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More Cholesky fixes.

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* Cholesky decs are NOT rank revealing so remove all the rank/isPositiveDefinite etc stuff.
* fix bug in LLT: s/return/continue/
* introduce machine_epsilon constants, they are actually needed for Higman's formula determining
  the cutoff in Cholesky. Btw fix the page reference to his book (chat with Keir).
* solve methods always return true, since this isn't a rank revealing dec. Actually... they already did always return true!! Now it's explicit.
* updated dox and unit-test
This commit is contained in:
Benoit Jacob
2009-04-01 00:21:16 +00:00
parent 8e2b191acf
commit 2f45eeb0c6
4 changed files with 35 additions and 99 deletions
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50
test/cholesky.cpp
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@@ -86,7 +86,6 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
{
LLT<SquareMatrixType> chol(symm);
VERIFY(chol.isPositiveDefinite());
VERIFY_IS_APPROX(symm, chol.matrixL() * chol.matrixL().adjoint());
chol.solve(vecB, &vecX);
VERIFY_IS_APPROX(symm * vecX, vecB);
@@ -103,18 +102,6 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
{
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);
@@ -123,15 +110,6 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
VERIFY_IS_APPROX(symm * matX, matB);
}
// test isPositiveDefinite on non definite matrix
if (rows>4)
{
SquareMatrixType symm = a0.block(0,0,rows,cols-4) * a0.block(0,0,rows,cols-4).adjoint();
LLT<SquareMatrixType> chol(symm);
VERIFY(!chol.isPositiveDefinite());
LDLT<SquareMatrixType> cholnosqrt(symm);
VERIFY(!cholnosqrt.isPositiveDefinite());
}
}
template<typename Derived>
@@ -156,29 +134,6 @@ void doSomeRankPreservingOperations(Eigen::MatrixBase<Derived>& m)
}
}
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()
{
@@ -191,9 +146,4 @@ void test_cholesky()
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>() );
}
}