ENH: Import (probability) Distribution class and test app from cvm.

applications/test/Distribution/DistributionTest.C

+/*---------------------------------------------------------------------------*\
+ =========                   |
+ \\      /   F ield          | OpenFOAM: The Open Source CFD Toolbox
+  \\    /    O peration      |
+   \\  /     A nd            | Copyright (C) 2008-2011 OpenCFD Ltd.
+    \\/      M anipulation   |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM 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 General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Application
+    DistributionTest
+
+Description
+    Test the Distribution class
+
+    Plot normal distribution test in gnuplot using:
+
+    @verbatim
+    normalDistribution(mean, sigma, x) = \
+        sqrt(1.0/(2.0*pi*sigma**2))*exp(-(x - mean)**2.0/(2.0*sigma**2))
+
+    plot normalDistribution(8.5, 2.5, x), "Distribution_scalar_test_x" w p
+    @endverbatim
+
+\*---------------------------------------------------------------------------*/
+
+#include "vector.H"
+#include "labelVector.H"
+#include "tensor.H"
+#include "Distribution.H"
+#include "Random.H"
+#include "dimensionedTypes.H"
+#include "argList.H"
+#include "PstreamReduceOps.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+using namespace Foam;
+
+int main(int argc, char *argv[])
+{
+    #   include "setRootCase.H"
+
+    Random R(918273);
+
+    {
+        // scalar
+        label randomDistributionTestSize = 50000000;
+
+        Distribution<scalar> dS(scalar(5e-2));
+
+        Info<< nl << "Distribution<scalar>" << nl
+            << "Sampling "
+            << randomDistributionTestSize
+            << " times from GaussNormal distribution."
+            << endl;
+
+        for (label i = 0; i < randomDistributionTestSize; i++)
+        {
+            dS.add(2.5*R.GaussNormal() + 8.5);
+        }
+
+        Info<< "Mean " << dS.mean() << nl
+            << "Median " << dS.median()
+            << endl;
+
+        dS.write("Distribution_scalar_test_1");
+
+        Distribution<scalar> dS2(scalar(1e-2));
+
+        Info<< nl << "Distribution<scalar>" << nl
+            << "Sampling "
+            << randomDistributionTestSize
+            << " times from GaussNormal distribution."
+            << endl;
+
+        for (label i = 0; i < randomDistributionTestSize; i++)
+        {
+            dS2.add(1.5*R.GaussNormal() -6.0);
+        }
+
+        Info<< "Mean " << dS2.mean() << nl
+            << "Median " << dS2.median()
+            << endl;
+
+        dS2.write("Distribution_scalar_test_2");
+
+        Info<< nl << "Adding previous two Distribution<scalar>" << endl;
+
+        dS = dS + dS2;
+
+        dS.write("Distribution_scalar_test_1+2");
+    }
+
+    if (Pstream::parRun())
+    {
+        // scalar in parallel
+        label randomDistributionTestSize = 100000000;
+
+        Distribution<scalar> dS(scalar(1e-1));
+
+        Pout<< "Distribution<scalar>" << nl
+            << "Sampling "
+            << randomDistributionTestSize
+            << " times from uniform distribution."
+            << endl;
+
+        for (label i = 0; i < randomDistributionTestSize; i++)
+        {
+            dS.add(R.scalar01() + 10*Pstream::myProcNo());
+        }
+
+        Pout<< "Mean " << dS.mean() << nl
+            << "Median " << dS.median()
+            << endl;
+
+        reduce(dS, sumOp< Distribution<scalar> >());
+
+        if (Pstream::master())
+        {
+            Info<< "Reducing parallel Distribution<scalar>" << nl
+                << "Mean " << dS.mean() << nl
+                << "Median " << dS.median()
+                << endl;
+
+            dS.write("Distribution_scalar_test_parallel_reduced");
+        }
+    }
+
+    {
+        // vector
+        Distribution<vector> dV(vector(0.1, 0.05, 0.15));
+
+        label randomDistributionTestSize = 1000000;
+
