11#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_H
12#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_H
52 :
public SolverBase<ColPivHouseholderQR<_MatrixType> >
125 template<
typename InputType>
146 template<
typename InputType>
161 #ifdef EIGEN_PARSED_BY_DOXYGEN
176 template<
typename Rhs>
210 template<
typename InputType>
417 #ifndef EIGEN_PARSED_BY_DOXYGEN
418 template<
typename RhsType,
typename DstType>
421 template<
bool Conjugate,
typename RhsType,
typename DstType>
449template<
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());
458template<
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();
472template<
typename MatrixType>
473template<
typename InputType>
481template<
typename MatrixType>
484 check_template_parameters();
491 Index rows = m_qr.rows();
492 Index cols = m_qr.cols();
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);
504 for (
Index k = 0; k < cols; ++k) {
507 m_colNormsDirect.coeffRef(k) = m_qr.col(k).norm();
508 m_colNormsUpdated.coeffRef(k) = m_colNormsDirect.coeffRef(k);
514 m_nonzero_pivots =
size;
515 m_maxpivot = RealScalar(0);
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;
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));
553 for (
Index j = k + 1; j < cols; ++j) {
558 if (m_colNormsUpdated.coeffRef(j) != RealScalar(0)) {
559 RealScalar temp =
abs(m_qr.coeffRef(k, j)) / m_colNormsUpdated.coeffRef(j);
560 temp = (RealScalar(1) + temp) * (RealScalar(1) - temp);
561 temp = temp < RealScalar(0) ? RealScalar(0) : temp;
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);
576 m_colsPermutation.setIdentity(PermIndexType(cols));
577 for(PermIndexType k = 0; k <
size; ++k)
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
585template<
typename _MatrixType>
586template<
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();
609template<
typename _MatrixType>
610template<
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>() );
637template<
typename DstXprType,
typename MatrixType>
653template<
typename MatrixType>
655 ::householderQ()
const
657 eigen_assert(m_isInitialized &&
"ColPivHouseholderQR is not initialized.");
665template<
typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Abs2ReturnType abs2() const
Definition: ArrayCwiseUnaryOps.h:80
#define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived)
Just a side note.
Definition: Macros.h:1274
#define eigen_assert(x)
Definition: Macros.h:1047
#define EIGEN_STATIC_ASSERT_NON_INTEGER(TYPE)
Definition: StaticAssert.h:187
constexpr common_return_t< T1, T2 > beta(const T1 a, const T2 b) noexcept
Compile-time beta function.
Definition: beta.hpp:36
Householder rank-revealing QR decomposition of a matrix with column-pivoting.
Definition: ColPivHouseholderQR.h:53
bool isInjective() const
Definition: ColPivHouseholderQR.h:285
PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime > PermutationType
Definition: ColPivHouseholderQR.h:66
ColPivHouseholderQR(const EigenBase< InputType > &matrix)
Constructs a QR factorization from a given matrix.
Definition: ColPivHouseholderQR.h:126
RowVectorType m_temp
Definition: ColPivHouseholderQR.h:440
const HCoeffsType & hCoeffs() const
Definition: ColPivHouseholderQR.h:334
HouseholderSequenceType householderQ() const
Definition: ColPivHouseholderQR.h:655
Index rank() const
Definition: ColPivHouseholderQR.h:255
HCoeffsType m_hCoeffs
Definition: ColPivHouseholderQR.h:437
Index m_det_pq
Definition: ColPivHouseholderQR.h:446
bool m_isInitialized
Definition: ColPivHouseholderQR.h:443
HouseholderSequence< MatrixType, typename internal::remove_all< typename HCoeffsType::ConjugateReturnType >::type > HouseholderSequenceType
Definition: ColPivHouseholderQR.h:70
internal::plain_diag_type< MatrixType >::type HCoeffsType
Definition: ColPivHouseholderQR.h:65
ColPivHouseholderQR(Index rows, Index cols)
Default Constructor with memory preallocation.
