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Port FullPivLU to PermutationMatrix

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This commit is contained in:
Benoit Jacob 2009-11-16 17:05:12 -05:00
parent 76c614f9bd
commit b90744dc05
4 changed files with 38 additions and 34 deletions
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43
Eigen/src/LU/FullPivLU.h
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@ -63,8 +63,8 @@ template<typename _MatrixType> class FullPivLU
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType; typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType; typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType; typedef PermutationMatrix<MatrixType::ColsAtCompileTime> PermutationQType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> ColVectorType; typedef PermutationMatrix<MatrixType::RowsAtCompileTime> PermutationPType;
/** /**
* \brief Default Constructor. * \brief Default Constructor.
@ -120,25 +120,21 @@ template<typename _MatrixType> class FullPivLU
*/ */
RealScalar maxPivot() const { return m_maxpivot; } RealScalar maxPivot() const { return m_maxpivot; }
/** \returns a vector of integers, whose size is the number of rows of the matrix being decomposed, /** \returns the permutation matrix P
* representing the P permutation i.e. the permutation of the rows. For its precise meaning,
* see the examples given in the documentation of class FullPivLU.
* *
* \sa permutationQ() * \sa permutationQ()
*/ */
inline const IntColVectorType& permutationP() const inline const PermutationPType& permutationP() const
{ {
ei_assert(m_isInitialized && "LU is not initialized."); ei_assert(m_isInitialized && "LU is not initialized.");
return m_p; return m_p;
} }
/** \returns a vector of integers, whose size is the number of columns of the matrix being /** \returns the permutation matrix Q
* decomposed, representing the Q permutation i.e. the permutation of the columns.
* For its precise meaning, see the examples given in the documentation of class FullPivLU.
* *
* \sa permutationP() * \sa permutationP()
*/ */
inline const IntRowVectorType& permutationQ() const inline const PermutationQType& permutationQ() const
{ {
ei_assert(m_isInitialized && "LU is not initialized."); ei_assert(m_isInitialized && "LU is not initialized.");
return m_q; return m_q;
@ -368,8 +364,8 @@ template<typename _MatrixType> class FullPivLU
protected: protected:
MatrixType m_lu; MatrixType m_lu;
IntColVectorType m_p; PermutationPType m_p;
IntRowVectorType m_q; PermutationQType m_q;
int m_det_pq, m_nonzero_pivots; int m_det_pq, m_nonzero_pivots;
RealScalar m_maxpivot, m_prescribedThreshold; RealScalar m_maxpivot, m_prescribedThreshold;
bool m_isInitialized, m_usePrescribedThreshold; bool m_isInitialized, m_usePrescribedThreshold;
@ -463,13 +459,13 @@ FullPivLU<MatrixType>& FullPivLU<MatrixType>::compute(const MatrixType& matrix)
// the main loop is over, we still have to accumulate the transpositions to find the // the main loop is over, we still have to accumulate the transpositions to find the
// permutations P and Q // permutations P and Q
for(int k = 0; k < matrix.rows(); ++k) m_p.coeffRef(k) = k; for(int k = 0; k < matrix.rows(); ++k) m_p.indices().coeffRef(k) = k;
for(int k = size-1; k >= 0; --k) for(int k = size-1; k >= 0; --k)
std::swap(m_p.coeffRef(k), m_p.coeffRef(rows_transpositions.coeff(k))); std::swap(m_p.indices().coeffRef(k), m_p.indices().coeffRef(rows_transpositions.coeff(k)));
for(int k = 0; k < matrix.cols(); ++k) m_q.coeffRef(k) = k; for(int k = 0; k < matrix.cols(); ++k) m_q.indices().coeffRef(k) = k;
for(int k = 0; k < size; ++k) for(int k = 0; k < size; ++k)
std::swap(m_q.coeffRef(k), m_q.coeffRef(cols_transpositions.coeff(k))); std::swap(m_q.indices().coeffRef(k), m_q.indices().coeffRef(cols_transpositions.coeff(k)));
m_det_pq = (number_of_transpositions%2) ? -1 : 1; m_det_pq = (number_of_transpositions%2) ? -1 : 1;
return *this; return *this;
@ -562,9 +558,9 @@ struct ei_kernel_retval<FullPivLU<_MatrixType> >
m.col(i).swap(m.col(pivots.coeff(i))); m.col(i).swap(m.col(pivots.coeff(i)));
// see the negative sign in the next line, that's what we were talking about above. // see the negative sign in the next line, that's what we were talking about above.
for(int i = 0; i < rank(); ++i) dst.row(dec().permutationQ().coeff(i)) = -m.row(i).end(dimker); for(int i = 0; i < rank(); ++i) dst.row(dec().permutationQ().indices().coeff(i)) = -m.row(i).end(dimker);
for(int i = rank(); i < cols; ++i) dst.row(dec().permutationQ().coeff(i)).setZero(); for(int i = rank(); i < cols; ++i) dst.row(dec().permutationQ().indices().coeff(i)).setZero();
for(int k = 0; k < dimker; ++k) dst.coeffRef(dec().permutationQ().coeff(rank()+k), k) = Scalar(1); for(int k = 0; k < dimker; ++k) dst.coeffRef(dec().permutationQ().indices().coeff(rank()+k), k) = Scalar(1);
} }
}; };
@ -600,8 +596,7 @@ struct ei_image_retval<FullPivLU<_MatrixType> >
pivots.coeffRef(p++) = i; pivots.coeffRef(p++) = i;
ei_internal_assert(p == rank()); ei_internal_assert(p == rank());
for(int i = 0; i < rank(); ++i) dst.block(0,0,dst.rows(),rank()) = (originalMatrix()*dec().permutationQ()).block(0,0,dst.rows(),rank());
dst.col(i) = originalMatrix().col(dec().permutationQ().coeff(pivots.coeff(i)));
} }
}; };
@ -638,7 +633,7 @@ struct ei_solve_retval<FullPivLU<_MatrixType>, Rhs>
// Step 1 // Step 1
for(int i = 0; i < rows; ++i) for(int i = 0; i < rows; ++i)
c.row(dec().permutationP().coeff(i)) = rhs().row(i); c.row(dec().permutationP().indices().coeff(i)) = rhs().row(i);
// Step 2 // Step 2
dec().matrixLU() dec().matrixLU()
@ -660,9 +655,9 @@ struct ei_solve_retval<FullPivLU<_MatrixType>, Rhs>
// Step 4 // Step 4
for(int i = 0; i < nonzero_pivots; ++i) for(int i = 0; i < nonzero_pivots; ++i)
dst.row(dec().permutationQ().coeff(i)) = c.row(i); dst.row(dec().permutationQ().indices().coeff(i)) = c.row(i);
for(int i = nonzero_pivots; i < dec().matrixLU().cols(); ++i) for(int i = nonzero_pivots; i < dec().matrixLU().cols(); ++i)
dst.row(dec().permutationQ().coeff(i)).setZero(); dst.row(dec().permutationQ().indices().coeff(i)).setZero();
} }
}; };