+        Info<< nl << "Distribution<vector>" << nl
+            << "Sampling "
+            << randomDistributionTestSize
+            << " times from uniform and GaussNormal distribution."
+            << endl;
+
+        for (label i = 0; i < randomDistributionTestSize; i++)
+        {
+            dV.add(R.vector01());
+
+            // Adding separate GaussNormal components with component
+            // weights
+
+            dV.add
+            (
+                vector
+                (
+                    R.GaussNormal()*3.0 + 1.5,
+                    R.GaussNormal()*0.25 + 4.0,
+                    R.GaussNormal()*3.0 - 1.5
+                ),
+                vector(1.0, 2.0, 5.0)
+            );
+        }
+
+        Info<< "Mean " << dV.mean() << nl
+            << "Median " << dV.median()
+            << endl;
+
+        dV.write("Distribution_vector_test");
+    }
+
+    // {
+    //     // labelVector
+    //     Distribution<labelVector> dLV(labelVector::one*10);
+
+    //     label randomDistributionTestSize = 2000000;
+
+    //     Info<< nl << "Distribution<labelVector>" << nl
+    //         << "Sampling "
+    //         << randomDistributionTestSize
+    //         << " times from uniform distribution."
+    //         << endl;
+
+    //     for (label i = 0; i < randomDistributionTestSize; i++)
+    //     {
+    //         dLV.add
+    //         (
+    //             labelVector
+    //             (
+    //                 R.integer(-1000, 1000),
+    //                 R.integer(-5000, 5000),
+    //                 R.integer(-2000, 7000)
+    //             )
+    //         );
+    //     }
+
+    //     Info<< "Mean " << dLV.mean() << nl
+    //         << "Median " << dLV.median()
+    //         << endl;
+
+    //     dLV.write("Distribution_labelVector_test");
+    // }
+
+    {
+        // tensor
+        Distribution<tensor> dT(tensor::one*1e-2);
+
+        label randomDistributionTestSize = 2000000;
+
+        Info<< nl << "Distribution<tensor>" << nl
+            << "Sampling "
+            << randomDistributionTestSize
+            << " times from uniform distribution."
+            << endl;
+
+        for (label i = 0; i < randomDistributionTestSize; i++)
+        {
+            dT.add(R.tensor01());
+        }
+
+        Info<< "Mean " << dT.mean() << nl
+            << "Median " << dT.median()
+            << endl;
+
+        dT.write("Distribution_tensor_test");
+    }
+
+    {
+        // symmTensor
+        Distribution<symmTensor> dSyT(symmTensor::one*1e-2);
+
+        label randomDistributionTestSize = 2000000;
+
+        Info<< nl << "Distribution<symmTensor>" << nl
+            << "Sampling "
+            << randomDistributionTestSize
+            << " times from uniform distribution."
+            << endl;
+
+        for (label i = 0; i < randomDistributionTestSize; i++)
+        {
+            dSyT.add(R.symmTensor01());
+        }
+
+        Info<< "Mean " << dSyT.mean() << nl
+            << "Median " << dSyT.median()
+            << endl;
+
+        dSyT.write("Distribution_symmTensor_test");
+    }
+
+    {
+        // sphericalTensor
+        Distribution<sphericalTensor> dSpT(sphericalTensor::one*1e-2);
+
+        label randomDistributionTestSize = 50000000;
+
+        Info<< nl << "Distribution<sphericalTensor>" << nl
+            << "Sampling "
+            << randomDistributionTestSize
+            << " times from uniform distribution."
+            << endl;
+
+        for (label i = 0; i < randomDistributionTestSize; i++)
+        {
+            dSpT.add(R.sphericalTensor01());
+        }
+
+        Info<< "Mean " << dSpT.mean() << nl
+            << "Median " << dSpT.median()
+            << endl;
+
+        dSpT.write("Distribution_sphericalTensor_test");
+    }
+
+    Info<< nl << "End" << nl << endl;
+
+    return 0;
+}
+
+
+// ************************************************************************* //

