1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library
2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// for linear algebra.
3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath//
4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath//
6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla
7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed
8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#ifndef EIGEN_JACOBISVD_H
11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#define EIGEN_JACOBISVD_H
12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathnamespace Eigen {
14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathnamespace internal {
16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// forward declaration (needed by ICC)
17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// the empty body is required by MSVC
18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType, int QRPreconditioner,
19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath         bool IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>
20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathstruct svd_precondition_2x2_block_to_be_real {};
21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/*** QR preconditioners (R-SVD)
23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ***
24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath *** Their role is to reduce the problem of computing the SVD to the case of a square matrix.
25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath *** This approach, known as R-SVD, is an optimization for rectangular-enough matrices, and is a requirement for
26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath *** JacobiSVD which by itself is only able to work on square matrices.
27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ***/
28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathenum { PreconditionIfMoreColsThanRows, PreconditionIfMoreRowsThanCols };
30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType, int QRPreconditioner, int Case>
32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathstruct qr_preconditioner_should_do_anything
33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{
34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  enum { a = MatrixType::RowsAtCompileTime != Dynamic &&
35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath             MatrixType::ColsAtCompileTime != Dynamic &&
36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath             MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime,
37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath         b = MatrixType::RowsAtCompileTime != Dynamic &&
38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath             MatrixType::ColsAtCompileTime != Dynamic &&
39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath             MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime,
40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath         ret = !( (QRPreconditioner == NoQRPreconditioner) ||
41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath                  (Case == PreconditionIfMoreColsThanRows && bool(a)) ||
42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath                  (Case == PreconditionIfMoreRowsThanCols && bool(b)) )
43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  };
44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath};
45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType, int QRPreconditioner, int Case,
47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath         bool DoAnything = qr_preconditioner_should_do_anything<MatrixType, QRPreconditioner, Case>::ret
48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath> struct qr_preconditioner_impl {};
49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType, int QRPreconditioner, int Case>
51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathclass qr_preconditioner_impl<MatrixType, QRPreconditioner, Case, false>
52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{
53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathpublic:
54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::Index Index;
55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  void allocate(const JacobiSVD<MatrixType, QRPreconditioner>&) {}
56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  bool run(JacobiSVD<MatrixType, QRPreconditioner>&, const MatrixType&)
57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    return false;
59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath};
61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/*** preconditioner using FullPivHouseholderQR ***/
63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType>
65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathclass qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{
67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathpublic:
68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::Index Index;
69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::Scalar Scalar;
70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  enum
71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime
74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  };
75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef Matrix<Scalar, 1, RowsAtCompileTime, RowMajor, 1, MaxRowsAtCompileTime> WorkspaceType;
76c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)
78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
817faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      m_qr.~QRType();
827faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      ::new (&m_qr) QRType(svd.rows(), svd.cols());
83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if (svd.m_computeFullU) m_workspace.resize(svd.rows());
85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if(matrix.rows() > matrix.cols())
90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      m_qr.compute(matrix);
92c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace);
94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      return true;
96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    return false;
98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathprivate:
1007faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  typedef FullPivHouseholderQR<MatrixType> QRType;
1017faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  QRType m_qr;
102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  WorkspaceType m_workspace;
103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath};
104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType>
106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathclass qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{
108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathpublic:
109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::Index Index;
110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::Scalar Scalar;
111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  enum
112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    Options = MatrixType::Options
118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  };
119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath          TransposeTypeWithSameStorageOrder;
121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)
123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
1267faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      m_qr.~QRType();
1277faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      ::new (&m_qr) QRType(svd.cols(), svd.rows());
128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    m_adjoint.resize(svd.cols(), svd.rows());
130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if (svd.m_computeFullV) m_workspace.resize(svd.cols());
131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if(matrix.cols() > matrix.rows())
136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      m_adjoint = matrix.adjoint();
138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      m_qr.compute(m_adjoint);
139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace);
141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      return true;
143c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
144c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    else return false;
145c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathprivate:
1477faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  typedef FullPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
1487faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  QRType m_qr;
149c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  TransposeTypeWithSameStorageOrder m_adjoint;
150c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typename internal::plain_row_type<MatrixType>::type m_workspace;
151c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath};
152c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
153c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/*** preconditioner using ColPivHouseholderQR ***/
154c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
155c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType>
156c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathclass qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
157c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{
158c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathpublic:
159c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::Index Index;
160c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
161c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)
162c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
163c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
164c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
1657faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      m_qr.~QRType();
1667faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      ::new (&m_qr) QRType(svd.rows(), svd.cols());
167c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
168c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if (svd.m_computeFullU) m_workspace.resize(svd.rows());
169c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
170c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
171c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
172c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
173c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
174c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if(matrix.rows() > matrix.cols())
175c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
176c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      m_qr.compute(matrix);
