block with a single vector case is working with IRBL

lib/algorithms/iterative/ImplicitlyRestartedBlockLanczos.h.bak

@@ -0,0 +1,835 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ImplicitlyRestartedBlockLanczos.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Chulwoo Jung
+Author: Yong-Chull Jang <ypj@quark.phy.bnl.gov> 
+Author: Guido Cossu
+
+    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 */
+#ifndef GRID_IRBL_H
+#define GRID_IRBL_H
+
+#include <string.h> //memset
+
+#define clog std::cout << GridLogMessage 
+
+namespace Grid {
+
+/////////////////////////////////////////////////////////////
+// Implicitly restarted block lanczos
+/////////////////////////////////////////////////////////////
+template<class Field> 
+class ImplicitlyRestartedBlockLanczos {
+
+private:       
+  
+  std::string cname = std::string("ImplicitlyRestartedBlockLanczos");
+  int MaxIter;   // Max iterations
+  int Nstop;     // Number of evecs checked for convergence
+  int Nu;        // Numbeer of vecs in the unit block
+  int Nk;        // Number of converged sought
+  int Nm;        // total number of vectors
+  int Nblock_k;    // Nk/Nu
+  int Nblock_m;    // Nm/Nu
+  RealD eresid;
+  IRLdiagonalisation diagonalisation;
+  ////////////////////////////////////
+  // Embedded objects
+  ////////////////////////////////////
+           SortEigen<Field> _sort;
+  LinearOperatorBase<Field> &_Linop;
+    OperatorFunction<Field> &_poly;
+
+  /////////////////////////
+  // Constructor
+  /////////////////////////
+public:       
+ ImplicitlyRestartedBlockLanczos(LinearOperatorBase<Field> &Linop, // op
+                                 OperatorFunction<Field> & poly,   // polynomial
+                                 int _Nstop, // really sought vecs
+                                 int _Nu,    // vecs in the unit block
+                                 int _Nk,    // sought vecs
+                                 int _Nm,    // total vecs
+                                 RealD _eresid, // resid in lmd deficit 
+                                 int _MaxIter,  // Max iterations
+                                 IRLdiagonalisation _diagonalisation = IRLdiagonaliseWithEigen)
+   : _Linop(Linop),    _poly(poly),
+      Nstop(_Nstop), Nu(_Nu), Nk(_Nk), Nm(_Nm), 
+      Nblock_m(_Nm/_Nu), Nblock_k(_Nk/_Nu),
+      //eresid(_eresid),  MaxIter(10),
+      eresid(_eresid),  MaxIter(_MaxIter),
+      diagonalisation(_diagonalisation)
+  { assert( (Nk%Nu==0) && (Nm%Nu==0) ); };
+
+  ////////////////////////////////
+  // Helpers
+  ////////////////////////////////
+  static RealD normalize(Field& v) 
+  {
+    RealD nn = norm2(v);
+    nn = sqrt(nn);
+    v = v * (1.0/nn);
+    return nn;
+  }
+  
+  void orthogonalize(Field& w, std::vector<Field>& evec, int k)
+  {
+    typedef typename Field::scalar_type MyComplex;
+    MyComplex ip;
+    
+    for(int j=0; j<k; ++j){
+      ip = innerProduct(evec[j],w); 
+      w = w - ip * evec[j];
+    }
+    normalize(w);
+  }
+
+/* Rudy Arthur's thesis pp.137
+------------------------
+Require: M > K P = M − K †
+Compute the factorization AVM = VM HM + fM eM 
+repeat
+  Q=I
+  for i = 1,...,P do
+    QiRi =HM −θiI Q = QQi
+    H M = Q †i H M Q i
+  end for
+  βK =HM(K+1,K) σK =Q(M,K)
+  r=vK+1βK +rσK
+  VK =VM(1:M)Q(1:M,1:K)
+  HK =HM(1:K,1:K)
+  →AVK =VKHK +fKe†K † Extend to an M = K + P step factorization AVM = VMHM + fMeM
+until convergence
+*/
+  void calc(std::vector<RealD>& eval,  
+            std::vector<Field>& evec, 
+            const std::vector<Field>& src, int& Nconv)
+  {
+    std::string fname = std::string(cname+"::calc()"); 
+    GridBase *grid = evec[0]._grid;
+    assert(grid == src[0]._grid);
+    assert( Nu = src.size() );
+    
+    clog << std::string(74,'*') << std::endl;
+    clog << fname + " starting iteration 0 /  "<< MaxIter<< std::endl;
+    clog << std::string(74,'*') << std::endl;
+    clog <<" -- seek   Nk    = "<< Nk    <<" vectors"<< std::endl;
+    clog <<" -- accept Nstop = "<< Nstop <<" vectors"<< std::endl;
+    clog <<" -- total  Nm    = "<< Nm    <<" vectors"<< std::endl;
+    clog <<" -- size of eval = "<< eval.size() << std::endl;
+    clog <<" -- size of evec = "<< evec.size() << std::endl;
+    if ( diagonalisation == IRLdiagonaliseWithEigen ) { 
+      clog << "Diagonalisation is Eigen "<< std::endl;
+    } else {
+      abort();
+    }
+    clog << std::string(74,'*') << std::endl;
+    
+    assert(Nm == evec.size() && Nm == eval.size());
+	
+    std::vector<std::vector<ComplexD>> lmd(Nu,std::vector<ComplexD>(Nm,0.0));  
+    std::vector<std::vector<ComplexD>> lme(Nu,std::vector<ComplexD>(Nm,0.0));  
+    std::vector<std::vector<ComplexD>> lmd2(Nu,std::vector<ComplexD>(Nm,0.0));  
+    std::vector<std::vector<ComplexD>> lme2(Nu,std::vector<ComplexD>(Nm,0.0));  
+    std::vector<RealD> eval2(Nm);
+
+    Eigen::MatrixXcd    Qt = Eigen::MatrixXcd::Zero(Nm,Nm);
+    Eigen::MatrixXcd    Q = Eigen::MatrixXcd::Zero(Nm,Nm);
+
+    std::vector<int>   Iconv(Nm);
+    std::vector<Field>  B(Nm,grid); // waste of space replicating
+    
+    std::vector<Field> f(Nu,grid);
+    std::vector<Field> f_copy(Nu,grid);
+    Field v(grid);
+    
+    Nconv = 0;
+    
+    RealD beta_k;
+  
+    // set initial vector
+    for (int i=0; i<Nu; ++i) {
+      clog << "norm2(src[" << i << "])= "<< norm2(src[i]) << std::endl;
+      evec[i] = src[i];
+      orthogonalize(evec[i],evec,i);
+      clog << "norm2(evec[" << i << "])= "<< norm2(evec[i]) << std::endl;
+    }
+    
+    // initial Nblock_k steps
+    for(int b=0; b<Nblock_k; ++b) blockwiseStep(lmd,lme,evec,f,f_copy,b);
+
+    // restarting loop begins
+    int iter;
+    for(iter = 0; iter<MaxIter; ++iter){
+      
+      clog <<" **********************"<< std::endl;
+      clog <<" Restart iteration = "<< iter << std::endl;
+      clog <<" **********************"<< std::endl;
+      
+      // additional (Nblock_m - Nblock_k) steps
+      for(int b=Nblock_k; b<Nblock_m; ++b) blockwiseStep(lmd,lme,evec,f,f_copy,b);
+      
+      for(int k=0; k<Nm; ++k) {
+        clog << "ckpt A1: lme[" << k << "] = " << lme[0][k] << '\n';
+      }
+      for(int k=0; k<Nm; ++k) {
+        clog << "ckpt A2: lmd[" << k << "] = " << lmd[0][k] << '\n';
+      }
+      
+      // residual vector
