Minimal model updating case

test-data/local/poly_example/POLY_EVAL

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+EXECUTABLE poly_eval.py

test-data/local/poly_example/README.md

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+## Polynomial curve fitting - A minimal model updating case
+A display of a truly minimal model updating case. It is done with a second
+degree polynomial as the _true reality_. The model is `ax^2 + bx + c` where
+`a`, `b` and `c` are the parameters.
+
+### Observed data
+The observed data was generated with the following _Python_ code:
+```
+def p(x):
+     return 0.5*x**2 + x + 3
+
+[(p(x)+random.gauss(0, 0.25*x**2+0.1), 0.25*x**2+0.1) for x in [0, 2, 4, 6, 8]]
+```
+
+This gives us observations (both a value and an uncertainty) for even `x` less
+than 10. These values appear in `poly_obs_data.txt`. Finally, these values are
+represented as an observation in `observations`. Here we give the data a name.
+And we specify that the values that should be used from the `forward_model` is only
+the even ones (the `forward model` spits out the image of the polynomial on the
+range `[0, 9]`). It also specifies that the time step to consider is `0`
+(`RESTART`). We do not really have a time concept in this setup and hence we
+only use `0` as a dummy value. We could of course have considered the values
+feed to the polynomial as time; but that is left as an exercise for the reader.
+
+### Parameters
+As mentioned above `a`, `b` and `c` forms the parameters of the model `ax^2 + bx + c`.
+They are all specified to be uniformly distributed over ranges in
+`coeff_priors` and are sampled by `GEN_KW` and dumped to the forward model
+following the `json`-template in `coeff.tmpl`.
+
+### Forward model
+After the parameters are dumped to the runpath, _forward model_'s are launched
+for each of the realizations. The forward model consists of a single script
+described in `poly_eval.py`, that loads the dumped parameters and outputs the
+values of the polynomial (given the parameters) for integer `x in [0, 10]` to the
+file `poly_0.out`.
+
+The very minimal job description file `POLY_EVAL` just points to the script.
+
+### Loading data
+The configuration specifies a `GEN_DATA` that expects there to be a result file
+`poly_%d.out` for report step `0`. In other words it expects to load data from
+`poly_0.out`, the exact file that the forward model produces.
+
+### Model update
+Then the loaded data is compared to the observed data and the parameters are
+updated accordingly.
+
+### Time
+Although we don't really have a clear concept of time in this case _ERT_
+expects us to have so. Since we have specified that all of our data is for time
+step `0`, we had to create an artificial time map `time_map` that specifies
+that the very first and only report step corresponds to `1/10/2006`. This could
+be any date, so we put it to the date of the first commit of the
+`ensembles/ert` repository on _Github_.

test-data/local/poly_example/coeff.tmpl

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+{
+  "a": <COEFF_A>,
+  "b": <COEFF_B>,
+  "c": <COEFF_C>
+}

test-data/local/poly_example/coeff_priors

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+COEFF_A UNIFORM 0 1
+COEFF_B UNIFORM 0 2
+COEFF_C UNIFORM 0 5

test-data/local/poly_example/observations

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+GENERAL_OBSERVATION POLY_OBS {
+   DATA       = POLY_RES;
+   INDEX_LIST = 0,2,4,6,8;
+   RESTART    = 0;
+   OBS_FILE   = poly_obs_data.txt;
+};

test-data/local/poly_example/poly.ert

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+JOBNAME poly_%d
+
+QUEUE_SYSTEM LOCAL
+QUEUE_OPTION LOCAL MAX_RUNNING 50
+
+RUNPATH poly_out/real_%d/iter_%d
+
+OBS_CONFIG observations
+TIME_MAP time_map
+
+NUM_REALIZATIONS 100
+
+GEN_KW COEFFS coeff.tmpl coeffs.json coeff_priors
+GEN_DATA POLY_RES RESULT_FILE:poly_%d.out REPORT_STEPS:0 INPUT_FORMAT:ASCII
+
+INSTALL_JOB poly_eval POLY_EVAL
+SIMULATION_JOB poly_eval

test-data/local/poly_example/poly_eval.py

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+#!/usr/bin/env python
+
+import json
+
+def _load_coeffs(filename):
+    with open(filename) as f:
+        return json.load(f)
+
+def _evaluate(coeffs, x):
+    return coeffs['a']*x**2 + coeffs['b']*x + coeffs['c']
+
+if __name__ == '__main__':
+    coeffs = _load_coeffs('coeffs.json')
+    output = [_evaluate(coeffs, x) for x in range(10)]
+    with open('poly_0.out', 'w') as f:
+        f.write('\n'.join(map(str, output)))

test-data/local/poly_example/poly_obs_data.txt

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+2.8532509308 0.1
+7.20311703432 1.1
+21.3864899107 4.1
+31.5145559347 9.1
+53.5676660405 16.1

test-data/local/poly_example/time_map

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+1/10/2006