mirror of
https://github.com/fverdugo/XM_40017.git
synced 2025-11-08 16:14:23 +01:00
991 lines
30 KiB
Plaintext
991 lines
30 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "f48b9a60",
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"metadata": {},
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"source": [
|
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"# Solutions to Notebook Exercises\n",
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"\n",
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"## Julia Basics: Exercise 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "a06fd02a",
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"metadata": {},
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"outputs": [],
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"source": [
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"function ex1(a)\n",
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" j = 1\n",
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" m = a[j]\n",
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" for (i,ai) in enumerate(a)\n",
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" if m < ai\n",
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" m = ai\n",
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" j = i\n",
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" end\n",
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" end\n",
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" (m,j)\n",
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"end"
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]
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},
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{
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"cell_type": "markdown",
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"id": "175b6c35",
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"metadata": {},
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"source": [
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"## Julia Basics: Exercise 2"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "bb289acd",
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"metadata": {},
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"outputs": [],
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"source": [
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"ex2(f,g) = x -> f(x) + g(x) "
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]
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},
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{
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"cell_type": "markdown",
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"id": "86250e27",
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"metadata": {},
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"source": [
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"## Julia Basics: Exercise 3"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "41b537ab",
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"metadata": {},
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"outputs": [],
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"source": [
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"function compute_values(n,max_iters)\n",
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" x = LinRange(-1.7,0.7,n)\n",
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" y = LinRange(-1.2,1.2,n)\n",
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" values = zeros(Int,n,n)\n",
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" for j in 1:n\n",
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" for i in 1:n\n",
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" values[i,j] = mandel(x[i],y[j],max_iters)\n",
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" end\n",
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" end\n",
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" values\n",
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"end\n",
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"values = compute_values(1000,10)\n",
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"using GLMakie\n",
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"heatmap(x,y,values)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d6d12733",
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"metadata": {},
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"source": [
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"## Matrix Multiplication : Exercise 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "be73e87a",
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"metadata": {},
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"outputs": [],
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"source": [
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"function matmul_dist_3!(C,A,B)\n",
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" m = size(C,1)\n",
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" n = size(C,2)\n",
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" l = size(A,2)\n",
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" @assert size(A,1) == m\n",
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" @assert size(B,2) == n\n",
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" @assert size(B,1) == l\n",
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" @assert mod(m,nworkers()) == 0\n",
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" # Implement here\n",
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" nrows_w = div(m,nworkers())\n",
