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modernize HouseholderQR too, uniformize all that stuff, update tests

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This commit is contained in:
Benoit Jacob 2009-08-24 13:46:14 -04:00
parent 7e4bd70157
commit 191d5275a7
7 changed files with 121 additions and 40 deletions
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2
Eigen/QR
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@ -35,7 +35,7 @@ namespace Eigen {
* \endcode
*/
#include "src/QR/QR.h"
#include "src/QR/HouseholderQR.h"
#include "src/QR/FullPivotingHouseholderQR.h"
#include "src/QR/ColPivotingHouseholderQR.h"
#include "src/QR/Tridiagonalization.h"

15
Eigen/src/QR/ColPivotingHouseholderQR.h
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@ -99,11 +99,15 @@ template<typename MatrixType> class ColPivotingHouseholderQR
template<typename OtherDerived, typename ResultType>
bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const;
MatrixType matrixQ(void) const;
MatrixQType matrixQ(void) const;
/** \returns a reference to the matrix where the Householder QR decomposition is stored
*/
const MatrixType& matrixQR() const { return m_qr; }
const MatrixType& matrixQR() const
{
ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized.");
return m_qr;
}
ColPivotingHouseholderQR& compute(const MatrixType& matrix);
@ -363,9 +367,10 @@ bool ColPivotingHouseholderQR<MatrixType>::solve(
// is c is in the image of R ?
RealScalar biggest_in_upper_part_of_c = c.corner(TopLeft, m_rank, c.cols()).cwise().abs().maxCoeff();
RealScalar biggest_in_lower_part_of_c = c.corner(BottomLeft, rows-m_rank, c.cols()).cwise().abs().maxCoeff();
if(!ei_isMuchSmallerThan(biggest_in_lower_part_of_c, biggest_in_upper_part_of_c, m_precision))
if(!ei_isMuchSmallerThan(biggest_in_lower_part_of_c, biggest_in_upper_part_of_c, m_precision*4))
return false;
}
m_qr.corner(TopLeft, m_rank, m_rank)
.template triangularView<UpperTriangular>()
.solveInPlace(c.corner(TopLeft, m_rank, c.cols()));
@ -377,7 +382,7 @@ bool ColPivotingHouseholderQR<MatrixType>::solve(
/** \returns the matrix Q */
template<typename MatrixType>
MatrixType ColPivotingHouseholderQR<MatrixType>::matrixQ() const
typename ColPivotingHouseholderQR<MatrixType>::MatrixQType ColPivotingHouseholderQR<MatrixType>::matrixQ() const
{
ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized.");
// compute the product H'_0 H'_1 ... H'_n-1,
@ -386,7 +391,7 @@ MatrixType ColPivotingHouseholderQR<MatrixType>::matrixQ() const
int rows = m_qr.rows();
int cols = m_qr.cols();
int size = std::min(rows,cols);
MatrixType res = MatrixType::Identity(rows, rows);
MatrixQType res = MatrixQType::Identity(rows, rows);
Matrix<Scalar,1,MatrixType::RowsAtCompileTime> temp(rows);
for (int k = size-1; k >= 0; k--)
{