177c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
178c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
179c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      else if(svd.m_computeThinU)
180c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      {
181c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
182c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
183c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      }
184c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
185c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      return true;
186c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
187c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    return false;
188c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
189c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
190c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathprivate:
1917faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  typedef ColPivHouseholderQR<MatrixType> QRType;
1927faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  QRType m_qr;
193c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typename internal::plain_col_type<MatrixType>::type m_workspace;
194c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath};
195c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
196c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType>
197c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathclass qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
198c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{
199c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathpublic:
200c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::Index Index;
201c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::Scalar Scalar;
202c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  enum
203c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
204c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
205c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
206c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
207c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
208c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    Options = MatrixType::Options
209c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  };
210c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
211c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
212c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath          TransposeTypeWithSameStorageOrder;
213c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
214c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)
215c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
216c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
217c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
2187faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      m_qr.~QRType();
2197faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      ::new (&m_qr) QRType(svd.cols(), svd.rows());
220c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
221c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if (svd.m_computeFullV) m_workspace.resize(svd.cols());
222c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
223c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    m_adjoint.resize(svd.cols(), svd.rows());
224c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
225c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
226c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
227c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
228c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if(matrix.cols() > matrix.rows())
229c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
230c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      m_adjoint = matrix.adjoint();
231c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      m_qr.compute(m_adjoint);
232c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
233c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
234c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
235c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      else if(svd.m_computeThinV)
236c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      {
237c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
238c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
239c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      }
240c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
241c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      return true;
242c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
243c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    else return false;
244c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
245c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
246c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathprivate:
2477faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  typedef ColPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
2487faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  QRType m_qr;
249c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  TransposeTypeWithSameStorageOrder m_adjoint;
250c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typename internal::plain_row_type<MatrixType>::type m_workspace;
251c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath};
252c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
253c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/*** preconditioner using HouseholderQR ***/
254c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
255c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType>
256c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathclass qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
257c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{
258c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathpublic:
259c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::Index Index;
260c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
261c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)
262c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
263c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
264c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
2657faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      m_qr.~QRType();
2667faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      ::new (&m_qr) QRType(svd.rows(), svd.cols());
267c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
268c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if (svd.m_computeFullU) m_workspace.resize(svd.rows());
269c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
270c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
271c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
272c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)
273c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
274c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if(matrix.rows() > matrix.cols())
275c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
276c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      m_qr.compute(matrix);
277c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
278c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
279c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      else if(svd.m_computeThinU)
280c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      {
281c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
282c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
283c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      }
284c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());
285c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      return true;
286c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
287c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    return false;
288c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
289c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathprivate:
2907faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  typedef HouseholderQR<MatrixType> QRType;
2917faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  QRType m_qr;
292c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typename internal::plain_col_type<MatrixType>::type m_workspace;
293c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath};
294c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
295c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType>
296c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathclass qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
297c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{
298c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathpublic:
299c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::Index Index;
300c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::Scalar Scalar;
301c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  enum
302c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
303c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
304c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
305c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
306c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
307c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    Options = MatrixType::Options
308c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  };
309c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
310c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
311c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath          TransposeTypeWithSameStorageOrder;
312c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
313c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)
314c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
315c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
316c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
3177faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      m_qr.~QRType();
3187faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      ::new (&m_qr) QRType(svd.cols(), svd.rows());
319c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
320c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if (svd.m_computeFullV) m_workspace.resize(svd.cols());
321c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
322c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    m_adjoint.resize(svd.cols(), svd.rows());
323c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
324c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
325c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)
326c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
327c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if(matrix.cols() > matrix.rows())
