mirror of
https://github.com/fverdugo/XM_40017.git
synced 2025-11-08 22:24:25 +01:00
176 lines
15 KiB
HTML
176 lines
15 KiB
HTML
<!DOCTYPE html>
|
|
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Solutions · XM_40017</title><meta name="title" content="Solutions · XM_40017"/><meta property="og:title" content="Solutions · XM_40017"/><meta property="twitter:title" content="Solutions · XM_40017"/><meta name="description" content="Documentation for XM_40017."/><meta property="og:description" content="Documentation for XM_40017."/><meta property="twitter:description" content="Documentation for XM_40017."/><meta property="og:url" content="https://fverdugo.github.io/XM_40017/solutions_for_all_notebooks/"/><meta property="twitter:url" content="https://fverdugo.github.io/XM_40017/solutions_for_all_notebooks/"/><link rel="canonical" href="https://fverdugo.github.io/XM_40017/solutions_for_all_notebooks/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../search_index.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-mocha.css" data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script><link href="../assets/favicon.ico" rel="icon" type="image/x-icon"/><script src="../assets/iframeResizer.min.js"></script><link href="../assets/custom.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img src="../assets/logo.png" alt="XM_40017 logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">XM_40017</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../getting_started_with_julia/">Getting started</a></li><li><span class="tocitem">Notebooks</span><ul><li><a class="tocitem" href="../julia_basics/">Julia Basics</a></li><li><a class="tocitem" href="../julia_async/">Asynchronous programming in Julia</a></li><li><a class="tocitem" href="../julia_distributed/">Distributed computing in Julia</a></li><li><a class="tocitem" href="../matrix_matrix/">Matrix-matrix multiplication</a></li><li><a class="tocitem" href="../julia_mpi/">MPI (point-to-point)</a></li><li><a class="tocitem" href="../mpi_collectives/">MPI (collectives)</a></li><li><a class="tocitem" href="../jacobi_method/">Jacobi method</a></li></ul></li><li class="is-active"><a class="tocitem" href>Solutions</a><ul class="internal"><li><a class="tocitem" href="#Julia-Basics"><span>Julia Basics</span></a></li><li><a class="tocitem" href="#Asynchronous-programming-in-Julia"><span>Asynchronous programming in Julia</span></a></li><li><a class="tocitem" href="#Distributed-computing-in-Julia"><span>Distributed computing in Julia</span></a></li><li><a class="tocitem" href="#Matrix-matrix-multiplication"><span>Matrix-matrix multiplication</span></a></li><li><a class="tocitem" href="#MPI-(Point-to-point)"><span>MPI (Point-to-point)</span></a></li><li><a class="tocitem" href="#Jacobi-method"><span>Jacobi method</span></a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Solutions</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Solutions</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/fverdugo/XM_40017/blob/main/docs/src/solutions_for_all_notebooks.md#" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Solutions"><a class="docs-heading-anchor" href="#Solutions">Solutions</a><a id="Solutions-1"></a><a class="docs-heading-anchor-permalink" href="#Solutions" title="Permalink"></a></h1><h2 id="Julia-Basics"><a class="docs-heading-anchor" href="#Julia-Basics">Julia Basics</a><a id="Julia-Basics-1"></a><a class="docs-heading-anchor-permalink" href="#Julia-Basics" title="Permalink"></a></h2><h3 id="Exercise-1"><a class="docs-heading-anchor" href="#Exercise-1">Exercise 1</a><a id="Exercise-1-1"></a><a class="docs-heading-anchor-permalink" href="#Exercise-1" title="Permalink"></a></h3><pre><code class="language-julia hljs">function ex1(a)
