Eigen  3.3.0
 
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Householder.h
1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
5// Copyright (C) 2009 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_HOUSEHOLDER_H
12#define EIGEN_HOUSEHOLDER_H
13
14namespace Eigen {
15
16namespace internal {
17template<int n> struct decrement_size
18{
19 enum {
20 ret = n==Dynamic ? n : n-1
21 };
22};
23}
24
41template<typename Derived>
43{
45 makeHouseholder(essentialPart, tau, beta);
46}
47
63template<typename Derived>
64template<typename EssentialPart>
66 EssentialPart& essential,
67 Scalar& tau,
68 RealScalar& beta) const
69{
70 using std::sqrt;
71 using numext::conj;
72
73 EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
75
76 RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm();
77 Scalar c0 = coeff(0);
78 const RealScalar tol = (std::numeric_limits<RealScalar>::min)();
79
80 if(tailSqNorm <= tol && numext::abs2(numext::imag(c0))<=tol)
81 {
82 tau = RealScalar(0);
83 beta = numext::real(c0);
84 essential.setZero();
85 }
86 else
87 {
88 beta = sqrt(numext::abs2(c0) + tailSqNorm);
89 if (numext::real(c0)>=RealScalar(0))
90 beta = -beta;
91 essential = tail / (c0 - beta);
92 tau = conj((beta - c0) / beta);
93 }
94}
95
111template<typename Derived>
112template<typename EssentialPart>
114 const EssentialPart& essential,
115 const Scalar& tau,
116 Scalar* workspace)
117{
118 if(rows() == 1)
119 {
120 *this *= Scalar(1)-tau;
121 }
122 else if(tau!=Scalar(0))
123 {
126 tmp.noalias() = essential.adjoint() * bottom;
127 tmp += this->row(0);
128 this->row(0) -= tau * tmp;
129 bottom.noalias() -= tau * essential * tmp;
130 }
131}
132
148template<typename Derived>
149template<typename EssentialPart>
151 const EssentialPart& essential,
152 const Scalar& tau,
153 Scalar* workspace)
154{
155 if(cols() == 1)
156 {
157 *this *= Scalar(1)-tau;
158 }
159 else if(tau!=Scalar(0))
160 {
163 tmp.noalias() = right * essential.conjugate();
164 tmp += this->col(0);
165 this->col(0) -= tau * tmp;
166 right.noalias() -= tau * tmp * essential.transpose();
167 }
168}
169
170} // end namespace Eigen
171
172#endif // EIGEN_HOUSEHOLDER_H
Expression of a fixed-size or dynamic-size block.
Definition: Block.h:105
internal::traits< Derived >::Scalar Scalar
Definition: DenseBase.h:66
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:90
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
Expression of a fixed-size or dynamic-size sub-vector.
Definition: VectorBlock.h:60
Namespace containing all symbols from the Eigen library.
Definition: Core:287
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_conjugate_op< typename Derived::Scalar >, const Derived > conj(const Eigen::ArrayBase< Derived > &x)
const int Dynamic
Definition: Constants.h:21