:start-after: UG_MEDCouplingFieldDouble_8
:end-before: UG_MEDCouplingFieldDouble_8
+Iterative statistics on fields
+------------------------------
+
+Statistical moments accross several *field* instances can be computed without having to store all fields in memory.
+The mean, standard-deviation, variance, and the variance-covariance matrix of field components
+on each field tuple can be computed by calling
+
+.. literalinclude:: ../../../src/Stat/Test/TestMEDCouplingIterativeStatistics.py
+ :start-after: UG_MEDCouplingIterativeStatistics_1
+ :end-before: UG_MEDCouplingIterativeStatistics_1
+
+In a similar fashion Sobol indices from *field* instances can be computed without having to store all fields in memory.
+The parameters of the fields must be sampled in a *pick-freeze* manner and the fields must be generated
+on the fly according to these generated parameters combinations.
+
+.. literalinclude:: ../../../src/Stat/Test/TestMEDCouplingIterativeStatistics.py
+ :start-after: UG_MEDCouplingIterativeStatistics_2
+ :end-before: UG_MEDCouplingIterativeStatistics_2
+
IF(MEDCOUPLING_ENABLE_PYTHON)
ADD_SUBDIRECTORY(MEDCoupling_Swig)
+
+ find_package(SalomeBasicIterativeStatistics)
+ if( BASICITERATIVESTATISTICS_FOUND )
+ add_subdirectory(Stat)
+ endif( BASICITERATIVESTATISTICS_FOUND )
+
ADD_SUBDIRECTORY(PyWrapping)
+
ENDIF(MEDCOUPLING_ENABLE_PYTHON)
IF(NOT MEDCOUPLING_MICROMED)
SUBDIRS(MEDPartitioner_Swig)
SUBDIRS(RENUMBER_Swig)
SUBDIRS(PyWrapping)
+SUBDIRS(Stat)
IF(WIN32 OR CYGWIN)
SWIG_LINK_LIBRARIES(${MEDCouling_target_name} ${PYTHON_LIBRARIES} ${PLATFORM_LIBS} medcouplingcpp)
-ELSE(WIN32)
+ELSE(WIN32 OR CYGWIN)
# ${PYTHON_LIBRARIES} not needed see https://www.python.org/dev/peps/pep-0513/#libpythonx-y-so-1
SWIG_LINK_LIBRARIES(${MEDCouling_target_name} ${PLATFORM_LIBS} medcouplingcpp)
-ENDIF(WIN32)
+ENDIF(WIN32 OR CYGWIN)
# ${PYTHON_LIBRARIES} not needed
SWIG_CHECK_GENERATION(${MEDCouling_target_name})
SET_SOURCE_FILES_PROPERTIES(MEDCouplingRemapper.i PROPERTIES CPLUSPLUS ON)
IF(WIN32 OR CYGWIN)
SWIG_LINK_LIBRARIES(MEDCouplingRemapper ${PYTHON_LIBRARIES} medcouplingremapper)
-ELSE(WIN32)
+ELSE(WIN32 OR CYGWIN)
# ${PYTHON_LIBRARIES} not needed see https://www.python.org/dev/peps/pep-0513/#libpythonx-y-so-1
SWIG_LINK_LIBRARIES(MEDCouplingRemapper medcouplingremapper)
-ENDIF(WIN32)
+ENDIF(WIN32 OR CYGWIN)
IF(WIN32)
SET_TARGET_PROPERTIES(_MEDCouplingRemapper PROPERTIES DEBUG_OUTPUT_NAME _MEDCouplingRemapper_d)
ELSE(WIN32)
# ${PYTHON_LIBRARIES} not needed see https://www.python.org/dev/peps/pep-0513/#libpythonx-y-so-1
SET(medcoupling_LIB_dependancies ${PLATFORM_LIBS} medcouplingremapper medicoco)
-ENDIF(WIN32)
+ENDIF(WIN32 OR CYGWIN)
IF(NOT MEDCOUPLING_MICROMED)
LIST(APPEND SWIG_MODULE_medcoupling_EXTRA_FLAGS -DWITH_MED_FILE)
LIST(APPEND medcoupling_LIB_dependancies paramedmem)
ENDIF(MEDCOUPLING_USE_MPI)
+if(BASICITERATIVESTATISTICS_FOUND)
+ LIST(APPEND SWIG_MODULE_medcoupling_EXTRA_FLAGS -DWITH_ITERATIVE_STATISTICS)
