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First working version of GMRES + a test for Wilson fermions

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This commit is contained in:
Daniel Richtmann 2017-11-08 13:56:41 +01:00
parent 56d32a4afb
commit 7f4ed6c2e5
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GPG Key ID: B33C490AF0772057
2 changed files with 92 additions and 226 deletions
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316
lib/algorithms/iterative/GeneralisedMinimalResidual.h
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@ -53,20 +53,40 @@ class GeneralisedMinimalResidual : public OperatorFunction<Field> {
public: public:
bool ErrorOnNoConverge; // Throw an assert when GMRES fails to converge, bool ErrorOnNoConverge; // Throw an assert when GMRES fails to converge,
// defaults to True. // defaults to True.
RealD Tolerance; RealD Tolerance;
Integer MaxIterations; Integer MaxIterations;
Integer RestartLength; Integer RestartLength;
Integer IterationsToComplete; // Number of iterations the GMRES took to Integer IterationCount; // Number of iterations the GMRES took to finish,
// finish. Filled in upon completion // filled in upon completion
GridStopWatch MatrixTimer; GridStopWatch MatrixTimer;
GridStopWatch PrecTimer; GridStopWatch PrecTimer;
GridStopWatch LinalgTimer; GridStopWatch LinalgTimer;
GridStopWatch QrTimer;
GridStopWatch CompSolutionTimer;
Eigen::MatrixXcd H;
std::vector<std::complex<double>> y;
std::vector<std::complex<double>> gamma;
std::vector<std::complex<double>> c;
std::vector<std::complex<double>> s;
GeneralisedMinimalResidual(RealD tol, GeneralisedMinimalResidual(RealD tol,
Integer maxit, Integer maxit,
Integer restart_length, Integer restart_length,
bool err_on_no_conv = true) bool err_on_no_conv = true)
: Tolerance(tol), MaxIterations(maxit), RestartLength(restart_length), ErrorOnNoConverge(err_on_no_conv){}; : Tolerance(tol)
, MaxIterations(maxit)
, RestartLength(restart_length)
, ErrorOnNoConverge(err_on_no_conv)
, H(Eigen::MatrixXcd::Zero(RestartLength, RestartLength + 1)) // sizes taken from DD-αAMG code base
, y(RestartLength + 1, 0.)
, gamma(RestartLength + 1, 0.)
, c(RestartLength + 1, 0.)
, s(RestartLength + 1, 0.) {};
void operator()(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi) { void operator()(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi) {
@ -82,17 +102,21 @@ class GeneralisedMinimalResidual : public OperatorFunction<Field> {
Field r(src._grid); Field r(src._grid);
std::cout << GridLogIterative << std::setprecision(4) << std::scientific << "MinimalResidual: guess " << guess << std::endl; std::cout << std::setprecision(4) << std::scientific << std::endl;
std::cout << GridLogIterative << std::setprecision(4) << std::scientific << "MinimalResidual: src " << ssq << std::endl; std::cout << GridLogIterative << "GeneralisedMinimalResidual: guess " << guess << std::endl;
std::cout << GridLogIterative << "GeneralisedMinimalResidual: src " << ssq << std::endl;
PrecTimer.Reset(); PrecTimer.Reset();
MatrixTimer.Reset(); MatrixTimer.Reset();
LinalgTimer.Reset(); LinalgTimer.Reset();
QrTimer.Reset();
CompSolutionTimer.Reset();
GridStopWatch SolverTimer; GridStopWatch SolverTimer;
SolverTimer.Start(); SolverTimer.Start();
int iterations = 0; IterationCount = 0;
for (int k=0; k<MaxIterations; k++) { for (int k=0; k<MaxIterations; k++) {
