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Update RealQZ to reduce 2x2 diagonal block of T corresponding to non reduced diagonal block of S to positive diagonal form.

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This step involve a real 2x2 SVD problem. The respective routine is thus in src/misc/ to be shared by both EVD and AVD modules.
This commit is contained in:
Gael Guennebaud
2016-06-09 17:11:03 +02:00
parent 15890c304e
commit c1f9ca9254
5 changed files with 87 additions and 33 deletions
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54
Eigen/src/misc/RealSvd2x2.h Normal file
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2013-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_REALSVD2X2_H
#define EIGEN_REALSVD2X2_H
namespace Eigen {
namespace internal {
template<typename MatrixType, typename RealScalar, typename Index>
void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
JacobiRotation<RealScalar> *j_left,
JacobiRotation<RealScalar> *j_right)
{
using std::sqrt;
using std::abs;
Matrix<RealScalar,2,2> m;
m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
JacobiRotation<RealScalar> rot1;
RealScalar t = m.coeff(0,0) + m.coeff(1,1);
RealScalar d = m.coeff(1,0) - m.coeff(0,1);
if(d == RealScalar(0))
{
rot1.s() = RealScalar(0);
rot1.c() = RealScalar(1);
}
else
{
// If d!=0, then t/d cannot overflow because the magnitude of the
// entries forming d are not too small compared to the ones forming t.
RealScalar u = t / d;
RealScalar tmp = sqrt(RealScalar(1) + numext::abs2(u));
rot1.s() = RealScalar(1) / tmp;
rot1.c() = u / tmp;
}
m.applyOnTheLeft(0,1,rot1);
j_right->makeJacobi(m,0,1);
*j_left = rot1 * j_right->transpose();
}
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_REALSVD2X2_H