Eigen
3.4.90 (git rev a4098ac676528a83cfb73d4d26ce1b42ec05f47c)
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Householder QR decomposition of a matrix.
MatrixType_ | the type of the matrix of which we are computing the QR decomposition |
This class performs a QR decomposition of a matrix A into matrices Q and R such that
\[ \mathbf{A} = \mathbf{Q} \, \mathbf{R} \]
by using Householder transformations. Here, Q a unitary matrix and R an upper triangular matrix. The result is stored in a compact way compatible with LAPACK.
Note that no pivoting is performed. This is not a rank-revealing decomposition. If you want that feature, use FullPivHouseholderQR or ColPivHouseholderQR instead.
This Householder QR decomposition is faster, but less numerically stable and less feature-full than FullPivHouseholderQR or ColPivHouseholderQR.
This class supports the inplace decomposition mechanism.
Public Member Functions | |
MatrixType::RealScalar | absDeterminant () const |
const HCoeffsType & | hCoeffs () const |
HouseholderSequenceType | householderQ () const |
HouseholderQR () | |
Default Constructor. More... | |
template<typename InputType > | |
HouseholderQR (const EigenBase< InputType > &matrix) | |
Constructs a QR factorization from a given matrix. More... | |
template<typename InputType > | |
HouseholderQR (EigenBase< InputType > &matrix) | |
Constructs a QR factorization from a given matrix. More... | |
HouseholderQR (Index rows, Index cols) | |
Default Constructor with memory preallocation. More... | |
MatrixType::RealScalar | logAbsDeterminant () const |
const MatrixType & | matrixQR () const |
template<typename Rhs > | |
const Solve< HouseholderQR, Rhs > | solve (const MatrixBase< Rhs > &b) const |
Public Member Functions inherited from Eigen::SolverBase< HouseholderQR< MatrixType_ > > | |
AdjointReturnType | adjoint () const |
HouseholderQR< MatrixType_ > & | derived () |
const HouseholderQR< MatrixType_ > & | derived () const |
const Solve< HouseholderQR< MatrixType_ >, Rhs > | solve (const MatrixBase< Rhs > &b) const |
SolverBase () | |
ConstTransposeReturnType | transpose () const |
Public Member Functions inherited from Eigen::EigenBase< Derived > | |
EIGEN_CONSTEXPR Index | cols () const EIGEN_NOEXCEPT |
Derived & | derived () |
const Derived & | derived () const |
EIGEN_CONSTEXPR Index | rows () const EIGEN_NOEXCEPT |
EIGEN_CONSTEXPR Index | size () const EIGEN_NOEXCEPT |
Protected Member Functions | |
void | computeInPlace () |
Additional Inherited Members | |
Public Types inherited from Eigen::EigenBase< Derived > | |
typedef Eigen::Index | Index |
The interface type of indices. More... | |
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Default Constructor.
The default constructor is useful in cases in which the user intends to perform decompositions via HouseholderQR::compute(const MatrixType&).
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Default Constructor with memory preallocation.
Like the default constructor but with preallocation of the internal data according to the specified problem size.
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inlineexplicit |
Constructs a QR factorization from a given matrix.
This constructor computes the QR factorization of the matrix matrix by calling the method compute(). It is a short cut for:
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inlineexplicit |
Constructs a QR factorization from a given matrix.
This overloaded constructor is provided for inplace decomposition when MatrixType
is a Eigen::Ref.
MatrixType::RealScalar Eigen::HouseholderQR< MatrixType >::absDeterminant |
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protected |
Performs the QR factorization of the given matrix matrix. The result of the factorization is stored into *this
, and a reference to *this
is returned.
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Q
.For advanced uses only.
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This method returns an expression of the unitary matrix Q as a sequence of Householder transformations.
The returned expression can directly be used to perform matrix products. It can also be assigned to a dense Matrix object. Here is an example showing how to recover the full or thin matrix Q, as well as how to perform matrix products using operator*:
Example:
Output:
The complete unitary matrix Q is: -0.0432 0.136 0.0214 0.546 0.825 -0.249 -0.521 -0.745 -0.229 0.244 0.715 0.264 -0.562 0.271 -0.171 0.169 -0.744 0.211 0.56 -0.245 0.629 -0.296 0.29 -0.512 0.413 The thin matrix Q is: -0.0432 0.136 0.0214 -0.249 -0.521 -0.745 0.715 0.264 -0.562 0.169 -0.744 0.211 0.629 -0.296 0.29
MatrixType::RealScalar Eigen::HouseholderQR< MatrixType >::logAbsDeterminant |
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This method finds a solution x to the equation Ax=b, where A is the matrix of which *this is the QR decomposition, if any exists.
b | the right-hand-side of the equation to solve. |
This method just tries to find as good a solution as possible. If you want to check whether a solution exists or if it is accurate, just call this function to get a result and then compute the error of this result, or use MatrixBase::isApprox() directly, for instance like this:
This method avoids dividing by zero, so that the non-existence of a solution doesn't by itself mean that you'll get inf
or nan
values.
If there exists more than one solution, this method will arbitrarily choose one.
Example:
Output:
Here is the matrix m: -1 -0.0827 -0.906 -0.737 0.0655 0.358 0.511 -0.562 0.359 Here is the matrix y: 0.869 0.662 0.0594 -0.233 -0.931 0.342 0.0388 -0.893 -0.985 Here is a solution x to the equation mx=y: -0.117 0.626 -0.278 -0.667 1.18 1.56 -0.77 -1.53 0.0985