generated from Nabla/LU_template
Calc done
This commit is contained in:
Sally Marcher
parent
bfc29d426d
commit
aa025c38b4
5 changed files with 406 additions and 11 deletions
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res/graphs/3D_4.1.png
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res/graphs/3D_4.1.png
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res/graphs/3D_4.4.png
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res/graphs/3D_4.4.png
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res/graphs/3d.py
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res/graphs/3d.py
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@ -0,0 +1,94 @@
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from saplotlib import match_t, eval_uncert, symbolize, plot_dataset_v2, format_uncert, latex_table_from_lists
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import numpy as np
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from sympy import *
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import sympy as sp
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import matplotlib.pyplot as plt
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from scipy.optimize import curve_fit
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import pyperclip
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clip = ""
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# Versuch 1
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# 1. Polarisator auf 0°
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# RS pro RS-12 DMM - range 200mV
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# maximum: ~138 => 185.5mV
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def calc_dphi(phi):
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return 1 # +- kleinste einheit / 2
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def calc_dU(U):
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return 0.1 * U + 0.2 # 200mV Range [Res 0.1mV] +- 0.5% (10%!) + 2 digits
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# (winkel, spannung [mV])
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data_1 = [(0, 46.7), (10, 22.9), (20, 4.8), (30, 1), (40, 8.9), (50, 30.5), (60, 57.5), (70, 85.9), (80, 132.4), (90, 160), (100, 176.1), (110, 192), (120, 193.4), (130, 173.1), (140, 190.3), (150, 146), (160, 118.8), (170, 80), (180, 51), (190, 22.5), (200, 6.6), (210, 0.8), (220, 7.9), (230, 29.8), (240, 63.5), (250, 98.8), (260, 128.8), (270, 161.7), (280, 171.2), (290, 182.3), (300, 199.5), (310, 191.6), (320, 169.4), (330, 158.3), (340, 119.7), (350, 73.9)]
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clip += "% Versuch 4.1 Werte Tabelle:\n"
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clip += latex_table_from_lists([[i[0] for i in data_1], [i[1] for i in data_1]], ["Winkel $\\phi$ / °", "Spannung $U$ / mV"], [calc_dphi, calc_dU]) + "\n\n"
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def I(_tex_phi, I_0, _tex_Delta_tex_phi):
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return I_0 * cos(_tex_phi + _tex_Delta_tex_phi) ** 2
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p = np.array([i[0] * (np.pi / 180) for i in data_1])
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U = np.array([i[1] * (np.pi / 180) for i in data_1])
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plt.polar()
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popt, perr = plot_dataset_v2(p, U, calc_dphi(p) * (np.pi / 180), calc_dU(U), I, "Messdaten", normalize=1)
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d_p = (popt[1] % np.pi) * (180/np.pi)
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dd_p = perr[1] * (180/np.pi)
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print(f"Verkippungswinkel der beiden Polarisatoren zueinander (delta phi): {format_uncert(d_p, dd_p)}°")
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plt.xlabel("$\\phi$ / °")
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plt.yticks([0.25, 0.5, 0.75, 1])
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plt.legend()
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plt.savefig('3D_4.1.png')
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plt.cla()
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# Versuch 2
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# -> Polarisatoren sind normal zueinander
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# Pol1: 0°; Pol2: 218°
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# Spannung 1.4mV
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# => Zucker Lösung in den Weg stellen, dann
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# > 47mV
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# Nomral stellen: 240°; 0.6mV
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pol_o = np.array([210, 209, 209, 209, 210]) # Ohne Zucker
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pol_m = np.array([238, 240, 238, 239, 239]) # Mit Zucker
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clip += "% Versuch 4.2 Werte Tabelle:\n"
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clip += latex_table_from_lists([pol_o, pol_m], ["Winkel $\\phi_o$ / °", "Winkel $\\phi_m$ / °"], [calc_dphi, calc_dphi]) + "\n\n"
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phi = np.mean(pol_m) - np.mean(pol_o)
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d_phi = 1
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phi_0 = 6.65
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l = 18.5 # [cm] +- 0.1cm
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dl = 0.1
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c = (phi / (phi_0 * l)) * 100
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dc = (1 / (phi_0 * l) * d_phi + dl * phi / (phi_0 * (l ** 2))) * 100
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print(f"Länge l {format_uncert(l, dl)}cm")
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print(f"Konzentration: {format_uncert(c, dc)}%")
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# Versuch 4
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# Polarisator 1: 0°
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# Polarisator 2: 28° => dann 0 transmission
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# (winkel, spannung [mV])
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data_2 = [(0, 0.5), (10, 3.6), (20, 16.1), (30, 37.7), (40, 66.8), (50, 97.2), (60, 128.9), (70, 152), (80, 152.6), (90, 151.7), (100, 139.9), (110, 137.9), (120, 128.8), (130, 109.2), (140, 81.1), (150, 52.1), (160, 25.9), (170, 8.4), (180, 0.8), (190, 3.2), (200, 14.9), (210, 34.5), (220, 65.4), (230, 97.2), (240, 119.1), (250, 153.6), (260, 162.4), (270, 153.2), (280, 154.2), (290, 154.2), (300, 140.8), (310, 123.5), (320, 92.6), (330, 57.3), (340, 28.2), (350, 7.7)]
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clip += "% Versuch 4.4 Werte Tabelle:\n"
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clip += latex_table_from_lists([[i[0] for i in data_2], [i[1] for i in data_2]], ["Winkel $\\phi$ / °", "Spannung $U$ / mV"], [calc_dphi, calc_dU]) + "\n\n"
