11 #ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_H 12 #define EIGEN_COLPIVOTINGHOUSEHOLDERQR_H 52 :
public SolverBase<ColPivHouseholderQR<_MatrixType> >
62 MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
63 MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
89 m_colsTranspositions(),
93 m_isInitialized(false),
94 m_usePrescribedThreshold(false) {}
104 m_hCoeffs((
std::
min)(rows,cols)),
105 m_colsPermutation(PermIndexType(cols)),
106 m_colsTranspositions(cols),
108 m_colNormsUpdated(cols),
109 m_colNormsDirect(cols),
110 m_isInitialized(false),
111 m_usePrescribedThreshold(false) {}
125 template<
typename InputType>
127 : m_qr(matrix.
rows(), matrix.
cols()),
129 m_colsPermutation(PermIndexType(matrix.
cols())),
130 m_colsTranspositions(matrix.
cols()),
131 m_temp(matrix.
cols()),
132 m_colNormsUpdated(matrix.
cols()),
133 m_colNormsDirect(matrix.
cols()),
134 m_isInitialized(false),
135 m_usePrescribedThreshold(false)
146 template<
typename InputType>
148 : m_qr(matrix.derived()),
150 m_colsPermutation(PermIndexType(matrix.
cols())),
151 m_colsTranspositions(matrix.
cols()),
152 m_temp(matrix.
cols()),
153 m_colNormsUpdated(matrix.
cols()),
154 m_colNormsDirect(matrix.
cols()),
155 m_isInitialized(false),
156 m_usePrescribedThreshold(false)
161 #ifdef EIGEN_PARSED_BY_DOXYGEN 176 template<
typename Rhs>
181 HouseholderSequenceType householderQ()
const;
184 return householderQ();
191 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
206 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
210 template<
typename InputType>
216 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
217 return m_colsPermutation;
258 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
259 RealScalar premultiplied_threshold =
abs(m_maxpivot) * threshold();
261 for(
Index i = 0;
i < m_nonzero_pivots; ++
i)
262 result += (
abs(m_qr.coeff(
i,
i)) > premultiplied_threshold);
274 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
275 return cols() - rank();
287 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
288 return rank() ==
cols();
300 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
301 return rank() ==
rows();
312 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
313 return isInjective() && isSurjective();
323 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
334 const HCoeffsType&
hCoeffs()
const {
return m_hCoeffs; }
355 m_usePrescribedThreshold =
true;
356 m_prescribedThreshold = threshold;
370 m_usePrescribedThreshold =
false;
380 eigen_assert(m_isInitialized || m_usePrescribedThreshold);
381 return m_usePrescribedThreshold ? m_prescribedThreshold
396 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
397 return m_nonzero_pivots;
413 eigen_assert(m_isInitialized &&
"Decomposition is not initialized.");
417 #ifndef EIGEN_PARSED_BY_DOXYGEN 418 template<
typename RhsType,
typename DstType>
419 void _solve_impl(
const RhsType &rhs, DstType &dst)
const;
421 template<
bool Conjugate,
typename RhsType,
typename DstType>
422 void _solve_impl_transposed(
const RhsType &rhs, DstType &dst)
const;
434 void computeInPlace();
449 template<
typename MatrixType>
453 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
454 eigen_assert(m_qr.rows() == m_qr.cols() &&
"You can't take the determinant of a non-square matrix!");
455 return abs(m_qr.diagonal().prod());
458 template<
typename MatrixType>
461 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
462 eigen_assert(m_qr.rows() == m_qr.cols() &&
"You can't take the determinant of a non-square matrix!");
463 return m_qr.diagonal().cwiseAbs().array().log().sum();
472 template<
typename MatrixType>
473 template<
typename InputType>
481 template<
typename MatrixType>
484 check_template_parameters();
495 m_hCoeffs.resize(size);
499 m_colsTranspositions.resize(m_qr.cols());
