chromium/third_party/eigen3/src/Eigen/src/Core/ConditionEstimator.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 Rasmus Munk Larsen ([email protected])
//
// 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_CONDITIONESTIMATOR_H
#define EIGEN_CONDITIONESTIMATOR_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

template <typename Vector, typename RealVector, bool IsComplex>
struct rcond_compute_sign { … };

// Partial specialization to avoid elementwise division for real vectors.
rcond_compute_sign<Vector, Vector, false>;

/**
 * \returns an estimate of ||inv(matrix)||_1 given a decomposition of
 * \a matrix that implements .solve() and .adjoint().solve() methods.
 *
 * This function implements Algorithms 4.1 and 5.1 from
 *   http://www.maths.manchester.ac.uk/~higham/narep/narep135.pdf
 * which also forms the basis for the condition number estimators in
 * LAPACK. Since at most 10 calls to the solve method of dec are
 * performed, the total cost is O(dims^2), as opposed to O(dims^3)
 * needed to compute the inverse matrix explicitly.
 *
 * The most common usage is in estimating the condition number
 * ||matrix||_1 * ||inv(matrix)||_1. The first term ||matrix||_1 can be
 * computed directly in O(n^2) operations.
 *
 * Supports the following decompositions: FullPivLU, PartialPivLU, LDLT, and
 * LLT.
 *
 * \sa FullPivLU, PartialPivLU, LDLT, LLT.
 */
template <typename Decomposition>
typename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomposition& dec) { … }

/** \brief Reciprocal condition number estimator.
 *
 * Computing a decomposition of a dense matrix takes O(n^3) operations, while
 * this method estimates the condition number quickly and reliably in O(n^2)
 * operations.
 *
 * \returns an estimate of the reciprocal condition number
 * (1 / (||matrix||_1 * ||inv(matrix)||_1)) of matrix, given ||matrix||_1 and
 * its decomposition. Supports the following decompositions: FullPivLU,
 * PartialPivLU, LDLT, and LLT.
 *
 * \sa FullPivLU, PartialPivLU, LDLT, LLT.
 */
template <typename Decomposition>
typename Decomposition::RealScalar rcond_estimate_helper(typename Decomposition::RealScalar matrix_norm,
                                                         const Decomposition& dec) { … }

}  // namespace internal

}  // namespace Eigen

#endif