xref: /petsc/src/mat/impls/fft/fftw/fftw.c (revision c8a8a4f0d4d51c20aa00b6c6fd97dc1f439daf51)

/*
    Provides an interface to the FFTW package.
    Testing examples can be found in ~src/mat/examples/tests
*/

#include <../src/mat/impls/fft/fft.h>   /*I "petscmat.h" I*/
EXTERN_C_BEGIN
#include <fftw3-mpi.h>
EXTERN_C_END

typedef struct {
  ptrdiff_t   ndim_fftw,*dim_fftw;
  PetscInt   partial_dim;
  fftw_plan   p_forward,p_backward;
  unsigned    p_flag; /* planner flags, FFTW_ESTIMATE,FFTW_MEASURE, FFTW_PATIENT, FFTW_EXHAUSTIVE */
  PetscScalar *finarray,*foutarray,*binarray,*boutarray; /* keep track of arrays becaue fftw plan should be
                                                            executed for the arrays with which the plan was created */
} Mat_FFTW;

extern PetscErrorCode MatMult_SeqFFTW(Mat,Vec,Vec);
extern PetscErrorCode MatMultTranspose_SeqFFTW(Mat,Vec,Vec);
extern PetscErrorCode MatMult_MPIFFTW(Mat,Vec,Vec);
extern PetscErrorCode MatMultTranspose_MPIFFTW(Mat,Vec,Vec);
extern PetscErrorCode MatDestroy_FFTW(Mat);
extern PetscErrorCode VecDestroy_MPIFFTW(Vec);
extern PetscErrorCode MatGetVecs_FFTW(Mat,Vec*,Vec*); // to be removed!

#undef __FUNCT__
#define __FUNCT__ "MatMult_SeqFFTW"
PetscErrorCode MatMult_SeqFFTW(Mat A,Vec x,Vec y)
{
  PetscErrorCode ierr;
  Mat_FFT        *fft  = (Mat_FFT*)A->data;
  Mat_FFTW       *fftw = (Mat_FFTW*)fft->data;
  PetscScalar    *x_array,*y_array;
  PetscInt       ndim=fft->ndim,*dim=fft->dim;

  PetscFunctionBegin;
  ierr = VecGetArray(x,&x_array);CHKERRQ(ierr);
  ierr = VecGetArray(y,&y_array);CHKERRQ(ierr);
  if (!fftw->p_forward){ /* create a plan, then excute it */
    switch (ndim){
    case 1:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_forward = fftw_plan_dft_1d(dim[0],(fftw_complex*)x_array,(fftw_complex*)y_array,FFTW_FORWARD,fftw->p_flag);
#else
      fftw->p_forward = fftw_plan_dft_r2c_1d(dim[0],(double *)x_array,(fftw_complex*)y_array,fftw->p_flag);
#endif
      break;
    case 2:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_forward = fftw_plan_dft_2d(dim[0],dim[1],(fftw_complex*)x_array,(fftw_complex*)y_array,FFTW_FORWARD,fftw->p_flag);
#else
      fftw->p_forward = fftw_plan_dft_r2c_2d(dim[0],dim[1],(double *)x_array,(fftw_complex*)y_array,fftw->p_flag);
#endif
      break;
    case 3:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_forward = fftw_plan_dft_3d(dim[0],dim[1],dim[2],(fftw_complex*)x_array,(fftw_complex*)y_array,FFTW_FORWARD,fftw->p_flag);
#else
      fftw->p_forward = fftw_plan_dft_r2c_3d(dim[0],dim[1],dim[2],(double *)x_array,(fftw_complex*)y_array,fftw->p_flag);
#endif
      break;
    default:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_forward = fftw_plan_dft(ndim,dim,(fftw_complex*)x_array,(fftw_complex*)y_array,FFTW_FORWARD,fftw->p_flag);
#else
      fftw->p_forward = fftw_plan_dft_r2c(ndim,dim,(double *)x_array,(fftw_complex*)y_array,fftw->p_flag);
#endif
      break;
    }
    fftw->finarray  = x_array;
    fftw->foutarray = y_array;
    /* Warning: if (fftw->p_flag!==FFTW_ESTIMATE) The data in the in/out arrays is overwritten!
                planning should be done before x is initialized! See FFTW manual sec2.1 or sec4 */
    fftw_execute(fftw->p_forward);
  } else { /* use existing plan */
    if (fftw->finarray != x_array || fftw->foutarray != y_array){ /* use existing plan on new arrays */
      fftw_execute_dft(fftw->p_forward,(fftw_complex*)x_array,(fftw_complex*)y_array);
    } else {
      fftw_execute(fftw->p_forward);
    }
  }
  ierr = VecRestoreArray(y,&y_array);CHKERRQ(ierr);
  ierr = VecRestoreArray(x,&x_array);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultTranspose_SeqFFTW"
PetscErrorCode MatMultTranspose_SeqFFTW(Mat A,Vec x,Vec y)
{
  PetscErrorCode ierr;
  Mat_FFT        *fft = (Mat_FFT*)A->data;
  Mat_FFTW       *fftw = (Mat_FFTW*)fft->data;
  PetscScalar    *x_array,*y_array;
  PetscInt       ndim=fft->ndim,*dim=fft->dim;

  PetscFunctionBegin;
  ierr = VecGetArray(x,&x_array);CHKERRQ(ierr);
  ierr = VecGetArray(y,&y_array);CHKERRQ(ierr);
  if (!fftw->p_backward){ /* create a plan, then excute it */
    switch (ndim){
    case 1:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_backward = fftw_plan_dft_1d(dim[0],(fftw_complex*)x_array,(fftw_complex*)y_array,FFTW_BACKWARD,fftw->p_flag);
#else
      fftw->p_backward= fftw_plan_dft_c2r_1d(dim[0],(fftw_complex*)x_array,(double *)y_array,fftw->p_flag);
#endif
      break;
    case 2:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_backward = fftw_plan_dft_2d(dim[0],dim[1],(fftw_complex*)x_array,(fftw_complex*)y_array,FFTW_BACKWARD,fftw->p_flag);
#else
      fftw->p_backward= fftw_plan_dft_c2r_2d(dim[0],dim[1],(fftw_complex*)x_array,(double *)y_array,fftw->p_flag);
#endif
      break;
    case 3:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_backward = fftw_plan_dft_3d(dim[0],dim[1],dim[2],(fftw_complex*)x_array,(fftw_complex*)y_array,FFTW_BACKWARD,fftw->p_flag);
#else
      fftw->p_backward= fftw_plan_dft_c2r_3d(dim[0],dim[1],dim[2],(fftw_complex*)x_array,(double *)y_array,fftw->p_flag);
#endif
      break;
    default:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_backward = fftw_plan_dft(ndim,dim,(fftw_complex*)x_array,(fftw_complex*)y_array,FFTW_BACKWARD,fftw->p_flag);
#else
      fftw->p_backward= fftw_plan_dft_c2r(ndim,dim,(fftw_complex*)x_array,(double *)y_array,fftw->p_flag);
#endif
      break;
    }
    fftw->binarray  = x_array;
    fftw->boutarray = y_array;
    fftw_execute(fftw->p_backward);CHKERRQ(ierr);
  } else { /* use existing plan */
    if (fftw->binarray != x_array || fftw->boutarray != y_array){ /* use existing plan on new arrays */
      fftw_execute_dft(fftw->p_backward,(fftw_complex*)x_array,(fftw_complex*)y_array);
    } else {
      fftw_execute(fftw->p_backward);CHKERRQ(ierr);
    }
  }
  ierr = VecRestoreArray(y,&y_array);CHKERRQ(ierr);
  ierr = VecRestoreArray(x,&x_array);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMult_MPIFFTW"
PetscErrorCode MatMult_MPIFFTW(Mat A,Vec x,Vec y)
{
  PetscErrorCode ierr;
  Mat_FFT        *fft  = (Mat_FFT*)A->data;
  Mat_FFTW       *fftw = (Mat_FFTW*)fft->data;
  PetscScalar    *x_array,*y_array;
  PetscInt       ndim=fft->ndim,*dim=fft->dim;
  MPI_Comm       comm=((PetscObject)A)->comm;

