{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Trasformata di Legendre di una funzione\n", "\n", "Usiamo il programma python *legendre.py* per calcolare *numericamente* la trasformata di Legendre di una funzione. \n", "\n", "Eseguiamo preventivamente la cella che segue per poter visualizzare la grafica direttamente in questa scheda del browser " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Carichiamo il programma *legendre* che deve essere presente nello stesso folder di questo notebook" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "%run legendre.py" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La funzione di cui si vuole fare la trasformata è:\n", "\n", "$$y=e^{-x}$$\n", "\n", "Questa è codificata nella funzione *func* nel file *legendre.py* ed è conservata come metodo all'interno della classe *function* allo scopo di poterla modificare con un metodo opportuno della classe, senza dover editare il programma e doverlo rilanciare; si veda più avanti. Per controllare la funzione inserita, usare il metodo *print* associato all'istanza $f$ della classe *function*:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "np.e**(-1*x)\n" ] } ], "source": [ "f.print()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La funzione *legendre(xmin,xmax,npoint)* definisce le rette tangenti alla funzione *y* in *npoint* punti, da *x=xmin* a *x=xmax*, e le disegna (rette in blu); la funzione *y* (curva in nero) è l'inviluppo dell'insieme di rette tangenti: " ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "legendre(0.0,5,10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Aumentando il parametro *npoint*, la ricostruzione della curva *y* appare più evidente" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "legendre(0,5,50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I valori numerici dei coefficienti angolari *m* e delle intercette *q* delle rette $r=mx+q$, tangenti alla curva *y* alle diverse ascisse *x*, si possono visualizzare chiamando la funzione *legendre* con il parametro opzionale *plot=False*:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "m -1.000, q 1.000\n", "m -0.574, q 0.893\n", "m -0.329, q 0.695\n", "m -0.189, q 0.504\n", "m -0.108, q 0.349\n", "m -0.062, q 0.235\n", "m -0.036, q 0.155\n", "m -0.020, q 0.100\n", "m -0.012, q 0.064\n", "m -0.007, q 0.040\n" ] } ], "source": [ "m,q=legendre(0,5,10,plot=False)\n", "for im in range(m.size):\n", " print(\"m %6.3f, q %6.3f\" % (m[im], q[im]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La trasformata di Legendre è la funzione *q(m)*: \n", "\n", "$$q(m)=y-\\frac{dy}{dx}x=y-mx$$ \n", "\n", "Questa può essere visualizzata con la funzione *legendre_plot(xmin,xmax,npoint)*:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "legendre_plot(0,5,100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Volendo eseguire la trasformata su una funzione diversa, usare il metodo *f.set* dando in input la nuova funzione. Per esempio, volendo fare la trasformata della funzione $y=log(x)$, scriviamo:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "np.log(x)\n" ] } ], "source": [ "f.set('np.log(x)')\n", "f.print()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Da notare che la funzione logaritmo (in base *e*) è una funzione della libreria *numpy*, quindi va invocata con il prefisso *np.*\n", "\n", "L'argomento di *f.set* è passato sotto forma di *stringa* racchiudendolo tra apici. Si procede poi come già visto sopra: " ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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