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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Pipeline · Documentation</title><meta name="title" content="Pipeline · Documentation"/><meta property="og:title" content="Pipeline · Documentation"/><meta property="twitter:title" content="Pipeline · Documentation"/><meta name="description" content="Documentation for Documentation."/><meta property="og:description" content="Documentation for Documentation."/><meta property="twitter:description" content="Documentation for Documentation."/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" 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rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">Documentation</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../cpd/">CPD</a></li><li><a class="tocitem" href="../tucker/">Tucker</a></li><li><a class="tocitem" href="../btd/">BTD</a></li><li><a class="tocitem" href="../join/">Join</a></li><li><a class="tocitem" href="../utils/">Utilities</a></li><li class="is-active"><a class="tocitem" href>Pipeline</a><ul class="internal"><li><a class="tocitem" href="#Public-entry-points"><span>Public entry points</span></a></li><li><a class="tocitem" href="#Default-behavior-(quick-reference)"><span>Default behavior (quick reference)</span></a></li><li><a class="tocitem" href="#Core-execution-architecture"><span>Core execution architecture</span></a></li><li><a class="tocitem" href="#API-flows"><span>API flows</span></a></li><li><a class="tocitem" href="#Generic-approx(...)-routing"><span>Generic <code>approx(...)</code> routing</span></a></li><li><a class="tocitem" href="#Result-types-and-post-processing"><span>Result types and post-processing</span></a></li><li><a class="tocitem" href="#File-map"><span>File map</span></a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Pipeline</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Pipeline</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/Harumaru58/TensorKitchen.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/Harumaru58/TensorKitchen.jl/blob/master/docs/src/PIPELINE.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="TensorKitchen-Pipeline"><a class="docs-heading-anchor" href="#TensorKitchen-Pipeline">TensorKitchen Pipeline</a><a id="TensorKitchen-Pipeline-1"></a><a class="docs-heading-anchor-permalink" href="#TensorKitchen-Pipeline" title="Permalink"></a></h1><p>This document explains how public APIs route into models, solvers, and result converters.</p><h2 id="Public-entry-points"><a class="docs-heading-anchor" href="#Public-entry-points">Public entry points</a><a id="Public-entry-points-1"></a><a class="docs-heading-anchor-permalink" href="#Public-entry-points" title="Permalink"></a></h2><ul><li><code>cpd(A, r; ...)</code> -&gt; <code>CPDResult</code></li><li><code>nncpd(A, r; ...)</code> -&gt; <code>CPDResult</code></li><li><code>btd(A, blocks, ranks; ...)</code> -&gt; <code>BTDResult</code></li><li><code>tucker(A, ranks; method=...)</code> -&gt; <code>TuckerResult</code></li><li><code>approx(...)</code> -&gt; <code>ApproxResult</code> or auto-routed <code>CPDResult</code>/<code>BTDResult</code></li></ul><h2 id="Default-behavior-(quick-reference)"><a class="docs-heading-anchor" href="#Default-behavior-(quick-reference)">Default behavior (quick reference)</a><a id="Default-behavior-(quick-reference)-1"></a><a class="docs-heading-anchor-permalink" href="#Default-behavior-(quick-reference)" title="Permalink"></a></h2><ul><li><code>cpd(A, r)</code>:<ul><li><code>init = :alswarm</code></li><li><code>solver = :rgd</code></li></ul></li><li><code>nncpd(A, r)</code>:<ul><li><code>init = :alswarm</code></li><li><code>solver = :rgd</code></li></ul></li><li><code>btd(A, blocks, ranks)</code>:<ul><li><code>init = :alswarm</code></li><li><code>warm_steps = 500</code></li><li><code>warm_init = BTDHOSVDMultistartInit(candidates=64, screening_steps=10, block_maxiter=12)</code></li><li><code>solver = :rgd</code></li><li>final BTD-ALS polish enabled by default for non-ALS solvers</li><li><code>max_stagnation_restarts = 1</code> (retry with stronger multistart when ALS fit-change stalls at high rel-error)</li></ul></li><li><code>tucker(A, ranks)</code>:<ul><li><code>method = :sthosvd</code></li></ul></li><li><code>approx(model::JoinModel)</code>:<ul><li><code>init = :alswarm</code></li><li><code>warm_steps = 500</code></li><li><code>solver = :rgd</code></li></ul></li></ul><h2 id="Core-execution-architecture"><a class="docs-heading-anchor" href="#Core-execution-architecture">Core execution architecture</a><a id="Core-execution-architecture-1"></a><a class="docs-heading-anchor-permalink" href="#Core-execution-architecture" title="Permalink"></a></h2><p>Most optimization APIs share this core pattern:</p><ol><li>Build a model (<code>JoinModel</code> + backend)</li><li>Call <code>_solve_model(...)</code></li><li>Convert to a public result struct</li></ol><p><code>_solve_model</code> lives in <code>src/solvers/solve_dispatch.jl</code> and is the common symbol-to-solver dispatch layer (<code>:rgd</code>, <code>:rcg</code>, <code>:lbfgs</code>, <code>:als</code>, <code>:btd_tsd</code>).