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Suppress some false negatives in SVD unit test

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This commit is contained in:
Gael Guennebaud 2015-03-27 10:55:53 +01:00
parent 1b8cc9af43
commit 7e225b6fa4
1 changed files with 50 additions and 14 deletions
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64
test/svd_common.h
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@ -49,18 +49,39 @@ void svd_compare_to_full(const MatrixType& m,
unsigned int computationOptions,
const SvdType& referenceSvd)
{
typedef typename MatrixType::Index Index;
typedef typename MatrixType::RealScalar RealScalar;
Index rows = m.rows();
Index cols = m.cols();
Index diagSize = (std::min)(rows, cols);
RealScalar prec = test_precision<RealScalar>();
SvdType svd(m, computationOptions);
VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
if(computationOptions & (ComputeFullV|ComputeThinV))
{
VERIFY( (svd.matrixV().transpose()*svd.matrixV()).isIdentity(prec) );
VERIFY_IS_APPROX( svd.matrixV().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).transpose(),
referenceSvd.matrixV().leftCols(diagSize) * referenceSvd.singularValues().asDiagonal() * referenceSvd.matrixV().leftCols(diagSize).transpose());
}
if(computationOptions & (ComputeFullU|ComputeThinU))
{
VERIFY( (svd.matrixU().transpose()*svd.matrixU()).isIdentity(prec) );
VERIFY_IS_APPROX( svd.matrixU().leftCols(diagSize) * svd.singularValues().cwiseAbs2().asDiagonal() * svd.matrixU().leftCols(diagSize).transpose(),
referenceSvd.matrixU().leftCols(diagSize) * referenceSvd.singularValues().cwiseAbs2().asDiagonal() * referenceSvd.matrixU().leftCols(diagSize).transpose());
}
// The following checks are not critical.
// For instance, with Dived&Conquer SVD, if only the factor 'V' is computedt then different matrix-matrix product implementation will be used
// and the resulting 'V' factor might be significantly different when the SVD decomposition is not unique, especially with single precision float.
++g_test_level;
if(computationOptions & ComputeFullU) VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
if(computationOptions & ComputeThinU) VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
if(computationOptions & ComputeFullV) VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV());
if(computationOptions & ComputeFullV) VERIFY_IS_APPROX(svd.matrixV().cwiseAbs(), referenceSvd.matrixV().cwiseAbs());
if(computationOptions & ComputeThinV) VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
--g_test_level;
}
//
@ -85,33 +106,48 @@ void svd_least_square(const MatrixType& m, unsigned int computationOptions)
SvdType svd(m, computationOptions);
if(internal::is_same<RealScalar,double>::value) svd.setThreshold(1e-8);
else if(internal::is_same<RealScalar,float>::value) svd.setThreshold(1e-4);
else if(internal::is_same<RealScalar,float>::value) svd.setThreshold(2e-4);
SolutionType x = svd.solve(rhs);
// evaluate normal equation which works also for least-squares solutions
if(internal::is_same<RealScalar,double>::value || svd.rank()==m.diagonal().size())
{
// This test is not stable with single precision.
// This is probably because squaring m signicantly affects the precision.
VERIFY_IS_APPROX(m.adjoint()*(m*x),m.adjoint()*rhs);
}
RealScalar residual = (m*x-rhs).norm();
// Check that there is no significantly better solution in the neighborhood of x
RealScalar rhs_norm = rhs.norm();
if(!test_isMuchSmallerThan(residual,rhs.norm()))
{
// ^^^ If the residual is very small, then we have an exact solution, so we are already good.
// evaluate normal equation which works also for least-squares solutions
if(internal::is_same<RealScalar,double>::value || svd.rank()==m.diagonal().size())
{
using std::sqrt;
// This test is not stable with single precision.
// This is probably because squaring m signicantly affects the precision.
if(internal::is_same<RealScalar,float>::value) ++g_test_level;
VERIFY_IS_APPROX(m.adjoint()*(m*x),m.adjoint()*rhs);
if(internal::is_same<RealScalar,float>::value) --g_test_level;
}
// Check that there is no significantly better solution in the neighborhood of x
for(Index k=0;k<x.rows();++k)
{
using std::abs;
SolutionType y(x);
y.row(k) = (1.+2*NumTraits<RealScalar>::epsilon())*x.row(k);
RealScalar residual_y = (m*y-rhs).norm();
VERIFY( test_isMuchSmallerThan(abs(residual_y-residual), rhs_norm) || residual < residual_y );
if(internal::is_same<RealScalar,float>::value) ++g_test_level;
VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
if(internal::is_same<RealScalar,float>::value) --g_test_level;
y.row(k) = (1.-2*NumTraits<RealScalar>::epsilon())*x.row(k);
residual_y = (m*y-rhs).norm();
VERIFY( test_isMuchSmallerThan(abs(residual_y-residual), rhs_norm) || residual < residual_y );
if(internal::is_same<RealScalar,float>::value) ++g_test_level;
VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
if(internal::is_same<RealScalar,float>::value) --g_test_level;
}
}
}