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Added ARPACK support for standard and generalized eigenvalue problems. Currently self-adjoint only.

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David Harmon 2012-10-06 17:18:09 -06:00
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 David Harmon <dharmon@gmail.com>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H
#define EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H
namespace Eigen {
namespace internal {
template<typename Scalar, typename RealScalar> struct arpack_wrapper;
template<typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD> struct OP;
}
template<typename MatrixType, typename MatrixSolver=SimplicialLLT<MatrixType>, bool BisSPD=false>
class ArpackGeneralizedSelfAdjointEigenSolver
{
public:
//typedef typename MatrixSolver::MatrixType MatrixType;
/** \brief Scalar type for matrices of type \p MatrixType. */
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::Index Index;
/** \brief Real scalar type for \p MatrixType.
*
* This is just \c Scalar if #Scalar is real (e.g., \c float or
* \c Scalar), and the type of the real part of \c Scalar if #Scalar is
* complex.
*/
typedef typename NumTraits<Scalar>::Real RealScalar;
/** \brief Type for vector of eigenvalues as returned by eigenvalues().
*
* This is a column vector with entries of type #RealScalar.
* The length of the vector is the size of \p nbrEigenvalues.
*/
typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVectorType;
/** \brief Default constructor.
*
* The default constructor is for cases in which the user intends to
* perform decompositions via compute().
*
*/
ArpackGeneralizedSelfAdjointEigenSolver()
: m_eivec(),
m_eivalues(),
m_isInitialized(false),
m_eigenvectorsOk(false),
m_nbrConverged(0),
m_nbrIterations(0)
{ }
/** \brief Constructor; computes generalized eigenvalues of given matrix with respect to another matrix.
*
* \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
* computed. By default, the upper triangular part is used, but can be changed
* through the template parameter.
* \param[in] B Self-adjoint matrix for the generalized eigenvalue problem.
* \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
* Must be less than the size of the input matrix, or an error is returned.
* \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
* respective meanings to find the largest magnitude , smallest magnitude,
* largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
* value can contain floating point value in string form, in which case the
* eigenvalues closest to this value will be found.
* \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
* \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
* means machine precision.
*
* This constructor calls compute(const MatrixType&, const MatrixType&, Index, string, int, RealScalar)
* to compute the eigenvalues of the matrix \p A with respect to \p B. The eigenvectors are computed if
* \p options equals #ComputeEigenvectors.
*
*/
ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A, const MatrixType& B,
Index nbrEigenvalues, std::string eigs_sigma="LM",
int options=ComputeEigenvectors, RealScalar tol=0.0)
: m_eivec(),
m_eivalues(),
m_isInitialized(false),
m_eigenvectorsOk(false),
m_nbrConverged(0),
m_nbrIterations(0)
{
compute(A, B, nbrEigenvalues, eigs_sigma, options, tol);
}
/** \brief Constructor; computes eigenvalues of given matrix.
*
* \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
* computed. By default, the upper triangular part is used, but can be changed
* through the template parameter.
* \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
* Must be less than the size of the input matrix, or an error is returned.
* \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
* respective meanings to find the largest magnitude , smallest magnitude,
* largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
* value can contain floating point value in string form, in which case the
* eigenvalues closest to this value will be found.
* \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
* \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
* means machine precision.
*
* This constructor calls compute(const MatrixType&, Index, string, int, RealScalar)
* to compute the eigenvalues of the matrix \p A. The eigenvectors are computed if
* \p options equals #ComputeEigenvectors.
*
*/
ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A,
Index nbrEigenvalues, std::string eigs_sigma="LM",
int options=ComputeEigenvectors, RealScalar tol=0.0)
: m_eivec(),
m_eivalues(),
m_isInitialized(false),
m_eigenvectorsOk(false),
m_nbrConverged(0),
m_nbrIterations(0)
{
compute(A, nbrEigenvalues, eigs_sigma, options, tol);
}
/** \brief Computes generalized eigenvalues / eigenvectors of given matrix using the external ARPACK library.
*
* \param[in] A Selfadjoint matrix whose eigendecomposition is to be computed.
