55e7da670c
- `tensor` and `tensor2D` returns complex eigenvalues/vectors
- `symmTensor` and `symmTensor2D` returns real eigenvalues/vectors
- adds new test routines for eigendecompositions
- improves numerical stability by:
- using new robust algorithms,
- reordering the conditional branches in root-type selection
981 lines
24 KiB
C
981 lines
24 KiB
C
/*---------------------------------------------------------------------------*\
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration |
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\\ / A nd | www.openfoam.com
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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Copyright (C) 2014 OpenFOAM Foundation
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Copyright (C) 2019-2020 OpenCFD Ltd.
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-------------------------------------------------------------------------------
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License
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This file is part of OpenFOAM.
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OpenFOAM is free software: you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received a copy of the GNU General Public License
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along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
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Application
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Test-Tensor2D
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Description
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Tests for \c Tensor2D constructors, member functions and operators
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using \c floatScalar, \c doubleScalar, and \c complex base types.
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Eigen decomposition tests for \c tensor2D, i.e. Tensor2D<scalar>.
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Cross-checks were obtained from 'NumPy 1.15.1' and 'SciPy 1.1.0' if no
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theoretical cross-check exists (like eigendecomposition relations), and
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were hard-coded for elementwise comparisons.
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For \c complex base type, the cross-checks do only involve zero imag part.
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\*---------------------------------------------------------------------------*/
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#include "vector2DField.H"
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#include "tensor2D.H"
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#include "symmTensor2D.H"
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#include "transform.H"
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#include "Random.H"
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#include "floatScalar.H"
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#include "doubleScalar.H"
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#include "complex.H"
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using namespace Foam;
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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// Total number of unit tests
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unsigned nTest_ = 0;
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// Total number of failed unit tests
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unsigned nFail_ = 0;
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// Create a random tensor2D
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tensor2D makeRandomContainer(Random& rnd)
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{
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tensor2D A(Zero);
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std::generate(A.begin(), A.end(), [&]{ return rnd.GaussNormal<scalar>(); });
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return A;
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}
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// Compare two floating point types, and print output.
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// Do ++nFail_ if values of two objects are not equal within a given tolerance.
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// The function is converted from PEP-485.
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template<class Type>
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typename std::enable_if
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<
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std::is_same<floatScalar, Type>::value ||
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std::is_same<doubleScalar, Type>::value ||
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std::is_same<complex, Type>::value,
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void
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>::type cmp
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(
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const word& msg,
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const Type& x,
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const Type& y,
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const scalar relTol = 1e-8, //<! are values the same within 8 decimals
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const scalar absTol = 0 //<! useful for cmps near zero
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)
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{
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Info<< msg << x << endl;
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unsigned nFail = 0;
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if (max(absTol, relTol*max(mag(x), mag(y))) < mag(x - y))
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{
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++nFail;
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}
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if (nFail)
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{
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Info<< nl
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<< " #### Fail in " << nFail << " comps ####" << nl << endl;
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++nFail_;
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}
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++nTest_;
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}
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// Compare two containers elementwise, and print output.
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// Do ++nFail_ if two components are not equal within a given tolerance.
