 2.000352, 3.000487]
731 Step 6 : J = 1.81641e+00 et X = [1.000247, 2.000651, 3.000156]
732 Step 7 : J = 1.81641e+00 et X = [1.000247, 2.000651, 3.000156]
733 Step 8 : J = 1.81569e+00 et X = [1.000015, 2.000432, 3.000364]
734 Step 9 : J = 1.81569e+00 et X = [1.000015, 2.000432, 3.000364]
735 Step 10 : J = 1.81568e+00 et X = [1.000013, 2.000458, 3.000390]
738 The state at the first step is the randomly generated background state
739 :math:`\mathbf{x}^b`. After completion, these printing on standard output is
740 available in the "*YACS Container Log*", obtained through the right click menu
741 of the "*proc*" window in the YACS scheme.
743 .. [#] For more information on YACS, see the the *YACS module User's Guide* available in the main "*Help*" menu of SALOME GUI.