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" @sync for (i,w) in enumerate(workers())\n",
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" rows_w = (1:nrows_w) .+ (i-1)*nrows_w\n",
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" Aw = A[rows_w,:]\n",
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" ftr = @spawnat w begin\n",
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" Cw = similar(Aw,nrows_w,n)\n",
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" matmul_seq!(Cw,Aw,B)\n",
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" Cw\n",
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" end\n",
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" @async C[rows_w,:] = fetch(ftr)\n",
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" end\n",
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" C\n",
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"end"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2d9f4813",
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"metadata": {},
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"source": [
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"## Jacobi Method : Exercise 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "cf3b1e72",
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"metadata": {},
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"outputs": [],
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"source": [
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"@mpi_do manager begin\n",
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" using MPI\n",
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" comm = MPI.Comm_dup(MPI.COMM_WORLD)\n",
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" nw = MPI.Comm_size(comm)\n",
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" iw = MPI.Comm_rank(comm)+1\n",
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" function jacobi_mpi(n,niters)\n",
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" if mod(n,nw) != 0\n",
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" println(\"n must be a multiple of nw\")\n",
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" MPI.Abort(comm,1)\n",
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" end\n",
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" n_own = div(n,nw)\n",
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" u = zeros(n_own+2)\n",
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" u[1] = -1\n",
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" u[end] = 1\n",
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" u_new = copy(u)\n",
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" for t in 1:niters\n",
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" reqs_snd = MPI.Request[]\n",
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" reqs_rcv = MPI.Request[]\n",
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" if iw != 1\n",
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" neig_rank = (iw-1)-1\n",
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" req = MPI.Isend(view(u,2:2),comm,dest=neig_rank,tag=0)\n",
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" push!(reqs_snd,req)\n",
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" req = MPI.Irecv!(view(u,1:1),comm,source=neig_rank,tag=0)\n",
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" push!(reqs_rcv,req)\n",
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" end\n",
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" if iw != nw\n",
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" neig_rank = (iw+1)-1\n",
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" s = n_own+1\n",
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" r = n_own+2\n",
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" req = MPI.Isend(view(u,s:s),comm,dest=neig_rank,tag=0)\n",
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" push!(reqs_snd,req)\n",
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" req = MPI.Irecv!(view(u,r:r),comm,source=neig_rank,tag=0)\n",
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" push!(reqs_rcv,req)\n",
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" end\n",
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" for i in 3:n_own\n",
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" u_new[i] = 0.5*(u[i-1]+u[i+1])\n",
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" end\n",
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" MPI.Waitall(reqs_rcv)\n",
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" for i in (2,n_own+1)\n",
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" u_new[i] = 0.5*(u[i-1]+u[i+1])\n",
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" end\n",
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" MPI.Waitall(reqs_snd)\n",
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" u, u_new = u_new, u\n",
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" end\n",
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" u\n",
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" @show u\n",
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" end\n",
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" niters = 100\n",
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" load = 4\n",
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" n = load*nw\n",
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" jacobi_mpi(n,niters)\n",
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"end"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2f343157",
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"metadata": {},
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"source": [
