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Upgrade Spectra to v1.1.0

release/4.3a0
Martin Valgur 2024-10-10 18:40:35 +03:00
parent 89fbe4bd2e
commit c99a8e1c1d
54 changed files with 5870 additions and 2381 deletions
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93
gtsam/3rdparty/Spectra/DavidsonSymEigsSolver.h vendored Normal file
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@ -0,0 +1,93 @@
// Copyright (C) 2020 Netherlands eScience Center <f.zapata@esciencecenter.nl>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_DAVIDSON_SYM_EIGS_SOLVER_H
#define SPECTRA_DAVIDSON_SYM_EIGS_SOLVER_H
#include <Eigen/Core>
#include "JDSymEigsBase.h"
#include "Util/SelectionRule.h"
namespace Spectra {
///
/// \ingroup EigenSolver
///
/// This class implement the DPR correction for the Davidson algorithms.
/// The algorithms in the Davidson family only differ in how the correction
/// vectors are computed and optionally in the initial orthogonal basis set.
///
/// the DPR correction compute the new correction vector using the following expression:
/// \f[ correction = -(\boldsymbol{D} - \rho \boldsymbol{I})^{-1} \boldsymbol{r} \f]
/// where
/// \f$D\f$ is the diagonal of the target matrix, \f$\rho\f$ the Ritz eigenvalue,
/// \f$I\f$ the identity matrix and \f$r\f$ the residue vector.
///
template <typename OpType>
class DavidsonSymEigsSolver : public JDSymEigsBase<DavidsonSymEigsSolver<OpType>, OpType>
{
private:
using Index = Eigen::Index;
using Scalar = typename OpType::Scalar;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
Vector m_diagonal;
public:
DavidsonSymEigsSolver(OpType& op, Index nev, Index nvec_init, Index nvec_max) :
JDSymEigsBase<DavidsonSymEigsSolver<OpType>, OpType>(op, nev, nvec_init, nvec_max)
{
m_diagonal.resize(this->m_matrix_operator.rows());
for (Index i = 0; i < op.rows(); i++)
{
m_diagonal(i) = op(i, i);
}
}
DavidsonSymEigsSolver(OpType& op, Index nev) :
DavidsonSymEigsSolver(op, nev, 2 * nev, 10 * nev) {}
/// Create initial search space based on the diagonal
/// and the spectrum'target (highest or lowest)
///
/// \param selection Spectrum section to target (e.g. lowest, etc.)
/// \return Matrix with the initial orthonormal basis
Matrix setup_initial_search_space(SortRule selection) const
{
std::vector<Eigen::Index> indices_sorted = argsort(selection, m_diagonal);
Matrix initial_basis = Matrix::Zero(this->m_matrix_operator.rows(), this->m_initial_search_space_size);
for (Index k = 0; k < this->m_initial_search_space_size; k++)
{
Index row = indices_sorted[k];
initial_basis(row, k) = 1.0;
}
return initial_basis;
}
/// Compute the corrections using the DPR method.
///
/// \return New correction vectors.
Matrix calculate_correction_vector() const
{
const Matrix& residues = this->m_ritz_pairs.residues();
const Vector& eigvals = this->m_ritz_pairs.ritz_values();
Matrix correction = Matrix::Zero(this->m_matrix_operator.rows(), this->m_correction_size);
for (Index k = 0; k < this->m_correction_size; k++)
{
Vector tmp = eigvals(k) - m_diagonal.array();
correction.col(k) = residues.col(k).array() / tmp.array();
}
return correction;
}
};
} // namespace Spectra
#endif // SPECTRA_DAVIDSON_SYM_EIGS_SOLVER_H

216
gtsam/3rdparty/Spectra/GenEigsBase.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2018-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2018-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef GEN_EIGS_BASE_H
#define GEN_EIGS_BASE_H
#ifndef SPECTRA_GEN_EIGS_BASE_H
#define SPECTRA_GEN_EIGS_BASE_H
#include <Eigen/Core>
#include <vector> // std::vector
@ -14,6 +14,7 @@
#include <complex> // std::complex, std::conj, std::norm, std::abs
#include <stdexcept> // std::invalid_argument
#include "Util/Version.h"
#include "Util/TypeTraits.h"
#include "Util/SelectionRule.h"
#include "Util/CompInfo.h"
@ -33,32 +34,30 @@ namespace Spectra {
/// It is kept here to provide the documentation for member functions of concrete eigen solvers
/// such as GenEigsSolver and GenEigsRealShiftSolver.
///
template <typename Scalar,
int SelectionRule,
typename OpType,
typename BOpType>
template <typename OpType, typename BOpType>
class GenEigsBase
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Array<Scalar, Eigen::Dynamic, 1> Array;
typedef Eigen::Array<bool, Eigen::Dynamic, 1> BoolArray;
typedef Eigen::Map<Matrix> MapMat;
typedef Eigen::Map<Vector> MapVec;
typedef Eigen::Map<const Vector> MapConstVec;
using Scalar = typename OpType::Scalar;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using Array = Eigen::Array<Scalar, Eigen::Dynamic, 1>;
using BoolArray = Eigen::Array<bool, Eigen::Dynamic, 1>;
using MapMat = Eigen::Map<Matrix>;
using MapVec = Eigen::Map<Vector>;
using MapConstVec = Eigen::Map<const Vector>;
typedef std::complex<Scalar> Complex;
typedef Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic> ComplexMatrix;
typedef Eigen::Matrix<Complex, Eigen::Dynamic, 1> ComplexVector;
using Complex = std::complex<Scalar>;
using ComplexMatrix = Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic>;
using ComplexVector = Eigen::Matrix<Complex, Eigen::Dynamic, 1>;
typedef ArnoldiOp<Scalar, OpType, BOpType> ArnoldiOpType;
typedef Arnoldi<Scalar, ArnoldiOpType> ArnoldiFac;
using ArnoldiOpType = ArnoldiOp<Scalar, OpType, BOpType>;
using ArnoldiFac = Arnoldi<Scalar, ArnoldiOpType>;
protected:
// clang-format off
OpType* m_op; // object to conduct matrix operation,
OpType& m_op; // object to conduct matrix operation,
// e.g. matrix-vector product
const Index m_n; // dimension of matrix A
const Index m_nev; // number of eigenvalues requested
@ -70,16 +69,11 @@ protected:
ComplexVector m_ritz_val; // Ritz values
ComplexMatrix m_ritz_vec; // Ritz vectors
ComplexVector m_ritz_est; // last row of m_ritz_vec
ComplexVector m_ritz_est; // last row of m_ritz_vec, also called the Ritz estimates
private:
BoolArray m_ritz_conv; // indicator of the convergence of Ritz values
int m_info; // status of the computation
const Scalar m_near_0; // a very small value, but 1.0 / m_near_0 does not overflow
// ~= 1e-307 for the "double" type
const Scalar m_eps; // the machine precision, ~= 1e-16 for the "double" type
const Scalar m_eps23; // m_eps^(2/3), used to test the convergence
CompInfo m_info; // status of the computation
// clang-format on
// Real Ritz values calculated from UpperHessenbergEigen have exact zero imaginary part
@ -89,7 +83,7 @@ private:
static bool is_conj(const Complex& v1, const Complex& v2) { return v1 == Eigen::numext::conj(v2); }
// Implicitly restarted Arnoldi factorization
void restart(Index k)
void restart(Index k, SortRule selection)
{
using std::norm;
@ -140,19 +134,27 @@ private:
m_fac.compress_V(Q);
m_fac.factorize_from(k, m_ncv, m_nmatop);
retrieve_ritzpair();
retrieve_ritzpair(selection);
}
// Calculates the number of converged Ritz values
Index num_converged(Scalar tol)
Index num_converged(const Scalar& tol)
{
// thresh = tol * max(m_eps23, abs(theta)), theta for Ritz value
Array thresh = tol * m_ritz_val.head(m_nev).array().abs().max(m_eps23);
using std::pow;
// The machine precision, ~= 1e-16 for the "double" type
const Scalar eps = TypeTraits<Scalar>::epsilon();
// std::pow() is not constexpr, so we do not declare eps23 to be constexpr
// But most compilers should be able to compute eps23 at compile time
const Scalar eps23 = pow(eps, Scalar(2) / 3);
// thresh = tol * max(eps23, abs(theta)), theta for Ritz value
Array thresh = tol * m_ritz_val.head(m_nev).array().abs().max(eps23);
Array resid = m_ritz_est.head(m_nev).array().abs() * m_fac.f_norm();
// Converged "wanted" Ritz values
m_ritz_conv = (resid < thresh);
return m_ritz_conv.cast<Index>().sum();
return m_ritz_conv.count();
}
// Returns the adjusted nev for restarting
@ -160,13 +162,17 @@ private:
{
using std::abs;
// A very small value, but 1.0 / near_0 does not overflow
// ~= 1e-307 for the "double" type
const Scalar near_0 = TypeTraits<Scalar>::min() * Scalar(10);
Index nev_new = m_nev;
for (Index i = m_nev; i < m_ncv; i++)
if (abs(m_ritz_est[i]) < m_near_0)
if (abs(m_ritz_est[i]) < near_0)
nev_new++;
// Adjust nev_new, according to dnaup2.f line 660~674 in ARPACK
nev_new += std::min(nconv, (m_ncv - nev_new) / 2);
nev_new += (std::min)(nconv, (m_ncv - nev_new) / 2);
if (nev_new == 1 && m_ncv >= 6)
nev_new = m_ncv / 2;
else if (nev_new == 1 && m_ncv > 3)
@ -187,14 +193,55 @@ private:
}
// Retrieves and sorts Ritz values and Ritz vectors
void retrieve_ritzpair()
void retrieve_ritzpair(SortRule selection)
{
UpperHessenbergEigen<Scalar> decomp(m_fac.matrix_H());
const ComplexVector& evals = decomp.eigenvalues();
ComplexMatrix evecs = decomp.eigenvectors();
SortEigenvalue<Complex, SelectionRule> sorting(evals.data(), evals.size());
std::vector<int> ind = sorting.index();
// Sort Ritz values and put the wanted ones at the beginning
std::vector<Index> ind;
switch (selection)
{
case SortRule::LargestMagn:
{
SortEigenvalue<Complex, SortRule::LargestMagn> sorting(evals.data(), m_ncv);
sorting.swap(ind);
break;
}
case SortRule::LargestReal:
{
SortEigenvalue<Complex, SortRule::LargestReal> sorting(evals.data(), m_ncv);
sorting.swap(ind);
break;
}
case SortRule::LargestImag:
{
SortEigenvalue<Complex, SortRule::LargestImag> sorting(evals.data(), m_ncv);
sorting.swap(ind);
break;
}
case SortRule::SmallestMagn:
{
SortEigenvalue<Complex, SortRule::SmallestMagn> sorting(evals.data(), m_ncv);
sorting.swap(ind);
break;
}
case SortRule::SmallestReal:
{
SortEigenvalue<Complex, SortRule::SmallestReal> sorting(evals.data(), m_ncv);
sorting.swap(ind);
break;
}
case SortRule::SmallestImag:
{
SortEigenvalue<Complex, SortRule::SmallestImag> sorting(evals.data(), m_ncv);
sorting.swap(ind);
break;
}
default:
throw std::invalid_argument("unsupported selection rule");
}
// Copy the Ritz values and vectors to m_ritz_val and m_ritz_vec, respectively
for (Index i = 0; i < m_ncv; i++)
@ -211,44 +258,45 @@ private:
protected:
// Sorts the first nev Ritz pairs in the specified order
// This is used to return the final results
virtual void sort_ritzpair(int sort_rule)
virtual void sort_ritzpair(SortRule sort_rule)
{
// First make sure that we have a valid index vector
SortEigenvalue<Complex, LARGEST_MAGN> sorting(m_ritz_val.data(), m_nev);
std::vector<int> ind = sorting.index();
std::vector<Index> ind;
switch (sort_rule)
{
case LARGEST_MAGN:
break;
case LARGEST_REAL:
case SortRule::LargestMagn:
{
SortEigenvalue<Complex, LARGEST_REAL> sorting(m_ritz_val.data(), m_nev);
ind = sorting.index();
SortEigenvalue<Complex, SortRule::LargestMagn> sorting(m_ritz_val.data(), m_nev);
sorting.swap(ind);
break;
}
case LARGEST_IMAG:
case SortRule::LargestReal:
{
SortEigenvalue<Complex, LARGEST_IMAG> sorting(m_ritz_val.data(), m_nev);
ind = sorting.index();
SortEigenvalue<Complex, SortRule::LargestReal> sorting(m_ritz_val.data(), m_nev);
sorting.swap(ind);
break;
}
case SMALLEST_MAGN:
case SortRule::LargestImag:
{
SortEigenvalue<Complex, SMALLEST_MAGN> sorting(m_ritz_val.data(), m_nev);
ind = sorting.index();
SortEigenvalue<Complex, SortRule::LargestImag> sorting(m_ritz_val.data(), m_nev);
sorting.swap(ind);
break;
}
case SMALLEST_REAL:
case SortRule::SmallestMagn:
{
SortEigenvalue<Complex, SMALLEST_REAL> sorting(m_ritz_val.data(), m_nev);
ind = sorting.index();
SortEigenvalue<Complex, SortRule::SmallestMagn> sorting(m_ritz_val.data(), m_nev);
sorting.swap(ind);
break;
}
case SMALLEST_IMAG:
case SortRule::SmallestReal:
{
SortEigenvalue<Complex, SMALLEST_IMAG> sorting(m_ritz_val.data(), m_nev);
ind = sorting.index();
SortEigenvalue<Complex, SortRule::SmallestReal> sorting(m_ritz_val.data(), m_nev);
sorting.swap(ind);
break;
}
case SortRule::SmallestImag:
{
SortEigenvalue<Complex, SortRule::SmallestImag> sorting(m_ritz_val.data(), m_nev);
sorting.swap(ind);
break;
}
default:
@ -274,18 +322,15 @@ protected:
public:
/// \cond
GenEigsBase(OpType* op, BOpType* Bop, Index nev, Index ncv) :
GenEigsBase(OpType& op, const BOpType& Bop, Index nev, Index ncv) :
m_op(op),
m_n(m_op->rows()),
m_n(m_op.rows()),
m_nev(nev),
m_ncv(ncv > m_n ? m_n : ncv),
m_nmatop(0),
m_niter(0),
m_fac(ArnoldiOpType(op, Bop), m_ncv),
m_info(NOT_COMPUTED),
m_near_0(TypeTraits<Scalar>::min() * Scalar(10)),
m_eps(Eigen::NumTraits<Scalar>::epsilon()),
m_eps23(Eigen::numext::pow(m_eps, Scalar(2.0) / 3))
m_info(CompInfo::NotComputed)
{
if (nev < 1 || nev > m_n - 2)
throw std::invalid_argument("nev must satisfy 1 <= nev <= n - 2, n is the size of matrix");
@ -348,28 +393,33 @@ public:
///
/// Conducts the major computation procedure.
///
/// \param selection An enumeration value indicating the selection rule of
/// the requested eigenvalues, for example `SortRule::LargestMagn`
/// to retrieve eigenvalues with the largest magnitude.
/// The full list of enumeration values can be found in
/// \ref Enumerations.
/// \param maxit Maximum number of iterations allowed in the algorithm.
/// \param tol Precision parameter for the calculated eigenvalues.
/// \param sort_rule Rule to sort the eigenvalues and eigenvectors.
/// \param sorting Rule to sort the eigenvalues and eigenvectors.
/// Supported values are
/// `Spectra::LARGEST_MAGN`, `Spectra::LARGEST_REAL`,
/// `Spectra::LARGEST_IMAG`, `Spectra::SMALLEST_MAGN`,
/// `Spectra::SMALLEST_REAL` and `Spectra::SMALLEST_IMAG`,
/// for example `LARGEST_MAGN` indicates that eigenvalues
/// `SortRule::LargestMagn`, `SortRule::LargestReal`,
/// `SortRule::LargestImag`, `SortRule::SmallestMagn`,
/// `SortRule::SmallestReal` and `SortRule::SmallestImag`,
/// for example `SortRule::LargestMagn` indicates that eigenvalues
/// with largest magnitude come first.
/// Note that this argument is only used to
/// **sort** the final result, and the **selection** rule
/// (e.g. selecting the largest or smallest eigenvalues in the
/// full spectrum) is specified by the template parameter
/// `SelectionRule` of GenEigsSolver.
/// full spectrum) is specified by the parameter `selection`.
///
/// \return Number of converged eigenvalues.
///
Index compute(Index maxit = 1000, Scalar tol = 1e-10, int sort_rule = LARGEST_MAGN)
Index compute(SortRule selection = SortRule::LargestMagn, Index maxit = 1000,
Scalar tol = 1e-10, SortRule sorting = SortRule::LargestMagn)
{
// The m-step Arnoldi factorization
m_fac.factorize_from(1, m_ncv, m_nmatop);
retrieve_ritzpair();
retrieve_ritzpair(selection);
// Restarting
Index i, nconv = 0, nev_adj;
for (i = 0; i < maxit; i++)
@ -379,22 +429,22 @@ public:
break;
nev_adj = nev_adjusted(nconv);
restart(nev_adj);
restart(nev_adj, selection);
}
// Sorting results
sort_ritzpair(sort_rule);
sort_ritzpair(sorting);
m_niter += i + 1;
m_info = (nconv >= m_nev) ? SUCCESSFUL : NOT_CONVERGING;
m_info = (nconv >= m_nev) ? CompInfo::Successful : CompInfo::NotConverging;
return std::min(m_nev, nconv);
return (std::min)(m_nev, nconv);
}
///
/// Returns the status of the computation.
/// The full list of enumeration values can be found in \ref Enumerations.
///
int info() const { return m_info; }
CompInfo info() const { return m_info; }
///
/// Returns the number of iterations used in the computation.
@ -446,7 +496,7 @@ public:
ComplexMatrix eigenvectors(Index nvec) const
{
const Index nconv = m_ritz_conv.cast<Index>().sum();
nvec = std::min(nvec, nconv);
nvec = (std::min)(nvec, nconv);
ComplexMatrix res(m_n, nvec);
if (!nvec)
@ -479,4 +529,4 @@ public:
} // namespace Spectra
#endif // GEN_EIGS_BASE_H
#endif // SPECTRA_GEN_EIGS_BASE_H

88
gtsam/3rdparty/Spectra/GenEigsComplexShiftSolver.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef GEN_EIGS_COMPLEX_SHIFT_SOLVER_H
#define GEN_EIGS_COMPLEX_SHIFT_SOLVER_H
#ifndef SPECTRA_GEN_EIGS_COMPLEX_SHIFT_SOLVER_H
#define SPECTRA_GEN_EIGS_COMPLEX_SHIFT_SOLVER_H
#include <Eigen/Core>
@ -23,33 +23,35 @@ namespace Spectra {
/// knowledge of the shift-and-invert mode can be found in the documentation
/// of the SymEigsShiftSolver class.
///
/// \tparam Scalar The element type of the matrix.
/// Currently supported types are `float`, `double` and `long double`.
/// \tparam SelectionRule An enumeration value indicating the selection rule of
/// the shifted-and-inverted eigenvalues.
/// The full list of enumeration values can be found in
/// \ref Enumerations.
/// \tparam OpType The name of the matrix operation class. Users could either
/// use the DenseGenComplexShiftSolve wrapper class, or define their
/// own that implements all the public member functions as in
/// DenseGenComplexShiftSolve.
/// \tparam OpType The name of the matrix operation class. Users could either
/// use the wrapper classes such as DenseGenComplexShiftSolve and
/// SparseGenComplexShiftSolve, or define their own that implements the type
/// definition `Scalar` and all the public member functions as in
/// DenseGenComplexShiftSolve.
///
template <typename Scalar = double,
int SelectionRule = LARGEST_MAGN,
typename OpType = DenseGenComplexShiftSolve<double> >
class GenEigsComplexShiftSolver : public GenEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>
template <typename OpType = DenseGenComplexShiftSolve<double>>
class GenEigsComplexShiftSolver : public GenEigsBase<OpType, IdentityBOp>
{
private:
typedef Eigen::Index Index;
typedef std::complex<Scalar> Complex;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Matrix<Complex, Eigen::Dynamic, 1> ComplexVector;
using Scalar = typename OpType::Scalar;
using Index = Eigen::Index;
using Complex = std::complex<Scalar>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using ComplexArray = Eigen::Array<Complex, Eigen::Dynamic, 1>;
using Base = GenEigsBase<OpType, IdentityBOp>;
using Base::m_op;
using Base::m_n;
using Base::m_nev;
using Base::m_fac;
using Base::m_ritz_val;
using Base::m_ritz_vec;
const Scalar m_sigmar;
const Scalar m_sigmai;
// First transform back the Ritz values, and then sort
void sort_ritzpair(int sort_rule)
void sort_ritzpair(SortRule sort_rule) override
{
using std::abs;
using std::sqrt;
@ -77,20 +79,20 @@ private:
SimpleRandom<Scalar> rng(0);
const Scalar shiftr = rng.random() * m_sigmar + rng.random();
const Complex shift = Complex(shiftr, Scalar(0));
this->m_op->set_shift(shiftr, Scalar(0));
m_op.set_shift(shiftr, Scalar(0));
// Calculate inv(A - r * I) * vj
Vector v_real(this->m_n), v_imag(this->m_n), OPv_real(this->m_n), OPv_imag(this->m_n);
const Scalar eps = Eigen::NumTraits<Scalar>::epsilon();
for (Index i = 0; i < this->m_nev; i++)
Vector v_real(m_n), v_imag(m_n), OPv_real(m_n), OPv_imag(m_n);
const Scalar eps = TypeTraits<Scalar>::epsilon();
for (Index i = 0; i < m_nev; i++)
{
v_real.noalias() = this->m_fac.matrix_V() * this->m_ritz_vec.col(i).real();
v_imag.noalias() = this->m_fac.matrix_V() * this->m_ritz_vec.col(i).imag();
this->m_op->perform_op(v_real.data(), OPv_real.data());
this->m_op->perform_op(v_imag.data(), OPv_imag.data());
v_real.noalias() = m_fac.matrix_V() * m_ritz_vec.col(i).real();
v_imag.noalias() = m_fac.matrix_V() * m_ritz_vec.col(i).imag();
m_op.perform_op(v_real.data(), OPv_real.data());
m_op.perform_op(v_imag.data(), OPv_imag.data());
// Two roots computed from the quadratic equation
const Complex nu = this->m_ritz_val[i];
const Complex nu = m_ritz_val[i];
const Complex root_part1 = m_sigmar + Scalar(0.5) / nu;
const Complex root_part2 = Scalar(0.5) * sqrt(Scalar(1) - Scalar(4) * m_sigmai * m_sigmai * (nu * nu)) / nu;
const Complex root1 = root_part1 + root_part2;
@ -98,7 +100,7 @@ private:
// Test roots
Scalar err1 = Scalar(0), err2 = Scalar(0);
for (int k = 0; k < this->m_n; k++)
for (int k = 0; k < m_n; k++)
{
const Complex rhs1 = Complex(v_real[k], v_imag[k]) / (root1 - shift);
const Complex rhs2 = Complex(v_real[k], v_imag[k]) / (root2 - shift);
@ -108,31 +110,31 @@ private:
}
const Complex lambdaj = (err1 < err2) ? root1 : root2;
this->m_ritz_val[i] = lambdaj;
m_ritz_val[i] = lambdaj;
if (abs(Eigen::numext::imag(lambdaj)) > eps)
{
this->m_ritz_val[i + 1] = Eigen::numext::conj(lambdaj);
m_ritz_val[i + 1] = Eigen::numext::conj(lambdaj);
i++;
}
else
{
this->m_ritz_val[i] = Complex(Eigen::numext::real(lambdaj), Scalar(0));
m_ritz_val[i] = Complex(Eigen::numext::real(lambdaj), Scalar(0));
}
}
GenEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>::sort_ritzpair(sort_rule);
Base::sort_ritzpair(sort_rule);
}
public:
///
/// Constructor to create a eigen solver object using the shift-and-invert mode.
///
/// \param op Pointer to the matrix operation object. This class should implement
/// \param op The matrix operation object that implements
/// the complex shift-solve operation of \f$A\f$: calculating
/// \f$\mathrm{Re}\{(A-\sigma I)^{-1}v\}\f$ for any vector \f$v\f$. Users could either
/// create the object from the DenseGenComplexShiftSolve wrapper class, or
/// define their own that implements all the public member functions
/// create the object from the wrapper class such as DenseGenComplexShiftSolve, or
/// define their own that implements all the public members
/// as in DenseGenComplexShiftSolve.
/// \param nev Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-2\f$,
/// where \f$n\f$ is the size of matrix.
@ -144,14 +146,14 @@ public:
/// \param sigmar The real part of the shift.
/// \param sigmai The imaginary part of the shift.
///
GenEigsComplexShiftSolver(OpType* op, Index nev, Index ncv, const Scalar& sigmar, const Scalar& sigmai) :
GenEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>(op, NULL, nev, ncv),
GenEigsComplexShiftSolver(OpType& op, Index nev, Index ncv, const Scalar& sigmar, const Scalar& sigmai) :
Base(op, IdentityBOp(), nev, ncv),
m_sigmar(sigmar), m_sigmai(sigmai)
{
this->m_op->set_shift(m_sigmar, m_sigmai);
op.set_shift(m_sigmar, m_sigmai);
}
};
} // namespace Spectra
#endif // GEN_EIGS_COMPLEX_SHIFT_SOLVER_H
#endif // SPECTRA_GEN_EIGS_COMPLEX_SHIFT_SOLVER_H

58
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef GEN_EIGS_REAL_SHIFT_SOLVER_H
#define GEN_EIGS_REAL_SHIFT_SOLVER_H
#ifndef SPECTRA_GEN_EIGS_REAL_SHIFT_SOLVER_H
#define SPECTRA_GEN_EIGS_REAL_SHIFT_SOLVER_H
#include <Eigen/Core>
@ -23,49 +23,45 @@ namespace Spectra {
/// knowledge of the shift-and-invert mode can be found in the documentation
/// of the SymEigsShiftSolver class.
///
/// \tparam Scalar The element type of the matrix.
/// Currently supported types are `float`, `double` and `long double`.
/// \tparam SelectionRule An enumeration value indicating the selection rule of
/// the shifted-and-inverted eigenvalues.
/// The full list of enumeration values can be found in
/// \ref Enumerations.
/// \tparam OpType The name of the matrix operation class. Users could either
/// use the wrapper classes such as DenseGenRealShiftSolve and
/// SparseGenRealShiftSolve, or define their
/// own that implements all the public member functions as in
/// DenseGenRealShiftSolve.
/// \tparam OpType The name of the matrix operation class. Users could either
/// use the wrapper classes such as DenseGenRealShiftSolve and
/// SparseGenRealShiftSolve, or define their own that implements the type
/// definition `Scalar` and all the public member functions as in
/// DenseGenRealShiftSolve.
///
template <typename Scalar = double,
int SelectionRule = LARGEST_MAGN,
typename OpType = DenseGenRealShiftSolve<double> >
class GenEigsRealShiftSolver : public GenEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>
template <typename OpType = DenseGenRealShiftSolve<double>>
class GenEigsRealShiftSolver : public GenEigsBase<OpType, IdentityBOp>
{
private:
typedef Eigen::Index Index;
typedef std::complex<Scalar> Complex;
typedef Eigen::Array<Complex, Eigen::Dynamic, 1> ComplexArray;
using Scalar = typename OpType::Scalar;
using Index = Eigen::Index;
using Complex = std::complex<Scalar>;
using ComplexArray = Eigen::Array<Complex, Eigen::Dynamic, 1>;
using Base = GenEigsBase<OpType, IdentityBOp>;
using Base::m_nev;
using Base::m_ritz_val;
const Scalar m_sigma;
// First transform back the Ritz values, and then sort
void sort_ritzpair(int sort_rule)
void sort_ritzpair(SortRule sort_rule) override
{
// The eigenvalues we get from the iteration is nu = 1 / (lambda - sigma)
// So the eigenvalues of the original problem is lambda = 1 / nu + sigma
ComplexArray ritz_val_org = Scalar(1.0) / this->m_ritz_val.head(this->m_nev).array() + m_sigma;
this->m_ritz_val.head(this->m_nev) = ritz_val_org;
GenEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>::sort_ritzpair(sort_rule);
m_ritz_val.head(m_nev) = Scalar(1) / m_ritz_val.head(m_nev).array() + m_sigma;
Base::sort_ritzpair(sort_rule);
}
public:
///
/// Constructor to create a eigen solver object using the shift-and-invert mode.
///
/// \param op Pointer to the matrix operation object. This class should implement
/// \param op The matrix operation object that implements
/// the shift-solve operation of \f$A\f$: calculating
/// \f$(A-\sigma I)^{-1}v\f$ for any vector \f$v\f$. Users could either
/// create the object from the wrapper class such as DenseGenRealShiftSolve, or
/// define their own that implements all the public member functions
/// define their own that implements all the public members
/// as in DenseGenRealShiftSolve.
/// \param nev Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-2\f$,
/// where \f$n\f$ is the size of matrix.
@ -76,14 +72,14 @@ public:
/// and is advised to take \f$ncv \ge 2\cdot nev + 1\f$.
/// \param sigma The real-valued shift.
///
GenEigsRealShiftSolver(OpType* op, Index nev, Index ncv, Scalar sigma) :
GenEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>(op, NULL, nev, ncv),
GenEigsRealShiftSolver(OpType& op, Index nev, Index ncv, const Scalar& sigma) :
Base(op, IdentityBOp(), nev, ncv),
m_sigma(sigma)
{
this->m_op->set_shift(m_sigma);
op.set_shift(m_sigma);
}
};
} // namespace Spectra
#endif // GEN_EIGS_REAL_SHIFT_SOLVER_H
#endif // SPECTRA_GEN_EIGS_REAL_SHIFT_SOLVER_H

59
gtsam/3rdparty/Spectra/GenEigsSolver.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef GEN_EIGS_SOLVER_H
#define GEN_EIGS_SOLVER_H
#ifndef SPECTRA_GEN_EIGS_SOLVER_H
#define SPECTRA_GEN_EIGS_SOLVER_H
#include <Eigen/Core>
@ -25,18 +25,11 @@ namespace Spectra {
/// also applies to the GenEigsSolver class here, except that the eigenvalues
/// and eigenvectors of a general matrix can now be complex-valued.
///
/// \tparam Scalar The element type of the matrix.
/// Currently supported types are `float`, `double` and `long double`.
/// \tparam SelectionRule An enumeration value indicating the selection rule of
/// the requested eigenvalues, for example `LARGEST_MAGN`
/// to retrieve eigenvalues with the largest magnitude.
/// The full list of enumeration values can be found in
/// \ref Enumerations.
/// \tparam OpType The name of the matrix operation class. Users could either
/// use the wrapper classes such as DenseGenMatProd and
/// SparseGenMatProd, or define their
/// own that implements all the public member functions as in
/// DenseGenMatProd.
/// \tparam OpType The name of the matrix operation class. Users could either
/// use the wrapper classes such as DenseGenMatProd and
/// SparseGenMatProd, or define their own that implements the type
/// definition `Scalar` and all the public member functions as in
/// DenseGenMatProd.
///
/// An example that illustrates the usage of GenEigsSolver is give below:
///
@ -58,15 +51,15 @@ namespace Spectra {
///
/// // Construct eigen solver object, requesting the largest
/// // (in magnitude, or norm) three eigenvalues
/// GenEigsSolver< double, LARGEST_MAGN, DenseGenMatProd<double> > eigs(&op, 3, 6);
/// GenEigsSolver<DenseGenMatProd<double>> eigs(op, 3, 6);
///
/// // Initialize and compute
/// eigs.init();
/// int nconv = eigs.compute();
/// int nconv = eigs.compute(SortRule::LargestMagn);
///
/// // Retrieve results
/// Eigen::VectorXcd evalues;
/// if(eigs.info() == SUCCESSFUL)
/// if (eigs.info() == CompInfo::Successful)
/// evalues = eigs.eigenvalues();
///
/// std::cout << "Eigenvalues found:\n" << evalues << std::endl;
@ -93,12 +86,12 @@ namespace Spectra {
/// const int n = 10;
/// Eigen::SparseMatrix<double> M(n, n);
/// M.reserve(Eigen::VectorXi::Constant(n, 3));
/// for(int i = 0; i < n; i++)
/// for (int i = 0; i < n; i++)
/// {
/// M.insert(i, i) = 1.0;
/// if(i > 0)
/// if (i > 0)
/// M.insert(i - 1, i) = 3.0;
/// if(i < n - 1)
/// if (i < n - 1)
/// M.insert(i + 1, i) = 2.0;
/// }
///
@ -106,15 +99,15 @@ namespace Spectra {
/// SparseGenMatProd<double> op(M);
///
/// // Construct eigen solver object, requesting the largest three eigenvalues
/// GenEigsSolver< double, LARGEST_MAGN, SparseGenMatProd<double> > eigs(&op, 3, 6);
/// GenEigsSolver<SparseGenMatProd<double>> eigs(op, 3, 6);
///
/// // Initialize and compute
/// eigs.init();
/// int nconv = eigs.compute();
/// int nconv = eigs.compute(SortRule::LargestMagn);
///
/// // Retrieve results
/// Eigen::VectorXcd evalues;
/// if(eigs.info() == SUCCESSFUL)
/// if (eigs.info() == CompInfo::Successful)
/// evalues = eigs.eigenvalues();
///
/// std::cout << "Eigenvalues found:\n" << evalues << std::endl;
@ -122,23 +115,21 @@ namespace Spectra {
/// return 0;
/// }
/// \endcode
template <typename Scalar = double,
int SelectionRule = LARGEST_MAGN,
typename OpType = DenseGenMatProd<double> >
class GenEigsSolver : public GenEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>
template <typename OpType = DenseGenMatProd<double>>
class GenEigsSolver : public GenEigsBase<OpType, IdentityBOp>
{
private:
typedef Eigen::Index Index;
using Index = Eigen::Index;
public:
///
/// Constructor to create a solver object.
///
/// \param op Pointer to the matrix operation object, which should implement
/// \param op The matrix operation object that implements
/// the matrix-vector multiplication operation of \f$A\f$:
/// calculating \f$Av\f$ for any vector \f$v\f$. Users could either
/// create the object from the wrapper class such as DenseGenMatProd, or
/// define their own that implements all the public member functions
/// define their own that implements all the public members
/// as in DenseGenMatProd.
/// \param nev Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-2\f$,
/// where \f$n\f$ is the size of matrix.
@ -148,11 +139,11 @@ public:
/// in each iteration. This parameter must satisfy \f$nev+2 \le ncv \le n\f$,
/// and is advised to take \f$ncv \ge 2\cdot nev + 1\f$.
///
GenEigsSolver(OpType* op, Index nev, Index ncv) :
GenEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>(op, NULL, nev, ncv)
GenEigsSolver(OpType& op, Index nev, Index ncv) :
GenEigsBase<OpType, IdentityBOp>(op, IdentityBOp(), nev, ncv)
{}
};
} // namespace Spectra
#endif // GEN_EIGS_SOLVER_H
#endif // SPECTRA_GEN_EIGS_SOLVER_H

477
gtsam/3rdparty/Spectra/HermEigsBase.h vendored Normal file
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@ -0,0 +1,477 @@
// Copyright (C) 2018-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_HERM_EIGS_BASE_H
#define SPECTRA_HERM_EIGS_BASE_H
#include <Eigen/Core>
#include <vector> // std::vector
#include <cmath> // std::abs, std::pow
#include <algorithm> // std::min
#include <stdexcept> // std::invalid_argument
#include <utility> // std::move
#include "Util/Version.h"
#include "Util/TypeTraits.h"
#include "Util/SelectionRule.h"
#include "Util/CompInfo.h"
#include "Util/SimpleRandom.h"
#include "MatOp/internal/ArnoldiOp.h"
#include "LinAlg/UpperHessenbergQR.h"
#include "LinAlg/TridiagEigen.h"
#include "LinAlg/Lanczos.h"
namespace Spectra {
///
/// \defgroup EigenSolver Eigen Solvers
///
/// Eigen solvers for different types of problems.
///
///
/// \ingroup EigenSolver
///
/// This is the base class for Hermitian (and real symmetric) eigen solvers,
/// mainly for internal use.
/// It is kept here to provide the documentation for member functions of
/// concrete eigen solvers such as SymEigsSolver, HermEigsSolver, SymEigsShiftSolver, etc.
///
template <typename OpType, typename BOpType>
class HermEigsBase
{
private:
using Scalar = typename OpType::Scalar;
// The real part type of the matrix element, e.g.,
// Scalar = double => RealScalar = double
// Scalar = std::complex<double> => RealScalar = double
using RealScalar = typename Eigen::NumTraits<Scalar>::Real;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using RealMatrix = Eigen::Matrix<RealScalar, Eigen::Dynamic, Eigen::Dynamic>;
using RealVector = Eigen::Matrix<RealScalar, Eigen::Dynamic, 1>;
using RealArray = Eigen::Array<RealScalar, Eigen::Dynamic, 1>;
using BoolArray = Eigen::Array<bool, Eigen::Dynamic, 1>;
using MapMat = Eigen::Map<Matrix>;
using MapVec = Eigen::Map<Vector>;
using MapConstVec = Eigen::Map<const Vector>;
using ArnoldiOpType = ArnoldiOp<Scalar, OpType, BOpType>;
using LanczosFac = Lanczos<Scalar, ArnoldiOpType>;
protected:
// clang-format off
// In SymEigsSolver and SymEigsShiftSolver, the A operator is an lvalue provided by
// the user. In SymGEigsSolver, the A operator is an rvalue. To avoid copying objects,
// we use the following scheme:
// 1. If the op parameter in the constructor is an lvalue, make m_op a const reference to op
// 2. If op is an rvalue, move op to m_op_container, and then make m_op a const
// reference to m_op_container[0]
std::vector<OpType> m_op_container;
const OpType& m_op; // matrix operator for A
const Index m_n; // dimension of matrix A
const Index m_nev; // number of eigenvalues requested
const Index m_ncv; // dimension of Krylov subspace in the Lanczos method
Index m_nmatop; // number of matrix operations called
Index m_niter; // number of restarting iterations
LanczosFac m_fac; // Lanczos factorization
RealVector m_ritz_val; // Ritz values
private:
RealMatrix m_ritz_vec; // Ritz vectors
RealVector m_ritz_est; // last row of m_ritz_vec, also called the Ritz estimates
BoolArray m_ritz_conv; // indicator of the convergence of Ritz values
CompInfo m_info; // status of the computation
// clang-format on
// Move rvalue object to the container
static std::vector<OpType> create_op_container(OpType&& rval)
{
std::vector<OpType> container;
container.emplace_back(std::move(rval));
return container;
}
// Implicitly restarted Lanczos factorization
void restart(Index k, SortRule selection)
{
using std::abs;
if (k >= m_ncv)
return;
// QR decomposition on a real symmetric matrix
TridiagQR<RealScalar> decomp(m_ncv);
// Q is a real orthogonal matrix
RealMatrix Q = RealMatrix::Identity(m_ncv, m_ncv);
// Apply large shifts first
const int nshift = m_ncv - k;
RealVector shifts = m_ritz_val.tail(nshift);
std::sort(shifts.data(), shifts.data() + nshift,
[](const RealScalar& v1, const RealScalar& v2) { return abs(v1) > abs(v2); });
for (Index i = 0; i < nshift; i++)
{
// QR decomposition of H-mu*I, mu is the shift
// H is known to be a real symmetric matrix
decomp.compute(m_fac.matrix_H().real(), shifts[i]);
// Q -> Q * Qi
decomp.apply_YQ(Q);
// H -> Q'HQ
// Since QR = H - mu * I, we have H = QR + mu * I
// and therefore Q'HQ = RQ + mu * I
m_fac.compress_H(decomp);
// Note that in our setting, mu is an eigenvalue of H,
// so after applying Q'HQ, H must have be of the following form
// H = [X 0 0]
// [0 mu 0]
// [0 0 D]
// Then we can force H[k, k-1] = H[k-1, k] = 0 and H[k, k] = mu,
// where k is the size of X
//
// Currently disabled due to numerical stability
//
// m_fac.deflate_H(m_ncv - i - 1, shifts[i]);
}
m_fac.compress_V(Q);
m_fac.factorize_from(k, m_ncv, m_nmatop);
retrieve_ritzpair(selection);
}
// Calculates the number of converged Ritz values
Index num_converged(const RealScalar& tol)
{
using std::pow;
// The machine precision, ~= 1e-16 for the "double" type
const RealScalar eps = TypeTraits<RealScalar>::epsilon();
// std::pow() is not constexpr, so we do not declare eps23 to be constexpr
// But most compilers should be able to compute eps23 at compile time
const RealScalar eps23 = pow(eps, RealScalar(2) / 3);
// thresh = tol * max(eps23, abs(theta)), theta for Ritz value
RealArray thresh = tol * m_ritz_val.head(m_nev).array().abs().max(eps23);
RealArray resid = m_ritz_est.head(m_nev).array().abs() * m_fac.f_norm();
// Converged "wanted" Ritz values
m_ritz_conv = (resid < thresh);
return m_ritz_conv.count();
}
// Returns the adjusted nev for restarting
Index nev_adjusted(Index nconv)
{
using std::abs;
// A very small value, but 1.0 / near_0 does not overflow
// ~= 1e-307 for the "double" type
const RealScalar near_0 = TypeTraits<RealScalar>::min() * RealScalar(10);
Index nev_new = m_nev;
for (Index i = m_nev; i < m_ncv; i++)
if (abs(m_ritz_est[i]) < near_0)
nev_new++;
// Adjust nev_new, according to dsaup2.f line 677~684 in ARPACK
nev_new += (std::min)(nconv, (m_ncv - nev_new) / 2);
if (nev_new == 1 && m_ncv >= 6)
nev_new = m_ncv / 2;
else if (nev_new == 1 && m_ncv > 2)
nev_new = 2;
if (nev_new > m_ncv - 1)
nev_new = m_ncv - 1;
return nev_new;
}
// Retrieves and sorts Ritz values and Ritz vectors
void retrieve_ritzpair(SortRule selection)
{
TridiagEigen<RealScalar> decomp(m_fac.matrix_H().real());
const RealVector& evals = decomp.eigenvalues();
const RealMatrix& evecs = decomp.eigenvectors();
// Sort Ritz values and put the wanted ones at the beginning
std::vector<Index> ind = argsort(selection, evals, m_ncv);
// Copy the Ritz values and vectors to m_ritz_val and m_ritz_vec, respectively
for (Index i = 0; i < m_ncv; i++)
{
m_ritz_val[i] = evals[ind[i]];
m_ritz_est[i] = evecs(m_ncv - 1, ind[i]);
}
for (Index i = 0; i < m_nev; i++)
{
m_ritz_vec.col(i).noalias() = evecs.col(ind[i]);
}
}
protected:
// Sorts the first nev Ritz pairs in the specified order
// This is used to return the final results
virtual void sort_ritzpair(SortRule sort_rule)
{
if ((sort_rule != SortRule::LargestAlge) && (sort_rule != SortRule::LargestMagn) &&
(sort_rule != SortRule::SmallestAlge) && (sort_rule != SortRule::SmallestMagn))
throw std::invalid_argument("unsupported sorting rule");
std::vector<Index> ind = argsort(sort_rule, m_ritz_val, m_nev);
RealVector new_ritz_val(m_ncv);
RealMatrix new_ritz_vec(m_ncv, m_nev);
BoolArray new_ritz_conv(m_nev);
for (Index i = 0; i < m_nev; i++)
{
new_ritz_val[i] = m_ritz_val[ind[i]];
new_ritz_vec.col(i).noalias() = m_ritz_vec.col(ind[i]);
new_ritz_conv[i] = m_ritz_conv[ind[i]];
}
m_ritz_val.swap(new_ritz_val);
m_ritz_vec.swap(new_ritz_vec);
m_ritz_conv.swap(new_ritz_conv);
}
public:
/// \cond
// If op is an lvalue
HermEigsBase(OpType& op, const BOpType& Bop, Index nev, Index ncv) :
m_op(op),
m_n(op.rows()),
m_nev(nev),
m_ncv(ncv > m_n ? m_n : ncv),
m_nmatop(0),
m_niter(0),
m_fac(ArnoldiOpType(op, Bop), m_ncv),
m_info(CompInfo::NotComputed)
{
if (nev < 1 || nev > m_n - 1)
throw std::invalid_argument("nev must satisfy 1 <= nev <= n - 1, n is the size of matrix");
if (ncv <= nev || ncv > m_n)
throw std::invalid_argument("ncv must satisfy nev < ncv <= n, n is the size of matrix");
}
// If op is an rvalue
HermEigsBase(OpType&& op, const BOpType& Bop, Index nev, Index ncv) :
m_op_container(create_op_container(std::move(op))),
m_op(m_op_container.front()),
m_n(m_op.rows()),
m_nev(nev),
m_ncv(ncv > m_n ? m_n : ncv),
m_nmatop(0),
m_niter(0),
m_fac(ArnoldiOpType(m_op, Bop), m_ncv),
m_info(CompInfo::NotComputed)
{
if (nev < 1 || nev > m_n - 1)
throw std::invalid_argument("nev must satisfy 1 <= nev <= n - 1, n is the size of matrix");
if (ncv <= nev || ncv > m_n)
throw std::invalid_argument("ncv must satisfy nev < ncv <= n, n is the size of matrix");
}
///
/// Virtual destructor
///
virtual ~HermEigsBase() {}
/// \endcond
///
/// Initializes the solver by providing an initial residual vector.
///
/// \param init_resid Pointer to the initial residual vector.
///
/// **Spectra** (and also **ARPACK**) uses an iterative algorithm
/// to find eigenvalues. This function allows the user to provide the initial
/// residual vector.
///
void init(const Scalar* init_resid)
{
// Reset all matrices/vectors to zero
m_ritz_val.resize(m_ncv);
m_ritz_vec.resize(m_ncv, m_nev);
m_ritz_est.resize(m_ncv);
m_ritz_conv.resize(m_nev);
m_ritz_val.setZero();
m_ritz_vec.setZero();
m_ritz_est.setZero();
m_ritz_conv.setZero();
m_nmatop = 0;
m_niter = 0;
// Initialize the Lanczos factorization
MapConstVec v0(init_resid, m_n);
m_fac.init(v0, m_nmatop);
}
///
/// Initializes the solver by providing a random initial residual vector.
///
/// This overloaded function generates a random initial residual vector
/// (with a fixed random seed) for the algorithm. Elements in the vector
/// follow independent Uniform(-0.5, 0.5) distribution.
///
void init()
{
SimpleRandom<Scalar> rng(0);
Vector init_resid = rng.random_vec(m_n);
init(init_resid.data());
}
///
/// Conducts the major computation procedure.
///
/// \param selection An enumeration value indicating the selection rule of
/// the requested eigenvalues, for example `SortRule::LargestMagn`
/// to retrieve eigenvalues with the largest magnitude.
/// The full list of enumeration values can be found in
/// \ref Enumerations.
/// \param maxit Maximum number of iterations allowed in the algorithm.
/// \param tol Precision parameter for the calculated eigenvalues.
/// \param sorting Rule to sort the eigenvalues and eigenvectors.
/// Supported values are
/// `SortRule::LargestAlge`, `SortRule::LargestMagn`,
/// `SortRule::SmallestAlge`, and `SortRule::SmallestMagn`.
/// For example, `SortRule::LargestAlge` indicates that largest eigenvalues
/// come first. Note that this argument is only used to
/// **sort** the final result, and the **selection** rule
/// (e.g. selecting the largest or smallest eigenvalues in the
/// full spectrum) is specified by the parameter `selection`.
///
/// \return Number of converged eigenvalues.
///
Index compute(SortRule selection = SortRule::LargestMagn, Index maxit = 1000,
RealScalar tol = 1e-10, SortRule sorting = SortRule::LargestAlge)
{
// The m-step Lanczos factorization
m_fac.factorize_from(1, m_ncv, m_nmatop);
retrieve_ritzpair(selection);
// Restarting
Index i, nconv = 0, nev_adj;
for (i = 0; i < maxit; i++)
{
nconv = num_converged(tol);
if (nconv >= m_nev)
break;
nev_adj = nev_adjusted(nconv);
restart(nev_adj, selection);
}
// Sorting results
sort_ritzpair(sorting);
m_niter += i + 1;
m_info = (nconv >= m_nev) ? CompInfo::Successful : CompInfo::NotConverging;
return (std::min)(m_nev, nconv);
}
///
/// Returns the status of the computation.
/// The full list of enumeration values can be found in \ref Enumerations.
///
CompInfo info() const { return m_info; }
///
/// Returns the number of iterations used in the computation.
///
Index num_iterations() const { return m_niter; }
///
/// Returns the number of matrix operations used in the computation.
///
Index num_operations() const { return m_nmatop; }
///
/// Returns the converged eigenvalues.
///
/// \return A vector containing the real-valued eigenvalues.
/// Returned vector type will be `Eigen::Vector<RealScalar, ...>`, depending on
/// the `Scalar` type defined in the matrix operation class.
/// For example, if `Scalar` is `double` or `std::complex<double>`,
/// then `RealScalar` would be `double`.
///
RealVector eigenvalues() const
{
const Index nconv = m_ritz_conv.count();
RealVector res(nconv);
if (!nconv)
return res;
Index j = 0;
for (Index i = 0; i < m_nev; i++)
{
if (m_ritz_conv[i])
{
res[j] = m_ritz_val[i];
j++;
}
}
return res;
}
///
/// Returns the eigenvectors associated with the converged eigenvalues.
///
/// \param nvec The number of eigenvectors to return.
///
/// \return A matrix containing the eigenvectors.
/// Returned matrix type will be `Eigen::Matrix<Scalar, ...>`,
/// depending on the `Scalar` type defined in the matrix operation class.
///
virtual Matrix eigenvectors(Index nvec) const
{
const Index nconv = m_ritz_conv.count();
nvec = (std::min)(nvec, nconv);
Matrix res(m_n, nvec);
if (!nvec)
return res;
RealMatrix ritz_vec_conv(m_ncv, nvec);
Index j = 0;
for (Index i = 0; i < m_nev && j < nvec; i++)
{
if (m_ritz_conv[i])
{
ritz_vec_conv.col(j).noalias() = m_ritz_vec.col(i);
j++;
}
}
res.noalias() = m_fac.matrix_V() * ritz_vec_conv;
return res;
}
///
/// Returns all converged eigenvectors.
///
virtual Matrix eigenvectors() const
{
return eigenvectors(m_nev);
}
};
} // namespace Spectra
#endif // SPECTRA_HERM_EIGS_BASE_H