+#if 1 // ypj[fixme] temporary to check a case when block has one vector
+      for ( int i=0; i<Nu; ++i) f_copy[i] = f[i];
+      for ( int i=0; i<Nu; ++i) {
+        f[i] = f_copy[0]*lme[0][Nm-Nu+i]; 
+        for ( int j=1; j<Nu; ++j) { 
+          f[i] += f_copy[j]*lme[j][Nm-Nu+i]; 
+        }
+        //clog << "ckpt C (i= " << i << ")" << '\n';
+        //clog << "norm2(f) = " << norm2(f[i]) << std::endl;
+      }
+#endif
+      
+      // getting eigenvalues
+      for(int u=0; u<Nu; ++u){
+        for(int k=0; k<Nm; ++k){
+          lmd2[u][k] = lmd[u][k];
+          lme2[u][k] = lme[u][k];
+        }
+      }
+      Qt = Eigen::MatrixXcd::Identity(Nm,Nm);
+      diagonalize(eval2,lmd2,lme2,Nu,Nm,Nm,Qt,grid);
+      
+      //for(int k=0; k<Nm; ++k){
+      //  clog << "ckpt D " << '\n';
+      //  clog << "eval2 [" << k << "] = " << eval2[k] << std::endl;
+      //}
+
+      // sorting
+      _sort.push(eval2,Nm);
+      
+      //for(int k=0; k<Nm; ++k){
+      //  clog << "ckpt E " << '\n';
+      //  clog << "eval2 [" << k << "] = " << eval2[k] << std::endl;
+      //}
+
+      // Implicitly shifted QR transformations
+      Eigen::MatrixXcd BTDM = Eigen::MatrixXcd::Identity(Nm,Nm);
+      Q = Eigen::MatrixXcd::Identity(Nm,Nm);
+      
+      unpackHermitBlockTriDiagMatToEigen(lmd,lme,Nu,Nblock_m,Nm,Nm,BTDM);
+
+      for(int ip=Nk; ip<Nm; ++ip){ 
+        clog << "ckpt B1: shift[" << ip << "] = " << eval2[ip] << endl;
+        shiftedQRDecompEigen(BTDM,Nm,eval2[ip],Q);
+      }
+      BTDM = Q.adjoint()*(BTDM*Q);
+      for (int i=0; i<Nm; ++i ) {
+        for (int j=i+1; j<Nm; ++j ) {
+          BTDM(i,j) = BTDM(j,i);
+        }
+        //BTDM(i,i) = real(BTDM(i,i));
+      }
+      
+      packHermitBlockTriDiagMatfromEigen(lmd,lme,Nu,Nblock_m,Nm,Nm,BTDM);
+
+      //for (int i=0; i<Nm; ++i) {
+      //  for (int j=0; j<Nm; ++j) {
+      //    clog << "ckpt G1: M[" << i << "," << j << "] = " << BTDM(i,j) << '\n';
+      //  }
+      //}
+      //for (int i=0; i<Nm; ++i) {
+      //  for (int j=0; j<Nm; ++j) {
+      //    clog << "ckpt G2: Q[" << i << "," << j << "] = " << Q(i,j) << '\n';
+      //  }
+      //}
+      for (int i=0; i<Nm; ++i) {
+        clog << "ckpt C1: lme[" << i << "] = " << lme[0][i] << '\n';
+      }
+      for (int i=0; i<Nm; ++i) {
+        clog << "ckpt C2: lmd[" << i << "] = " << lmd[0][i] << '\n';
+      }
+
+      for(int i=0; i<Nk+Nu; ++i) B[i] = 0.0;
+      for(int j=0; j<Nk+Nu; ++j){
+	for(int k=0; k<Nm; ++k){
+	  B[j].checkerboard = evec[k].checkerboard;
+	  B[j] += evec[k]*Q(k,j);
+	}
+      }
+      for(int i=0; i<Nk+Nu; ++i) { 
+        evec[i] = B[i];
+        //clog << "ckpt F: norm2_evec[= " << i << "]" << norm2(evec[i]) << std::endl;
+      }
+
+#if 1 // ypj[fixme] temporary to check a case when block has one vector
+      // Compressed vector f and beta(k2)
+      f[0] *= Q(Nm-1,Nk-1);
+      f[0] += lme[0][Nk-1] * evec[Nk]; // was commented out
+      std::cout<< GridLogMessage<<"ckpt D1: Q[Nm-1,Nk-1] = "<<Q(Nm-1,Nk-1)<<std::endl;
+      beta_k = norm2(f[0]);
+      beta_k = sqrt(beta_k);
+      std::cout<< GridLogMessage<<"ckpt D2: beta(k) = "<<beta_k<<std::endl;
+      
+      RealD betar = 1.0/beta_k;
+      evec[Nk] = betar * f[0];
+      lme[0][Nk-1] = beta_k;
+#endif
+
+      // Convergence test
+      for(int u=0; u<Nu; ++u){
+        for(int k=0; k<Nm; ++k){
+          lmd2[u][k] = lmd[u][k];
+          lme2[u][k] = lme[u][k];
+        }
+      }
+      Qt = Eigen::MatrixXcd::Identity(Nm,Nm);
+      diagonalize(eval2,lmd2,lme2,Nu,Nk,Nm,Qt,grid);
+      
+      for(int k = 0; k<Nk; ++k) B[k]=0.0;
+      for(int j = 0; j<Nk; ++j){
+	for(int k = 0; k<Nk; ++k){
+	  B[j].checkerboard = evec[k].checkerboard;
+	  B[j] += evec[k]*Qt(k,j);
+	}
+      }
+      
+      //for (int i=0; i<Nk; ++i) {
+      //  for (int j=0; j<Nk; ++j) {
+      //    clog << "ckpt H1: R[" << i << "," << j << "] = " << Qt(i,j) << '\n';
+      //  }
+      //}
+      //for (int i=0; i<Nk; ++i) {
+      //  clog << "ckpt H2: eval2[" << i << "] = " << eval2[i] << '\n';
+      //}
+      
+      //for(int j=0; j<Nk; ++j) {
+      //  clog << "ckpt I: norm2_B[ " << j << "]" << norm2(B[j]) << std::endl;
+      //}
+
+      Nconv = 0;
+      for(int i=0; i<Nk; ++i){
+	
+	_Linop.HermOp(B[i],v);
+	    
+	RealD vnum = real(innerProduct(B[i],v)); // HermOp.
+	RealD vden = norm2(B[i]);
+	eval2[i] = vnum/vden;
+	v -= eval2[i]*B[i];
+	RealD vv = norm2(v);
+	
+	std::cout.precision(13);
+	clog << "[" << std::setw(3)<< std::setiosflags(std::ios_base::right) <<i<<"] ";
+	std::cout << "eval = "<<std::setw(25)<< std::setiosflags(std::ios_base::left)<< eval2[i];
+	std::cout << " |H B[i] - eval[i]B[i]|^2 "<< std::setw(25)<< std::setiosflags(std::ios_base::right)<< vv<< std::endl;
+	
+	// change the criteria as evals are supposed to be sorted, all evals smaller(larger) than Nstop should have converged
+	if( (vv<eresid*eresid) && (i == Nconv) ){
+	//if( (vv<eresid*eresid) ){
+	  Iconv[Nconv] = i;
+	  ++Nconv;
+	}
+	
+      }  // i-loop end
+      
+      clog <<" #modes converged: "<<Nconv<<std::endl;
+
+      if( Nconv>=Nstop ){
+	goto converged;
+      }
+
+    } // end of iter loop
+    
+    clog <<"**************************************************************************"<< std::endl;
+    std::cout<< GridLogError    << fname + " NOT converged.";
+    clog <<"**************************************************************************"<< std::endl;
+    abort();
+	
+  converged:
+    // Sorting
+    eval.resize(Nconv);
+    evec.resize(Nconv,grid);
+    for(int i=0; i<Nconv; ++i){
+      eval[i] = eval2[Iconv[i]];
+      evec[i] = B[Iconv[i]];
+    }
+    _sort.push(eval,evec,Nconv);
+    
+    clog <<"**************************************************************************"<< std::endl;
+    clog << fname + " CONVERGED ; Summary :\n";
+    clog <<"**************************************************************************"<< std::endl;
+    clog << " -- Iterations  = "<< iter   << "\n";
+    clog << " -- beta(k)     = "<< beta_k << "\n";
+    clog << " -- Nconv       = "<< Nconv  << "\n";
+    clog <<"**************************************************************************"<< std::endl;
+  }
+
+private:
+/* Saad PP. 195
+1. Choose an initial vector v1 of 2-norm unity. Set β1 ≡ 0, v0 ≡ 0
+2. For k = 1,2,...,m Do:
