\n",
"\n",
"Ebben a notebookban bemutatjuk, hogy lehet függvényeket írni, miként lehet az adatpontokra elvégezni az illesztési feladatokat."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline\n",
"figsize(6,6) #Képméret megváltoztatása"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Függvények (function)\n",
"\n",
"A számítógép-programozásban a függvény (function) egy nagyobb program forráskódjának egy viszonylag jól felismerhető része, amely egy adott feladatot hajt végre. A kód többi részétől viszonylag független egység, és többször felhasználható anélkül, hogy a program kódjának több példányban is tartalmaznia kellene, azaz többször, több helyen is hivatkozhatunk ugyanarra a függvényre. Hasonló fogalmat jelölnek a eljárás, szubrutin, metódus, procedúra vagy alprogram nevek is."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A függvények és eljárások használatnak előnyei\n",
"\n",
"- csökkenthető a kódismétlődés\n",
"- ugyanaz a függvény más programban is használható\n",
"- összetett problémák egyszerűbb részekre bonthatók, ami könnyebbé teszi a kód frissítését és bővítését\n",
"- javítható a program olvashatósága\n",
"- elrejthetők és szabályozhatók a program egyes részei"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Az eddig megismert parancsokat felfoghatjuk már előre definiált függvényként. Például a `exp` parancs, olyan függvény, ami kiszámolja az `e` hatványait. Vagy a `plot` egy olyan eljárás, ami ábrázolja az adatokat. Néhány programozási nyelvben szokás különbséget tenni eljárás és függvény között. A függvény egy csoportja az eljárások halmazának. Olyan speciális eljárások, melyeknek van valamilyen visszatérési értéke (csinál valami, és az eredményt visszaadja a programnak). Tehát a `plot` inkább csak szimpla eljárás, míg az `exp`, vagy `sqrt` igazi függvények. A C-ben és a pythonban a két fogalmat szinonimaként használhatjuk. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A következőkben bemutatjuk, hogyan lehet egyszerűen a függvények használni. \n",
"\n",
"A függvények szintaktikájára jellemző, hogy 3 fő része van.\n",
"* Beolvasott adatok, paraméterek\n",
"* Műveletvégzés\n",
"* A kész eredmény visszaadása a fő programnak (oda ahol megvolt hívva a függvény): **`return`** rész\n",
"\n",
"A következő példában a `func` függvény kiszámolja a beadott szám reciprokát, majd az eredményt visszaadja meghívás helyének, ez esetben a plot parancs y adatsorának."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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/+2xeYPX5z8M++8DDDxedrPos8pIaxsorw6mnwvPPwxZb5INLRo3KUzHLemid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\nsf8DKfiApy4tuksAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"############################\n",
"\n",
"def func(x): # A fügvényünk megkapja az \"x\" adatokat\n",
" return 1/x # A visszadás és a művelevégézés ez esetben egybe van olvasztva\n",
"\n",
"############################\n",
"\n",
"\n",
"x=arange(1,2,0.01) # Geneáljuk az x adatokat\n",
"\n",
"plot(x, func(x)) # Ábároljuk az \"x\" fügvényében, a \"func(x)\" számokat"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lehet több függvényünk is: (f1 és f2 nevű)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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1b0Bb5e3QcgSjYVpkCkNcmiIifjNZ4sayAwBSpJLoOJC5bB9p4TqshSKkWrCH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\nwWcYhgkJbPAZhmFCwv8PUqAQ0FqfwFoAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"########################################################\n",
"def f1(t): # Egy \"sima\" koszinusz függvény\n",
" y=cos(2*pi*t)\n",
" return y\n",
"########################################################\n",
"########################################################\n",
"def f2(t):\n",
" y=f1(t) * exp(-t) # Adjunk hozzá \"exp(-t)\" csillapítást\n",
" return y\n",
"########################################################\n",
"\n",
"t1 = arange(0.0, 5.0, 0.05)\n",
"\n",
"plot(t1, f1(t1), 'r')\n",
"plot(t1, f2(t1), 'bo')\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Egy másik példa függvények használatára: \n",
"Figyeljük meg, hogy a függvény hívásakor több paramétert is meg kell adni! (x,a,b-t is, ahol `x` egy vektor, míg `a` és `b` konstansok). A konstansok átadása a következő módon történik: \n",
">`func(x, *(a,b))`"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(2.5, 100)\n"
]
},
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def func(x,a,b):\n",
" return (x**a)+b\n",
"\n",
"x=arange(1,2,0.01)\n",
"zz=(2.5,100)\n",
"print(zz)\n",
"\n",
"plot(x, func(x, *(zz)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Összetettebb feladat\n",
"\n",
"A következő példában a \"Mandelbrot-halmaz\" kiszámolás és ábrázolása a feladat. A Mandelbrot-halmaz (fraktál) egy síkbeli alakzat, amelyet egy alapvetően nagyon egyszerű algebrai összefüggés bonyolultabb (végtelennel kapcsolatos, analitikus fogalmakat, határérték-számítást igénylő) elemzése ad meg, rajzol ki.\n",
"\n",
"A matematikában a Mandelbrot-halmaz azon c komplex számokból áll (a „komplex számsík” azon pontjainak mértani helye, halmaza), melyekre az alábbi (komplex szám értékű) $x_{n}$ rekurzív sorozat:\n",
"$$ x_1 := c$$\n",
"$$ x_{n+1} := (x_n)^2+c$$\n",
"nem tart végtelenbe, azaz abszolút értékben (hosszára nézve) korlátos.\n",
"