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Merged latest updates from trunk

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Benoit Steiner 2016-04-14 15:25:20 -07:00
commit 00dfe18487
2 changed files with 34 additions and 20 deletions
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42
Eigen/src/SVD/JacobiSVD.h
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@ -350,7 +350,8 @@ template<typename MatrixType, int QRPreconditioner>
struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, false> struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, false>
{ {
typedef JacobiSVD<MatrixType, QRPreconditioner> SVD; typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
static bool run(typename SVD::WorkMatrixType&, SVD&, Index, Index, const typename MatrixType::RealScalar&) { return true; } typedef typename MatrixType::RealScalar RealScalar;
static bool run(typename SVD::WorkMatrixType&, SVD&, Index, Index, RealScalar&) { return true; }
}; };
template<typename MatrixType, int QRPreconditioner> template<typename MatrixType, int QRPreconditioner>
@ -359,25 +360,30 @@ struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
typedef JacobiSVD<MatrixType, QRPreconditioner> SVD; typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
typedef typename MatrixType::Scalar Scalar; typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar; typedef typename MatrixType::RealScalar RealScalar;
static bool run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q, const typename MatrixType::RealScalar& precision) static bool run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q, RealScalar& maxDiagEntry)
{ {
using std::sqrt; using std::sqrt;
using std::abs;
Scalar z; Scalar z;
JacobiRotation<Scalar> rot; JacobiRotation<Scalar> rot;
RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p))); RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));
const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
const RealScalar precision = NumTraits<Scalar>::epsilon();
if(n==0) if(n==0)
{ {
// make sure first column is zero // make sure first column is zero
work_matrix.coeffRef(p,p) = work_matrix.coeffRef(q,p) = Scalar(0); work_matrix.coeffRef(p,p) = work_matrix.coeffRef(q,p) = Scalar(0);
if(work_matrix.coeff(p,q)!=Scalar(0))
if(abs(numext::imag(work_matrix.coeff(p,q)))>considerAsZero)
{ {
// work_matrix.coeff(p,q) can be zero if work_matrix.coeff(q,p) is not zero but small enough to underflow when computing n // work_matrix.coeff(p,q) can be zero if work_matrix.coeff(q,p) is not zero but small enough to underflow when computing n
z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q); z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
work_matrix.row(p) *= z; work_matrix.row(p) *= z;
if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z); if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
} }
if(work_matrix.coeff(q,q)!=Scalar(0)) if(abs(numext::imag(work_matrix.coeff(q,q)))>considerAsZero)
{ {
z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q); z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
work_matrix.row(q) *= z; work_matrix.row(q) *= z;
@ -391,13 +397,13 @@ struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
rot.s() = work_matrix.coeff(q,p) / n; rot.s() = work_matrix.coeff(q,p) / n;
work_matrix.applyOnTheLeft(p,q,rot); work_matrix.applyOnTheLeft(p,q,rot);
if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint()); if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());
if(work_matrix.coeff(p,q) != Scalar(0)) if(abs(numext::imag(work_matrix.coeff(p,q)))>considerAsZero)
{ {
z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q); z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
work_matrix.col(q) *= z; work_matrix.col(q) *= z;
if(svd.computeV()) svd.m_matrixV.col(q) *= z; if(svd.computeV()) svd.m_matrixV.col(q) *= z;
} }
if(work_matrix.coeff(q,q) != Scalar(0)) if(abs(numext::imag(work_matrix.coeff(q,q)))>considerAsZero)
{ {
z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q); z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
work_matrix.row(q) *= z; work_matrix.row(q) *= z;
@ -405,11 +411,11 @@ struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
} }
} }
const RealScalar considerAsZero = RealScalar(2) * std::numeric_limits<RealScalar>::denorm_min(); // update largest diagonal entry
RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, maxDiagEntry = numext::maxi(maxDiagEntry,numext::maxi(abs(work_matrix.coeff(p,p)), abs(work_matrix.coeff(q,q))));
precision * numext::maxi<RealScalar>(abs(work_matrix.coeff(p,p)), abs(work_matrix.coeff(q,q)))); // and check whether the 2x2 block is already diagonal
// return true if we still have some work to do RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, precision * maxDiagEntry);
return numext::abs(work_matrix(p,q)) > threshold || numext::abs(work_matrix(q,p)) > threshold; return abs(work_matrix.coeff(p,q))>threshold || abs(work_matrix.coeff(q,p)) > threshold;
} }
}; };
@ -426,7 +432,6 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
JacobiRotation<RealScalar> rot1; JacobiRotation<RealScalar> rot1;
RealScalar t = m.coeff(0,0) + m.coeff(1,1); RealScalar t = m.coeff(0,0) + m.coeff(1,1);
RealScalar d = m.coeff(1,0) - m.coeff(0,1); RealScalar d = m.coeff(1,0) - m.coeff(0,1);
if(d == RealScalar(0)) if(d == RealScalar(0))
{ {
rot1.s() = RealScalar(0); rot1.s() = RealScalar(0);
@ -719,6 +724,7 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
} }
/*** step 2. The main Jacobi SVD iteration. ***/ /*** step 2. The main Jacobi SVD iteration. ***/
RealScalar maxDiagEntry = m_workMatrix.cwiseAbs().diagonal().maxCoeff();
bool finished = false; bool finished = false;
while(!finished) while(!finished)
@ -734,16 +740,13 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
// if this 2x2 sub-matrix is not diagonal already... // if this 2x2 sub-matrix is not diagonal already...
// notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't // notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't
// keep us iterating forever. Similarly, small denormal numbers are considered zero. // keep us iterating forever. Similarly, small denormal numbers are considered zero.
RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, precision * maxDiagEntry);
precision * numext::maxi<RealScalar>(abs(m_workMatrix.coeff(p,p)),
abs(m_workMatrix.coeff(q,q))));
// We compare both values to threshold instead of calling max to be robust to NaN (See bug 791)
if(abs(m_workMatrix.coeff(p,q))>threshold || abs(m_workMatrix.coeff(q,p)) > threshold) if(abs(m_workMatrix.coeff(p,q))>threshold || abs(m_workMatrix.coeff(q,p)) > threshold)
{ {
finished = false; finished = false;
// perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal // perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal
// the complex to real operation returns true is the updated 2x2 block is not already diagonal // the complex to real operation returns true is the updated 2x2 block is not already diagonal
if(internal::svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner>::run(m_workMatrix, *this, p, q, precision)) if(internal::svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner>::run(m_workMatrix, *this, p, q, maxDiagEntry))
{ {
JacobiRotation<RealScalar> j_left, j_right; JacobiRotation<RealScalar> j_left, j_right;
internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right); internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right);
@ -754,6 +757,9 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
m_workMatrix.applyOnTheRight(p,q,j_right); m_workMatrix.applyOnTheRight(p,q,j_right);
if(computeV()) m_matrixV.applyOnTheRight(p,q,j_right); if(computeV()) m_matrixV.applyOnTheRight(p,q,j_right);
// keep track of the largest diagonal coefficient
maxDiagEntry = numext::maxi(maxDiagEntry,numext::maxi(abs(m_workMatrix.coeff(p,p)), abs(m_workMatrix.coeff(q,q))));
} }
} }
} }

12
test/svd_fill.h
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@ -80,6 +80,8 @@ void svd_fill_random(MatrixType &m, int Option = 0)
Index i = internal::random<Index>(0,m.rows()-1); Index i = internal::random<Index>(0,m.rows()-1);
Index j = internal::random<Index>(0,m.cols()-1); Index j = internal::random<Index>(0,m.cols()-1);
m(j,i) = m(i,j) = samples(internal::random<Index>(0,samples.size()-1)); m(j,i) = m(i,j) = samples(internal::random<Index>(0,samples.size()-1));
if(NumTraits<Scalar>::IsComplex)
*(&numext::real_ref(m(j,i))+1) = *(&numext::real_ref(m(i,j))+1) = samples.real()(internal::random<Index>(0,samples.size()-1));
} }
} }
} }
@ -91,8 +93,14 @@ void svd_fill_random(MatrixType &m, int Option = 0)
if(!(dup && unit_uv)) if(!(dup && unit_uv))
{ {
Index n = internal::random<Index>(0,m.size()-1); Index n = internal::random<Index>(0,m.size()-1);
for(Index i=0; i<n; ++i) for(Index k=0; k<n; ++k)
m(internal::random<Index>(0,m.rows()-1), internal::random<Index>(0,m.cols()-1)) = samples(internal::random<Index>(0,samples.size()-1)); {
Index i = internal::random<Index>(0,m.rows()-1);
Index j = internal::random<Index>(0,m.cols()-1);
m(i,j) = samples(internal::random<Index>(0,samples.size()-1));
if(NumTraits<Scalar>::IsComplex)
*(&numext::real_ref(m(i,j))+1) = samples.real()(internal::random<Index>(0,samples.size()-1));
}
} }
} }
} }