+endif(BASICITERATIVESTATISTICS_FOUND)
+
IF(${CMAKE_VERSION} VERSION_LESS "3.8.0")
SWIG_ADD_MODULE(medcoupling python medcoupling.i)
ELSE()
static const char RENUM_EXT[]="Renumberer";
static const char PART_EXT[]="Partitioner";
static const char PAR_INTERPOL_EXT[]="Parallel interpolator (SPMD paradigm)";
+ static const char IT_STATS_EXT[] = "Iterative statistics";
- static const char *EXTENSIONS[]={SEQ_INTERPOL_EXT,MEDFILEIO_EXT,RENUM_EXT,PART_EXT,PAR_INTERPOL_EXT};
+ static const char *EXTENSIONS[]={SEQ_INTERPOL_EXT,MEDFILEIO_EXT,RENUM_EXT,PART_EXT,PAR_INTERPOL_EXT,IT_STATS_EXT};
static const int NB_OF_EXTENSIONS=sizeof(EXTENSIONS)/sizeof(const char *);
%}
#endif
#ifdef WITH_PARALLEL_INTERPOLATOR
ret.push_back(std::string(PAR_INTERPOL_EXT));
+#endif
+#ifdef WITH_ITERATIVE_STATISTICS
+ ret.push_back(std::string(IT_STATS_EXT));
#endif
return ret;
}
--- /dev/null
+# Copyright (C) 2024 CEA, EDF
+#
+# 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.
+#
+# This library is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+# Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public
+# License along with this library; if not, write to the Free Software
+# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+#
+# See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
+#
+
+install(FILES MEDCouplingIterativeStatistics.py DESTINATION ${MEDCOUPLING_INSTALL_PYTHON})
+
+if (MEDCOUPLING_BUILD_PY_TESTS)
+ add_subdirectory(Test)
+endif ()
+
--- /dev/null
+#! /usr/bin/env python3
+# -*- coding: utf-8 -*-
+# Copyright (C) 2021-2024 CEA, EDF
+#
+# 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.
+#
+# This library is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+# Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public
+# License along with this library; if not, write to the Free Software
+# 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 : Anthony GEAY (EDF R&D)
+
+from iterative_stats.iterative_mean import IterativeMean
+from iterative_stats.iterative_variance import IterativeVariance
+from iterative_stats.iterative_covariance import IterativeCovariance
+from iterative_stats.sensitivity.sensitivity_saltelli import IterativeSensitivitySaltelli
+
+import numpy as np
+try:
+ import openturns as ot
+ have_ot = True
+except ImportError:
+ have_ot = False
+
+
+class IterativeFieldMoments:
+ """
+ Compute statistics over fields.
+
+ Parameters
+ ----------
+ enable_mean : bool, optional
+ Whether to aggregate mean
+ Default is True
+ enable_variance : bool, optional
+ Whether to aggregate variance
+ Default is True
+ enable_covariance : bool, optional
+ Whether to aggregate covariance
+ Default is True
+ """
+
+ def __init__(self, enable_mean=True, enable_variance=True, enable_covariance=True):
+ self._dim = None
+ self._size = None
+ self._enable_mean = enable_mean
+ self._enable_variance = enable_variance
+ self._enable_covariance = enable_covariance
+
+ def increment(self, field):
+ """
+ Increment state.
