GitHub-Proxy/eigen
1
0
Fork 0
mirror of https://gitlab.com/libeigen/eigen.git synced 2025-05-13 16:28:06 +08:00
Code Issues Packages Projects Releases Wiki Activity

integrate Hauke's 2x2 direct symmetric eigenvalues solver

Browse Source
This commit is contained in:
Gael Guennebaud 2011-07-22 09:43:14 +02:00
parent 26d7dad138
commit 47a2bca89f
1 changed files with 88 additions and 3 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

91
Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
View File

@ -500,10 +500,10 @@ template<typename SolverType,int Size,bool IsComplex> struct direct_selfadjoint_
template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3,false>
{
typedef typename SolverType::MatrixType MatrixType;
typedef typename SolverType::RealVectorType VectorType;
typedef typename SolverType::Scalar Scalar;
template<typename Roots>
inline static void computeRoots(const MatrixType& m, Roots& roots)
inline static void computeRoots(const MatrixType& m, VectorType& roots)
{
using std::sqrt;
using std::atan2;
@ -561,7 +561,7 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
MatrixType& eivecs = solver.m_eivec;
typename SolverType::RealVectorType& eivals = solver.m_eivalues;
VectorType& eivals = solver.m_eivalues;
// map the matrix coefficients to [-1:1] to avoid over- and underflow.
Scalar scale = mat.cwiseAbs().maxCoeff();
@ -610,6 +610,91 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
}
};
// 2x2 direct eigenvalues decomposition, code from Hauke Heibel
template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,2,false>
{
typedef typename SolverType::MatrixType MatrixType;
typedef typename SolverType::RealVectorType VectorType;
typedef typename SolverType::Scalar Scalar;
inline static void run(SolverType& solver, const MatrixType& mat, int options)
{
eigen_assert(mat.cols() == 2 && mat.cols() == mat.rows());
eigen_assert((options&~(EigVecMask|GenEigMask))==0
&& (options&EigVecMask)!=EigVecMask
&& "invalid option parameter");
bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
MatrixType& eivecs = solver.m_eivec;
VectorType& eivals = solver.m_eivalues;
// map the matrix coefficients to [-1:1] to avoid over- and underflow.
Scalar scale = mat.cwiseAbs().maxCoeff();
scale = std::max(scale,Scalar(1));
MatrixType scaledMat = mat / scale;
// Compute the eigenvalues
const Scalar xx = scaledMat(0,0);
const Scalar yy = scaledMat(1,1);
const Scalar xy = scaledMat(1,0);
const Scalar root = std::sqrt((xx-yy)*(xx-yy)+Scalar(4.0)*xy*xy);
const Scalar eig_val1 = Scalar(0.5)*(xx+yy+root);
const Scalar eig_val2 = Scalar(0.5)*(xx+yy-root);
using std::sqrt;
using std::abs;
// compute the eigen vectors
if(computeEigenvectors)
{
Scalar nx, ny;
if (xx-yy > 0)
{
Scalar len(1.0);
if (-yy+xx+root != Scalar(0.0))
{
ny = -Scalar(2.0)*xy/(-yy+xx+root);
len = Scalar(1.0)/sqrt(1+ny*ny);
ny *= len;
}
else
ny = Scalar(0.0);
nx = -len;
}
else
{
Scalar len = Scalar(1.0);
if (-yy+xx-root != Scalar(0.0))
{
nx = -Scalar(2.0)*xy/(-yy+xx-root);
len = Scalar(1.0)/sqrt(1+nx*nx);
nx *= len;
}
else
nx = Scalar(0.0);
ny = len;
}
int id0(0), id1(1);
if(eig_val1>eig_val2)
std::swap(id0,id1);
eivecs.col(id0) << nx, ny;
eivecs.col(id1) << -ny, nx;
eivals(id0) = eig_val1;
eivals(id1) = eig_val2;
}
// Rescale back to the original size.
eivals *= scale;
solver.m_info = Success;
solver.m_isInitialized = true;
solver.m_eigenvectorsOk = computeEigenvectors;
}
};
}
template<typename MatrixType>