applications/test/Distribution/Make/files

+DistributionTest.C
+
+EXE = $(FOAM_USER_APPBIN)/DistributionTest

applications/test/Distribution/Make/options

+/* EXE_INC = */
+/* EXE_LIBS = */

src/OpenFOAM/containers/Lists/Distribution/Distribution.C

+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2009-2011 OpenCFD Ltd.
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM 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 General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+\*---------------------------------------------------------------------------*/
+
+#include "Distribution.H"
+#include "OFstream.H"
+#include "ListOps.H"
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+template<class Type>
+Foam::Distribution<Type>::Distribution()
+:
+    List< List<scalar> >(pTraits<Type>::nComponents),
+    binWidth_(pTraits<Type>::one),
+    listStarts_(pTraits<Type>::nComponents, 0)
+{}
+
+
+template<class Type>
+Foam::Distribution<Type>::Distribution(const Type& binWidth)
+:
+    List< List<scalar> >(pTraits<Type>::nComponents),
+    binWidth_(binWidth),
+    listStarts_(pTraits<Type>::nComponents, 0)
+{}
+
+
+template<class Type>
+Foam::Distribution<Type>::Distribution(const Distribution<Type>& d)
+:
+    List< List<scalar> >(static_cast< const List< List<scalar> >& >(d)),
+    binWidth_(d.binWidth()),
+    listStarts_(d.listStarts())
+{}
+
+
+// * * * * * * * * * * * * * * * * Destructor  * * * * * * * * * * * * * * * //
+
+template<class Type>
+Foam::Distribution<Type>::~Distribution()
+{}
+
+
+// * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * * //
+
+template<class Type>
+Foam::scalar Foam::Distribution<Type>::totalWeight(direction cmpt) const
+{
+    const List<scalar>& cmptDistribution = (*this)[cmpt];
+
+    scalar sumOfWeights = 0.0;
+
+    forAll(cmptDistribution, i)
+    {
+        sumOfWeights += cmptDistribution[i];
+    }
+
+    return sumOfWeights;
+}
+
+
+template<class Type>
+Foam::List<Foam::label> Foam::Distribution<Type>::keys(direction cmpt) const
+{
+    List<label> keys = identity((*this)[cmpt].size());
+
+    forAll(keys, k)
+    {
+        keys[k] += listStarts_[cmpt];
+    }
+
+    return keys;
+}
+
+
+template<class Type>
+Foam::label Foam::Distribution<Type>::index
+(
+    direction cmpt,
+    label n
+)
+{
+    List<scalar>& cmptDistribution = (*this)[cmpt];
+
+    if (cmptDistribution.empty())
+    {
+        // Initialise this list with this value
+
+        cmptDistribution.setSize(2, 0.0);
+
+        listStarts_[cmpt] = n;
+
+        return 0;
+    }
+
+    label listIndex = -1;
+
+    label& listStart  = listStarts_[cmpt];
+
+    label testIndex = n - listStart;
+
+    if (testIndex < 0)
+    {
+        // Underflow of this List, storage increase and remapping
+        // required
+
+        List<scalar> newCmptDistribution(2*cmptDistribution.size(), 0.0);
+
+        label sOld = cmptDistribution.size();
+
+        forAll(cmptDistribution, i)
+        {
+            newCmptDistribution[i + sOld] = cmptDistribution[i];
+        }
+
+        cmptDistribution = newCmptDistribution;
+
+        listStart -= sOld;
+
+        // Recursively call this function in case another remap is required.
+        listIndex = index(cmpt, n);
+    }
+    else if (testIndex > cmptDistribution.size() - 1)
+    {
+        // Overflow of this List, storage increase required
+
+        cmptDistribution.setSize(2*cmptDistribution.size(), 0.0);
+
+        // Recursively call this function in case another storage
+        // alteration is required.
+        listIndex = index(cmpt, n);
+    }
+    else
+    {
+        listIndex = n - listStart;
+    }
+
+    return listIndex;
+}
+
+
+template<class Type>
+Foam::Pair<Foam::label> Foam::Distribution<Type>::validLimits
+(
+    direction cmpt
+) const
+{
+    const List<scalar>& cmptDistribution = (*this)[cmpt];