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"## Exercise: Ring communication - MPI"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "a49be691",
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"metadata": {},
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"outputs": [],
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"source": [
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"using MPI\n",
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"using Test\n",
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"\n",
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"MPI.Init()\n",
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"comm = MPI.COMM_WORLD\n",
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"rank = MPI.Comm_rank(comm)\n",
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"id = rank + 1\n",
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"root = 0\n",
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"size = MPI.Comm_size(comm)\n",
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"\n",
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"dst = mod(rank + 1, size)\n",
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"src = mod(rank - 1, size)\n",
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"\n",
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"send_buf = id\n",
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"recv_buf = 1\n",
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"\n",
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"if rank == root \n",
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" # Proc 1: Send id async to destination, then wait for receive\n",
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" MPI.isend(send_buf, comm; dest=dst, tag=0)\n",
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" recv_buf = MPI.recv(comm; source=src, tag=0)\n",
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" @show recv_buf == factorial(size)\n",
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" @test recv_buf == factorial(size)\n",
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"else\n",
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" # Other procs: receive sync and send async to next process\n",
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" recv_buf = MPI.recv(comm; source=src, tag=0)\n",
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" send_buf = recv_buf * id\n",
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" MPI.isend(send_buf, comm; dest=dst, tag=0)\n",
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"end\n",
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"\n",
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"MPI.Finalize()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "6cbbf074",
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"metadata": {},
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"source": [
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"## Exercise: Ring communication - Distributed.jl"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "dc156523",
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"metadata": {},
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"outputs": [],
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"source": [
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"using Distributed \n",
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"using Test\n",
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"\n",
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"np = 4\n",
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"add_n = np - nprocs() \n",
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"addprocs(add_n)\n",
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"worker_ids = workers()\n",
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"@assert nprocs() > nworkers()\n",
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"\n",
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"# Initialize id channel\n",
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"id_chnl = RemoteChannel(()->Channel{Int}(1))\n",
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"put!(id_chnl, 1)\n",
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"\n",
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"# Initialize data channel\n",
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"job_chnl = RemoteChannel(()->Channel{Int}(1))\n",
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"put!(job_chnl, 1)\n",
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"\n",
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"@sync for w in workers()\n",
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" @spawnat w begin\n",
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" pos = findfirst(worker_ids .== w) + 1\n",
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" dst = mod(pos, np) + 1\n",
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" src = mod(pos-2, np) + 1\n",
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" while true \n",
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" pred = fetch(id_chnl)\n",
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" if pred == src\n",
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" take!(id_chnl)\n",
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" value = take!(job_chnl)\n",
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" put!(job_chnl, value * pos) \n",
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" put!(id_chnl, pos) \n",
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" break\n",
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" end\n",