  PetscFunctionBegin;
  ierr = VecGetArray(x,&x_array);CHKERRQ(ierr);
  ierr = VecGetArray(y,&y_array);CHKERRQ(ierr);
  if (!fftw->p_forward){ /* create a plan, then excute it */
    switch (ndim){
    case 1:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_forward = fftw_mpi_plan_dft_1d(dim[0],(fftw_complex*)x_array,(fftw_complex*)y_array,comm,FFTW_FORWARD,fftw->p_flag);
#else
      SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"not support for real numbers yet");
#endif
      break;
    case 2:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_forward = fftw_mpi_plan_dft_2d(dim[0],dim[1],(fftw_complex*)x_array,(fftw_complex*)y_array,comm,FFTW_FORWARD,fftw->p_flag);
#else
      fftw->p_forward = fftw_mpi_plan_dft_r2c_2d(dim[0],dim[1],(double *)x_array,(fftw_complex*)y_array,comm,FFTW_ESTIMATE);
#endif
      break;
    case 3:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_forward = fftw_mpi_plan_dft_3d(dim[0],dim[1],dim[2],(fftw_complex*)x_array,(fftw_complex*)y_array,comm,FFTW_FORWARD,fftw->p_flag);
#else
      fftw->p_forward = fftw_mpi_plan_dft_r2c_3d(dim[0],dim[1],dim[2],(double *)x_array,(fftw_complex*)y_array,comm,FFTW_ESTIMATE);
#endif
      break;
    default:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_forward = fftw_mpi_plan_dft(fftw->ndim_fftw,fftw->dim_fftw,(fftw_complex*)x_array,(fftw_complex*)y_array,comm,FFTW_FORWARD,fftw->p_flag);
#else
      fftw->p_forward = fftw_mpi_plan_dft_r2c(fftw->ndim_fftw,fftw->dim_fftw,(double *)x_array,(fftw_complex*)y_array,comm,FFTW_ESTIMATE);
#endif
      break;
    }
    fftw->finarray  = x_array;
    fftw->foutarray = y_array;
    /* Warning: if (fftw->p_flag!==FFTW_ESTIMATE) The data in the in/out arrays is overwritten!
                planning should be done before x is initialized! See FFTW manual sec2.1 or sec4 */
    fftw_execute(fftw->p_forward);
  } else { /* use existing plan */
    if (fftw->finarray != x_array || fftw->foutarray != y_array){ /* use existing plan on new arrays */
      fftw_execute_dft(fftw->p_forward,(fftw_complex*)x_array,(fftw_complex*)y_array);
    } else {
      fftw_execute(fftw->p_forward);
    }
  }
  ierr = VecRestoreArray(y,&y_array);CHKERRQ(ierr);
  ierr = VecRestoreArray(x,&x_array);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultTranspose_MPIFFTW"
PetscErrorCode MatMultTranspose_MPIFFTW(Mat A,Vec x,Vec y)
{
  PetscErrorCode ierr;
  Mat_FFT        *fft  = (Mat_FFT*)A->data;
  Mat_FFTW       *fftw = (Mat_FFTW*)fft->data;
  PetscScalar    *x_array,*y_array;
  PetscInt       ndim=fft->ndim,*dim=fft->dim;
  MPI_Comm       comm=((PetscObject)A)->comm;

  PetscFunctionBegin;
  ierr = VecGetArray(x,&x_array);CHKERRQ(ierr);
  ierr = VecGetArray(y,&y_array);CHKERRQ(ierr);
  if (!fftw->p_backward){ /* create a plan, then excute it */
    switch (ndim){
    case 1:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_backward = fftw_mpi_plan_dft_1d(dim[0],(fftw_complex*)x_array,(fftw_complex*)y_array,comm,FFTW_BACKWARD,fftw->p_flag);
#else
      SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"not support for real numbers yet");
#endif
      break;
    case 2:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_backward = fftw_mpi_plan_dft_2d(dim[0],dim[1],(fftw_complex*)x_array,(fftw_complex*)y_array,comm,FFTW_BACKWARD,fftw->p_flag);
#else
      fftw->p_backward = fftw_mpi_plan_dft_c2r_2d(dim[0],dim[1],(fftw_complex*)x_array,(double *)y_array,comm,FFTW_ESTIMATE);
#endif
      break;
    case 3:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_backward = fftw_mpi_plan_dft_3d(dim[0],dim[1],dim[2],(fftw_complex*)x_array,(fftw_complex*)y_array,comm,FFTW_BACKWARD,fftw->p_flag);
#else
      fftw->p_backward = fftw_mpi_plan_dft_c2r_3d(dim[0],dim[1],dim[2],(fftw_complex*)x_array,(double *)y_array,comm,FFTW_ESTIMATE);
#endif
      break;
    default:
#if defined(PETSC_USE_COMPLEX)
      fftw->p_backward = fftw_mpi_plan_dft(fftw->ndim_fftw,fftw->dim_fftw,(fftw_complex*)x_array,(fftw_complex*)y_array,comm,FFTW_BACKWARD,fftw->p_flag);
#else
      fftw->p_backward = fftw_mpi_plan_dft_c2r(fftw->ndim_fftw,fftw->dim_fftw,(fftw_complex*)x_array,(double *)y_array,comm,FFTW_ESTIMATE);
#endif
      break;
    }
    fftw->binarray  = x_array;
    fftw->boutarray = y_array;
    fftw_execute(fftw->p_backward);CHKERRQ(ierr);
  } else { /* use existing plan */
    if (fftw->binarray != x_array || fftw->boutarray != y_array){ /* use existing plan on new arrays */
      fftw_execute_dft(fftw->p_backward,(fftw_complex*)x_array,(fftw_complex*)y_array);
    } else {
      fftw_execute(fftw->p_backward);CHKERRQ(ierr);
    }
  }
  ierr = VecRestoreArray(y,&y_array);CHKERRQ(ierr);
  ierr = VecRestoreArray(x,&x_array);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDestroy_FFTW"
PetscErrorCode MatDestroy_FFTW(Mat A)
{
  Mat_FFT        *fft = (Mat_FFT*)A->data;
  Mat_FFTW       *fftw = (Mat_FFTW*)fft->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  fftw_destroy_plan(fftw->p_forward);
  fftw_destroy_plan(fftw->p_backward);
  ierr = PetscFree(fftw->dim_fftw);CHKERRQ(ierr);
  ierr = PetscFree(fft->data);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#include <../src/vec/vec/impls/mpi/pvecimpl.h>   /*I  "petscvec.h"   I*/
#undef __FUNCT__
#define __FUNCT__ "VecDestroy_MPIFFTW"
PetscErrorCode VecDestroy_MPIFFTW(Vec v)
{
  PetscErrorCode  ierr;
  PetscScalar     *array;

  PetscFunctionBegin;
  ierr = VecGetArray(v,&array);CHKERRQ(ierr);
  fftw_free((fftw_complex*)array);CHKERRQ(ierr);
  ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
  ierr = VecDestroy_MPI(v);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetVecsFFTW_1DC"
/*
    - Get Vectors(s) compatible with matrix, i.e. with the
     parallel layout determined by FFTW-1D

*/
PetscErrorCode MatGetVecsFFTW_1DC(Mat A,Vec *fin,Vec *fout,Vec *bout)
{
  PetscErrorCode ierr;
  PetscMPIInt    size,rank;
  MPI_Comm       comm=((PetscObject)A)->comm;
  Mat_FFT        *fft = (Mat_FFT*)A->data;
//  Mat_FFTW       *fftw = (Mat_FFTW*)fft->data;
  PetscInt       N=fft->N;
  PetscInt       ndim=fft->ndim,*dim=fft->dim;
  ptrdiff_t      f_alloc_local,f_local_n0,f_local_0_start;
  ptrdiff_t      f_local_n1,f_local_1_end;
  ptrdiff_t      b_alloc_local,b_local_n0,b_local_0_start;
  ptrdiff_t      b_local_n1,b_local_1_end;
  fftw_complex   *data_fin,*data_fout,*data_bout;

  PetscFunctionBegin;
#if !defined(PETSC_USE_COMPLEX)
  SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"not support for real numbers");
#endif
  ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  if (size == 1){
    SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Works only for parallel 1D");
  }
  else {
      if (ndim>1){
        SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Works only for parallel 1D");}
      else {
          f_alloc_local = fftw_mpi_local_size_1d(dim[0],comm,FFTW_FORWARD,FFTW_ESTIMATE,&f_local_n0,&f_local_0_start,&f_local_n1,&f_local_1_end);
          b_alloc_local = fftw_mpi_local_size_1d(dim[0],comm,FFTW_BACKWARD,FFTW_ESTIMATE,&b_local_n0,&b_local_0_start,&b_local_n1,&b_local_1_end);
          if (fin) {
            data_fin  = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*f_alloc_local);
            ierr = VecCreateMPIWithArray(comm,f_local_n0,N,(const PetscScalar*)data_fin,fin);CHKERRQ(ierr);
            (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
          }
          if (fout) {
            data_fout = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*f_alloc_local);
            ierr = VecCreateMPIWithArray(comm,f_local_n1,N,(const PetscScalar*)data_fout,fout);CHKERRQ(ierr);
            (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
          }
          if (bout) {
            data_bout = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*b_alloc_local);
            ierr = VecCreateMPIWithArray(comm,b_local_n1,N,(const PetscScalar*)data_bout,bout);CHKERRQ(ierr);
            (*bout)->ops->destroy   = VecDestroy_MPIFFTW;
          }
  }
  if (fin){
    ierr = PetscLayoutReference(A->cmap,&(*fin)->map);CHKERRQ(ierr);
  }
  if (fout){
    ierr = PetscLayoutReference(A->rmap,&(*fout)->map);CHKERRQ(ierr);
  }
  if (bout){
    ierr = PetscLayoutReference(A->rmap,&(*bout)->map);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}


}

#undef __FUNCT__
#define __FUNCT__ "MatGetVecsFFTW"
/*@
   MatGetVecsFFTW - Get vector(s) compatible with the matrix, i.e. with the
     parallel layout determined by FFTW

   Collective on Mat

   Input Parameter:
.  mat - the matrix

   Output Parameter:
+   fin - (optional) input vector of forward FFTW
-   fout - (optional) output vector of forward FFTW

