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Daniel Richtmann
Daniel Richtmann
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@ -29,7 +29,6 @@ directory
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#ifndef GRID_GENERALISED_MINIMAL_RESIDUAL_H
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#define GRID_GENERALISED_MINIMAL_RESIDUAL_H
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///////////////////////////////////////////////////////////////////////////////////////////////////////
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// from Y. Saad - Iterative Methods for Sparse Linear Systems, PP 172
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// Compute r0 = b − Ax0 , β := ||r0||2 , and v1 := r0 /β
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// For j = 1, 2, ..., m Do:
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@ -47,156 +46,274 @@ directory
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// want to solve Ax = b -> A = LinOp, psi = x, b = src
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namespace Grid
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{
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template< class Field >
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class GeneralisedMinimalResidual : public OperatorFunction< Field >
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{
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public:
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bool ErrorOnNoConverge; // Throw an assert when GMRES fails to converge,
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// defaults to True.
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RealD Tolerance;
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Integer MaxIterations;
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Integer IterationsToComplete; // Number of iterations the GMRES took to
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// finish. Filled in upon completion
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namespace Grid {
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GeneralisedMinimalResidual( RealD tol,
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Integer maxit,
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bool err_on_no_conv = true )
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: Tolerance( tol )
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, MaxIterations( maxit )
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, ErrorOnNoConverge( err_on_no_conv ){};
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template<class Field>
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class GeneralisedMinimalResidual : public OperatorFunction<Field> {
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public:
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bool ErrorOnNoConverge; // Throw an assert when GMRES fails to converge,
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// defaults to True.
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RealD Tolerance;
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Integer MaxIterations;
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Integer IterationsToComplete; // Number of iterations the GMRES took to
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// finish. Filled in upon completion
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// want to solve Ax = b -> A = LinOp, psi = x, b = src
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GeneralisedMinimalResidual(RealD tol,
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Integer maxit,
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bool err_on_no_conv = true)
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: Tolerance(tol), MaxIterations(maxit), ErrorOnNoConverge(err_on_no_conv){};
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void operator()( LinearOperatorBase< Field > &LinOp,
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const Field & src,
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Field & psi )
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{
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std::cout << GridLogMessage
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<< "GeneralisedMinimalResidual: Start of operator()"
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<< std::endl;
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psi.checkerboard = src.checkerboard;
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conformable( psi, src );
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// want to solve Ax = b -> A = LinOp, psi = x, b = src
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Field r( src );
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Field mmv( src );
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/* void */
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/* operator()(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi)
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* { */
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/* typedef typename Eigen::MatrixXcd MyMatrix; */
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/* typedef typename Eigen::VectorXcd MyVector; */
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std::vector< Field > v( MaxIterations + 1, src );
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/* Field r(src); */
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/* Field w(src); */
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/* Field mmv(src); */
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RealD beta{};
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RealD b{};
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RealD d{};
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/* std::vector<Field> V(MaxIterations + 1, src); */
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/* std::vector<std::complex<double>> y(MaxIterations + 1, 0.); */
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/* std::vector<std::complex<double>> gamma(MaxIterations + 1, 0.); */
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/* std::vector<std::complex<double>> c(MaxIterations + 1, 0.); */
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/* std::vector<std::complex<double>> s(MaxIterations + 1, 0.); */
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Eigen::MatrixXcd H
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= Eigen::MatrixXcd::Zero( MaxIterations + 1, MaxIterations );
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/* int m = MaxIterations; */
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// Compute r0 = b − Ax0 , β := ||r0||2 , and v1 := r0 /β
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LinOp.Op( psi, mmv );
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/* RealD gamma0{}; */
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r = src - mmv;
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beta = norm2( r );
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V[ 0 ] = ( 1 / beta ) * r;
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/* MyMatrix H = Eigen::MatrixXcd::Zero(MaxIterations + 1, MaxIterations); */
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for( auto j = 0; j < MaxIterations; ++j )
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{
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LinOp.Op( V[ j ], mmv );
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/* RealD normPsiSq = norm2(psi); */
