[petsc-users] Usage of parallel FFT for doing batch 1d-FFTs over the columns of a dense 2d-matrix
Matthew Knepley
knepley at gmail.com
Tue Dec 8 07:55:21 CST 2020
On Tue, Dec 8, 2020 at 8:40 AM Roland Richter <roland.richter at ntnu.no>
wrote:
> Dear all,
>
> I tried the following code:
>
> *int main(int argc, char **args) {*
> * Mat C, F;*
> * Vec x, y, z;*
> * PetscViewer viewer;*
> * PetscMPIInt rank, size;*
> * PetscInitialize(&argc, &args, (char*) 0, help);*
>
> * MPI_Comm_size(PETSC_COMM_WORLD, &size);*
> * MPI_Comm_rank(PETSC_COMM_WORLD, &rank);*
>
> * PetscPrintf(PETSC_COMM_WORLD,"Number of processors = %d, rank =
> %d\n", size, rank);*
> * // std::cout << "From rank " << rank << '\n';*
>
> * //MatCreate(PETSC_COMM_WORLD, &C);*
> * PetscViewerCreate(PETSC_COMM_WORLD, &viewer);*
> * PetscViewerSetType(viewer, PETSCVIEWERASCII);*
> * arma::cx_mat local_mat, local_zero_mat;*
> * const size_t matrix_size = 5;*
>
> * MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE,
> matrix_size, matrix_size, NULL, &C);*
> * MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE,
> matrix_size, matrix_size, NULL, &F);*
> * if(rank == 0) {*
> * arma::Col<int> indices = arma::linspace<arma::Col<int>>(0,
> matrix_size - 1, matrix_size);*
> * //if(rank == 0) {*
> * local_mat = arma::randu<arma::cx_mat>(matrix_size, matrix_size);*
> * local_zero_mat = arma::zeros<arma::cx_mat>(matrix_size,
> matrix_size);*
> * arma::cx_mat tmp_mat = local_mat.st <http://local_mat.st>();*
> * MatSetValues(C, matrix_size, indices.memptr(), matrix_size,
> indices.memptr(), tmp_mat.memptr(), INSERT_VALUES);*
> * MatSetValues(F, matrix_size, indices.memptr(), matrix_size,
> indices.memptr(), local_zero_mat.memptr(), INSERT_VALUES);*
> * }*
>
> * MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY);*
> * MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY);*
> * MatAssemblyBegin(F, MAT_FINAL_ASSEMBLY);*
> * MatAssemblyEnd(F, MAT_FINAL_ASSEMBLY);*
>
> * //FFT test*
> * Mat FFT_A;*
> * Vec input, output;*
> * int first_owned_row_index = 0, last_owned_row_index = 0;*
> * const int FFT_length[] = {matrix_size};*
>
>
> * MatCreateFFT(PETSC_COMM_WORLD, 1, FFT_length, MATFFTW, &FFT_A);*
> * MatCreateVecsFFTW(FFT_A, &x, &y, &z);*
> * VecCreate(PETSC_COMM_WORLD, &input);*
> * VecSetFromOptions(input);*
> * VecSetSizes(input, PETSC_DECIDE, matrix_size);*
> * VecCreate(PETSC_COMM_WORLD, &output);*
> * VecSetFromOptions(output);*
> * VecSetSizes(output, PETSC_DECIDE, matrix_size);*
> * MatGetOwnershipRange(C, &first_owned_row_index,
> &last_owned_row_index);*
> * std::cout << "Rank " << rank << " owns row " << first_owned_row_index
> << " to row " << last_owned_row_index << '\n';*
>
> * //Testing FFT*
>
> * /*---------------------------------------------------------*/*
> * fftw_plan fplan,bplan;*
> * fftw_complex *data_in,*data_out,*data_out2;*
> * ptrdiff_t alloc_local, local_ni, local_i_start,
> local_n0,local_0_start;*
> * PetscRandom rdm;*
>
> * // if (!rank)*
> * // printf("Use FFTW without PETSc-FFTW interface\n");*
> * fftw_mpi_init();*
> * int N = matrix_size * matrix_size;*
> * int N0 = matrix_size;*
> * int N1 = matrix_size;*
> * const ptrdiff_t n_data[] = {N0, 1};*
> * //alloc_local =
> fftw_mpi_local_size_2d(N0,N1,PETSC_COMM_WORLD,&local_n0,&local_0_start);*
> * alloc_local = fftw_mpi_local_size_many(1, n_data,*
> * matrix_size,*
> * FFTW_MPI_DEFAULT_BLOCK,*
> * PETSC_COMM_WORLD,*
> * &local_n0,*
> * &local_0_start);*
> * //data_in =
