text: #!/usr/bin/python
  
  # interpolate scalar gradient onto nedelec space
  from dolfin import *
  
  import petsc4py
  import sys
  
  petsc4py.init(sys.argv)
  
  from petsc4py import PETSc
  Print = PETSc.Sys.Print
  # from MatrixOperations import *
  import numpy as np
  #import matplotlib.pylab as plt
  import PETScIO as IO
  import common
  import scipy
  import scipy.io
  import time
  
  import BiLinear as forms
  import IterOperations as Iter
  import MatrixOperations as MO
  import CheckPetsc4py as CP
  import ExactSol
  import Solver as S
  import MHDmatrixPrecondSetup as PrecondSetup
  import NSprecondSetup
  m = 6
  
  
  errL2u =np.zeros((m-1,1))
  errH1u =np.zeros((m-1,1))
  errL2p =np.zeros((m-1,1))
  errL2b =np.zeros((m-1,1))
  errCurlb =np.zeros((m-1,1))
  errL2r =np.zeros((m-1,1))
  errH1r =np.zeros((m-1,1))
  
  
  
  l2uorder =  np.zeros((m-1,1))
  H1uorder =np.zeros((m-1,1))
  l2porder =  np.zeros((m-1,1))
  l2border =  np.zeros((m-1,1))
  Curlborder =np.zeros((m-1,1))
  l2rorder =  np.zeros((m-1,1))
  H1rorder = np.zeros((m-1,1))
  
  NN = np.zeros((m-1,1))
  DoF = np.zeros((m-1,1))
  Velocitydim = np.zeros((m-1,1))
  Magneticdim = np.zeros((m-1,1))
  Pressuredim = np.zeros((m-1,1))
  Lagrangedim = np.zeros((m-1,1))
  Wdim = np.zeros((m-1,1))
  iterations = np.zeros((m-1,1))
  SolTime = np.zeros((m-1,1))
  udiv = np.zeros((m-1,1))
  MU = np.zeros((m-1,1))
  level = np.zeros((m-1,1))
  NSave = np.zeros((m-1,1))
  Mave = np.zeros((m-1,1))
  TotalTime = np.zeros((m-1,1))
  nn = 2
  
  dim = 2
  ShowResultPlots = 'yes'
  split = 'Linear'
  
  MU[0]= 1e0
  for xx in xrange(1,m):
      print xx
      level[xx-1] = xx+1
      nn = 2**(level[xx-1])
  
  
      # Create mesh and define function space
      nn = int(nn)
      NN[xx-1] = nn/2
      # parameters["form_compiler"]["quadrature_degree"] = 6
      # parameters = CP.ParameterSetup()
      mesh = UnitSquareMesh(nn,nn)
  
      order = 1
      parameters['reorder_dofs_serial'] = False
      Velocity = VectorFunctionSpace(mesh, "CG", order)
      Pressure = FunctionSpace(mesh, "DG", order-1)
      Magnetic = FunctionSpace(mesh, "N1curl", order)
      Lagrange = FunctionSpace(mesh, "CG", order)
      W = MixedFunctionSpace([Magnetic, Velocity,Pressure, Lagrange])
      # W = Velocity*Pressure*Magnetic*Lagrange
      Velocitydim[xx-1] = Velocity.dim()
      Pressuredim[xx-1] = Pressure.dim()
      Magneticdim[xx-1] = Magnetic.dim()
      Lagrangedim[xx-1] = Lagrange.dim()
      Wdim[xx-1] = W.dim()
      print "\n\nW:  ",Wdim[xx-1],"Velocity:  ",Velocitydim[xx-1],"Pressure:  ",Pressuredim[xx-1],"Magnetic:  ",Magneticdim[xx-1],"Lagrange:  ",Lagrangedim[xx-1],"\n\n"
      dim = [Magnetic.dim(), Velocity.dim(), Pressure.dim(), Lagrange.dim()]
  
  
      def boundary(x, on_boundary):
          return on_boundary
  
      u0, p0,b0, r0, Laplacian, Advection, gradPres,CurlCurl, gradR, NS_Couple, M_Couple = ExactSol.MHD2D(4,1)
  
  
      bcu = DirichletBC(W.sub(1),u0, boundary)
      bcb = DirichletBC(W.sub(0),b0, boundary)
      bcr = DirichletBC(W.sub(3),r0, boundary)
  
