build based on eef9b49

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-03-13T23:00:23","documenter_version":"1.3.0"}}
+{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-03-26T17:29:56","documenter_version":"1.3.0"}}

dev/index.html

@@ -14,4 +14,4 @@
 using Plots; gr()
 plot(range(inf(a), stop=sup(a), length=1000), x->f(x), label="f(x)", lw=2, xaxis="x", yaxis="f(x)")
 plot!(ftm6, label="6th order")
-plot!(ftm7, label=&quot;7th order&quot;)</code></pre><p><img src="assets/intro_plot.png" alt="intro_plot"/></p><h3 id="Authors"><a class="docs-heading-anchor" href="#Authors">Authors</a><a id="Authors-1"></a><a class="docs-heading-anchor-permalink" href="#Authors" title="Permalink"></a></h3><ul><li><a href="http://www.cicc.unam.mx/~benet/">Luis Benet</a>, Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México (UNAM)</li><li><a href="http://sistemas.fciencias.unam.mx/~dsanders">David P. Sanders</a>, Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM)</li></ul><h2 id="Bibliography"><a class="docs-heading-anchor" href="#Bibliography">Bibliography</a><a id="Bibliography-1"></a><a class="docs-heading-anchor-permalink" href="#Bibliography" title="Permalink"></a></h2><ul><li><a href="https://tel.archives-ouvertes.fr/tel-00657843"><em>Rigorous Polynomial Approximations and Applications</em></a>, Mioara Maria Joldes, Ecole normale supérieure de lyon - ENS LYON (2011)</li></ul><h2 id="Acknowledgements"><a class="docs-heading-anchor" href="#Acknowledgements">Acknowledgements</a><a id="Acknowledgements-1"></a><a class="docs-heading-anchor-permalink" href="#Acknowledgements" title="Permalink"></a></h2><p>Financial support is acknowledged from DGAPA-UNAM PAPIIT grants IN-117117, IG-100616 and IG-100819. DPS acknowledges support through a <em>Cátedra Marcos Moshinsky</em> (2018).</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="range_bounding/">Range bounding »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 13 March 2024 23:00">Wednesday 13 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+plot!(ftm7, label=&quot;7th order&quot;)</code></pre><p><img src="assets/intro_plot.png" alt="intro_plot"/></p><h3 id="Authors"><a class="docs-heading-anchor" href="#Authors">Authors</a><a id="Authors-1"></a><a class="docs-heading-anchor-permalink" href="#Authors" title="Permalink"></a></h3><ul><li><a href="http://www.cicc.unam.mx/~benet/">Luis Benet</a>, Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México (UNAM)</li><li><a href="http://sistemas.fciencias.unam.mx/~dsanders">David P. Sanders</a>, Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM)</li></ul><h2 id="Bibliography"><a class="docs-heading-anchor" href="#Bibliography">Bibliography</a><a id="Bibliography-1"></a><a class="docs-heading-anchor-permalink" href="#Bibliography" title="Permalink"></a></h2><ul><li><a href="https://tel.archives-ouvertes.fr/tel-00657843"><em>Rigorous Polynomial Approximations and Applications</em></a>, Mioara Maria Joldes, Ecole normale supérieure de lyon - ENS LYON (2011)</li></ul><h2 id="Acknowledgements"><a class="docs-heading-anchor" href="#Acknowledgements">Acknowledgements</a><a id="Acknowledgements-1"></a><a class="docs-heading-anchor-permalink" href="#Acknowledgements" title="Permalink"></a></h2><p>Financial support is acknowledged from DGAPA-UNAM PAPIIT grants IN-117117, IG-100616 and IG-100819. DPS acknowledges support through a <em>Cátedra Marcos Moshinsky</em> (2018).</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="range_bounding/">Range bounding »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 26 March 2024 17:29">Tuesday 26 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/range_bounding/index.html

