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This commit is contained in:
Gael Guennebaud 2015-06-09 15:23:08 +02:00
parent 04665ef9e1
commit cacbc5679d
1 changed files with 150 additions and 148 deletions
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48
unsupported/Eigen/src/IterativeSolvers/GMRES.h
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@ -78,7 +78,8 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
const RealScalar r0Norm = r0.norm(); const RealScalar r0Norm = r0.norm();
// is initial guess already good enough? // is initial guess already good enough?
if(r0Norm == 0) { if(r0Norm == 0)
{
tol_error = 0; tol_error = 0;
return true; return true;
} }
@ -95,10 +96,10 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
Ref<VectorType> H0_tail = H.col(0).tail(m - 1); Ref<VectorType> H0_tail = H.col(0).tail(m - 1);
RealScalar beta; RealScalar beta;
r0.makeHouseholder(H0_tail, tau.coeffRef(0), beta); r0.makeHouseholder(H0_tail, tau.coeffRef(0), beta);
w(0)=(Scalar) beta; w(0) = Scalar(beta);
for (Index k = 1; k <= restart; ++k) {
for (Index k = 1; k <= restart; ++k)
{
++iters; ++iters;
v = VectorType::Unit(m, k - 1); v = VectorType::Unit(m, k - 1);
@ -117,29 +118,30 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
v.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data()); v.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data());
} }
if (v.tail(m - k).norm() != 0.0) { if (v.tail(m - k).norm() != 0.0)
if (k <= restart) { {
if (k <= restart)
{
// generate new Householder vector // generate new Householder vector
Ref<VectorType> Hk_tail = H.col(k).tail(m - k - 1); Ref<VectorType> Hk_tail = H.col(k).tail(m - k - 1);
v.tail(m - k).makeHouseholder(Hk_tail, tau.coeffRef(k), beta); v.tail(m - k).makeHouseholder(Hk_tail, tau.coeffRef(k), beta);
// apply Householder reflection H_{k} to v // apply Householder reflection H_{k} to v
v.tail(m - k).applyHouseholderOnTheLeft(Hk_tail, tau.coeffRef(k), workspace.data()); v.tail(m - k).applyHouseholderOnTheLeft(Hk_tail, tau.coeffRef(k), workspace.data());
} }
} }
if (k > 1) { if (k > 1)
for (Index i = 0; i < k - 1; ++i) { {
for (Index i = 0; i < k - 1; ++i)
{
// apply old Givens rotations to v // apply old Givens rotations to v
v.applyOnTheLeft(i, i + 1, G[i].adjoint()); v.applyOnTheLeft(i, i + 1, G[i].adjoint());
} }
} }
if (k<m && v(k) != (Scalar) 0) { if (k<m && v(k) != (Scalar) 0)
{
// determine next Givens rotation // determine next Givens rotation
G[k - 1].makeGivens(v(k - 1), v(k)); G[k - 1].makeGivens(v(k - 1), v(k));
@ -153,11 +155,11 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
bool stop = (k==m || abs(w(k)) < tol * r0Norm || iters == maxIters); bool stop = (k==m || abs(w(k)) < tol * r0Norm || iters == maxIters);
if (stop || k == restart) { if (stop || k == restart)
{
// solve upper triangular system // solve upper triangular system
VectorType y = w.head(k); VectorType y = w.head(k);
H.topLeftCorner(k, k).template triangularView < Eigen::Upper > ().solveInPlace(y); H.topLeftCorner(k, k).template triangularView <Upper>().solveInPlace(y);
// use Horner-like scheme to calculate solution vector // use Horner-like scheme to calculate solution vector
VectorType x_new = y(k - 1) * VectorType::Unit(m, k - 1); VectorType x_new = y(k - 1) * VectorType::Unit(m, k - 1);
@ -165,7 +167,8 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
// apply Householder reflection H_{k} to x_new // apply Householder reflection H_{k} to x_new
x_new.tail(m - k + 1).applyHouseholderOnTheLeft(H.col(k - 1).tail(m - k), tau.coeffRef(k - 1), workspace.data()); x_new.tail(m - k + 1).applyHouseholderOnTheLeft(H.col(k - 1).tail(m - k), tau.coeffRef(k - 1), workspace.data());
for (Index i = k - 2; i >= 0; --i) { for (Index i = k - 2; i >= 0; --i)
{
x_new += y(i) * VectorType::Unit(m, i); x_new += y(i) * VectorType::Unit(m, i);
// apply Householder reflection H_{i} to x_new // apply Householder reflection H_{i} to x_new
x_new.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data()); x_new.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data());
@ -173,9 +176,12 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
x += x_new; x += x_new;
if (stop) { if (stop)
{
return true; return true;
} else { }
else
{
k=0; k=0;
// reset data for restart // reset data for restart
@ -190,12 +196,8 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
// generate first Householder vector // generate first Householder vector
r0.makeHouseholder(H0_tail, tau.coeffRef(0), beta); r0.makeHouseholder(H0_tail, tau.coeffRef(0), beta);
w(0)=(Scalar) beta; w(0)=(Scalar) beta;
} }
} }
} }
return false; return false;