+3. wk:=Avk−βkv_{k−1}      
+4. αk:=(wk,vk)       // 
+5. wk:=wk−αkvk       // wk orthog vk 
+6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
+7. vk+1 := wk/βk+1
+8. EndDo
+ */
+  void blockwiseStep(std::vector<std::vector<ComplexD>>& lmd,
+	             std::vector<std::vector<ComplexD>>& lme, 
+	             std::vector<Field>& evec,
+	             std::vector<Field>& w, 
+	             std::vector<Field>& w_copy, 
+                     int b)
+  {
+    const RealD tiny = 1.0e-20;
+    
+    int Nu = w.size();
+    int Nm = evec.size();
+    assert( b < Nm/Nu );
+    
+    // converts block index to full indicies for an interval [L,R)
+    int L = Nu*b;
+    int R = Nu*(b+1);
+
+    Real beta;
+    
+    // 3. wk:=Avk−βkv_{k−1}
+    for (int k=L, u=0; k<R; ++k, ++u) {
+      _poly(_Linop,evec[k],w[u]);      
+    }
+    
+    if (b>0) {
+      for (int u=0; u<Nu; ++u) {
+        for (int k=L-Nu; k<L; ++k) {
+          w[u] = w[u] - evec[k] * conjugate(lme[u][k]);
+          //clog << "ckpt A (k= " << k+1 << ")" << '\n';
+          //clog << "lme = " << lme[u][k] << '\n';
+          //clog << "lme = " << conjugate(lme[u][k]) << '\n';
+        }
+        //clog << "norm(w) = " << norm2(w[u]) << std::endl;
+      }
+    }
+    
+    // 4. αk:=(vk,wk)
+    for (int u=0; u<Nu; ++u) {
+      for (int k=L; k<R; ++k) {
+        lmd[u][k] = innerProduct(evec[k],w[u]);  // lmd = transpose of alpha
+      }
+      lmd[u][L+u] = real(lmd[u][L+u]);  // force diagonal to be real
+      //clog << "ckpt B (k= " << L+u << ")" << '\n';
+      //clog << "lmd = " << lmd[u][L+u] << std::endl;
+    }
+    
+    // 5. wk:=wk−αkvk
+    for (int u=0; u<Nu; ++u) {
+      for (int k=L; k<R; ++k) {
+        w[u] = w[u] - evec[k]*lmd[u][k];
+      }
+      w_copy[u] = w[u];
+    }
+    
+    // In block version, the steps 6 and 7 in Lanczos construction is
+    // replaced by the QR decomposition of new basis block.
+    // It results block version beta and orthonormal block basis. 
+    // Here, QR decomposition is done by using Gram-Schmidt
+    for (int u=0; u<Nu; ++u) {
+      for (int k=L; k<R; ++k) {
+        lme[u][k] = 0.0;
+      }
+    }
+
+    beta = normalize(w[0]);
+    for (int u=1; u<Nu; ++u) {
+      //orthogonalize(w[u],w_copy,u);
+      orthogonalize(w[u],w,u);
+    }
+    
+    for (int u=0; u<Nu; ++u) {
+      for (int v=0; v<Nu; ++v) {
+        lme[u][L+v] = innerProduct(w[u],w_copy[v]);
+      }
+    }
+    lme[0][L] = beta;
+    
+#if 0
+    for (int u=0; u<Nu; ++u) {
+      for (int k=L+u; k<R; ++k) {
+        if (lme[u][k] < tiny) {
+          clog <<" In block "<< b << ","; 
+          std::cout <<" beta[" << u << "," << k-L << "] = ";
+          std::cout << lme[u][k] << std::endl;
+        }
+      }
+    }
+#else
+    for (int u=0; u<Nu; ++u) {
+      clog << "norm2(w[" << u << "])= "<< norm2(w[u]) << std::endl;
+      for (int k=L+u; k<R; ++k) {
+        clog <<" In block "<< b << ","; 
+        std::cout <<" beta[" << u << "," << k-L << "] = ";
+        std::cout << lme[u][k] << std::endl;
+      }
+    }
+#endif
+    
+    // re-orthogonalization for numerical stability
+    if (b>0) {
+      for (int u=0; u<Nu; ++u) {
+        orthogonalize(w[u],evec,R);
+      }
+    }
+
+    if (b < Nm/Nu-1) {
+      for (int u=0; u<Nu; ++u) {
+        evec[R+u] = w[u];
+      }
+    }
+
+  }
+  
+
+  void diagonalize_Eigen(std::vector<RealD>& eval, 
+                         std::vector<std::vector<ComplexD>>& lmd,
+                         std::vector<std::vector<ComplexD>>& lme, 
+			 int Nu, int Nk, int Nm,
+			 Eigen::MatrixXcd & Qt, // Nm x Nm
+			 GridBase *grid)
+  {
+    assert( Nk%Nu == 0 && Nm%Nu == 0 );
+    assert( Nk <= Nm );
+    Eigen::MatrixXcd BlockTriDiag = Eigen::MatrixXcd::Zero(Nk,Nk);
+    
+    for ( int u=0; u<Nu; ++u ) {
+      for (int k=0; k<Nk; ++k ) {
+        BlockTriDiag(k,u+(k/Nu)*Nu) = lmd[u][k];
+      }
+    }
+    
+    for ( int u=0; u<Nu; ++u ) {
+      for (int k=Nu; k<Nk; ++k ) {
+        BlockTriDiag(k-Nu,u+(k/Nu)*Nu) = conjugate(lme[u][k-Nu]);
+        BlockTriDiag(u+(k/Nu)*Nu,k-Nu) = lme[u][k-Nu];
+      }
+    }
+    //std::cout << BlockTriDiag << std::endl;
+    
+    Eigen::SelfAdjointEigenSolver<Eigen::MatrixXcd> eigensolver(BlockTriDiag);
+
+    for (int i = 0; i < Nk; i++) {
+      eval[Nk-1-i] = eigensolver.eigenvalues()(i);
+    }
+    for (int i = 0; i < Nk; i++) {
+      for (int j = 0; j < Nk; j++) {
+	Qt(j,Nk-1-i) = eigensolver.eigenvectors()(j,i);
+	//Qt(Nk-1-i,j) = eigensolver.eigenvectors()(i,j);
+	//Qt(i,j) = eigensolver.eigenvectors()(i,j);
+      }
+    }
+  }
+
+
+  void diagonalize(std::vector<RealD>& eval, 
+                   std::vector<std::vector<ComplexD>>& lmd, 
+                   std::vector<std::vector<ComplexD>>& lme, 
+		   int Nu, int Nk, int Nm,   
+		   Eigen::MatrixXcd & Qt,
+		   GridBase *grid)
+  {
+    Qt = Eigen::MatrixXcd::Identity(Nm,Nm);
+    if ( diagonalisation == IRLdiagonaliseWithEigen ) { 
+      diagonalize_Eigen(eval,lmd,lme,Nu,Nk,Nm,Qt,grid);
+    } else { 
+      assert(0);
+    }
+  }
+  
+
+  void unpackHermitBlockTriDiagMatToEigen(
+         std::vector<std::vector<ComplexD>>& lmd,  
+         std::vector<std::vector<ComplexD>>& lme,
+         int Nu, int Nb, int Nk, int Nm,
+         Eigen::MatrixXcd& M)
+  {
+    //clog << "unpackHermitBlockTriDiagMatToEigen() begin" << '\n'; 
+    assert( Nk%Nu == 0 && Nm%Nu == 0 );
+    assert( Nk <= Nm );
+    M = Eigen::MatrixXcd::Zero(Nk,Nk);
+    
+    // rearrange 
+    for ( int u=0; u<Nu; ++u ) {
+      for (int k=0; k<Nk; ++k ) {
+        M(k,u+(k/Nu)*Nu) = lmd[u][k];
+      }
+    }
+
+    for ( int u=0; u<Nu; ++u ) {
+      for (int k=Nu; k<Nk; ++k ) {
+        M(k-Nu,u+(k/Nu)*Nu) = conjugate(lme[u][k-Nu]);
+        M(u+(k/Nu)*Nu,k-Nu) = lme[u][k-Nu];
+      }
+    }
+    //clog << "unpackHermitBlockTriDiagMatToEigen() end" << endl; 
+  }
+ 
+
+  void packHermitBlockTriDiagMatfromEigen(
+         std::vector<std::vector<ComplexD>>& lmd,
+         std::vector<std::vector<ComplexD>>& lme,
+         int Nu, int Nb, int Nk, int Nm,
+         Eigen::MatrixXcd& M)
+  {
+    //clog << "packHermitBlockTriDiagMatfromEigen() begin" << '\n'; 
+    assert( Nk%Nu == 0 && Nm%Nu == 0 );
+    assert( Nk <= Nm );
+    
+    // rearrange 
+    for ( int u=0; u<Nu; ++u ) {
+      for (int k=0; k<Nk; ++k ) {