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// The function is converted from PEP-485
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template<class Type>
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typename std::enable_if
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<
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!std::is_same<floatScalar, Type>::value &&
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!std::is_same<doubleScalar, Type>::value &&
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!std::is_same<complex, Type>::value,
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void
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>::type cmp
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(
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const word& msg,
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const Type& x,
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const Type& y,
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const scalar relTol = 1e-8,
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const scalar absTol = 0
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)
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{
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Info<< msg << x << endl;
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unsigned nFail = 0;
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for (label i = 0; i < pTraits<Type>::nComponents; ++i)
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{
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if (max(absTol, relTol*max(mag(x[i]), mag(y[i]))) < mag(x[i] - y[i]))
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{
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++nFail;
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}
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}
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if (nFail)
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{
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Info<< nl
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<< " #### Fail in " << nFail << " comps ####" << nl << endl;
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++nFail_;
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}
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++nTest_;
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}
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// Create each constructor of Tensor2D<Type>, and print output
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template<class Type>
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void test_constructors(Type)
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{
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{
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Info<< "# Construct initialized to zero:" << nl;
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const Tensor2D<Type> T(Zero);
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Info<< T << endl;
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}
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{
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Info<< "# Construct given VectorSpace:" << nl;
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const VectorSpace<Tensor2D<Type>, Type, 4> V(Zero);
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const Tensor2D<Type> T(V);
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Info<< T << endl;
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}
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{
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Info<< "# Construct given SymmTensor2D:" << nl;
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const SymmTensor2D<Type> S
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(
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Type(1), Type(2),
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Type(3)
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);
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const Tensor2D<Type> T(S);
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Info<< T << endl;
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}
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{
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Info<< "# Construct given SphericalTensor2D:" << nl;
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const SphericalTensor2D<Type> Sp(Type(5));
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const Tensor2D<Type> T(Sp);
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Info<< T << endl;
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}
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{
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Info<< "# Construct given the two row vectors:" << nl;
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const Vector2D<Type> x(Type(1), Type(2));
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const Vector2D<Type> y(Type(3), Type(4));
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const Tensor2D<Type> T(x, y);
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Info<< T << endl;
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}
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{
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Info<< "# Construct given the four components:" << nl;
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const Tensor2D<Type> T
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(
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Type(1), Type(2),
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Type(3), Type(4)
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);
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Info<< T << endl;
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}
