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Correct GMRES:

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* Fix error in calculation of residual at restart.
* Use relative residual as stopping criterion.
* Improve documentation.
This commit is contained in:
Kolja Brix 2014-08-02 18:39:15 +02:00
parent e51da9c3a8
commit 953ec08089
1 changed files with 80 additions and 76 deletions
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34
unsupported/Eigen/src/IterativeSolvers/GMRES.h
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@ -27,7 +27,7 @@ namespace internal {
* \param iters on input: maximum number of iterations to perform
* on output: number of iterations performed
* \param restart number of iterations for a restart
* \param tol_error on input: residual tolerance
* \param tol_error on input: relative residual tolerance
* on output: residuum achieved
*
* \sa IterativeMethods::bicgstab()
@ -70,18 +70,24 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
const int m = mat.rows();
VectorType p0 = rhs - mat*x;
// residual and preconditioned residual
const VectorType p0 = rhs - mat*x;
VectorType r0 = precond.solve(p0);
const RealScalar r0Norm = r0.norm();
// is initial guess already good enough?
if(abs(r0.norm()) < tol) {
if(r0Norm == 0) {
tol_error=0;
return true;
}
// storage for Hessenberg matrix and Householder data
FMatrixType H = FMatrixType::Zero(m, restart + 1);
VectorType w = VectorType::Zero(restart + 1);
FMatrixType H = FMatrixType::Zero(m, restart + 1); // Hessenberg matrix
VectorType tau = VectorType::Zero(restart + 1);
// storage for Jacobi rotations
std::vector < JacobiRotation < Scalar > > G(restart);
// generate first Householder vector
@ -112,7 +118,6 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
}
if (v.tail(m - k).norm() != 0.0) {
if (k <= restart) {
// generate new Householder vector
@ -135,19 +140,19 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
}
if (k<m && v(k) != (Scalar) 0) {
// determine next Givens rotation
G[k - 1].makeGivens(v(k - 1), v(k));
// apply Givens rotation to v and w
v.applyOnTheLeft(k - 1, k, G[k - 1].adjoint());
w.applyOnTheLeft(k - 1, k, G[k - 1].adjoint());
}
// insert coefficients into upper matrix triangle
H.col(k - 1).head(k) = v.head(k);
bool stop=(k==m || abs(w(k)) < tol || iters == maxIters);
bool stop=(k==m || abs(w(k)) < tol * r0Norm || iters == maxIters);
if (stop || k == restart) {
@ -174,13 +179,13 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
} else {
k=0;
// reset data for a restart r0 = rhs - mat * x;
VectorType p0=mat*x;
VectorType p1=precond.solve(p0);
r0 = rhs - p1;
// r0_sqnorm = r0.squaredNorm();
w = VectorType::Zero(restart + 1);
// reset data for restart
const VectorType p0 = rhs - mat*x;
r0 = precond.solve(p0);
// clear Hessenberg matrix and Householder data
H = FMatrixType::Zero(m, restart + 1);
w = VectorType::Zero(restart + 1);
tau = VectorType::Zero(restart + 1);
// generate first Householder vector
@ -194,7 +199,6 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
}
}
return false;