1225 lines
No EOL
37 KiB
HTML
1225 lines
No EOL
37 KiB
HTML
|
||
<!doctype html>
|
||
<html lang="en" class="no-js">
|
||
<head>
|
||
|
||
<meta charset="utf-8">
|
||
<meta name="viewport" content="width=device-width,initial-scale=1">
|
||
|
||
<meta name="description" content="Electromagnetic simulation tools">
|
||
|
||
|
||
|
||
<link rel="canonical" href="https://mpxd.net/docs/meanas/api/eigensolvers/">
|
||
|
||
|
||
<link rel="prev" href="../meanas/">
|
||
|
||
|
||
<link rel="next" href="../fdfd/">
|
||
|
||
|
||
|
||
|
||
|
||
<link rel="icon" href="../../assets/images/favicon.png">
|
||
<meta name="generator" content="mkdocs-1.6.1, mkdocs-material-9.7.6">
|
||
|
||
|
||
|
||
<title>eigensolvers - meanas</title>
|
||
|
||
|
||
|
||
<link rel="stylesheet" href="../../assets/stylesheets/main.484c7ddc.min.css">
|
||
|
||
|
||
<link rel="stylesheet" href="../../assets/stylesheets/palette.ab4e12ef.min.css">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<link rel="stylesheet" href="../../css/print-site.css">
|
||
|
||
<link rel="stylesheet" href="../../css/print-site-material.css">
|
||
|
||
<link rel="stylesheet" href="../../assets/_mkdocstrings.css">
|
||
|
||
<link rel="stylesheet" href="../../stylesheets/extra.css">
|
||
|
||
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,_)=>(e<<5)-e+_.charCodeAt(0)),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script>
|
||
|
||
|
||
|
||
|
||
|
||
</head>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<body dir="ltr" data-md-color-scheme="slate" data-md-color-primary="blue-grey" data-md-color-accent="cyan">
|
||
|
||
|
||
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
|
||
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
|
||
<label class="md-overlay" for="__drawer"></label>
|
||
<div data-md-component="skip">
|
||
|
||
|
||
<a href="#eigensolvers" class="md-skip">
|
||
Skip to content
|
||
</a>
|
||
|
||
</div>
|
||
<div data-md-component="announce">
|
||
|
||
</div>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<header class="md-header md-header--shadow" data-md-component="header">
|
||
<nav class="md-header__inner md-grid" aria-label="Header">
|
||
<a href="../.." title="meanas" class="md-header__button md-logo" aria-label="meanas" data-md-component="logo">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54"/></svg>
|
||
|
||
</a>
|
||
<label class="md-header__button md-icon" for="__drawer">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z"/></svg>
|
||
</label>
|
||
<div class="md-header__title" data-md-component="header-title">
|
||
<div class="md-header__ellipsis">
|
||
<div class="md-header__topic">
|
||
<span class="md-ellipsis">
|
||
meanas
|
||
</span>
|
||
</div>
|
||
<div class="md-header__topic" data-md-component="header-topic">
|
||
<span class="md-ellipsis">
|
||
|
||
eigensolvers
|
||
|
||
</span>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
<form class="md-header__option" data-md-component="palette">
|
||
|
||
|
||
|
||
|
||
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="blue-grey" data-md-color-accent="cyan" aria-label="Switch to light mode" type="radio" name="__palette" id="__palette_0">
|
||
|
||
<label class="md-header__button md-icon" title="Switch to light mode" for="__palette_1" hidden>
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5s-1.65.15-2.39.42zM3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29zm.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14zM20.65 7l-1.77 3.79a7.02 7.02 0 0 0-2.38-4.15zm-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29zM12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44z"/></svg>
|
||
</label>
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="teal" data-md-color-accent="indigo" aria-label="Switch to dark mode" type="radio" name="__palette" id="__palette_1">
|
||
|
||
<label class="md-header__button md-icon" title="Switch to dark mode" for="__palette_0" hidden>
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3zm3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95zm-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31"/></svg>
|
||
</label>
|
||
|
||
|
||
</form>
|
||
|
||
|
||
|
||
<script>var palette=__md_get("__palette");if(palette&&palette.color){if("(prefers-color-scheme)"===palette.color.media){var media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']");palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent")}for(var[key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-header__button md-icon" for="__search">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
|
||
</label>
|
||
<div class="md-search" data-md-component="search" role="dialog">
|
||
<label class="md-search__overlay" for="__search"></label>
|
||
<div class="md-search__inner" role="search">
|
||
<form class="md-search__form" name="search">
|
||
<input type="text" class="md-search__input" name="query" aria-label="Search" placeholder="Search" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
|
||
<label class="md-search__icon md-icon" for="__search">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
|
||
</label>
|
||
<nav class="md-search__options" aria-label="Search">
|
||
|
||
<button type="reset" class="md-search__icon md-icon" title="Clear" aria-label="Clear" tabindex="-1">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
