{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Kapitel 1. Einstieg in die Welt von Python:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In Ihrer Vorbereitung haben Sie bisher die folgenden Konzepte kennen gelernt:\n",
"\n",
"* Aufbau eines Jupyter-Notebooks (Aufgabe 1).\n",
"* Einfache Rechenoperationen (Aufgabe 2 a.)\n",
"* Einfache Zeichenketten (engl. Strings) und formatierte Strings (Aufgabe 2 b.).\n",
"* Das definieren von Funktionen (Aufgabe 3.)\n",
"* Das definieren von Messtabellen.\n",
"\n",
"Hierauf wollen wir an unserem heutigen Versuchstag aufbauen."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Arbeiten mit Messreihen:\n",
"\n",
"Bisher hat uns das programmieren eher mehr Arbeit gemacht als uns welche abgenommen. Zeitersparnis bekommen wir sofern wir viele Rechnungen hintereinander ausführen müssen. Hierfür gibt es die **for**-Schleife. Diese Schleife führt die gleichen Zeilen eins Codes wiederholt für die Elemente in einer Liste aus:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:07:49.905202Z",
"start_time": "2019-11-04T12:07:49.889579Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wert: 1\n",
"Wert: 2\n",
"Wert: 3\n",
"Wert: 4\n",
"Ergebnis: 6\n"
]
}
],
"source": [
"liste = [1, 2, 3, 4]\n",
"\n",
"for wert in liste:\n",
" print('Wert:', wert)\n",
" rechnung = wert + 2\n",
" \n",
"print('Ergebnis:', rechnung)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Bei einer Schleife ist darauf zu achten, dass der Anweisungsblock welcher wiederholt ausgeführt werden soll mit 4x Leerzeichen eingrückt wurde. Dies entspricht einmal "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:08:53.901374Z",
"start_time": "2019-11-04T12:08:53.885753Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Hier läuft das Hauptprogramm\n",
"Schleife\n",
"Wert: 1\n",
"Schleife\n",
"Wert: 2\n",
"Schleife\n",
"Wert: 3\n",
"Schleife\n",
"Wert: 4\n",
"Hier läuft wieder das Hauptprogramm\n",
"Letztes Ergebnis + 5: 11\n"
]
}
],
"source": [
"liste = [1, 2, 3, 4]\n",
"print('Hier läuft das Hauptprogramm')\n",
"\n",
"for wert in liste:\n",
" print('Schleife')\n",
" print('Wert:', wert)\n",
" rechnung = wert + 2\n",
" \n",
"print('Hier läuft wieder das Hauptprogramm')\n",
"rechnung = rechnung + 5\n",
"print('Letztes Ergebnis + 5: ', rechnung)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Statt das Ergebnis lediglich per `print`-Anweisung darstellen zu lassen, können wir auch unser Wissen um Listen benutzen und die berechneten Werte einer neuen Liste anfügen:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# (Funktion haben wir bereits in der Vorbereitung definiert)\n",
"def Spannung(Strom, Widerstand):\n",
" '''\n",
" Diese Funktion berechnet die Spannung eines Ohmschen \n",
" Widerstands.\n",
" \n",
" Args:\n",
" Strom (float): Der gemessene Strom in mA.\n",
" Widerstand (float): Der Wert des verwendeten Widerstands\n",
" in Ohm.\n",
" \n",
" Returns:\n",
" float: Die Berechnete Spannung in V.\n",
" '''\n",
" return Widerstand * Strom/1000"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:10:08.503300Z",
"start_time": "2019-11-04T12:10:08.472059Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[10.1, 10.5, 9.8, 8.7, 11.2]"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Stromwerte = [101, 105, 98, 87, 112] # mA\n",
"Widerstand = 100 # Ohm\n",
"\n",
"Spannungswerte = []# Einheit? <-- Deshlab Docstrings und Help!\n",
"for Strom in Stromwerte:\n",
" res = Spannung(Strom, Widerstand)\n",
" Spannungswerte.append(res)\n",
"\n",
"Spannungswerte"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Python ermöglicht uns auch eine kompaktere Schreibweise die so genannte \"list comprehension\": "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:11:40.799393Z",
"start_time": "2019-11-04T12:11:40.783772Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[10.1, 10.5, 9.8, 8.7, 11.2]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Spannungswerte = [Spannung(Strom, 100) for Strom in Stromwerte]\n",
"Spannungswerte"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wir können auch über mehre Daten gleichzeitig loopen. Hierzu kann die `zip` Anweisung genutzt werden. `zip` verbindet hierbei die einzelnen Elemente einer Liste wie bei einem Reißverschluss miteinander:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:12:42.522873Z",
"start_time": "2019-11-04T12:12:42.507254Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A und 0\n",
"B und 1\n",
"C und 2\n",
"D und 3\n"
]
}
],
"source": [
"Werte1 = ['A', 'B', 'C', 'D']\n",
"Werte2 = [0, 1, 2, 3]\n",
"\n",
"for w1, w2 in zip(Werte1, Werte2):\n",
" print(w1, ' und ', w2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Dies kann zum Beispiel dann hilfreich sein wenn sich mehr als eine Variable ändern soll, z.B. bei einer Messreihe für die Schallgeschwindigkeit in Luft:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:13:30.363510Z",
"start_time": "2019-11-04T12:13:30.347888Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[335.4904, 347.3442, 343.6145, 337.275, 331.6212, 342.0115, 336.2262]\n",
"[335.4904, 347.3442, 343.6145, 337.275, 331.6212, 342.0115, 336.2262]\n"
]
}
],
"source": [
"# Gemessene Werte:\n",
"frequenzen = [30.17, 30.63, 30.01, 29.98, 30.12, 29.87, 29.94] #kHz\n",
"wellenlängen = [11.12, 11.34, 11.45, 11.25, 11.01, 11.45, 11.23] # mm\n",
"\n",
"# Variante 1:\n",
"schallgeschindigkeiten = [] # m/s\n",
"\n",
"for f, l in zip(frequenzen, wellenlängen):\n",
" schallgeschindigkeiten.append(f*l)\n",
"\n",
"print(schallgeschindigkeiten)\n",
"\n",
"# oder Variante 2:\n",
"schallgeschindigkeiten2 = [f*l for f,l in zip(frequenzen, wellenlängen)]\n",
"print(schallgeschindigkeiten2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wir können auch die `zip`-Anweisung mit mehr als nur zwei Listen verwenden:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:13:49.912658Z",
