build based on 73ebb10

Author: zeptodoctor

dev/dev/index.html

@@ -34,4 +34,4 @@
 </code></pre><p>Then we wait for the friendly folks at <a href="https://github.com/JuliaPackaging">JuliaPackaging</a> to merge the pull request to Yggdrasil, triggering a new release of the <a href="https://github.com/JuliaBinaryWrappers/FastTransforms_jll.jl">FastTransforms_jll.jl</a> meta package that stores all precompiled binaries. With this release, we update the FastTransforms.jl <a href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/Project.toml">Project.toml</a> to point to the latest release and register the new version.</p><p>Since development of Yggdrasil is quite rapid, a fork may easily become stale. Git permits the developer to forcibly make a master branch on a fork even with upstream master:</p><pre><code class="language-none">git fetch upstream
 git checkout master
 git reset --hard upstream/master
-git push origin master --force</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../generated/annulus/">Integration on an annulus »</a></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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Tuesday 26 November 2024 18:45">Tuesday 26 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+git push origin master --force</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../generated/annulus/">Integration on an annulus »</a></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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 12 December 2024 20:41">Thursday 12 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/generated/annulus.html

@@ -1,7 +1,7 @@
-<script src="https://cdn.plot.ly/plotly-2.6.3.min.js"></script>    <div id="7fa18bd7-b8b8-486e-abdf-c5c385a25ecb" style="width:600px;height:400px;"></div>
+<script src="https://cdn.plot.ly/plotly-2.6.3.min.js"></script>    <div id="5d6f2daa-b496-4f12-856e-b39debed00f0" style="width:600px;height:400px;"></div>
     <script>
 
-    Plotly.newPlot('7fa18bd7-b8b8-486e-abdf-c5c385a25ecb', [
+    Plotly.newPlot('5d6f2daa-b496-4f12-856e-b39debed00f0', [
     {
         "xaxis": "x",
         "colorbar": {

dev/generated/annulus/index.html

@@ -35,4 +35,4 @@
  -1.96208e-17   7.71573e-19   0.00458845   -2.03822e-18   1.86344e-17   3.19547e-18   0.00369818   -1.86152e-18  -3.29302e-18   8.11326e-19  -4.97022e-21  -1.77139e-18   1.47439e-18  -6.8012e-18    2.63512e-18  -4.24712e-18   5.7017e-18   -7.2048e-18    7.38785e-18  -4.72462e-18   1.59607e-17  -5.27319e-18   1.44348e-17  -1.67467e-18  -4.59916e-19   8.00009e-19   5.99498e-18  -3.34661e-18  -2.03062e-18
   1.3498e-17    1.71852e-19  -0.00150441    7.97602e-19  -9.38596e-18  -3.21855e-18  -0.00121128   -4.47164e-19  -1.76175e-17  -4.83245e-18   6.52956e-18  -5.47568e-18   5.27089e-18  -2.9175e-18    5.23985e-18  -5.70705e-18  -3.147e-18    -3.85137e-19  -3.05417e-18  -5.31797e-19  -4.09175e-18   3.59849e-18   4.48894e-18   3.4972e-18    1.74387e-18   1.53405e-18   8.8938e-18    4.33464e-18   5.85819e-18
   5.24011e-17  -4.20047e-18   0.000517281  -2.62968e-18   1.29799e-17  -9.06153e-18   0.000424358  -4.57265e-18   2.49476e-18  -6.80939e-18  -6.07451e-18  -2.399e-18     1.03771e-18   6.6648e-19   -1.96393e-17   1.69496e-20  -1.42128e-18   5.37575e-18  -1.16727e-17   3.57204e-19  -7.01129e-18   2.48838e-18  -1.17285e-17   4.39475e-19   5.83824e-18  -1.63971e-18  -3.91773e-19   1.39577e-18   1.02075e-17
- -8.95802e-18   6.39707e-19  -0.000162126   3.55753e-18   7.44168e-18   4.28763e-18  -5.40419e-5    5.16629e-18   8.97839e-18   5.4486e-18    3.6724e-18    4.64571e-18  -1.67417e-18   6.04678e-19   5.73104e-18  -2.13942e-18  -1.44968e-17  -3.57457e-18   1.24167e-17  -5.67995e-18  -1.09651e-17  -4.98049e-18   6.22788e-18  -2.89642e-18  -1.52622e-17  -2.30036e-18   1.82749e-18  -1.26575e-18  -9.91876e-18</code></pre><p>The annulus coefficients are useful for integration. The integral of <span>$[f(x,y)]^2$</span> over the annulus is approximately the square of the 2-norm of the coefficients:</p><pre><code class="language-julia">norm(U)^2, 5π/8*(1675/4536+9*log(3)/32-3*log(7)/32)</code></pre><pre><code class="language-none">(0.9735516844404257, 0.973547572736036)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../dev/">« Development</a><a class="docs-footer-nextpage" href="../automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms »</a></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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Tuesday 26 November 2024 18:45">Tuesday 26 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ -8.95802e-18   6.39707e-19  -0.000162126   3.55753e-18   7.44168e-18   4.28763e-18  -5.40419e-5    5.16629e-18   8.97839e-18   5.4486e-18    3.6724e-18    4.64571e-18  -1.67417e-18   6.04678e-19   5.73104e-18  -2.13942e-18  -1.44968e-17  -3.57457e-18   1.24167e-17  -5.67995e-18  -1.09651e-17  -4.98049e-18   6.22788e-18  -2.89642e-18  -1.52622e-17  -2.30036e-18   1.82749e-18  -1.26575e-18  -9.91876e-18</code></pre><p>The annulus coefficients are useful for integration. The integral of <span>$[f(x,y)]^2$</span> over the annulus is approximately the square of the 2-norm of the coefficients:</p><pre><code class="language-julia">norm(U)^2, 5π/8*(1675/4536+9*log(3)/32-3*log(7)/32)</code></pre><pre><code class="language-none">(0.9735516844404257, 0.973547572736036)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../dev/">« Development</a><a class="docs-footer-nextpage" href="../automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms »</a></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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 12 December 2024 20:41">Thursday 12 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/generated/automaticdifferentiation/index.html