  Level: advanced

.seealso: MatCreateFFTW()
@*/
PetscErrorCode MatGetVecsFFTW(Mat A,Vec *x,Vec *y,Vec *z)
{
  PetscErrorCode ierr;
  PetscFunctionBegin;
  ierr = PetscTryMethod(A,"MatGetVecsFFTW_C",(Mat,Vec*,Vec*,Vec*),(A,x,y,z));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatGetVecsFFTW_FFTW"
PetscErrorCode  MatGetVecsFFTW_FFTW(Mat A,Vec *fin,Vec *fout,Vec *bout)
{
  PetscErrorCode ierr;
  PetscMPIInt    size,rank;
  MPI_Comm       comm=((PetscObject)A)->comm;
  Mat_FFT        *fft = (Mat_FFT*)A->data;
  Mat_FFTW       *fftw = (Mat_FFTW*)fft->data;
  PetscInt       N=fft->N;
  PetscInt       ndim=fft->ndim,*dim=fft->dim,n=fft->n;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);

  ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
  if (size == 1){ /* sequential case */
  printf("Routine is getting called\n");
#if defined(PETSC_USE_COMPLEX)
    if (fin) {ierr = VecCreateSeq(PETSC_COMM_SELF,N,fin);CHKERRQ(ierr);}
    if (fout){ierr = VecCreateSeq(PETSC_COMM_SELF,N,fout);CHKERRQ(ierr);}
    if (bout){ierr = VecCreateSeq(PETSC_COMM_SELF,N,bout);CHKERRQ(ierr);}
#else
    if (fin) {ierr = VecCreateSeq(PETSC_COMM_SELF,2*N*(dim[ndim-1]/2+1)/dim[ndim-1],fin);CHKERRQ(ierr);}
    if (fout){ierr = VecCreateSeq(PETSC_COMM_SELF,2*N*(dim[ndim-1]/2+1)/dim[ndim-1],fout);CHKERRQ(ierr);}
    if (bout){ierr = VecCreateSeq(PETSC_COMM_SELF,2*N*(dim[ndim-1]/2+1)/dim[ndim-1],bout);CHKERRQ(ierr);}
#endif
  } else {
    ptrdiff_t      alloc_local,local_n0,local_0_start;
    ptrdiff_t      local_n1;
    fftw_complex   *data_fout;
    ptrdiff_t      local_1_start;
#if defined(PETSC_USE_COMPLEX)
    fftw_complex   *data_fin,*data_bout;
#else
    double         *data_finr,*data_boutr;
    PetscInt       n1,N1,vsize;
    ptrdiff_t      temp;
#endif

    switch (ndim){
          case 1:
#if !defined(PETSC_USE_COMPLEX)
                 SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"FFTW does not allow parallel real 1D transform");
#else
                 //SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Not implemented yet");
                 alloc_local = fftw_mpi_local_size_1d(dim[0],comm,FFTW_FORWARD,FFTW_ESTIMATE,&local_n0,&local_0_start,&local_n1,&local_1_start);
                 if (fin) {
                         data_fin  = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                         ierr = VecCreateMPIWithArray(comm,local_n0,N,(const PetscScalar*)data_fin,fin);CHKERRQ(ierr);
                         (*fin)->ops->destroy = VecDestroy_MPIFFTW;
                         }
                 if (fout) {
                          data_fout = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                          ierr = VecCreateMPIWithArray(comm,local_n1,N,(const PetscScalar*)data_fout,fout);CHKERRQ(ierr);
                          (*fout)->ops->destroy = VecDestroy_MPIFFTW;
                         }
                 alloc_local = fftw_mpi_local_size_1d(dim[0],comm,FFTW_BACKWARD,FFTW_ESTIMATE,&local_n0,&local_0_start,&local_n1,&local_1_start);
                 if (bout) {
                          data_bout = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                          ierr = VecCreateMPIWithArray(comm,local_n1,N,(const PetscScalar*)data_bout,bout);CHKERRQ(ierr);
                          (*bout)->ops->destroy = VecDestroy_MPIFFTW;
                         }
          break;
#endif
          case 2:
#if !defined(PETSC_USE_COMPLEX)
                 alloc_local =  fftw_mpi_local_size_2d_transposed(dim[0],dim[1]/2+1,comm,&local_n0,&local_0_start,&local_n1,&local_1_start);
                 N1 = 2*dim[0]*(dim[1]/2+1); n1 = 2*local_n0*(dim[1]/2+1);
                 if (fin) {
                           data_finr=(double *)fftw_malloc(sizeof(double)*alloc_local*2);
                           ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,(PetscInt)n1,N1,(PetscScalar*)data_finr,fin);CHKERRQ(ierr);
                           (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
                          }
                 if (bout) {
                           data_boutr=(double *)fftw_malloc(sizeof(double)*alloc_local*2);
                           ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,(PetscInt)n1,N1,(PetscScalar*)data_boutr,bout);CHKERRQ(ierr);
                           ierr = VecGetSize(*bout,&vsize);CHKERRQ(ierr);
                           (*bout)->ops->destroy   = VecDestroy_MPIFFTW;
                          }
                 //n1 = 2*local_n1*dim[0];
                 if (fout) {
                            data_fout=(fftw_complex *)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                            ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,(PetscInt)n1,N1,(PetscScalar*)data_fout,fout);CHKERRQ(ierr);
                            (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
                           }
#else
      /* Get local size */
                 alloc_local = fftw_mpi_local_size_2d(dim[0],dim[1],comm,&local_n0,&local_0_start);
                 if (fin) {
                           data_fin  = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                           ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_fin,fin);CHKERRQ(ierr);
                           (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
                          }
                 if (fout) {
                            data_fout = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                            ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_fout,fout);CHKERRQ(ierr);
                            (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
                           }
                 if (bout) {
                           data_bout  = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                           ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_bout,bout);CHKERRQ(ierr);
                           (*bout)->ops->destroy   = VecDestroy_MPIFFTW;
                          }
#endif
          break;
          case 3:
#if !defined(PETSC_USE_COMPLEX)
                 alloc_local =  fftw_mpi_local_size_3d_transposed(dim[0],dim[1],dim[2]/2+1,comm,&local_n0,&local_0_start,&local_n1,&local_1_start);
                 N1 = 2*dim[0]*dim[1]*(dim[2]/2+1); n1 = 2*local_n0*dim[1]*(dim[2]/2+1);
                 if (fin) {
                         data_finr=(double *)fftw_malloc(sizeof(double)*alloc_local*2);
                         ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,(PetscInt)n1,N1,(PetscScalar*)data_finr,fin);CHKERRQ(ierr);
                         (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
                         }
                 if (bout) {
                         data_boutr=(double *)fftw_malloc(sizeof(double)*alloc_local*2);
                         ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,(PetscInt)n1,N1,(PetscScalar*)data_boutr,bout);CHKERRQ(ierr);
                         (*bout)->ops->destroy   = VecDestroy_MPIFFTW;
                          }
                 //n1 = 2*local_n1*dim[0]*(dim[2]/2+1);
                 if (fout) {
                          data_fout=(fftw_complex *)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                          ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,n1,N1,(PetscScalar*)data_fout,fout);CHKERRQ(ierr);
                          (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
                          }
#else
                 alloc_local = fftw_mpi_local_size_3d(dim[0],dim[1],dim[2],comm,&local_n0,&local_0_start);
                 if (fin) {
                         data_fin  = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                         ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_fin,fin);CHKERRQ(ierr);
                         (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
                         }
                 if (fout) {
                          data_fout = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                          ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_fout,fout);CHKERRQ(ierr);
                          (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
                         }
                 if (bout) {
                         data_bout  = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                         ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_bout,bout);CHKERRQ(ierr);
                         (*bout)->ops->destroy   = VecDestroy_MPIFFTW;
                         }
#endif
          break;
          default:
#if !defined(PETSC_USE_COMPLEX)
                 temp = (fftw->dim_fftw)[fftw->ndim_fftw-1];
                 (fftw->dim_fftw)[fftw->ndim_fftw-1] = temp/2 + 1;
                 alloc_local = fftw_mpi_local_size_transposed(fftw->ndim_fftw,fftw->dim_fftw,comm,&local_n0,&local_0_start,&local_n1,&local_1_start);
                 N1 = 2*N*(PetscInt)((fftw->dim_fftw)[fftw->ndim_fftw-1])/((PetscInt) temp);
                 (fftw->dim_fftw)[fftw->ndim_fftw-1] = temp;

                 if (fin) {
                         data_finr=(double *)fftw_malloc(sizeof(double)*alloc_local*2);
                         ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,(PetscInt)n,N1,(PetscScalar*)data_finr,fin);CHKERRQ(ierr);
                         (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
                        }
                 if (bout) {
                         data_boutr=(double *)fftw_malloc(sizeof(double)*alloc_local*2);
                         ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,(PetscInt)n,N1,(PetscScalar*)data_boutr,bout);CHKERRQ(ierr);
                         (*bout)->ops->destroy   = VecDestroy_MPIFFTW;
                        }
                 //temp = fftw->partial_dim;
                 //fftw->partial_dim = fftw->partial_dim * ((fftw->dim_fftw)[fftw->ndim_fftw-1]/2+1)*(fftw->dim_fftw)[1]/((fftw->dim_fftw)[2]*(fftw->dim_fftw)[fftw->ndim_fftw-1]);
                 //n1 = 2*local_n1*(fftw->partial_dim);  fftw->partial_dim = temp;
                 if (fout) {
                          data_fout=(fftw_complex *)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                          ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,n,N1,(PetscScalar*)data_fout,fout);CHKERRQ(ierr);
                          (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
                        }
#else
                alloc_local = fftw_mpi_local_size(fftw->ndim_fftw,fftw->dim_fftw,comm,&local_n0,&local_0_start);
                if (fin) {
                       data_fin  = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                       ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_fin,fin);CHKERRQ(ierr);
                       (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
                       }
                if (fout) {
                         data_fout = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                         ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_fout,fout);CHKERRQ(ierr);
                         (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
                       }
                if (bout) {
                       data_bout  = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
                       ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_bout,bout);CHKERRQ(ierr);
                       (*bout)->ops->destroy   = VecDestroy_MPIFFTW;
                       }
#endif
            break;
          }
  }
  PetscFunctionReturn(0);
}
EXTERN_C_END

