Merge pull request BlackSamorez#46 from intex2dx/master

Лаба 1.4.5. Подробно расписана теор. часть.

1.4.5/Artemov_I/lab 1 4 5 график квадрата.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def xi2(x,y, y_err):
+    #y = a + bx
+    N = len(x)
+    avx = sum(x/(y_err**2))/sum(1/(y_err**2))
+    avy = sum(y/(y_err**2))/sum(1/(y_err**2))
+    av2x = sum(x*x/(y_err**2))/sum(1/(y_err**2))
+    av2y = sum(y*y/(y_err**2))/sum(1/(y_err**2))
+    R_xy = (sum(x*y/(y_err**2))/sum(1/(y_err**2))-avx*avy)
+    S_x = av2x - avx**2
+    S_y = av2y - avy**2
+    b = R_xy/S_x
+    a = avy - b * avx
+    r = R_xy/(np.sqrt(S_x*S_y))
+    delta_b = np.sqrt(1/(N-2)) * np.sqrt(S_y/S_x - b**2)
+    delta_a = delta_b * np.sqrt(av2x)
+    f = a + b * x
+    xi = sum(((y-f)/y_err)**2)
+    return a, b, delta_a, delta_b, xi,  r
+
+T = np.array([10.3, 15.1, 19.9, 23.2, 28.0])
+u2 = np.array([183.10, 261.0, 341.1, 396.0, 478.7])
+delta_u2 = np.array([0.8, 1.0, 0.7, 0.8, 1.3])
+a, b, delta_a, delta_b, xi, r = xi2(T, u2, delta_u2)
+plt.errorbar(T, u2,  delta_u2, [0]*5, ls='none', fmt='o-', elinewidth=2, markersize=4, color='black', capsize=2)
+plt.xlabel(r"$T$, Н")
+plt.ylabel(r'$u^2, 10^{2} \cdot м^2/с^2$')
+T1 = np.array([9, 10.3, 15.1, 19.9, 23.2, 28.0, 30])
+u2_normal = a + b * T1
+print(a)
+print(b)
+print(delta_a)
+print(delta_b)
+print(r)
+print(xi/3)
+plt.plot(T1, u2_normal, color='red', linewidth=1, label=r'''$u^2(T) = (11 \pm 2)\cdot 10^2 + (16.61 \pm 0.10) \cdot T$
+$r = 0.99994$
+$\frac{\chi^2}{d.o.f.} = 2.27$
+''')
+plt.grid(which='major',
+        color = 'k')
+plt.legend()
+plt.show()

1.4.5/Artemov_I/lab 1 4 5.csv

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+ n;nu;nu;nu;nu;nu
+1;134.6;161.5;186.7;201.4;223
+2;271.2;325;373.5;404.3;444
+3;405.3;488.7;563;607.5;667.5
+4;543.6;653.6;750.4;810.4;891.6
+5;681.9;811.9;940.3;1013.5;1113
+6;819.3;982.4;1129.6;1215;1338
+7;957.1;1149;1317.5;1418;1559
+8;1096;1313;1505;1622;1783
+9;1238.4;1479;1695;1825;2008
+10;1378;1645;1881;2031;2233

