From 0a992f5328b3bcc60c5c8f21297629a2dfe024b5 Mon Sep 17 00:00:00 2001 From: maxbarsukov Date: Tue, 26 Dec 2023 13:24:20 +0300 Subject: [PATCH] feat(pt): :sparkles: upload new hw and lectures --- 3 теорвер/дз/2/19.1/1.png | Bin 0 -> 22595 bytes 3 теорвер/дз/2/19.1/2.png | Bin 0 -> 14641 bytes 3 теорвер/дз/2/19.1/3.png | Bin 0 -> 28190 bytes 3 теорвер/дз/2/19.1/README.md | 19 ++ 3 теорвер/дз/2/19.1/calculations.py | 245 ++++++++++++++++++ 3 теорвер/дз/2/19.1/result.pdf | Bin 0 -> 177074 bytes 3 теорвер/дз/2/19.1/template.tex | 20 ++ 3 теорвер/дз/2/19.2/calculation.xlsx | Bin 0 -> 23869 bytes 3 теорвер/дз/2/ДЗ 19.1.docx | Bin 0 -> 109419 bytes 3 теорвер/дз/2/ДЗ 19.2.docx | Bin 0 -> 37898 bytes 3 теорвер/лекции/Лекция 6.pdf | Bin 0 -> 1543571 bytes 3 теорвер/лекции/Лекция 7.pdf | Bin 0 -> 1171412 bytes 3 теорвер/практические работы/6/data.xlsx | Bin 0 -> 11624 bytes .../практические работы/6/Практическая работа 6.pdf | Bin 0 -> 1506488 bytes .../практические работы/6/практическая 6.docx | 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z`%xq(PX+)ysCaRd8o(zF1eS?OsIGg70I|8Fn=KqTV4<$g6BQLj7?-5b1d~#QaCQl7 z52P8p!8f^0h&%!tHf*Reqq!xLE3NenLcCk%D931isGUY8kf1VzfvFDozNhfaV;W5wk8ZFooC(v1h~%^kkuM zLrO`ua}Z#BoWBH|p83(ytko^cT^wTM_?M5mfsuxBf-tZz%||V(H|^QRo0;Z^p#$e} zwI!}pF?N+9Mnpik%dNk>y3K!tt78S?>wJ5AK8X1EkTHRu(1Y&xRkPPD9tK7Hm)J&YO`wZ-`JR>IJX6?d&0)BS__!VOoy3_mM^}ucbMvV7E zX=tYRB4@#?mne|gHB~r{5eN>RapaI9R30UBah=JwAh?kdms!(8G1`VggC83^_+~o? z;gtq2V&)%)wa}LKfC=eLUq)0?9v0{gNZc1RvCr&$iYvN`K%Tjm| zU^-c)@6T3#VFbI<4%L8`<9QC(Y-`kRu-WYgCoOh#wDa&#+!z$pR=9Gu;iiXfXR3eb z|1Rm3I%lTUcXde%N$b`O_trxjnFPg4U)B3=vegPI0#)D6we(R2xe#b;0YyAFH|n_@ z@N8uD$7tZf*7>f-n8nn4OIhHiQ;-HG(br`% +Для работы скрипта надо записать значения из варианта, номер варианта и имя: +```python +if __name__ == "__main__": + # Значения из варианта + values = """ + """ + + variant = "" # Номер варианта + name = "" # Имя автора + + values = make_table(values) + template_handler = TemplateHandler(variant, name) + process(values, template_handler, True) +``` +После можно запускать скрипт. +Для работы нужен `matplotlib`. diff --git a/3 теорвер/дз/2/19.1/calculations.py b/3 теорвер/дз/2/19.1/calculations.py new file mode 100644 index 0000000..0f53e51 --- /dev/null +++ b/3 теорвер/дз/2/19.1/calculations.py @@ -0,0 +1,245 @@ +import bisect +import matplotlib.pyplot as plt +from math import sqrt, pi, exp + +N = 100 + + +class TemplateHandler: + def __init__(self, variant, name) -> None: + self.template = self.load_tex_template(variant, name) + + def get_template(self): + return self.template + + def load_tex_template(self, variant, name): + with open('template.tex', 'r', encoding='utf-8') as f: + text = f.read() + text = text.replace("??", str(variant), 1) + text = text.replace("??", name, 1) + return text + + def save_template(self, name): + with open(name + '.tex', 'w', encoding='utf-8') as f: + f.write(self.template) + print("༼ つ ◕_◕ ༽つ Saved result in `" + name + ".tex`") + + def end_text(self): + self.template = self.template.replace("??", "") + + def add_text(self, text, newline=False): + if newline: + postfix = "\n\n??" + else: + postfix = "\n??" + self.template = self.template.replace("??", text + postfix, 1) + + def add_picture(self, name): + text = "\\centerline{\\includegraphics[scale=0.7]{" + name + ".png}}" + self.add_text(text, True) + + def generate_table(self, top_row, bottom_row, values): + table_text = "\\begin{center}\n\\begin{tabular}{ |" + table_text += "c|" * len(top_row) + " }" + table_text += "\n\\hline\n" + table_text += " & ".join(top_row) + " \\\\\n" + + for val in values: + table_text += " & ".join(val) + table_text += " \\\\\n" + + if bottom_row: + table_text += " & ".join(bottom_row) + " \\\\\n" + table_text += "\\hline\n" + table_text += "\\end{tabular}\n\\end{center}" + + self.add_text(table_text, True) + + def generate_first_table(self, intervals, middles, freqs, relative_freqs, F, mf, m2f): + top_row = [ + "Интервал", + "Середина интервала $x_i$", + "Частота $f_i$", + "$w_i=\\frac{f_i}{n}$", + "$w_i^{HAK}$", + "$x_if_i$", + "$x_i^2f_i$"] + tuple_intervals = zip(intervals[:-1], intervals[1:]) + rows = zip(tuple_intervals, middles, freqs, relative_freqs, F, mf, m2f) + values = [] + for row in rows: + values.append([]) + for el in row: + if type(el) == tuple: + values[-1].append(f"{el[0]} - {el[1]}") + else: + values[-1].append(str(el)) + bottom_row = ["\\quad", "$\\sum$", "$n=100$", "1", "\\quad", str(sum(mf)), str(sum(m2f))] + self.generate_table(top_row, bottom_row, values) + + def generate_second_table(self, middles, t, f, ft): + top_row = ["$x_i$", "$t_i$", "$f(t_i)$", "$f_i^T$"] + rows = list(map(list, zip(middles, t, f, ft))) + + values = [list(map(lambda x: str(round(x, 2)), row)) for row in rows] + self.generate_table(top_row, None, values) + + def generate_third_table(self, f, fT, crit): + top_row = ["$f_i$", "$f_i^T$", "$\\chi^2$"] + rows = list(map(list, zip(f, fT, crit))) + + values = [list(map(lambda x: str(round(x, 2)), row)) for row in rows] + self.generate_table(top_row, None, values) + + +def print_table(values): + for i in range(0, len(values), 10): + for j in range(10): + try: + print(values[i + j], end=' ') + except BaseException: + break + print() + print() + + +def make_table(string): + correct_string = string.replace(',', '.') + values = list(map(float, correct_string.split())) + assert len(values) == N, f"must be {N} vallues, check the table." + + print("Given table:") + print_table(values) + + return sorted(values) + + +def find_ni(values, l, r): + lower_bound = bisect.bisect_right(values, l) if l > values[0] else 0 + upper_bound = bisect.bisect_right(values, r, lower_bound) + return upper_bound - lower_bound + + +def draw_graph(x, y, name, save=False, saveName=''): + plt.title(name) + plt.xticks(x) + plt.yticks(y) + plt.plot(x, y, marker='o') + if save: + plt.savefig(saveName + '.png') + plt.clf() + else: + plt.show() + + +def draw_histogram(data, intervals, r_freqs, name, save=False, saveName=''): + plt.title(name) + plt.xticks(intervals) + plt.yticks(r_freqs) + plt.hist(data, bins=intervals, weights=r_freqs) + if save: + plt.savefig(saveName + '.png') + plt.clf() + else: + plt.show() + + +def process(values, th, save=False): + w = max(values) - min(values) + h = round(w / (10 - 1), 2) + intervals = [round(min(values) + i * h, 2) for i in range(10)] + middles = [(x1 + x2) / 2 for x1, x2 in zip(intervals[:-1], intervals[1:])] + freqs = [find_ni(values, x1, x2) for x1, x2 in zip(intervals[:-1], intervals[1:])] + relative_freqs = [f / N for f in freqs] + m = [sum(freqs[:i + 1]) for i in range(len(freqs))] + F = [mx / N for mx in m] + mf = [m * f for m, f in zip(middles, freqs)] + m2f = [m * m * f for m, f in zip(middles, freqs)] + x_overline = round(sum(mf) / N, 2) + D_chosen = round(sum(m2f) / N - x_overline ** 2, 2) + sigma_chosen = round(sqrt(D_chosen), 2) + t = [(m - x_overline) / sigma_chosen for m in middles] + f = [1 / sqrt(2 * pi) * exp(-(ti ** 2 / 2)) for ti in t] + fT = [round(h * N / sigma_chosen * fi) for fi in f] + crit = [(fr - fTi) ** 2 / fTi for fr, fTi in zip(freqs, fT)] + ty = round(2.31 * sigma_chosen / 10, 2) + dk1 = sqrt(2 * N) / (sqrt(2 * N - 3) + 2.31) * sigma_chosen + dk2 = sqrt(2 * N) / (sqrt(2 * N - 3) - 2.31) * sigma_chosen + + draw_graph(middles, freqs, name='Полигон частот', save=save, saveName="1") + draw_histogram(middles, intervals, [fi / N for fi in freqs], name='Гистограмма относительных частот', save=save, saveName="2") + draw_graph(intervals, [0] + F, name='Эмпирическая