+
+ Parameters
+ ----------
+ field : medcoupling.MEDCouplingFieldDouble
+ Field to compute statistics from
+ """
+ values = field.getArray()
+
+ if self._dim is None:
+ self._dim = values.getNumberOfComponents()
+ self._size = values.getNumberOfTuples()
+ if have_ot:
+ self._agg_mean = [ot.IterativeMoments(1, self._dim) for k in range(self._size)] if self._enable_mean else None
+ self._agg_variance = [ot.IterativeMoments(2, self._dim) for k in range(self._size)] if self._enable_variance else None
+ else:
+ self._agg_mean = [IterativeMean(dim=self._dim) for k in range(self._size)] if self._enable_mean else None
+ self._agg_variance = [IterativeVariance(dim=self._dim) for k in range(self._size)] if self._enable_variance else None
+
+ if self._enable_covariance:
+ n_tri = (self._dim * (self._dim + 1) // 2)
+ self._agg_covariance = [[IterativeCovariance(dim=1) for i in range(n_tri)] for k in range(self._size)]
+ else:
+ self._agg_covariance = None
+
+ if values.getNumberOfComponents() != self._dim:
+ raise ValueError(f"Incorrect number of components {values.getNumberOfComponents()} expected {self._dim}")
+ if values.getNumberOfTuples() != self._size:
+ raise ValueError(f"Incorrect number of tuples {values.getNumberOfTuples()} expected {self._size}")
+ for k in range(self._size):
+ tk = values.getTuple(k)
+ if self._enable_mean:
+ self._agg_mean[k].increment(tk)
+ if self._enable_variance:
+ self._agg_variance[k].increment(tk)
+ if self._enable_covariance:
+ for i in range(self._dim):
+ for j in range(i + 1):
+ self._agg_covariance[k][i * (i + 1) // 2 + j].increment(tk[i], tk[j])
+
+ def mean(self):
+ """
+ Mean.
+
+ Returns
+ -------
+ mean : numpy.array of shape (n, d)
+ Mean field
+ """
+ if self._agg_mean is None:
+ raise ValueError(f"No data aggregated")
+
+ mean = np.zeros((self._size, self._dim))
+ for i in range(self._size):
+ if have_ot:
+ mean[i] = self._agg_mean[i].getMean()
+ else:
+ mean[i] = self._agg_mean[i].get_stats()
+ return mean
+
+ def variance(self):
+ """
+ Variance.
+
+ Returns
+ -------
+ variance : numpy.array
+ Variance per component
+ """
+ if self._agg_variance is None:
+ raise ValueError(f"No data aggregated")
+
+ variance = np.zeros((self._size, self._dim))
+ for i in range(self._size):
+ if have_ot:
+ variance[i] = self._agg_variance[i].getVariance()
+ else:
+ variance[i] = self._agg_variance[i].get_stats()
+ return variance
+
+ def stddev(self):
+ """
+ Standard deviation.
+
+ Returns
+ -------
+ stddev : numpy.array of shape (n, d)
+ Standard deviation per component
+ """
+ return np.sqrt(self.variance())
+
+ def covariance(self):
+ """
+ Compute the variance-covariance matrix.
+
+ Returns
+ -------
+ cov : numpy.array of shape (n, d, d)
+ Variance-covariance matrix
+ """
+ if self._agg_covariance is None:
+ raise ValueError(f"No data aggregated")
+
+ covariance = np.zeros((self._size, self._dim, self._dim))
+ for k in range(self._size):
+ for i in range(self._dim):
+ for j in range(i + 1):
+ covij = self._agg_covariance[k][i * (i + 1) // 2 + j].get_stats()[0]
+ covariance[k, i, j] = covij
+ if i != j:
+ covariance[k, j, i] = covij
+ return covariance
+
+
+class IterativeFieldSobol:
+ """
+ Iterative Sobol indices.
