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Many improvements in LLT and LDLT:

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* in LDLT, support the negative semidefinite case
* fix bad floating-point comparisons, improves greatly the accuracy of methods like
  isPositiveDefinite() and rank()
* simplifications
* identify (but not resolve) bug: claim that only triangular part is used, is inaccurate
* expanded unit-tests
This commit is contained in:
Benoit Jacob
2009-03-30 21:45:45 +00:00
parent df9dfa1455
commit a1ba995f05
3 changed files with 142 additions and 52 deletions
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101
test/cholesky.cpp
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@@ -25,7 +25,7 @@
#define EIGEN_NO_ASSERTION_CHECKING
#include "main.h"
#include <Eigen/Cholesky>
#include <Eigen/LU>
#include <Eigen/QR>
#ifdef HAS_GSL
#include "gsl_helper.h"
@@ -52,6 +52,10 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
MatrixType a1 = MatrixType::Random(rows,cols);
symm += a1 * a1.adjoint();
// to test if really Cholesky only uses the upper triangular part, uncomment the following
// FIXME: currently that fails !!
//symm.template part<StrictlyLowerTriangular>().setZero();
#ifdef HAS_GSL
if (ei_is_same_type<RealScalar,double>::ret)
{
@@ -80,17 +84,6 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
}
#endif
{
LDLT<SquareMatrixType> ldlt(symm);
VERIFY(ldlt.isPositiveDefinite());
// TODO(keir): This doesn't make sense now that LDLT pivots.
//VERIFY_IS_APPROX(symm, ldlt.matrixL() * ldlt.vectorD().asDiagonal() * ldlt.matrixL().adjoint());
ldlt.solve(vecB, &vecX);
VERIFY_IS_APPROX(symm * vecX, vecB);
ldlt.solve(matB, &matX);
VERIFY_IS_APPROX(symm * matX, matB);
}
{
LLT<SquareMatrixType> chol(symm);
VERIFY(chol.isPositiveDefinite());
@@ -101,6 +94,35 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
VERIFY_IS_APPROX(symm * matX, matB);
}
int sign = ei_random<int>()%2 ? 1 : -1;
if(sign == -1)
{
symm = -symm; // test a negative matrix
}
{
LDLT<SquareMatrixType> ldlt(symm);
VERIFY(ldlt.isInvertible());
if(sign == 1)
{
VERIFY(ldlt.isPositive());
VERIFY(ldlt.isPositiveDefinite());
}
if(sign == -1)
{
VERIFY(ldlt.isNegative());
VERIFY(ldlt.isNegativeDefinite());
}
// TODO(keir): This doesn't make sense now that LDLT pivots.
//VERIFY_IS_APPROX(symm, ldlt.matrixL() * ldlt.vectorD().asDiagonal() * ldlt.matrixL().adjoint());
ldlt.solve(vecB, &vecX);
VERIFY_IS_APPROX(symm * vecX, vecB);
ldlt.solve(matB, &matX);
VERIFY_IS_APPROX(symm * matX, matB);
}
// test isPositiveDefinite on non definite matrix
if (rows>4)
{
@@ -112,6 +134,52 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
}
}
template<typename Derived>
void doSomeRankPreservingOperations(Eigen::MatrixBase<Derived>& m)
{
typedef typename Derived::RealScalar RealScalar;
for(int a = 0; a < 3*(m.rows()+m.cols()); a++)
{
RealScalar d = Eigen::ei_random<RealScalar>(-1,1);
int i = Eigen::ei_random<int>(0,m.rows()-1); // i is a random row number
int j;
do {
j = Eigen::ei_random<int>(0,m.rows()-1);
} while (i==j); // j is another one (must be different)
m.row(i) += d * m.row(j);
i = Eigen::ei_random<int>(0,m.cols()-1); // i is a random column number
do {
j = Eigen::ei_random<int>(0,m.cols()-1);
} while (i==j); // j is another one (must be different)
m.col(i) += d * m.col(j);
}
}
template<typename MatrixType> void ldlt_rank()
{
// NOTE there seems to be a problem with too small sizes -- could easily lie in the doSomeRankPreservingOperations function
int rows = ei_random<int>(50,200);
int rank = ei_random<int>(40, rows-1);
// generate a random positive matrix a of given rank
MatrixType m = MatrixType::Random(rows,rows);
QR<MatrixType> qr(m);
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> DiagVectorType;
DiagVectorType d(rows);
d.setZero();
for(int i = 0; i < rank; i++) d(i)=RealScalar(1);
MatrixType a = qr.matrixQ() * d.asDiagonal() * qr.matrixQ().adjoint();
LDLT<MatrixType> ldlt(a);
VERIFY( ei_abs(ldlt.rank() - rank) <= rank / 20 ); // yes, LDLT::rank is a bit inaccurate...
}
void test_cholesky()
{
for(int i = 0; i < g_repeat; i++) {
@@ -120,7 +188,12 @@ void test_cholesky()
CALL_SUBTEST( cholesky(Matrix3f()) );
CALL_SUBTEST( cholesky(Matrix4d()) );
CALL_SUBTEST( cholesky(MatrixXcd(7,7)) );
CALL_SUBTEST( cholesky(MatrixXf(17,17)) );
CALL_SUBTEST( cholesky(MatrixXd(33,33)) );
CALL_SUBTEST( cholesky(MatrixXd(17,17)) );
CALL_SUBTEST( cholesky(MatrixXf(200,200)) );
}
for(int i = 0; i < g_repeat/3; i++) {
CALL_SUBTEST( ldlt_rank<MatrixXd>() );
CALL_SUBTEST( ldlt_rank<MatrixXf>() );
CALL_SUBTEST( ldlt_rank<MatrixXcd>() );
}
}