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@ -0,0 +1,146 @@
// Copyright (C) 2024-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_HERM_EIGS_SOLVER_H
#define SPECTRA_HERM_EIGS_SOLVER_H
#include <Eigen/Core>
#include "HermEigsBase.h"
#include "Util/SelectionRule.h"
#include "MatOp/DenseHermMatProd.h"
namespace Spectra {
///
/// \ingroup EigenSolver
///
/// This class implements the eigen solver for Hermitian matrices, i.e.,
/// to solve \f$Ax=\lambda x\f$ where \f$A\f$ is Hermitian.
/// An Hermitian matrix is a complex square matrix that is equal to its
/// own conjugate transpose. It is known that all Hermitian matrices have
/// real-valued eigenvalues.
///
/// \tparam OpType The name of the matrix operation class. Users could either
/// use the wrapper classes such as DenseHermMatProd and
/// SparseHermMatProd, or define their own that implements the type
/// definition `Scalar` and all the public member functions as in
/// DenseHermMatProd.
///
/// Below is an example that demonstrates the usage of this class.
///
/// \code{.cpp}
/// #include <Eigen/Core>
/// #include <Spectra/HermEigsSolver.h>
/// // <Spectra/MatOp/DenseHermMatProd.h> is implicitly included
/// #include <iostream>
///
/// using namespace Spectra;
///
/// int main()
/// {
/// // We are going to calculate the eigenvalues of M
/// Eigen::MatrixXcd A = Eigen::MatrixXcd::Random(10, 10);
/// Eigen::MatrixXcd M = A + A.adjoint();
///
/// // Construct matrix operation object using the wrapper class DenseHermMatProd
/// using OpType = DenseHermMatProd<std::complex<double>>;
/// OpType op(M);
///
/// // Construct eigen solver object, requesting the largest three eigenvalues
/// HermEigsSolver<OpType> eigs(op, 3, 6);
///
/// // Initialize and compute
/// eigs.init();
/// int nconv = eigs.compute(SortRule::LargestAlge);
///
/// // Retrieve results
/// // Eigenvalues are real-valued, and eigenvectors are complex-valued
/// Eigen::VectorXd evalues;
/// if (eigs.info() == CompInfo::Successful)
/// evalues = eigs.eigenvalues();
///
/// std::cout << "Eigenvalues found:\n" << evalues << std::endl;
///
/// return 0;
/// }
/// \endcode
///
/// And here is an example for user-supplied matrix operation class.
///
/// \code{.cpp}
/// #include <Eigen/Core>
/// #include <Spectra/HermEigsSolver.h>
/// #include <iostream>
///
/// using namespace Spectra;
///
/// // M = diag(1+0i, 2+0i, ..., 10+0i)
/// class MyDiagonalTen
/// {
/// public:
/// using Scalar = std::complex<double>; // A typedef named "Scalar" is required
/// int rows() const { return 10; }
/// int cols() const { return 10; }
/// // y_out = M * x_in
/// void perform_op(Scalar *x_in, Scalar *y_out) const
/// {
/// for (int i = 0; i < rows(); i++)
/// {
/// y_out[i] = x_in[i] * Scalar(i + 1, 0);
/// }
/// }
/// };
///
/// int main()
/// {
/// MyDiagonalTen op;
/// HermEigsSolver<MyDiagonalTen> eigs(op, 3, 6);
/// eigs.init();
/// eigs.compute(SortRule::LargestAlge);
/// if (eigs.info() == CompInfo::Successful)
/// {
/// Eigen::VectorXd evalues = eigs.eigenvalues();
/// // Will get (10, 9, 8)
/// std::cout << "Eigenvalues found:\n" << evalues << std::endl;
/// }
///
/// return 0;
/// }
/// \endcode
///
template <typename OpType = DenseHermMatProd<double>>
class HermEigsSolver : public HermEigsBase<OpType, IdentityBOp>
{
private:
using Index = Eigen::Index;
public:
///
/// Constructor to create a solver object.
///
/// \param op The matrix operation object that implements
/// the matrix-vector multiplication operation of \f$A\f$:
/// calculating \f$Av\f$ for any vector \f$v\f$. Users could either
/// create the object from the wrapper class such as DenseHermMatProd, or
/// define their own that implements all the public members
/// as in DenseHermMatProd.
/// \param nev Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-1\f$,
/// where \f$n\f$ is the size of matrix.
/// \param ncv Parameter that controls the convergence speed of the algorithm.
/// Typically a larger `ncv` means faster convergence, but it may
/// also result in greater memory use and more matrix operations
/// in each iteration. This parameter must satisfy \f$nev < ncv \le n\f$,
/// and is advised to take \f$ncv \ge 2\cdot nev\f$.
///
HermEigsSolver(OpType& op, Index nev, Index ncv) :
HermEigsBase<OpType, IdentityBOp>(op, IdentityBOp(), nev, ncv)
{}
};
} // namespace Spectra
#endif // SPECTRA_HERM_EIGS_SOLVER_H

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// Copyright (C) 2020 Netherlands eScience Center <J.Wehner@esciencecenter.nl>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_JD_SYM_EIGS_BASE_H
#define SPECTRA_JD_SYM_EIGS_BASE_H
#include <Eigen/Core>
#include <vector> // std::vector
#include <cmath> // std::abs, std::pow
#include <algorithm> // std::min
#include <stdexcept> // std::invalid_argument
#include <iostream>
#include "Util/SelectionRule.h"
#include "Util/CompInfo.h"
#include "LinAlg/SearchSpace.h"
#include "LinAlg/RitzPairs.h"
namespace Spectra {
///
/// \ingroup EigenSolver
///
/// This is the base class for symmetric JD eigen solvers, mainly for internal use.
/// It is kept here to provide the documentation for member functions of concrete eigen solvers
/// such as DavidsonSymEigsSolver.
///
/// This class uses the CRTP method to call functions from the derived class.
///
template <typename Derived, typename OpType>
class JDSymEigsBase
{
protected:
using Index = Eigen::Index;
using Scalar = typename OpType::Scalar;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
const OpType& m_matrix_operator; // object to conduct matrix operation,
// e.g. matrix-vector product
Index niter_ = 0;
const Index m_number_eigenvalues; // number of eigenvalues requested
Index m_max_search_space_size;
Index m_initial_search_space_size;
Index m_correction_size; // how many correction vectors are added in each iteration
RitzPairs<Scalar> m_ritz_pairs; // Ritz eigen pair structure
SearchSpace<Scalar> m_search_space; // search space
private:
CompInfo m_info = CompInfo::NotComputed; // status of the computation
void check_argument() const
{
if (m_number_eigenvalues < 1 || m_number_eigenvalues > m_matrix_operator.cols() - 1)
throw std::invalid_argument("nev must satisfy 1 <= nev <= n - 1, n is the size of matrix");
}
void initialize()
{
// TODO better input validation and checks
if (m_matrix_operator.cols() < m_max_search_space_size)
{
m_max_search_space_size = m_matrix_operator.cols();
}
if (m_matrix_operator.cols() < m_initial_search_space_size + m_correction_size)
{
m_initial_search_space_size = m_matrix_operator.cols() / 3;
m_correction_size = m_matrix_operator.cols() / 3;
}
}
public:
JDSymEigsBase(OpType& op, Index nev, Index nvec_init, Index nvec_max) :
m_matrix_operator(op),
m_number_eigenvalues(nev),
m_max_search_space_size(nvec_max < op.rows() ? nvec_max : 10 * m_number_eigenvalues),
m_initial_search_space_size(nvec_init < op.rows() ? nvec_init : 2 * m_number_eigenvalues),
m_correction_size(m_number_eigenvalues)
{
check_argument();
initialize();
}
JDSymEigsBase(OpType& op, Index nev) :
JDSymEigsBase(op, nev, 2 * nev, 10 * nev) {}
///
/// Sets the Maxmium SearchspaceSize after which is deflated
///
void set_max_search_space_size(Index max_search_space_size)
{
m_max_search_space_size = max_search_space_size;
}
///
/// Sets how many correction vectors are added in each iteration
///
void set_correction_size(Index correction_size)
{
m_correction_size = correction_size;
}
///
/// Sets the Initial SearchspaceSize for Ritz values
///
void set_initial_search_space_size(Index initial_search_space_size)
{
m_initial_search_space_size = initial_search_space_size;
}
///
/// Virtual destructor
///
virtual ~JDSymEigsBase() {}
///
/// Returns the status of the computation.
/// The full list of enumeration values can be found in \ref Enumerations.
///
CompInfo info() const { return m_info; }
///
/// Returns the number of iterations used in the computation.
///
Index num_iterations() const { return niter_; }
Vector eigenvalues() const { return m_ritz_pairs.ritz_values().head(m_number_eigenvalues); }
Matrix eigenvectors() const { return m_ritz_pairs.ritz_vectors().leftCols(m_number_eigenvalues); }
Index compute(SortRule selection = SortRule::LargestMagn, Index maxit = 100,
Scalar tol = 100 * Eigen::NumTraits<Scalar>::dummy_precision())
{
Derived& derived = static_cast<Derived&>(*this);
Matrix intial_space = derived.setup_initial_search_space(selection);
return compute_with_guess(intial_space, selection, maxit, tol);
}
Index compute_with_guess(const Eigen::Ref<const Matrix>& initial_space,
SortRule selection = SortRule::LargestMagn,
Index maxit = 100,
Scalar tol = 100 * Eigen::NumTraits<Scalar>::dummy_precision())
{
m_search_space.initialize_search_space(initial_space);
niter_ = 0;
for (niter_ = 0; niter_ < maxit; niter_++)
{
bool do_restart = (m_search_space.size() > m_max_search_space_size);
if (do_restart)
{
m_search_space.restart(m_ritz_pairs, m_initial_search_space_size);
}
m_search_space.update_operator_basis_product(m_matrix_operator);
Eigen::ComputationInfo small_problem_info = m_ritz_pairs.compute_eigen_pairs(m_search_space);
if (small_problem_info != Eigen::ComputationInfo::Success)
{
m_info = CompInfo::NumericalIssue;
break;
}
m_ritz_pairs.sort(selection);
bool converged = m_ritz_pairs.check_convergence(tol, m_number_eigenvalues);
if (converged)
{
m_info = CompInfo::Successful;
break;
}
else if (niter_ == maxit - 1)
{
m_info = CompInfo::NotConverging;
break;
}
Derived& derived = static_cast<Derived&>(*this);
Matrix corr_vect = derived.calculate_correction_vector();
m_search_space.extend_basis(corr_vect);
}
return (m_ritz_pairs.converged_eigenvalues()).template cast<Index>().head(m_number_eigenvalues).sum();
}
};
} // namespace Spectra
#endif // SPECTRA_JD_SYM_EIGS_BASE_H

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@ -1,16 +1,16 @@
// Copyright (C) 2018-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2018-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef ARNOLDI_H
#define ARNOLDI_H
#ifndef SPECTRA_ARNOLDI_H
#define SPECTRA_ARNOLDI_H
#include <Eigen/Core>
#include <cmath> // std::sqrt
#include <utility> // std::move
#include <stdexcept> // std::invalid_argument
#include <sstream> // std::stringstream
#include "../MatOp/internal/ArnoldiOp.h"
#include "../Util/TypeTraits.h"
@ -31,92 +31,127 @@ template <typename Scalar, typename ArnoldiOpType>
class Arnoldi
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<Matrix> MapMat;
typedef Eigen::Map<Vector> MapVec;
typedef Eigen::Map<const Matrix> MapConstMat;
typedef Eigen::Map<const Vector> MapConstVec;
// The real part type of the matrix element
using RealScalar = typename Eigen::NumTraits<Scalar>::Real;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapVec = Eigen::Map<Vector>;
using MapConstMat = Eigen::Map<const Matrix>;
using MapConstVec = Eigen::Map<const Vector>;
protected:
// clang-format off
ArnoldiOpType m_op; // Operators for the Arnoldi factorization
// A very small value, but 1.0 / m_near_0 does not overflow
// ~= 1e-307 for the "double" type
const RealScalar m_near_0 = TypeTraits<RealScalar>::min() * RealScalar(10);
// The machine precision, ~= 1e-16 for the "double" type
const RealScalar m_eps = TypeTraits<RealScalar>::epsilon();
const Index m_n; // dimension of A
const Index m_m; // maximum dimension of subspace V
Index m_k; // current dimension of subspace V
ArnoldiOpType m_op; // Operators for the Arnoldi factorization
const Index m_n; // dimension of A
const Index m_m; // maximum dimension of subspace V
Index m_k; // current dimension of subspace V
Matrix m_fac_V; // V matrix in the Arnoldi factorization
Matrix m_fac_H; // H matrix in the Arnoldi factorization
Vector m_fac_f; // residual in the Arnoldi factorization
RealScalar m_beta; // ||f||, B-norm of f
Matrix m_fac_V; // V matrix in the Arnoldi factorization
Matrix m_fac_H; // H matrix in the Arnoldi factorization
Vector m_fac_f; // residual in the Arnoldi factorization
Scalar m_beta; // ||f||, B-norm of f
const Scalar m_near_0; // a very small value, but 1.0 / m_near_0 does not overflow
// ~= 1e-307 for the "double" type
const Scalar m_eps; // the machine precision, ~= 1e-16 for the "double" type
// clang-format on
// Given orthonormal basis functions V, find a nonzero vector f such that V'Bf = 0
// Given orthonormal basis V (w.r.t. B), find a nonzero vector f such that (V^H)Bf = 0
// With rounding errors, we hope ||(V^H)Bf|| < eps * ||f||
// Assume that f has been properly allocated
void expand_basis(MapConstMat& V, const Index seed, Vector& f, Scalar& fnorm)
void expand_basis(MapConstMat& V, const Index seed, Vector& f, RealScalar& fnorm, Index& op_counter)
{
using std::sqrt;
const Scalar thresh = m_eps * sqrt(Scalar(m_n));
Vector Vf(V.cols());
Vector v(m_n), Vf(V.cols());
for (Index iter = 0; iter < 5; iter++)
{
// Randomly generate a new vector and orthogonalize it against V
SimpleRandom<Scalar> rng(seed + 123 * iter);
f.noalias() = rng.random_vec(m_n);
// f <- f - V * V'Bf, so that f is orthogonal to V in B-norm
m_op.trans_product(V, f, Vf);
// The first try forces f to be in the range of A
if (iter == 0)
{
rng.random_vec(v);
m_op.perform_op(v.data(), f.data());
op_counter++;
}
else
{
rng.random_vec(f);
}
// f <- f - V * (V^H)Bf, so that f is orthogonal to V in B-norm
m_op.adjoint_product(V, f, Vf);
f.noalias() -= V * Vf;
// fnorm <- ||f||
fnorm = m_op.norm(f);
// If fnorm is too close to zero, we try a new random vector,
// otherwise return the result
if (fnorm >= thresh)
// Compute (V^H)Bf again
m_op.adjoint_product(V, f, Vf);
// Test whether ||(V^H)Bf|| < eps * ||f||
RealScalar ortho_err = Vf.cwiseAbs().maxCoeff();
// If not, iteratively correct the residual
int count = 0;
while (count < 3 && ortho_err >= m_eps * fnorm)
{
// f <- f - V * Vf
f.noalias() -= V * Vf;
// beta <- ||f||
fnorm = m_op.norm(f);
m_op.adjoint_product(V, f, Vf);
ortho_err = Vf.cwiseAbs().maxCoeff();
count++;
}
// If the condition is satisfied, simply return
// Otherwise, go to the next iteration and try a new random vector
if (ortho_err < m_eps * fnorm)
return;
}
}
public:
// Copy an ArnoldiOp
Arnoldi(const ArnoldiOpType& op, Index m) :
m_op(op), m_n(op.rows()), m_m(m), m_k(0),
m_near_0(TypeTraits<Scalar>::min() * Scalar(10)),
m_eps(Eigen::NumTraits<Scalar>::epsilon())
m_op(op), m_n(op.rows()), m_m(m), m_k(0)
{}
virtual ~Arnoldi() {}
// Move an ArnoldiOp
Arnoldi(ArnoldiOpType&& op, Index m) :
m_op(std::move(op)), m_n(op.rows()), m_m(m), m_k(0)
{}
// Const-reference to internal structures
const Matrix& matrix_V() const { return m_fac_V; }
const Matrix& matrix_H() const { return m_fac_H; }
const Vector& vector_f() const { return m_fac_f; }
Scalar f_norm() const { return m_beta; }
RealScalar f_norm() const { return m_beta; }
Index subspace_dim() const { return m_k; }
// Initialize with an operator and an initial vector
void init(MapConstVec& v0, Index& op_counter)
{
using std::abs;
m_fac_V.resize(m_n, m_m);
m_fac_H.resize(m_m, m_m);
m_fac_f.resize(m_n);
m_fac_H.setZero();
// Verify the initial vector
const Scalar v0norm = m_op.norm(v0);
const RealScalar v0norm = m_op.norm(v0);
if (v0norm < m_near_0)
throw std::invalid_argument("initial residual vector cannot be zero");
// Points to the first column of V
MapVec v(m_fac_V.data(), m_n);
// Force v to be in the range of A, i.e., v = A * v0
m_op.perform_op(v0.data(), v.data());
op_counter++;
// Normalize
v.noalias() = v0 / v0norm;
const RealScalar vnorm = m_op.norm(v);
v /= vnorm;
// Compute H and f
Vector w(m_n);
@ -126,12 +161,14 @@ public:
m_fac_H(0, 0) = m_op.inner_product(v, w);
m_fac_f.noalias() = w - v * m_fac_H(0, 0);
// In some cases f is zero in exact arithmetics, but due to rounding errors
// it may contain tiny fluctuations. When this happens, we force f to be zero
if (m_fac_f.cwiseAbs().maxCoeff() < m_eps)
// In some cases, H[1,1] is already an eigenvalue of A,
// so f would be zero in exact arithmetics. But due to rounding errors,
// it may contain tiny fluctuations. When this happens, we force f to be zero,
// so that it can be restarted in the subsequent Arnoldi factorization
if (m_fac_f.cwiseAbs().maxCoeff() < m_eps * abs(m_fac_H(0, 0)))
{
m_fac_f.setZero();
m_beta = Scalar(0);
m_beta = RealScalar(0);
}
else
{
@ -152,12 +189,12 @@ public:
if (from_k > m_k)
{
std::stringstream msg;
msg << "Arnoldi: from_k (= " << from_k << ") is larger than the current subspace dimension (= " << m_k << ")";
throw std::invalid_argument(msg.str());
std::string msg = "Arnoldi: from_k (= " + std::to_string(from_k) +
") is larger than the current subspace dimension (= " + std::to_string(m_k) + ")";
throw std::invalid_argument(msg);
}
const Scalar beta_thresh = m_eps * sqrt(Scalar(m_n));
const RealScalar beta_thresh = m_eps * sqrt(RealScalar(m_n));
// Pre-allocate vectors
Vector Vf(to_m);
@ -176,7 +213,7 @@ public:
if (m_beta < m_near_0)
{
MapConstMat V(m_fac_V.data(), m_n, i); // The first i columns
expand_basis(V, 2 * i, m_fac_f, m_beta);
expand_basis(V, 2 * i, m_fac_f, m_beta, op_counter);
restart = true;
}
@ -184,7 +221,7 @@ public:
m_fac_V.col(i).noalias() = m_fac_f / m_beta; // The (i+1)-th column
// Note that H[i+1, i] equals to the unrestarted beta
m_fac_H(i, i - 1) = restart ? Scalar(0) : m_beta;
m_fac_H(i, i - 1) = restart ? Scalar(0) : Scalar(m_beta);
// w <- A * v, v = m_fac_V.col(i)
m_op.perform_op(&m_fac_V(0, i), w.data());
@ -195,20 +232,20 @@ public:
MapConstMat Vs(m_fac_V.data(), m_n, i1);
// h = m_fac_H(0:i, i)
MapVec h(&m_fac_H(0, i), i1);
// h <- V'Bw
m_op.trans_product(Vs, w, h);
// h <- (V^H)Bw
m_op.adjoint_product(Vs, w, h);
// f <- w - V * h
m_fac_f.noalias() = w - Vs * h;
m_beta = m_op.norm(m_fac_f);
if (m_beta > Scalar(0.717) * m_op.norm(h))
if (m_beta > RealScalar(0.717) * m_op.norm(h))
continue;
// f/||f|| is going to be the next column of V, so we need to test
// whether V'B(f/||f||) ~= 0
m_op.trans_product(Vs, m_fac_f, Vf.head(i1));
Scalar ortho_err = Vf.head(i1).cwiseAbs().maxCoeff();
// whether (V^H)B(f/||f||) ~= 0
m_op.adjoint_product(Vs, m_fac_f, Vf.head(i1));
RealScalar ortho_err = Vf.head(i1).cwiseAbs().maxCoeff();
// If not, iteratively correct the residual
int count = 0;
while (count < 5 && ortho_err > m_eps * m_beta)
@ -221,7 +258,7 @@ public:
if (m_beta < beta_thresh)
{
m_fac_f.setZero();
m_beta = Scalar(0);
m_beta = RealScalar(0);
break;
}
@ -232,7 +269,7 @@ public:
// beta <- ||f||
m_beta = m_op.norm(m_fac_f);
m_op.trans_product(Vs, m_fac_f, Vf.head(i1));
m_op.adjoint_product(Vs, m_fac_f, Vf.head(i1));
ortho_err = Vf.head(i1).cwiseAbs().maxCoeff();
count++;
}
@ -261,13 +298,21 @@ public:
// Only need to update the first k+1 columns of V
// The first (m - k + i) elements of the i-th column of Q are non-zero,
// and the rest are zero
void compress_V(const Matrix& Q)
//
// When V has a complex type, Q can be either real or complex
// Hense we use a generic implementation
template <typename Derived>
void compress_V(const Eigen::MatrixBase<Derived>& Q)
{
using QScalar = typename Derived::Scalar;
using QVector = Eigen::Matrix<QScalar, Eigen::Dynamic, 1>;
using QMapConstVec = Eigen::Map<const QVector>;
Matrix Vs(m_n, m_k + 1);
for (Index i = 0; i < m_k; i++)
{
const Index nnz = m_m - m_k + i + 1;
MapConstVec q(&Q(0, i), nnz);
QMapConstVec q(&Q(0, i), nnz);
Vs.col(i).noalias() = m_fac_V.leftCols(nnz) * q;
}
Vs.col(m_k).noalias() = m_fac_V * Q.col(m_k);
@ -281,4 +326,4 @@ public:
} // namespace Spectra
#endif // ARNOLDI_H
#endif // SPECTRA_ARNOLDI_H

348
gtsam/3rdparty/Spectra/LinAlg/BKLDLT.h vendored
View File

@ -1,20 +1,58 @@
// Copyright (C) 2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2019-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef BK_LDLT_H
#define BK_LDLT_H
#ifndef SPECTRA_BK_LDLT_H
#define SPECTRA_BK_LDLT_H
#include <Eigen/Core>
#include <vector>
#include <stdexcept>
#include <type_traits> // std::is_same
#include "../Util/CompInfo.h"
namespace Spectra {
// We need a generic conj() function for both real and complex values,
// and hope that conj(x) == x if x is real-valued. However, in STL,
// conj(x) == std::complex(x, 0) for such cases, meaning that the
// return value type is not necessarily the same as x. To avoid this
// inconvenience, we define a simple class that does this task
//
// Similarly, define a real(x) function that returns x itself if
// x is real-valued, and returns std::complex(x, 0) if x is complex-valued
template <typename Scalar>
struct ScalarOp
{
static Scalar conj(const Scalar& x)
{
return x;
}
static Scalar real(const Scalar& x)
{
return x;
}
};
// Specialization for complex values
template <typename RealScalar>
struct ScalarOp<std::complex<RealScalar>>
{
static std::complex<RealScalar> conj(const std::complex<RealScalar>& x)
{
using std::conj;
return conj(x);
}
static std::complex<RealScalar> real(const std::complex<RealScalar>& x)
{
return std::complex<RealScalar>(x.real(), RealScalar(0));
}
};
// Bunch-Kaufman LDLT decomposition
// References:
// 1. Bunch, J. R., & Kaufman, L. (1977). Some stable methods for calculating inertia and solving symmetric linear systems.
@ -27,26 +65,24 @@ template <typename Scalar = double>
class BKLDLT
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<Vector> MapVec;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Matrix<Index, Eigen::Dynamic, 1> IntVector;
typedef Eigen::Ref<Vector> GenericVector;
typedef Eigen::Ref<Matrix> GenericMatrix;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
typedef const Eigen::Ref<const Vector> ConstGenericVector;
// The real part type of the matrix element
using RealScalar = typename Eigen::NumTraits<Scalar>::Real;
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapVec = Eigen::Map<Vector>;
using MapConstVec = Eigen::Map<const Vector>;
using IntVector = Eigen::Matrix<Index, Eigen::Dynamic, 1>;
using GenericVector = Eigen::Ref<Vector>;
using ConstGenericVector = const Eigen::Ref<const Vector>;
Index m_n;
Vector m_data; // storage for a lower-triangular matrix
std::vector<Scalar*> m_colptr; // pointers to columns
IntVector m_perm; // [-2, -1, 3, 1, 4, 5]: 0 <-> 2, 1 <-> 1, 2 <-> 3, 3 <-> 1, 4 <-> 4, 5 <-> 5
std::vector<std::pair<Index, Index> > m_permc; // compressed version of m_perm: [(0, 2), (2, 3), (3, 1)]
Vector m_data; // storage for a lower-triangular matrix
std::vector<Scalar*> m_colptr; // pointers to columns
IntVector m_perm; // [-2, -1, 3, 1, 4, 5]: 0 <-> 2, 1 <-> 1, 2 <-> 3, 3 <-> 1, 4 <-> 4, 5 <-> 5
std::vector<std::pair<Index, Index>> m_permc; // compressed version of m_perm: [(0, 2), (2, 3), (3, 1)]
bool m_computed;
int m_info;
CompInfo m_info;
// Access to elements
// Pointer to the k-th column
@ -73,28 +109,38 @@ private:
}
// Copy mat - shift * I to m_data
void copy_data(ConstGenericMatrix& mat, int uplo, const Scalar& shift)
template <typename Derived>
void copy_data(const Eigen::MatrixBase<Derived>& mat, int uplo, const RealScalar& shift)
{
if (uplo == Eigen::Lower)
// If mat is an expression, first evaluate it into a temporary object
// This can be achieved by assigning mat to a const Eigen::Ref<const Matrix>&
// If mat is a plain object, no temporary object is created
const Eigen::Ref<const typename Derived::PlainObject>& src(mat);
// Efficient copying for column-major matrices with lower triangular part
if ((!Derived::PlainObject::IsRowMajor) && uplo == Eigen::Lower)
{
for (Index j = 0; j < m_n; j++)
{
const Scalar* begin = &mat.coeffRef(j, j);
const Scalar* begin = &src.coeffRef(j, j);
const Index len = m_n - j;
std::copy(begin, begin + len, col_pointer(j));
diag_coeff(j) -= shift;
diag_coeff(j) -= Scalar(shift);
}
}
else
{
Scalar* dest = m_data.data();
for (Index i = 0; i < m_n; i++)
for (Index j = 0; j < m_n; j++)
{
for (Index j = i; j < m_n; j++, dest++)
for (Index i = j; i < m_n; i++, dest++)
{
*dest = mat.coeff(i, j);
if (uplo == Eigen::Lower)
*dest = src.coeff(i, j);
else
*dest = ScalarOp<Scalar>::conj(src.coeff(j, i));
}
diag_coeff(i) -= shift;
diag_coeff(j) -= Scalar(shift);
}
}
}
@ -116,12 +162,11 @@ private:
// Assume r >= k
void pivoting_1x1(Index k, Index r)
{
m_perm[k] = r;
// No permutation
if (k == r)
{
m_perm[k] = r;
return;
}
// A[k, k] <-> A[r, r]
std::swap(diag_coeff(k), diag_coeff(r));
@ -130,13 +175,32 @@ private:
std::swap_ranges(&coeff(r + 1, k), col_pointer(k + 1), &coeff(r + 1, r));
// A[(k+1):(r-1), k] <-> A[r, (k+1):(r-1)]
// Note: for Hermitian matrices, also need to do conjugate
Scalar* src = &coeff(k + 1, k);
for (Index j = k + 1; j < r; j++, src++)
if (std::is_same<Scalar, RealScalar>::value)
{
std::swap(*src, coeff(r, j));
// Simple swapping for real values
for (Index j = k + 1; j < r; j++, src++)
{
std::swap(*src, coeff(r, j));
}
}
else
{
// For complex values
for (Index j = k + 1; j < r; j++, src++)
{
const Scalar src_conj = ScalarOp<Scalar>::conj(*src);
*src = ScalarOp<Scalar>::conj(coeff(r, j));
coeff(r, j) = src_conj;
}
}
m_perm[k] = r;
// A[r, k] <- Conj(A[r, k])
if (!std::is_same<Scalar, RealScalar>::value)
{
coeff(r, k) = ScalarOp<Scalar>::conj(coeff(r, k));
}
}
// Working on the A[k:end, k:end] submatrix
@ -173,7 +237,7 @@ private:
// Largest (in magnitude) off-diagonal element in the first column of the current reduced matrix
// r is the row index
// Assume k < end
Scalar find_lambda(Index k, Index& r)
RealScalar find_lambda(Index k, Index& r)
{
using std::abs;
@ -181,11 +245,11 @@ private:
const Scalar* end = col_pointer(k + 1);
// Start with r=k+1, lambda=A[k+1, k]
r = k + 1;
Scalar lambda = abs(head[1]);
RealScalar lambda = abs(head[1]);
// Scan remaining elements
for (const Scalar* ptr = head + 2; ptr < end; ptr++)
{
const Scalar abs_elem = abs(*ptr);
const RealScalar abs_elem = abs(*ptr);
if (lambda < abs_elem)
{
lambda = abs_elem;
@ -200,20 +264,20 @@ private:
// Largest (in magnitude) off-diagonal element in the r-th column of the current reduced matrix
// p is the row index
// Assume k < r < end
Scalar find_sigma(Index k, Index r, Index& p)
RealScalar find_sigma(Index k, Index r, Index& p)
{
using std::abs;
// First search A[r+1, r], ..., A[end, r], which has the same task as find_lambda()
// If r == end, we skip this search
Scalar sigma = Scalar(-1);
RealScalar sigma = RealScalar(-1);
if (r < m_n - 1)
sigma = find_lambda(r, p);
// Then search A[k, r], ..., A[r-1, r], which maps to A[r, k], ..., A[r, r-1]
for (Index j = k; j < r; j++)
{
const Scalar abs_elem = abs(coeff(r, j));
const RealScalar abs_elem = abs(coeff(r, j));
if (sigma < abs_elem)
{
sigma = abs_elem;
@ -226,21 +290,21 @@ private:
// Generate permutations and apply to A
// Return true if the resulting pivoting is 1x1, and false if 2x2
bool permutate_mat(Index k, const Scalar& alpha)
bool permutate_mat(Index k, const RealScalar& alpha)
{
using std::abs;
Index r = k, p = k;
const Scalar lambda = find_lambda(k, r);
const RealScalar lambda = find_lambda(k, r);
// If lambda=0, no need to interchange
if (lambda > Scalar(0))
if (lambda > RealScalar(0))
{
const Scalar abs_akk = abs(diag_coeff(k));
const RealScalar abs_akk = abs(diag_coeff(k));
// If |A[k, k]| >= alpha * lambda, no need to interchange
if (abs_akk < alpha * lambda)
{
const Scalar sigma = find_sigma(k, r, p);
const RealScalar sigma = find_sigma(k, r, p);
// If sigma * |A[k, k]| >= alpha * lambda^2, no need to interchange
if (sigma * abs_akk < alpha * lambda * lambda)
@ -272,7 +336,7 @@ private:
// r = k+1, so that only one permutation needs to be performed
/* const Index rp_min = std::min(r, p);
const Index rp_max = std::max(r, p);
if(rp_min == k + 1)
if (rp_min == k + 1)
{
r = rp_min; p = rp_max;
} else {
@ -283,6 +347,7 @@ private:
// Permutation on A
pivoting_2x2(k, r, p);
// Permutation on L
interchange_rows(k, p, 0, k - 1);
interchange_rows(k + 1, r, 0, k - 1);
@ -302,51 +367,138 @@ private:
{
// inv(E) = [d11, d12], d11 = e22/delta, d21 = -e21/delta, d22 = e11/delta
// [d21, d22]
const Scalar delta = e11 * e22 - e21 * e21;
// delta = e11 * e22 - e12 * e21
const Scalar e12 = ScalarOp<Scalar>::conj(e21);
const Scalar delta = e11 * e22 - e12 * e21;
std::swap(e11, e22);
e11 /= delta;
e22 /= delta;
e21 = -e21 / delta;
}
// Return value is the status, SUCCESSFUL/NUMERICAL_ISSUE
int gaussian_elimination_1x1(Index k)
// E = [e11, e12]
// [e21, e22]
// Overwrite b with x = inv(E) * b, which is equivalent to solving E * x = b
void solve_inplace_2x2(
const Scalar& e11, const Scalar& e21, const Scalar& e22,
Scalar& b1, Scalar& b2) const
{
// D = 1 / A[k, k]
const Scalar akk = diag_coeff(k);
// Return NUMERICAL_ISSUE if not invertible
using std::abs;
const Scalar e12 = ScalarOp<Scalar>::conj(e21);
const RealScalar e11_abs = abs(e11);
const RealScalar e21_abs = abs(e21);
// If |e11| >= |e21|, no need to exchange rows
if (e11_abs >= e21_abs)
{
const Scalar fac = e21 / e11;
const Scalar x2 = (b2 - fac * b1) / (e22 - fac * e12);
const Scalar x1 = (b1 - e12 * x2) / e11;
b1 = x1;
b2 = x2;
}
else
{
// Exchange row 1 and row 2, so the system becomes
// E* = [e21, e22], b* = [b2], x* = [x1]
// [e11, e12] [b1] [x2]
const Scalar fac = e11 / e21;
const Scalar x2 = (b1 - fac * b2) / (e12 - fac * e22);
const Scalar x1 = (b2 - e22 * x2) / e21;
b1 = x1;
b2 = x2;
}
}
// Compute C * inv(E), which is equivalent to solving X * E = C
// X [n x 2], E [2 x 2], C [n x 2]
// X = [x1, x2], E = [e11, e12], C = [c1 c2]
// [e21, e22]
void solve_left_2x2(
const Scalar& e11, const Scalar& e21, const Scalar& e22,
const MapVec& c1, const MapVec& c2,
Eigen::Matrix<Scalar, Eigen::Dynamic, 2>& x) const
{
using std::abs;
const Scalar e12 = ScalarOp<Scalar>::conj(e21);
const RealScalar e11_abs = abs(e11);
const RealScalar e12_abs = abs(e12);
// If |e11| >= |e12|, no need to exchange rows
if (e11_abs >= e12_abs)
{
const Scalar fac = e12 / e11;
// const Scalar x2 = (c2 - fac * c1) / (e22 - fac * e21);
// const Scalar x1 = (c1 - e21 * x2) / e11;
x.col(1).array() = (c2 - fac * c1).array() / (e22 - fac * e21);
x.col(0).array() = (c1 - e21 * x.col(1)).array() / e11;
}
else
{
// Exchange column 1 and column 2, so the system becomes
// X* = [x1, x2], E* = [e12, e11], C* = [c2 c1]
// [e22, e21]
const Scalar fac = e11 / e12;
// const Scalar x2 = (c1 - fac * c2) / (e21 - fac * e22);
// const Scalar x1 = (c2 - e22 * x2) / e12;
x.col(1).array() = (c1 - fac * c2).array() / (e21 - fac * e22);
x.col(0).array() = (c2 - e22 * x.col(1)).array() / e12;
}
}
// Return value is the status, CompInfo::Successful/NumericalIssue
CompInfo gaussian_elimination_1x1(Index k)
{
// A[k, k] is known to be real-valued, so we force its imaginary
// part to be zero when Scalar is a complex type
// Interestingly, this has a significant effect on the accuracy
// and numerical stability of the final solution
const Scalar akk = ScalarOp<Scalar>::real(diag_coeff(k));
diag_coeff(k) = akk;
// Return CompInfo::NumericalIssue if not invertible
if (akk == Scalar(0))
return NUMERICAL_ISSUE;
return CompInfo::NumericalIssue;
diag_coeff(k) = Scalar(1) / akk;
// [inverse]
// diag_coeff(k) = Scalar(1) / akk;
// B -= l * l' / A[k, k], B := A[(k+1):end, (k+1):end], l := L[(k+1):end, k]
// B -= l * l^H / A[k, k], B := A[(k+1):end, (k+1):end], l := L[(k+1):end, k]
Scalar* lptr = col_pointer(k) + 1;
const Index ldim = m_n - k - 1;
MapVec l(lptr, ldim);
for (Index j = 0; j < ldim; j++)
{
MapVec(col_pointer(j + k + 1), ldim - j).noalias() -= (lptr[j] / akk) * l.tail(ldim - j);
Scalar l_conj = ScalarOp<Scalar>::conj(lptr[j]);
MapVec(col_pointer(j + k + 1), ldim - j).noalias() -= (l_conj / akk) * l.tail(ldim - j);
}
// l /= A[k, k]
l /= akk;
return SUCCESSFUL;
return CompInfo::Successful;
}
// Return value is the status, SUCCESSFUL/NUMERICAL_ISSUE
int gaussian_elimination_2x2(Index k)
// Return value is the status, CompInfo::Successful/NumericalIssue
CompInfo gaussian_elimination_2x2(Index k)
{
// D = inv(E)
Scalar& e11 = diag_coeff(k);
Scalar& e21 = coeff(k + 1, k);
Scalar& e22 = diag_coeff(k + 1);
// Return NUMERICAL_ISSUE if not invertible
if (e11 * e22 - e21 * e21 == Scalar(0))
return NUMERICAL_ISSUE;
inverse_inplace_2x2(e11, e21, e22);
// A[k, k] and A[k+1, k+1] are known to be real-valued,
// so we force their imaginary parts to be zero when Scalar
// is a complex type
// Interestingly, this has a significant effect on the accuracy
// and numerical stability of the final solution
e11 = ScalarOp<Scalar>::real(e11);
e22 = ScalarOp<Scalar>::real(e22);
Scalar e12 = ScalarOp<Scalar>::conj(e21);
// Return CompInfo::NumericalIssue if not invertible
if (e11 * e22 - e12 * e21 == Scalar(0))
return CompInfo::NumericalIssue;
// [inverse]
// inverse_inplace_2x2(e11, e21, e22);
// X = l * inv(E), l := L[(k+2):end, k:(k+1)]
Scalar* l1ptr = &coeff(k + 2, k);
@ -355,35 +507,43 @@ private:
MapVec l1(l1ptr, ldim), l2(l2ptr, ldim);
Eigen::Matrix<Scalar, Eigen::Dynamic, 2> X(ldim, 2);
X.col(0).noalias() = l1 * e11 + l2 * e21;
X.col(1).noalias() = l1 * e21 + l2 * e22;
// [inverse]
// e12 = ScalarOp<Scalar>::conj(e21);
// X.col(0).noalias() = l1 * e11 + l2 * e21;
// X.col(1).noalias() = l1 * e12 + l2 * e22;
// [solve]
solve_left_2x2(e11, e21, e22, l1, l2, X);
// B -= l * inv(E) * l' = X * l', B = A[(k+2):end, (k+2):end]
// B -= l * inv(E) * l^H = X * l^H, B = A[(k+2):end, (k+2):end]
for (Index j = 0; j < ldim; j++)
{
MapVec(col_pointer(j + k + 2), ldim - j).noalias() -= (X.col(0).tail(ldim - j) * l1ptr[j] + X.col(1).tail(ldim - j) * l2ptr[j]);
const Scalar l1j_conj = ScalarOp<Scalar>::conj(l1ptr[j]);
const Scalar l2j_conj = ScalarOp<Scalar>::conj(l2ptr[j]);
MapVec(col_pointer(j + k + 2), ldim - j).noalias() -= (X.col(0).tail(ldim - j) * l1j_conj + X.col(1).tail(ldim - j) * l2j_conj);
}
// l = X
l1.noalias() = X.col(0);
l2.noalias() = X.col(1);
return SUCCESSFUL;
return CompInfo::Successful;
}
public:
BKLDLT() :
m_n(0), m_computed(false), m_info(NOT_COMPUTED)
m_n(0), m_computed(false), m_info(CompInfo::NotComputed)
{}
// Factorize mat - shift * I
BKLDLT(ConstGenericMatrix& mat, int uplo = Eigen::Lower, const Scalar& shift = Scalar(0)) :
m_n(mat.rows()), m_computed(false), m_info(NOT_COMPUTED)
template <typename Derived>
BKLDLT(const Eigen::MatrixBase<Derived>& mat, int uplo = Eigen::Lower, const RealScalar& shift = RealScalar(0)) :
m_n(mat.rows()), m_computed(false), m_info(CompInfo::NotComputed)
{
compute(mat, uplo, shift);
}
void compute(ConstGenericMatrix& mat, int uplo = Eigen::Lower, const Scalar& shift = Scalar(0))
template <typename Derived>
void compute(const Eigen::MatrixBase<Derived>& mat, int uplo = Eigen::Lower, const RealScalar& shift = RealScalar(0))
{
using std::abs;
@ -399,7 +559,7 @@ public:
compute_pointer();
copy_data(mat, uplo, shift);
const Scalar alpha = (1.0 + std::sqrt(17.0)) / 8.0;
const RealScalar alpha = (1.0 + std::sqrt(17.0)) / 8.0;
Index k = 0;
for (k = 0; k < m_n - 1; k++)
{
@ -418,17 +578,19 @@ public:
}
// 3. Check status
if (m_info != SUCCESSFUL)
if (m_info != CompInfo::Successful)
break;
}
// Invert the last 1x1 block if it exists
if (k == m_n - 1)
{
const Scalar akk = diag_coeff(k);
const Scalar akk = ScalarOp<Scalar>::real(diag_coeff(k));
diag_coeff(k) = akk;
if (akk == Scalar(0))
m_info = NUMERICAL_ISSUE;
m_info = CompInfo::NumericalIssue;
diag_coeff(k) = Scalar(1) / diag_coeff(k);
// [inverse]
// diag_coeff(k) = Scalar(1) / diag_coeff(k);
}
compress_permutation();
@ -442,7 +604,8 @@ public:
if (!m_computed)
throw std::logic_error("BKLDLT: need to call compute() first");
// PAP' = LDL'
// PAP' = LD(L^H), A = P'LD(L^H)P
// Ax = b ==> P'LD(L^H)Px = b ==> LD(L^H)Px = Pb
// 1. b -> Pb
Scalar* x = b.data();
MapVec res(x, m_n);
@ -452,6 +615,7 @@ public:
std::swap(x[m_permc[i].first], x[m_permc[i].second]);
}
// z = D(L^H)Px
// 2. Lz = Pb
// If m_perm[end] < 0, then end with m_n - 3, otherwise end with m_n - 2
const Index end = (m_perm[m_n - 1] < 0) ? (m_n - 3) : (m_n - 2);
@ -473,37 +637,47 @@ public:
}
}
// w = (L^H)Px
// 3. Dw = z
for (Index i = 0; i < m_n; i++)
{
const Scalar e11 = diag_coeff(i);
if (m_perm[i] >= 0)
{
x[i] *= e11;
// [inverse]
// x[i] *= e11;
// [solve]
x[i] /= e11;
}
else
{
const Scalar e21 = coeff(i + 1, i), e22 = diag_coeff(i + 1);
const Scalar wi = x[i] * e11 + x[i + 1] * e21;
x[i + 1] = x[i] * e21 + x[i + 1] * e22;
x[i] = wi;
// [inverse]
// const Scalar e12 = ScalarOp<Scalar>::conj(e21);
// const Scalar wi = x[i] * e11 + x[i + 1] * e12;
// x[i + 1] = x[i] * e21 + x[i + 1] * e22;
// x[i] = wi;
// [solve]
solve_inplace_2x2(e11, e21, e22, x[i], x[i + 1]);
i++;
}
}
// 4. L'y = w
// y = Px
// 4. (L^H)y = w
// If m_perm[end] < 0, then start with m_n - 3, otherwise start with m_n - 2
Index i = (m_perm[m_n - 1] < 0) ? (m_n - 3) : (m_n - 2);
for (; i >= 0; i--)
{
const Index ldim = m_n - i - 1;
MapConstVec l(&coeff(i + 1, i), ldim);
x[i] -= res.segment(i + 1, ldim).dot(l);
x[i] -= l.dot(res.segment(i + 1, ldim));
if (m_perm[i] < 0)
{
MapConstVec l2(&coeff(i + 1, i - 1), ldim);
x[i - 1] -= res.segment(i + 1, ldim).dot(l2);
x[i - 1] -= l2.dot(res.segment(i + 1, ldim));
i--;
}
}
@ -522,9 +696,9 @@ public:
return res;
}
int info() const { return m_info; }
CompInfo info() const { return m_info; }
};
} // namespace Spectra
#endif // BK_LDLT_H
#endif // SPECTRA_BK_LDLT_H