|
||
</button>
|
||
</nav>
|
||
|
||
</form>
|
||
<div class="md-search__output">
|
||
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
|
||
<div class="md-search-result" data-md-component="search-result">
|
||
<div class="md-search-result__meta">
|
||
Initializing search
|
||
</div>
|
||
<ol class="md-search-result__list" role="presentation"></ol>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-header__source">
|
||
<a href="https://mpxd.net/code/jan/meanas" title="Go to repository" class="md-source" data-md-component="source">
|
||
<div class="md-source__icon md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M439.6 236.1 244 40.5c-5.4-5.5-12.8-8.5-20.4-8.5s-15 3-20.4 8.4L162.5 81l51.5 51.5c27.1-9.1 52.7 16.8 43.4 43.7l49.7 49.7c34.2-11.8 61.2 31 35.5 56.7-26.5 26.5-70.2-2.9-56-37.3L240.3 199v121.9c25.3 12.5 22.3 41.8 9.1 55-6.4 6.4-15.2 10.1-24.3 10.1s-17.8-3.6-24.3-10.1c-17.6-17.6-11.1-46.9 11.2-56v-123c-20.8-8.5-24.6-30.7-18.6-45L142.6 101 8.5 235.1C3 240.6 0 247.9 0 255.5s3 15 8.5 20.4l195.6 195.7c5.4 5.4 12.7 8.4 20.4 8.4s15-3 20.4-8.4l194.7-194.7c5.4-5.4 8.4-12.8 8.4-20.4s-3-15-8.4-20.4"/></svg>
|
||
</div>
|
||
<div class="md-source__repository">
|
||
meanas
|
||
</div>
|
||
</a>
|
||
</div>
|
||
|
||
</nav>
|
||
|
||
</header>
|
||
|
||
<div class="md-container" data-md-component="container">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<main class="md-main" data-md-component="main">
|
||
<div class="md-main__inner md-grid">
|
||
|
||
|
||
|
||
<div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
|
||
<div class="md-sidebar__scrollwrap">
|
||
<div class="md-sidebar__inner">
|
||
|
||
|
||
|
||
|
||
<nav class="md-nav md-nav--primary" aria-label="Navigation" data-md-level="0">
|
||
<label class="md-nav__title" for="__drawer">
|
||
<a href="../.." title="meanas" class="md-nav__button md-logo" aria-label="meanas" data-md-component="logo">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54"/></svg>
|
||
|
||
</a>
|
||
meanas
|
||
</label>
|
||
|
||
<div class="md-nav__source">
|
||
<a href="https://mpxd.net/code/jan/meanas" title="Go to repository" class="md-source" data-md-component="source">
|
||
<div class="md-source__icon md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M439.6 236.1 244 40.5c-5.4-5.5-12.8-8.5-20.4-8.5s-15 3-20.4 8.4L162.5 81l51.5 51.5c27.1-9.1 52.7 16.8 43.4 43.7l49.7 49.7c34.2-11.8 61.2 31 35.5 56.7-26.5 26.5-70.2-2.9-56-37.3L240.3 199v121.9c25.3 12.5 22.3 41.8 9.1 55-6.4 6.4-15.2 10.1-24.3 10.1s-17.8-3.6-24.3-10.1c-17.6-17.6-11.1-46.9 11.2-56v-123c-20.8-8.5-24.6-30.7-18.6-45L142.6 101 8.5 235.1C3 240.6 0 247.9 0 255.5s3 15 8.5 20.4l195.6 195.7c5.4 5.4 12.7 8.4 20.4 8.4s15-3 20.4-8.4l194.7-194.7c5.4-5.4 8.4-12.8 8.4-20.4s-3-15-8.4-20.4"/></svg>
|
||
</div>
|
||
<div class="md-source__repository">
|
||
meanas
|
||
</div>
|
||
</a>
|
||
</div>
|
||
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../.." class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
Home
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" checked>
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../" class="md-nav__link ">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
API
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="true">
|
||
<label class="md-nav__title" for="__nav_2">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
API
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../meanas/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
meanas
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--active">
|
||
|
||
<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link md-nav__link--active" for="__toc">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
eigensolvers
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<a href="./" class="md-nav__link md-nav__link--active">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
eigensolvers
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="Table of contents">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
Table of contents
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.eigensolvers" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> eigensolvers
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" eigensolvers">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.eigensolvers.power_iteration" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> power_iteration
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.eigensolvers.rayleigh_quotient_iteration" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> rayleigh_quotient_iteration
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.eigensolvers.signed_eigensolve" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> signed_eigensolve
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../fdfd/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
fdfd
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../waveguides/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
waveguides
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../fdtd/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
fdtd
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../fdmath/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
fdmath
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
