build based on bc91deb

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.3","generation_timestamp":"2024-05-24T09:00:30","documenter_version":"1.4.1"}}
+{"documenter":{"julia_version":"1.10.3","generation_timestamp":"2024-05-24T09:21:01","documenter_version":"1.4.1"}}

dev/examples/multi_ad/index.html

@@ -41,19 +41,19 @@
 qrcomp = QRCompress(; tol=1e-9)
 rbres = assemble(H, grid_train, greedy, lobpcg, qrcomp);</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">n      max. err    ‖BᵀB-I‖     time      μ
 ------------------------------------------------------------
-1      NaN         5.68e-15     217ms    [-1.0, 0.0]
-2      2.33        5.7e-15      233ms    [2.231, 0.538]
-3      0.946       5.8e-15     85.1ms    [0.795, 0.897]
-4      0.508       5.91e-15    72.7ms    [1.154, 1.795]
-5      0.472       6.21e-15    81.1ms    [2.5, 1.077]
-6      0.385       6.51e-15    81.2ms    [0.346, 0.179]
-7      0.0727      1.23e-14    78.8ms    [-0.551, 0.0]
-8      0.0554      1.93e-14    86.5ms    [-0.462, 0.269]
-9      0.0163      9.5e-14     99.3ms    [1.423, 0.538]
-10     0.00522     1.61e-13     110ms    [-0.372, 0.449]
-11     0.004       3.05e-13     123ms    [1.692, 1.346]
-12     0.00151     4.61e-13     138ms    [-0.821, 0.0]
-13     0.00039     1.08e-12     155ms    [-0.821, 0.09]
+1      NaN         5.68e-15     197ms    [-1.0, 0.0]
+2      2.33        5.7e-15      224ms    [2.231, 0.538]
+3      0.946       5.8e-15     75.3ms    [0.795, 0.897]
+4      0.508       5.91e-15    87.4ms    [1.154, 1.795]
+5      0.472       6.21e-15    64.6ms    [2.5, 1.077]
+6      0.385       6.51e-15    92.1ms    [0.346, 0.179]
+7      0.0727      1.23e-14    79.5ms    [-0.551, 0.0]
+8      0.0554      1.93e-14    83.7ms    [-0.462, 0.269]
+9      0.0163      9.5e-14     95.4ms    [1.423, 0.538]
+10     0.00522     1.61e-13     102ms    [-0.372, 0.449]
+11     0.004       3.05e-13     120ms    [1.692, 1.346]
+12     0.00151     4.61e-13     133ms    [-0.821, 0.0]
+13     0.00039     1.08e-12     147ms    [-0.821, 0.09]
 reached residual target</code></pre><p>Now the task is to implement the double-sum in <span>$\mathcal{S}$</span>, as well as the <span>$k$</span>-dependency in the coefficients. The double-sum can be encoded by putting all <span>$S^z_r S^z_{r&#39;}$</span> combinations into an <span>$L \times L$</span> matrix:</p><pre><code class="language-julia hljs">terms = map(idx -&gt; to_global(σz, L, idx[1]) * to_global(σz, L, idx[2]),
             Iterators.product(1:L, 1:L));</code></pre><p>Correspondingly, the coefficient function now has to map one <span>$k$</span> value to a matrix of coefficients of the same size as the <code>terms</code> matrix:</p><pre><code class="language-julia hljs">coefficients = k -&gt; map(idx -&gt; cis(-(idx[1] - idx[2]) * k) / L,
                         Iterators.product(1:L, 1:L));</code></pre><p>One feature of the structure factor that also shows up in many other affine decompositions with double-sums is that the term indices commute, i.e. <span>$O_{r,r&#39;} = O_{r&#39;,r}$</span>. In that case, only the upper triangular matrix has to be computed since <span>$B^\dagger O_{r,r&#39;} B = B^\dagger O_{r&#39;,r} B$</span> are the same in the compressed affine decomposition. So let&#39;s create the <a href="../../api/#ReducedBasis.AffineDecomposition"><code>AffineDecomposition</code></a> and compress, exploiting this symmetry using the <code>symmetric_terms</code> keyword argument:</p><pre><code class="language-julia hljs">SFspin    = AffineDecomposition(terms, coefficients)
@@ -75,4 +75,4 @@
     push!(hms, heatmap(grid_online.ranges[1], grid_online.ranges[2], sf[i]&#39;;
                        title=&quot;\$k = $(round(q/π; digits=3))\\pi\$&quot;, kwargs...))
 end
-plot(hms...)</code></pre><img src="eef9cae0.svg" alt="Example block output"/><p>It can be nicely seen that the spin structure factor indicates the ferromagnetic phase at <span>$k=0$</span> and then moves through the magnetization plateaus until it reaches the antiferromagnetic plateau at <span>$k=\pi$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../xxz_pod/">« Basis assembly using Proper Orthogonal Decomposition</a><a class="docs-footer-nextpage" href="../basis_analysis/">Analyzing and modifying a reduced basis after assembly »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Friday 24 May 2024 09:00">Friday 24 May 2024</span>. Using Julia version 1.10.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+plot(hms...)</code></pre><img src="ab5ec462.svg" alt="Example block output"/><p>It can be nicely seen that the spin structure factor indicates the ferromagnetic phase at <span>$k=0$</span> and then moves through the magnetization plateaus until it reaches the antiferromagnetic plateau at <span>$k=\pi$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../xxz_pod/">« Basis assembly using Proper Orthogonal Decomposition</a><a class="docs-footer-nextpage" href="../basis_analysis/">Analyzing and modifying a reduced basis after assembly »</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 1.4.1 on <span class="colophon-date" title="Friday 24 May 2024 09:21">Friday 24 May 2024</span>. Using Julia version 1.10.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/examples/xxz_dmrg/index.html