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p = np.array([i[0] * (np.pi / 180) for i in data_2])
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U = np.array([i[1] for i in data_2])
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plt.polar()
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popt, perr = plot_dataset_v2(p, U, calc_dphi(p) * (np.pi / 180), calc_dU(U), I, "Messdaten", normalize=1)
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plt.xlabel("$\\phi$ / °")
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plt.gca().set_theta_zero_location("N")
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plt.yticks([0.25, 0.5, 0.75, 1])
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plt.legend()
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plt.savefig('3D_4.4.png')
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plt.cla()
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d_p = (popt[1] % np.pi) * (180/np.pi)
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dd_p = perr[1] * (180/np.pi)
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print(f"delta phi Brille: {format_uncert(d_p, dd_p)}°")
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pyperclip.copy(clip)
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180
res/graphs/out.txt
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180
res/graphs/out.txt
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@ -0,0 +1,180 @@
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% Versuch 4.1 Werte Tabelle:
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\begin{tabular}{|c||c|}
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\hline
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Winkel $\phi$ / ° ($\pm 1.0$) & Spannung $U$ / mV \\
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\hline
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$0.0$ & $47\pm5$ \\
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\hline
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$10.0$ & $23\pm3$ \\
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\hline
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$20.0$ & $4.8\pm0.7$ \\
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\hline
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$30.0$ & $1.0\pm0.4$ \\
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\hline
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$40.0$ & $8.9\pm1.1$ \\
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\hline
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$50.0$ & $30\pm4$ \\
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\hline
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$60.0$ & $58\pm6$ \\
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\hline
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$70.0$ & $86\pm9$ \\
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\hline
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$80.0$ & $132\pm14$ \\
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\hline
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$90.0$ & $160\pm17$ \\
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\hline
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$100.0$ & $176\pm18$ \\
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\hline
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$110.0$ & $192\pm20$ \\
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\hline
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$120.0$ & $193\pm20$ \\
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\hline
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$130.0$ & $173\pm18$ \\
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\hline
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$140.0$ & $190\pm20$ \\
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\hline
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$150.0$ & $146\pm15$ \\
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\hline
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$160.0$ & $119\pm13$ \\
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\hline
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$170.0$ & $80\pm9$ \\
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\hline
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$180.0$ & $51\pm6$ \\
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\hline
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$190.0$ & $22\pm3$ \\
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\hline
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$200.0$ & $6.6\pm0.9$ \\
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\hline
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$210.0$ & $0.8\pm0.3$ \\
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\hline
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$220.0$ & $7.9\pm1.0$ \\
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\hline
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$230.0$ & $30\pm4$ \\
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\hline
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$240.0$ & $64\pm7$ \\
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\hline
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$250.0$ & $99\pm11$ \\
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\hline
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$260.0$ & $129\pm14$ \\
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\hline
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$270.0$ & $162\pm17$ \\
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\hline
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$280.0$ & $171\pm18$ \\
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\hline
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$290.0$ & $182\pm19$ \\
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\hline
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$300.0$ & $200\pm30$ \\
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\hline
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$310.0$ & $192\pm20$ \\
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\hline
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$320.0$ & $169\pm18$ \\
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\hline
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$330.0$ & $158\pm17$ \\
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\hline
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$340.0$ & $120\pm13$ \\
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\hline
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$350.0$ & $74\pm8$ \\
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\hline
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\end{tabular}
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% Versuch 4.2 Werte Tabelle:
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\begin{tabular}{|c||c|}
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\hline
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Winkel $\phi_o$ / ° ($\pm 1.0$) & Winkel $\phi_m$ / ° ($\pm 1.0$) \\
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\hline
