How to use MPI derived data type for 3D array?

Question

I want to write a parallel code that works on a 3D matrix where each processes has it's own sub matrix but for doing their jobs they need some information about their neighbouring processes' sub matrix (just boundary planes). I send these informations with point to point communication but I know that for large matrix it is not a good idea so I decide to use derived data type for communication. I have problem with mpi_type_vector: for example I have a NX*NY*NZ matrix and I want to send plane with constant NY to another process I write these lines for doing this:

MPI_Datatype sub;

MPI_Type_vector(NX, NZ, NY*NZ, MPI_DOUBLE, &sub);

MPI_Type_commit(&sub);

but it doesn't work (can not send my desired plane). What is wrong? my test code is here:

#include <mpi.h>
#include <iostream>

using namespace std;

int main(int argc,char ** argv)
{

    int const IE=100,JE=25,KE=100;
    int size,rank;
    MPI_Status status;

    MPI_Init(&argc,&argv);
    MPI_Comm_size(MPI_COMM_WORLD,&size);
    MPI_Comm_rank(MPI_COMM_WORLD,&rank);
    MPI_Datatype sub;
    MPI_Type_vector(KE,IE,IE+(JE-1)*IE,MPI_DOUBLE,&sub);
    MPI_Type_commit(&sub);

    if (rank==0){

        double*** a=new double**[IE];

        for(int i=0;i<IE;i++){
            a[i]=new double *[JE];
            for(int j=0;j<JE;j++){
                a[i][j]=new double [KE];
            }
        }

        for(int i=0;i<IE;i++){
            for(int j=0;j<JE;j++){
                for(int k=0;k<KE;k++){
                    a[i][j][k]=2;
                }}}

        for(int i=0;i<IE;i++){
            for(int j=0;j<JE;j++){
                a[i][j][0]=2;
            }}

        MPI_Send(&a[0][0][0],1,sub,1,52,MPI_COMM_WORLD);

    }

    if (rank==1){

        double*** b=new double**[IE];

        for(int i=0;i<IE;i++){
            b[i]=new double *[JE];
            for(int j=0;j<JE;j++){
                b[i][j]=new double [KE];
            }
        }

        for(int i=0;i<IE;i++){
            for(int j=0;j<JE;j++){
                for(int k=0;k<KE;k++){
                    b[i][j][k]=0;
                }}}

        MPI_Recv(&b[0][0][0][0],1,sub,0,52,MPI_COMM_WORLD,&status);

        for(int i=0;i<IE;i++){
            for(int j=0;j<JE;j++){
                for(int k=0;k<KE;k++){
                    if(b[i][j][k]>0){
                        cout<<"b["<<i<<"]["<<j<<"]["<<k<<"]="<<b[i][j][k]<<endl;
                    }}}}

    }

    MPI_Finalize();

}

Answer 1

With a 3d matrix, in general you'd have to use a vector of vectors (because there are two strides involved) - which is possible, but much simpler is to use MPI_Type_create_subarray() which just lets you carve out the slab of a multidimensional array you want.

Update: One problem in the above code is that the 3d array you allocate isn't contiguous; it's a collection of IE*JE allocated 1d arrays which may or may not be anywhere near each other. So there's no reliable way of extracting a plane of data out of it.

You need to do something like this:

double ***alloc3d(int l, int m, int n) {
    double *data = new double [l*m*n];
    double ***array = new double **[l];
    for (int i=0; i<l; i++) {
        array[i] = new double *[m];
        for (int j=0; j<m; j++) {
            array[i][j] = &(data[(i*m+j)*n]);
        }
    }
    return array;
}

Then the data is in one big cube, like you'd expect, with an array of pointers pointing into it. This - the fact that C doesn't have real multidimensional arrays - comes up all the time with C + MPI.

Answer 2

Thanks to Jonathan Dursi. Here I want to publish complete code that creates a 3d matrix and uses derived datatypes for communication (only plane with constant y will be sent from one process to another).I used Jonathan Dursi's function posted above.

#include <mpi.h>
#include <iostream>
#include <math.h>
#include <fstream>
#include <vector>
using namespace std;
#define IE 100
#define JE 50
#define KE 100

#define JE_loc 52
double ***alloc3d(int l, int m, int n) {
double *data = new double [l*m*n];
double ***array = new double **[l];
for (int i=0; i<l; i++) {
    array[i] = new double *[m];
    for (int j=0; j<m; j++) {
        array[i][j] = &(data[(i*m+j)*n]);
    }
}
return array;
}




int main(int argc ,char ** argv)
{
//////////////////////declartion/////////////////////////////
int const NFREQS=100,ia=7,ja=7,ka=7;
double const pi=3.14159;
int i,j,size,rank,k;
//MPI_Status status[10];
MPI_Status status;
MPI_Request request[10];
MPI_Init(&argc, &argv);
MPI_Comm_size(MPI_COMM_WORLD, &size);
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
MPI_Datatype sub;
MPI_Type_vector(KE,IE,IE+(JE-1)*IE,MPI_DOUBLE,&sub);
MPI_Type_commit(&sub);


double ***a=alloc3d(IE,JE,KE);
for (i=0; i<IE; i++) {
    for (j=0; j<JE; j++) {
        for (k=0; k<KE; k++) {
            a[i][j][k]=0.0;
        }
    }
}
if (rank==0) {
    for (i=0; i<IE; i++) {
        for (j=0; j<JE; j++) {
            for (k=0; k<KE; k++) {
                a[i][j][k]=2;
            }
        }
    }
    MPI_Send(&a[0][0][0],1,sub,1,52,MPI_COMM_WORLD);

}
if (rank==1) {
    MPI_Recv(&a[0][49][0],1,sub,0,52,MPI_COMM_WORLD,&status);
    for (i=0; i<IE; i++) {
        for (j=0; j<JE; j++) {
            for (k=0; k<KE; k++) {
                if (a[i][j][k]>0) {
                    cout<<"a["<<i<<"]["<<j<<"]["<<k<<"]="<<a[i][j][k]<<endl;
                }
            }
        }
    }

}
MPI_Finalize();
}