cp = outerLoopBody(LinOp, src, psi, rsd_sq); cp = outerLoopBody(LinOp, src, psi, rsd_sq);
@ -109,21 +133,23 @@ class GeneralisedMinimalResidual : public OperatorFunction<Field> {
RealD resnorm = sqrt(norm2(r)); RealD resnorm = sqrt(norm2(r));
RealD true_residual = resnorm / srcnorm; RealD true_residual = resnorm / srcnorm;
std::cout << GridLogMessage << "GeneralizedMinimalResidual: Converged on iteration " << k << std::endl; std::cout << GridLogMessage << "GeneralisedMinimalResidual: Converged on iteration " << IterationCount << std::endl;
std::cout << GridLogMessage << "\tComputed residual " << sqrt(cp / ssq) << std::endl; std::cout << GridLogMessage << "\tComputed residual " << sqrt(cp / ssq) << std::endl;
std::cout << GridLogMessage << "\tTrue residual " << true_residual << std::endl; std::cout << GridLogMessage << "\tTrue residual " << true_residual << std::endl;
std::cout << GridLogMessage << "\tTarget " << Tolerance << std::endl; std::cout << GridLogMessage << "\tTarget " << Tolerance << std::endl;
std::cout << GridLogMessage << "GeneralizedMinimalResidual Time breakdown" << std::endl; std::cout << GridLogMessage << "GeneralisedMinimalResidual Time breakdown" << std::endl;
std::cout << GridLogMessage << "\tElapsed " << SolverTimer.Elapsed() << std::endl; std::cout << GridLogMessage << "\tElapsed " << SolverTimer.Elapsed() << std::endl;
std::cout << GridLogMessage << "\tPrecon " << PrecTimer.Elapsed() << std::endl; std::cout << GridLogMessage << "\tPrecon " << PrecTimer.Elapsed() << std::endl;
std::cout << GridLogMessage << "\tMatrix " << MatrixTimer.Elapsed() << std::endl; std::cout << GridLogMessage << "\tMatrix " << MatrixTimer.Elapsed() << std::endl;
std::cout << GridLogMessage << "\tLinalg " << LinalgTimer.Elapsed() << std::endl; std::cout << GridLogMessage << "\tLinalg " << LinalgTimer.Elapsed() << std::endl;
std::cout << GridLogMessage << "\tQR " << QrTimer.Elapsed() << std::endl;
std::cout << GridLogMessage << "\tCompSol " << CompSolutionTimer.Elapsed() << std::endl;
return; return;
} }
} }
std::cout << GridLogMessage << "GeneralizedMinimalResidual did NOT converge" << std::endl; std::cout << GridLogMessage << "GeneralisedMinimalResidual did NOT converge" << std::endl;
if (ErrorOnNoConverge) if (ErrorOnNoConverge)
assert(0); assert(0);
@ -136,45 +162,43 @@ class GeneralisedMinimalResidual : public OperatorFunction<Field> {
Field w(src._grid); Field w(src._grid);
Field r(src._grid); Field r(src._grid);
auto whatDoWePutHere = 1; std::vector<Field> v(RestartLength + 1, src._grid);
std::vector<Field> v(whatDoWePutHere, src._grid); // in MG code: m + 1
std::vector<std::complex<double>> gamma(whatDoWePutHere, 0.); // in MG code: m + 1
MatrixTimer.Start(); MatrixTimer.Start();
LinOp.Op(psi, w); // w = D * psi LinOp.Op(psi, w);
MatrixTimer.Stop(); MatrixTimer.Stop();
LinalgTimer.Start(); LinalgTimer.Start();
r = src - w; r = src - w;
gamma[0] = norm2(r); // do we need an explicit cast? // in MG code: sqrt around/within the norm gamma[0] = sqrt(norm2(r));
v[0] = (1. / gamma[0]) * r; v[0] = (1. / gamma[0]) * r;
LinalgTimer.Stop(); LinalgTimer.Stop();
for (int i=0; i<whatDoWePutHere; i++) { // in MG code: p->restart_length for (int i=0; i<RestartLength; i++) {
arnoldiStep(LinOp, v, w, whatDoWePutHere); // in MG code: j IterationCount++;
/////////////////////////////////////////////////////////////////////// arnoldiStep(LinOp, v, w, i);
