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/*! For license information please see bundle.731f9.esm.js.LICENSE.txt */
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/*! For license information please see bundle.bde4a.esm.js.LICENSE.txt */
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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><title>Appunti Web</title><meta name="viewport" content="width=device-width,initial-scale=1"><meta name="mobile-web-app-capable" content="yes"><meta name="apple-mobile-web-app-capable" content="yes"><link rel="apple-touch-icon" href="./assets/icons/apple-touch-icon.png"><link rel="manifest" href="/manifest.json"><meta name="theme-color" content="#a0ccff"><link rel="shortcut icon" href="/favicon.ico"><style>*{box-sizing:border-box}body{background-color:#0d193b;color:#a0ccff;font-family:Arial,sans-serif}</style><link href="/bundle.0c633.css" rel="preload" as="style" onload="this.rel='stylesheet'"><noscript><link rel="stylesheet" href="/bundle.0c633.css"></noscript></head><body><script type="__PREACT_CLI_DATA__">{"preRenderData":{"url":"/"}}</script><script nomodule="">!function(){var e=document,t=e.createElement("script");if(!("noModule"in t)&&"onbeforeload"in t){var n=!1;e.addEventListener("beforeload",function(e){if(e.target===t)n=!0;else if(!e.target.hasAttribute("nomodule")||!n)return;e.preventDefault()},!0),t.type="module",t.src=".",e.head.appendChild(t),t.remove()}}();</script><script crossorigin="anonymous" src="/bundle.731f9.esm.js" type="module"></script><script nomodule="" src="/polyfills.b70a1.js"></script><script nomodule="" defer="defer" src="/bundle.2ef69.js"></script></body></html>
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|
||||
`)))))),l(e.a,{title:"Dualità"},l(a.a,{title:"Duale"},l("p",null,"Il sistema che ",l("b",null,l(d.a,null,"massimizza"),"/",l(b.a,null,"minimizza")," i moltiplicatori di rilassamento")," di un problema detto ",l("i",null,"primale"),".")),l(a.a,{title:"In termini matriciali"},l("p",null,"Possiamo ",l("b",null,"trasporre")," il tableau e sostituire le variabili ",l(t.b,null,yl(ml||(ml=Il`x_n`)))," con variabili ",l(t.b,null,yl(fl||(fl=Il`u_n`)))," per ottenere il sistema duale!"),l("p",null,"I maggiori e minori dei vincoli diventeranno maggiori e minori delle variabili e viceversa.")),l(a.a,{title:"Feasibility del duale"},l("ul",null,l("li",null,"Se un problema ha una ",l("b",null,"soluzione finita"),", allora anche il suo duale la avrà."),l("li",null,"Se un problema è ",l("b",null,l(s.a,null)),", allora il suo duale potrà essere ",l(s.a,null)," oppure ",l(c.a,null),"."),l("li",null,"Se un problema è ",l("b",null,l(c.a,null)),", allora il suo duale sarà certamente ",l(s.a,null),".")))),l(e.a,{title:"Un po' di teoria"},l(a.a,{title:"Lemma di Farkas"},l("p",null,"Una disuguaglianza lineare ",l(t.b,null,yl(hl||(hl=Il`c_0 \leq \mathbf{c}^T \mathbf{x}`)))," è verificata da tutti i punti di un poliedro non-",l(s.a,null)," se e solo se esiste un vettore ",l(t.b,null,yl(pl||(pl=Il`u \in \mathfrak{R}^m`)))," tale che:"),l(m.a,null,yl(_l||(_l=Il`\mathbf{c}^T \geq \mathbf{u}^T \mathbf{A}`))),l(m.a,null,yl(vl||(vl=Il`c_0 \leq \mathbf{u}^T \mathbf{b}`))),l("p",null,l(u.a,null,"TODO: Cioè?"))),l(a.a,{title:"Dualità forte"},l("p",null,"Il