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Idrs refactoring
This commit is contained in:
Jens Wehner
Rasmus Munk Larsen
parent
f63c6dd1f9
commit
4ee2e9b340
@ -9,17 +9,14 @@
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_IDRS_H
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#define EIGEN_IDRS_H
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#include "./InternalHeaderCheck.h"
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namespace Eigen
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{
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namespace Eigen {
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namespace internal
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{
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namespace internal {
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/** \internal Low-level Induced Dimension Reduction algorithm
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\param A The matrix A
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\param b The right hand side vector b
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@ -31,16 +28,15 @@ namespace Eigen
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\param S On input Number of the dimension of the shadow space.
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\param smoothing switches residual smoothing on.
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\param angle small omega lead to faster convergence at the expense of numerical stability
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\param replacement switches on a residual replacement strategy to increase accuracy of residual at the expense of more Mat*vec products
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\return false in the case of numerical issue, for example a break down of IDRS.
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\param replacement switches on a residual replacement strategy to increase accuracy of residual at the
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expense of more Mat*vec products \return false in the case of numerical issue, for example a break down of IDRS.
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*/
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template <typename Vector, typename RealScalar>
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typename Vector::Scalar omega(const Vector& t, const Vector& s, RealScalar angle)
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{
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typename Vector::Scalar omega(const Vector& t, const Vector& s, RealScalar angle) {
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using numext::abs;
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typedef typename Vector::Scalar Scalar;
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const RealScalar ns = s.norm();
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const RealScalar nt = t.norm();
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const RealScalar ns = s.StableNorm();
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const RealScalar nt = t.StableNorm();
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const Scalar ts = t.dot(s);
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const RealScalar rho = abs(ts / (nt * ns));
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@ -58,10 +54,9 @@ namespace Eigen
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}
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template <typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
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bool idrs(const MatrixType& A, const Rhs& b, Dest& x, const Preconditioner& precond,
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Index& iter,
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typename Dest::RealScalar& relres, Index S, bool smoothing, typename Dest::RealScalar angle, bool replacement)
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{
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bool idrs(const MatrixType& A, const Rhs& b, Dest& x, const Preconditioner& precond, Index& iter,
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typename Dest::RealScalar& relres, Index S, bool smoothing, typename Dest::RealScalar angle,
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bool replacement) {
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typedef typename Dest::RealScalar RealScalar;
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typedef typename Dest::Scalar Scalar;
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typedef Matrix<Scalar, Dynamic, 1> VectorType;
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@ -82,10 +77,9 @@ namespace Eigen
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P = (qr.householderQ() * DenseMatrixType::Identity(N, S));
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}
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const RealScalar normb = b.norm();
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const RealScalar normb = b.StableNorm();
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if (internal::isApprox(normb, RealScalar(0)))
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{
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if (internal::isApprox(normb, RealScalar(0))) {
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// Solution is the zero vector
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x.setZero();
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iter = 0;
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@ -105,24 +99,20 @@ namespace Eigen
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// It only happens if things go very wrong. Too many restarts may ruin the convergence.