+
+ Parameters
+ ----------
+ nb_params : int
+ Number of parameters of the field
+ """
+ def __init__(self, nb_parms: int):
+ if nb_parms < 2:
+ raise ValueError(f"Got {nb_parms} parameters, expected at least 2")
+ self._nb_parms = nb_parms
+ self._dim = None
+ self._size = None
+ self._agg_sobol = None
+
+ def increment(self, fields):
+ """
+ Update data.
+
+ Parameters
+ ----------
+ fields : List[medcoupling.MEDCouplingFieldDouble]
+ List of fields for each pick-freeze combination of the parameters
+ """
+
+ if len(fields) != self._nb_parms + 2:
+ raise ValueError(f"Got {len(fields)} fields, expected {self._nb_parms + 2}")
+ if self._dim == None:
+ self._dim = fields[0].getArray().getNumberOfComponents()
+ self._size = fields[0].getArray().getNumberOfTuples()
+ self._agg_sobol = [IterativeSensitivitySaltelli(self._nb_parms, dim=self._dim) for k in range(self._size)]
+
+ for k in range(self._size):
+ tks = np.array([field.getArray().getTuple(k) for field in fields])
+ self._agg_sobol[k].increment(tks.reshape((self._nb_parms + 2,)))
+
+ def indices(self, k):
+ """
+ Sobol indices accessor.
+
+ Parameters
+ ----------
+ k : int
+ Tuple index in the field
+
+ Returns
+ -------
+ first, total : np.array
+ First and total order Sobol' indices of shape (nb_parms, dim)
+ """
+ if self._agg_sobol is None:
+ raise ValueError("No data aggregated")
+ result = self._agg_sobol[k].getFirstOrderIndices(), self._agg_sobol[k].getTotalOrderIndices()
+ return result
--- /dev/null
+
+# Copyright (C) 2024 CEA, EDF
+#
+# 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.
+#
+# This library is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+# Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public
+# License along with this library; if not, write to the Free Software
+# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+#
+# See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
+#
+
+SALOME_ACCUMULATE_ENVIRONMENT(PYTHONPATH NOCHECK ${CMAKE_CURRENT_BINARY_DIR}/../../Stat)
+SALOME_GENERATE_TESTS_ENVIRONMENT(tests_env)
+
+set(TEST_INSTALL_DIRECTORY ${MEDCOUPLING_INSTALL_TESTS}/Stat)
+
+ADD_TEST(NAME MEDCouplingIterativeStatistics COMMAND ${PYTHON_EXECUTABLE} ${CMAKE_CURRENT_SOURCE_DIR}/TestMEDCouplingIterativeStatistics.py)
+SET_TESTS_PROPERTIES(MEDCouplingIterativeStatistics PROPERTIES ENVIRONMENT "${tests_env}")
+
+install(FILES TestMEDCouplingIterativeStatistics.py DESTINATION ${TEST_INSTALL_DIRECTORY})
+install(FILES CTestTestfileInstall.cmake DESTINATION ${TEST_INSTALL_DIRECTORY} RENAME CTestTestfile.cmake)
--- /dev/null
+# Copyright (C) 2024 CEA, EDF
+#
+# 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.
+#
+# This library is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+# Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public
+# License along with this library; if not, write to the Free Software
+# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+#
+# See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
+#
+
+SET(TEST_NAMES
+ TestMEDCouplingIterativeStatistics
+)
+
+SET(PYTHONPATH $ENV{PYTHONPATH})
+CMAKE_PATH(APPEND PYTHONPATH "../../bin")
+FOREACH(tfile ${TEST_NAMES})
+ SET(TEST_NAME ${COMPONENT_NAME}_${tfile})
+ ADD_TEST(${TEST_NAME} python3 ${tfile}.py)
+ SET(TEST_ENVIRONMENT)
+ SET_TESTS_PROPERTIES(${TEST_NAME} PROPERTIES
+ LABELS "${COMPONENT_NAME}"
+ TIMEOUT ${TIMEOUT}
+ ENVIRONMENT "${PYTHONPATH}"
+ )
+ENDFOREACH()
--- /dev/null
+#! /usr/bin/env python3
+# -*- coding: utf-8 -*-
+# Copyright (C) 2021-2024 CEA, EDF
+#
+# 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.