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" end\n",
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" end\n",
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"end\n",
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"\n",
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"res = take!(job_chnl)\n",
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"@show res\n",
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"@test res == factorial(np)\n",
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"\n",
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"rmprocs(workers())"
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]
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},
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{
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"cell_type": "markdown",
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"id": "508125f9",
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"metadata": {},
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"source": [
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"### New ring example"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "7af4cfd0",
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"metadata": {},
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"outputs": [],
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"source": [
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"@everywhere workers() begin\n",
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" using MPI\n",
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" MPI.Init()\n",
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" comm = MPI.Comm_dup(MPI.COMM_WORLD)\n",
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" rank = MPI.Comm_rank(comm)\n",
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" nranks = MPI.Comm_size(comm)\n",
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" buffer = Ref(0)\n",
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" if rank == 0\n",
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" msg = rand(1:10)\n",
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" buffer[] = msg\n",
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" println(\"msg = $(buffer[])\")\n",
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" MPI.Send(buffer,comm;dest=rank+1,tag=0)\n",
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" MPI.Recv!(buffer,comm;source=nranks-1,tag=0)\n",
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" println(\"msg = $(buffer[])\")\n",
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" else\n",
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" dest = (rank != nranks-1) ? rank+1 : 0\n",
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" MPI.Recv!(buffer,comm;source=rank-1,tag=0)\n",
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" buffer[] += 1\n",
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" println(\"msg = $(buffer[])\")\n",
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" MPI.Send(buffer,comm;dest,tag=0)\n",
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" end\n",
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "30ece423",
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"metadata": {},
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"outputs": [],
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"source": [
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"ftrs = Vector{Future}(undef,nprocs())\n",
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"for p in 1:nprocs()\n",
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" ftrs[p] = @spawnat p RemoteChannel(()->Channel{Int}(1))\n",
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"end\n",
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"for p in 1:nprocs()\n",
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" @spawnat p begin \n",
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" chnl_snd = fetch(ftrs[p])\n",
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" source = (p != 1) ? p-1 : nprocs()\n",
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" chnl_rcv = fetch(ftrs[source])\n",
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" if p == 1\n",
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" msg = rand(1:10)\n",
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" @show msg\n",
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" put!(chnl_snd,msg)\n",
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" msg = take!(chnl_rcv)\n",
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" @show msg\n",
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" else\n",
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" msg = take!(chnl_rcv)\n",
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" msg += 1\n",
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" @show msg\n",
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" put!(chnl_snd,msg)\n",
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" end\n",
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" end\n",
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "761ce452",
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"metadata": {},
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"outputs": [],
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"source": [
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"@everywhere function work(msg)\n",
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" msg += 1\n",
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" println(\"msg = $msg\")\n",
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" if myid() == nprocs()\n",
