static char help[] = "This program illustrates the use of PETSc-fftw interface for real 2D DFT.\n\
                    See ~petsc/src/mat/tests/ex158.c for general cases. \n\n";

#include <petscmat.h>

int main(int argc, char **args)
{
  PetscMPIInt rank, size;
  PetscInt    N0 = 50, N1 = 50, N = N0 * N1;
  PetscRandom rdm;
  PetscReal   enorm;
  Vec         x, y, z, input, output;
  Mat         A;
  PetscInt    DIM, dim[2];
  PetscReal   fac;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &args, NULL, help));
#if defined(PETSC_USE_COMPLEX)
  SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "This example requires real numbers");
#endif

  PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));

  /* Create and set PETSc vectors 'input' and 'output' */
  PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rdm));
  PetscCall(PetscRandomSetFromOptions(rdm));

  PetscCall(VecCreate(PETSC_COMM_WORLD, &input));
  PetscCall(VecSetSizes(input, PETSC_DECIDE, N0 * N1));
  PetscCall(VecSetFromOptions(input));
  PetscCall(VecSetRandom(input, rdm));
  PetscCall(VecDuplicate(input, &output));
  PetscCall(PetscObjectSetName((PetscObject)input, "Real space vector"));
  PetscCall(PetscObjectSetName((PetscObject)output, "Reconstructed vector"));

  /* Get FFTW vectors 'x', 'y' and 'z' */
  DIM    = 2;
  dim[0] = N0;
  dim[1] = N1;
  PetscCall(MatCreateFFT(PETSC_COMM_WORLD, DIM, dim, MATFFTW, &A));
  PetscCall(MatCreateVecsFFTW(A, &x, &y, &z));

  /* Scatter PETSc vector 'input' to FFTW vector 'x' */
  PetscCall(VecScatterPetscToFFTW(A, input, x));

  /* Apply forward FFT */
  PetscCall(MatMult(A, x, y));

  /* Apply backward FFT */
  PetscCall(MatMultTranspose(A, y, z));

  /* Scatter FFTW vector 'z' to PETSc vector 'output' */
  PetscCall(VecScatterFFTWToPetsc(A, z, output));

  /* Check accuracy */
  fac = 1.0 / (PetscReal)N;
  PetscCall(VecScale(output, fac));
  PetscCall(VecAXPY(output, -1.0, input));
  PetscCall(VecNorm(output, NORM_1, &enorm));
  if (enorm > 1.e-11 && rank == 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Error norm of |x - z| %e\n", enorm));

  /* Free spaces */
  PetscCall(PetscRandomDestroy(&rdm));
  PetscCall(VecDestroy(&input));
  PetscCall(VecDestroy(&output));
  PetscCall(VecDestroy(&x));
  PetscCall(VecDestroy(&y));
  PetscCall(VecDestroy(&z));
  PetscCall(MatDestroy(&A));

  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   build:
      requires: fftw !complex

   test:
      output_file: output/empty.out

   test:
      suffix: 2
      nsize: 3
      output_file: output/empty.out

TEST*/