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* fix the QR module to use extract/part instead of the previous triangular stuff

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* added qr and eigensolver tests
* fix a compilation warning in Matrix copy constructor
This commit is contained in:
Gael Guennebaud
2008-05-27 09:16:27 +00:00
parent 5aa00f6870
commit 559233c73e
7 changed files with 138 additions and 19 deletions
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25
Eigen/src/QR/EigenSolver.h
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@@ -32,7 +32,7 @@
* \param MatrixType the type of the matrix of which we are computing the eigen decomposition
* \param IsSelfadjoint tells the input matrix is guaranteed to be selfadjoint (hermitian). In that case the
* return type of eigenvalues() is a real vector.
*
*
* Currently it only support real matrices.
*
* \note this code was adapted from JAMA (public domain)
@@ -49,6 +49,7 @@ template<typename _MatrixType, bool IsSelfadjoint=false> class EigenSolver
typedef std::complex<RealScalar> Complex;
typedef Matrix<typename ei_meta_if<IsSelfadjoint, Scalar, Complex>::ret, MatrixType::ColsAtCompileTime, 1> EigenvalueType;
typedef Matrix<RealScalar, MatrixType::ColsAtCompileTime, 1> RealVectorType;
typedef Matrix<RealScalar, Dynamic, 1> RealVectorTypeX;
EigenSolver(const MatrixType& matrix)
: m_eivec(matrix.rows(), matrix.cols()),
@@ -74,7 +75,7 @@ template<typename _MatrixType, bool IsSelfadjoint=false> class EigenSolver
void tql2(RealVectorType& eivalr, RealVectorType& eivali);
void orthes(MatrixType& matH, RealVectorType& ort);
void hqr2(MatrixType& matH, RealVectorType& ort);
void hqr2(MatrixType& matH);
protected:
MatrixType m_eivec;
@@ -87,7 +88,7 @@ void EigenSolver<MatrixType,IsSelfadjoint>::computeImpl(const MatrixType& matrix
assert(matrix.cols() == matrix.rows());
int n = matrix.cols();
m_eivalues.resize(n,1);
RealVectorType eivali(n);
m_eivec = matrix;
@@ -115,25 +116,25 @@ void EigenSolver<MatrixType,IsSelfadjoint>::computeImpl(const MatrixType& matrix
RealVectorType eivalr(n);
RealVectorType eivali(n);
m_eivec = matrix;
// Tridiagonalize.
tridiagonalization(eivalr, eivali);
// Diagonalize.
tql2(eivalr, eivali);
m_eivalues = eivalr.template cast<Complex>();
}
else
{
MatrixType matH = matrix;
RealVectorType ort(n);
// Reduce to Hessenberg form.
orthes(matH, ort);
// Reduce Hessenberg to real Schur form.
hqr2(matH, ort);
hqr2(matH);
}
}
@@ -198,7 +199,7 @@ void EigenSolver<MatrixType,IsSelfadjoint>::tridiagonalization(RealVectorType& e
f = (eivali.start(i).transpose() * eivalr.start(i))(0,0);
eivali.start(i) = (eivali.start(i) - (f / (h + h)) * eivalr.start(i))/h;
m_eivec.corner(TopLeft, i, i).lower() -=
m_eivec.corner(TopLeft, i, i).template part<Lower>() -=
( (eivali.start(i) * eivalr.start(i).transpose()).lazy()
+ (eivalr.start(i) * eivali.start(i).transpose()).lazy());
@@ -279,7 +280,7 @@ void EigenSolver<MatrixType,IsSelfadjoint>::tql2(RealVectorType& eivalr, RealVec
Scalar dl1 = eivalr[l+1];
Scalar h = g - eivalr[l];
if (l+2<n)
eivalr.end(n-l-2) -= RealVectorType::constant(n-l-2, h);
eivalr.end(n-l-2) -= RealVectorTypeX::constant(n-l-2, h);
f = f + h;
// Implicit QL transformation.
@@ -432,7 +433,7 @@ std::complex<Scalar> cdiv(Scalar xr, Scalar xi, Scalar yr, Scalar yi)
// Nonsymmetric reduction from Hessenberg to real Schur form.
template<typename MatrixType, bool IsSelfadjoint>
void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH, RealVectorType& ort)
void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
{
// This is derived from the Algol procedure hqr2,
// by Martin and Wilkinson, Handbook for Auto. Comp.,