* \param[in] B Selfadjoint matrix for generalized eigenvalues.
* \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
* Must be less than the size of the input matrix, or an error is returned.
* \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
* respective meanings to find the largest magnitude , smallest magnitude,
* largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
* value can contain floating point value in string form, in which case the
* eigenvalues closest to this value will be found.
* \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
* \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
* means machine precision.
*
* \returns Reference to \c *this
*
* This function computes the generalized eigenvalues of \p A with respect to \p B using ARPACK. The eigenvalues()
* function can be used to retrieve them. If \p options equals #ComputeEigenvectors,
* then the eigenvectors are also computed and can be retrieved by
* calling eigenvectors().
*
*/
ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A, const MatrixType& B,
Index nbrEigenvalues, std::string eigs_sigma="LM",
int options=ComputeEigenvectors, RealScalar tol=0.0);
/** \brief Computes eigenvalues / eigenvectors of given matrix using the external ARPACK library.
*
* \param[in] A Selfadjoint matrix whose eigendecomposition is to be computed.
* \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
* Must be less than the size of the input matrix, or an error is returned.
* \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
* respective meanings to find the largest magnitude , smallest magnitude,
* largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
* value can contain floating point value in string form, in which case the
* eigenvalues closest to this value will be found.
* \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
* \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
* means machine precision.
*
* \returns Reference to \c *this
*
* This function computes the eigenvalues of \p A using ARPACK. The eigenvalues()
* function can be used to retrieve them. If \p options equals #ComputeEigenvectors,
* then the eigenvectors are also computed and can be retrieved by
* calling eigenvectors().
*
*/
ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A,
Index nbrEigenvalues, std::string eigs_sigma="LM",
int options=ComputeEigenvectors, RealScalar tol=0.0);
/** \brief Returns the eigenvectors of given matrix.
*
* \returns A const reference to the matrix whose columns are the eigenvectors.
*
* \pre The eigenvectors have been computed before.
*
* Column \f$ k \f$ of the returned matrix is an eigenvector corresponding
* to eigenvalue number \f$ k \f$ as returned by eigenvalues(). The
* eigenvectors are normalized to have (Euclidean) norm equal to one. If
* this object was used to solve the eigenproblem for the selfadjoint
* matrix \f$ A \f$, then the matrix returned by this function is the
* matrix \f$ V \f$ in the eigendecomposition \f$ A V = D V \f$.
* For the generalized eigenproblem, the matrix returned is the solution \f$A V = D B V
*
* Example: \include SelfAdjointEigenSolver_eigenvectors.cpp
* Output: \verbinclude SelfAdjointEigenSolver_eigenvectors.out
*
* \sa eigenvalues()
*/
const Matrix<Scalar, Dynamic, Dynamic>& eigenvectors() const
{
eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
return m_eivec;
}
/** \brief Returns the eigenvalues of given matrix.
*
* \returns A const reference to the column vector containing the eigenvalues.
*
* \pre The eigenvalues have been computed before.
*
* The eigenvalues are repeated according to their algebraic multiplicity,
* so there are as many eigenvalues as rows in the matrix. The eigenvalues
* are sorted in increasing order.
*
* Example: \include SelfAdjointEigenSolver_eigenvalues.cpp
* Output: \verbinclude SelfAdjointEigenSolver_eigenvalues.out
*
* \sa eigenvectors(), MatrixBase::eigenvalues()
*/
const Matrix<Scalar, Dynamic, 1>& eigenvalues() const
{
eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
return m_eivalues;
}
/** \brief Computes the positive-definite square root of the matrix.
*
* \returns the positive-definite square root of the matrix
*
* \pre The eigenvalues and eigenvectors of a positive-definite matrix
* have been computed before.
*
* The square root of a positive-definite matrix \f$ A \f$ is the
* positive-definite matrix whose square equals \f$ A \f$. This function
* uses the eigendecomposition \f$ A = V D V^{-1} \f$ to compute the
* square root as \f$ A^{1/2} = V D^{1/2} V^{-1} \f$.