Definition: ColPivHouseholderQR.h:102
static void check_template_parameters()
Definition: ColPivHouseholderQR.h:429
ComputationInfo info() const
Reports whether the QR factorization was successful.
Definition: ColPivHouseholderQR.h:411
Index cols() const
Definition: ColPivHouseholderQR.h:328
ColPivHouseholderQR(EigenBase< InputType > &matrix)
Constructs a QR factorization from a given matrix.
Definition: ColPivHouseholderQR.h:147
RealScalar m_maxpivot
Definition: ColPivHouseholderQR.h:444
const Inverse< ColPivHouseholderQR > inverse() const
Definition: ColPivHouseholderQR.h:321
IntRowVectorType m_colsTranspositions
Definition: ColPivHouseholderQR.h:439
@ MaxColsAtCompileTime
Definition: ColPivHouseholderQR.h:63
@ MaxRowsAtCompileTime
Definition: ColPivHouseholderQR.h:62
RealScalar threshold() const
Returns the threshold that will be used by certain methods such as rank().
Definition: ColPivHouseholderQR.h:378
Index nonzeroPivots() const
Definition: ColPivHouseholderQR.h:394
Index rows() const
Definition: ColPivHouseholderQR.h:327
const PermutationType & colsPermutation() const
Definition: ColPivHouseholderQR.h:214
void computeInPlace()
Definition: ColPivHouseholderQR.h:482
Index dimensionOfKernel() const
Definition: ColPivHouseholderQR.h:272
_MatrixType MatrixType
Definition: ColPivHouseholderQR.h:56
internal::plain_row_type< MatrixType, Index >::type IntRowVectorType
Definition: ColPivHouseholderQR.h:67
bool isSurjective() const
Definition: ColPivHouseholderQR.h:298
HouseholderSequenceType matrixQ() const
Definition: ColPivHouseholderQR.h:182
bool isInvertible() const
Definition: ColPivHouseholderQR.h:310
RealScalar m_prescribedThreshold
Definition: ColPivHouseholderQR.h:444
ColPivHouseholderQR()
Default Constructor.
Definition: ColPivHouseholderQR.h:85
MatrixType::PlainObject PlainObject
Definition: ColPivHouseholderQR.h:71
RealRowVectorType m_colNormsUpdated
Definition: ColPivHouseholderQR.h:441
RealScalar maxPivot() const
Definition: ColPivHouseholderQR.h:403
ColPivHouseholderQR & setThreshold(const RealScalar &threshold)
Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine ...
Definition: ColPivHouseholderQR.h:353
const MatrixType & matrixR() const
Definition: ColPivHouseholderQR.h:204
ColPivHouseholderQR & setThreshold(Default_t)
Allows to come back to the default behavior, letting Eigen use its default formula for determining th...
Definition: ColPivHouseholderQR.h:368
Index m_nonzero_pivots
Definition: ColPivHouseholderQR.h:445
MatrixType::RealScalar absDeterminant() const
Definition: ColPivHouseholderQR.h:450
bool m_usePrescribedThreshold
Definition: ColPivHouseholderQR.h:443
internal::plain_row_type< MatrixType >::type RowVectorType
Definition: ColPivHouseholderQR.h:68
internal::plain_row_type< MatrixType, RealScalar >::type RealRowVectorType
Definition: ColPivHouseholderQR.h:69
const MatrixType & matrixQR() const
Definition: ColPivHouseholderQR.h:189
void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const
Definition: ColPivHouseholderQR.h:611
MatrixType m_qr
Definition: ColPivHouseholderQR.h:436
void _solve_impl(const RhsType &rhs, DstType &dst) const
Definition: ColPivHouseholderQR.h:587
ColPivHouseholderQR & compute(const EigenBase< InputType > &matrix)
PermutationType m_colsPermutation
Definition: ColPivHouseholderQR.h:438
SolverBase< ColPivHouseholderQR > Base
Definition: ColPivHouseholderQR.h:57
RealRowVectorType m_colNormsDirect
Definition: ColPivHouseholderQR.h:442
MatrixType::RealScalar logAbsDeterminant() const
Definition: ColPivHouseholderQR.h:459
Complete orthogonal decomposition (COD) of a matrix.
