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Diffstat (limited to 'runtimes/nn/depend/external/eigen/Eigen/src/Householder/Householder.h')
| -rw-r--r-- | runtimes/nn/depend/external/eigen/Eigen/src/Householder/Householder.h | 172 |
1 files changed, 172 insertions, 0 deletions
diff --git a/runtimes/nn/depend/external/eigen/Eigen/src/Householder/Householder.h b/runtimes/nn/depend/external/eigen/Eigen/src/Householder/Householder.h new file mode 100644 index 000000000..80de2c305 --- /dev/null +++ b/runtimes/nn/depend/external/eigen/Eigen/src/Householder/Householder.h @@ -0,0 +1,172 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com> +// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_HOUSEHOLDER_H +#define EIGEN_HOUSEHOLDER_H + +namespace Eigen { + +namespace internal { +template<int n> struct decrement_size +{ + enum { + ret = n==Dynamic ? n : n-1 + }; +}; +} + +/** Computes the elementary reflector H such that: + * \f$ H *this = [ beta 0 ... 0]^T \f$ + * where the transformation H is: + * \f$ H = I - tau v v^*\f$ + * and the vector v is: + * \f$ v^T = [1 essential^T] \f$ + * + * The essential part of the vector \c v is stored in *this. + * + * On output: + * \param tau the scaling factor of the Householder transformation + * \param beta the result of H * \c *this + * + * \sa MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(), + * MatrixBase::applyHouseholderOnTheRight() + */ +template<typename Derived> +void MatrixBase<Derived>::makeHouseholderInPlace(Scalar& tau, RealScalar& beta) +{ + VectorBlock<Derived, internal::decrement_size<Base::SizeAtCompileTime>::ret> essentialPart(derived(), 1, size()-1); + makeHouseholder(essentialPart, tau, beta); +} + +/** Computes the elementary reflector H such that: + * \f$ H *this = [ beta 0 ... 0]^T \f$ + * where the transformation H is: + * \f$ H = I - tau v v^*\f$ + * and the vector v is: + * \f$ v^T = [1 essential^T] \f$ + * + * On output: + * \param essential the essential part of the vector \c v + * \param tau the scaling factor of the Householder transformation + * \param beta the result of H * \c *this + * + * \sa MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(), + * MatrixBase::applyHouseholderOnTheRight() + */ +template<typename Derived> +template<typename EssentialPart> +void MatrixBase<Derived>::makeHouseholder( + EssentialPart& essential, + Scalar& tau, + RealScalar& beta) const +{ + using std::sqrt; + using numext::conj; + + EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart) + VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1); + + RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm(); + Scalar c0 = coeff(0); + const RealScalar tol = (std::numeric_limits<RealScalar>::min)(); + + if(tailSqNorm <= tol && numext::abs2(numext::imag(c0))<=tol) + { + tau = RealScalar(0); + beta = numext::real(c0); + essential.setZero(); + } + else + { + beta = sqrt(numext::abs2(c0) + tailSqNorm); + if (numext::real(c0)>=RealScalar(0)) + beta = -beta; + essential = tail / (c0 - beta); + tau = conj((beta - c0) / beta); + } +} + +/** Apply the elementary reflector H given by + * \f$ H = I - tau v v^*\f$ + * with + * \f$ v^T = [1 essential^T] \f$ + * from the left to a vector or matrix. + * + * On input: + * \param essential the essential part of the vector \c v + * \param tau the scaling factor of the Householder transformation + * \param workspace a pointer to working space with at least + * this->cols() * essential.size() entries + * + * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), + * MatrixBase::applyHouseholderOnTheRight() + */ +template<typename Derived> +template<typename EssentialPart> +void MatrixBase<Derived>::applyHouseholderOnTheLeft( + const EssentialPart& essential, + const Scalar& tau, + Scalar* workspace) +{ + if(rows() == 1) + { + *this *= Scalar(1)-tau; + } + else if(tau!=Scalar(0)) + { + Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace,cols()); + Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols()); + tmp.noalias() = essential.adjoint() * bottom; + tmp += this->row(0); + this->row(0) -= tau * tmp; + bottom.noalias() -= tau * essential * tmp; + } +} + +/** Apply the elementary reflector H given by + * \f$ H = I - tau v v^*\f$ + * with + * \f$ v^T = [1 essential^T] \f$ + * from the right to a vector or matrix. + * + * On input: + * \param essential the essential part of the vector \c v + * \param tau the scaling factor of the Householder transformation + * \param workspace a pointer to working space with at least + * this->cols() * essential.size() entries + * + * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), + * MatrixBase::applyHouseholderOnTheLeft() + */ +template<typename Derived> +template<typename EssentialPart> +void MatrixBase<Derived>::applyHouseholderOnTheRight( + const EssentialPart& essential, + const Scalar& tau, + Scalar* workspace) +{ + if(cols() == 1) + { + *this *= Scalar(1)-tau; + } + else if(tau!=Scalar(0)) + { + Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace,rows()); + Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1); + tmp.noalias() = right * essential.conjugate(); + tmp += this->col(0); + this->col(0) -= tau * tmp; + right.noalias() -= tau * tmp * essential.transpose(); + } +} + +} // end namespace Eigen + +#endif // EIGEN_HOUSEHOLDER_H |