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openfoam/src/OpenFOAM/primitives/Tensor/TensorI.H

1375 lines
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C++

/*---------------------------------------------------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration |
\\ / A nd | www.openfoam.com
\\/ M anipulation |
-------------------------------------------------------------------------------
Copyright (C) 2011-2016 OpenFOAM Foundation
Copyright (C) 2016-2023 OpenCFD Ltd.
-------------------------------------------------------------------------------
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 <type_traits>
#include "SymmTensor.H"
// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
template<class Cmpt>
inline Foam::Tensor<Cmpt>::Tensor(const Foam::zero)
:
Tensor::msType(Zero)
{}
template<class Cmpt>
template<class Cmpt2>
inline Foam::Tensor<Cmpt>::Tensor
(
const MatrixSpace<Tensor<Cmpt2>, Cmpt2, 3, 3>& vs
)
:
Tensor::msType(vs)
{}
template<class Cmpt>
template<class Cmpt2>
inline Foam::Tensor<Cmpt>::Tensor
(
const VectorSpace<Tensor<Cmpt2>, Cmpt2, 9>& vs
)
:
Tensor::msType(vs)
{}
template<class Cmpt>
inline Foam::Tensor<Cmpt>::Tensor(const SphericalTensor<Cmpt>& st)
{
this->v_[XX] = st.ii(); this->v_[XY] = Zero; this->v_[XZ] = Zero;
this->v_[YX] = Zero; this->v_[YY] = st.ii(); this->v_[YZ] = Zero;
this->v_[ZX] = Zero; this->v_[ZY] = Zero; this->v_[ZZ] = st.ii();
}
template<class Cmpt>
inline Foam::Tensor<Cmpt>::Tensor(const SymmTensor<Cmpt>& st)
{
this->v_[XX] = st.xx(); this->v_[XY] = st.xy(); this->v_[XZ] = st.xz();
this->v_[YX] = st.xy(); this->v_[YY] = st.yy(); this->v_[YZ] = st.yz();
this->v_[ZX] = st.xz(); this->v_[ZY] = st.yz(); this->v_[ZZ] = st.zz();
}
template<class Cmpt>
inline Foam::Tensor<Cmpt>::Tensor
(
const Vector<Vector<Cmpt>>& vecs,
const bool transposed
)
:
Tensor<Cmpt>(vecs.x(), vecs.y(), vecs.z(), transposed)
{}
template<class Cmpt>
inline Foam::Tensor<Cmpt>::Tensor
(
const Vector<Cmpt>& x,
const Vector<Cmpt>& y,
const Vector<Cmpt>& z,
const bool transposed
)
{
if (transposed)
{
this->cols(x, y, z);
}
else
{
this->rows(x, y, z);
}
}
template<class Cmpt>
inline Foam::Tensor<Cmpt>::Tensor
(
const Cmpt txx, const Cmpt txy, const Cmpt txz,
const Cmpt tyx, const Cmpt tyy, const Cmpt tyz,
const Cmpt tzx, const Cmpt tzy, const Cmpt tzz
)
{
this->v_[XX] = txx; this->v_[XY] = txy; this->v_[XZ] = txz;
this->v_[YX] = tyx; this->v_[YY] = tyy; this->v_[YZ] = tyz;
this->v_[ZX] = tzx; this->v_[ZY] = tzy; this->v_[ZZ] = tzz;
}
template<class Cmpt>
template
<
template<class, Foam::direction, Foam::direction> class Block2,
Foam::direction BRowStart,
Foam::direction BColStart
>
inline Foam::Tensor<Cmpt>::Tensor
(
const Block2<Tensor<Cmpt>, BRowStart, BColStart>& block
)
:
Tensor::msType(block)
{}
template<class Cmpt>
inline Foam::Tensor<Cmpt>::Tensor(Istream& is)
:
Tensor::msType(is)
{}
// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
template<class Cmpt>
inline Foam::Vector<Cmpt> Foam::Tensor<Cmpt>::x() const
{
return Vector<Cmpt>(this->v_[XX], this->v_[XY], this->v_[XZ]);
}
template<class Cmpt>
inline Foam::Vector<Cmpt> Foam::Tensor<Cmpt>::y() const
{
return Vector<Cmpt>(this->v_[YX], this->v_[YY], this->v_[YZ]);
}
template<class Cmpt>
inline Foam::Vector<Cmpt> Foam::Tensor<Cmpt>::z() const
{
return Vector<Cmpt>(this->v_[ZX], this->v_[ZY], this->v_[ZZ]);
}
template<class Cmpt>
inline Foam::Vector<Cmpt> Foam::Tensor<Cmpt>::cx() const
{
return Vector<Cmpt>(this->v_[XX], this->v_[YX], this->v_[ZX]);
}
template<class Cmpt>
inline Foam::Vector<Cmpt> Foam::Tensor<Cmpt>::cy() const
