11 #ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_H 12 #define EIGEN_COLPIVOTINGHOUSEHOLDERQR_H 17 template<
typename _MatrixType>
struct traits<ColPivHouseholderQR<_MatrixType> >
48 template<
typename _MatrixType>
class ColPivHouseholderQR
52 typedef _MatrixType MatrixType;
54 RowsAtCompileTime = MatrixType::RowsAtCompileTime,
55 ColsAtCompileTime = MatrixType::ColsAtCompileTime,
56 MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
57 MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
59 typedef typename MatrixType::Scalar Scalar;
60 typedef typename MatrixType::RealScalar RealScalar;
62 typedef typename MatrixType::StorageIndex StorageIndex;
63 typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
64 typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType;
65 typedef typename internal::plain_row_type<MatrixType, Index>::type IntRowVectorType;
66 typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
67 typedef typename internal::plain_row_type<MatrixType, RealScalar>::type RealRowVectorType;
68 typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> HouseholderSequenceType;
69 typedef typename MatrixType::PlainObject PlainObject;
73 typedef typename PermutationType::StorageIndex PermIndexType;
87 m_colsTranspositions(),
91 m_isInitialized(false),
92 m_usePrescribedThreshold(false) {}
102 m_hCoeffs((
std::min)(rows,cols)),
103 m_colsPermutation(PermIndexType(cols)),
104 m_colsTranspositions(cols),
106 m_colNormsUpdated(cols),
107 m_colNormsDirect(cols),
108 m_isInitialized(false),
109 m_usePrescribedThreshold(false) {}
123 template<
typename InputType>
125 : m_qr(matrix.rows(), matrix.cols()),
126 m_hCoeffs((
std::min)(matrix.rows(),matrix.cols())),
127 m_colsPermutation(PermIndexType(matrix.cols())),
128 m_colsTranspositions(matrix.cols()),
129 m_temp(matrix.cols()),
130 m_colNormsUpdated(matrix.cols()),
131 m_colNormsDirect(matrix.cols()),
132 m_isInitialized(false),
133 m_usePrescribedThreshold(false)
144 template<
typename InputType>
146 : m_qr(matrix.derived()),
147 m_hCoeffs((
std::min)(matrix.rows(),matrix.cols())),
148 m_colsPermutation(PermIndexType(matrix.cols())),
149 m_colsTranspositions(matrix.cols()),
150 m_temp(matrix.cols()),
151 m_colNormsUpdated(matrix.cols()),
152 m_colNormsDirect(matrix.cols()),
153 m_isInitialized(false),
154 m_usePrescribedThreshold(false)
176 template<
typename Rhs>
180 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
184 HouseholderSequenceType householderQ()
const;
185 HouseholderSequenceType matrixQ()
const 187 return householderQ();
194 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
209 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
213 template<
typename InputType>
219 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
220 return m_colsPermutation;
236 typename MatrixType::RealScalar absDeterminant()
const;
250 typename MatrixType::RealScalar logAbsDeterminant()
const;
261 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
262 RealScalar premultiplied_threshold =
abs(m_maxpivot) * threshold();
264 for(
Index i = 0; i < m_nonzero_pivots; ++i)
265 result += (
abs(m_qr.coeff(i,i)) > premultiplied_threshold);
277 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
278 return cols() - rank();
290 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
291 return rank() == cols();
303 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
304 return rank() == rows();
315 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
316 return isInjective() && isSurjective();
326 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
330 inline Index rows()
const {
return m_qr.rows(); }
331 inline Index cols()
const {
return m_qr.cols(); }
337 const HCoeffsType&
hCoeffs()
const {
return m_hCoeffs; }
358 m_usePrescribedThreshold =
true;
359 m_prescribedThreshold = threshold;
373 m_usePrescribedThreshold =
false;
383 eigen_assert(m_isInitialized || m_usePrescribedThreshold);
384 return m_usePrescribedThreshold ? m_prescribedThreshold
399 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
400 return m_nonzero_pivots;
416 eigen_assert(m_isInitialized &&
"Decomposition is not initialized.");
420 #ifndef EIGEN_PARSED_BY_DOXYGEN 421 template<
typename RhsType,
typename DstType>
423 void _solve_impl(
const RhsType &rhs, DstType &dst)
const;
430 static void check_template_parameters()
432 EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
435 void computeInPlace();
438 HCoeffsType m_hCoeffs;
439 PermutationType m_colsPermutation;
440 IntRowVectorType m_colsTranspositions;
441 RowVectorType m_temp;
442 RealRowVectorType m_colNormsUpdated;
