Eigen
3.2.9

Householder rankrevealing QR decomposition of a matrix with columnpivoting.
MatrixType  the type of the matrix of which we are computing the QR decomposition 
This class performs a rankrevealing QR decomposition of a matrix A into matrices P, Q and R such that
by using Householder transformations. Here, P is a permutation matrix, Q a unitary matrix and R an upper triangular matrix.
This decomposition performs column pivoting in order to be rankrevealing and improve numerical stability. It is slower than HouseholderQR, and faster than FullPivHouseholderQR.
Public Member Functions  
MatrixType::RealScalar  absDeterminant () const 
ColPivHouseholderQR ()  
Default Constructor. More...  
ColPivHouseholderQR (Index rows, Index cols)  
Default Constructor with memory preallocation. More...  
ColPivHouseholderQR (const MatrixType &matrix)  
Constructs a QR factorization from a given matrix. More...  
const PermutationType &  colsPermutation () const 
ColPivHouseholderQR &  compute (const MatrixType &matrix) 
Index  dimensionOfKernel () const 
const HCoeffsType &  hCoeffs () const 
HouseholderSequenceType  householderQ (void) const 
ComputationInfo  info () const 
Reports whether the QR factorization was succesful. More...  
const internal::solve_retval < ColPivHouseholderQR, typename MatrixType::IdentityReturnType >  inverse () const 
bool  isInjective () const 
bool  isInvertible () const 
bool  isSurjective () const 
MatrixType::RealScalar  logAbsDeterminant () const 
const MatrixType &  matrixQR () const 
const MatrixType &  matrixR () const 
RealScalar  maxPivot () const 
Index  nonzeroPivots () const 
Index  rank () const 
ColPivHouseholderQR &  setThreshold (const RealScalar &threshold) 
ColPivHouseholderQR &  setThreshold (Default_t) 
template<typename Rhs >  
const internal::solve_retval < ColPivHouseholderQR, Rhs >  solve (const MatrixBase< Rhs > &b) const 
RealScalar  threshold () const 

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Default Constructor.
The default constructor is useful in cases in which the user intends to perform decompositions via ColPivHouseholderQR::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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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:
References ColPivHouseholderQR< MatrixType >::compute().
MatrixType::RealScalar absDeterminant  (  )  const 

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ColPivHouseholderQR< MatrixType > & compute  (  const MatrixType &  matrix  ) 
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.
Referenced by ColPivHouseholderQR< MatrixType >::ColPivHouseholderQR().

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References ColPivHouseholderQR< MatrixType >::rank().

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Q
.For advanced uses only.
ColPivHouseholderQR< MatrixType >::HouseholderSequenceType householderQ  (  void  )  const 

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Reports whether the QR factorization was succesful.
Success
. It is provided for compatibility with other factorization routines. Success
References Eigen::Success.

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References ColPivHouseholderQR< MatrixType >::rank().
Referenced by ColPivHouseholderQR< MatrixType >::isInvertible().

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References ColPivHouseholderQR< MatrixType >::isInjective(), and ColPivHouseholderQR< MatrixType >::isSurjective().

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References ColPivHouseholderQR< MatrixType >::rank().
Referenced by ColPivHouseholderQR< MatrixType >::isInvertible().
MatrixType::RealScalar logAbsDeterminant  (  )  const 

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References ColPivHouseholderQR< MatrixType >::threshold().
Referenced by ColPivHouseholderQR< MatrixType >::dimensionOfKernel(), ColPivHouseholderQR< MatrixType >::isInjective(), and ColPivHouseholderQR< MatrixType >::isSurjective().

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Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine when pivots are to be considered nonzero. This is not used for the QR decomposition itself.
When it needs to get the threshold value, Eigen calls threshold(). By default, this uses a formula to automatically determine a reasonable threshold. Once you have called the present method setThreshold(const RealScalar&), your value is used instead.
threshold  The new value to use as the threshold. 
A pivot will be considered nonzero if its absolute value is strictly greater than where maxpivot is the biggest pivot.
If you want to come back to the default behavior, call setThreshold(Default_t)
References ColPivHouseholderQR< MatrixType >::threshold().

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Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold.
You should pass the special object Eigen::Default as parameter here.
See the documentation of setThreshold(const RealScalar&).

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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 righthandside 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 nonexistence 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: 0.68 0.597 0.33 0.211 0.823 0.536 0.566 0.605 0.444 Here is the matrix y: 0.108 0.27 0.832 0.0452 0.0268 0.271 0.258 0.904 0.435 Here is a solution x to the equation mx=y: 0.609 2.68 1.67 0.231 1.57 0.0713 0.51 3.51 1.05

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Returns the threshold that will be used by certain methods such as rank().
See the documentation of setThreshold(const RealScalar&).
Referenced by ColPivHouseholderQR< MatrixType >::rank(), and ColPivHouseholderQR< MatrixType >::setThreshold().