+#
+# This library is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+# Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public
+# License along with this library; if not, write to the Free Software
+# 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 : Anthony GEAY (EDF R&D)
+
+import medcoupling as mc
+from MEDCouplingIterativeStatistics import IterativeFieldMoments, IterativeFieldSobol
+from iterative_stats.experimental_design.experiment import AbstractExperiment
+from numpy.testing import assert_allclose
+import numpy as np
+import unittest
+
+
+class MEDCouplingIterativeStatisticsTest(unittest.TestCase):
+ def test1(self):
+ #! [UG_MEDCouplingIterativeStatistics_1]
+ # check moments on simple linear 3-d field defined on an 1-d mesh
+ import medcoupling as mc
+ from MEDCouplingIterativeStatistics import IterativeFieldMoments
+
+ # 1-d mesh
+ size = int(1e1)
+ coords = [i / size for i in range(size)]
+ arrX = mc.DataArrayDouble(coords, size, 1)
+ mesh = mc.MEDCouplingCMesh()
+ mesh.setCoords(arrX)
+
+ # compute statistics
+ istats = IterativeFieldMoments()
+
+ # aggregate 3-d fields
+ sampling_size = 10
+ dim = 3
+ for i in range(sampling_size):
+ coeff = 1.0 + i / sampling_size
+ field = mesh.fillFromAnalytic(mc.ON_NODES, dim, f"2*x*IVec + 3*x*{coeff}*JVec + 5*KVec")
+ istats.increment(field)
+
+ # check moments on last node
+ mean = istats.mean()
+ variance = istats.variance()
+ stddev = istats.stddev()
+ covariance = istats.covariance()
+ #! [UG_MEDCouplingIterativeStatistics_1]
+
+ print(f"mean={mean[-1]}")
+ assert mean.shape == (size, dim), f"wrong shape: {mean.shape}"
+ assert_allclose(mean[-1], [1.8, 3.915, 5.0])
+
+ print(f"variance={variance[-1]}")
+ assert variance.shape == (size, dim), f"wrong shape: {variance.shape}"
+ assert_allclose(variance[-1], [0., 0.66825, 0.], atol=1e-9)
+
+ print(f"stddev={stddev[-1]}")
+ assert stddev.shape == (size, dim), f"wrong shape: {stddev.shape}"
+ assert_allclose(stddev[-1], [0., 0.8174656, 0.], atol=1e-9)
+
+ print(f"covariance={covariance[-1]}")
+ assert covariance.shape == (size, dim, dim), f"wrong shape: {covariance.shape}"
+ assert_allclose(
+ covariance[-1].flatten(), [0.0, 0.0, 0.0, 0.0, 0.66825, 0.0, 0.0, 0.0, 0.0]
+ )
+
+ def test2(self):
+ # check ref values with OT-only
+ try:
+ import openturns as ot
+ except ImportError:
+ return
+
+ size = int(1e1)
+ mesh = ot.RegularGrid(0.0, 1.0 / size, size)
+
+ sampling_size = 10
+ sample = ot.Sample(sampling_size, 3)
+ for i in range(sampling_size):
+ coeff = 1.0 + i / sampling_size
+ f = ot.SymbolicFunction(["x"], ["2*x", f"3*x*{coeff}", "5"])
+ values = f(mesh.getVertices())
+ sample[i] = values[-1]
+
+ # check moments on last node
+ mean = sample.computeMean()
+ print(f"mean={mean}")
+ assert_allclose(np.asarray(mean), [1.8, 3.915, 5.0], atol=1e-9)
+
+ variance = sample.computeVariance()
+ print(f"variance={variance}")
+ assert_allclose(np.asarray(variance), [0., 0.668250, 0.], atol=1e-9)