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{
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Info<< "# Copy construct:" << nl;
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const Tensor2D<Type> T(Zero);
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const Tensor2D<Type> Tcopy(T);
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Info<< T << endl;
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}
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}
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// Execute each member function of Tensor2D<Type>, and print output
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template<class Type>
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void test_member_funcs(Type)
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{
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Tensor2D<Type> T
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(
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Type(1), Type(2),
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Type(4), Type(5)
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);
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Tensor2D<Type> Tbak = T;
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const Tensor2D<Type> cT
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(
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Type(-9), Type(8),
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Type(-6), Type(5)
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);
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Info<< "# Operand: " << nl
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<< " Tensor2D = " << T << endl;
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{
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Info<< "# Component access:" << nl;
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Tensor2D<Type> cpT
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(
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T.xx(), T.xy(),
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T.yx(), T.yy()
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);
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cmp(" 'Tensor2D' access:", T, cpT);
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const Tensor2D<Type> cpcT
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(
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cT.xx(), cT.xy(),
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cT.yx(), cT.yy()
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);
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cmp(" 'const Tensor2D' access:", cT, cpcT);
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}
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{
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Info<< "# Column-vector access:" << nl;
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cmp(" cx():", T.cx(), Vector2D<Type>(Type(1), Type(4)));
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cmp(" cy():", T.cy(), Vector2D<Type>(Type(2), Type(5)));
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cmp(" col(0):", T.col(0), Vector2D<Type>(Type(1), Type(4)));
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cmp(" col(1):", T.col(1), Vector2D<Type>(Type(2), Type(5)));
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cmp
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(
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" col<0>:",
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T.template col<0>(),
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Vector2D<Type>(Type(1), Type(4))
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);
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cmp
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(
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" col<1>:",
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T.template col<1>(),
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Vector2D<Type>(Type(2), Type(5))
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);
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// Compilation error: Info << " col<2> = " << T.col<2>() << nl;
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Info<< "# Column-vector manipulation:" << nl;
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T.col(1, Vector2D<Type>(Type(0), Type(1)));
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cmp
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(
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" col(1, Vector):",
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T.col(1),
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Vector2D<Type>(Type(0), Type(1))
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);
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T.cols
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(
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Vector2D<Type>(Type(1), Type(1)),
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Vector2D<Type>(Type(-1), Type(1))
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);
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cmp
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(
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" cols(Vectors):",
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T,
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Tensor2D<Type>
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(
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Type(1), Type(-1),
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Type(1), Type(1)
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)
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);
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}
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{