221
gtsam/3rdparty/Spectra/LinAlg/DoubleShiftQR.h vendored
View File

@ -1,15 +1,16 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef DOUBLE_SHIFT_QR_H
#define DOUBLE_SHIFT_QR_H
#ifndef SPECTRA_DOUBLE_SHIFT_QR_H
#define SPECTRA_DOUBLE_SHIFT_QR_H
#include <Eigen/Core>
#include <vector> // std::vector
#include <algorithm> // std::min, std::fill, std::copy
#include <utility> // std::swap
#include <cmath> // std::abs, std::sqrt, std::pow
#include <stdexcept> // std::invalid_argument, std::logic_error
@ -21,31 +22,87 @@ template <typename Scalar = double>
class DoubleShiftQR
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, 3, Eigen::Dynamic> Matrix3X;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Array<unsigned char, Eigen::Dynamic, 1> IntArray;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Matrix3X = Eigen::Matrix<Scalar, 3, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using IntArray = Eigen::Array<unsigned char, Eigen::Dynamic, 1>;
typedef Eigen::Ref<Matrix> GenericMatrix;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
using GenericMatrix = Eigen::Ref<Matrix>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
Index m_n; // Dimension of the matrix
Matrix m_mat_H; // A copy of the matrix to be factorized
Scalar m_shift_s; // Shift constant
Scalar m_shift_t; // Shift constant
Matrix3X m_ref_u; // Householder reflectors
IntArray m_ref_nr; // How many rows does each reflector affects
// 3 - A general reflector
// 2 - A Givens rotation
// 1 - An identity transformation
const Scalar m_near_0; // a very small value, but 1.0 / m_safe_min does not overflow
// ~= 1e-307 for the "double" type
const Scalar m_eps; // the machine precision,
// e.g. ~= 1e-16 for the "double" type
const Scalar m_eps_rel;
const Scalar m_eps_abs;
bool m_computed; // Whether matrix has been factorized
// A very small value, but 1.0 / m_near_0 does not overflow
// ~= 1e-307 for the "double" type
const Scalar m_near_0 = TypeTraits<Scalar>::min() * Scalar(10);
// The machine precision, ~= 1e-16 for the "double" type
const Scalar m_eps = TypeTraits<Scalar>::epsilon();
Index m_n; // Dimension of the matrix
Matrix m_mat_H; // A copy of the matrix to be factorized
Scalar m_shift_s; // Shift constant
Scalar m_shift_t; // Shift constant
Matrix3X m_ref_u; // Householder reflectors
IntArray m_ref_nr; // How many rows does each reflector affects
// 3 - A general reflector
// 2 - A Givens rotation
// 1 - An identity transformation
bool m_computed; // Whether matrix has been factorized
// Compute sqrt(x1^2 + x2^2 + x3^2) wit high precision
static Scalar stable_norm3(Scalar x1, Scalar x2, Scalar x3)
{
using std::abs;
using std::sqrt;
x1 = abs(x1);
x2 = abs(x2);
x3 = abs(x3);
// Make x1 >= {x2, x3}
if (x1 < x2)
std::swap(x1, x2);
if (x1 < x3)
std::swap(x1, x3);
// If x1 is too small, return 0
const Scalar near_0 = TypeTraits<Scalar>::min() * Scalar(10);
if (x1 < near_0)
return Scalar(0);
const Scalar r2 = x2 / x1, r3 = x3 / x1;
// We choose a cutoff such that cutoff^4 < eps
// If max(r2, r3) > cutoff, use the standard way; otherwise use Taylor series expansion
// to avoid an explicit sqrt() call that may lose precision
const Scalar eps = TypeTraits<Scalar>::epsilon();
const Scalar cutoff = Scalar(0.1) * pow(eps, Scalar(0.25));
Scalar r = r2 * r2 + r3 * r3;
r = (r2 >= cutoff || r3 >= cutoff) ?
sqrt(Scalar(1) + r) :
(Scalar(1) + r * (Scalar(0.5) - Scalar(0.125) * r)); // sqrt(1 + t) ~= 1 + t/2 - t^2/8
return x1 * r;
}
// x[i] <- x[i] / r, r = sqrt(x1^2 + x2^2 + x3^2)
// Assume |x1| >= {|x2|, |x3|}, x1 != 0
static void stable_scaling(Scalar& x1, Scalar& x2, Scalar& x3)
{
using std::abs;
using std::pow;
using std::sqrt;
const Scalar x1sign = (x1 > Scalar(0)) ? Scalar(1) : Scalar(-1);
x1 = abs(x1);
// Use the same method as in stable_norm3()
const Scalar r2 = x2 / x1, r3 = x3 / x1;
const Scalar eps = TypeTraits<Scalar>::epsilon();
const Scalar cutoff = Scalar(0.1) * pow(eps, Scalar(0.25));
Scalar r = r2 * r2 + r3 * r3;
// r = 1/sqrt(1 + r2^2 + r3^2)
r = (abs(r2) >= cutoff || abs(r3) >= cutoff) ?
Scalar(1) / sqrt(Scalar(1) + r) :
(Scalar(1) - r * (Scalar(0.5) - Scalar(0.375) * r)); // 1/sqrt(1 + t) ~= 1 - t * (1/2 - (3/8) * t)
x1 = x1sign * r;
x2 = r2 * r;
x3 = r3 * r;
}
void compute_reflector(const Scalar& x1, const Scalar& x2, const Scalar& x3, Index ind)
{
@ -53,42 +110,39 @@ private:
Scalar* u = &m_ref_u.coeffRef(0, ind);
unsigned char* nr = m_ref_nr.data();
// In general case the reflector affects 3 rows
nr[ind] = 3;
Scalar x2x3 = Scalar(0);
// If x3 is zero, decrease nr by 1
if (abs(x3) < m_near_0)
{
// If x2 is also zero, nr will be 1, and we can exit this function
if (abs(x2) < m_near_0)
{
nr[ind] = 1;
return;
}
else
{
nr[ind] = 2;
}
x2x3 = abs(x2);
}
else
{
x2x3 = Eigen::numext::hypot(x2, x3);
}
// x1' = x1 - rho * ||x||
// rho = -sign(x1), if x1 == 0, we choose rho = 1
Scalar x1_new = x1 - ((x1 <= 0) - (x1 > 0)) * Eigen::numext::hypot(x1, x2x3);
Scalar x_norm = Eigen::numext::hypot(x1_new, x2x3);
// Double check the norm of new x
if (x_norm < m_near_0)
const Scalar x2m = abs(x2), x3m = abs(x3);
// If both x2 and x3 are zero, nr is 1, and we early exit
if (x2m < m_near_0 && x3m < m_near_0)
{
nr[ind] = 1;
return;
}
u[0] = x1_new / x_norm;
u[1] = x2 / x_norm;
u[2] = x3 / x_norm;
// In general case the reflector affects 3 rows
// If x3 is zero, decrease nr by 1
nr[ind] = (x3m < m_near_0) ? 2 : 3;
const Scalar x_norm = (x3m < m_near_0) ? Eigen::numext::hypot(x1, x2) : stable_norm3(x1, x2, x3);
// x1' = x1 - rho * ||x||
// rho = -sign(x1), if x1 == 0, we choose rho = 1
const Scalar rho = (x1 <= Scalar(0)) - (x1 > Scalar(0));
const Scalar x1_new = x1 - rho * x_norm, x1m = abs(x1_new);
// Copy x to u
u[0] = x1_new;
u[1] = x2;
u[2] = x3;
if (x1m >= x2m && x1m >= x3m)
{
stable_scaling(u[0], u[1], u[2]);
}
else if (x2m >= x1m && x2m >= x3m)
{
stable_scaling(u[1], u[0], u[2]);
}
else
{
stable_scaling(u[2], u[0], u[1]);
}
}
void compute_reflector(const Scalar* x, Index ind)
@ -138,7 +192,7 @@ private:
// Apply the first reflector
apply_PX(m_mat_H.block(il, il, 3, m_n - il), m_n, il);
apply_XP(m_mat_H.block(0, il, il + std::min(bsize, Index(4)), 3), m_n, il);
apply_XP(m_mat_H.block(0, il, il + (std::min)(bsize, Index(4)), 3), m_n, il);
// Calculate the following reflectors
// If entering this loop, block size is at least 4.
@ -147,7 +201,7 @@ private:
compute_reflector(&m_mat_H.coeffRef(il + i, il + i - 1), il + i);
// Apply the reflector to X
apply_PX(m_mat_H.block(il + i, il + i - 1, 3, m_n - il - i + 1), m_n, il + i);
apply_XP(m_mat_H.block(0, il + i, il + std::min(bsize, Index(i + 4)), 3), m_n, il + i);
apply_XP(m_mat_H.block(0, il + i, il + (std::min)(bsize, Index(i + 4)), 3), m_n, il + i);
}
// The last reflector
@ -168,10 +222,8 @@ private:
if (nr == 1)
return;
const Scalar u0 = m_ref_u.coeff(0, u_ind),
u1 = m_ref_u.coeff(1, u_ind);
const Scalar u0_2 = Scalar(2) * u0,
u1_2 = Scalar(2) * u1;
const Scalar u0 = m_ref_u.coeff(0, u_ind), u1 = m_ref_u.coeff(1, u_ind);
const Scalar u0_2 = Scalar(2) * u0, u1_2 = Scalar(2) * u1;
const Index nrow = X.rows();
const Index ncol = X.cols();
@ -228,10 +280,8 @@ private:
if (nr == 1)
return;
const Scalar u0 = m_ref_u.coeff(0, u_ind),
u1 = m_ref_u.coeff(1, u_ind);
const Scalar u0_2 = Scalar(2) * u0,
u1_2 = Scalar(2) * u1;
const Scalar u0 = m_ref_u.coeff(0, u_ind), u1 = m_ref_u.coeff(1, u_ind);
const Scalar u0_2 = Scalar(2) * u0, u1_2 = Scalar(2) * u1;
const int nrow = X.rows();
const int ncol = X.cols();
@ -267,10 +317,6 @@ private:
public:
DoubleShiftQR(Index size) :
m_n(size),
m_near_0(TypeTraits<Scalar>::min() * Scalar(10)),
m_eps(Eigen::NumTraits<Scalar>::epsilon()),
m_eps_rel(m_eps),
m_eps_abs(m_near_0 * (m_n / m_eps)),
m_computed(false)
{}
@ -281,10 +327,6 @@ public:
m_shift_t(t),
m_ref_u(3, m_n),
m_ref_nr(m_n),
m_near_0(TypeTraits<Scalar>::min() * Scalar(10)),
m_eps(Eigen::NumTraits<Scalar>::epsilon()),
m_eps_rel(m_eps),
m_eps_abs(m_near_0 * (m_n / m_eps)),
m_computed(false)
{
compute(mat, s, t);
@ -305,19 +347,25 @@ public:
m_ref_nr.resize(m_n);
// Make a copy of mat
std::copy(mat.data(), mat.data() + mat.size(), m_mat_H.data());
m_mat_H.noalias() = mat;
// Obtain the indices of zero elements in the subdiagonal,
// so that H can be divided into several blocks
const Scalar eps_abs = m_near_0 * (m_n / m_eps);
const Scalar eps_rel = m_eps;
std::vector<int> zero_ind;
zero_ind.reserve(m_n - 1);
zero_ind.push_back(0);
Scalar* Hii = m_mat_H.data();
for (Index i = 0; i < m_n - 2; i++, Hii += (m_n + 1))
for (Index i = 0; i < m_n - 1; i++, Hii += (m_n + 1))
{
// Hii[0] => m_mat_H(i, i)
// Hii[1] => m_mat_H(i + 1, i)
// Hii[m_n + 1] => m_mat_H(i + 1, i + 1)
const Scalar h = abs(Hii[1]);
if (h <= 0 || h <= m_eps_rel * (abs(Hii[0]) + abs(Hii[m_n + 1])))
// Deflate small sub-diagonal elements
const Scalar diag = abs(Hii[0]) + abs(Hii[m_n + 1]);
if (h <= eps_abs || h <= eps_rel * diag)
{
Hii[1] = 0;
zero_ind.push_back(i + 1);
@ -328,7 +376,8 @@ public:
}
zero_ind.push_back(m_n);
for (std::vector<int>::size_type i = 0; i < zero_ind.size() - 1; i++)
const Index len = zero_ind.size() - 1;
for (Index i = 0; i < len; i++)
{
const Index start = zero_ind[i];
const Index end = zero_ind[i + 1] - 1;
@ -336,6 +385,16 @@ public:
update_block(start, end);
}
// Deflation on the computed result
Hii = m_mat_H.data();
for (Index i = 0; i < m_n - 1; i++, Hii += (m_n + 1))
{
const Scalar h = abs(Hii[1]);
const Scalar diag = abs(Hii[0]) + abs(Hii[m_n + 1]);
if (h <= eps_abs || h <= eps_rel * diag)
Hii[1] = 0;
}
m_computed = true;
}
@ -381,4 +440,4 @@ public:
} // namespace Spectra
#endif // DOUBLE_SHIFT_QR_H
#endif // SPECTRA_DOUBLE_SHIFT_QR_H

138
gtsam/3rdparty/Spectra/LinAlg/Lanczos.h vendored
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@ -1,16 +1,16 @@
// Copyright (C) 2018-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2018-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef LANCZOS_H
#define LANCZOS_H
#ifndef SPECTRA_LANCZOS_H
#define SPECTRA_LANCZOS_H
#include <Eigen/Core>
#include <cmath> // std::sqrt
#include <utility> // std::forward
#include <stdexcept> // std::invalid_argument
#include <sstream> // std::stringstream
#include "Arnoldi.h"
@ -27,13 +27,15 @@ template <typename Scalar, typename ArnoldiOpType>
class Lanczos : public Arnoldi<Scalar, ArnoldiOpType>
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<Matrix> MapMat;
typedef Eigen::Map<Vector> MapVec;
typedef Eigen::Map<const Matrix> MapConstMat;
typedef Eigen::Map<const Vector> MapConstVec;
// The real part type of the matrix element
using RealScalar = typename Eigen::NumTraits<Scalar>::Real;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapMat = Eigen::Map<Matrix>;
using MapVec = Eigen::Map<Vector>;
using MapConstMat = Eigen::Map<const Matrix>;
using RealMatrix = Eigen::Matrix<RealScalar, Eigen::Dynamic, Eigen::Dynamic>;
using Arnoldi<Scalar, ArnoldiOpType>::m_op;
using Arnoldi<Scalar, ArnoldiOpType>::m_n;
@ -47,13 +49,16 @@ private:
using Arnoldi<Scalar, ArnoldiOpType>::m_eps;
public:
Lanczos(const ArnoldiOpType& op, Index m) :
Arnoldi<Scalar, ArnoldiOpType>(op, m)
// Forward parameter `op` to the constructor of Arnoldi
template <typename T>
Lanczos(T&& op, Index m) :
Arnoldi<Scalar, ArnoldiOpType>(std::forward<T>(op), m)
{}
// Lanczos factorization starting from step-k
void factorize_from(Index from_k, Index to_m, Index& op_counter)
void factorize_from(Index from_k, Index to_m, Index& op_counter) override
{
using std::abs;
using std::sqrt;
if (to_m <= from_k)
@ -61,12 +66,13 @@ public:
if (from_k > m_k)
{
std::stringstream msg;
msg << "Lanczos: from_k (= " << from_k << ") is larger than the current subspace dimension (= " << m_k << ")";
throw std::invalid_argument(msg.str());
std::string msg = "Lanczos: from_k (= " + std::to_string(from_k) +
") is larger than the current subspace dimension (= " + std::to_string(m_k) + ")";
throw std::invalid_argument(msg);
}
const Scalar beta_thresh = m_eps * sqrt(Scalar(m_n));
const RealScalar beta_thresh = m_eps * sqrt(RealScalar(m_n));
const RealScalar eps_sqrt = sqrt(m_eps);
// Pre-allocate vectors
Vector Vf(to_m);
@ -78,47 +84,70 @@ public:
for (Index i = from_k; i <= to_m - 1; i++)
{
bool restart = false;
// If beta = 0, then the next V is not full rank
// We need to generate a new residual vector that is orthogonal
// to the current V, which we call a restart
if (m_beta < m_near_0)
//
// A simple criterion is beta < near_0, but it may be too stringent
// Another heuristic is to test whether (V^H)B(f/||f||) ~= 0 when ||f|| is small,
// and to reduce the computational cost, we only use the latest Vi
// Test the first criterion
bool restart = (m_beta < m_near_0);
// If not met, test the second criterion
// v is the (i+1)-th column of V
MapVec v(&m_fac_V(0, i), m_n);
if (!restart)
{
MapConstMat V(m_fac_V.data(), m_n, i); // The first i columns
this->expand_basis(V, 2 * i, m_fac_f, m_beta);
restart = true;
// Save v <- f / ||f|| to the (i+1)-th column of V
v.noalias() = m_fac_f / m_beta;
if (m_beta < eps_sqrt)
{
// Test (Vi^H)v
const Scalar Viv = m_op.inner_product(m_fac_V.col(i - 1), v);
// Restart V if (Vi^H)v is much larger than eps
restart = (abs(Viv) > eps_sqrt);
}
}
// v <- f / ||f||
MapVec v(&m_fac_V(0, i), m_n); // The (i+1)-th column
v.noalias() = m_fac_f / m_beta;
if (restart)
{
MapConstMat V(m_fac_V.data(), m_n, i); // The first i columns
this->expand_basis(V, 2 * i, m_fac_f, m_beta, op_counter);
v.noalias() = m_fac_f / m_beta;
}
// Whether there is a restart or not, right now the (i+1)-th column of V
// contains f / ||f||
// Note that H[i+1, i] equals to the unrestarted beta
m_fac_H(i, i - 1) = restart ? Scalar(0) : m_beta;
m_fac_H(i, i - 1) = restart ? Scalar(0) : Scalar(m_beta);
m_fac_H(i - 1, i) = m_fac_H(i, i - 1); // Due to symmetry
// w <- A * v
m_op.perform_op(v.data(), w.data());
op_counter++;
// H[i+1, i+1] = <v, w> = v'Bw
m_fac_H(i - 1, i) = m_fac_H(i, i - 1); // Due to symmetry
// f <- w - V * (V^H)Bw = w - H[i+1, i] * V{i} - H[i+1, i+1] * V{i+1}
// If restarting, we know that H[i+1, i] = 0
// First do w <- w - H[i+1, i] * V{i}, see the discussions in Section 2.3 of
// Cullum and Willoughby (2002). Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Vol. 1
if (!restart)
w.noalias() -= m_fac_H(i, i - 1) * m_fac_V.col(i - 1);
// H[i+1, i+1] = <v, w> = (v^H)Bw
m_fac_H(i, i) = m_op.inner_product(v, w);
// f <- w - V * V'Bw = w - H[i+1, i] * V{i} - H[i+1, i+1] * V{i+1}
// If restarting, we know that H[i+1, i] = 0
if (restart)
m_fac_f.noalias() = w - m_fac_H(i, i) * v;
else
m_fac_f.noalias() = w - m_fac_H(i, i - 1) * m_fac_V.col(i - 1) - m_fac_H(i, i) * v;
// f <- w - H[i+1, i+1] * V{i+1}
m_fac_f.noalias() = w - m_fac_H(i, i) * v;
m_beta = m_op.norm(m_fac_f);
// f/||f|| is going to be the next column of V, so we need to test
// whether V'B(f/||f||) ~= 0
// whether (V^H)B(f/||f||) ~= 0
const Index i1 = i + 1;
MapMat Vs(m_fac_V.data(), m_n, i1); // The first (i+1) columns
m_op.trans_product(Vs, m_fac_f, Vf.head(i1));
Scalar ortho_err = Vf.head(i1).cwiseAbs().maxCoeff();
m_op.adjoint_product(Vs, m_fac_f, Vf.head(i1));
RealScalar ortho_err = Vf.head(i1).cwiseAbs().maxCoeff();
// If not, iteratively correct the residual
int count = 0;
while (count < 5 && ortho_err > m_eps * m_beta)
@ -131,7 +160,7 @@ public:
if (m_beta < beta_thresh)
{
m_fac_f.setZero();
m_beta = Scalar(0);
m_beta = RealScalar(0);
break;
}
@ -144,7 +173,7 @@ public:
// beta <- ||f||
m_beta = m_op.norm(m_fac_f);
m_op.trans_product(Vs, m_fac_f, Vf.head(i1));
m_op.adjoint_product(Vs, m_fac_f, Vf.head(i1));
ortho_err = Vf.head(i1).cwiseAbs().maxCoeff();
count++;
}
@ -155,13 +184,36 @@ public:
}
// Apply H -> Q'HQ, where Q is from a tridiagonal QR decomposition
void compress_H(const TridiagQR<Scalar>& decomp)
// Function overloading here, not overriding
//
// Note that H is by nature a real symmetric matrix, but it may be stored
// as a complex matrix (e.g. in HermEigsSolver).
// Therefore, if m_fac_H has a real type (as in SymEigsSolver), then we
// directly overwrite m_fac_H. Otherwise, m_fac_H has a complex type
// (as in HermEigsSolver), so we first compute the real-typed result,
// and then cast to the complex type. This is done in the TridiagQR class
void compress_H(const TridiagQR<RealScalar>& decomp)
{
decomp.matrix_QtHQ(m_fac_H);
m_k--;
}
// In some cases we know that H has the form H = [X e 0],
// [e' s 0]
// [0 0 D]
// where X is an irreducible tridiagonal matrix, D is a diagonal matrix,
// s is a scalar, and e = (0, ..., 0, eps), eps ~= 0
//
// In this case we can force H[m+1, m] = H[m, m+1] = 0 and H[m+1, m+1] = s,
// where m is the size of X
void deflate_H(Index irr_size, const Scalar& s)
{
m_fac_H(irr_size, irr_size - 1) = Scalar(0);
m_fac_H(irr_size - 1, irr_size) = Scalar(0);
m_fac_H(irr_size, irr_size) = s;
}
};
} // namespace Spectra
#endif // LANCZOS_H
#endif // SPECTRA_LANCZOS_H

141
gtsam/3rdparty/Spectra/LinAlg/Orthogonalization.h vendored Normal file
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@ -0,0 +1,141 @@
// Copyright (C) 2020 Netherlands eScience Center <f.zapata@esciencecenter.nl>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_ORTHOGONALIZATION_H
#define SPECTRA_ORTHOGONALIZATION_H
#include <Eigen/Core>
#include <Eigen/QR>
namespace Spectra {
/// Check if the number of columns to skip is
/// larger than 0 but smaller than the total number
/// of columns of the matrix
/// \param in_output Matrix to be orthogonalized
/// \param left_cols_to_skip Number of left columns to be left untouched
template <typename Matrix>
void assert_left_cols_to_skip(Matrix& in_output, Eigen::Index left_cols_to_skip)
{
assert(in_output.cols() > left_cols_to_skip && "left_cols_to_skip is larger than columns of matrix");
assert(left_cols_to_skip >= 0 && "left_cols_to_skip is negative");
}
/// If the the number of columns to skip is null,
/// normalize the first column and set left_cols_to_skip=1
/// \param in_output Matrix to be orthogonalized
/// \param left_cols_to_skip Number of left columns to be left untouched
/// \return Actual number of left columns to skip
template <typename Matrix>
Eigen::Index treat_first_col(Matrix& in_output, Eigen::Index left_cols_to_skip)
{
if (left_cols_to_skip == 0)
{
in_output.col(0).normalize();
left_cols_to_skip = 1;
}
return left_cols_to_skip;
}
/// Orthogonalize the in_output matrix using a QR decomposition
/// \param in_output Matrix to be orthogonalized
template <typename Matrix>
void QR_orthogonalisation(Matrix& in_output)
{
using InternalMatrix = Eigen::Matrix<typename Matrix::Scalar, Eigen::Dynamic, Eigen::Dynamic>;
Eigen::Index nrows = in_output.rows();
Eigen::Index ncols = in_output.cols();
ncols = (std::min)(nrows, ncols);
InternalMatrix I = InternalMatrix::Identity(nrows, ncols);
Eigen::HouseholderQR<Matrix> qr(in_output);
in_output.leftCols(ncols).noalias() = qr.householderQ() * I;
}
/// Orthogonalize the in_output matrix using a modified Gram Schmidt process
/// \param in_output matrix to be orthogonalized
/// \param left_cols_to_skip Number of left columns to be left untouched
template <typename Matrix>
void MGS_orthogonalisation(Matrix& in_output, Eigen::Index left_cols_to_skip = 0)
{
assert_left_cols_to_skip(in_output, left_cols_to_skip);
left_cols_to_skip = treat_first_col(in_output, left_cols_to_skip);
for (Eigen::Index k = left_cols_to_skip; k < in_output.cols(); ++k)
{
for (Eigen::Index j = 0; j < k; j++)
{
in_output.col(k) -= in_output.col(j).dot(in_output.col(k)) * in_output.col(j);
}
in_output.col(k).normalize();
}
}
/// Orthogonalize the in_output matrix using a Gram Schmidt process
/// \param in_output matrix to be orthogonalized
/// \param left_cols_to_skip Number of left columns to be left untouched
template <typename Matrix>
void GS_orthogonalisation(Matrix& in_output, Eigen::Index left_cols_to_skip = 0)
{
assert_left_cols_to_skip(in_output, left_cols_to_skip);
left_cols_to_skip = treat_first_col(in_output, left_cols_to_skip);
for (Eigen::Index j = left_cols_to_skip; j < in_output.cols(); ++j)
{
in_output.col(j) -= in_output.leftCols(j) * (in_output.leftCols(j).transpose() * in_output.col(j));
in_output.col(j).normalize();
}
}
/// Orthogonalize the subspace spanned by right columns of in_output
/// against the subspace spanned by left columns
/// It assumes that the left columns are already orthogonal and normalized,
/// and it does not orthogonalize the left columns against each other
/// \param in_output Matrix to be orthogonalized
/// \param left_cols_to_skip Number of left columns to be left untouched
template <typename Matrix>
void subspace_orthogonalisation(Matrix& in_output, Eigen::Index left_cols_to_skip)
{
assert_left_cols_to_skip(in_output, left_cols_to_skip);
if (left_cols_to_skip == 0)
{
return;
}
Eigen::Index right_cols_to_ortho = in_output.cols() - left_cols_to_skip;
in_output.rightCols(right_cols_to_ortho) -= in_output.leftCols(left_cols_to_skip) *
(in_output.leftCols(left_cols_to_skip).transpose() * in_output.rightCols(right_cols_to_ortho));
}
/// Orthogonalize the in_output matrix using a Jens process
/// The subspace spanned by right columns are first orthogonalized
/// agains the left columns, and then a QR decomposition is applied on the right columns
/// to make them orthogonalized agains each other
/// \param in_output Matrix to be orthogonalized
/// \param left_cols_to_skip Number of left columns to be left untouched
template <typename Matrix>
void JensWehner_orthogonalisation(Matrix& in_output, Eigen::Index left_cols_to_skip = 0)
{
assert_left_cols_to_skip(in_output, left_cols_to_skip);
Eigen::Index right_cols_to_ortho = in_output.cols() - left_cols_to_skip;
subspace_orthogonalisation(in_output, left_cols_to_skip);
Eigen::Ref<Matrix> right_cols = in_output.rightCols(right_cols_to_ortho);
QR_orthogonalisation(right_cols);
}
/// Orthogonalize the in_output matrix using a twice-is-enough Jens process
/// \param in_output Matrix to be orthogonalized
/// \param left_cols_to_skip Number of left columns to be left untouched
template <typename Matrix>
void twice_is_enough_orthogonalisation(Matrix& in_output, Eigen::Index left_cols_to_skip = 0)
{
JensWehner_orthogonalisation(in_output, left_cols_to_skip);
JensWehner_orthogonalisation(in_output, left_cols_to_skip);
}
} // namespace Spectra
#endif // SPECTRA_ORTHOGONALIZATION_H

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@ -0,0 +1,130 @@
// Copyright (C) 2020 Netherlands eScience Center <n.renauld@esciencecenter.nl>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_RITZ_PAIRS_H
#define SPECTRA_RITZ_PAIRS_H
#include <Eigen/Core>
#include <Eigen/Eigenvalues>
#include "../Util/SelectionRule.h"
namespace Spectra {
template <typename Scalar>
class SearchSpace;
/// This class handles the creation and manipulation of Ritz eigen pairs
/// for iterative eigensolvers such as Davidson, Jacobi-Davidson, etc.
template <typename Scalar>
class RitzPairs
{
private:
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using Array = Eigen::Array<Scalar, Eigen::Dynamic, 1>;
using BoolArray = Eigen::Array<bool, Eigen::Dynamic, 1>;
Vector m_values; // eigenvalues
Matrix m_small_vectors; // eigenvectors of the small problem, makes restart cheaper.
Matrix m_vectors; // Ritz (or harmonic Ritz) eigenvectors
Matrix m_residues; // residues of the pairs
BoolArray m_root_converged;
public:
RitzPairs() = default;
/// Compute the eigen values/vectors
///
/// \param search_space Instance of the class handling the search space
/// \return Eigen::ComputationalInfo Whether small eigenvalue problem worked
Eigen::ComputationInfo compute_eigen_pairs(const SearchSpace<Scalar>& search_space);
/// Returns the size of the ritz eigen pairs
///
/// \return Eigen::Index Number of pairs
Index size() const { return m_values.size(); }
/// Sort the eigen pairs according to the selection rule
///
/// \param selection Sorting rule
void sort(SortRule selection)
{
std::vector<Index> ind = argsort(selection, m_values);
RitzPairs<Scalar> temp = *this;
for (Index i = 0; i < size(); i++)
{
m_values[i] = temp.m_values[ind[i]];
m_vectors.col(i) = temp.m_vectors.col(ind[i]);
m_residues.col(i) = temp.m_residues.col(ind[i]);
m_small_vectors.col(i) = temp.m_small_vectors.col(ind[i]);
}
}
/// Checks if the algorithm has converged and updates root_converged
///
/// \param tol Tolerance for convergence
/// \param number_eigenvalue Number of request eigenvalues
/// \return bool true if all eigenvalues are converged
bool check_convergence(Scalar tol, Index number_eigenvalues)
{
const Array norms = m_residues.colwise().norm();
bool converged = true;
m_root_converged = BoolArray::Zero(norms.size());
for (Index j = 0; j < norms.size(); j++)
{
m_root_converged[j] = (norms[j] < tol);
if (j < number_eigenvalues)
{
converged &= (norms[j] < tol);
}
}
return converged;
}
const Matrix& ritz_vectors() const { return m_vectors; }
const Vector& ritz_values() const { return m_values; }
const Matrix& small_ritz_vectors() const { return m_small_vectors; }
const Matrix& residues() const { return m_residues; }
const BoolArray& converged_eigenvalues() const { return m_root_converged; }
};
} // namespace Spectra
#include "SearchSpace.h"
namespace Spectra {
/// Creates the small space matrix and computes its eigen pairs
/// Also computes the ritz vectors and residues
///
/// \param search_space Instance of the SearchSpace class
template <typename Scalar>
Eigen::ComputationInfo RitzPairs<Scalar>::compute_eigen_pairs(const SearchSpace<Scalar>& search_space)
{
const Matrix& basis_vectors = search_space.basis_vectors();
const Matrix& op_basis_prod = search_space.operator_basis_product();
// Form the small eigenvalue
Matrix small_matrix = basis_vectors.transpose() * op_basis_prod;
// Small eigenvalue problem
Eigen::SelfAdjointEigenSolver<Matrix> eigen_solver(small_matrix);
m_values = eigen_solver.eigenvalues();
m_small_vectors = eigen_solver.eigenvectors();
// Ritz vectors
m_vectors = basis_vectors * m_small_vectors;
// Residues
m_residues = op_basis_prod * m_small_vectors - m_vectors * m_values.asDiagonal();
return eigen_solver.info();
}
} // namespace Spectra
#endif // SPECTRA_RITZ_PAIRS_H

