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| <html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Index · MultivariateMoments</title><meta name="title" content="Index · MultivariateMoments"/><meta property="og:title" content="Index · MultivariateMoments"/><meta property="twitter:title" content="Index · MultivariateMoments"/><meta name="description" content="Documentation for MultivariateMoments."/><meta property="og:description" content="Documentation for MultivariateMoments."/><meta property="twitter:description" content="Documentation for MultivariateMoments."/><script data-outdated-warner src="assets/warner.js"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" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="search_index.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><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>MultivariateMoments</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 class="is-active"><a class="tocitem" href>Index</a><ul class="internal"><li><a class="tocitem" href="#Contents"><span>Contents</span></a></li></ul></li><li><a class="tocitem" href="moments/">Moments and expectation</a></li><li><a class="tocitem" href="atoms/">Atoms extraction</a></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>Index</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Index</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaAlgebra/MultivariateMoments.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/JuliaAlgebra/MultivariateMoments.jl/blob/master/docs/src/index.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="MultivariateMoments-–-Multivariate-Moments-for-Julia"><a class="docs-heading-anchor" href="#MultivariateMoments-–-Multivariate-Moments-for-Julia">MultivariateMoments –- Multivariate Moments for Julia</a><a id="MultivariateMoments-–-Multivariate-Moments-for-Julia-1"></a><a class="docs-heading-anchor-permalink" href="#MultivariateMoments-–-Multivariate-Moments-for-Julia" title="Permalink"></a></h1><p>Extension of <a href="https://github.com/JuliaAlgebra/MultivariatePolynomials.jl">MultivariatePolynomials</a> to moments of multivariate measures and their scalar product with polynomials. It also includes the extraction of atomic measures from moment matrices which is related to the <a href="https://en.wikipedia.org/wiki/Moment_problem">moment problem</a>.</p><h2 id="Contents"><a class="docs-heading-anchor" href="#Contents">Contents</a><a id="Contents-1"></a><a class="docs-heading-anchor-permalink" href="#Contents" title="Permalink"></a></h2><ul><li><a href="moments/#Moments-and-expectation">Moments and expectation</a></li><li class="no-marker"><ul><li><a href="moments/#Moment">Moment</a></li><li><a href="moments/#Measure">Measure</a></li><li><a href="moments/#Expectation">Expectation</a></li></ul></li><li><a href="atoms/#Atoms-extration">Atoms extration</a></li><li class="no-marker"><ul><li><a href="atoms/#Vectorized-matrix">Vectorized matrix</a></li><li><a href="atoms/#Moment-matrix">Moment matrix</a></li><li><a href="atoms/#Atomic-measure">Atomic measure</a></li><li><a href="atoms/#Atoms-extraction">Atoms extraction</a></li></ul></li></ul></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="moments/">Moments and expectation »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Tuesday 28 November 2023 15:51">Tuesday 28 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> | ||
| <html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Index · MultivariateMoments</title><meta name="title" content="Index · MultivariateMoments"/><meta property="og:title" content="Index · MultivariateMoments"/><meta property="twitter:title" content="Index · MultivariateMoments"/><meta name="description" content="Documentation for MultivariateMoments."/><meta property="og:description" content="Documentation for MultivariateMoments."/><meta property="twitter:description" content="Documentation for MultivariateMoments."/><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" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="search_index.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><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>MultivariateMoments</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 class="is-active"><a class="tocitem" href>Index</a><ul class="internal"><li><a class="tocitem" href="#Contents"><span>Contents</span></a></li></ul></li><li><a class="tocitem" href="moments/">Moments and expectation</a></li><li><a class="tocitem" href="atoms/">Atoms extraction</a></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>Index</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Index</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaAlgebra/MultivariateMoments.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/JuliaAlgebra/MultivariateMoments.jl/blob/master/docs/src/index.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="MultivariateMoments-–-Multivariate-Moments-for-Julia"><a class="docs-heading-anchor" href="#MultivariateMoments-–-Multivariate-Moments-for-Julia">MultivariateMoments –- Multivariate Moments for Julia</a><a id="MultivariateMoments-–-Multivariate-Moments-for-Julia-1"></a><a class="docs-heading-anchor-permalink" href="#MultivariateMoments-–-Multivariate-Moments-for-Julia" title="Permalink"></a></h1><p>Extension of <a href="https://github.com/JuliaAlgebra/MultivariatePolynomials.jl">MultivariatePolynomials</a> to moments of multivariate measures and their scalar product with polynomials. It also includes the extraction of atomic measures from moment matrices which is related to the <a href="https://en.wikipedia.org/wiki/Moment_problem">moment problem</a>.</p><h2 id="Contents"><a class="docs-heading-anchor" href="#Contents">Contents</a><a id="Contents-1"></a><a class="docs-heading-anchor-permalink" href="#Contents" title="Permalink"></a></h2><ul><li><a href="moments/#Moments-and-expectation">Moments and expectation</a></li><li class="no-marker"><ul><li><a href="moments/#Moment">Moment</a></li><li><a href="moments/#Measure">Measure</a></li><li><a href="moments/#Expectation">Expectation</a></li></ul></li><li><a href="atoms/#Atoms-extration">Atoms extration</a></li><li class="no-marker"><ul><li><a href="atoms/#Vectorized-matrix">Vectorized matrix</a></li><li><a href="atoms/#Moment-matrix">Moment matrix</a></li><li><a href="atoms/#Atomic-measure">Atomic measure</a></li><li><a href="atoms/#Atoms-extraction">Atoms extraction</a></li></ul></li></ul></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="moments/">Moments and expectation »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Thursday 7 December 2023 14:52">Thursday 7 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> |
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