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" @spawnat 1 println(\"msg = $msg\")\n",
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" else\n",
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" next = myid() + 1\n",
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" @spawnat next work(msg)\n",
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" end\n",
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"end"
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]
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},
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{
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"cell_type": "markdown",
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"id": "48e594e7",
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"metadata": {},
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"source": [
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"## LEQ: Exercise 1\n",
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"### Blockwise partitioning: "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "5d890006",
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"metadata": {},
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"outputs": [],
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"source": [
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"function ge_par_block!(B,n,m,comm)\n",
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" nranks = MPI.Comm_size(comm)\n",
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" rank = MPI.Comm_rank(comm)\n",
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" # Init buffers\n",
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" T = eltype(B)\n",
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" if rank == 0\n",
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" buffer_root = Vector{T}(undef,n*m)\n",
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" buffer_root[:] = transpose(B)[:]\n",
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" else\n",
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" buffer_root = Vector{T}(undef,0)\n",
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" end \n",
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" nw = div(n,nranks)\n",
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" buffer = Vector{T}(undef,nw*m)\n",
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" # Send local matrices to workers\n",
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" MPI.Scatter!(buffer_root,buffer,comm;root=0)\n",
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" Bw = Matrix{T}(undef,nw,m)\n",
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" transpose(Bw)[:] = buffer\n",
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" MPI.Barrier(comm)\n",
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" # time calcultation\n",
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" t = @elapsed ge_block_worker!(Bw,n,comm)\n",
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" # Gather results\n",
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" buffer[:] = transpose(Bw)[:]\n",
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" MPI.Gather!(buffer,buffer_root,comm;root=0)\n",
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" Tf = typeof(t)\n",
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" if rank == 0\n",
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" transpose(B)[:] = buffer_root[:]\n",
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" ts = Vector{Tf}(undef,nranks)\n",
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" else\n",
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" ts = Vector{Tf}(undef,0)\n",
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" end\n",
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" MPI.Gather!([t],ts,comm;root=0)\n",
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" B, ts\n",
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"end \n",
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"\n",
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"function ge_block_worker!(Bw,n,comm)\n",
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" rank = MPI.Comm_rank(comm)\n",
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" nranks = MPI.Comm_size(comm)\n",
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" nw,m = size(Bw)\n",
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" B_k = similar(Bw,m)\n",
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" lb = nw*rank + 1\n",
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" ub = nw*(rank+1)\n",
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" @inbounds for k in 1:n\n",
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" # If I have row k\n",
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" if k in lb:ub\n",
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" myk = k - lb + 1\n",
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" # Update just row k\n",
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" #@show Bw[myk,k]\n",
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" for t in (k+1):m\n",
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" Bw[myk,t] = Bw[myk,t]/Bw[myk,k]\n",
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" end\n",
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" Bw[myk,k] = 1\n",
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" # Send k to other procs\n",
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" B_k .= view(Bw,myk,:)\n",
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" MPI.Bcast!(B_k,comm;root=rank)\n",
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" else\n",