96
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@ -0,0 +1,96 @@
// Copyright (C) 2020 Netherlands eScience Center <n.renauld@esciencecenter.nl>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_SEARCH_SPACE_H
#define SPECTRA_SEARCH_SPACE_H
#include <Eigen/Core>
#include "RitzPairs.h"
#include "Orthogonalization.h"
namespace Spectra {
/// This class handles the creation and manipulation of the search space
/// for iterative eigensolvers such as Davidson, Jacobi-Davidson, etc.
template <typename Scalar>
class SearchSpace
{
private:
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
Matrix m_basis_vectors;
Matrix m_op_basis_product;
/// Append new vector to the basis
///
/// \param new_vect Matrix of new correction vectors
void append_new_vectors_to_basis(const Matrix& new_vect)
{
Index num_update = new_vect.cols();
m_basis_vectors.conservativeResize(Eigen::NoChange, m_basis_vectors.cols() + num_update);
m_basis_vectors.rightCols(num_update).noalias() = new_vect;
}
public:
SearchSpace() = default;
/// Returns the current size of the search space
Index size() const { return m_basis_vectors.cols(); }
void initialize_search_space(const Eigen::Ref<const Matrix>& initial_vectors)
{
m_basis_vectors = initial_vectors;
m_op_basis_product = Matrix(initial_vectors.rows(), 0);
}
/// Updates the matrix formed by the operator applied to the search space
/// after the addition of new vectors in the search space. Only the product
/// of the operator with the new vectors is computed and the result is appended
/// to the op_basis_product member variable
///
/// \param OpType Operator representing the matrix
template <typename OpType>
void update_operator_basis_product(OpType& op)
{
Index nvec = m_basis_vectors.cols() - m_op_basis_product.cols();
m_op_basis_product.conservativeResize(Eigen::NoChange, m_basis_vectors.cols());
m_op_basis_product.rightCols(nvec).noalias() = op * m_basis_vectors.rightCols(nvec);
}
/// Restart the search space by reducing the basis vector to the last
/// Ritz eigenvector
///
/// \param ritz_pair Instance of a RitzPair class
/// \param size Size of the restart
void restart(const RitzPairs<Scalar>& ritz_pairs, Index size)
{
m_basis_vectors = ritz_pairs.ritz_vectors().leftCols(size);
m_op_basis_product = m_op_basis_product * ritz_pairs.small_ritz_vectors().leftCols(size);
}
/// Append new vectors to the search space and
/// orthogonalize the resulting matrix
///
/// \param new_vect Matrix of new correction vectors
void extend_basis(const Matrix& new_vect)
{
Index left_cols_to_skip = size();
append_new_vectors_to_basis(new_vect);
twice_is_enough_orthogonalisation(m_basis_vectors, left_cols_to_skip);
}
/// Returns the basis vectors
const Matrix& basis_vectors() const { return m_basis_vectors; }
/// Returns the operator applied to basis vector
const Matrix& operator_basis_product() const { return m_op_basis_product; }
};
} // namespace Spectra
#endif // SPECTRA_SEARCH_SPACE_H

77
gtsam/3rdparty/Spectra/LinAlg/TridiagEigen.h vendored
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@ -2,14 +2,14 @@
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef TRIDIAG_EIGEN_H
#define TRIDIAG_EIGEN_H
#ifndef SPECTRA_TRIDIAG_EIGEN_H
#define SPECTRA_TRIDIAG_EIGEN_H
#include <Eigen/Core>
#include <Eigen/Jacobi>
@ -23,25 +23,22 @@ template <typename Scalar = double>
class TridiagEigen
{
private:
typedef Eigen::Index Index;
using Index = Eigen::Index;
// For convenience in adapting the tridiagonal_qr_step() function
typedef Scalar RealScalar;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Ref<Matrix> GenericMatrix;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
using RealScalar = Scalar;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using GenericMatrix = Eigen::Ref<Matrix>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
Index m_n;
Vector m_main_diag; // Main diagonal elements of the matrix
Vector m_sub_diag; // Sub-diagonal elements of the matrix
Matrix m_evecs; // To store eigenvectors
bool m_computed;
const Scalar m_near_0; // a very small value, ~= 1e-307 for the "double" type
// Adapted from Eigen/src/Eigenvaleus/SelfAdjointEigenSolver.h
// Francis implicit QR step.
static void tridiagonal_qr_step(RealScalar* diag,
RealScalar* subdiag, Index start,
Index end, Scalar* matrixQ,
@ -49,6 +46,7 @@ private:
{
using std::abs;
// Wilkinson Shift.
RealScalar td = (diag[end - 1] - diag[end]) * RealScalar(0.5);
RealScalar e = subdiag[end - 1];
// Note that thanks to scaling, e^2 or td^2 cannot overflow, however they can still
@ -57,14 +55,14 @@ private:
// RealScalar mu = diag[end] - e2 / (td + (td>0 ? 1 : -1) * sqrt(td*td + e2));
// This explain the following, somewhat more complicated, version:
RealScalar mu = diag[end];
if (td == Scalar(0))
if (td == RealScalar(0))
mu -= abs(e);
else
else if (e != RealScalar(0))
{
RealScalar e2 = Eigen::numext::abs2(subdiag[end - 1]);
RealScalar h = Eigen::numext::hypot(td, e);
const RealScalar e2 = Eigen::numext::abs2(e);
const RealScalar h = Eigen::numext::hypot(td, e);
if (e2 == RealScalar(0))
mu -= (e / (td + (td > RealScalar(0) ? RealScalar(1) : RealScalar(-1)))) * (e / h);
mu -= e / ((td + (td > RealScalar(0) ? h : -h)) / e);
else
mu -= e2 / (td + (td > RealScalar(0) ? h : -h));
}
@ -72,7 +70,9 @@ private:
RealScalar x = diag[start] - mu;
RealScalar z = subdiag[start];
Eigen::Map<Matrix> q(matrixQ, n, n);
for (Index k = start; k < end; ++k)
// If z ever becomes zero, the Givens rotation will be the identity and
// z will stay zero for all future iterations.
for (Index k = start; k < end && z != RealScalar(0); ++k)
{
Eigen::JacobiRotation<RealScalar> rot;
rot.makeGivens(x, z);
@ -91,8 +91,8 @@ private:
if (k > start)
subdiag[k - 1] = c * subdiag[k - 1] - s * z;
// "Chasing the bulge" to return to triangular form.
x = subdiag[k];
if (k < end - 1)
{
z = -s * subdiag[k + 1];
@ -107,13 +107,11 @@ private:
public:
TridiagEigen() :
m_n(0), m_computed(false),
m_near_0(TypeTraits<Scalar>::min() * Scalar(10))
m_n(0), m_computed(false)
{}
TridiagEigen(ConstGenericMatrix& mat) :
m_n(mat.rows()), m_computed(false),
m_near_0(TypeTraits<Scalar>::min() * Scalar(10))
m_n(mat.rows()), m_computed(false)
{
compute(mat);
}
@ -122,6 +120,10 @@ public:
{
using std::abs;
// A very small value, but 1.0 / near_0 does not overflow
// ~= 1e-307 for the "double" type
const Scalar near_0 = TypeTraits<Scalar>::min() * Scalar(10);
m_n = mat.rows();
if (m_n != mat.cols())
throw std::invalid_argument("TridiagEigen: matrix must be square");
@ -132,10 +134,10 @@ public:
m_evecs.setIdentity();
// Scale matrix to improve stability
const Scalar scale = std::max(mat.diagonal().cwiseAbs().maxCoeff(),
mat.diagonal(-1).cwiseAbs().maxCoeff());
const Scalar scale = (std::max)(mat.diagonal().cwiseAbs().maxCoeff(),
mat.diagonal(-1).cwiseAbs().maxCoeff());
// If scale=0, mat is a zero matrix, so we can early stop
if (scale < m_near_0)
if (scale < near_0)
{
// m_main_diag contains eigenvalues
m_main_diag.setZero();
@ -156,16 +158,25 @@ public:
int info = 0; // 0 for success, 1 for failure
const Scalar considerAsZero = TypeTraits<Scalar>::min();
const Scalar precision = Scalar(2) * Eigen::NumTraits<Scalar>::epsilon();
const Scalar precision_inv = Scalar(1) / Eigen::NumTraits<Scalar>::epsilon();
while (end > 0)
{
for (Index i = start; i < end; i++)
if (abs(subdiag[i]) <= considerAsZero ||
abs(subdiag[i]) <= (abs(diag[i]) + abs(diag[i + 1])) * precision)
subdiag[i] = 0;
{
if (abs(subdiag[i]) <= considerAsZero)
subdiag[i] = Scalar(0);
else
{
// abs(subdiag[i]) <= epsilon * sqrt(abs(diag[i]) + abs(diag[i+1]))
// Scaled to prevent underflows.
const Scalar scaled_subdiag = precision_inv * subdiag[i];
if (scaled_subdiag * scaled_subdiag <= (abs(diag[i]) + abs(diag[i + 1])))
subdiag[i] = Scalar(0);
}
}
// find the largest unreduced block
// find the largest unreduced block at the end of the matrix.
while (end > 0 && subdiag[end - 1] == Scalar(0))
end--;
@ -216,4 +227,4 @@ public:
} // namespace Spectra
#endif // TRIDIAG_EIGEN_H
#endif // SPECTRA_TRIDIAG_EIGEN_H

45
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@ -2,42 +2,41 @@
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef UPPER_HESSENBERG_EIGEN_H
#define UPPER_HESSENBERG_EIGEN_H
#ifndef SPECTRA_UPPER_HESSENBERG_EIGEN_H
#define SPECTRA_UPPER_HESSENBERG_EIGEN_H
#include <Eigen/Core>
#include <Eigen/Eigenvalues>
#include <stdexcept>
#include "UpperHessenbergSchur.h"
namespace Spectra {
template <typename Scalar = double>
class UpperHessenbergEigen
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using GenericMatrix = Eigen::Ref<Matrix>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
typedef Eigen::Ref<Matrix> GenericMatrix;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
typedef std::complex<Scalar> Complex;
typedef Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic> ComplexMatrix;
typedef Eigen::Matrix<Complex, Eigen::Dynamic, 1> ComplexVector;
using Complex = std::complex<Scalar>;
using ComplexMatrix = Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic>;
using ComplexVector = Eigen::Matrix<Complex, Eigen::Dynamic, 1>;
Index m_n; // Size of the matrix
Eigen::RealSchur<Matrix> m_realSchur; // Schur decomposition solver
UpperHessenbergSchur<Scalar> m_schur; // Schur decomposition solver
Matrix m_matT; // Schur T matrix
Matrix m_eivec; // Storing eigenvectors
ComplexVector m_eivalues; // Eigenvalues
bool m_computed;
void doComputeEigenvectors()
@ -177,7 +176,7 @@ private:
}
// Overflow control
Scalar t = std::max(abs(m_matT.coeff(i, n - 1)), abs(m_matT.coeff(i, n)));
Scalar t = (std::max)(abs(m_matT.coeff(i, n - 1)), abs(m_matT.coeff(i, n)));
if ((eps * t) * t > Scalar(1))
m_matT.block(i, n - 1, size - i, 2) /= t;
}
@ -221,13 +220,9 @@ public:
const Scalar scale = mat.cwiseAbs().maxCoeff();
// Reduce to real Schur form
Matrix Q = Matrix::Identity(m_n, m_n);
m_realSchur.computeFromHessenberg(mat / scale, Q, true);
if (m_realSchur.info() != Eigen::Success)
throw std::runtime_error("UpperHessenbergEigen: eigen decomposition failed");
m_matT = m_realSchur.matrixT();
m_eivec = m_realSchur.matrixU();
m_schur.compute(mat / scale);
m_schur.swap_T(m_matT);
m_schur.swap_U(m_eivec);
// Compute eigenvalues from matT
m_eivalues.resize(m_n);
@ -249,7 +244,7 @@ public:
{
Scalar t0 = m_matT.coeff(i + 1, i);
Scalar t1 = m_matT.coeff(i, i + 1);
Scalar maxval = std::max(abs(p), std::max(abs(t0), abs(t1)));
Scalar maxval = (std::max)(abs(p), (std::max)(abs(t0), abs(t1)));
t0 /= maxval;
t1 /= maxval;
Scalar p0 = p / maxval;
@ -316,4 +311,4 @@ public:
} // namespace Spectra
#endif // UPPER_HESSENBERG_EIGEN_H
#endif // SPECTRA_UPPER_HESSENBERG_EIGEN_H

443
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@ -1,17 +1,19 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef UPPER_HESSENBERG_QR_H
#define UPPER_HESSENBERG_QR_H
#ifndef SPECTRA_UPPER_HESSENBERG_QR_H
#define SPECTRA_UPPER_HESSENBERG_QR_H
#include <Eigen/Core>
#include <cmath> // std::sqrt
#include <algorithm> // std::fill, std::copy
#include <cmath> // std::abs, std::sqrt, std::pow
#include <algorithm> // std::fill
#include <stdexcept> // std::logic_error
#include "../Util/TypeTraits.h"
namespace Spectra {
///
@ -43,16 +45,16 @@ template <typename Scalar = double>
class UpperHessenbergQR
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Matrix<Scalar, 1, Eigen::Dynamic> RowVector;
typedef Eigen::Array<Scalar, Eigen::Dynamic, 1> Array;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using RowVector = Eigen::Matrix<Scalar, 1, Eigen::Dynamic>;
using Array = Eigen::Array<Scalar, Eigen::Dynamic, 1>;
typedef Eigen::Ref<Matrix> GenericMatrix;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
using GenericMatrix = Eigen::Ref<Matrix>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
Matrix m_mat_T;
Matrix m_mat_R;
protected:
Index m_n;
@ -64,40 +66,107 @@ protected:
Array m_rot_sin;
bool m_computed;
// Given x and y, compute 1) r = sqrt(x^2 + y^2), 2) c = x / r, 3) s = -y / r
// If both x and y are zero, set c = 1 and s = 0
// We must implement it in a numerically stable way
static void compute_rotation(const Scalar& x, const Scalar& y, Scalar& r, Scalar& c, Scalar& s)
// Given a >= b > 0, compute r = sqrt(a^2 + b^2), c = a / r, and s = b / r with high precision
static void stable_scaling(const Scalar& a, const Scalar& b, Scalar& r, Scalar& c, Scalar& s)
{
using std::sqrt;
using std::pow;
const Scalar xsign = (x > Scalar(0)) - (x < Scalar(0));
const Scalar ysign = (y > Scalar(0)) - (y < Scalar(0));
const Scalar xabs = x * xsign;
const Scalar yabs = y * ysign;
if (xabs > yabs)
// Let t = b / a, then 0 < t <= 1
// c = 1 / sqrt(1 + t^2)
// s = t * c
// r = a * sqrt(1 + t^2)
const Scalar t = b / a;
// We choose a cutoff such that cutoff^4 < eps
// If t > cutoff, use the standard way; otherwise use Taylor series expansion
// to avoid an explicit sqrt() call that may lose precision
const Scalar eps = TypeTraits<Scalar>::epsilon();
// std::pow() is not constexpr, so we do not declare cutoff to be constexpr
// But most compilers should be able to compute cutoff at compile time
const Scalar cutoff = Scalar(0.1) * pow(eps, Scalar(0.25));
if (t >= cutoff)
{
// In this case xabs != 0
const Scalar ratio = yabs / xabs; // so that 0 <= ratio < 1
const Scalar common = sqrt(Scalar(1) + ratio * ratio);
c = xsign / common;
r = xabs * common;
s = -y / r;
const Scalar denom = sqrt(Scalar(1) + t * t);
c = Scalar(1) / denom;
s = t * c;
r = a * denom;
}
else
{
if (yabs == Scalar(0))
{
r = Scalar(0);
c = Scalar(1);
s = Scalar(0);
return;
}
const Scalar ratio = xabs / yabs; // so that 0 <= ratio <= 1
const Scalar common = sqrt(Scalar(1) + ratio * ratio);
s = -ysign / common;
r = yabs * common;
c = x / r;
// 1 / sqrt(1 + t^2) ~= 1 - (1/2) * t^2 + (3/8) * t^4
// 1 / sqrt(1 + l^2) ~= 1 / l - (1/2) / l^3 + (3/8) / l^5
// == t - (1/2) * t^3 + (3/8) * t^5, where l = 1 / t
// sqrt(1 + t^2) ~= 1 + (1/2) * t^2 - (1/8) * t^4 + (1/16) * t^6
//
// c = 1 / sqrt(1 + t^2) ~= 1 - t^2 * (1/2 - (3/8) * t^2)
// s = 1 / sqrt(1 + l^2) ~= t * (1 - t^2 * (1/2 - (3/8) * t^2))
// r = a * sqrt(1 + t^2) ~= a + (1/2) * b * t - (1/8) * b * t^3 + (1/16) * b * t^5
// == a + (b/2) * t * (1 - t^2 * (1/4 - 1/8 * t^2))
const Scalar c1 = Scalar(1);
const Scalar c2 = Scalar(0.5);
const Scalar c4 = Scalar(0.25);
const Scalar c8 = Scalar(0.125);
const Scalar c38 = Scalar(0.375);
const Scalar t2 = t * t;
const Scalar tc = t2 * (c2 - c38 * t2);
c = c1 - tc;
s = t - t * tc;
r = a + c2 * b * t * (c1 - t2 * (c4 - c8 * t2));
/* const Scalar t_2 = Scalar(0.5) * t;
const Scalar t2_2 = t_2 * t;
const Scalar t3_2 = t2_2 * t;
const Scalar t4_38 = Scalar(1.5) * t2_2 * t2_2;
const Scalar t5_16 = Scalar(0.25) * t3_2 * t2_2;
c = Scalar(1) - t2_2 + t4_38;
s = t - t3_2 + Scalar(6) * t5_16;
r = a + b * (t_2 - Scalar(0.25) * t3_2 + t5_16); */
}
}
// Given x and y, compute 1) r = sqrt(x^2 + y^2), 2) c = x / r, 3) s = -y / r
// If both x and y are zero, set c = 1 and s = 0
// We must implement it in a numerically stable way
// The implementation below is shown to be more accurate than directly computing
// r = std::hypot(x, y); c = x / r; s = -y / r;
static void compute_rotation(const Scalar& x, const Scalar& y, Scalar& r, Scalar& c, Scalar& s)
{
using std::abs;
// Only need xsign when x != 0
const Scalar xsign = (x > Scalar(0)) ? Scalar(1) : Scalar(-1);
const Scalar xabs = abs(x);
if (y == Scalar(0))
{
c = (x == Scalar(0)) ? Scalar(1) : xsign;
s = Scalar(0);
r = xabs;
return;
}
// Now we know y != 0
const Scalar ysign = (y > Scalar(0)) ? Scalar(1) : Scalar(-1);
const Scalar yabs = abs(y);
if (x == Scalar(0))
{
c = Scalar(0);
s = -ysign;
r = yabs;
return;
}
// Now we know x != 0, y != 0
if (xabs > yabs)
{
stable_scaling(xabs, yabs, r, c, s);
c = xsign * c;
s = -ysign * s;
}
else
{
stable_scaling(yabs, xabs, r, s, c);
c = xsign * c;
s = -ysign * s;
}
}
@ -108,6 +177,7 @@ public:
///
UpperHessenbergQR(Index size) :
m_n(size),
m_shift(0),
m_rot_cos(m_n - 1),
m_rot_sin(m_n - 1),
m_computed(false)
@ -122,7 +192,7 @@ public:
/// \param mat Matrix type can be `Eigen::Matrix<Scalar, ...>` (e.g.
/// `Eigen::MatrixXd` and `Eigen::MatrixXf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
/// Only the upper triangular and the lower subdiagonal parts of
/// Only the upper triangular and the subdiagonal elements of
/// the matrix are used.
///
UpperHessenbergQR(ConstGenericMatrix& mat, const Scalar& shift = Scalar(0)) :
@ -138,16 +208,16 @@ public:
///
/// Virtual destructor.
///
virtual ~UpperHessenbergQR(){};
virtual ~UpperHessenbergQR() {}
///
/// Conduct the QR factorization of an upper Hessenberg matrix with
/// Compute the QR decomposition of an upper Hessenberg matrix with
/// an optional shift.
///
/// \param mat Matrix type can be `Eigen::Matrix<Scalar, ...>` (e.g.
/// `Eigen::MatrixXd` and `Eigen::MatrixXf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
/// Only the upper triangular and the lower subdiagonal parts of
/// Only the upper triangular and the subdiagonal elements of
/// the matrix are used.
///
virtual void compute(ConstGenericMatrix& mat, const Scalar& shift = Scalar(0))
@ -157,54 +227,54 @@ public:
throw std::invalid_argument("UpperHessenbergQR: matrix must be square");
m_shift = shift;
m_mat_T.resize(m_n, m_n);
m_mat_R.resize(m_n, m_n);
m_rot_cos.resize(m_n - 1);
m_rot_sin.resize(m_n - 1);
// Make a copy of mat - s * I
std::copy(mat.data(), mat.data() + mat.size(), m_mat_T.data());
m_mat_T.diagonal().array() -= m_shift;
m_mat_R.noalias() = mat;
m_mat_R.diagonal().array() -= m_shift;
Scalar xi, xj, r, c, s;
Scalar *Tii, *ptr;
Scalar *Rii, *ptr;
const Index n1 = m_n - 1;
for (Index i = 0; i < n1; i++)
{
Tii = &m_mat_T.coeffRef(i, i);
Rii = &m_mat_R.coeffRef(i, i);
// Make sure mat_T is upper Hessenberg
// Zero the elements below mat_T(i + 1, i)
std::fill(Tii + 2, Tii + m_n - i, Scalar(0));
// Make sure R is upper Hessenberg
// Zero the elements below R[i + 1, i]
std::fill(Rii + 2, Rii + m_n - i, Scalar(0));
xi = Tii[0]; // mat_T(i, i)
xj = Tii[1]; // mat_T(i + 1, i)
xi = Rii[0]; // R[i, i]
xj = Rii[1]; // R[i + 1, i]
compute_rotation(xi, xj, r, c, s);
m_rot_cos[i] = c;
m_rot_sin[i] = s;
m_rot_cos.coeffRef(i) = c;
m_rot_sin.coeffRef(i) = s;
// For a complete QR decomposition,
// we first obtain the rotation matrix
// G = [ cos sin]
// [-sin cos]
// and then do T[i:(i + 1), i:(n - 1)] = G' * T[i:(i + 1), i:(n - 1)]
// and then do R[i:(i + 1), i:(n - 1)] = G' * R[i:(i + 1), i:(n - 1)]
// Gt << c, -s, s, c;
// m_mat_T.block(i, i, 2, m_n - i) = Gt * m_mat_T.block(i, i, 2, m_n - i);
Tii[0] = r; // m_mat_T(i, i) => r
Tii[1] = 0; // m_mat_T(i + 1, i) => 0
ptr = Tii + m_n; // m_mat_T(i, k), k = i+1, i+2, ..., n-1
// m_mat_R.block(i, i, 2, m_n - i) = Gt * m_mat_R.block(i, i, 2, m_n - i);
Rii[0] = r; // R[i, i] => r
Rii[1] = 0; // R[i + 1, i] => 0
ptr = Rii + m_n; // R[i, k], k = i+1, i+2, ..., n-1
for (Index j = i + 1; j < m_n; j++, ptr += m_n)
{
Scalar tmp = ptr[0];
const Scalar tmp = ptr[0];
ptr[0] = c * tmp - s * ptr[1];
ptr[1] = s * tmp + c * ptr[1];
}
// If we do not need to calculate the R matrix, then
// only the cos and sin sequences are required.
// In such case we only update T[i + 1, (i + 1):(n - 1)]
// m_mat_T.block(i + 1, i + 1, 1, m_n - i - 1) *= c;
// m_mat_T.block(i + 1, i + 1, 1, m_n - i - 1) += s * mat_T.block(i, i + 1, 1, m_n - i - 1);
// In such case we only update R[i + 1, (i + 1):(n - 1)]
// m_mat_R.block(i + 1, i + 1, 1, m_n - i - 1) *= c;
// m_mat_R.block(i + 1, i + 1, 1, m_n - i - 1) += s * m_mat_R.block(i, i + 1, 1, m_n - i - 1);
}
m_computed = true;
@ -222,7 +292,7 @@ public:
if (!m_computed)
throw std::logic_error("UpperHessenbergQR: need to call compute() first");
return m_mat_T;
return m_mat_R;
}
///
@ -239,7 +309,7 @@ public:
// Make a copy of the R matrix
dest.resize(m_n, m_n);
std::copy(m_mat_T.data(), m_mat_T.data() + m_mat_T.size(), dest.data());
dest.noalias() = m_mat_R;
// Compute the RQ matrix
const Index n1 = m_n - 1;
@ -252,7 +322,7 @@ public:
// [-sin[i] cos[i]]
Scalar *Yi, *Yi1;
Yi = &dest.coeffRef(0, i);
Yi1 = Yi + m_n; // RQ(0, i + 1)
Yi1 = Yi + m_n; // RQ[0, i + 1]
const Index i2 = i + 2;
for (Index j = 0; j < i2; j++)
{
@ -475,16 +545,23 @@ template <typename Scalar = double>
class TridiagQR : public UpperHessenbergQR<Scalar>
{
private:
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
using ComplexMatrix = Eigen::Matrix<std::complex<Scalar>, Eigen::Dynamic, Eigen::Dynamic>;
typedef typename Matrix::Index Index;
using UpperHessenbergQR<Scalar>::m_n;
using UpperHessenbergQR<Scalar>::m_shift;
using UpperHessenbergQR<Scalar>::m_rot_cos;
using UpperHessenbergQR<Scalar>::m_rot_sin;
using UpperHessenbergQR<Scalar>::m_computed;
Vector m_T_diag; // diagonal elements of T
Vector m_T_lsub; // lower subdiagonal of T
Vector m_T_usub; // upper subdiagonal of T
Vector m_T_usub2; // 2nd upper subdiagonal of T
Vector m_T_subd; // 1st subdiagonal of T
Vector m_R_diag; // diagonal elements of R, where T = QR
Vector m_R_supd; // 1st superdiagonal of R
Vector m_R_supd2; // 2nd superdiagonal of R
public:
///
@ -497,15 +574,14 @@ public:
///
/// Constructor to create an object that performs and stores the
/// QR decomposition of an upper Hessenberg matrix `mat`, with an
/// optional shift: \f$H-sI=QR\f$. Here \f$H\f$ stands for the matrix
/// QR decomposition of a tridiagonal matrix `mat`, with an
/// optional shift: \f$T-sI=QR\f$. Here \f$T\f$ stands for the matrix
/// `mat`, and \f$s\f$ is the shift.
///
/// \param mat Matrix type can be `Eigen::Matrix<Scalar, ...>` (e.g.
/// `Eigen::MatrixXd` and `Eigen::MatrixXf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
/// Only the major- and sub- diagonal parts of
/// the matrix are used.
/// Only the diagonal and subdiagonal elements of the matrix are used.
///
TridiagQR(ConstGenericMatrix& mat, const Scalar& shift = Scalar(0)) :
UpperHessenbergQR<Scalar>(mat.rows())
@ -514,70 +590,84 @@ public:
}
///
/// Conduct the QR factorization of a tridiagonal matrix with an
/// Compute the QR decomposition of a tridiagonal matrix with an
/// optional shift.
///
/// \param mat Matrix type can be `Eigen::Matrix<Scalar, ...>` (e.g.
/// `Eigen::MatrixXd` and `Eigen::MatrixXf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
/// Only the major- and sub- diagonal parts of
/// the matrix are used.
/// Only the diagonal and subdiagonal elements of the matrix are used.
///
void compute(ConstGenericMatrix& mat, const Scalar& shift = Scalar(0))
void compute(ConstGenericMatrix& mat, const Scalar& shift = Scalar(0)) override
{
this->m_n = mat.rows();
if (this->m_n != mat.cols())
using std::abs;
m_n = mat.rows();
if (m_n != mat.cols())
throw std::invalid_argument("TridiagQR: matrix must be square");
this->m_shift = shift;
m_T_diag.resize(this->m_n);
m_T_lsub.resize(this->m_n - 1);
m_T_usub.resize(this->m_n - 1);
m_T_usub2.resize(this->m_n - 2);
this->m_rot_cos.resize(this->m_n - 1);
this->m_rot_sin.resize(this->m_n - 1);
m_shift = shift;
m_rot_cos.resize(m_n - 1);
m_rot_sin.resize(m_n - 1);
m_T_diag.array() = mat.diagonal().array() - this->m_shift;
m_T_lsub.noalias() = mat.diagonal(-1);
m_T_usub.noalias() = m_T_lsub;
// Save the diagonal and subdiagonal elements of T
m_T_diag.resize(m_n);
m_T_subd.resize(m_n - 1);
m_T_diag.noalias() = mat.diagonal();
m_T_subd.noalias() = mat.diagonal(-1);
// Deflation of small sub-diagonal elements
const Scalar eps = TypeTraits<Scalar>::epsilon();
for (Index i = 0; i < m_n - 1; i++)
{
if (abs(m_T_subd[i]) <= eps * (abs(m_T_diag[i]) + abs(m_T_diag[i + 1])))
m_T_subd[i] = Scalar(0);
}
// Apply shift and copy T to R
m_R_diag.resize(m_n);
m_R_supd.resize(m_n - 1);
m_R_supd2.resize(m_n - 2);
m_R_diag.array() = m_T_diag.array() - m_shift;
m_R_supd.noalias() = m_T_subd;
// A number of pointers to avoid repeated address calculation
Scalar *c = this->m_rot_cos.data(), // pointer to the cosine vector
*s = this->m_rot_sin.data(), // pointer to the sine vector
Scalar *c = m_rot_cos.data(), // pointer to the cosine vector
*s = m_rot_sin.data(), // pointer to the sine vector
r;
const Index n1 = this->m_n - 1;
const Index n1 = m_n - 1, n2 = m_n - 2;
for (Index i = 0; i < n1; i++)
{
// diag[i] == T[i, i]
// lsub[i] == T[i + 1, i]
// r = sqrt(T[i, i]^2 + T[i + 1, i]^2)
// c = T[i, i] / r, s = -T[i + 1, i] / r
this->compute_rotation(m_T_diag.coeff(i), m_T_lsub.coeff(i), r, *c, *s);
// Rdiag[i] == R[i, i]
// Tsubd[i] == R[i + 1, i]
// r = sqrt(R[i, i]^2 + R[i + 1, i]^2)
// c = R[i, i] / r, s = -R[i + 1, i] / r
this->compute_rotation(m_R_diag.coeff(i), m_T_subd.coeff(i), r, *c, *s);
// For a complete QR decomposition,
// we first obtain the rotation matrix
// G = [ cos sin]
// [-sin cos]
// and then do T[i:(i + 1), i:(i + 2)] = G' * T[i:(i + 1), i:(i + 2)]
// and then do R[i:(i + 1), i:(i + 2)] = G' * R[i:(i + 1), i:(i + 2)]
// Update T[i, i] and T[i + 1, i]
// The updated value of T[i, i] is known to be r
// The updated value of T[i + 1, i] is known to be 0
m_T_diag.coeffRef(i) = r;
m_T_lsub.coeffRef(i) = Scalar(0);
// Update T[i, i + 1] and T[i + 1, i + 1]
// usub[i] == T[i, i + 1]
// diag[i + 1] == T[i + 1, i + 1]
const Scalar tmp = m_T_usub.coeff(i);
m_T_usub.coeffRef(i) = (*c) * tmp - (*s) * m_T_diag.coeff(i + 1);
m_T_diag.coeffRef(i + 1) = (*s) * tmp + (*c) * m_T_diag.coeff(i + 1);
// Update T[i, i + 2] and T[i + 1, i + 2]
// usub2[i] == T[i, i + 2]
// usub[i + 1] == T[i + 1, i + 2]
if (i < n1 - 1)
// Update R[i, i] and R[i + 1, i]
// The updated value of R[i, i] is known to be r
// The updated value of R[i + 1, i] is known to be 0
m_R_diag.coeffRef(i) = r;
// Update R[i, i + 1] and R[i + 1, i + 1]
// Rsupd[i] == R[i, i + 1]
// Rdiag[i + 1] == R[i + 1, i + 1]
const Scalar Tii1 = m_R_supd.coeff(i);
const Scalar Ti1i1 = m_R_diag.coeff(i + 1);
m_R_supd.coeffRef(i) = (*c) * Tii1 - (*s) * Ti1i1;
m_R_diag.coeffRef(i + 1) = (*s) * Tii1 + (*c) * Ti1i1;
// Update R[i, i + 2] and R[i + 1, i + 2]
// Rsupd2[i] == R[i, i + 2]
// Rsupd[i + 1] == R[i + 1, i + 2]
if (i < n2)
{
m_T_usub2.coeffRef(i) = -(*s) * m_T_usub.coeff(i + 1);
m_T_usub.coeffRef(i + 1) *= (*c);
m_R_supd2.coeffRef(i) = -(*s) * m_R_supd.coeff(i + 1);
m_R_supd.coeffRef(i + 1) *= (*c);
}
c++;
@ -585,12 +675,12 @@ public:
// If we do not need to calculate the R matrix, then
// only the cos and sin sequences are required.
// In such case we only update T[i + 1, (i + 1):(i + 2)]
// T[i + 1, i + 1] = c * T[i + 1, i + 1] + s * T[i, i + 1];
// T[i + 1, i + 2] *= c;
// In such case we only update R[i + 1, (i + 1):(i + 2)]
// R[i + 1, i + 1] = c * R[i + 1, i + 1] + s * R[i, i + 1];
// R[i + 1, i + 2] *= c;
}
this->m_computed = true;
m_computed = true;
}
///
@ -600,64 +690,107 @@ public:
/// \return Returned matrix type will be `Eigen::Matrix<Scalar, ...>`, depending on
/// the template parameter `Scalar` defined.
///
Matrix matrix_R() const
Matrix matrix_R() const override
{
if (!this->m_computed)
if (!m_computed)
throw std::logic_error("TridiagQR: need to call compute() first");
Matrix R = Matrix::Zero(this->m_n, this->m_n);
R.diagonal().noalias() = m_T_diag;
R.diagonal(1).noalias() = m_T_usub;
R.diagonal(2).noalias() = m_T_usub2;
Matrix R = Matrix::Zero(m_n, m_n);
R.diagonal().noalias() = m_R_diag;
R.diagonal(1).noalias() = m_R_supd;
R.diagonal(2).noalias() = m_R_supd2;
return R;
}
///
/// Overwrite `dest` with \f$Q'HQ = RQ + sI\f$, where \f$H\f$ is the input matrix `mat`,
/// Overwrite `dest` with \f$Q'TQ = RQ + sI\f$, where \f$T\f$ is the input matrix `mat`,
/// and \f$s\f$ is the shift. The result is a tridiagonal matrix.
///
/// \param mat The matrix to be overwritten, whose type should be `Eigen::Matrix<Scalar, ...>`,
/// depending on the template parameter `Scalar` defined.
///
void matrix_QtHQ(Matrix& dest) const
void matrix_QtHQ(Matrix& dest) const override
{
if (!this->m_computed)
using std::abs;
if (!m_computed)
throw std::logic_error("TridiagQR: need to call compute() first");
// Make a copy of the R matrix
dest.resize(this->m_n, this->m_n);
// In exact arithmetics, Q'TQ = RQ + sI, so we can just apply Q to R and add the shift.
// However, some numerical examples show that this algorithm decreases the precision,
// so we directly apply Q' and Q to T.
// Copy the saved diagonal and subdiagonal elements of T to `dest`
dest.resize(m_n, m_n);
dest.setZero();
dest.diagonal().noalias() = m_T_diag;
// The upper diagonal refers to m_T_usub
// The 2nd upper subdiagonal will be zero in RQ
dest.diagonal(-1).noalias() = m_T_subd;
// Compute the RQ matrix
// [m11 m12] points to RQ[i:(i+1), i:(i+1)]
// [0 m22]
// Ti = [x y 0], Gi = [ cos[i] sin[i] 0], Gi' * Ti * Gi = [x' y' o']
// [y z w] [-sin[i] cos[i] 0] [y' z' w']
// [0 w u] [ 0 0 1] [o' w' u']
//
// Gi = [ cos[i] sin[i]]
// [-sin[i] cos[i]]
const Index n1 = this->m_n - 1;
// x' = c2*x - 2*c*s*y + s2*z
// y' = c*s*(x-z) + (c2-s2)*y
// z' = s2*x + 2*c*s*y + c2*z
// o' = -s*w, w' = c*w, u' = u
//
// In iteration (i+1), (y', o') will be further updated to (y'', o''),
// where o'' = 0, y'' = cos[i+1]*y' - sin[i+1]*o'
const Index n1 = m_n - 1, n2 = m_n - 2;
for (Index i = 0; i < n1; i++)
{
const Scalar c = this->m_rot_cos.coeff(i);
const Scalar s = this->m_rot_sin.coeff(i);
const Scalar m11 = dest.coeff(i, i),
m12 = m_T_usub.coeff(i),
m22 = m_T_diag.coeff(i + 1);
const Scalar c = m_rot_cos.coeff(i);
const Scalar s = m_rot_sin.coeff(i);
const Scalar cs = c * s, c2 = c * c, s2 = s * s;
const Scalar x = dest.coeff(i, i),
y = dest.coeff(i + 1, i),
z = dest.coeff(i + 1, i + 1);
const Scalar c2x = c2 * x, s2x = s2 * x, c2z = c2 * z, s2z = s2 * z;
const Scalar csy2 = Scalar(2) * c * s * y;
// Update the diagonal and the lower subdiagonal of dest
dest.coeffRef(i, i) = c * m11 - s * m12;
dest.coeffRef(i + 1, i) = -s * m22;
dest.coeffRef(i + 1, i + 1) = c * m22;
dest.coeffRef(i, i) = c2x - csy2 + s2z; // x'
dest.coeffRef(i + 1, i) = cs * (x - z) + (c2 - s2) * y; // y'
dest.coeffRef(i + 1, i + 1) = s2x + csy2 + c2z; // z'
if (i < n2)
{
const Scalar ci1 = m_rot_cos.coeff(i + 1);
const Scalar si1 = m_rot_sin.coeff(i + 1);
const Scalar o = -s * m_T_subd.coeff(i + 1); // o'
dest.coeffRef(i + 2, i + 1) *= c; // w'
dest.coeffRef(i + 1, i) = ci1 * dest.coeff(i + 1, i) - si1 * o; // y''
}
}
// Deflation of small sub-diagonal elements
const Scalar eps = TypeTraits<Scalar>::epsilon();
for (Index i = 0; i < n1; i++)
{
const Scalar diag = abs(dest.coeff(i, i)) + abs(dest.coeff(i + 1, i + 1));
if (abs(dest.coeff(i + 1, i)) <= eps * diag)
dest.coeffRef(i + 1, i) = Scalar(0);
}
// Copy the lower subdiagonal to upper subdiagonal
dest.diagonal(1).noalias() = dest.diagonal(-1);
}
// Add the shift to the diagonal
dest.diagonal().array() += this->m_shift;
///
/// The version of matrix_QtHQ() when `dest` has a complex value type.
///
/// This is used in Hermitian eigen solvers where the result is stored
/// as a complex matrix.
///
void matrix_QtHQ(ComplexMatrix& dest) const
{
// Simply compute the real-typed result and copy to the complex one
Matrix dest_real;
this->matrix_QtHQ(dest_real);
dest.resize(m_n, m_n);
dest.noalias() = dest_real.template cast<std::complex<Scalar>>();
}
};
@ -667,4 +800,4 @@ public:
} // namespace Spectra
#endif // UPPER_HESSENBERG_QR_H
#endif // SPECTRA_UPPER_HESSENBERG_QR_H