+
+ covariance = sample.computeCovariance()
+ print(f"covariance={covariance}")
+ assert_allclose(
+ np.asarray(covariance).flatten(), [0.0, 0.0, 0.0, 0.0, 0.66825, 0.0, 0.0, 0.0, 0.0],
+ atol=1e-9
+ )
+
+ def test3(self):
+ # test on bigger mesh
+
+ # 1-d mesh
+ size = int(1e4)
+ coords = [i / size for i in range(size)]
+ arrX = mc.DataArrayDouble(coords, size, 1)
+ mesh = mc.MEDCouplingCMesh()
+ mesh.setCoords(arrX)
+
+ # compute mean only
+ istats = IterativeFieldMoments(enable_variance=False, enable_covariance=False)
+
+ # aggregate 2-d fields
+ sampling_size = 10
+ dim = 2
+ for i in range(sampling_size):
+ coeff = 1.0 + i / sampling_size
+ field = mesh.fillFromAnalytic(mc.ON_NODES, dim, f"2*x*IVec + 3*x*{coeff}*JVec")
+ istats.increment(field)
+
+ mean = istats.mean()
+ print(f"mean={mean[-1]}")
+ assert mean.shape == (size, dim), f"wrong shape: {mean.shape}"
+ assert_allclose(mean[-1], [1.9998 , 4.349565])
+
+ def test4(self):
+ #! [UG_MEDCouplingIterativeStatistics_2]
+
+ # Sobol' test over an 1-d mesh
+ import medcoupling as mc
+ from MEDCouplingIterativeStatistics import IterativeFieldSobol
+ from iterative_stats.experimental_design.experiment import AbstractExperiment
+
+ # 1-d mesh [-1; -1]
+ size = int(1e2)
+ coords = [-1 + 2*i / size for i in range(size)]
+ arrX = mc.DataArrayDouble(coords, size, 1)
+ mesh = mc.MEDCouplingCMesh()
+ mesh.setCoords(arrX)
+
+ # class to sample 2 parameters: in [0,1]^2 for nb_sim repetitions in a pick-freeze manner
+ nb_parms = 2
+ nb_sim = 300
+ class ABSampler(AbstractExperiment):
+ def __init__(self):
+ super(ABSampler, self).__init__(nb_parms, nb_sim)
+ np.random.seed(42)
+ def draw(self):
+ return np.random.rand(1, self.nb_parms)
+
+ # aggregate the nb_sim simulations
+ isobol = IterativeFieldSobol(nb_parms)
+ for pf_sample in ABSampler().generator():
+ # build the fields of the time-series f(a, b)_x=a+bx^2 for each (a,b) tuple in the pick-freeze sample
+ fields = [mesh.fillFromAnalytic(mc.ON_NODES, 1, f"({a}+{b}*x*x)*IVec") for a,b in pf_sample]
+ # note that for each simulation we need to instanciate nb_parms+2 fields
+ isobol.increment(fields)
+
+ # retrieve the Sobol' indices of f(a, b)_x in the beginning (x=-1) and middle (x=0) tuples of the time grid
+ first_beg, total_beg = isobol.indices(0)
+ print(f"at 0 : first={first_beg} total={total_beg}")
+
+ first_mid, total_mid = isobol.indices(size // 2)
+ print(f"at mid: first={first_mid} total={total_mid}")
+
+ #! [UG_MEDCouplingIterativeStatistics_2]
+
+ assert_allclose(first_beg[0], [0.59680837, 0.56303733])
+ assert_allclose(total_beg[0], [0.52188301, 0.47895543])
+
+ assert_allclose(first_mid[0], [0.94759752, -0.00683533], rtol=1e-6)
+ assert_allclose(total_mid[0], [1.00739829e+00, -9.41396650e-07])
+
+
+if __name__ == "__main__":
+ import logging
+ from iterative_stats.utils.logger import logger
+ logger.level = logging.INFO
+ unittest.main()