{
return Vector<Cmpt>(this->v_[XY], this->v_[YY], this->v_[ZY]);
}
template<class Cmpt>
inline Foam::Vector<Cmpt> Foam::Tensor<Cmpt>::cz() const
{
return Vector<Cmpt>(this->v_[XZ], this->v_[YZ], this->v_[ZZ]);
}
template<class Cmpt>
template<Foam::direction Idx>
inline Foam::Vector<Cmpt> Foam::Tensor<Cmpt>::col() const
{
if (Idx == 0) return cx();
else if (Idx == 1) return cy();
else if (Idx == 2) return cz();
static_assert(Idx < 3, "Invalid column access");
return Zero;
}
template<class Cmpt>
inline Foam::Vector<Cmpt> Foam::Tensor<Cmpt>::col(const direction c) const
{
switch (c)
{
case 0: return cx(); break;
case 1: return cy(); break;
case 2: return cz(); break;
default:
FatalErrorInFunction
<< "Invalid column access " << c << abort(FatalError);
}
return Zero;
}
template<class Cmpt>
template<Foam::direction Idx>
inline Foam::Vector<Cmpt> Foam::Tensor<Cmpt>::row() const
{
if (Idx == 0) return x();
else if (Idx == 1) return y();
else if (Idx == 2) return z();
static_assert(Idx < 3, "Invalid row access");
return Zero;
}
template<class Cmpt>
inline Foam::Vector<Cmpt> Foam::Tensor<Cmpt>::row(const direction r) const
{
switch (r)
{
case 0: return x(); break;
case 1: return y(); break;
case 2: return z(); break;
default:
FatalErrorInFunction
<< "Invalid row access " << r << abort(FatalError);
}
return Zero;
}
template<class Cmpt>
template<Foam::direction Idx>
inline void Foam::Tensor<Cmpt>::col(const Vector<Cmpt>& v)
{
if (Idx == 0)
{
this->v_[XX] = v.x();
this->v_[YX] = v.y();
this->v_[ZX] = v.z();
}
else if (Idx == 1)
{
this->v_[XY] = v.x();
this->v_[YY] = v.y();
this->v_[ZY] = v.z();
}
else if (Idx == 2)
{
this->v_[XZ] = v.x();
this->v_[YZ] = v.y();
this->v_[ZZ] = v.z();
}
static_assert(Idx < 3, "Invalid column access");
}
template<class Cmpt>
template<Foam::direction Idx>
inline void Foam::Tensor<Cmpt>::row(const Vector<Cmpt>& v)
{
if (Idx == 0)
{
this->v_[XX] = v.x(); this->v_[XY] = v.y(); this->v_[XZ] = v.z();
}
else if (Idx == 1)
{
this->v_[YX] = v.x(); this->v_[YY] = v.y(); this->v_[YZ] = v.z();
}
else if (Idx == 2)
{
this->v_[ZX] = v.x(); this->v_[ZY] = v.y(); this->v_[ZZ] = v.z();
}
static_assert(Idx < 3, "Invalid row access");
}
template<class Cmpt>
inline void Foam::Tensor<Cmpt>::cols
(
const Vector<Cmpt>& x,
const Vector<Cmpt>& y,
const Vector<Cmpt>& z
)
{
this->v_[XX] = x.x(); this->v_[XY] = y.x(); this->v_[XZ] = z.x();
this->v_[YX] = x.y(); this->v_[YY] = y.y(); this->v_[YZ] = z.y();
this->v_[ZX] = x.z(); this->v_[ZY] = y.z(); this->v_[ZZ] = z.z();
}
template<class Cmpt>
inline void Foam::Tensor<Cmpt>::rows
(
const Vector<Cmpt>& x,
const Vector<Cmpt>& y,
const Vector<Cmpt>& z
)
{
this->v_[XX] = x.x(); this->v_[XY] = x.y(); this->v_[XZ] = x.z();
this->v_[YX] = y.x(); this->v_[YY] = y.y(); this->v_[YZ] = y.z();
this->v_[ZX] = z.x(); this->v_[ZY] = z.y(); this->v_[ZZ] = z.z();
}
template<class Cmpt>
inline void Foam::Tensor<Cmpt>::col
(
const direction c,
const Vector<Cmpt>& v
)
{
switch (c)
{
case 0: col<0>(v); break;
case 1: col<1>(v); break;
case 2: col<2>(v); break;
default:
FatalErrorInFunction
<< "Invalid column access " << c << abort(FatalError);
}
}
template<class Cmpt>
inline void Foam::Tensor<Cmpt>::row
(
const direction r,
const Vector<Cmpt>& v
)
{
switch (r)
{
case 0: row<0>(v); break;
case 1: row<1>(v); break;
case 2: row<2>(v); break;
default:
FatalErrorInFunction
<< "Invalid row access " << r << abort(FatalError);
}
}
template<class Cmpt>
inline Foam::Vector<Cmpt> Foam::Tensor<Cmpt>::diag() const
{
return Vector<Cmpt>(this->v_[XX], this->v_[YY], this->v_[ZZ]);
}
template<class Cmpt>
inline void Foam::Tensor<Cmpt>::diag(const Vector<Cmpt>& v)
{
this->v_[XX] = v.x(); this->v_[YY] = v.y(); this->v_[ZZ] = v.z();
}
template<class Cmpt>
inline void Foam::Tensor<Cmpt>::addDiag(const Vector<Cmpt>& v)
{
this->v_[XX] += v.x(); this->v_[YY] += v.y(); this->v_[ZZ] += v.z();
}
template<class Cmpt>
inline void Foam::Tensor<Cmpt>::subtractDiag(const Vector<Cmpt>& v)
{
this->v_[XX] -= v.x(); this->v_[YY] -= v.y(); this->v_[ZZ] -= v.z();
}
template<class Cmpt>
inline Foam::scalar Foam::Tensor<Cmpt>::diagSqr() const
{
return
(
Foam::magSqr(this->xx())
+ Foam::magSqr(this->yy())
+ Foam::magSqr(this->zz())
);
}
template<class Cmpt>
inline bool Foam::Tensor<Cmpt>::is_identity(const scalar tol) const
{
return
(
Foam::mag(xx() - pTraits<Cmpt>::one) < tol
&& Foam::mag(yy() - pTraits<Cmpt>::one) < tol
&& Foam::mag(zz() - pTraits<Cmpt>::one) < tol
&& Foam::mag(xy()) < tol && Foam::mag(xz()) < tol
&& Foam::mag(yx()) < tol && Foam::mag(yz()) < tol
&& Foam::mag(zx()) < tol && Foam::mag(zy()) < tol
);
}
// * * * * * * * * * * * * * * * Member Operations * * * * * * * * * * * * * //
template<class Cmpt>
inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::T() const
{
return Tensor<Cmpt>
(
xx(), yx(), zx(),
xy(), yy(), zy(),
xz(), yz(), zz()
);
}
template<class Cmpt>
inline Cmpt Foam::Tensor<Cmpt>::det() const
{
return
(
xx()*yy()*zz() + xy()*yz()*zx()
+ xz()*yx()*zy() - xx()*yz()*zy()
- xy()*yx()*zz() - xz()*yy()*zx()
);
}
template<class Cmpt>
inline Cmpt Foam::Tensor<Cmpt>::det2D(const direction excludeCmpt) const
{
switch (excludeCmpt)
{
case 0: // Eliminate x
{
return (yy()*zz() - yz()*zy());
}
case 1: // Eliminate y
{
return (xx()*zz() - xz()*zx());
}
}
// Fall-through: Eliminate z
return (xx()*yy() - xy()*yx());
}
template<class Cmpt>
inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::adjunct() const
{
return Tensor<Cmpt>
(
yy()*zz() - zy()*yz(), xz()*zy() - xy()*zz(), xy()*yz() - xz()*yy(),
zx()*yz() - yx()*zz(), xx()*zz() - xz()*zx(), yx()*xz() - xx()*yz(),
yx()*zy() - yy()*zx(), xy()*zx() - xx()*zy(), xx()*yy() - yx()*xy()
);
}
template<class Cmpt>
inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::cof() const
{
return this->adjunct().T();
}
template<class Cmpt>
inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::adjunct2D
(
const direction excludeCmpt
) const
{
switch (excludeCmpt)
{
case 0: // Eliminate x
{
return Tensor<Cmpt>
(
Zero, Zero, Zero,
Zero, zz(), -yz(),
Zero, -zy(), yy()
);
}
case 1: // Eliminate y
{
return Tensor<Cmpt>
(
zz(), Zero, -xz(),
Zero, Zero, Zero,
-zx(), Zero, xx()
);
}
}
// Fall-through: Eliminate z
return Tensor<Cmpt>
(
yy(), -xy(), Zero,
-yx(), xx(), Zero,
Zero, Zero, Zero
);
}
template<class Cmpt>
inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::inv2D
(
const direction excludeCmpt
) const
{
const Cmpt detval = this->det2D(excludeCmpt);
return this->adjunct2D(excludeCmpt)/detval;
}
template<class Cmpt>
#if defined(__GNUC__) && !defined(__clang__)
// Workaround for gcc (11+) that fails to handle tensor dot vector
__attribute__((optimize("no-tree-vectorize")))
#endif
inline Foam::Tensor<Cmpt>
Foam::Tensor<Cmpt>::inner(const Tensor<Cmpt>& t2) const
{
const Tensor<Cmpt>& t1 = *this;
return Tensor<Cmpt>
(
t1.xx()*t2.xx() + t1.xy()*t2.yx() + t1.xz()*t2.zx(),
t1.xx()*t2.xy() + t1.xy()*t2.yy() + t1.xz()*t2.zy(),
t1.xx()*t2.xz() + t1.xy()*t2.yz() + t1.xz()*t2.zz(),
t1.yx()*t2.xx() + t1.yy()*t2.yx() + t1.yz()*t2.zx(),
t1.yx()*t2.xy() + t1.yy()*t2.yy() + t1.yz()*t2.zy(),
t1.yx()*t2.xz() + t1.yy()*t2.yz() + t1.yz()*t2.zz(),
t1.zx()*t2.xx() + t1.zy()*t2.yx() + t1.zz()*t2.zx(),
t1.zx()*t2.xy() + t1.zy()*t2.yy() + t1.zz()*t2.zy(),
t1.zx()*t2.xz() + t1.zy()*t2.yz() + t1.zz()*t2.zz()
);
}
template<class Cmpt>
#if defined(__GNUC__) && !defined(__clang__)
// Workaround for gcc (11+) that fails to handle tensor dot vector
__attribute__((optimize("no-tree-vectorize")))
#endif
inline Foam::Tensor<Cmpt>
Foam::Tensor<Cmpt>::schur(const Tensor<Cmpt>& t2) const
{
const Tensor<Cmpt>& t1 = *this;
return Tensor<Cmpt>
(
t1.xx()*t2.xx(), t1.xy()*t2.xy(), t1.xz()*t2.xz(),
t1.yx()*t2.yx(), t1.yy()*t2.yy(), t1.yz()*t2.yz(),
t1.zx()*t2.zx(), t1.zy()*t2.zy(), t1.zz()*t2.zz()
);
}
// Invert without much error handling
template<class Cmpt>
inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::inv() const
{
const Cmpt detval = this->det();
#ifdef FULLDEBUG
if (mag(detval) < VSMALL)
{
FatalErrorInFunction
<< "Tensor not properly invertible, determinant:"
<< detval << " tensor:" << *this << nl
<< abort(FatalError);
}
#endif
return this->adjunct()/detval;
}
// Invert with some error handling
template<class Cmpt>
inline Foam::Tensor<Cmpt> Foam::Tensor<Cmpt>::safeInv() const
{
{
// Attempt to identify and handle 2-D cases
// - use diagSqr instead of magSqr for fewer operations
const scalar magSqr_xx = Foam::magSqr(xx());
const scalar magSqr_yy = Foam::magSqr(yy());
const scalar magSqr_zz = Foam::magSqr(zz());
// SMALL: 1e-15 (double), 1e-6 (float), but 1e-6 may be adequate
const scalar threshold = SMALL * (magSqr_xx + magSqr_yy + magSqr_zz);
const bool small_xx = (magSqr_xx < threshold);
const bool small_yy = (magSqr_yy < threshold);
const bool small_zz = (magSqr_zz < threshold);
if (small_xx || small_yy || small_zz)
{
Tensor<Cmpt> work(*this);
if (small_xx) { work.xx() += pTraits<Cmpt>::one; }
if (small_yy) { work.yy() += pTraits<Cmpt>::one; }
if (small_zz) { work.zz() += pTraits<Cmpt>::one; }
const Cmpt detval = work.det();
if (mag(detval) < ROOTVSMALL)
{
// Appears to be nearly zero - leave untouched?
return Tensor<Cmpt>(Zero);
}
work = work.adjunct()/detval;
if (small_xx) { work.xx() -= pTraits<Cmpt>::one; }
if (small_yy) { work.yy() -= pTraits<Cmpt>::one; }
if (small_zz) { work.zz() -= pTraits<Cmpt>::one; }
return work;
}
}
const Cmpt detval = this->det();
if (mag(detval) < ROOTVSMALL)
{
// Appears to be nearly zero - leave untouched?
return Tensor<Cmpt>(Zero);
}
return this->adjunct()/detval;
}
// * * * * * * * * * * * * * * * Member Operators * * * * * * * * * * * * * //
template<class Cmpt>
inline void Foam::Tensor<Cmpt>::operator&=(const Tensor<Cmpt>& t)
{
*this = this->inner(t);
}
template<class Cmpt>
template<class Cmpt2>
inline void Foam::Tensor<Cmpt>::operator=
(
const VectorSpace<Tensor<Cmpt2>, Cmpt2, 9>& vs
)
{
VectorSpace<Tensor<Cmpt>, Cmpt, 9>::operator=(vs);
}
template<class Cmpt>
inline void Foam::Tensor<Cmpt>::operator=(const SphericalTensor<Cmpt>& st)
{
this->v_[XX] = st.ii(); this->v_[XY] = Zero; this->v_[XZ] = Zero;
this->v_[YX] = Zero; this->v_[YY] = st.ii(); this->v_[YZ] = Zero;
this->v_[ZX] = Zero; this->v_[ZY] = Zero; this->v_[ZZ] = st.ii();
}
template<class Cmpt>
inline void Foam::Tensor<Cmpt>::operator=(const SymmTensor<Cmpt>& st)
{
this->v_[XX] = st.xx(); this->v_[XY] = st.xy(); this->v_[XZ] = st.xz();
this->v_[YX] = st.xy(); this->v_[YY] = st.yy(); this->v_[YZ] = st.yz();
this->v_[ZX] = st.xz(); this->v_[ZY] = st.yz(); this->v_[ZZ] = st.zz();
}
template<class Cmpt>
inline void Foam::Tensor<Cmpt>::operator=(const Vector<Vector<Cmpt>>& tr)
{
this->v_[XX] = tr.x().x();
this->v_[XY] = tr.x().y();
this->v_[XZ] = tr.x().z();
this->v_[YX] = tr.y().x();
this->v_[YY] = tr.y().y();
this->v_[YZ] = tr.y().z();
this->v_[ZX] = tr.z().x();
this->v_[ZY] = tr.z().y();
this->v_[ZZ] = tr.z().z();
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
namespace Foam
{
// * * * * * * * * * * * * * * * Global Functions * * * * * * * * * * * * * //
//- Return the trace of a Tensor
template<class Cmpt>
inline Cmpt tr(const Tensor<Cmpt>& t)
{
return t.xx() + t.yy() + t.zz();
}
//- Return the spherical part of a Tensor
template<class Cmpt>
inline SphericalTensor<Cmpt> sph(const Tensor<Cmpt>& t)
{
return SphericalTensor<Cmpt>
(
(1.0/3.0)*tr(t)
);
}
//- Return the symmetric part of a Tensor
template<class Cmpt>
inline SymmTensor<Cmpt> symm(const Tensor<Cmpt>& t)
{
return SymmTensor<Cmpt>
(
t.xx(), 0.5*(t.xy() + t.yx()), 0.5*(t.xz() + t.zx()),
t.yy(), 0.5*(t.yz() + t.zy()),
t.zz()
);
}
//- Return twice the symmetric part of a Tensor
template<class Cmpt>
inline SymmTensor<Cmpt> twoSymm(const Tensor<Cmpt>& t)
{
return SymmTensor<Cmpt>
(
2*t.xx(), (t.xy() + t.yx()), (t.xz() + t.zx()),
2*t.yy(), (t.yz() + t.zy()),
2*t.zz()
);
}
//- Return the deviatoric part of the symmetric part of a Tensor
template<class Cmpt>
inline SymmTensor<Cmpt> devSymm(const Tensor<Cmpt>& t)
{
const Cmpt sph(tr(t)/3.0);
return SymmTensor<Cmpt>
(
t.xx() - sph, 0.5*(t.xy() + t.yx()), 0.5*(t.xz() + t.zx()),
t.yy() - sph, 0.5*(t.yz() + t.zy()),
t.zz() - sph
);
}
//- Return the deviatoric part of twice the symmetric part of a Tensor
template<class Cmpt>
inline SymmTensor<Cmpt> devTwoSymm(const Tensor<Cmpt>& t)
{
const Cmpt sph((2.0/3.0)*tr(t));
return SymmTensor<Cmpt>
(
2*t.xx() - sph, (t.xy() + t.yx()), (t.xz() + t.zx()),
2*t.yy() - sph, (t.yz() + t.zy()),
2*t.zz() - sph
);
}
//- Return the skew-symmetric part of a Tensor
template<class Cmpt>
inline Tensor<Cmpt> skew(const Tensor<Cmpt>& t)
{
return Tensor<Cmpt>
(
Zero, 0.5*(t.xy() - t.yx()), 0.5*(t.xz() - t.zx()),
0.5*(t.yx() - t.xy()), Zero, 0.5*(t.yz() - t.zy()),
0.5*(t.zx() - t.xz()), 0.5*(t.zy() - t.yz()), Zero
);
}
//- Return the skew-symmetric part of a SymmTensor as a Tensor
template<class Cmpt>
inline const Tensor<Cmpt>& skew(const SymmTensor<Cmpt>& st)
{
return Tensor<Cmpt>::zero;
}
//- Return the deviatoric part of a Tensor
template<class Cmpt>
inline Tensor<Cmpt> dev(const Tensor<Cmpt>& t)
{
return t - sph(t);
}
//- Return the two-third deviatoric part of a Tensor
template<class Cmpt>
inline Tensor<Cmpt> dev2(const Tensor<Cmpt>& t)
{
return t - 2*sph(t);
}
//- Return the determinant of a Tensor
template<class Cmpt>
inline Cmpt det(const Tensor<Cmpt>& t)
{
return t.det();
}
//- Return the cofactor Tensor of a Tensor
template<class Cmpt>
inline Tensor<Cmpt> cof(const Tensor<Cmpt>& t)
{
return t.cof();
}
//- Return the inverse of a Tensor, using the given determinant value
template<class Cmpt>
inline Tensor<Cmpt> inv(const Tensor<Cmpt>& t, const Cmpt detval)
{
#ifdef FULLDEBUG
if (mag(detval) < VSMALL)
{
FatalErrorInFunction
<< "Tensor not properly invertible, determinant:"
<< detval << " tensor:" << t << nl
<< abort(FatalError);
}
#endif
return t.adjunct()/detval;
}
//- Return the inverse of a Tensor
template<class Cmpt>
inline Tensor<Cmpt> inv(const Tensor<Cmpt>& t)
{
return t.inv();
}
//- Return the 1st invariant of a Tensor
template<class Cmpt>
inline Cmpt invariantI(const Tensor<Cmpt>& t)
{
return tr(t);
}
//- Return the 2nd invariant of a Tensor
template<class Cmpt>
inline Cmpt invariantII(const Tensor<Cmpt>& t)
{
return
(
t.xx()*t.yy() + t.yy()*t.zz() + t.xx()*t.zz()
- t.xy()*t.yx() - t.yz()*t.zy() - t.xz()*t.zx()
);
}
//- Return the 3rd invariant of a Tensor
template<class Cmpt>
inline Cmpt invariantIII(const Tensor<Cmpt>& t)
{
return det(t);
}
//- Linear interpolation of tensors a and b by factor t
template<class Cmpt>
inline Tensor<Cmpt> lerp
(
const Tensor<Cmpt>& a,
const Tensor<Cmpt>& b,
const scalar t
)
{
const scalar onet = (1-t);
return Tensor<Cmpt>
(
onet*a.xx() + t*b.xx(),
onet*a.xy() + t*b.xy(),
onet*a.xz() + t*b.xz(),
onet*a.yx() + t*b.yx(),
onet*a.yy() + t*b.yy(),
onet*a.yz() + t*b.yz(),
onet*a.zx() + t*b.zx(),
onet*a.zy() + t*b.zy(),
onet*a.zz() + t*b.zz()
);
}
// * * * * * * * * * * * * * * * Global Operators * * * * * * * * * * * * * //
//- Sum of a SphericalTensor and a Tensor
template<class Cmpt>
inline Tensor<Cmpt>
operator+(const SphericalTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
{
return Tensor<Cmpt>
(
st1.ii() + t2.xx(), t2.xy(), t2.xz(),
t2.yx(), st1.ii() + t2.yy(), t2.yz(),
t2.zx(), t2.zy(), st1.ii() + t2.zz()
);
}
//- Sum of a Tensor and a SphericalTensor
template<class Cmpt>
inline Tensor<Cmpt>
operator+(const Tensor<Cmpt>& t1, const SphericalTensor<Cmpt>& st2)
{
return Tensor<Cmpt>
(
t1.xx() + st2.ii(), t1.xy(), t1.xz(),
t1.yx(), t1.yy() + st2.ii(), t1.yz(),
t1.zx(), t1.zy(), t1.zz() + st2.ii()
);
}
//- Sum of a SymmTensor and a Tensor
template<class Cmpt>
inline Tensor<Cmpt>
operator+(const SymmTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
{
return Tensor<Cmpt>
(
st1.xx() + t2.xx(), st1.xy() + t2.xy(), st1.xz() + t2.xz(),
st1.xy() + t2.yx(), st1.yy() + t2.yy(), st1.yz() + t2.yz(),
st1.xz() + t2.zx(), st1.yz() + t2.zy(), st1.zz() + t2.zz()
);
}
//- Sum of a Tensor and a SymmTensor
template<class Cmpt>
inline Tensor<Cmpt>
operator+(const Tensor<Cmpt>& t1, const SymmTensor<Cmpt>& st2)
{
return Tensor<Cmpt>
(
t1.xx() + st2.xx(), t1.xy() + st2.xy(), t1.xz() + st2.xz(),
t1.yx() + st2.xy(), t1.yy() + st2.yy(), t1.yz() + st2.yz(),
t1.zx() + st2.xz(), t1.zy() + st2.yz(), t1.zz() + st2.zz()
);
}
//- Subtract a Tensor from a SphericalTensor
template<class Cmpt>
inline Tensor<Cmpt>
operator-(const SphericalTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
{
return Tensor<Cmpt>
(
st1.ii() - t2.xx(), -t2.xy(), -t2.xz(),
-t2.yx(), st1.ii() - t2.yy(), -t2.yz(),
-t2.zx(), -t2.zy(), st1.ii() - t2.zz()
);
}
//- Subtract a SphericalTensor from a Tensor
template<class Cmpt>
inline Tensor<Cmpt>
operator-(const Tensor<Cmpt>& t1, const SphericalTensor<Cmpt>& st2)
{
return Tensor<Cmpt>
(
t1.xx() - st2.ii(), t1.xy(), t1.xz(),
t1.yx(), t1.yy() - st2.ii(), t1.yz(),
t1.zx(), t1.zy(), t1.zz() - st2.ii()
);
}
//- Subtract a Tensor from a SymmTensor
template<class Cmpt>
inline Tensor<Cmpt>
operator-(const SymmTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
{
return Tensor<Cmpt>
(
st1.xx() - t2.xx(), st1.xy() - t2.xy(), st1.xz() - t2.xz(),
st1.xy() - t2.yx(), st1.yy() - t2.yy(), st1.yz() - t2.yz(),
st1.xz() - t2.zx(), st1.yz() - t2.zy(), st1.zz() - t2.zz()
);
}
//- Subtract a SymmTensor from a Tensor
template<class Cmpt>
inline Tensor<Cmpt>
operator-(const Tensor<Cmpt>& t1, const SymmTensor<Cmpt>& st2)
{
return Tensor<Cmpt>
(
t1.xx() - st2.xx(), t1.xy() - st2.xy(), t1.xz() - st2.xz(),
t1.yx() - st2.xy(), t1.yy() - st2.yy(), t1.yz() - st2.yz(),
t1.zx() - st2.xz(), t1.zy() - st2.yz(), t1.zz() - st2.zz()
);
}
//- Return the Hodge dual of a Tensor as a Vector
template<class Cmpt>
inline Vector<Cmpt> operator*(const Tensor<Cmpt>& t)
{
return Vector<Cmpt>(t.yz(), -t.xz(), t.xy());
}
//- Return the Hodge dual of a Vector as a Tensor
template<class Cmpt>
inline Tensor<Cmpt> operator*(const Vector<Cmpt>& v)
{
return Tensor<Cmpt>
(
Zero, -v.z(), v.y(),
v.z(), Zero, -v.x(),
-v.y(), v.x(), Zero
);
}
//- Division of a Vector by a Tensor
template<class Cmpt>
inline typename innerProduct<Vector<Cmpt>, Tensor<Cmpt>>::type
operator/(const Vector<Cmpt>& v, const Tensor<Cmpt>& t)
{
return inv(t) & v;
}
//- Division of a Tensor by a Cmpt
template<class Cmpt>
inline Tensor<Cmpt>
operator/(const Tensor<Cmpt>& t, const Cmpt s)
{
#ifdef FULLDEBUG
if (mag(s) < VSMALL)
{
FatalErrorInFunction
<< "Tensor = " << t
<< " is not divisible due to a zero value in Cmpt:"
<< "Cmpt = " << s
<< abort(FatalError);
}
#endif
return Tensor<Cmpt>
(
t.xx()/s, t.xy()/s, t.xz()/s,
t.yx()/s, t.yy()/s, t.yz()/s,
t.zx()/s, t.zy()/s, t.zz()/s
);
}
//- Inner-product of a Tensor and a Tensor
template<class Cmpt>
inline typename innerProduct<Tensor<Cmpt>, Tensor<Cmpt>>::type
operator&(const Tensor<Cmpt>& t1, const Tensor<Cmpt>& t2)
{
return t1.inner(t2);
}
//- Inner-product of a SphericalTensor and a Tensor
template<class Cmpt>
#if defined(__GNUC__) && !defined(__clang__)
// Workaround for gcc (11+) that fails to handle tensor dot vector
__attribute__((optimize("no-tree-vectorize")))
#endif
inline Tensor<Cmpt>
operator&(const SphericalTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
{
return Tensor<Cmpt>
(
st1.ii()*t2.xx(), st1.ii()*t2.xy(), st1.ii()*t2.xz(),
st1.ii()*t2.yx(), st1.ii()*t2.yy(), st1.ii()*t2.yz(),
st1.ii()*t2.zx(), st1.ii()*t2.zy(), st1.ii()*t2.zz()
);
}
//- Inner-product of a Tensor and a SphericalTensor
template<class Cmpt>
#if defined(__GNUC__) && !defined(__clang__)
// Workaround for gcc (11+) that fails to handle tensor dot vector
__attribute__((optimize("no-tree-vectorize")))
#endif
inline Tensor<Cmpt>
operator&(const Tensor<Cmpt>& t1, const SphericalTensor<Cmpt>& st2)
{
return Tensor<Cmpt>
(
t1.xx()*st2.ii(), t1.xy()*st2.ii(), t1.xz()*st2.ii(),
t1.yx()*st2.ii(), t1.yy()*st2.ii(), t1.yz()*st2.ii(),
t1.zx()*st2.ii(), t1.zy()*st2.ii(), t1.zz()*st2.ii()
);
}
//- Inner-product of a SymmTensor and a Tensor
template<class Cmpt>
#if defined(__GNUC__) && !defined(__clang__)
// Workaround for gcc (11+) that fails to handle tensor dot vector
__attribute__((optimize("no-tree-vectorize")))
#endif
inline Tensor<Cmpt>
operator&(const SymmTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
{
return Tensor<Cmpt>
(
st1.xx()*t2.xx() + st1.xy()*t2.yx() + st1.xz()*t2.zx(),
st1.xx()*t2.xy() + st1.xy()*t2.yy() + st1.xz()*t2.zy(),
st1.xx()*t2.xz() + st1.xy()*t2.yz() + st1.xz()*t2.zz(),
st1.xy()*t2.xx() + st1.yy()*t2.yx() + st1.yz()*t2.zx(),
st1.xy()*t2.xy() + st1.yy()*t2.yy() + st1.yz()*t2.zy(),
st1.xy()*t2.xz() + st1.yy()*t2.yz() + st1.yz()*t2.zz(),
st1.xz()*t2.xx() + st1.yz()*t2.yx() + st1.zz()*t2.zx(),
st1.xz()*t2.xy() + st1.yz()*t2.yy() + st1.zz()*t2.zy(),
st1.xz()*t2.xz() + st1.yz()*t2.yz() + st1.zz()*t2.zz()
);
}
//- Inner-product of a Tensor and a SymmTensor
template<class Cmpt>
#if defined(__GNUC__) && !defined(__clang__)
// Workaround for gcc (11+) that fails to handle tensor dot vector
__attribute__((optimize("no-tree-vectorize")))
#endif
inline Tensor<Cmpt>
operator&(const Tensor<Cmpt>& t1, const SymmTensor<Cmpt>& st2)
{
return Tensor<Cmpt>
(
t1.xx()*st2.xx() + t1.xy()*st2.xy() + t1.xz()*st2.xz(),
t1.xx()*st2.xy() + t1.xy()*st2.yy() + t1.xz()*st2.yz(),
t1.xx()*st2.xz() + t1.xy()*st2.yz() + t1.xz()*st2.zz(),
t1.yx()*st2.xx() + t1.yy()*st2.xy() + t1.yz()*st2.xz(),
t1.yx()*st2.xy() + t1.yy()*st2.yy() + t1.yz()*st2.yz(),
t1.yx()*st2.xz() + t1.yy()*st2.yz() + t1.yz()*st2.zz(),
t1.zx()*st2.xx() + t1.zy()*st2.xy() + t1.zz()*st2.xz(),
t1.zx()*st2.xy() + t1.zy()*st2.yy() + t1.zz()*st2.yz(),