*
* Example: \include SelfAdjointEigenSolver_operatorSqrt.cpp
* Output: \verbinclude SelfAdjointEigenSolver_operatorSqrt.out
*
* \sa operatorInverseSqrt(),
* \ref MatrixFunctions_Module "MatrixFunctions Module"
*/
Matrix<Scalar, Dynamic, Dynamic> operatorSqrt() const
{
eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint();
}
/** \brief Computes the inverse square root of the matrix.
*
* \returns the inverse positive-definite square root of the matrix
*
* \pre The eigenvalues and eigenvectors of a positive-definite matrix
* have been computed before.
*
* This function uses the eigendecomposition \f$ A = V D V^{-1} \f$ to
* compute the inverse square root as \f$ V D^{-1/2} V^{-1} \f$. This is
* cheaper than first computing the square root with operatorSqrt() and
* then its inverse with MatrixBase::inverse().
*
* Example: \include SelfAdjointEigenSolver_operatorInverseSqrt.cpp
* Output: \verbinclude SelfAdjointEigenSolver_operatorInverseSqrt.out
*
* \sa operatorSqrt(), MatrixBase::inverse(),
* \ref MatrixFunctions_Module "MatrixFunctions Module"
*/
Matrix<Scalar, Dynamic, Dynamic> operatorInverseSqrt() const
{
eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
return m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint();
}
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was succesful, \c NoConvergence otherwise.
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
return m_info;
}
size_t getNbrConvergedEigenValues() const
{ return m_nbrConverged; }
size_t getNbrIterations() const
{ return m_nbrIterations; }
protected:
Matrix<Scalar, Dynamic, Dynamic> m_eivec;
Matrix<Scalar, Dynamic, 1> m_eivalues;
ComputationInfo m_info;
bool m_isInitialized;
bool m_eigenvectorsOk;
size_t m_nbrConverged;
size_t m_nbrIterations;
};
template<typename MatrixType, typename MatrixSolver, bool BisSPD>
ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>&
ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>
::compute(const MatrixType& A, Index nbrEigenvalues,
std::string eigs_sigma, int options, RealScalar tol)
{
MatrixType B(0,0);
compute(A, B, nbrEigenvalues, eigs_sigma, options, tol);
}
template<typename MatrixType, typename MatrixSolver, bool BisSPD>
ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>&
ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>
::compute(const MatrixType& A, const MatrixType& B, Index nbrEigenvalues,
std::string eigs_sigma, int options, RealScalar tol)
{
eigen_assert(A.cols() == A.rows());
eigen_assert(B.cols() == B.rows());
eigen_assert(B.rows() == 0 || A.cols() == B.rows());
eigen_assert((options &~ (EigVecMask | GenEigMask)) == 0
&& (options & EigVecMask) != EigVecMask
&& "invalid option parameter");
bool isBempty = (B.rows() == 0) || (B.cols() == 0);
// For clarity, all parameters match their ARPACK name
//
// Always 0 on the first call
//
int ido = 0;
int n = (int)A.cols();
// User options: "LA", "SA", "SM", "LM", "BE"
//
char whch[3] = "LM";
// Specifies the shift if iparam[6] = { 3, 4, 5 }, not used if iparam[6] = { 1, 2 }
//
RealScalar sigma = 0.0;
if (eigs_sigma.length() >= 2 && isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1]))
{
eigs_sigma[0] = toupper(eigs_sigma[0]);
eigs_sigma[1] = toupper(eigs_sigma[1]);
// In the following special case we're going to invert the problem, since solving
// for larger magnitude is much much faster
// i.e., if 'SM' is specified, we're going to really use 'LM', the default
//
if (eigs_sigma.substr(0,2) != "SM")
{
whch[0] = eigs_sigma[0];
whch[1] = eigs_sigma[1];
}
}
else
{
eigen_assert(false && "Specifying clustered eigenvalues is not yet supported!");
// If it's not scalar values, then the user may be explicitly
