1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
5// Copyright (C) 2013-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
6//
7// This Source Code Form is subject to the terms of the Mozilla
8// Public License v. 2.0. If a copy of the MPL was not distributed
9// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11#ifndef EIGEN_REALSVD2X2_H
12#define EIGEN_REALSVD2X2_H
13
14namespace Eigen {
15
16namespace internal {
17
18template<typename MatrixType, typename RealScalar, typename Index>
19void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
20 JacobiRotation<RealScalar> *j_left,
21 JacobiRotation<RealScalar> *j_right)
22{
23 using std::sqrt;
24 using std::abs;
25 Matrix<RealScalar,2,2> m;
26 m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
27 numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
28 JacobiRotation<RealScalar> rot1;
29 RealScalar t = m.coeff(0,0) + m.coeff(1,1);
30 RealScalar d = m.coeff(1,0) - m.coeff(0,1);
31
32 if(abs(d) < (std::numeric_limits<RealScalar>::min)())
33 {
34 rot1.s() = RealScalar(0);
35 rot1.c() = RealScalar(1);
36 }
37 else
38 {
39 // If d!=0, then t/d cannot overflow because the magnitude of the
40 // entries forming d are not too small compared to the ones forming t.
41 RealScalar u = t / d;
42 RealScalar tmp = sqrt(RealScalar(1) + numext::abs2(u));
43 rot1.s() = RealScalar(1) / tmp;
44 rot1.c() = u / tmp;
45 }
46 m.applyOnTheLeft(0,1,rot1);
47 j_right->makeJacobi(m,0,1);
48 *j_left = rot1 * j_right->transpose();
49}
50
51} // end namespace internal
52
53} // end namespace Eigen
54
55#endif // EIGEN_REALSVD2X2_H
56