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/* RealD normSrcSq = norm2(src); */
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/* RealD TargetResSq = Tolerance * Tolerance * normSrcSq; */
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for( auto i = 0; i < j; ++i )
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{
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std::cout
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<< GridLogMessage
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<< "GeneralisedMinimalResidual: End of inner iteration "
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<< i << std::endl;
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H( i, j ) = innerProduct( mmv, v[ i ] );
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mmv = mmv - H( i, j ) * V[ i ];
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}
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/* LinOp.Op(psi, mmv); */
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H( j + 1, j ) = norm2( mmv );
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/* r = src - mmv; */
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/* gamma[0] = norm2(r); */
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/* std::cout << gamma[0] << std::endl; */
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/* gamma0 = std::real(gamma[0]); */
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/* V[0] = (1. / gamma[0]) * r; */
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std::cout << GridLogMessage << "GeneralisedMinimalResidual: H"
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<< j + 1 << "," << j << "= " << H( j + 1, j )
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<< std::endl;
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if( H( j + 1, j ) == 0. )
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{
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IterationsToComplete = j;
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break;
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}
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/* std::cout << GridLogMessage << std::setprecision(4) */
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/* << "GeneralisedMinimalResidual: psi " << normPsiSq */
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/* << std::endl; */
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/* std::cout << GridLogMessage << std::setprecision(4) */
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/* << "GeneralisedMinimalResidual: src " << normSrcSq */
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/* << std::endl; */
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/* std::cout << GridLogMessage << std::setprecision(4) */
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/* << "GeneralisedMinimalResidual: target " << TargetResSq */
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/* << std::endl; */
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/* std::cout << GridLogMessage << std::setprecision(4) */
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/* << "GeneralisedMinimalResidual: r " << gamma0 <<
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* std::endl; */
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V[ j + 1 ] = ( 1. / H( j + 1, j ) ) * mmv;
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std::cout << GridLogMessage
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<< "GeneralisedMinimalResidual: End of outer iteration "
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<< j << std::endl;
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}
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std::cout << GridLogMessage
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<< "GeneralisedMinimalResidual: End of operator()"
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<< std::endl;
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/* std::cout */
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/* << GridLogIterative << std::setprecision(4) */
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/* << "GeneralisedMinimalResidual: before starting to iterate residual "
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*/
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/* << gamma0 << " target " << TargetResSq << std::endl; */
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/* for(auto j = 0; j < m; ++j) { */
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/* LinOp.Op(V[j], w); */
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/* for(auto i = 0; i <= j; ++i) { */
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/* H(i, j) = innerProduct(V[i], w); */
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/* w = w - H(i, j) * V[i]; */
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/* } */
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/* H(j + 1, j) = norm2(w); */
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/* V[j + 1] = (1. / H(j + 1, j)) * w; */
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/* if(std::abs(H(j + 1, j)) > 1e-15) { */
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/* qrUpdate(gamma, c, s, H, j); */
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/* } */
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/* /\* std::cout << GridLogMessage << "GeneralisedMinimalResidual: H( "
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* *\/ */
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/* /\* << j + 1 << "," << j << " ) = " << H( j + 1, j ) *\/ */
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/* /\* << std::endl; *\/ */
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/* std::cout << GridLogIterative << "GeneralisedMinimalResidual: Iteration
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* " */
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/* << j << " residual " << std::abs(gamma[j + 1]) << " target "
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*/
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/* << TargetResSq << std::endl; */
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/* if(std::abs(gamma[j + 1]) / gamma0 < Tolerance) { */
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/* IterationsToComplete = j; */
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/* break; */
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/* } */
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/* } */
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/* computeSolution(y, gamma, H, V, psi, IterationsToComplete); */
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/* std::cout << GridLogMessage */
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/* << "GeneralisedMinimalResidual: End of operator() after " */
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/* << IterationsToComplete << " iterations" << std::endl; */
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/* RealD normSrc = sqrt(normSrcSq); */
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/* RealD resnorm = sqrt(norm2(mmv)); */
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/* RealD true_residual = resnorm / srcnorm; */
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/* Field result = mmv; */
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/* Field Dx(src); */
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/* Field tmp(src); */
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/* // Test the correctness */
