diff options
Diffstat (limited to 'unsupported/Eigen/src/IterativeSolvers/MINRES.h')
| -rw-r--r-- | unsupported/Eigen/src/IterativeSolvers/MINRES.h | 70 |
1 files changed, 39 insertions, 31 deletions
diff --git a/unsupported/Eigen/src/IterativeSolvers/MINRES.h b/unsupported/Eigen/src/IterativeSolvers/MINRES.h index 0e56342a8..30f26aa50 100644 --- a/unsupported/Eigen/src/IterativeSolvers/MINRES.h +++ b/unsupported/Eigen/src/IterativeSolvers/MINRES.h @@ -37,22 +37,31 @@ namespace Eigen { typedef typename Dest::Scalar Scalar; typedef Matrix<Scalar,Dynamic,1> VectorType; + // Check for zero rhs + const RealScalar rhsNorm2(rhs.squaredNorm()); + if(rhsNorm2 == 0) + { + x.setZero(); + iters = 0; + tol_error = 0; + return; + } + // initialize const int maxIters(iters); // initialize maxIters to iters const int N(mat.cols()); // the size of the matrix - const RealScalar rhsNorm2(rhs.squaredNorm()); const RealScalar threshold2(tol_error*tol_error*rhsNorm2); // convergence threshold (compared to residualNorm2) // Initialize preconditioned Lanczos -// VectorType v_old(N); // will be initialized inside loop + VectorType v_old(N); // will be initialized inside loop VectorType v( VectorType::Zero(N) ); //initialize v VectorType v_new(rhs-mat*x); //initialize v_new RealScalar residualNorm2(v_new.squaredNorm()); -// VectorType w(N); // will be initialized inside loop + VectorType w(N); // will be initialized inside loop VectorType w_new(precond.solve(v_new)); // initialize w_new // RealScalar beta; // will be initialized inside loop RealScalar beta_new2(v_new.dot(w_new)); - eigen_assert(beta_new2 >= 0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE"); + eigen_assert(beta_new2 >= 0.0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE"); RealScalar beta_new(sqrt(beta_new2)); const RealScalar beta_one(beta_new); v_new /= beta_new; @@ -62,14 +71,14 @@ namespace Eigen { RealScalar c_old(1.0); RealScalar s(0.0); // the sine of the Givens rotation RealScalar s_old(0.0); // the sine of the Givens rotation -// VectorType p_oold(N); // will be initialized in loop + VectorType p_oold(N); // will be initialized in loop VectorType p_old(VectorType::Zero(N)); // initialize p_old=0 VectorType p(p_old); // initialize p=0 RealScalar eta(1.0); iters = 0; // reset iters - while ( iters < maxIters ){ - + while ( iters < maxIters ) + { // Preconditioned Lanczos /* Note that there are 4 variants on the Lanczos algorithm. These are * described in Paige, C. C. (1972). Computational variants of @@ -81,17 +90,17 @@ namespace Eigen { * A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM (1987). */ const RealScalar beta(beta_new); -// v_old = v; // update: at first time step, this makes v_old = 0 so value of beta doesn't matter - const VectorType v_old(v); // NOT SURE IF CREATING v_old EVERY ITERATION IS EFFICIENT + v_old = v; // update: at first time step, this makes v_old = 0 so value of beta doesn't matter +// const VectorType v_old(v); // NOT SURE IF CREATING v_old EVERY ITERATION IS EFFICIENT v = v_new; // update -// w = w_new; // update - const VectorType w(w_new); // NOT SURE IF CREATING w EVERY ITERATION IS EFFICIENT + w = w_new; // update +// const VectorType w(w_new); // NOT SURE IF CREATING w EVERY ITERATION IS EFFICIENT v_new.noalias() = mat*w - beta*v_old; // compute v_new const RealScalar alpha = v_new.dot(w); v_new -= alpha*v; // overwrite v_new w_new = precond.solve(v_new); // overwrite w_new beta_new2 = v_new.dot(w_new); // compute beta_new - eigen_assert(beta_new2 >= 0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE"); + eigen_assert(beta_new2 >= 0.0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE"); beta_new = sqrt(beta_new2); // compute beta_new v_new /= beta_new; // overwrite v_new for next iteration w_new /= beta_new; // overwrite w_new for next iteration @@ -107,21 +116,28 @@ namespace Eigen { s=beta_new/r1; // new sine // Update solution -// p_oold = p_old; - const VectorType p_oold(p_old); // NOT SURE IF CREATING p_oold EVERY ITERATION IS EFFICIENT + p_oold = p_old; +// const VectorType p_oold(p_old); // NOT SURE IF CREATING p_oold EVERY ITERATION IS EFFICIENT p_old = p; p.noalias()=(w-r2*p_old-r3*p_oold) /r1; // IS NOALIAS REQUIRED? x += beta_one*c*eta*p; + + /* Update the squared residual. Note that this is the estimated residual. + The real residual |Ax-b|^2 may be slightly larger */ residualNorm2 *= s*s; - if ( residualNorm2 < threshold2){ + if ( residualNorm2 < threshold2) + { break; } eta=-s*eta; // update eta iters++; // increment iteration number (for output purposes) } - tol_error = std::sqrt(residualNorm2 / rhsNorm2); // return error. Note that this is the estimated error. The real error |Ax-b|/|b| may be slightly larger + + /* Compute error. Note that this is the estimated error. The real + error |Ax-b|/|b| may be slightly larger */ + tol_error = std::sqrt(residualNorm2 / rhsNorm2); } } @@ -174,20 +190,7 @@ namespace Eigen { * \endcode * * By default the iterations start with x=0 as an initial guess of the solution. - * One can control the start using the solveWithGuess() method. Here is a step by - * step execution example starting with a random guess and printing the evolution - * of the estimated error: - * * \code - * x = VectorXd::Random(n); - * mr.setMaxIterations(1); - * int i = 0; - * do { - * x = mr.solveWithGuess(b,x); - * std::cout << i << " : " << mr.error() << std::endl; - * ++i; - * } while (mr.info()!=Success && i<100); - * \endcode - * Note that such a step by step excution is slightly slower. + * One can control the start using the solveWithGuess() method. * * \sa class ConjugateGradient, BiCGSTAB, SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner */ @@ -250,6 +253,11 @@ namespace Eigen { template<typename Rhs,typename Dest> void _solveWithGuess(const Rhs& b, Dest& x) const { + typedef typename internal::conditional<UpLo==(Lower|Upper), + const MatrixType&, + SparseSelfAdjointView<const MatrixType, UpLo> + >::type MatrixWrapperType; + m_iterations = Base::maxIterations(); m_error = Base::m_tolerance; @@ -259,7 +267,7 @@ namespace Eigen { m_error = Base::m_tolerance; typename Dest::ColXpr xj(x,j); - internal::minres(mp_matrix->template selfadjointView<UpLo>(), b.col(j), xj, + internal::minres(MatrixWrapperType(*mp_matrix), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error); } |