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Merged in rmlarsen/eigen (pull request PR-161)

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Change Eigen's ColPivHouseholderQR to use  numerically stable norm downdate formula
This commit is contained in:
Gael Guennebaud
2016-02-03 21:37:06 +01:00
parent 70dc14e4e1 5fb04ab2da
commit b70db60e4d
2 changed files with 159 additions and 52 deletions
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84
test/qr_colpivoting.cpp
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@@ -19,6 +19,7 @@ template<typename MatrixType> void qr()
Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
MatrixType m1;
createRandomPIMatrixOfRank(rank,rows,cols,m1);
@@ -36,6 +37,24 @@ template<typename MatrixType> void qr()
MatrixType c = q * r * qr.colsPermutation().inverse();
VERIFY_IS_APPROX(m1, c);
// Verify that the absolute value of the diagonal elements in R are
// non-increasing until they reach the singularity threshold.
RealScalar threshold =
std::sqrt(RealScalar(rows)) * (std::abs)(r(0, 0)) * NumTraits<Scalar>::epsilon();
for (Index i = 0; i < (std::min)(rows, cols) - 1; ++i) {
RealScalar x = (std::abs)(r(i, i));
RealScalar y = (std::abs)(r(i + 1, i + 1));
if (x < threshold && y < threshold) continue;
if (test_isApproxOrLessThan(x, y)) {
for (Index j = 0; j < (std::min)(rows, cols); ++j) {
std::cout << "i = " << j << ", |r_ii| = " << (std::abs)(r(j, j)) << std::endl;
}
std::cout << "Failure at i=" << i << ", rank=" << rank
<< ", threshold=" << threshold << std::endl;
}
VERIFY_IS_APPROX_OR_LESS_THAN(y, x);
}
MatrixType m2 = MatrixType::Random(cols,cols2);
MatrixType m3 = m1*m2;
m2 = MatrixType::Random(cols,cols2);
@@ -47,6 +66,7 @@ template<typename MatrixType, int Cols2> void qr_fixedsize()
{
enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
int rank = internal::random<int>(1, (std::min)(int(Rows), int(Cols))-1);
Matrix<Scalar,Rows,Cols> m1;
createRandomPIMatrixOfRank(rank,Rows,Cols,m1);
@@ -66,6 +86,67 @@ template<typename MatrixType, int Cols2> void qr_fixedsize()
m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
m2 = qr.solve(m3);
VERIFY_IS_APPROX(m3, m1*m2);
// Verify that the absolute value of the diagonal elements in R are
// non-increasing until they reache the singularity threshold.
RealScalar threshold =
std::sqrt(RealScalar(Rows)) * (std::abs)(r(0, 0)) * NumTraits<Scalar>::epsilon();
for (Index i = 0; i < (std::min)(int(Rows), int(Cols)) - 1; ++i) {
RealScalar x = (std::abs)(r(i, i));
RealScalar y = (std::abs)(r(i + 1, i + 1));
if (x < threshold && y < threshold) continue;
if (test_isApproxOrLessThan(x, y)) {
for (Index j = 0; j < (std::min)(int(Rows), int(Cols)); ++j) {
std::cout << "i = " << j << ", |r_ii| = " << (std::abs)(r(j, j)) << std::endl;
}
std::cout << "Failure at i=" << i << ", rank=" << rank
<< ", threshold=" << threshold << std::endl;
}
VERIFY_IS_APPROX_OR_LESS_THAN(y, x);
}
}
// This test is meant to verify that pivots are chosen such that
// even for a graded matrix, the diagonal of R falls of roughly
// monotonically until it reaches the threshold for singularity.
// We use the so-called Kahan matrix, which is a famous counter-example
// for rank-revealing QR. See
// http://www.netlib.org/lapack/lawnspdf/lawn176.pdf
// page 3 for more detail.
template<typename MatrixType> void qr_kahan_matrix()
{
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
Index rows = 300, cols = rows;
MatrixType m1;
m1.setZero(rows,cols);
RealScalar s = std::pow(NumTraits<RealScalar>::epsilon(), 1.0 / rows);
RealScalar c = std::sqrt(1 - s*s);
for (Index i = 0; i < rows; ++i) {
m1(i, i) = pow(s, i);
m1.row(i).tail(rows - i - 1) = -pow(s, i) * c * MatrixType::Ones(1, rows - i - 1);
}
m1 = (m1 + m1.transpose()).eval();
ColPivHouseholderQR<MatrixType> qr(m1);
MatrixType r = qr.matrixQR().template triangularView<Upper>();
RealScalar threshold =
std::sqrt(RealScalar(rows)) * (std::abs)(r(0, 0)) * NumTraits<Scalar>::epsilon();
for (Index i = 0; i < (std::min)(rows, cols) - 1; ++i) {
RealScalar x = (std::abs)(r(i, i));
RealScalar y = (std::abs)(r(i + 1, i + 1));
if (x < threshold && y < threshold) continue;
if (test_isApproxOrLessThan(x, y)) {
for (Index j = 0; j < (std::min)(rows, cols); ++j) {
std::cout << "i = " << j << ", |r_ii| = " << (std::abs)(r(j, j)) << std::endl;
}
std::cout << "Failure at i=" << i << ", rank=" << qr.rank()
<< ", threshold=" << threshold << std::endl;
}
VERIFY_IS_APPROX_OR_LESS_THAN(y, x);
}
}
template<typename MatrixType> void qr_invertible()
@@ -147,4 +228,7 @@ void test_qr_colpivoting()
// Test problem size constructors
CALL_SUBTEST_9(ColPivHouseholderQR<MatrixXf>(10, 20));
CALL_SUBTEST_1( qr_kahan_matrix<MatrixXf>() );
CALL_SUBTEST_2( qr_kahan_matrix<MatrixXd>() );
}