static char help[] = "Tests MATHTOOL\n\n";

#include <petscmat.h>

static PetscErrorCode GenEntries(PetscInt sdim, PetscInt M, PetscInt N, const PetscInt *J, const PetscInt *K, PetscScalar *ptr, PetscCtx ctx)
{
  PetscInt  d, j, k;
  PetscReal diff = 0.0, *coords = (PetscReal *)(ctx);

  PetscFunctionBeginUser;
  for (j = 0; j < M; j++) {
    for (k = 0; k < N; k++) {
      diff = 0.0;
      for (d = 0; d < sdim; d++) diff += (coords[J[j] * sdim + d] - coords[K[k] * sdim + d]) * (coords[J[j] * sdim + d] - coords[K[k] * sdim + d]);
      ptr[j + M * k] = 1.0 / (1.0e-2 + PetscSqrtReal(diff));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GenEntriesRectangular(PetscInt sdim, PetscInt M, PetscInt N, const PetscInt *J, const PetscInt *K, PetscScalar *ptr, PetscCtx ctx)
{
  PetscInt  d, j, k;
  PetscReal diff = 0.0, **coords = (PetscReal **)(ctx);

  PetscFunctionBeginUser;
  for (j = 0; j < M; j++) {
    for (k = 0; k < N; k++) {
      diff = 0.0;
      for (d = 0; d < sdim; d++) diff += (coords[0][J[j] * sdim + d] - coords[1][K[k] * sdim + d]) * (coords[0][J[j] * sdim + d] - coords[1][K[k] * sdim + d]);
      ptr[j + M * k] = 1.0 / (1.0e-2 + PetscSqrtReal(diff));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