> (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);*
> * PetscScalar *C_ptr, *F_ptr;*
> * MatDenseGetArray(C, &C_ptr);*
> * MatDenseGetArray(F, &F_ptr);*
> * data_in = reinterpret_cast<fftw_complex*>(C_ptr);*
> * data_out = reinterpret_cast<fftw_complex*>(F_ptr);*
> * data_out2 =
> (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);*
>
>
> * VecCreateMPIWithArray(PETSC_COMM_WORLD,1,(PetscInt)local_n0 *
> N1,(PetscInt)N,(const PetscScalar*)data_in,&x);*
> * PetscObjectSetName((PetscObject) x, "Real Space vector");*
> * VecCreateMPIWithArray(PETSC_COMM_WORLD,1,(PetscInt)local_n0 *
> N1,(PetscInt)N,(const PetscScalar*)data_out,&y);*
> * PetscObjectSetName((PetscObject) y, "Frequency space vector");*
> * VecCreateMPIWithArray(PETSC_COMM_WORLD,1,(PetscInt)local_n0 *
> N1,(PetscInt)N,(const PetscScalar*)data_out2,&z);*
> * PetscObjectSetName((PetscObject) z, "Reconstructed vector");*
>
> * int FFT_rank = 1;*
> * const ptrdiff_t FFTW_size[] = {matrix_size};*
> * int howmany = last_owned_row_index - first_owned_row_index;*
> * //std::cout << "Rank " << rank << " processes " << howmany << "
> rows\n";*
> * int idist = matrix_size;//1;*
> * int odist = matrix_size;//1;*
> * int istride = 1;//matrix_size;*
> * int ostride = 1;//matrix_size;*
> * const ptrdiff_t *inembed = FFTW_size, *onembed = FFTW_size;*
> * fplan = fftw_mpi_plan_many_dft(FFT_rank, FFTW_size,*
> * howmany,*
> * FFTW_MPI_DEFAULT_BLOCK,
> FFTW_MPI_DEFAULT_BLOCK,*
> * data_in, data_out,*
> * PETSC_COMM_WORLD,*
> * FFTW_FORWARD, FFTW_ESTIMATE);*
> * bplan = fftw_mpi_plan_many_dft(FFT_rank, FFTW_size,*
> * howmany,*
> * FFTW_MPI_DEFAULT_BLOCK,
> FFTW_MPI_DEFAULT_BLOCK,*
> * data_out, data_out2,*
> * PETSC_COMM_WORLD,*
> * FFTW_BACKWARD, FFTW_ESTIMATE);*
>
> * if (false) {VecView(x,PETSC_VIEWER_STDOUT_WORLD);}*
>
> * fftw_execute(fplan);*
> * if (false) {VecView(y,PETSC_VIEWER_STDOUT_WORLD);}*
>
> * fftw_execute(bplan);*
>
> * double a = 1.0 / matrix_size;*
> * double enorm = 0;*
> * VecScale(z,a);*
> * if (false) {VecView(z, PETSC_VIEWER_STDOUT_WORLD);}*
> * VecAXPY(z,-1.0,x);*
> * VecNorm(z,NORM_1,&enorm);*
> * if (enorm > 1.e-11) {*
> * PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z|
> %g\n",(double)enorm);*
> * }*
>
> * /* Free spaces */*
> * fftw_destroy_plan(fplan);*
> * fftw_destroy_plan(bplan);*
> * fftw_free(data_out2);*
>
> * //Generate test matrix for comparison*
> * arma::cx_mat fft_test_mat = local_mat;*
> * fft_test_mat.each_row([&](arma::cx_rowvec &a){*
> * a = arma::fft(a);*
> * });*
> * std::cout <<
> "-----------------------------------------------------\n";*
> * std::cout << "Input matrix:\n" << local_mat << '\n';*
> * MatView(C, viewer);*
> * std::cout <<
> "-----------------------------------------------------\n";*
> * std::cout << "Expected output matrix:\n" << fft_test_mat << '\n';*
> * MatView(F, viewer);*
> * std::cout <<
> "-----------------------------------------------------\n";*
> * MatDestroy(&FFT_A);*
> * VecDestroy(&input);*
> * VecDestroy(&output);*
> * VecDestroy(&x);*
> * VecDestroy(&y);*
> * VecDestroy(&z);*
> * MatDestroy(&C);*
> * MatDestroy(&F);*
> * PetscViewerDestroy(&viewer);*
> * PetscFinalize();*
> * return 0;*
> *}*
>
> For *mpirun -n 1* I get the expected output (i.e. armadillo and
> PETSc/FFTW return the same result), but for *mpirun -n x* with x > 1
> every value which is not assigned to rank 0 is lost and set to zero
> instead. Every value assigned to rank 0 is calculated correctly, as far as
> I can see. Did I forget something here?
>
> I do not understand why your FFTW calls use the WORLD communicator. Aren't
they serial FFTs over the local rows?
THanks,
Matt
> Thanks,
>
> Roland
> Am 05.12.20 um 01:59 schrieb Barry Smith:
>
>
> Roland,
>
> If you store your matrix as described in a parallel PETSc dense matrix
> then you should be able to call
>
> fftw_plan_many_dft() directly on the value obtained with
> MatDenseGetArray(). You just need to pass the arguments regarding column
> major ordering appropriately. Probably identically to what you do with your
> previous code.
>
> Barry
>
>
> On Dec 4, 2020, at 6:47 AM, Roland Richter <roland.richter at ntnu.no> wrote:
>
> Ideally those FFTs could be handled in parallel, after they are not
> depending on each other. Is that possible with MatFFT, or should I rather
> use FFTW for that?
>
> Thanks,
>
> Roland
> Am 04.12.20 um 13:19 schrieb Matthew Knepley:
>
> On Fri, Dec 4, 2020 at 5:32 AM Roland Richter <roland.richter at ntnu.no>
> wrote:
>
>> Hei,
>>
>> I am currently working on a problem which requires a large amount of
>> transformations of a field E(r, t) from time space to Fourier space E(r,
>> w) and back. The field is described in a 2d-matrix, with the r-dimension
>> along the columns and the t-dimension along the rows.
>>
>> For the transformation from time to frequency space and back I therefore
>> have to apply a 1d-FFT operation over each row of my matrix. For my
>> earlier attempts I used armadillo as matrix library and FFTW for doing
>> the transformations. Here I could use fftw_plan_many_dft to do all FFTs
>> at the same time. Unfortunately, armadillo does not support MPI, and
>> therefore I had to switch to PETSc for larger matrices.
>>
>> Based on the examples (such as example 143) PETSc has a way of doing
>> FFTs internally by creating an FFT object (using MatCreateFFT).
>> Unfortunately, I can not see how I could use that object to conduct the
>> operation described above without having to iterate over each row in my
>> original matrix (i.e. doing it sequential, not in parallel).
>>
>> Ideally I could distribute the FFTs such over my nodes that each node
>> takes several rows of the original matrix and applies the FFT to each of
>> them. As example, for a matrix with a size of 4x4 and two nodes node 0
>> would take row 0 and 1, while node 1 takes row 2 and 3, to avoid
>> unnecessary memory transfer between the nodes while conducting the FFTs.
>> Is that something PETSc can do, too?
>>
>
> The way I understand our setup (I did not write it), we use plan_many_dft
> to handle
> multiple dof FFTs, but these would be interlaced. You want many FFTs for
> non-interlaced
> storage, which is not something we do right now. You could definitely call
> FFTW directly
> if you want.
>
> Second, above it seems like you just want serial FFTs. You can definitely
> create a MatFFT
> with PETSC_COMM_SELF, and apply it to each row in the local rows, or
> create the plan
> yourself for the stack of rows.
>
> Thanks,
>
> Matt
>
>
>> Thanks!
>>
>> Regards,
>>
>> Roland
>>
>>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
>
>
--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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