MatrixBase_impl.h

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          https://www.mrpt.org/                         |
   |                                                                        |
   | Copyright (c) 2005-2019, Individual contributors, see AUTHORS file     |
   | See: https://www.mrpt.org/Authors - All rights reserved.               |
   | Released under BSD License. See: https://www.mrpt.org/License          |
   +------------------------------------------------------------------------+ */
#pragma once

#include <mrpt/core/exceptions.h>
#include <mrpt/math/CVectorDynamic.h>
#include <mrpt/math/MatrixBase.h>
#include <Eigen/Eigenvalues>  // EigenSolver
#include <cstdint>
#include <stdexcept>
#include <vector>

namespace mrpt::math
{
template <typename Scalar, class Derived>
void MatrixBase<Scalar, Derived>::unsafeRemoveColumns(
    const std::vector<std::size_t>& idxs)
{
    std::size_t k = 1;
    const auto nR = mbDerived().rows();
    for (auto it = idxs.rbegin(); it != idxs.rend(); ++it, ++k)
    {
        const auto nC = mbDerived().cols() - *it - k;
        if (nC > 0)
            mbDerived().asEigen().block(0, *it, nR, nC) =
                mbDerived().asEigen().block(0, *it + 1, nR, nC).eval();
    }
    mbDerived().setSize(nR, mbDerived().cols() - idxs.size());
}

template <typename Scalar, class Derived>
void MatrixBase<Scalar, Derived>::removeColumns(
    const std::vector<std::size_t>& idxsToRemove)
{
    std::vector<std::size_t> idxs = idxsToRemove;
    std::sort(idxs.begin(), idxs.end());
    auto itEnd = std::unique(idxs.begin(), idxs.end());
    idxs.resize(itEnd - idxs.begin());
    unsafeRemoveColumns(idxs);
}

template <typename Scalar, class Derived>
void MatrixBase<Scalar, Derived>::unsafeRemoveRows(
    const std::vector<size_t>& idxs)
{
    std::size_t k = 1;
    const auto nC = mbDerived().cols();
    for (auto it = idxs.rbegin(); it != idxs.rend(); ++it, ++k)
    {
        const auto nR = mbDerived().rows() - *it - k;
        if (nR > 0)
            mbDerived().asEigen().block(*it, 0, nR, nC) =
                mbDerived().asEigen().block(*it + 1, 0, nR, nC).eval();
    }
    mbDerived().setSize(mbDerived().rows() - idxs.size(), nC);
}

template <typename Scalar, class Derived>
void MatrixBase<Scalar, Derived>::removeRows(
    const std::vector<size_t>& idxsToRemove)
{
    std::vector<std::size_t> idxs = idxsToRemove;
    std::sort(idxs.begin(), idxs.end());
    auto itEnd = std::unique(idxs.begin(), idxs.end());
    idxs.resize(itEnd - idxs.begin());
    unsafeRemoveRows(idxs);
}

template <typename Scalar, class Derived>
Scalar MatrixBase<Scalar, Derived>::det() const
{
    return mbDerived().asEigen().eval().determinant();
}

namespace detail
{
// Aux func to sort by ascending eigenvalues:
template <typename Scalar, typename VEC1, typename MATRIX1, typename MATRIX2>
void sortEigResults(
    const VEC1& eVals, const MATRIX1& eVecs, std::vector<Scalar>& sorted_eVals,
    MATRIX2& sorted_eVecs)
{
    const int64_t N = static_cast<int64_t>(eVals.size());
    std::vector<std::pair<Scalar, int64_t>> D;
    D.reserve(N);
    for (int64_t i = 0; i < N; i++) D.emplace_back(eVals[i], i);
    std::sort(D.begin(), D.end());

