Error while implementing matrix vector multiplication with MPI in C

Question

I am new to MPI and have only learnt the basics. While performing the matrix vector multiplication based on the following algorithm, an error message appears that I can not understand and thus cannot fix.

The error message : Signal : Segmentation fault (11) Signal Code: Address not mapped (1)

/* Matrix-vector product Ab = c with parallel inner products*/
/* Row-oriented blockwise distribution of A */
/* Replicated distribution of vectors b and c */
local n = n/p;
for (i=0; i<local n; i++) local c[i] = 0;
for (i=0; i<local n; i++)
for (j=0; j<m; j++)
local c[i] = local c[i] + local A[i][j] * b[j];
multi broadcast(local c,local n,c);
/* Multi-broadcast operation of (c[0]; :::; c[localn]) to globalc*/

This is my code:

#include<stdio.h>
#include<stdlib.h>
#include "mpi.h"

#define n 4
#define m 4

void matrix_vector_product(double **matrix, double *vector, double *result, int rows, int cols)
{
  for(int i=0; i<rows; i++)
    result[i] = 0;
  for(int i=0; i<rows; i++)
    for(int j=0; j<cols; j++)
      result[i] += matrix[i][j] * vector[j];
}

int main(int argc, char *argv[])
{
  int rank, size;
  MPI_Init(&argc, &argv);
  MPI_Comm_size(MPI_COMM_WORLD, &size);
  MPI_Comm_rank(MPI_COMM_WORLD, &rank);
 
  double **matrix;
  matrix = (double **)calloc(n,sizeof(double *));
  for (int i=0; i<n; i++)
  {
    matrix[i] = (double *)calloc(m, sizeof(double));
  }
 
  double *b;
  b = (double *)calloc(m, sizeof(double));
 
  double *c = NULL;
  double *local_c = (double *)calloc(n, sizeof(double));
  int local_n = n/size;
 
  if (rank == 0)
  {
    for(int i=0; i<n; i++)
      for(int j =0; j<m; j++)
        matrix[i][j] = i+j;
   
    for(int j =0; j<m; j++)
        b[j] = j+1;
   
    c = (double *)calloc(m, sizeof(double));
  }
 
  MPI_Scatter(&matrix, local_n*m, MPI_DOUBLE, &matrix, local_n*m, MPI_DOUBLE, 0, MPI_COMM_WORLD);
   
  MPI_Bcast(b, m, MPI_DOUBLE, 0, MPI_COMM_WORLD);
 
  matrix_vector_product(matrix, b, local_c, local_n, m);
 
  MPI_Gather(local_c, local_n, MPI_DOUBLE, c, local_n, MPI_DOUBLE, 0, MPI_COMM_WORLD);
 
  if(rank==0){
    printf(" Result = ");
    for(int i=0; i<n; i++)
      printf(" .2%f", c[i]);
  }
   
  MPI_Finalize();
 
  free(matrix);
  free(b);
  free(c);
  free(local_c);
 
  return 0;
}

If you could also explain as to why this is happening that would be great since I want to clear my concepts.

I tried to multiply a *matrix *of size n x m with a vector of size m. Since a distributed memory distribution is assumed, I used MPI_Scatter operation to assign blocks of memory of rows of matrix to achieve row-wise block-wise distribution of A. b is replicated using MPI_Bcast operation. The result is calculated using a function matrix_vector_product() and the content of the local buffer(array here) c are gathered in c. I was expecting the output to be Result = 8 10 12 14

Answer 1

1. Any MPI buffer needs to be a simpletype*, in your case double*. So you can not pass matrix which is a double**.
2. You don't have a matrix: you have an array of arrays. Please allocate double *matrix and use a conversion from 2D indexing to 1D. Then pass MPI_Scatter(matrix,....`
3. Don't use scatter to spread your matrix: for good parallel performance each process needs to create its own part of the matrix. You have a time and memory bottleneck.