+        lmd[u][k] = M(k,u+(k/Nu)*Nu);
+      }
+    }
+
+    for ( int u=0; u<Nu; ++u ) {
+      for (int k=Nu; k<Nk; ++k ) {
+        lme[u][k-Nu] = M(u+(k/Nu)*Nu,k-Nu);
+      }
+    }
+    //clog << "packHermitBlockTriDiagMatfromEigen() end" << endl; 
+  }
+
+
+//  void shiftedQRDecompEigen(Eigen::MatrixXcd& M, int Nm,
+//		            RealD Dsh,
+//		            Eigen::MatrixXcd& Qprod, int Nk)
+//  {
+//    //clog << "shiftedQRDecompEigen() begin" << '\n'; 
+//    Eigen::MatrixXcd Mtmp = Eigen::MatrixXcd::Zero(Nm,Nm);
+//    Eigen::MatrixXcd Q = Eigen::MatrixXcd::Zero(Nm,Nm);
+//     
+//    Mtmp = M;
+//    for (int i=0; i<Nm; ++i ) {
+//      Mtmp(i,i) = M(i,i) - Dsh;
+//    }
+//    
+//    Eigen::HouseholderQR<Eigen::MatrixXcd> QRD(Mtmp);
+//    Q = QRD.householderQ();
+//
+//    M = Q.adjoint()*(M*Q);
+//#if 0
+//    Qprod *= Q;
+//#else
+//    Mtmp = Qprod*Q;
+//    
+//    Eigen::HouseholderQR<Eigen::MatrixXcd> QRD2(Mtmp);
+//    Qprod = QRD2.householderQ();
+//
+//    Mtmp -= Qprod;
+//    clog << "Frobenius norm ||Qprod(after) - Qprod|| = " << Mtmp.norm() << std::endl;
+//#endif
+//    //clog << "shiftedQRDecompEigen() end" << endl; 
+//  }
+  void shiftedQRDecompEigen(Eigen::MatrixXcd& M, int Nm,
+		            RealD Dsh,
+		            Eigen::MatrixXcd& Qprod)
+  {
+    //clog << "shiftedQRDecompEigen() begin" << '\n'; 
+    Eigen::MatrixXcd Mtmp = Eigen::MatrixXcd::Zero(Nm,Nm);
+    //Eigen::MatrixXcd Qtmp = Eigen::MatrixXcd::Zero(Nm,Nm);
+    
+    Mtmp = Qprod.adjoint()*(M*Qprod);
+    for (int i=0; i<Nm; ++i ) {
+      for (int j=i+1; j<Nm; ++j ) {
+        Mtmp(i,j) = Mtmp(j,i);
+      }
+    }
+    
+    for (int i=0; i<Nm; ++i ) {
+      Mtmp(i,i) -= Dsh;
+      //Mtmp(i,i) = real(Mtmp(i,i)-Dsh);
+    }
+    
+    Eigen::HouseholderQR<Eigen::MatrixXcd> QRD(Mtmp);
+    //Qtmp = Qprod*QRD.householderQ();
+    
+    //Eigen::HouseholderQR<Eigen::MatrixXcd> QRD2(Qtmp);
+    //Qprod = QRD2.householderQ();
+
+    Qprod *= QRD.householderQ();
+    //ComplexD p;
+    //RealD r;
+
+    //r = 0.;
+    //for (int k=0; k<Nm; ++k) r += real(conj(Qprod(k,0))*Qprod(k,0));
+    //r = sqrt(r);
+    //for (int k=0; k<Nm; ++k) Qprod(k,0) /= r;
+    //
+    //for (int i=1; i<Nm; ++i) {
+    //  for (int j=0; j<i; ++j) {
+    //    p = 0.;
+    //    for (int k=0; k<Nm; ++k) {
+    //      p += conj(Qprod(k,j))*Qprod(k,i);
+    //    }
+    //    for (int k=0; k<Nm; ++k) {
+    //      Qprod(k,i) -= p*Qprod(k,j);
+    //    }
+    //  }
+    //  r = 0.;
+    //  for (int k=0; k<Nm; ++k) r += real(conj(Qprod(k,i))*Qprod(k,i));
+    //  r = sqrt(r);
+    //  for (int k=0; k<Nm; ++k) Qprod(k,i) /= r;
+    //}
+
+    //clog << "shiftedQRDecompEigen() end" << endl; 
+  }
+  
+
+  void exampleQRDecompEigen(void)
+  {
+    Eigen::MatrixXd A = Eigen::MatrixXd::Zero(3,3);
+    Eigen::MatrixXd Q = Eigen::MatrixXd::Zero(3,3);
+    Eigen::MatrixXd R = Eigen::MatrixXd::Zero(3,3);
+    Eigen::MatrixXd P = Eigen::MatrixXd::Zero(3,3);
+
+    A(0,0) = 12.0;
+    A(0,1) = -51.0;
+    A(0,2) = 4.0;
+    A(1,0) = 6.0;
+    A(1,1) = 167.0;
+    A(1,2) = -68.0;
+    A(2,0) = -4.0;
+    A(2,1) = 24.0;
+    A(2,2) = -41.0;
+    
+    clog << "matrix A before ColPivHouseholder" << std::endl;
+    for ( int i=0; i<3; i++ ) {
+      for ( int j=0; j<3; j++ ) {
+        clog << "A[" << i << "," << j << "] = " << A(i,j) << '\n';
+      }
+    }
+    clog << std::endl;
+
+    Eigen::ColPivHouseholderQR<Eigen::MatrixXd> QRD(A);
+    
+    clog << "matrix A after ColPivHouseholder" << std::endl;
+    for ( int i=0; i<3; i++ ) {
+      for ( int j=0; j<3; j++ ) {
+        clog << "A[" << i << "," << j << "] = " << A(i,j) << '\n';
+      }
+    }
+    clog << std::endl;
+    
+    clog << "HouseholderQ with sequence lenth = nonzeroPiviots" << std::endl;
+    Q = QRD.householderQ().setLength(QRD.nonzeroPivots());
+    for ( int i=0; i<3; i++ ) {
+      for ( int j=0; j<3; j++ ) {
+        clog << "Q[" << i << "," << j << "] = " << Q(i,j) << '\n';
+      }
+    }
+    clog << std::endl;
+    
+    clog << "HouseholderQ with sequence lenth = 1" << std::endl;
+    Q = QRD.householderQ().setLength(1);
+    for ( int i=0; i<3; i++ ) {
+      for ( int j=0; j<3; j++ ) {
+        clog << "Q[" << i << "," << j << "] = " << Q(i,j) << '\n';
+      }
+    }
+    clog << std::endl;
+    
+    clog << "HouseholderQ with sequence lenth = 2" << std::endl;
+    Q = QRD.householderQ().setLength(2);
+    for ( int i=0; i<3; i++ ) {
+      for ( int j=0; j<3; j++ ) {
+        clog << "Q[" << i << "," << j << "] = " << Q(i,j) << '\n';
+      }
+    }
+    clog << std::endl;
+    
+    clog << "matrixR" << std::endl;
+    R = QRD.matrixR();
+    for ( int i=0; i<3; i++ ) {
+      for ( int j=0; j<3; j++ ) {
+        clog << "R[" << i << "," << j << "] = " << R(i,j) << '\n';
+      }
+    }
+    clog << std::endl;
+
+    clog << "rank = " << QRD.rank() << std::endl;
+    clog << "threshold = " << QRD.threshold() << std::endl;
+    
+    clog << "matrixP" << std::endl;
+    P = QRD.colsPermutation();
+    for ( int i=0; i<3; i++ ) {
+      for ( int j=0; j<3; j++ ) {
+        clog << "P[" << i << "," << j << "] = " << P(i,j) << '\n';
+      }
+    }
+    clog << std::endl;
+
+
+    clog << "QR decomposition without column pivoting" << std::endl;
+    
+    A(0,0) = 12.0;
+    A(0,1) = -51.0;
+    A(0,2) = 4.0;
+    A(1,0) = 6.0;
+    A(1,1) = 167.0;
+    A(1,2) = -68.0;
+    A(2,0) = -4.0;
+    A(2,1) = 24.0;
+    A(2,2) = -41.0;
+    
+    clog << "matrix A before Householder" << std::endl;
+    for ( int i=0; i<3; i++ ) {
+      for ( int j=0; j<3; j++ ) {
+        clog << "A[" << i << "," << j << "] = " << A(i,j) << '\n';
+      }
+    }
+    clog << std::endl;
+    
+    Eigen::HouseholderQR<Eigen::MatrixXd> QRDplain(A);
+    
+    clog << "HouseholderQ" << std::endl;
+    Q = QRDplain.householderQ();
+    for ( int i=0; i<3; i++ ) {
+      for ( int j=0; j<3; j++ ) {
+        clog << "Q[" << i << "," << j << "] = " << Q(i,j) << '\n';
+      }
+    }
+    clog << std::endl;
+    
+    clog << "matrix A after Householder" << std::endl;
+    for ( int i=0; i<3; i++ ) {
+      for ( int j=0; j<3; j++ ) {
+        clog << "A[" << i << "," << j << "] = " << A(i,j) << '\n';
+      }
+    }
+    clog << std::endl;
+  }
+
+ };
+}
+#undef clog
+#endif