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$210.0$ & $238.0$ \\
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\hline
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$209.0$ & $240.0$ \\
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\hline
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$209.0$ & $238.0$ \\
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\hline
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$209.0$ & $239.0$ \\
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\hline
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$210.0$ & $239.0$ \\
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\hline
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\end{tabular}
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% Versuch 4.4 Werte Tabelle:
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\begin{tabular}{|c||c|}
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\hline
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Winkel $\phi$ / ° ($\pm 1.0$) & Spannung $U$ / mV \\
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\hline
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$0.0$ & $0.5\pm0.3$ \\
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\hline
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$10.0$ & $3.6\pm0.6$ \\
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\hline
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$20.0$ & $16.1\pm1.9$ \\
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\hline
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$30.0$ & $38\pm4$ \\
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\hline
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$40.0$ & $67\pm7$ \\
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\hline
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$50.0$ & $97\pm10$ \\
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\hline
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$60.0$ & $129\pm14$ \\
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\hline
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$70.0$ & $152\pm16$ \\
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\hline
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$80.0$ & $153\pm16$ \\
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\hline
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$90.0$ & $152\pm16$ \\
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\hline
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$100.0$ & $140\pm15$ \\
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\hline
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$110.0$ & $138\pm14$ \\
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\hline
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$120.0$ & $129\pm14$ \\
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\hline
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$130.0$ & $109\pm12$ \\
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\hline
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$140.0$ & $81\pm9$ \\
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\hline
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$150.0$ & $52\pm6$ \\
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\hline
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$160.0$ & $26\pm3$ \\
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\hline
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$170.0$ & $8.4\pm1.1$ \\
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\hline
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$180.0$ & $0.8\pm0.3$ \\
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\hline
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$190.0$ & $3.2\pm0.6$ \\
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\hline
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$200.0$ & $14.9\pm1.7$ \\
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\hline
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$210.0$ & $34\pm4$ \\
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\hline
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$220.0$ & $65\pm7$ \\
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\hline
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$230.0$ & $97\pm10$ \\
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\hline
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$240.0$ & $119\pm13$ \\
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\hline
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$250.0$ & $154\pm16$ \\
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\hline
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$260.0$ & $162\pm17$ \\
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\hline
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$270.0$ & $153\pm16$ \\
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\hline
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$280.0$ & $154\pm16$ \\
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\hline
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$290.0$ & $154\pm16$ \\
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\hline
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$300.0$ & $141\pm15$ \\
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\hline
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$310.0$ & $124\pm13$ \\
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\hline
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$320.0$ & $93\pm10$ \\
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\hline
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$330.0$ & $57\pm6$ \\
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\hline
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$340.0$ & $28\pm4$ \\
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\hline
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$350.0$ & $7.7\pm1.0$ \\
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\hline
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\end{tabular}
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Verkippungswinkel der beiden Polarisatoren zueinander (delta phi): (61.5 ± 0.5)°
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Länge l (18.50 ± 0.10)cm
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Konzentration: (23.9 ± 1.0)%
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delta phi Brille: (87.4 ± 0.8)°
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@ -2,6 +2,7 @@ import numpy as np
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from scipy.optimize import curve_fit
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import matplotlib.pyplot as plt
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from sympy import *
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import math
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plt.rcParams['text.usetex'] = True
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@ -30,6 +31,30 @@ def match_t(arr, sigma_mult):
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print(f"Matched Student t multiplier: {t}! Using {sigma_mult} Sigma width!")