+
+    // limits.first(): lower bound, i.e. the first non-zero entry
+    // limits.second(): upper bound, i.e. the last non-zero entry
+    Pair<label> limits(-1, -1);
+
+    forAll(cmptDistribution, i)
+    {
+        if (cmptDistribution[i] > 0.0)
+        {
+            if (limits.first() == -1)
+            {
+                limits.first() = i;
+                limits.second() = i;
+            }
+            else
+            {
+                limits.second() = i;
+            }
+        }
+    }
+
+    return limits;
+}
+
+
+template<class Type>
+Type Foam::Distribution<Type>::mean() const
+{
+    Type meanValue(pTraits<Type>::zero);
+
+    for (direction cmpt = 0; cmpt < pTraits<Type>::nComponents; cmpt++)
+    {
+        const List<scalar>& cmptDistribution = (*this)[cmpt];
+
+        scalar totalCmptWeight = totalWeight(cmpt);
+
+        List<label> theKeys = keys(cmpt);
+
+        forAll(theKeys, k)
+        {
+            label key = theKeys[k];
+
+            setComponent(meanValue, cmpt) +=
+                (0.5 + scalar(key))
+               *component(binWidth_, cmpt)
+               *cmptDistribution[k]
+               /totalCmptWeight;
+        }
+    }
+
+    return meanValue;
+}
+
+
+template<class Type>
+Type Foam::Distribution<Type>::median() const
+{
+    Type medianValue(pTraits<Type>::zero);
+
+    List< List < Pair<scalar> > > normDistribution = normalised();
+
+    for (direction cmpt = 0; cmpt < pTraits<Type>::nComponents; cmpt++)
+    {
+        List< Pair<scalar> >& normDist = normDistribution[cmpt];
+
+        if (normDist.size())
+        {
+            if (normDist.size() == 1)
+            {
+                setComponent(medianValue, cmpt) = normDist[0].first();
+            }
+            else if
+            (
+                normDist.size() > 1
+             && normDist[0].second()*component(binWidth_, cmpt) > 0.5
+            )
+            {
+                scalar xk =
+                    normDist[0].first()
+                  + 0.5*component(binWidth_, cmpt);
+
+                scalar xkm1 =
+                    normDist[0].first()
+                  - 0.5*component(binWidth_, cmpt);
+
+                scalar Sk = (normDist[0].second())*component(binWidth_, cmpt);
+
+                setComponent(medianValue, cmpt) = 0.5*(xk - xkm1)/(Sk) + xkm1;
+            }
+            else
+            {
+                label previousNonZeroIndex = 0;
+
+                scalar cumulative = 0.0;
+
+                forAll(normDist, nD)
+                {
+                    if
+                    (
+                        cumulative
+                      + (normDist[nD].second()*component(binWidth_, cmpt))
+                      > 0.5
+                    )
+                    {
+                        scalar xk =
+                            normDist[nD].first()
+                          + 0.5*component(binWidth_, cmpt);
+
+                        scalar xkm1 =
+                            normDist[previousNonZeroIndex].first()
+                          + 0.5*component(binWidth_, cmpt);
+
+                        scalar Sk =
+                            cumulative
+                          + (normDist[nD].second()*component(binWidth_, cmpt));
+
+                        scalar Skm1 = cumulative;
+
+                        setComponent(medianValue, cmpt) =
+                            (0.5 - Skm1)*(xk - xkm1)/(Sk - Skm1) + xkm1;
+
+                        break;
+                    }
+                    else if (mag(normDist[nD].second()) > VSMALL)
+                    {
+                        cumulative +=
+                            normDist[nD].second()*component(binWidth_, cmpt);
+
+                        previousNonZeroIndex = nD;
+                    }
+                }
+            }
+        }
+
+    }
+