Lines Matching defs:iu
195 Index findSmallSubdiagEntry(Index iu, Scalar norm);
196 void splitOffTwoRows(Index iu, bool computeU, Scalar exshift);
197 void computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo);
198 void initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector);
199 void performFrancisQRStep(Index il, Index im, Index iu, bool computeU, const Vector3s& firstHouseholderVector, Scalar* workspace);
220 // Rows il,...,iu is the part we are working on (the active window).
221 // Rows iu+1,...,end are already brought in triangular form.
222 Index iu = m_matT.cols() - 1;
229 while (iu >= 0)
231 Index il = findSmallSubdiagEntry(iu, norm);
234 if (il == iu) // One root found
236 m_matT.coeffRef(iu,iu) = m_matT.coeff(iu,iu) + exshift;
237 if (iu > 0)
238 m_matT.coeffRef(iu, iu-1) = Scalar(0);
239 iu--;
242 else if (il == iu-1) // Two roots found
244 splitOffTwoRows(iu, computeU, exshift);
245 iu -= 2;
252 computeShift(iu, iter, exshift, shiftInfo);
256 initFrancisQRStep(il, iu, shiftInfo, im, firstHouseholderVector);
257 performFrancisQRStep(il, im, iu, computeU, firstHouseholderVector, workspace);
287 inline typename MatrixType::Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu, Scalar norm)
289 Index res = iu;
302 /** \internal Update T given that rows iu-1 and iu decouple from the rest. */
304 inline void RealSchur<MatrixType>::splitOffTwoRows(Index iu, bool computeU, Scalar exshift)
310 Scalar p = Scalar(0.5) * (m_matT.coeff(iu-1,iu-1) - m_matT.coeff(iu,iu));
311 Scalar q = p * p + m_matT.coeff(iu,iu-1) * m_matT.coeff(iu-1,iu); // q = tr^2 / 4 - det = discr/4
312 m_matT.coeffRef(iu,iu) += exshift;
313 m_matT.coeffRef(iu-1,iu-1) += exshift;
320 rot.makeGivens(p + z, m_matT.coeff(iu, iu-1));
322 rot.makeGivens(p - z, m_matT.coeff(iu, iu-1));
324 m_matT.rightCols(size-iu+1).applyOnTheLeft(iu-1, iu, rot.adjoint());
325 m_matT.topRows(iu+1).applyOnTheRight(iu-1, iu, rot);
326 m_matT.coeffRef(iu, iu-1) = Scalar(0);
328 m_matU.applyOnTheRight(iu-1, iu, rot);
331 if (iu > 1)
332 m_matT.coeffRef(iu-1, iu-2) = Scalar(0);
337 inline void RealSchur<MatrixType>::computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo)
339 shiftInfo.coeffRef(0) = m_matT.coeff(iu,iu);
340 shiftInfo.coeffRef(1) = m_matT.coeff(iu-1,iu-1);
341 shiftInfo.coeffRef(2) = m_matT.coeff(iu,iu-1) * m_matT.coeff(iu-1,iu);
347 for (Index i = 0; i <= iu; ++i)
349 Scalar s = internal::abs(m_matT.coeff(iu,iu-1)) + internal::abs(m_matT.coeff(iu-1,iu-2));
368 for (Index i = 0; i <= iu; ++i)
377 inline void RealSchur<MatrixType>::initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector)
381 for (im = iu-2; im >= il; --im)
401 /** \internal Perform a Francis QR step involving rows il:iu and columns im:iu. */
403 inline void RealSchur<MatrixType>::performFrancisQRStep(Index il, Index im, Index iu, bool computeU, const Vector3s& firstHouseholderVector, Scalar* workspace)
406 assert(im <= iu-2);
410 for (Index k = im; k <= iu-2; ++k)
433 m_matT.block(0, k, (std::min)(iu
439 Matrix<Scalar, 2, 1> v = m_matT.template block<2,1>(iu-1, iu-2);
446 m_matT.coeffRef(iu-1, iu-2) = beta;
447 m_matT.block(iu-1, iu-1, 2, size-iu+1).applyHouseholderOnTheLeft(ess, tau, workspace);
448 m_matT.block(0, iu-1, iu+1, 2).applyHouseholderOnTheRight(ess, tau, workspace);
450 m_matU.block(0, iu-1, size, 2).applyHouseholderOnTheRight(ess, tau, workspace);
454 for (Index i = im+2; i <= iu; ++i)
