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{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-25T18:55:28","documenter_version":"1.1.2"}}
{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-27T23:27:13","documenter_version":"1.1.2"}}
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# s, squash = use commit, but meld into previous commit
#
# If you remove a line here THAT COMMIT WILL BE LOST.
# However, if you remove everything, the rebase will be aborted.</code></pre><p>Then in the next screen that appears, we can just delete all messages that we do not want to show in the commit. After this is done and we are back to the console, we have to force push. We need to force push because we rewrote the local commit history.</p><pre><code class="nohighlight hljs">$ git push -uf origin &lt;name_of_local_branch&gt;</code></pre><p>You can find more information about squashing <a href="https://github.com/edx/edx-platform/wiki/How-to-Rebase-a-Pull-Request#squash-your-changes">here</a>.</p><h3 id="Unit-testing"><a class="docs-heading-anchor" href="#Unit-testing">Unit testing</a><a id="Unit-testing-1"></a><a class="docs-heading-anchor-permalink" href="#Unit-testing" title="Permalink"></a></h3><p>Currently a number of checks are run per commit for a given PR.</p><ul><li><code>JuliaFormatter</code> checks if the PR is formatted with <code>.dev/climaformat.jl</code>.</li><li><code>Documentation</code> rebuilds the documentation for the PR and checks if the docs are consistent and generate valid output.</li><li><code>Unit Tests</code> run subsets of the unit tests defined in <code>tests/</code>, using <code>Pkg.test()</code>. The tests are run in parallel to ensure that they finish in a reasonable time. The tests only run the latest commit for a PR, branch and will kill any stale jobs on push. These tests are only run on linux (Ubuntu LTS).</li></ul><p>Unit tests are run against every new commit for a given PR, the status of the unit-tests are not checked during the merge process but act as a sanity check for developers and reviewers. Depending on the content changed in the PR, some CI checks that are not necessary will be skipped. For example doc only changes do not require the unit tests to be run.</p><h3 id="The-merge-process"><a class="docs-heading-anchor" href="#The-merge-process">The merge process</a><a id="The-merge-process-1"></a><a class="docs-heading-anchor-permalink" href="#The-merge-process" title="Permalink"></a></h3><p>We use <a href="https://bors.tech/"><code>bors</code></a> to manage merging PR&#39;s in the the <code>EnsembleKalmanProcesses</code> repo. If you&#39;re a collaborator and have the necessary permissions, you can type <code>bors try</code> in a comment on a PR to have integration test suite run on that PR, or <code>bors r+</code> to try and merge the code. Bors ensures that all integration tests for a given PR always pass before merging into <code>main</code>. The integration tests currently run example cases in <code>examples/</code>. Any breaking changes will need to also update the <code>examples/</code>, else bors will fail.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../API/Localizers/">« Localizers</a><a class="docs-footer-nextpage" href="../glossary/">Glossary »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Wednesday 25 October 2023 18:55">Wednesday 25 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
# However, if you remove everything, the rebase will be aborted.</code></pre><p>Then in the next screen that appears, we can just delete all messages that we do not want to show in the commit. After this is done and we are back to the console, we have to force push. We need to force push because we rewrote the local commit history.</p><pre><code class="nohighlight hljs">$ git push -uf origin &lt;name_of_local_branch&gt;</code></pre><p>You can find more information about squashing <a href="https://github.com/edx/edx-platform/wiki/How-to-Rebase-a-Pull-Request#squash-your-changes">here</a>.</p><h3 id="Unit-testing"><a class="docs-heading-anchor" href="#Unit-testing">Unit testing</a><a id="Unit-testing-1"></a><a class="docs-heading-anchor-permalink" href="#Unit-testing" title="Permalink"></a></h3><p>Currently a number of checks are run per commit for a given PR.</p><ul><li><code>JuliaFormatter</code> checks if the PR is formatted with <code>.dev/climaformat.jl</code>.</li><li><code>Documentation</code> rebuilds the documentation for the PR and checks if the docs are consistent and generate valid output.</li><li><code>Unit Tests</code> run subsets of the unit tests defined in <code>tests/</code>, using <code>Pkg.test()</code>. The tests are run in parallel to ensure that they finish in a reasonable time. The tests only run the latest commit for a PR, branch and will kill any stale jobs on push. These tests are only run on linux (Ubuntu LTS).</li></ul><p>Unit tests are run against every new commit for a given PR, the status of the unit-tests are not checked during the merge process but act as a sanity check for developers and reviewers. Depending on the content changed in the PR, some CI checks that are not necessary will be skipped. For example doc only changes do not require the unit tests to be run.</p><h3 id="The-merge-process"><a class="docs-heading-anchor" href="#The-merge-process">The merge process</a><a id="The-merge-process-1"></a><a class="docs-heading-anchor-permalink" href="#The-merge-process" title="Permalink"></a></h3><p>We use <a href="https://bors.tech/"><code>bors</code></a> to manage merging PR&#39;s in the the <code>EnsembleKalmanProcesses</code> repo. If you&#39;re a collaborator and have the necessary permissions, you can type <code>bors try</code> in a comment on a PR to have integration test suite run on that PR, or <code>bors r+</code> to try and merge the code. Bors ensures that all integration tests for a given PR always pass before merging into <code>main</code>. The integration tests currently run example cases in <code>examples/</code>. Any breaking changes will need to also update the <code>examples/</code>, else bors will fail.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../API/Localizers/">« Localizers</a><a class="docs-footer-nextpage" href="../glossary/">Glossary »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Friday 27 October 2023 23:27">Friday 27 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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initial_ensemble = construct_initial_ensemble(prior, J) # Initialize ensemble from prior

