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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 
14 namespace Eigen {
15 
16 namespace internal {
17 
18 template<typename MatrixType, typename RealScalar, typename Index>
real_2x2_jacobi_svd(const MatrixType & matrix,Index p,Index q,JacobiRotation<RealScalar> * j_left,JacobiRotation<RealScalar> * j_right)19 void 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