4
Eigen/src/LU/PartialPivLU.h
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@ -103,9 +103,7 @@ template<typename _MatrixType> class PartialPivLU
return m_lu; return m_lu;
} }
/** \returns a vector of integers, whose size is the number of rows of the matrix being decomposed, /** \returns the permutation matrix P.
* representing the P permutation i.e. the permutation of the rows. For its precise meaning,
* see the examples given in the documentation of class FullPivLU.
*/ */
inline const PermutationType& permutationP() const inline const PermutationType& permutationP() const
{ {

6
doc/snippets/class_FullPivLU.cpp
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@ -13,8 +13,4 @@ cout << "Here is the U part:" << endl;
Matrix5x3 u = lu.matrixLU().part<UpperTriangular>(); Matrix5x3 u = lu.matrixLU().part<UpperTriangular>();
cout << u << endl; cout << u << endl;
cout << "Let us now reconstruct the original matrix m:" << endl; cout << "Let us now reconstruct the original matrix m:" << endl;
Matrix5x3 x = l * u; cout << lu.permutationP().inverse() * l * u * lu.permutationQ().inverse() << endl;
Matrix5x3 y;
for(int i = 0; i < 5; i++) for(int j = 0; j < 3; j++)
y(i, lu.permutationQ()[j]) = x(lu.permutationP()[i], j);
cout << y << endl; // should be equal to the original matrix m

17
test/lu.cpp
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@ -24,9 +24,11 @@
#include "main.h" #include "main.h"
#include <Eigen/LU> #include <Eigen/LU>
using namespace std;
template<typename MatrixType> void lu_non_invertible() template<typename MatrixType> void lu_non_invertible()
{ {
typedef typename MatrixType::Scalar Scalar;
/* this test covers the following files: /* this test covers the following files:
LU.h LU.h
*/ */
@ -65,7 +67,20 @@ template<typename MatrixType> void lu_non_invertible()
createRandomMatrixOfRank(rank, rows, cols, m1); createRandomMatrixOfRank(rank, rows, cols, m1);
FullPivLU<MatrixType> lu(m1); FullPivLU<MatrixType> lu(m1);
std::cout << lu.kernel().rows() << " " << lu.kernel().cols() << std::endl; // FIXME need better way to construct trapezoid matrices. extend triangularView to support rectangular.
DynamicMatrixType u(rows,cols);
for(int i = 0; i < rows; i++)
for(int j = 0; j < cols; j++)
u(i,j) = i>j ? Scalar(0) : lu.matrixLU()(i,j);
DynamicMatrixType l(rows,rows);
for(int i = 0; i < rows; i++)
for(int j = 0; j < rows; j++)
l(i,j) = (i<j || j>=cols) ? Scalar(0)
: i==j ? Scalar(1)
: lu.matrixLU()(i,j);
VERIFY_IS_APPROX(lu.permutationP() * m1 * lu.permutationQ(), l*u);
KernelMatrixType m1kernel = lu.kernel(); KernelMatrixType m1kernel = lu.kernel();
ImageMatrixType m1image = lu.image(m1); ImageMatrixType m1image = lu.image(m1);