      # bc = [u0,p0,b0,r0]
      bcs = [bcu,bcb,bcr]
      FSpaces = [Velocity,Pressure,Magnetic,Lagrange]
  
  
      (u, p, b, r) = TrialFunctions(W)
      (v, q, c,s ) = TestFunctions(W)
  
      kappa = 1.0
      Mu_m =1e1
      MU = 1.0
      IterType = 'Full'
  
      F_NS = -MU*Laplacian+Advection+gradPres-kappa*NS_Couple
      if kappa == 0:
          F_M = Mu_m*CurlCurl+gradR -kappa*M_Couple
      else:
          F_M = Mu_m*kappa*CurlCurl+gradR -kappa*M_Couple
      params = [kappa,Mu_m,MU]
  
  
      # MO.PrintStr("Preconditioning MHD setup",5,"+","\n\n","\n\n")
      HiptmairMatrices = PrecondSetup.MagneticSetup(Magnetic, Lagrange, b0, r0, 1e-6)
  
  
      MO.PrintStr("Setting up MHD initial guess",5,"+","\n\n","\n\n")
      u_k,p_k,b_k,r_k = common.InitialGuess(FSpaces,[u0,p0,b0,r0],[F_NS,F_M],params,HiptmairMatrices,1e-6,Neumann=Expression(("0","0")),options ="New", FS = "DG")
  
      ones = Function(Pressure)
      ones.vector()[:]=(0*ones.vector().array()+1)
      # pConst = - assemble(p_k*dx)/assemble(ones*dx)
      p_k.vector()[:] += - assemble(p_k*dx)/assemble(ones*dx)
      x = Iter.u_prev(u_k,b_k,p_k,r_k)
  
      KSPlinearfluids, MatrixLinearFluids = PrecondSetup.FluidLinearSetup(Pressure, MU)
      kspFp, Fp = PrecondSetup.FluidNonLinearSetup(Pressure, MU, u_k)
      # plot(b_k)
  
      ns,maxwell,CoupleTerm,Lmaxwell,Lns = forms.MHD2D(mesh, W,F_M,F_NS, u_k,b_k,params,IterType,"DG", SaddlePoint = "number2")
      RHSform = forms.PicardRHS(mesh, W, u_k, p_k, b_k, r_k, params,"DG",SaddlePoint = "number2")
  
  
      bcu = DirichletBC(W.sub(0),Expression(("0.0","0.0")), boundary)
      bcb = DirichletBC(W.sub(1),Expression(("0.0","0.0")), boundary)
      bcr = DirichletBC(W.sub(3),Expression(("0.0")), boundary)
      bcs = [bcu,bcb,bcr]
  
      eps = 1.0           # error measure ||u-u_k||
      tol = 1.0E-4     # tolerance
      iter = 0            # iteration counter
      maxiter = 40       # max no of iterations allowed
      SolutionTime = 0
      outer = 0
      # parameters['linear_algebra_backend'] = 'uBLAS'
  
      # FSpaces = [Velocity,Magnetic,Pressure,Lagrange]
  
      if IterType == "CD":
          AA, bb = assemble_system(maxwell+ns, (Lmaxwell + Lns) - RHSform,  bcs)
          A,b = CP.Assemble(AA,bb)
          # u = b.duplicate()
          # P = CP.Assemble(PP)
  
  
      u_is = PETSc.IS().createGeneral(range(Velocity.dim()))
      NS_is = PETSc.IS().createGeneral(range(Velocity.dim()+Pressure.dim()))
      M_is = PETSc.IS().createGeneral(range(Velocity.dim()+Pressure.dim(),W.dim()))
      OuterTol = 1e-5
      InnerTol = 1e-3
      NSits =0
      Mits =0
      TotalStart =time.time()
      SolutionTime = 0
      while eps > tol  and iter < maxiter:
          iter += 1
          MO.PrintStr("Iter "+str(iter),7,"=","\n\n","\n\n")
          tic()
          if IterType == "CD":
              bb = assemble((Lmaxwell + Lns) - RHSform)
              for bc in bcs:
                  bc.apply(bb)
              A,b = CP.Assemble(AA,bb)
              # if iter == 1
              if iter == 1:
                  u = b.duplicate()
                  F = A.getSubMatrix(u_is,u_is)
                  kspF = NSprecondSetup.LSCKSPnonlinear(F)
          else:
              AA, bb = assemble_system(maxwell+ns+CoupleTerm, (Lmaxwell + Lns) - RHSform,  bcs)
              A,b = CP.Assemble(AA,bb)
              F = A.getSubMatrix(u_is,u_is)
              kspF = NSprecondSetup.LSCKSPnonlinear(F)
          # if iter == 1:
              if iter == 1:
                  u = b.duplicate()
          print ("{:40}").format("MHD assemble, time: "), " ==>  ",("{:4f}").format(toc()),  ("{:9}").format("   time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
  