"start_time": "2019-11-04T12:13:49.897039Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a und 1 und x\n",
"b und 2 und y\n",
"c und 3 und z\n"
]
}
],
"source": [
"l1 = ['a', 'b', 'c']\n",
"l2 = [1, 2, 3]\n",
"l3 = ['x', 'y', 'z']\n",
"\n",
"for i, j, k in zip(l1, l2, l3):\n",
" print(i, 'und', j, 'und', k)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"#### Aufgabe 4.b.: Werte berechnen:\n",
"Kopiert eure Aufgabe 4.a. aus der Vorbereitung in das Notebook und berechnet nun für die Messwerte aus Aufgabe 4 a. die Leistung $P$ und den Widerstand $R$ sowie deren Fehler. Nutzt hierfür die ausführliche schrebweise der **for**-Schleife im Fall des Widerstands $R$ und den list-comprehension Syntax für die Leistung $P$. Fügt die berechneten Werte als neue Spalten and die Liste *daten* an. \n",
"
"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"ExecuteTime": {
"end_time": "2020-08-25T12:29:42.611010Z",
"start_time": "2020-08-25T12:29:42.589070Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Spalte mit Index 0: [1, 2, 3, 4, 5, 6]\n",
"Spalte mit Index 1: [12.0, 11.78, 12.56, 12.34, 12.01, 11.94]\n",
"Spalte mit Index 2: [110, 98, 102, 124, 105, 95]\n",
"Spalte mit Index 3: [0.32, 0.15, 0.63, 0.12, 0.2, 0.17]\n",
"Spalte mit Index 4: [10, 10, 10, 10, 10, 10]\n",
"Spalte mit Index 5: [0.10909090909090909, 0.12020408163265306, 0.12313725490196079, 0.09951612903225807, 0.11438095238095237, 0.1256842105263158]\n",
"Spalte mit Index 6: [0.010335218792552269, 0.012360854546774054, 0.01356055790616861, 0.008083630548247704, 0.01105869816696616, 0.013350390150906498]\n",
"Spalte mit Index 7: [1320.0, 1154.4399999999998, 1281.1200000000001, 1530.16, 1261.05, 1134.3]\n",
"Spalte mit Index 8: [125.05614738988244, 118.71364706721802, 141.0840444557782, 124.29390330985667, 121.92214729080192, 120.48727111193115]\n"
]
}
],
"source": [
"messwert_nummer = list(range(1,7,1))\n",
"spannungs_wert = [12., 11.78, 12.56, 12.34, 12.01, 11.94]\n",
"strom_werte = [110, 98, 102, 124, 105, 95]\n",
"dspannung_wetre = [0.32, 0.15, 0.63, 0.12, 0.20, 0.17]\n",
"dstrom_werte = [10]*len(messwert_nummer)\n",
"daten = [messwert_nummer, spannungs_wert, strom_werte, dspannung_wetre, dstrom_werte]\n",
"\n",
"def res(i, u):\n",
" r = u/i\n",
" return r\n",
"\n",
"# Widerstand:\n",
"widerstand = []\n",
"dwiderstand = []\n",
"\n",
"for strom, spannung in zip(daten[2], daten[1]):\n",
" widerstand.append(res(strom, spannung))\n",
"daten.append(widerstand)\n",
"\n",
"# Fehler des Widerstands:\n",
"for strom, spannung, dstrom, dspannung in zip(daten[2], daten[1], daten[4], daten[3]):\n",
" dwiderstand.append(((dstrom * spannung/(strom)**2)**2 + (dspannung/strom)**2)**0.5)\n",
"daten.append(dwiderstand)\n",
"\n",
"# Leistung:\n",
"p = [u*i for u,i in zip(daten[1], daten[2])]\n",
"\n",
"# Fehler der Leistung:\n",
"dp = [((u*di)**2 + (du*i)**2 )**0.5 for u,i,du,di in zip(daten[1], daten[2], daten[3], daten[4])]\n",
"daten.append(p)\n",
"daten.append(dp)\n",
"\n",
"for ind, spalte in enumerate(daten): \n",
" # enumerate ist hilfreich falls man noch zusätzlich einen Index braucht\n",
" print(f'Spalte mit Index {ind}: ', spalte)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Das Darstellen von Messdaten mittels `matplotlib`:\n",
"Das Plotten von Daten ist eines der wichtigsten Mittel um eine Fülle von Informationen kompakt und verständlich seinem Gegenüber darzubieten. Gute Plots zu erstellen kann eine regelrechte Kunst sein und ist für ein gutes Paper, bzw. eine gute Bachelor- bzw. Masterarbeit unverzichtbar. \n",
"\n",
"\n",
"\n",
"Resultate des XENON1T Dunkle Materie Experiments. Die Graphik wurde mittels Matplotlib in Python erstellt. \n",
"\n",
"\n",
"Jede Programmiersprache verfügt über zusätzliche Pakete (im Englischen \"packages\") welche die Funktionalität der verwendeten Programmiersprache erweitern. **Matplotlib** ist ein umfangreiches Package, welches das Zeichnen von 2D und 3D Grafiken ermöglicht. Alle Parameter und Einstellungen einer Grafik werden entsprechend des Python-Codes eingestellt. Dadurch wird das Erstellen der Grafik reproduzierbar und man kann schnell dieselbe Grafik mit neuen Daten füttern.\n",
"\n",
"Es ist unmöglich alle Möglichkeiten und Einstellungen die euch **Matplotlib** bietet auswendig zu kennen. Mit der Zeit werdet ihr ein solides Grundwissen der gängisten Befehle haben. Für alles weitere hilft euch die [Dokumentation und ihre Beispiele](http://matplotlib.org/). Des Weiteren ist insbesondere hier die **IPython Hilfe** und das **automatische Vervollständigen von Befehlen** besonders hilfreich.\n",
"\n",
"Für das Praktikum wollen wir uns zunächst lediglich drei unterschiedliche Arten von Plots angucken:\n",
"\n",
"* Normale Liniengrafiken\n",
"* Plots mit Fehlerbalken\n",
"* Histogramme "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Zunächst müssen wir Python mitteilen, dass wir das **Matplotlib** package nutzen möchten:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:52:38.927838Z",
"start_time": "2019-11-04T12:52:36.881444Z"
}
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`import` läd für und aus dem package matplotlib das Modul `pyplot`. Mit Hilfe des Zusatzes `as plt` wird ein alias erstellt. Dieser Alias erspart uns im nachfolgenden Arbeit, wie wir im nachfolgenden Beispiel sehen können:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:53:06.331480Z",
"start_time": "2019-11-04T12:53:05.987810Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot([1,2,3,4,5], # <-- x-Daten\n",
" [1,2,3,4,5] # <-- y-Daten\n",
" )\n",
"plt.show() # <-- Zeigen des Plots"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Hätten wir den Alias nicht definiert hätten wir den folgenden etwas länglichen Code benötigt:\n",