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" myk = 0\n",
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" owner = div(k-1,nw)\n",
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" MPI.Bcast!(B_k,comm;root=owner)\n",
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" end\n",
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" # Do nothing if I only have rows < k \n",
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" if k <= ub\n",
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" for i in (myk+1):nw\n",
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" for j in (k+1):m\n",
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" Bw[i,j] = Bw[i,j] - Bw[i,k]*B_k[j]\n",
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" end\n",
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" Bw[i,k] = 0\n",
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" end\n",
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" end\n",
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" end\n",
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" Bw\n",
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"end"
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]
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},
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{
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"cell_type": "markdown",
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"id": "18c688ac",
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"metadata": {},
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"source": [
|
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"### Cyclic partitioning: "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "6ba555b2",
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|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"function ge_par_cyclic!(B,n,m,comm)\n",
|
|
" nranks = MPI.Comm_size(comm)\n",
|
|
" rank = MPI.Comm_rank(comm)\n",
|
|
" nw = div(n,nranks)\n",
|
|
" # Init buffers\n",
|
|
" T = eltype(B)\n",
|
|
" if rank == 0\n",
|
|
" buffer_root = Vector{T}(undef,n*m)\n",
|
|
" # Fill buffer cyclicly\n",
|
|
" for i in 1:n\n",
|
|
" ub = i * m \n",
|
|
" lb = ub - m + 1\n",
|
|
" j = mod(i-1,nw)*nranks + div(i-1,nw) +1\n",
|
|
" buffer_root[lb:ub] = transpose(B)[:,j]\n",
|
|
" end\n",
|
|
" else\n",
|
|
" buffer_root = Vector{T}(undef,0)\n",
|
|
" end \n",
|
|
" buffer = Vector{T}(undef,nw*m)\n",
|
|
" # Send local matrices to workers\n",
|
|
" MPI.Scatter!(buffer_root,buffer,comm;root=0)\n",
|
|
" Bw = Matrix{T}(undef,nw,m)\n",
|
|
" transpose(Bw)[:] = buffer\n",
|
|
" MPI.Barrier(comm)\n",
|
|
" # time calcultation\n",
|
|
" t = @elapsed ge_cyclic_worker!(Bw,n,comm)\n",
|
|
" # Gather results\n",
|
|
" buffer[:] = transpose(Bw)[:]\n",
|
|
" MPI.Gather!(buffer,buffer_root,comm;root=0)\n",
|
|
" Tf = typeof(t)\n",
|
|
" if rank == 0\n",
|
|
" for i in 1:n\n",
|
|
" ub = i * m \n",
|
|
" lb = ub - m + 1\n",
|
|
" j = mod(i-1,nw)*nranks + div(i-1,nw) +1\n",
|
|
" transpose(B)[:,j] = buffer_root[lb:ub]\n",
|
|
" end\n",
|
|
" ts = Vector{Tf}(undef,nranks)\n",
|
|
" else\n",
|
|
" ts = Vector{Tf}(undef,0)\n",
|
|
" end\n",
|
|
" MPI.Gather!([t],ts,comm;root=0)\n",
|
|
" B, ts\n",
|
|
"end\n",
|
|
"\n",
|
|
"function ge_cyclic_worker!(Bw,n,comm)\n",
|
|
" rank = MPI.Comm_rank(comm)\n",
|
|
" nranks = MPI.Comm_size(comm)\n",
|
|
" nw,m = size(Bw)\n",
|
|
" B_k = similar(Bw,m)\n",
|
|
" my_rows = [i*nranks+(rank+1) for i in 0:(nw-1)]\n",
|
|
" @inbounds for k in 1:n\n",
|
|
" # If I have row k\n",
|
|
" if k in my_rows\n",
|
|
" myk = findfirst(my_rows .== k)[2]\n",
|
|
" # Update just row k\n",
|
|
" for t in (k+1):m\n",
|
|
" Bw[myk,t] = Bw[myk,t]/Bw[myk,k]\n",
|
|
" end\n",
|
|
" Bw[myk,k] = 1\n",
|
|
" # Send k to other procs\n",
|
|
" B_k .= view(Bw,myk,:)\n",
|
|
" MPI.Bcast!(B_k,comm;root=rank)\n",
|
|
" else\n",
|
|
" owner = mod(k-1,nranks)\n",
|
|
" MPI.Bcast!(B_k,comm;root=owner)\n",
|
|
" end\n",
|
|
" # Do nothing if I only have rows < k \n",
|
|
" if k < maximum(my_rows)\n",
|
|
" cutoff = findfirst(my_rows .> k)[2]\n",
|
|
" for i in cutoff:length(my_rows)\n",
|
|
" for j in (k+1):m\n",
|
|
" Bw[i,j] = Bw[i,j] - Bw[i,k]*B_k[j]\n",
|
|
" end\n",
|
|
" Bw[i,k] = 0\n",
|
|
" end\n",
|
|
" end\n",
|
|
" end\n",
|
|
" Bw\n",
|
|
"end"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "fe0bb4ab",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Main Function to run code and test performance: "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "4d00c192",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"using MPI\n",
|
|
"using Test\n",
|
|
"MPI.Init()\n",
|
|
"\n",
|
|
"\n",
|
|
"function tridiagonal_matrix(n)\n",
|
|
" C = zeros(n,n)\n",
|
|
" stencil = [(-1,2,-1),(-1,0,1)]\n",
|
|
" for i in 1:n\n",
|
|
" for (coeff,o) in zip((-1,2,-1),(-1,0,1))\n",
|
|
" j = i+o\n",
|
|
" if j in 1:n\n",
|
|
" C[i,j] = coeff\n",
|
|
" end\n",
|
|
" end\n",
|
|
" end\n",
|
|
" C\n",
|
|
"end\n",
|
|
"\n",
|
|
"function ge_seq!(B)\n",
|
|
" n,m = size(B)\n",
|
|
" @inbounds for k in 1:n\n",
|
|
" for t in (k+1):m\n",
|
|
" B[k,t] = B[k,t]/B[k,k]\n",
|
|
" end\n",
|
|
" B[k,k] = 1\n",
|
|
" for i in (k+1):n \n",
|
|
" for j in (k+1):m\n",
|
|
" B[i,j] = B[i,j] - B[i,k]*B[k,j]\n",
|
|
" end\n",
|
|
" B[i,k] = 0\n",
|
|
" end\n",
|
|
" end\n",
|
|
" B\n",
|
|
"end\n",
|
|
"\n",
|
|
"function main_check()\n",
|
|
" # Create communicator \n",
|
|
" comm = MPI.Comm_dup(MPI.COMM_WORLD)\n",
|
|
" rank = MPI.Comm_rank(comm)\n",
|
|
" nranks = MPI.Comm_size(comm)\n",
|
|
" n = 10*nranks\n",
|
|
" # create matrix B such that mod(n, nprocs) == 0\n",
|
|
" if rank == 0 \n",
|
|