|
|
j = 1
|
|
m = a[j]
|
|
for (i,ai) in enumerate(a)
|
|
if m < ai
|
|
m = ai
|
|
j = i
|
|
end
|
|
end
|
|
(m,j)
|
|
end</code></pre><h3 id="Exercise-2"><a class="docs-heading-anchor" href="#Exercise-2">Exercise 2</a><a id="Exercise-2-1"></a><a class="docs-heading-anchor-permalink" href="#Exercise-2" title="Permalink"></a></h3><pre><code class="language-julia hljs">ex2(f,g) = x -> f(x) + g(x)</code></pre><h3 id="Exercise-3"><a class="docs-heading-anchor" href="#Exercise-3">Exercise 3</a><a id="Exercise-3-1"></a><a class="docs-heading-anchor-permalink" href="#Exercise-3" title="Permalink"></a></h3><pre><code class="language-julia hljs">using GLMakie
|
|
max_iters = 100
|
|
n = 1000
|
|
x = LinRange(-1.7,0.7,n)
|
|
y = LinRange(-1.2,1.2,n)
|
|
heatmap(x,y,(i,j)->mandel(i,j,max_iters))</code></pre><h2 id="Asynchronous-programming-in-Julia"><a class="docs-heading-anchor" href="#Asynchronous-programming-in-Julia">Asynchronous programming in Julia</a><a id="Asynchronous-programming-in-Julia-1"></a><a class="docs-heading-anchor-permalink" href="#Asynchronous-programming-in-Julia" title="Permalink"></a></h2><h2 id="Distributed-computing-in-Julia"><a class="docs-heading-anchor" href="#Distributed-computing-in-Julia">Distributed computing in Julia</a><a id="Distributed-computing-in-Julia-1"></a><a class="docs-heading-anchor-permalink" href="#Distributed-computing-in-Julia" title="Permalink"></a></h2><h3 id="Exercise-1-2"><a class="docs-heading-anchor" href="#Exercise-1-2">Exercise 1</a><a class="docs-heading-anchor-permalink" href="#Exercise-1-2" title="Permalink"></a></h3><pre><code class="language-julia hljs">f = () -> Channel{Int}(1)
|
|
chnls = [ RemoteChannel(f,w) for w in workers() ]
|
|
@sync for (iw,w) in enumerate(workers())
|
|
@spawnat w begin
|
|
chnl_snd = chnls[iw]
|
|
if w == 2
|
|
chnl_rcv = chnls[end]
|
|
msg = 2
|
|
println("msg = $msg")
|
|
put!(chnl_snd,msg)
|
|
msg = take!(chnl_rcv)
|
|
println("msg = $msg")
|
|
else
|
|
chnl_rcv = chnls[iw-1]
|
|
msg = take!(chnl_rcv)
|
|
msg += 1
|
|
println("msg = $msg")
|
|
put!(chnl_snd,msg)
|
|
end
|
|
end
|
|
end</code></pre><p>This is another possible solution.</p><pre><code class="language-julia hljs">@everywhere function work(msg)
|
|
println("msg = $msg")
|
|
if myid() != nprocs()
|
|
next = myid() + 1
|
|
@fetchfrom next work(msg+1)
|
|
else
|
|
@fetchfrom 2 println("msg = $msg")
|
|
end
|
|
end
|
|
msg = 2
|
|
@fetchfrom 2 work(msg)</code></pre><h2 id="Matrix-matrix-multiplication"><a class="docs-heading-anchor" href="#Matrix-matrix-multiplication">Matrix-matrix multiplication</a><a id="Matrix-matrix-multiplication-1"></a><a class="docs-heading-anchor-permalink" href="#Matrix-matrix-multiplication" title="Permalink"></a></h2><h3 id="Exercise-1-3"><a class="docs-heading-anchor" href="#Exercise-1-3">Exercise 1</a><a class="docs-heading-anchor-permalink" href="#Exercise-1-3" title="Permalink"></a></h3><pre><code class="language-julia hljs">function matmul_dist_3!(C,A,B)
|
|
m = size(C,1)
|
|
n = size(C,2)
|
|
l = size(A,2)
|
|
@assert size(A,1) == m
|
|
@assert size(B,2) == n
|
|
@assert size(B,1) == l
|
|
@assert mod(m,nworkers()) == 0
|
|
nrows_w = div(m,nworkers())
|
|
@sync for (iw,w) in enumerate(workers())
|
|
lb = 1 + (iw-1)*nrows_w
|
|
ub = iw*nrows_w
|
|
A_w = A[lb:ub,:]
|
|
ftr = @spawnat w begin
|
|
C_w = similar(A_w)
|
|
matmul_seq!(C_w,A_w,B)
|
|
C_w
|
|
end
|
|
@async C[lb:ub,:] = fetch(ftr)
|
|
end
|
|
C
|
|
end
|
