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  {
   "cell_type": "markdown",
   "id": "d6d12733",
   "metadata": {},
   "source": [
    "# Solutions to Notebook Exercises\n",
    "\n",
    "## Matrix Multiplication : Implementation of Algorithm 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "be73e87a",
   "metadata": {},
   "outputs": [],
   "source": [
    "function matmul_dist_3!(C,A,B)\n",
    "    m = size(C,1)\n",
    "    n = size(C,2)\n",
    "    l = size(A,2)\n",
    "    @assert size(A,1) == m\n",
    "    @assert size(B,2) == n\n",
    "    @assert size(B,1) == l\n",
    "    @assert mod(m,nworkers()) == 0\n",
    "    # Implement here\n",
    "    nrows_w = div(m,nworkers())\n",
    "    @sync for (i,w) in enumerate(workers())\n",
    "        rows_w = (1:nrows_w) .+ (i-1)*nrows_w\n",
    "        Aw = A[rows_w,:]\n",
    "        ftr = @spawnat w begin\n",
    "            Cw = similar(Aw,nrows_w,n)\n",
    "            matmul_seq!(Cw,Aw,B)\n",
    "            Cw\n",
    "        end\n",
    "        @async C[rows_w,:] = fetch(ftr)\n",
    "    end\n",
    "    C\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d9f4813",
   "metadata": {},
   "source": [
    "## Jacobi Method : Exercise 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cf3b1e72",
   "metadata": {},
   "outputs": [],
   "source": [
    "@mpi_do manager begin\n",
    "    using MPI\n",
    "    comm = MPI.Comm_dup(MPI.COMM_WORLD)\n",
    "    nw = MPI.Comm_size(comm)\n",
    "    iw = MPI.Comm_rank(comm)+1\n",
    "    function jacobi_mpi(n,niters)\n",
    "        if mod(n,nw) != 0\n",
    "            println(\"n must be a multiple of nw\")\n",
    "            MPI.Abort(comm,1)\n",
    "        end\n",
    "        n_own = div(n,nw)\n",
    "        u = zeros(n_own+2)\n",
    "        u[1] = -1\n",
    "        u[end] = 1\n",
    "        u_new = copy(u)\n",
    "        for t in 1:niters\n",
    "            reqs_snd = MPI.Request[]\n",
    "            reqs_rcv = MPI.Request[]\n",
    "            if iw != 1\n",
    "                neig_rank = (iw-1)-1\n",
    "                req = MPI.Isend(view(u,2:2),comm,dest=neig_rank,tag=0)\n",
    "                push!(reqs_snd,req)\n",
    "                req = MPI.Irecv!(view(u,1:1),comm,source=neig_rank,tag=0)\n",
    "                push!(reqs_rcv,req)\n",
    "            end\n",
    "            if iw != nw\n",
    "                neig_rank = (iw+1)-1\n",
    "                s = n_own+1\n",
    "                r = n_own+2\n",
    "                req = MPI.Isend(view(u,s:s),comm,dest=neig_rank,tag=0)\n",
    "                push!(reqs_snd,req)\n",
    "                req = MPI.Irecv!(view(u,r:r),comm,source=neig_rank,tag=0)\n",
    "                push!(reqs_rcv,req)\n",
    "            end\n",
    "            for i in 3:n_own\n",
    "                u_new[i] = 0.5*(u[i-1]+u[i+1])\n",
    "            end\n",
    "            MPI.Waitall(reqs_rcv)\n",
    "            for i in (2,n_own+1)\n",
    "                u_new[i] = 0.5*(u[i-1]+u[i+1])\n",
    "            end\n",
    "            MPI.Waitall(reqs_snd)\n",
    "            u, u_new = u_new, u\n",
    "        end\n",
    "        u\n",
    "        @show u\n",
    "    end\n",
    "    niters = 100\n",
    "    load = 4\n",
    "    n = load*nw\n",
    "    jacobi_mpi(n,niters)\n",
    "end"
   ]
  }
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