@@ -27,30 +27,30 @@
 
 rbres = assemble(H, grid_train, greedy, dm, edcomp);</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">n      max. err    ‖BᵀB-I‖     time      μ
 ------------------------------------------------------------
-1      NaN         8.88e-16     465ms    [-1.0, 0.0]
-2      6.3         2.29e-16     642ms    [2.5, 3.5]
-3      3.36        3.91e-16     370ms    [2.5, 0.538]
-4      1.52        1.74e-14     598ms    [-0.282, 0.09]
-5      1.87        1.91e-13     240ms    [2.5, 2.513]
-6      0.934       7.49e-15     222ms    [0.795, 0.0]
-7      0.726       6.06e-15     224ms    [0.077, 0.718]
-8      0.868       5.91e-15     203ms    [2.5, 3.141]
-9      0.723       6.31e-15     228ms    [0.795, 0.538]
-10     0.814       1.43e-14     250ms    [2.5, 0.897]
-11     0.708       1.12e-14     208ms    [2.051, 2.423]
-12     0.538       5.14e-14     235ms    [0.705, 0.897]
-13     0.443       3.19e-14     337ms    [-0.103, 0.0]
-14     0.274       3.78e-14     324ms    [-0.372, 0.269]
-15     0.233       1.16e-13     815ms    [-0.91, 0.0]
-16     0.229       8.77e-14     303ms    [-0.462, 0.449]
-17     0.113       1.1e-13      354ms    [-0.641, 0.09]
-18     0.103       1.44e-13     1.02s    [-0.821, 0.09]
-19     0.079       9.01e-13     439ms    [1.782, 0.359]
-20     0.0748      8.76e-13     427ms    [-0.731, 0.09]
-21     0.041       1.05e-11     452ms    [1.692, 1.256]
-22     0.0393      2.46e-12     501ms    [-0.641, 0.0]
-23     0.0269      3.72e-12     475ms    [0.526, 1.436]
-24     0.0933      7.78e-12     479ms    [2.5, 3.41]</code></pre><p>The returned <code>basis</code> now has snapshot vectors of <code>ITensors.MPS</code> type, which we have to keep in mind when we want to compress observables. That is to say, the observables have to be constructed as <a href="../../api/#ReducedBasis.AffineDecomposition"><code>AffineDecomposition</code></a>s with <a href="../../api/#ReducedBasis.ApproxMPO"><code>ApproxMPO</code></a> terms as we did for the Hamiltonian. Again, we want to compute the magnetization so that we can reuse the third term of <code>H</code>:</p><pre><code class="language-julia hljs">M    = AffineDecomposition([H.terms[3]], [2 / L])
+1      NaN         8.88e-16     430ms    [-1.0, 0.0]
+2      6.3         2.29e-16     613ms    [2.5, 3.5]
+3      3.36        3.91e-16     362ms    [2.5, 0.538]
+4      1.52        1.74e-14     567ms    [-0.282, 0.09]
+5      1.87        1.91e-13     228ms    [2.5, 2.513]
+6      0.934       7.49e-15     216ms    [0.795, 0.0]
+7      0.726       6.06e-15     218ms    [0.077, 0.718]
+8      0.868       5.91e-15     212ms    [2.5, 3.141]
+9      0.723       6.31e-15     223ms    [0.795, 0.538]
+10     0.814       1.43e-14     242ms    [2.5, 0.897]
+11     0.708       1.12e-14     214ms    [2.051, 2.423]
+12     0.538       5.14e-14     247ms    [0.705, 0.897]
+13     0.443       3.19e-14     313ms    [-0.103, 0.0]
+14     0.274       3.78e-14     306ms    [-0.372, 0.269]
+15     0.233       1.16e-13     782ms    [-0.91, 0.0]
+16     0.229       8.77e-14     300ms    [-0.462, 0.449]
+17     0.113       1.1e-13      336ms    [-0.641, 0.09]
+18     0.103       1.44e-13     992ms    [-0.821, 0.09]
+19     0.079       9.01e-13     418ms    [1.782, 0.359]
+20     0.0748      8.76e-13     419ms    [-0.731, 0.09]
+21     0.041       1.05e-11     440ms    [1.692, 1.256]