500 Index number_of_transpositions = 0;
502 m_colNormsUpdated.resize(cols);
503 m_colNormsDirect.resize(cols);
507 m_colNormsDirect.coeffRef(k) = m_qr.col(k).norm();
508 m_colNormsUpdated.coeffRef(k) = m_colNormsDirect.coeffRef(k);
514 m_nonzero_pivots =
size;
520 Index biggest_col_index;
521 RealScalar biggest_col_sq_norm =
numext::abs2(m_colNormsUpdated.tail(cols-k).maxCoeff(&biggest_col_index));
522 biggest_col_index += k;
526 if(m_nonzero_pivots==size && biggest_col_sq_norm < threshold_helper *
RealScalar(rows-k))
527 m_nonzero_pivots = k;
530 m_colsTranspositions.coeffRef(k) = biggest_col_index;
531 if(k != biggest_col_index) {
532 m_qr.col(k).swap(m_qr.col(biggest_col_index));
533 std::swap(m_colNormsUpdated.coeffRef(k), m_colNormsUpdated.coeffRef(biggest_col_index));
534 std::swap(m_colNormsDirect.coeffRef(k), m_colNormsDirect.coeffRef(biggest_col_index));
535 ++number_of_transpositions;
540 m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
543 m_qr.coeffRef(k,k) = beta;
546 if(
abs(beta) > m_maxpivot) m_maxpivot =
abs(beta);
549 m_qr.bottomRightCorner(rows-k, cols-k-1)
550 .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));
558 if (m_colNormsUpdated.coeffRef(
j) !=
RealScalar(0)) {
559 RealScalar temp =
abs(m_qr.coeffRef(k,
j)) / m_colNormsUpdated.coeffRef(
j);
562 RealScalar temp2 = temp * numext::abs2<RealScalar>(m_colNormsUpdated.coeffRef(
j) /
563 m_colNormsDirect.coeffRef(
j));
564 if (temp2 <= norm_downdate_threshold) {
567 m_colNormsDirect.coeffRef(
j) = m_qr.col(
j).tail(rows - k - 1).norm();
568 m_colNormsUpdated.coeffRef(
j) = m_colNormsDirect.coeffRef(
j);
578 m_colsPermutation.applyTranspositionOnTheRight(k,
PermIndexType(m_colsTranspositions.coeff(k)));
580 m_det_pq = (number_of_transpositions%2) ? -1 : 1;
581 m_isInitialized =
true;
584 #ifndef EIGEN_PARSED_BY_DOXYGEN 585 template<
typename _MatrixType>
586 template<
typename RhsType,
typename DstType>
589 const Index nonzero_pivots = nonzeroPivots();
591 if(nonzero_pivots == 0)
597 typename RhsType::PlainObject
c(rhs);
599 c.applyOnTheLeft(householderQ().setLength(nonzero_pivots).
adjoint() );
601 m_qr.topLeftCorner(nonzero_pivots, nonzero_pivots)
602 .template triangularView<Upper>()
603 .solveInPlace(c.topRows(nonzero_pivots));
605 for(
Index i = 0;
i < nonzero_pivots; ++
i) dst.row(m_colsPermutation.indices().coeff(
i)) = c.row(
i);
606 for(
Index i = nonzero_pivots;
i <
cols(); ++
i) dst.row(m_colsPermutation.indices().coeff(
i)).
setZero();
609 template<
typename _MatrixType>
610 template<
bool Conjugate,
typename RhsType,
typename DstType>
613 const Index nonzero_pivots = nonzeroPivots();
615 if(nonzero_pivots == 0)
621 typename RhsType::PlainObject
c(m_colsPermutation.transpose()*rhs);
623 m_qr.topLeftCorner(nonzero_pivots, nonzero_pivots)
624 .template triangularView<Upper>()
625 .transpose().template conjugateIf<Conjugate>()
626 .solveInPlace(
c.topRows(nonzero_pivots));
628 dst.topRows(nonzero_pivots) =
c.topRows(nonzero_pivots);
629 dst.bottomRows(
rows()-nonzero_pivots).setZero();
631 dst.applyOnTheLeft(householderQ().setLength(nonzero_pivots).
template conjugateIf<!Conjugate>() );
637 template<
typename DstXprType,
typename MatrixType>
653 template<
typename MatrixType>
657 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
665 template<
typename Derived>
674 #endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_H PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime > PermutationType
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT
Inverse< QrType > SrcXprType
SolverBase< ColPivHouseholderQR > Base
#define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived)
bool isSurjective() const
ColPivHouseholderQR(EigenBase< InputType > &matrix)
Constructs a QR factorization from a given matrix.
