1*bf2c3715SXin Li // This file is part of Eigen, a lightweight C++ template library
2*bf2c3715SXin Li // for linear algebra.
3*bf2c3715SXin Li //
4*bf2c3715SXin Li // Copyright (C) 2009-2010 Benoit Jacob <[email protected]>
5*bf2c3715SXin Li // Copyright (C) 2013-2016 Gael Guennebaud <[email protected]>
6*bf2c3715SXin Li //
7*bf2c3715SXin Li // This Source Code Form is subject to the terms of the Mozilla
8*bf2c3715SXin Li // Public License v. 2.0. If a copy of the MPL was not distributed
9*bf2c3715SXin Li // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10*bf2c3715SXin Li
11*bf2c3715SXin Li #ifndef EIGEN_REALSVD2X2_H
12*bf2c3715SXin Li #define EIGEN_REALSVD2X2_H
13*bf2c3715SXin Li
14*bf2c3715SXin Li namespace Eigen {
15*bf2c3715SXin Li
16*bf2c3715SXin Li namespace internal {
17*bf2c3715SXin Li
18*bf2c3715SXin Li 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*bf2c3715SXin Li void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
20*bf2c3715SXin Li JacobiRotation<RealScalar> *j_left,
21*bf2c3715SXin Li JacobiRotation<RealScalar> *j_right)
22*bf2c3715SXin Li {
23*bf2c3715SXin Li using std::sqrt;
24*bf2c3715SXin Li using std::abs;
25*bf2c3715SXin Li Matrix<RealScalar,2,2> m;
26*bf2c3715SXin Li m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
27*bf2c3715SXin Li numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
28*bf2c3715SXin Li JacobiRotation<RealScalar> rot1;
29*bf2c3715SXin Li RealScalar t = m.coeff(0,0) + m.coeff(1,1);
30*bf2c3715SXin Li RealScalar d = m.coeff(1,0) - m.coeff(0,1);
31*bf2c3715SXin Li
32*bf2c3715SXin Li if(abs(d) < (std::numeric_limits<RealScalar>::min)())
33*bf2c3715SXin Li {
34*bf2c3715SXin Li rot1.s() = RealScalar(0);
35*bf2c3715SXin Li rot1.c() = RealScalar(1);
36*bf2c3715SXin Li }
37*bf2c3715SXin Li else
38*bf2c3715SXin Li {
39*bf2c3715SXin Li // If d!=0, then t/d cannot overflow because the magnitude of the
40*bf2c3715SXin Li // entries forming d are not too small compared to the ones forming t.
41*bf2c3715SXin Li RealScalar u = t / d;
42*bf2c3715SXin Li RealScalar tmp = sqrt(RealScalar(1) + numext::abs2(u));
43*bf2c3715SXin Li rot1.s() = RealScalar(1) / tmp;
44*bf2c3715SXin Li rot1.c() = u / tmp;
45*bf2c3715SXin Li }
46*bf2c3715SXin Li m.applyOnTheLeft(0,1,rot1);
47*bf2c3715SXin Li j_right->makeJacobi(m,0,1);
48*bf2c3715SXin Li *j_left = rot1 * j_right->transpose();
49*bf2c3715SXin Li }
50*bf2c3715SXin Li
51*bf2c3715SXin Li } // end namespace internal
52*bf2c3715SXin Li
53*bf2c3715SXin Li } // end namespace Eigen
54*bf2c3715SXin Li
55*bf2c3715SXin Li #endif // EIGEN_REALSVD2X2_H
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