@@ -27,4 +27,4 @@
 
 R16 = reduce(hull, evaluate.(s, mince(D, 16)))
 plot!(fig, Dt, t -> sup(R16), lab="N = 16", c=:orange, style=:dash)
-plot!(fig, Dt, t -&gt; inf(R16), c=:orange, lab=&quot;&quot;, style=:dash)</code></pre><img src="c80d881f.svg" alt="Example block output"/><h2 id="Internal-representation"><a class="docs-heading-anchor" href="#Internal-representation">Internal representation</a><a id="Internal-representation-1"></a><a class="docs-heading-anchor-permalink" href="#Internal-representation" title="Permalink"></a></h2><p>Consider again the Taylor model variable from the <a href="#Taylor-model-variables-and-range-bounding">Taylor model variables and range bounding</a> example.</p><pre><code class="language-julia hljs">t</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi"> [1, 1] t + [0, 0]</code></pre><p>Such constructor is an alias for</p><pre><code class="language-julia hljs">    TaylorModel1(x0 + Taylor1(eltype(x0), ord), zero(dom), interval(x0), dom)</code></pre><p>Taylor models in one variable are internally represented using four fields: a Taylor series (<code>pol</code>) in one variable that holds the polynomial approximation of order <code>ord</code>; the interval remainder (<code>rem</code>); the expansion point (<code>x0</code>), and the interval domain of interest (<code>dom</code>). Getter functions are defined for each of these fields:</p><pre><code class="language-julia hljs">get_order(t)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">3</code></pre><pre><code class="language-julia hljs">remainder(t)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">[0, 0]</code></pre><pre><code class="language-julia hljs">polynomial(t)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi"> [1, 1] t + 𝒪(t⁴)</code></pre><pre><code class="language-julia hljs">domain(t)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">[-0.5, 0.5]</code></pre><pre><code class="language-julia hljs">expansion_point(t)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">[0, 0]</code></pre><p>Finally, note that the Taylor model type has two parameters, <code>T</code> and <code>S</code>. The first parameter, <code>T</code>, refers to the numeric type of the coefficients of the polynomial, in this case an interval with double precision floating point values (<code>Interval{Float64}</code>). The second parameter, <code>S</code>, refers to the numeric type of the interval that holds the remainder, expansion point and domain of interest (in this case <code>Float64</code>).</p><pre><code class="language-julia hljs">typeof(t)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">TaylorModel1{Interval{Float64}, Float64}</code></pre><p>If we had defined the expansion point using <code>0.0</code> instead of <code>interval(0)</code>, the coefficients of (the polynomial part of) this Taylor model variable would be floats instead of intervals.</p><pre><code class="language-julia hljs">z = TaylorModel1(3, 0.0, -0.5..0.5)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi"> 1.0 t + [0, 0]</code></pre><pre><code class="language-julia hljs">typeof(z)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">TaylorModel1{Float64, Float64}</code></pre><pre><code class="language-julia hljs">polynomial(z)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi"> 1.0 t + 𝒪(t⁴)</code></pre><p>Using a polynomial with interval coefficients guarantees that all arithmetic operations involving <code>t</code> are conservative, or rigorous, with respect to floating point arithmetic.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../api/">API »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 13 March 2024 23:00">Wednesday 13 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+plot!(fig, Dt, t -&gt; inf(R16), c=:orange, lab=&quot;&quot;, style=:dash)</code></pre><img src="7be32035.svg" alt="Example block output"/><h2 id="Internal-representation"><a class="docs-heading-anchor" href="#Internal-representation">Internal representation</a><a id="Internal-representation-1"></a><a class="docs-heading-anchor-permalink" href="#Internal-representation" title="Permalink"></a></h2><p>Consider again the Taylor model variable from the <a href="#Taylor-model-variables-and-range-bounding">Taylor model variables and range bounding</a> example.</p><pre><code class="language-julia hljs">t</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi"> [1, 1] t + [0, 0]</code></pre><p>Such constructor is an alias for</p><pre><code class="language-julia hljs">    TaylorModel1(x0 + Taylor1(eltype(x0), ord), zero(dom), interval(x0), dom)</code></pre><p>Taylor models in one variable are internally represented using four fields: a Taylor series (<code>pol</code>) in one variable that holds the polynomial approximation of order <code>ord</code>; the interval remainder (<code>rem</code>); the expansion point (<code>x0</code>), and the interval domain of interest (<code>dom</code>). Getter functions are defined for each of these fields:</p><pre><code class="language-julia hljs">get_order(t)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">3</code></pre><pre><code class="language-julia hljs">remainder(t)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">[0, 0]</code></pre><pre><code class="language-julia hljs">polynomial(t)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi"> [1, 1] t + 𝒪(t⁴)</code></pre><pre><code class="language-julia hljs">domain(t)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">[-0.5, 0.5]</code></pre><pre><code class="language-julia hljs">expansion_point(t)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">[0, 0]</code></pre><p>Finally, note that the Taylor model type has two parameters, <code>T</code> and <code>S</code>. The first parameter, <code>T</code>, refers to the numeric type of the coefficients of the polynomial, in this case an interval with double precision floating point values (<code>Interval{Float64}</code>). The second parameter, <code>S</code>, refers to the numeric type of the interval that holds the remainder, expansion point and domain of interest (in this case <code>Float64</code>).</p><pre><code class="language-julia hljs">typeof(t)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">TaylorModel1{Interval{Float64}, Float64}</code></pre><p>If we had defined the expansion point using <code>0.0</code> instead of <code>interval(0)</code>, the coefficients of (the polynomial part of) this Taylor model variable would be floats instead of intervals.</p><pre><code class="language-julia hljs">z = TaylorModel1(3, 0.0, -0.5..0.5)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi"> 1.0 t + [0, 0]</code></pre><pre><code class="language-julia hljs">typeof(z)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">TaylorModel1{Float64, Float64}</code></pre><pre><code class="language-julia hljs">polynomial(z)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi"> 1.0 t + 𝒪(t⁴)</code></pre><p>Using a polynomial with interval coefficients guarantees that all arithmetic operations involving <code>t</code> are conservative, or rigorous, with respect to floating point arithmetic.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../api/">API »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 26 March 2024 17:29">Tuesday 26 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>