From 58a31f0763d9c5f06a4df38e47ed5919eb58c8fb Mon Sep 17 00:00:00 2001
From: Peter Boyle <paboyle@ph.ed.ac.uk>
Date: Mon, 9 Dec 2019 02:59:13 -0500
Subject: [PATCH] QMR implemented, preserve even if not used much

---
 .../iterative/QuasiMinimalResidual.h          | 371 ++++++++++++++++++
 1 file changed, 371 insertions(+)
 create mode 100644 Grid/algorithms/iterative/QuasiMinimalResidual.h

diff --git a/Grid/algorithms/iterative/QuasiMinimalResidual.h b/Grid/algorithms/iterative/QuasiMinimalResidual.h
new file mode 100644
index 00000000..ea5531b6
--- /dev/null
+++ b/Grid/algorithms/iterative/QuasiMinimalResidual.h
@@ -0,0 +1,371 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithmsf/iterative/QuasiMinimalResidual.h
+
+Copyright (C) 2019
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+template<class Field> 
+RealD innerG5ProductReal(Field &l, Field &r)
+{
+  Gamma G5(Gamma::Algebra::Gamma5);
+  Field tmp(l.Grid());
+  //  tmp = G5*r;
+  G5R5(tmp,r);
+  ComplexD ip =innerProduct(l,tmp);
+  std::cout << "innerProductRealG5R5 "<<ip<<std::endl;
+  return ip.real();
+}
+
+template<class Field>
+class QuasiMinimalResidual : public OperatorFunction<Field> {
+ public:
+  using OperatorFunction<Field>::operator();
+
+  bool ErrorOnNoConverge; 
+  RealD   Tolerance;
+  Integer MaxIterations;
+  Integer IterationCount;
+
+  QuasiMinimalResidual(RealD   tol,
+		       Integer maxit,
+		       bool    err_on_no_conv = true)
+      : Tolerance(tol)
+      , MaxIterations(maxit)
+      , ErrorOnNoConverge(err_on_no_conv) 
+  {};
+
+#if 1
+  void operator()(LinearOperatorBase<Field> &LinOp, const Field &b, Field &x) 
+  {
+    RealD resid;
+    IterationCount=0;
+
+    RealD  rho, rho_1, xi, gamma, gamma_1, theta, theta_1;
+    RealD  eta, delta, ep, beta; 
+
+    GridBase *Grid = b.Grid();
+    Field r(Grid), d(Grid), s(Grid);
+    Field v(Grid), w(Grid), y(Grid),  z(Grid);
+    Field v_tld(Grid), w_tld(Grid), y_tld(Grid), z_tld(Grid);
+    Field p(Grid), q(Grid), p_tld(Grid);
+
+    Real normb = norm2(b);
+
+    LinOp.Op(x,r); r = b - r;
+
+    assert(normb> 0.0);
+
+    resid = norm2(r)/normb;
+    if (resid <= Tolerance) {
+      return;
+    }
+
+    v_tld = r;
+    y = v_tld;
+    rho = norm2(y);
+
+    // Take Gamma5 conjugate
+    //    Gamma G5(Gamma::Algebra::Gamma5);
+    //    G5R5(w_tld,r);
+    //    w_tld = G5* v_tld;
+    w_tld=v_tld;
+    z = w_tld;
+    xi = norm2(z);
+
+    gamma = 1.0;
+    eta   = -1.0;
+    theta = 0.0;
+
+    for (int i = 1; i <= MaxIterations; i++) {
+
+      // Breakdown tests
+      assert( rho != 0.0);
+      assert( xi  != 0.0);
+
+      v = (1. / rho) * v_tld;
+      y = (1. / rho) * y;
+
+      w = (1. / xi) * w_tld;
+      z = (1. / xi) * z;
+
+      ComplexD Zdelta = innerProduct(z, y); // Complex?