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/* LinOp.Op(result, Dx); */
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/* tmp = Dx - src; */
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/* std::cout << norm2(tmp) << " " << norm2(tmp) / gamma0 << std::endl; */
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/* } */
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void
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operator()(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi) {
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std::cout << "GMRES: Start of operator()" << std::endl;
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int m = MaxIterations;
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Field r(src);
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Field w(src);
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Field Dpsi(src);
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Field Dv(src);
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std::vector<Field> v(m + 1, src);
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Eigen::MatrixXcd H = Eigen::MatrixXcd::Zero(m + 1, m);
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std::vector<std::complex<double>> y(m + 1, 0.);
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std::vector<std::complex<double>> gamma(m + 1, 0.);
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std::vector<std::complex<double>> c(m + 1, 0.);
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std::vector<std::complex<double>> s(m + 1, 0.);
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LinOp.Op(psi, Dpsi);
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r = src - Dpsi;
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RealD beta = norm2(r);
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gamma[0] = beta;
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std::cout << "beta " << beta << std::endl;
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v[0] = (1. / beta) * r;
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// Begin iterating
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for(auto j = 0; j < m; ++j) {
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LinOp.Op(v[j], Dv);
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w = Dv;
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for(auto i = 0; i <= j; ++i) {
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H(i, j) = innerProduct(v[i], w);
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w = w - H(i, j) * v[i];
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}
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H(j + 1, j) = norm2(w);
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v[j + 1] = (1. / H(j + 1, j)) * w;
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// end of arnoldi process, begin of givens rotations
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// apply old Givens rotation
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for(auto i = 0; i < j ; ++i) {
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auto tmp = -s[i] * H(i, j) + c[i] * H(i + 1, j);
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H(i, j) = std::conj(c[i]) * H(i, j) + std::conj(s[i]) * H(i + 1, j);
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H(i + 1, j) = tmp;
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}
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// compute new Givens Rotation
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ComplexD nu = sqrt(std::norm(H(j, j)) + std::norm(H(j + 1, j)));
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c[j] = H(j, j) / nu;
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s[j] = H(j + 1, j) / nu;
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std::cout << "nu" << nu << std::endl;
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std::cout << "H("<<j<<","<<j<<")" << H(j,j) << std::endl;
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std::cout << "H("<<j+1<<","<<j<<")" << H(j+1,j) << std::endl;
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// apply new Givens rotation
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H(j, j) = nu;
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H(j + 1, j) = 0.;
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/* ORDERING??? */
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gamma[j + 1] = -s[j] * gamma[j];
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gamma[j] = std::conj(c[j]) * gamma[j];
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/* for(auto k = 0; k <= j+1 ; ++k) */
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/* std::cout << "k " << k << "nu " << nu << " c["<<k<<"]" << c[k]<< " s["<<k<<"]" << s[k] << " gamma["<<k<<"]" << gamma[k] << std::endl; */
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std::cout << GridLogIterative << "GeneralisedMinimalResidual: Iteration "
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<< j << " residual " << std::abs(gamma[j + 1]) << std::endl; //" target "
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/* << TargetResSq << std::endl; */
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if(std::abs(gamma[j + 1]) / sqrt(beta) < Tolerance) {
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IterationsToComplete = j;
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break;
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}
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}
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// backward substitution
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computeSolution(y, gamma, H, v, psi, IterationsToComplete);
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std::cout << "GMRES: End of operator()" << std::endl;
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}
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private:
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/* void qrUpdate(std::vector<std::complex<double>> &gamma, */
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/* std::vector<std::complex<double>> &c, */
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/* std::vector<std::complex<double>> &s, */
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/* Eigen::MatrixXcd & H, */
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/* int j) { */
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/* ComplexD beta{}; */
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/* // update QR factorization */
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/* // apply previous Givens rotation */
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/* for(auto i = 0; i < j; i++) { */
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/* beta = -s[i] * H(i, j) + c[i] * H(i + 1, j); */
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/* H(i, j) = std::conj(c[i]) * H(i, j) + std::conj(s[i]) * H(i + 1,
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* j); */
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/* H(i + 1, j) = beta; */
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/* } */
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/* // compute current Givens rotation */
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/* beta = sqrt(std::norm(H(j, j)) + std::norm(H(j + 1, j))); */
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/* s[j] = H(j + 1, j) / beta; */
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/* c[j] = H(j, j) / beta; */