|
||
<div class="md-sidebar__scrollwrap">
|
||
<div class="md-sidebar__inner">
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="Table of contents">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
Table of contents
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.eigensolvers" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-module"></code> eigensolvers
|
||
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label=" eigensolvers">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.eigensolvers.power_iteration" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> power_iteration
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.eigensolvers.rayleigh_quotient_iteration" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> rayleigh_quotient_iteration
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#meanas.eigensolvers.signed_eigensolve" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
<code class="doc-symbol doc-symbol-toc doc-symbol-function"></code> signed_eigensolve
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-content" data-md-component="content">
|
||
|
||
<article class="md-content__inner md-typeset">
|
||
|
||
|
||
|
||
|
||
|
||
<h1 id="eigensolvers">eigensolvers<a class="headerlink" href="#eigensolvers" title="Permanent link">¶</a></h1>
|
||
|
||
|
||
<div class="doc doc-object doc-module">
|
||
|
||
|
||
|
||
<h2 id="meanas.eigensolvers" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-module"></code> <span class="doc doc-object-name doc-module-name">meanas.eigensolvers</span>
|
||
|
||
|
||
<a href="#meanas.eigensolvers" class="headerlink" title="Permanent link">¶</a></h2>
|
||
|
||
<div class="doc doc-contents first">
|
||
|
||
<p>Solvers for eigenvalue / eigenvector problems</p>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="doc doc-children">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.eigensolvers.power_iteration" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">power_iteration</span>
|
||
|
||
|
||
<a href="#meanas.eigensolvers.power_iteration" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">power_iteration</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">operator</span><span class="p">:</span> <span class="n">spmatrix</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">guess_vector</span><span class="p">:</span> <span class="n">NDArray</span><span class="p">[</span><span class="n">complex128</span><span class="p">]</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">iterations</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">20</span><span class="p">,</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="p">)</span> <span class="o">-></span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">complex</span><span class="p">,</span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">complex128</span><span class="p">]]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Use power iteration to estimate the dominant eigenvector of a matrix.</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>operator</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="scipy.sparse.spmatrix">spmatrix</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Matrix to analyze.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>guess_vector</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="numpy.typing.NDArray">NDArray</span>[<span title="numpy.complex128">complex128</span>] | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Starting point for the eigenvector. Default is a randomly chosen vector.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>iterations</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="int">int</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Number of iterations to perform. Default 20.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>20</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="tuple">tuple</span>[<span title="complex">complex</span>, <span title="numpy.typing.NDArray">NDArray</span>[<span title="numpy.complex128">complex128</span>]]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>(Largest-magnitude eigenvalue, Corresponding eigenvector estimate)</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.eigensolvers.rayleigh_quotient_iteration" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">rayleigh_quotient_iteration</span>
|
||
|
||
|
||
<a href="#meanas.eigensolvers.rayleigh_quotient_iteration" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">rayleigh_quotient_iteration</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">operator</span><span class="p">:</span> <span class="n">spmatrix</span> <span class="o">|</span> <span class="n">LinearOperator</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">guess_vector</span><span class="p">:</span> <span class="n">NDArray</span><span class="p">[</span><span class="n">complex128</span><span class="p">],</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">iterations</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">40</span><span class="p">,</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">tolerance</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">1e-13</span><span class="p">,</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">solver</span><span class="p">:</span> <span class="n">Callable</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">NDArray</span><span class="p">[</span><span class="n">complex128</span><span class="p">]]</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="p">)</span> <span class="o">-></span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">complex</span><span class="p">,</span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">complex128</span><span class="p">]]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Use Rayleigh quotient iteration to refine an eigenvector guess.