lib/algorithms/iterative/ImplicitlyRestartedLanczos.h

@@ -32,6 +32,8 @@ Author: Guido Cossu
 
 #include <string.h> //memset
 
+#define clog std::cout << GridLogMessage 
+
 namespace Grid {
 
   enum IRLdiagonalisation { 
@@ -229,7 +231,16 @@ until convergence
       
       for(int k=Nk; k<Nm; ++k) step(eval,lme,evec,f,Nm,k);
       
+      for(int k=0; k<Nm; ++k) {
+        clog << "ckpt A1: lme[" << k << "] = " << lme[k] << '\n';
+      }
+      for(int k=0; k<Nm; ++k) {
+        clog << "ckpt A2: lmd[" << k << "] = " << eval[k] << '\n';
+      }
+      
       f *= lme[Nm-1];
+      //clog << "ckpt C " << '\n';
+      //clog << "norm2(f) = " << norm2(f) << std::endl;
       
       // getting eigenvalues
       for(int k=0; k<Nm; ++k){
@@ -238,16 +249,39 @@ until convergence
       }
       Qt = Eigen::MatrixXd::Identity(Nm,Nm);
       diagonalize(eval2,lme2,Nm,Nm,Qt,grid);
+      
+      //for(int k=0; k<Nm; ++k){
+      //  clog << "ckpt D " << '\n';
+      //  clog << "eval2 [" << k << "] = " << eval2[k] << std::endl;
+      //}
 
       // sorting
       _sort.push(eval2,Nm);
       
+      //for(int k=0; k<Nm; ++k){
+      //  clog << "ckpt E " << '\n';
+      //  clog << "eval2 [" << k << "] = " << eval2[k] << std::endl;
+      //}
+      
       // Implicitly shifted QR transformations
       Qt = Eigen::MatrixXd::Identity(Nm,Nm);
       for(int ip=k2; ip<Nm; ++ip){ 
 	// Eigen replacement for qr_decomp ???
+        clog << "ckpt B1: shift[" << ip << "] = " << eval2[ip] << endl;
 	qr_decomp(eval,lme,Nm,Nm,Qt,eval2[ip],k1,Nm);
       }
+      
+      //for (int i=0; i<Nm; ++i) {
+      //  for (int j=0; j<Nm; ++j) {
+      //    clog << "ckpt G2: Q[" << i << "," << j << "] = " << Qt(j,i) << '\n';
+      //  }
+      //}
+      for (int i=0; i<Nm; ++i) {
+        clog << "ckpt C1: lme[" << i << "] = " << lme[i] << '\n';
+      }
+      for (int i=0; i<Nm; ++i) {
+        clog << "ckpt C2: lmd[" << i << "] = " << eval[i] << '\n';
+      }
     
       for(int i=0; i<(Nk+1); ++i) B[i] = 0.0;
 	  
@@ -257,14 +291,18 @@ until convergence
 	  B[j] += Qt(j,k) * evec[k];
 	}
       }
-      for(int j=k1-1; j<k2+1; ++j) evec[j] = B[j];
+      for(int j=k1-1; j<k2+1; ++j) {
+        evec[j] = B[j];
+        //clog << "ckpt F: norm2_evec[ " << j << "]" << norm2(evec[j]) << std::endl;
+      }
       
       // Compressed vector f and beta(k2)
       f *= Qt(k2-1,Nm-1);
-      f += lme[k2-1] * evec[k2];
+      f += lme[k2-1] * evec[k2]; // was commented out
+      std::cout<< GridLogMessage<<"ckpt D1: Q[Nm-1,Nk-1] = "<<Qt(Nk-1,Nm-1)<<std::endl;
       beta_k = norm2(f);
       beta_k = sqrt(beta_k);
-      std::cout<< GridLogMessage<<" beta(k) = "<<beta_k<<std::endl;
+      std::cout<< GridLogMessage<<"ckpt D2: beta(k) = "<<beta_k<<std::endl;
       
       RealD betar = 1.0/beta_k;
       evec[k2] = betar * f;
@@ -286,6 +324,19 @@ until convergence
 	  B[j] += Qt(j,k) * evec[k];
 	}
       }
+      
+      //for (int i=0; i<Nk; ++i) {
+      //  for (int j=0; j<Nk; ++j) {
+      //    clog << "ckpt H1: R[" << i << "," << j << "] = " << Qt(j,i) << '\n';
+      //  }
+      //}
+      //for (int i=0; i<Nk; ++i) {
+      //  clog << "ckpt H2: eval2[" << i << "] = " << eval2[i] << '\n';
+      //}
+      
+      //for(int j=0; j<Nk; ++j) {
+      //  clog << "ckpt I: norm2_B[ " << j << "]" << norm2(B[j]) << std::endl;
+      //}
 
       Nconv = 0;
       for(int i=0; i<Nk; ++i){
@@ -363,10 +414,17 @@ private:
     
     _poly(_Linop,evec[k],w);      // 3. wk:=Avk−βkv_{k−1}
     
-    if(k>0) w -= lme[k-1] * evec[k-1];
+    if(k>0) { 
+      w -= lme[k-1] * evec[k-1];
+      //clog << "ckpt A (k= " << k << ")" << '\n';
+      //clog << "lme = " << lme[k-1] << '\n';
+      //clog << "norm(w) = " << norm2(w) << std::endl;
+    }
     
     ComplexD zalph = innerProduct(evec[k],w); // 4. αk:=(wk,vk)
     RealD     alph = real(zalph);
+    //clog << "ckpt B (k= " << k << ")" << '\n';
+    //clog << "lmd = " << alph << std::endl;
     