#undef __FUNCT__
#define __FUNCT__ "MatGetVecs_FFTW"
/*
   MatGetVecs_FFTW - Get vector(s) compatible with the matrix, i.e. with the
     parallel layout determined by FFTW

   Collective on Mat

   Input Parameter:
.  mat - the matrix

   Output Parameter:
+   fin - (optional) input vector of forward FFTW
-   fout - (optional) output vector of forward FFTW

  Level: advanced

.seealso: MatCreateFFTW()
*/
PetscErrorCode  MatGetVecs_FFTW(Mat A,Vec *fin,Vec *fout)
{
  PetscErrorCode ierr;
  PetscMPIInt    size,rank;
  MPI_Comm       comm=((PetscObject)A)->comm;
  Mat_FFT        *fft = (Mat_FFT*)A->data;
  Mat_FFTW       *fftw = (Mat_FFTW*)fft->data;
  PetscInt       N=fft->N;
  PetscInt       ndim=fft->ndim,*dim=fft->dim,n=fft->n;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);

  ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  if (size == 1){ /* sequential case */
#if defined(PETSC_USE_COMPLEX)
    if (fin) {ierr = VecCreateSeq(PETSC_COMM_SELF,N,fin);CHKERRQ(ierr);}
    if (fout){ierr = VecCreateSeq(PETSC_COMM_SELF,N,fout);CHKERRQ(ierr);}
#else
    if (fin) {ierr = VecCreateSeq(PETSC_COMM_SELF,N*2*(dim[ndim-1]/2+1)/dim[ndim-1],fin);CHKERRQ(ierr);}
    if (fout){ierr = VecCreateSeq(PETSC_COMM_SELF,2*N*(dim[ndim-1]/2+1)/dim[ndim-1],fout);CHKERRQ(ierr);}
#endif
  } else {        /* mpi case */
    ptrdiff_t      alloc_local,local_n0,local_0_start;
    ptrdiff_t      local_n1,local_1_end;
    fftw_complex   *data_fin,*data_fout;
#if !defined(PETSC_USE_COMPLEX)
    double         *data_finr ;
    ptrdiff_t      local_1_start,temp;
    PetscInt       vsize,n1,N1;
#endif

//    PetscInt ctr;
//    ptrdiff_t      ndim1,*pdim;
//    ndim1=(ptrdiff_t) ndim;
//    pdim = (ptrdiff_t *)calloc(ndim,sizeof(ptrdiff_t));

//    for(ctr=0;ctr<ndim;ctr++)
//        {k
//           pdim[ctr] = dim[ctr];
//       }



    switch (ndim){
    case 1:
      /* Get local size */
      /* We need to write an error message here saying that one cannot call this routine when doing parallel 1D real FFTW */
//      SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Works only for parallel Multi-dimensional FFTW, Dimension>1. Check Documentation for MatGetVecs_FFTW1D routine");
      alloc_local = fftw_mpi_local_size_1d(dim[0],comm,FFTW_FORWARD,FFTW_ESTIMATE,&local_n0,&local_0_start,&local_n1,&local_1_end);
      printf("The values of local_n0 and local_n1 are %ld and %ld\n",local_n0,local_n1);
      if (fin) {
        data_fin  = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
        ierr = VecCreateMPIWithArray(comm,local_n0,N,(const PetscScalar*)data_fin,fin);CHKERRQ(ierr);
        (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
      }
      if (fout) {
        data_fout = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
        ierr = VecCreateMPIWithArray(comm,local_n1,N,(const PetscScalar*)data_fout,fout);CHKERRQ(ierr);
        (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
      }
      break;
    case 2:
#if !defined(PETSC_USE_COMPLEX)
      alloc_local =  fftw_mpi_local_size_2d_transposed(dim[0],dim[1]/2+1,comm,&local_n0,&local_0_start,&local_n1,&local_1_start);
      N1 = 2*dim[0]*(dim[1]/2+1); n1 = 2*local_n0*(dim[1]/2+1);
      if (fin) {
        data_finr=(double *)fftw_malloc(sizeof(double)*alloc_local*2);
        ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,(PetscInt)n1,N1,(PetscScalar*)data_finr,fin);CHKERRQ(ierr);
        ierr = VecGetSize(*fin,&vsize);CHKERRQ(ierr);
        //printf("The code comes here with vector size %d\n",vsize);
        (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
      }
      n1 = 2*local_n1*(dim[0]);
      //n1 = 2*local_n1*dim[1];
      printf("The values are %ld\n",local_n1);
      if (fout) {
        data_fout=(fftw_complex *)fftw_malloc(sizeof(fftw_complex)*alloc_local);
        ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,n1,N1,(PetscScalar*)data_fout,fout);CHKERRQ(ierr);
        (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
      }
      printf("Vector size from fftw.c is  given by %d, %d\n",n1,N1);

#else
      /* Get local size */
     //printf("Hope this does not come here");
      alloc_local = fftw_mpi_local_size_2d(dim[0],dim[1],comm,&local_n0,&local_0_start);
      if (fin) {
        data_fin  = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
        ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_fin,fin);CHKERRQ(ierr);
        (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
      }
      if (fout) {
        data_fout = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
        ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_fout,fout);CHKERRQ(ierr);
        (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
      }
     //printf("Hope this does not come here");
#endif
      break;
    case 3:
      /* Get local size */
#if !defined(PETSC_USE_COMPLEX)
      alloc_local =  fftw_mpi_local_size_3d_transposed(dim[0],dim[1],dim[2]/2+1,comm,&local_n0,&local_0_start,&local_n1,&local_1_start);
      N1 = 2*dim[0]*dim[1]*(dim[2]/2+1); n1 = 2*local_n0*dim[1]*(dim[2]/2+1);
      if (fin) {
        data_finr=(double *)fftw_malloc(sizeof(double)*alloc_local*2);
        ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,(PetscInt)n1,N1,(PetscScalar*)data_finr,fin);CHKERRQ(ierr);
        ierr = VecGetSize(*fin,&vsize);CHKERRQ(ierr);
        //printf("The code comes here with vector size %d\n",vsize);
        (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
      }
      printf("The value is %ld",local_n1);
      n1 = 2*local_n1*dim[0]*(dim[2]/2+1);
      if (fout) {
        data_fout=(fftw_complex *)fftw_malloc(sizeof(fftw_complex)*alloc_local);
        ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,n1,N1,(PetscScalar*)data_fout,fout);CHKERRQ(ierr);
        (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
      }
      printf("Vector size from fftw.c is  given by %d, %d\n",n1,N1);


#else
      alloc_local = fftw_mpi_local_size_3d(dim[0],dim[1],dim[2],comm,&local_n0,&local_0_start);
//      printf("The quantity n is %d",n);
      if (fin) {
        data_fin  = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
        ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_fin,fin);CHKERRQ(ierr);
        (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
      }
      if (fout) {
        data_fout = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
        ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_fout,fout);CHKERRQ(ierr);
        (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
      }
#endif
      break;
    default:
      /* Get local size */
#if !defined(PETSC_USE_COMPLEX)
      temp = (fftw->dim_fftw)[fftw->ndim_fftw-1];
      printf("The value of temp is %ld\n",temp);
      (fftw->dim_fftw)[fftw->ndim_fftw-1] = temp/2 + 1;
      alloc_local = fftw_mpi_local_size_transposed(fftw->ndim_fftw,fftw->dim_fftw,comm,&local_n0,&local_0_start,&local_n1,&local_1_start);
      N1 = 2*N*(PetscInt)((fftw->dim_fftw)[fftw->ndim_fftw-1])/((PetscInt) temp);
      (fftw->dim_fftw)[fftw->ndim_fftw-1] = temp;
      if (fin) {
        data_finr=(double *)fftw_malloc(sizeof(double)*alloc_local*2);
        ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,(PetscInt)n,N1,(PetscScalar*)data_finr,fin);CHKERRQ(ierr);
        ierr = VecGetSize(*fin,&vsize);CHKERRQ(ierr);
        //printf("The code comes here with vector size %d\n",vsize);
        (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
      }
      printf("The value is %ld. Global length is %d \n",local_n1,N1);
      temp = fftw->partial_dim;
      fftw->partial_dim = fftw->partial_dim * ((fftw->dim_fftw)[fftw->ndim_fftw-1]/2+1)*(fftw->dim_fftw)[1]/((fftw->dim_fftw)[2]*(fftw->dim_fftw)[fftw->ndim_fftw-1]);

      n1 = 2*local_n1*(fftw->partial_dim);  fftw->partial_dim = temp;
      if (fout) {
        data_fout=(fftw_complex *)fftw_malloc(sizeof(fftw_complex)*alloc_local);
        ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,n1,N1,(PetscScalar*)data_fout,fout);CHKERRQ(ierr);
        (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
      }