12
Eigen/src/QR/FullPivotingHouseholderQR.h
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@ -97,11 +97,15 @@ template<typename MatrixType> class FullPivotingHouseholderQR
template<typename OtherDerived, typename ResultType>
bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const;
MatrixType matrixQ(void) const;
MatrixQType matrixQ(void) const;
/** \returns a reference to the matrix where the Householder QR decomposition is stored
*/
const MatrixType& matrixQR() const { return m_qr; }
const MatrixType& matrixQR() const
{
ei_assert(m_isInitialized && "FullPivotingHouseholderQR is not initialized.");
return m_qr;
}
FullPivotingHouseholderQR& compute(const MatrixType& matrix);
@ -391,7 +395,7 @@ bool FullPivotingHouseholderQR<MatrixType>::solve(
/** \returns the matrix Q */
template<typename MatrixType>
MatrixType FullPivotingHouseholderQR<MatrixType>::matrixQ() const
typename FullPivotingHouseholderQR<MatrixType>::MatrixQType FullPivotingHouseholderQR<MatrixType>::matrixQ() const
{
ei_assert(m_isInitialized && "FullPivotingHouseholderQR is not initialized.");
// compute the product H'_0 H'_1 ... H'_n-1,
@ -400,7 +404,7 @@ MatrixType FullPivotingHouseholderQR<MatrixType>::matrixQ() const
int rows = m_qr.rows();
int cols = m_qr.cols();
int size = std::min(rows,cols);
MatrixType res = MatrixType::Identity(rows, rows);
MatrixQType res = MatrixQType::Identity(rows, rows);
Matrix<Scalar,1,MatrixType::RowsAtCompileTime> temp(rows);
for (int k = size-1; k >= 0; k--)
{