int main(int argc, char **argv)
{
  Mat               A, AT, D, B, P, R, RT;
  PetscInt          m = 100, dim = 3, M, K = 10, begin, n = 0, N, bs;
  PetscMPIInt       size;
  PetscScalar      *ptr;
  PetscReal        *coords, *gcoords, *scoords, *gscoords, *ctx[2], norm, epsilon = PetscSqrtReal(PETSC_SMALL);
  MatHtoolKernelFn *kernel = GenEntries;
  PetscBool         flg, sym = PETSC_FALSE, recompression = PETSC_FALSE;
  PetscRandom       rdm;
  IS                iss, ist, is[2];
  Vec               right, left, perm;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, (char *)NULL, help));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-m_local", &m, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-n_local", &n, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-dim", &dim, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-K", &K, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-symmetric", &sym, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-recompression", &recompression, NULL));
  PetscCall(PetscOptionsGetReal(NULL, NULL, "-mat_htool_epsilon", &epsilon, NULL));
  PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
  M = size * m;
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-M", &M, NULL));
  PetscCall(PetscMalloc1(m * dim, &coords));
  PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rdm));
  PetscCall(PetscRandomGetValuesReal(rdm, m * dim, coords));
  PetscCall(PetscCalloc1(M * dim, &gcoords));
  PetscCall(MatCreateDense(PETSC_COMM_WORLD, m, PETSC_DECIDE, M, K, NULL, &B));
  PetscCall(MatSetRandom(B, rdm));
  PetscCall(MatGetOwnershipRange(B, &begin, NULL));
  PetscCall(PetscArraycpy(gcoords + begin * dim, coords, m * dim));
  PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, gcoords, M * dim, MPIU_REAL, MPI_SUM, PETSC_COMM_WORLD));
  PetscCall(MatCreateHtoolFromKernel(PETSC_COMM_WORLD, m, m, M, M, dim, coords, coords, kernel, gcoords, &A));
  PetscCall(MatSetOption(A, MAT_SYMMETRIC, sym));
  PetscCall(MatHtoolUseRecompression(A, recompression));
  PetscCall(MatSetFromOptions(A));
  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatViewFromOptions(A, NULL, "-A_view"));
  PetscCall(MatGetOwnershipIS(A, is, NULL));
  PetscCall(ISDuplicate(is[0], is + 1));
  PetscCall(MatIncreaseOverlap(A, 1, is, 2));
  PetscCall(MatSetBlockSize(A, 2));
  PetscCall(MatIncreaseOverlap(A, 1, is + 1, 1));
  PetscCall(ISGetBlockSize(is[1], &bs));
  PetscCheck(bs == 2, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Incorrect block size %" PetscInt_FMT " != 2", bs);
  PetscCall(MatSetBlockSize(A, 1));
  PetscCall(ISEqual(is[0], is[1], &flg));
  PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unequal index sets");
  PetscCall(ISDestroy(is));
  PetscCall(ISDestroy(is + 1));
  PetscCall(MatCreateVecs(A, &right, &left));
  PetscCall(VecSetRandom(right, rdm));
  PetscCall(MatMult(A, right, left));
  PetscCall(MatHtoolGetPermutationSource(A, &iss));
  PetscCall(MatHtoolGetPermutationTarget(A, &ist));
  PetscCall(VecDuplicate(left, &perm));
  PetscCall(VecCopy(left, perm));
  PetscCall(VecPermute(perm, ist, PETSC_FALSE));
  PetscCall(VecPermute(right, iss, PETSC_FALSE));
  PetscCall(MatHtoolUsePermutation(A, PETSC_FALSE));
  PetscCall(MatMult(A, right, left));
  PetscCall(VecAXPY(left, -1.0, perm));
  PetscCall(VecNorm(left, NORM_INFINITY, &norm));
  PetscCheck(PetscAbsReal(norm) <= PETSC_SMALL, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "||y(with permutation)-y(without permutation)|| = %g (> %g)", (double)PetscAbsReal(norm), (double)PETSC_SMALL);
  PetscCall(MatHtoolUsePermutation(A, PETSC_TRUE));
  PetscCall(VecDestroy(&perm));
  PetscCall(VecDestroy(&left));
  PetscCall(VecDestroy(&right));
  PetscCall(ISDestroy(&ist));
  PetscCall(ISDestroy(&iss));
  if (PetscAbsReal(epsilon) >= PETSC_SMALL) { /* when there is compression, it is more difficult to check against MATDENSE, so just compare symmetric and nonsymmetric assemblies */
    PetscReal relative;
    PetscCall(MatDestroy(&B));
    PetscCall(MatCreateHtoolFromKernel(PETSC_COMM_WORLD, m, m, M, M, dim, coords, coords, kernel, gcoords, &B));
    PetscCall(MatSetOption(B, MAT_SYMMETRIC, (PetscBool)!sym));
    PetscCall(MatHtoolUseRecompression(B, recompression));
    PetscCall(MatSetFromOptions(B));
    PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    PetscCall(MatViewFromOptions(B, NULL, "-B_view"));
    PetscCall(MatConvert(A, MATDENSE, MAT_INITIAL_MATRIX, &P));
    PetscCall(MatNorm(P, NORM_FROBENIUS, &relative));
    PetscCall(MatConvert(B, MATDENSE, MAT_INITIAL_MATRIX, &R));
    PetscCall(MatAXPY(R, -1.0, P, SAME_NONZERO_PATTERN));
    PetscCall(MatNorm(R, NORM_INFINITY, &norm));
    PetscCheck(PetscAbsReal(norm / relative) <= epsilon, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "||A(!symmetric)-A(symmetric)|| = %g (> %g)", (double)PetscAbsReal(norm / relative), (double)epsilon);
    PetscCall(MatDestroy(&B));
    PetscCall(MatDestroy(&R));
    PetscCall(MatDestroy(&P));
  } else {
    PetscCall(MatConvert(A, MATDENSE, MAT_INITIAL_MATRIX, &D));
    PetscCall(MatViewFromOptions(D, NULL, "-D_view"));
    PetscCall(MatMultEqual(A, D, 10, &flg));
    PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Ax != Dx");
    PetscCall(MatMultTransposeEqual(A, D, 10, &flg));
    PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "A^Tx != D^Tx");
    PetscCall(MatMultAddEqual(A, D, 10, &flg));
    PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "y+Ax != y+Dx");
    PetscCall(MatGetOwnershipRange(B, &begin, NULL));
    PetscCall(MatDenseGetArrayWrite(D, &ptr));
    for (PetscInt i = begin; i < m + begin; ++i)
      for (PetscInt j = 0; j < M; ++j) PetscCall(GenEntries(dim, 1, 1, &i, &j, ptr + i - begin + j * m, gcoords));
    PetscCall(MatDenseRestoreArrayWrite(D, &ptr));