     w = w - alph * evec[k];// 5. wk:=wk−αkvk
     
@@ -622,4 +680,5 @@ void diagonalize_lapack(std::vector<RealD>& lmd,
 
  };
 }
+#undef clog
 #endif

lib/algorithms/iterative/ImplicitlyRestartedLanczos.h.bak

@@ -0,0 +1,625 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ImplicitlyRestartedLanczos.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Chulwoo Jung
+Author: Guido Cossu
+
+    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 */
+#ifndef GRID_IRL_H
+#define GRID_IRL_H
+
+#include <string.h> //memset
+
+namespace Grid {
+
+  enum IRLdiagonalisation { 
+    IRLdiagonaliseWithDSTEGR,
+    IRLdiagonaliseWithQR,
+    IRLdiagonaliseWithEigen
+  };
+
+////////////////////////////////////////////////////////////////////////////////
+// Helper class for sorting the evalues AND evectors by Field
+// Use pointer swizzle on vectors
+////////////////////////////////////////////////////////////////////////////////
+template<class Field>
+class SortEigen {
+ private:
+  static bool less_lmd(RealD left,RealD right){
+    return left > right;
+  }  
+  static bool less_pair(std::pair<RealD,Field const*>& left,
+                        std::pair<RealD,Field const*>& right){
+    return left.first > (right.first);
+  }  
+  
+ public:
+  void push(std::vector<RealD>& lmd,std::vector<Field>& evec,int N) {
+    
+    ////////////////////////////////////////////////////////////////////////
+    // PAB: FIXME: VERY VERY VERY wasteful: takes a copy of the entire vector set.
+    //    : The vector reorder should be done by pointer swizzle somehow
+    ////////////////////////////////////////////////////////////////////////
+    std::vector<Field> cpy(lmd.size(),evec[0]._grid);
+    for(int i=0;i<lmd.size();i++) cpy[i] = evec[i];
+    
+    std::vector<std::pair<RealD, Field const*> > emod(lmd.size());    
+
+    for(int i=0;i<lmd.size();++i)  emod[i] = std::pair<RealD,Field const*>(lmd[i],&cpy[i]);
+
+    partial_sort(emod.begin(),emod.begin()+N,emod.end(),less_pair);
+
+    typename std::vector<std::pair<RealD, Field const*> >::iterator it = emod.begin();
+    for(int i=0;i<N;++i){
+      lmd[i]=it->first;
+      evec[i]=*(it->second);
+      ++it;
+    }
+  }
+  void push(std::vector<RealD>& lmd,int N) {
+    std::partial_sort(lmd.begin(),lmd.begin()+N,lmd.end(),less_lmd);
+  }
+  bool saturated(RealD lmd, RealD thrs) {
+    return fabs(lmd) > fabs(thrs);
+  }
+};
+
+/////////////////////////////////////////////////////////////
+// Implicitly restarted lanczos
+/////////////////////////////////////////////////////////////
+template<class Field> 
+class ImplicitlyRestartedLanczos {
+
+private:       
+
+  int MaxIter;   // Max iterations
+  int Nstop;     // Number of evecs checked for convergence
+  int Nk;        // Number of converged sought
+  int Nm;        // Nm -- total number of vectors
+  RealD eresid;
+  IRLdiagonalisation diagonalisation;
+  ////////////////////////////////////
+  // Embedded objects
+  ////////////////////////////////////
+           SortEigen<Field> _sort;
+  LinearOperatorBase<Field> &_Linop;
+    OperatorFunction<Field> &_poly;
+
+  /////////////////////////
+  // Constructor
+  /////////////////////////
+public:       
+ ImplicitlyRestartedLanczos(LinearOperatorBase<Field> &Linop, // op
+			    OperatorFunction<Field> & poly,   // polynomial
+			    int _Nstop, // really sought vecs
+			    int _Nk,    // sought vecs
+			    int _Nm,    // total vecs
+			    RealD _eresid, // resid in lmd deficit 
+			    int _MaxIter,  // Max iterations
+			    IRLdiagonalisation _diagonalisation= IRLdiagonaliseWithEigen ) :
+    _Linop(Linop),    _poly(poly),
+      Nstop(_Nstop), Nk(_Nk), Nm(_Nm),
+      eresid(_eresid),  MaxIter(_MaxIter),
+      diagonalisation(_diagonalisation)
+      { };
+
+  ////////////////////////////////
+  // Helpers
+  ////////////////////////////////
+  static RealD normalise(Field& v) 
+  {
+    RealD nn = norm2(v);
+    nn = sqrt(nn);
+    v = v * (1.0/nn);
+    return nn;
+  }
+  
+  void orthogonalize(Field& w, std::vector<Field>& evec, int k)
+  {
+    typedef typename Field::scalar_type MyComplex;
+    MyComplex ip;
+    
+    for(int j=0; j<k; ++j){
+      ip = innerProduct(evec[j],w); 
+      w = w - ip * evec[j];
+    }
+    normalise(w);
+  }
+
+/* Rudy Arthur's thesis pp.137
+------------------------
+Require: M > K P = M − K †
+Compute the factorization AVM = VM HM + fM eM 
+repeat
+  Q=I
+  for i = 1,...,P do
+    QiRi =HM −θiI Q = QQi
+    H M = Q †i H M Q i
+  end for
+  βK =HM(K+1,K) σK =Q(M,K)
+  r=vK+1βK +rσK
+  VK =VM(1:M)Q(1:M,1:K)
+  HK =HM(1:K,1:K)
+  →AVK =VKHK +fKe†K † Extend to an M = K + P step factorization AVM = VMHM + fMeM
+until convergence
+*/
+  void calc(std::vector<RealD>& eval,  std::vector<Field>& evec, const Field& src, int& Nconv)
+  {
+    
+    GridBase *grid = evec[0]._grid;
+    assert(grid == src._grid);
+    
+    std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
+    std::cout << GridLogMessage <<" ImplicitlyRestartedLanczos::calc() starting iteration 0 /  "<< MaxIter<< std::endl;
+    std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
+    std::cout << GridLogMessage <<" -- seek   Nk    = " << Nk    <<" vectors"<< std::endl;
+    std::cout << GridLogMessage <<" -- accept Nstop = " << Nstop <<" vectors"<< std::endl;
+    std::cout << GridLogMessage <<" -- total  Nm    = " << Nm    <<" vectors"<< std::endl;
+    std::cout << GridLogMessage <<" -- size of eval = " << eval.size() << std::endl;
+    std::cout << GridLogMessage <<" -- size of evec = " << evec.size() << std::endl;
+    if ( diagonalisation == IRLdiagonaliseWithDSTEGR ) {
+      std::cout << GridLogMessage << "Diagonalisation is DSTEGR "<<std::endl;
+    } else if ( diagonalisation == IRLdiagonaliseWithQR ) { 
+      std::cout << GridLogMessage << "Diagonalisation is QR "<<std::endl;
+    }  else if ( diagonalisation == IRLdiagonaliseWithEigen ) { 
+      std::cout << GridLogMessage << "Diagonalisation is Eigen "<<std::endl;
+    }
+    std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
+    
+    assert(Nm == evec.size() && Nm == eval.size());
+	
+    std::vector<RealD> lme(Nm);  
+    std::vector<RealD> lme2(Nm);
+    std::vector<RealD> eval2(Nm);
+
+    Eigen::MatrixXd    Qt = Eigen::MatrixXd::Zero(Nm,Nm);
+
+    std::vector<int>   Iconv(Nm);
+    std::vector<Field>  B(Nm,grid); // waste of space replicating
+    
+    Field f(grid);
+    Field v(grid);
+    
+    int k1 = 1;
+    int k2 = Nk;
+    
+    Nconv = 0;
+    
+    RealD beta_k;
+  
+    // Set initial vector
+    evec[0] = src;
+    std::cout << GridLogMessage <<"norm2(src)= " << norm2(src)<<std::endl;
+    
+    normalise(evec[0]);
+    std::cout << GridLogMessage <<"norm2(evec[0])= " << norm2(evec[0]) <<std::endl;
+    
+    // Initial Nk steps
+    for(int k=0; k<Nk; ++k) step(eval,lme,evec,f,Nm,k);
+    
+    // Restarting loop begins
+    int iter;
+    for(iter = 0; iter<MaxIter; ++iter){
+      
+      std::cout<< GridLogMessage <<" **********************"<< std::endl;
+      std::cout<< GridLogMessage <<" Restart iteration = "<< iter << std::endl;
+      std::cout<< GridLogMessage <<" **********************"<< std::endl;
+      
+      for(int k=Nk; k<Nm; ++k) step(eval,lme,evec,f,Nm,k);
+      
+      f *= lme[Nm-1];
+      
+      // getting eigenvalues
+      for(int k=0; k<Nm; ++k){
+	eval2[k] = eval[k+k1-1];
+	lme2[k] = lme[k+k1-1];
+      }
+      Qt = Eigen::MatrixXd::Identity(Nm,Nm);
+      diagonalize(eval2,lme2,Nm,Nm,Qt,grid);
+
+      // sorting
+      _sort.push(eval2,Nm);
+      
+      // Implicitly shifted QR transformations
+      Qt = Eigen::MatrixXd::Identity(Nm,Nm);
+      for(int ip=k2; ip<Nm; ++ip){ 
+	// Eigen replacement for qr_decomp ???
+	qr_decomp(eval,lme,Nm,Nm,Qt,eval2[ip],k1,Nm);
+      }
+    
+      for(int i=0; i<(Nk+1); ++i) B[i] = 0.0;
+	  
+      for(int j=k1-1; j<k2+1; ++j){
+	for(int k=0; k<Nm; ++k){
+	  B[j].checkerboard = evec[k].checkerboard;
+	  B[j] += Qt(j,k) * evec[k];
+	}
+      }
+      for(int j=k1-1; j<k2+1; ++j) evec[j] = B[j];
+      
+      // Compressed vector f and beta(k2)
+      f *= Qt(k2-1,Nm-1);
+      f += lme[k2-1] * evec[k2];
+      beta_k = norm2(f);
+      beta_k = sqrt(beta_k);
+      std::cout<< GridLogMessage<<" beta(k) = "<<beta_k<<std::endl;
+      
+      RealD betar = 1.0/beta_k;
+      evec[k2] = betar * f;
+      lme[k2-1] = beta_k;
+      
+      // Convergence test
+      for(int k=0; k<Nm; ++k){    
+	eval2[k] = eval[k];
+	lme2[k] = lme[k];
+      }
+      Qt = Eigen::MatrixXd::Identity(Nm,Nm);
+      diagonalize(eval2,lme2,Nk,Nm,Qt,grid);
+      
+      for(int k = 0; k<Nk; ++k) B[k]=0.0;
+      
+      for(int j = 0; j<Nk; ++j){
+	for(int k = 0; k<Nk; ++k){
+	  B[j].checkerboard = evec[k].checkerboard;
+	  B[j] += Qt(j,k) * evec[k];
+	}
+      }
+
+      Nconv = 0;
+      for(int i=0; i<Nk; ++i){
+	
+	_Linop.HermOp(B[i],v);
+	    
+	RealD vnum = real(innerProduct(B[i],v)); // HermOp.
+	RealD vden = norm2(B[i]);
+	eval2[i] = vnum/vden;
+	v -= eval2[i]*B[i];
+	RealD vv = norm2(v);
+	
+	std::cout.precision(13);
+	std::cout << GridLogMessage << "[" << std::setw(3)<< std::setiosflags(std::ios_base::right) <<i<<"] ";
+	std::cout << "eval = "<<std::setw(25)<< std::setiosflags(std::ios_base::left)<< eval2[i];
+	std::cout << " |H B[i] - eval[i]B[i]|^2 "<< std::setw(25)<< std::setiosflags(std::ios_base::right)<< vv<< std::endl;
+	
+	// change the criteria as evals are supposed to be sorted, all evals smaller(larger) than Nstop should have converged
