/*******************************************************************************
 * For each run, the input filename and restart information (if needed) must   *
 * be given on the command line.  For non-restarted case, command line is:     *
 *                                                                             *
 *    executable <input file name>                                             *
 *                                                                             *
 * For restarted run, command line is:                                         *
 *                                                                             *
 *    executable <input file name> <restart directory> <restart number>        *
 *                                                                             *
 *******************************************************************************/
bool
run_example(int argc, char* argv[])
{
    // Initialize PETSc, MPI, and SAMRAI.
    PetscInitialize(&argc, &argv, NULL, NULL);
    SAMRAI_MPI::setCommunicator(PETSC_COMM_WORLD);
    SAMRAI_MPI::setCallAbortInSerialInsteadOfExit();
    SAMRAIManager::startup();

    { // cleanup dynamically allocated objects prior to shutdown

        // Parse command line options, set some standard options from the input
        // file, initialize the restart database (if this is a restarted run),
        // and enable file logging.
        Pointer<AppInitializer> app_initializer = new AppInitializer(argc, argv, "IB.log");
        Pointer<Database> input_db = app_initializer->getInputDatabase();

        // Get various standard options set in the input file.
        const bool dump_viz_data = app_initializer->dumpVizData();
        const int viz_dump_interval = app_initializer->getVizDumpInterval();
        const bool uses_visit = dump_viz_data && !app_initializer->getVisItDataWriter().isNull();

        const bool dump_restart_data = app_initializer->dumpRestartData();
        const int restart_dump_interval = app_initializer->getRestartDumpInterval();
        const string restart_dump_dirname = app_initializer->getRestartDumpDirectory();

        const bool dump_postproc_data = app_initializer->dumpPostProcessingData();
        const int postproc_data_dump_interval = app_initializer->getPostProcessingDataDumpInterval();
        const string postproc_data_dump_dirname = app_initializer->getPostProcessingDataDumpDirectory();
        if (dump_postproc_data && (postproc_data_dump_interval > 0) && !postproc_data_dump_dirname.empty())
        {
            Utilities::recursiveMkdir(postproc_data_dump_dirname);
        }

        const bool dump_timer_data = app_initializer->dumpTimerData();
        const int timer_dump_interval = app_initializer->getTimerDumpInterval();

        // Create major algorithm and data objects that comprise the
        // application.  These objects are configured from the input database
        // and, if this is a restarted run, from the restart database.
        Pointer<INSHierarchyIntegrator> navier_stokes_integrator = new INSStaggeredHierarchyIntegrator(
            "INSStaggeredHierarchyIntegrator",
            app_initializer->getComponentDatabase("INSStaggeredHierarchyIntegrator"));

        const int num_structures = input_db->getIntegerWithDefault("num_structures", 1);
        Pointer<ConstraintIBMethod> ib_method_ops = new ConstraintIBMethod(
            "ConstraintIBMethod", app_initializer->getComponentDatabase("ConstraintIBMethod"), num_structures);
        Pointer<IBHierarchyIntegrator> time_integrator =
            new IBExplicitHierarchyIntegrator("IBHierarchyIntegrator",
                                              app_initializer->getComponentDatabase("IBHierarchyIntegrator"),
                                              ib_method_ops,
                                              navier_stokes_integrator);

        Pointer<CartesianGridGeometry<NDIM> > grid_geometry = new CartesianGridGeometry<NDIM>(
            "CartesianGeometry", app_initializer->getComponentDatabase("CartesianGeometry"));
        Pointer<PatchHierarchy<NDIM> > patch_hierarchy = new PatchHierarchy<NDIM>("PatchHierarchy", grid_geometry);

        Pointer<StandardTagAndInitialize<NDIM> > error_detector =
            new StandardTagAndInitialize<NDIM>("StandardTagAndInitialize",
                                               time_integrator,
                                               app_initializer->getComponentDatabase("StandardTagAndInitialize"));
        Pointer<BergerRigoutsos<NDIM> > box_generator = new BergerRigoutsos<NDIM>();
        Pointer<LoadBalancer<NDIM> > load_balancer =
            new LoadBalancer<NDIM>("LoadBalancer", app_initializer->getComponentDatabase("LoadBalancer"));
        Pointer<GriddingAlgorithm<NDIM> > gridding_algorithm =
            new GriddingAlgorithm<NDIM>("GriddingAlgorithm",
                                        app_initializer->getComponentDatabase("GriddingAlgorithm"),
                                        error_detector,
                                        box_generator,
                                        load_balancer);

        // Configure the IB solver.
        Pointer<IBStandardInitializer> ib_initializer = new IBStandardInitializer(
            "IBStandardInitializer", app_initializer->getComponentDatabase("IBStandardInitializer"));
        ib_method_ops->registerLInitStrategy(ib_initializer);
        Pointer<IBStandardForceGen> ib_force_fcn = new IBStandardForceGen();
        ib_method_ops->registerIBLagrangianForceFunction(ib_force_fcn);

        // Create Eulerian initial condition specification objects.
        if (input_db->keyExists("VelocityInitialConditions"))
        {
            Pointer<CartGridFunction> u_init = new muParserCartGridFunction(
                "u_init", app_initializer->getComponentDatabase("VelocityInitialConditions"), grid_geometry);
            navier_stokes_integrator->registerVelocityInitialConditions(u_init);
        }

        if (input_db->keyExists("PressureInitialConditions"))
        {
            Pointer<CartGridFunction> p_init = new muParserCartGridFunction(
//.........这里部分代码省略.........

