static char help[] ="Tests sequential and parallel DMCreateMatrix(), MatMatMult() and MatPtAP()\n\
  -Mx <xg>, where <xg> = number of coarse grid points in the x-direction\n\
  -My <yg>, where <yg> = number of coarse grid points in the y-direction\n\
  -Mz <zg>, where <zg> = number of coarse grid points in the z-direction\n\
  -Npx <npx>, where <npx> = number of processors in the x-direction\n\
  -Npy <npy>, where <npy> = number of processors in the y-direction\n\
  -Npz <npz>, where <npz> = number of processors in the z-direction\n\n";

/*
    This test is modified from ~src/ksp/tests/ex19.c.
    Example of usage: mpiexec -n 3 ./ex96 -Mx 10 -My 10 -Mz 10
*/

#include <petscdm.h>
#include <petscdmda.h>

/* User-defined application contexts */
typedef struct {
  PetscInt mx,my,mz;            /* number grid points in x, y and z direction */
  Vec      localX,localF;       /* local vectors with ghost region */
  DM       da;
  Vec      x,b,r;               /* global vectors */
  Mat      J;                   /* Jacobian on grid */
} GridCtx;
typedef struct {
  GridCtx  fine;
  GridCtx  coarse;
  PetscInt ratio;
  Mat      Ii;                  /* interpolation from coarse to fine */
} AppCtx;

#define COARSE_LEVEL 0
#define FINE_LEVEL   1

/*
      Mm_ratio - ration of grid lines between fine and coarse grids.
*/
int main(int argc,char **argv)
{
  AppCtx         user;
  PetscInt       Npx=PETSC_DECIDE,Npy=PETSC_DECIDE,Npz=PETSC_DECIDE;
  PetscMPIInt    size,rank;
  PetscInt       m,n,M,N,i,nrows;
  PetscScalar    one = 1.0;
  PetscReal      fill=2.0;
  Mat            A,A_tmp,P,C,C1,C2;
  PetscScalar    *array,none = -1.0,alpha;
  Vec            x,v1,v2,v3,v4;
  PetscReal      norm,norm_tmp,norm_tmp1,tol=100.*PETSC_MACHINE_EPSILON;
  PetscRandom    rdm;
  PetscBool      Test_MatMatMult=PETSC_TRUE,Test_MatPtAP=PETSC_TRUE,Test_3D=PETSC_TRUE,flg;
  const PetscInt *ia,*ja;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc,&argv,NULL,help));
  PetscCall(PetscOptionsGetReal(NULL,NULL,"-tol",&tol,NULL));

  user.ratio     = 2;
  user.coarse.mx = 20; user.coarse.my = 20; user.coarse.mz = 20;

  PetscCall(PetscOptionsGetInt(NULL,NULL,"-Mx",&user.coarse.mx,NULL));
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-My",&user.coarse.my,NULL));
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-Mz",&user.coarse.mz,NULL));
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-ratio",&user.ratio,NULL));

  if (user.coarse.mz) Test_3D = PETSC_TRUE;

  PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size));
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD,&rank));
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-Npx",&Npx,NULL));
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-Npy",&Npy,NULL));
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-Npz",&Npz,NULL));

  /* Set up distributed array for fine grid */
  if (!Test_3D) {
    PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.coarse.mx,user.coarse.my,Npx,Npy,1,1,NULL,NULL,&user.coarse.da));
  } else {
    PetscCall(DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.coarse.mx,user.coarse.my,user.coarse.mz,Npx,Npy,Npz,1,1,NULL,NULL,NULL,&user.coarse.da));
  }
  PetscCall(DMSetFromOptions(user.coarse.da));
  PetscCall(DMSetUp(user.coarse.da));

  /* This makes sure the coarse DMDA has the same partition as the fine DMDA */
  PetscCall(DMRefine(user.coarse.da,PetscObjectComm((PetscObject)user.coarse.da),&user.fine.da));

  /* Test DMCreateMatrix()                                         */
  /*------------------------------------------------------------*/
  PetscCall(DMSetMatType(user.fine.da,MATAIJ));
  PetscCall(DMCreateMatrix(user.fine.da,&A));
  PetscCall(DMSetMatType(user.fine.da,MATBAIJ));
  PetscCall(DMCreateMatrix(user.fine.da,&C));