450
gtsam/3rdparty/Spectra/LinAlg/UpperHessenbergSchur.h vendored Normal file
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@ -0,0 +1,450 @@
// The code was adapted from Eigen/src/Eigenvaleus/RealSchur.h
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
// Copyright (C) 2021-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_UPPER_HESSENBERG_SCHUR_H
#define SPECTRA_UPPER_HESSENBERG_SCHUR_H
#include <Eigen/Core>
#include <Eigen/Jacobi>
#include <Eigen/Householder>
#include <stdexcept>
#include "../Util/TypeTraits.h"
namespace Spectra {
template <typename Scalar = double>
class UpperHessenbergSchur
{
private:
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using Vector2s = Eigen::Matrix<Scalar, 2, 1>;
using Vector3s = Eigen::Matrix<Scalar, 3, 1>;
using GenericMatrix = Eigen::Ref<Matrix>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
Index m_n; // Size of the matrix
Matrix m_T; // T matrix, A = UTU'
Matrix m_U; // U matrix, A = UTU'
bool m_computed;
// L1 norm of an upper Hessenberg matrix
static Scalar upper_hessenberg_l1_norm(ConstGenericMatrix& x)
{
const Index n = x.cols();
Scalar norm(0);
for (Index j = 0; j < n; j++)
norm += x.col(j).segment(0, (std::min)(n, j + 2)).cwiseAbs().sum();
return norm;
}
// Look for single small sub-diagonal element and returns its index
Index find_small_subdiag(Index iu, const Scalar& near_0) const
{
using std::abs;
const Scalar eps = Eigen::NumTraits<Scalar>::epsilon();
Index res = iu;
while (res > 0)
{
Scalar s = abs(m_T.coeff(res - 1, res - 1)) + abs(m_T.coeff(res, res));
s = Eigen::numext::maxi<Scalar>(s * eps, near_0);
if (abs(m_T.coeff(res, res - 1)) <= s)
break;
res--;
}
return res;
}
// Update T given that rows iu-1 and iu decouple from the rest
void split_off_two_rows(Index iu, const Scalar& ex_shift)
{
using std::sqrt;
using std::abs;
// The eigenvalues of the 2x2 matrix [a b; c d] are
// trace +/- sqrt(discr/4) where discr = tr^2 - 4*det, tr = a + d, det = ad - bc
Scalar p = Scalar(0.5) * (m_T.coeff(iu - 1, iu - 1) - m_T.coeff(iu, iu));
Scalar q = p * p + m_T.coeff(iu, iu - 1) * m_T.coeff(iu - 1, iu); // q = tr^2 / 4 - det = discr/4
m_T.coeffRef(iu, iu) += ex_shift;
m_T.coeffRef(iu - 1, iu - 1) += ex_shift;
if (q >= Scalar(0)) // Two real eigenvalues
{
Scalar z = sqrt(abs(q));
Eigen::JacobiRotation<Scalar> rot;
rot.makeGivens((p >= Scalar(0)) ? (p + z) : (p - z), m_T.coeff(iu, iu - 1));
m_T.rightCols(m_n - iu + 1).applyOnTheLeft(iu - 1, iu, rot.adjoint());
m_T.topRows(iu + 1).applyOnTheRight(iu - 1, iu, rot);
m_T.coeffRef(iu, iu - 1) = Scalar(0);
m_U.applyOnTheRight(iu - 1, iu, rot);
}
if (iu > 1)
m_T.coeffRef(iu - 1, iu - 2) = Scalar(0);
}
// Form shift in shift_info, and update ex_shift if an exceptional shift is performed
void compute_shift(Index iu, Index iter, Scalar& ex_shift, Vector3s& shift_info)
{
using std::sqrt;
using std::abs;
shift_info.coeffRef(0) = m_T.coeff(iu, iu);
shift_info.coeffRef(1) = m_T.coeff(iu - 1, iu - 1);
shift_info.coeffRef(2) = m_T.coeff(iu, iu - 1) * m_T.coeff(iu - 1, iu);
// Wilkinson's original ad hoc shift
if (iter == 10)
{
ex_shift += shift_info.coeff(0);
for (Index i = 0; i <= iu; ++i)
m_T.coeffRef(i, i) -= shift_info.coeff(0);
Scalar s = abs(m_T.coeff(iu, iu - 1)) + abs(m_T.coeff(iu - 1, iu - 2));
shift_info.coeffRef(0) = Scalar(0.75) * s;
shift_info.coeffRef(1) = Scalar(0.75) * s;
shift_info.coeffRef(2) = Scalar(-0.4375) * s * s;
}
// MATLAB's new ad hoc shift
if (iter == 30)
{
Scalar s = (shift_info.coeff(1) - shift_info.coeff(0)) / Scalar(2);
s = s * s + shift_info.coeff(2);
if (s > Scalar(0))
{
s = sqrt(s);
if (shift_info.coeff(1) < shift_info.coeff(0))
s = -s;
s = s + (shift_info.coeff(1) - shift_info.coeff(0)) / Scalar(2);
s = shift_info.coeff(0) - shift_info.coeff(2) / s;
ex_shift += s;
for (Index i = 0; i <= iu; ++i)
m_T.coeffRef(i, i) -= s;
shift_info.setConstant(Scalar(0.964));
}
}
}
// Compute index im at which Francis QR step starts and the first Householder vector
void init_francis_qr_step(Index il, Index iu, const Vector3s& shift_info, Index& im, Vector3s& first_householder_vec) const
{
using std::abs;
const Scalar eps = Eigen::NumTraits<Scalar>::epsilon();
Vector3s& v = first_householder_vec; // alias to save typing
for (im = iu - 2; im >= il; --im)
{
const Scalar Tmm = m_T.coeff(im, im);
const Scalar r = shift_info.coeff(0) - Tmm;
const Scalar s = shift_info.coeff(1) - Tmm;
v.coeffRef(0) = (r * s - shift_info.coeff(2)) / m_T.coeff(im + 1, im) + m_T.coeff(im, im + 1);
v.coeffRef(1) = m_T.coeff(im + 1, im + 1) - Tmm - r - s;
v.coeffRef(2) = m_T.coeff(im + 2, im + 1);
if (im == il)
break;
const Scalar lhs = m_T.coeff(im, im - 1) * (abs(v.coeff(1)) + abs(v.coeff(2)));
const Scalar rhs = v.coeff(0) * (abs(m_T.coeff(im - 1, im - 1)) + abs(Tmm) + abs(m_T.coeff(im + 1, im + 1)));
if (abs(lhs) < eps * rhs)
break;
}
}
// P = I - tau * v * v' = P'
// PX = X - tau * v * (v'X), X [3 x c]
static void apply_householder_left(const Vector2s& ess, const Scalar& tau, Scalar* x, Index ncol, Index stride)
{
const Scalar v1 = ess.coeff(0), v2 = ess.coeff(1);
const Scalar* const x_end = x + ncol * stride;
for (; x < x_end; x += stride)
{
const Scalar tvx = tau * (x[0] + v1 * x[1] + v2 * x[2]);
x[0] -= tvx;
x[1] -= tvx * v1;
x[2] -= tvx * v2;
}
}
// P = I - tau * v * v' = P'
// XP = X - tau * (X * v) * v', X [r x 3]
static void apply_householder_right(const Vector2s& ess, const Scalar& tau, Scalar* x, Index nrow, Index stride)
{
const Scalar v1 = ess.coeff(0), v2 = ess.coeff(1);
Scalar* x0 = x;
Scalar* x1 = x + stride;
Scalar* x2 = x1 + stride;
for (Index i = 0; i < nrow; i++)
{
const Scalar txv = tau * (x0[i] + v1 * x1[i] + v2 * x2[i]);
x0[i] -= txv;
x1[i] -= txv * v1;
x2[i] -= txv * v2;
}
}
// SIMD version of apply_householder_right()
// Inspired by apply_rotation_in_the_plane_selector() in Eigen/src/Jacobi/Jacobi.h
static void apply_householder_right_simd(const Vector2s& ess, const Scalar& tau, Scalar* x, Index nrow, Index stride)
{
// Packet type
using Eigen::internal::ploadu;
using Eigen::internal::pstoreu;
using Eigen::internal::pset1;
using Eigen::internal::padd;
using Eigen::internal::psub;
using Eigen::internal::pmul;
using Packet = typename Eigen::internal::packet_traits<Scalar>::type;
constexpr unsigned char PacketSize = Eigen::internal::packet_traits<Scalar>::size;
constexpr unsigned char Peeling = 2;
constexpr unsigned char Increment = Peeling * PacketSize;
// Column heads
Scalar* x0 = x;
Scalar* x1 = x + stride;
Scalar* x2 = x1 + stride;
// Pointers for the current row
Scalar* px0 = x0;
Scalar* px1 = x1;
Scalar* px2 = x2;
// Householder reflectors
const Scalar v1 = ess.coeff(0), v2 = ess.coeff(1);
// Vectorized versions
const Packet vtau = pset1<Packet>(tau);
const Packet vv1 = pset1<Packet>(v1);
const Packet vv2 = pset1<Packet>(v2);
// n % (2^k) == n & (2^k-1), see https://stackoverflow.com/q/3072665
// const Index peeling_end = nrow - nrow % Increment;
const Index aligned_end = nrow - (nrow & (PacketSize - 1));
const Index peeling_end = nrow - (nrow & (Increment - 1));
for (Index i = 0; i < peeling_end; i += Increment)
{
Packet vx01 = ploadu<Packet>(px0);
Packet vx02 = ploadu<Packet>(px0 + PacketSize);
Packet vx11 = ploadu<Packet>(px1);
Packet vx12 = ploadu<Packet>(px1 + PacketSize);
Packet vx21 = ploadu<Packet>(px2);
Packet vx22 = ploadu<Packet>(px2 + PacketSize);
// Packet txv1 = vtau * (vx01 + vv1 * vx11 + vv2 * vx21);
Packet txv1 = pmul(vtau, padd(padd(vx01, pmul(vv1, vx11)), pmul(vv2, vx21)));
Packet txv2 = pmul(vtau, padd(padd(vx02, pmul(vv1, vx12)), pmul(vv2, vx22)));
pstoreu(px0, psub(vx01, txv1));
pstoreu(px0 + PacketSize, psub(vx02, txv2));
pstoreu(px1, psub(vx11, pmul(txv1, vv1)));
pstoreu(px1 + PacketSize, psub(vx12, pmul(txv2, vv1)));
pstoreu(px2, psub(vx21, pmul(txv1, vv2)));
pstoreu(px2 + PacketSize, psub(vx22, pmul(txv2, vv2)));
px0 += Increment;
px1 += Increment;
px2 += Increment;
}
if (aligned_end != peeling_end)
{
px0 = x0 + peeling_end;
px1 = x1 + peeling_end;
px2 = x2 + peeling_end;
Packet x0_p = ploadu<Packet>(px0);
Packet x1_p = ploadu<Packet>(px1);
Packet x2_p = ploadu<Packet>(px2);
Packet txv = pmul(vtau, padd(padd(x0_p, pmul(vv1, x1_p)), pmul(vv2, x2_p)));
pstoreu(px0, psub(x0_p, txv));
pstoreu(px1, psub(x1_p, pmul(txv, vv1)));
pstoreu(px2, psub(x2_p, pmul(txv, vv2)));
}
// Remaining rows
for (Index i = aligned_end; i < nrow; i++)
{
const Scalar txv = tau * (x0[i] + v1 * x1[i] + v2 * x2[i]);
x0[i] -= txv;
x1[i] -= txv * v1;
x2[i] -= txv * v2;
}
}
// Perform a Francis QR step involving rows il:iu and columns im:iu
void perform_francis_qr_step(Index il, Index im, Index iu, const Vector3s& first_householder_vec, const Scalar& near_0)
{
using std::abs;
for (Index k = im; k <= iu - 2; ++k)
{
const bool first_iter = (k == im);
Vector3s v;
if (first_iter)
v = first_householder_vec;
else
v = m_T.template block<3, 1>(k, k - 1);
Scalar tau, beta;
Vector2s ess;
v.makeHouseholder(ess, tau, beta);
if (abs(beta) > near_0) // if v is not zero
{
if (first_iter && k > il)
m_T.coeffRef(k, k - 1) = -m_T.coeff(k, k - 1);
else if (!first_iter)
m_T.coeffRef(k, k - 1) = beta;
// These Householder transformations form the O(n^3) part of the algorithm
// m_T.block(k, k, 3, m_n - k).applyHouseholderOnTheLeft(ess, tau, workspace);
// m_T.block(0, k, (std::min)(iu, k + 3) + 1, 3).applyHouseholderOnTheRight(ess, tau, workspace);
// m_U.block(0, k, m_n, 3).applyHouseholderOnTheRight(ess, tau, workspace);
apply_householder_left(ess, tau, &m_T.coeffRef(k, k), m_n - k, m_n);
apply_householder_right_simd(ess, tau, &m_T.coeffRef(0, k), (std::min)(iu, k + 3) + 1, m_n);
apply_householder_right_simd(ess, tau, &m_U.coeffRef(0, k), m_n, m_n);
}
}
// The last 2-row block
Eigen::JacobiRotation<Scalar> rot;
Scalar beta;
rot.makeGivens(m_T.coeff(iu - 1, iu - 2), m_T.coeff(iu, iu - 2), &beta);
if (abs(beta) > near_0) // if v is not zero
{
m_T.coeffRef(iu - 1, iu - 2) = beta;
m_T.rightCols(m_n - iu + 1).applyOnTheLeft(iu - 1, iu, rot.adjoint());
m_T.topRows(iu + 1).applyOnTheRight(iu - 1, iu, rot);
m_U.applyOnTheRight(iu - 1, iu, rot);
}
// clean up pollution due to round-off errors
for (Index i = im + 2; i <= iu; ++i)
{
m_T.coeffRef(i, i - 2) = Scalar(0);
if (i > im + 2)
m_T.coeffRef(i, i - 3) = Scalar(0);
}
}
public:
UpperHessenbergSchur() :
m_n(0), m_computed(false)
{}
UpperHessenbergSchur(ConstGenericMatrix& mat) :
m_n(mat.rows()), m_computed(false)
{
compute(mat);
}
void compute(ConstGenericMatrix& mat)
{
using std::abs;
using std::sqrt;
if (mat.rows() != mat.cols())
throw std::invalid_argument("UpperHessenbergSchur: matrix must be square");
m_n = mat.rows();
m_T.resize(m_n, m_n);
m_U.resize(m_n, m_n);
constexpr Index max_iter_per_row = 40;
const Index max_iter = m_n * max_iter_per_row;
m_T.noalias() = mat;
m_U.setIdentity();
// The matrix m_T is divided in three parts.
// Rows 0,...,il-1 are decoupled from the rest because m_T(il,il-1) is zero.
// Rows il,...,iu is the part we are working on (the active window).
// Rows iu+1,...,end are already brought in triangular form.
Index iu = m_n - 1;
Index iter = 0; // iteration count for current eigenvalue
Index total_iter = 0; // iteration count for whole matrix
Scalar ex_shift(0); // sum of exceptional shifts
const Scalar norm = upper_hessenberg_l1_norm(m_T);
// sub-diagonal entries smaller than near_0 will be treated as zero.
// We use eps^2 to enable more precision in small eigenvalues.
const Scalar eps = Eigen::NumTraits<Scalar>::epsilon();
const Scalar near_0 = Eigen::numext::maxi<Scalar>(norm * eps * eps, TypeTraits<Scalar>::min());
if (norm != Scalar(0))
{
while (iu >= 0)
{
Index il = find_small_subdiag(iu, near_0);
// Check for convergence
if (il == iu) // One root found
{
m_T.coeffRef(iu, iu) += ex_shift;
if (iu > 0)
m_T.coeffRef(iu, iu - 1) = Scalar(0);
iu--;
iter = 0;
}
else if (il == iu - 1) // Two roots found
{
split_off_two_rows(iu, ex_shift);
iu -= 2;
iter = 0;
}
else // No convergence yet
{
Vector3s first_householder_vec = Vector3s::Zero(), shift_info;
compute_shift(iu, iter, ex_shift, shift_info);
iter++;
total_iter++;
if (total_iter > max_iter)
break;
Index im;
init_francis_qr_step(il, iu, shift_info, im, first_householder_vec);
perform_francis_qr_step(il, im, iu, first_householder_vec, near_0);
}
}
}
if (total_iter > max_iter)
throw std::runtime_error("UpperHessenbergSchur: Schur decomposition failed");
m_computed = true;
}
const Matrix& matrix_T() const
{
if (!m_computed)
throw std::logic_error("UpperHessenbergSchur: need to call compute() first");
return m_T;
}
const Matrix& matrix_U() const
{
if (!m_computed)
throw std::logic_error("UpperHessenbergSchur: need to call compute() first");
return m_U;
}
void swap_T(Matrix& other)
{
m_T.swap(other);
}
void swap_U(Matrix& other)
{
m_U.swap(other);
}
};
} // namespace Spectra
#endif // SPECTRA_UPPER_HESSENBERG_SCHUR_H

55
gtsam/3rdparty/Spectra/MatOp/DenseCholesky.h vendored
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@ -1,15 +1,16 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef DENSE_CHOLESKY_H
#define DENSE_CHOLESKY_H
#ifndef SPECTRA_DENSE_CHOLESKY_H
#define SPECTRA_DENSE_CHOLESKY_H
#include <Eigen/Core>
#include <Eigen/Cholesky>
#include <stdexcept>
#include "../Util/CompInfo.h"
namespace Spectra {
@ -22,21 +23,32 @@ namespace Spectra {
/// matrix. It is mainly used in the SymGEigsSolver generalized eigen solver
/// in the Cholesky decomposition mode.
///
template <typename Scalar, int Uplo = Eigen::Lower>
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Uplo Either `Eigen::Lower` or `Eigen::Upper`, indicating which
/// triangular part of the matrix is used.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
///
template <typename Scalar_, int Uplo = Eigen::Lower, int Flags = Eigen::ColMajor>
class DenseCholesky
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Matrix> MapConstMat;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flags>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
const Index m_n;
Eigen::LLT<Matrix, Uplo> m_decomp;
int m_info; // status of the decomposition
CompInfo m_info; // status of the decomposition
public:
///
@ -47,16 +59,21 @@ public:
/// `Eigen::MatrixXf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
///
DenseCholesky(ConstGenericMatrix& mat) :
m_n(mat.rows()), m_info(NOT_COMPUTED)
template <typename Derived>
DenseCholesky(const Eigen::MatrixBase<Derived>& mat) :
m_n(mat.rows()), m_info(CompInfo::NotComputed)
{
if (mat.rows() != mat.cols())
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(Matrix::IsRowMajor),
"DenseCholesky: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
if (m_n != mat.cols())
throw std::invalid_argument("DenseCholesky: matrix must be square");
m_decomp.compute(mat);
m_info = (m_decomp.info() == Eigen::Success) ?
SUCCESSFUL :
NUMERICAL_ISSUE;
CompInfo::Successful :
CompInfo::NumericalIssue;
}
///
@ -72,7 +89,7 @@ public:
/// Returns the status of the computation.
/// The full list of enumeration values can be found in \ref Enumerations.
///
int info() const { return m_info; }
CompInfo info() const { return m_info; }
///
/// Performs the lower triangular solving operation \f$y=L^{-1}x\f$.
@ -105,4 +122,4 @@ public:
} // namespace Spectra
#endif // DENSE_CHOLESKY_H
#endif // SPECTRA_DENSE_CHOLESKY_H

54
gtsam/3rdparty/Spectra/MatOp/DenseGenComplexShiftSolve.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef DENSE_GEN_COMPLEX_SHIFT_SOLVE_H
#define DENSE_GEN_COMPLEX_SHIFT_SOLVE_H
#ifndef SPECTRA_DENSE_GEN_COMPLEX_SHIFT_SOLVE_H
#define SPECTRA_DENSE_GEN_COMPLEX_SHIFT_SOLVE_H
#include <Eigen/Core>
#include <Eigen/LU>
@ -21,27 +21,38 @@ namespace Spectra {
/// \f$\sigma\f$ and real-valued vector \f$x\f$. It is mainly used in the
/// GenEigsComplexShiftSolver eigen solver.
///
template <typename Scalar>
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
///
template <typename Scalar_, int Flags = Eigen::ColMajor>
class DenseGenComplexShiftSolve
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flags>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
typedef std::complex<Scalar> Complex;
typedef Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic> ComplexMatrix;
typedef Eigen::Matrix<Complex, Eigen::Dynamic, 1> ComplexVector;
using Complex = std::complex<Scalar>;
using ComplexMatrix = Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic, Flags>;
using ComplexVector = Eigen::Matrix<Complex, Eigen::Dynamic, 1>;
typedef Eigen::PartialPivLU<ComplexMatrix> ComplexSolver;
using ComplexSolver = Eigen::PartialPivLU<ComplexMatrix>;
ConstGenericMatrix m_mat;
const Index m_n;
ComplexSolver m_solver;
ComplexVector m_x_cache;
mutable ComplexVector m_x_cache;
public:
///
@ -52,9 +63,14 @@ public:
/// `Eigen::MatrixXf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
///
DenseGenComplexShiftSolve(ConstGenericMatrix& mat) :
template <typename Derived>
DenseGenComplexShiftSolve(const Eigen::MatrixBase<Derived>& mat) :
m_mat(mat), m_n(mat.rows())
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(Matrix::IsRowMajor),
"DenseGenComplexShiftSolve: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
if (mat.rows() != mat.cols())
throw std::invalid_argument("DenseGenComplexShiftSolve: matrix must be square");
}
@ -74,7 +90,7 @@ public:
/// \param sigmar Real part of \f$\sigma\f$.
/// \param sigmai Imaginary part of \f$\sigma\f$.
///
void set_shift(Scalar sigmar, Scalar sigmai)
void set_shift(const Scalar& sigmar, const Scalar& sigmai)
{
m_solver.compute(m_mat.template cast<Complex>() - Complex(sigmar, sigmai) * ComplexMatrix::Identity(m_n, m_n));
m_x_cache.resize(m_n);
@ -89,7 +105,7 @@ public:
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = Re( inv(A - sigma * I) * x_in )
void perform_op(const Scalar* x_in, Scalar* y_out)
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
m_x_cache.real() = MapConstVec(x_in, m_n);
MapVec y(y_out, m_n);
@ -99,4 +115,4 @@ public:
} // namespace Spectra
#endif // DENSE_GEN_COMPLEX_SHIFT_SOLVE_H
#endif // SPECTRA_DENSE_GEN_COMPLEX_SHIFT_SOLVE_H

58
gtsam/3rdparty/Spectra/MatOp/DenseGenMatProd.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef DENSE_GEN_MAT_PROD_H
#define DENSE_GEN_MAT_PROD_H
#ifndef SPECTRA_DENSE_GEN_MAT_PROD_H
#define SPECTRA_DENSE_GEN_MAT_PROD_H
#include <Eigen/Core>
@ -25,16 +25,27 @@ namespace Spectra {
/// \f$x\f$. It is mainly used in the GenEigsSolver and
/// SymEigsSolver eigen solvers.
///
template <typename Scalar>
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
///
template <typename Scalar_, int Flags = Eigen::ColMajor>
class DenseGenMatProd
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flags>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
ConstGenericMatrix m_mat;
@ -47,9 +58,14 @@ public:
/// `Eigen::MatrixXf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
///
DenseGenMatProd(ConstGenericMatrix& mat) :
template <typename Derived>
DenseGenMatProd(const Eigen::MatrixBase<Derived>& mat) :
m_mat(mat)
{}
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(Matrix::IsRowMajor),
"DenseGenMatProd: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
}
///
/// Return the number of rows of the underlying matrix.
@ -73,8 +89,24 @@ public:
MapVec y(y_out, m_mat.rows());
y.noalias() = m_mat * x;
}
///
/// Perform the matrix-matrix multiplication operation \f$y=Ax\f$.
///
Matrix operator*(const Eigen::Ref<const Matrix>& mat_in) const
{
return m_mat * mat_in;
}
///
/// Extract (i,j) element of the underlying matrix.
///
Scalar operator()(Index i, Index j) const
{
return m_mat(i, j);
}
};
} // namespace Spectra
#endif // DENSE_GEN_MAT_PROD_H
#endif // SPECTRA_DENSE_GEN_MAT_PROD_H

42
gtsam/3rdparty/Spectra/MatOp/DenseGenRealShiftSolve.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef DENSE_GEN_REAL_SHIFT_SOLVE_H
#define DENSE_GEN_REAL_SHIFT_SOLVE_H
#ifndef SPECTRA_DENSE_GEN_REAL_SHIFT_SOLVE_H
#define SPECTRA_DENSE_GEN_REAL_SHIFT_SOLVE_H
#include <Eigen/Core>
#include <Eigen/LU>
@ -20,16 +20,27 @@ namespace Spectra {
/// i.e., calculating \f$y=(A-\sigma I)^{-1}x\f$ for any real \f$\sigma\f$ and
/// vector \f$x\f$. It is mainly used in the GenEigsRealShiftSolver eigen solver.
///
template <typename Scalar>
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
///
template <typename Scalar_, int Flags = Eigen::ColMajor>
class DenseGenRealShiftSolve
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flags>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
ConstGenericMatrix m_mat;
const Index m_n;
@ -44,9 +55,14 @@ public:
/// `Eigen::MatrixXf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
///
DenseGenRealShiftSolve(ConstGenericMatrix& mat) :
template <typename Derived>
DenseGenRealShiftSolve(const Eigen::MatrixBase<Derived>& mat) :
m_mat(mat), m_n(mat.rows())
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(Matrix::IsRowMajor),
"DenseGenRealShiftSolve: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
if (mat.rows() != mat.cols())
throw std::invalid_argument("DenseGenRealShiftSolve: matrix must be square");
}
@ -63,7 +79,7 @@ public:
///
/// Set the real shift \f$\sigma\f$.
///
void set_shift(Scalar sigma)
void set_shift(const Scalar& sigma)
{
m_solver.compute(m_mat - sigma * Matrix::Identity(m_n, m_n));
}
@ -85,4 +101,4 @@ public:
} // namespace Spectra
#endif // DENSE_GEN_REAL_SHIFT_SOLVE_H
#endif // SPECTRA_DENSE_GEN_REAL_SHIFT_SOLVE_H

92
gtsam/3rdparty/Spectra/MatOp/DenseHermMatProd.h vendored Normal file
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@ -0,0 +1,92 @@
// Copyright (C) 2024-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_DENSE_HERM_MAT_PROD_H
#define SPECTRA_DENSE_HERM_MAT_PROD_H
#include <Eigen/Core>
namespace Spectra {
///
/// \ingroup MatOp
///
/// This class defines the matrix-vector multiplication operation on a
/// Hermitian complex matrix \f$A\f$, i.e., calculating \f$y=Ax\f$ for any vector
/// \f$x\f$. It is mainly used in the HermEigsSolver eigen solver.
///
/// \tparam Scalar_ The element type of the matrix, for example,
/// `std::complex<float>`, `std::complex<double>`,
/// and `std::complex<long double>`.
/// \tparam Uplo Either `Eigen::Lower` or `Eigen::Upper`, indicating which
/// triangular part of the matrix is used.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
///
template <typename Scalar_, int Uplo = Eigen::Lower, int Flags = Eigen::ColMajor>
class DenseHermMatProd
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flags>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
ConstGenericMatrix m_mat;
public:
///
/// Constructor to create the matrix operation object.
///
/// \param mat An **Eigen** matrix object, whose type can be
/// `Eigen::Matrix<Scalar, ...>` (e.g. `Eigen::MatrixXcd` and
/// `Eigen::MatrixXcf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXcd>`).
///
template <typename Derived>
DenseHermMatProd(const Eigen::MatrixBase<Derived>& mat) :
m_mat(mat)
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(Matrix::IsRowMajor),
"DenseHermMatProd: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
}
///
/// Return the number of rows of the underlying matrix.
///
Index rows() const { return m_mat.rows(); }
///
/// Return the number of columns of the underlying matrix.
///
Index cols() const { return m_mat.cols(); }
///
/// Perform the matrix-vector multiplication operation \f$y=Ax\f$.
///
/// \param x_in Pointer to the \f$x\f$ vector.
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = A * x_in
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
MapConstVec x(x_in, m_mat.cols());
MapVec y(y_out, m_mat.rows());
y.noalias() = m_mat.template selfadjointView<Uplo>() * x;
}
};
} // namespace Spectra
#endif // SPECTRA_DENSE_HERM_MAT_PROD_H

60
gtsam/3rdparty/Spectra/MatOp/DenseSymMatProd.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef DENSE_SYM_MAT_PROD_H
#define DENSE_SYM_MAT_PROD_H
#ifndef SPECTRA_DENSE_SYM_MAT_PROD_H
#define SPECTRA_DENSE_SYM_MAT_PROD_H
#include <Eigen/Core>
@ -18,16 +18,29 @@ namespace Spectra {
/// symmetric real matrix \f$A\f$, i.e., calculating \f$y=Ax\f$ for any vector
/// \f$x\f$. It is mainly used in the SymEigsSolver eigen solver.
///
template <typename Scalar, int Uplo = Eigen::Lower>
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Uplo Either `Eigen::Lower` or `Eigen::Upper`, indicating which
/// triangular part of the matrix is used.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
///
template <typename Scalar_, int Uplo = Eigen::Lower, int Flags = Eigen::ColMajor>
class DenseSymMatProd
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flags>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
ConstGenericMatrix m_mat;
@ -40,9 +53,14 @@ public:
/// `Eigen::MatrixXf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
///
DenseSymMatProd(ConstGenericMatrix& mat) :
template <typename Derived>
DenseSymMatProd(const Eigen::MatrixBase<Derived>& mat) :
m_mat(mat)
{}
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(Matrix::IsRowMajor),
"DenseSymMatProd: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
}
///
/// Return the number of rows of the underlying matrix.
@ -66,8 +84,24 @@ public:
MapVec y(y_out, m_mat.rows());
y.noalias() = m_mat.template selfadjointView<Uplo>() * x;
}
///
/// Perform the matrix-matrix multiplication operation \f$y=Ax\f$.
///
Matrix operator*(const Eigen::Ref<const Matrix>& mat_in) const
{
return m_mat.template selfadjointView<Uplo>() * mat_in;
}
///
/// Extract (i,j) element of the underlying matrix.
///
Scalar operator()(Index i, Index j) const
{
return m_mat(i, j);
}
};
} // namespace Spectra
#endif // DENSE_SYM_MAT_PROD_H
#endif // SPECTRA_DENSE_SYM_MAT_PROD_H

50
gtsam/3rdparty/Spectra/MatOp/DenseSymShiftSolve.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef DENSE_SYM_SHIFT_SOLVE_H
#define DENSE_SYM_SHIFT_SOLVE_H
#ifndef SPECTRA_DENSE_SYM_SHIFT_SOLVE_H
#define SPECTRA_DENSE_SYM_SHIFT_SOLVE_H
#include <Eigen/Core>
#include <stdexcept>
@ -22,19 +22,32 @@ namespace Spectra {
/// i.e., calculating \f$y=(A-\sigma I)^{-1}x\f$ for any real \f$\sigma\f$ and
/// vector \f$x\f$. It is mainly used in the SymEigsShiftSolver eigen solver.
///
template <typename Scalar, int Uplo = Eigen::Lower>
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Uplo Either `Eigen::Lower` or `Eigen::Upper`, indicating which
/// triangular part of the matrix is used.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
///
template <typename Scalar_, int Uplo = Eigen::Lower, int Flags = Eigen::ColMajor>
class DenseSymShiftSolve
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flags>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using ConstGenericMatrix = const Eigen::Ref<const Matrix>;
ConstGenericMatrix m_mat;
const int m_n;
const Index m_n;
BKLDLT<Scalar> m_solver;
public:
@ -46,10 +59,15 @@ public:
/// `Eigen::MatrixXf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
///
DenseSymShiftSolve(ConstGenericMatrix& mat) :
template <typename Derived>
DenseSymShiftSolve(const Eigen::MatrixBase<Derived>& mat) :
m_mat(mat), m_n(mat.rows())
{
if (mat.rows() != mat.cols())
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(Matrix::IsRowMajor),
"DenseSymShiftSolve: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
if (m_n != mat.cols())
throw std::invalid_argument("DenseSymShiftSolve: matrix must be square");
}
@ -65,10 +83,10 @@ public:
///
/// Set the real shift \f$\sigma\f$.
///
void set_shift(Scalar sigma)
void set_shift(const Scalar& sigma)
{
m_solver.compute(m_mat, Uplo, sigma);
if (m_solver.info() != SUCCESSFUL)
if (m_solver.info() != CompInfo::Successful)
throw std::invalid_argument("DenseSymShiftSolve: factorization failed with the given shift");
}
@ -89,4 +107,4 @@ public:
} // namespace Spectra
#endif // DENSE_SYM_SHIFT_SOLVE_H
#endif // SPECTRA_DENSE_SYM_SHIFT_SOLVE_H

51
gtsam/3rdparty/Spectra/MatOp/SparseCholesky.h vendored
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@ -1,16 +1,17 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPARSE_CHOLESKY_H
#define SPARSE_CHOLESKY_H
#ifndef SPECTRA_SPARSE_CHOLESKY_H
#define SPECTRA_SPARSE_CHOLESKY_H
#include <Eigen/Core>
#include <Eigen/SparseCore>
#include <Eigen/SparseCholesky>
#include <stdexcept>
#include "../Util/CompInfo.h"
namespace Spectra {
@ -23,20 +24,33 @@ namespace Spectra {
/// matrix. It is mainly used in the SymGEigsSolver generalized eigen solver
/// in the Cholesky decomposition mode.
///
template <typename Scalar, int Uplo = Eigen::Lower, int Flags = 0, typename StorageIndex = int>
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Uplo Either `Eigen::Lower` or `Eigen::Upper`, indicating which
/// triangular part of the matrix is used.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
/// \tparam StorageIndex The type of the indices for the sparse matrix.
///
template <typename Scalar_, int Uplo = Eigen::Lower, int Flags = Eigen::ColMajor, typename StorageIndex = int>
class SparseCholesky
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef Eigen::SparseMatrix<Scalar, Flags, StorageIndex> SparseMatrix;
typedef const Eigen::Ref<const SparseMatrix> ConstGenericSparseMatrix;
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using SparseMatrix = Eigen::SparseMatrix<Scalar, Flags, StorageIndex>;
const Index m_n;
Eigen::SimplicialLLT<SparseMatrix, Uplo> m_decomp;
int m_info; // status of the decomposition
CompInfo m_info; // status of the decomposition
public:
///
@ -46,16 +60,21 @@ public:
/// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
/// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
///
SparseCholesky(ConstGenericSparseMatrix& mat) :
template <typename Derived>
SparseCholesky(const Eigen::SparseMatrixBase<Derived>& mat) :
m_n(mat.rows())
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(SparseMatrix::IsRowMajor),
"SparseCholesky: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
if (mat.rows() != mat.cols())
throw std::invalid_argument("SparseCholesky: matrix must be square");
m_decomp.compute(mat);
m_info = (m_decomp.info() == Eigen::Success) ?
SUCCESSFUL :
NUMERICAL_ISSUE;
CompInfo::Successful :
CompInfo::NumericalIssue;
}
///
@ -71,7 +90,7 @@ public:
/// Returns the status of the computation.
/// The full list of enumeration values can be found in \ref Enumerations.
///
int info() const { return m_info; }
CompInfo info() const { return m_info; }
///
/// Performs the lower triangular solving operation \f$y=L^{-1}x\f$.
@ -106,4 +125,4 @@ public:
} // namespace Spectra
#endif // SPARSE_CHOLESKY_H
#endif // SPECTRA_SPARSE_CHOLESKY_H

124
gtsam/3rdparty/Spectra/MatOp/SparseGenComplexShiftSolve.h vendored Normal file
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@ -0,0 +1,124 @@
// Copyright (C) 2020-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_SPARSE_GEN_COMPLEX_SHIFT_SOLVE_H
#define SPECTRA_SPARSE_GEN_COMPLEX_SHIFT_SOLVE_H
#include <Eigen/Core>
#include <Eigen/SparseCore>
#include <Eigen/SparseLU>
#include <stdexcept>
namespace Spectra {
///
/// \ingroup MatOp
///
/// This class defines the complex shift-solve operation on a sparse real matrix \f$A\f$,
/// i.e., calculating \f$y=\mathrm{Re}\{(A-\sigma I)^{-1}x\}\f$ for any complex-valued
/// \f$\sigma\f$ and real-valued vector \f$x\f$. It is mainly used in the
/// GenEigsComplexShiftSolver eigen solver.
///
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
/// \tparam StorageIndex The type of the indices for the sparse matrix.
///
template <typename Scalar_, int Flags = Eigen::ColMajor, typename StorageIndex = int>
class SparseGenComplexShiftSolve
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using SparseMatrix = Eigen::SparseMatrix<Scalar, Flags, StorageIndex>;
using ConstGenericSparseMatrix = const Eigen::Ref<const SparseMatrix>;
using Complex = std::complex<Scalar>;
using ComplexVector = Eigen::Matrix<Complex, Eigen::Dynamic, 1>;
using SparseComplexMatrix = Eigen::SparseMatrix<Complex, Flags, StorageIndex>;
using ComplexSolver = Eigen::SparseLU<SparseComplexMatrix>;
ConstGenericSparseMatrix m_mat;
const Index m_n;
ComplexSolver m_solver;
mutable ComplexVector m_x_cache;
public:
///
/// Constructor to create the matrix operation object.
///
/// \param mat An **Eigen** sparse matrix object, whose type can be
/// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
/// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
///
template <typename Derived>
SparseGenComplexShiftSolve(const Eigen::SparseMatrixBase<Derived>& mat) :
m_mat(mat), m_n(mat.rows())
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(SparseMatrix::IsRowMajor),
"SparseGenComplexShiftSolve: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
if (mat.rows() != mat.cols())
throw std::invalid_argument("SparseGenComplexShiftSolve: matrix must be square");
}
///
/// Return the number of rows of the underlying matrix.
///
Index rows() const { return m_n; }
///
/// Return the number of columns of the underlying matrix.
///
Index cols() const { return m_n; }
///
/// Set the complex shift \f$\sigma\f$.
///
/// \param sigmar Real part of \f$\sigma\f$.
/// \param sigmai Imaginary part of \f$\sigma\f$.
///
void set_shift(const Scalar& sigmar, const Scalar& sigmai)
{
// Create a sparse idendity matrix (1 + 0i on diagonal)
SparseComplexMatrix I(m_n, m_n);
I.setIdentity();
// Sparse LU decomposition
m_solver.compute(m_mat.template cast<Complex>() - Complex(sigmar, sigmai) * I);
// Set cache to zero
m_x_cache.resize(m_n);
m_x_cache.setZero();
}
///
/// Perform the complex shift-solve operation
/// \f$y=\mathrm{Re}\{(A-\sigma I)^{-1}x\}\f$.
///
/// \param x_in Pointer to the \f$x\f$ vector.
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = Re( inv(A - sigma * I) * x_in )
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
m_x_cache.real() = MapConstVec(x_in, m_n);
MapVec y(y_out, m_n);
y.noalias() = m_solver.solve(m_x_cache).real();
}
};
} // namespace Spectra
#endif // SPECTRA_SPARSE_GEN_COMPLEX_SHIFT_SOLVE_H

61
gtsam/3rdparty/Spectra/MatOp/SparseGenMatProd.h vendored
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@ -1,17 +1,16 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPARSE_GEN_MAT_PROD_H
#define SPARSE_GEN_MAT_PROD_H
#ifndef SPECTRA_SPARSE_GEN_MAT_PROD_H
#define SPECTRA_SPARSE_GEN_MAT_PROD_H
#include <Eigen/Core>
#include <Eigen/SparseCore>
namespace Spectra {
///
/// \ingroup MatOp
///
@ -20,16 +19,29 @@ namespace Spectra {
/// \f$x\f$. It is mainly used in the GenEigsSolver and SymEigsSolver
/// eigen solvers.
///
template <typename Scalar, int Flags = 0, typename StorageIndex = int>
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
/// \tparam StorageIndex The type of the indices for the sparse matrix.
///
template <typename Scalar_, int Flags = Eigen::ColMajor, typename StorageIndex = int>
class SparseGenMatProd
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef Eigen::SparseMatrix<Scalar, Flags, StorageIndex> SparseMatrix;
typedef const Eigen::Ref<const SparseMatrix> ConstGenericSparseMatrix;
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using SparseMatrix = Eigen::SparseMatrix<Scalar, Flags, StorageIndex>;
using ConstGenericSparseMatrix = const Eigen::Ref<const SparseMatrix>;
ConstGenericSparseMatrix m_mat;
@ -41,9 +53,14 @@ public:
/// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
/// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
///
SparseGenMatProd(ConstGenericSparseMatrix& mat) :
template <typename Derived>
SparseGenMatProd(const Eigen::SparseMatrixBase<Derived>& mat) :
m_mat(mat)
{}
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(SparseMatrix::IsRowMajor),
"SparseGenMatProd: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
}
///
/// Return the number of rows of the underlying matrix.
@ -67,8 +84,24 @@ public:
MapVec y(y_out, m_mat.rows());
y.noalias() = m_mat * x;
}
///
/// Perform the matrix-matrix multiplication operation \f$y=Ax\f$.
///
Matrix operator*(const Eigen::Ref<const Matrix>& mat_in) const
{
return m_mat * mat_in;
}
///
/// Extract (i,j) element of the underlying matrix.
///
Scalar operator()(Index i, Index j) const
{
return m_mat.coeff(i, j);
}
};
} // namespace Spectra
#endif // SPARSE_GEN_MAT_PROD_H
#endif // SPECTRA_SPARSE_GEN_MAT_PROD_H

45
gtsam/3rdparty/Spectra/MatOp/SparseGenRealShiftSolve.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPARSE_GEN_REAL_SHIFT_SOLVE_H
#define SPARSE_GEN_REAL_SHIFT_SOLVE_H
#ifndef SPECTRA_SPARSE_GEN_REAL_SHIFT_SOLVE_H
#define SPECTRA_SPARSE_GEN_REAL_SHIFT_SOLVE_H
#include <Eigen/Core>
#include <Eigen/SparseCore>
@ -21,19 +21,31 @@ namespace Spectra {
/// i.e., calculating \f$y=(A-\sigma I)^{-1}x\f$ for any real \f$\sigma\f$ and
/// vector \f$x\f$. It is mainly used in the GenEigsRealShiftSolver eigen solver.
///
template <typename Scalar, int Flags = 0, typename StorageIndex = int>
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
/// \tparam StorageIndex The type of the indices for the sparse matrix.
///
template <typename Scalar_, int Flags = Eigen::ColMajor, typename StorageIndex = int>
class SparseGenRealShiftSolve
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef Eigen::SparseMatrix<Scalar, Flags, StorageIndex> SparseMatrix;
typedef const Eigen::Ref<const SparseMatrix> ConstGenericSparseMatrix;
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using SparseMatrix = Eigen::SparseMatrix<Scalar, Flags, StorageIndex>;
using ConstGenericSparseMatrix = const Eigen::Ref<const SparseMatrix>;
ConstGenericSparseMatrix m_mat;
const int m_n;
const Index m_n;
Eigen::SparseLU<SparseMatrix> m_solver;
public:
@ -44,9 +56,14 @@ public:
/// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
/// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
///
SparseGenRealShiftSolve(ConstGenericSparseMatrix& mat) :
template <typename Derived>
SparseGenRealShiftSolve(const Eigen::SparseMatrixBase<Derived>& mat) :
m_mat(mat), m_n(mat.rows())
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(SparseMatrix::IsRowMajor),
"SparseGenRealShiftSolve: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
if (mat.rows() != mat.cols())
throw std::invalid_argument("SparseGenRealShiftSolve: matrix must be square");
}
@ -63,7 +80,7 @@ public:
///
/// Set the real shift \f$\sigma\f$.
///
void set_shift(Scalar sigma)
void set_shift(const Scalar& sigma)
{
SparseMatrix I(m_n, m_n);
I.setIdentity();
@ -90,4 +107,4 @@ public:
} // namespace Spectra
#endif // SPARSE_GEN_REAL_SHIFT_SOLVE_H
#endif // SPECTRA_SPARSE_GEN_REAL_SHIFT_SOLVE_H

92
gtsam/3rdparty/Spectra/MatOp/SparseHermMatProd.h vendored Normal file
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@ -0,0 +1,92 @@
// Copyright (C) 2024-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_SPARSE_HERM_MAT_PROD_H
#define SPECTRA_SPARSE_HERM_MAT_PROD_H
#include <Eigen/Core>
#include <Eigen/SparseCore>
namespace Spectra {
///
/// \ingroup MatOp
///
/// This class defines the matrix-vector multiplication operation on a
/// sparse real symmetric matrix \f$A\f$, i.e., calculating \f$y=Ax\f$ for any vector
/// \f$x\f$. It is mainly used in the SymEigsSolver eigen solver.
///
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Uplo Either `Eigen::Lower` or `Eigen::Upper`, indicating which
/// triangular part of the matrix is used.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
/// \tparam StorageIndex The type of the indices for the sparse matrix.
///
template <typename Scalar_, int Uplo = Eigen::Lower, int Flags = Eigen::ColMajor, typename StorageIndex = int>
class SparseHermMatProd
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using SparseMatrix = Eigen::SparseMatrix<Scalar, Flags, StorageIndex>;
using ConstGenericSparseMatrix = const Eigen::Ref<const SparseMatrix>;
ConstGenericSparseMatrix m_mat;
public:
///
/// Constructor to create the matrix operation object.
///
/// \param mat An **Eigen** sparse matrix object, whose type can be
/// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
/// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
///
template <typename Derived>
SparseHermMatProd(const Eigen::SparseMatrixBase<Derived>& mat) :
m_mat(mat)
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(SparseMatrix::IsRowMajor),
"SparseHermMatProd: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
}
///
/// Return the number of rows of the underlying matrix.
///
Index rows() const { return m_mat.rows(); }
///
/// Return the number of columns of the underlying matrix.
///
Index cols() const { return m_mat.cols(); }
///
/// Perform the matrix-vector multiplication operation \f$y=Ax\f$.
///
/// \param x_in Pointer to the \f$x\f$ vector.
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = A * x_in
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
MapConstVec x(x_in, m_mat.cols());
MapVec y(y_out, m_mat.rows());
y.noalias() = m_mat.template selfadjointView<Uplo>() * x;
}
};
} // namespace Spectra
#endif // SPECTRA_SPARSE_HERM_MAT_PROD_H

