Estimate steady heterogeneous parameters

Here we demonstrate how to estimate parameters of heterogeneity, namely mean, variance and correlation length of log-transmissivity, with the aid the the extended Thiem solution in 2D.

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Out:

Initializing the  Shuffled Complex Evolution (SCE-UA) algorithm  with  5000  repetitions
The objective function will be minimized
Starting burn-in sampling...
Initialize database...
['csv', 'hdf5', 'ram', 'sql', 'custom', 'noData']
* Database file '/home/docs/checkouts/readthedocs.org/user_builds/welltestpy/checkouts/v1.0.3/examples/Est_steady_het/2021-02-18_17-00-53_db.csv' created.
Burn-in sampling completed...
Starting Complex Evolution...
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*** OPTIMIZATION SEARCH TERMINATED BECAUSE THE LIMIT
ON THE MAXIMUM NUMBER OF TRIALS
5000
HAS BEEN EXCEEDED.
SEARCH WAS STOPPED AT TRIAL NUMBER: 5109
NUMBER OF DISCARDED TRIALS: 42
NORMALIZED GEOMETRIC RANGE = 0.013639
THE BEST POINT HAS IMPROVED IN LAST 100 LOOPS BY 100000.000000 PERCENT

*** Final SPOTPY summary ***
Total Duration: 0.97 seconds
Total Repetitions: 5109
Minimal objective value: 0.000151716
Corresponding parameter setting:
mu: -9.18609
var: 0.0484952
len_scale: 42.1287
******************************

Best parameter set:
mu=-9.186761848511011, var=0.04715748703394454, len_scale=41.45292299149325
/home/docs/.pyenv/versions/3.7.9/lib/python3.7/site-packages/numpy/core/_asarray.py:136: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray
  return array(a, dtype, copy=False, order=order, subok=True)
Initializing the  Fourier Amplitude Sensitivity Test (FAST)  with  1158  repetitions
Starting the FAST algotrithm with 1158 repetitions...
Creating FAST Matrix
Initialize database...
['csv', 'hdf5', 'ram', 'sql', 'custom', 'noData']
* Database file '/home/docs/checkouts/readthedocs.org/user_builds/welltestpy/checkouts/v1.0.3/examples/Est_steady_het/2021-02-18_17-00-57_sensitivity_db.csv' created.

*** Final SPOTPY summary ***
Total Duration: 0.22 seconds
Total Repetitions: 1158
Minimal objective value: 16.6143
Corresponding parameter setting:
mu: -6.23099
var: 5.98156
len_scale: 39.9276
Maximal objective value: 1.88561e+08
Corresponding parameter setting:
mu: -15.8922
var: 9.01653
len_scale: 17.8871
******************************

1158
Parameter First Total
mu 0.450328 0.888768
var 0.085536 0.598273
len_scale 0.000183 0.015598
1158

import welltestpy as wtp

campaign = wtp.load_campaign("Cmp_UFZ-campaign.cmp")
estimation = wtp.estimate.ExtThiem2D("Est_steady_het", campaign, generate=True)
estimation.run()
estimation.sensitivity()