triennale-appunti-steffo/docs/route-ottimizzazioneLineare.chunk.5ecfe.js.map

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rcesContent":["// extracted by mini-css-extract-plugin\nmodule.exports = {\"latex\":\"latex__3Esv7\"};","import {Component} from 'preact'\nimport Split from \"../components/split\";\nimport Latex from \"../components/latex\";\nimport Panel from \"../components/panel\";\nimport Example from \"../components/example\";\nimport Todo from \"../components/todo\";\nimport Minus from \"../components/minus\";\nimport Plus from \"../components/plus\";\n\nconst r = String.raw;\n\nexport default class OttimizzazioneLineare extends Component {\n    render() {\n        return (\n            <div>\n                <h1>Ottimizzazione lineare intera</h1>\n                <Split title={\"Materiale\"}>\n                    <Panel title={\"Videolezioni su YouTube\"}>\n                        <p>\n                            Ho rimosso il rumore in sottofondo da tutti i video di Ricerca Operativa!\n                        </p>\n                        <p>\n                            <b><a href={\"https://www.youtube.com/playlist?list=PLh93e8qjTszffkHNn-19CqUOhHFbhBlBh\"}>Guardate i video qui!</a></b>\n                        </p>\n                    </Panel>\n                </Split>\n                <Split title={\"Le basi\"}>\n                    <Panel title={\"Funzione obiettivo\"}>\n                        <p>\n                            La funzione obiettivo è la funzione con valore noto sconosciuto:\n                        </p>\n                        <p>\n                            <Latex>{r`z = C_1 \\cdot x_1 + C_2 \\cdot x_2 + C_n \\cdot x_n`}</Latex>\n                        </p>\n                    </Panel>\n                    <Panel title={\"Gradiente\"}>\n                        <p>\n                            Funzione della funzione obiettivo che indica la direzione del suo aumento più veloce.\n                        </p>\n                        <p>\n                            <Latex>{r`\\nabla f = \\frac{\\delta f}{\\delta x_1} e_1 + \\frac{\\delta f}{\\delta x_2} e_2 + \\frac{\\delta f}{\\delta x_n} e_n`}</Latex>\n                        </p>\n                        <p>\n                            <Latex>{r`e_i`}</Latex> è la direzione della coordinata i-esima.\n                        </p>\n                        <Example>\n                            Se <Latex>{r`n = 3`}</Latex>, allora:\n                            <ul>\n                                <li><Latex>{r`e_1 = (1, 0, 0)`}</Latex></li>\n                                <li><Latex>{r`e_2 = (0, 1, 0)`}</Latex></li>\n                                <li><Latex>{r`e_3 = (0, 0, 1)`}</Latex></li>\n                            </ul>\n                        </Example>\n                        <Example>\n                            Se la funzione obiettivo è <Latex>z = 2w + 3x + 4y</Latex>, il suo gradiente è <Latex>{r`\\nabla z = (2, 3, 4)`}</Latex>.\n                        </Example>\n                    </Panel>\n                </Split>\n                <Split title={\"La forma standard\"}>\n                    <Panel title={\"Condizioni\"}>\n                        <p>\n                            Un sistema è in <i>forma standard</i> quando ha:\n                        </p>\n                        <ul>\n                            <li>Solo equazioni</li>\n                            <li>Tutte le variabili maggiori di zero</li>\n                        </ul>\n                    </Panel>\n                    <Panel title={\"Slack\"}>\n                        <p>\n                            Possiamo trasformare una disequazione in equazione introducendo variabili <i>slack</i>:\n                        </p>\n                        <p>\n                            <Latex>{r`3x + 2y \\leq 15 \\implies 3x + 2y + s_1 = 15`}</Latex>\n                        </p>\n                        <p>\n                            In seguito, possiamo riscrivere tutte le funzioni in termini delle variabili slack.\n                        </p>\n                        <Example>\n                            Si ottiene qualcosa come <Latex>{r`z = -2 s_1 - 3 s_2 + 40`}</Latex>.\n                        </Example>\n                    </Panel>\n                    <Panel title={\"Tableu\"}>\n                        <p>\n                            Un modo per rappresentare sistemi in forma standard.