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Info<< "# Row-vector access:" << nl;
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T = Tbak;
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cmp(" x():", T.x(), Vector2D<Type>(Type(1), Type(2)));
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cmp(" y():", T.y(), Vector2D<Type>(Type(4), Type(5)));
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cmp(" row(0):", T.row(0), Vector2D<Type>(Type(1), Type(2)));
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cmp(" row(1):", T.row(1), Vector2D<Type>(Type(4), Type(5)));
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cmp
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(
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" row<0>:",
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T.template row<0>(),
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Vector2D<Type>(Type(1), Type(2))
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);
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cmp
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(
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" row<1>:",
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T.template row<1>(),
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Vector2D<Type>(Type(4), Type(5))
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);
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// Compilation error: Info << " row<2> = " << T.row<2>() << nl;
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Info<< "# Row-vector manipulation:" << nl;
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T.row(1, Vector2D<Type>(Type(0), Type(1)));
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cmp
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(
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" row(1, Vector):",
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T.row(1),
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Vector2D<Type>(Type(0), Type(1))
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);
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T.rows
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(
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Vector2D<Type>(Type(1), Type(1)),
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Vector2D<Type>(Type(-1), Type(1))
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);
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cmp
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(
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" rows(Vectors):",
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T,
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Tensor2D<Type>
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(
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Type(1), Type(1),
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Type(-1), Type(1)
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)
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);
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}
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{
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Info<< "# Diagonal access:" << nl;
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T = Tbak;
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cmp
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(
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" 'Tensor2D'.diag():",
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T.diag(),
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Vector2D<Type>(Type(1), Type(5))
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);
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cmp
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(
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" 'const Tensor2D'.diag():",
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cT.diag(),
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Vector2D<Type>(Type(-9), Type(5))
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);
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Info<< "# Diagonal manipulation:" << nl;
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T.diag(Vector2D<Type>(Type(-10), Type(-15)));
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cmp
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(
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" 'Tensor2D'.diag('Vector'):",
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T.diag(),
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Vector2D<Type>(Type(-10), Type(-15))
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);
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}
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{
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Info<< "# Tensor operations:" << nl;
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T = Tbak;
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cmp(" Transpose:", T, (T.T()).T());
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cmp
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(
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" Inner-product:",
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T.inner(T),
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Tensor2D<Type>
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(
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Type(9), Type(12),
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Type(24), Type(33)
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)
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);
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cmp
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(
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" Schur-product:",
