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* FullPivLU: replace "remaining==0" termination condition (from Golub) by a fuzzy compare

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(fixes lu test failures when testing solve())
* LU test: set appropriate threshold and limit the number of times that a specially tricky test
  is run. (fixes lu test failures when testing rank()).
* Tests: rename createRandomMatrixOfRank to createRandomProjectionOfRank
This commit is contained in:
Benoit Jacob 2010-02-23 09:04:59 -05:00
parent 4a0d41c5fb
commit 7dc75380c1
6 changed files with 37 additions and 12 deletions
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6
Eigen/src/LU/FullPivLU.h
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@ -404,6 +404,7 @@ FullPivLU<MatrixType>& FullPivLU<MatrixType>::compute(const MatrixType& matrix)
m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)
m_maxpivot = RealScalar(0);
RealScalar cutoff(0);
for(int k = 0; k < size; ++k)
{
@ -418,8 +419,11 @@ FullPivLU<MatrixType>& FullPivLU<MatrixType>::compute(const MatrixType& matrix)
row_of_biggest_in_corner += k; // correct the values! since they were computed in the corner,
col_of_biggest_in_corner += k; // need to add k to them.
// when k==0, biggest_in_corner is the biggest coeff absolute value in the original matrix
if(k == 0) cutoff = biggest_in_corner * NumTraits<Scalar>::epsilon();
// if the pivot (hence the corner) is exactly zero, terminate to avoid generating nan/inf values
if(biggest_in_corner == RealScalar(0))
if(ei_abs(biggest_in_corner) < cutoff)
{
// before exiting, make sure to initialize the still uninitialized transpositions
// in a sane state without destroying what we already have.

2
test/inverse.cpp
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@ -42,7 +42,7 @@ template<typename MatrixType> void inverse(const MatrixType& m)
m2(rows, cols),
mzero = MatrixType::Zero(rows, cols),
identity = MatrixType::Identity(rows, rows);
createRandomMatrixOfRank(rows,rows,rows,m1);
createRandomProjectionOfRank(rows,rows,rows,m1);
m2 = m1.inverse();
VERIFY_IS_APPROX(m1, m2.inverse() );

31
test/lu.cpp
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@ -28,7 +28,11 @@ using namespace std;
template<typename MatrixType> void lu_non_invertible()
{
static int times_called = 0;
times_called++;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
/* this test covers the following files:
LU.h
*/
@ -64,9 +68,15 @@ template<typename MatrixType> void lu_non_invertible()
MatrixType m1(rows, cols), m3(rows, cols2);
CMatrixType m2(cols, cols2);
createRandomMatrixOfRank(rank, rows, cols, m1);
createRandomProjectionOfRank(rank, rows, cols, m1);
FullPivLU<MatrixType> lu;
// The special value 0.01 below works well in tests. Keep in mind that we're only computing the rank of projections.
// So it's not clear at all the epsilon should play any role there.
lu.setThreshold(RealScalar(0.01));
lu.compute(m1);
FullPivLU<MatrixType> lu(m1);
// FIXME need better way to construct trapezoid matrices. extend triangularView to support rectangular.
DynamicMatrixType u(rows,cols);
for(int i = 0; i < rows; i++)
@ -91,9 +101,20 @@ template<typename MatrixType> void lu_non_invertible()
VERIFY(!lu.isSurjective());
VERIFY((m1 * m1kernel).isMuchSmallerThan(m1));
VERIFY(m1image.fullPivLu().rank() == rank);
DynamicMatrixType sidebyside(m1.rows(), m1.cols() + m1image.cols());
sidebyside << m1, m1image;
VERIFY(sidebyside.fullPivLu().rank() == rank);
// The following test is damn hard to get to succeed over a large number of repetitions.
// We're checking that the image is indeed the image, i.e. adding it as new columns doesn't increase the rank.
// Since we've already tested rank() above, the point here is not to test rank(), it is to test image().
// Since image() is implemented in a very simple way that doesn't leave much room for choice, the occasional
// errors that we get here (one in 1e+4 repetitions roughly) are probably just a sign that it's a really
// hard test, so we just limit how many times it's run.
if(times_called < 100)
{
DynamicMatrixType sidebyside(m1.rows(), m1.cols() + m1image.cols());
sidebyside << m1, m1image;
VERIFY(sidebyside.fullPivLu().rank() == rank);
}
m2 = CMatrixType::Random(cols,cols2);
m3 = m1*m2;
m2 = CMatrixType::Random(cols,cols2);

4
test/main.h
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@ -148,7 +148,7 @@ namespace Eigen
#define EIGEN_INTERNAL_DEBUGGING
#define EIGEN_NICE_RANDOM
#include <Eigen/QR> // required for createRandomMatrixOfRank
#include <Eigen/QR> // required for createRandomProjectionOfRank
#define VERIFY(a) do { if (!(a)) { \
@ -343,7 +343,7 @@ inline bool test_isUnitary(const MatrixBase<Derived>& m)
}
template<typename MatrixType>
void createRandomMatrixOfRank(int desired_rank, int rows, int cols, MatrixType& m)
void createRandomProjectionOfRank(int desired_rank, int rows, int cols, MatrixType& m)
{
typedef typename ei_traits<MatrixType>::Scalar Scalar;
enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };

4
test/qr_colpivoting.cpp
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@ -36,7 +36,7 @@ template<typename MatrixType> void qr()
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
MatrixType m1;
createRandomMatrixOfRank(rank,rows,cols,m1);
createRandomProjectionOfRank(rank,rows,cols,m1);
ColPivHouseholderQR<MatrixType> qr(m1);
VERIFY_IS_APPROX(rank, qr.rank());
VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
@ -64,7 +64,7 @@ template<typename MatrixType, int Cols2> void qr_fixedsize()
typedef typename MatrixType::Scalar Scalar;
int rank = ei_random<int>(1, std::min(int(Rows), int(Cols))-1);
Matrix<Scalar,Rows,Cols> m1;
createRandomMatrixOfRank(rank,Rows,Cols,m1);
createRandomProjectionOfRank(rank,Rows,Cols,m1);
ColPivHouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
VERIFY_IS_APPROX(rank, qr.rank());
VERIFY(Cols - qr.rank() == qr.dimensionOfKernel());

2
test/qr_fullpivoting.cpp
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@ -35,7 +35,7 @@ template<typename MatrixType> void qr()
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
MatrixType m1;
createRandomMatrixOfRank(rank,rows,cols,m1);
createRandomProjectionOfRank(rank,rows,cols,m1);
FullPivHouseholderQR<MatrixType> qr(m1);
VERIFY_IS_APPROX(rank, qr.rank());
VERIFY(cols - qr.rank() == qr.dimensionOfKernel());