/*******************************************************************************
 * For each run, the input filename and restart information (if needed) must   *
 * be given on the command line.  For non-restarted case, command line is:     *
 *                                                                             *
 *    executable <input file name>                                             *
 *                                                                             *
 * For restarted run, command line is:                                         *
 *                                                                             *
 *    executable <input file name> <restart directory> <restart number>        *
 *                                                                             *
 *******************************************************************************/
int main(int argc, char* argv[])
{
    // Initialize PETSc, MPI, and SAMRAI.
    PetscInitialize(&argc, &argv, NULL, NULL);
    SAMRAI_MPI::setCommunicator(PETSC_COMM_WORLD);
    SAMRAI_MPI::setCallAbortInSerialInsteadOfExit();
    SAMRAIManager::startup();

    { // cleanup dynamically allocated objects prior to shutdown

        // Parse command line options, set some standard options from the input
        // file, initialize the restart database (if this is a restarted run),
        // and enable file logging.
        Pointer<AppInitializer> app_initializer = new AppInitializer(argc, argv, "INS.log");
        Pointer<Database> input_db = app_initializer->getInputDatabase();

        // Get various standard options set in the input file.
        const bool dump_viz_data = app_initializer->dumpVizData();
        const int viz_dump_interval = app_initializer->getVizDumpInterval();
        const bool uses_visit = dump_viz_data && app_initializer->getVisItDataWriter();

        const bool dump_restart_data = app_initializer->dumpRestartData();
        const int restart_dump_interval = app_initializer->getRestartDumpInterval();
        const string restart_dump_dirname = app_initializer->getRestartDumpDirectory();

        const bool dump_postproc_data = app_initializer->dumpPostProcessingData();
        const int postproc_data_dump_interval = app_initializer->getPostProcessingDataDumpInterval();
        const string postproc_data_dump_dirname = app_initializer->getPostProcessingDataDumpDirectory();

        const bool dump_timer_data = app_initializer->dumpTimerData();
        const int timer_dump_interval = app_initializer->getTimerDumpInterval();

        // Create major algorithm and data objects that comprise the
        // application.  These objects are configured from the input database
        // and, if this is a restarted run, from the restart database.
        Pointer<INSHierarchyIntegrator> time_integrator;
        const string solver_type =
            app_initializer->getComponentDatabase("Main")->getStringWithDefault("solver_type", "STAGGERED");
        if (solver_type == "STAGGERED")
        {
            time_integrator = new INSStaggeredHierarchyIntegrator(
                "INSStaggeredHierarchyIntegrator",
                app_initializer->getComponentDatabase("INSStaggeredHierarchyIntegrator"));
        }
        else if (solver_type == "COLLOCATED")
        {
            time_integrator = new INSCollocatedHierarchyIntegrator(
                "INSCollocatedHierarchyIntegrator",
                app_initializer->getComponentDatabase("INSCollocatedHierarchyIntegrator"));
        }
        else
        {
            TBOX_ERROR("Unsupported solver type: " << solver_type << "\n"
                                                   << "Valid options are: COLLOCATED, STAGGERED");
        }
        Pointer<CartesianGridGeometry<NDIM> > grid_geometry = new CartesianGridGeometry<NDIM>(
            "CartesianGeometry", app_initializer->getComponentDatabase("CartesianGeometry"));
        Pointer<PatchHierarchy<NDIM> > patch_hierarchy = new PatchHierarchy<NDIM>("PatchHierarchy", grid_geometry);
        Pointer<StandardTagAndInitialize<NDIM> > error_detector =
            new StandardTagAndInitialize<NDIM>("StandardTagAndInitialize", time_integrator,
                                               app_initializer->getComponentDatabase("StandardTagAndInitialize"));
        Pointer<BergerRigoutsos<NDIM> > box_generator = new BergerRigoutsos<NDIM>();
        Pointer<LoadBalancer<NDIM> > load_balancer =
            new LoadBalancer<NDIM>("LoadBalancer", app_initializer->getComponentDatabase("LoadBalancer"));
        Pointer<GriddingAlgorithm<NDIM> > gridding_algorithm =
            new GriddingAlgorithm<NDIM>("GriddingAlgorithm", app_initializer->getComponentDatabase("GriddingAlgorithm"),
                                        error_detector, box_generator, load_balancer);

        // Create initial condition specification objects.
        if (input_db->keyExists("VelocityInitialConditions"))
        {
            Pointer<CartGridFunction> u_init = new muParserCartGridFunction(
                "u_init", app_initializer->getComponentDatabase("VelocityInitialConditions"), grid_geometry);
            time_integrator->registerVelocityInitialConditions(u_init);
        }

        // Create boundary condition specification objects (when necessary).
        const IntVector<NDIM>& periodic_shift = grid_geometry->getPeriodicShift();
        vector<RobinBcCoefStrategy<NDIM>*> u_bc_coefs(NDIM);
        if (periodic_shift.min() > 0)
        {
            for (unsigned int d = 0; d < NDIM; ++d)
            {
                u_bc_coefs[d] = NULL;
            }
        }
        else
        {
            for (unsigned int d = 0; d < NDIM; ++d)
//.........这里部分代码省略.........

int main(int argc,char **argv)
{
  AppCtx         user;                /* user-defined work context */
  PetscInt       mx,my,its;
  PetscErrorCode ierr;
  MPI_Comm       comm;
  SNES           snes;
  DM             da;
  Vec            x,X,b;
  PetscBool      youngflg,poissonflg,muflg,lambdaflg,view=PETSC_FALSE,viewline=PETSC_FALSE;
  PetscReal      poisson=0.2,young=4e4;
  char           filename[PETSC_MAX_PATH_LEN] = "ex16.vts";
  char           filename_def[PETSC_MAX_PATH_LEN] = "ex16_def.vts";

  ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
  ierr = FormElements();CHKERRQ(ierr);
  comm = PETSC_COMM_WORLD;
  ierr = SNESCreate(comm,&snes);CHKERRQ(ierr);
  ierr = DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,11,2,2,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,3,1,NULL,NULL,NULL,&da);CHKERRQ(ierr);
  ierr = DMSetFromOptions(da);CHKERRQ(ierr);
  ierr = DMSetUp(da);CHKERRQ(ierr);
  ierr = SNESSetDM(snes,(DM)da);CHKERRQ(ierr);

  ierr = SNESSetNGS(snes,NonlinearGS,&user);CHKERRQ(ierr);

  ierr = DMDAGetInfo(da,0,&mx,&my,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
  user.loading     = 0.0;
  user.arc         = PETSC_PI/3.;
  user.mu          = 4.0;
  user.lambda      = 1.0;
  user.rad         = 100.0;
  user.height      = 3.;
  user.width       = 1.;
  user.ploading    = -5e3;

  ierr = PetscOptionsGetReal(NULL,NULL,"-arc",&user.arc,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,&muflg);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-lambda",&user.lambda,&lambdaflg);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-rad",&user.rad,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-height",&user.height,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-width",&user.width,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-loading",&user.loading,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-ploading",&user.ploading,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-poisson",&poisson,&poissonflg);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-young",&young,&youngflg);CHKERRQ(ierr);
  if ((youngflg || poissonflg) || !(muflg || lambdaflg)) {
    /* set the lame' parameters based upon the poisson ratio and young's modulus */
    user.lambda = poisson*young / ((1. + poisson)*(1. - 2.*poisson));
    user.mu     = young/(2.*(1. + poisson));
  }
  ierr = PetscOptionsGetBool(NULL,NULL,"-view",&view,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetBool(NULL,NULL,"-view_line",&viewline,NULL);CHKERRQ(ierr);

  ierr = DMDASetFieldName(da,0,"x_disp");CHKERRQ(ierr);
  ierr = DMDASetFieldName(da,1,"y_disp");CHKERRQ(ierr);
  ierr = DMDASetFieldName(da,2,"z_disp");CHKERRQ(ierr);

  ierr = DMSetApplicationContext(da,&user);CHKERRQ(ierr);
  ierr = DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);CHKERRQ(ierr);
  ierr = DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)FormJacobianLocal,&user);CHKERRQ(ierr);
  ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
  ierr = FormCoordinates(da,&user);CHKERRQ(ierr);

  ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
  ierr = DMCreateGlobalVector(da,&b);CHKERRQ(ierr);
  ierr = InitialGuess(da,&user,x);CHKERRQ(ierr);
  ierr = FormRHS(da,&user,b);CHKERRQ(ierr);

  ierr = PetscPrintf(comm,"lambda: %f mu: %f\n",(double)user.lambda,(double)user.mu);CHKERRQ(ierr);

  /* show a cross-section of the initial state */
  if (viewline) {
    ierr = DisplayLine(snes,x);CHKERRQ(ierr);
  }

  /* get the loaded configuration */
  ierr = SNESSolve(snes,b,x);CHKERRQ(ierr);

  ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr);
  ierr = PetscPrintf(comm,"Number of SNES iterations = %D\n", its);CHKERRQ(ierr);
  ierr = SNESGetSolution(snes,&X);CHKERRQ(ierr);
  /* show a cross-section of the final state */
  if (viewline) {
    ierr = DisplayLine(snes,X);CHKERRQ(ierr);
  }

  if (view) {
    PetscViewer viewer;
    Vec         coords;
    ierr = PetscViewerVTKOpen(PETSC_COMM_WORLD,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
    ierr = VecView(x,viewer);CHKERRQ(ierr);
    ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
    ierr = DMGetCoordinates(da,&coords);CHKERRQ(ierr);
    ierr = VecAXPY(coords,1.0,x);CHKERRQ(ierr);
    ierr = PetscViewerVTKOpen(PETSC_COMM_WORLD,filename_def,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
    ierr = VecView(x,viewer);CHKERRQ(ierr);
    ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
  }

  ierr = VecDestroy(&x);CHKERRQ(ierr);
//.........这里部分代码省略.........

int main(int argc,char **args)
{
  Vec            x,y,u,s1,s2;
  Mat            A,sA,sB;
  PetscRandom    rctx;
  PetscReal      r1,r2,rnorm,tol=1.e-10;
  PetscScalar    one=1.0, neg_one=-1.0, value[3], four=4.0,alpha=0.1;
  PetscInt       n,col[3],n1,block,row,i,j,i2,j2,Ii,J,rstart,rend,bs=1,mbs=16,d_nz=3,o_nz=3,prob=2;
  PetscErrorCode ierr;
  PetscMPIInt    size,rank;
  PetscBool      flg;
  MatType        type;

  PetscInitialize(&argc,&args,(char*)0,help);
  ierr = PetscOptionsGetInt(NULL,"-mbs",&mbs,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(NULL,"-bs",&bs,NULL);CHKERRQ(ierr);

  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);

  n = mbs*bs;

  /* Assemble MPISBAIJ matrix sA */
  ierr = MatCreate(PETSC_COMM_WORLD,&sA);CHKERRQ(ierr);
  ierr = MatSetSizes(sA,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
  ierr = MatSetType(sA,MATSBAIJ);CHKERRQ(ierr);
  ierr = MatSetFromOptions(sA);CHKERRQ(ierr);
  ierr = MatGetType(sA,&type);CHKERRQ(ierr);
  /* printf(" mattype: %s\n",type); */
  ierr = MatMPISBAIJSetPreallocation(sA,bs,d_nz,NULL,o_nz,NULL);CHKERRQ(ierr);
  ierr = MatSeqSBAIJSetPreallocation(sA,bs,d_nz,NULL);CHKERRQ(ierr);
  ierr = MatSetOption(sA,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);

  if (bs == 1) {
    if (prob == 1) { /* tridiagonal matrix */
      value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
      for (i=1; i<n-1; i++) {
        col[0] = i-1; col[1] = i; col[2] = i+1;
        ierr   = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
      }
      i       = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;
      value[0]= 0.1; value[1]=-1; value[2]=2;
      ierr    = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);