+22     0.0393      2.46e-12     483ms    [-0.641, 0.0]
+23     0.0269      3.72e-12     472ms    [0.526, 1.436]
+24     0.0933      7.78e-12     478ms    [2.5, 3.41]</code></pre><p>The returned <code>basis</code> now has snapshot vectors of <code>ITensors.MPS</code> type, which we have to keep in mind when we want to compress observables. That is to say, the observables have to be constructed as <a href="../../api/#ReducedBasis.AffineDecomposition"><code>AffineDecomposition</code></a>s with <a href="../../api/#ReducedBasis.ApproxMPO"><code>ApproxMPO</code></a> terms as we did for the Hamiltonian. Again, we want to compute the magnetization so that we can reuse the third term of <code>H</code>:</p><pre><code class="language-julia hljs">M    = AffineDecomposition([H.terms[3]], [2 / L])
 m, _ = compress(M, rbres.basis);</code></pre><p>And at that point, we continue as before since we have arrived at the online phase where we only operate in the low-dimensional RB space, agnostic of the snapshot solver method. We have to make sure, however, to choose matching degeneracy settings for the <a href="../../api/#ReducedBasis.FullDiagonalization"><code>FullDiagonalization</code></a> solver in the online phase:</p><pre><code class="language-julia hljs">fulldiag = FullDiagonalization(dm);</code></pre><p>Then we can define an online grid and compute the magnetization at all grid points, again constructing <code>m</code> at an arbitrary parameter point since its coefficient is parameter-independent:</p><pre><code class="language-julia hljs">m_reduced = m()
 Δ_online = range(first(Δ), last(Δ); length=100)
 hJ_online = range(first(hJ), last(hJ); length=100)
@@ -66,4 +66,4 @@
              colorbar=true, clims=(0.0, 1.0), leg=false)
 params = unique(rbres.basis.parameters)
 scatter!(hm, [μ[1] for μ in params], [μ[2] for μ in params];
-         markershape=:xcross, color=:springgreen, ms=3.0, msw=2.0)</code></pre><img src="3dc08666.svg" alt="Example block output"/><p>We reproduce the ground-state phase diagram, but this time with more magnetization plateaus (due to increased system size) and we see that the greedy algorithm chose different parameter points to solve using DMRG.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../xxz_ed/">« The reduced basis workflow</a><a class="docs-footer-nextpage" href="../xxz_pod/">Basis assembly using Proper Orthogonal Decomposition »</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 1.4.1 on <span class="colophon-date" title="Friday 24 May 2024 09:00">Friday 24 May 2024</span>. Using Julia version 1.10.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+         markershape=:xcross, color=:springgreen, ms=3.0, msw=2.0)</code></pre><img src="71af1085.svg" alt="Example block output"/><p>We reproduce the ground-state phase diagram, but this time with more magnetization plateaus (due to increased system size) and we see that the greedy algorithm chose different parameter points to solve using DMRG.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../xxz_ed/">« The reduced basis workflow</a><a class="docs-footer-nextpage" href="../xxz_pod/">Basis assembly using Proper Orthogonal Decomposition »</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 1.4.1 on <span class="colophon-date" title="Friday 24 May 2024 09:21">Friday 24 May 2024</span>. Using Julia version 1.10.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>