@@ -16,4 +16,4 @@
 λ: 0.5010383094167955 and the 2-norm: 1.0000000000187363
 λ: 0.5010383094167954 and the 2-norm: 1.0000000000000002
 λ: 0.5010383094167955 and the 2-norm: 0.9999999999999999
-</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../annulus/">« Integration on an annulus</a><a class="docs-footer-nextpage" href="../chebyshev/">Chebyshev transform »</a></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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Tuesday 26 November 2024 18:45">Tuesday 26 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../annulus/">« Integration on an annulus</a><a class="docs-footer-nextpage" href="../chebyshev/">Chebyshev transform »</a></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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 12 December 2024 20:41">Thursday 12 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/generated/chebyshev/index.html

@@ -16,4 +16,4 @@
 f = exp.(p_2)
 f̌ = chebyshevutransform(f, Val(2))
 f̃ = x -> [sin((k+1)*acos(x))/sin(acos(x)) for k=0:n-3]' * f̌
-f̃(0.1) ≈ exp(0.1)</code></pre><pre><code class="language-none">true</code></pre><p>Second kind polynomials <span>$\to$</span> second kind points</p><pre><code class="language-julia">ichebyshevutransform(f̌, Val(2)) ≈ exp.(p_2)</code></pre><pre><code class="language-none">true</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../automaticdifferentiation/">« Automatic differentiation through spherical harmonic transforms</a><a class="docs-footer-nextpage" href="../disk/">Holomorphic integration on the unit disk »</a></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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Tuesday 26 November 2024 18:45">Tuesday 26 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+f̃(0.1) ≈ exp(0.1)</code></pre><pre><code class="language-none">true</code></pre><p>Second kind polynomials <span>$\to$</span> second kind points</p><pre><code class="language-julia">ichebyshevutransform(f̌, Val(2)) ≈ exp.(p_2)</code></pre><pre><code class="language-none">true</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../automaticdifferentiation/">« Automatic differentiation through spherical harmonic transforms</a><a class="docs-footer-nextpage" href="../disk/">Holomorphic integration on the unit disk »</a></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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 12 December 2024 20:41">Thursday 12 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/generated/disk/index.html