teorema che dimostra l'equivalenza tra primale e duale."),l("p",null,"Se uno dei due problemi è finito, la soluzione di uno coincide con la soluzione dell'altro."),l("p",null,l(t.b,null,yl(gl||(gl=Il`\mathbf{c}^T \mathbf{x} = \mathbf{u}^T \mathbf{b}`)))),l("p",null,l(u.a,null,"TODO: Anche qui c'è una lunga dimostrazione..."))),l(a.a,{title:"Dualità debole"},l("p",null,"Il teorema che dimostra che il valore della funzione obiettivo del duale (di un qualsiasi tableau) è sempre ",l(d.a,null,"minore o uguale"),"/",l(b.a,null,"maggiore o uguale")," alla soluzione del corrispettivo primale."),l("p",null,l(u.a,null,"TODO: Dimostrazione cortina, ma sembra complicata."))),l(a.a,{title:"Condizioni di ottimalità"},l("p",null,"Il teorema che ci permette di passare dalla soluzione del duale alla soluzione del primale. ",l(u.a,null,"TODO: credo?")),l("p",null,"Si deriva combinando le seguenti condizioni:"),l("ul",null,l("li",null,"Ammissibilità del primale: ",l(t.b,null,yl(zl||(zl=Il`\mathbf{A} \mathbf{X} \geq \mathbf{b}, \quad \mathbf{x} \geq 0`)))),l("li",null,"Ammissibilità del duale: ",l(t.b,null,yl(xl||(xl=Il`\mathbf{u}^T \mathbf{A} \leq \mathbf{c}^T, \quad \mathbf{u} \geq 0`)))),l("li",null,"Teorema della dualità forte: ",l(t.b,null,yl(ql||(ql=Il`\mathbf{c}^T \mathbf{x} = \mathbf{u}^T \mathbf{b}`)))," (alla soluzione ottima)")),l("p",null,"Ne risulta che una soluzione è ottima se e solo se:"),l(m.a,null,yl(Ll||(Ll=Il`\left( \mathbf{c}^T - \mathbf{u}^T \mathbf{A} \right) \mathbf{x} = 0`))),l(m.a,null,yl(wl||(wl=Il`\mathbf{u}^T \left( \mathbf{A} \mathbf{x} - \mathbf{b} \right) = 0`))))),l(e.a,{title:"Simplex duale"},l(a.a,{title:"Cos'è?"},l("p",null,"Un'estensione al Simplex primale che opera sul problema duale.")),l(a.a,{title:"Come funziona?"},l("p",null,"Funziona esattamente come il Simplex primale, ma opera sulle righe invece che sulle colonne, cercando di rendere ",l(d.a,null,"positivi"),"/",l(b.a,null,"negativi")," tutti i termini noti."),l(o.a,null,"Significa che si possono moltiplicare tutti i valori di una riga per lo stesso numero e il risultato non cambia...?"))),l(e.a,{title:"Analisi di sensibilità"},l(a.a,{title:"Cos'è?"},l("p",null,"Un procedimento che misura di ",l("b",null,"quanto può variare")," il termine noto di un vincolo ",l(t.b,null,yl(Tl||(Tl=Il`b_i`)))," o il coefficiente della funzione obiettivo ",l(t.b,null,yl(Sl||(Sl=Il`c_i`)))," prima che la base degeneri. ",l(u.a,null,"TODO: verificare")))))}}.call(this,i("hosL").h)},htlC:function(l){l.exports={splitparent:"splitparent__3-wBs",splitchild:"splitchild__begkX"}},imVn:function(l,n,i){"use strict";(function(l){var e=i("OmdA"),t=i.n(e),a=i("Y9Ml");n.a=function(n){return l(a.a,{color:n.color},l("h3",{class:t.a.title},n.title),l("div",{class:t.a.contents},n.children))}}).call(this,i("hosL").h)},wQ73:function(l,n,i){"use strict";var e=i("hosL");n.a=Object(e.createContext)(!0)},zDbI:function(l,n,i){"use strict";(function(l){var e=i("Q7TX");n.a=function(n){return l(e.b,{inline:!1,display:e.a.BLOCK},n.children)}}).call(this,i("hosL").h)}}]);
|
||||
//# sourceMappingURL=route-OttimizzazioneLineare.chunk.55518.esm.js.map
|
||||
//# sourceMappingURL=route-OttimizzazioneLineare.chunk.ae44a.esm.js.map
|
||||
|
|
@ -1 +1 @@
|
|||