    // store:
    sorted_eVecs.resize(eVecs.rows(), eVecs.cols());
    sorted_eVals.resize(N);
    for (int64_t i = 0; i < N; i++)
    {
        sorted_eVals[i] = D[i].first;
        sorted_eVecs.col(i) = eVecs.col(D[i].second);
    }
}
}  // namespace detail

template <typename Scalar, class Derived>
bool MatrixBase<Scalar, Derived>::eig(
    Derived& eVecs, std::vector<Scalar>& eVals, bool sorted) const
{
    Eigen::EigenSolver<typename Derived::eigen_t> es(mbDerived().asEigen());
    if (es.info() != Eigen::Success) return false;
    const auto eigenVal = es.eigenvalues().real();
    ASSERT_EQUAL_(eigenVal.rows(), mbDerived().rows());
    const auto N = eigenVal.rows();

    if (sorted)
    {
        detail::sortEigResults(
            eigenVal, es.eigenvectors().real(), eVals, eVecs);
    }
    else
    {
        eVals.resize(N);
        eVecs = es.eigenvectors().real();
        for (int i = 0; i < N; i++) eVals[i] = eigenVal[i];
    }
    return true;
}

template <typename Scalar, class Derived>
bool MatrixBase<Scalar, Derived>::eig_symmetric(
    Derived& eVecs, std::vector<Scalar>& eVals, bool sorted) const
{
    Eigen::SelfAdjointEigenSolver<typename Derived::eigen_t> es(
        mbDerived().asEigen());
    if (es.info() != Eigen::Success) return false;
    const auto eigenVal = es.eigenvalues().real();
    ASSERT_EQUAL_(eigenVal.rows(), mbDerived().rows());
    const auto N = eigenVal.rows();

    if (sorted)
    {
        detail::sortEigResults(
            eigenVal, es.eigenvectors().real(), eVals, eVecs);
    }
    else
    {
        eVals.resize(N);
        eVecs = es.eigenvectors().real();
        for (int i = 0; i < N; i++) eVals[i] = eigenVal[i];
    }
    return true;
}

template <typename Scalar, class Derived>
int MatrixBase<Scalar, Derived>::rank(Scalar threshold) const
{
    Eigen::FullPivLU<typename Derived::eigen_t> lu(
        mbDerived().asEigen().eval());
    if (threshold > 0) lu.setThreshold(threshold);
    return lu.rank();
}

template <typename Scalar, class Derived>
bool MatrixBase<Scalar, Derived>::chol(Derived& U) const
{
    Eigen::LLT<typename Derived::eigen_t> Chol =
        mbDerived().asEigen().template selfadjointView<Eigen::Lower>().llt();
    if (Chol.info() == Eigen::NoConvergence) return false;
    U = typename Derived::eigen_t(Chol.matrixU());
    return true;
}

template <typename Scalar, class Derived>
void MatrixBase<Scalar, Derived>::matProductOf_AB(
    const Derived& A, const Derived& B)
{
    mbDerived().resize(A.rows(), B.cols());
    mbDerived().asEigen() = (A.asEigen() * B.asEigen()).eval();
}

template <typename Scalar, class Derived>
Derived MatrixBase<Scalar, Derived>::inverse() const
{
    ASSERT_EQUAL_(mbDerived().cols(), mbDerived().rows());
    const auto N = mbDerived().cols();
    const auto I = Derived::eigen_t::Identity(N, N);
    Derived inv(mrpt::math::UNINITIALIZED_MATRIX);
    inv.resize(N, N);
    inv.asEigen() = mbDerived().asEigen().lu().solve(I).eval();
    return inv;
}

template <typename Scalar, class Derived>
Derived MatrixBase<Scalar, Derived>::inverse_LLt() const
{
    ASSERT_EQUAL_(mbDerived().cols(), mbDerived().rows());
    const auto N = mbDerived().cols();
    const auto I = Derived::eigen_t::Identity(N, N);
    Derived inv(mrpt::math::UNINITIALIZED_MATRIX);
    inv.resize(N, N);
    inv.asEigen() = mbDerived().asEigen().llt().solve(I).eval();
    return inv;
}

template <typename Scalar, class Derived>
Scalar MatrixBase<Scalar, Derived>::maximumDiagonal() const
{
    return mbDerived().asEigen().diagonal().maxCoeff();
}

template <typename Scalar, class Derived>
Scalar MatrixBase<Scalar, Derived>::minimumDiagonal() const
{
    return mbDerived().asEigen().diagonal().minCoeff();
}

template <typename Scalar, class Derived>
Scalar MatrixBase<Scalar, Derived>::trace() const
{
    return mbDerived().asEigen().trace();
}

}  // namespace mrpt::math