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Fix real schur and polynomial solver.

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This commit is contained in:
Antonio Sánchez 2024-02-17 15:22:11 +00:00
parent 8a4118746e
commit b14c5d0fa1
3 changed files with 33 additions and 22 deletions
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45
Eigen/src/Eigenvalues/RealSchur.h
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@ -408,28 +408,29 @@ inline void RealSchur<MatrixType>::computeShift(Index iu, Index iter, Scalar& ex
shiftInfo.coeffRef(1) = m_matT.coeff(iu - 1, iu - 1);
shiftInfo.coeffRef(2) = m_matT.coeff(iu, iu - 1) * m_matT.coeff(iu - 1, iu);
// Wilkinson's original ad hoc shift
if (iter == 10) {
exshift += shiftInfo.coeff(0);
for (Index i = 0; i <= iu; ++i) m_matT.coeffRef(i, i) -= shiftInfo.coeff(0);
Scalar s = abs(m_matT.coeff(iu, iu - 1)) + abs(m_matT.coeff(iu - 1, iu - 2));
shiftInfo.coeffRef(0) = Scalar(0.75) * s;
shiftInfo.coeffRef(1) = Scalar(0.75) * s;
shiftInfo.coeffRef(2) = Scalar(-0.4375) * s * s;
}
// MATLAB's new ad hoc shift
if (iter == 30) {
Scalar s = (shiftInfo.coeff(1) - shiftInfo.coeff(0)) / Scalar(2.0);
s = s * s + shiftInfo.coeff(2);
if (s > Scalar(0)) {
s = sqrt(s);
if (shiftInfo.coeff(1) < shiftInfo.coeff(0)) s = -s;
s = s + (shiftInfo.coeff(1) - shiftInfo.coeff(0)) / Scalar(2.0);
s = shiftInfo.coeff(0) - shiftInfo.coeff(2) / s;
exshift += s;
for (Index i = 0; i <= iu; ++i) m_matT.coeffRef(i, i) -= s;
shiftInfo.setConstant(Scalar(0.964));
// Alternate exceptional shifting strategy every 16 iterations.
if (iter % 16 == 0) {
// Wilkinson's original ad hoc shift
if (iter % 32 != 0) {
exshift += shiftInfo.coeff(0);
for (Index i = 0; i <= iu; ++i) m_matT.coeffRef(i, i) -= shiftInfo.coeff(0);
Scalar s = abs(m_matT.coeff(iu, iu - 1)) + abs(m_matT.coeff(iu - 1, iu - 2));
shiftInfo.coeffRef(0) = Scalar(0.75) * s;
shiftInfo.coeffRef(1) = Scalar(0.75) * s;
shiftInfo.coeffRef(2) = Scalar(-0.4375) * s * s;
} else {
// MATLAB's new ad hoc shift
Scalar s = (shiftInfo.coeff(1) - shiftInfo.coeff(0)) / Scalar(2.0);
s = s * s + shiftInfo.coeff(2);
if (s > Scalar(0)) {
s = sqrt(s);
if (shiftInfo.coeff(1) < shiftInfo.coeff(0)) s = -s;
s = s + (shiftInfo.coeff(1) - shiftInfo.coeff(0)) / Scalar(2.0);
s = shiftInfo.coeff(0) - shiftInfo.coeff(2) / s;
exshift += s;
for (Index i = 0; i <= iu; ++i) m_matT.coeffRef(i, i) -= s;
shiftInfo.setConstant(Scalar(0.964));
}
}
}
}

9
test/schur_real.cpp
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@ -97,6 +97,13 @@ void schur(int size = MatrixType::ColsAtCompileTime) {
}
}
void test_bug2633() {
Eigen::MatrixXd A(4, 4);
A << 0, 0, 0, -2, 1, 0, 0, -0, 0, 1, 0, 2, 0, 0, 2, -0;
RealSchur<Eigen::MatrixXd> schur(A);
VERIFY(schur.info() == Eigen::Success);
}
EIGEN_DECLARE_TEST(schur_real) {
CALL_SUBTEST_1((schur<Matrix4f>()));
CALL_SUBTEST_2((schur<MatrixXd>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4))));
@ -105,4 +112,6 @@ EIGEN_DECLARE_TEST(schur_real) {
// Test problem size constructors
CALL_SUBTEST_5(RealSchur<MatrixXf>(10));
CALL_SUBTEST_6((test_bug2633()));
}

1
unsupported/Eigen/src/Polynomials/PolynomialSolver.h
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@ -320,6 +320,7 @@ class PolynomialSolver : public PolynomialSolverBase<Scalar_, Deg_> {
internal::companion<Scalar, Deg_> companion(poly);
companion.balance();
m_eigenSolver.compute(companion.denseMatrix());
eigen_assert(m_eigenSolver.info() == Eigen::Success);
m_roots = m_eigenSolver.eigenvalues();
// cleanup noise in imaginary part of real roots:
// if the imaginary part is rather small compared to the real part