12 #ifndef EIGEN_COMPLEX_SCHUR_H 13 #define EIGEN_COMPLEX_SCHUR_H 15 #include "./HessenbergDecomposition.h" 20 template<
typename MatrixType,
bool IsComplex>
struct complex_schur_reduce_to_hessenberg;
54 typedef _MatrixType MatrixType;
56 RowsAtCompileTime = MatrixType::RowsAtCompileTime,
57 ColsAtCompileTime = MatrixType::ColsAtCompileTime,
58 Options = MatrixType::Options,
59 MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
60 MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
64 typedef typename MatrixType::Scalar
Scalar;
98 m_isInitialized(false),
99 m_matUisUptodate(false),
112 template<
typename InputType>
114 : m_matT(matrix.rows(),matrix.cols()),
115 m_matU(matrix.rows(),matrix.cols()),
116 m_hess(matrix.rows()),
117 m_isInitialized(false),
118 m_matUisUptodate(false),
140 eigen_assert(m_isInitialized &&
"ComplexSchur is not initialized.");
141 eigen_assert(m_matUisUptodate &&
"The matrix U has not been computed during the ComplexSchur decomposition.");
164 eigen_assert(m_isInitialized &&
"ComplexSchur is not initialized.");
190 template<
typename InputType>
210 template<
typename HessMatrixType,
typename OrthMatrixType>
219 eigen_assert(m_isInitialized &&
"ComplexSchur is not initialized.");
230 m_maxIters = maxIters;
251 bool m_isInitialized;
252 bool m_matUisUptodate;
256 bool subdiagonalEntryIsNeglegible(
Index i);
258 void reduceToTriangularForm(
bool computeU);
259 friend struct internal::complex_schur_reduce_to_hessenberg<MatrixType,
NumTraits<
Scalar>::IsComplex>;
265 template<typename MatrixType>
266 inline bool
ComplexSchur<MatrixType>::subdiagonalEntryIsNeglegible(Index i)
268 RealScalar d = numext::norm1(m_matT.
coeff(i,i)) + numext::norm1(m_matT.
coeff(i+1,i+1));
269 RealScalar sd = numext::norm1(m_matT.
coeff(i+1,i));
280 template<
typename MatrixType>
284 if (iter == 10 || iter == 20)
287 return abs(numext::real(m_matT.
coeff(iu,iu-1))) +
abs(numext::real(m_matT.
coeff(iu-1,iu-2)));
292 Matrix<ComplexScalar,2,2> t = m_matT.template block<2,2>(iu-1,iu-1);
293 RealScalar normt = t.cwiseAbs().sum();
304 if(numext::norm1(eival1) > numext::norm1(eival2))
305 eival2 = det / eival1;
307 eival1 = det / eival2;
310 if(numext::norm1(eival1-t.coeff(1,1)) < numext::norm1(eival2-t.coeff(1,1)))
311 return normt * eival1;
313 return normt * eival2;
317 template<
typename MatrixType>
318 template<
typename InputType>
321 m_matUisUptodate =
false;
322 eigen_assert(matrix.cols() == matrix.rows());
324 if(matrix.cols() == 1)
326 m_matT = matrix.derived().template cast<ComplexScalar>();
327 if(computeU) m_matU = ComplexMatrixType::Identity(1,1);
329 m_isInitialized =
true;
330 m_matUisUptodate = computeU;
334 internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>::run(*
this, matrix.derived(), computeU);
339 template<
typename MatrixType>
340 template<
typename HessMatrixType,
typename OrthMatrixType>
346 reduceToTriangularForm(computeU);
352 template<
typename MatrixType,
bool IsComplex>
353 struct complex_schur_reduce_to_hessenberg
356 static void run(ComplexSchur<MatrixType>& _this,
const MatrixType& matrix,
bool computeU)
358 _this.m_hess.compute(matrix);
359 _this.m_matT = _this.m_hess.matrixH();
360 if(computeU) _this.m_matU = _this.m_hess.matrixQ();
364 template<
typename MatrixType>
365 struct complex_schur_reduce_to_hessenberg<MatrixType, false>
367 static void run(ComplexSchur<MatrixType>& _this,
const MatrixType& matrix,
bool computeU)
372 _this.m_hess.compute(matrix);
373 _this.m_matT = _this.m_hess.matrixH().template cast<ComplexScalar>();
377 MatrixType Q = _this.m_hess.matrixQ();
378 _this.m_matU = Q.template cast<ComplexScalar>();
386 template<
typename MatrixType>
387 void ComplexSchur<MatrixType>::reduceToTriangularForm(
bool computeU)
389 Index maxIters = m_maxIters;
397 Index iu = m_matT.cols() - 1;
407 if(!subdiagonalEntryIsNeglegible(iu-1))
break;
418 if(totalIter > maxIters)
break;
422 while(il > 0 && !subdiagonalEntryIsNeglegible(il-1))
432 JacobiRotation<ComplexScalar> rot;
433 rot.makeGivens(m_matT.