{"version":3,"sources":[],"names":[],"mappings":"","file":"route-OttimizzazioneLineare.chunk.55518.esm.js","sourceRoot":""}
|
||||
{"version":3,"sources":[],"names":[],"mappings":"","file":"route-OttimizzazioneLineare.chunk.ae44a.esm.js","sourceRoot":""}
|
||||
2
docs/sw-esm.js
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2
docs/sw.js
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docs/sw.js
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|
|
@ -1,7 +1,7 @@
|
|||
{
|
||||
"private": true,
|
||||
"name": "appuntiweb",
|
||||
"version": "0.3.11",
|
||||
"version": "0.3.12",
|
||||
"license": "AGPL-3.0-or-later",
|
||||
"scripts": {
|
||||
"start": "preact watch",
|
||||
|
|
|
|||
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|
|
@ -42,6 +42,7 @@
|
|||
|
||||
.unknown {
|
||||
color: @magenta;
|
||||
border: 2px solid fade(@magenta, 20%);
|
||||
|
||||
.count {
|
||||
color: @magenta;
|
||||
|
|
@ -50,6 +51,7 @@
|
|||
|
||||
.expired {
|
||||
color: @red;
|
||||
border: 2px solid fade(@red, 20%);
|
||||
|
||||
.count {
|
||||
color: @red;
|
||||
|
|
|
|||
|
|
@ -2,6 +2,11 @@ import {Component} from 'preact'
|
|||
import Section from "../components/Elements/Section";
|
||||
import Panel from "../components/Elements/Panel";
|
||||
import Timer from "../components/Elements/Timer";
|
||||
import ILatex from "../components/Rendering/ILatex";
|
||||
import TablePanel from "../components/Elements/TablePanel";
|
||||
import BLatex from "../components/Rendering/BLatex";
|
||||
import PLatex from "../components/Rendering/PLatex";
|
||||
import Example from "../components/Elements/Example";
|
||||
|
||||
const r = String.raw;
|
||||
|
||||
|
|
@ -71,6 +76,203 @@ export default class BasiDiDati extends Component {
|
|||
</p>
|
||||
</Panel>
|
||||
</Section>
|
||||
<Section title={"Calcolo dei costi delle query"}>
|
||||
<TablePanel>
|
||||
<thead>
|
||||
<tr>
|
||||
<th>Simbolo</th>
|
||||
<th>Descrizione</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><BLatex>{r`N_{tuple}`}</BLatex></td>
|
||||
<td>Numero di tuple di una tabella</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><BLatex>{r`N_{blocchi}`}</BLatex></td>
|
||||
<td>Numero di blocchi di una tabella</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><BLatex>{r`N_{foglie}`}</BLatex></td>
|
||||
<td>Numero di foglie di un indice</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><BLatex>{r`N_{indici}`}</BLatex></td>
|
||||
<td>Numero di indici presenti in una tabella</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><BLatex>{r`N_{unici}`}</BLatex></td>
|
||||
<td>Numero di valori unici presenti in una colonna</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><BLatex>{r`F`}</BLatex></td>
|
||||
<td>Fattore di selettività di una condizione</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><BLatex>{r`C`}</BLatex></td>
|
||||
<td>Costo di accesso a una o più tuple</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><BLatex>{r`N_{selezionati}`}</BLatex></td>
|
||||
<td>Numero di tuple del risultato</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</TablePanel>
|
||||
</Section>
|
||||
<Section>
|
||||
<Panel title={"Fattore booleano"}>
|
||||
<p>
|
||||
Espressione formata da <b>una o più condizioni moltiplicate tra loro</b>.
