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Documenter.jl
@@ -212,67 +212,98 @@ end</code></pre><p>This other solution uses a column partition instead of a row
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MPI.Gather!(myC,C,comm;root)
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C
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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-1-6"><a class="docs-heading-anchor" href="#Exercise-1-6">Exercise 1</a><a class="docs-heading-anchor-permalink" href="#Exercise-1-6" title="Permalink"></a></h3><pre><code class="language-julia hljs">function jacobi_mpi(n,niters)
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comm = MPI.COMM_WORLD
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nranks = MPI.Comm_size(comm)
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u, u_new = init(n,comm)
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load = length(u)-2
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rank = MPI.Comm_rank(comm)
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if mod(n,nranks) != 0
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println("n must be a multiple of nranks")
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MPI.Abort(comm,1)
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end
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load = div(n,nranks)
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u = zeros(load+2)
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u[1] = -1
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u[end] = 1
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u_new = copy(u)
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nranks = MPI.Comm_size(comm)
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nreqs = 2*((rank != 0) + (rank != (nranks-1)))
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reqs = MPI.MultiRequest(nreqs)
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for t in 1:niters
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reqs = MPI.Request[]
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ireq = 0
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if rank != 0
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neig_rank = rank-1
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req = MPI.Isend(view(u,2:2),comm,dest=neig_rank,tag=0)
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push!(reqs,req)
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req = MPI.Irecv!(view(u,1:1),comm,source=neig_rank,tag=0)
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push!(reqs,req)
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u_snd = view(u,2:2)
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u_rcv = view(u,1:1)
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dest = neig_rank
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source = neig_rank
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ireq += 1
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MPI.Isend(u_snd,comm,reqs[ireq];dest)
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ireq += 1
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MPI.Irecv!(u_rcv,comm,reqs[ireq];source)
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end
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if rank != (nranks-1)
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neig_rank = rank+1
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s = load+1
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r = load+2
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req = MPI.Isend(view(u,s:s),comm,dest=neig_rank,tag=0)
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push!(reqs,req)
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req = MPI.Irecv!(view(u,r:r),comm,source=neig_rank,tag=0)
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push!(reqs,req)
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u_snd = view(u,(load+1):(load+1))
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u_rcv = view(u,(load+2):(load+2))
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dest = neig_rank
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source = neig_rank
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ireq += 1
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MPI.Isend(u_snd,comm,reqs[ireq];dest)
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ireq += 1
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MPI.Irecv!(u_rcv,comm,reqs[ireq];source)
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end
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# Upload interior cells
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for i in 3:load
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u_new[i] = 0.5*(u[i-1]+u[i+1])
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end
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# Wait for the communications to finish
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MPI.Waitall(reqs)
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# Update boundaries
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for i in (2,load+1)
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u_new[i] = 0.5*(u[i-1]+u[i+1])
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end
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u, u_new = u_new, u
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end
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# Gather the results
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if rank !=0
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lb = 2
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ub = load+1
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MPI.Send(view(u,lb:ub),comm,dest=0)
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u_all = zeros(0) # This will nevel be used
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else
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u_all = zeros(n+2)
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# Set boundary
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u_all[1] = -1
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u_all[end] = 1
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# Set data for rank 0
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lb = 2
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ub = load+1
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u_all[lb:ub] = view(u,lb:ub)
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# Set data for other ranks
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for other_rank in 1:(nranks-1)
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lb += load
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ub += load
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MPI.Recv!(view(u_all,lb:ub),comm;source=other_rank)
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return u
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end</code></pre><h3 id="Exercise-2-3"><a class="docs-heading-anchor" href="#Exercise-2-3">Exercise 2</a><a class="docs-heading-anchor-permalink" href="#Exercise-2-3" title="Permalink"></a></h3><pre><code class="language-julia hljs">function jacobi_mpi(n,niters,tol,comm) # new tol arg
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u, u_new = init(n,comm)
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load = length(u)-2
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rank = MPI.Comm_rank(comm)
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nranks = MPI.Comm_size(comm)
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nreqs = 2*((rank != 0) + (rank != (nranks-1)))
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reqs = MPI.MultiRequest(nreqs)
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for t in 1:niters
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ireq = 0
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if rank != 0
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neig_rank = rank-1
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u_snd = view(u,2:2)
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u_rcv = view(u,1:1)
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dest = neig_rank
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source = neig_rank
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ireq += 1
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MPI.Isend(u_snd,comm,reqs[ireq];dest)
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ireq += 1
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MPI.Irecv!(u_rcv,comm,reqs[ireq];source)
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end
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if rank != (nranks-1)
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neig_rank = rank+1
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u_snd = view(u,(load+1):(load+1))
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u_rcv = view(u,(load+2):(load+2))
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dest = neig_rank
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source = neig_rank
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ireq += 1
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MPI.Isend(u_snd,comm,reqs[ireq];dest)
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ireq += 1
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MPI.Irecv!(u_rcv,comm,reqs[ireq];source)
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end
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MPI.Waitall(reqs)
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# Compute the max diff in the current
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# rank while doing the local update
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mydiff = 0.0
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for i in 2:load+1
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u_new[i] = 0.5*(u[i-1]+u[i+1])
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diff_i = abs(u_new[i] - u[i])
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mydiff = max(mydiff,diff_i)
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end
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# Now we need to find the global diff
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diff_ref = Ref(mydiff)
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MPI.Allreduce!(diff_ref,max,comm)
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diff = diff_ref[]
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# If global diff below tol, stop!
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if diff < tol
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return u_new
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end
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u, u_new = u_new, u
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end
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return u_all
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end</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tsp/">« Traveling salesperson problem</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 23 September 2024 12:01">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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return u
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end</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tsp/">« Traveling salesperson problem</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 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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