// Begin of QR Update /////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
qrUpdate(whatDoWePutHere); // in MG code: j qrUpdate(i);
/////////////////////////////////////////////////////////////////////// cp = std::norm(gamma[i+1]);
// End of QR Update ///////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
if ((whatDoWePutHere) || (cp < rsd_sq)) { // in VPGCR code: (k == nstep-1) std::cout << GridLogIterative << "GeneralisedMinimalResidual: Iteration " << IterationCount
<< " residual " << cp << " target " << rsd_sq << std::endl;
// compute solution if ((i == RestartLength - 1) || (cp <= rsd_sq)) {
computeSolution(v, psi, i);
return cp; return cp;
} }
} }
assert(0); // Never reached
return cp;
} }
void arnoldiStep(LinearOperatorBase<Field> &LinOp, std::vector<Field> &v, Field &w, int iter) { void arnoldiStep(LinearOperatorBase<Field> &LinOp, std::vector<Field> &v, Field &w, int iter) {
@ -184,223 +208,65 @@ class GeneralisedMinimalResidual : public OperatorFunction<Field> {
MatrixTimer.Stop(); MatrixTimer.Stop();
LinalgTimer.Start(); LinalgTimer.Start();
for(int i = 0; i <= iter; ++i) { for (int i = 0; i <= iter; ++i) {
H(i, iter) = innerProduct(v[i], w); H(iter, i) = innerProduct(v[i], w);
w = w - H(i, iter) * v[i]; w = w - H(iter, i) * v[i];
} }
H(iter + 1, iter) = norm2(w); // in MG code: sqrt around/within the norm H(iter, iter + 1) = sqrt(norm2(w));
v[iter + 1] = (1. / H(iter + 1, iter)) * w; v[iter + 1] = (1. / H(iter, iter + 1)) * w;
LinalgTimer.Stop(); LinalgTimer.Stop();
} }
void qrUpdate(int iter) { void qrUpdate(int iter) {
for(int i = 0; i < iter ; ++i) { QrTimer.Start();
auto tmp = -s[i] * H(i, iter) + c[i] * H(i + 1, iter); for (int i = 0; i < iter ; ++i) {
H(i, iter) = std::conj(c[i]) * H(i, iter) + std::conj(s[i]) * H(i + 1, iter); auto tmp = -s[i] * H(iter, i) + c[i] * H(iter, i + 1);
H(i + 1, iter) = tmp; H(iter, i) = std::conj(c[i]) * H(iter, i) + std::conj(s[i]) * H(iter, i + 1);
H(iter, i + 1) = tmp;
} }
// compute new Givens Rotation // Compute new Givens Rotation
ComplexD nu = sqrt(std::norm(H(iter, iter)) + std::norm(H(iter + 1, iter))); ComplexD nu = sqrt(std::norm(H(iter, iter)) + std::norm(H(iter, iter + 1)));
c[iter] = H(iter, iter) / nu; c[iter] = H(iter, iter) / nu;
s[iter] = H(iter + 1, iter) / nu; s[iter] = H(iter, iter + 1) / nu;
// apply new Givens rotation // Apply new Givens rotation
H(iter, iter) = nu; H(iter, iter) = nu;
H(iter + 1, iter) = 0.; H(iter, iter + 1) = 0.;
/* ORDERING??? */
gamma[iter + 1] = -s[iter] * gamma[iter]; gamma[iter + 1] = -s[iter] * gamma[iter];
gamma[iter] = std::conj(c[iter]) * gamma[iter]; gamma[iter] = std::conj(c[iter]) * gamma[iter];
QrTimer.Stop();
} }
void Step() { void computeSolution(std::vector< Field > const &v, Field &psi, int iter) {
int m = MaxIterations; CompSolutionTimer.Start();
for (int i = iter; i >= 0; i--) {
Field r(src);
Field w(src);
Field Dpsi(src);
Field Dv(src);
std::vector<Field> v(m + 1, src);
Eigen::MatrixXcd H = Eigen::MatrixXcd::Zero(m + 1, m);
std::vector<std::complex<double>> y(m + 1, 0.);
std::vector<std::complex<double>> gamma(m + 1, 0.);
std::vector<std::complex<double>> c(m + 1, 0.);
std::vector<std::complex<double>> s(m + 1, 0.);
// Initial residual computation & set up
RealD guess = norm2(psi);
assert(std::isnan(guess) == 0);
RealD ssq = norm2(src); // flopcount.addSiteFlops(4*Nc*Ns,s); // stands for "source squared"
