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{
"cells": [
{
"cell_type": "markdown",
"id": "f48b9a60",
"metadata": {},
"source": [
"# Solutions to Notebook Exercises\n",
"\n",
"## Julia Basics: Exercise 1"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a06fd02a",
"metadata": {},
"outputs": [],
"source": [
"function ex1(a)\n",
" j = 1\n",
" m = a[j]\n",
" for (i,ai) in enumerate(a)\n",
" if m < ai\n",
" m = ai\n",
" j = i\n",
" end\n",
" end\n",
" (m,j)\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "175b6c35",
"metadata": {},
"source": [
"## Julia Basics: Exercise 2"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bb289acd",
"metadata": {},
"outputs": [],
"source": [
"ex2(f,g) = x -> f(x) + g(x) "
]
},
{
"cell_type": "markdown",
"id": "86250e27",
"metadata": {},
"source": [
"## Julia Basics: Exercise 3"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "41b537ab",
"metadata": {},
"outputs": [],
"source": [
"function compute_values(n,max_iters)\n",
" x = LinRange(-1.7,0.7,n)\n",
" y = LinRange(-1.2,1.2,n)\n",
" values = zeros(Int,n,n)\n",
" for j in 1:n\n",
" for i in 1:n\n",
" values[i,j] = mandel(x[i],y[j],max_iters)\n",
" end\n",
" end\n",
" values\n",
"end\n",
"values = compute_values(1000,10)\n",
"using GLMakie\n",
"heatmap(x,y,values)"
]
},
{
"cell_type": "markdown",
"id": "d6d12733",
"metadata": {},
"source": [
"## Matrix Multiplication : Exercise 1"
]
},
{
"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"
]
},
{
"cell_type": "markdown",
"id": "2f343157",
"metadata": {},
"source": [
"## Exercise: Ring communication - MPI"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a49be691",
"metadata": {},
"outputs": [],
"source": [
"using MPI\n",
"using Test\n",
"\n",
"MPI.Init()\n",
"comm = MPI.COMM_WORLD\n",
"rank = MPI.Comm_rank(comm)\n",
"id = rank + 1\n",
"root = 0\n",
"size = MPI.Comm_size(comm)\n",
"\n",
"dst = mod(rank + 1, size)\n",
"src = mod(rank - 1, size)\n",
"\n",
"send_buf = id\n",
"recv_buf = 1\n",
"\n",
"if rank == root \n",
" # Proc 1: Send id async to destination, then wait for receive\n",
" MPI.isend(send_buf, comm; dest=dst, tag=0)\n",
" recv_buf = MPI.recv(comm; source=src, tag=0)\n",
" @show recv_buf == factorial(size)\n",
" @test recv_buf == factorial(size)\n",
"else\n",
" # Other procs: receive sync and send async to next process\n",
" recv_buf = MPI.recv(comm; source=src, tag=0)\n",
" send_buf = recv_buf * id\n",
" MPI.isend(send_buf, comm; dest=dst, tag=0)\n",
"end\n",
"\n",
"MPI.Finalize()"
]
},
{
"cell_type": "markdown",
"id": "6cbbf074",
"metadata": {},
"source": [
"## Exercise: Ring communication - Distributed.jl"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "dc156523",
"metadata": {},
"outputs": [],
"source": [
"using Distributed \n",
"using Test\n",
"\n",
"np = 4\n",
"add_n = np - nprocs() \n",
"addprocs(add_n)\n",
"worker_ids = workers()\n",
"@assert nprocs() > nworkers()\n",
"\n",
"# Initialize id channel\n",
"id_chnl = RemoteChannel(()->Channel{Int}(1))\n",
"put!(id_chnl, 1)\n",
"\n",
"# Initialize data channel\n",
"job_chnl = RemoteChannel(()->Channel{Int}(1))\n",
"put!(job_chnl, 1)\n",
"\n",
"@sync for w in workers()\n",
" @spawnat w begin\n",
" pos = findfirst(worker_ids .== w) + 1\n",
" dst = mod(pos, np) + 1\n",
" src = mod(pos-2, np) + 1\n",
" while true \n",
" pred = fetch(id_chnl)\n",
" if pred == src\n",
" take!(id_chnl)\n",
" value = take!(job_chnl)\n",
" put!(job_chnl, value * pos) \n",
" put!(id_chnl, pos) \n",
" break\n",
" end\n",
" end\n",
" end\n",
"end\n",
"\n",
"res = take!(job_chnl)\n",
"@show res\n",
"@test res == factorial(np)\n",
"\n",
"rmprocs(workers())"
]
},
{
"cell_type": "markdown",
"id": "47d88e7a",
"metadata": {},
"source": [
"# License\n",
"\n",
"TODO: replace link to website\n",
"\n",
"This notebook is part of the course [Programming Large Scale Parallel Systems](http://localhost:8000/) at Vrije Universiteit Amsterdam and may be used under a [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/) license."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "968304a6",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.9.0",
"language": "julia",
"name": "julia-1.9"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.9.0"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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