"\n",
"```python\n",
"matplotlib.pyplot.plot([1,2,3,4,5], [1,2,3,4,5])\n",
"matplotlib.pyplot.show()\n",
"```\n",
"\n",
"Innerhalb der Python-Community haben sich ein paar Standards etabliert an welche man sich halten sollte. So ist für `matplotlib.pyplot` der Alias `plt` zu verwenden. \n",
"\n",
"Im oberen Beispiel habt ihr nun auch bereits gesehen wie wir einfache Liniengrafiken erstellen können. Dabei sieht der Plot noch etwas blass aus. Dies können wir mit ein paar zusätzlichen Befehlen ändern."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:54:21.547247Z",
"start_time": "2019-11-04T12:54:21.226301Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xdaten = [1,2,3,4,5]\n",
"ydaten = [1,2,2,4,5]\n",
"\n",
"plt.plot(xdaten, ydaten, # <-- Wie eben die x und y daten\n",
" color = 'red', # <-- Farbe der Linie\n",
" linestyle='dashed', # <-- Linientyp\n",
" label='Spannungskurve' # <-- Name der Linie\n",
" )\n",
"plt.xlabel('X-Achse') # <-- Beschriftung der x-Achse\n",
"plt.ylabel('Y-Achse') # <-- Beschiftung der y-Achse\n",
"plt.legend() # <-- Hinzufügen der Legend mit den \n",
" # in plot definierten labels\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Viele der eben verwendeten Optionen bieten euch unterschiedliche Auswahlmöglichkeiten:\n",
"\n",
"**Linestyle:**\n",
"* `''`: keine Linie\n",
"* `'-'`: durchgehende Linie\n",
"* `'--'`: gestrichelte Linie\n",
"* `'-.'`: Strich-Punktlinie\n",
"* `':'`: Punktlinie\n",
"* `'steps'`: Treppenfunktion\n",
"\n",
"**Color**:\n",
"* red, blue, yellow, \n",
"* RGB Werte von 0 bis 1 (statt von 0 bis 255): (1, 1, 1), (1, 0.2, 0.4)\n",
"\n",
"Darüber hinaus gibt es auch noch andere nützliche Styleoptionen wie `alpha` was die Transparenz eurer Linie ändert (Werte zwischen 0-1), oder `linewidth`-Option mit dessen Hilfe ihr die Linienbreite ändern könnt. \n",
"\n",
"Auch die anderen Befehle welche wir verwendetet haben verfügen über zusätzliche Optionen:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:55:35.863633Z",
"start_time": "2019-11-04T12:55:35.535586Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xdaten = [1,2,3,4,5]\n",
"ydaten = [1,2,2,4,5]\n",
"\n",
"plt.plot(xdaten, ydaten,\n",
" color = 'red',\n",
" linestyle='dashed',\n",
" label='Graph 1'\n",
" )\n",
"plt.xlabel('X-Achse',\n",
" color = (0,1,0) # <-- Beschriftungsfrabe\n",
" )\n",
"\n",
"plt.ylabel('Y-Achse',\n",
" fontsize=14) # <-- Beschiftungsgröße\n",
"\n",
"plt.legend(title='Messwerte', # <-- Legendentitel\n",
" loc=3) # <-- Legendenposition:\n",
" # 0: Best,\n",
" # 1: Oben Rechts\n",
" # 2: Oben Links\n",
" # 3: Unten Links\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sofern ihr mehrere Graphen in einen Plot zeichnen möchtet geht dies auch ganz einfach."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:56:56.976082Z",
"start_time": "2019-11-04T12:56:56.644588Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xdaten = [-3, -2, -1, 0, 1, 2, 3]\n",
"ydaten1 = xdaten\n",
"ydaten2 = [x**2 for x in xdaten]\n",
"ydaten3 = [x**3 for x in xdaten]\n",
"\n",
"plt.plot(xdaten, ydaten1, label='Linear')\n",
"plt.plot(xdaten, ydaten2, label='Quadratisch')\n",
"plt.plot(xdaten, ydaten3, label='Cubisch')\n",
"\n",
"plt.legend(title='Exponent')\n",
"plt.xlabel('X-Werte')\n",
"plt.ylabel('Y-Werte')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Ihr seht, das `plot` zwischen den angegebene Werte interpoliert. Möchtet ihr eine glatte Kurve zeichnen so müsst ihr die Anzahl an Punkten für die Interpolation erhöhen."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:58:19.439740Z",
"start_time": "2019-11-04T12:58:19.116107Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def cubic(x):\n",
" '''\n",
" Funktion welche den cubischen Wert einer Zahl zurück gibt.\n",
" '''\n",
" return x**3\n",
"\n",
"\n",
"x1 = list(range(-3, 4, 1)) # <- Werte zwischen -3 und 3\n",
"x2 = [i/10 for i in range(-30, 31, 1)] # <- 10 mal mehr Werte\n",
"\n",
"y1 = [cubic(j) for j in x1]\n",
"y2 = [cubic(value) for value in x2]\n",
"\n",
"\n",
"plt.plot(x1, y1, label='Werte 1', linestyle='dashed')\n",
"plt.plot(x2, y2, label='Werte 2')\n",
"plt.xlabel('x-Werte')\n",
"plt.ylabel('y-Werte')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Errorbarplot\n",
"\n",
"In der Physik gehören zu jedem gemessen Wert ein Messunsicherheit/Messfehler. Diese Fehler sollten natürlich auch in unseren Grafiken korrekt dargestellt werden. Hierfür können wir den `errorbar`-Plot verwenden."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"ExecuteTime": {
"end_time": "2020-08-25T11:01:53.690343Z",
"start_time": "2020-08-25T11:01:53.511857Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"spannung = [0.9, 2.0, 3.0, 4.1, 4.9, 6.2] # [V]\n",
"strom = [105, 204, 298, 391, 506, 601] # [mA]\n",
"spannung_error = [0.3]*len(spannung) # Konstanter Ablesefehler [V]\n",
"strom_error = [14, 9, 12, 8, 7, 11] # gemessener schwankender Fehler[mA]\n",
"\n",
"plt.errorbar(spannung, strom,\n",
" yerr=strom_error, \n",
" xerr=spannung_error,\n",
" ) \n",
"\n",
"plt.xlabel('Spannung [V]')\n",
"plt.ylabel('Strom [mA]')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"#### Aufgabe 5.: Erstelle eine `errorbar`-Plot :\n",
"\n",
"Editiert die obere Zelle so, dass ihr mit Hilfe des Befehls \n",
"\n",
"```python\n",
"plt.errorbar()\n",
"```\n",
"\n",
"einen Errorbarplot erstellt. Verwende hier für die IPython help-funktion um den exakten Syntax zu erfahren. \n",
"\n",
"**Erinnerung:**\n",
