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add Threshold API to FullPivHouseholderQR

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This commit is contained in:
Benoit Jacob 2011-01-27 10:17:52 -05:00
parent a954a0fbd5
commit b69b6a9db2
1 changed files with 108 additions and 21 deletions
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129
Eigen/src/QR/FullPivHouseholderQR.h
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@ -82,7 +82,8 @@ template<typename _MatrixType> class FullPivHouseholderQR
m_cols_transpositions(),
m_cols_permutation(),
m_temp(),
m_isInitialized(false) {}
m_isInitialized(false),
m_usePrescribedThreshold(false) {}
/** \brief Default Constructor with memory preallocation
*
@ -97,7 +98,8 @@ template<typename _MatrixType> class FullPivHouseholderQR
m_cols_transpositions(cols),
m_cols_permutation(cols),
m_temp(std::min(rows,cols)),
m_isInitialized(false) {}
m_isInitialized(false),
m_usePrescribedThreshold(false) {}
FullPivHouseholderQR(const MatrixType& matrix)
: m_qr(matrix.rows(), matrix.cols()),
@ -106,7 +108,8 @@ template<typename _MatrixType> class FullPivHouseholderQR
m_cols_transpositions(matrix.cols()),
m_cols_permutation(matrix.cols()),
m_temp(std::min(matrix.rows(), matrix.cols())),
m_isInitialized(false)
m_isInitialized(false),
m_usePrescribedThreshold(false)
{
compute(matrix);
}
@ -191,54 +194,63 @@ template<typename _MatrixType> class FullPivHouseholderQR
/** \returns the rank of the matrix of which *this is the QR decomposition.
*
* \note This is computed at the time of the construction of the QR decomposition. This
* method does not perform any further computation.
* \note This method has to determine which pivots should be considered nonzero.
* For that, it uses the threshold value that you can control by calling
* setThreshold(const RealScalar&).
*/
inline Index rank() const
{
eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
return m_rank;
RealScalar premultiplied_threshold = internal::abs(m_maxpivot) * threshold();
Index result = 0;
for(Index i = 0; i < m_nonzero_pivots; ++i)
result += (internal::abs(m_qr.coeff(i,i)) > premultiplied_threshold);
return result;
}
/** \returns the dimension of the kernel of the matrix of which *this is the QR decomposition.
*
* \note Since the rank is computed at the time of the construction of the QR decomposition, this
* method almost does not perform any further computation.
* \note This method has to determine which pivots should be considered nonzero.
* For that, it uses the threshold value that you can control by calling
* setThreshold(const RealScalar&).
*/
inline Index dimensionOfKernel() const
{
eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
return m_qr.cols() - m_rank;
return cols() - rank();
}
/** \returns true if the matrix of which *this is the QR decomposition represents an injective
* linear map, i.e. has trivial kernel; false otherwise.
*
* \note Since the rank is computed at the time of the construction of the QR decomposition, this
* method almost does not perform any further computation.
* \note This method has to determine which pivots should be considered nonzero.
* For that, it uses the threshold value that you can control by calling
* setThreshold(const RealScalar&).
*/
inline bool isInjective() const
{
eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
return m_rank == m_qr.cols();
return rank() == cols();
}
/** \returns true if the matrix of which *this is the QR decomposition represents a surjective
* linear map; false otherwise.
*
* \note Since the rank is computed at the time of the construction of the QR decomposition, this
* method almost does not perform any further computation.
* \note This method has to determine which pivots should be considered nonzero.
* For that, it uses the threshold value that you can control by calling
* setThreshold(const RealScalar&).
*/
inline bool isSurjective() const
{
eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
return m_rank == m_qr.rows();
return rank() == rows();
}
/** \returns true if the matrix of which *this is the QR decomposition is invertible.
*
* \note Since the rank is computed at the time of the construction of the QR decomposition, this
* method almost does not perform any further computation.
* \note This method has to determine which pivots should be considered nonzero.