|
||||
</p>
|
||||
</Panel>
|
||||
<Panel title={"Argomenti di ricerca attraverso indice"}>
|
||||
<p>
|
||||
Condizioni che soddisfano i seguenti requisiti:
|
||||
</p>
|
||||
<ul>
|
||||
<li>
|
||||
Usa uno dei seguenti <b>operatori</b>:
|
||||
<ul>
|
||||
<li><ILatex>{r`<`}</ILatex></li>
|
||||
<li><ILatex>{r`\leq`}</ILatex></li>
|
||||
<li><ILatex>{r`=`}</ILatex></li>
|
||||
<li><ILatex>{r`\geq`}</ILatex></li>
|
||||
<li><ILatex>{r`>`}</ILatex></li>
|
||||
<li><b><code>{r`BETWEEN`}</code></b></li>
|
||||
<li><b><code>{r`OR`}</code></b> (solo in alcuni DBMS)</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li>Uno dei due termini del confronto è <b>una colonna</b> della tabella</li>
|
||||
<li>L'altro termine del confronto è <b>una costante numerica</b></li>
|
||||
</ul>
|
||||
</Panel>
|
||||
<Panel title={"Indici"}>
|
||||
<p>
|
||||
È possibile costruire indici sulle colonne di una tabella per velocizzare le query che riguardano quelle colonne.
|
||||
</p>
|
||||
<p>
|
||||
In particolare, ogni tabella può avere <b>un</b> <i>indice clustered</i> e <b>infiniti</b> <i>indici unclustered</i>.
|
||||
</p>
|
||||
<p>
|
||||
Generalmente, l'indice clustered è costruito sulla colonna della primary key, ma <a href={"https://stackoverflow.com/questions/15051869/relationship-of-primary-key-and-clustered-index"}>non è sempre quello il caso</a>.
|
||||
</p>
|
||||
<p>
|
||||
Gli indici vanno tenuti aggiornati, e ciò ha un <b>costo di manutenzione</b>:
|
||||
</p>
|
||||
<ul>
|
||||
<li><code>DELETE</code>: <ILatex>{r`N_{indici} \cdot 2 \cdot N_{selezionati}`}</ILatex></li>
|
||||
<li><code>UPDATE</code>: <ILatex>{r`N_{indici} \cdot 4 \cdot N_{selezionati}`}</ILatex></li>
|
||||
</ul>
|
||||
<p>
|
||||
È possibile usare gli indici nelle query solo per gli <b>argomenti di ricerca attraverso indice</b>.
|
||||
</p>
|
||||
</Panel>
|
||||
</Section>
|
||||
<Section>
|
||||
<Panel title={"Fattore di selettività"}>
|
||||
<p>
|
||||
La percentuale di tuple di una tabella che soddisfano una condizione.