#else
      alloc_local = fftw_mpi_local_size(fftw->ndim_fftw,fftw->dim_fftw,comm,&local_n0,&local_0_start);
//      printf("The value of alloc local is %d from process %d\n",alloc_local,rank);
//      printf("The value of alloc local is %d",alloc_local);
//      pdim=(ptrdiff_t *)calloc(ndim,sizeof(ptrdiff_t));
//      for(i=0;i<ndim;i++)
//         {
//          pdim[i]=dim[i];printf("%d",pdim[i]);
//         }
//      alloc_local = fftw_mpi_local_size(ndim,pdim,comm,&local_n0,&local_0_start);
//      printf("The quantity n is %d",n);
      if (fin) {
        data_fin  = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
        ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_fin,fin);CHKERRQ(ierr);
        (*fin)->ops->destroy   = VecDestroy_MPIFFTW;
      }
      if (fout) {
        data_fout = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
        ierr = VecCreateMPIWithArray(comm,n,N,(const PetscScalar*)data_fout,fout);CHKERRQ(ierr);
        (*fout)->ops->destroy   = VecDestroy_MPIFFTW;
      }
#endif
      break;
    }
  }
//  if (fin){
//    ierr = PetscLayoutReference(A->cmap,&(*fin)->map);CHKERRQ(ierr);
//  }
//  if (fout){
//    ierr = PetscLayoutReference(A->rmap,&(*fout)->map);CHKERRQ(ierr);
//  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "InputTransformFFT"
PetscErrorCode InputTransformFFT(Mat A,Vec x,Vec y)
{
  PetscErrorCode ierr;
  PetscFunctionBegin;
  ierr = PetscTryMethod(A,"InputTransformFFT_C",(Mat,Vec,Vec),(A,x,y));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*
      InputTransformFFT_FFTW - Copies the user data to the vector that goes into FFTW block. For real
      parallel FFT, this routine also performs padding of right number of zeros at the end of the fastetst
      changing dimension.
  Input A, x, y
  A - FFTW matrix
  x - user data
  Options Database Keys:
+ -mat_fftw_plannerflags - set FFTW planner flags

   Level: intermediate

*/

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "InputTransformFFT_FTTW"
PetscErrorCode InputTransformFFT_FFTW(Mat A,Vec x,Vec y)
{
  PetscErrorCode ierr;
  MPI_Comm       comm=((PetscObject)A)->comm;
  Mat_FFT        *fft = (Mat_FFT*)A->data;
  Mat_FFTW       *fftw = (Mat_FFTW*)fft->data;
  PetscInt       N=fft->N;
  PetscInt       ndim=fft->ndim,*dim=fft->dim;//n=fft->n;
  PetscInt       low;
  PetscInt       rank,size;
  ptrdiff_t      alloc_local,local_n0,local_0_start;
  ptrdiff_t      local_n1,local_1_start;
  VecScatter     vecscat;
  IS             list1,list2;
#if !defined(PETSC_USE_COMPLEX)
  PetscInt       i,j,k,partial_dim;
  PetscInt       *indx1, *indx2, tempindx, tempindx1;
  PetscInt       N1, n1 ,NM;
  ptrdiff_t      temp;
#endif

  ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(y,&low,PETSC_NULL);

  if (size==1)
    {
/*     switch (ndim){
     case 1:
          ierr = PetscMalloc(sizeof(PetscInt)*dim[0],&indx1);CHKERRQ(ierr);
          for (i=0;i<dim[0];i++)
             {
              indx1[i] = i;
             }
          ierr = ISCreateGeneral(comm,dim[0],indx1,PETSC_COPY_VALUES,&list1);CHKERRQ(ierr);
          ierr = VecScatterCreate(x,list1,y,list1,&vecscat);CHKERRQ(ierr);
          ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
          ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
          ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
          ierr = ISDestroy(&list1);CHKERRQ(ierr);
          ierr = PetscFree(indx1);CHKERRQ(ierr);
     break;

     case 2:
          ierr = PetscMalloc(sizeof(PetscInt)*dim[0]*dim[1],&indx1);CHKERRQ(ierr);
          for (i=0;i<dim[0];i++){
             for (j=0;j<dim[1];j++){
                indx1[i*dim[1]+j] = i*dim[1] + j;
             }
          }
          ierr = ISCreateGeneral(comm,dim[0]*dim[1],indx1,PETSC_COPY_VALUES,&list1);CHKERRQ(ierr);
          ierr = VecScatterCreate(x,list1,y,list1,&vecscat);CHKERRQ(ierr);
          ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
          ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
          ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
          ierr = ISDestroy(&list1);CHKERRQ(ierr);
          ierr = PetscFree(indx1);CHKERRQ(ierr);
          break;
     case 3:
          ierr = PetscMalloc(sizeof(PetscInt)*dim[0]*dim[1]*dim[2],&indx1);CHKERRQ(ierr);
          for (i=0;i<dim[0];i++){
             for (j=0;j<dim[1];j++){
                for (k=0;k<dim[2];k++){
                   indx1[i*dim[1]*dim[2]+j*dim[2]+k] = i*dim[1]*dim[2] + j*dim[2] + k;
                }
             }
          }
          ierr = ISCreateGeneral(comm,dim[0]*dim[1]*dim[2],indx1,PETSC_COPY_VALUES,&list1);CHKERRQ(ierr);
          ierr = VecScatterCreate(x,list1,y,list1,&vecscat);CHKERRQ(ierr);
          ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
          ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
          ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
          ierr = ISDestroy(&list1);CHKERRQ(ierr);
          ierr = PetscFree(indx1);CHKERRQ(ierr);
          break;
     default:
*/
          ierr = ISCreateStride(PETSC_COMM_SELF,N,0,1,&list1);CHKERRQ(ierr);
          ierr = VecScatterCreate(x,list1,y,list1,&vecscat);CHKERRQ(ierr);
          ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
          ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
          ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
          ierr = ISDestroy(&list1);CHKERRQ(ierr);
 //         break;
  //    }
    }

 else{

 switch (ndim){
 case 1:
#if defined(PETSC_USE_COMPLEX)
      alloc_local = fftw_mpi_local_size_1d(dim[0],comm,FFTW_FORWARD,FFTW_ESTIMATE,&local_n0,&local_0_start,&local_n1,&local_1_start);
      ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0,local_0_start,1,&list1);
      ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0,low,1,&list2);
      ierr = VecScatterCreate(x,list1,y,list2,&vecscat);CHKERRQ(ierr);
      ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
      ierr = ISDestroy(&list1);CHKERRQ(ierr);
      ierr = ISDestroy(&list2);CHKERRQ(ierr);
#else
      SETERRQ(comm,PETSC_ERR_SUP,"FFTW does not support parallel 1D real transform");
#endif
 break;
 case 2:
#if defined(PETSC_USE_COMPLEX)
      alloc_local = fftw_mpi_local_size_2d(dim[0],dim[1],comm,&local_n0,&local_0_start);
      ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0*dim[1],local_0_start*dim[1],1,&list1);
      ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0*dim[1],low,1,&list2);
      ierr = VecScatterCreate(x,list1,y,list2,&vecscat);CHKERRQ(ierr);
      ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
      ierr = ISDestroy(&list1);CHKERRQ(ierr);
      ierr = ISDestroy(&list2);CHKERRQ(ierr);
#else
      alloc_local =  fftw_mpi_local_size_2d_transposed(dim[0],dim[1]/2+1,comm,&local_n0,&local_0_start,&local_n1,&local_1_start);
      N1 = 2*dim[0]*(dim[1]/2+1); n1 = 2*local_n0*(dim[1]/2+1);
      //ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*N1,&indx1);CHKERRQ(ierr);
      //ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*N1,&indx2);CHKERRQ(ierr);
      ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*dim[1],&indx1);CHKERRQ(ierr);
      ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*dim[1],&indx2);CHKERRQ(ierr);

      if (dim[1]%2==0)
        NM = dim[1]+2;
      else
        NM = dim[1]+1;

      for (i=0;i<local_n0;i++){
         for (j=0;j<dim[1];j++){
            tempindx = i*dim[1] + j;
            tempindx1 = i*NM + j;
            indx1[tempindx]=local_0_start*dim[1]+tempindx;
            indx2[tempindx]=low+tempindx1;
        }
     }

      ierr = ISCreateGeneral(comm,local_n0*dim[1],indx1,PETSC_COPY_VALUES,&list1);CHKERRQ(ierr);
      ierr = ISCreateGeneral(comm,local_n0*dim[1],indx2,PETSC_COPY_VALUES,&list2);CHKERRQ(ierr);

      ierr = VecScatterCreate(x,list1,y,list2,&vecscat);CHKERRQ(ierr);
      ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
      ierr = ISDestroy(&list1);CHKERRQ(ierr);
      ierr = ISDestroy(&list2);CHKERRQ(ierr);
      ierr = PetscFree(indx1);CHKERRQ(ierr);
      ierr = PetscFree(indx2);CHKERRQ(ierr);
#endif
 break;

 case 3:
#if defined(PETSC_USE_COMPLEX)
      alloc_local = fftw_mpi_local_size_3d(dim[0],dim[1],dim[2],comm,&local_n0,&local_0_start);
      ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0*dim[1]*dim[2],local_0_start*dim[1]*dim[2],1,&list1);
      ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0*dim[1]*dim[2],low,1,&list2);
      //ierr = ISView(list1,PETSC_VIEWER_STDOUT_WORLD);
      //ierr = ISView(list2,PETSC_VIEWER_STDOUT_WORLD);
      ierr = VecScatterCreate(x,list1,y,list2,&vecscat);CHKERRQ(ierr);
      ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
      ierr = ISDestroy(&list1);CHKERRQ(ierr);
      ierr = ISDestroy(&list2);CHKERRQ(ierr);
#else
      alloc_local =  fftw_mpi_local_size_3d_transposed(dim[0],dim[1],dim[2]/2+1,comm,&local_n0,&local_0_start,&local_n1,&local_1_start);
      N1 = 2*dim[0]*dim[1]*(dim[2]/2+1); n1 = 2*local_n0*dim[1]*(dim[2]/2+1);