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/* /\* std::cout << "beta= " << beta << std::endl; *\/ */
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/* /\* std::cout << "s[j]= " << s[ j ] << std::endl; *\/ */
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/* /\* std::cout << "c[j]= " << c[ j ] << std::endl; *\/ */
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/* /\* std::cout << "gamma[j+1]= " << gamma[ j + 1 ] << std::endl; *\/ */
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/* /\* std::cout << "gamma[j]= " << gamma[ j ] << std::endl; *\/ */
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/* // update right column */
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/* gamma[j + 1] = -s[j] * gamma[j]; */
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/* gamma[j] = std::conj(c[j]) * gamma[j]; */
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/* /\* std::cout << "gamma[j+1]= " << gamma[ j + 1 ] << std::endl; *\/ */
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/* /\* std::cout << "gamma[j]= " << gamma[ j ] << std::endl; *\/ */
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/* // apply current Givens rotation */
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/* H(j, j) = beta; */
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/* H(j + 1, j) = 0.; */
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/* /\* std::cout << "H(j,j)= " << H( j, j ) << std::endl; *\/ */
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/* /\* std::cout << "H(j+1,j)= " << H( j + 1, j ) << std::endl; *\/ */
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/* } */
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void computeSolution(std::vector<std::complex<double>> & y,
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std::vector<std::complex<double>> const &gamma,
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Eigen::MatrixXcd const & H,
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std::vector<Field> const & v,
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Field & x,
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int j) {
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for(auto i = j; i >= 0; i--) {
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y[i] = gamma[i];
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for(auto k = i + 1; k <= j; k++)
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y[i] -= H(i, k) * y[k];
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y[i] /= H(i, i);
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}
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/* if(true) // TODO ??? */
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/* { */
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/* for(auto i = 0; i <= j; i++) */
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/* x = x + v[i] * y[i]; */
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/* } else { */
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x = y[0] * v[0];
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for(auto i = 1; i <= j; i++)
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x = x + v[i] * y[i];
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/* } */
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}
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};
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}
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#endif
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// Note: The DD-αAMG codebase turns around the Hessenberg matrix
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void arnoldiStep()
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{
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w = D * V[ j ];
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for( auto i = 0; i <= j; ++i )
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H( i, j ) = innerProduct( V[ j + 1 ], w );
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w = w - H( i, j ) * V[ i ];
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H( j + 1, j ) = norm2( w );
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V[ j + 1 ] = w / H( j + 1, j );
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}
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void qr_update_PRECISION()
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{
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// update QR factorization
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// apply previous Givens rotation
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for( auto i = 0; i < j; i++ )
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{
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beta = -s[ i ] * H( i, j ) + c[ i ] * H( i + 1, j );
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H( i, j ) = std::conj( c[ i ] ) * H( i, j )
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+ std::conj( s[ i ] ) * H( i + 1, j );
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H( i + 1, j ) = beta;
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}
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// compute current Givens rotation
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beta = sqrt( std::norm( H( j, j ) ) + std::norm( H( j, j + 1 ) ) );
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s[ j ] = H( j + 1, j ) / beta;
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c[ j ] = H( j, j ) / beta;
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// update right column
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gamma[ j + 1 ] = -s[ j ] * gamma[ j ];
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gamma[ j ] = std::conj( c[ j ] ) * gamma[ j ];
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// apply current Givens rotation
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H( j, j ) = beta;
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H( j + 1, j ) = 0;
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}
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// check
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void compute_solution_PRECISION()
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{
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for( auto i = j; i >= 0; i-- )
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{
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y[ i ] = gamma[ i ];
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for( auto k = i + 1; k <= j; k++ )
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y[ i ] -= H( i, k ) * y[ k ];
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y[ i ] /= H( i, i );
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}
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if( true ) // TODO ???
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{
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for( i = 0; i <= j; i++ )
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x = x + V[ i ] * y[ i ];
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}
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else
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{
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x = y[ 0 ] * V[ 0 ];
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for( i = 1; i <= j; i++ )
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x = x + V[ i ] * y[ i ];
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}
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}
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