      i        = 0; col[0] = 0; col[1] = 1; col[2]=n-1;
      value[0] = 2.0; value[1] = -1.0; value[2]=0.1;
      ierr     = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
    } else if (prob ==2) { /* matrix for the five point stencil */
      n1 =  (int) PetscSqrtReal((PetscReal)n);
      if (n1*n1 != n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n must be a perfect square of n1");

      for (i=0; i<n1; i++) {
        for (j=0; j<n1; j++) {
          Ii = j + n1*i;
          if (i>0)    {J = Ii - n1; ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);}
          if (i<n1-1) {J = Ii + n1; ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);}
          if (j>0)    {J = Ii - 1;  ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);}
          if (j<n1-1) {J = Ii + 1;  ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);}
          ierr = MatSetValues(sA,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
        }
      }
    }
    /* end of if (bs == 1) */
  } else {  /* bs > 1 */
    for (block=0; block<n/bs; block++) {
      /* diagonal blocks */
      value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
      for (i=1+block*bs; i<bs-1+block*bs; i++) {
        col[0] = i-1; col[1] = i; col[2] = i+1;
        ierr   = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
      }
      i       = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;
      value[0]=-1.0; value[1]=4.0;
      ierr    = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);

      i       = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;
      value[0]=4.0; value[1] = -1.0;
      ierr    = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
    }
    /* off-diagonal blocks */
    value[0]=-1.0;
    for (i=0; i<(n/bs-1)*bs; i++) {
      col[0]=i+bs;
      ierr  = MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
      col[0]=i; row=i+bs;
      ierr  = MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
    }
  }
  ierr = MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* Test MatView() */
  /*
  ierr = MatView(sA, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  ierr = MatView(sA, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
  */
  /* Assemble MPIBAIJ matrix A */
  ierr = MatCreateBAIJ(PETSC_COMM_WORLD,bs,PETSC_DECIDE,PETSC_DECIDE,n,n,d_nz,NULL,o_nz,NULL,&A);CHKERRQ(ierr);
  ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);

//.........这里部分代码省略.........

int main(int argc,char **argv)
{
  PetscMPIInt      rank;
  PetscErrorCode   ierr;
  PetscInt         M = 10,N = 8,m = PETSC_DECIDE;
  PetscInt         s=2,w=2,n = PETSC_DECIDE,nloc,l,i,j,kk;
  PetscInt         Xs,Xm,Ys,Ym,iloc,*iglobal,*ltog;
  PetscInt         *lx = PETSC_NULL,*ly = PETSC_NULL;
  PetscBool        testorder = PETSC_FALSE,flg;
  DMDABoundaryType bx = DMDA_BOUNDARY_NONE,by= DMDA_BOUNDARY_NONE;
  DM               da;
  PetscViewer      viewer;
  Vec              local,global;
  PetscScalar      value;
  DMDAStencilType  st = DMDA_STENCIL_BOX;
  AO               ao;

  ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
  ierr = PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"",300,0,400,400,&viewer);CHKERRQ(ierr);

  /* Readoptions */
  ierr = PetscOptionsGetInt(PETSC_NULL,"-NX",&M,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-NY",&N,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-s",&s,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-w",&w,PETSC_NULL);CHKERRQ(ierr);

  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-xperiodic",&flg,PETSC_NULL);CHKERRQ(ierr); if (flg) bx = DMDA_BOUNDARY_PERIODIC;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-yperiodic",&flg,PETSC_NULL);CHKERRQ(ierr); if (flg) by = DMDA_BOUNDARY_PERIODIC;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-xghosted",&flg,PETSC_NULL);CHKERRQ(ierr); if (flg) bx = DMDA_BOUNDARY_GHOSTED;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-yghosted",&flg,PETSC_NULL);CHKERRQ(ierr); if (flg) by = DMDA_BOUNDARY_GHOSTED;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-star",&flg,PETSC_NULL);CHKERRQ(ierr); if (flg) st = DMDA_STENCIL_STAR;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-box",&flg,PETSC_NULL);CHKERRQ(ierr); if (flg) st = DMDA_STENCIL_BOX;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-testorder",&testorder,PETSC_NULL);CHKERRQ(ierr);
  /*
      Test putting two nodes in x and y on each processor, exact last processor
      in x and y gets the rest.
  */
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-distribute",&flg,PETSC_NULL);CHKERRQ(ierr);
  if (flg) {
    if (m == PETSC_DECIDE) SETERRQ(PETSC_COMM_WORLD,1,"Must set -m option with -distribute option");
    ierr = PetscMalloc(m*sizeof(PetscInt),&lx);CHKERRQ(ierr);
    for (i=0; i<m-1; i++) { lx[i] = 4;}
    lx[m-1] = M - 4*(m-1);
    if (n == PETSC_DECIDE) SETERRQ(PETSC_COMM_WORLD,1,"Must set -n option with -distribute option");
    ierr = PetscMalloc(n*sizeof(PetscInt),&ly);CHKERRQ(ierr);
    for (i=0; i<n-1; i++) { ly[i] = 2;}
    ly[n-1] = N - 2*(n-1);
  }


  /* Create distributed array and get vectors */
  ierr = DMDACreate2d(PETSC_COMM_WORLD,bx,by,st,M,N,m,n,w,s,lx,ly,&da);CHKERRQ(ierr);
  ierr = PetscFree(lx);CHKERRQ(ierr);
  ierr = PetscFree(ly);CHKERRQ(ierr);

  ierr = DMView(da,viewer);CHKERRQ(ierr);
  ierr = DMCreateGlobalVector(da,&global);CHKERRQ(ierr);
  ierr = DMCreateLocalVector(da,&local);CHKERRQ(ierr);

  /* Set global vector; send ghost points to local vectors */
  value = 1;
  ierr = VecSet(global,value);CHKERRQ(ierr);
  ierr = DMGlobalToLocalBegin(da,global,INSERT_VALUES,local);CHKERRQ(ierr);
  ierr = DMGlobalToLocalEnd(da,global,INSERT_VALUES,local);CHKERRQ(ierr);

