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 true</code></pre><p><strong>Advanced input for different block approximations</strong></p><p>Instead of defining the approximation option uniformly for each block, we can define different approximations for different blocks. For this purpose, the argument <code>block_options</code> can also be a mapping from block index (in the partition) to the corresponding approximation option.</p><p>For example, we can approximate the first block with a <code>Hyperrectangle</code> and the second block with <span>$ε$</span>-close approximation for <span>$ε = 0.1$</span>:</p><pre><code class="language-julia-repl hljs">julia&gt; res = array(decompose(S, P2d, Dict(1 =&gt; Hyperrectangle, 2 =&gt; 0.1)));
 
 julia&gt; typeof(res[1]), typeof(res[2])
-(Hyperrectangle{Float64, Vector{Float64}, Vector{Float64}}, HPolygon{Float64, Vector{Float64}})</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaReach/LazySets.jl/blob/337c25762daacdc246a780cbfb71a38ed5440b03/src/Approximations/decompositions.jl#L1-L151">source</a></section><section><div><pre><code class="language-julia hljs">decompose(S::LazySet, block_options; [block_size]::Int=1)</code></pre><p>Decompose a high-dimensional set into a Cartesian product of overapproximations of the projections over uniformly-sized subspaces.</p><p><strong>Input</strong></p><ul><li><code>S</code>             – set</li><li><code>block_options</code> – overapproximation option or mapping from block indices to a                    corresponding overapproximation option</li><li><code>block_size</code>    – (optional; default: <code>1</code>) size of the blocks</li></ul><p><strong>Output</strong></p><p>A <code>CartesianProductArray</code> containing the low-dimensional approximated projections.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaReach/LazySets.jl/blob/337c25762daacdc246a780cbfb71a38ed5440b03/src/Approximations/decompositions.jl#L181-L198">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../approximate/">« Approximation</a><a class="docs-footer-nextpage" href="../hausdorff_distance/">Hausdorff Distance »</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><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Thursday 28 November 2024 09:43">Thursday 28 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+(Hyperrectangle{Float64, Vector{Float64}, Vector{Float64}}, HPolygon{Float64, Vector{Float64}})</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaReach/LazySets.jl/blob/6fc2bb47d1d7a46afe6ba1bd8f2837c4d0eb97d3/src/Approximations/decompositions.jl#L1-L151">source</a></section><section><div><pre><code class="language-julia hljs">decompose(S::LazySet, block_options; [block_size]::Int=1)</code></pre><p>Decompose a high-dimensional set into a Cartesian product of overapproximations of the projections over uniformly-sized subspaces.</p><p><strong>Input</strong></p><ul><li><code>S</code>             – set</li><li><code>block_options</code> – overapproximation option or mapping from block indices to a                    corresponding overapproximation option</li><li><code>block_size</code>    – (optional; default: <code>1</code>) size of the blocks</li></ul><p><strong>Output</strong></p><p>A <code>CartesianProductArray</code> containing the low-dimensional approximated projections.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaReach/LazySets.jl/blob/6fc2bb47d1d7a46afe6ba1bd8f2837c4d0eb97d3/src/Approximations/decompositions.jl#L181-L198">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../approximate/">« Approximation</a><a class="docs-footer-nextpage" href="../hausdorff_distance/">Hausdorff Distance »</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><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Thursday 28 November 2024 20:34">Thursday 28 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>