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T.schur(T),
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Tensor2D<Type>
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(
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Type(1), Type(4),
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Type(16), Type(25)
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)
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);
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}
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{
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Info<< "# Member operators:" << nl;
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T = SphericalTensor2D<Type>(Type(5));
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cmp
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(
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" Assign to a SphericalTensor2D:",
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T,
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Tensor2D<Type>
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(
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Type(5), Zero,
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Zero, Type(5)
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)
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);
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T = SymmTensor2D<Type>
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(
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Type(1), Type(2),
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Type(5)
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);
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cmp
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(
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" Assign to a SymmTensor2D:",
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T,
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Tensor2D<Type>
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(
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Type(1), Type(2),
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Type(2), Type(5)
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)
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);
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}
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}
|
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|
|
|
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// Execute each global function of Tensor2D<Type>, and print output
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template<class Type>
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void test_global_funcs(Type)
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{
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const Tensor2D<Type> T
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(
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Type(-1), Type(2),
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Type(4), Type(5)
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);
|
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|
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Info<< "# Operand: " << nl
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<< " Tensor2D = " << T << endl;
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|
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cmp(" Trace = ", tr(T), Type(4));
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cmp(" Spherical part = ", sph(T), SphericalTensor2D<Type>(tr(T)/Type(2)));
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cmp
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(
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" Symmetric part = ",
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symm(T),
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SymmTensor2D<Type>
|
|
(
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Type(-1), Type(3),
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Type(5)
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)
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);
|
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cmp
|
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(
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" Twice the symmetric part = ",
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twoSymm(T),
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SymmTensor2D<Type>
|
|
(
|
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Type(-2), Type(6),
|
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Type(10)
|
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)
|
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);
|
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cmp
|
|
(
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" Skew-symmetric part = ",
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skew(T),
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|
Tensor2D<Type>
|
|
(
|
|
Type(0), Type(-1),
|
|
Type(1), Type(0)
|
|
)
|
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);
|
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cmp
|
|
(
|
|
" Deviatoric part = ",
|
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dev(T),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(-3), Type(2),
|
|
Type(4), Type(3)
|
|
)
|
|
);
|
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cmp(" Two-third deviatoric part = ", dev2(T), T - 2*sph(T));
|
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cmp(" Determinant = ", det(T), Type(-13));
|
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cmp
|
|
(
|
|
" Cofactor tensor2D = ",
|
|
cof(T),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(5), Type(-4),
|
|
Type(-2), Type(-1)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Inverse = ",
|
