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merge with default branch

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This commit is contained in:
Gael Guennebaud
2014-07-10 22:04:45 +02:00
parent 61b88d2feb d1460d9278
commit 296cb40161
49 changed files with 263 additions and 167 deletions
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37
Eigen/src/Cholesky/LDLT.h
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@@ -276,23 +276,13 @@ template<> struct ldlt_inplace<Lower>
return true;
}
RealScalar cutoff(0), biggest_in_corner;
for (Index k = 0; k < size; ++k)
{
// Find largest diagonal element
Index index_of_biggest_in_corner;
biggest_in_corner = mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
index_of_biggest_in_corner += k;
if(k == 0)
{
// The biggest overall is the point of reference to which further diagonals
// are compared; if any diagonal is negligible compared
// to the largest overall, the algorithm bails.
cutoff = abs(NumTraits<Scalar>::epsilon() * biggest_in_corner);
}
transpositions.coeffRef(k) = index_of_biggest_in_corner;
if(k != index_of_biggest_in_corner)
{
@@ -323,16 +313,20 @@ template<> struct ldlt_inplace<Lower>
if(k>0)
{
temp.head(k) = mat.diagonal().head(k).asDiagonal() * A10.adjoint();
temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint();
mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();
if(rs>0)
A21.noalias() -= A20 * temp.head(k);
}
if((rs>0) && (abs(mat.coeffRef(k,k)) > cutoff))
A21 /= mat.coeffRef(k,k);
// In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot
// was smaller than the cutoff value. However, soince LDLT is not rank-revealing
// we should only make sure we do not introduce INF or NaN values.
// LAPACK also uses 0 as the cutoff value.
RealScalar realAkk = numext::real(mat.coeffRef(k,k));
if((rs>0) && (abs(realAkk) > RealScalar(0)))
A21 /= realAkk;
if (sign == PositiveSemiDef) {
if (realAkk < 0) sign = Indefinite;
} else if (sign == NegativeSemiDef) {
@@ -504,9 +498,14 @@ void LDLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) cons
// more precisely, use pseudo-inverse of D (see bug 241)
using std::abs;
EIGEN_USING_STD_MATH(max);
const Diagonal<const MatrixType> vecD = vectorD();
RealScalar tolerance = (max)( vecD.array().abs().maxCoeff() * NumTraits<Scalar>::epsilon(),
RealScalar(1) / NumTraits<RealScalar>::highest()); // motivated by LAPACK's xGELSS
const typename Diagonal<const MatrixType>::RealReturnType vecD(vectorD());
// In some previous versions, tolerance was set to the max of 1/highest and the maximal diagonal entry * epsilon
// as motivated by LAPACK's xGELSS:
// RealScalar tolerance = (max)(vectorD.array().abs().maxCoeff() *NumTraits<RealScalar>::epsilon(),RealScalar(1) / NumTraits<RealScalar>::highest());
// However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest
// diagonal element is not well justified and to numerical issues in some cases.
// Moreover, Lapack's xSYTRS routines use 0 for the tolerance.
RealScalar tolerance = RealScalar(1) / NumTraits<RealScalar>::highest();
for (Index i = 0; i < vecD.size(); ++i)
{
@@ -582,7 +581,7 @@ MatrixType LDLT<MatrixType,_UpLo>::reconstructedMatrix() const
// L^* P
res = matrixU() * res;
// D(L^*P)
res = vectorD().asDiagonal() * res;
res = vectorD().real().asDiagonal() * res;
// L(DL^*P)
res = matrixL() * res;
// P^T (LDL^*P)