63
gtsam/3rdparty/Spectra/MatOp/SparseRegularInverse.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2017-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2017-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPARSE_REGULAR_INVERSE_H
#define SPARSE_REGULAR_INVERSE_H
#ifndef SPECTRA_SPARSE_REGULAR_INVERSE_H
#define SPECTRA_SPARSE_REGULAR_INVERSE_H
#include <Eigen/Core>
#include <Eigen/SparseCore>
@ -25,20 +25,35 @@ namespace Spectra {
/// This class is intended to be used with the SymGEigsSolver generalized eigen solver
/// in the regular inverse mode.
///
template <typename Scalar, int Uplo = Eigen::Lower, int Flags = 0, typename StorageIndex = int>
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Uplo Either `Eigen::Lower` or `Eigen::Upper`, indicating which
/// triangular part of the matrix is used.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
/// \tparam StorageIndex The type of the indices for the sparse matrix.
///
template <typename Scalar_, int Uplo = Eigen::Lower, int Flags = Eigen::ColMajor, typename StorageIndex = int>
class SparseRegularInverse
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef Eigen::SparseMatrix<Scalar, Flags, StorageIndex> SparseMatrix;
typedef const Eigen::Ref<const SparseMatrix> ConstGenericSparseMatrix;
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using SparseMatrix = Eigen::SparseMatrix<Scalar, Flags, StorageIndex>;
using ConstGenericSparseMatrix = const Eigen::Ref<const SparseMatrix>;
ConstGenericSparseMatrix m_mat;
const int m_n;
const Index m_n;
Eigen::ConjugateGradient<SparseMatrix> m_cg;
mutable CompInfo m_info;
public:
///
@ -48,13 +63,21 @@ public:
/// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
/// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
///
SparseRegularInverse(ConstGenericSparseMatrix& mat) :
template <typename Derived>
SparseRegularInverse(const Eigen::SparseMatrixBase<Derived>& mat) :
m_mat(mat), m_n(mat.rows())
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(SparseMatrix::IsRowMajor),
"SparseRegularInverse: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
if (mat.rows() != mat.cols())
throw std::invalid_argument("SparseRegularInverse: matrix must be square");
m_cg.compute(mat);
m_info = (m_cg.info() == Eigen::Success) ?
CompInfo::Successful :
CompInfo::NumericalIssue;
}
///
@ -66,6 +89,12 @@ public:
///
Index cols() const { return m_n; }
///
/// Returns the status of the computation.
/// The full list of enumeration values can be found in \ref Enumerations.
///
CompInfo info() const { return m_info; }
///
/// Perform the solving operation \f$y=B^{-1}x\f$.
///
@ -78,6 +107,12 @@ public:
MapConstVec x(x_in, m_n);
MapVec y(y_out, m_n);
y.noalias() = m_cg.solve(x);
m_info = (m_cg.info() == Eigen::Success) ?
CompInfo::Successful :
CompInfo::NotConverging;
if (m_info != CompInfo::Successful)
throw std::runtime_error("SparseRegularInverse: CG solver does not converge");
}
///
@ -87,7 +122,7 @@ public:
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = B * x_in
void mat_prod(const Scalar* x_in, Scalar* y_out) const
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
MapConstVec x(x_in, m_n);
MapVec y(y_out, m_n);
@ -97,4 +132,4 @@ public:
} // namespace Spectra
#endif // SPARSE_REGULAR_INVERSE_H
#endif // SPECTRA_SPARSE_REGULAR_INVERSE_H

63
gtsam/3rdparty/Spectra/MatOp/SparseSymMatProd.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPARSE_SYM_MAT_PROD_H
#define SPARSE_SYM_MAT_PROD_H
#ifndef SPECTRA_SPARSE_SYM_MAT_PROD_H
#define SPECTRA_SPARSE_SYM_MAT_PROD_H
#include <Eigen/Core>
#include <Eigen/SparseCore>
@ -19,16 +19,31 @@ namespace Spectra {
/// sparse real symmetric matrix \f$A\f$, i.e., calculating \f$y=Ax\f$ for any vector
/// \f$x\f$. It is mainly used in the SymEigsSolver eigen solver.
///
template <typename Scalar, int Uplo = Eigen::Lower, int Flags = 0, typename StorageIndex = int>
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Uplo Either `Eigen::Lower` or `Eigen::Upper`, indicating which
/// triangular part of the matrix is used.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
/// \tparam StorageIndex The type of the indices for the sparse matrix.
///
template <typename Scalar_, int Uplo = Eigen::Lower, int Flags = Eigen::ColMajor, typename StorageIndex = int>
class SparseSymMatProd
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef Eigen::SparseMatrix<Scalar, Flags, StorageIndex> SparseMatrix;
typedef const Eigen::Ref<const SparseMatrix> ConstGenericSparseMatrix;
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using SparseMatrix = Eigen::SparseMatrix<Scalar, Flags, StorageIndex>;
using ConstGenericSparseMatrix = const Eigen::Ref<const SparseMatrix>;
ConstGenericSparseMatrix m_mat;
@ -40,9 +55,14 @@ public:
/// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
/// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
///
SparseSymMatProd(ConstGenericSparseMatrix& mat) :
template <typename Derived>
SparseSymMatProd(const Eigen::SparseMatrixBase<Derived>& mat) :
m_mat(mat)
{}
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(SparseMatrix::IsRowMajor),
"SparseSymMatProd: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
}
///
/// Return the number of rows of the underlying matrix.
@ -66,8 +86,23 @@ public:
MapVec y(y_out, m_mat.rows());
y.noalias() = m_mat.template selfadjointView<Uplo>() * x;
}
};
///
/// Perform the matrix-matrix multiplication operation \f$y=Ax\f$.
///
Matrix operator*(const Eigen::Ref<const Matrix>& mat_in) const
{
return m_mat.template selfadjointView<Uplo>() * mat_in;
}
///
/// Extract (i,j) element of the underlying matrix.
///
Scalar operator()(Index i, Index j) const
{
return m_mat.coeff(i, j);
}
};
} // namespace Spectra
#endif // SPARSE_SYM_MAT_PROD_H
#endif // SPECTRA_SPARSE_SYM_MAT_PROD_H

47
gtsam/3rdparty/Spectra/MatOp/SparseSymShiftSolve.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPARSE_SYM_SHIFT_SOLVE_H
#define SPARSE_SYM_SHIFT_SOLVE_H
#ifndef SPECTRA_SPARSE_SYM_SHIFT_SOLVE_H
#define SPECTRA_SPARSE_SYM_SHIFT_SOLVE_H
#include <Eigen/Core>
#include <Eigen/SparseCore>
@ -21,19 +21,33 @@ namespace Spectra {
/// i.e., calculating \f$y=(A-\sigma I)^{-1}x\f$ for any real \f$\sigma\f$ and
/// vector \f$x\f$. It is mainly used in the SymEigsShiftSolver eigen solver.
///
template <typename Scalar, int Uplo = Eigen::Lower, int Flags = 0, typename StorageIndex = int>
/// \tparam Scalar_ The element type of the matrix, for example,
/// `float`, `double`, and `long double`.
/// \tparam Uplo Either `Eigen::Lower` or `Eigen::Upper`, indicating which
/// triangular part of the matrix is used.
/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
/// the storage format of the input matrix.
/// \tparam StorageIndex The type of the indices for the sparse matrix.
///
template <typename Scalar_, int Uplo = Eigen::Lower, int Flags = Eigen::ColMajor, typename StorageIndex = int>
class SparseSymShiftSolve
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef Eigen::SparseMatrix<Scalar, Flags, StorageIndex> SparseMatrix;
typedef const Eigen::Ref<const SparseMatrix> ConstGenericSparseMatrix;
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using SparseMatrix = Eigen::SparseMatrix<Scalar, Flags, StorageIndex>;
using ConstGenericSparseMatrix = const Eigen::Ref<const SparseMatrix>;
ConstGenericSparseMatrix m_mat;
const int m_n;
const Index m_n;
Eigen::SparseLU<SparseMatrix> m_solver;
public:
@ -44,9 +58,14 @@ public:
/// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
/// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
///
SparseSymShiftSolve(ConstGenericSparseMatrix& mat) :
template <typename Derived>
SparseSymShiftSolve(const Eigen::SparseMatrixBase<Derived>& mat) :
m_mat(mat), m_n(mat.rows())
{
static_assert(
static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(SparseMatrix::IsRowMajor),
"SparseSymShiftSolve: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
if (mat.rows() != mat.cols())
throw std::invalid_argument("SparseSymShiftSolve: matrix must be square");
}
@ -63,7 +82,7 @@ public:
///
/// Set the real shift \f$\sigma\f$.
///
void set_shift(Scalar sigma)
void set_shift(const Scalar& sigma)
{
SparseMatrix mat = m_mat.template selfadjointView<Uplo>();
SparseMatrix identity(m_n, m_n);
@ -92,4 +111,4 @@ public:
} // namespace Spectra
#endif // SPARSE_SYM_SHIFT_SOLVE_H
#endif // SPECTRA_SPARSE_SYM_SHIFT_SOLVE_H

245
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@ -0,0 +1,245 @@
// Copyright (C) 2020-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_SYM_SHIFT_INVERT_H
#define SPECTRA_SYM_SHIFT_INVERT_H
#include <Eigen/Core>
#include <Eigen/SparseCore>
#include <Eigen/SparseLU>
#include <stdexcept>
#include <type_traits> // std::conditional, std::is_same
#include "../LinAlg/BKLDLT.h"
#include "../Util/CompInfo.h"
namespace Spectra {
/// \cond
// Compute and factorize A-sigma*B without unnecessary copying
// Default case: A is sparse, B is sparse
template <bool AIsSparse, bool BIsSparse, int UploA, int UploB>
class SymShiftInvertHelper
{
public:
template <typename Scalar, typename Fac, typename ArgA, typename ArgB>
static bool factorize(Fac& fac, const ArgA& A, const ArgB& B, const Scalar& sigma)
{
using SpMat = typename ArgA::PlainObject;
SpMat matA = A.template selfadjointView<UploA>();
SpMat matB = B.template selfadjointView<UploB>();
SpMat mat = matA - sigma * matB;
// SparseLU solver
fac.isSymmetric(true);
fac.compute(mat);
// Return true if successful
return fac.info() == Eigen::Success;
}
};
// A is dense, B is dense or sparse
template <bool BIsSparse, int UploA, int UploB>
class SymShiftInvertHelper<false, BIsSparse, UploA, UploB>
{
public:
template <typename Scalar, typename Fac, typename ArgA, typename ArgB>
static bool factorize(Fac& fac, const ArgA& A, const ArgB& B, const Scalar& sigma)
{
using Matrix = typename ArgA::PlainObject;
// Make a copy of the <UploA> triangular part of A
Matrix mat(A.rows(), A.cols());
mat.template triangularView<UploA>() = A;
// Update <UploA> triangular part of mat
if (UploA == UploB)
mat -= (B * sigma).template triangularView<UploA>();
else
mat -= (B * sigma).template triangularView<UploB>().transpose();
// BKLDLT solver
fac.compute(mat, UploA);
// Return true if successful
return fac.info() == CompInfo::Successful;
}
};
// A is sparse, B is dense
template <int UploA, int UploB>
class SymShiftInvertHelper<true, false, UploA, UploB>
{
public:
template <typename Scalar, typename Fac, typename ArgA, typename ArgB>
static bool factorize(Fac& fac, const ArgA& A, const ArgB& B, const Scalar& sigma)
{
using Matrix = typename ArgB::PlainObject;
// Construct the <UploB> triangular part of -sigma*B
Matrix mat(B.rows(), B.cols());
mat.template triangularView<UploB>() = -sigma * B;
// Update <UploB> triangular part of mat
if (UploA == UploB)
mat += A.template triangularView<UploB>();
else
mat += A.template triangularView<UploA>().transpose();
// BKLDLT solver
fac.compute(mat, UploB);
// Return true if successful
return fac.info() == CompInfo::Successful;
}
};
/// \endcond
///
/// \ingroup MatOp
///
/// This class defines matrix operations required by the generalized eigen solver
/// in the shift-and-invert mode. Given two symmetric matrices \f$A\f$ and \f$B\f$,
/// it solves the linear equation \f$y=(A-\sigma B)^{-1}x\f$, where \f$\sigma\f$ is a real shift.
/// Each of \f$A\f$ and \f$B\f$ can be a dense or sparse matrix.
///
/// This class is intended to be used with the SymGEigsShiftSolver generalized eigen solver.
///
/// \tparam Scalar_ The element type of the matrices.
/// Currently supported types are `float`, `double`, and `long double`.
/// \tparam TypeA The type of the \f$A\f$ matrix, indicating whether \f$A\f$ is
/// dense or sparse. Possible values are `Eigen::Dense` and `Eigen::Sparse`.
/// \tparam TypeB The type of the \f$B\f$ matrix, indicating whether \f$B\f$ is
/// dense or sparse. Possible values are `Eigen::Dense` and `Eigen::Sparse`.
/// \tparam UploA Whether the lower or upper triangular part of \f$A\f$ should be used.
/// Possible values are `Eigen::Lower` and `Eigen::Upper`.
/// \tparam UploB Whether the lower or upper triangular part of \f$B\f$ should be used.
/// Possible values are `Eigen::Lower` and `Eigen::Upper`.
/// \tparam FlagsA Additional flags for the matrix class of \f$A\f$.
/// Possible values are `Eigen::ColMajor` and `Eigen::RowMajor`.
/// \tparam FlagsB Additional flags for the matrix class of \f$B\f$.
/// Possible values are `Eigen::ColMajor` and `Eigen::RowMajor`.
/// \tparam StorageIndexA The storage index type of the \f$A\f$ matrix, only used when \f$A\f$
/// is a sparse matrix.
/// \tparam StorageIndexB The storage index type of the \f$B\f$ matrix, only used when \f$B\f$
/// is a sparse matrix.
///
template <typename Scalar_, typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse,
int UploA = Eigen::Lower, int UploB = Eigen::Lower,
int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor,
typename StorageIndexA = int, typename StorageIndexB = int>
class SymShiftInvert
{
public:
///
/// Element type of the matrix.
///
using Scalar = Scalar_;
private:
using Index = Eigen::Index;
// Hypothetical type of the A matrix, either dense or sparse
using DenseTypeA = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, FlagsA>;
using SparseTypeA = Eigen::SparseMatrix<Scalar, FlagsA, StorageIndexA>;
// Whether A is sparse
using ASparse = std::is_same<TypeA, Eigen::Sparse>;
// Actual type of the A matrix
using MatrixA = typename std::conditional<ASparse::value, SparseTypeA, DenseTypeA>::type;
// Hypothetical type of the B matrix, either dense or sparse
using DenseTypeB = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, FlagsB>;
using SparseTypeB = Eigen::SparseMatrix<Scalar, FlagsB, StorageIndexB>;
// Whether B is sparse
using BSparse = std::is_same<TypeB, Eigen::Sparse>;
// Actual type of the B matrix
using MatrixB = typename std::conditional<BSparse::value, SparseTypeB, DenseTypeB>::type;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
// The type of A-sigma*B if one of A and B is dense
// DenseType = if (A is dense) MatrixA else MatrixB
using DenseType = typename std::conditional<ASparse::value, MatrixB, MatrixA>::type;
// The type of A-sigma*B
// If both A and B are sparse, the result is MatrixA; otherwise the result is DenseType
using ResType = typename std::conditional<ASparse::value && BSparse::value, MatrixA, DenseType>::type;
// If both A and B are sparse, then the result A-sigma*B is sparse, so we use
// sparseLU for factorization; otherwise A-sigma*B is dense, and we use BKLDLT
using FacType = typename std::conditional<
ASparse::value && BSparse::value,
Eigen::SparseLU<ResType>,
BKLDLT<Scalar>>::type;
using ConstGenericMatrixA = const Eigen::Ref<const MatrixA>;
using ConstGenericMatrixB = const Eigen::Ref<const MatrixB>;
ConstGenericMatrixA m_matA;
ConstGenericMatrixB m_matB;
const Index m_n;
FacType m_solver;
public:
///
/// Constructor to create the matrix operation object.
///
/// \param A A dense or sparse matrix object, whose type can be `Eigen::Matrix<...>`,
/// `Eigen::SparseMatrix<...>`, `Eigen::Map<Eigen::Matrix<...>>`,
/// `Eigen::Map<Eigen::SparseMatrix<...>>`, `Eigen::Ref<Eigen::Matrix<...>>`,
/// `Eigen::Ref<Eigen::SparseMatrix<...>>`, etc.
/// \param B A dense or sparse matrix object.
///
template <typename DerivedA, typename DerivedB>
SymShiftInvert(const Eigen::EigenBase<DerivedA>& A, const Eigen::EigenBase<DerivedB>& B) :
m_matA(A.derived()), m_matB(B.derived()), m_n(A.rows())
{
static_assert(
static_cast<int>(DerivedA::PlainObject::IsRowMajor) == static_cast<int>(MatrixA::IsRowMajor),
"SymShiftInvert: the \"FlagsA\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
static_assert(
static_cast<int>(DerivedB::PlainObject::IsRowMajor) == static_cast<int>(MatrixB::IsRowMajor),
"SymShiftInvert: the \"FlagsB\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
if (m_n != A.cols() || m_n != B.rows() || m_n != B.cols())
throw std::invalid_argument("SymShiftInvert: A and B must be square matrices of the same size");
}
///
/// Return the number of rows of the underlying matrix.
///
Index rows() const { return m_n; }
///
/// Return the number of columns of the underlying matrix.
///
Index cols() const { return m_n; }
///
/// Set the real shift \f$\sigma\f$.
///
void set_shift(const Scalar& sigma)
{
constexpr bool AIsSparse = ASparse::value;
constexpr bool BIsSparse = BSparse::value;
using Helper = SymShiftInvertHelper<AIsSparse, BIsSparse, UploA, UploB>;
const bool success = Helper::factorize(m_solver, m_matA, m_matB, sigma);
if (!success)
throw std::invalid_argument("SymShiftInvert: factorization failed with the given shift");
}
///
/// Perform the shift-invert operation \f$y=(A-\sigma B)^{-1}x\f$.
///
/// \param x_in Pointer to the \f$x\f$ vector.
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = inv(A - sigma * B) * x_in
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
MapConstVec x(x_in, m_n);
MapVec y(y_out, m_n);
y.noalias() = m_solver.solve(x);
}
};
} // namespace Spectra
#endif // SPECTRA_SYM_SHIFT_INVERT_H

86
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@ -1,14 +1,15 @@
// Copyright (C) 2018-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2018-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef ARNOLDI_OP_H
#define ARNOLDI_OP_H
#ifndef SPECTRA_ARNOLDI_OP_H
#define SPECTRA_ARNOLDI_OP_H
#include <Eigen/Core>
#include <cmath> // std::sqrt
#include <cmath> // std::sqrt
#include <complex> // std::real
namespace Spectra {
@ -32,51 +33,62 @@ template <typename Scalar, typename OpType, typename BOpType>
class ArnoldiOp
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
// The real part type of the matrix element
using RealScalar = typename Eigen::NumTraits<Scalar>::Real;
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
OpType& m_op;
BOpType& m_Bop;
Vector m_cache;
const OpType& m_op;
const BOpType& m_Bop;
mutable Vector m_cache;
public:
ArnoldiOp(OpType* op, BOpType* Bop) :
m_op(*op), m_Bop(*Bop), m_cache(op->rows())
ArnoldiOp(const OpType& op, const BOpType& Bop) :
m_op(op), m_Bop(Bop), m_cache(op.rows())
{}
// Move constructor
ArnoldiOp(ArnoldiOp&& other) :
m_op(other.m_op), m_Bop(other.m_Bop)
{
// We emulate the move constructor for Vector using Vector::swap()
m_cache.swap(other.m_cache);
}
inline Index rows() const { return m_op.rows(); }
// In generalized eigenvalue problem Ax=lambda*Bx, define the inner product to be <x, y> = x'By.
// For regular eigenvalue problems, it is the usual inner product <x, y> = x'y
// In generalized eigenvalue problem Ax=lambda*Bx, define the inner product to be <x, y> = (x^H)By.
// For regular eigenvalue problems, it is the usual inner product <x, y> = (x^H)y
// Compute <x, y> = x'By
// Compute <x, y> = (x^H)By
// x and y are two vectors
template <typename Arg1, typename Arg2>
Scalar inner_product(const Arg1& x, const Arg2& y)
Scalar inner_product(const Arg1& x, const Arg2& y) const
{
m_Bop.mat_prod(y.data(), m_cache.data());
m_Bop.perform_op(y.data(), m_cache.data());
return x.dot(m_cache);
}
// Compute res = <X, y> = X'By
// Compute res = <X, y> = (X^H)By
// X is a matrix, y is a vector, res is a vector
template <typename Arg1, typename Arg2>
void trans_product(const Arg1& x, const Arg2& y, Eigen::Ref<Vector> res)
void adjoint_product(const Arg1& x, const Arg2& y, Eigen::Ref<Vector> res) const
{
m_Bop.mat_prod(y.data(), m_cache.data());
res.noalias() = x.transpose() * m_cache;
m_Bop.perform_op(y.data(), m_cache.data());
res.noalias() = x.adjoint() * m_cache;
}
// B-norm of a vector, ||x||_B = sqrt(x'Bx)
// B-norm of a vector, ||x||_B = sqrt((x^H)Bx)
template <typename Arg>
Scalar norm(const Arg& x)
RealScalar norm(const Arg& x) const
{
using std::sqrt;
return sqrt(inner_product<Arg, Arg>(x, x));
using std::real;
return sqrt(real(inner_product<Arg, Arg>(x, x)));
}
// The "A" operator to generate the Krylov subspace
inline void perform_op(const Scalar* x_in, Scalar* y_out)
inline void perform_op(const Scalar* x_in, Scalar* y_out) const
{
m_op.perform_op(x_in, y_out);
}
@ -99,19 +111,21 @@ template <typename Scalar, typename OpType>
class ArnoldiOp<Scalar, OpType, IdentityBOp>
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
// The real part type of the matrix element
using RealScalar = typename Eigen::NumTraits<Scalar>::Real;
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
OpType& m_op;
const OpType& m_op;
public:
ArnoldiOp<Scalar, OpType, IdentityBOp>(OpType* op, IdentityBOp* /*Bop*/) :
m_op(*op)
ArnoldiOp(const OpType& op, const IdentityBOp& /*Bop*/) :
m_op(op)
{}
inline Index rows() const { return m_op.rows(); }
// Compute <x, y> = x'y
// Compute <x, y> = (x^H)y
// x and y are two vectors
template <typename Arg1, typename Arg2>
Scalar inner_product(const Arg1& x, const Arg2& y) const
@ -119,23 +133,23 @@ public:
return x.dot(y);
}
// Compute res = <X, y> = X'y
// Compute res = <X, y> = (X^H)y
// X is a matrix, y is a vector, res is a vector
template <typename Arg1, typename Arg2>
void trans_product(const Arg1& x, const Arg2& y, Eigen::Ref<Vector> res) const
void adjoint_product(const Arg1& x, const Arg2& y, Eigen::Ref<Vector> res) const
{
res.noalias() = x.transpose() * y;
res.noalias() = x.adjoint() * y;
}
// B-norm of a vector. For regular eigenvalue problems it is simply the L2 norm
template <typename Arg>
Scalar norm(const Arg& x)
RealScalar norm(const Arg& x) const
{
return x.norm();
}
// The "A" operator to generate the Krylov subspace
inline void perform_op(const Scalar* x_in, Scalar* y_out)
inline void perform_op(const Scalar* x_in, Scalar* y_out) const
{
m_op.perform_op(x_in, y_out);
}
@ -147,4 +161,4 @@ public:
} // namespace Spectra
#endif // ARNOLDI_OP_H
#endif // SPECTRA_ARNOLDI_OP_H

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@ -0,0 +1,95 @@
// Copyright (C) 2020-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_SYM_GEIGS_BUCKLING_OP_H
#define SPECTRA_SYM_GEIGS_BUCKLING_OP_H
#include <Eigen/Core>
#include "../SymShiftInvert.h"
#include "../SparseSymMatProd.h"
namespace Spectra {
///
/// \ingroup Operators
///
/// This class defines the matrix operation for generalized eigen solver in the
/// buckling mode. It computes \f$y=(K-\sigma K_G)^{-1}Kx\f$ for any
/// vector \f$x\f$, where \f$K\f$ is positive definite, \f$K_G\f$ is symmetric,
/// and \f$\sigma\f$ is a real shift.
/// This class is intended for internal use.
///
template <typename OpType = SymShiftInvert<double>,
typename BOpType = SparseSymMatProd<double>>
class SymGEigsBucklingOp
{
public:
using Scalar = typename OpType::Scalar;
private:
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
OpType& m_op;
const BOpType& m_Bop;
mutable Vector m_cache; // temporary working space
public:
///
/// Constructor to create the matrix operation object.
///
/// \param op The \f$(K-\sigma K_G)^{-1}\f$ matrix operation object.
/// \param Bop The \f$K\f$ matrix operation object.
///
SymGEigsBucklingOp(OpType& op, const BOpType& Bop) :
m_op(op), m_Bop(Bop), m_cache(op.rows())
{}
///
/// Move constructor.
///
SymGEigsBucklingOp(SymGEigsBucklingOp&& other) :
m_op(other.m_op), m_Bop(other.m_Bop)
{
// We emulate the move constructor for Vector using Vector::swap()
m_cache.swap(other.m_cache);
}
///
/// Return the number of rows of the underlying matrix.
///
Index rows() const { return m_op.rows(); }
///
/// Return the number of columns of the underlying matrix.
///
Index cols() const { return m_op.rows(); }
///
/// Set the real shift \f$\sigma\f$.
///
void set_shift(const Scalar& sigma)
{
m_op.set_shift(sigma);
}
///
/// Perform the matrix operation \f$y=(K-\sigma K_G)^{-1}Kx\f$.
///
/// \param x_in Pointer to the \f$x\f$ vector.
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = inv(K - sigma * K_G) * K * x_in
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
m_Bop.perform_op(x_in, m_cache.data());
m_op.perform_op(m_cache.data(), y_out);
}
};
} // namespace Spectra
#endif // SPECTRA_SYM_GEIGS_BUCKLING_OP_H

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@ -0,0 +1,105 @@
// Copyright (C) 2020-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_SYM_GEIGS_CAYLEY_OP_H
#define SPECTRA_SYM_GEIGS_CAYLEY_OP_H
#include <Eigen/Core>
#include "../SymShiftInvert.h"
#include "../SparseSymMatProd.h"
namespace Spectra {
///
/// \ingroup Operators
///
/// This class defines the matrix operation for generalized eigen solver in the
/// Cayley mode. It computes \f$y=(A-\sigma B)^{-1}(A+\sigma B)x\f$ for any
/// vector \f$x\f$, where \f$A\f$ is a symmetric matrix, \f$B\f$ is positive definite,
/// and \f$\sigma\f$ is a real shift.
/// This class is intended for internal use.
///
template <typename OpType = SymShiftInvert<double>,
typename BOpType = SparseSymMatProd<double>>
class SymGEigsCayleyOp
{
public:
using Scalar = typename OpType::Scalar;
private:
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
OpType& m_op;
const BOpType& m_Bop;
mutable Vector m_cache; // temporary working space
Scalar m_sigma;
public:
///
/// Constructor to create the matrix operation object.
///
/// \param op The \f$(A-\sigma B)^{-1}\f$ matrix operation object.
/// \param Bop The \f$B\f$ matrix operation object.
///
SymGEigsCayleyOp(OpType& op, const BOpType& Bop) :
m_op(op), m_Bop(Bop), m_cache(op.rows())
{}
///
/// Move constructor.
///
SymGEigsCayleyOp(SymGEigsCayleyOp&& other) :
m_op(other.m_op), m_Bop(other.m_Bop), m_sigma(other.m_sigma)
{
// We emulate the move constructor for Vector using Vector::swap()
m_cache.swap(other.m_cache);
}
///
/// Return the number of rows of the underlying matrix.
///
Index rows() const { return m_op.rows(); }
///
/// Return the number of columns of the underlying matrix.
///
Index cols() const { return m_op.rows(); }
///
/// Set the real shift \f$\sigma\f$.
///
void set_shift(const Scalar& sigma)
{
m_op.set_shift(sigma);
m_sigma = sigma;
}
///
/// Perform the matrix operation \f$y=(A-\sigma B)^{-1}(A+\sigma B)x\f$.
///
/// \param x_in Pointer to the \f$x\f$ vector.
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = inv(A - sigma * B) * (A + sigma * B) * x_in
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
// inv(A - sigma * B) * (A + sigma * B) * x
// = inv(A - sigma * B) * (A - sigma * B + 2 * sigma * B) * x
// = x + 2 * sigma * inv(A - sigma * B) * B * x
m_Bop.perform_op(x_in, m_cache.data());
m_op.perform_op(m_cache.data(), y_out);
MapConstVec x(x_in, this->rows());
MapVec y(y_out, this->rows());
y.noalias() = x + (Scalar(2) * m_sigma) * y;
}
};
} // namespace Spectra
#endif // SPECTRA_SYM_GEIGS_CAYLEY_OP_H

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@ -1,13 +1,14 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SYM_GEIGS_CHOLESKY_OP_H
#define SYM_GEIGS_CHOLESKY_OP_H
#ifndef SPECTRA_SYM_GEIGS_CHOLESKY_OP_H
#define SPECTRA_SYM_GEIGS_CHOLESKY_OP_H
#include <Eigen/Core>
#include "../DenseSymMatProd.h"
#include "../DenseCholesky.h"
@ -21,31 +22,42 @@ namespace Spectra {
/// vector \f$x\f$, where \f$L\f$ is the Cholesky decomposition of \f$B\f$.
/// This class is intended for internal use.
///
template <typename Scalar = double,
typename OpType = DenseSymMatProd<double>,
typename BOpType = DenseCholesky<double> >
template <typename OpType = DenseSymMatProd<double>,
typename BOpType = DenseCholesky<double>>
class SymGEigsCholeskyOp
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
public:
using Scalar = typename OpType::Scalar;
OpType& m_op;
BOpType& m_Bop;
Vector m_cache; // temporary working space
private:
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
const OpType& m_op;
const BOpType& m_Bop;
mutable Vector m_cache; // temporary working space
public:
///
/// Constructor to create the matrix operation object.
///
/// \param op Pointer to the \f$A\f$ matrix operation object.
/// \param Bop Pointer to the \f$B\f$ matrix operation object.
/// \param op The \f$A\f$ matrix operation object.
/// \param Bop The \f$B\f$ matrix operation object.
///
SymGEigsCholeskyOp(OpType& op, BOpType& Bop) :
SymGEigsCholeskyOp(const OpType& op, const BOpType& Bop) :
m_op(op), m_Bop(Bop), m_cache(op.rows())
{}
///
/// Move constructor.
///
SymGEigsCholeskyOp(SymGEigsCholeskyOp&& other) :
m_op(other.m_op), m_Bop(other.m_Bop)
{
// We emulate the move constructor for Vector using Vector::swap()
m_cache.swap(other.m_cache);
}
///
/// Return the number of rows of the underlying matrix.
///
@ -62,7 +74,7 @@ public:
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = inv(L) * A * inv(L') * x_in
void perform_op(const Scalar* x_in, Scalar* y_out)
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
m_Bop.upper_triangular_solve(x_in, y_out);
m_op.perform_op(y_out, m_cache.data());
@ -72,4 +84,4 @@ public:
} // namespace Spectra
#endif // SYM_GEIGS_CHOLESKY_OP_H
#endif // SPECTRA_SYM_GEIGS_CHOLESKY_OP_H

48
gtsam/3rdparty/Spectra/MatOp/internal/SymGEigsRegInvOp.h vendored
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@ -1,13 +1,14 @@
// Copyright (C) 2017-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2017-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SYM_GEIGS_REG_INV_OP_H
#define SYM_GEIGS_REG_INV_OP_H
#ifndef SPECTRA_SYM_GEIGS_REG_INV_OP_H
#define SPECTRA_SYM_GEIGS_REG_INV_OP_H
#include <Eigen/Core>
#include "../SparseSymMatProd.h"
#include "../SparseRegularInverse.h"
@ -19,31 +20,42 @@ namespace Spectra {
/// This class defines the matrix operation for generalized eigen solver in the
/// regular inverse mode. This class is intended for internal use.
///
template <typename Scalar = double,
typename OpType = SparseSymMatProd<double>,
typename BOpType = SparseRegularInverse<double> >
template <typename OpType = SparseSymMatProd<double>,
typename BOpType = SparseRegularInverse<double>>
class SymGEigsRegInvOp
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
public:
using Scalar = typename OpType::Scalar;
OpType& m_op;
BOpType& m_Bop;
Vector m_cache; // temporary working space
private:
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
const OpType& m_op;
const BOpType& m_Bop;
mutable Vector m_cache; // temporary working space
public:
///
/// Constructor to create the matrix operation object.
///
/// \param op Pointer to the \f$A\f$ matrix operation object.
/// \param Bop Pointer to the \f$B\f$ matrix operation object.
/// \param op The \f$A\f$ matrix operation object.
/// \param Bop The \f$B\f$ matrix operation object.
///
SymGEigsRegInvOp(OpType& op, BOpType& Bop) :
SymGEigsRegInvOp(const OpType& op, const BOpType& Bop) :
m_op(op), m_Bop(Bop), m_cache(op.rows())
{}
///
/// Move constructor.
///
SymGEigsRegInvOp(SymGEigsRegInvOp&& other) :
m_op(other.m_op), m_Bop(other.m_Bop)
{
// We emulate the move constructor for Vector using Vector::swap()
m_cache.swap(other.m_cache);
}
///
/// Return the number of rows of the underlying matrix.
///
@ -60,7 +72,7 @@ public:
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = inv(B) * A * x_in
void perform_op(const Scalar* x_in, Scalar* y_out)
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
m_op.perform_op(x_in, m_cache.data());
m_Bop.solve(m_cache.data(), y_out);
@ -69,4 +81,4 @@ public:
} // namespace Spectra
#endif // SYM_GEIGS_REG_INV_OP_H
#endif // SPECTRA_SYM_GEIGS_REG_INV_OP_H

95
gtsam/3rdparty/Spectra/MatOp/internal/SymGEigsShiftInvertOp.h vendored Normal file
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@ -0,0 +1,95 @@
// Copyright (C) 2020-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_SYM_GEIGS_SHIFT_INVERT_OP_H
#define SPECTRA_SYM_GEIGS_SHIFT_INVERT_OP_H
#include <Eigen/Core>
#include "../SymShiftInvert.h"
#include "../SparseSymMatProd.h"
namespace Spectra {
///
/// \ingroup Operators
///
/// This class defines the matrix operation for generalized eigen solver in the
/// shift-and-invert mode. It computes \f$y=(A-\sigma B)^{-1}Bx\f$ for any
/// vector \f$x\f$, where \f$A\f$ is a symmetric matrix, \f$B\f$ is positive definite,
/// and \f$\sigma\f$ is a real shift.
/// This class is intended for internal use.
///
template <typename OpType = SymShiftInvert<double>,
typename BOpType = SparseSymMatProd<double>>
class SymGEigsShiftInvertOp
{
public:
using Scalar = typename OpType::Scalar;
private:
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
OpType& m_op;
const BOpType& m_Bop;
mutable Vector m_cache; // temporary working space
public:
///
/// Constructor to create the matrix operation object.
///
/// \param op The \f$(A-\sigma B)^{-1}\f$ matrix operation object.
/// \param Bop The \f$B\f$ matrix operation object.
///
SymGEigsShiftInvertOp(OpType& op, const BOpType& Bop) :
m_op(op), m_Bop(Bop), m_cache(op.rows())
{}
///
/// Move constructor.
///
SymGEigsShiftInvertOp(SymGEigsShiftInvertOp&& other) :
m_op(other.m_op), m_Bop(other.m_Bop)
{
// We emulate the move constructor for Vector using Vector::swap()
m_cache.swap(other.m_cache);
}
///
/// Return the number of rows of the underlying matrix.
///
Index rows() const { return m_op.rows(); }
///
/// Return the number of columns of the underlying matrix.
///
Index cols() const { return m_op.rows(); }
///
/// Set the real shift \f$\sigma\f$.
///
void set_shift(const Scalar& sigma)
{
m_op.set_shift(sigma);
}
///
/// Perform the matrix operation \f$y=(A-\sigma B)^{-1}Bx\f$.
///
/// \param x_in Pointer to the \f$x\f$ vector.
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = inv(A - sigma * B) * B * x_in
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
m_Bop.perform_op(x_in, m_cache.data());
m_op.perform_op(m_cache.data(), y_out);
}
};
} // namespace Spectra
#endif // SPECTRA_SYM_GEIGS_SHIFT_INVERT_OP_H

448
gtsam/3rdparty/Spectra/SymEigsBase.h vendored
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@ -1,448 +0,0 @@
// Copyright (C) 2018-2019 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SYM_EIGS_BASE_H
#define SYM_EIGS_BASE_H
#include <Eigen/Core>
#include <vector> // std::vector
#include <cmath> // std::abs, std::pow, std::sqrt
#include <algorithm> // std::min, std::copy
#include <stdexcept> // std::invalid_argument
#include "Util/TypeTraits.h"
#include "Util/SelectionRule.h"
#include "Util/CompInfo.h"
#include "Util/SimpleRandom.h"
#include "MatOp/internal/ArnoldiOp.h"
#include "LinAlg/UpperHessenbergQR.h"
#include "LinAlg/TridiagEigen.h"
#include "LinAlg/Lanczos.h"
namespace Spectra {
///
/// \defgroup EigenSolver Eigen Solvers
///
/// Eigen solvers for different types of problems.
///
///
/// \ingroup EigenSolver
///
/// This is the base class for symmetric eigen solvers, mainly for internal use.
/// It is kept here to provide the documentation for member functions of concrete eigen solvers
/// such as SymEigsSolver and SymEigsShiftSolver.
///
template <typename Scalar,
int SelectionRule,
typename OpType,
typename BOpType>
class SymEigsBase
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Array<Scalar, Eigen::Dynamic, 1> Array;
typedef Eigen::Array<bool, Eigen::Dynamic, 1> BoolArray;
typedef Eigen::Map<Matrix> MapMat;
typedef Eigen::Map<Vector> MapVec;
typedef Eigen::Map<const Vector> MapConstVec;
typedef ArnoldiOp<Scalar, OpType, BOpType> ArnoldiOpType;
typedef Lanczos<Scalar, ArnoldiOpType> LanczosFac;
protected:
// clang-format off
OpType* m_op; // object to conduct matrix operation,
// e.g. matrix-vector product
const Index m_n; // dimension of matrix A
const Index m_nev; // number of eigenvalues requested
const Index m_ncv; // dimension of Krylov subspace in the Lanczos method
Index m_nmatop; // number of matrix operations called
Index m_niter; // number of restarting iterations
LanczosFac m_fac; // Lanczos factorization
Vector m_ritz_val; // Ritz values
private:
Matrix m_ritz_vec; // Ritz vectors
Vector m_ritz_est; // last row of m_ritz_vec, also called the Ritz estimates
BoolArray m_ritz_conv; // indicator of the convergence of Ritz values
int m_info; // status of the computation
const Scalar m_near_0; // a very small value, but 1.0 / m_near_0 does not overflow
// ~= 1e-307 for the "double" type
const Scalar m_eps; // the machine precision, ~= 1e-16 for the "double" type
const Scalar m_eps23; // m_eps^(2/3), used to test the convergence
// clang-format on
// Implicitly restarted Lanczos factorization
void restart(Index k)
{
if (k >= m_ncv)
return;
TridiagQR<Scalar> decomp(m_ncv);
Matrix Q = Matrix::Identity(m_ncv, m_ncv);
for (Index i = k; i < m_ncv; i++)
{
// QR decomposition of H-mu*I, mu is the shift
decomp.compute(m_fac.matrix_H(), m_ritz_val[i]);
// Q -> Q * Qi
decomp.apply_YQ(Q);
// H -> Q'HQ
// Since QR = H - mu * I, we have H = QR + mu * I
// and therefore Q'HQ = RQ + mu * I
m_fac.compress_H(decomp);
}
m_fac.compress_V(Q);
m_fac.factorize_from(k, m_ncv, m_nmatop);
retrieve_ritzpair();
}
// Calculates the number of converged Ritz values
Index num_converged(Scalar tol)
{
// thresh = tol * max(m_eps23, abs(theta)), theta for Ritz value
Array thresh = tol * m_ritz_val.head(m_nev).array().abs().max(m_eps23);
Array resid = m_ritz_est.head(m_nev).array().abs() * m_fac.f_norm();
// Converged "wanted" Ritz values
m_ritz_conv = (resid < thresh);
return m_ritz_conv.cast<Index>().sum();
}
// Returns the adjusted nev for restarting
Index nev_adjusted(Index nconv)
{
using std::abs;
Index nev_new = m_nev;
for (Index i = m_nev; i < m_ncv; i++)
if (abs(m_ritz_est[i]) < m_near_0)
nev_new++;
// Adjust nev_new, according to dsaup2.f line 677~684 in ARPACK
nev_new += std::min(nconv, (m_ncv - nev_new) / 2);
if (nev_new == 1 && m_ncv >= 6)
nev_new = m_ncv / 2;
else if (nev_new == 1 && m_ncv > 2)
nev_new = 2;
if (nev_new > m_ncv - 1)
nev_new = m_ncv - 1;
return nev_new;
}
// Retrieves and sorts Ritz values and Ritz vectors
void retrieve_ritzpair()
{
TridiagEigen<Scalar> decomp(m_fac.matrix_H());
const Vector& evals = decomp.eigenvalues();
const Matrix& evecs = decomp.eigenvectors();
SortEigenvalue<Scalar, SelectionRule> sorting(evals.data(), evals.size());
std::vector<int> ind = sorting.index();
// For BOTH_ENDS, the eigenvalues are sorted according
// to the LARGEST_ALGE rule, so we need to move those smallest
// values to the left
// The order would be
// Largest => Smallest => 2nd largest => 2nd smallest => ...
// We keep this order since the first k values will always be
// the wanted collection, no matter k is nev_updated (used in restart())
// or is nev (used in sort_ritzpair())
if (SelectionRule == BOTH_ENDS)
{
std::vector<int> ind_copy(ind);
for (Index i = 0; i < m_ncv; i++)
{
// If i is even, pick values from the left (large values)
// If i is odd, pick values from the right (small values)
if (i % 2 == 0)
ind[i] = ind_copy[i / 2];
else
ind[i] = ind_copy[m_ncv - 1 - i / 2];
}
}
// Copy the Ritz values and vectors to m_ritz_val and m_ritz_vec, respectively
for (Index i = 0; i < m_ncv; i++)
{
m_ritz_val[i] = evals[ind[i]];
m_ritz_est[i] = evecs(m_ncv - 1, ind[i]);
}
for (Index i = 0; i < m_nev; i++)
{
m_ritz_vec.col(i).noalias() = evecs.col(ind[i]);
}
}
protected:
// Sorts the first nev Ritz pairs in the specified order
// This is used to return the final results
virtual void sort_ritzpair(int sort_rule)
{
// First make sure that we have a valid index vector
SortEigenvalue<Scalar, LARGEST_ALGE> sorting(m_ritz_val.data(), m_nev);
std::vector<int> ind = sorting.index();
switch (sort_rule)
{
case LARGEST_ALGE:
break;
case LARGEST_MAGN:
{
SortEigenvalue<Scalar, LARGEST_MAGN> sorting(m_ritz_val.data(), m_nev);
ind = sorting.index();
break;
}
case SMALLEST_ALGE:
{
SortEigenvalue<Scalar, SMALLEST_ALGE> sorting(m_ritz_val.data(), m_nev);
ind = sorting.index();
break;
}
case SMALLEST_MAGN:
{
SortEigenvalue<Scalar, SMALLEST_MAGN> sorting(m_ritz_val.data(), m_nev);
ind = sorting.index();
break;
}
default:
throw std::invalid_argument("unsupported sorting rule");
}
Vector new_ritz_val(m_ncv);
Matrix new_ritz_vec(m_ncv, m_nev);
BoolArray new_ritz_conv(m_nev);
for (Index i = 0; i < m_nev; i++)
{
new_ritz_val[i] = m_ritz_val[ind[i]];
new_ritz_vec.col(i).noalias() = m_ritz_vec.col(ind[i]);
new_ritz_conv[i] = m_ritz_conv[ind[i]];
}
m_ritz_val.swap(new_ritz_val);
m_ritz_vec.swap(new_ritz_vec);
m_ritz_conv.swap(new_ritz_conv);
}
public:
/// \cond
SymEigsBase(OpType* op, BOpType* Bop, Index nev, Index ncv) :
m_op(op),
m_n(m_op->rows()),
m_nev(nev),
m_ncv(ncv > m_n ? m_n : ncv),
m_nmatop(0),
m_niter(0),
m_fac(ArnoldiOpType(op, Bop), m_ncv),
m_info(NOT_COMPUTED),
m_near_0(TypeTraits<Scalar>::min() * Scalar(10)),
m_eps(Eigen::NumTraits<Scalar>::epsilon()),
m_eps23(Eigen::numext::pow(m_eps, Scalar(2.0) / 3))
{
if (nev < 1 || nev > m_n - 1)
throw std::invalid_argument("nev must satisfy 1 <= nev <= n - 1, n is the size of matrix");
if (ncv <= nev || ncv > m_n)
throw std::invalid_argument("ncv must satisfy nev < ncv <= n, n is the size of matrix");
}
///
/// Virtual destructor
///
virtual ~SymEigsBase() {}
/// \endcond
///
/// Initializes the solver by providing an initial residual vector.
///
/// \param init_resid Pointer to the initial residual vector.
///
/// **Spectra** (and also **ARPACK**) uses an iterative algorithm
/// to find eigenvalues. This function allows the user to provide the initial
/// residual vector.
///
void init(const Scalar* init_resid)
{
// Reset all matrices/vectors to zero
m_ritz_val.resize(m_ncv);
m_ritz_vec.resize(m_ncv, m_nev);
m_ritz_est.resize(m_ncv);
m_ritz_conv.resize(m_nev);
m_ritz_val.setZero();
m_ritz_vec.setZero();
m_ritz_est.setZero();
m_ritz_conv.setZero();
m_nmatop = 0;
m_niter = 0;
// Initialize the Lanczos factorization
MapConstVec v0(init_resid, m_n);
m_fac.init(v0, m_nmatop);
}
///
/// Initializes the solver by providing a random initial residual vector.
///
/// This overloaded function generates a random initial residual vector
/// (with a fixed random seed) for the algorithm. Elements in the vector
/// follow independent Uniform(-0.5, 0.5) distribution.
///
void init()
{
SimpleRandom<Scalar> rng(0);
Vector init_resid = rng.random_vec(m_n);
init(init_resid.data());
}
///
/// Conducts the major computation procedure.
///
/// \param maxit Maximum number of iterations allowed in the algorithm.
/// \param tol Precision parameter for the calculated eigenvalues.
/// \param sort_rule Rule to sort the eigenvalues and eigenvectors.
/// Supported values are
/// `Spectra::LARGEST_ALGE`, `Spectra::LARGEST_MAGN`,
/// `Spectra::SMALLEST_ALGE` and `Spectra::SMALLEST_MAGN`,
/// for example `LARGEST_ALGE` indicates that largest eigenvalues
/// come first. Note that this argument is only used to
/// **sort** the final result, and the **selection** rule
/// (e.g. selecting the largest or smallest eigenvalues in the
/// full spectrum) is specified by the template parameter
/// `SelectionRule` of SymEigsSolver.
///
/// \return Number of converged eigenvalues.
///
Index compute(Index maxit = 1000, Scalar tol = 1e-10, int sort_rule = LARGEST_ALGE)
{
// The m-step Lanczos factorization
m_fac.factorize_from(1, m_ncv, m_nmatop);
retrieve_ritzpair();
// Restarting
Index i, nconv = 0, nev_adj;
for (i = 0; i < maxit; i++)
{
nconv = num_converged(tol);
if (nconv >= m_nev)
break;
nev_adj = nev_adjusted(nconv);
restart(nev_adj);
}
// Sorting results
sort_ritzpair(sort_rule);
m_niter += i + 1;
m_info = (nconv >= m_nev) ? SUCCESSFUL : NOT_CONVERGING;
return std::min(m_nev, nconv);
}
///
/// Returns the status of the computation.
/// The full list of enumeration values can be found in \ref Enumerations.
///
int info() const { return m_info; }
///
/// Returns the number of iterations used in the computation.
///
Index num_iterations() const { return m_niter; }
///
/// Returns the number of matrix operations used in the computation.
///
Index num_operations() const { return m_nmatop; }
///
/// Returns the converged eigenvalues.
///
/// \return A vector containing the eigenvalues.
/// Returned vector type will be `Eigen::Vector<Scalar, ...>`, depending on
/// the template parameter `Scalar` defined.
///
Vector eigenvalues() const
{
const Index nconv = m_ritz_conv.cast<Index>().sum();
Vector res(nconv);
if (!nconv)
return res;
Index j = 0;
for (Index i = 0; i < m_nev; i++)
{
if (m_ritz_conv[i])
{
res[j] = m_ritz_val[i];
j++;
}
}
return res;
}
///
/// Returns the eigenvectors associated with the converged eigenvalues.
///
/// \param nvec The number of eigenvectors to return.
///
/// \return A matrix containing the eigenvectors.
/// Returned matrix type will be `Eigen::Matrix<Scalar, ...>`,
/// depending on the template parameter `Scalar` defined.
///
virtual Matrix eigenvectors(Index nvec) const
{
const Index nconv = m_ritz_conv.cast<Index>().sum();
nvec = std::min(nvec, nconv);
Matrix res(m_n, nvec);
if (!nvec)
return res;
Matrix ritz_vec_conv(m_ncv, nvec);
Index j = 0;
for (Index i = 0; i < m_nev && j < nvec; i++)
{
if (m_ritz_conv[i])
{
ritz_vec_conv.col(j).noalias() = m_ritz_vec.col(i);
j++;
}
}
res.noalias() = m_fac.matrix_V() * ritz_vec_conv;
return res;
}
///
/// Returns all converged eigenvectors.
///
virtual Matrix eigenvectors() const
{
return eigenvectors(m_nev);
}
};
} // namespace Spectra
#endif // SYM_EIGS_BASE_H

