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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-05T16:18:15","documenter_version":"1.2.1"}}
{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-05T16:50:14","documenter_version":"1.2.1"}}
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1024 9.6e-13 1.1e-12 3.4e-15 4.8e-15 1.3e-03 1.4e-03
2048 1.0e-12 1.2e-12 5.1e-15 4.5e-15 7.2e-03 6.8e-03
4096 2.1e-12 2.1e-12 6.6e-15 7.5e-15 2.4e-02 2.5e-02
8192 3.3e-12 3.2e-12 9.0e-15 1.0e-14 8.4e-02 8.9e-02 </code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Termination/">« Terminating the while loop</a><a class="docs-footer-nextpage" href="../../functions/MPArray/">MPArray: constructor »</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 1.2.1 on <span class="colophon-date" title="Tuesday 5 December 2023 16:18">Tuesday 5 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
8192 3.3e-12 3.2e-12 9.0e-15 1.0e-14 8.4e-02 8.9e-02 </code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Termination/">« Terminating the while loop</a><a class="docs-footer-nextpage" href="../../functions/MPArray/">MPArray: constructor »</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 1.2.1 on <span class="colophon-date" title="Tuesday 5 December 2023 16:50">Tuesday 5 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2 changes: 1 addition & 1 deletion dev/Details/Stats/index.html
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1.21892e-04
5.25805e-11
2.56462e-14
1.33227e-15</code></pre><p>As you can see, IR does well for this problem. The package uses an initial iterate of <span>$x = 0$</span> and so the initial residual is simply <span>$r = b$</span> and the first entry in the residual history is <span>$|| b ||_\infty$</span>. The iteration terminates successfully after four matrix-vector products.</p><p>There are more examples for this in [<a href="../../References/#ctk:mparraysdocs">2</a>].</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../functions/mpglu/">« mpglu: Combine MPGArray construction and factorization</a><a class="docs-footer-nextpage" href="../../functions/mpgeslir/">mpgeslir: IR solver »</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 1.2.1 on <span class="colophon-date" title="Tuesday 5 December 2023 16:18">Tuesday 5 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
1.33227e-15</code></pre><p>As you can see, IR does well for this problem. The package uses an initial iterate of <span>$x = 0$</span> and so the initial residual is simply <span>$r = b$</span> and the first entry in the residual history is <span>$|| b ||_\infty$</span>. The iteration terminates successfully after four matrix-vector products.</p><p>There are more examples for this in [<a href="../../References/#ctk:mparraysdocs">2</a>].</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../functions/mpglu/">« mpglu: Combine MPGArray construction and factorization</a><a class="docs-footer-nextpage" href="../../functions/mpgeslir/">mpgeslir: IR solver »</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 1.2.1 on <span class="colophon-date" title="Tuesday 5 December 2023 16:50">Tuesday 5 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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0.2875508 0.004160166

julia&gt; println(norm(b-A*z,Inf)/norm(b,Inf),&quot; &quot;,norm(b-A*y,Inf)/norm(b,Inf))
0.0012593127 1.4025759e-5</code></pre><p>So, the relative error and relative residual norm for GMRES-IR is much smaller than that for IR.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../Details/Termination/">Terminating the while loop »</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 1.2.1 on <span class="colophon-date" title="Tuesday 5 December 2023 16:18">Tuesday 5 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
0.0012593127 1.4025759e-5</code></pre><p>So, the relative error and relative residual norm for GMRES-IR is much smaller than that for IR.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../Details/Termination/">Terminating the while loop »</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 1.2.1 on <span class="colophon-date" title="Tuesday 5 December 2023 16:50">Tuesday 5 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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2 changes: 1 addition & 1 deletion dev/functions/MPArray/index.html
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AL::Array{TL,2}
residual::Vector{TH}
onthefly::Bool
end</code></pre><p>The constructor just builds an MPArray with TH=Float64. Set TL=Float16 to get double/half IR.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/ctkelley/MultiPrecisionArrays.jl/blob/ceef3b9758096cfe11a766b8e27f98609fce4a28/src/Structs4MP/MPArray.jl#L1-L21">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="MultiPrecisionArrays.MPArray-Tuple{Matrix{Float32}}" href="#MultiPrecisionArrays.MPArray-Tuple{Matrix{Float32}}"><code>MultiPrecisionArrays.MPArray</code></a> — <span class="docstring-category">Method</span></header><section><div><p>MPArray(AH::Array{Float32,2}; TL = Float16, onthefly=true) Default single precision constructor for MPArray with TL=Float16</p><p>If your high precision array is single, then your low precision array is half (Duh!). </p><p>We do the triangular solves with on-the-fly interprecision transfer in this case because the bit of extra accuracy makes a difference and, at least for now, on-the-fly interprecision transfers are cheaper.</p><p>Data structures etc are the same as in the double-single/half case, but you don&#39;t have the option to go lower than half.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/ctkelley/MultiPrecisionArrays.jl/blob/ceef3b9758096cfe11a766b8e27f98609fce4a28/src/Structs4MP/MPArray.jl#L31-L46">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../Details/Interprecision_1/">« Interprecision Transfers: Part I</a><a class="docs-footer-nextpage" href="../MPGArray/">MPGArray: constructor »</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 1.2.1 on <span class="colophon-date" title="Tuesday 5 December 2023 16:18">Tuesday 5 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
end</code></pre><p>The constructor just builds an MPArray with TH=Float64. Set TL=Float16 to get double/half IR.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/ctkelley/MultiPrecisionArrays.jl/blob/d768d09fb66afa5500ee13ebed1dc5226eb554e4/src/Structs4MP/MPArray.jl#L1-L21">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="MultiPrecisionArrays.MPArray-Tuple{Matrix{Float32}}" href="#MultiPrecisionArrays.MPArray-Tuple{Matrix{Float32}}"><code>MultiPrecisionArrays.MPArray</code></a> — <span class="docstring-category">Method</span></header><section><div><p>MPArray(AH::Array{Float32,2}; TL = Float16, onthefly=true) Default single precision constructor for MPArray with TL=Float16</p><p>If your high precision array is single, then your low precision array is half (Duh!). </p><p>We do the triangular solves with on-the-fly interprecision transfer in this case because the bit of extra accuracy makes a difference and, at least for now, on-the-fly interprecision transfers are cheaper.</p><p>Data structures etc are the same as in the double-single/half case, but you don&#39;t have the option to go lower than half.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/ctkelley/MultiPrecisionArrays.jl/blob/d768d09fb66afa5500ee13ebed1dc5226eb554e4/src/Structs4MP/MPArray.jl#L31-L46">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../Details/Interprecision_1/">« Interprecision Transfers: Part I</a><a class="docs-footer-nextpage" href="../MPGArray/">MPGArray: constructor »</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 1.2.1 on <span class="colophon-date" title="Tuesday 5 December 2023 16:50">Tuesday 5 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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