+      std::cout << "Zdelta "<<Zdelta<<std::endl;
+      delta = Zdelta.real();
+
+      y_tld = y; 
+      z_tld = z;
+
+      if (i > 1) {
+	p = y_tld - (xi  * delta / ep) * p;
+	q = z_tld - (rho * delta / ep) * q;
+      } else {
+	p = y_tld;
+	q = z_tld;
+      }
+
+      LinOp.Op(p,p_tld);      //     p_tld = A * p;
+      ComplexD Zep = innerProduct(q, p_tld);
+      ep=Zep.real();
+      std::cout << "Zep "<<Zep <<std::endl;
+      // Complex Audit
+      assert(abs(ep)>0);
+
+      beta = ep / delta;
+      assert(abs(beta)>0);
+
+      v_tld = p_tld - beta * v;
+      y = v_tld;
+
+      rho_1 = rho;
+      rho   = norm2(y);
+      LinOp.AdjOp(q,w_tld);
+      w_tld = w_tld - beta * w;
+      z = w_tld;
+
+      xi = norm2(z);
+
+      gamma_1 = gamma;
+      theta_1 = theta;
+
+      theta   = rho / (gamma_1 * beta);
+      gamma   = 1.0 / sqrt(1.0 + theta * theta);
+      std::cout << "theta "<<theta<<std::endl;
+      std::cout << "gamma "<<gamma<<std::endl;
+
+      assert(abs(gamma)> 0.0);
+
+      eta = -eta * rho_1 * gamma* gamma / (beta * gamma_1 * gamma_1);
+
+      if (i > 1) {
+	d = eta * p + (theta_1 * theta_1 * gamma * gamma) * d;
+	s = eta * p_tld + (theta_1 * theta_1 * gamma * gamma) * s;
+      } else {
+	d = eta * p;
+	s = eta * p_tld;
+      }
+
+      x =x+d;                            // update approximation vector
+      r =r-s;                            // compute residual
+
+      if ((resid = norm2(r) / normb) <= Tolerance) {
+	return;
+      }
+      std::cout << "Iteration "<<i<<" resid " << resid<<std::endl;
+    }
+    assert(0);
+    return;                            // no convergence
+  }
+#else
+  // QMRg5 SMP thesis
+  void operator()(LinearOperatorBase<Field> &LinOp, const Field &b, Field &x) 
+  {
+    // Real scalars
+    GridBase *grid = b.Grid();
+
+    Field    r(grid);
+    Field    p_m(grid), p_m_minus_1(grid), p_m_minus_2(grid);
+    Field    v_m(grid), v_m_minus_1(grid), v_m_plus_1(grid);
+    Field    tmp(grid);
+
+    RealD    w;
+    RealD    z1, z2;
+    RealD    delta_m, delta_m_minus_1;
+    RealD    c_m_plus_1, c_m, c_m_minus_1;
+    RealD    s_m_plus_1, s_m, s_m_minus_1;
+    RealD    alpha, beta, gamma, epsilon;
+    RealD    mu, nu, rho, theta, xi, chi;
+    RealD    mod2r, mod2b;
+    RealD    tau2, target2;
+
+    mod2b=norm2(b);
+
+    /////////////////////////
+    // Initial residual
+    /////////////////////////
+    LinOp.Op(x,tmp);
+    r = b - tmp;
+
+    /////////////////////////
+    // \mu = \rho = |r_0|
+    /////////////////////////
+    mod2r = norm2(r);
+    rho = sqrt( mod2r);
+    mu=rho;
+    
+    std::cout << "QuasiMinimalResidual rho "<< rho<<std::endl;
+    /////////////////////////
+    // Zero negative history
+    /////////////////////////
+    v_m_plus_1  = Zero();
+    v_m_minus_1 = Zero();
+    p_m_minus_1 = Zero();
+    p_m_minus_2 = Zero();
+
+    // v0
+    v_m = (1.0/rho)*r;
+
+    /////////////////////////
+    // Initial coeffs
+    /////////////////////////
+    delta_m_minus_1 = 1.0;
+    c_m_minus_1     = 1.0;
+    c_m             = 1.0;
+    s_m_minus_1     = 0.0;
+    s_m             = 0.0;
+
+    /////////////////////////
+    // Set up convergence check
+    /////////////////////////
+    tau2    = mod2r;
+    target2 = mod2b * Tolerance*Tolerance;
+ 
+    for(int iter = 0 ; iter < MaxIterations; iter++){
+
+      /////////////////////////
+      // \delta_m = (v_m, \gamma_5 v_m) 
+      /////////////////////////
+      delta_m = innerG5ProductReal(v_m,v_m);
+      std::cout << "QuasiMinimalResidual delta_m "<< delta_m<<std::endl;
+
+      /////////////////////////
+      // tmp = A v_m
+      /////////////////////////
+      LinOp.Op(v_m,tmp);
+
+      /////////////////////////
+      // \alpha = (v_m, \gamma_5 temp) / \delta_m 
+      /////////////////////////
+      alpha = innerG5ProductReal(v_m,tmp);
+      alpha = alpha/delta_m ;
+      std::cout << "QuasiMinimalResidual alpha "<< alpha<<std::endl;
+
+      /////////////////////////
+      // \beta = \rho \delta_m / \delta_{m-1}
+      /////////////////////////
+      beta = rho * delta_m / delta_m_minus_1;
+      std::cout << "QuasiMinimalResidual beta "<< beta<<std::endl;
+
+      /////////////////////////
+      // \tilde{v}_{m+1} = temp - \alpha v_m - \beta v_{m-1}
+      /////////////////////////
+      v_m_plus_1 = tmp - alpha*v_m - beta*v_m_minus_1;
+
+      ///////////////////////////////
+      // \rho = || \tilde{v}_{m+1} ||
+      ///////////////////////////////
+      rho = sqrt( norm2(v_m_plus_1) );
+      std::cout << "QuasiMinimalResidual rho "<< rho<<std::endl;
+
+      ///////////////////////////////
+      //      v_{m+1} = \tilde{v}_{m+1}
+      ///////////////////////////////
+      v_m_plus_1 = (1.0 / rho) * v_m_plus_1;
+
+      ////////////////////////////////
+      // QMR recurrence coefficients.