</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>operator</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="scipy.sparse.spmatrix">spmatrix</span> | <span title="scipy.sparse.linalg.LinearOperator">LinearOperator</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Matrix to analyze.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>guess_vector</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="numpy.typing.NDArray">NDArray</span>[<span title="numpy.complex128">complex128</span>]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Eigenvector to refine.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>iterations</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="int">int</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Maximum number of iterations to perform. Default 40.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>40</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>tolerance</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="float">float</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Stop iteration if <code>(A - I*eigenvalue) @ v < num_vectors * tolerance</code>,
|
||
Default 1e-13.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>1e-13</code>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>solver</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="collections.abc.Callable">Callable</span>[..., <span title="numpy.typing.NDArray">NDArray</span>[<span title="numpy.complex128">complex128</span>]] | None</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Solver function of the form <code>x = solver(A, b)</code>.
|
||
By default, use scipy.sparse.spsolve for sparse matrices and
|
||
scipy.sparse.bicgstab for general LinearOperator instances.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>None</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="tuple">tuple</span>[<span title="complex">complex</span>, <span title="numpy.typing.NDArray">NDArray</span>[<span title="numpy.complex128">complex128</span>]]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>(eigenvalues, eigenvectors)</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
<div class="doc doc-object doc-function">
|
||
|
||
|
||
<h3 id="meanas.eigensolvers.signed_eigensolve" class="doc doc-heading">
|
||
<code class="doc-symbol doc-symbol-heading doc-symbol-function"></code> <span class="doc doc-object-name doc-function-name">signed_eigensolve</span>
|
||
|
||
|
||
<a href="#meanas.eigensolvers.signed_eigensolve" class="headerlink" title="Permanent link">¶</a></h3>
|
||
<div class="doc-signature highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">signed_eigensolve</span><span class="p">(</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">operator</span><span class="p">:</span> <span class="n">spmatrix</span> <span class="o">|</span> <span class="n">LinearOperator</span><span class="p">,</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">how_many</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">negative</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="p">)</span> <span class="o">-></span> <span class="nb">tuple</span><span class="p">[</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">complex128</span><span class="p">],</span> <span class="n">NDArray</span><span class="p">[</span><span class="n">numpy</span><span class="o">.</span><span class="n">complex128</span><span class="p">]</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="p">]</span>
|
||
</code></pre></div>
|
||
|
||
<div class="doc doc-contents ">
|
||
|
||
<p>Find the largest-magnitude positive-only (or negative-only) eigenvalues and
|
||
eigenvectors of the provided matrix.</p>
|
||
|
||
|
||
<p><span class="doc-section-title">Parameters:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Name</th>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
<th>Default</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>operator</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="scipy.sparse.spmatrix">spmatrix</span> | <span title="scipy.sparse.linalg.LinearOperator">LinearOperator</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Matrix to analyze.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>how_many</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="int">int</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>How many eigenvalues to find.</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<em>required</em>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code>negative</code>
|
||
</td>
|
||
<td>
|
||
<code><span title="bool">bool</span></code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>Whether to find negative-only eigenvalues.