1.4.5/Artemov_I/lab 1 4 5.py

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+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+def xi2(x,y, y_err):
+    #y = a + bx
+    N = len(x)
+    avx = sum(x/y_err)/N
+    avy = sum(y/y_err)/N
+    av2x = sum(x*x/y_err)/N
+    av2y = sum(y*y/y_err)/N
+    R_xy = (sum(x*y/y_err)/N-avx*avy)
+    S_x = av2x - avx**2
+    S_y = av2y - avy**2
+    b = R_xy/S_x
+    a = avy - b * avx
+    r = R_xy/(S_x*S_y)
+    delta_b = np.sqrt(1/(N-2)) * np.sqrt(S_y/S_x - b**2)
+    delta_a = delta_b * np.sqrt(av2x)
+    f = a + b * x
+    xi = sum(((y-f)/y_err)**2)
+    return a, b, delta_a, delta_b, xi, r
+
+
+df = pd.read_csv("lab 1 4 5.csv", encoding="utf-8", sep=";")
+n = df.iloc[:, [0]]
+nu_1 = df.iloc[:, [1]]
+nu_1_list = np.array((nu_1["nu"]))
+
+x = np.array(range(1, 11))
+print(x)
+plt.plot(x, nu_1_list, color="black", marker='o', ls="none", markersize= 4.5)
+plt.xlabel("n")
+plt.ylabel(r"$\nu_n(n), Гц$")
+print(x)
+print(nu_1_list)
+res = xi2(x, nu_1_list, np.array([1]*10))
+plt.plot([0, 11], [res[0], res[0] + res[1]*11], color="black", label=r"$\nu_n = (-7.2 \pm 1.9) + (138.1 \pm 0.3) \cdot n$", linewidth=0.8)
+print(res)
+
+
+nu_1 = df.iloc[:, [2]]
+nu_1_list = np.array((nu_1["nu.1"]))
+
+x = np.array(range(1, 11))
+print(x)
+plt.plot(x, nu_1_list, color="red", marker='o', ls="none", markersize= 4.5)
+plt.xlabel("n")
+plt.ylabel(r"$\nu_n(n), Гц$")
+print(x)
+print(nu_1_list)
+res = xi2(x, nu_1_list, np.array([1]*10))
+plt.plot([0, 11], [res[0], res[0] + res[1]*11], color="red", label=r"$\nu_n = (-6.0 \pm 1.8) + (164.9 \pm 0.3) \cdot n$",linewidth=0.8)
+print(res)
+
+
+nu_1 = df.iloc[:, [3]]
+nu_1_list = np.array((nu_1["nu.2"]))
+
+x = np.array(range(1, 11))
+print(x)
+plt.plot(x, nu_1_list, color="grey", marker='o', ls="none", markersize= 4.5)
+plt.xlabel("n")
+plt.ylabel(r"$\nu_n(n), Гц$")
+print(x)
+print(nu_1_list)
+res = xi2(x, nu_1_list, np.array([1]*10))
+plt.plot([0, 11], [res[0], res[0] + res[1]*11], color="grey", label=r"$\nu_n = (-2.5 \pm 0.7) + (188.48 \pm 0.11) \cdot n$",linewidth=0.8)
+print(res)
+
+
+nu_1 = df.iloc[:, [4]]
+nu_1_list = np.array((nu_1["nu.3"]))
+
+x = np.array(range(1, 11))
+print(x)
+plt.plot(x, nu_1_list, color="green", marker='o', ls="none", markersize= 4.5)
+plt.xlabel("n")
+plt.ylabel(r"$\nu_n(n), Гц$")
+print(x)
+print(nu_1_list)
+res = xi2(x, nu_1_list, np.array([1]*10))
+plt.plot([0, 11], [res[0], res[0] + res[1]*11], color="green", label=r"$\nu_n = (-2.1 \pm 0.8) + (203.08 \pm 0.13) \cdot n$",linewidth=0.8)
+print(res)
+
+
+nu_1 = df.iloc[:, [5]]
+nu_1_list = np.array((nu_1["nu.4"]))
+
+x = np.array(range(1, 11))
+print(x)
+plt.plot(x, nu_1_list, color="darkblue", marker='o', ls="none", markersize= 4.5)
+plt.xlabel("n")
+plt.ylabel(r"$\nu_n(n), Гц$")
+print(x)
+print(nu_1_list)
+res = xi2(x, nu_1_list, np.array([1]*10))
+plt.plot([0, 11], [res[0], res[0] + res[1]*11], color="darkblue", label=r"$\nu_n = (-2.1 \pm 1.0) + (223.29 \pm 0.16) \cdot n$",linewidth=0.8)
+print(res)
+
+
+plt.legend()
+plt.grid(which='major',
+        color = 'k')
+plt.show()