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return t
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def format_uncert(val, err, p=False):
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if err == 0:
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return f"{val}"
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exponent = math.floor(math.log10(abs(err)))
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first_digit = int(abs(err) / (10**exponent))
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sig = 2 if first_digit == 1 else 1
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factor = 10**(exponent - sig + 1)
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rounded_err = math.ceil(abs(err) / factor) * factor
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rounded_val = round(val, -(exponent - sig + 1))
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decimals = max(0, -(exponent - sig + 1))
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val_str = f"{rounded_val:.{decimals}f}"
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err_str = f"{rounded_err:.{decimals}f}"
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if p:
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return f"{val_str};{err_str}"
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return f"({val_str} ± {err_str})"
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def symbolize(func):
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"""
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Arguments:
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@ -39,6 +64,9 @@ def symbolize(func):
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"""
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return func(*[Symbol(label) for label in func.__code__.co_varnames])
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def symbolize_tex(func):
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return func(*[Symbol(label.replace("_tex_", "\\")) for label in func.__code__.co_varnames])
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def conv_to_f_args(args):
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f_args = {}
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for key in args.keys():
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@ -68,18 +96,111 @@ def eval_uncert(f, args, typ="B"):
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result = symf.evalf(subs=f_args)
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return result, uncert
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def plot_dataset(x, y, xerr, yerr, func, label, n=100, log=0):
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symfunc = symbolize(func)
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def plot_dataset(x, y, xerr, yerr, func, label, n=100, log=0, fit_range=(0, None), plot_fit_range=None):
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if str(type(func)) != "<class 'NoneType'>":
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symfunc = symbolize(func)
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plt.errorbar(x, y, yerr=yerr, xerr=xerr, marker="o", ls="", capsize=5, label=label)
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if log:
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fitx = np.logspace(min(x), max(x), n)
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else:
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fitx = np.linspace(min(x), max(x), n)
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symbols = func.__code__.co_varnames
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npfunc = lambdify(symbols, symfunc, "numpy")
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popt, pcov = curve_fit(npfunc, x, y)
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plt.plot(fitx, npfunc(fitx, *popt), label="Fit: $"+latex(symfunc)+"$")
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print(f"Optimized {symbols[1:]} with values {popt}")
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if str(type(func)) != "<class 'NoneType'>":
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if log:
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if plot_fit_range:
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fitx = np.logspace(plot_fit_range[0], plot_fit_range[1], n)
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else:
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fitx = np.logspace(min(x[fit_range[0]:fit_range[1]]), max(x[fit_range[0]:fit_range[1]]), n)
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else:
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if plot_fit_range:
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fitx = np.linspace(plot_fit_range[0], plot_fit_range[1], n)
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else:
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fitx = np.linspace(min(x[fit_range[0]:fit_range[1]]), max(x[fit_range[0]:fit_range[1]]), n)
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symbols = func.__code__.co_varnames
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npfunc = lambdify(symbols, symfunc, "numpy")
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popt, pcov = curve_fit(npfunc, x[fit_range[0]:fit_range[1]], y[fit_range[0]:fit_range[1]])
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plt.plot(fitx, npfunc(fitx, *popt), label="Fit: $"+latex(symfunc)+"$")
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print(f"Optimized {symbols[1:]} with values {popt}")
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return popt
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def plot_dataset_v2(x, y, xerr, yerr, func, label, *, n: int = 100, log: int = 0, fit_range: tuple = (0, None), plot_fit_range=None, normalize: int = 0):
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if str(type(func)) != "<class 'NoneType'>":
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symfunc = symbolize(func)
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if normalize == 0:
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plt.errorbar(x, y, yerr=yerr, xerr=xerr, marker="o", ls="", capsize=5, label=label)
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if str(type(func)) != "<class 'NoneType'>":
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if log:
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if plot_fit_range:
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fitx = np.logspace(plot_fit_range[0], plot_fit_range[1], n)
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else:
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fitx = np.logspace(min(x[fit_range[0]:fit_range[1]]), max(x[fit_range[0]:fit_range[1]]), n)
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else:
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if plot_fit_range:
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fitx = np.linspace(plot_fit_range[0], plot_fit_range[1], n)
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else:
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fitx = np.linspace(min(x[fit_range[0]:fit_range[1]]), max(x[fit_range[0]:fit_range[1]]), n)
|
||||
symbols = func.__code__.co_varnames
|
||||
npfunc = lambdify(symbols, symfunc, "numpy")
|
||||
popt, pcov = curve_fit(npfunc, x[fit_range[0]:fit_range[1]], y[fit_range[0]:fit_range[1]])
|
||||
I_0 = 1
|
||||
if normalize:
|
||||
try:
|
||||
I_0 = popt[func.__code__.co_varnames.index("I_0")-1]
|
||||
plt.errorbar(x, [i/I_0 for i in y], yerr=[i/I_0 for i in yerr], xerr=xerr, marker="o", ls="", capsize=5, label=label)
|
||||
except ValueError:
|
||||
plt.errorbar(x, y, yerr=yerr, xerr=xerr, marker="o", ls="", capsize=5, label=label)
|
||||
symfunc = symbolize_tex(func)
|
||||
plt.plot(fitx, [i/I_0 for i in npfunc(fitx, *popt)], label="Fit: $"+latex(symfunc)+"$")
|
||||
#print(f"Optimized {symbols[1:]} with values {popt}")
|
||||
perr = np.sqrt(np.diag(pcov))
|
||||
return popt, perr
|
||||
|
||||
|
||||
def latex_table_from_lists(
|
||||
data_lists,
|
||||
column_names=None,
|
||||
uncertainty_func=None,
|
||||
):
|
||||
n_cols = len(data_lists)
|
||||
n_rows = len(data_lists[0])
|
||||
|
||||
common_uncertainties=[]
|
||||
for i in range(0, n_cols):
|
||||
uncertainties = [format_uncert(v, uncertainty_func[i](v), True).split(";")[1] for v in data_lists[i]]
|
||||
|
||||
if all(u == uncertainties[0] for u in uncertainties):
|
||||
common_uncertainties.append(uncertainties[0])
|
||||
else:
|
||||
common_uncertainties.append(None)
|
||||
|
||||
header = []
|
||||
for i in range(n_cols):
|
||||
if common_uncertainties and common_uncertainties[i] is not None:
|
||||
header.append(f"{column_names[i]} ($\\pm {common_uncertainties[i]}$)")
|
||||
else:
|
||||
header.append(column_names[i])
|
||||
|
||||
rows = []
|
||||
for row_idx in range(n_rows):
|
||||
row_entries = []
|
||||
for col_idx in range(n_cols):
|
||||
value = data_lists[col_idx][row_idx]
|
||||
u = uncertainty_func[col_idx](value)
|
||||
if common_uncertainties[col_idx]:
|
||||
entry = "$"+format_uncert(value, u, True).split(";")[0]+"$"
|
||||
else:
|
||||
entry = "$"+format_uncert(value, u, True).replace(";", "\\pm")+"$"
|
||||
|
||||
row_entries.append(entry)
|
||||
|
||||
rows.append(" & ".join(row_entries) + " \\\\")
|
||||
|
||||
latex = "\\begin{tabular}{" + "|c|" * n_cols + "}\n"
|
||||
latex += "\\hline\n"
|
||||
latex += " & ".join(header) + " \\\\\n"
|
||||
latex += "\\hline\n"
|
||||
latex += "\n\\hline\n".join(rows) + "\n"
|
||||
latex += "\\hline\n"
|
||||
latex += "\\end{tabular}"
|
||||
|
||||
return latex
|
||||
|
||||
|
||||
"""
|
||||
Sources:
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue