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ENH: improve analytic eigen for small off-diagonals

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This commit is contained in:
Kutalmis Bercin
2020-02-20 16:00:23 +00:00
committed by Andrew Heather
parent b476dd92e6
commit 6576397e81
9 changed files with 638 additions and 226 deletions
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91
applications/test/Tensor2D/Test-Tensor2D.C
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@ -86,11 +86,11 @@ typename std::enable_if
const word& msg,
const Type& x,
const Type& y,
const scalar relTol = 1e-8, //<! are values the same within 8 decimals
const scalar absTol = 0 //<! useful for cmps near zero
const scalar absTol = 0, //<! useful for cmps near zero
const scalar relTol = 1e-8 //<! are values the same within 8 decimals
)
{
Info<< msg << x << endl;
Info<< msg << x << "?=" << y << endl;
unsigned nFail = 0;
@ -124,11 +124,11 @@ typename std::enable_if
const word& msg,
const Type& x,
const Type& y,
const scalar relTol = 1e-8,
const scalar absTol = 0
const scalar absTol = 0,
const scalar relTol = 1e-8
)
{
Info<< msg << x << endl;
Info<< msg << x << "?=" << y << endl;
unsigned nFail = 0;
@ -725,7 +725,7 @@ void test_eigenvalues(const tensor2D& T, const Vector2D<complex>& EVals)
// 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);
cmp("# Product of eigenvalues = det(T):", EValsProd, determinant, 1e-7);
}
{
@ -737,7 +737,7 @@ void test_eigenvalues(const tensor2D& T, const Vector2D<complex>& EVals)
{
EValsSum += val.real();
}
cmp("# Sum of eigenvalues = trace(sT):", EValsSum, trace, 1e-8, 1e-8);
cmp("# Sum of eigenvalues = trace(T):", EValsSum, trace, 1e-8);
}
}
@ -767,7 +767,7 @@ void test_characteristic_equation
for (const auto x : X)
{
cmp(" (Tc & EVec - EVal*EVec) = 0:", mag(x), 0.0, 1e-8, 1e-6);
cmp(" (Tc & EVec - EVal*EVec) = 0:", mag(x), 0.0, 1e-5);
}
}
}
@ -861,14 +861,13 @@ int main(int argc, char *argv[])
}
{
Info<< nl << " ## Test eigen functions by a zero tensor2D: ##"<< nl;
Info<< nl << " ## A zero tensor2D: ##"<< nl;
const tensor2D zeroT(Zero);
test_eigen_funcs(zeroT);
}
{
Info<< nl
<< " ## Test eigen functions by a tensor2D consisting of"
<< " repeated eigenvalues: ##"
<< " ## A tensor2D with repeated eigenvalues: ##"
<< nl;
const tensor2D T
(
@ -879,8 +878,7 @@ int main(int argc, char *argv[])
}
{
Info<< nl
<< " ## Test eigen functions by a skew-symmetric tensor2D"
<< " consisting of no-real eigenvalues: ##"
<< " ## A skew-symmetric tensor2D with no-real eigenvalues: ##"
<< nl;
const tensor2D T
(
@ -891,7 +889,7 @@ int main(int argc, char *argv[])
}
{
Info<< nl
<< " ## Test eigen functions by a stiff tensor2D: ##"
<< " ## A stiff tensor2D: ##"
<< nl;
const tensor2D stiff
(
@ -900,6 +898,68 @@ int main(int argc, char *argv[])
);
test_eigen_funcs(stiff);
}
{
Info<< nl
<< " ## Random tensor2D with tiny off-diag elements: ##"
<< nl;
const List<scalar> epsilons
({
0, SMALL, Foam::sqrt(SMALL), sqr(SMALL), Foam::cbrt(SMALL),
-SMALL, -Foam::sqrt(SMALL), -sqr(SMALL), -Foam::cbrt(SMALL)
});
for (label i = 0; i < numberOfTests; ++i)
{
for (const auto& eps : epsilons)
{
{
tensor2D T(makeRandomContainer(rndGen));
T.xy() = eps*rndGen.GaussNormal<scalar>();
test_eigen_funcs(T);
}
{
tensor2D T(makeRandomContainer(rndGen));
T.yx() = eps*rndGen.GaussNormal<scalar>();
test_eigen_funcs(T);
}
{
tensor2D T(makeRandomContainer(rndGen));
T.xy() = eps*rndGen.GaussNormal<scalar>();
T.yx() = eps*rndGen.GaussNormal<scalar>();
test_eigen_funcs(T);
}
{
tensor2D T(makeRandomContainer(rndGen));
T.xy() = 0;
T.yx() = eps*rndGen.GaussNormal<scalar>();
test_eigen_funcs(T);
}
{
tensor2D T(makeRandomContainer(rndGen));
T.xy() = eps*rndGen.GaussNormal<scalar>();
T.yx() = 0;
test_eigen_funcs(T);
}
{
tensor2D T(makeRandomContainer(rndGen));
T.xy() = eps;
test_eigen_funcs(T);
}
{
tensor2D T(makeRandomContainer(rndGen));
T.yx() = eps;
test_eigen_funcs(T);
}
{
tensor2D T(makeRandomContainer(rndGen));
T.xy() = eps;
T.yx() = eps;
test_eigen_funcs(T);
}
}
}
}
{
@ -963,6 +1023,7 @@ int main(int argc, char *argv[])
}
}
if (nFail_)
{
Info<< nl << " #### "