ColPivHouseholderQR()
Default Constructor.
void adjoint(const MatrixType &m)
ColPivHouseholderQR(Index rows, Index cols)
Default Constructor with memory preallocation.
internal::traits< ColPivHouseholderQR< TransposeTypeWithSameStorageOrder > >::Scalar Scalar
RealScalar m_prescribedThreshold
const HCoeffsType & hCoeffs() const
PermutationType::StorageIndex PermIndexType
const ColPivHouseholderQR< PlainObject > colPivHouseholderQr() const
internal::plain_diag_type< MatrixType >::type HCoeffsType
HouseholderSequence< MatrixType, typename internal::remove_all< typename HCoeffsType::ConjugateReturnType >::type > HouseholderSequenceType
Namespace containing all symbols from the Eigen library.
PermutationType m_colsPermutation
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
ComputationInfo info() const
Reports whether the QR factorization was successful.
Complete orthogonal decomposition (COD) of a matrix.
Eigen::Index Index
The interface type of indices.
RealRowVectorType m_colNormsUpdated
Sequence of Householder reflections acting on subspaces with decreasing size.
ColPivHouseholderQR(const EigenBase< InputType > &matrix)
Constructs a QR factorization from a given matrix.
Expression of the inverse of another expression.
HouseholderSequenceType householderQ() const
ColPivHouseholderQR & compute(const EigenBase< InputType > &matrix)
RealScalar maxPivot() const
ColPivHouseholderQR & setThreshold(Default_t)
internal::plain_row_type< MatrixType >::type RowVectorType
Householder rank-revealing QR decomposition of a matrix with column-pivoting.
const MatrixType & matrixR() const
static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op< typename DstXprType::Scalar, typename QrType::Scalar > &)
#define EIGEN_STATIC_ASSERT_NON_INTEGER(TYPE)
void _solve_impl(const RhsType &rhs, DstType &dst) const
bool m_usePrescribedThreshold
NumTraits< Scalar >::Real RealScalar
bool isInvertible() const
MatrixType::PlainObject PlainObject
internal::plain_row_type< MatrixType, RealScalar >::type RealRowVectorType
void swap(GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &a, GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &b)
MatrixType::RealScalar absDeterminant() const
RealRowVectorType m_colNormsDirect
ColPivHouseholderQR & setThreshold(const RealScalar &threshold)
CleanedUpDerType< DerType >::type() min(const AutoDiffScalar< DerType > &x, const T &y)
ColPivHouseholderQR< MatrixType > QrType
EIGEN_CONSTEXPR Index size(const T &x)
SolverStorage StorageKind
RealScalar threshold() const
HouseholderSequenceType matrixQ() const
MatrixType::RealScalar logAbsDeterminant() const
Index dimensionOfKernel() const
static void check_template_parameters()
internal::plain_row_type< MatrixType, Index >::type IntRowVectorType
Index nonzeroPivots() const
Traits::StorageIndex StorageIndex
internal::nested_eval< T, 1 >::type eval(const T &xpr)
void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const
Pseudo expression representing a solving operation.
IntRowVectorType m_colsTranspositions
Generic expression where a coefficient-wise unary operator is applied to an expression.
EIGEN_DONT_INLINE void compute(Solver &solver, const MatrixType &A)
Map< Matrix< T, Dynamic, Dynamic, ColMajor >, 0, OuterStride<> > matrix(T *data, int rows, int cols, int stride)
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float sqrt(const float &x)
const MatrixType & matrixQR() const
A base class for matrix decomposition and solvers.
const PermutationType & colsPermutation() const
EIGEN_DEVICE_FUNC bool abs2(bool x)
EIGEN_DEVICE_FUNC Derived & derived()
Base class for all dense matrices, vectors, and expressions.
const Inverse< ColPivHouseholderQR > inverse() const
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT
EIGEN_DEVICE_FUNC const XprTypeNestedCleaned & nestedExpression() const