// specifying the sigma value to cluster the evs around
//
sigma = atof(eigs_sigma.c_str());
// If atof fails, it returns 0.0, which is a fine default
//
}
// "I" means normal eigenvalue problem, "G" means generalized
//
char bmat[2] = "I";
if (eigs_sigma.substr(0,2) == "SM" || !(isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])) || (!isBempty && !BisSPD))
bmat[0] = 'G';
// Now we determine the mode to use
//
int mode = (bmat[0] == 'G') + 1;
if (eigs_sigma.substr(0,2) == "SM" || !(isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])))
{
// We're going to use shift-and-invert mode, and basically find
// the largest eigenvalues of the inverse operator
//
mode = 3;
}
// The user-specified number of eigenvalues/vectors to compute
//
int nev = (int)nbrEigenvalues;
// Allocate space for ARPACK to store the residual
//
Scalar *resid = new Scalar[n];
// Number of Lanczos vectors, must satisfy nev < ncv <= n
// Note that this indicates that nev != n, and we cannot compute
// all eigenvalues of a mtrix
//
int ncv = std::min(std::max(2*nev, 20), n);
// The working n x ncv matrix, also store the final eigenvectors (if computed)
//
Scalar *v = new Scalar[n*ncv];
int ldv = n;
// Working space
//
Scalar *workd = new Scalar[3*n];
int lworkl = ncv*ncv+8*ncv; // Must be at least this length
Scalar *workl = new Scalar[lworkl];
int *iparam= new int[11];
iparam[0] = 1; // 1 means we let ARPACK perform the shifts, 0 means we'd have to do it
iparam[2] = std::max(300, (int)std::ceil(2*n/std::max(ncv,1)));
iparam[6] = mode; // The mode, 1 is standard ev problem, 2 for generalized ev, 3 for shift-and-invert
// Used during reverse communicate to notify where arrays start
//
int *ipntr = new int[11];
// Error codes are returned in here, initial value of 0 indicates a random initial
// residual vector is used, any other values means resid contains the initial residual
// vector, possibly from a previous run
//
int info = 0;
Scalar scale = 1.0;
//if (!isBempty)
//{
//Scalar scale = B.norm() / std::sqrt(n);
//scale = std::pow(2, std::floor(std::log(scale+1)));
////M /= scale;
//for (size_t i=0; i<(size_t)B.outerSize(); i++)
// for (typename MatrixType::InnerIterator it(B, i); it; ++it)
// it.valueRef() /= scale;
//}
MatrixSolver OP;
if (mode == 1 || mode == 2)
{
if (!isBempty)
OP.compute(B);
}
else if (mode == 3)
{
if (sigma == 0.0)
{
OP.compute(A);
}
else
{
// Note: We will never enter here because sigma must be 0.0
//
if (isBempty)
{
MatrixType AminusSigmaB(A);
for (Index i=0; i<A.rows(); ++i)
AminusSigmaB.coeffRef(i,i) -= sigma;
OP.compute(AminusSigmaB);
}
else
{
MatrixType AminusSigmaB = A - sigma * B;
OP.compute(AminusSigmaB);
}
}
}
if (!(mode == 1 && isBempty) && !(mode == 2 && isBempty) && OP.info() != Success)
std::cout << "Error factoring matrix" << std::endl;
do
{
internal::arpack_wrapper<Scalar, RealScalar>::saupd(&ido, bmat, &n, whch, &nev, &tol, resid,
&ncv, v, &ldv, iparam, ipntr, workd, workl,
&lworkl, &info);
if (ido == -1 || ido == 1)
{
Scalar *in = workd + ipntr[0] - 1;
Scalar *out = workd + ipntr[1] - 1;
if (ido == 1 && mode != 2)
{
Scalar *out2 = workd + ipntr[2] - 1;
if (isBempty || mode == 1)
Matrix<Scalar, Dynamic, 1>::Map(out2, n) = Matrix<Scalar, Dynamic, 1>::Map(in, n);
else
Matrix<Scalar, Dynamic, 1>::Map(out2, n) = B * Matrix<Scalar, Dynamic, 1>::Map(in, n);
in = workd + ipntr[2] - 1;
}
if (mode == 1)
{
if (isBempty)
{
// OP = A
//
Matrix<Scalar, Dynamic, 1>::Map(out, n) = A * Matrix<Scalar, Dynamic, 1>::Map(in, n);
}
else
{
// OP = L^{-1}AL^{-T}
//
internal::OP<MatrixSolver, MatrixType, Scalar, BisSPD>::applyOP(OP, A, n, in, out);
}
}
else if (mode == 2)
{
if (ido == 1)