328c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
329c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      m_adjoint = matrix.adjoint();
330c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      m_qr.compute(m_adjoint);
331c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
332c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
333c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
334c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      else if(svd.m_computeThinV)
335c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      {
336c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
337c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
338c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      }
339c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());
340c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      return true;
341c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
342c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    else return false;
343c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
344c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
345c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathprivate:
3467faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  typedef HouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
3477faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  QRType m_qr;
348c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  TransposeTypeWithSameStorageOrder m_adjoint;
349c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typename internal::plain_row_type<MatrixType>::type m_workspace;
350c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath};
351c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
352c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/*** 2x2 SVD implementation
353c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ***
354c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath *** JacobiSVD consists in performing a series of 2x2 SVD subproblems
355c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ***/
356c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
357c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType, int QRPreconditioner>
358c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathstruct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, false>
359c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{
360c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
361c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename SVD::Index Index;
362c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  static void run(typename SVD::WorkMatrixType&, SVD&, Index, Index) {}
363c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath};
364c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
365c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType, int QRPreconditioner>
366c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathstruct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
367c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{
368c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
369c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::Scalar Scalar;
370c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename MatrixType::RealScalar RealScalar;
371c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  typedef typename SVD::Index Index;
372c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  static void run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q)
373c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
3747faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    using std::sqrt;
375c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    Scalar z;
376c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    JacobiRotation<Scalar> rot;
3777faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));
3787faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez
379c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    if(n==0)
380c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
381c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
382c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      work_matrix.row(p) *= z;
383c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
3847faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      if(work_matrix.coeff(q,q)!=Scalar(0))
3857faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      {
3867faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez        z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
3877faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez        work_matrix.row(q) *= z;
3887faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez        if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
3897faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      }
3907faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      // otherwise the second row is already zero, so we have nothing to do.
391c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
392c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    else
393c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
394c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      rot.c() = conj(work_matrix.coeff(p,p)) / n;
395c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      rot.s() = work_matrix.coeff(q,p) / n;
396c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      work_matrix.applyOnTheLeft(p,q,rot);
397c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());
398c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(work_matrix.coeff(p,q) != Scalar(0))
399c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      {
400c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        Scalar z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
401c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        work_matrix.col(q) *= z;
402c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        if(svd.computeV()) svd.m_matrixV.col(q) *= z;
403c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      }
404c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      if(work_matrix.coeff(q,q) != Scalar(0))
405c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      {
406c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
407c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        work_matrix.row(q) *= z;
408c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
409c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      }
410c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
411c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
412c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath};
413c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
414c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType, typename RealScalar, typename Index>
415c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathvoid real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
416c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath                            JacobiRotation<RealScalar> *j_left,
417c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath                            JacobiRotation<RealScalar> *j_right)
418c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{
4197faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  using std::sqrt;
4207faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  using std::abs;
421c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  Matrix<RealScalar,2,2> m;
4227faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez  m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
4237faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez       numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
424c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  JacobiRotation<RealScalar> rot1;
425c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  RealScalar t = m.coeff(0,0) + m.coeff(1,1);
426c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  RealScalar d = m.coeff(1,0) - m.coeff(0,1);
427c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  if(t == RealScalar(0))
428c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
429c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    rot1.c() = RealScalar(0);
430c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    rot1.s() = d > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
431c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
432c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  else
433c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  {
4347faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    RealScalar t2d2 = numext::hypot(t,d);
4357faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    rot1.c() = abs(t)/t2d2;
4367faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    rot1.s() = d/t2d2;
4377faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    if(t<RealScalar(0))
4387faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      rot1.s() = -rot1.s();
439c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  }
440c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  m.applyOnTheLeft(0,1,rot1);
441c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  j_right->makeJacobi(m,0,1);
442c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *j_left  = rot1 * j_right->transpose();
443c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}
444c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
445c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} // end namespace internal
446c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
447c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \ingroup SVD_Module
448c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
449c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
450c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * \class JacobiSVD
451c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
452c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * \brief Two-sided Jacobi SVD decomposition of a rectangular matrix
453c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
454c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * \param MatrixType the type of the matrix of which we are computing the SVD decomposition
455c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * \param QRPreconditioner this optional parameter allows to specify the type of QR decomposition that will be used internally
456c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *                        for the R-SVD step for non-square matrices. See discussion of possible values below.