coeff(il,il) - shift, m_matT.
coeff(il+1,il));
434 m_matT.rightCols(m_matT.cols()-il).applyOnTheLeft(il, il+1, rot.adjoint());
435 m_matT.topRows((std::min)(il+2,iu)+1).applyOnTheRight(il, il+1, rot);
436 if(computeU) m_matU.applyOnTheRight(il, il+1, rot);
438 for(
Index i=il+1 ; i<iu ; i++)
442 m_matT.rightCols(m_matT.cols()-i).applyOnTheLeft(i, i+1, rot.adjoint());
443 m_matT.topRows((std::min)(i+2,iu)+1).applyOnTheRight(i, i+1, rot);
444 if(computeU) m_matU.applyOnTheRight(i, i+1, rot);
448 if(totalIter <= maxIters)
453 m_isInitialized =
true;
454 m_matUisUptodate = computeU;
459 #endif // EIGEN_COMPLEX_SCHUR_H ComplexSchur(const EigenBase< InputType > &matrix, bool computeU=true)
Constructor; computes Schur decomposition of given matrix.
Definition: ComplexSchur.h:113
ComplexSchur & setMaxIterations(Index maxIters)
Sets the maximum number of iterations allowed.
Definition: ComplexSchur.h:228
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)
Namespace containing all symbols from the Eigen library.
Definition: Core:306
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:150
Derived & derived()
Definition: EigenBase.h:45
ComplexSchur & computeFromHessenberg(const HessMatrixType &matrixH, const OrthMatrixType &matrixQ, bool computeU=true)
Compute Schur decomposition from a given Hessenberg matrix.
std::complex< RealScalar > ComplexScalar
Complex scalar type for _MatrixType.
Definition: ComplexSchur.h:74
ComplexSchur & compute(const EigenBase< InputType > &matrix, bool computeU=true)
Computes Schur decomposition of given matrix.
ComputationInfo info() const
Reports whether previous computation was successful.
Definition: ComplexSchur.h:217
Definition: EigenBase.h:29
Matrix< ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime > ComplexMatrixType
Type for the matrices in the Schur decomposition.
Definition: ComplexSchur.h:81
MatrixType::Scalar Scalar
Scalar type for matrices of type _MatrixType.
Definition: ComplexSchur.h:64
Scalar & coeffRef(Index rowId, Index colId)
Definition: PlainObjectBase.h:183
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
Index getMaxIterations()
Returns the maximum number of iterations.
Definition: ComplexSchur.h:235
ComplexSchur(Index size=RowsAtCompileTime==Dynamic ? 1 :RowsAtCompileTime)
Default constructor.
Definition: ComplexSchur.h:94
Definition: Constants.h:432
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_abs_op< typename Derived::Scalar >, const Derived > abs(const Eigen::ArrayBase< Derived > &x)
const Scalar & coeff(Index rowId, Index colId) const
Definition: PlainObjectBase.h:160
const ComplexMatrixType & matrixU() const
Returns the unitary matrix in the Schur decomposition.
Definition: ComplexSchur.h:138
Eigen::Index Index
Definition: ComplexSchur.h:66
const int Dynamic
Definition: Constants.h:21
Performs a complex Schur decomposition of a real or complex square matrix.
Definition: ComplexSchur.h:51
ComputationInfo
Definition: Constants.h:430
Definition: Constants.h:436
const ComplexMatrixType & matrixT() const
Returns the triangular matrix in the Schur decomposition.
Definition: ComplexSchur.h:162
static const int m_maxIterationsPerRow
Maximum number of iterations per row.
Definition: ComplexSchur.h:245