          kspFp, Fp = PrecondSetup.FluidNonLinearSetup(Pressure, MU, u_k)
  
          print "Inititial guess norm: ", u.norm()
          # ksp.solve(b, u)
          # u,it1,it2 = S.solve(A,b,u,[NS_is,M_is],FSpaces,IterType,OuterTol,InnerTol,HiptmairMatrices,KSPlinearfluids,kspF,Fp,MatrixLinearFluids,kspFp)
  
  
          ksp = PETSc.KSP()
          ksp.create(comm=PETSc.COMM_WORLD)
          pcF = ksp.getPC()
          ksp.setType('preonly')
          pcF.setType('lu')
          OptDB = PETSc.Options()
          OptDB['pc_factor_mat_solver_package']  = "mumps"
          OptDB['pc_factor_mat_ordering_type']  = "rcm"
          ksp.setFromOptions()
          ksp.setOperators(A)
          stime = time.time()
          ksp.solve(b,u)
          Soltime = time.time()- stime
          # NSits += it1
          # Mits +=dodim
  
          SolutionTime = SolutionTime +Soltime
  
          u1, p1, b1, r1, eps= Iter.PicardToleranceDecouple(u,x,FSpaces,dim,"2",iter, SaddlePoint = "Yes")
          p1.vector()[:] += - assemble(p1*dx)/assemble(ones*dx)
          u_k.assign(u1)
          p_k.assign(p1)
          b_k.assign(b1)
          r_k.assign(r1)
          # if eps > 100 and iter > 3:
          #     print 22222
          #     break
          uOld= np.concatenate((u_k.vector().array(),b_k.vector().array(),p_k.vector().array(),r_k.vector().array()), axis=0)
          x = IO.arrayToVec(uOld)
          # iter = 10000
  
  
          # u_k,b_k,epsu,epsb=Iter.PicardTolerance(x,u_k,b_k,FSpaces,dim,"inf",iter)
  
      XX= np.concatenate((u_k.vector().array(),p_k.vector().array(),b_k.vector().array(),r_k.vector().array()), axis=0)
      print SolTime
      SolTime[xx-1] = SolutionTime/iter
      NSave[xx-1] = (float(NSits)/iter)
      Mave[xx-1] = (float(Mits)/iter)
      iterations[xx-1] = iter
      TotalTime[xx-1] = time.time() - TotalStart
      ue =u0
      pe = p0
      be = b0
      re = r0
  
  
  
  
      dim = [Velocity.dim(), Pressure.dim(), Magnetic.dim(),Lagrange.dim()]
  
      ExactSolution = [ue,pe,be,re]
      errL2u[xx-1], errH1u[xx-1], errL2p[xx-1], errL2b[xx-1], errCurlb[xx-1], errL2r[xx-1], errH1r[xx-1] = Iter.Errors(XX,mesh,FSpaces,ExactSolution,order,dim, "DG")
  
      if xx > 1:
          l2uorder[xx-1] =  np.abs(np.log2(errL2u[xx-2]/errL2u[xx-1]))
          H1uorder[xx-1] =  np.abs(np.log2(errH1u[xx-2]/errH1u[xx-1]))
  
          l2porder[xx-1] =  np.abs(np.log2(errL2p[xx-2]/errL2p[xx-1]))
  
          l2border[xx-1] =  np.abs(np.log2(errL2b[xx-2]/errL2b[xx-1]))
          Curlborder[xx-1] =  np.abs(np.log2(errCurlb[xx-2]/errCurlb[xx-1]))
  
          l2rorder[xx-1] =  np.abs(np.log2(errL2r[xx-2]/errL2r[xx-1]))
          H1rorder[xx-1] =  np.abs(np.log2(errH1r[xx-2]/errH1r[xx-1]))
  
  
  
  
  import pandas as pd
  
  
  
