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Fix numerical issues with BiCGSTAB.

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This commit is contained in:
Antonio Sánchez 2025-02-11 19:41:59 +00:00
parent ef475f2770
commit 809d266b49
2 changed files with 87 additions and 17 deletions
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49
Eigen/src/IterativeLinearSolvers/BiCGSTAB.h
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@ -31,8 +31,6 @@ namespace internal {
template <typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x, const Preconditioner& precond, Index& iters,
typename Dest::RealScalar& tol_error) {
using std::abs;
using std::sqrt;
typedef typename Dest::RealScalar RealScalar;
typedef typename Dest::Scalar Scalar;
typedef Matrix<Scalar, Dynamic, 1> VectorType;
@ -43,14 +41,15 @@ bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x, const Precondition
VectorType r = rhs - mat * x;
VectorType r0 = r;
RealScalar r0_sqnorm = r0.squaredNorm();
RealScalar rhs_sqnorm = rhs.squaredNorm();
if (rhs_sqnorm == 0) {
RealScalar r0_norm = r0.stableNorm();
RealScalar r_norm = r0_norm;
RealScalar rhs_norm = rhs.stableNorm();
if (rhs_norm == 0) {
x.setZero();
return true;
}
Scalar rho(1);
Scalar alpha(1);
Scalar alpha(0);
Scalar w(1);
VectorType v = VectorType::Zero(n), p = VectorType::Zero(n);
@ -59,21 +58,22 @@ bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x, const Precondition
VectorType s(n), t(n);
RealScalar tol2 = tol * tol * rhs_sqnorm;
RealScalar eps2 = NumTraits<Scalar>::epsilon() * NumTraits<Scalar>::epsilon();
RealScalar eps = NumTraits<Scalar>::epsilon();
Index i = 0;
Index restarts = 0;
while (r.squaredNorm() > tol2 && i < maxIters) {
while (r_norm > tol && i < maxIters) {
Scalar rho_old = rho;
rho = r0.dot(r);
if (abs(rho) < eps2 * r0_sqnorm) {
if (Eigen::numext::abs(rho) / Eigen::numext::maxi(r0_norm, r_norm) < eps * Eigen::numext::mini(r0_norm, r_norm)) {
// The new residual vector became too orthogonal to the arbitrarily chosen direction r0
// Let's restart with a new r0:
r = rhs - mat * x;
r0 = r;
rho = r0_sqnorm = r.squaredNorm();
rho = r.squaredNorm();
r0_norm = r.stableNorm();
alpha = Scalar(0);
w = Scalar(1);
if (restarts++ == 0) i = 0;
}
Scalar beta = (rho / rho_old) * (alpha / w);
@ -82,23 +82,38 @@ bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x, const Precondition
y = precond.solve(p);
v.noalias() = mat * y;
alpha = rho / r0.dot(v);
Scalar theta = r0.dot(v);
// For small angles ∠(r0, v) < eps, random restart.
RealScalar v_norm = v.stableNorm();
if (Eigen::numext::abs(theta) / Eigen::numext::maxi(r0_norm, v_norm) < eps * Eigen::numext::mini(r0_norm, v_norm)) {
r = rhs - mat * x;
r0.setRandom();
r0_norm = r0.stableNorm();
rho = Scalar(1);
alpha = Scalar(0);
w = Scalar(1);
if (restarts++ == 0) i = 0;
continue;
}
alpha = rho / theta;
s = r - alpha * v;
z = precond.solve(s);
t.noalias() = mat * z;
RealScalar tmp = t.squaredNorm();
if (tmp > RealScalar(0))
if (tmp > RealScalar(0)) {
w = t.dot(s) / tmp;
else
} else {
w = Scalar(0);
}
x += alpha * y + w * z;
r = s - w * t;
r_norm = r.stableNorm();
++i;
}
tol_error = sqrt(r.squaredNorm() / rhs_sqnorm);
tol_error = r_norm / rhs_norm;
iters = i;
return true;
}

55
test/bicgstab.cpp
View File

@ -26,8 +26,63 @@ void test_bicgstab_T() {
// CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_ssor) );
}
// https://gitlab.com/libeigen/eigen/-/issues/2856
void test_2856() {
Eigen::MatrixXd D = Eigen::MatrixXd::Identity(14, 14);
D(6, 13) = 1;
D(13, 12) = 1;
using CSRMatrix = Eigen::SparseMatrix<double, Eigen::RowMajor>;
CSRMatrix A = D.sparseView();
Eigen::VectorXd b = Eigen::VectorXd::Zero(14);
b(12) = -1001;
Eigen::BiCGSTAB<CSRMatrix> solver;
solver.compute(A);
Eigen::VectorXd x = solver.solve(b);
Eigen::VectorXd expected = Eigen::VectorXd::Zero(14);
expected(6) = -1001;
expected(12) = -1001;
expected(13) = 1001;
VERIFY_IS_EQUAL(x, expected);
Eigen::VectorXd residual = b - A * x;
VERIFY(residual.isZero());
}
// https://gitlab.com/libeigen/eigen/-/issues/2899
void test_2899() {
Eigen::MatrixXd A(4, 4);
A(0, 0) = 1;
A(1, 0) = -1.0 / 6;
A(1, 1) = 2.0 / 3;
A(1, 2) = -1.0 / 6;
A(1, 3) = -1.0 / 3;
A(2, 1) = -1.0 / 3;
A(2, 2) = 1;
A(2, 3) = -2.0 / 3;
A(3, 1) = -1.0 / 3;
A(3, 2) = -1.0 / 3;
A(3, 3) = 2.0 / 3;
Eigen::VectorXd b(4);
b(0) = 0;
b(1) = 1;
b(2) = 1;
b(3) = 1;
Eigen::BiCGSTAB<Eigen::MatrixXd> solver;
solver.compute(A);
Eigen::VectorXd x = solver.solve(b);
Eigen::VectorXd expected(4);
expected << 0, 15, 18, 18;
VERIFY_IS_APPROX(x, expected);
Eigen::VectorXd residual = b - A * x;
VERIFY(residual.isZero());
}
EIGEN_DECLARE_TEST(bicgstab) {
CALL_SUBTEST_1((test_bicgstab_T<double, int>()));
CALL_SUBTEST_2((test_bicgstab_T<std::complex<double>, int>()));
CALL_SUBTEST_3((test_bicgstab_T<double, long int>()));
CALL_SUBTEST_4(test_2856());
CALL_SUBTEST_5(test_2899());
}