  PetscCall(MatConvert(C,MATAIJ,MAT_INITIAL_MATRIX,&A_tmp)); /* not work for mpisbaij matrix! */
  PetscCall(MatEqual(A,A_tmp,&flg));
  PetscCheck(flg,PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"A != C");
  PetscCall(MatDestroy(&C));
  PetscCall(MatDestroy(&A_tmp));

  /*------------------------------------------------------------*/

  PetscCall(MatGetLocalSize(A,&m,&n));
  PetscCall(MatGetSize(A,&M,&N));
  /* if (rank == 0) printf("A %d, %d\n",M,N); */

  /* set val=one to A */
  if (size == 1) {
    PetscCall(MatGetRowIJ(A,0,PETSC_FALSE,PETSC_FALSE,&nrows,&ia,&ja,&flg));
    if (flg) {
      PetscCall(MatSeqAIJGetArray(A,&array));
      for (i=0; i<ia[nrows]; i++) array[i] = one;
      PetscCall(MatSeqAIJRestoreArray(A,&array));
    }
    PetscCall(MatRestoreRowIJ(A,0,PETSC_FALSE,PETSC_FALSE,&nrows,&ia,&ja,&flg));
  } else {
    Mat AA,AB;
    PetscCall(MatMPIAIJGetSeqAIJ(A,&AA,&AB,NULL));
    PetscCall(MatGetRowIJ(AA,0,PETSC_FALSE,PETSC_FALSE,&nrows,&ia,&ja,&flg));
    if (flg) {
      PetscCall(MatSeqAIJGetArray(AA,&array));
      for (i=0; i<ia[nrows]; i++) array[i] = one;
      PetscCall(MatSeqAIJRestoreArray(AA,&array));
    }
    PetscCall(MatRestoreRowIJ(AA,0,PETSC_FALSE,PETSC_FALSE,&nrows,&ia,&ja,&flg));
    PetscCall(MatGetRowIJ(AB,0,PETSC_FALSE,PETSC_FALSE,&nrows,&ia,&ja,&flg));
    if (flg) {
      PetscCall(MatSeqAIJGetArray(AB,&array));
      for (i=0; i<ia[nrows]; i++) array[i] = one;
      PetscCall(MatSeqAIJRestoreArray(AB,&array));
    }
    PetscCall(MatRestoreRowIJ(AB,0,PETSC_FALSE,PETSC_FALSE,&nrows,&ia,&ja,&flg));
  }
  /* PetscCall(MatView(A, PETSC_VIEWER_STDOUT_WORLD)); */

  /* Create interpolation between the fine and coarse grids */
  PetscCall(DMCreateInterpolation(user.coarse.da,user.fine.da,&P,NULL));
  PetscCall(MatGetLocalSize(P,&m,&n));
  PetscCall(MatGetSize(P,&M,&N));
  /* if (rank == 0) printf("P %d, %d\n",M,N); */

  /* Create vectors v1 and v2 that are compatible with A */
  PetscCall(VecCreate(PETSC_COMM_WORLD,&v1));
  PetscCall(MatGetLocalSize(A,&m,NULL));
  PetscCall(VecSetSizes(v1,m,PETSC_DECIDE));
  PetscCall(VecSetFromOptions(v1));
  PetscCall(VecDuplicate(v1,&v2));
  PetscCall(PetscRandomCreate(PETSC_COMM_WORLD,&rdm));
  PetscCall(PetscRandomSetFromOptions(rdm));

  /* Test MatMatMult(): C = A*P */
  /*----------------------------*/
  if (Test_MatMatMult) {
    PetscCall(MatDuplicate(A,MAT_COPY_VALUES,&A_tmp));
    PetscCall(MatMatMult(A_tmp,P,MAT_INITIAL_MATRIX,fill,&C));