|
||
Default False (positive only).</p>
|
||
</div>
|
||
</td>
|
||
<td>
|
||
<code>False</code>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
<p><span class="doc-section-title">Returns:</span></p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Type</th>
|
||
<th>Description</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="numpy.typing.NDArray">NDArray</span>[<span title="numpy.complex128">complex128</span>]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p>(sorted list of eigenvalues, 2D ndarray of corresponding eigenvectors)</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
<tr class="doc-section-item">
|
||
<td>
|
||
<code><span title="numpy.typing.NDArray">NDArray</span>[<span title="numpy.complex128">complex128</span>]</code>
|
||
</td>
|
||
<td>
|
||
<div class="doc-md-description">
|
||
<p><code>eigenvectors[:, k]</code> corresponds to the k-th eigenvalue</p>
|
||
</div>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
</article>
|
||
</div>
|
||
|
||
|
||
<script>var target=document.getElementById(location.hash.slice(1));target&&target.name&&(target.checked=target.name.startsWith("__tabbed_"))</script>
|
||
</div>
|
||
|
||
<button type="button" class="md-top md-icon" data-md-component="top" hidden>
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 20h-2V8l-5.5 5.5-1.42-1.42L12 4.16l7.92 7.92-1.42 1.42L13 8z"/></svg>
|
||
Back to top
|
||
</button>
|
||
|
||
</main>
|
||
|
||
<footer class="md-footer">
|
||
|
||
<div class="md-footer-meta md-typeset">
|
||
<div class="md-footer-meta__inner md-grid">
|
||
<div class="md-copyright">
|
||
|
||
|
||
Made with
|
||
<a href="https://squidfunk.github.io/mkdocs-material/" target="_blank" rel="noopener">
|
||
Material for MkDocs
|
||
</a>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
</div>
|
||
</footer>
|
||
|
||
</div>
|
||
<div class="md-dialog" data-md-component="dialog">
|
||
<div class="md-dialog__inner md-typeset"></div>
|
||
</div>
|
||
|
||
|
||
|
||
|
||
|
||
<script id="__config" type="application/json">{"annotate": null, "base": "../..", "features": ["navigation.indexes", "navigation.sections", "navigation.top", "content.code.copy", "toc.follow"], "search": "../../assets/javascripts/workers/search.2c215733.min.js", "tags": null, "translations": {"clipboard.copied": "Copied to clipboard", "clipboard.copy": "Copy to clipboard", "search.result.more.one": "1 more on this page", "search.result.more.other": "# more on this page", "search.result.none": "No matching documents", "search.result.one": "1 matching document", "search.result.other": "# matching documents", "search.result.placeholder": "Type to start searching", "search.result.term.missing": "Missing", "select.version": "Select version"}, "version": null}</script>
|
||
|
||
|
||
<script src="../../assets/javascripts/bundle.79ae519e.min.js"></script>
|
||
|
||
<script src="../../js/print-site.js"></script>
|
||
|
||
<script src="../../javascripts/mathjax.js"></script>
|
||
|
||
<script src="../../assets/vendor/mathjax/startup.js"></script>
|
||
|
||
|
||
</body>
|
||
</html> |