t1.zx()*st2.xz() + t1.zy()*st2.yz() + t1.zz()*st2.zz()
);
}
//- Inner-product of a Tensor and a Vector
template<class Cmpt>
#if defined(__GNUC__) && !defined(__clang__)
// Workaround for gcc (11+) that fails to handle tensor dot vector
__attribute__((optimize("no-tree-vectorize")))
#endif
inline Vector<Cmpt>
operator&(const Tensor<Cmpt>& t, const Vector<Cmpt>& v)
{
return Vector<Cmpt>
(
t.xx()*v.x() + t.xy()*v.y() + t.xz()*v.z(),
t.yx()*v.x() + t.yy()*v.y() + t.yz()*v.z(),
t.zx()*v.x() + t.zy()*v.y() + t.zz()*v.z()
);
}
//- Inner-product of a Vector and a Tensor
template<class Cmpt>
#if defined(__GNUC__) && !defined(__clang__)
// Workaround for gcc (11+) that fails to handle tensor dot vector
__attribute__((optimize("no-tree-vectorize")))
#endif
inline Vector<Cmpt>
operator&(const Vector<Cmpt>& v, const Tensor<Cmpt>& t)
{
return Vector<Cmpt>
(
v.x()*t.xx() + v.y()*t.yx() + v.z()*t.zx(),
v.x()*t.xy() + v.y()*t.yy() + v.z()*t.zy(),
v.x()*t.xz() + v.y()*t.yz() + v.z()*t.zz()
);
}
//- Double-inner-product of a SphericalTensor and a Tensor
template<class Cmpt>
inline Cmpt
operator&&(const SphericalTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
{
return (st1.ii()*t2.xx() + st1.ii()*t2.yy() + st1.ii()*t2.zz());
}
//- Double-inner-product of a Tensor and a SphericalTensor
template<class Cmpt>
inline Cmpt
operator&&(const Tensor<Cmpt>& t1, const SphericalTensor<Cmpt>& st2)
{
return (t1.xx()*st2.ii() + t1.yy()*st2.ii() + t1.zz()*st2.ii());
}
//- Double-inner-product of a SymmTensor and a Tensor
template<class Cmpt>
inline Cmpt
operator&&(const SymmTensor<Cmpt>& st1, const Tensor<Cmpt>& t2)
{
return
(
st1.xx()*t2.xx() + st1.xy()*t2.xy() + st1.xz()*t2.xz() +
st1.xy()*t2.yx() + st1.yy()*t2.yy() + st1.yz()*t2.yz() +
st1.xz()*t2.zx() + st1.yz()*t2.zy() + st1.zz()*t2.zz()
);
}
//- Double-inner-product of a Tensor and a SymmTensor
template<class Cmpt>
inline Cmpt
operator&&(const Tensor<Cmpt>& t1, const SymmTensor<Cmpt>& st2)
{
return
(
t1.xx()*st2.xx() + t1.xy()*st2.xy() + t1.xz()*st2.xz() +
t1.yx()*st2.xy() + t1.yy()*st2.yy() + t1.yz()*st2.yz() +
t1.zx()*st2.xz() + t1.zy()*st2.yz() + t1.zz()*st2.zz()
);
}
//- Outer-product of a Vector and a Vector
template<class Cmpt>
inline typename outerProduct<Vector<Cmpt>, Vector<Cmpt>>::type
operator*(const Vector<Cmpt>& v1, const Vector<Cmpt>& v2)
{
return Tensor<Cmpt>
(
v1.x()*v2.x(), v1.x()*v2.y(), v1.x()*v2.z(),
v1.y()*v2.x(), v1.y()*v2.y(), v1.y()*v2.z(),
v1.z()*v2.x(), v1.z()*v2.y(), v1.z()*v2.z()
);
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
template<class Cmpt>
class typeOfSum<SphericalTensor<Cmpt>, Tensor<Cmpt>>
{
public:
typedef Tensor<Cmpt> type;
};
template<class Cmpt>
class typeOfSum<Tensor<Cmpt>, SphericalTensor<Cmpt>>
{
public:
typedef Tensor<Cmpt> type;
};
template<class Cmpt>
class innerProduct<SphericalTensor<Cmpt>, Tensor<Cmpt>>
{
public:
typedef Tensor<Cmpt> type;
};
template<class Cmpt>
class innerProduct<Tensor<Cmpt>, SphericalTensor<Cmpt>>
{
public:
typedef Tensor<Cmpt> type;
};
template<class Cmpt>
class typeOfSum<SymmTensor<Cmpt>, Tensor<Cmpt>>
{
public:
typedef Tensor<Cmpt> type;
};
template<class Cmpt>
class typeOfSum<Tensor<Cmpt>, SymmTensor<Cmpt>>
{
public:
typedef Tensor<Cmpt> type;
};
template<class Cmpt>
class innerProduct<SymmTensor<Cmpt>, Tensor<Cmpt>>
{
public:
typedef Tensor<Cmpt> type;
};
template<class Cmpt>
class innerProduct<Tensor<Cmpt>, SymmTensor<Cmpt>>
{
public:
typedef Tensor<Cmpt> type;
};
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
} // End namespace Foam
// ************************************************************************* //