"Ihr könnt die IPython-Hilfe aufrufen in dem ihr euren Cursor innerhalb das Wort errorbar von plt.errorbar bewegt und die Tastenkombination shift + tab verwendet. Lest nun nach wie ihr die x- und y-Werte und deren Fehler an die Funktion übergeben müsst.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Leider ist diese Standardvariante des Errorbar plots noch nicht das was wir möchten. Die Messwerte sind linear interpoliert und die errorbars sehen noch etwas eigenartig aus. Dies können wir jedoch im Handumdrehen ändern. Kümmern wir uns zunächst um die Plotmarker:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"ExecuteTime": {
"end_time": "2020-08-25T11:00:51.750584Z",
"start_time": "2020-08-25T11:00:51.717716Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.errorbar(strom, spannung,\n",
" xerr=strom_error, \n",
" yerr=spannung_error, \n",
" # Änderungen für plotmarker: | Kurzform:\n",
" linestyle='', # <-- Schaltet den Linienstyle aus | ls=''\n",
" marker='d', # <-- Ändert den Markertyp in Diamanten | -----\n",
" markerfacecolor='orange', # <-- Ändert die Markerfarbe zu Orange | mfc='orange'\n",
" markeredgecolor='k', # <-- Setzt die Kantenfarbe auf schwarz | mec='k'\n",
" markersize=7 # <-- Ändert die Markergröße | ms='7'\n",
" )\n",
"\n",
"plt.ylabel('Spannung [V]')\n",
"plt.xlabel('Strom [mA]')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All die Optionen welche wir hier für die Plotmarker verwendet haben können wir auch in der normalen `plt.plot`-Anweisung verwenden. Dabei gibt es eine ganze fülle an unterschiedlichen [marker Symbole](http://matplotlib.org/api/markers_api.html):\n",
" \n",
"* `+`: Plus\n",
"* `o`: Kreis\n",
"* `*`: Stern\n",
"* `,`,`.`: kleiner und sehr kleiner Punkt\n",
"* `s`: Quadrat\n",
"* `p`: Pentagon\n",
"* `h`: Hexagon\n",
"* `1`, `2`, `3`, `4`: nach unten, oben, links, rechts zeigendes Dreieck\n",
" \n",
"Nach dem wir uns um unsere Marker gekümmert haben müssen wir nun auch noch unsere Fehlerbalken enstprechend anpassen:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T13:11:52.919783Z",
"start_time": "2019-11-04T13:11:52.638600Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.errorbar(strom, \n",
" spannung,\n",
" xerr=strom_error,\n",
" yerr=spannung_error, \n",
" ls='', \n",
" marker='d', \n",
" mfc='orange', \n",
" mec='k', \n",
" ms=7,\n",
" # Fehlerbalken optionen:\n",
" ecolor='k', # <-- Ändert die Linienfarbe der errorbars\n",
" elinewidth=2, # <-- Ändert die Fehlerbalkenbreite\n",
" capsize=5, # <-- Ändert die Breite der Endkappen der Fehlerbalken\n",
" capthick=2 # <-- Ändert die Dicke der Endkappen\n",
" ) \n",
"\n",
"plt.ylabel('Spannung [V]')\n",
"plt.xlabel('Strom [mA]')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Histogramme:\n",
"\n",
"Ein weiterer Plottyp welcher häufig Verwendung findet ist das Histogramm. Um unser Histogramm mit Pseudozufallszahlen zu bestücken müssen wir diese erst erzeugen. Hierfür können wir das `numpy`-Modul verwenden. `numpy` ist ein weiteres Standardmodul welches viele nützliche Funktionen mit sich bringt. Hier wollen wir uns jedoch nur auf das erstellen von Zufallszahlen beschränken. "
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T13:13:40.357937Z",
"start_time": "2019-11-04T13:13:40.342316Z"
}
},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T13:13:40.844488Z",
"start_time": "2019-11-04T13:13:40.828850Z"
}
},
"outputs": [],
"source": [
"rnd_numbers = np.random.normal(0,1,1000) # <-- Hier werden 1000 gausförmig verteile Zufallszahlen\n",
" # mit einem Mittelwert von 0 und einer Standardabweichung \n",
" # von 1 erzeugt."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Das histgrom lässt sich ganz einfach mit der `plt.hist`-Anweisung erstellt."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T13:13:52.473958Z",
"start_time": "2019-11-04T13:13:52.177152Z"
}
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.hist(rnd_numbers)\n",
"\n",
"plt.xlabel('Zufallswert')\n",
"plt.ylabel('Anzahl der Einträge')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Auch für Histogramme gibt es viele unterschiedlichen Optionen welche ihr entweder mit Hilfe der Help-Funktion oder den Beispielen in der [Matplolibdokumentation](http://matplotlib.org/) herrausfinden könnt."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T13:15:09.390753Z",
"start_time": "2019-11-04T13:15:09.031464Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rnd_numbers2 = np.random.normal(1, 2, 1000)\n",
"\n",
"\n",
"plt.hist(rnd_numbers, \n",
" bins=13, \n",
" range=(-3,5), # <-- Achtung im Gegensatz zur range-Anweisung ist \n",
" # das Intervall hier geschlossen [-3, 5]\n",
" histtype='step', # Ändert den Balkentyp in Stufen\n",
" linestyle='dashed',\n",
" label='Verteilung 1'\n",
" )\n",
"\n",
"plt.hist(rnd_numbers2, \n",
" bins=13, \n",
" range=(-3,5),\n",
" alpha=0.5, # Ändert die Transparenz der Balken \n",
" label='Verteilung 2'\n",
" )\n",
"\n",
"plt.legend()\n",
"plt.xlabel('Zufallswert')\n",
"plt.ylabel('Anzahl der Einträge')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Bei Histogrammen solltet ihr immer darauf achten, dass euer binning sinnvoll gewählt ist. Weder zu viele noch zu wenig Bins führen zu einer sinnvollen Darstellung eurer Daten."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T13:15:48.283946Z",
"start_time": "2019-11-04T13:15:47.327389Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.hist(rnd_numbers, \n",
" bins=100, \n",
" range=(-3,3),\n",
" label='Zu viele bins'\n",
" )\n",
"\n",
"plt.legend()\n",
"plt.xlabel('Zufallswert')\n",
"plt.ylabel('Anzahl der Einträge')\n",
"plt.show()\n",
"\n",
"plt.hist(rnd_numbers, \n",
" bins=3, \n",
" range=(-3,3),\n",
" label='Zu wenig bins'\n",
" )\n",
"\n",
"plt.legend()\n",
"plt.xlabel('Zufallswert')\n",
"plt.ylabel('Anzahl der Einträge')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Nach dem wir jetzt die verschiedenen Plottypen mit ihren unterschiedlichen Optionen kennen gelernt haben möchten wir diese natürlich auch speichern können. Dies können wir auf zwei unterschiedliche Arten machen.\n",
"\n",