    PetscCall(MatMultEqual(A, D, 10, &flg));
    PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Ax != Dx");
    PetscCall(MatTranspose(D, MAT_INPLACE_MATRIX, &D));
    PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &AT));
    PetscCall(MatMultEqual(AT, D, 10, &flg));
    PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "A^Tx != D^Tx");
    PetscCall(MatTranspose(A, MAT_REUSE_MATRIX, &AT));
    PetscCall(MatMultEqual(AT, D, 10, &flg));
    PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "A^Tx != D^Tx");
    PetscCall(MatAXPY(D, -1.0, AT, SAME_NONZERO_PATTERN));
    PetscCall(MatNorm(D, NORM_INFINITY, &norm));
    PetscCheck(PetscAbsReal(norm) <= PETSC_SMALL, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "||A-D|| = %g (> %g)", (double)norm, (double)PETSC_SMALL);
    PetscCall(MatDestroy(&AT));
    PetscCall(MatDestroy(&D));
    PetscCall(MatMatMult(A, B, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &P));
    PetscCall(MatAssemblyBegin(P, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(P, MAT_FINAL_ASSEMBLY));
    PetscCall(MatMatMultEqual(A, B, P, 10, &flg));
    PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "ABx != Px");
    PetscCall(MatTransposeMatMultEqual(A, B, P, 10, &flg));
    PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "A^TBx != P^Tx");
    PetscCall(MatDestroy(&B));
    PetscCall(MatDestroy(&P));
    if (n) {
      PetscCall(PetscMalloc1(n * dim, &scoords));
      PetscCall(PetscRandomGetValuesReal(rdm, n * dim, scoords));
      N = n;
      PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &N, 1, MPIU_INT, MPI_SUM, PETSC_COMM_WORLD));
      PetscCall(PetscCalloc1(N * dim, &gscoords));
      PetscCallMPI(MPI_Exscan(&n, &begin, 1, MPIU_INT, MPI_SUM, PETSC_COMM_WORLD));
      PetscCall(PetscArraycpy(gscoords + begin * dim, scoords, n * dim));
      PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, gscoords, N * dim, MPIU_REAL, MPI_SUM, PETSC_COMM_WORLD));
      kernel = GenEntriesRectangular;
      ctx[0] = gcoords;
      ctx[1] = gscoords;
      PetscCall(MatCreateHtoolFromKernel(PETSC_COMM_WORLD, m, n, M, N, dim, coords, scoords, kernel, ctx, &R));
      PetscCall(MatSetFromOptions(R));
      PetscCall(MatHtoolUseRecompression(R, recompression));
      PetscCall(MatAssemblyBegin(R, MAT_FINAL_ASSEMBLY));
      PetscCall(MatAssemblyEnd(R, MAT_FINAL_ASSEMBLY));
      PetscCall(MatViewFromOptions(R, NULL, "-R_view"));
      PetscCall(MatConvert(R, MATDENSE, MAT_INITIAL_MATRIX, &D));
      PetscCall(MatViewFromOptions(D, NULL, "-D_view"));
      PetscCall(MatMultEqual(R, D, 10, &flg));
      PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Rx != Dx");
      PetscCall(MatTranspose(D, MAT_INPLACE_MATRIX, &D));
      PetscCall(MatTranspose(R, MAT_INITIAL_MATRIX, &RT));
      PetscCall(MatMultEqual(RT, D, 10, &flg));
      PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "R^Tx != D^Tx");
      PetscCall(MatTranspose(R, MAT_REUSE_MATRIX, &RT));
      PetscCall(MatMultEqual(RT, D, 10, &flg));
      PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "R^Tx != D^Tx");
      PetscCall(MatDestroy(&RT));
      PetscCall(MatDestroy(&D));
      PetscCall(MatCreateDense(PETSC_COMM_WORLD, n, PETSC_DECIDE, PETSC_DETERMINE, K, NULL, &B));
      PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
      PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
      PetscCall(MatSetRandom(B, rdm));
      PetscCall(MatMatMult(R, B, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &P));
      PetscCall(MatAssemblyBegin(P, MAT_FINAL_ASSEMBLY));
      PetscCall(MatAssemblyEnd(P, MAT_FINAL_ASSEMBLY));
      PetscCall(MatMatMultEqual(R, B, P, 10, &flg));
      PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "RBx != Px");
      PetscCall(MatDestroy(&B));
      PetscCall(MatDestroy(&P));
      PetscCall(MatCreateVecs(R, &right, &left));
      PetscCall(VecSetRandom(right, rdm));
      PetscCall(MatMult(R, right, left));
      PetscCall(MatHtoolGetPermutationSource(R, &iss));
      PetscCall(MatHtoolGetPermutationTarget(R, &ist));
      PetscCall(VecDuplicate(left, &perm));
      PetscCall(VecCopy(left, perm));
      PetscCall(VecPermute(perm, ist, PETSC_FALSE));
      PetscCall(VecPermute(right, iss, PETSC_FALSE));
      PetscCall(MatHtoolUsePermutation(R, PETSC_FALSE));
      PetscCall(MatMult(R, right, left));
      PetscCall(VecAXPY(left, -1.0, perm));
      PetscCall(VecNorm(left, NORM_INFINITY, &norm));
      PetscCheck(PetscAbsReal(norm) <= PETSC_SMALL, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "||y(with permutation)-y(without permutation)|| = %g (> %g)", (double)PetscAbsReal(norm), (double)PETSC_SMALL);
      PetscCall(MatHtoolUsePermutation(R, PETSC_TRUE));
      PetscCall(VecDestroy(&perm));
      PetscCall(VecDestroy(&left));
      PetscCall(VecDestroy(&right));
      PetscCall(ISDestroy(&ist));
      PetscCall(ISDestroy(&iss));
      PetscCall(MatDestroy(&R));
      PetscCall(PetscFree(gscoords));
      PetscCall(PetscFree(scoords));
    }
  }
  PetscCall(PetscRandomDestroy(&rdm));
  PetscCall(MatDestroy(&A));
  PetscCall(PetscFree(gcoords));
  PetscCall(PetscFree(coords));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   build:
      requires: htool

   test:
      requires: htool
      suffix: 1
      nsize: 4
      args: -m_local 80 -n_local 25 -mat_htool_epsilon 1.0e-11 -symmetric {{false true}shared output} -recompression {{false true}shared output}
      output_file: output/empty.out

   test:
      requires: htool
      suffix: 2
      nsize: 4
      args: -m_local 120 -mat_htool_epsilon 1.0e-2 -mat_htool_compressor {{sympartialACA fullACA SVD}shared output} -mat_htool_clustering {{PCARegular PCAGeometric BoundingBox1Regular BoundingBox1Geometric}shared output}
      output_file: output/empty.out

TEST*/