457c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
458c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
459c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *   \f[ A = U S V^* \f]
460c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal;
461c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * the diagonal entries of S are known as the \em singular \em values of \a A and the columns of \a U and \a V are known as the left
462c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * and right \em singular \em vectors of \a A respectively.
463c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
464c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * Singular values are always sorted in decreasing order.
465c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
466c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * This JacobiSVD decomposition computes only the singular values by default. If you want \a U or \a V, you need to ask for them explicitly.
467c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
468c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \a m be the
469c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * smaller value among \a n and \a p, there are only \a m singular vectors; the remaining columns of \a U and \a V do not correspond to actual
470c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix,
471c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving.
472c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
473c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * Here's an example demonstrating basic usage:
474c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * \include JacobiSVD_basic.cpp
475c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * Output: \verbinclude JacobiSVD_basic.out
476c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
477c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * This JacobiSVD class is a two-sided Jacobi R-SVD decomposition, ensuring optimal reliability and accuracy. The downside is that it's slower than
478c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * bidiagonalizing SVD algorithms for large square matrices; however its complexity is still \f$ O(n^2p) \f$ where \a n is the smaller dimension and
479c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * \a p is the greater dimension, meaning that it is still of the same order of complexity as the faster bidiagonalizing R-SVD algorithms.
480c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * In particular, like any R-SVD, it takes advantage of non-squareness in that its complexity is only linear in the greater dimension.
481c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
482c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to
483c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * terminate in finite (and reasonable) time.
484c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
485c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * The possible values for QRPreconditioner are:
486c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * \li ColPivHouseholderQRPreconditioner is the default. In practice it's very safe. It uses column-pivoting QR.
487c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * \li FullPivHouseholderQRPreconditioner, is the safest and slowest. It uses full-pivoting QR.
488c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *     Contrary to other QRs, it doesn't allow computing thin unitaries.
489c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * \li HouseholderQRPreconditioner is the fastest, and less safe and accurate than the pivoting variants. It uses non-pivoting QR.
490c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *     This is very similar in safety and accuracy to the bidiagonalization process used by bidiagonalizing SVD algorithms (since bidiagonalization
491c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *     is inherently non-pivoting). However the resulting SVD is still more reliable than bidiagonalizing SVDs because the Jacobi-based iterarive
492c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *     process is more reliable than the optimized bidiagonal SVD iterations.
493c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * \li NoQRPreconditioner allows not to use a QR preconditioner at all. This is useful if you know that you will only be computing
494c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *     JacobiSVD decompositions of square matrices. Non-square matrices require a QR preconditioner. Using this option will result in
495c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *     faster compilation and smaller executable code. It won't significantly speed up computation, since JacobiSVD is always checking
496c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *     if QR preconditioning is needed before applying it anyway.