+      ////////////////////////////////
+      theta      = s_m_minus_1 * beta;
+      gamma      = c_m_minus_1 * beta;
+      epsilon    =  c_m * gamma + s_m * alpha;
+      xi         = -s_m * gamma + c_m * alpha;
+      nu         = sqrt( xi*xi + rho*rho );
+      c_m_plus_1 = fabs(xi) / nu;
+      if ( xi == 0.0 ) {
+	s_m_plus_1 = 1.0;
+      } else {
+	s_m_plus_1 = c_m_plus_1 * rho / xi;
+      }
+      chi = c_m_plus_1 * xi + s_m_plus_1 * rho;
+
+      std::cout << "QuasiMinimalResidual coeffs "<< theta <<" "<<gamma<<" "<< epsilon<<" "<< xi<<" "<< nu<<std::endl;
+      std::cout << "QuasiMinimalResidual coeffs "<< chi   <<std::endl;
+
+      ////////////////////////////////
+      //p_m=(v_m - \epsilon p_{m-1} - \theta p_{m-2}) / \chi
+      ////////////////////////////////
+      p_m = (1.0/chi) * v_m - (epsilon/chi) * p_m_minus_1 - (theta/chi) * p_m_minus_2;
+
+      ////////////////////////////////////////////////////////////////
+      //      \psi = \psi + c_{m+1} \mu p_m	
+      ////////////////////////////////////////////////////////////////
+      x = x + ( c_m_plus_1 * mu ) * p_m;
+
+      ////////////////////////////////////////
+      //
+      ////////////////////////////////////////
+      mu              = -s_m_plus_1 * mu;
+      delta_m_minus_1 = delta_m;
+      c_m_minus_1     = c_m;
+      c_m             = c_m_plus_1;
+      s_m_minus_1     = s_m;
+      s_m             = s_m_plus_1;
+
+      ////////////////////////////////////
+      // Could use pointer swizzle games.
+      ////////////////////////////////////
+      v_m_minus_1 = v_m;
+      v_m         = v_m_plus_1;
+      p_m_minus_2 = p_m_minus_1;
+      p_m_minus_1 = p_m;
+
+
+      /////////////////////////////////////
+      // Convergence checks
+      /////////////////////////////////////
+      z1 = RealD(iter+1.0);
+      z2 = z1 + 1.0;
+      tau2 = tau2 *( z2 / z1 ) * s_m * s_m;
+      std::cout << " QuasiMinimumResidual iteration "<< iter<<std::endl;
+      std::cout << " QuasiMinimumResidual tau bound "<< tau2<<std::endl;
+
+      // Compute true residual
+      mod2r = tau2;
+      if ( 1 || (tau2 < (100.0 * target2)) ) {
+	LinOp.Op(x,tmp);
+	r = b - tmp;
+	mod2r = norm2(r);
+	std::cout << " QuasiMinimumResidual true residual is "<< mod2r<<std::endl;
+      }
+
+
+      if ( mod2r < target2 ) { 
+
+	std::cout << " QuasiMinimumResidual has converged"<<std::endl;
+	return;
+
+      }
+
+    }
+
+
+  }
+#endif
+};
+
+NAMESPACE_END(Grid);