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inv(T, det(T)),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(-0.38461538), Type(0.15384615),
|
|
Type(0.30769231), Type(0.07692308)
|
|
),
|
|
1e-6,
|
|
1e-6
|
|
);
|
|
cmp
|
|
(
|
|
" Inverse (another) = ",
|
|
inv(T),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(-0.38461538), Type(0.15384615),
|
|
Type(0.30769231), Type(0.07692308)
|
|
),
|
|
1e-6,
|
|
1e-6
|
|
);
|
|
cmp(" First invariant = ", invariantI(T), Type(4));
|
|
cmp(" Second invariant = ", invariantII(T), Type(-13));
|
|
}
|
|
|
|
|
|
// Execute each global operator of Tensor2D<Type>, and print output
|
|
template<class Type>
|
|
void test_global_opers(Type)
|
|
{
|
|
const Tensor2D<Type> T
|
|
(
|
|
Type(-1), Type(2),
|
|
Type(4), Type(5)
|
|
);
|
|
const SymmTensor2D<Type> sT
|
|
(
|
|
Type(1), Type(2),
|
|
Type(5)
|
|
);
|
|
const SphericalTensor2D<Type> spT(Type(1));
|
|
const Vector2D<Type> v(Type(3), Type(2));
|
|
const Type x(4);
|
|
|
|
Info<< "# Operands:" << nl
|
|
<< " Tensor2D = " << T << nl
|
|
<< " SymmTensor2D = " << sT << nl
|
|
<< " SphericalTensor2D = " << spT << nl
|
|
<< " Vector2D = " << v << nl
|
|
<< " Type = " << x << endl;
|
|
|
|
|
|
cmp
|
|
(
|
|
" Sum of SpTensor2D-Tensor2D = ",
|
|
(spT + T),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(0), Type(2),
|
|
Type(4), Type(6)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Sum of Tensor2D-SpTensor2D = ",
|
|
(T + spT),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(0), Type(2),
|
|
Type(4), Type(6)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Sum of SymmTensor2D-Tensor2D = ",
|
|
(sT + T),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(0), Type(4),
|
|
Type(6), Type(10)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Sum of Tensor2D-SymmTensor2D = ",
|
|
(T + sT),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(0), Type(4),
|
|
Type(6), Type(10)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Subtract Tensor2D from SpTensor2D = ",
|
|
(spT - T),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(2), Type(-2),
|
|
Type(-4), Type(-4)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Subtract SpTensor2D from Tensor2D = ",
|
|
(T - spT),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(-2), Type(2),
|
|
Type(4), Type(4)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Subtract Tensor2D from SymmTensor2D = ",
|
|
(sT - T),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(2), Type(0),
|
|
Type(-2), Type(0)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Subtract SymmTensor2D from Tensor2D = ",
|
|
(T - sT),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(-2), Type(0),
|
|
Type(2), Type(0)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Division of Tensor2D by Type = ",
|
|
(T/x),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(-0.25), Type(0.5),
|
|
Type(1), Type(1.25)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Inner-product of Tensor2D-Tensor2D = ",
|
|
(T & T),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(9), Type(8),
|
|
Type(16), Type(33)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Inner-product of SpTensor2D-Tensor2D = ",
|
|
(spT & T),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(-1), Type(2),
|
|
Type(4), Type(5)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Inner-product of Tensor2D-SpTensor2D = ",
|
|
(T & spT),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(-1), Type(2),
|
|
Type(4), Type(5)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Inner-product of SymmTensor2D-Tensor2D = ",
|
|
(sT & T),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(7), Type(12),
|
|
Type(18), Type(29)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Inner-product of Tensor2D-SymmTensor2D = ",
|
|
(T & sT),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(3), Type(8),
|
|
Type(14), Type(33)
|
|
)
|
|
);
|
|
cmp
|
|
(
|
|
" Inner-product of Tensor2D-Vector2D = ",
|
|
(T & v),
|
|
Vector2D<Type>(Type(1), Type(22)) // Column-vector
|
|
);
|
|
cmp
|
|
(
|
|
" Inner-product of Vector2D-Tensor2D = ",
|
|
(v & T),
|
|
Vector2D<Type>(Type(5), Type(16)) // Row-vector
|
|
);
|
|
cmp(" D-inner-product of SpTensor2D-Tensor2D = ", (spT && T), Type(4));
|
|
cmp(" D-inner-product of Tensor2D-SpTensor2D = ", (T && spT), Type(4));
|
|
cmp(" D-inner-product of SymmTensor2D-Tensor2D = ", (sT && T), Type(36));
|
|
cmp(" D-inner-product of Tensor2D-SymmTensor2D = ", (T && sT), Type(36));
|
|
cmp
|
|
(
|
|
" Outer-product of Vector2D-Vector2D = ",
|
|
(v*v),
|
|
Tensor2D<Type>
|
|
(
|
|
Type(9), Type(6),
|
|
Type(6), Type(4)
|
|
)
|
|
);
|
|
}
|
|
|
|
|
|
// Return false if given eigenvalues fail to satisy eigenvalue relations
|
|
// Relations: (Beauregard & Fraleigh (1973), ISBN 0-395-14017-X, p. 307)
|
|
void test_eigenvalues(const tensor2D& T, const Vector2D<complex>& EVals)
|
|
{
|
|
{
|
|
const scalar determinant = det(T);
|
|
// In case of complex EVals, the production is effectively scalar
|
|
// due to the (complex*complex conjugate) results in zero imag part
|
|
const scalar EValsProd = ((EVals.x()*EVals.y()).real());
|
|
cmp("# Product of eigenvalues = det(sT):", EValsProd, determinant);
|
|
}
|
|
|
|
{
|
|
const scalar trace = tr(T);
|
|
scalar EValsSum = 0.0;
|
|
// In case of complex EVals, the summation is effectively scalar
|
|
// due to the (complex+complex conjugate) results in zero imag part
|
|
for (const auto& val : EVals)
|
|
{
|
|
EValsSum += val.real();
|
|
}
|
|
cmp("# Sum of eigenvalues = trace(sT):", EValsSum, trace, 1e-8, 1e-8);
|
|
}
|
|
}
|
|
|
|
|
|
// Return false if a given eigenvalue-eigenvector pair
|
|
// fails to satisfy the characteristic equation
|
|
void test_characteristic_equation
|
|
(
|
|
const tensor2D& T,
|
|
const Vector2D<complex>& EVals,
|
|
const Tensor2D<complex>& EVecs
|
|
)
|
|
{
|
|
Info<< "# Characteristic equation:" << nl;
|
|
|
|
Tensor2D<complex> Tc(Zero);