85
gtsam/3rdparty/Spectra/SymEigsShiftSolver.h vendored
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@ -1,15 +1,15 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SYM_EIGS_SHIFT_SOLVER_H
#define SYM_EIGS_SHIFT_SOLVER_H
#ifndef SPECTRA_SYM_EIGS_SHIFT_SOLVER_H
#define SPECTRA_SYM_EIGS_SHIFT_SOLVER_H
#include <Eigen/Core>
#include "SymEigsBase.h"
#include "HermEigsBase.h"
#include "Util/SelectionRule.h"
#include "MatOp/DenseSymShiftSolve.h"
@ -54,17 +54,11 @@ namespace Spectra {
/// returning \f$\lambda\f$ rather than \f$\nu\f$), and eigenvectors are the
/// same for both the original problem and the shifted-and-inverted problem.
///
/// \tparam Scalar The element type of the matrix.
/// Currently supported types are `float`, `double` and `long double`.
/// \tparam SelectionRule An enumeration value indicating the selection rule of
/// the shifted-and-inverted eigenvalues.
/// The full list of enumeration values can be found in
/// \ref Enumerations.
/// \tparam OpType The name of the matrix operation class. Users could either
/// use the wrapper classes such as DenseSymShiftSolve and
/// SparseSymShiftSolve, or define their
/// own that implements all the public member functions as in
/// DenseSymShiftSolve.
/// \tparam OpType The name of the matrix operation class. Users could either
/// use the wrapper classes such as DenseSymShiftSolve and
/// SparseSymShiftSolve, or define their own that implements the type
/// definition `Scalar` and all the public member functions as in
/// DenseSymShiftSolve.
///
/// Below is an example that illustrates the use of the shift-and-invert mode:
///
@ -80,7 +74,7 @@ namespace Spectra {
/// {
/// // A size-10 diagonal matrix with elements 1, 2, ..., 10
/// Eigen::MatrixXd M = Eigen::MatrixXd::Zero(10, 10);
/// for(int i = 0; i < M.rows(); i++)
/// for (int i = 0; i < M.rows(); i++)
/// M(i, i) = i + 1;
///
/// // Construct matrix operation object using the wrapper class
@ -88,12 +82,11 @@ namespace Spectra {
///
/// // Construct eigen solver object with shift 0
/// // This will find eigenvalues that are closest to 0
/// SymEigsShiftSolver< double, LARGEST_MAGN,
/// DenseSymShiftSolve<double> > eigs(&op, 3, 6, 0.0);
/// SymEigsShiftSolver<DenseSymShiftSolve<double>> eigs(op, 3, 6, 0.0);
///
/// eigs.init();
/// eigs.compute();
/// if(eigs.info() == SUCCESSFUL)
/// eigs.compute(SortRule::LargestMagn);
/// if (eigs.info() == CompInfo::Successful)
/// {
/// Eigen::VectorXd evalues = eigs.eigenvalues();
/// // Will get (3.0, 2.0, 1.0)
@ -119,14 +112,15 @@ namespace Spectra {
/// private:
/// double sigma_;
/// public:
/// int rows() { return 10; }
/// int cols() { return 10; }
/// using Scalar = double; // A typedef named "Scalar" is required
/// int rows() const { return 10; }
/// int cols() const { return 10; }
/// void set_shift(double sigma) { sigma_ = sigma; }
/// // y_out = inv(A - sigma * I) * x_in
/// // inv(A - sigma * I) = diag(1/(1-sigma), 1/(2-sigma), ...)
/// void perform_op(double *x_in, double *y_out)
/// void perform_op(double *x_in, double *y_out) const
/// {
/// for(int i = 0; i < rows(); i++)
/// for (int i = 0; i < rows(); i++)
/// {
/// y_out[i] = x_in[i] / (i + 1 - sigma_);
/// }
@ -137,11 +131,10 @@ namespace Spectra {
/// {
/// MyDiagonalTenShiftSolve op;
/// // Find three eigenvalues that are closest to 3.14
/// SymEigsShiftSolver<double, LARGEST_MAGN,
/// MyDiagonalTenShiftSolve> eigs(&op, 3, 6, 3.14);
/// SymEigsShiftSolver<MyDiagonalTenShiftSolve> eigs(op, 3, 6, 3.14);
/// eigs.init();
/// eigs.compute();
/// if(eigs.info() == SUCCESSFUL)
/// eigs.compute(SortRule::LargestMagn);
/// if (eigs.info() == CompInfo::Successful)
/// {
/// Eigen::VectorXd evalues = eigs.eigenvalues();
/// // Will get (4.0, 3.0, 2.0)
@ -152,34 +145,38 @@ namespace Spectra {
/// }
/// \endcode
///
template <typename Scalar = double,
int SelectionRule = LARGEST_MAGN,
typename OpType = DenseSymShiftSolve<double> >
class SymEigsShiftSolver : public SymEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>
template <typename OpType = DenseSymShiftSolve<double>>
class SymEigsShiftSolver : public HermEigsBase<OpType, IdentityBOp>
{
private:
typedef Eigen::Index Index;
typedef Eigen::Array<Scalar, Eigen::Dynamic, 1> Array;
using Scalar = typename OpType::Scalar;
using Index = Eigen::Index;
using Array = Eigen::Array<Scalar, Eigen::Dynamic, 1>;
using Base = HermEigsBase<OpType, IdentityBOp>;
using Base::m_nev;
using Base::m_ritz_val;
const Scalar m_sigma;
// First transform back the Ritz values, and then sort
void sort_ritzpair(int sort_rule)
void sort_ritzpair(SortRule sort_rule) override
{
Array m_ritz_val_org = Scalar(1.0) / this->m_ritz_val.head(this->m_nev).array() + m_sigma;
this->m_ritz_val.head(this->m_nev) = m_ritz_val_org;
SymEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>::sort_ritzpair(sort_rule);
// The eigenvalues we get from the iteration is nu = 1 / (lambda - sigma)
// So the eigenvalues of the original problem is lambda = 1 / nu + sigma
m_ritz_val.head(m_nev).array() = Scalar(1) / m_ritz_val.head(m_nev).array() + m_sigma;
Base::sort_ritzpair(sort_rule);
}
public:
///
/// Constructor to create a eigen solver object using the shift-and-invert mode.
///
/// \param op Pointer to the matrix operation object, which should implement
/// \param op The matrix operation object that implements
/// the shift-solve operation of \f$A\f$: calculating
/// \f$(A-\sigma I)^{-1}v\f$ for any vector \f$v\f$. Users could either
/// create the object from the wrapper class such as DenseSymShiftSolve, or
/// define their own that implements all the public member functions
/// define their own that implements all the public members
/// as in DenseSymShiftSolve.
/// \param nev Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-1\f$,
/// where \f$n\f$ is the size of matrix.
@ -190,14 +187,14 @@ public:
/// and is advised to take \f$ncv \ge 2\cdot nev\f$.
/// \param sigma The value of the shift.
///
SymEigsShiftSolver(OpType* op, Index nev, Index ncv, Scalar sigma) :
SymEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>(op, NULL, nev, ncv),
SymEigsShiftSolver(OpType& op, Index nev, Index ncv, const Scalar& sigma) :
Base(op, IdentityBOp(), nev, ncv),
m_sigma(sigma)
{
this->m_op->set_shift(m_sigma);
op.set_shift(m_sigma);
}
};
} // namespace Spectra
#endif // SYM_EIGS_SHIFT_SOLVER_H
#endif // SPECTRA_SYM_EIGS_SHIFT_SOLVER_H

71
gtsam/3rdparty/Spectra/SymEigsSolver.h vendored
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@ -1,15 +1,15 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SYM_EIGS_SOLVER_H
#define SYM_EIGS_SOLVER_H
#ifndef SPECTRA_SYM_EIGS_SOLVER_H
#define SPECTRA_SYM_EIGS_SOLVER_H
#include <Eigen/Core>
#include "SymEigsBase.h"
#include "HermEigsBase.h"
#include "Util/SelectionRule.h"
#include "MatOp/DenseSymMatProd.h"
@ -34,27 +34,21 @@ namespace Spectra {
/// the constructor of SymEigsSolver.
///
/// If the matrix \f$A\f$ is already stored as a matrix object in **Eigen**,
/// for example `Eigen::MatrixXd`, then there is an easy way to construct such
/// for example `Eigen::MatrixXd`, then there is an easy way to construct such a
/// matrix operation class, by using the built-in wrapper class DenseSymMatProd
/// which wraps an existing matrix object in **Eigen**. This is also the
/// that wraps an existing matrix object in **Eigen**. This is also the
/// default template parameter for SymEigsSolver. For sparse matrices, the
/// wrapper class SparseSymMatProd can be used similarly.
///
/// If the users need to define their own matrix-vector multiplication operation
/// class, it should implement all the public member functions as in DenseSymMatProd.
/// class, it should define a public type `Scalar` to indicate the element type,
/// and implement all the public member functions as in DenseSymMatProd.
///
/// \tparam Scalar The element type of the matrix.
/// Currently supported types are `float`, `double` and `long double`.
/// \tparam SelectionRule An enumeration value indicating the selection rule of
/// the requested eigenvalues, for example `LARGEST_MAGN`
/// to retrieve eigenvalues with the largest magnitude.
/// The full list of enumeration values can be found in
/// \ref Enumerations.
/// \tparam OpType The name of the matrix operation class. Users could either
/// use the wrapper classes such as DenseSymMatProd and
/// SparseSymMatProd, or define their
/// own that implements all the public member functions as in
/// DenseSymMatProd.
/// \tparam OpType The name of the matrix operation class. Users could either
/// use the wrapper classes such as DenseSymMatProd and
/// SparseSymMatProd, or define their own that implements the type
/// definition `Scalar` and all the public member functions as in
/// DenseSymMatProd.
///
/// Below is an example that demonstrates the usage of this class.
///
@ -76,15 +70,15 @@ namespace Spectra {
/// DenseSymMatProd<double> op(M);
///
/// // Construct eigen solver object, requesting the largest three eigenvalues
/// SymEigsSolver< double, LARGEST_ALGE, DenseSymMatProd<double> > eigs(&op, 3, 6);
/// SymEigsSolver<DenseSymMatProd<double>> eigs(op, 3, 6);
///
/// // Initialize and compute
/// eigs.init();
/// int nconv = eigs.compute();
/// int nconv = eigs.compute(SortRule::LargestAlge);
///
/// // Retrieve results
/// Eigen::VectorXd evalues;
/// if(eigs.info() == SUCCESSFUL)
/// if (eigs.info() == CompInfo::Successful)
/// evalues = eigs.eigenvalues();
///
/// std::cout << "Eigenvalues found:\n" << evalues << std::endl;
@ -106,12 +100,13 @@ namespace Spectra {
/// class MyDiagonalTen
/// {
/// public:
/// int rows() { return 10; }
/// int cols() { return 10; }
/// using Scalar = double; // A typedef named "Scalar" is required
/// int rows() const { return 10; }
/// int cols() const { return 10; }
/// // y_out = M * x_in
/// void perform_op(double *x_in, double *y_out)
/// void perform_op(double *x_in, double *y_out) const
/// {
/// for(int i = 0; i < rows(); i++)
/// for (int i = 0; i < rows(); i++)
/// {
/// y_out[i] = x_in[i] * (i + 1);
/// }
@ -121,10 +116,10 @@ namespace Spectra {
/// int main()
/// {
/// MyDiagonalTen op;
/// SymEigsSolver<double, LARGEST_ALGE, MyDiagonalTen> eigs(&op, 3, 6);
/// SymEigsSolver<MyDiagonalTen> eigs(op, 3, 6);
/// eigs.init();
/// eigs.compute();
/// if(eigs.info() == SUCCESSFUL)
/// eigs.compute(SortRule::LargestAlge);
/// if (eigs.info() == CompInfo::Successful)
/// {
/// Eigen::VectorXd evalues = eigs.eigenvalues();
/// // Will get (10, 9, 8)
@ -135,23 +130,21 @@ namespace Spectra {
/// }
/// \endcode
///
template <typename Scalar = double,
int SelectionRule = LARGEST_MAGN,
typename OpType = DenseSymMatProd<double> >
class SymEigsSolver : public SymEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>
template <typename OpType = DenseSymMatProd<double>>
class SymEigsSolver : public HermEigsBase<OpType, IdentityBOp>
{
private:
typedef Eigen::Index Index;
using Index = Eigen::Index;
public:
///
/// Constructor to create a solver object.
///
/// \param op Pointer to the matrix operation object, which should implement
/// \param op The matrix operation object that implements
/// the matrix-vector multiplication operation of \f$A\f$:
/// calculating \f$Av\f$ for any vector \f$v\f$. Users could either
/// create the object from the wrapper class such as DenseSymMatProd, or
/// define their own that implements all the public member functions
/// define their own that implements all the public members
/// as in DenseSymMatProd.
/// \param nev Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-1\f$,
/// where \f$n\f$ is the size of matrix.
@ -161,11 +154,11 @@ public:
/// in each iteration. This parameter must satisfy \f$nev < ncv \le n\f$,
/// and is advised to take \f$ncv \ge 2\cdot nev\f$.
///
SymEigsSolver(OpType* op, Index nev, Index ncv) :
SymEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>(op, NULL, nev, ncv)
SymEigsSolver(OpType& op, Index nev, Index ncv) :
HermEigsBase<OpType, IdentityBOp>(op, IdentityBOp(), nev, ncv)
{}
};
} // namespace Spectra
#endif // SYM_EIGS_SOLVER_H
#endif // SPECTRA_SYM_EIGS_SOLVER_H

463
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@ -0,0 +1,463 @@
// Copyright (C) 2020-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_SYM_GEIGS_SHIFT_SOLVER_H
#define SPECTRA_SYM_GEIGS_SHIFT_SOLVER_H
#include <utility> // std::move
#include "HermEigsBase.h"
#include "Util/GEigsMode.h"
#include "MatOp/internal/SymGEigsShiftInvertOp.h"
#include "MatOp/internal/SymGEigsBucklingOp.h"
#include "MatOp/internal/SymGEigsCayleyOp.h"
namespace Spectra {
///
/// \ingroup GEigenSolver
///
/// This class implements the generalized eigen solver for real symmetric
/// matrices, i.e., to solve \f$Ax=\lambda Bx\f$ where \f$A\f$ and \f$B\f$ are symmetric
/// matrices. A spectral transform is applied to seek interior
/// generalized eigenvalues with respect to some shift \f$\sigma\f$.
///
/// There are different modes of this solver, specified by the template parameter `Mode`.
/// See the pages for the specialized classes for details.
/// - The shift-and-invert mode transforms the problem into \f$(A-\sigma B)^{-1}Bx=\nu x\f$,
/// where \f$\nu=1/(\lambda-\sigma)\f$. This mode assumes that \f$B\f$ is positive definite.
/// See \ref SymGEigsShiftSolver<OpType, BOpType, GEigsMode::ShiftInvert>
/// "SymGEigsShiftSolver (Shift-and-invert mode)" for more details.
/// - The buckling mode transforms the problem into \f$(A-\sigma B)^{-1}Ax=\nu x\f$,
/// where \f$\nu=\lambda/(\lambda-\sigma)\f$. This mode assumes that \f$A\f$ is positive definite.
/// See \ref SymGEigsShiftSolver<OpType, BOpType, GEigsMode::Buckling>
/// "SymGEigsShiftSolver (Buckling mode)" for more details.
/// - The Cayley mode transforms the problem into \f$(A-\sigma B)^{-1}(A+\sigma B)x=\nu x\f$,
/// where \f$\nu=(\lambda+\sigma)/(\lambda-\sigma)\f$. This mode assumes that \f$B\f$ is positive definite.
/// See \ref SymGEigsShiftSolver<OpType, BOpType, GEigsMode::Cayley>
/// "SymGEigsShiftSolver (Cayley mode)" for more details.
// Empty class template
template <typename OpType, typename BOpType, GEigsMode Mode>
class SymGEigsShiftSolver
{};
///
/// \ingroup GEigenSolver
///
/// This class implements the generalized eigen solver for real symmetric
/// matrices using the shift-and-invert spectral transformation. The original problem is
/// to solve \f$Ax=\lambda Bx\f$, where \f$A\f$ is symmetric and \f$B\f$ is positive definite.
/// The transformed problem is \f$(A-\sigma B)^{-1}Bx=\nu x\f$, where
/// \f$\nu=1/(\lambda-\sigma)\f$, and \f$\sigma\f$ is a user-specified shift.
///
/// This solver requires two matrix operation objects: one to compute \f$y=(A-\sigma B)^{-1}x\f$
/// for any vector \f$v\f$, and one for the matrix multiplication \f$Bv\f$.
///
/// If \f$A\f$ and \f$B\f$ are stored as Eigen matrices, then the first operation object
/// can be created using the SymShiftInvert class, and the second one can be created
/// using the DenseSymMatProd or SparseSymMatProd classes. If the users need to define their
/// own operation classes, then they should implement all the public member functions as
/// in those built-in classes.
///
/// \tparam OpType The type of the first operation object. Users could either
/// use the wrapper class SymShiftInvert, or define their own that implements
/// the type definition `Scalar` and all the public member functions as in SymShiftInvert.
/// \tparam BOpType The name of the matrix operation class for \f$B\f$. Users could either
/// use the wrapper classes such as DenseSymMatProd and
/// SparseSymMatProd, or define their own that implements all the
/// public member functions as in DenseSymMatProd.
/// \tparam Mode Mode of the generalized eigen solver. In this solver
/// it is Spectra::GEigsMode::ShiftInvert.
///
/// Below is an example that demonstrates the usage of this class.
///
/// \code{.cpp}
/// #include <Eigen/Core>
/// #include <Eigen/SparseCore>
/// #include <Spectra/SymGEigsShiftSolver.h>
/// #include <Spectra/MatOp/SymShiftInvert.h>
/// #include <Spectra/MatOp/SparseSymMatProd.h>
/// #include <iostream>
///
/// using namespace Spectra;
///
/// int main()
/// {
/// // We are going to solve the generalized eigenvalue problem
/// // A * x = lambda * B * x,
/// // where A is symmetric and B is positive definite
/// const int n = 100;
///
/// // Define the A matrix
/// Eigen::MatrixXd M = Eigen::MatrixXd::Random(n, n);
/// Eigen::MatrixXd A = M + M.transpose();
///
/// // Define the B matrix, a tridiagonal matrix with 2 on the diagonal
/// // and 1 on the subdiagonals
/// Eigen::SparseMatrix<double> B(n, n);
/// B.reserve(Eigen::VectorXi::Constant(n, 3));
/// for (int i = 0; i < n; i++)
/// {
/// B.insert(i, i) = 2.0;
/// if (i > 0)
/// B.insert(i - 1, i) = 1.0;
/// if (i < n - 1)
/// B.insert(i + 1, i) = 1.0;
/// }
///
/// // Construct matrix operation objects using the wrapper classes
/// // A is dense, B is sparse
/// using OpType = SymShiftInvert<double, Eigen::Dense, Eigen::Sparse>;
/// using BOpType = SparseSymMatProd<double>;
/// OpType op(A, B);
/// BOpType Bop(B);
///
/// // Construct generalized eigen solver object, seeking three generalized
/// // eigenvalues that are closest to zero. This is equivalent to specifying
/// // a shift sigma = 0.0 combined with the SortRule::LargestMagn selection rule
/// SymGEigsShiftSolver<OpType, BOpType, GEigsMode::ShiftInvert>
/// geigs(op, Bop, 3, 6, 0.0);
///
/// // Initialize and compute
/// geigs.init();
/// int nconv = geigs.compute(SortRule::LargestMagn);
///
/// // Retrieve results
/// Eigen::VectorXd evalues;
/// Eigen::MatrixXd evecs;
/// if (geigs.info() == CompInfo::Successful)
/// {
/// evalues = geigs.eigenvalues();
/// evecs = geigs.eigenvectors();
/// }
///
/// std::cout << "Number of converged generalized eigenvalues: " << nconv << std::endl;
/// std::cout << "Generalized eigenvalues found:\n" << evalues << std::endl;
/// std::cout << "Generalized eigenvectors found:\n" << evecs.topRows(10) << std::endl;
///
/// return 0;
/// }
/// \endcode
// Partial specialization for mode = GEigsMode::ShiftInvert
template <typename OpType, typename BOpType>
class SymGEigsShiftSolver<OpType, BOpType, GEigsMode::ShiftInvert> :
public HermEigsBase<SymGEigsShiftInvertOp<OpType, BOpType>, BOpType>
{
private:
using Scalar = typename OpType::Scalar;
using Index = Eigen::Index;
using Array = Eigen::Array<Scalar, Eigen::Dynamic, 1>;
using ModeMatOp = SymGEigsShiftInvertOp<OpType, BOpType>;
using Base = HermEigsBase<ModeMatOp, BOpType>;
using Base::m_nev;
using Base::m_ritz_val;
const Scalar m_sigma;
// Set shift and forward
static ModeMatOp set_shift_and_move(ModeMatOp&& op, const Scalar& sigma)
{
op.set_shift(sigma);
return std::move(op);
}
// First transform back the Ritz values, and then sort
void sort_ritzpair(SortRule sort_rule) override
{
// The eigenvalues we get from the iteration is nu = 1 / (lambda - sigma)
// So the eigenvalues of the original problem is lambda = 1 / nu + sigma
m_ritz_val.head(m_nev).array() = Scalar(1) / m_ritz_val.head(m_nev).array() + m_sigma;
Base::sort_ritzpair(sort_rule);
}
public:
///
/// Constructor to create a solver object.
///
/// \param op The matrix operation object that computes \f$y=(A-\sigma B)^{-1}v\f$
/// for any vector \f$v\f$. Users could either create the object from the
/// wrapper class SymShiftInvert, or define their own that implements all
/// the public members as in SymShiftInvert.
/// \param Bop The \f$B\f$ matrix operation object that implements the matrix-vector
/// multiplication \f$Bv\f$. Users could either create the object from the
/// wrapper classes such as DenseSymMatProd and SparseSymMatProd, or
/// define their own that implements all the public member functions
/// as in DenseSymMatProd. \f$B\f$ needs to be positive definite.
/// \param nev Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-1\f$,
/// where \f$n\f$ is the size of matrix.
/// \param ncv Parameter that controls the convergence speed of the algorithm.
/// Typically a larger `ncv` means faster convergence, but it may
/// also result in greater memory use and more matrix operations
/// in each iteration. This parameter must satisfy \f$nev < ncv \le n\f$,
/// and is advised to take \f$ncv \ge 2\cdot nev\f$.
/// \param sigma The value of the shift.
///
SymGEigsShiftSolver(OpType& op, BOpType& Bop, Index nev, Index ncv, const Scalar& sigma) :
Base(set_shift_and_move(ModeMatOp(op, Bop), sigma), Bop, nev, ncv),
m_sigma(sigma)
{}
};
///
/// \ingroup GEigenSolver
///
/// This class implements the generalized eigen solver for real symmetric
/// matrices in the buckling mode. The original problem is
/// to solve \f$Kx=\lambda K_G x\f$, where \f$K\f$ is positive definite and \f$K_G\f$ is symmetric.
/// The transformed problem is \f$(K-\sigma K_G)^{-1}Kx=\nu x\f$, where
/// \f$\nu=\lambda/(\lambda-\sigma)\f$, and \f$\sigma\f$ is a user-specified shift.
///
/// This solver requires two matrix operation objects: one to compute \f$y=(K-\sigma K_G)^{-1}x\f$
/// for any vector \f$v\f$, and one for the matrix multiplication \f$Kv\f$.
///
/// If \f$K\f$ and \f$K_G\f$ are stored as Eigen matrices, then the first operation object
/// can be created using the SymShiftInvert class, and the second one can be created
/// using the DenseSymMatProd or SparseSymMatProd classes. If the users need to define their
/// own operation classes, then they should implement all the public member functions as
/// in those built-in classes.
///
/// \tparam OpType The type of the first operation object. Users could either
/// use the wrapper class SymShiftInvert, or define their own that implements
/// the type definition `Scalar` and all the public member functions as in SymShiftInvert.
/// \tparam BOpType The name of the matrix operation class for \f$K\f$. Users could either
/// use the wrapper classes such as DenseSymMatProd and
/// SparseSymMatProd, or define their own that implements all the
/// public member functions as in DenseSymMatProd.
/// \tparam Mode Mode of the generalized eigen solver. In this solver
/// it is Spectra::GEigsMode::Buckling.
///
/// Below is an example that demonstrates the usage of this class.
///
/// \code{.cpp}
/// #include <Eigen/Core>
/// #include <Eigen/SparseCore>
/// #include <Spectra/SymGEigsShiftSolver.h>
/// #include <Spectra/MatOp/SymShiftInvert.h>
/// #include <Spectra/MatOp/SparseSymMatProd.h>
/// #include <iostream>
///
/// using namespace Spectra;
///
/// int main()
/// {
/// // We are going to solve the generalized eigenvalue problem
/// // K * x = lambda * KG * x,
/// // where K is positive definite, and KG is symmetric
/// const int n = 100;
///
/// // Define the K matrix, a tridiagonal matrix with 2 on the diagonal
/// // and 1 on the subdiagonals
/// Eigen::SparseMatrix<double> K(n, n);
/// K.reserve(Eigen::VectorXi::Constant(n, 3));
/// for (int i = 0; i < n; i++)
/// {
/// K.insert(i, i) = 2.0;
/// if (i > 0)
/// K.insert(i - 1, i) = 1.0;
/// if (i < n - 1)
/// K.insert(i + 1, i) = 1.0;
/// }
///
/// // Define the KG matrix
/// Eigen::MatrixXd M = Eigen::MatrixXd::Random(n, n);
/// Eigen::MatrixXd KG = M + M.transpose();
///
/// // Construct matrix operation objects using the wrapper classes
/// // K is sparse, KG is dense
/// using OpType = SymShiftInvert<double, Eigen::Sparse, Eigen::Dense>;
/// using BOpType = SparseSymMatProd<double>;
/// OpType op(K, KG);
/// BOpType Bop(K);
///
/// // Construct generalized eigen solver object, seeking three generalized
/// // eigenvalues that are closest to and larger than 1.0. This is equivalent to
/// // specifying a shift sigma = 1.0 combined with the SortRule::LargestAlge
/// // selection rule
/// SymGEigsShiftSolver<OpType, BOpType, GEigsMode::Buckling>
/// geigs(op, Bop, 3, 6, 1.0);
///
/// // Initialize and compute
/// geigs.init();
/// int nconv = geigs.compute(SortRule::LargestAlge);
///
/// // Retrieve results
/// Eigen::VectorXd evalues;
/// Eigen::MatrixXd evecs;
/// if (geigs.info() == CompInfo::Successful)
/// {
/// evalues = geigs.eigenvalues();
/// evecs = geigs.eigenvectors();
/// }
///
/// std::cout << "Number of converged generalized eigenvalues: " << nconv << std::endl;
/// std::cout << "Generalized eigenvalues found:\n" << evalues << std::endl;
/// std::cout << "Generalized eigenvectors found:\n" << evecs.topRows(10) << std::endl;
///
/// return 0;
/// }
/// \endcode
// Partial specialization for mode = GEigsMode::Buckling
template <typename OpType, typename BOpType>
class SymGEigsShiftSolver<OpType, BOpType, GEigsMode::Buckling> :
public HermEigsBase<SymGEigsBucklingOp<OpType, BOpType>, BOpType>
{
private:
using Scalar = typename OpType::Scalar;
using Index = Eigen::Index;
using Array = Eigen::Array<Scalar, Eigen::Dynamic, 1>;
using ModeMatOp = SymGEigsBucklingOp<OpType, BOpType>;
using Base = HermEigsBase<ModeMatOp, BOpType>;
using Base::m_nev;
using Base::m_ritz_val;
const Scalar m_sigma;
// Set shift and forward
static ModeMatOp set_shift_and_move(ModeMatOp&& op, const Scalar& sigma)
{
if (sigma == Scalar(0))
throw std::invalid_argument("SymGEigsShiftSolver: sigma cannot be zero in the buckling mode");
op.set_shift(sigma);
return std::move(op);
}
// First transform back the Ritz values, and then sort
void sort_ritzpair(SortRule sort_rule) override
{
// The eigenvalues we get from the iteration is nu = lambda / (lambda - sigma)
// So the eigenvalues of the original problem is lambda = sigma * nu / (nu - 1)
m_ritz_val.head(m_nev).array() = m_sigma * m_ritz_val.head(m_nev).array() /
(m_ritz_val.head(m_nev).array() - Scalar(1));
Base::sort_ritzpair(sort_rule);
}
public:
///
/// Constructor to create a solver object.
///
/// \param op The matrix operation object that computes \f$y=(K-\sigma K_G)^{-1}v\f$
/// for any vector \f$v\f$. Users could either create the object from the
/// wrapper class SymShiftInvert, or define their own that implements all
/// the public members as in SymShiftInvert.
/// \param Bop The \f$K\f$ matrix operation object that implements the matrix-vector
/// multiplication \f$Kv\f$. Users could either create the object from the
/// wrapper classes such as DenseSymMatProd and SparseSymMatProd, or
/// define their own that implements all the public member functions
/// as in DenseSymMatProd. \f$K\f$ needs to be positive definite.
/// \param nev Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-1\f$,
/// where \f$n\f$ is the size of matrix.
/// \param ncv Parameter that controls the convergence speed of the algorithm.
/// Typically a larger `ncv` means faster convergence, but it may
/// also result in greater memory use and more matrix operations
/// in each iteration. This parameter must satisfy \f$nev < ncv \le n\f$,
/// and is advised to take \f$ncv \ge 2\cdot nev\f$.
/// \param sigma The value of the shift.
///
SymGEigsShiftSolver(OpType& op, BOpType& Bop, Index nev, Index ncv, const Scalar& sigma) :
Base(set_shift_and_move(ModeMatOp(op, Bop), sigma), Bop, nev, ncv),
m_sigma(sigma)
{}
};
///
/// \ingroup GEigenSolver
///
/// This class implements the generalized eigen solver for real symmetric
/// matrices using the Cayley spectral transformation. The original problem is
/// to solve \f$Ax=\lambda Bx\f$, where \f$A\f$ is symmetric and \f$B\f$ is positive definite.
/// The transformed problem is \f$(A-\sigma B)^{-1}(A+\sigma B)x=\nu x\f$, where
/// \f$\nu=(\lambda+\sigma)/(\lambda-\sigma)\f$, and \f$\sigma\f$ is a user-specified shift.
///
/// This solver requires two matrix operation objects: one to compute \f$y=(A-\sigma B)^{-1}x\f$
/// for any vector \f$v\f$, and one for the matrix multiplication \f$Bv\f$.
///
/// If \f$A\f$ and \f$B\f$ are stored as Eigen matrices, then the first operation object
/// can be created using the SymShiftInvert class, and the second one can be created
/// using the DenseSymMatProd or SparseSymMatProd classes. If the users need to define their
/// own operation classes, then they should implement all the public member functions as
/// in those built-in classes.
///
/// \tparam OpType The type of the first operation object. Users could either
/// use the wrapper class SymShiftInvert, or define their own that implements
/// the type definition `Scalar` and all the public member functions as in SymShiftInvert.
/// \tparam BOpType The name of the matrix operation class for \f$B\f$. Users could either
/// use the wrapper classes such as DenseSymMatProd and
/// SparseSymMatProd, or define their own that implements all the
/// public member functions as in DenseSymMatProd.
/// \tparam Mode Mode of the generalized eigen solver. In this solver
/// it is Spectra::GEigsMode::Cayley.
// Partial specialization for mode = GEigsMode::Cayley
template <typename OpType, typename BOpType>
class SymGEigsShiftSolver<OpType, BOpType, GEigsMode::Cayley> :
public HermEigsBase<SymGEigsCayleyOp<OpType, BOpType>, BOpType>
{
private:
using Scalar = typename OpType::Scalar;
using Index = Eigen::Index;
using Array = Eigen::Array<Scalar, Eigen::Dynamic, 1>;
using ModeMatOp = SymGEigsCayleyOp<OpType, BOpType>;
using Base = HermEigsBase<ModeMatOp, BOpType>;
using Base::m_nev;
using Base::m_ritz_val;
const Scalar m_sigma;
// Set shift and forward
static ModeMatOp set_shift_and_move(ModeMatOp&& op, const Scalar& sigma)
{
if (sigma == Scalar(0))
throw std::invalid_argument("SymGEigsShiftSolver: sigma cannot be zero in the Cayley mode");
op.set_shift(sigma);
return std::move(op);
}
// First transform back the Ritz values, and then sort
void sort_ritzpair(SortRule sort_rule) override
{
// The eigenvalues we get from the iteration is nu = (lambda + sigma) / (lambda - sigma)
// So the eigenvalues of the original problem is lambda = sigma * (nu + 1) / (nu - 1)
m_ritz_val.head(m_nev).array() = m_sigma * (m_ritz_val.head(m_nev).array() + Scalar(1)) /
(m_ritz_val.head(m_nev).array() - Scalar(1));
Base::sort_ritzpair(sort_rule);
}
public:
///
/// Constructor to create a solver object.
///
/// \param op The matrix operation object that computes \f$y=(A-\sigma B)^{-1}v\f$
/// for any vector \f$v\f$. Users could either create the object from the
/// wrapper class SymShiftInvert, or define their own that implements all
/// the public members as in SymShiftInvert.
/// \param Bop The \f$B\f$ matrix operation object that implements the matrix-vector
/// multiplication \f$Bv\f$. Users could either create the object from the
/// wrapper classes such as DenseSymMatProd and SparseSymMatProd, or
/// define their own that implements all the public member functions
/// as in DenseSymMatProd. \f$B\f$ needs to be positive definite.
/// \param nev Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-1\f$,
/// where \f$n\f$ is the size of matrix.
/// \param ncv Parameter that controls the convergence speed of the algorithm.
/// Typically a larger `ncv` means faster convergence, but it may
/// also result in greater memory use and more matrix operations
/// in each iteration. This parameter must satisfy \f$nev < ncv \le n\f$,
/// and is advised to take \f$ncv \ge 2\cdot nev\f$.
/// \param sigma The value of the shift.
///
SymGEigsShiftSolver(OpType& op, BOpType& Bop, Index nev, Index ncv, const Scalar& sigma) :
Base(set_shift_and_move(ModeMatOp(op, Bop), sigma), Bop, nev, ncv),
m_sigma(sigma)
{}
};
} // namespace Spectra
#endif // SPECTRA_SYM_GEIGS_SHIFT_SOLVER_H