|
|
|
@everywhere function matmul_seq!(C,A,B)
|
|
m = size(C,1)
|
|
n = size(C,2)
|
|
l = size(A,2)
|
|
@assert size(A,1) == m
|
|
@assert size(B,2) == n
|
|
@assert size(B,1) == l
|
|
z = zero(eltype(C))
|
|
for j in 1:n
|
|
for i in 1:m
|
|
Cij = z
|
|
for k in 1:l
|
|
@inbounds Cij = Cij + A[i,k]*B[k,j]
|
|
end
|
|
C[i,j] = Cij
|
|
end
|
|
end
|
|
C
|
|
end</code></pre><h2 id="MPI-(Point-to-point)"><a class="docs-heading-anchor" href="#MPI-(Point-to-point)">MPI (Point-to-point)</a><a id="MPI-(Point-to-point)-1"></a><a class="docs-heading-anchor-permalink" href="#MPI-(Point-to-point)" title="Permalink"></a></h2><h3 id="Exercise-2-2"><a class="docs-heading-anchor" href="#Exercise-2-2">Exercise 2</a><a class="docs-heading-anchor-permalink" href="#Exercise-2-2" title="Permalink"></a></h3><pre><code class="language-julia hljs">using MPI
|
|
MPI.Init()
|
|
comm = MPI.COMM_WORLD
|
|
rank = MPI.Comm_rank(comm)
|
|
nranks = MPI.Comm_size(comm)
|
|
buffer = Ref(0)
|
|
if rank == 0
|
|
msg = 2
|
|
buffer[] = msg
|
|
println("msg = $(buffer[])")
|
|
MPI.Send(buffer,comm;dest=rank+1,tag=0)
|
|
MPI.Recv!(buffer,comm;source=nranks-1,tag=0)
|
|
println("msg = $(buffer[])")
|
|
else
|
|
dest = if (rank != nranks-1)
|
|
rank+1
|
|
else
|
|
0
|
|
end
|
|
MPI.Recv!(buffer,comm;source=rank-1,tag=0)
|
|
buffer[] += 1
|
|
println("msg = $(buffer[])")
|
|
MPI.Send(buffer,comm;dest,tag=0)
|
|
end</code></pre><h2 id="Jacobi-method"><a class="docs-heading-anchor" href="#Jacobi-method">Jacobi method</a><a id="Jacobi-method-1"></a><a class="docs-heading-anchor-permalink" href="#Jacobi-method" title="Permalink"></a></h2><h3 id="Exercise-1-4"><a class="docs-heading-anchor" href="#Exercise-1-4">Exercise 1</a><a class="docs-heading-anchor-permalink" href="#Exercise-1-4" title="Permalink"></a></h3><pre><code class="language-julia hljs">function jacobi_mpi(n,niters)
|
|
comm = MPI.COMM_WORLD
|
|
nranks = MPI.Comm_size(comm)
|
|
rank = MPI.Comm_rank(comm)
|
|
if mod(n,nranks) != 0
|
|
println("n must be a multiple of nranks")
|
|
MPI.Abort(comm,1)
|
|
end
|
|
load = div(n,nranks)
|
|
u = zeros(load+2)
|
|
u[1] = -1
|
|
u[end] = 1
|
|
u_new = copy(u)
|
|
for t in 1:niters
|
|
reqs = MPI.Request[]
|
|
if rank != 0
|
|
neig_rank = rank-1
|
|
req = MPI.Isend(view(u,2:2),comm,dest=neig_rank,tag=0)
|
|
push!(reqs,req)
|
|
req = MPI.Irecv!(view(u,1:1),comm,source=neig_rank,tag=0)
|
|
push!(reqs,req)
|
|
end
|
|
if rank != (nranks-1)
|
|
neig_rank = rank+1
|
|
s = load+1
|
|
r = load+2
|
|
req = MPI.Isend(view(u,s:s),comm,dest=neig_rank,tag=0)
|
|
push!(reqs,req)
|
|
req = MPI.Irecv!(view(u,r:r),comm,source=neig_rank,tag=0)
|
|
push!(reqs,req)
|
|
end
|
|
for i in 3:load
|
|
u_new[i] = 0.5*(u[i-1]+u[i+1])
|
|
end
|
|
MPI.Waitall(reqs)
|
|
for i in (2,load+1)
|
|
u_new[i] = 0.5*(u[i-1]+u[i+1])
|
|
end
|
|
u, u_new = u_new, u
|
|
|
|
end
|
|
# Gather the results
|
|
if rank !=0
|
|
lb = 2
|
|
ub = load+1
|
|
MPI.Send(view(u,lb:ub),comm,dest=0)
|
|
u_all = zeros(0) # This will nevel be used
|
|
else
|
|
u_all = zeros(n+2)
|
|
# Set boundary
|
|
u_all[1] = -1
|
|
u_all[end] = 1
|
|
# Set data for rank 0
|
|
lb = 2
|
|
ub = load+1
|
|
u_all[lb:ub] = view(u,lb:ub)
|
|
# Set data for other ranks
|
|
for other_rank in 1:(nranks-1)
|
|
lb += load
|
|
ub += load
|
|
MPI.Recv!(view(u_all,lb:ub),comm;source=other_rank)
|
|
end
|
|
end
|
|
return u_all
|
|
end</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../jacobi_method/">« Jacobi method</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 9 September 2024 15:08">Monday 9 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|