+	if((vv<eresid*eresid) && (i == Nconv) ){
+	  Iconv[Nconv] = i;
+	  ++Nconv;
+	}
+	
+      }  // i-loop end
+      
+      std::cout<< GridLogMessage <<" #modes converged: "<<Nconv<<std::endl;
+
+      if( Nconv>=Nstop ){
+	goto converged;
+      }
+    } // end of iter loop
+    
+    std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
+    std::cout<< GridLogError    <<" ImplicitlyRestartedLanczos::calc() NOT converged.";
+    std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
+    abort();
+	
+  converged:
+    // Sorting
+    eval.resize(Nconv);
+    evec.resize(Nconv,grid);
+    for(int i=0; i<Nconv; ++i){
+      eval[i] = eval2[Iconv[i]];
+      evec[i] = B[Iconv[i]];
+    }
+    _sort.push(eval,evec,Nconv);
+    
+    std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
+    std::cout << GridLogMessage << "ImplicitlyRestartedLanczos CONVERGED ; Summary :\n";
+    std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
+    std::cout << GridLogMessage << " -- Iterations  = "<< iter   << "\n";
+    std::cout << GridLogMessage << " -- beta(k)     = "<< beta_k << "\n";
+    std::cout << GridLogMessage << " -- Nconv       = "<< Nconv  << "\n";
+    std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
+  }
+
+private:
+/* Saad PP. 195
+1. Choose an initial vector v1 of 2-norm unity. Set β1 ≡ 0, v0 ≡ 0
+2. For k = 1,2,...,m Do:
+3. wk:=Avk−βkv_{k−1}      
+4. αk:=(wk,vk)       // 
+5. wk:=wk−αkvk       // wk orthog vk 
+6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
+7. vk+1 := wk/βk+1
+8. EndDo
+ */
+  void step(std::vector<RealD>& lmd,
+	    std::vector<RealD>& lme, 
+	    std::vector<Field>& evec,
+	    Field& w,int Nm,int k)
+  {
+    const RealD tiny = 1.0e-20;
+    assert( k< Nm );
+    
+    _poly(_Linop,evec[k],w);      // 3. wk:=Avk−βkv_{k−1}
+    
+    if(k>0) w -= lme[k-1] * evec[k-1];
+    
+    ComplexD zalph = innerProduct(evec[k],w); // 4. αk:=(wk,vk)
+    RealD     alph = real(zalph);
+    
+    w = w - alph * evec[k];// 5. wk:=wk−αkvk
+    
+    RealD beta = normalise(w); // 6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
+    // 7. vk+1 := wk/βk+1
+    
+    lmd[k] = alph;
+    lme[k] = beta;
+    
+    if ( k > 0 ) orthogonalize(w,evec,k); // orthonormalise
+    if ( k < Nm-1) evec[k+1] = w;
+    
+    if ( beta < tiny ) std::cout << GridLogMessage << " beta is tiny "<<beta<<std::endl;
+  }
+      
+  void diagonalize_Eigen(std::vector<RealD>& lmd, std::vector<RealD>& lme, 
+			 int Nk, int Nm,  
+			 Eigen::MatrixXd & Qt, // Nm x Nm
+			 GridBase *grid)
+  {
+    Eigen::MatrixXd TriDiag = Eigen::MatrixXd::Zero(Nk,Nk);
+
+    for(int i=0;i<Nk;i++)   TriDiag(i,i)   = lmd[i];
+    for(int i=0;i<Nk-1;i++) TriDiag(i,i+1) = lme[i];
+    for(int i=0;i<Nk-1;i++) TriDiag(i+1,i) = lme[i];
+    
+    Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eigensolver(TriDiag);
+
+    for (int i = 0; i < Nk; i++) {
+      lmd[Nk-1-i] = eigensolver.eigenvalues()(i);
+    }
+    for (int i = 0; i < Nk; i++) {
+      for (int j = 0; j < Nk; j++) {
+	Qt(Nk-1-i,j) = eigensolver.eigenvectors()(j,i);
+      }
+    }
+  }
+  ///////////////////////////////////////////////////////////////////////////
+  // File could end here if settle on Eigen ???
+  ///////////////////////////////////////////////////////////////////////////
+
+  void qr_decomp(std::vector<RealD>& lmd,   // Nm 
+		 std::vector<RealD>& lme,   // Nm 
+		 int Nk, int Nm,            // Nk, Nm
+		 Eigen::MatrixXd& Qt,       // Nm x Nm matrix
+		 RealD Dsh, int kmin, int kmax)
+  {
+    int k = kmin-1;
+    RealD x;
+    
+    RealD Fden = 1.0/hypot(lmd[k]-Dsh,lme[k]);
+    RealD c = ( lmd[k] -Dsh) *Fden;
+    RealD s = -lme[k] *Fden;
+      
+    RealD tmpa1 = lmd[k];
+    RealD tmpa2 = lmd[k+1];
+    RealD tmpb  = lme[k];
+
+    lmd[k]   = c*c*tmpa1 +s*s*tmpa2 -2.0*c*s*tmpb;
+    lmd[k+1] = s*s*tmpa1 +c*c*tmpa2 +2.0*c*s*tmpb;
+    lme[k]   = c*s*(tmpa1-tmpa2) +(c*c-s*s)*tmpb;
+    x        =-s*lme[k+1];
+    lme[k+1] = c*lme[k+1];
+      
+    for(int i=0; i<Nk; ++i){
+      RealD Qtmp1 = Qt(k,i);
+      RealD Qtmp2 = Qt(k+1,i);
+      Qt(k,i)  = c*Qtmp1 - s*Qtmp2;
+      Qt(k+1,i)= s*Qtmp1 + c*Qtmp2; 
+    }
+
+    // Givens transformations
+    for(int k = kmin; k < kmax-1; ++k){
+      
+      RealD Fden = 1.0/hypot(x,lme[k-1]);
+      RealD c = lme[k-1]*Fden;
+      RealD s = - x*Fden;
+	
+      RealD tmpa1 = lmd[k];
+      RealD tmpa2 = lmd[k+1];
+      RealD tmpb  = lme[k];
+
+      lmd[k]   = c*c*tmpa1 +s*s*tmpa2 -2.0*c*s*tmpb;
+      lmd[k+1] = s*s*tmpa1 +c*c*tmpa2 +2.0*c*s*tmpb;
+      lme[k]   = c*s*(tmpa1-tmpa2) +(c*c-s*s)*tmpb;
+      lme[k-1] = c*lme[k-1] -s*x;
+
+      if(k != kmax-2){
+	x = -s*lme[k+1];
+	lme[k+1] = c*lme[k+1];
+      }
+
+      for(int i=0; i<Nk; ++i){
+	RealD Qtmp1 = Qt(k,i);
+	RealD Qtmp2 = Qt(k+1,i);
+	Qt(k,i)     = c*Qtmp1 -s*Qtmp2;
+	Qt(k+1,i)   = s*Qtmp1 +c*Qtmp2;
+      }
+    }
+  }
+
+  void diagonalize(std::vector<RealD>& lmd, std::vector<RealD>& lme, 
+		   int Nk, int Nm,   
+		   Eigen::MatrixXd & Qt,
+		   GridBase *grid)
+  {
+    Qt = Eigen::MatrixXd::Identity(Nm,Nm);
+    if ( diagonalisation == IRLdiagonaliseWithDSTEGR ) {
+      diagonalize_lapack(lmd,lme,Nk,Nm,Qt,grid);
+    } else if ( diagonalisation == IRLdiagonaliseWithQR ) { 
+      diagonalize_QR(lmd,lme,Nk,Nm,Qt,grid);
+    }  else if ( diagonalisation == IRLdiagonaliseWithEigen ) { 
+      diagonalize_Eigen(lmd,lme,Nk,Nm,Qt,grid);
+    } else { 
+      assert(0);
+    }
+  }
+
+#ifdef USE_LAPACK
+void LAPACK_dstegr(char *jobz, char *range, int *n, double *d, double *e,
+                   double *vl, double *vu, int *il, int *iu, double *abstol,
+                   int *m, double *w, double *z, int *ldz, int *isuppz,
+                   double *work, int *lwork, int *iwork, int *liwork,
+                   int *info);
+#endif
+
+void diagonalize_lapack(std::vector<RealD>& lmd,
+			std::vector<RealD>& lme, 
+			int Nk, int Nm,  
+			Eigen::MatrixXd& Qt,
+			GridBase *grid)
+{
+#ifdef USE_LAPACK
+  const int size = Nm;
+  int NN = Nk;
+  double evals_tmp[NN];
+  double evec_tmp[NN][NN];
+  memset(evec_tmp[0],0,sizeof(double)*NN*NN);
+  double DD[NN];
+  double EE[NN];
+  for (int i = 0; i< NN; i++) {
+    for (int j = i - 1; j <= i + 1; j++) {
+      if ( j < NN && j >= 0 ) {
+	if (i==j) DD[i] = lmd[i];
+	if (i==j) evals_tmp[i] = lmd[i];
+	if (j==(i-1)) EE[j] = lme[j];
+      }
+    }
+  }
+  int evals_found;
+  int lwork = ( (18*NN) > (1+4*NN+NN*NN)? (18*NN):(1+4*NN+NN*NN)) ;
+  int liwork =  3+NN*10 ;
+  int iwork[liwork];
+  double work[lwork];
+  int isuppz[2*NN];
+  char jobz = 'V'; // calculate evals & evecs
+  char range = 'I'; // calculate all evals
+  //    char range = 'A'; // calculate all evals
+  char uplo = 'U'; // refer to upper half of original matrix
+  char compz = 'I'; // Compute eigenvectors of tridiagonal matrix
+  int ifail[NN];
+  int info;
+  int total = grid->_Nprocessors;
+  int node  = grid->_processor;
+  int interval = (NN/total)+1;
+  double vl = 0.0, vu = 0.0;
+  int il = interval*node+1 , iu = interval*(node+1);
+  if (iu > NN)  iu=NN;
+  double tol = 0.0;
+  if (1) {
+    memset(evals_tmp,0,sizeof(double)*NN);
+    if ( il <= NN){
+      LAPACK_dstegr(&jobz, &range, &NN,
+		    (double*)DD, (double*)EE,
+		    &vl, &vu, &il, &iu, // these four are ignored if second parameteris 'A'
+		    &tol, // tolerance
+		    &evals_found, evals_tmp, (double*)evec_tmp, &NN,
+		    isuppz,
+		    work, &lwork, iwork, &liwork,
+		    &info);
+      for (int i = iu-1; i>= il-1; i--){
+	evals_tmp[i] = evals_tmp[i - (il-1)];
+	if (il>1) evals_tmp[i-(il-1)]=0.;
+	for (int j = 0; j< NN; j++){
+	  evec_tmp[i][j] = evec_tmp[i - (il-1)][j];
+	  if (il>1) evec_tmp[i-(il-1)][j]=0.;
+	}
+      }
+    }
+    {
+      grid->GlobalSumVector(evals_tmp,NN);
+      grid->GlobalSumVector((double*)evec_tmp,NN*NN);
+    }
+  } 
+  // Safer to sort instead of just reversing it, 
+  // but the document of the routine says evals are sorted in increasing order. 
+  // qr gives evals in decreasing order.
+  for(int i=0;i<NN;i++){
+    lmd [NN-1-i]=evals_tmp[i];
+    for(int j=0;j<NN;j++){
+      Qt((NN-1-i),j)=evec_tmp[i][j];
+    }
+  }
+#else 
+  assert(0);
+#endif
+}
+
+  void diagonalize_QR(std::vector<RealD>& lmd, std::vector<RealD>& lme, 
+		      int Nk, int Nm,   
+		      Eigen::MatrixXd & Qt,
+		      GridBase *grid)
+  {
+    int Niter = 100*Nm;
+    int kmin = 1;
+    int kmax = Nk;
+
+    // (this should be more sophisticated)
+    for(int iter=0; iter<Niter; ++iter){
+      
+      // determination of 2x2 leading submatrix
+      RealD dsub = lmd[kmax-1]-lmd[kmax-2];
+      RealD dd = sqrt(dsub*dsub + 4.0*lme[kmax-2]*lme[kmax-2]);
+      RealD Dsh = 0.5*(lmd[kmax-2]+lmd[kmax-1] +dd*(dsub/fabs(dsub)));
+      // (Dsh: shift)
+	
+      // transformation
+      qr_decomp(lmd,lme,Nk,Nm,Qt,Dsh,kmin,kmax); // Nk, Nm
+	
+      // Convergence criterion (redef of kmin and kamx)
+      for(int j=kmax-1; j>= kmin; --j){
+	RealD dds = fabs(lmd[j-1])+fabs(lmd[j]);
+	if(fabs(lme[j-1])+dds > dds){
+	  kmax = j+1;
+	  goto continued;
+	}
+      }
+      Niter = iter;
+      return;
+
+    continued:
+      for(int j=0; j<kmax-1; ++j){
+	RealD dds = fabs(lmd[j])+fabs(lmd[j+1]);
+	if(fabs(lme[j])+dds > dds){
+	  kmin = j+1;
+	  break;
+	}
+      }
+    }
+    std::cout << GridLogError << "[QL method] Error - Too many iteration: "<<Niter<<"\n";
+    abort();
+  }
+
+ };
+}
+#endif