Definition: CompleteOrthogonalDecomposition.h:52
\householder_module
Definition: HouseholderSequence.h:121
Expression of the inverse of another expression.
Definition: Inverse.h:44
EIGEN_DEVICE_FUNC const XprTypeNestedCleaned & nestedExpression() const
Definition: Inverse.h:60
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT
Definition: Inverse.h:58
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT
Definition: Inverse.h:57
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
Traits::StorageIndex StorageIndex
Definition: PermutationMatrix.h:307
Pseudo expression representing a solving operation.
Definition: Solve.h:63
A base class for matrix decomposition and solvers.
Definition: SolverBase.h:69
internal::traits< ColPivHouseholderQR< _MatrixType > >::Scalar Scalar
Definition: SolverBase.h:73
const Solve< ColPivHouseholderQR< _MatrixType >, Rhs > solve(const MatrixBase< Rhs > &b) const
Definition: SolverBase.h:106
EIGEN_DEVICE_FUNC ColPivHouseholderQR< _MatrixType > & derived()
Definition: EigenBase.h:46
UnitType abs(const UnitType x) noexcept
Compute absolute value.
Definition: math.h:721
auto sqrt(const UnitType &value) noexcept -> unit_t< square_root< typename units::traits::unit_t_traits< UnitType >::unit_type >, typename units::traits::unit_t_traits< UnitType >::underlying_type, linear_scale >
computes the square root of value
Definition: math.h:483
ComputationInfo
Enum for reporting the status of a computation.
Definition: Constants.h:440
@ Success
Computation was successful.
Definition: Constants.h:442
constexpr common_t< T1, T2 > min(const T1 x, const T2 y) noexcept
Compile-time pairwise minimum function.
Definition: min.hpp:35
EIGEN_CONSTEXPR Index size(const T &x)
Definition: Meta.h:479
Namespace containing all symbols from the Eigen library.
Definition: MatrixExponential.h:16
Default_t
Definition: Constants.h:362
result
Definition: format.h:2556
Definition: Eigen_Colamd.h:50
Definition: StdDeque.h:50
void swap(wpi::SmallVectorImpl< T > &LHS, wpi::SmallVectorImpl< T > &RHS)
Implement std::swap in terms of SmallVector swap.
Definition: SmallVector.h:1299
static constexpr const velocity::meters_per_second_t c(299792458.0)
Speed of light in vacuum.
Common base class for all classes T such that MatrixBase has an operator=(T) and a constructor Matrix...
Definition: EigenBase.h:30
Eigen::Index Index
The interface type of indices.
Definition: EigenBase.h:39
EIGEN_DEVICE_FUNC Derived & derived()
Definition: EigenBase.h:46
The type used to identify a matrix expression.
Definition: Constants.h:522
Holds information about the various numeric (i.e.
Definition: NumTraits.h:233
The type used to identify a general solver (factored) storage.
Definition: Constants.h:513
ColPivHouseholderQR< MatrixType > QrType
Definition: ColPivHouseholderQR.h:640
Inverse< QrType > SrcXprType
Definition: ColPivHouseholderQR.h:641
static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op< typename DstXprType::Scalar, typename QrType::Scalar > &)
Definition: ColPivHouseholderQR.h:642
Definition: AssignEvaluator.h:824
Definition: AssignEvaluator.h:814
Definition: AssignmentFunctors.h:21
int StorageIndex
Definition: ColPivHouseholderQR.h:22
SolverStorage StorageKind
Definition: ColPivHouseholderQR.h:21
MatrixXpr XprKind
Definition: ColPivHouseholderQR.h:20
Definition: ForwardDeclarations.h:17