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const RealScalar mp = RealScalar(1e3) * NumTraits<Scalar>::epsilon();
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// Compute initial residual
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const RealScalar tolb = tol * normb; // Relative tolerance
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VectorType r = b - A * x;
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VectorType x_s, r_s;
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if (smoothing)
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{
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if (smoothing) {
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x_s = x;
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r_s = r;
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}
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RealScalar normr = r.norm();
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RealScalar normr = r.StableNorm();
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if (normr <= tolb)
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{
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if (normr <= tolb) {
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// Initial guess is a good enough solution
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iter = 0;
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relres = normr / normb;
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@ -138,13 +128,11 @@ namespace Eigen
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// Main iteration loop, guild G-spaces:
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iter = 0;
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while (normr > tolb && iter < maxit)
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{
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while (normr > tolb && iter < maxit) {
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// New right hand size for small system:
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VectorType f = (r.adjoint() * P).adjoint();
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for (Index k = 0; k < S; ++k)
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{
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for (Index k = 0; k < S; ++k) {
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// Solve small system and make v orthogonal to P:
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// c = M(k:s,k:s)\f(k:s);
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lu_solver.compute(M.block(k, k, S - k, S - k));
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@ -159,8 +147,7 @@ namespace Eigen
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G.col(k) = A * U.col(k);
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// Bi-Orthogonalise the new basis vectors:
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for (Index i = 0; i < k-1 ; ++i)
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{
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for (Index i = 0; i < k - 1; ++i) {
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// alpha = ( P(:,i)'*G(:,k) )/M(i,i);
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Scalar alpha = P.col(i).dot(G.col(k)) / M(i, i);
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G.col(k) = G.col(k) - alpha * G.col(i);
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@ -171,8 +158,7 @@ namespace Eigen
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// M(k:s,k) = (G(:,k)'*P(:,k:s))';
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M.block(k, k, S - k, 1) = (G.col(k).adjoint() * P.rightCols(S - k)).adjoint();
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if (internal::isApprox(M(k,k), Scalar(0)))
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{
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if (internal::isApprox(M(k, k), Scalar(0))) {
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return false;
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}
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@ -180,38 +166,33 @@ namespace Eigen
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Scalar beta = f(k) / M(k, k);
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r = r - beta * G.col(k);
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x = x + beta * U.col(k);
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normr = r.norm();
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normr = r.StableNorm();
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if (replacement && normr > tolb / mp)
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{
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if (replacement && normr > tolb / mp) {
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trueres = true;
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}
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// Smoothing:
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if (smoothing)
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{
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if (smoothing) {
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t = r_s - r;
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// gamma is a Scalar, but the conversion is not allowed
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Scalar gamma = t.dot(r_s) / t.norm();
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Scalar gamma = t.dot(r_s) / t.StableNorm();
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r_s = r_s - gamma * t;
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x_s = x_s - gamma * (x_s - x);
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normr = r_s.norm();
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normr = r_s.StableNorm();
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}
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if (normr < tolb || iter == maxit)
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{
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if (normr < tolb || iter == maxit) {
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break;
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}
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// New f = P'*r (first k components are zero)
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if (k < S-1)
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{
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if (k < S - 1) {
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f.segment(k + 1, S - (k + 1)) = f.segment(k + 1, S - (k + 1)) - beta * M.block(k + 1, k, S - (k + 1), 1);
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}
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} // end for
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if (normr < tolb || iter == maxit)
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{
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if (normr < tolb || iter == maxit) {
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break;
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}
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@ -227,44 +208,39 @@ namespace Eigen
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// Computation of a new omega
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om = internal::omega(t, r, angle);
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if (om == RealScalar(0.0))
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{
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if (om == RealScalar(0.0)) {
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return false;
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}
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r = r - om * t;
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x = x + om * v;
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normr = r.norm();
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normr = r.StableNorm();
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if (replacement && normr > tolb / mp)
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{
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if (replacement && normr > tolb / mp) {
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trueres = true;
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}
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// Residual replacement?
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if (trueres && normr < normb)
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{
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if (trueres && normr < normb) {
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r = b - A * x;
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trueres = false;
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replacements++;
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}
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// Smoothing:
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if (smoothing)
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{
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if (smoothing) {
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t = r_s - r;
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Scalar gamma = t.dot(r_s) /t.norm();
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Scalar gamma = t.dot(r_s) / t.StableNorm();
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r_s = r_s - gamma * t;
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x_s = x_s - gamma * (x_s - x);
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normr = r_s.norm();
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normr = r_s.StableNorm();
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}
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iter++;
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} // end while
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if (smoothing)
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{
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if (smoothing) {
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x = x_s;
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}
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relres = normr / normb;
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@ -276,21 +252,19 @@ namespace Eigen
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template <typename MatrixType_, typename Preconditioner_ = DiagonalPreconditioner<typename MatrixType_::Scalar> >
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class IDRS;
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namespace internal
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{
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namespace internal {
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template <typename MatrixType_, typename Preconditioner_>
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struct traits<Eigen::IDRS<MatrixType_, Preconditioner_> >
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{
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struct traits<Eigen::IDRS<MatrixType_, Preconditioner_> > {
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typedef MatrixType_ MatrixType;
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typedef Preconditioner_ Preconditioner;
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};
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} // namespace internal
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/** \ingroup IterativeLinearSolvers_Module
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* \brief The Induced Dimension Reduction method (IDR(s)) is a short-recurrences Krylov method for sparse square problems.