"Entweder ihr macht mit eurer Maus einen Rechtsklick auf eure Grafik und wählt \"Grafik speichern als\" aus, oder ihr verwendet statt der `plt.show`- die `plt.savefig`-Anweisung dafür."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"#### Aufgabe 6.: Erstellen einer gauss'schen Wahrscheinlichkeitsdichte:\n",
"\n",
"Im folgenden wollen wir ein Plot mit einer gauss'schen Wahrscheinlichkeitsdichte erstellen. Geht hierfür wie folgt vor:\n",
"\n",
"1. Erstellt euch 500000 pseudo-Zufallszahlen, welche einer Gaußverteilung mit $µ=5$ und $sigma=2$ folgen.\n",
"2. Tragt die Zufallszahlen in ein Histogramm ein und normiert dieses so dass die Gesamtfläche eins beträgt. **Tipp: `plt.hist` hat hierfür einen optionalen Parameter benutzt die Help oder das Internet um herrauszufinden welcher es ist.**\n",
"3. Wählt ein geeignete `range` und ein `binning` von 100 für das Histogram.\n",
"4. Plottet anschließend die dazugehörige Gaußverteilung als Funktion. Geht dabei wie folgt vor:\n",
" 1. Erstellt eine Gaußfunktion. *Erinnerung:* eine Gaußverteilung ist gegeben durch:\n",
" $$g(x, \\mu, \\sigma) = \\frac{1}{\\sqrt{2 \\pi} \\, \\sigma} \\exp\\bigg( \\frac{ -(x - \\mu)^2}{2 \\sigma^2}\\bigg) $$\n",
" **Tipp:** Das Numpy package beinhaltet die Zahlen pi und die Exponentialfunktion bereit. Ihr könnt diese über `np.pi` und `np.exp()` verwenden. \n",
" 2. Erstellt euch eine liste von x-Werten in der von euch gewählten range in 0.1er Schritten. Verwendetet hierfür die `range`-Funktion zusammen mit der listcomprehension.\n",
" 3. Erstellt den plot.\n",
"Das Ergebnis sollte wie folgt aussehen:\n",
"\n",
"\n",
"\n",
""
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"ExecuteTime": {
"end_time": "2020-08-25T10:59:12.527496Z",
"start_time": "2020-08-25T10:59:11.830137Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"rnd = np.random.normal(5, 2, 500000)\n",
"\n",
"# Histogram:\n",
"plt.figure(dpi=100)\n",
"plt.hist(rnd, bins=100, range=(0, 10), density=True, label='Zufallszahlen')\n",
"\n",
"# Gaussfunktion:\n",
"def gauss(x, mu, sig):\n",
" return 1/((2 * np.pi)**0.5 * sig) * np.exp(-(x - mu)**2/(2*sig**2))\n",
"\n",
"# x-Werte mittels listcomprehension:\n",
"xdata = [i/10 for i in range(0, 100, 1)]\n",
"\n",
"# Plot:\n",
"plt.plot(xdata, [gauss(x, 5, 2) for x in xdata], ls='dashed', color='k', label='gauss(x, 5, 2)')\n",
"plt.legend()\n",
"plt.ylabel('Wahrscheinlichkeitsdichte P')\n",
"plt.xlabel('x-Werte')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitten von Messdaten:\n",
"\n",
"### Methode der kleinsten Quadrate\n",
"\n",
"Im folgenden wolllen wir die **Methode der kleinsten Quadrate (Least Squares)** näher beleuchten. Diese Methode wird oft benutzt um eine Funktion $\\lambda(x; \\ $**$\\phi$**$)$ mit den Funktionsparametern $\\mathbf{\\phi}$ an die gemessenen Punkte **$(x,y)$** anzupassen. Um jedoch die **Methode der kleinsten Quadrate** zu verstehen wollen wir sie erst einmal anschaulich und mathematisch herleiten. Dabei stüzen wir uns im folgenden auf eine Herleitung aus dem Buch **\"Statistical Data Analysis\"** von **Glen Cowan**.\n",
"\n",
"In unserem Grundpraktikum haben wir bereits gelernt, dass Messwerte durch Zufallszahlen $x_i$ representiert werden und einer gewissen **Wahrscheinlichkeitsdichtefunktion (probability density function)** $f(x)$ unterliegen. \n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"Eine **pdf** gibt an mit welcher **Wahrscheinlichkeit ein Wert $x_i$** innerhalb eines **infinitesimalen Intervals $\\text{d}x_i$** zu finden ist. Des Weitren gilt das die Gesamtwahrscheinlichkeit gegeben ist durch $\\int_S f(x) dx = 1$. \n",
"\n",
"Nun betrachten wir folgendes Beispiel: In unserem Labor messen wir genau drei mal die Raumtemperartur T. Auch hier gilt, dass unsere Messung der einzelnen $T_i$ einer gewissen **Wahrscheinlichkeitsdichtefunktion** folgen. Betrachtet nun das folgende Bild; welche **Wahrscheinlichkeitsdichtefunktion** passt besser zu den gezeigten Daten und **Warum?**\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"Die rechte Verteilung spiegelt unsere Messdaten besser wieder. Dies können wir auch mathematisch ausdrücken. Für $N$ voreinander unabhängige Zufallszahlen bzw. Messpunkte (in unserem Beispiel $N = 3$) ist die Gesamtwahrscheinlichkeit gegeben durch das Produkt der einzelnen Wahrscheinlichkeitsdichten $f(x_i, \\theta)$ multipliziert mit dem jeweiligen infinitesimalen element $dx_i$\n",
"\n",
"$$\\prod_{i = 1}^{N} f(x_i,\\theta) \\ dx_i \\text{ für alle } x_i \\text{ in } [x_i, x_i + dx_i]$$\n",
"\n",
"wobei $x_i$ in unserem Beispiel den Messpunkten $T_i$ und $f(x_i,\\theta)$ unserer Gausverteilung mit $\\theta = (\\mu, \\sigma)$ entspricht. Sprich sofern unsere Werte gut von der jeweiligen **Wahrscheinlichkeitsdichtefunktion** repräsentiert werden, d.h. wir die richtigen Parameter $\\theta$ gewählt haben (wie im rechten oberen Plot), gilt \n",
"\n",
"$$ \\prod_{i = 1}^{N} f(x_i,\\theta) dx_i$$ \n",
"\n",
"ist **maximal**. Da die einzelnen $dx_i$ von unseren Parametern $\\theta$ unabhängig sind gilt die gleiche Argumentation auch für \n",
"\n",
"$$ \\mathcal{L}(x_1 ... x_N; \\theta_1 ... \\theta_N) = \\prod_{i = 1}^{N} f(x_i,\\theta)$$ \n",
"\n",
"wobei $\\mathcal{L}(x_1 ... x_N; \\theta_1 ... \\theta_N)$ die sogenannte **likely hood function** darstellt."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wie kommen wir nun von der **likely hood function** auf unsere **Methode der kleinsten Quadrate** und dem fitten einer Funktion $\\lambda(x; \\ $**$\\phi$**$)$ an die gemessenen Punkte **$(x,y)$**? Dazu brauche wir noch einen Zwischenschritt. Oftmals ist es einfacher statt die **likely hood function** zu maximieren die so genannte **log likely hood function**\n",
"\n",
"$$ \\log( \\mathcal{L}(x_1 ... x_N; \\theta_1 ... \\theta_N)) = \\sum_{i = 1}^{N} \\log(f(x_i,\\theta))$$\n",