93
Eigen/src/QR/QR.h → Eigen/src/QR/HouseholderQR.h
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@ -2,6 +2,7 @@
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
@ -38,6 +39,10 @@
* stored in a compact way compatible with LAPACK.
*
* Note that no pivoting is performed. This is \b not a rank-revealing decomposition.
* If you want that feature, use FullPivotingHouseholderQR or ColPivotingHouseholderQR instead.
*
* This Householder QR decomposition is faster, but less numerically stable and less feature-full than
* FullPivotingHouseholderQR or ColPivotingHouseholderQR.
*
* \sa MatrixBase::householderQr()
*/
@ -46,15 +51,17 @@ template<typename MatrixType> class HouseholderQR
public:
enum {
MinSizeAtCompileTime = EIGEN_ENUM_MIN(MatrixType::ColsAtCompileTime,MatrixType::RowsAtCompileTime)
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
Options = MatrixType::Options,
DiagSizeAtCompileTime = EIGEN_ENUM_MIN(ColsAtCompileTime,RowsAtCompileTime)
};
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef Block<MatrixType, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> MatrixRBlockType;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> MatrixTypeR;
typedef Matrix<Scalar, MinSizeAtCompileTime, 1> HCoeffsType;
typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;
typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixQType;
typedef Matrix<Scalar, DiagSizeAtCompileTime, 1> HCoeffsType;
typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
/**
* \brief Default Constructor.
@ -72,15 +79,6 @@ template<typename MatrixType> class HouseholderQR
compute(matrix);
}
/** \returns a read-only expression of the matrix R of the actual the QR decomposition */
const TriangularView<NestByValue<MatrixRBlockType>, UpperTriangular>
matrixR(void) const
{
ei_assert(m_isInitialized && "HouseholderQR is not initialized.");
int cols = m_qr.cols();
return MatrixRBlockType(m_qr, 0, 0, cols, cols).nestByValue().template triangularView<UpperTriangular>();
}
/** 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.
*
@ -99,15 +97,48 @@ template<typename MatrixType> class HouseholderQR
template<typename OtherDerived, typename ResultType>
void solve(const MatrixBase<OtherDerived>& b, ResultType *result) const;
MatrixType matrixQ(void) const;
MatrixQType matrixQ(void) const;
/** \returns a reference to the matrix where the Householder QR decomposition is stored
* in a LAPACK-compatible way.
*/
const MatrixType& matrixQR() const { return m_qr; }
const MatrixType& matrixQR() const
{
ei_assert(m_isInitialized && "HouseholderQR is not initialized.");
return m_qr;
}
HouseholderQR& compute(const MatrixType& matrix);
/** \returns the absolute value of the determinant of the matrix of which
* *this is the QR decomposition. It has only linear complexity
* (that is, O(n) where n is the dimension of the square matrix)
* as the QR decomposition has already been computed.
*
* \note This is only for square matrices.
*
* \warning a determinant can be very big or small, so for matrices
* of large enough dimension, there is a risk of overflow/underflow.
* One way to work around that is to use logAbsDeterminant() instead.
*
* \sa logAbsDeterminant(), MatrixBase::determinant()
*/
typename MatrixType::RealScalar absDeterminant() const;
/** \returns the natural log of the absolute value of the determinant of the matrix of which
* *this is the QR decomposition. It has only linear complexity
* (that is, O(n) where n is the dimension of the square matrix)
* as the QR decomposition has already been computed.
*
* \note This is only for square matrices.
*
* \note This method is useful to work around the risk of overflow/underflow that's inherent
* to determinant computation.
*
* \sa absDeterminant(), MatrixBase::determinant()
*/
typename MatrixType::RealScalar logAbsDeterminant() const;
protected:
MatrixType m_qr;
HCoeffsType m_hCoeffs;
@ -116,6 +147,22 @@ template<typename MatrixType> class HouseholderQR
#ifndef EIGEN_HIDE_HEAVY_CODE
template<typename MatrixType>
typename MatrixType::RealScalar HouseholderQR<MatrixType>::absDeterminant() const
{
ei_assert(m_isInitialized && "HouseholderQR is not initialized.");
ei_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
return ei_abs(m_qr.diagonal().prod());
}
template<typename MatrixType>
typename MatrixType::RealScalar HouseholderQR<MatrixType>::logAbsDeterminant() const
{
ei_assert(m_isInitialized && "HouseholderQR is not initialized.");
ei_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
return m_qr.diagonal().cwise().abs().cwise().log().sum();
}
template<typename MatrixType>
HouseholderQR<MatrixType>& HouseholderQR<MatrixType>::compute(const MatrixType& matrix)
{
@ -177,7 +224,7 @@ void HouseholderQR<MatrixType>::solve(
/** \returns the matrix Q */
template<typename MatrixType>
MatrixType HouseholderQR<MatrixType>::matrixQ() const
typename HouseholderQR<MatrixType>::MatrixQType HouseholderQR<MatrixType>::matrixQ() const
{
ei_assert(m_isInitialized && "HouseholderQR is not initialized.");
// compute the product H'_0 H'_1 ... H'_n-1,
@ -185,13 +232,13 @@ MatrixType HouseholderQR<MatrixType>::matrixQ() const
// and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...]
int rows = m_qr.rows();
int cols = m_qr.cols();
MatrixType res = MatrixType::Identity(rows, cols);
Matrix<Scalar,1,MatrixType::ColsAtCompileTime> temp(cols);
for (int k = cols-1; k >= 0; k--)
int size = std::min(rows,cols);
MatrixQType res = MatrixQType::Identity(rows, rows);
Matrix<Scalar,1,MatrixType::RowsAtCompileTime> temp(rows);
for (int k = size-1; k >= 0; k--)
{
int remainingSize = rows-k;
res.corner(BottomRight, remainingSize, cols-k)
.applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), ei_conj(m_hCoeffs.coeff(k)), &temp.coeffRef(k));
res.block(k, k, rows-k, rows-k)
.applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), ei_conj(m_hCoeffs.coeff(k)), &temp.coeffRef(k));
}
return res;
}