RealD rsd_sq = Tolerance * Tolerance * ssq; // flopcount.addSiteFlops(4*Nc*Ns,s); // stands for "residual squared"
LinOp.Op(psi, Dpsi);
r = src - Dpsi;
RealD cp = norm2(r); // cp = beta in WMG nomenclature, in WMG there is no norm2 but a sqrt(norm2) here
gamma[0] = cp;
std::cout << GridLogIterative << "cp " << cp << std::endl;
v[0] = (1. / cp) * r;
std::cout << GridLogIterative << std::setprecision(4) << "GeneralizedMinimalResidual: guess " << guess << std::endl;
std::cout << GridLogIterative << std::setprecision(4) << "GeneralizedMinimalResidual: src " << ssq << std::endl;
// std::cout << GridLogIterative << std::setprecision(4) << "GeneralizedMinimalResidual: mp " << d << std::endl;
std::cout << GridLogIterative << std::setprecision(4) << "GeneralizedMinimalResidual: cp,r " << cp << std::endl;
if (cp <= rsd_sq) {
return;
}
std::cout << GridLogIterative << std::setprecision(4)
<< "GeneralizedMinimalResidual: k=0 residual " << cp << " target " << rsd_sq << std::endl;
GridStopWatch SolverTimer;
GridStopWatch MatrixTimer;
SolverTimer.Start();
for(auto j = 0; j < m; ++j) {
// std::cout << GridLogIterative << "GeneralizedMinimalResidual: Start of outer loop with index j = " << j << std::endl;
MatrixTimer.Start();
LinOp.Op(v[j], Dv);
MatrixTimer.Stop();
w = Dv;
for(auto i = 0; i <= j; ++i) {
H(i, j) = innerProduct(v[i], w);
w = w - H(i, j) * v[i];
}
H(j + 1, j) = norm2(w);
v[j + 1] = (1. / H(j + 1, j)) * w;
// end of arnoldi process, begin of givens rotations
// apply old Givens rotation
for(auto i = 0; i < j ; ++i) {
auto tmp = -s[i] * H(i, j) + c[i] * H(i + 1, j);
H(i, j) = std::conj(c[i]) * H(i, j) + std::conj(s[i]) * H(i + 1, j);
H(i + 1, j) = tmp;
}
// compute new Givens Rotation
ComplexD nu = sqrt(std::norm(H(j, j)) + std::norm(H(j + 1, j)));
c[j] = H(j, j) / nu;
s[j] = H(j + 1, j) / nu;
std::cout << GridLogIterative << "GeneralizedMinimalResidual: nu" << nu << std::endl;
std::cout << GridLogIterative << "GeneralizedMinimalResidual: H("<<j<<","<<j<<")" << H(j,j) << std::endl;
std::cout << GridLogIterative << "GeneralizedMinimalResidual: H("<<j+1<<","<<j<<")" << H(j+1,j) << std::endl;
// apply new Givens rotation
H(j, j) = nu;
H(j + 1, j) = 0.;
/* ORDERING??? */
gamma[j + 1] = -s[j] * gamma[j];
gamma[j] = std::conj(c[j]) * gamma[j];
/* for(auto k = 0; k <= j+1 ; ++k) */
/* std::cout << GridLogIterative << "k " << k << "nu " << nu << " c["<<k<<"]" << c[k]<< " s["<<k<<"]" << s[k] << " gamma["<<k<<"]" << gamma[k] << std::endl; */
std::cout << GridLogIterative << "GeneralisedMinimalResidual: Iteration "
<< j << " residual " << std::abs(gamma[j + 1]) << std::endl; //" target "
/* << TargetResSq << std::endl; */
if(std::abs(gamma[j + 1]) / sqrt(cp) < Tolerance) {
SolverTimer.Stop();
std::cout << GridLogMessage << "GeneralizedMinimalResidual Converged on iteration " << j << std::endl;
// std::cout << GridLogMessage << "\tComputed residual " << sqrt(cp / ssq) << std::endl;
// std::cout << GridLogMessage << "\tTrue residual " << true_residual << std::endl;
std::cout << GridLogMessage << "\tTarget " << Tolerance << std::endl;
std::cout << GridLogMessage << "Time breakdown " << std::endl;
std::cout << GridLogMessage << "\tElapsed " << SolverTimer.Elapsed() << std::endl;
std::cout << GridLogMessage << "\tMatrix " << MatrixTimer.Elapsed() << std::endl;
// std::cout << GridLogMessage << "\tLinalg " << LinalgTimer.Elapsed() << std::endl;