//      ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*N1,&indx1);CHKERRQ(ierr);
//      ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*N1,&indx2);CHKERRQ(ierr);
      ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*dim[1]*dim[2],&indx1);CHKERRQ(ierr);
      ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*dim[1]*dim[2],&indx2);CHKERRQ(ierr);

      if (dim[2]%2==0)
        NM = dim[2]+2;
      else
        NM = dim[2]+1;

      for (i=0;i<local_n0;i++){
         for (j=0;j<dim[1];j++){
            for (k=0;k<dim[2];k++){
               tempindx = i*dim[1]*dim[2] + j*dim[2] + k;
               tempindx1 = i*dim[1]*NM + j*NM + k;
               indx1[tempindx]=local_0_start*dim[1]*dim[2]+tempindx;
               indx2[tempindx]=low+tempindx1;
            }
         }
      }

      ierr = ISCreateGeneral(comm,local_n0*dim[1]*dim[2],indx1,PETSC_COPY_VALUES,&list1);CHKERRQ(ierr);
      ierr = ISCreateGeneral(comm,local_n0*dim[1]*dim[2],indx2,PETSC_COPY_VALUES,&list2);CHKERRQ(ierr);
      ierr = VecScatterCreate(x,list1,y,list2,&vecscat);CHKERRQ(ierr);
      ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
      ierr = ISDestroy(&list1);CHKERRQ(ierr);
      ierr = ISDestroy(&list2);CHKERRQ(ierr);
      ierr = PetscFree(indx1);CHKERRQ(ierr);
      ierr = PetscFree(indx2);CHKERRQ(ierr);
#endif
 break;

 default:
#if defined(PETSC_USE_COMPLEX)
      alloc_local = fftw_mpi_local_size(fftw->ndim_fftw,fftw->dim_fftw,comm,&local_n0,&local_0_start);
      ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0*(fftw->partial_dim),local_0_start*(fftw->partial_dim),1,&list1);
      ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0*(fftw->partial_dim),low,1,&list2);
      ierr = VecScatterCreate(x,list1,y,list2,&vecscat);CHKERRQ(ierr);
      ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
      ierr = ISDestroy(&list1);CHKERRQ(ierr);
      ierr = ISDestroy(&list2);CHKERRQ(ierr);
#else
      temp = (fftw->dim_fftw)[fftw->ndim_fftw-1];
      (fftw->dim_fftw)[fftw->ndim_fftw-1] = temp/2 + 1;
      alloc_local = fftw_mpi_local_size_transposed(fftw->ndim_fftw,fftw->dim_fftw,comm,&local_n0,&local_0_start,&local_n1,&local_1_start);
      N1 = 2*N*(PetscInt)((fftw->dim_fftw)[fftw->ndim_fftw-1])/((PetscInt) temp);
      (fftw->dim_fftw)[fftw->ndim_fftw-1] = temp;

      partial_dim = fftw->partial_dim;

      ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*partial_dim,&indx1);CHKERRQ(ierr);
      ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*partial_dim,&indx2);CHKERRQ(ierr);

      if (dim[ndim-1]%2==0)
        NM = 2;
      else
        NM = 1;

      j = low;
      for (i=0,k=1; i<((PetscInt)local_n0)*partial_dim;i++,k++)
         {
          indx1[i] = local_0_start*partial_dim + i;
          indx2[i] = j;
          if (k%dim[ndim-1]==0)
            { j+=NM;}
          j++;
         }
      ierr = ISCreateGeneral(comm,local_n0*partial_dim,indx1,PETSC_COPY_VALUES,&list1);CHKERRQ(ierr);
      ierr = ISCreateGeneral(comm,local_n0*partial_dim,indx2,PETSC_COPY_VALUES,&list2);CHKERRQ(ierr);
      ierr = VecScatterCreate(x,list1,y,list2,&vecscat);CHKERRQ(ierr);
      ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
      ierr = ISDestroy(&list1);CHKERRQ(ierr);
      ierr = ISDestroy(&list2);CHKERRQ(ierr);
      ierr = PetscFree(indx1);CHKERRQ(ierr);
      ierr = PetscFree(indx2);CHKERRQ(ierr);
#endif
 break;
  }
 }

 return 0;
}
EXTERN_C_END

#undef __FUNCT__
#define __FUNCT__ "OutputTransformFFT"
PetscErrorCode OutputTransformFFT(Mat A,Vec x,Vec y)
{
  PetscErrorCode ierr;
  PetscFunctionBegin;
  ierr = PetscTryMethod(A,"OutputTransformFFT_C",(Mat,Vec,Vec),(A,x,y));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*
      OutputTransformFFT_FFTW - Copies the FFTW output to the PETSc vector that user can use
  Input A, x, y
  A - FFTW matrix
  x - FFTW vector
  y - PETSc vector that user can read
  Options Database Keys:
+ -mat_fftw_plannerflags - set FFTW planner flags

   Level: intermediate

*/

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "OutputTransformFFT_FTTW"
PetscErrorCode OutputTransformFFT_FFTW(Mat A,Vec x,Vec y)
{
  PetscErrorCode ierr;
  MPI_Comm       comm=((PetscObject)A)->comm;
  Mat_FFT        *fft = (Mat_FFT*)A->data;
  Mat_FFTW       *fftw = (Mat_FFTW*)fft->data;
  PetscInt       N=fft->N;
  PetscInt       ndim=fft->ndim,*dim=fft->dim;
  PetscInt       low;
  PetscInt       rank,size;
  ptrdiff_t      alloc_local,local_n0,local_0_start;
  ptrdiff_t      local_n1,local_1_start;
  VecScatter     vecscat;
  IS             list1,list2;
#if !defined(PETSC_USE_COMPLEX)
  PetscInt       i,j,k,partial_dim;
  PetscInt       *indx1, *indx2, tempindx, tempindx1;
  PetscInt       N1, n1 ,NM;
  ptrdiff_t      temp;
#endif


  ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(x,&low,PETSC_NULL);CHKERRQ(ierr);

  if (size==1){
/*
    switch (ndim){
    case 1:
           ierr = PetscMalloc(sizeof(PetscInt)*dim[0],&indx1);CHKERRQ(ierr);
          for (i=0;i<dim[0];i++)
             {
              indx1[i] = i;
             }
          ierr = ISCreateGeneral(comm,dim[0],indx1,PETSC_COPY_VALUES,&list1);CHKERRQ(ierr);
          ierr = VecScatterCreate(x,list1,y,list1,&vecscat);CHKERRQ(ierr);
          ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
          ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
          ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
          ierr = ISDestroy(&list1);CHKERRQ(ierr);
          ierr = PetscFree(indx1);CHKERRQ(ierr);
          break;

    case 2:
         ierr = PetscMalloc(sizeof(PetscInt)*dim[0]*dim[1],&indx1);CHKERRQ(ierr);
          for (i=0;i<dim[0];i++){
             for (j=0;j<dim[1];j++){
                indx1[i*dim[1]+j] = i*dim[1] + j;
             }
          }
         ierr = ISCreateGeneral(comm,dim[0]*dim[1],indx1,PETSC_COPY_VALUES,&list1);CHKERRQ(ierr);
         ierr = VecScatterCreate(x,list1,y,list1,&vecscat);CHKERRQ(ierr);
         ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
         ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
         ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
         ierr = ISDestroy(&list1);CHKERRQ(ierr);
         ierr = PetscFree(indx1);CHKERRQ(ierr);
         break;
    case 3:
         ierr = PetscMalloc(sizeof(PetscInt)*dim[0]*dim[1]*dim[2],&indx1);CHKERRQ(ierr);
         for (i=0;i<dim[0];i++){
            for (j=0;j<dim[1];j++){
               for (k=0;k<dim[2];k++){
                  indx1[i*dim[1]*dim[2]+j*dim[2]+k] = i*dim[1]*dim[2] + j*dim[2] + k;
               }
            }
         }
         ierr = ISCreateGeneral(comm,dim[0]*dim[1]*dim[2],indx1,PETSC_COPY_VALUES,&list1);CHKERRQ(ierr);
         ierr = VecScatterCreate(x,list1,y,list1,&vecscat);CHKERRQ(ierr);
         ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
         ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
         ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
         ierr = ISDestroy(&list1);CHKERRQ(ierr);
         ierr = PetscFree(indx1);CHKERRQ(ierr);
         break;
    default:
*/
    ierr = ISCreateStride(comm,N,0,1,&list1);CHKERRQ(ierr);
    //ierr = ISView(list1,PETSC_VIEWER_STDOUT_SELF);
    ierr = VecScatterCreate(x,list1,y,list1,&vecscat);CHKERRQ(ierr);
    ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
    ierr = ISDestroy(&list1);CHKERRQ(ierr);
  //       break;
   // }
  }
  else{

 switch (ndim){
 case 1:
#if defined(PETSC_USE_COMPLEX)
      alloc_local = fftw_mpi_local_size_1d(dim[0],comm,FFTW_BACKWARD,FFTW_ESTIMATE,&local_n0,&local_0_start,&local_n1,&local_1_start);
      ierr = ISCreateStride(PETSC_COMM_WORLD,local_n1,local_1_start,1,&list1);
      ierr = ISCreateStride(PETSC_COMM_WORLD,local_n1,low,1,&list2);
      //ierr = ISView(list1,PETSC_VIEWER_STDOUT_WORLD);
      //ierr = ISView(list2,PETSC_VIEWER_STDOUT_WORLD);
      ierr = VecScatterCreate(x,list1,y,list2,&vecscat);CHKERRQ(ierr);
      ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
      ierr = ISDestroy(&list1);CHKERRQ(ierr);
      ierr = ISDestroy(&list2);CHKERRQ(ierr);
#else
      SETERRQ(comm,PETSC_ERR_SUP,"No support for real parallel 1D FFT");
#endif
 break;
 case 2:
#if defined(PETSC_USE_COMPLEX)
      alloc_local = fftw_mpi_local_size_2d(dim[0],dim[1],comm,&local_n0,&local_0_start);
      ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0*dim[1],local_0_start*dim[1],1,&list1);
      ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0*dim[1],low,1,&list2);
      ierr = VecScatterCreate(x,list2,y,list1,&vecscat);CHKERRQ(ierr);
      ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
      ierr = ISDestroy(&list1);CHKERRQ(ierr);
      ierr = ISDestroy(&list2);CHKERRQ(ierr);
#else
      alloc_local =  fftw_mpi_local_size_2d_transposed(dim[0],dim[1]/2+1,comm,&local_n0,&local_0_start,&local_n1,&local_1_start);
      N1 = 2*dim[0]*(dim[1]/2+1); n1 = 2*local_n0*(dim[1]/2+1);

      ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*dim[1],&indx1);CHKERRQ(ierr);
      ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*dim[1],&indx2);CHKERRQ(ierr);

      if (dim[1]%2==0)
        NM = dim[1]+2;
      else
        NM = dim[1]+1;

      for (i=0;i<local_n0;i++){
         for (j=0;j<dim[1];j++){
            tempindx = i*dim[1] + j;
            tempindx1 = i*NM + j;
            indx1[tempindx]=local_0_start*dim[1]+tempindx;
            indx2[tempindx]=low+tempindx1;
         }
       }

       ierr = ISCreateGeneral(comm,local_n0*dim[1],indx1,PETSC_COPY_VALUES,&list1);CHKERRQ(ierr);
       ierr = ISCreateGeneral(comm,local_n0*dim[1],indx2,PETSC_COPY_VALUES,&list2);CHKERRQ(ierr);

       ierr = VecScatterCreate(x,list2,y,list1,&vecscat);CHKERRQ(ierr);
       ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
       ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
       ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
       ierr = ISDestroy(&list1);CHKERRQ(ierr);
       ierr = ISDestroy(&list2);CHKERRQ(ierr);
       ierr = PetscFree(indx1);CHKERRQ(ierr);
       ierr = PetscFree(indx2);CHKERRQ(ierr);
#endif
 break;
 case 3:
#if defined(PETSC_USE_COMPLEX)
       alloc_local = fftw_mpi_local_size_3d(dim[0],dim[1],dim[2],comm,&local_n0,&local_0_start);
       ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0*dim[1]*dim[2],local_0_start*dim[1]*dim[2],1,&list1);
       ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0*dim[1]*dim[2],low,1,&list2);
       ierr = VecScatterCreate(x,list1,y,list2,&vecscat);CHKERRQ(ierr);
       ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
       ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
       ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
       ierr = ISDestroy(&list1);CHKERRQ(ierr);
       ierr = ISDestroy(&list2);CHKERRQ(ierr);
#else

       alloc_local =  fftw_mpi_local_size_3d_transposed(dim[0],dim[1],dim[2]/2+1,comm,&local_n0,&local_0_start,&local_n1,&local_1_start);
       N1 = 2*dim[0]*dim[1]*(dim[2]/2+1); n1 = 2*local_n0*dim[1]*(dim[2]/2+1);

//     ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*N1,&indx1);CHKERRQ(ierr);
//     ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*N1,&indx2);CHKERRQ(ierr);
       ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*dim[1]*dim[2],&indx1);CHKERRQ(ierr);
       ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*dim[1]*dim[2],&indx2);CHKERRQ(ierr);

       if (dim[2]%2==0)
        NM = dim[2]+2;
       else
        NM = dim[2]+1;

       for (i=0;i<local_n0;i++){
          for (j=0;j<dim[1];j++){
             for (k=0;k<dim[2];k++){
                tempindx = i*dim[1]*dim[2] + j*dim[2] + k;
                tempindx1 = i*dim[1]*NM + j*NM + k;
                indx1[tempindx]=local_0_start*dim[1]*dim[2]+tempindx;
                indx2[tempindx]=low+tempindx1;
             }
        //    printf("Val tempindx1 = %d\n",tempindx1);
        //    printf("index1 %d from proc %d is \n",indx1[tempindx],rank);
        //    printf("index2 %d from proc %d is \n",indx2[tempindx],rank);
        //    printf("-------------------------\n",indx2[tempindx],rank);
          }
       }

       ierr = ISCreateGeneral(comm,local_n0*dim[1]*dim[2],indx1,PETSC_COPY_VALUES,&list1);CHKERRQ(ierr);
       ierr = ISCreateGeneral(comm,local_n0*dim[1]*dim[2],indx2,PETSC_COPY_VALUES,&list2);CHKERRQ(ierr);

       ierr = VecScatterCreate(x,list2,y,list1,&vecscat);CHKERRQ(ierr);
       ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
       ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
       ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
       ierr = ISDestroy(&list1);CHKERRQ(ierr);
       ierr = ISDestroy(&list2);CHKERRQ(ierr);
       ierr = PetscFree(indx1);CHKERRQ(ierr);
       ierr = PetscFree(indx2);CHKERRQ(ierr);
#endif
 break;
 default:
#if defined(PETSC_USE_COMPLEX)
       alloc_local = fftw_mpi_local_size(fftw->ndim_fftw,fftw->dim_fftw,comm,&local_n0,&local_0_start);
       ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0*(fftw->partial_dim),local_0_start*(fftw->partial_dim),1,&list1);
       ierr = ISCreateStride(PETSC_COMM_WORLD,local_n0*(fftw->partial_dim),low,1,&list2);
      //ierr = ISView(list1,PETSC_VIEWER_STDOUT_WORLD);
      //ierr = ISView(list2,PETSC_VIEWER_STDOUT_WORLD);
       ierr = VecScatterCreate(x,list1,y,list2,&vecscat);CHKERRQ(ierr);
       ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
       ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
       ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
       ierr = ISDestroy(&list1);CHKERRQ(ierr);
       ierr = ISDestroy(&list2);CHKERRQ(ierr);
#else
       temp = (fftw->dim_fftw)[fftw->ndim_fftw-1];
       (fftw->dim_fftw)[fftw->ndim_fftw-1] = temp/2 + 1;
       alloc_local = fftw_mpi_local_size_transposed(fftw->ndim_fftw,fftw->dim_fftw,comm,&local_n0,&local_0_start,&local_n1,&local_1_start);
       N1 = 2*N*(PetscInt)((fftw->dim_fftw)[fftw->ndim_fftw-1])/((PetscInt) temp);
       (fftw->dim_fftw)[fftw->ndim_fftw-1] = temp;

       partial_dim = fftw->partial_dim;

       ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*partial_dim,&indx1);CHKERRQ(ierr);
       ierr = PetscMalloc(sizeof(PetscInt)*((PetscInt)local_n0)*partial_dim,&indx2);CHKERRQ(ierr);

       if (dim[ndim-1]%2==0)
         NM = 2;
       else
         NM = 1;

       j = low;
       for (i=0,k=1; i<((PetscInt)local_n0)*partial_dim;i++,k++)
          {
           indx1[i] = local_0_start*partial_dim + i;
           indx2[i] = j;
           if (k%dim[ndim-1]==0)
             { j+=NM;}
           j++;
          }
       ierr = ISCreateGeneral(comm,local_n0*partial_dim,indx1,PETSC_COPY_VALUES,&list1);CHKERRQ(ierr);
       ierr = ISCreateGeneral(comm,local_n0*partial_dim,indx2,PETSC_COPY_VALUES,&list2);CHKERRQ(ierr);

       ierr = VecScatterCreate(x,list2,y,list1,&vecscat);CHKERRQ(ierr);
       ierr = VecScatterBegin(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
       ierr = VecScatterEnd(vecscat,x,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
       ierr = VecScatterDestroy(&vecscat);CHKERRQ(ierr);
       ierr = ISDestroy(&list1);CHKERRQ(ierr);
       ierr = ISDestroy(&list2);CHKERRQ(ierr);
       ierr = PetscFree(indx1);CHKERRQ(ierr);
       ierr = PetscFree(indx2);CHKERRQ(ierr);
#endif
 break;
 }
 }
 return 0;
}
EXTERN_C_END