497c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  *
498c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  * \sa MatrixBase::jacobiSvd()
499c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  */
500c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename _MatrixType, int QRPreconditioner> class JacobiSVD
501c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{
502c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath  public:
503c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
504c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    typedef _MatrixType MatrixType;
505c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    typedef typename MatrixType::Scalar Scalar;
506c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
507c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    typedef typename MatrixType::Index Index;
508c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    enum {
509c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      RowsAtCompileTime = MatrixType::RowsAtCompileTime,
510c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
511c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),
512c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
513c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
514c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),
515c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      MatrixOptions = MatrixType::Options
516c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    };
517c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
518c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
519c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath                   MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
520c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath            MatrixUType;
521c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
522c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath                   MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
523c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath            MatrixVType;
524c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
525c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    typedef typename internal::plain_row_type<MatrixType>::type RowType;
526c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    typedef typename internal::plain_col_type<MatrixType>::type ColType;
527c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
528c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath                   MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime>
529c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath            WorkMatrixType;
530c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
531c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    /** \brief Default Constructor.
532c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      *
533c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      * The default constructor is useful in cases in which the user intends to
534c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      * perform decompositions via JacobiSVD::compute(const MatrixType&).
535c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      */
536c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    JacobiSVD()
537c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      : m_isInitialized(false),
538c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        m_isAllocated(false),
5397faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez        m_usePrescribedThreshold(false),
540c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        m_computationOptions(0),
5417faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez        m_rows(-1), m_cols(-1), m_diagSize(0)
542c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {}
543c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
544c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
545c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    /** \brief Default Constructor with memory preallocation
546c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      *
547c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      * Like the default constructor but with preallocation of the internal data
548c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      * according to the specified problem size.
549c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      * \sa JacobiSVD()
550c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      */
551c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0)
552c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      : m_isInitialized(false),
553c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        m_isAllocated(false),
5547faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez        m_usePrescribedThreshold(false),
555c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        m_computationOptions(0),
556c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        m_rows(-1), m_cols(-1)
557c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
558c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      allocate(rows, cols, computationOptions);
559c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
560c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
561c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    /** \brief Constructor performing the decomposition of given matrix.
562c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
563c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * \param matrix the matrix to decompose
564c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
565c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *                           By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
566c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *                           #ComputeFullV, #ComputeThinV.
567c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
568c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
569c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * available with the (non-default) FullPivHouseholderQR preconditioner.
570c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     */
571c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
572c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      : m_isInitialized(false),
573c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        m_isAllocated(false),
5747faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez        m_usePrescribedThreshold(false),
575c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        m_computationOptions(0),
576c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath        m_rows(-1), m_cols(-1)
577c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
578c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      compute(matrix, computationOptions);
579c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
580c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
581c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    /** \brief Method performing the decomposition of given matrix using custom options.
582c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
583c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * \param matrix the matrix to decompose
584c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
585c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *                           By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
586c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *                           #ComputeFullV, #ComputeThinV.
587c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
588c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
589c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * available with the (non-default) FullPivHouseholderQR preconditioner.
590c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     */
591c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    JacobiSVD& compute(const MatrixType& matrix, unsigned int computationOptions);
592c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
593c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    /** \brief Method performing the decomposition of given matrix using current options.
594c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
595c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * \param matrix the matrix to decompose
596c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
597c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
598c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     */
599c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    JacobiSVD& compute(const MatrixType& matrix)
600c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
601c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      return compute(matrix, m_computationOptions);
602c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
603c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
604c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    /** \returns the \a U matrix.
605c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
606c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
607c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
608c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
609c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
610c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
611c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * This method asserts that you asked for \a U to be computed.
612c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     */
613c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    const MatrixUType& matrixU() const
614c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
615c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
616c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      eigen_assert(computeU() && "This JacobiSVD decomposition didn't compute U. Did you ask for it?");
617c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      return m_matrixU;
618c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
619c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
620c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    /** \returns the \a V matrix.
621c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
622c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
623c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.
624c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
625c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
626c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
627c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * This method asserts that you asked for \a V to be computed.
628c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     */
629c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    const MatrixVType& matrixV() const
630c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
631c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
632c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      eigen_assert(computeV() && "This JacobiSVD decomposition didn't compute V. Did you ask for it?");
633c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      return m_matrixV;
634c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
635c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
636c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    /** \returns the vector of singular values.
637c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     *
638c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
639c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     * returned vector has size \a m.  Singular values are always sorted in decreasing order.