* For that, it uses the threshold value that you can control by calling
* setThreshold(const RealScalar&).
*/
inline bool isInvertible() const
{
@ -263,6 +275,75 @@ template<typename _MatrixType> class FullPivHouseholderQR
inline Index cols() const { return m_qr.cols(); }
const HCoeffsType& hCoeffs() const { return m_hCoeffs; }
/** 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.
*
* \param threshold The new value to use as the threshold.
*
* A pivot will be considered nonzero if its absolute value is strictly greater than
* \f$ \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \f$
* where maxpivot is the biggest pivot.
*
* If you want to come back to the default behavior, call setThreshold(Default_t)
*/
FullPivHouseholderQR& setThreshold(const RealScalar& threshold)
{
m_usePrescribedThreshold = true;
m_prescribedThreshold = threshold;
return *this;
}
/** 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.
* \code qr.setThreshold(Eigen::Default); \endcode
*
* See the documentation of setThreshold(const RealScalar&).
*/
FullPivHouseholderQR& setThreshold(Default_t)
{
m_usePrescribedThreshold = false;
return *this;
}
/** Returns the threshold that will be used by certain methods such as rank().
*
* See the documentation of setThreshold(const RealScalar&).
*/
RealScalar threshold() const
{
eigen_assert(m_isInitialized || m_usePrescribedThreshold);
return m_usePrescribedThreshold ? m_prescribedThreshold
// this formula comes from experimenting (see "LU precision tuning" thread on the list)
// and turns out to be identical to Higham's formula used already in LDLt.
: NumTraits<Scalar>::epsilon() * m_qr.diagonalSize();
}
/** \returns the number of nonzero pivots in the QR decomposition.
* Here nonzero is meant in the exact sense, not in a fuzzy sense.
* So that notion isn't really intrinsically interesting, but it is
* still useful when implementing algorithms.
*
* \sa rank()
*/
inline Index nonzeroPivots() const
{
eigen_assert(m_isInitialized && "LU is not initialized.");
return m_nonzero_pivots;
}
/** \returns the absolute value of the biggest pivot, i.e. the biggest
* diagonal coefficient of U.
*/
RealScalar maxPivot() const { return m_maxpivot; }
protected:
MatrixType m_qr;
HCoeffsType m_hCoeffs;
@ -270,9 +351,10 @@ template<typename _MatrixType> class FullPivHouseholderQR
IntRowVectorType m_cols_transpositions;
PermutationType m_cols_permutation;
RowVectorType m_temp;
bool m_isInitialized;
bool m_isInitialized, m_usePrescribedThreshold;
RealScalar m_prescribedThreshold, m_maxpivot;
Index m_nonzero_pivots;
RealScalar m_precision;
Index m_rank;
Index m_det_pq;
};
@ -298,7 +380,6 @@ FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(cons
Index rows = matrix.rows();
Index cols = matrix.cols();
Index size = std::min(rows,cols);
m_rank = size;
m_qr = matrix;
m_hCoeffs.resize(size);
@ -313,6 +394,9 @@ FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(cons
RealScalar biggest(0);
m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)
m_maxpivot = RealScalar(0);
for (Index k = 0; k < size; ++k)
{
Index row_of_biggest_in_corner, col_of_biggest_in_corner;
@ -328,7 +412,7 @@ FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(cons
// if the corner is negligible, then we have less than full rank, and we can finish early
if(internal::isMuchSmallerThan(biggest_in_corner, biggest, m_precision))
{
m_rank = k;
m_nonzero_pivots = k;
for(Index i = k; i < size; i++)
{
m_rows_transpositions.coeffRef(i) = i;
@ -353,6 +437,9 @@ FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(cons
m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
m_qr.coeffRef(k,k) = beta;
// remember the maximum absolute value of diagonal coefficients
if(internal::abs(beta) > m_maxpivot) m_maxpivot = internal::abs(beta);
m_qr.bottomRightCorner(rows-k, cols-k-1)
.applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));
}