"\n",
"zu maximieren. Dies ist im Grunde das Gleiche, da der logarithmus eine monoton-steigende Funktion ist. Auch in unserem Fall der **Methode der kleinsten Quadrate** benötigen wir die **log likely hood function**. \n",
"\n",
"Stellt euch nun vor wir haben eine Messung mit $N$ voneinander unabhängigen Messpunkten (x,y). Des Weiteren nehmen wir an, dass alle $x_i$ ohne Fehler sind und das unsere $y_i$ gaußförmig um einen unbekannten Wahrenwert $\\lambda_i$ (sprich $\\lambda_i$ entspricht dem Erwartungswert $\\mu_i$ unserer Gaußverteilung) mit einer bekannten Varianz $\\Delta y_i^2$ verteilt sind (Diese Annahme lässt sich mit dem zentralen Grenzwertsatz begründen, so lange der Fehler sich aus der Summe kleinen Fehlern zusammensetzt). Die dazugehörige **likely hood function** ist dann gegeben durch:\n",
"\n",
"$$ \\mathcal{L}(y_1 ... y_N; \\lambda_1 ... \\lambda_N, \\Delta y_1 ... \\Delta y_N)) = \\prod_{i = 1}^{N}\\frac{1}{\\sqrt{2 \\pi \\Delta y_i^2}} \\cdot \\exp \\bigg( \\frac{ -(y_i - \\lambda_i)^2}{2 \\cdot \\Delta y_i^2}\\bigg)$$\n",
"\n",
"Beziehungsweise die **log likely hood function** mit $\\lambda_i = \\lambda(x_i; \\phi)$ ergibt sich zu\n",
"\n",
"$$ \\log(\\mathcal{L}(y, \\theta)) \\approx -\\frac{1}{2} \\sum_{i = 1}^{N}\\bigg( \\frac{ (y_i - \\lambda(x_i; \\phi))^2}{\\Delta y_i^2}\\bigg)$$\n",
"\n",
"wobei die konstanten Terme welche nicht von unserer Funktion $\\lambda(x_i; \\phi)$ abhängen vernachlässigt worden sind. Durch den Faktor $-\\frac{1}{2}$ ist das maximieren dieser **log likely hood function** gleich dem minnimieren von\n",
"\n",
"$$ \\chi(\\phi_1 ... \\phi_N)^2 = \\sum_{i = 1}^{N} \\frac{ (y_i - \\lambda(x_i; \\phi))^2}{\\Delta y_i^2}$$\n",
"\n",
"Diese Funktion ist unsere gesuchte **Methode der kleinsten Quadrate**. Mit ihrer Hilfe kann eine beliebige Funktion $\\lambda(x; \\phi)$, welche liniear in ihren Parametern $\\phi$ ist, an unsere Messdaten $(x,y\\pm\\Delta y)$ gefittet werden. Dabei stellt der Fitprozess selbst lediglich ein Minimierungsproblem dar. Im folgenden sind unsere Annahmen noch einmal grafisch in einem Beispiel dargestellt.\n",
"\n",
"\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Es gibt verschiedene Arten von Algorithmen um Minimierungsprobleme zu lösen. Wie diese genau Aufgebaut sind lernt ihr in anderen Progrmmierkursen wie zum Beispiel *Programmieren für Physiker* oder *Computer in der Wissenschaft*. Zum Glück haben uns bereits in Python andere Menschen diese Arbeit abgenommen und wir können aus dem Package `scipy.optimize` die Funktion `curve_fit` verwenden. \n",
"\n",
"Hierbei stellt curve_fit eine Methode dar, Fit-Funktionen nach der obigen vorgestellten Methode der *kleinsten Quadraten* zu bestimmen. Dies hat zur Folge, dass lediglich die y-Fehler eurer Messwerte für den Fit verwendet werden können. "
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T14:03:03.767521Z",
"start_time": "2019-11-04T14:03:02.583918Z"
}
},
"outputs": [],
"source": [
"from scipy.optimize import curve_fit"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Gucken wir uns einen Fit ohne Messfehler an um die Funktion etwas näher kennen zu lernen."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T14:04:02.759738Z",
"start_time": "2019-11-04T14:04:02.714523Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10.098259801145538\n",
"0.15780378609977405\n",
"Widerstand R 10.10 +/- 0.16 Ohm\n"
]
}
],
"source": [
"# Und jetzt fitten wir:\n",
"para, pcov = curve_fit(Spannung, # <-- Funktion die an die Messdaten gefittet werden soll\n",
" strom, # <-- gemessenen \"X\"-Werte\n",
" spannung # <-- gemessenen \"Y\"-Werte \n",
" )\n",
"\n",
"print(para[0])\n",
"print(pcov[0,0]**0.5)\n",
"\n",
"print(f'Widerstand R {para[0]:.2f} +/- {pcov[0,0]**0.5:.2f} Ohm')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Ihr seht `curve_fit` gibt uns zwei unterschiedliche Listen zurück. Die erste Liste `para` beinhaltet die berechneten Fitparameter. `pcov` hingegen ist eine [Kovarianzmatrix](https://de.wikipedia.org/wiki/Kovarianzmatrix) auf deren Diagonalen ihr die Varianzen ($\\sigma^2$) der einzelnen Parameter findet (auf der Nebendiagonalen befinden sich die Kovarianzen). D.h. bei einer Funktion mit drei Parametern `def f(x, p1, p2, p3):` würde `para` und `pcov` allgemein so aussehen:\n",
"\n",
"```\n",
"para = [p1, p2, p3]\n",
"pcov = [[cov_1,1, cov_1,2, cov_1,3], \n",
" [cov_2,1, cov_2,2, cov_2,3],\n",
" [cov_3,1, cov_3,2, cov_3,3]]\n",
"```\n",
"wobei `cov_i,i` wie bereits erwähnt die einzelnen Kovarianzen bzw. Varianzen sind. Aber was genau macht jetzt curve_fit eigentlich um auf diese Werte zu kommen? Wie bereits erklärt basiert `curve_fit` auf der Methode der kleinsten Quadrate. D.h. die Funktion probiert etliche verschiedene Varianten eurer Parameter durch bis es die Kombination gefunden hat bei der das $\\chi^2$ klein wird. Gucken wir uns doch mal ein paar Zwischenschritte für unser Beispiel des ohm'schen Widerstandes an: \n",
"\n",
"\n",
"\n",
"\n",
"\n",
"Nach dem wir nun wissen, was genau `curve_fit` macht wollen wir unser Resultat etwas schöner darstellen:"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T14:06:00.969312Z",
"start_time": "2019-11-04T14:06:00.676047Z"
}
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(strom, \n",
" spannung, \n",
" ls='', \n",
" marker='d', \n",
" mfc='orange', \n",
" mec='k', \n",
" ms=7,\n",
" label='Messwerte aus A. 5 (ohne Fehler)'\n",
" ) \n",
"plt.plot(strom, \n",
" [Spannung(value, para[0]) for value in strom], \n",
" ls ='dashed',\n",
" color='orange',\n",
" label = f'Fitgerade mit R = {para[0]:0.2f} +/- {pcov[0,0]**(1/2):0.2f} ohm'\n",
" )\n",
"\n",
"plt.legend()\n",
"plt.ylabel('Spannung [V]')\n",