25
test/qr.cpp
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@ -27,7 +27,6 @@
template<typename MatrixType> void qr(const MatrixType& m)
{
/* this test covers the following files: QR.h */
int rows = m.rows();
int cols = m.cols();
@ -37,8 +36,11 @@ template<typename MatrixType> void qr(const MatrixType& m)
MatrixType a = MatrixType::Random(rows,cols);
HouseholderQR<MatrixType> qrOfA(a);
VERIFY_IS_APPROX(a, qrOfA.matrixQ() * qrOfA.matrixR().toDense());
VERIFY_IS_NOT_APPROX(a+MatrixType::Identity(rows, cols), qrOfA.matrixQ() * qrOfA.matrixR().toDense());
MatrixType r = qrOfA.matrixQR();
// FIXME need better way to construct trapezoid
for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);
VERIFY_IS_APPROX(a, qrOfA.matrixQ() * r);
SquareMatrixType b = a.adjoint() * a;
@ -57,8 +59,9 @@ template<typename MatrixType> void qr(const MatrixType& m)
template<typename MatrixType> void qr_invertible()
{
/* this test covers the following files: QR.h */
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef typename MatrixType::Scalar Scalar;
int size = ei_random<int>(10,50);
MatrixType m1(size, size), m2(size, size), m3(size, size);
@ -75,6 +78,16 @@ template<typename MatrixType> void qr_invertible()
m3 = MatrixType::Random(size,size);
qr.solve(m3, &m2);
VERIFY_IS_APPROX(m3, m1*m2);
// now construct a matrix with prescribed determinant
m1.setZero();
for(int i = 0; i < size; i++) m1(i,i) = ei_random<Scalar>();
RealScalar absdet = ei_abs(m1.diagonal().prod());
m3 = qr.matrixQ(); // get a unitary
m1 = m3 * m1 * m3;
qr.compute(m1);
VERIFY_IS_APPROX(absdet, qr.absDeterminant());
VERIFY_IS_APPROX(ei_log(absdet), qr.logAbsDeterminant());
}
template<typename MatrixType> void qr_verify_assert()
@ -82,9 +95,11 @@ template<typename MatrixType> void qr_verify_assert()
MatrixType tmp;
HouseholderQR<MatrixType> qr;
VERIFY_RAISES_ASSERT(qr.matrixR())
VERIFY_RAISES_ASSERT(qr.matrixQR())
VERIFY_RAISES_ASSERT(qr.solve(tmp,&tmp))
VERIFY_RAISES_ASSERT(qr.matrixQ())
VERIFY_RAISES_ASSERT(qr.absDeterminant())
VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}
void test_qr()

10
test/qr_colpivoting.cpp
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@ -101,9 +101,17 @@ template<typename MatrixType> void qr_verify_assert()
MatrixType tmp;
ColPivotingHouseholderQR<MatrixType> qr;
VERIFY_RAISES_ASSERT(qr.matrixR())
VERIFY_RAISES_ASSERT(qr.matrixQR())
VERIFY_RAISES_ASSERT(qr.solve(tmp,&tmp))
VERIFY_RAISES_ASSERT(qr.matrixQ())
VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
VERIFY_RAISES_ASSERT(qr.isInjective())
VERIFY_RAISES_ASSERT(qr.isSurjective())
VERIFY_RAISES_ASSERT(qr.isInvertible())
VERIFY_RAISES_ASSERT(qr.computeInverse(&tmp))
VERIFY_RAISES_ASSERT(qr.inverse())
VERIFY_RAISES_ASSERT(qr.absDeterminant())
VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}
void test_qr_colpivoting()

4
test/qr_fullpivoting.cpp
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@ -105,7 +105,7 @@ template<typename MatrixType> void qr_verify_assert()
MatrixType tmp;
FullPivotingHouseholderQR<MatrixType> qr;
VERIFY_RAISES_ASSERT(qr.matrixR())
VERIFY_RAISES_ASSERT(qr.matrixQR())
VERIFY_RAISES_ASSERT(qr.solve(tmp,&tmp))
VERIFY_RAISES_ASSERT(qr.matrixQ())
VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
@ -114,6 +114,8 @@ template<typename MatrixType> void qr_verify_assert()
VERIFY_RAISES_ASSERT(qr.isInvertible())
VERIFY_RAISES_ASSERT(qr.computeInverse(&tmp))
VERIFY_RAISES_ASSERT(qr.inverse())
VERIFY_RAISES_ASSERT(qr.absDeterminant())
VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}
void test_qr_fullpivoting()