640c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath     */
641c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    const SingularValuesType& singularValues() const
642c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
643c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
644c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      return m_singularValues;
645c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
646c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
647c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    /** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
648c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    inline bool computeU() const { return m_computeFullU || m_computeThinU; }
649c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    /** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
650c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    inline bool computeV() const { return m_computeFullV || m_computeThinV; }
651c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
652c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    /** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
653c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      *
654c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      * \param b the right-hand-side of the equation to solve.
655c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      *
656c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      * \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
657c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      *
658c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      * \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving.
659c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      * In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$.
660c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      */
661c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    template<typename Rhs>
662c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    inline const internal::solve_retval<JacobiSVD, Rhs>
663c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    solve(const MatrixBase<Rhs>& b) const
664c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
665c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
666c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      eigen_assert(computeU() && computeV() && "JacobiSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
667c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      return internal::solve_retval<JacobiSVD, Rhs>(*this, b.derived());
668c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
669c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
670c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    /** \returns the number of singular values that are not exactly 0 */
671c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    Index nonzeroSingularValues() const
672c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    {
673c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
674c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath      return m_nonzeroSingularValues;
675c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath    }
6767faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez
6777faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    /** \returns the rank of the matrix of which \c *this is the SVD.
6787faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      *
6797faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * \note This method has to determine which singular values should be considered nonzero.
6807faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      *       For that, it uses the threshold value that you can control by calling
6817faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      *       setThreshold(const RealScalar&).
6827faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      */
6837faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    inline Index rank() const
6847faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    {
6857faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      using std::abs;
6867faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
6877faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      if(m_singularValues.size()==0) return 0;
6887faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      RealScalar premultiplied_threshold = m_singularValues.coeff(0) * threshold();
6897faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      Index i = m_nonzeroSingularValues-1;
6907faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
6917faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      return i+1;
6927faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    }
6937faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez
6947faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    /** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
6957faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * which need to determine when singular values are to be considered nonzero.
6967faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * This is not used for the SVD decomposition itself.
6977faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      *
6987faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * When it needs to get the threshold value, Eigen calls threshold().
6997faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * The default is \c NumTraits<Scalar>::epsilon()
7007faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      *
7017faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * \param threshold The new value to use as the threshold.
7027faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      *
7037faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * A singular value will be considered nonzero if its value is strictly greater than
7047faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      *  \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
7057faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      *
7067faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * If you want to come back to the default behavior, call setThreshold(Default_t)
7077faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      */
7087faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    JacobiSVD& setThreshold(const RealScalar& threshold)
7097faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    {
7107faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      m_usePrescribedThreshold = true;
7117faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      m_prescribedThreshold = threshold;
7127faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      return *this;
7137faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    }
7147faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez
7157faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    /** Allows to come back to the default behavior, letting Eigen use its default formula for
7167faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * determining the threshold.
7177faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      *
7187faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * You should pass the special object Eigen::Default as parameter here.
7197faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * \code svd.setThreshold(Eigen::Default); \endcode
7207faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      *
7217faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * See the documentation of setThreshold(const RealScalar&).
7227faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      */
7237faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    JacobiSVD& setThreshold(Default_t)
7247faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    {
7257faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      m_usePrescribedThreshold = false;
7267faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      return *this;
7277faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    }
7287faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez
7297faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    /** Returns the threshold that will be used by certain methods such as rank().
7307faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      *
7317faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      * See the documentation of setThreshold(const RealScalar&).
7327faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      */
7337faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    RealScalar threshold() const
7347faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    {
7357faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      eigen_assert(m_isInitialized || m_usePrescribedThreshold);
7367faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez      return m_usePrescribedThreshold ? m_prescribedThreshold
7377faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez                                      : (std::max<Index>)(1,m_diagSize)*NumTraits<Scalar>::epsilon();
7387faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez    }
739c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath
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