|
||||
</p>
|
||||
<table>
|
||||
<thead>
|
||||
<tr>
|
||||
<th>Condizione</th>
|
||||
<th>Fattore di selettività</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><code>col = $costante</code></td>
|
||||
<td><BLatex>{r`F = \frac{1}{N_{unici}`}</BLatex></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><code>col != $costante</code></td>
|
||||
<td><BLatex>{r`F = 1 - \frac{1}{N_{unici}`}</BLatex></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><code>col1 != col2</code></td>
|
||||
<td><BLatex>{r`F = \frac{1}{max(N_{unici_A}, N_{unici_B})`}</BLatex></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><code>IN</code></td>
|
||||
<td><BLatex>{r`F = \frac{n_{IN}}{N_{unici}}`}</BLatex></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><code>col > $costante</code></td>
|
||||
<td><BLatex>{r`F = \frac{ max(col) - \$costante }{ max(col) - min(col) }`}</BLatex></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><code>{r`col < $costante`}</code></td>
|
||||
<td><BLatex>{r`F = \frac{ \$costante - min(col) }{ max(col) - min(col) }`}</BLatex></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><code>col BETWEEN $lower AND $upper</code></td>
|
||||
<td><BLatex>{r`F = \frac{ \$upper - \$lower }{ max(col) - min(col) }`}</BLatex></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><code>cond1 OR cond2</code></td>
|
||||
<td><BLatex>{r`F = F_{cond1} + F_{cond2} - ( F_{cond1} \cdot F_{cond2} )`}</BLatex></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
</Panel>
|
||||
<Panel title={"Costo di accesso"}>
|
||||
<p>
|
||||
Quante <i>unità di lavoro</i> costa accedere a una specifica relazione:
|
||||
</p>
|
||||
<PLatex>{r`
|
||||
C = {\color{yellow} {C_{indice}}} + {\color{Orange} C_{relazione}}
|
||||
`}</PLatex>
|
||||
<p>
|
||||
Per accedere attraverso un indice a una specifica tupla della relazione, si spenderà:
|
||||
</p>
|
||||
<PLatex>{r`
|
||||
C = {\color{yellow} 1} + {\color{Orange} 1}
|
||||
`}</PLatex>
|
||||
<p>
|
||||
Se le tuple a cui si vuole accedere sono più di una, allora, il costo dipenderà da se l'indice è clustered o non-clustered.
|
||||
</p>
|
||||
<Example>
|
||||
Nel calcolo del costo di una query, si considerano tutti i cambi di pagina come <b>page fault</b>.
|
||||
</Example>
|
||||
<p>
|
||||
Per gli indici <b>clustered</b>, visto che basta caricare in memoria i blocchi in sequenza, il costo sarà:
|
||||
</p>
|
||||
<PLatex>{r`
|
||||
C = {\color{yellow} ( F \cdot N_{foglie} ) } + {\color{Orange} ( F \cdot N_{blocchi} ) }
|
||||
`}</PLatex>
|
||||
<p>
|
||||
Per gli indici <b>unclustered</b>, per i quali potremmo dover caricare e rimuovere lo stesso blocco dalla memoria più volte, il costo sarà:
|
||||
</p>
|
||||
<PLatex>{r`
|
||||
C = {\color{yellow} ( F \cdot N_{foglie} ) } + {\color{Orange} ( F \cdot N_{tuple} ) }
|
||||
`}</PLatex>
|
||||
<p>
|
||||
Se si stanno effettuando query su più indici unclustered, il costo sarà:
|
||||
</p>
|
||||
<PLatex>{r`
|
||||
C = {\color{yellow}\sum_k ( F_k \cdot N_{foglie_k} )} + {\color{Orange} \left( \prod_k F_k \cdot N_{tuple} \right)}
|
||||
`}</PLatex>
|
||||
</Panel>
|
||||
<Panel title={"Costo di join"}>
|
||||
<p>
|
||||
Quante <i>unità di lavoro</i> costa effettuare un join tra due relazioni.
|
||||
</p>
|
||||
<p>
|
||||
Varia in base al metodo di join utilizzato.
|
||||
</p>
|
||||
<p>
|
||||
Utilizzando il metodo del <b>nested loop</b>:
|
||||
</p>
|
||||
<PLatex>{r`
|
||||
C_{1 \times 2} = C_1 + ( N_{selezionati_1} \cdot C_2 )
|
||||
`}</PLatex>
|
||||
<p>
|
||||
La scelta della colonna su cui iterare è quindi importante!
|
||||
</p>
|
||||
</Panel>
|
||||
</Section>
|
||||
</div>
|
||||
)
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in a new issue