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatCreate_FFTW"
/*
      MatCreate_FFTW - Creates a matrix object that provides FFT
  via the external package FFTW
  Options Database Keys:
+ -mat_fftw_plannerflags - set FFTW planner flags

   Level: intermediate

*/

PetscErrorCode MatCreate_FFTW(Mat A)
{
  PetscErrorCode ierr;
  MPI_Comm       comm=((PetscObject)A)->comm;
  Mat_FFT        *fft=(Mat_FFT*)A->data;
  Mat_FFTW       *fftw;
  PetscInt       n=fft->n,N=fft->N,ndim=fft->ndim,*dim = fft->dim;
  const char     *p_flags[]={"FFTW_ESTIMATE","FFTW_MEASURE","FFTW_PATIENT","FFTW_EXHAUSTIVE"};
  PetscBool      flg;
  PetscInt       p_flag,partial_dim=1,ctr,n1;
  PetscMPIInt    size,rank;
  ptrdiff_t      *pdim;
  ptrdiff_t      local_n1,local_1_start;
#if !defined(PETSC_USE_COMPLEX)
   ptrdiff_t     temp;
   PetscInt      N1;
#endif


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

  pdim = (ptrdiff_t *)calloc(ndim,sizeof(ptrdiff_t));
  pdim[0] = dim[0];
  for (ctr=1;ctr<ndim;ctr++)
     {
          partial_dim *= dim[ctr];
          pdim[ctr] = dim[ctr];
     }

  if (size == 1) {
#if defined(PETSC_USE_COMPLEX)
    ierr = MatSetSizes(A,N,N,N,N);CHKERRQ(ierr);
    n = N;
#else
    PetscInt tot_dim = N*2*(dim[ndim-1]/2+1)/dim[ndim-1];
    ierr = MatSetSizes(A,tot_dim,tot_dim,tot_dim,tot_dim);CHKERRQ(ierr);
    n = tot_dim;
#endif

  } else {
    ptrdiff_t alloc_local,local_n0,local_0_start;//local_1_end;
    switch (ndim){
    case 1:
#if !defined(PETSC_USE_COMPLEX)
   SETERRQ(comm,PETSC_ERR_SUP,"FFTW does not support parallel 1D real transform");
#else
      alloc_local = fftw_mpi_local_size_1d(dim[0],comm,FFTW_FORWARD,FFTW_ESTIMATE,&local_n0,&local_0_start,&local_n1,&local_1_start);
      n = (PetscInt)local_n0;
      n1 = (PetscInt) local_n1;
      ierr = MatSetSizes(A,n1,n,N,N);CHKERRQ(ierr);
#endif
      break;
    case 2:
#if defined(PETSC_USE_COMPLEX)
      alloc_local = fftw_mpi_local_size_2d(dim[0],dim[1],comm,&local_n0,&local_0_start);
      /*
       PetscMPIInt    rank;
       PetscSynchronizedPrintf(comm,"[%d] MatCreateSeqFFTW: local_n0, local_0_start %d %d, N %d,dim %d, %d\n",rank,(PetscInt)local_n0*dim[1],(PetscInt)local_0_start,m,dim[0],dim[1]);
       PetscSynchronizedFlush(comm);
       */
      n = (PetscInt)local_n0*dim[1];
      ierr = MatSetSizes(A,n,n,N,N);CHKERRQ(ierr);
#else
      alloc_local = fftw_mpi_local_size_2d_transposed(dim[0],dim[1]/2+1,PETSC_COMM_WORLD,&local_n0,&local_0_start,&local_n1,&local_1_start);
      n = 2*(PetscInt)local_n0*(dim[1]/2+1);
//      n1 = 2*(PetscInt)local_n1*(dim[0]);
//      ierr = MatSetSizes(A,n1,n,2*dim[0]*(dim[1]/2+1),2*dim[0]*(dim[1]/2+1));
      ierr = MatSetSizes(A,n,n,2*dim[0]*(dim[1]/2+1),2*dim[0]*(dim[1]/2+1));
#endif
      break;
    case 3:
#if defined(PETSC_USE_COMPLEX)
      alloc_local = fftw_mpi_local_size_3d(dim[0],dim[1],dim[2],comm,&local_n0,&local_0_start);
      n = (PetscInt)local_n0*dim[1]*dim[2];
      ierr = MatSetSizes(A,n,n,N,N);CHKERRQ(ierr);
#else
      alloc_local = fftw_mpi_local_size_3d_transposed(dim[0],dim[1],dim[2]/2+1,PETSC_COMM_WORLD,&local_n0,&local_0_start,&local_n1,&local_1_start);
      n = 2*(PetscInt)local_n0*dim[1]*(dim[2]/2+1);
//      n1 = 2*local_n1*dim[0]*(dim[2]/2+1);
//      ierr = MatSetSizes(A,n1,n,2*dim[0]*dim[1]*(dim[2]/2+1),2*dim[0]*dim[1]*(dim[2]/2+1));
      ierr = MatSetSizes(A,n,n,2*dim[0]*dim[1]*(dim[2]/2+1),2*dim[0]*dim[1]*(dim[2]/2+1));
#endif
      break;
    default:
#if defined(PETSC_USE_COMPLEX)
      alloc_local = fftw_mpi_local_size(ndim,pdim,comm,&local_n0,&local_0_start);
      n = (PetscInt)local_n0*partial_dim;
      ierr = MatSetSizes(A,n,n,N,N);CHKERRQ(ierr);
#else
      temp = pdim[ndim-1];
      pdim[ndim-1] = temp/2 + 1;
      alloc_local = fftw_mpi_local_size_transposed(ndim,pdim,PETSC_COMM_WORLD,&local_n0,&local_0_start,&local_n1,&local_1_start);
      n = 2*(PetscInt)local_n0*partial_dim*pdim[ndim-1]/temp;
      N1 = 2*N*(PetscInt)pdim[ndim-1]/((PetscInt) temp);
      pdim[ndim-1] = temp;
//      temp = partial_dim*(dim[ndim-1]/2+1)*dim[0]/(dim[1]*dim[ndim-1]);
//      n1 = 2*local_n1*temp;
//      ierr = MatSetSizes(A,n1,n,N1,N1);CHKERRQ(ierr);
      ierr = MatSetSizes(A,n,n,N1,N1);CHKERRQ(ierr);
#endif
      break;
    }
  }
  ierr = PetscObjectChangeTypeName((PetscObject)A,MATFFTW);CHKERRQ(ierr);
  ierr = PetscNewLog(A,Mat_FFTW,&fftw);CHKERRQ(ierr);
  fft->data = (void*)fftw;

  fft->n           = n;
  fftw->ndim_fftw  = (ptrdiff_t)ndim; // This is dimension of fft
  fftw->partial_dim = partial_dim;
  ierr = PetscMalloc(ndim*sizeof(ptrdiff_t), (ptrdiff_t *)&(fftw->dim_fftw));CHKERRQ(ierr);
  for(ctr=0;ctr<ndim;ctr++) (fftw->dim_fftw)[ctr]=dim[ctr];

  fftw->p_forward  = 0;
  fftw->p_backward = 0;
  fftw->p_flag     = FFTW_ESTIMATE;

  if (size == 1){
    A->ops->mult          = MatMult_SeqFFTW;
    A->ops->multtranspose = MatMultTranspose_SeqFFTW;
  } else {
    A->ops->mult          = MatMult_MPIFFTW;
    A->ops->multtranspose = MatMultTranspose_MPIFFTW;
  }
  fft->matdestroy          = MatDestroy_FFTW;
  // if(ndim=1 && size>1) and also if it is complex then getvecs should be attached to MatGetVecs_FFTW1D
  //A->ops->getvecs       = MatGetVecs_FFTW;
  A->assembled          = PETSC_TRUE;
  PetscObjectComposeFunctionDynamic((PetscObject)A,"MatGetVecsFFTW_C","MatGetVecsFFTW_FFTW",MatGetVecsFFTW_FFTW);
  PetscObjectComposeFunctionDynamic((PetscObject)A,"InputTransformFFT_C","InputTransformFFT_FFTW",InputTransformFFT_FFTW);
  PetscObjectComposeFunctionDynamic((PetscObject)A,"OutputTransformFFT_C","OutputTransformFFT_FFTW",OutputTransformFFT_FFTW);

  /* get runtime options */
  ierr = PetscOptionsBegin(((PetscObject)A)->comm,((PetscObject)A)->prefix,"FFTW Options","Mat");CHKERRQ(ierr);
    ierr = PetscOptionsEList("-mat_fftw_plannerflags","Planner Flags","None",p_flags,4,p_flags[0],&p_flag,&flg);CHKERRQ(ierr);
    if (flg) {fftw->p_flag = (unsigned)p_flag;}
  PetscOptionsEnd();
  PetscFunctionReturn(0);
}
EXTERN_C_END