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bug #1036: implement verify_is_approx_upto_permutation through a combinatorial search.

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The previous implementation was subject to numerical cancellation issues.
This commit is contained in:
Gael Guennebaud 2015-07-20 15:34:06 +02:00
parent ab8b497a7e
commit 87f3e533f5
1 changed files with 47 additions and 7 deletions
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54
test/eigensolver_complex.cpp
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@ -13,20 +13,60 @@
#include <Eigen/Eigenvalues>
#include <Eigen/LU>
/* Check that two column vectors are approximately equal upto permutations,
by checking that the k-th power sums are equal for k = 1, ..., vec1.rows() */
template<typename MatrixType> bool find_pivot(typename MatrixType::Scalar tol, MatrixType &diffs, Index col=0)
{
typedef typename MatrixType::Scalar Scalar;
bool match = diffs.diagonal().sum() <= tol;
if(match || col==diffs.cols())
{
return match;
}
else
{
Index n = diffs.cols();
std::vector<std::pair<Index,Index> > transpositions;
for(Index i=col; i<n; ++i)
{
Index best_index(0);
if(diffs.col(col).segment(col,n-i).minCoeff(&best_index) > tol)
break;
best_index += col;
diffs.row(col).swap(diffs.row(best_index));
if(find_pivot(tol,diffs,col+1)) return true;
diffs.row(col).swap(diffs.row(best_index));
// move current pivot to the end
diffs.row(n-(i-col)-1).swap(diffs.row(best_index));
transpositions.push_back(std::pair<Index,Index>(n-(i-col)-1,best_index));
}
// restore
for(Index k=transpositions.size()-1; k>=0; --k)
diffs.row(transpositions[k].first).swap(diffs.row(transpositions[k].second));
}
return false;
}
/* Check that two column vectors are approximately equal upto permutations.
* Initially, this method checked that the k-th power sums are equal for all k = 1, ..., vec1.rows(),
* however this strategy is numerically inacurate because of numerical cancellation issues.
*/
template<typename VectorType>
void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2)
{
typedef typename NumTraits<typename VectorType::Scalar>::Real RealScalar;
typedef typename VectorType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
VERIFY(vec1.cols() == 1);
VERIFY(vec2.cols() == 1);
VERIFY(vec1.rows() == vec2.rows());
for (int k = 1; k <= vec1.rows(); ++k)
{
VERIFY_IS_APPROX(vec1.array().pow(RealScalar(k)).sum(), vec2.array().pow(RealScalar(k)).sum());
}
Index n = vec1.rows();
RealScalar tol = test_precision<RealScalar>()*test_precision<RealScalar>()*numext::maxi(vec1.squaredNorm(),vec2.squaredNorm());
Matrix<RealScalar,Dynamic,Dynamic> diffs = (vec1.rowwise().replicate(n) - vec2.rowwise().replicate(n).transpose()).cwiseAbs2();
VERIFY( find_pivot(tol, diffs) );
}