ekiobj = EnsembleKalmanProcess(initial_ensemble, y, obs_noise_cov,
TransformInversion(inv(obs_noise_cov)))</code></pre><p>The rest of the inversion process is the same as for regular EKI.</p><h1 id="seki"><a class="docs-heading-anchor" href="#seki">Sparsity-Inducing Ensemble Kalman Inversion</a><a id="seki-1"></a><a class="docs-heading-anchor-permalink" href="#seki" title="Permalink"></a></h1><p>We include Sparsity-inducing Ensemble Kalman Inversion (SEKI) to add approximate <span>$L^0$</span> and <span>$L^1$</span> penalization to the EKI (<a href="https://doi.org/10.48550/arXiv.2007.06175">Schneider, Stuart, Wu, 2020</a>).</p><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p>The algorithm suffers from robustness issues, and therefore we urge caution in using the tool</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../examples/template_example/">« Template</a><a class="docs-footer-nextpage" href="../ensemble_kalman_sampler/">Ensemble Kalman Sampler »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Wednesday 25 October 2023 18:55">Wednesday 25 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
TransformInversion(inv(obs_noise_cov)))</code></pre><p>The rest of the inversion process is the same as for regular EKI.</p><h1 id="seki"><a class="docs-heading-anchor" href="#seki">Sparsity-Inducing Ensemble Kalman Inversion</a><a id="seki-1"></a><a class="docs-heading-anchor-permalink" href="#seki" title="Permalink"></a></h1><p>We include Sparsity-inducing Ensemble Kalman Inversion (SEKI) to add approximate <span>$L^0$</span> and <span>$L^1$</span> penalization to the EKI (<a href="https://doi.org/10.48550/arXiv.2007.06175">Schneider, Stuart, Wu, 2020</a>).</p><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p>The algorithm suffers from robustness issues, and therefore we urge caution in using the tool</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../examples/template_example/">« Template</a><a class="docs-footer-nextpage" href="../ensemble_kalman_sampler/">Ensemble Kalman Sampler »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Friday 27 October 2023 23:27">Friday 27 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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Γ_post = get_u_cov_final(eksobj)</code></pre><p>To obtain samples of this approximate posterior in the constrained space, we first sample the distribution, then transform using the constraints contained within the prior </p><pre><code class="language-julia hljs">using Random, Distributions

ten_post_samples = rand(MvNormal(θ_post,Γ_post), 10)
ten_post_samples_phys = transform_unconstrained_to_constrained(prior, ten_post_samples) # the optimal physical parameter value</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../ensemble_kalman_inversion/">« Ensemble Kalman Inversion</a><a class="docs-footer-nextpage" href="../unscented_kalman_inversion/">Unscented Kalman Inversion »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Wednesday 25 October 2023 18:55">Wednesday 25 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
ten_post_samples_phys = transform_unconstrained_to_constrained(prior, ten_post_samples) # the optimal physical parameter value</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../ensemble_kalman_inversion/">« Ensemble Kalman Inversion</a><a class="docs-footer-nextpage" href="../unscented_kalman_inversion/">Unscented Kalman Inversion »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Friday 27 October 2023 23:27">Friday 27 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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θ = load(&quot;ekp_clima.jld&quot;)[&quot;ekp_u&quot;]
println(typeof(θ)) # Array{Array{Float64,2},1}, outer dimension is N_iter, inner Array{Float64,2} of size = (J, p)</code></pre><p>The optimal parameter vector determined by the ensemble Kalman inversion is the ensemble mean of the particles after the last iteration. Following the previous script,</p><pre><code class="language-julia hljs">using Statistics

θ_opt = mean(θ[end], dims=1)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../sinusoid_example_toml/">« TOML interface</a><a class="docs-footer-nextpage" href="../template_example/">Template »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Wednesday 25 October 2023 18:55">Wednesday 25 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
θ_opt = mean(θ[end], dims=1)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../sinusoid_example_toml/">« TOML interface</a><a class="docs-footer-nextpage" href="../template_example/">Template »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Friday 27 October 2023 23:27">Friday 27 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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