  /* Scale local vectors according to processor rank; pass to global vector */
  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
  value = rank;
  ierr = VecScale(local,value);CHKERRQ(ierr);
  ierr = DMLocalToGlobalBegin(da,local,INSERT_VALUES,global);CHKERRQ(ierr);
  ierr = DMLocalToGlobalEnd(da,local,INSERT_VALUES,global);CHKERRQ(ierr);

  if (!testorder) { /* turn off printing when testing ordering mappings */
    ierr = PetscPrintf (PETSC_COMM_WORLD,"\nGlobal Vectors:\n");CHKERRQ(ierr);
    ierr = VecView(global,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscPrintf (PETSC_COMM_WORLD,"\n\n");CHKERRQ(ierr);
  }

  /* Send ghost points to local vectors */
  ierr = DMGlobalToLocalBegin(da,global,INSERT_VALUES,local);CHKERRQ(ierr);
  ierr = DMGlobalToLocalEnd(da,global,INSERT_VALUES,local);CHKERRQ(ierr);

  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-local_print",&flg,PETSC_NULL);CHKERRQ(ierr);
  if (flg) {
    PetscViewer sviewer;
    ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"\nLocal Vector: processor %d\n",rank);CHKERRQ(ierr);
    ierr = PetscViewerGetSingleton(PETSC_VIEWER_STDOUT_WORLD,&sviewer);CHKERRQ(ierr);
    ierr = VecView(local,sviewer);CHKERRQ(ierr);
    ierr = PetscViewerRestoreSingleton(PETSC_VIEWER_STDOUT_WORLD,&sviewer);CHKERRQ(ierr);
//.........这里部分代码省略.........

int main(int argc,char **argv)
{
  TS             ts;            /* ODE integrator */
  Vec            U;             /* solution will be stored here */
  Mat            A;             /* Jacobian matrix */
  PetscErrorCode ierr;
  PetscMPIInt    size;
  PetscInt       n = 2,idx;
  AppCtx         user;
  PetscScalar    *u;
  SNES           snes;
  PetscScalar       *mat;
  const PetscScalar *x;
  Mat         B;
  PetscScalar *amat;
  PetscViewer viewer;



  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize program
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
  if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Create necessary matrix and vectors
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
  ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = MatSetFromOptions(A);CHKERRQ(ierr);
  ierr = MatSetUp(A);CHKERRQ(ierr);

  ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr);

  /* Create wind speed data using Weibull distribution */
  ierr = WindSpeeds(&user);CHKERRQ(ierr);
  /* Set parameters for wind turbine and induction generator */
  ierr = SetWindTurbineParams(&user);CHKERRQ(ierr);
  ierr = SetInductionGeneratorParams(&user);CHKERRQ(ierr);

  ierr = VecGetArray(U,&u);CHKERRQ(ierr);
  u[0] = vwa;
  u[1] = s;
  ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);

  /* Create matrix to save solutions at each time step */
  user.stepnum = 0;

  ierr = MatCreateSeqDense(PETSC_COMM_SELF,3,2010,NULL,&user.Sol);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
  ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
  ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);
  ierr = TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&user);CHKERRQ(ierr);

  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESSetJacobian(snes,A,A,SNESComputeJacobianDefault,NULL);CHKERRQ(ierr);
  /*  ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&user);CHKERRQ(ierr); */
  ierr = TSSetApplicationContext(ts,&user);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSetSolution(ts,U);CHKERRQ(ierr);

  /* Save initial solution */
  idx=3*user.stepnum;

  ierr = MatDenseGetArray(user.Sol,&mat);CHKERRQ(ierr);
  ierr = VecGetArrayRead(U,&x);CHKERRQ(ierr);

  mat[idx] = 0.0;

  ierr = PetscMemcpy(mat+idx+1,x,2*sizeof(PetscScalar));CHKERRQ(ierr);
  ierr = MatDenseRestoreArray(user.Sol,&mat);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(U,&x);CHKERRQ(ierr);
  user.stepnum++;


  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set solver options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSetDuration(ts,2000,20.0);CHKERRQ(ierr);
  ierr = TSSetInitialTimeStep(ts,0.0,.01);CHKERRQ(ierr);
  ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
  ierr = TSSetPostStep(ts,SaveSolution);CHKERRQ(ierr);
  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Solve nonlinear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSolve(ts,U);CHKERRQ(ierr);

  ierr = MatCreateSeqDense(PETSC_COMM_SELF,3,user.stepnum,NULL,&B);CHKERRQ(ierr);
  ierr = MatDenseGetArray(user.Sol,&mat);CHKERRQ(ierr);
  ierr = MatDenseGetArray(B,&amat);CHKERRQ(ierr);
  ierr = PetscMemcpy(amat,mat,user.stepnum*3*sizeof(PetscScalar));CHKERRQ(ierr);
//.........这里部分代码省略.........

int main(int argc,char **argv)
{
  PetscErrorCode ierr;
  KSP            ksp;
  PC             pc;
  Vec            x,b;
  DM             da;
  Mat            A,Atrans;
  PetscInt       dof=1,M=-8;
  PetscBool      flg,trans=PETSC_FALSE;

  PetscInitialize(&argc,&argv,(char *)0,help);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-dof",&dof,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetBool(PETSC_NULL,"-trans",&trans,PETSC_NULL);CHKERRQ(ierr);

  ierr = DMDACreate(PETSC_COMM_WORLD,&da);CHKERRQ(ierr);
  ierr = DMDASetDim(da,3);CHKERRQ(ierr);
  ierr = DMDASetBoundaryType(da,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE);CHKERRQ(ierr);
  ierr = DMDASetStencilType(da,DMDA_STENCIL_STAR);CHKERRQ(ierr);
  ierr = DMDASetSizes(da,M,M,M);CHKERRQ(ierr);
  ierr = DMDASetNumProcs(da,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
  ierr = DMDASetDof(da,dof);CHKERRQ(ierr);
  ierr = DMDASetStencilWidth(da,1);CHKERRQ(ierr);
  ierr = DMDASetOwnershipRanges(da,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
  ierr = DMSetFromOptions(da);CHKERRQ(ierr);
  ierr = DMSetUp(da);CHKERRQ(ierr);

  ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
  ierr = DMCreateGlobalVector(da,&b);CHKERRQ(ierr);
  ierr = ComputeRHS(da,b);CHKERRQ(ierr);
  ierr = DMCreateMatrix(da,MATBAIJ,&A);CHKERRQ(ierr);
  ierr = ComputeMatrix(da,A);CHKERRQ(ierr);


  /* A is non-symmetric. Make A = 0.5*(A + Atrans) symmetric for testing icc and cholesky */
  ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&Atrans);CHKERRQ(ierr);
  ierr = MatAXPY(A,1.0,Atrans,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
  ierr = MatScale(A,0.5);CHKERRQ(ierr);
  ierr = MatDestroy(&Atrans);CHKERRQ(ierr);

  /* Test sbaij matrix */
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL, "-test_sbaij1", &flg,PETSC_NULL);CHKERRQ(ierr);
  if (flg){
    Mat sA;
    PetscBool issymm;
    ierr = MatIsTranspose(A,A,0.0,&issymm);CHKERRQ(ierr);
    if (issymm) {
      ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
    } else {
      printf("Warning: A is non-symmetric\n");
    }
    ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
    ierr = MatDestroy(&A);CHKERRQ(ierr);
    A = sA;
  }

  ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
  ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
  ierr = KSPSetOperators(ksp,A,A,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
  ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
  ierr = PCSetDM(pc,(DM)da);CHKERRQ(ierr);
 
  if (trans) {
    ierr = KSPSolveTranspose(ksp,b,x);CHKERRQ(ierr);
  } else {
    ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
  }

  /* check final residual */
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL, "-check_final_residual", &flg,PETSC_NULL);CHKERRQ(ierr);
  if (flg){
    Vec            b1;
    PetscReal      norm;
    ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr);
    ierr = VecDuplicate(b,&b1);CHKERRQ(ierr);
    ierr = MatMult(A,x,b1);CHKERRQ(ierr);
    ierr = VecAXPY(b1,-1.0,b);CHKERRQ(ierr);
    ierr = VecNorm(b1,NORM_2,&norm);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"Final residual %g\n",norm);CHKERRQ(ierr);
    ierr = VecDestroy(&b1);CHKERRQ(ierr);
  }
   
  ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
  ierr = VecDestroy(&x);CHKERRQ(ierr);
  ierr = VecDestroy(&b);CHKERRQ(ierr);
  ierr = MatDestroy(&A);CHKERRQ(ierr);
  ierr = DMDestroy(&da);CHKERRQ(ierr);
  ierr = PetscFinalize();
  return 0;
}

int main(int argc,char **args)
{
  Mat          C;
  int          i,m = 5,rank,size,N,start,end,M;
  int          ierr,idx[4];
  PetscScalar  Ke[16];
  PetscReal    h;
  Vec          u,b;
  KSP          ksp;
  MatNullSpace nullsp;

  ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
  ierr = PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);CHKERRQ(ierr);
  N    = (m+1)*(m+1); /* dimension of matrix */
  M    = m*m; /* number of elements */
  h    = 1.0/m;    /* mesh width */
  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);

  /* Create stiffness matrix */
  ierr  = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
  ierr  = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
  ierr  = MatSetFromOptions(C);CHKERRQ(ierr);
  ierr  = MatSetUp(C);CHKERRQ(ierr);
  start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
  end   = start + M/size + ((M%size) > rank);

  /* Assemble matrix */
  ierr = FormElementStiffness(h*h,Ke);   /* element stiffness for Laplacian */
  for (i=start; i<end; i++) {
    /* location of lower left corner of element */
    /* node numbers for the four corners of element */
    idx[0] = (m+1)*(i/m) + (i % m);
    idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
    ierr   = MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* Create right-hand-side and solution vectors */
  ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
  ierr = VecSetSizes(u,PETSC_DECIDE,N);CHKERRQ(ierr);
  ierr = VecSetFromOptions(u);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)u,"Approx. Solution");CHKERRQ(ierr);
  ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)b,"Right hand side");CHKERRQ(ierr);

  ierr = VecSet(b,1.0);CHKERRQ(ierr);
  ierr = VecSetValue(b,0,1.2,ADD_VALUES);CHKERRQ(ierr);
  ierr = VecSet(u,0.0);CHKERRQ(ierr);

  /* Solve linear system */
  ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
  ierr = KSPSetOperators(ksp,C,C);CHKERRQ(ierr);
  ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
  ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);

  ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,NULL,&nullsp);CHKERRQ(ierr);
  /*
     The KSP solver will remove this nullspace from the solution at each iteration
  */
  ierr = MatSetNullSpace(C,nullsp);CHKERRQ(ierr);
  /*
     The KSP solver will remove from the right hand side any portion in this nullspace, thus making the linear system consistent.
  */
  ierr = MatSetTransposeNullSpace(C,nullsp);CHKERRQ(ierr);
  ierr = MatNullSpaceDestroy(&nullsp);CHKERRQ(ierr);

  ierr = KSPSolve(ksp,b,u);CHKERRQ(ierr);


  /* Free work space */
  ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
  ierr = VecDestroy(&u);CHKERRQ(ierr);
  ierr = VecDestroy(&b);CHKERRQ(ierr);
  ierr = MatDestroy(&C);CHKERRQ(ierr);
  ierr = PetscFinalize();
  return ierr;
}