@@ -186,4 +186,4 @@
   0.000104898  -1.01818e-18  -4.97719e-5   -7.29653e-19  -1.14056e-5    5.87956e-19  -1.12136e-5    4.60098e-19  -8.949e-6      4.53171e-19  -5.82665e-6   -2.44462e-19  -3.11536e-6   -6.1681e-19   -1.37708e-6    5.61031e-19  -5.04943e-7   -8.46536e-20  -1.52739e-7   -3.66863e-19  -3.7074e-8    -2.38249e-19  -6.54014e-9    1.24858e-19  -4.49338e-10   7.25589e-19   2.34081e-10  -4.87718e-19   1.39557e-10  -5.94023e-19
  -3.13646e-18  -0.000389793  -3.28188e-18  -8.04943e-5   -1.37241e-19  -3.68665e-5   -2.30965e-18   8.03845e-6   -6.09189e-19   2.97453e-5   -5.0944e-19    2.89916e-5    1.05019e-18   1.86472e-5    6.3629e-19    8.99472e-6    1.43239e-18   3.37228e-6   -1.20318e-18   9.75922e-7    4.1214e-20    2.02668e-7   -1.14334e-19   2.00821e-8    1.81185e-19  -5.36499e-9   -1.23364e-19  -3.68864e-9    4.2811e-20   -1.00792e-9
   1.54054e-5    1.23828e-18   1.00144e-6    1.84463e-19   1.23964e-6   -8.43152e-20   1.21824e-6    5.74481e-20   9.71898e-7   -1.03935e-19   6.32656e-7   -8.20175e-20   3.38215e-7    1.5389e-19    1.49487e-7   -1.12048e-19   5.48103e-8   -2.06987e-19   1.65791e-8    6.79198e-20   4.02426e-9    1.22785e-19   7.09969e-10  -6.46596e-20   4.88112e-11  -5.51333e-20  -2.53943e-11   1.23995e-19  -1.51441e-11   7.96269e-20
- -1.5778e-18    0.000145153   1.32424e-19   0.000143445  -7.6147e-20    6.55677e-5    2.22587e-19  -1.45469e-5    3.01577e-19  -5.3233e-5     3.22253e-20  -5.18305e-5   -8.36085e-22  -3.33247e-5   -1.86065e-19  -1.60719e-5   -4.43286e-19  -6.0251e-6     8.63083e-20  -1.74358e-6    5.65738e-21  -3.62096e-7    4.33784e-20  -3.58901e-8   -1.49965e-19   9.57958e-9    1.3012e-20    6.5884e-9     3.28648e-19   1.80042e-9</code></pre><p>The Dunkl-Xu coefficients are useful for integration. The integral of <span>$f(x,y)$</span> over the disk should be <span>$\pi/2$</span> by harmonicity. The coefficient of <span>$P_{0,0}$</span> multiplied by <code>√π</code> is:</p><pre><code class="language-julia">U[1, 1]*sqrt(π)</code></pre><pre><code class="language-none">1.5707955409153043</code></pre><p>Using an orthonormal basis, the integral of <span>$[f(x,y)]^2$</span> over the disk is approximately the square of the 2-norm of the coefficients:</p><pre><code class="language-julia">norm(U)^2, π/(2*sqrt(2))*log1p(sqrt(2))</code></pre><pre><code class="language-none">(0.978937045726087, 0.9789599179781414)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../chebyshev/">« Chebyshev transform</a><a class="docs-footer-nextpage" href="../halfrange/">Half-range Chebyshev polynomials »</a></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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Tuesday 26 November 2024 18:45">Tuesday 26 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ -1.5778e-18    0.000145153   1.32424e-19   0.000143445  -7.6147e-20    6.55677e-5    2.22587e-19  -1.45469e-5    3.01577e-19  -5.3233e-5     3.22253e-20  -5.18305e-5   -8.36085e-22  -3.33247e-5   -1.86065e-19  -1.60719e-5   -4.43286e-19  -6.0251e-6     8.63083e-20  -1.74358e-6    5.65738e-21  -3.62096e-7    4.33784e-20  -3.58901e-8   -1.49965e-19   9.57958e-9    1.3012e-20    6.5884e-9     3.28648e-19   1.80042e-9</code></pre><p>The Dunkl-Xu coefficients are useful for integration. The integral of <span>$f(x,y)$</span> over the disk should be <span>$\pi/2$</span> by harmonicity. The coefficient of <span>$P_{0,0}$</span> multiplied by <code>√π</code> is:</p><pre><code class="language-julia">U[1, 1]*sqrt(π)</code></pre><pre><code class="language-none">1.5707955409153043</code></pre><p>Using an orthonormal basis, the integral of <span>$[f(x,y)]^2$</span> over the disk is approximately the square of the 2-norm of the coefficients:</p><pre><code class="language-julia">norm(U)^2, π/(2*sqrt(2))*log1p(sqrt(2))</code></pre><pre><code class="language-none">(0.978937045726087, 0.9789599179781414)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../chebyshev/">« Chebyshev transform</a><a class="docs-footer-nextpage" href="../halfrange/">Half-range Chebyshev polynomials »</a></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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 12 December 2024 20:41">Thursday 12 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>