"plt.xlabel('Strom [mA]')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Das Ergebnis sieht bereits ganz gut aus, allerdings kennt hier unsere Funktion `curve_fit` die Fehler unserer Messwerte noch garnicht. Da dies sehr unphysikalisch ist lasst uns das ganze nochmal mit Unsicherheiten wiederholen: "
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T14:08:11.387120Z",
"start_time": "2019-11-04T14:08:11.137181Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"para2, pcov2 = curve_fit(Spannung, \n",
" strom, \n",
" spannung,\n",
" sigma=spannung_error, # <-- Diesesmal mit Fehler\n",
" absolute_sigma=True # <-- Diesen Option müssen wir auf Wahr setzen, da \n",
" # wir in der Regel absolute und keine relativen \n",
" # Unsicherheiten messen.\n",
" )\n",
"\n",
"plt.plot(strom, \n",
" [Spannung(value, para2[0]) for value in strom], \n",
" ls ='dashed',\n",
" color='orange',\n",
" label = f'Fitgerade mit R = {para2[0]:0.2f} +/- {pcov2[0,0]**(1/2):0.2f} ohm'\n",
" )\n",
"plt.errorbar(strom, \n",
" spannung,\n",
" xerr=strom_error,\n",
" yerr=spannung_error, \n",
" ls='', \n",
" marker='d', \n",
" mfc='orange', \n",
" mec='k', \n",
" ms=7,\n",
" ecolor='k', \n",
" elinewidth=2, \n",
" capsize=5, \n",
" capthick=2, \n",
" label='Messwerte aus A. 5'\n",
" ) \n",
"\n",
"\n",
"plt.legend()\n",
"plt.ylabel('Spannung [V]')\n",
"plt.xlabel('Strom [mA]')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wie ihr sehen könnt ist der Wert für den Widerstand zwar gleich geblieben, jedoch die Unsicherheit des Wertes hat sich erhöht.\n",
"\n",
"Wie gut denkt ihr fittet unsere obige Funktion unsere Messdaten? Sehr gut? Gut? Befriedigend? Oder doch eher schlecht? Wäre es nicht gut ein Maß für die Güte des Fits zu haben? Wie könnte ein solches Maß aussehen?\n",
"\n",
"Ihr habt das entscheiden Kriterium bereits kennen gelernt, bei der Methode der kleinsten Quadrate geht es darum das $\\chi^2$ zu minimieren sprich klein zu machen. Gucken wir uns hierzu erst noch einmal an wie sich das $\\chi^2$ berechnet:\n",
"\n",
"$$ \\chi(\\phi_1 ... \\phi_N)^2 = \\sum_{i = 1}^{N} \\frac{ (y_i - \\lambda(x_i; \\phi))^2}{\\Delta y_i^2}$$\n",
"\n",
"Dies bedeute in unserem Fall:\n",
"\n",
"$$ \\chi(R)^2 = \\sum_{i = 1}^{N} \\frac{ (U_i - u(I_i; R))^2}{\\Delta U_i^2}$$\n",
"\n",
"wobei hier groß $U$ unsere gemessenen Spannung und klein $u$ unsere Funktion entspricht."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T14:09:37.708408Z",
"start_time": "2019-11-04T14:09:37.683983Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Das chi-qudrat ist 1.26\n"
]
}
],
"source": [
"chi_2 = [ (u - Spannung(i, para2[0]))**2/du**2 for i,u,du in zip(strom, spannung, spannung_error)]\n",
"chi_2 = sum(chi_2)\n",
"print(f'Das chi-qudrat ist {chi_2:.2f}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wie vergleicht sich dieses $\\chi^2$ nun mit einer Funktion welche unsere Daten schlechter beschreibt. Zum Beispiel sofern wir die Spannung über die Funktion \n",
"\n",
"$$ U(R,I) = R \\cdot I $$\n",
"\n",
"$$ U(R,I) = R \\cdot I + U0 $$\n",
"\n",
"$$ U(R,I) = R \\cdot I^2 $$\n",
"\n",
"beschreiben würden."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T14:10:02.649772Z",
"start_time": "2019-11-04T14:10:02.619695Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Chi-qudrat nach URI: 1.26\n",
"Chi-qudrat nach URI-Parabel: 60.68\n"
]
}
],
"source": [
"def Spannung2(I, R):\n",
" return R * I**2\n",
"\n",
"\n",
"\n",
"para3, pcov3 = curve_fit(Spannung2,\n",
" strom,\n",
" spannung,\n",
" sigma=spannung_error,\n",
" absolute_sigma=True\n",
" )\n",
"\n",
"chi_2_new = [ (u - Spannung2(I, *para3))**2/du**2 for I,u,du in zip(strom, spannung, spannung_error)]\n",
"chi_2_new = sum(chi_2_new)\n",
"print(f'Chi-qudrat nach URI: {chi_2:.2f}\\nChi-qudrat nach URI-Parabel: {chi_2_new:.2f}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wie ihr sehen könnt ist das $\\chi^2$ für unsere zweite Funktion etwas größer als für das klassische ohm'sche Gesetzt. Somit würden wir unsere zweiten Ansatz verwerfen. \n",
"\n",
"Damit man für einen gegebene Datensatz nicht hunderte von verschiedene Funktionen durchprobieren muss gibt es für das $\\chi^2$ eine allgemeine Faustregel, welche den berechneten $\\chi^2$-Wert mit der Anzahl unserer Freiheitsgrade vergleicht. Die Anzahl an Freiheitsgrade ist allgemeinhin gegeben als *Anzahl der Messwerte - Anzahl der Funktionsparameter* ($m - n$).\n",
"\n",
"1. Sofern $\\chi^2/\\text{ndof} >> 1$: sollte die Hypothese bzw. die Fitfunktion angezweifelt werden. Sie beschreibt in diesem Fall die Messdaten nur unzureichend. (Bzw. sollte $\\chi^2/\\text{ndof} > 1$ kann dies auch bedeuten, dass eure Unsicherheiten unterschätzt sind)\n",
"2. Sofern $\\chi^2/\\text{ndof} \\approx 1$: beschreibt die Hypothese bzw. die Fitfunktion die Daten wie erwartet und wird nicht abgelehnt. \n",
"3. Falls $\\chi^2/\\text{ndof} << 1$ beschreibt die Hypothese bzw. die Fitfunktion die Daten wesentlich besser als erwartet. In diesem Fall heißt es nicht, dass unsere Hypothese falsch ist, aber man sollte überprüfen ob die gemessenen Fehler nicht überschätzt worden sind (oder eine Korrelation zwischen denn Messfehlern vor liegt). \n",
"\n",
"Sofern ihr eine Arbeit schreibt und eure **Goodness-of-the-Fit** ($\\chi^2/\\text{ndof}$) angeben wollt so gebt immer beides an, das $\\chi^2$ und die Anzahl an Freiheitsgraden ndof. Beide Werte getrennt habne einen größeren Informationsgehalt als der Resultierende Quotient (genaueres lernt ihr in z.B. in der Vorlesung *Statistik, Datenanalyse und Simulationen* im Master)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"#### Aufgabe 7.: PGP Auswertung:\n",
"\n",
"Jetzt seid ihr ein letztes mal gefordert. In dieser Aufgabe wollen wir alles was wir heute gelernt haben nochmal reflektieren und anwenden. Erstellt hierfür ein neues Jupyter-Notebook und bearbeitet die Aufgaben im Skript. Sofern ihr Fragen bzw. Probleme habt vergesst nicht auf die folgenden Hilfsmöglichkeiten zurückzugreifen:\n",