  -m # : the size of the vectors\n					\
  -n # : the numer of indices (with n<=m)\n				\
  -toFirst # : the starting index of the output vector for strided scatters\n \
  -toStep # : the step size into the output vector for strided scatters\n \
  -fromFirst # : the starting index of the input vector for strided scatters\n\
  -fromStep # : the step size into the input vector for strided scatters\n\n";

int main(int argc, char * argv[]) {

  Vec            X,Y;
  PetscInt       m,n,i,n1,n2;
  PetscInt       toFirst,toStep,fromFirst,fromStep;
  PetscInt       *idx,*idy;
  PetscBool      flg;
  IS             toISStrided,fromISStrided,toISGeneral,fromISGeneral;
  VecScatter     vscatSStoSS,vscatSStoSG,vscatSGtoSS,vscatSGtoSG;
  ScatterMode    mode;
  InsertMode     addv;
  PetscErrorCode ierr;

  ierr = PetscInitialize(&argc,&argv,0,help);if (ierr) return ierr;
  ierr = PetscOptionsGetInt(NULL,NULL,"-m",&m,&flg);CHKERRQ(ierr);
  if (!flg) m = 100;

  ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,&flg);CHKERRQ(ierr);
  if (!flg) n = 30;

  ierr = PetscOptionsGetInt(NULL,NULL,"-toFirst",&toFirst,&flg);CHKERRQ(ierr);
  if (!flg) toFirst = 3;

  ierr = PetscOptionsGetInt(NULL,NULL,"-toStep",&toStep,&flg);CHKERRQ(ierr);
  if (!flg) toStep = 3;

  ierr = PetscOptionsGetInt(NULL,NULL,"-fromFirst",&fromFirst,&flg);CHKERRQ(ierr);
  if (!flg) fromFirst = 2;

  ierr = PetscOptionsGetInt(NULL,NULL,"-fromStep",&fromStep,&flg);CHKERRQ(ierr);
  if (!flg) fromStep = 2;

  if (n>m) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"The vector sizes are %D. The number of elements being scattered is %D\n",m,n);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"Adjust the parameters such that m>=n\n");CHKERRQ(ierr);
  } else if (toFirst+(n-1)*toStep >=m) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"The vector sizes are %D. The number of elements being scattered is %D\n",m,n);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"For the Strided Scatter, toFirst=%D and toStep=%D.\n",toFirst,toStep);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"This produces an index (toFirst+(n-1)*toStep)>=m\n");CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"Adjust the parameterrs accordingly with -m, -n, -toFirst, or -toStep\n");CHKERRQ(ierr);
  } else if (fromFirst+(n-1)*fromStep>=m) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"The vector sizes are %D. The number of elements being scattered is %D\n",m,n);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"For the Strided Scatter, fromFirst=%D and fromStep=%D.\n",fromFirst,toStep);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"This produces an index (fromFirst+(n-1)*fromStep)>=m\n");CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"Adjust the parameterrs accordingly with -m, -n, -fromFirst, or -fromStep\n");CHKERRQ(ierr);
  } else {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"m=%D\tn=%D\tfromFirst=%D\tfromStep=%D\ttoFirst=%D\ttoStep=%D\n",m,n,fromFirst,fromStep,toFirst,toStep);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"fromFirst+(n-1)*fromStep=%D\ttoFirst+(n-1)*toStep=%D\n",fromFirst+(n-1)*fromStep,toFirst+(n-1)*toStep);CHKERRQ(ierr);

    /* Build the vectors */
    ierr = VecCreate(PETSC_COMM_WORLD,&Y);CHKERRQ(ierr);
    ierr = VecSetSizes(Y,m,PETSC_DECIDE);CHKERRQ(ierr);
    ierr = VecCreate(PETSC_COMM_WORLD,&X);CHKERRQ(ierr);
    ierr = VecSetSizes(X,m,PETSC_DECIDE);CHKERRQ(ierr);

    ierr = VecSetFromOptions(Y);CHKERRQ(ierr);
    ierr = VecSetFromOptions(X);CHKERRQ(ierr);
    ierr = VecSet(X,2.0);CHKERRQ(ierr);
    ierr = VecSet(Y,1.0);CHKERRQ(ierr);

    /* Build the strided index sets */
    ierr = ISCreate(PETSC_COMM_WORLD,&toISStrided);CHKERRQ(ierr);
    ierr = ISCreate(PETSC_COMM_WORLD,&fromISStrided);CHKERRQ(ierr);
    ierr = ISSetType(toISStrided, ISSTRIDE);CHKERRQ(ierr);
    ierr = ISSetType(fromISStrided, ISSTRIDE);CHKERRQ(ierr);
    ierr = ISStrideSetStride(fromISStrided,n,fromFirst,fromStep);CHKERRQ(ierr);
    ierr = ISStrideSetStride(toISStrided,n,toFirst,toStep);CHKERRQ(ierr);

    /* Build the general index sets */
    ierr = PetscMalloc1(n,&idx);CHKERRQ(ierr);
    ierr = PetscMalloc1(n,&idy);CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      idx[i] = i % m;
      idy[i] = (i+m) % m;
    }
    n1 = n;
    n2 = n;
    ierr = PetscSortRemoveDupsInt(&n1,idx);CHKERRQ(ierr);
    ierr = PetscSortRemoveDupsInt(&n2,idy);CHKERRQ(ierr);

    ierr = ISCreateGeneral(PETSC_COMM_WORLD,n1,idx,PETSC_COPY_VALUES,&toISGeneral);CHKERRQ(ierr);
    ierr = ISCreateGeneral(PETSC_COMM_WORLD,n2,idy,PETSC_COPY_VALUES,&fromISGeneral);CHKERRQ(ierr);

    /* set the mode and the insert/add parameter */
    mode = SCATTER_FORWARD;
    addv = ADD_VALUES;

    /* VecScatter : Seq Strided to Seq Strided */
    ierr = VecScatterCreate(X,fromISStrided,Y,toISStrided,&vscatSStoSS);CHKERRQ(ierr);
    ierr = VecScatterBegin(vscatSStoSS,X,Y,addv,mode);CHKERRQ(ierr);
    ierr = VecScatterEnd(vscatSStoSS,X,Y,addv,mode);CHKERRQ(ierr);
    ierr = VecScatterDestroy(&vscatSStoSS);CHKERRQ(ierr);