" A = tridiagonal_matrix(n)\n",
|
|
" b = ones(n)\n",
|
|
" B = [A b]\n",
|
|
" else \n",
|
|
" B = tridiagonal_matrix(0)\n",
|
|
" end\n",
|
|
" # call parallel method \n",
|
|
" B_block, ts_block = ge_par_block!(copy(B),n,n+1,comm)\n",
|
|
" B_cyclic, ts_cyclic = ge_par_cyclic!(copy(B),n,n+1,comm)\n",
|
|
" # test if results is equal to sequential \n",
|
|
" if rank == 0\n",
|
|
" B_seq = ge_seq!(copy(B))\n",
|
|
" @test B_seq == B_block\n",
|
|
" @test B_seq == B_cyclic\n",
|
|
" # print timings\n",
|
|
" println(\"No workers: $nranks| Blockwise: min $(minimum(ts_block))| Cyclic: min $(minimum(ts_cyclic))\")\n",
|
|
" end\n",
|
|
"end\n",
|
|
"\n",
|
|
"main_check()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "cbbd3b8f",
|
|
"metadata": {},
|
|
"source": [
|
|
"## ASP : Exercise 1\n",
|
|
"Implementation of parallel ASP using only `MPI.Bcast!`. "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "ec5f932f",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"@everywhere function floyd_worker_bcast!(Cw,comm)\n",
|
|
" rank = MPI.Comm_rank(comm)\n",
|
|
" nranks = MPI.Comm_size(comm)\n",
|
|
" Nw,N = size(Cw)\n",
|
|
" C_k = similar(Cw,N)\n",
|
|
" lb = Nw*rank + 1\n",
|
|
" ub = Nw*(rank+1)\n",
|
|
" for k in 1:N\n",
|
|
" if k in lb:ub\n",
|
|
" myk = k - lb + 1\n",
|
|
" C_k .= view(Cw,myk,:)\n",
|
|
" MPI.Bcast!(C_k,comm;root=rank)\n",
|
|
" else\n",
|
|
" owner = div(k-1,Nw)\n",
|
|
" MPI.Bcast!(C_k,comm;root=owner)\n",
|
|
" end\n",
|
|
" for j in 1:N\n",
|
|
" for i in 1:Nw\n",
|
|
" @inbounds Cw[i,j] = min(Cw[i,j],Cw[i,k]+C_k[j])\n",
|
|
" end\n",
|
|
" end\n",
|
|
" end\n",
|
|
" Cw\n",
|
|
"end"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "19641daf",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Exercise: Measure search overhead\n",
|
|
"Modify the code of the serial and parallel algorithms so that the functions return the number of nodes in the search tree that they visit. You can then compare how many more nodes are visited by the parallel algorithm compared with the serial algorithm (known as _search overhead_). You can then use the third cell to gather some statistics about the search overhead using your altered version of the functions. "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "22ccce39",
|
|
"metadata": {},
|
|
"source": [
|
|
"## TSP: Exercise x (Measure search overhead)\n",
|
|
"This is the solution of how the code can be altered to measure the search overhead:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "a4d5ab70",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"using Distributed\n",
|
|
"\n",
|
|
"if procs() == workers()\n",
|
|
" addprocs(4)\n",
|
|
"end\n",
|
|
"\n",
|
|
"@everywhere function visited(city,hops,path)\n",
|
|
" for i = 1:hops\n",
|
|
" if path[i] == city\n",
|
|
" return true\n",
|
|
" end\n",
|
|
" end\n",
|
|
" return false\n",
|
|
"end"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "bcee99f0",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"## TSP serial \n",
|
|
"function tsp_serial_impl(connections,hops,path,current_distance, min_path, min_distance, node_count)\n",
|
|
" num_cities = length(connections)\n",
|
|
" if hops == num_cities\n",
|
|
" if current_distance < min_distance\n",
|
|
" min_path .= path\n",
|
|
" return min_path, current_distance, node_count\n",
|
|
" end\n",
|
|
" else\n",
|
|
" current_city = path[hops]\n",
|
|
" next_hops = hops + 1\n",
|
|
" for (next_city,distance_increment) in connections[current_city]\n",
|
|
" if !visited(next_city,hops,path)\n",
|
|
" node_count += 1\n",
|
|
" path[next_hops] = next_city\n",
|
|
" next_distance = current_distance + distance_increment\n",
|
|
" if next_distance < min_distance\n",
|
|
" min_path, min_distance, node_count = tsp_serial_impl(connections,next_hops,path,next_distance,min_path,min_distance, node_count)\n",
|
|
" end\n",
|
|
" end\n",
|
|
" end \n",
|
|
" end\n",
|
|
" return min_path, min_distance, node_count\n",
|
|
"end\n",
|
|
"\n",
|
|
"function tsp_serial(connections,city)\n",
|
|
" num_cities = length(connections)\n",
|
|
" path=zeros(Int,num_cities)\n",
|
|
" hops = 1\n",
|
|
" path[hops] = city\n",
|
|
" min_path = zeros(Int, num_cities)\n",
|
|
" current_distance = 0\n",
|
|
" min_distance = typemax(Int)\n",
|
|
" node_count = 1\n",
|
|
" # Count the number of nodes visited in recursive function and return\n",
|
|
" min_path, min_distance, node_count = tsp_serial_impl(connections,hops,path,current_distance, min_path, min_distance, node_count)\n",
|
|
" (;path=min_path,distance=min_distance, node_count)\n",
|
|
"end"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "327f5349",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"## TSP distributed\n",
|
|
"@everywhere function tsp_dist_impl(connections,hops,path,current_distance,min_dist_chnl, max_hops,jobs_chnl,ftr_result,node_count)\n",
|
|
" num_cities = length(connections)\n",
|
|
" if hops == num_cities\n",
|
|
" min_distance = fetch(min_dist_chnl)\n",
|
|
" if current_distance < min_distance\n",
|
|
" take!(min_dist_chnl)\n",
|
|
" if ftr_result !== nothing\n",
|
|
" @spawnat 1 begin\n",
|
|
" result = fetch(ftr_result)\n",
|
|
" result.path .= path\n",
|
|
" result.min_distance_ref[] = current_distance\n",
|
|
" end |> wait\n",
|
|
" end\n",
|
|
" put!(min_dist_chnl, current_distance)\n",
|
|
" end\n",
|
|
" elseif hops <= max_hops\n",
|
|
" current_city = path[hops]\n",
|
|
" next_hops = hops + 1\n",
|
|
" for (next_city,distance_increment) in connections[current_city]\n",
|
|
" if !visited(next_city,hops,path)\n",
|
|
" path[next_hops] = next_city\n",
|
|
" node_count += 1\n",
|
|
" next_distance = current_distance + distance_increment\n",
|
|
" min_distance = fetch(min_dist_chnl)\n",