|
|
forAll(T, i)
|
|
{
|
|
Tc[i] = complex(T[i], 0);
|
|
}
|
|
|
|
for (direction dir = 0; dir < pTraits<vector2D>::nComponents; ++dir)
|
|
{
|
|
const Vector2D<complex> leftSide(Tc & EVecs.row(dir));
|
|
const Vector2D<complex> rightSide(EVals[dir]*EVecs.row(dir));
|
|
const Vector2D<complex> X(leftSide - rightSide);
|
|
|
|
for (const auto x : X)
|
|
{
|
|
cmp(" (Tc & EVec - EVal*EVec) = 0:", mag(x), 0.0, 1e-8, 1e-6);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
// Return false if the eigen functions fail to satisfy relations
|
|
void test_eigen_funcs(const tensor2D& T)
|
|
{
|
|
Info<< "# Operand:" << nl
|
|
<< " tensor2D = " << T << nl;
|
|
|
|
|
|
Info<< "# Return eigenvalues of a given tensor2D:" << nl;
|
|
const Vector2D<complex> EVals(eigenValues(T));
|
|
Info<< EVals << endl;
|
|
test_eigenvalues(T, EVals);
|
|
|
|
Info<< "# Return an eigenvector of a given tensor2D in a given direction"
|
|
<< " corresponding to a given eigenvalue:" << nl;
|
|
const Vector2D<complex> standardBasis(pTraits<complex>::one, Zero);
|
|
const Vector2D<complex> EVec(eigenVector(T, EVals.x(), standardBasis));
|
|
Info<< EVec << endl;
|
|
|
|
Info<< "# Return eigenvectors of a given tensor2D corresponding to"
|
|
<< " given eigenvalues:" << nl;
|
|
const Tensor2D<complex> EVecs0(eigenVectors(T, EVals));
|
|
Info<< EVecs0 << endl;
|
|
test_characteristic_equation(T, EVals, EVecs0);
|
|
|
|
Info<< "# Return eigenvectors of a given tensor2D by computing"
|
|
<< " the eigenvalues of the tensor2D in the background:" << nl;
|
|
const Tensor2D<complex> EVecs1(eigenVectors(T));
|
|
Info<< EVecs1 << endl;
|
|
}
|
|
|
|
|
|
// Do compile-time recursion over the given types
|
|
template<std::size_t I = 0, typename... Tp>
|
|
inline typename std::enable_if<I == sizeof...(Tp), void>::type
|
|
run_tests(const std::tuple<Tp...>& types, const List<word>& typeID){}
|
|
|
|
|
|
template<std::size_t I = 0, typename... Tp>
|
|
inline typename std::enable_if<I < sizeof...(Tp), void>::type
|
|
run_tests(const std::tuple<Tp...>& types, const List<word>& typeID)
|
|
{
|
|
Info<< nl << " ## Test constructors: "<< typeID[I] <<" ##" << nl;
|
|
test_constructors(std::get<I>(types));
|
|
|
|
Info<< nl << " ## Test member functions: "<< typeID[I] <<" ##" << nl;
|
|
test_member_funcs(std::get<I>(types));
|
|
|
|
Info<< nl << " ## Test global functions: "<< typeID[I] << " ##" << nl;
|
|
test_global_funcs(std::get<I>(types));
|
|
|
|
Info<< nl << " ## Test global operators: "<< typeID[I] <<" ##" << nl;
|
|
test_global_opers(std::get<I>(types));
|
|
|
|
run_tests<I + 1, Tp...>(types, typeID);
|
|
}
|
|
|
|
|
|
// * * * * * * * * * * * * * * * Main Program * * * * * * * * * * * * * * * //
|
|
|
|
int main(int argc, char *argv[])
|
|
{
|
|
|
|
const std::tuple<floatScalar, doubleScalar, complex> types
|
|
(
|
|
std::make_tuple(Zero, Zero, Zero)
|
|
);
|
|
|
|
const List<word> typeID
|
|
({
|
|
"Tensor2D<floatScalar>",
|
|
"Tensor2D<doubleScalar>",
|
|
"Tensor2D<complex>"
|
|
});
|
|
|
|
run_tests(types, typeID);
|
|
|
|
|
|
Info<< nl << " ## Test tensor2D eigen functions: ##" << nl;
|
|
const label numberOfTests = 10000;
|
|
Random rndGen(1234);
|
|
|
|
for (label i = 0; i < numberOfTests; ++i)
|
|
{
|
|
const tensor2D T(makeRandomContainer(rndGen));
|
|
test_eigen_funcs(T);
|
|
}
|
|
|
|
{
|
|
Info<< nl << " ## Test eigen functions by a zero tensor2D: ##"<< nl;
|
|
const tensor2D zeroT(Zero);
|
|
test_eigen_funcs(zeroT);
|
|
}
|
|
{
|
|
Info<< nl
|
|
<< " ## Test eigen functions by a tensor2D consisting of"
|
|
<< " repeated eigenvalues: ##"
|
|
<< nl;
|
|
const tensor2D T
|
|
(
|
|
-1.0, 2.0,
|
|
0.0, -1.0
|
|
);
|
|
test_eigen_funcs(T);
|
|
}
|
|
{
|
|
Info<< nl
|
|
<< " ## Test eigen functions by a skew-symmetric tensor2D"
|
|
<< " consisting of no-real eigenvalues: ##"
|
|
<< nl;
|
|
const tensor2D T
|
|
(
|
|
0.0, 1.0,
|
|
-1.0, 0.0
|
|
);
|
|
test_eigen_funcs(T);
|
|
}
|
|
{
|
|
Info<< nl
|
|
<< " ## Test eigen functions by a stiff tensor2D: ##"
|
|
<< nl;
|
|
const tensor2D stiff
|
|
(
|
|
pow(10.0, 10), pow(10.0, 8),
|
|
pow(10.0, -8), pow(10.0, 9)
|
|
);
|
|
test_eigen_funcs(stiff);
|
|
}
|
|
|
|
|
|
{
|
|
Info<< "# Pre-v2006 tests:" << nl;
|
|
vector2D v1(1, 2), v2(3, 4);
|
|
tensor2D t3 = v1*v2;
|
|
|
|
Info<< v1 << "*" << v2 << " = " << t3 << endl;
|
|
|
|
{
|
|
Info<< "rows:" << nl;
|
|
for (direction i = 0; i < 2; ++i)
|
|
{
|
|
Info<< " (" << i << ") = " << t3.row(i) << nl;
|
|
}
|
|
}
|
|
|
|
{
|
|
Info<< "cols:" << nl;
|
|
for (direction i = 0; i < 2; ++i)
|
|
{
|
|
Info<< " (" << i << ") = " << t3.col(i) << nl;
|
|
}
|
|
Info<< "col<0> = " << t3.col<0>() << nl;
|
|
Info<< "col<1> = " << t3.col<1>() << nl;
|
|
// Compilation error: Info << "col<3> = " << t3.col<3>() << nl;
|
|
|
|
t3.col<0>({0, 2});
|
|
Info<< "replaced col<0> = " << t3.col<0>() << nl;
|
|
Info<< "tensor " << t3 << nl;
|
|
|
|
t3.row<1>(Zero);
|
|
Info<< "replaced row<1> = " << t3.row<1>() << nl;
|
|
Info<< "tensor " << t3 << nl;
|
|
}
|
|
|
|
|
|
{
|
|
vector2DField vfld1(8, Zero);
|
|
|
|
forAll(vfld1, i)
|
|
{
|
|
vfld1[i] = (i + 1) * ((i % 2) ? v1 : v2);
|
|
}
|
|
|
|
Info<< "vector: " << flatOutput(vfld1) << nl;
|
|
|
|
scalarField xvals(8);
|
|
scalarField yvals(8);
|
|
unzip(vfld1, xvals, yvals);
|
|
|
|
Info<< "unzip" << nl
|
|
<< " x => " << flatOutput(xvals) << nl
|
|
<< " y => " << flatOutput(yvals) << nl;
|
|
|
|
reverse(xvals);
|
|
zip(vfld1, xvals, yvals);
|
|
|
|
Info<< "rezip (with reversed x)" << nl
|
|
<< " => " << flatOutput(vfld1) << nl;
|
|
}
|
|
}
|
|
|
|
if (nFail_)
|
|
{
|
|
Info<< nl << " #### "
|
|
<< "Failed in " << nFail_ << " tests "
|
|
<< "out of total " << nTest_ << " tests "
|
|
<< "####\n" << endl;
|
|
return 1;
|
|
}
|
|
|
|
Info<< nl << " #### Passed all " << nTest_ <<" tests ####\n" << endl;
|
|
return 0;
|
|
}
|
|
|
|
|
|
// ************************************************************************* //
|