443 RealRowVectorType m_colNormsDirect;
444 bool m_isInitialized, m_usePrescribedThreshold;
445 RealScalar m_prescribedThreshold, m_maxpivot;
446 Index m_nonzero_pivots;
450 template<
typename MatrixType>
454 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
455 eigen_assert(m_qr.rows() == m_qr.cols() &&
"You can't take the determinant of a non-square matrix!");
456 return abs(m_qr.diagonal().prod());
459 template<
typename MatrixType>
462 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
463 eigen_assert(m_qr.rows() == m_qr.cols() &&
"You can't take the determinant of a non-square matrix!");
464 return m_qr.diagonal().cwiseAbs().array().log().sum();
473 template<
typename MatrixType>
474 template<
typename InputType>
482 template<
typename MatrixType>
485 check_template_parameters();
492 Index rows = m_qr.rows();
493 Index cols = m_qr.cols();
494 Index size = m_qr.diagonalSize();
496 m_hCoeffs.resize(size);
500 m_colsTranspositions.resize(m_qr.cols());
501 Index number_of_transpositions = 0;
503 m_colNormsUpdated.resize(cols);
504 m_colNormsDirect.resize(cols);
505 for (
Index k = 0; k < cols; ++k) {
508 m_colNormsDirect.coeffRef(k) = m_qr.col(k).norm();
509 m_colNormsUpdated.coeffRef(k) = m_colNormsDirect.coeffRef(k);
515 m_nonzero_pivots = size;
516 m_maxpivot = RealScalar(0);
518 for(
Index k = 0; k < size; ++k)
521 Index biggest_col_index;
522 RealScalar biggest_col_sq_norm = numext::abs2(m_colNormsUpdated.tail(cols-k).maxCoeff(&biggest_col_index));
523 biggest_col_index += k;
527 if(m_nonzero_pivots==size && biggest_col_sq_norm < threshold_helper * RealScalar(rows-k))
528 m_nonzero_pivots = k;
531 m_colsTranspositions.coeffRef(k) = biggest_col_index;
532 if(k != biggest_col_index) {
533 m_qr.col(k).swap(m_qr.col(biggest_col_index));
534 std::swap(m_colNormsUpdated.coeffRef(k), m_colNormsUpdated.coeffRef(biggest_col_index));
535 std::swap(m_colNormsDirect.coeffRef(k), m_colNormsDirect.coeffRef(biggest_col_index));
536 ++number_of_transpositions;
541 m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
544 m_qr.coeffRef(k,k) = beta;
547 if(
abs(beta) > m_maxpivot) m_maxpivot =
abs(beta);
550 m_qr.bottomRightCorner(rows-k, cols-k-1)
551 .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));
554 for (
Index j = k + 1; j < cols; ++j) {
559 if (m_colNormsUpdated.coeffRef(j) != 0) {
560 RealScalar temp =
abs(m_qr.coeffRef(k, j)) / m_colNormsUpdated.coeffRef(j);
561 temp = (RealScalar(1) + temp) * (RealScalar(1) - temp);
562 temp = temp < 0 ? 0 : temp;
563 RealScalar temp2 = temp * numext::abs2(m_colNormsUpdated.coeffRef(j) /
564 m_colNormsDirect.coeffRef(j));
565 if (temp2 <= norm_downdate_threshold) {
568 m_colNormsDirect.coeffRef(j) = m_qr.col(j).tail(rows - k - 1).norm();
569 m_colNormsUpdated.coeffRef(j) = m_colNormsDirect.coeffRef(j);
571 m_colNormsUpdated.coeffRef(j) *= numext::sqrt(temp);
577 m_colsPermutation.setIdentity(PermIndexType(cols));
578 for(PermIndexType k = 0; k < size; ++k)
579 m_colsPermutation.applyTranspositionOnTheRight(k, PermIndexType(m_colsTranspositions.coeff(k)));
581 m_det_pq = (number_of_transpositions%2) ? -1 : 1;
582 m_isInitialized =
true;
585 #ifndef EIGEN_PARSED_BY_DOXYGEN 586 template<
typename _MatrixType>
587 template<
typename RhsType,
typename DstType>
590 eigen_assert(rhs.rows() == rows());
592 const Index nonzero_pivots = nonzeroPivots();
594 if(nonzero_pivots == 0)
600 typename RhsType::PlainObject c(rhs);
604 .setLength(nonzero_pivots)
608 m_qr.topLeftCorner(nonzero_pivots, nonzero_pivots)
609 .template triangularView<Upper>()
610 .solveInPlace(c.topRows(nonzero_pivots));
612 for(
Index i = 0; i < nonzero_pivots; ++i) dst.row(m_colsPermutation.indices().coeff(i)) = c.row(i);
613 for(
Index i = nonzero_pivots; i < cols(); ++i) dst.row(m_colsPermutation.indices().coeff(i)).setZero();
619 template<
typename DstXprType,
typename MatrixType,
typename Scalar>
620 struct Assignment<DstXprType, Inverse<ColPivHouseholderQR<MatrixType> >, internal::assign_op<Scalar,Scalar>, Dense2Dense>
624 static void run(DstXprType &dst,
const SrcXprType &src,
const internal::assign_op<Scalar,Scalar> &)
626 dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));
635 template<
typename MatrixType>
639 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
648 template<
typename Derived>
658 #endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_H Index rank() const
Definition: ColPivHouseholderQR.h:258
bool isSurjective() const
Definition: ColPivHouseholderQR.h:301
ColPivHouseholderQR(EigenBase< InputType > &matrix)
Constructs a QR factorization from a given matrix.
