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* add LU unit-test. Seems like we have very good numerical stability!

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* some cleanup, and grant me a copyright line on the determinant test.
This commit is contained in:
Benoit Jacob
2008-08-09 19:26:14 +00:00
parent 4fa40367e9
commit d6e88f8155
5 changed files with 146 additions and 15 deletions
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2
Eigen/src/LU/Inverse.h
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@@ -161,7 +161,7 @@ struct ei_compute_inverse
static inline void run(const MatrixType& matrix, MatrixType* result)
{
LU<MatrixType> lu(matrix);
lu.solve(MatrixType::Identity(matrix.rows(), matrix.cols()), result);
lu.computeInverse(result);
}
};

38
Eigen/src/LU/LU.h
View File

@@ -38,12 +38,9 @@
* are permutation matrices.
*
* This decomposition provides the generic approach to solving systems of linear equations, computing
* the rank, invertibility, inverse, and determinant. However for the case when invertibility is
* assumed, we have a specialized variant (see MatrixBase::inverse()) achieving better performance.
* the rank, invertibility, inverse, kernel, and determinant.
*
* \sa MatrixBase::lu(), MatrixBase::determinant(), MatrixBase::rank(), MatrixBase::kernelDim(),
* MatrixBase::kernelBasis(), MatrixBase::solve(), MatrixBase::isInvertible(),
* MatrixBase::inverse(), MatrixBase::computeInverse()
* \sa MatrixBase::lu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse()
*/
template<typename MatrixType> class LU
{
@@ -141,6 +138,18 @@ template<typename MatrixType> class LU
return isInjective() && isSurjective();
}
inline void computeInverse(MatrixType *result) const
{
solve(MatrixType::Identity(m_lu.rows(), m_lu.cols()), result);
}
inline MatrixType inverse() const
{
MatrixType result;
computeInverse(&result);
return result;
}
protected:
MatrixType m_lu;
IntColVectorType m_p;
@@ -163,7 +172,7 @@ LU<MatrixType>::LU(const MatrixType& matrix)
IntRowVectorType cols_transpositions(matrix.cols());
int number_of_transpositions = 0;
RealScalar biggest;
RealScalar biggest = RealScalar(0);
for(int k = 0; k < size; k++)
{
int row_of_biggest_in_corner, col_of_biggest_in_corner;
@@ -224,7 +233,7 @@ void LU<MatrixType>::computeKernel(Matrix<typename MatrixType::Scalar,
> *result) const
{
ei_assert(!isInvertible());
const int dimker = dimensionOfKernel(), rows = m_lu.rows(), cols = m_lu.cols();
const int dimker = dimensionOfKernel(), cols = m_lu.cols();
result->resize(cols, dimker);
/* Let us use the following lemma:
@@ -284,21 +293,22 @@ bool LU<MatrixType>::solve(
* Step 4: result = Qd;
*/
ei_assert(b.rows() == m_lu.rows());
const int smalldim = std::min(m_lu.rows(), m_lu.cols());
const int rows = m_lu.rows();
ei_assert(b.rows() == rows);
const int smalldim = std::min(rows, m_lu.cols());
typename OtherDerived::Eval c(b.rows(), b.cols());
// Step 1
for(int i = 0; i < m_lu.rows(); i++) c.row(m_p.coeff(i)) = b.row(i);
for(int i = 0; i < rows; i++) c.row(m_p.coeff(i)) = b.row(i);
// Step 2
Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime,
MatrixType::MaxRowsAtCompileTime,
MatrixType::MaxRowsAtCompileTime> l(m_lu.rows(), m_lu.rows());
MatrixType::MaxRowsAtCompileTime> l(rows, rows);
l.setZero();
l.corner(Eigen::TopLeft,m_lu.rows(),smalldim)
= m_lu.corner(Eigen::TopLeft,m_lu.rows(),smalldim);
l.corner(Eigen::TopLeft,rows,smalldim)
= m_lu.corner(Eigen::TopLeft,rows,smalldim);
l.template marked<UnitLower>().inverseProductInPlace(c);
// Step 3
@@ -330,7 +340,7 @@ bool LU<MatrixType>::solve(
* \sa class LU
*/
template<typename Derived>
const LU<typename MatrixBase<Derived>::EvalType>
inline const LU<typename MatrixBase<Derived>::EvalType>
MatrixBase<Derived>::lu() const
{
return eval();