    /* Test MAT_REUSE_MATRIX - reuse symbolic C */
    alpha=1.0;
    for (i=0; i<2; i++) {
      alpha -= 0.1;
      PetscCall(MatScale(A_tmp,alpha));
      PetscCall(MatMatMult(A_tmp,P,MAT_REUSE_MATRIX,fill,&C));
    }
    /* Free intermediate data structures created for reuse of C=Pt*A*P */
    PetscCall(MatProductClear(C));

    /* Test MatDuplicate()        */
    /*----------------------------*/
    PetscCall(MatDuplicate(C,MAT_COPY_VALUES,&C1));
    PetscCall(MatDuplicate(C1,MAT_COPY_VALUES,&C2));
    PetscCall(MatDestroy(&C1));
    PetscCall(MatDestroy(&C2));

    /* Create vector x that is compatible with P */
    PetscCall(VecCreate(PETSC_COMM_WORLD,&x));
    PetscCall(MatGetLocalSize(P,NULL,&n));
    PetscCall(VecSetSizes(x,n,PETSC_DECIDE));
    PetscCall(VecSetFromOptions(x));

    norm = 0.0;
    for (i=0; i<10; i++) {
      PetscCall(VecSetRandom(x,rdm));
      PetscCall(MatMult(P,x,v1));
      PetscCall(MatMult(A_tmp,v1,v2)); /* v2 = A*P*x */
      PetscCall(MatMult(C,x,v1));  /* v1 = C*x   */
      PetscCall(VecAXPY(v1,none,v2));
      PetscCall(VecNorm(v1,NORM_1,&norm_tmp));
      PetscCall(VecNorm(v2,NORM_1,&norm_tmp1));
      norm_tmp /= norm_tmp1;
      if (norm_tmp > norm) norm = norm_tmp;
    }
    if (norm >= tol && rank == 0) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF,"Error: MatMatMult(), |v1 - v2|/|v2|: %g\n",(double)norm));
    }

    PetscCall(VecDestroy(&x));
    PetscCall(MatDestroy(&C));
    PetscCall(MatDestroy(&A_tmp));
  }

  /* Test P^T * A * P - MatPtAP() */
  /*------------------------------*/
  if (Test_MatPtAP) {
    PetscCall(MatPtAP(A,P,MAT_INITIAL_MATRIX,fill,&C));
    PetscCall(MatGetLocalSize(C,&m,&n));

    /* Test MAT_REUSE_MATRIX - reuse symbolic C */
    alpha=1.0;
    for (i=0; i<1; i++) {
      alpha -= 0.1;
      PetscCall(MatScale(A,alpha));
      PetscCall(MatPtAP(A,P,MAT_REUSE_MATRIX,fill,&C));
    }

    /* Free intermediate data structures created for reuse of C=Pt*A*P */
    PetscCall(MatProductClear(C));

    /* Test MatDuplicate()        */
    /*----------------------------*/
    PetscCall(MatDuplicate(C,MAT_COPY_VALUES,&C1));
    PetscCall(MatDuplicate(C1,MAT_COPY_VALUES,&C2));
    PetscCall(MatDestroy(&C1));
    PetscCall(MatDestroy(&C2));

    /* Create vector x that is compatible with P */
    PetscCall(VecCreate(PETSC_COMM_WORLD,&x));
    PetscCall(MatGetLocalSize(P,&m,&n));
    PetscCall(VecSetSizes(x,n,PETSC_DECIDE));
    PetscCall(VecSetFromOptions(x));

    PetscCall(VecCreate(PETSC_COMM_WORLD,&v3));
    PetscCall(VecSetSizes(v3,n,PETSC_DECIDE));
    PetscCall(VecSetFromOptions(v3));
    PetscCall(VecDuplicate(v3,&v4));

    norm = 0.0;
    for (i=0; i<10; i++) {
      PetscCall(VecSetRandom(x,rdm));
      PetscCall(MatMult(P,x,v1));
      PetscCall(MatMult(A,v1,v2));  /* v2 = A*P*x */

