11 #ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_H 12 #define EIGEN_COLPIVOTINGHOUSEHOLDERQR_H 37 template<
typename _MatrixType>
class ColPivHouseholderQR
41 typedef _MatrixType MatrixType;
43 RowsAtCompileTime = MatrixType::RowsAtCompileTime,
44 ColsAtCompileTime = MatrixType::ColsAtCompileTime,
45 Options = MatrixType::Options,
46 MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
47 MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
49 typedef typename MatrixType::Scalar Scalar;
50 typedef typename MatrixType::RealScalar RealScalar;
51 typedef typename MatrixType::Index Index;
52 typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, Options, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixQType;
53 typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
54 typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType;
55 typedef typename internal::plain_row_type<MatrixType, Index>::type IntRowVectorType;
56 typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
57 typedef typename internal::plain_row_type<MatrixType, RealScalar>::type RealRowVectorType;
58 typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> HouseholderSequenceType;
62 typedef typename PermutationType::Index PermIndexType;
76 m_colsTranspositions(),
79 m_isInitialized(false),
80 m_usePrescribedThreshold(false) {}
90 m_hCoeffs((
std::min)(rows,cols)),
91 m_colsPermutation(PermIndexType(cols)),
92 m_colsTranspositions(cols),
95 m_isInitialized(false),
96 m_usePrescribedThreshold(false) {}
111 : m_qr(matrix.rows(), matrix.cols()),
112 m_hCoeffs((
std::min)(matrix.rows(),matrix.cols())),
113 m_colsPermutation(PermIndexType(matrix.cols())),
114 m_colsTranspositions(matrix.cols()),
115 m_temp(matrix.cols()),
116 m_colSqNorms(matrix.cols()),
117 m_isInitialized(false),
118 m_usePrescribedThreshold(false)
137 template<
typename Rhs>
138 inline const internal::solve_retval<ColPivHouseholderQR, Rhs>
141 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
142 return internal::solve_retval<ColPivHouseholderQR, Rhs>(*
this, b.derived());
146 HouseholderSequenceType matrixQ(
void)
const 155 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
170 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
179 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
180 return m_colsPermutation;
221 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
222 RealScalar premultiplied_threshold = abs(m_maxpivot) *
threshold();
224 for(Index i = 0; i < m_nonzero_pivots; ++i)
225 result += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);
237 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
238 return cols() -
rank();
250 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
251 return rank() == cols();
263 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
264 return rank() == rows();
275 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
285 internal::solve_retval<ColPivHouseholderQR, typename MatrixType::IdentityReturnType>
288 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
289 return internal::solve_retval<ColPivHouseholderQR,typename MatrixType::IdentityReturnType>
290 (*
this, MatrixType::Identity(m_qr.rows(), m_qr.cols()));
293 inline Index rows()
const {
return m_qr.rows(); }
294 inline Index cols()
const {
return m_qr.cols(); }
300 const HCoeffsType&
hCoeffs()
const {
return m_hCoeffs; }
321 m_usePrescribedThreshold =
true;
336 m_usePrescribedThreshold =
false;
346 eigen_assert(m_isInitialized || m_usePrescribedThreshold);
347 return m_usePrescribedThreshold ? m_prescribedThreshold
362 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
363 return m_nonzero_pivots;
379 eigen_assert(m_isInitialized &&
"Decomposition is not initialized.");
385 static void check_template_parameters()
387 EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
391 HCoeffsType m_hCoeffs;
392 PermutationType m_colsPermutation;
393 IntRowVectorType m_colsTranspositions;
394 RowVectorType m_temp;
395 RealRowVectorType m_colSqNorms;
396 bool m_isInitialized, m_usePrescribedThreshold;
397 RealScalar m_prescribedThreshold, m_maxpivot;
398 Index m_nonzero_pivots;
402 template<
typename MatrixType>
406 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
407 eigen_assert(m_qr.rows() == m_qr.cols() &&
"You can't take the determinant of a non-square matrix!");
408 return abs(m_qr.diagonal().prod());
411 template<
typename MatrixType>
414 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
415 eigen_assert(m_qr.rows() == m_qr.cols() &&
"You can't take the determinant of a non-square matrix!");
416 return m_qr.diagonal().cwiseAbs().array().log().sum();
425 template<
typename MatrixType>
428 check_template_parameters();
431 Index rows = matrix.rows();
432 Index cols = matrix.cols();
433 Index size = matrix.diagonalSize();
439 m_hCoeffs.resize(size);
443 m_colsTranspositions.resize(matrix.cols());
444 Index number_of_transpositions = 0;
446 m_colSqNorms.resize(cols);
447 for(Index k = 0; k < cols; ++k)
448 m_colSqNorms.coeffRef(k) = m_qr.col(k).squaredNorm();
452 m_nonzero_pivots = size;
453 m_maxpivot = RealScalar(0);
455 for(Index k = 0; k < size; ++k)
458 Index biggest_col_index;
459 RealScalar biggest_col_sq_norm = m_colSqNorms.tail(cols-k).maxCoeff(&biggest_col_index);
460 biggest_col_index += k;
466 biggest_col_sq_norm = m_qr.col(biggest_col_index).tail(rows-k).squaredNorm();
469 m_colSqNorms.coeffRef(biggest_col_index) = biggest_col_sq_norm;
473 if(m_nonzero_pivots==size && biggest_col_sq_norm < threshold_helper * RealScalar(rows-k))
474 m_nonzero_pivots = k;
477 m_colsTranspositions.coeffRef(k) = biggest_col_index;
478 if(k != biggest_col_index) {
479 m_qr.col(k).swap(m_qr.col(biggest_col_index));
480 std::swap(m_colSqNorms.coeffRef(k), m_colSqNorms.coeffRef(biggest_col_index));
481 ++number_of_transpositions;
486 m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
489 m_qr.coeffRef(k,k) = beta;
492 if(abs(beta) > m_maxpivot) m_maxpivot = abs(beta);
495 m_qr.bottomRightCorner(rows-k, cols-k-1)
496 .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));
499 m_colSqNorms.tail(cols-k-1) -= m_qr.row(k).tail(cols-k-1).cwiseAbs2();
502 m_colsPermutation.