</p><h2 id="API-flows"><a class="docs-heading-anchor" href="#API-flows">API flows</a><a id="API-flows-1"></a><a class="docs-heading-anchor-permalink" href="#API-flows" title="Permalink"></a></h2><h3 id="CPD-(cpd,-nncpd)"><a class="docs-heading-anchor" href="#CPD-(cpd,-nncpd)">CPD (<code>cpd</code>, <code>nncpd</code>)</a><a id="CPD-(cpd,-nncpd)-1"></a><a class="docs-heading-anchor-permalink" href="#CPD-(cpd,-nncpd)" title="Permalink"></a></h3><p><code>cpd(A, r; ...)</code>:</p><ol><li>Build <code>JoinModel(A, r; geometry=...)</code> with <code>CPDBackend</code></li><li>Normalize/validate options (<code>solver</code>, <code>geometry</code>, <code>gradient_mode</code>, normalization policy)</li><li>Solve through <code>_solve_model(...)</code></li><li>Optionally run nonnegative ALS polishing (for selected nonnegative paths)</li><li>Convert to <code>CPDResult</code></li></ol><p>Notes:</p><ul><li><code>:als</code> means CP-ALS.</li><li>Manifold solvers (<code>:rgd</code>, <code>:rgd_fixed</code>, <code>:rcg</code>, <code>:lbfgs</code>) share dispatch with other pipelines.</li></ul><h3 id="BTD-(btd)"><a class="docs-heading-anchor" href="#BTD-(btd)">BTD (<code>btd</code>)</a><a id="BTD-(btd)-1"></a><a class="docs-heading-anchor-permalink" href="#BTD-(btd)" title="Permalink"></a></h3><p><code>btd(A, blocks, ranks; ...)</code>:</p><ol><li>Build a uniform Tucker family via <code>TuckerJoin(...)</code></li><li>Wrap as <code>JoinModel</code> with <code>BTDBackend</code></li><li>Choose effective initializer:<ul><li><code>solver == :als</code>: use requested init directly (default multistart)</li><li><code>solver != :als</code>: use <code>BTDALSWarmStartInit(...)</code> so first-order methods start from a good BTD-ALS warm point</li></ul></li><li>Solve through <code>_solve_model(...)</code></li><li>If <code>solver != :als</code>, optionally polish with BTD-ALS (<code>btd_als_polish_maxiter</code>)</li><li>Convert to <code>BTDResult</code></li></ol><p>BTD-specific initialization options:</p><ul><li><code>:hosvd</code>: sequential block initialization on residual</li><li><code>:hosvd_multistart</code>: HOSVD subspace split candidates, optional screening ALS, keep lowest-cost candidate</li><li><code>:alswarm</code>: short BTD-ALS warm-start wrapper around base initializer</li></ul><p>BTD-ALS stabilization behavior:</p><ul><li>Tracks per-iteration fit change (<code>|rel_t - rel_{t-1}|</code>)</li><li>Detects stagnation when fit change is tiny but <code>rel_error</code> remains high</li><li>Can restart from fresh multistart pool (<code>max_stagnation_restarts</code>)</li><li>Reports true final Riemannian gradient norm (<code>grad_norm</code>) instead of a placeholder</li></ul><h3 id="Tucker-(tucker)"><a class="docs-heading-anchor" href="#Tucker-(tucker)">Tucker (<code>tucker</code>)</a><a id="Tucker-(tucker)-1"></a><a class="docs-heading-anchor-permalink" href="#Tucker-(tucker)" title="Permalink"></a></h3><p><code>tucker(A, ranks; method=...)</code> does not use <code>_solve_model</code>. It dispatches directly to decomposition routines:</p><ul><li><code>:sthosvd</code></li><li><code>:thosvd</code> / <code>:hosvd</code></li><li><code>:hooi</code></li></ul><h2 id="Generic-approx(...)-routing"><a class="docs-heading-anchor" href="#Generic-approx(...)-routing">Generic <code>approx(...)</code> routing</a><a id="Generic-approx(...)-routing-1"></a><a class="docs-heading-anchor-permalink" href="#Generic-approx(...)-routing" title="Permalink"></a></h2><p><code>approx(manifolds, target; dispatch=:auto)</code> routes by manifold family:</p><ul><li>uniform <code>Manifolds.Segre</code> -&gt; <code>cpd(...)</code></li><li>uniform <code>Manifolds.Tucker</code> matching target shape/rank -&gt; <code>btd(...)</code></li><li>mixed or non-uniform family -&gt; generic <code>JoinModel(...)</code> path -&gt; <code>ApproxResult</code></li></ul><p><code>dispatch=:cpd</code>, <code>:btd</code>, and <code>:generic</code> force behavior.</p><h2 id="Result-types-and-post-processing"><a class="docs-heading-anchor" href="#Result-types-and-post-processing">Result types and post-processing</a><a id="Result-types-and-post-processing-1"></a><a class="docs-heading-anchor-permalink" href="#Result-types-and-post-processing" title="Permalink"></a></h2><ul><li><code>CPDResult</code></li><li><code>BTDResult</code></li><li><code>TuckerResult</code></li><li><code>ApproxResult</code></li></ul><p>Common utilities:</p><ul><li><code>reconstruct(result)</code></li><li><code>rel_error(A, result)</code></li></ul><h2 id="File-map"><a class="docs-heading-anchor" href="#File-map">File map</a><a id="File-map-1"></a><a class="docs-heading-anchor-permalink" href="#File-map" title="Permalink"></a></h2><ul><li>API entry points: <code>src/api/approx.jl</code>, <code>src/api/cpd.jl</code>, <code>src/api/nncpd.jl</code>, <code>src/api/btd.jl</code></li><li>Routing helpers: <code>src/dispatch/approx_routing.jl</code></li><li>Solver dispatch core: <code>src/solvers/solve_dispatch.jl</code></li><li>BTD backend/init details: <code>src/btd/model.jl</code>, <code>src/solvers/btd_als.jl</code></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../utils/">« Utilities</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 1.17.0 on <span class="colophon-date" title="Wednesday 29 April 2026 17:30">Wednesday 29 April 2026</span>. 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