"\n",
"1. Verwenden der IPython-Hilfe unter Verwendung der shift + tab Tasten.\n",
"2. Die ausführlichen Dokumentation von Python und das Angebot etlicher nützlicher Hilfsbeiträge in verschiedenen Foren (z.B. stackoverflow) im Internet.\n",
"3. Fragt bei den Assistenten nach während der Stunde nach bzw. nutzt den Emailkontakt auf der [gitlab Seite](https://gitlab.rlp.net/hoek/pgp1-python-einfuehrung/tree/master). \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.8"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
![\"Tab-Taste\"](\"images/Tab-Key.png\")
"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:08:53.901374Z",
"start_time": "2019-11-04T12:08:53.885753Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Hier läuft das Hauptprogramm\n",
"Schleife\n",
"Wert: 1\n",
"Schleife\n",
"Wert: 2\n",
"Schleife\n",
"Wert: 3\n",
"Schleife\n",
"Wert: 4\n",
"Hier läuft wieder das Hauptprogramm\n",
"Letztes Ergebnis + 5: 11\n"
]
}
],
"source": [
"liste = [1, 2, 3, 4]\n",
"print('Hier läuft das Hauptprogramm')\n",
"\n",
"for wert in liste:\n",
" print('Schleife')\n",
" print('Wert:', wert)\n",
" rechnung = wert + 2\n",
" \n",
"print('Hier läuft wieder das Hauptprogramm')\n",
"rechnung = rechnung + 5\n",
"print('Letztes Ergebnis + 5: ', rechnung)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Statt das Ergebnis lediglich per `print`-Anweisung darstellen zu lassen, können wir auch unser Wissen um Listen benutzen und die berechneten Werte einer neuen Liste anfügen:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# (Funktion haben wir bereits in der Vorbereitung definiert)\n",
"def Spannung(Strom, Widerstand):\n",
" '''\n",
" Diese Funktion berechnet die Spannung eines Ohmschen \n",
" Widerstands.\n",
" \n",
" Args:\n",
" Strom (float): Der gemessene Strom in mA.\n",
" Widerstand (float): Der Wert des verwendeten Widerstands\n",
" in Ohm.\n",
" \n",
" Returns:\n",
" float: Die Berechnete Spannung in V.\n",
" '''\n",
" return Widerstand * Strom/1000"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:10:08.503300Z",
"start_time": "2019-11-04T12:10:08.472059Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[10.1, 10.5, 9.8, 8.7, 11.2]"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Stromwerte = [101, 105, 98, 87, 112] # mA\n",
"Widerstand = 100 # Ohm\n",
"\n",
"Spannungswerte = []# Einheit? <-- Deshlab Docstrings und Help!\n",
"for Strom in Stromwerte:\n",
" res = Spannung(Strom, Widerstand)\n",
" Spannungswerte.append(res)\n",
"\n",
"Spannungswerte"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Python ermöglicht uns auch eine kompaktere Schreibweise die so genannte \"list comprehension\": "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:11:40.799393Z",
"start_time": "2019-11-04T12:11:40.783772Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[10.1, 10.5, 9.8, 8.7, 11.2]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Spannungswerte = [Spannung(Strom, 100) for Strom in Stromwerte]\n",
"Spannungswerte"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wir können auch über mehre Daten gleichzeitig loopen. Hierzu kann die `zip` Anweisung genutzt werden. `zip` verbindet hierbei die einzelnen Elemente einer Liste wie bei einem Reißverschluss miteinander:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:12:42.522873Z",
"start_time": "2019-11-04T12:12:42.507254Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A und 0\n",
"B und 1\n",
"C und 2\n",
"D und 3\n"
]
}
],
"source": [
"Werte1 = ['A', 'B', 'C', 'D']\n",
"Werte2 = [0, 1, 2, 3]\n",
"\n",
"for w1, w2 in zip(Werte1, Werte2):\n",
" print(w1, ' und ', w2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Dies kann zum Beispiel dann hilfreich sein wenn sich mehr als eine Variable ändern soll, z.B. bei einer Messreihe für die Schallgeschwindigkeit in Luft:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:13:30.363510Z",
"start_time": "2019-11-04T12:13:30.347888Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[335.4904, 347.3442, 343.6145, 337.275, 331.6212, 342.0115, 336.2262]\n",
"[335.4904, 347.3442, 343.6145, 337.275, 331.6212, 342.0115, 336.2262]\n"
]
}
],
"source": [
"# Gemessene Werte:\n",
"frequenzen = [30.17, 30.63, 30.01, 29.98, 30.12, 29.87, 29.94] #kHz\n",
"wellenlängen = [11.12, 11.34, 11.45, 11.25, 11.01, 11.45, 11.23] # mm\n",
"\n",
"# Variante 1:\n",
"schallgeschindigkeiten = [] # m/s\n",
"\n",
"for f, l in zip(frequenzen, wellenlängen):\n",
" schallgeschindigkeiten.append(f*l)\n",
"\n",
"print(schallgeschindigkeiten)\n",
"\n",
"# oder Variante 2:\n",
"schallgeschindigkeiten2 = [f*l for f,l in zip(frequenzen, wellenlängen)]\n",
"print(schallgeschindigkeiten2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wir können auch die `zip`-Anweisung mit mehr als nur zwei Listen verwenden:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-04T12:13:49.912658Z",
"start_time": "2019-11-04T12:13:49.897039Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a und 1 und x\n",
"b und 2 und y\n",
"c und 3 und z\n"
]
}
],
"source": [
"l1 = ['a', 'b', 'c']\n",
"l2 = [1, 2, 3]\n",
"l3 = ['x', 'y', 'z']\n",
"\n",
"for i, j, k in zip(l1, l2, l3):\n",
" print(i, 'und', j, 'und', k)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![\"{{](\"images/MaterialPythonkurs092018/Xenon1tResults1yearx1texposure.png\")
\n",
"![\"{{](\"images/MaterialPythonkurs092018/Gaußverteilung.png\")
\n",
"![\"{{](\"images/MaterialPythonkurs092018/PorbDensFun.png\")
\n",
"![\"{{](\"images/MaterialPythonkurs092018/ProbMaxTemp.png\")
\n",
"![\"{{](\"images/MaterialPythonkurs092018/LeastSquare.png\")
\n",
"![\"{{](\"images/MaterialPythonkurs092018/Fitting_gif.gif\")
\n",
"