static char help[] = "Test PC redistribute on matrix with load imbalance. \n\
                      Modified from src/ksp/ksp/tutorials/ex2.c.\n\
Input parameters include:\n\
  -random_exact_sol : use a random exact solution vector\n\
  -view_exact_sol   : write exact solution vector to stdout\n\
  -n <mesh_y>       : number of mesh points\n\n";
/*
Example:
  mpiexec -n 8 ./ex3 -n 10000 -ksp_type cg -pc_type bjacobi -sub_pc_type icc -ksp_rtol 1.e-8 -log_view
  mpiexec -n 8 ./ex3 -n 10000 -ksp_type preonly -pc_type redistribute -redistribute_ksp_type cg -redistribute_pc_type bjacobi -redistribute_sub_pc_type icc -redistribute_ksp_rtol 1.e-8 -log_view
*/

#include <petscksp.h>

int main(int argc, char **args)
{
  Vec           x, b, u; /* approx solution, RHS, exact solution */
  Mat           A;       /* linear system matrix */
  KSP           ksp;     /* linear solver context */
  PetscRandom   rctx;    /* random number generator context */
  PetscReal     norm;    /* norm of solution error */
  PetscInt      i, j, Ii, J, Istart, Iend, m, n = 7, its, nloc, matdistribute = 0;
  PetscBool     flg = PETSC_FALSE;
  PetscScalar   v;
  PetscMPIInt   rank, size;
  PetscLogStage stage;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
  PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
  PetscCheck(size > 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This example requires at least 2 MPI processes!");

  PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-matdistribute", &matdistribute, NULL));
  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
         Compute the matrix and right-hand-side vector that define
         the linear system, Ax = b.
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  switch (matdistribute) {
  case 1: /* very imbalanced process load for matrix A */
    m    = (1 + size) * size;
    nloc = (rank + 1) * n;
    if (rank == size - 1) { /* proc[size-1] stores all remaining rows */
      nloc = m * n;
      for (i = 0; i < size - 1; i++) nloc -= (i + 1) * n;
    }
    break;
  default: /* proc[0] and proc[1] load much smaller row blocks, the rest processes have same loads */
    if (rank == 0 || rank == 1) {
      nloc = n;
    } else {
      nloc = 10 * n; /* 10x larger load */
    }
    m = 2 + (size - 2) * 10;
    break;
  }
  PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
  PetscCall(MatSetSizes(A, nloc, nloc, PETSC_DECIDE, PETSC_DECIDE));
  PetscCall(MatSetFromOptions(A));
  PetscCall(MatMPIAIJSetPreallocation(A, 5, NULL, 5, NULL));
  PetscCall(MatSeqAIJSetPreallocation(A, 5, NULL));
  PetscCall(MatSetUp(A));

  PetscCall(MatGetOwnershipRange(A, &Istart, &Iend));
  nloc = Iend - Istart;
  PetscCall(PetscSynchronizedPrintf(PETSC_COMM_WORLD, "[%d] A Istart,Iend: %" PetscInt_FMT " %" PetscInt_FMT "; nloc %" PetscInt_FMT "\n", rank, Istart, Iend, nloc));
  PetscCall(PetscSynchronizedFlush(PETSC_COMM_WORLD, PETSC_STDOUT));

  PetscCall(PetscLogStageRegister("Assembly", &stage));
  PetscCall(PetscLogStagePush(stage));
  for (Ii = Istart; Ii < Iend; Ii++) {
    v = -1.0;
    i = Ii / n;
    j = Ii - i * n;
    if (i > 0) {
      J = Ii - n;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
    }
    if (i < m - 1) {
      J = Ii + n;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
    }
    if (j > 0) {
      J = Ii - 1;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
    }
    if (j < n - 1) {
      J = Ii + 1;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
    }
    v = 4.0;
    PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
  }
  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  PetscCall(PetscLogStagePop());

  /* A is symmetric. Set symmetric flag to enable ICC/Cholesky preconditioner */
  PetscCall(MatSetOption(A, MAT_SYMMETRIC, PETSC_TRUE));

  /* Create parallel vectors. */
  PetscCall(VecCreate(PETSC_COMM_WORLD, &u));
  PetscCall(VecSetSizes(u, nloc, PETSC_DECIDE));
  PetscCall(VecSetFromOptions(u));
  PetscCall(VecDuplicate(u, &b));
  PetscCall(VecDuplicate(b, &x));

  /* Set exact solution; then compute right-hand-side vector. */
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-random_exact_sol", &flg, NULL));
  if (flg) {
    PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rctx));
    PetscCall(PetscRandomSetFromOptions(rctx));
    PetscCall(VecSetRandom(u, rctx));
    PetscCall(PetscRandomDestroy(&rctx));
  } else {
    PetscCall(VecSet(u, 1.0));
  }
  PetscCall(MatMult(A, u, b));

  /* View the exact solution vector if desired */
  flg = PETSC_FALSE;
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_exact_sol", &flg, NULL));
  if (flg) PetscCall(VecView(u, PETSC_VIEWER_STDOUT_WORLD));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                Create the linear solver and set various options
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
  PetscCall(KSPSetOperators(ksp, A, A));
  PetscCall(KSPSetTolerances(ksp, 1.e-2 / ((m + 1) * (n + 1)), PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT));
  PetscCall(KSPSetFromOptions(ksp));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Solve the linear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(KSPSolve(ksp, b, x));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Check solution and clean up
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(VecAXPY(x, -1.0, u));
  PetscCall(VecNorm(x, NORM_2, &norm));
  PetscCall(KSPGetIterationNumber(ksp, &its));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g iterations %" PetscInt_FMT "\n", (double)norm, its));

  /* Free work space. */
  PetscCall(KSPDestroy(&ksp));
  PetscCall(VecDestroy(&u));
  PetscCall(VecDestroy(&x));
  PetscCall(VecDestroy(&b));
  PetscCall(MatDestroy(&A));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   test:
      nsize: 8
      args: -n 100 -ksp_type cg -pc_type bjacobi -sub_pc_type icc -ksp_rtol 1.e-8

   test:
      suffix: 2
      nsize: 8
      args: -n 100 -ksp_type preonly -pc_type redistribute -redistribute_ksp_type cg -redistribute_pc_type bjacobi -redistribute_sub_pc_type icc -redistribute_ksp_rtol 1.e-8

TEST*/