IterationsToComplete = j;
break;
}
}
// backward substitution
computeSolution(y, gamma, H, v, psi, IterationsToComplete);
std::cout << GridLogIterative << "GeneralizedMinimalResidual: End of operator()" << std::endl;
}
private:
/* void qrUpdate(std::vector<std::complex<double>> &gamma, */
/* std::vector<std::complex<double>> &c, */
/* std::vector<std::complex<double>> &s, */
/* Eigen::MatrixXcd & H, */
/* int j) { */
/* ComplexD cp{}; */
/* // update QR factorization */
/* // apply previous Givens rotation */
/* for(auto i = 0; i < j; i++) { */
/* cp = -s[i] * H(i, j) + c[i] * H(i + 1, j); */
/* H(i, j) = std::conj(c[i]) * H(i, j) + std::conj(s[i]) * H(i + 1,
* j); */
/* H(i + 1, j) = cp; */
/* } */
/* // compute current Givens rotation */
/* cp = sqrt(std::norm(H(j, j)) + std::norm(H(j + 1, j))); */
/* s[j] = H(j + 1, j) / cp; */
/* c[j] = H(j, j) / cp; */
/* /\* std::cout << GridLogIterative << "cp= " << cp << std::endl; *\/ */
/* /\* std::cout << GridLogIterative << "s[j]= " << s[ j ] << std::endl; *\/ */
/* /\* std::cout << GridLogIterative << "c[j]= " << c[ j ] << std::endl; *\/ */
/* /\* std::cout << GridLogIterative << "gamma[j+1]= " << gamma[ j + 1 ] << std::endl; *\/ */
/* /\* std::cout << GridLogIterative << "gamma[j]= " << gamma[ j ] << std::endl; *\/ */
/* // update right column */
/* gamma[j + 1] = -s[j] * gamma[j]; */
/* gamma[j] = std::conj(c[j]) * gamma[j]; */
/* /\* std::cout << GridLogIterative << "gamma[j+1]= " << gamma[ j + 1 ] << std::endl; *\/ */
/* /\* std::cout << GridLogIterative << "gamma[j]= " << gamma[ j ] << std::endl; *\/ */
/* // apply current Givens rotation */
/* H(j, j) = cp; */
/* H(j + 1, j) = 0.; */
/* /\* std::cout << GridLogIterative << "H(j,j)= " << H( j, j ) << std::endl; *\/ */
/* /\* std::cout << GridLogIterative << "H(j+1,j)= " << H( j + 1, j ) << std::endl; *\/ */
/* } */
void computeSolution(std::vector<std::complex<double>> & y,
std::vector<std::complex<double>> const &gamma,
Eigen::MatrixXcd const & H,
std::vector<Field> const & v,
Field & x,
int j) {
for(auto i = iter; i >= 0; i--) {
y[i] = gamma[i]; y[i] = gamma[i];
for(auto k = i + 1; k <= iter; k++) for (int k = i + 1; k <= iter; k++)
y[i] -= H(i, k) * y[k]; y[i] -= H(k, i) * y[k];
y[i] /= H(i, i); y[i] /= H(i, i);
} }
/* if(true) // TODO ??? */ // TODO: Use axpys or similar for these
/* { */ // TODO: Fix the condition
/* for(auto i = 0; i <= iter; i++) */ if (true) {
/* x = x + v[i] * y[i]; */ for (int i = 0; i <= iter; i++)
/* } else { */ psi = psi + v[i] * y[i];
x = y[0] * v[0]; }
for(auto i = 1; i <= j; i++) else {
x = x + v[i] * y[i]; psi = y[0] * v[0];
/* } */ for (int i = 1; i <= iter; i++)
psi = psi + v[i] * y[i];
}
CompSolutionTimer.Stop();
} }
}; };
} }
#endif #endif
// Possible problems/TODOs for this implementation
// * correct the stopping criterion

2
tests/solver/Test_wilson_gmres_unprec.cc
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@ -58,7 +58,7 @@ int main (int argc, char ** argv)
WilsonFermionR Dw(Umu,Grid,RBGrid,mass); WilsonFermionR Dw(Umu,Grid,RBGrid,mass);
MdagMLinearOperator<WilsonFermionR,LatticeFermion> HermOp(Dw); MdagMLinearOperator<WilsonFermionR,LatticeFermion> HermOp(Dw);
GeneralisedMinimalResidual<LatticeFermion> GMRES(1.0e-8, 10000, 5); GeneralisedMinimalResidual<LatticeFermion> GMRES(1.0e-8, 50, 25);
GMRES(HermOp,src,result); GMRES(HermOp,src,result);
Grid_finalize(); Grid_finalize();