Matrix<Scalar, Dynamic, 1>::Map(in, n) = A * Matrix<Scalar, Dynamic, 1>::Map(in, n);
// OP = B^{-1} A
//
Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
}
else if (mode == 3)
{
// OP = (A-\sigmaB)B (\sigma could be 0, and B could be I)
// The B * in is already computed and stored at in if ido == 1
//
if (ido == 1 || isBempty)
Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
else
Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(B * Matrix<Scalar, Dynamic, 1>::Map(in, n));
}
}
else if (ido == 2)
{
Scalar *in = workd + ipntr[0] - 1;
Scalar *out = workd + ipntr[1] - 1;
if (isBempty || mode == 1)
Matrix<Scalar, Dynamic, 1>::Map(out, n) = Matrix<Scalar, Dynamic, 1>::Map(in, n);
else
Matrix<Scalar, Dynamic, 1>::Map(out, n) = B * Matrix<Scalar, Dynamic, 1>::Map(in, n);
}
} while (ido != 99);
if (info == 1)
m_info = NoConvergence;
else if (info == 3)
m_info = NumericalIssue;
else if (info < 0)
m_info = InvalidInput;
else if (info != 0)
eigen_assert(false && "Unknown ARPACK return value!");
else
{
// Do we compute eigenvectors or not?
//
int rvec = (options & ComputeEigenvectors) == ComputeEigenvectors;
// "A" means "All", use "S" to choose specific eigenvalues (not yet supported in ARPACK))
//
char howmny[2] = "A";
// if howmny == "S", specifies the eigenvalues to compute (not implemented in ARPACK)
//
int *select = new int[ncv];
// Final eigenvalues
//
m_eivalues.resize(nev, 1);
internal::arpack_wrapper<Scalar, RealScalar>::seupd(&rvec, howmny, select, m_eivalues.data(), v, &ldv,
&sigma, bmat, &n, whch, &nev, &tol, resid, &ncv,
v, &ldv, iparam, ipntr, workd, workl, &lworkl, &info);
if (info == -14)
m_info = NoConvergence;
else if (info != 0)
m_info = InvalidInput;
else
{
if (rvec)
{
m_eivec.resize(A.rows(), nev);
for (int i=0; i<nev; i++)
for (int j=0; j<n; j++)
m_eivec(j,i) = v[i*n+j] / scale;
if (mode == 1 && !isBempty && BisSPD)
internal::OP<MatrixSolver, MatrixType, Scalar, BisSPD>::project(OP, n, nev, m_eivec.data());
m_eigenvectorsOk = true;
}
m_nbrIterations = iparam[2];
m_nbrConverged = iparam[4];
m_info = Success;
}
delete select;
}
delete v;
delete iparam;
delete ipntr;
delete workd;
delete workl;
delete resid;
m_isInitialized = true;
return *this;
}
// Single precision
//
extern "C" void ssaupd_(int *ido, char *bmat, int *n, char *which,
int *nev, float *tol, float *resid, int *ncv,
float *v, int *ldv, int *iparam, int *ipntr,
float *workd, float *workl, int *lworkl,
int *info);
extern "C" void sseupd_(int *rvec, char *All, int *select, float *d,
float *z, int *ldz, float *sigma,
char *bmat, int *n, char *which, int *nev,
float *tol, float *resid, int *ncv, float *v,
int *ldv, int *iparam, int *ipntr, float *workd,
float *workl, int *lworkl, int *ierr);
// Double precision
//
extern "C" void dsaupd_(int *ido, char *bmat, int *n, char *which,
int *nev, double *tol, double *resid, int *ncv,
double *v, int *ldv, int *iparam, int *ipntr,
double *workd, double *workl, int *lworkl,
int *info);
extern "C" void dseupd_(int *rvec, char *All, int *select, double *d,
double *z, int *ldz, double *sigma,
char *bmat, int *n, char *which, int *nev,
double *tol, double *resid, int *ncv, double *v,
int *ldv, int *iparam, int *ipntr, double *workd,
double *workl, int *lworkl, int *ierr);
namespace internal {
template<typename Scalar, typename RealScalar> struct arpack_wrapper
{
static inline void saupd(int *ido, char *bmat, int *n, char *which,
int *nev, RealScalar *tol, Scalar *resid, int *ncv,
Scalar *v, int *ldv, int *iparam, int *ipntr,
Scalar *workd, Scalar *workl, int *lworkl, int *info)
{ EIGEN_STATIC_ASSERT(false, static_assertion<true>::NUMERIC_TYPE_MUST_BE_REAL); }
static inline void seupd(int *rvec, char *All, int *select, Scalar *d,