\n                        </p>\n                        <p>\n                            <table class={\"right\"}>\n                                <thead>\n                                    <tr>\n                                        <th/>\n                                        <th><Latex>x</Latex></th>\n                                        <th><Latex>y</Latex></th>\n                                        <th><Latex>s_1</Latex></th>\n                                        <th><Latex>s_2</Latex></th>\n                                    </tr>\n                                </thead>\n                                <tbody>\n                                    <tr>\n                                        <td>obj:</td>\n                                        <td><Latex>80</Latex></td>\n                                        <td><Latex>70</Latex></td>\n                                        <td><Latex>0</Latex></td>\n                                        <td><Latex>0</Latex></td>\n                                    </tr>\n                                    <tr>\n                                        <td/>\n                                        <td><Latex>3</Latex></td>\n                                        <td><Latex>2</Latex></td>\n                                        <td><Latex>1</Latex></td>\n                                        <td><Latex>0</Latex></td>\n                                    </tr>\n                                    <tr>\n                                        <td/>\n                                        <td><Latex>2</Latex></td>\n                                        <td><Latex>3</Latex></td>\n                                        <td><Latex>0</Latex></td>\n                                        <td><Latex>1</Latex></td>\n                                    </tr>\n                                </tbody>\n                            </table>\n                        </p>\n                        <Example>\n                            E' la matrice equivalente completa del sistema!\n                        </Example>\n                        <p>\n                            Riscrivendo in termini delle variabili slack, otteniamo:\n                        </p>\n                        <p>\n                            <table class={\"right\"}>\n                                <thead>\n                                <tr>\n                                    <th/>\n                                    <th><Latex>x</Latex></th>\n                                    <th><Latex>y</Latex></th>\n                                    <th><Latex>s_1</Latex></th>\n                                    <th><Latex>s_2</Latex></th>\n                                </tr>\n                                </thead>\n                                <tbody>\n                                <tr>\n                                    <td>obj:</td>\n                                    <td><Latex>0</Latex></td>\n                                    <td><Latex>0</Latex></td>\n                                    <td><Latex>-20</Latex></td>\n                                    <td><Latex>-10</Latex></td>\n                                </tr>\n                                <tr>\n                                    <td/>\n                                    <td><Latex>1</Latex></td>\n                                    <td><Latex>0</Latex></td>\n                                    <td><Latex>{r`-\\frac{3}{5}`}</Latex></td>\n                                    <td><Latex>{r`\\frac{2}{5}`}</Latex></td>\n                                </tr>\n                                <tr>\n                                    <td/>\n                                    <td><Latex>0</Latex></td>\n                                    <td><Latex>1</Latex></td>\n                                    <td><Latex>{r`\\frac{2}{5}`}</Latex></td>\n                                    <td><Latex>{r`-\\frac{3}{5}`}</Latex></td>\n                                </tr>\n                                </tbody>\n                            </table>\n                        </p>\n                        <Example>\n                            Abbiamo appena applicato Gauss-Jordan, trovando la matrice inversa.\n                        </Example>\n                    </Panel>\n                </Split>\n                <Split title={\"Un po' di Algebra Lineare\"}>\n                    <Panel title={\"Base\"}>\n                        <p>\n                            Insieme di <Latex>n</Latex> colonne lunghe <Latex>n</Latex> linearmente indipendenti.\n                        </p>\n                    </Panel>\n                    <Panel title={\"Soluzione di base\"}>\n                        <p>\n                            Soluzione ottenuta dalla seguente formula:\n                        </p>\n                        <ol>\n                            <li><Latex>{r`A \\cdot x = B`}</Latex></li>\n                            <li><Latex>{r`B \\cdot x_B + F \\cdot x_F = b`}</Latex></li>\n                            <li><Latex>{r`x_B = B^{-1} \\cdot b - B^{-1} \\cdot x_F`}</Latex></li>\n                        </ol>\n                        <p>\n                            Dove:\n                        </p>\n                        <ul>\n                            <li><Latex>{r`A`}</Latex> è la matrice equivalente</li>\n                            <li><Latex>{r`b`}</Latex> è la colonna dei valori noti</li>\n                            <li><Latex>{r`B`}</Latex> è la matrice delle colonne della base</li>\n                            <li><Latex>{r`F`}</Latex> è la matrice delle colonne fuoribase</li>\n                            <li><Latex>{r`x_B`}</Latex> sono le incognite relative alla base</li>\n                            <li><Latex>{r`x_F`}</Latex> sono le incognite relative ai valori fuoribase</li>\n                        </ul>\n                    </Panel>\n                </Split>\n                <Split title={\"Forme\"}>\n                    <Panel title={\"Forma standard\"}>\n                        <ul>\n                            <li><Minus>Solo equazioni</Minus></li>\n                            <li><Minus>Tutte le variabili maggiori di zero</Minus></li>\n                        </ul>\n                    </Panel>\n                    <Panel title={\"Forma canonica\"}>\n                        <ul>\n                            <li><Plus>Equazioni e disequazioni</Plus></li>\n                            <li><Minus>Tutte le variabili maggiori di zero</Minus></li>\n                        </ul>\n                    </Panel>\n                    <Panel title={\"Forma generale\"}>\n                        <ul>\n                            <li><Plus>Equazioni e disequazioni</Plus></li>\n                            <li><Plus>Tutte le variabili maggiori di zero</Plus></li>\n                        </ul>\n                    </Panel>\n                </Split>\n                <Split title={\"Equivalenza di forma\"}>\n                    <Panel title={\"Da generale a canonica\"}>\n                        <p>\n                            Sostituiamo le variabili potenzialmente negative (unconstrained) <Latex>{r`x_j`}</Latex> con due variabili <Latex>{r`x_j^+`}</Latex> e <Latex>{r`x_j^-`}</Latex>.\n                        </p>\n                    </Panel>\n                    <Panel title={\"Da canonica a standard\"}>\n                        <p>\n                            Convertiamo le disequazioni in equazioni aggiungendo una variabile slack.\n                        </p>\n                    </Panel>\n                    <Panel title={\"Da standard a generale\"}>\n                        <p>\n                            Convertiamo ogni equazione <Latex>{r`=`}</Latex> in due disequazioni <Latex>{r`\\leq`}</Latex> e <Latex>{r`\\geq`}</Latex>,\n                        </p>\n                    </Panel>\n                </Split>\n            </div>\n        )\n    }\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"panel\":\"panel__1ubJw\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__P0_NL\"};","import style from \"./todo.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Todo extends Component {\r\n\trender() {\r\n\t\treturn <span class={style.todo}>{this.props.children}</span>;\r\n\t}\r\n}\r\n","import style from \"./panel.css\";\nimport { Component } from 'preact';\n\nexport default class Panel extends Component {\n\tgetStyle() {\n\t\treturn style.panel;\n\t};\n\n\trender() {\n\t\tlet title = null;\n\t\tif(this.props.title !== undefined) {\n\t\t\ttitle = (<h3>{this.props.title}</h3>);\n\t\t}\n\n\t\treturn (\n\t\t\t<div class={this.getStyle()} id={this.props.id}>\n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t</div>\n\t\t);\n\t}\n}\n","import style from \"./minus.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Minus extends Component {\r\n\trender() {\r\n\t\treturn <span class={style.minus}>{this.props.children}</span>;\r\n\t}\r\n}\r\n","import style from \"./example.css\";\nimport {Component} from \"preact\";\n\nexport default class Example extends Component {\n    render() {\n        return (\n            <blockquote class={style.example}>\n                {this.props.children}\n            </blockquote>\n        )\n    }\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"plus\":\"plus__29_QM\"};","import style from './latex.css';\nimport { Component } from 'preact';\n\nexport default class Latex extends Component {\n\trender() {\n\t\tlet equation = `{\\\\color{White} ${this.props.children} }`;\n\t\treturn (\n\t\t\t<img src={`https://latex.codecogs.com/svg.latex?${equation}`}\n\t\t\t\t alt={this.props.children}\n\t\t\t     title={this.props.children}\n\t\t\t     class={style.latex}\n\t\t\t/>);\n\t}\n}","import style from \"./plus.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Plus extends Component {\r\n\trender() {\r\n\t\treturn <span class={style.plus}>{this.props.children}</span>;\r\n\t}\r\n}\r\n","import style from \"./split.css\";\nimport { Component } from 'preact';\n\nexport default class Split extends Component {\n\trender() {\n\t    let title = null;\n\t    if(this.props.title !== undefined) {\n            title = (<h2>{this.props.title}</h2>)\n        }\n\n        let children;\n        if(Array.isArray(this.props.children)) {\n            children = this.props.children.map(element => {\n                return (<div class={style.splitchild}>{element}</div>);\n            });\n        }\n        else {\n            children = <div class={style.splitchild}>{this.props.children}</div>;\n        }\n\t\treturn (\n\t        <div class={style.split}>\n                {title}\n                <div class={style.splitparent}>{children}</div>\n            </div>\n        );\n\t}\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"minus\":\"minus__2Ld4F\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"todo\":\"todo__1pOoN\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"split\":\"split__3qCWp\",\"splitparent\":\"splitparent__2xagg\",\"splitchild\":\"splitchild__3cEoc\"};"],"sourceRoot":""}