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* \brief The Induced Dimension Reduction method (IDR(s)) is a short-recurrences Krylov method for sparse square
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* problems.
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*
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* This class allows to solve for A.x = b sparse linear problems. The vectors x and b can be either dense or sparse.
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* he Induced Dimension Reduction method, IDR(), is a robust and efficient short-recurrence Krylov subspace method for
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@ -330,9 +304,7 @@ namespace Eigen
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* \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
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*/
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template <typename MatrixType_, typename Preconditioner_>
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class IDRS : public IterativeSolverBase<IDRS<MatrixType_, Preconditioner_> >
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{
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class IDRS : public IterativeSolverBase<IDRS<MatrixType_, Preconditioner_> > {
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public:
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typedef MatrixType_ MatrixType;
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typedef typename MatrixType::Scalar Scalar;
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@ -366,9 +338,8 @@ namespace Eigen
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matrix A, or modify a copy of A.
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*/
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template <typename MatrixDerived>
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explicit IDRS(const EigenBase<MatrixDerived>& A) : Base(A.derived()), m_S(4), m_smoothing(false),
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m_angle(RealScalar(0.7)), m_residual(false) {}
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explicit IDRS(const EigenBase<MatrixDerived>& A)
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: Base(A.derived()), m_S(4), m_smoothing(false), m_angle(RealScalar(0.7)), m_residual(false) {}
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/** \internal */
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/** Loops over the number of columns of b and does the following:
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@ -376,21 +347,19 @@ namespace Eigen
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2. Calls the function that has the core solver routine
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*/
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template <typename Rhs, typename Dest>
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void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const
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{
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void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const {
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m_iterations = Base::maxIterations();
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m_error = Base::m_tolerance;
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bool ret = internal::idrs(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error, m_S,m_smoothing,m_angle,m_residual);
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bool ret = internal::idrs(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error, m_S, m_smoothing, m_angle,
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m_residual);
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m_info = (!ret) ? NumericalIssue : m_error <= Base::m_tolerance ? Success : NoConvergence;
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}
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/** Sets the parameter S, indicating the dimension of the shadow space. Default is 4*/
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void setS(Index S)
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{
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if (S < 1)
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{
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void setS(Index S) {
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if (S < 1) {
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S = 4;
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}
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@ -403,10 +372,7 @@ namespace Eigen
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operations. Although monotonic decrease of the residual norms is a
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desirable property, the rate of convergence of the unsmoothed process and
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the smoothed process is basically the same. Default is off */
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void setSmoothing(bool smoothing)
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{
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m_smoothing=smoothing;
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}
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void setSmoothing(bool smoothing) { m_smoothing = smoothing; }
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/** The angle must be a real scalar. In IDR(s), a value for the
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iteration parameter omega must be chosen in every s+1th step. The most
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@ -418,19 +384,12 @@ namespace Eigen
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between accurate computations and reduction of the residual norm. The
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parameter angle =0.7 (”maintaining the convergence strategy”)
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results in such a compromise. */
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void setAngle(RealScalar angle)
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{
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m_angle=angle;
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}
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void setAngle(RealScalar angle) { m_angle = angle; }
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/** The parameter replace is a logical that determines whether a
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residual replacement strategy is employed to increase the accuracy of the
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solution. */
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void setResidualUpdate(bool update)
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{
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m_residual=update;
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}
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void setResidualUpdate(bool update) { m_residual = update; }
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};
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} // namespace Eigen
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