|
|
" if next_distance < min_distance\n",
|
|
" node_count = tsp_dist_impl(connections,next_hops,path,next_distance,min_dist_chnl,max_hops,jobs_chnl,ftr_result,node_count)\n",
|
|
" end\n",
|
|
" end\n",
|
|
" end \n",
|
|
" else\n",
|
|
" if jobs_chnl !== nothing \n",
|
|
" path_copy = copy(path) \n",
|
|
" put!(jobs_chnl,(;hops,path=path_copy,current_distance))\n",
|
|
" end\n",
|
|
" end\n",
|
|
" return node_count\n",
|
|
"end\n",
|
|
"\n",
|
|
"function tsp_dist(connections,city)\n",
|
|
" max_hops = 2\n",
|
|
" num_cities = length(connections)\n",
|
|
" path=zeros(Int,num_cities)\n",
|
|
" result_path=zeros(Int, num_cities)\n",
|
|
" hops = 1\n",
|
|
" path[hops] = city\n",
|
|
" current_distance = 0\n",
|
|
" min_distance = typemax(Int)\n",
|
|
" node_count = 1\n",
|
|
" jobs_chnl = RemoteChannel(()->Channel{Any}(10))\n",
|
|
" min_dist_chnl = RemoteChannel(()->Channel{Int}(1))\n",
|
|
" put!(min_dist_chnl, min_distance)\n",
|
|
" ftr_result = @spawnat 1 (;path=result_path,min_distance_ref=Ref(min_distance))\n",
|
|
" # Add another future to store number of visited nodes\n",
|
|
" ftr_node_count = @spawnat 1 node_count_ref = Ref(node_count)\n",
|
|
" @async begin\n",
|
|
" ncount = 0\n",
|
|
" ncount += tsp_dist_impl(connections,hops,path,current_distance,min_dist_chnl,max_hops,jobs_chnl,nothing, ncount)\n",
|
|
" # Update node counter\n",
|
|
" node_count_ref = fetch(ftr_node_count)\n",
|
|
" node_count_ref[] += ncount \n",
|
|
" for w in workers()\n",
|
|
" put!(jobs_chnl,nothing)\n",
|
|
" end\n",
|
|
" end\n",
|
|
" @sync for w in workers()\n",
|
|
" @spawnat w begin\n",
|
|
" path = zeros(Int, num_cities)\n",
|
|
" max_hops = typemax(Int)\n",
|
|
" while true\n",
|
|
" job = take!(jobs_chnl)\n",
|
|
" if job == nothing\n",
|
|
" break\n",
|
|
" end\n",
|
|
" hops = job.hops\n",
|
|
" path = job.path \n",
|
|
" current_distance = job.current_distance\n",
|
|
" ncount = 0\n",
|
|
" min_distance = fetch(min_dist_chnl)\n",
|
|
" if current_distance < min_distance\n",
|
|
" ncount += tsp_dist_impl(connections,hops,path,current_distance,min_dist_chnl,max_hops,nothing,ftr_result, ncount)\n",
|
|
" # Update node counter\n",
|
|
" @spawnat 1 begin \n",
|
|
" node_count_ref = fetch(ftr_node_count)\n",
|
|
" node_count_ref[] += ncount \n",
|
|
" end\n",
|
|
" end\n",
|
|
" end\n",
|
|
" end\n",
|
|
" end \n",
|
|
" result = fetch(ftr_result)\n",
|
|
" # Fetch number of visited nodes for return\n",
|
|
" node_count_ref = fetch(ftr_node_count)\n",
|
|
" (;path = result.path, distance = result.min_distance_ref[], node_count=node_count_ref[])\n",
|
|
"end"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "706242f2",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"using Distributed\n",
|
|
"using Plots\n",
|
|
"using Statistics\n",
|
|
"\n",
|
|
"# Generate random matrices\n",
|
|
"function rand_symmetric_distance_table(n)\n",
|
|
" threshold = 0.2\n",
|
|
" mincost = 3\n",
|
|
" maxcost = 10\n",
|
|
" infinity = 10000*maxcost\n",
|
|
" C = fill(infinity,n,n)\n",
|
|
" for j in 1:n\n",
|
|
" for i in 1:j\n",
|
|
" if rand() > threshold\n",
|
|
" C[i,j] = rand(mincost:maxcost)\n",
|
|
" C[j,i] = C[i,j]\n",
|
|
" end\n",
|
|
" end\n",
|
|
" C[j,j] = 0\n",
|
|
" end\n",
|
|
" C,infinity\n",
|
|
"end\n",
|
|
"\n",
|
|
"# Sort to get ascending distance weights\n",
|
|
"function sort_neighbors(C)\n",
|
|
" n = size(C,1)\n",
|
|
" map(1:n) do i\n",
|
|
" Ci = C[i,:]\n",
|
|
" cities = sortperm(Ci)\n",
|
|
" distances = Ci[cities]\n",
|
|
" collect(zip(cities,distances))[2:end]\n",
|
|
" end\n",
|
|
"end\n",
|
|
"\n",
|
|
"n_cities = [4, 6, 8, 10]\n",
|
|
"n_rep = 10\n",
|
|
"city = 1\n",
|
|
"node_count_serial = zeros(Union{Missing,Int64},length(n_cities), n_rep)\n",
|
|
"node_count_dist = zeros(Union{Missing,Int64},length(n_cities), n_rep)\n",
|
|
"for (i, n) in enumerate(n_cities)\n",
|
|
" @show n\n",
|
|
" for j in 1:n_rep\n",
|
|
" # Generate random connections matrix\n",
|
|
" C, inf = rand_symmetric_distance_table(n)\n",
|
|
" C = sort_neighbors(C)\n",
|
|
" # Run serial algorithm\n",
|
|
" path, distance, ncount_serial = tsp_serial(C, city)\n",
|
|
" # Check if graph is connected \n",
|
|
" if distance >= inf\n",
|
|
" println(\"The input graph size $n, it $j is not connected\")\n",
|
|
" node_count_serial[i,j] = missing\n",
|
|
" node_count_dist[i,j] = missing\n",
|
|
" else\n",
|
|
" path, distance, ncount_dist = tsp_dist(C, city)\n",
|
|
" node_count_serial[i,j] = ncount_serial\n",
|
|
" node_count_dist[i,j] = ncount_dist\n",
|
|
" end\n",
|
|
" end\n",
|
|
"end\n",
|
|
"\n",
|
|
"# Calculate average and confidence interval\n",
|
|
"search_overhead_perc = (node_count_dist .- node_count_serial)./node_count_serial\n",
|
|
"avg_search_overhead = [mean(skipmissing(search_overhead_perc[i,:])) for i in axes(search_overhead_perc,1)]\n",
|
|
"conf_int = [1.96*std(skipmissing(search_overhead_perc[i,:]))/\n",
|
|
" sqrt(count(!ismissing,search_overhead_perc[i,:])) \n",
|
|
" for i in axes(search_overhead_perc,1)]\n",
|
|
"\n",
|
|
"# Plot\n",
|
|
"plot(n_cities, avg_search_overhead, ribbon=conf_int, markershape=:circle, legend=false)\n",
|
|
"title!(\"Average search overhead (%) and 95%-CI \\nin parallel algorithm\")\n",
|
|
"ylabel!(\"Average % extra nodes visited \\n in parallel algorithm\")\n",
|
|
"xlabel!(\"Number of cities\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "968304a6",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Julia 1.9.1",
|
|
"language": "julia",
|
|
"name": "julia-1.9"
|
|
},
|
|
"language_info": {
|
|
"file_extension": ".jl",
|
|
"mimetype": "application/julia",
|
|
"name": "julia",
|
|
"version": "1.9.1"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|