Definition: ColPivHouseholderQR.h:145
ColPivHouseholderQR()
Default Constructor.
Definition: ColPivHouseholderQR.h:83
ColPivHouseholderQR(Index rows, Index cols)
Default Constructor with memory preallocation.
Definition: ColPivHouseholderQR.h:100
const HCoeffsType & hCoeffs() const
Definition: ColPivHouseholderQR.h:337
const ColPivHouseholderQR< PlainObject > colPivHouseholderQr() const
Definition: ColPivHouseholderQR.h:650
Namespace containing all symbols from the Eigen library.
Definition: Core:271
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:167
ComputationInfo info() const
Reports whether the QR factorization was succesful.
Definition: ColPivHouseholderQR.h:414
Derived & derived()
Definition: EigenBase.h:44
Complete orthogonal decomposition (COD) of a matrix.
Definition: ForwardDeclarations.h:257
HouseholderSequence< VectorsType, CoeffsType > householderSequence(const VectorsType &v, const CoeffsType &h)
Convenience function for constructing a Householder sequence.
Definition: HouseholderSequence.h:451
Definition: EigenBase.h:28
Sequence of Householder reflections acting on subspaces with decreasing size.
Definition: ForwardDeclarations.h:262
ColPivHouseholderQR(const EigenBase< InputType > &matrix)
Constructs a QR factorization from a given matrix.
Definition: ColPivHouseholderQR.h:124
Expression of the inverse of another expression.
Definition: Inverse.h:43
HouseholderSequenceType householderQ() const
Definition: ColPivHouseholderQR.h:637
RealScalar maxPivot() const
Definition: ColPivHouseholderQR.h:406
ColPivHouseholderQR & setThreshold(Default_t)
Definition: ColPivHouseholderQR.h:371
Householder rank-revealing QR decomposition of a matrix with column-pivoting.
Definition: ForwardDeclarations.h:255
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: XprHelper.h:35
const MatrixType & matrixR() const
Definition: ColPivHouseholderQR.h:207
bool isInjective() const
Definition: ColPivHouseholderQR.h:288
const Solve< ColPivHouseholderQR, Rhs > solve(const MatrixBase< Rhs > &b) const
Definition: ColPivHouseholderQR.h:178
bool isInvertible() const
Definition: ColPivHouseholderQR.h:313
Definition: Constants.h:432
MatrixType::RealScalar absDeterminant() const
Definition: ColPivHouseholderQR.h:451
ColPivHouseholderQR & setThreshold(const RealScalar &threshold)
Definition: ColPivHouseholderQR.h:356
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_abs_op< typename Derived::Scalar >, const Derived > abs(const Eigen::ArrayBase< Derived > &x)
Definition: Eigen_Colamd.h:50
RealScalar threshold() const
Definition: ColPivHouseholderQR.h:381
MatrixType::RealScalar logAbsDeterminant() const
Definition: ColPivHouseholderQR.h:460
Index dimensionOfKernel() const
Definition: ColPivHouseholderQR.h:275
Index nonzeroPivots() const
Definition: ColPivHouseholderQR.h:397
Pseudo expression representing a solving operation.
Definition: Solve.h:62
const MatrixType & matrixQR() const
Definition: ColPivHouseholderQR.h:192
ComputationInfo
Definition: Constants.h:430
const PermutationType & colsPermutation() const
Definition: ColPivHouseholderQR.h:217
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
const Inverse< ColPivHouseholderQR > inverse() const
Definition: ColPivHouseholderQR.h:324