tests/lanczos/Test_dwf_block_lanczos.cc

@@ -51,9 +51,9 @@ int main (int argc, char ** argv)
   std::vector<int> seeds5({5,6,7,8});
   GridParallelRNG          RNG5(FGrid);  RNG5.SeedFixedIntegers(seeds5);
   GridParallelRNG          RNG4(UGrid);  RNG4.SeedFixedIntegers(seeds4);
-  //GridParallelRNG          RNG5rb(FrbGrid);  RNG5.SeedFixedIntegers(seeds5); 
+  GridParallelRNG          RNG5rb(FrbGrid);  RNG5.SeedFixedIntegers(seeds5); 
   // ypj [note] why seed RNG5 again? bug? In this case, run with a default seed().
-  GridParallelRNG          RNG5rb(FrbGrid);  //RNG5rb.SeedFixedIntegers(seeds5);
+  //GridParallelRNG          RNG5rb(FrbGrid);  //RNG5rb.SeedFixedIntegers(seeds5);
 
   LatticeGaugeField Umu(UGrid); 
   SU3::HotConfiguration(RNG4, Umu);
@@ -77,19 +77,19 @@ int main (int argc, char ** argv)
   SchurDiagTwoOperator<GparityMobiusFermionR,FermionField> HermOp(Ddwf);
 //  SchurDiagMooeeOperator<DomainWallFermionR,LatticeFermion> HermOp(Ddwf);
 
-  const int Nstop = 30;
+  const int Nstop = 50;
-  const int Nu = 4;
+  const int Nu = 1;
-  const int Nk = 60;
+  const int Nk = 200;
-  const int Np = 60;
+  const int Np = 200;
   const int Nm = Nk+Np;
-  const int MaxIt= 10000;
+  const int MaxIt= 10;
   RealD resid = 1.0e-8;
 
   //std::vector<double> Coeffs { 0.,-1.}; 
   // ypj [note] this may not be supported by some compilers
-  std::vector<double> Coeffs({ 0.,1.}); 
+  std::vector<double> Coeffs({ 0.,-1.}); 
   Polynomial<FermionField> PolyX(Coeffs);
-  Chebyshev<FermionField> Cheb(0.2,5.,11);
+  Chebyshev<FermionField> Cheb(0.2,5.5,11);
 //  ChebyshevLanczos<LatticeFermion> Cheb(9.,1.,0.,20);
 //  Cheb.csv(std::cout);
 //  exit(-24);

tests/lanczos/Test_dwf_lanczos.cc

@@ -75,16 +75,16 @@ int main (int argc, char ** argv)
   SchurDiagTwoOperator<GparityMobiusFermionR,FermionField> HermOp(Ddwf);
 //  SchurDiagMooeeOperator<DomainWallFermionR,LatticeFermion> HermOp(Ddwf);
 
-  const int Nstop = 30;
+  const int Nstop = 50;
-  const int Nk = 40;
+  const int Nk = 200;
-  const int Np = 40;
+  const int Np = 200;
   const int Nm = Nk+Np;
-  const int MaxIt= 10000;
+  const int MaxIt= 100;
   RealD resid = 1.0e-8;
 
   std::vector<double> Coeffs { 0.,-1.};
   Polynomial<FermionField> PolyX(Coeffs);
-  Chebyshev<FermionField> Cheb(0.2,5.,11);
+  Chebyshev<FermionField> Cheb(0.2,5.5,11);
 //  ChebyshevLanczos<LatticeFermion> Cheb(9.,1.,0.,20);
 //  Cheb.csv(std::cout);
 //  exit(-24);