setIdentity(PermIndexType(cols));
503 for(PermIndexType k = 0; k < size; ++k)
506 m_det_pq = (number_of_transpositions%2) ? -1 : 1;
507 m_isInitialized =
true;
514 template<
typename _MatrixType,
typename Rhs>
515 struct solve_retval<ColPivHouseholderQR<_MatrixType>, Rhs>
516 : solve_retval_base<ColPivHouseholderQR<_MatrixType>, Rhs>
520 template<
typename Dest>
void evalTo(Dest& dst)
const 522 eigen_assert(rhs().rows() == dec().rows());
524 const Index cols = dec().cols(),
525 nonzero_pivots = dec().nonzeroPivots();
527 if(nonzero_pivots == 0)
533 typename Rhs::PlainObject c(rhs());
542 .topLeftCorner(nonzero_pivots, nonzero_pivots)
543 .template triangularView<Upper>()
544 .solveInPlace(c.topRows(nonzero_pivots));
546 for(Index i = 0; i < nonzero_pivots; ++i) dst.row(dec().
colsPermutation().indices().coeff(i)) = c.row(i);
547 for(Index i = nonzero_pivots; i < cols; ++i) dst.row(dec().
colsPermutation().indices().coeff(i)).setZero();
556 template<
typename MatrixType>
560 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
568 template<
typename Derived>
577 #endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_H const MatrixType & matrixQR() const
Definition: ColPivHouseholderQR.h:153
bool isInvertible() const
Definition: ColPivHouseholderQR.h:273
void setIdentity()
Definition: PermutationMatrix.h:148
Derived & applyTranspositionOnTheRight(Index i, Index j)
Definition: PermutationMatrix.h:190
bool isSurjective() const
Definition: ColPivHouseholderQR.h:261
HouseholderSequenceType householderQ(void) const
Definition: ColPivHouseholderQR.h:558
const PermutationType & colsPermutation() const
Definition: ColPivHouseholderQR.h:177
Definition: StdDeque.h:50
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:88
MatrixType::RealScalar absDeterminant() const
Definition: ColPivHouseholderQR.h:403
Index nonzeroPivots() const
Definition: ColPivHouseholderQR.h:360
HouseholderSequence< VectorsType, CoeffsType > householderSequence(const VectorsType &v, const CoeffsType &h)
Convenience function for constructing a Householder sequence.
Definition: HouseholderSequence.h:423
ComputationInfo info() const
Reports whether the QR factorization was succesful.
Definition: ColPivHouseholderQR.h:377
ColPivHouseholderQR()
Default Constructor.
Definition: ColPivHouseholderQR.h:72
ColPivHouseholderQR(const MatrixType &matrix)
Constructs a QR factorization from a given matrix.
Definition: ColPivHouseholderQR.h:110
Sequence of Householder reflections acting on subspaces with decreasing size.
Definition: ForwardDeclarations.h:227
const MatrixType & matrixR() const
Definition: ColPivHouseholderQR.h:168
ColPivHouseholderQR & compute(const MatrixType &matrix)
Definition: ColPivHouseholderQR.h:426
const internal::solve_retval< ColPivHouseholderQR, Rhs > solve(const MatrixBase< Rhs > &b) const
Definition: ColPivHouseholderQR.h:139
Index rank() const
Definition: ColPivHouseholderQR.h:218
Householder rank-revealing QR decomposition of a matrix with column-pivoting.
Definition: ForwardDeclarations.h:222
const HCoeffsType & hCoeffs() const
Definition: ColPivHouseholderQR.h:300
ColPivHouseholderQR & setThreshold(Default_t)
Definition: ColPivHouseholderQR.h:334
ColPivHouseholderQR & setThreshold(const RealScalar &threshold)
Definition: ColPivHouseholderQR.h:319
Definition: Eigen_Colamd.h:50
MatrixType::RealScalar logAbsDeterminant() const
Definition: ColPivHouseholderQR.h:412
const ColPivHouseholderQR< PlainObject > colPivHouseholderQr() const
Definition: ColPivHouseholderQR.h:570
RealScalar threshold() const
Definition: ColPivHouseholderQR.h:344
RealScalar maxPivot() const
Definition: ColPivHouseholderQR.h:369
Index dimensionOfKernel() const
Definition: ColPivHouseholderQR.h:235
Definition: Constants.h:376
ColPivHouseholderQR(Index rows, Index cols)
Default Constructor with memory preallocation.
Definition: ColPivHouseholderQR.h:88
ComputationInfo
Definition: Constants.h:374
const internal::solve_retval< ColPivHouseholderQR, typename MatrixType::IdentityReturnType > inverse() const
Definition: ColPivHouseholderQR.h:286
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
bool isInjective() const
Definition: ColPivHouseholderQR.h:248