[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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| 5 | // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 6 | //
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| 7 | // This Source Code Form is subject to the terms of the Mozilla
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| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 10 |
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| 11 | #ifndef EIGEN_HOUSEHOLDER_H
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| 12 | #define EIGEN_HOUSEHOLDER_H
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| 13 |
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| 14 | namespace Eigen {
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| 15 |
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| 16 | namespace internal {
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| 17 | template<int n> struct decrement_size
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| 18 | {
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| 19 | enum {
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| 20 | ret = n==Dynamic ? n : n-1
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| 21 | };
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| 22 | };
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| 23 | }
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| 24 |
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| 25 | /** Computes the elementary reflector H such that:
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| 26 | * \f$ H *this = [ beta 0 ... 0]^T \f$
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| 27 | * where the transformation H is:
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| 28 | * \f$ H = I - tau v v^*\f$
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| 29 | * and the vector v is:
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| 30 | * \f$ v^T = [1 essential^T] \f$
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| 31 | *
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| 32 | * The essential part of the vector \c v is stored in *this.
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| 33 | *
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| 34 | * On output:
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| 35 | * \param tau the scaling factor of the Householder transformation
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| 36 | * \param beta the result of H * \c *this
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| 37 | *
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| 38 | * \sa MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(),
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| 39 | * MatrixBase::applyHouseholderOnTheRight()
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| 40 | */
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| 41 | template<typename Derived>
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| 42 | void MatrixBase<Derived>::makeHouseholderInPlace(Scalar& tau, RealScalar& beta)
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| 43 | {
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| 44 | VectorBlock<Derived, internal::decrement_size<Base::SizeAtCompileTime>::ret> essentialPart(derived(), 1, size()-1);
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| 45 | makeHouseholder(essentialPart, tau, beta);
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| 46 | }
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| 47 |
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| 48 | /** Computes the elementary reflector H such that:
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| 49 | * \f$ H *this = [ beta 0 ... 0]^T \f$
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| 50 | * where the transformation H is:
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| 51 | * \f$ H = I - tau v v^*\f$
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| 52 | * and the vector v is:
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| 53 | * \f$ v^T = [1 essential^T] \f$
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| 54 | *
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| 55 | * On output:
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| 56 | * \param essential the essential part of the vector \c v
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| 57 | * \param tau the scaling factor of the Householder transformation
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| 58 | * \param beta the result of H * \c *this
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| 59 | *
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| 60 | * \sa MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(),
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| 61 | * MatrixBase::applyHouseholderOnTheRight()
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| 62 | */
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| 63 | template<typename Derived>
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| 64 | template<typename EssentialPart>
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| 65 | void MatrixBase<Derived>::makeHouseholder(
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| 66 | EssentialPart& essential,
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| 67 | Scalar& tau,
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| 68 | RealScalar& beta) const
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| 69 | {
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| 70 | using std::sqrt;
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| 71 | using numext::conj;
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| 72 |
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| 73 | EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
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| 74 | VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
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| 75 |
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| 76 | RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm();
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| 77 | Scalar c0 = coeff(0);
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| 78 | const RealScalar tol = (std::numeric_limits<RealScalar>::min)();
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| 79 |
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| 80 | if(tailSqNorm <= tol && numext::abs2(numext::imag(c0))<=tol)
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| 81 | {
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| 82 | tau = RealScalar(0);
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| 83 | beta = numext::real(c0);
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| 84 | essential.setZero();
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| 85 | }
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| 86 | else
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| 87 | {
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| 88 | beta = sqrt(numext::abs2(c0) + tailSqNorm);
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| 89 | if (numext::real(c0)>=RealScalar(0))
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| 90 | beta = -beta;
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| 91 | essential = tail / (c0 - beta);
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| 92 | tau = conj((beta - c0) / beta);
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| 93 | }
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| 94 | }
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| 95 |
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| 96 | /** Apply the elementary reflector H given by
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| 97 | * \f$ H = I - tau v v^*\f$
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| 98 | * with
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| 99 | * \f$ v^T = [1 essential^T] \f$
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| 100 | * from the left to a vector or matrix.
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| 101 | *
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| 102 | * On input:
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| 103 | * \param essential the essential part of the vector \c v
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| 104 | * \param tau the scaling factor of the Householder transformation
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| 105 | * \param workspace a pointer to working space with at least
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| 106 | * this->cols() * essential.size() entries
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| 107 | *
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| 108 | * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(),
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| 109 | * MatrixBase::applyHouseholderOnTheRight()
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| 110 | */
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| 111 | template<typename Derived>
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| 112 | template<typename EssentialPart>
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| 113 | void MatrixBase<Derived>::applyHouseholderOnTheLeft(
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| 114 | const EssentialPart& essential,
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| 115 | const Scalar& tau,
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| 116 | Scalar* workspace)
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| 117 | {
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| 118 | if(rows() == 1)
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| 119 | {
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| 120 | *this *= Scalar(1)-tau;
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| 121 | }
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| 122 | else
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| 123 | {
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| 124 | Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace,cols());
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| 125 | Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols());
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| 126 | tmp.noalias() = essential.adjoint() * bottom;
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| 127 | tmp += this->row(0);
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| 128 | this->row(0) -= tau * tmp;
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| 129 | bottom.noalias() -= tau * essential * tmp;
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| 130 | }
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| 131 | }
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| 132 |
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| 133 | /** Apply the elementary reflector H given by
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| 134 | * \f$ H = I - tau v v^*\f$
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| 135 | * with
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| 136 | * \f$ v^T = [1 essential^T] \f$
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| 137 | * from the right to a vector or matrix.
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| 138 | *
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| 139 | * On input:
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| 140 | * \param essential the essential part of the vector \c v
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| 141 | * \param tau the scaling factor of the Householder transformation
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| 142 | * \param workspace a pointer to working space with at least
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| 143 | * this->cols() * essential.size() entries
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| 144 | *
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| 145 | * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(),
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| 146 | * MatrixBase::applyHouseholderOnTheLeft()
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| 147 | */
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| 148 | template<typename Derived>
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| 149 | template<typename EssentialPart>
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| 150 | void MatrixBase<Derived>::applyHouseholderOnTheRight(
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| 151 | const EssentialPart& essential,
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| 152 | const Scalar& tau,
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| 153 | Scalar* workspace)
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| 154 | {
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| 155 | if(cols() == 1)
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| 156 | {
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| 157 | *this *= Scalar(1)-tau;
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| 158 | }
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| 159 | else
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| 160 | {
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| 161 | Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace,rows());
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| 162 | Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1);
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| 163 | tmp.noalias() = right * essential.conjugate();
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| 164 | tmp += this->col(0);
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| 165 | this->col(0) -= tau * tmp;
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| 166 | right.noalias() -= tau * tmp * essential.transpose();
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| 167 | }
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| 168 | }
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| 169 |
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| 170 | } // end namespace Eigen
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| 171 |
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| 172 | #endif // EIGEN_HOUSEHOLDER_H
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