Scalar *z, int *ldz, RealScalar *sigma,
char *bmat, int *n, char *which, int *nev,
RealScalar *tol, Scalar *resid, int *ncv, Scalar *v,
int *ldv, int *iparam, int *ipntr, Scalar *workd,
Scalar *workl, int *lworkl, int *ierr)
{ EIGEN_STATIC_ASSERT(false, static_assertion<true>::NUMERIC_TYPE_MUST_BE_REAL); }
};
template <> struct arpack_wrapper<float, float>
{
static inline void saupd(int *ido, char *bmat, int *n, char *which,
int *nev, float *tol, float *resid, int *ncv,
float *v, int *ldv, int *iparam, int *ipntr,
float *workd, float *workl, int *lworkl, int *info)
{
ssaupd_(ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, info);
}
static inline void seupd(int *rvec, char *All, int *select, float *d,
float *z, int *ldz, float *sigma,
char *bmat, int *n, char *which, int *nev,
float *tol, float *resid, int *ncv, float *v,
int *ldv, int *iparam, int *ipntr, float *workd,
float *workl, int *lworkl, int *ierr)
{
sseupd_(rvec, All, select, d, z, ldz, sigma, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr,
workd, workl, lworkl, ierr);
}
};
template <> struct arpack_wrapper<double, double>
{
static inline void saupd(int *ido, char *bmat, int *n, char *which,
int *nev, double *tol, double *resid, int *ncv,
double *v, int *ldv, int *iparam, int *ipntr,
double *workd, double *workl, int *lworkl, int *info)
{
dsaupd_(ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, info);
}
static inline void seupd(int *rvec, char *All, int *select, double *d,
double *z, int *ldz, double *sigma,
char *bmat, int *n, char *which, int *nev,
double *tol, double *resid, int *ncv, double *v,
int *ldv, int *iparam, int *ipntr, double *workd,
double *workl, int *lworkl, int *ierr)
{
dseupd_(rvec, All, select, d, v, ldv, sigma, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr,
workd, workl, lworkl, ierr);
}
};
template<typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD>
struct OP
{
static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out);
static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs);
};
template<typename MatrixSolver, typename MatrixType, typename Scalar>
struct OP<MatrixSolver, MatrixType, Scalar, true>
{
static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out)
{
// OP = L^{-1} A L^{-T} (B = LL^T)
//
// First solve L^T out = in
//
Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixU().solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.permutationPinv() * Matrix<Scalar, Dynamic, 1>::Map(out, n);
// Then compute out = A out
//
Matrix<Scalar, Dynamic, 1>::Map(out, n) = A * Matrix<Scalar, Dynamic, 1>::Map(out, n);
// Then solve L out = out
//
Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.permutationP() * Matrix<Scalar, Dynamic, 1>::Map(out, n);
Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixL().solve(Matrix<Scalar, Dynamic, 1>::Map(out, n));
}
static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs)
{
// Solve L^T out = in
//
Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.matrixU().solve(Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k));
Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.permutationPinv() * Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k);
}
};
template<typename MatrixSolver, typename MatrixType, typename Scalar>
struct OP<MatrixSolver, MatrixType, Scalar, false>
{
static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out)
{
eigen_assert(false && "Should never be in here...");
}
static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs)
{
eigen_assert(false && "Should never be in here...");
}
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_ARPACKSELFADJOINTEIGENSOLVER_H