200
gtsam/3rdparty/Spectra/SymGEigsSolver.h vendored
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@ -1,13 +1,13 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SYM_GEIGS_SOLVER_H
#define SYM_GEIGS_SOLVER_H
#ifndef SPECTRA_SYM_GEIGS_SOLVER_H
#define SPECTRA_SYM_GEIGS_SOLVER_H
#include "SymEigsBase.h"
#include "HermEigsBase.h"
#include "Util/GEigsMode.h"
#include "MatOp/internal/SymGEigsCholeskyOp.h"
#include "MatOp/internal/SymGEigsRegInvOp.h"
@ -27,25 +27,21 @@ namespace Spectra {
/// matrices, i.e., to solve \f$Ax=\lambda Bx\f$ where \f$A\f$ is symmetric and
/// \f$B\f$ is positive definite.
///
/// There are two modes of this solver, specified by the template parameter
/// GEigsMode. See the pages for the specialized classes for details.
/// There are two modes of this solver, specified by the template parameter `Mode`.
/// See the pages for the specialized classes for details.
/// - The Cholesky mode assumes that \f$B\f$ can be factorized using Cholesky
/// decomposition, which is the preferred mode when the decomposition is
/// available. (This can be easily done in Eigen using the dense or sparse
/// Cholesky solver.)
/// See \ref SymGEigsSolver<Scalar, SelectionRule, OpType, BOpType, GEIGS_CHOLESKY> "SymGEigsSolver (Cholesky mode)" for more details.
/// See \ref SymGEigsSolver<OpType, BOpType, GEigsMode::Cholesky> "SymGEigsSolver (Cholesky mode)" for more details.
/// - The regular inverse mode requires the matrix-vector product \f$Bv\f$ and the
/// linear equation solving operation \f$B^{-1}v\f$. This mode should only be
/// used when the Cholesky decomposition of \f$B\f$ is hard to implement, or
/// when computing \f$B^{-1}v\f$ is much faster than the Cholesky decomposition.
/// See \ref SymGEigsSolver<Scalar, SelectionRule, OpType, BOpType, GEIGS_REGULAR_INVERSE> "SymGEigsSolver (Regular inverse mode)" for more details.
/// See \ref SymGEigsSolver<OpType, BOpType, GEigsMode::RegularInverse> "SymGEigsSolver (Regular inverse mode)" for more details.
// Empty class template
template <typename Scalar,
int SelectionRule,
typename OpType,
typename BOpType,
int GEigsMode>
template <typename OpType, typename BOpType, GEigsMode Mode>
class SymGEigsSolver
{};
@ -67,25 +63,17 @@ class SymGEigsSolver
/// classes. If the users need to define their own operation classes, then they
/// should implement all the public member functions as in those built-in classes.
///
/// \tparam Scalar The element type of the matrix.
/// Currently supported types are `float`, `double` and `long double`.
/// \tparam SelectionRule An enumeration value indicating the selection rule of
/// the requested eigenvalues, for example `LARGEST_MAGN`
/// to retrieve eigenvalues with the largest magnitude.
/// The full list of enumeration values can be found in
/// \ref Enumerations.
/// \tparam OpType The name of the matrix operation class for \f$A\f$. Users could either
/// use the wrapper classes such as DenseSymMatProd and
/// SparseSymMatProd, or define their
/// own that implements all the public member functions as in
/// DenseSymMatProd.
/// \tparam BOpType The name of the matrix operation class for \f$B\f$. Users could either
/// use the wrapper classes such as DenseCholesky and
/// SparseCholesky, or define their
/// own that implements all the public member functions as in
/// DenseCholesky.
/// \tparam GEigsMode Mode of the generalized eigen solver. In this solver
/// it is Spectra::GEIGS_CHOLESKY.
/// \tparam OpType The name of the matrix operation class for \f$A\f$. Users could either
/// use the wrapper classes such as DenseSymMatProd and
/// SparseSymMatProd, or define their own that implements the type
/// definition `Scalar` and all the public member functions as in
/// DenseSymMatProd.
/// \tparam BOpType The name of the matrix operation class for \f$B\f$. Users could either
/// use the wrapper classes such as DenseCholesky and
/// SparseCholesky, or define their own that implements all the
/// public member functions as in DenseCholesky.
/// \tparam Mode Mode of the generalized eigen solver. In this solver
/// it is Spectra::GEigsMode::Cholesky.
///
/// Below is an example that demonstrates the usage of this class.
///
@ -112,31 +100,31 @@ class SymGEigsSolver
/// // Define the B matrix, a band matrix with 2 on the diagonal and 1 on the subdiagonals
/// Eigen::SparseMatrix<double> B(n, n);
/// B.reserve(Eigen::VectorXi::Constant(n, 3));
/// for(int i = 0; i < n; i++)
/// for (int i = 0; i < n; i++)
/// {
/// B.insert(i, i) = 2.0;
/// if(i > 0)
/// if (i > 0)
/// B.insert(i - 1, i) = 1.0;
/// if(i < n - 1)
/// if (i < n - 1)
/// B.insert(i + 1, i) = 1.0;
/// }
///
/// // Construct matrix operation object using the wrapper classes
/// // Construct matrix operation objects using the wrapper classes
/// DenseSymMatProd<double> op(A);
/// SparseCholesky<double> Bop(B);
///
/// // Construct generalized eigen solver object, requesting the largest three generalized eigenvalues
/// SymGEigsSolver<double, LARGEST_ALGE, DenseSymMatProd<double>, SparseCholesky<double>, GEIGS_CHOLESKY>
/// geigs(&op, &Bop, 3, 6);
/// SymGEigsSolver<DenseSymMatProd<double>, SparseCholesky<double>, GEigsMode::Cholesky>
/// geigs(op, Bop, 3, 6);
///
/// // Initialize and compute
/// geigs.init();
/// int nconv = geigs.compute();
/// int nconv = geigs.compute(SortRule::LargestAlge);
///
/// // Retrieve results
/// Eigen::VectorXd evalues;
/// Eigen::MatrixXd evecs;
/// if(geigs.info() == SUCCESSFUL)
/// if (geigs.info() == CompInfo::Successful)
/// {
/// evalues = geigs.eigenvalues();
/// evecs = geigs.eigenvectors();
@ -156,39 +144,39 @@ class SymGEigsSolver
/// }
/// \endcode
// Partial specialization for GEigsMode = GEIGS_CHOLESKY
template <typename Scalar,
int SelectionRule,
typename OpType,
typename BOpType>
class SymGEigsSolver<Scalar, SelectionRule, OpType, BOpType, GEIGS_CHOLESKY> :
public SymEigsBase<Scalar, SelectionRule, SymGEigsCholeskyOp<Scalar, OpType, BOpType>, IdentityBOp>
// Partial specialization for mode = GEigsMode::Cholesky
template <typename OpType, typename BOpType>
class SymGEigsSolver<OpType, BOpType, GEigsMode::Cholesky> :
public HermEigsBase<SymGEigsCholeskyOp<OpType, BOpType>, IdentityBOp>
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
using Scalar = typename OpType::Scalar;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
BOpType* m_Bop;
using ModeMatOp = SymGEigsCholeskyOp<OpType, BOpType>;
using Base = HermEigsBase<ModeMatOp, IdentityBOp>;
const BOpType& m_Bop;
public:
///
/// Constructor to create a solver object.
///
/// \param op Pointer to the \f$A\f$ matrix operation object. It
/// should implement the matrix-vector multiplication operation of \f$A\f$:
/// \param op The \f$A\f$ matrix operation object that implements the matrix-vector
/// multiplication operation of \f$A\f$:
/// calculating \f$Av\f$ for any vector \f$v\f$. Users could either
/// create the object from the wrapper classes such as DenseSymMatProd, or
/// define their own that implements all the public member functions
/// define their own that implements all the public members
/// as in DenseSymMatProd.
/// \param Bop Pointer to the \f$B\f$ matrix operation object. It
/// represents a Cholesky decomposition of \f$B\f$, and should
/// implement the lower and upper triangular solving operations:
/// \param Bop The \f$B\f$ matrix operation object that represents a Cholesky decomposition of \f$B\f$.
/// It should implement the lower and upper triangular solving operations:
/// calculating \f$L^{-1}v\f$ and \f$(L')^{-1}v\f$ for any vector
/// \f$v\f$, where \f$LL'=B\f$. Users could either
/// create the object from the wrapper classes such as DenseCholesky, or
/// define their own that implements all the public member functions
/// as in DenseCholesky.
/// as in DenseCholesky. \f$B\f$ needs to be positive definite.
/// \param nev Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-1\f$,
/// where \f$n\f$ is the size of matrix.
/// \param ncv Parameter that controls the convergence speed of the algorithm.
@ -197,37 +185,30 @@ public:
/// in each iteration. This parameter must satisfy \f$nev < ncv \le n\f$,
/// and is advised to take \f$ncv \ge 2\cdot nev\f$.
///
SymGEigsSolver(OpType* op, BOpType* Bop, Index nev, Index ncv) :
SymEigsBase<Scalar, SelectionRule, SymGEigsCholeskyOp<Scalar, OpType, BOpType>, IdentityBOp>(
new SymGEigsCholeskyOp<Scalar, OpType, BOpType>(*op, *Bop), NULL, nev, ncv),
SymGEigsSolver(OpType& op, BOpType& Bop, Index nev, Index ncv) :
Base(ModeMatOp(op, Bop), IdentityBOp(), nev, ncv),
m_Bop(Bop)
{}
/// \cond
~SymGEigsSolver()
Matrix eigenvectors(Index nvec) const override
{
// m_op contains the constructed SymGEigsCholeskyOp object
delete this->m_op;
}
Matrix eigenvectors(Index nvec) const
{
Matrix res = SymEigsBase<Scalar, SelectionRule, SymGEigsCholeskyOp<Scalar, OpType, BOpType>, IdentityBOp>::eigenvectors(nvec);
Matrix res = Base::eigenvectors(nvec);
Vector tmp(res.rows());
const Index nconv = res.cols();
for (Index i = 0; i < nconv; i++)
{
m_Bop->upper_triangular_solve(&res(0, i), tmp.data());
m_Bop.upper_triangular_solve(&res(0, i), tmp.data());
res.col(i).noalias() = tmp;
}
return res;
}
Matrix eigenvectors() const
Matrix eigenvectors() const override
{
return SymGEigsSolver<Scalar, SelectionRule, OpType, BOpType, GEIGS_CHOLESKY>::eigenvectors(this->m_nev);
return SymGEigsSolver<OpType, BOpType, GEigsMode::Cholesky>::eigenvectors(this->m_nev);
}
/// \endcond
@ -252,53 +233,45 @@ public:
/// is always preferred. If the users need to define their own operation classes, then they
/// should implement all the public member functions as in those built-in classes.
///
/// \tparam Scalar The element type of the matrix.
/// Currently supported types are `float`, `double` and `long double`.
/// \tparam SelectionRule An enumeration value indicating the selection rule of
/// the requested eigenvalues, for example `LARGEST_MAGN`
/// to retrieve eigenvalues with the largest magnitude.
/// The full list of enumeration values can be found in
/// \ref Enumerations.
/// \tparam OpType The name of the matrix operation class for \f$A\f$. Users could either
/// use the wrapper classes such as DenseSymMatProd and
/// SparseSymMatProd, or define their
/// own that implements all the public member functions as in
/// DenseSymMatProd.
/// \tparam BOpType The name of the matrix operation class for \f$B\f$. Users could either
/// use the wrapper class SparseRegularInverse, or define their
/// own that implements all the public member functions as in
/// SparseRegularInverse.
/// \tparam GEigsMode Mode of the generalized eigen solver. In this solver
/// it is Spectra::GEIGS_REGULAR_INVERSE.
/// \tparam OpType The name of the matrix operation class for \f$A\f$. Users could either
/// use the wrapper classes such as DenseSymMatProd and
/// SparseSymMatProd, or define their own that implements the type
/// definition `Scalar` and all the public member functions as in
/// DenseSymMatProd.
/// \tparam BOpType The name of the matrix operation class for \f$B\f$. Users could either
/// use the wrapper class SparseRegularInverse, or define their
/// own that implements all the public member functions as in
/// SparseRegularInverse.
/// \tparam Mode Mode of the generalized eigen solver. In this solver
/// it is Spectra::GEigsMode::RegularInverse.
///
// Partial specialization for GEigsMode = GEIGS_REGULAR_INVERSE
template <typename Scalar,
int SelectionRule,
typename OpType,
typename BOpType>
class SymGEigsSolver<Scalar, SelectionRule, OpType, BOpType, GEIGS_REGULAR_INVERSE> :
public SymEigsBase<Scalar, SelectionRule, SymGEigsRegInvOp<Scalar, OpType, BOpType>, BOpType>
// Partial specialization for mode = GEigsMode::RegularInverse
template <typename OpType, typename BOpType>
class SymGEigsSolver<OpType, BOpType, GEigsMode::RegularInverse> :
public HermEigsBase<SymGEigsRegInvOp<OpType, BOpType>, BOpType>
{
private:
typedef Eigen::Index Index;
using Index = Eigen::Index;
using ModeMatOp = SymGEigsRegInvOp<OpType, BOpType>;
using Base = HermEigsBase<ModeMatOp, BOpType>;
public:
///
/// Constructor to create a solver object.
///
/// \param op Pointer to the \f$A\f$ matrix operation object. It
/// should implement the matrix-vector multiplication operation of \f$A\f$:
/// \param op The \f$A\f$ matrix operation object that implements the matrix-vector
/// multiplication operation of \f$A\f$:
/// calculating \f$Av\f$ for any vector \f$v\f$. Users could either
/// create the object from the wrapper classes such as DenseSymMatProd, or
/// define their own that implements all the public member functions
/// define their own that implements all the public members
/// as in DenseSymMatProd.
/// \param Bop Pointer to the \f$B\f$ matrix operation object. It should
/// implement the multiplication operation \f$Bv\f$ and the linear equation
/// solving operation \f$B^{-1}v\f$ for any vector \f$v\f$. Users could either
/// create the object from the wrapper class SparseRegularInverse, or
/// \param Bop The \f$B\f$ matrix operation object that implements the multiplication operation
/// \f$Bv\f$ and the linear equation solving operation \f$B^{-1}v\f$ for any vector \f$v\f$.
/// Users could either create the object from the wrapper class SparseRegularInverse, or
/// define their own that implements all the public member functions
/// as in SparseRegularInverse.
/// as in SparseRegularInverse. \f$B\f$ needs to be positive definite.
/// \param nev Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-1\f$,
/// where \f$n\f$ is the size of matrix.
/// \param ncv Parameter that controls the convergence speed of the algorithm.
@ -307,20 +280,11 @@ public:
/// in each iteration. This parameter must satisfy \f$nev < ncv \le n\f$,
/// and is advised to take \f$ncv \ge 2\cdot nev\f$.
///
SymGEigsSolver(OpType* op, BOpType* Bop, Index nev, Index ncv) :
SymEigsBase<Scalar, SelectionRule, SymGEigsRegInvOp<Scalar, OpType, BOpType>, BOpType>(
new SymGEigsRegInvOp<Scalar, OpType, BOpType>(*op, *Bop), Bop, nev, ncv)
SymGEigsSolver(OpType& op, BOpType& Bop, Index nev, Index ncv) :
Base(ModeMatOp(op, Bop), Bop, nev, ncv)
{}
/// \cond
~SymGEigsSolver()
{
// m_op contains the constructed SymGEigsRegInvOp object
delete this->m_op;
}
/// \endcond
};
} // namespace Spectra
#endif // SYM_GEIGS_SOLVER_H
#endif // SPECTRA_SYM_GEIGS_SOLVER_H

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gtsam/3rdparty/Spectra/Util/CompInfo.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef COMP_INFO_H
#define COMP_INFO_H
#ifndef SPECTRA_COMP_INFO_H
#define SPECTRA_COMP_INFO_H
namespace Spectra {
@ -14,22 +14,23 @@ namespace Spectra {
///
/// The enumeration to report the status of computation.
///
enum COMPUTATION_INFO
enum class CompInfo
{
SUCCESSFUL = 0, ///< Computation was successful.
Successful, ///< Computation was successful.
NOT_COMPUTED, ///< Used in eigen solvers, indicating that computation
///< has not been conducted. Users should call
///< the `compute()` member function of solvers.
NotComputed, ///< Used in eigen solvers, indicating that computation
///< has not been conducted. Users should call
///< the `compute()` member function of solvers.
NOT_CONVERGING, ///< Used in eigen solvers, indicating that some eigenvalues
///< did not converge. The `compute()`
///< function returns the number of converged eigenvalues.
NotConverging, ///< Used in eigen solvers, indicating that some eigenvalues
///< did not converge. The `compute()`
///< function returns the number of converged eigenvalues.
NUMERICAL_ISSUE ///< Used in Cholesky decomposition, indicating that the
///< matrix is not positive definite.
NumericalIssue ///< Used in various matrix factorization classes, for example in
///< Cholesky decomposition it indicates that the
///< matrix is not positive definite.
};
} // namespace Spectra
#endif // COMP_INFO_H
#endif // SPECTRA_COMP_INFO_H

24
gtsam/3rdparty/Spectra/Util/GEigsMode.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef GEIGS_MODE_H
#define GEIGS_MODE_H
#ifndef SPECTRA_GEIGS_MODE_H
#define SPECTRA_GEIGS_MODE_H
namespace Spectra {
@ -14,19 +14,15 @@ namespace Spectra {
///
/// The enumeration to specify the mode of generalized eigenvalue solver.
///
enum GEIGS_MODE
enum class GEigsMode
{
GEIGS_CHOLESKY = 0, ///< Using Cholesky decomposition to solve generalized eigenvalues.
GEIGS_REGULAR_INVERSE, ///< Regular inverse mode for generalized eigenvalue solver.
GEIGS_SHIFT_INVERT, ///< Shift-and-invert mode for generalized eigenvalue solver.
GEIGS_BUCKLING, ///< Buckling mode for generalized eigenvalue solver.
GEIGS_CAYLEY ///< Cayley transformation mode for generalized eigenvalue solver.
Cholesky, ///< Using Cholesky decomposition to solve generalized eigenvalues.
RegularInverse, ///< Regular inverse mode for generalized eigenvalue solver.
ShiftInvert, ///< Shift-and-invert mode for generalized eigenvalue solver.
Buckling, ///< Buckling mode for generalized eigenvalue solver.
Cayley ///< Cayley transformation mode for generalized eigenvalue solver.
};
} // namespace Spectra
#endif // GEIGS_MODE_H
#endif // SPECTRA_GEIGS_MODE_H

265
gtsam/3rdparty/Spectra/Util/SelectionRule.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SELECTION_RULE_H
#define SELECTION_RULE_H
#ifndef SPECTRA_SELECTION_RULE_H
#define SPECTRA_SELECTION_RULE_H
#include <vector> // std::vector
#include <cmath> // std::abs
@ -14,10 +14,13 @@
#include <utility> // std::pair
#include <stdexcept> // std::invalid_argument
#include <Eigen/Core>
#include "TypeTraits.h"
namespace Spectra {
///
/// \defgroup Enumerations
/// \defgroup Enumerations Enumerations
///
/// Enumeration types for the selection rule of eigenvalues.
///
@ -27,81 +30,46 @@ namespace Spectra {
///
/// The enumeration of selection rules of desired eigenvalues.
///
enum SELECT_EIGENVALUE
enum class SortRule
{
LARGEST_MAGN = 0, ///< Select eigenvalues with largest magnitude. Magnitude
///< means the absolute value for real numbers and norm for
///< complex numbers. Applies to both symmetric and general
///< eigen solvers.
LargestMagn, ///< Select eigenvalues with largest magnitude. Magnitude
///< means the absolute value for real numbers and norm for
///< complex numbers. Applies to both symmetric and general
///< eigen solvers.
LARGEST_REAL, ///< Select eigenvalues with largest real part. Only for general eigen solvers.
LargestReal, ///< Select eigenvalues with largest real part. Only for general eigen solvers.
LARGEST_IMAG, ///< Select eigenvalues with largest imaginary part (in magnitude). Only for general eigen solvers.
LargestImag, ///< Select eigenvalues with largest imaginary part (in magnitude). Only for general eigen solvers.
LARGEST_ALGE, ///< Select eigenvalues with largest algebraic value, considering
///< any negative sign. Only for symmetric eigen solvers.
LargestAlge, ///< Select eigenvalues with largest algebraic value, considering
///< any negative sign. Only for symmetric eigen solvers.
SMALLEST_MAGN, ///< Select eigenvalues with smallest magnitude. Applies to both symmetric and general
///< eigen solvers.
SmallestMagn, ///< Select eigenvalues with smallest magnitude. Applies to both symmetric and general
///< eigen solvers.
SMALLEST_REAL, ///< Select eigenvalues with smallest real part. Only for general eigen solvers.
SmallestReal, ///< Select eigenvalues with smallest real part. Only for general eigen solvers.
SMALLEST_IMAG, ///< Select eigenvalues with smallest imaginary part (in magnitude). Only for general eigen solvers.
SmallestImag, ///< Select eigenvalues with smallest imaginary part (in magnitude). Only for general eigen solvers.
SMALLEST_ALGE, ///< Select eigenvalues with smallest algebraic value. Only for symmetric eigen solvers.
SmallestAlge, ///< Select eigenvalues with smallest algebraic value. Only for symmetric eigen solvers.
BOTH_ENDS ///< Select eigenvalues half from each end of the spectrum. When
///< `nev` is odd, compute more from the high end. Only for symmetric eigen solvers.
};
///
/// \ingroup Enumerations
///
/// The enumeration of selection rules of desired eigenvalues. Alias for `SELECT_EIGENVALUE`.
///
enum SELECT_EIGENVALUE_ALIAS
{
WHICH_LM = 0, ///< Alias for `LARGEST_MAGN`
WHICH_LR, ///< Alias for `LARGEST_REAL`
WHICH_LI, ///< Alias for `LARGEST_IMAG`
WHICH_LA, ///< Alias for `LARGEST_ALGE`
WHICH_SM, ///< Alias for `SMALLEST_MAGN`
WHICH_SR, ///< Alias for `SMALLEST_REAL`
WHICH_SI, ///< Alias for `SMALLEST_IMAG`
WHICH_SA, ///< Alias for `SMALLEST_ALGE`
WHICH_BE ///< Alias for `BOTH_ENDS`
BothEnds ///< Select eigenvalues half from each end of the spectrum. When
///< `nev` is odd, compute more from the high end. Only for symmetric eigen solvers.
};
/// \cond
// Get the element type of a "scalar"
// ElemType<double> => double
// ElemType< std::complex<double> > => double
template <typename T>
class ElemType
{
public:
typedef T type;
};
template <typename T>
class ElemType<std::complex<T> >
{
public:
typedef T type;
};
// When comparing eigenvalues, we first calculate the "target"
// to sort. For example, if we want to choose the eigenvalues with
// When comparing eigenvalues, we first calculate the "target" to sort.
// For example, if we want to choose the eigenvalues with
// largest magnitude, the target will be -abs(x).
// The minus sign is due to the fact that std::sort() sorts in ascending order.
// Default target: throw an exception
template <typename Scalar, int SelectionRule>
template <typename Scalar, SortRule Rule>
class SortingTarget
{
public:
static typename ElemType<Scalar>::type get(const Scalar& val)
static ElemType<Scalar> get(const Scalar& val)
{
using std::abs;
throw std::invalid_argument("incompatible selection rule");
@ -109,23 +77,23 @@ public:
}
};
// Specialization for LARGEST_MAGN
// This covers [float, double, complex] x [LARGEST_MAGN]
// Specialization for SortRule::LargestMagn
// This covers [float, double, complex] x [SortRule::LargestMagn]
template <typename Scalar>
class SortingTarget<Scalar, LARGEST_MAGN>
class SortingTarget<Scalar, SortRule::LargestMagn>
{
public:
static typename ElemType<Scalar>::type get(const Scalar& val)
static ElemType<Scalar> get(const Scalar& val)
{
using std::abs;
return -abs(val);
}
};
// Specialization for LARGEST_REAL
// This covers [complex] x [LARGEST_REAL]
// Specialization for SortRule::LargestReal
// This covers [complex] x [SortRule::LargestReal]
template <typename RealType>
class SortingTarget<std::complex<RealType>, LARGEST_REAL>
class SortingTarget<std::complex<RealType>, SortRule::LargestReal>
{
public:
static RealType get(const std::complex<RealType>& val)
@ -134,10 +102,10 @@ public:
}
};
// Specialization for LARGEST_IMAG
// This covers [complex] x [LARGEST_IMAG]
// Specialization for SortRule::LargestImag
// This covers [complex] x [SortRule::LargestImag]
template <typename RealType>
class SortingTarget<std::complex<RealType>, LARGEST_IMAG>
class SortingTarget<std::complex<RealType>, SortRule::LargestImag>
{
public:
static RealType get(const std::complex<RealType>& val)
@ -147,10 +115,10 @@ public:
}
};
// Specialization for LARGEST_ALGE
// This covers [float, double] x [LARGEST_ALGE]
// Specialization for SortRule::LargestAlge
// This covers [float, double] x [SortRule::LargestAlge]
template <typename Scalar>
class SortingTarget<Scalar, LARGEST_ALGE>
class SortingTarget<Scalar, SortRule::LargestAlge>
{
public:
static Scalar get(const Scalar& val)
@ -159,12 +127,12 @@ public:
}
};
// Here BOTH_ENDS is the same as LARGEST_ALGE, but
// Here SortRule::BothEnds is the same as SortRule::LargestAlge, but
// we need some additional steps, which are done in
// SymEigsSolver.h => retrieve_ritzpair().
// There we move the smallest values to the proper locations.
template <typename Scalar>
class SortingTarget<Scalar, BOTH_ENDS>
class SortingTarget<Scalar, SortRule::BothEnds>
{
public:
static Scalar get(const Scalar& val)
@ -173,23 +141,23 @@ public:
}
};
// Specialization for SMALLEST_MAGN
// This covers [float, double, complex] x [SMALLEST_MAGN]
// Specialization for SortRule::SmallestMagn
// This covers [float, double, complex] x [SortRule::SmallestMagn]
template <typename Scalar>
class SortingTarget<Scalar, SMALLEST_MAGN>
class SortingTarget<Scalar, SortRule::SmallestMagn>
{
public:
static typename ElemType<Scalar>::type get(const Scalar& val)
static ElemType<Scalar> get(const Scalar& val)
{
using std::abs;
return abs(val);
}
};
// Specialization for SMALLEST_REAL
// This covers [complex] x [SMALLEST_REAL]
// Specialization for SortRule::SmallestReal
// This covers [complex] x [SortRule::SmallestReal]
template <typename RealType>
class SortingTarget<std::complex<RealType>, SMALLEST_REAL>
class SortingTarget<std::complex<RealType>, SortRule::SmallestReal>
{
public:
static RealType get(const std::complex<RealType>& val)
@ -198,10 +166,10 @@ public:
}
};
// Specialization for SMALLEST_IMAG
// This covers [complex] x [SMALLEST_IMAG]
// Specialization for SortRule::SmallestImag
// This covers [complex] x [SortRule::SmallestImag]
template <typename RealType>
class SortingTarget<std::complex<RealType>, SMALLEST_IMAG>
class SortingTarget<std::complex<RealType>, SortRule::SmallestImag>
{
public:
static RealType get(const std::complex<RealType>& val)
@ -211,10 +179,10 @@ public:
}
};
// Specialization for SMALLEST_ALGE
// This covers [float, double] x [SMALLEST_ALGE]
// Specialization for SortRule::SmallestAlge
// This covers [float, double] x [SortRule::SmallestAlge]
template <typename Scalar>
class SortingTarget<Scalar, SMALLEST_ALGE>
class SortingTarget<Scalar, SortRule::SmallestAlge>
{
public:
static Scalar get(const Scalar& val)
@ -223,53 +191,110 @@ public:
}
};
// Sort eigenvalues and return the order index
template <typename PairType>
class PairComparator
{
public:
bool operator()(const PairType& v1, const PairType& v2)
{
return v1.first < v2.first;
}
};
template <typename T, int SelectionRule>
// Sort eigenvalues
template <typename T, SortRule Rule>
class SortEigenvalue
{
private:
typedef typename ElemType<T>::type TargetType; // Type of the sorting target, will be
// a floating number type, e.g. "double"
typedef std::pair<TargetType, int> PairType; // Type of the sorting pair, including
// the sorting target and the index
using Index = Eigen::Index;
using IndexArray = std::vector<Index>;
std::vector<PairType> pair_sort;
const T* m_evals;
IndexArray m_index;
public:
SortEigenvalue(const T* start, int size) :
pair_sort(size)
// Sort indices according to the eigenvalues they point to
inline bool operator()(Index i, Index j)
{
for (int i = 0; i < size; i++)
return SortingTarget<T, Rule>::get(m_evals[i]) < SortingTarget<T, Rule>::get(m_evals[j]);
}
SortEigenvalue(const T* start, Index size) :
m_evals(start), m_index(size)
{
for (Index i = 0; i < size; i++)
{
pair_sort[i].first = SortingTarget<T, SelectionRule>::get(start[i]);
pair_sort[i].second = i;
m_index[i] = i;
}
PairComparator<PairType> comp;
std::sort(pair_sort.begin(), pair_sort.end(), comp);
std::sort(m_index.begin(), m_index.end(), *this);
}
std::vector<int> index()
{
std::vector<int> ind(pair_sort.size());
for (unsigned int i = 0; i < ind.size(); i++)
ind[i] = pair_sort[i].second;
return ind;
}
inline IndexArray index() const { return m_index; }
inline void swap(IndexArray& other) { m_index.swap(other); }
};
// Sort values[:len] according to the selection rule, and return the indices
template <typename Scalar>
std::vector<Eigen::Index> argsort(SortRule selection, const Eigen::Matrix<Scalar, Eigen::Dynamic, 1>& values, Eigen::Index len)
{
using Index = Eigen::Index;
// Sort Ritz values and put the wanted ones at the beginning
std::vector<Index> ind;
switch (selection)
{
case SortRule::LargestMagn:
{
SortEigenvalue<Scalar, SortRule::LargestMagn> sorting(values.data(), len);
sorting.swap(ind);
break;
}
case SortRule::BothEnds:
case SortRule::LargestAlge:
{
SortEigenvalue<Scalar, SortRule::LargestAlge> sorting(values.data(), len);
sorting.swap(ind);
break;
}
case SortRule::SmallestMagn:
{
SortEigenvalue<Scalar, SortRule::SmallestMagn> sorting(values.data(), len);
sorting.swap(ind);
break;
}
case SortRule::SmallestAlge:
{
SortEigenvalue<Scalar, SortRule::SmallestAlge> sorting(values.data(), len);
sorting.swap(ind);
break;
}
default:
throw std::invalid_argument("unsupported selection rule");
}
// For SortRule::BothEnds, the eigenvalues are sorted according to the
// SortRule::LargestAlge rule, so we need to move those smallest values to the left
// The order would be
// Largest => Smallest => 2nd largest => 2nd smallest => ...
// We keep this order since the first k values will always be
// the wanted collection, no matter k is nev_updated (used in SymEigsBase::restart())
// or is nev (used in SymEigsBase::sort_ritzpair())
if (selection == SortRule::BothEnds)
{
std::vector<Index> ind_copy(ind);
for (Index i = 0; i < len; i++)
{
// If i is even, pick values from the left (large values)
// If i is odd, pick values from the right (small values)
if (i % 2 == 0)
ind[i] = ind_copy[i / 2];
else
ind[i] = ind_copy[len - 1 - i / 2];
}
}
return ind;
}
// Default vector length
template <typename Scalar>
std::vector<Eigen::Index> argsort(SortRule selection, const Eigen::Matrix<Scalar, Eigen::Dynamic, 1>& values)
{
return argsort<Scalar>(selection, values, values.size());
}
/// \endcond
} // namespace Spectra
#endif // SELECTION_RULE_H
#endif // SPECTRA_SELECTION_RULE_H

128
gtsam/3rdparty/Spectra/Util/SimpleRandom.h vendored
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@ -1,13 +1,14 @@
// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2016-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SIMPLE_RANDOM_H
#define SIMPLE_RANDOM_H
#ifndef SPECTRA_SIMPLE_RANDOM_H
#define SPECTRA_SIMPLE_RANDOM_H
#include <Eigen/Core>
#include <complex>
/// \cond
@ -25,61 +26,98 @@ namespace Spectra {
// 5. Based on public domain code by Ray Gardner
// http://stjarnhimlen.se/snippets/rg_rand.c
// Given a 32-bit integer as the seed, generate a pseudo random 32-bit integer
inline long next_long_rand(long seed)
{
constexpr unsigned int m_a = 16807; // multiplier
constexpr unsigned long m_max = 2147483647L; // 2^31 - 1
unsigned long lo, hi;
lo = m_a * (long) (seed & 0xFFFF);
hi = m_a * (long) ((unsigned long) seed >> 16);
lo += (hi & 0x7FFF) << 16;
if (lo > m_max)
{
lo &= m_max;
++lo;
}
lo += hi >> 15;
if (lo > m_max)
{
lo &= m_max;
++lo;
}
return (long) lo;
}
// Generate a random scalar from the given random seed
// Also overwrite seed with the new random integer
template <typename Scalar>
struct RandomScalar
{
static Scalar run(long& seed)
{
constexpr unsigned long m_max = 2147483647L; // 2^31 - 1
seed = next_long_rand(seed);
return Scalar(seed) / Scalar(m_max) - Scalar(0.5);
}
};
// Specialization for complex values
template <typename RealScalar>
struct RandomScalar<std::complex<RealScalar>>
{
static std::complex<RealScalar> run(long& seed)
{
RealScalar r = RandomScalar<RealScalar>::run(seed);
RealScalar i = RandomScalar<RealScalar>::run(seed);
return std::complex<RealScalar>(r, i);
}
};
// A simple random generator class
template <typename Scalar = double>
class SimpleRandom
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
// The real part type of the matrix element
using RealScalar = typename Eigen::NumTraits<Scalar>::Real;
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
const unsigned int m_a; // multiplier
const unsigned long m_max; // 2^31 - 1
long m_rand;
inline long next_long_rand(long seed)
{
unsigned long lo, hi;
lo = m_a * (long) (seed & 0xFFFF);
hi = m_a * (long) ((unsigned long) seed >> 16);
lo += (hi & 0x7FFF) << 16;
if (lo > m_max)
{
lo &= m_max;
++lo;
}
lo += hi >> 15;
if (lo > m_max)
{
lo &= m_max;
++lo;
}
return (long) lo;
}
long m_rand; // RNG state
public:
SimpleRandom(unsigned long init_seed) :
m_a(16807),
m_max(2147483647L),
m_rand(init_seed ? (init_seed & m_max) : 1)
{}
Scalar random()
SimpleRandom(unsigned long init_seed)
{
m_rand = next_long_rand(m_rand);
return Scalar(m_rand) / Scalar(m_max) - Scalar(0.5);
constexpr unsigned long m_max = 2147483647L; // 2^31 - 1
m_rand = init_seed ? (init_seed & m_max) : 1;
}
// Vector of random numbers of type Scalar
// Return a single random number, ranging from -0.5 to 0.5
Scalar random()
{
return RandomScalar<Scalar>::run(m_rand);
}
// Fill the given vector with random numbers
// Ranging from -0.5 to 0.5
void random_vec(Vector& vec)
{
const Index len = vec.size();
for (Index i = 0; i < len; i++)
{
vec[i] = random();
}
}
// Return a vector of random numbers
// Ranging from -0.5 to 0.5
Vector random_vec(const Index len)
{
Vector res(len);
for (Index i = 0; i < len; i++)
{
m_rand = next_long_rand(m_rand);
res[i] = Scalar(m_rand) / Scalar(m_max) - Scalar(0.5);
}
random_vec(res);
return res;
}
};
@ -88,4 +126,4 @@ public:
/// \endcond
#endif // SIMPLE_RANDOM_H
#endif // SPECTRA_SIMPLE_RANDOM_H

52
gtsam/3rdparty/Spectra/Util/TypeTraits.h vendored
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@ -1,17 +1,23 @@
// Copyright (C) 2018-2019 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2018-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef TYPE_TRAITS_H
#define TYPE_TRAITS_H
#ifndef SPECTRA_TYPE_TRAITS_H
#define SPECTRA_TYPE_TRAITS_H
#include <Eigen/Core>
#include <limits>
/// \cond
// Clang-Format will have unintended effects:
// static constexpr Scalar(min)()
// So we turn it off here
//
// clang-format off
namespace Spectra {
// For a real value type "Scalar", we want to know its smallest
@ -30,9 +36,13 @@ namespace Spectra {
template <typename Scalar>
struct TypeTraits
{
static inline Scalar min()
static constexpr Scalar epsilon()
{
return Eigen::numext::pow(Eigen::NumTraits<Scalar>::epsilon(), Scalar(3));
return Eigen::numext::numeric_limits<Scalar>::epsilon();
}
static constexpr Scalar (min)()
{
return epsilon() * epsilon() * epsilon();
}
};
@ -40,32 +50,50 @@ struct TypeTraits
template <>
struct TypeTraits<float>
{
static inline float min()
static constexpr float epsilon()
{
return std::numeric_limits<float>::min();
return std::numeric_limits<float>::epsilon();
}
static constexpr float (min)()
{
return (std::numeric_limits<float>::min)();
}
};
template <>
struct TypeTraits<double>
{
static inline double min()
static constexpr double epsilon()
{
return std::numeric_limits<double>::min();
return std::numeric_limits<double>::epsilon();
}
static constexpr double (min)()
{
return (std::numeric_limits<double>::min)();
}
};
template <>
struct TypeTraits<long double>
{
static inline long double min()
static constexpr long double epsilon()
{
return std::numeric_limits<long double>::min();
return std::numeric_limits<long double>::epsilon();
}
static constexpr long double (min)()
{
return (std::numeric_limits<long double>::min)();
}
};
// Get the element type of a "scalar"
// ElemType<double> => double
// ElemType<std::complex<double>> => double
template <typename T>
using ElemType = typename Eigen::NumTraits<T>::Real;
} // namespace Spectra
/// \endcond
#endif // TYPE_TRAITS_H
#endif // SPECTRA_TYPE_TRAITS_H

16
gtsam/3rdparty/Spectra/Util/Version.h vendored Normal file
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@ -0,0 +1,16 @@
// Copyright (C) 2020-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPECTRA_VERSION_H
#define SPECTRA_VERSION_H
#define SPECTRA_MAJOR_VERSION 1
#define SPECTRA_MINOR_VERSION 1
#define SPECTRA_PATCH_VERSION 0
#define SPECTRA_VERSION (SPECTRA_MAJOR_VERSION * 10000 + SPECTRA_MINOR_VERSION * 100 + SPECTRA_PATCH_VERSION)
#endif // SPECTRA_VERSION_H

1103
gtsam/3rdparty/Spectra/contrib/LOBPCGSolver.h vendored
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99
gtsam/3rdparty/Spectra/contrib/PartialSVDSolver.h vendored
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@ -1,11 +1,11 @@
// Copyright (C) 2018 Yixuan Qiu <yixuan.qiu@cos.name>
// Copyright (C) 2018-2025 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef PARTIAL_SVD_SOLVER_H
#define PARTIAL_SVD_SOLVER_H
#ifndef SPECTRA_PARTIAL_SVD_SOLVER_H
#define SPECTRA_PARTIAL_SVD_SOLVER_H
#include <Eigen/Core>
#include "../SymEigsSolver.h"
@ -13,15 +13,21 @@
namespace Spectra {
// Abstract class for matrix operation
template <typename Scalar>
template <typename Scalar_>
class SVDMatOp
{
public:
virtual int rows() const = 0;
virtual int cols() const = 0;
using Scalar = Scalar_;
private:
using Index = Eigen::Index;
public:
virtual Index rows() const = 0;
virtual Index cols() const = 0;
// y_out = A' * A * x_in or y_out = A * A' * x_in
virtual void perform_op(const Scalar* x_in, Scalar* y_out) = 0;
virtual void perform_op(const Scalar* x_in, Scalar* y_out) const = 0;
virtual ~SVDMatOp() {}
};
@ -33,29 +39,30 @@ template <typename Scalar, typename MatrixType>
class SVDTallMatOp : public SVDMatOp<Scalar>
{
private:
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef const Eigen::Ref<const MatrixType> ConstGenericMatrix;
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using ConstGenericMatrix = const Eigen::Ref<const MatrixType>;
ConstGenericMatrix m_mat;
const int m_dim;
Vector m_cache;
const Index m_dim;
mutable Vector m_cache;
public:
// Constructor
SVDTallMatOp(ConstGenericMatrix& mat) :
m_mat(mat),
m_dim(std::min(mat.rows(), mat.cols())),
m_dim((std::min)(mat.rows(), mat.cols())),
m_cache(mat.rows())
{}
// These are the rows and columns of A' * A
int rows() const { return m_dim; }
int cols() const { return m_dim; }
Index rows() const override { return m_dim; }
Index cols() const override { return m_dim; }
// y_out = A' * A * x_in
void perform_op(const Scalar* x_in, Scalar* y_out)
void perform_op(const Scalar* x_in, Scalar* y_out) const override
{
MapConstVec x(x_in, m_mat.cols());
MapVec y(y_out, m_mat.cols());
@ -71,29 +78,30 @@ template <typename Scalar, typename MatrixType>
class SVDWideMatOp : public SVDMatOp<Scalar>
{
private:
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef const Eigen::Ref<const MatrixType> ConstGenericMatrix;
using Index = Eigen::Index;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using MapConstVec = Eigen::Map<const Vector>;
using MapVec = Eigen::Map<Vector>;
using ConstGenericMatrix = const Eigen::Ref<const MatrixType>;
ConstGenericMatrix m_mat;
const int m_dim;
Vector m_cache;
const Index m_dim;
mutable Vector m_cache;
public:
// Constructor
SVDWideMatOp(ConstGenericMatrix& mat) :
m_mat(mat),
m_dim(std::min(mat.rows(), mat.cols())),
m_dim((std::min)(mat.rows(), mat.cols())),
m_cache(mat.cols())
{}
// These are the rows and columns of A * A'
int rows() const { return m_dim; }
int cols() const { return m_dim; }
Index rows() const override { return m_dim; }
Index cols() const override { return m_dim; }
// y_out = A * A' * x_in
void perform_op(const Scalar* x_in, Scalar* y_out)
void perform_op(const Scalar* x_in, Scalar* y_out) const override
{
MapConstVec x(x_in, m_mat.rows());
MapVec y(y_out, m_mat.rows());
@ -104,26 +112,27 @@ public:
// Partial SVD solver
// MatrixType is either Eigen::Matrix<Scalar, ...> or Eigen::SparseMatrix<Scalar, ...>
template <typename Scalar = double,
typename MatrixType = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> >
template <typename MatrixType = Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>>
class PartialSVDSolver
{
private:
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef const Eigen::Ref<const MatrixType> ConstGenericMatrix;
using Scalar = typename MatrixType::Scalar;
using Index = Eigen::Index;
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
using ConstGenericMatrix = const Eigen::Ref<const MatrixType>;
ConstGenericMatrix m_mat;
const int m_m;
const int m_n;
const Index m_m;
const Index m_n;
SVDMatOp<Scalar>* m_op;
SymEigsSolver<Scalar, LARGEST_ALGE, SVDMatOp<Scalar> >* m_eigs;
int m_nconv;
SymEigsSolver<SVDMatOp<Scalar>>* m_eigs;
Index m_nconv;
Matrix m_evecs;
public:
// Constructor
PartialSVDSolver(ConstGenericMatrix& mat, int ncomp, int ncv) :
PartialSVDSolver(ConstGenericMatrix& mat, Index ncomp, Index ncv) :
m_mat(mat), m_m(mat.rows()), m_n(mat.cols()), m_evecs(0, 0)
{
// Determine the matrix type, tall or wide
@ -137,7 +146,7 @@ public:
}
// Solver object
m_eigs = new SymEigsSolver<Scalar, LARGEST_ALGE, SVDMatOp<Scalar> >(m_op, ncomp, ncv);
m_eigs = new SymEigsSolver<SVDMatOp<Scalar>>(*m_op, ncomp, ncv);
}
// Destructor
@ -148,10 +157,10 @@ public:
}
// Computation
int compute(int maxit = 1000, Scalar tol = 1e-10)
Index compute(Index maxit = 1000, Scalar tol = 1e-10)
{
m_eigs->init();
m_nconv = m_eigs->compute(maxit, tol);
m_nconv = m_eigs->compute(SortRule::LargestAlge, maxit, tol);
return m_nconv;
}
@ -165,13 +174,13 @@ public:
}
// The converged left singular vectors
Matrix matrix_U(int nu)
Matrix matrix_U(Index nu)
{
if (m_evecs.cols() < 1)
{
m_evecs = m_eigs->eigenvectors();
}
nu = std::min(nu, m_nconv);
nu = (std::min)(nu, m_nconv);
if (m_m <= m_n)
{
return m_evecs.leftCols(nu);
@ -181,13 +190,13 @@ public:
}
// The converged right singular vectors
Matrix matrix_V(int nv)
Matrix matrix_V(Index nv)
{
if (m_evecs.cols() < 1)
{
m_evecs = m_eigs->eigenvectors();
}
nv = std::min(nv, m_nconv);
nv = (std::min)(nv, m_nconv);
if (m_m > m_n)
{
return m_evecs.leftCols(nv);
@ -199,4 +208,4 @@ public:
} // namespace Spectra
#endif // PARTIAL_SVD_SOLVER_H
#endif // SPECTRA_PARTIAL_SVD_SOLVER_H