public static CGetHessCoarseResiIterImpl Do
                    (object[] atoms
                    , HessMatrix H
                    , List <int>[] lstNewIdxRemv
                    , double thres_zeroblk
                    , ILinAlg ila
                    , bool cloneH
                    , string[] options
                    )
                {
                    //HDebug.ToDo();

                    ila    = null;
                    cloneH = true;
                    if (cloneH)
                    {
                        H = H.CloneHess();
                    }

                    bool process_disp_console = true;

                    if (options != null && options.Contains("print process"))
                    {
                        process_disp_console = true;
                    }

                    bool parallel = false;

                    /// keep only lower triangle of H (lower block triangles)
                    {
                        HashSet <Tuple <int, int, MatrixByArr> > lstUppTrig = new HashSet <Tuple <int, int, MatrixByArr> >();
                        foreach (ValueTuple <int, int, MatrixByArr> bc_br_bval in H.EnumBlocks())
                        {
                            int bc = bc_br_bval.Item1;
                            int br = bc_br_bval.Item2;
                            if (bc < br)
                            {
                                lstUppTrig.Add(bc_br_bval.ToTuple());
                            }
                        }
                        foreach (Tuple <int, int, MatrixByArr> bc_br_bval in lstUppTrig)
                        {
                            int bc = bc_br_bval.Item1;
                            int br = bc_br_bval.Item2;
                            HDebug.Assert(bc < br);
                            H.SetBlock(bc, br, null);
                        }
                    }
                    GC.Collect();

                    DateTime[] process_time = new DateTime[6];

                    //System.Console.WriteLine("begin coarse-graining");
                    List <HessCoarseResiIterInfo> iterinfos = new List <HessCoarseResiIterInfo>();

                    for (int iter = lstNewIdxRemv.Length - 1; iter >= 0; iter--)
                    {
                        bool lprocess_disp_console = (process_disp_console && iter % 5 == 0);
                        lprocess_disp_console = true;
                        if (lprocess_disp_console)
                        {
                            process_time[0] = DateTime.UtcNow;
                            System.Console.Write(" - {0:000} : ", iter);
                        }

                        //int[] ikeep = lstNewIdxRemv[iter].Item1;

                        HessCoarseResiIterInfo iterinfo = new HessCoarseResiIterInfo();
                        iterinfo.sizeHessBlkMat  = 1;
                        iterinfo.numAtomsRemoved = 1;
                        iterinfo.time0           = DateTime.UtcNow;
                        int _count_update = 0;
                        {
                            HDebug.Assert(lstNewIdxRemv[iter].Count == 1);
                            int iremv = lstNewIdxRemv[iter][0];

                            HessMatrix         A         = H;
                            MatrixByArr        D         = null;
                            double             D_absmin  = 0;
                            List <int>         C_lstbr   = new List <int>();
                            List <MatrixByArr> C_lstbval = new List <MatrixByArr>();
                            {
                                // get C and D
                                foreach (var(bc, br, bval) in H.EnumBlocksInCols(new int[] { iremv }))
                                {
                                    HDebug.Assert(iremv == bc);
                                    if (bc == br)
                                    {
                                        HDebug.Assert(D == null);
                                        D        = bval;
                                        D_absmin = D.HAbsMin();
                                    }
                                    else
                                    {
                                        if (bval.HAbsMin() >= thres_zeroblk)
                                        {
                                            C_lstbr.Add(br);
                                            C_lstbval.Add(bval);
                                        }
                                    }
                                }
                                // remove C and D
                                {
                                    int bc = iremv;
                                    H.SetBlock(bc, bc, null);
                                    foreach (int br in C_lstbr)
                                    {
                                        H.SetBlock(bc, br, null);
                                    }
                                }
                            }
                            if (lprocess_disp_console)
                            {
                                process_time[1] = process_time[2] = DateTime.UtcNow;
                                System.Console.Write("CD({0:00.00} min), ", (process_time[2] - process_time[0]).TotalMinutes);
                            }

                            double threshold = thres_zeroblk / lstNewIdxRemv.Length;

                            //  DD ={ { d00,d01,d02},{ d10,d11,d12},{ d20,d21,d22} }; MatrixForm[DD]
                            //  BB ={ { b00,b01,b02},{ b10,b11,b12},{ b20,b21,b22} }; MatrixForm[BB]
                            //  CC ={ { c00,c01,c02},{ c10,c11,c12},{ c20,c21,c22} }; MatrixForm[CC]
                            //  object[]    dbginfo = null; // new object[] { iremv, atoms, H, D, C_lstbr, C_lstbval };

                            Action <ValueTuple <int, int, MatrixByArr, MatrixByArr> > Update_A_B_invD_C = delegate(ValueTuple <int, int, MatrixByArr, MatrixByArr> info)
                            {
                                int         bc = info.Item1; // bc
                                int         br = info.Item2; // br
                                MatrixByArr DC = info.Item3; // invDD_CC  // XX ={ { x00,x01,x02},{ x10,x11,x12},{ x20,x21,x22} }; MatrixForm[CC]
                                MatrixByArr B  = info.Item4; // BB        // BB ={ { b00,b01,b02},{ b10,b11,b12},{ b20,b21,b22} }; MatrixForm[BB]
                                //var _iremv                      = (int)dbginfo[0];
                                //var _atoms                      = dbginfo[1] as Universe.Atom[]  ;
                                //var _H                          = dbginfo[2] as HessMatrix       ;
                                //var _D                          = dbginfo[3] as MatrixByArr      ;
                                //var _C_lstbr                    = dbginfo[4] as List<int>        ;
                                //var _C_lstbval                  = dbginfo[5] as List<MatrixByArr>;

                                //MatrixByArr BB_invDD_CC = BB * invDD_CC;
                                double _BDC00 = 0 - B[0, 0] * DC[0, 0] - B[0, 1] * DC[1, 0] - B[0, 2] * DC[2, 0]; // { { b00 x00 +b01 x10 + b02 x20
                                double _BDC01 = 0 - B[0, 0] * DC[0, 1] - B[0, 1] * DC[1, 1] - B[0, 2] * DC[2, 1]; //   , b00 x01 +b01 x11 + b02 x21
                                double _BDC02 = 0 - B[0, 0] * DC[0, 2] - B[0, 1] * DC[1, 2] - B[0, 2] * DC[2, 2]; //   , b00 x02 +b01 x12 + b02 x22
                                double _BDC10 = 0 - B[1, 0] * DC[0, 0] - B[1, 1] * DC[1, 0] - B[1, 2] * DC[2, 0]; // },{ b10 x00 +b11 x10 + b12 x20
                                double _BDC11 = 0 - B[1, 0] * DC[0, 1] - B[1, 1] * DC[1, 1] - B[1, 2] * DC[2, 1]; //   , b10 x01 +b11 x11 + b12 x21
                                double _BDC12 = 0 - B[1, 0] * DC[0, 2] - B[1, 1] * DC[1, 2] - B[1, 2] * DC[2, 2]; //   , b10 x02 +b11 x12 + b12 x22
                                double _BDC20 = 0 - B[2, 0] * DC[0, 0] - B[2, 1] * DC[1, 0] - B[2, 2] * DC[2, 0]; // },{ b20 x00 +b21 x10 + b22 x20
                                double _BDC21 = 0 - B[2, 0] * DC[0, 1] - B[2, 1] * DC[1, 1] - B[2, 2] * DC[2, 1]; //   , b20 x01 +b21 x11 + b22 x21
                                double _BDC22 = 0 - B[2, 0] * DC[0, 2] - B[2, 1] * DC[1, 2] - B[2, 2] * DC[2, 2]; //   , b20 x02 +b21 x12 + b22 x22 }}

                                if (A.HasBlockLock(bc, br))
                                {
                                    MatrixByArr A_bc_br = A.GetBlockLock(bc, br);
                                    A_bc_br[0, 0] += _BDC00; // A = A + (-B.invD.C)
                                    A_bc_br[0, 1] += _BDC01; // A = A + (-B.invD.C)
                                    A_bc_br[0, 2] += _BDC02; // A = A + (-B.invD.C)
                                    A_bc_br[1, 0] += _BDC10; // A = A + (-B.invD.C)
                                    A_bc_br[1, 1] += _BDC11; // A = A + (-B.invD.C)
                                    A_bc_br[1, 2] += _BDC12; // A = A + (-B.invD.C)
                                    A_bc_br[2, 0] += _BDC20; // A = A + (-B.invD.C)
                                    A_bc_br[2, 1] += _BDC21; // A = A + (-B.invD.C)
                                    A_bc_br[2, 2] += _BDC22; // A = A + (-B.invD.C)
                                    // (small && small && small) == !(large || large || large)
                                    bool toosmall = !(Math.Abs(A_bc_br[0, 0]) > threshold || Math.Abs(A_bc_br[0, 1]) > threshold || Math.Abs(A_bc_br[0, 2]) > threshold ||
                                                      Math.Abs(A_bc_br[1, 0]) > threshold || Math.Abs(A_bc_br[1, 1]) > threshold || Math.Abs(A_bc_br[1, 2]) > threshold ||
                                                      Math.Abs(A_bc_br[2, 0]) > threshold || Math.Abs(A_bc_br[2, 1]) > threshold || Math.Abs(A_bc_br[2, 2]) > threshold);
                                    if (toosmall)
                                    {
                                        HDebug.Assert(bc != br);
                                        A.SetBlockLock(bc, br, null);
                                    }
                                }
                                else
                                {
                                    // (small && small && small) == !(large || large || large)
                                    bool toosmall = !(Math.Abs(_BDC00) > threshold || Math.Abs(_BDC01) > threshold || Math.Abs(_BDC02) > threshold ||
                                                      Math.Abs(_BDC10) > threshold || Math.Abs(_BDC11) > threshold || Math.Abs(_BDC12) > threshold ||
                                                      Math.Abs(_BDC20) > threshold || Math.Abs(_BDC21) > threshold || Math.Abs(_BDC22) > threshold);
                                    if (!toosmall)
                                    {
                                        MatrixByArr A_bc_br = new double[3, 3]
                                        {
                                            { _BDC00, _BDC01, _BDC02 }   // A = 0 + (-B.invD.C)
                                            , { _BDC10, _BDC11, _BDC12 } // A = 0 + (-B.invD.C)
                                            , { _BDC20, _BDC21, _BDC22 } // A = 0 + (-B.invD.C)
                                        };
                                        A.SetBlockLock(bc, br, A_bc_br);
                                    }
                                }

                                System.Threading.Interlocked.Increment(ref _count_update);
                            };

                            var lstCompInfo = EnumComput(D, C_lstbr, C_lstbval, threshold);
                            if (parallel)
                            {
                                Parallel.ForEach(lstCompInfo, Update_A_B_invD_C);
                            }
                            else
                            {
                                foreach (var info in lstCompInfo)
                                {
                                    Update_A_B_invD_C(info);
                                }
                            }

                            //GC.Collect(0);

                            if (lprocess_disp_console)
                            {
                                process_time[4] = DateTime.UtcNow;
                                System.Console.Write("B.invD.C({0:00.00} min), ", (process_time[4] - process_time[3]).TotalMinutes);
                            }

                            H = A;
                        }
                        iterinfo.usedMemoryByte = GC.GetTotalMemory(false);
                        iterinfo.time1          = DateTime.UtcNow;
                        iterinfos.Add(iterinfo);

                        if (lprocess_disp_console)
                        {
                            System.Console.WriteLine("summary(makezero {0,5}, nonzero {1,5}, numIgnMul {2,7}, numRemvAtoms {3,3}, {4,5:0.00} sec, {5} mb, {6}x{6}, nzeroBlk/Atom {7:0.00}, cntUpdateBlk({8}))"
                                                     , iterinfo.numSetZeroBlock
                                                     , iterinfo.numNonZeroBlock
                                                     , iterinfo.numAddIgnrBlock
                                                     , iterinfo.numAtomsRemoved
                                                     , iterinfo.compSec
                                                     , iterinfo.usedMemoryByte / (1024 * 1024)
                                                     , (0 * 3)
                                                     , 0//((double)iterinfo.numNonZeroBlock / idxremv.Length)
                                                     , _count_update
                                                     );
                        }
                    }
                    int numca = H.ColBlockSize - lstNewIdxRemv.HListCount().Sum();

                    //System.Console.WriteLine("finish coarse-graining");
                    {
                        int[] idxkeep = HEnum.HEnumCount(numca).ToArray();
                        H = H.SubMatrixByAtoms(false, idxkeep, idxkeep, false);
                    }
                    {
                        H.MakeNearZeroBlockAsZero(thres_zeroblk);
                    }
                    GC.Collect(0);
                    //System.Console.WriteLine("finish resizing");

                    return(new CGetHessCoarseResiIterImpl
                    {
                        iterinfos = iterinfos,
                        H = H,
                    });
                }