  LatexTitles = ["l","DoFu","Dofp","V-L2","L2-order","V-H1","H1-order","P-L2","PL2-order"]
  LatexValues = np.concatenate((level,Velocitydim,Pressuredim,errL2u,l2uorder,errH1u,H1uorder,errL2p,l2porder), axis=1)
  LatexTable = pd.DataFrame(LatexValues, columns = LatexTitles)
  pd.set_option('precision',3)
  LatexTable = MO.PandasFormat(LatexTable,"V-L2","%2.4e")
  LatexTable = MO.PandasFormat(LatexTable,'V-H1',"%2.4e")
  LatexTable = MO.PandasFormat(LatexTable,"H1-order","%1.2f")
  LatexTable = MO.PandasFormat(LatexTable,'L2-order',"%1.2f")
  LatexTable = MO.PandasFormat(LatexTable,"P-L2","%2.4e")
  LatexTable = MO.PandasFormat(LatexTable,'PL2-order',"%1.2f")
  print LatexTable
  
  
  print "\n\n   Magnetic convergence"
  MagneticTitles = ["l","B DoF","R DoF","B-L2","L2-order","B-Curl","HCurl-order"]
  MagneticValues = np.concatenate((level,Magneticdim,Lagrangedim,errL2b,l2border,errCurlb,Curlborder),axis=1)
  MagneticTable= pd.DataFrame(MagneticValues, columns = MagneticTitles)
  pd.set_option('precision',3)
  MagneticTable = MO.PandasFormat(MagneticTable,"B-Curl","%2.4e")
  MagneticTable = MO.PandasFormat(MagneticTable,'B-L2',"%2.4e")
  MagneticTable = MO.PandasFormat(MagneticTable,"L2-order","%1.2f")
  MagneticTable = MO.PandasFormat(MagneticTable,'HCurl-order',"%1.2f")
  print MagneticTable
  
  # print "\n\n   Lagrange convergence"
  # LagrangeTitles = ["l","SolTime","B DoF","R DoF","R-L2","L2-order","R-H1","H1-order"]
  # LagrangeValues = np.concatenate((level,SolTime,Magneticdim,Lagrangedim,errL2r,l2rorder,errH1r,H1rorder),axis=1)
  # LagrangeTable= pd.DataFrame(LagrangeValues, columns = LagrangeTitles)
  # pd.set_option('precision',3)
  # LagrangeTable = MO.PandasFormat(LagrangeTable,"R-L2","%2.4e")
  # LagrangeTable = MO.PandasFormat(LagrangeTable,'R-H1',"%2.4e")
  # LagrangeTable = MO.PandasFormat(LagrangeTable,"H1-order","%1.2f")
  # LagrangeTable = MO.PandasFormat(LagrangeTable,'L2-order',"%1.2f")
  # print LagrangeTable
  
  # print "\n\n   Iteration table"
  # if IterType == "Full":
  #     IterTitles = ["l","DoF","AV solve Time","Total picard time","picard iterations","Av Outer its","Av Inner its",]
  # else:
  #     IterTitles = ["l","DoF","AV solve Time","Total picard time","picard iterations","Av NS iters","Av M iters"]
  # IterValues = np.concatenate((level,Wdim,SolTime,TotalTime,iterations,NSave,Mave),axis=1)
  # IterTable= pd.DataFrame(IterValues, columns = IterTitles)
  # if IterType == "Full":
  #     IterTable = MO.PandasFormat(IterTable,'Av Outer its',"%2.1f")
  #     IterTable = MO.PandasFormat(IterTable,'Av Inner its',"%2.1f")
  # else:
  #     IterTable = MO.PandasFormat(IterTable,'Av NS iters',"%2.1f")
  #     IterTable = MO.PandasFormat(IterTable,'Av M iters',"%2.1f")
  # print IterTable.to_latex()
  # print " \n  Outer Tol:  ",OuterTol, "Inner Tol:   ", InnerTol
  
  
  
  
  # # # if (ShowResultPlots == 'yes'):
  
  # plot(u_k)
  # plot(interpolate(ue,Velocity))
  
  # plot(p_k)
  
  # plot(interpolate(pe,Pressure))
  
  # plot(b_k)
  # plot(interpolate(be,Magnetic))
  
  # plot(r_k)
  # plot(interpolate(re,Lagrange))
  
  # interactive()
  
  interactive()
  