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LDLT is not rank-revealing, so we should not attempt to use the biggest diagonal elements as thresholds.

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This commit is contained in:
Gael Guennebaud
2014-07-02 23:04:46 +02:00
parent b18a7ff6be
commit bbe9e22d60
2 changed files with 70 additions and 23 deletions
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52
test/cholesky.cpp
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@@ -68,6 +68,7 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
Index cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
@@ -179,6 +180,57 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
// restore
if(sign == -1)
symm = -symm;
// check matrices coming from linear constraints with Lagrange multipliers
if(rows>=3)
{
SquareMatrixType A = symm;
int c = internal::random<int>(0,rows-2);
A.bottomRightCorner(c,c).setZero();
// Make sure a solution exists:
vecX.setRandom();
vecB = A * vecX;
vecX.setZero();
ldltlo.compute(A);
VERIFY_IS_APPROX(A, ldltlo.reconstructedMatrix());
vecX = ldltlo.solve(vecB);
VERIFY_IS_APPROX(A * vecX, vecB);
}
// check non-full rank matrices
if(rows>=3)
{
int r = internal::random<int>(1,rows-1);
Matrix<Scalar,Dynamic,Dynamic> a = Matrix<Scalar,Dynamic,Dynamic>::Random(rows,r);
SquareMatrixType A = a * a.adjoint();
// Make sure a solution exists:
vecX.setRandom();
vecB = A * vecX;
vecX.setZero();
ldltlo.compute(A);
VERIFY_IS_APPROX(A, ldltlo.reconstructedMatrix());
vecX = ldltlo.solve(vecB);
VERIFY_IS_APPROX(A * vecX, vecB);
}
// check matrices with wide spectrum
if(rows>=3)
{
RealScalar s = (std::min)(16,std::numeric_limits<RealScalar>::max_exponent10/8);
Matrix<Scalar,Dynamic,Dynamic> a = Matrix<Scalar,Dynamic,Dynamic>::Random(rows,rows);
Matrix<RealScalar,Dynamic,1> d = Matrix<RealScalar,Dynamic,1>::Random(rows);
for(int k=0; k<rows; ++k)
d(k) = d(k)*std::pow(RealScalar(10),internal::random<RealScalar>(-s,s));
SquareMatrixType A = a * d.asDiagonal() * a.adjoint();
// Make sure a solution exists:
vecX.setRandom();
vecB = A * vecX;
vecX.setZero();
ldltlo.compute(A);
VERIFY_IS_APPROX(A, ldltlo.reconstructedMatrix());
vecX = ldltlo.solve(vecB);
VERIFY_IS_APPROX(A * vecX, vecB);
}
}
// update/downdate