//.........这里部分代码省略.........

int main(int argc,char **args)
{
  Mat             A;
  PetscErrorCode  ierr;
  PetscMPIInt     rank,size;
  PetscInt        *ia,*ja;
  MatPartitioning part;
  IS              is,isn;

  PetscInitialize(&argc,&args,(char*)0,help);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
  if (size != 4) SETERRQ(PETSC_COMM_WORLD,1,"Must run with 4 processors");
  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);

  ierr = PetscMalloc(5*sizeof(PetscInt),&ia);CHKERRQ(ierr);
  ierr = PetscMalloc(16*sizeof(PetscInt),&ja);CHKERRQ(ierr);
  if (!rank) {
    ja[0] = 1; ja[1] = 4; ja[2] = 0; ja[3] = 2; ja[4] = 5; ja[5] = 1; ja[6] = 3; ja[7] = 6;
    ja[8] = 2; ja[9] = 7;
    ia[0] = 0; ia[1] = 2; ia[2] = 5; ia[3] = 8; ia[4] = 10;
  } else if (rank == 1) {
    ja[0] = 0; ja[1] = 5; ja[2] = 8; ja[3] = 1; ja[4] = 4; ja[5] = 6; ja[6] = 9; ja[7] = 2;
    ja[8] = 5; ja[9] = 7; ja[10] = 10; ja[11] = 3; ja[12] = 6; ja[13] = 11;
    ia[0] = 0; ia[1] = 3; ia[2] = 7; ia[3] = 11; ia[4] = 14;
  } else if (rank == 2) {
    ja[0] = 4; ja[1] = 9; ja[2] = 12; ja[3] = 5; ja[4] = 8; ja[5] = 10; ja[6] = 13; ja[7] = 6;
    ja[8] = 9; ja[9] = 11; ja[10] = 14; ja[11] = 7; ja[12] = 10; ja[13] = 15;
    ia[0] = 0; ia[1] = 3; ia[2] = 7; ia[3] = 11; ia[4] = 14;
  } else {
    ja[0] = 8; ja[1] = 13; ja[2] = 9; ja[3] = 12; ja[4] = 14; ja[5] = 10; ja[6] = 13; ja[7] = 15;
    ja[8] = 11; ja[9] = 14;
    ia[0] = 0; ia[1] = 2; ia[2] = 5; ia[3] = 8; ia[4] = 10;
  }

  ierr = MatCreateMPIAdj(PETSC_COMM_WORLD,4,16,ia,ja,NULL,&A);CHKERRQ(ierr);
  ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);

  /*
       Partition the graph of the matrix
  */
  ierr = MatPartitioningCreate(PETSC_COMM_WORLD,&part);CHKERRQ(ierr);
  ierr = MatPartitioningSetAdjacency(part,A);CHKERRQ(ierr);
  ierr = MatPartitioningSetFromOptions(part);CHKERRQ(ierr);
  /* get new processor owner number of each vertex */
  ierr = MatPartitioningApply(part,&is);CHKERRQ(ierr);
  /* get new global number of each old global number */
  ierr = ISPartitioningToNumbering(is,&isn);CHKERRQ(ierr);
  ierr = ISView(isn,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  ierr = ISDestroy(&is);CHKERRQ(ierr);

  ierr = ISDestroy(&isn);CHKERRQ(ierr);
  ierr = MatPartitioningDestroy(&part);CHKERRQ(ierr);

  /*
       Free work space.  All PETSc objects should be destroyed when they
       are no longer needed.
  */
  ierr = MatDestroy(&A);CHKERRQ(ierr);


  ierr = PetscFinalize();
  return 0;
}

Example: mpiexec -n <np> ./ex130 -f <matrix binary file> -mat_solver_type 1 -mat_superlu_equil \n\n";

#include <petscmat.h>

int main(int argc,char **args)
{
  Mat            A,F;
  Vec            u,x,b;
  PetscErrorCode ierr;
  PetscMPIInt    rank,size;
  PetscInt       m,n,nfact,ipack=0;
  PetscReal      norm,tol=1.e-12,Anorm;
  IS             perm,iperm;
  MatFactorInfo  info;
  PetscBool      flg,testMatSolve=PETSC_TRUE;
  PetscViewer    fd;              /* viewer */
  char           file[PETSC_MAX_PATH_LEN]; /* input file name */

  ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
  ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);

  /* Determine file from which we read the matrix A */
  ierr = PetscOptionsGetString(NULL,NULL,"-f",file,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
  if (!flg) SETERRQ(PETSC_COMM_WORLD,1,"Must indicate binary file with the -f option");

  /* Load matrix A */
  ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr);
  ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
  ierr = MatLoad(A,fd);CHKERRQ(ierr);
  ierr = VecCreate(PETSC_COMM_WORLD,&b);CHKERRQ(ierr);
  ierr = VecLoad(b,fd);CHKERRQ(ierr);
  ierr = PetscViewerDestroy(&fd);CHKERRQ(ierr);
  ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
  if (m != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ, "This example is not intended for rectangular matrices (%d, %d)", m, n);
  ierr = MatNorm(A,NORM_INFINITY,&Anorm);CHKERRQ(ierr);

  /* Create vectors */
  ierr = VecDuplicate(b,&x);CHKERRQ(ierr);
  ierr = VecDuplicate(x,&u);CHKERRQ(ierr); /* save the true solution */

  /* Test LU Factorization */
  ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iperm);CHKERRQ(ierr);

  ierr = PetscOptionsGetInt(NULL,NULL,"-mat_solver_type",&ipack,NULL);CHKERRQ(ierr);
  switch (ipack) {
  case 1:
#if defined(PETSC_HAVE_SUPERLU)
    if (!rank) printf(" SUPERLU LU:\n");