      PetscCall(MatMultTranspose(P,v2,v3)); /* v3 = Pt*A*P*x */
      PetscCall(MatMult(C,x,v4));           /* v3 = C*x   */
      PetscCall(VecAXPY(v4,none,v3));
      PetscCall(VecNorm(v4,NORM_1,&norm_tmp));
      PetscCall(VecNorm(v3,NORM_1,&norm_tmp1));

      norm_tmp /= norm_tmp1;
      if (norm_tmp > norm) norm = norm_tmp;
    }
    if (norm >= tol && rank == 0) {
      PetscCall(PetscPrintf(PETSC_COMM_SELF,"Error: MatPtAP(), |v3 - v4|/|v3|: %g\n",(double)norm));
    }
    PetscCall(MatDestroy(&C));
    PetscCall(VecDestroy(&v3));
    PetscCall(VecDestroy(&v4));
    PetscCall(VecDestroy(&x));
  }

  /* Clean up */
  PetscCall(MatDestroy(&A));
  PetscCall(PetscRandomDestroy(&rdm));
  PetscCall(VecDestroy(&v1));
  PetscCall(VecDestroy(&v2));
  PetscCall(DMDestroy(&user.fine.da));
  PetscCall(DMDestroy(&user.coarse.da));
  PetscCall(MatDestroy(&P));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   test:
      args: -Mx 10 -My 5 -Mz 10
      output_file: output/ex96_1.out

   test:
      suffix: nonscalable
      nsize: 3
      args: -Mx 10 -My 5 -Mz 10
      output_file: output/ex96_1.out

   test:
      suffix: scalable
      nsize: 3
      args: -Mx 10 -My 5 -Mz 10 -matmatmult_via scalable -matptap_via scalable
      output_file: output/ex96_1.out

   test:
     suffix: seq_scalable
     nsize: 3
     args: -Mx 10 -My 5 -Mz 10 -matmatmult_via scalable -matptap_via scalable -inner_diag_mat_product_algorithm scalable -inner_offdiag_mat_product_algorithm scalable
     output_file: output/ex96_1.out

   test:
     suffix: seq_sorted
     nsize: 3
     args: -Mx 10 -My 5 -Mz 10 -matmatmult_via scalable -matptap_via scalable -inner_diag_mat_product_algorithm sorted -inner_offdiag_mat_product_algorithm sorted
     output_file: output/ex96_1.out

   test:
     suffix: seq_scalable_fast
     nsize: 3
     args: -Mx 10 -My 5 -Mz 10 -matmatmult_via scalable -matptap_via scalable -inner_diag_mat_product_algorithm scalable_fast -inner_offdiag_mat_product_algorithm scalable_fast
     output_file: output/ex96_1.out

   test:
     suffix: seq_heap
     nsize: 3
     args: -Mx 10 -My 5 -Mz 10 -matmatmult_via scalable -matptap_via scalable -inner_diag_mat_product_algorithm heap -inner_offdiag_mat_product_algorithm heap
     output_file: output/ex96_1.out

   test:
     suffix: seq_btheap
     nsize: 3
     args: -Mx 10 -My 5 -Mz 10 -matmatmult_via scalable -matptap_via scalable -inner_diag_mat_product_algorithm btheap -inner_offdiag_mat_product_algorithm btheap
     output_file: output/ex96_1.out

   test:
     suffix: seq_llcondensed
     nsize: 3
     args: -Mx 10 -My 5 -Mz 10 -matmatmult_via scalable -matptap_via scalable -inner_diag_mat_product_algorithm llcondensed -inner_offdiag_mat_product_algorithm llcondensed
     output_file: output/ex96_1.out

   test:
     suffix: seq_rowmerge
     nsize: 3
     args: -Mx 10 -My 5 -Mz 10 -matmatmult_via scalable -matptap_via scalable -inner_diag_mat_product_algorithm rowmerge -inner_offdiag_mat_product_algorithm rowmerge
     output_file: output/ex96_1.out

   test:
     suffix: allatonce
     nsize: 3
     args: -Mx 10 -My 5 -Mz 10 -matmatmult_via scalable -matptap_via allatonce
     output_file: output/ex96_1.out

   test:
     suffix: allatonce_merged
     nsize: 3
     args: -Mx 10 -My 5 -Mz 10 -matmatmult_via scalable -matptap_via allatonce_merged
     output_file: output/ex96_1.out

TEST*/