функция распределения', save=save, saveName="3") + + th.add_text("а-б)") + th.generate_first_table(intervals, middles, freqs, relative_freqs, F, mf, m2f) + th.add_text("в)", True) + th.add_picture("1") + th.add_picture("2") + th.add_picture("3") + th.add_text("г)", True) + th.add_text("Вычислим среднюю арифметическую:") + th.add_text(f"\\[\\overline{{x}}=\\frac{{\\sum x_i f_i}}{{n}}={x_overline}\\]") + th.add_text(f"\\[D=\\frac{{\\sum x_i^2 f_i}}{{n}} - \\overline{{x}}={D_chosen}\\]", True) + th.add_text("д)", True) + th.add_text("Найдем значение теоретических частот $f_i^T$ используя формулу:") + th.add_text("$f_i^T=\\frac{hn}{\\sigma}f(t)$", True) + th.add_text("где $f(t)=\\frac{1}{\\sqrt{2\\pi}}e^{-\\frac{t^2}{2}}, t=\\frac{x_i-\\overline{x}}{\\sigma}$") + th.add_text(f"$\\sigma=\\sqrt{{D}}={sigma_chosen}$", True) + th.add_text("Расчетная таблица") + th.generate_second_table(middles, t, f, fT) + th.add_text("Расчетное значение критерия вычислим по формуле:") + th.add_text("$\\chi^2=\\sum_{i=1}^l\\frac{(f_i-f^T_i)^2}{f_i^T}$.", True) + th.add_text("где $l$ - количество интервалов\\\\", True) + th.add_text("Расчетная таблица") + th.generate_third_table(f, fT, crit) + th.add_text(f"Таким образом $\\chi^2 = {round(sum(crit), 2)}$.", True) + th.add_text("Теоретическое значение критерия возьмем из таблицы. Оно равно $14.4$.") + th.add_text(f"Таким образом $\\chi ^ 2 = {round(sum(crit), 2)} < 14.4$, то есть на уровне значимости") + th.add_text("$\\alpha=0.025$ принимаем нулевую гипотезу о том, что генеральная совокупность,") + th.add_text("из которой извлечена выборка, имеет нормальное распределение.", True) + th.add_text("е)", True) + th.add_text("Доверительный интервал истинного значения генеральной средней вычислим по формуле") + th.add_text("\\[\\overline{x}-\\frac{t_{\\gamma}\\sigma}{\\sqrt{n}} < \\tilde{x} <") + th.add_text("\\overline{x} + \\frac{t_{\\gamma}\\sigma}{\\sqrt{n}}\\]") + th.add_text("Выберем уровень доверительной вероятности $\\gamma = 0.05$.") + th.add_text("По таблице распределения Стъюдента находим $t_{\\gamma}=2.31$.\\\\", True) + th.add_text("Вычислим точность оценки:") + th.add_text("\\[\\frac{t_{\\gamma}\\sigma}{\\sqrt{n}} \\approx " + str(ty) + "\\]", True) + th.add_text("Таким образом") + th.add_text(f"\\[{round(x_overline - ty, 2)} < \\tilde{{x}} < {round(x_overline + ty, 2)}\\]", True) + th.add_text("с вероятностью $95\\%$ данный интервал накроет истинное значение $\\tilde{x}$") + th.add_text("генеральной средней.\\\\", True) + th.add_text("Доверительный интервал для генерального среднего квадратического отклонения") + th.add_text("определяется по формуле") + th.add_text("\\[\\frac{\\sqrt{2n}}{\\sqrt{2n}-3+t_{\\gamma}}\\sigma<\\tilde{\\sigma}<") + th.add_text("\\frac{\\sqrt{2n}}{\\sqrt{2n}-3-t_{\\gamma}}\\sigma\\]", True) + th.add_text("Таким образом") + th.add_text(f"\\[{round(dk1, 2)} < \\tilde{{\\sigma}} < {round(dk2, 2)}\\]", True) + th.add_text("с вероятностью $95\\%$ данный интервал накроет истинное значение $\\tilde{\\sigma}$") + th.add_text("генерального среднего квадратического отклонения.") + th.end_text() + th.save_template("result") + + +if __name__ == "__main__": + # starting values + values = """ + 16,8 17,9 21,4 14,1 19,1 18,1 15,1 18,2 20,3 16,7 + 19,5 18,5 22,5 18,4 16,2 18,3 19,1 21,4 14,5 16,1 + 21,5 14,9 18,6 20,4 15,2 18,5 17,1 22,4 20,8 19,8 + 17,2 19,7 16,3 18,7 14,4 18,8 19,5 21,6 15,3 17,3 + 22,8 17,4 22,2 16,5 21,7 15,4 21,3 14,3 20,5 16,4 + 20,6 15,5 19,4 17,5 20,9 23,0 18,9 15,9 18,2 20,7 + 17,9 21,8 14,2 21,2 16,1 18,4 17,5 19,3 22,7 19,6 + 22,1 17,6 16,7 20,4 15,7 18,1 16,6 18,3 15,5 17,7 + 19,2 14,8 19,7 17,7 16,5 17,8 18,5 14,0 21,9 16,9 + 15,8 20,8 17,1 20,1 22,6 18,9 15,6 21,1 20,2 15,1 + """.replace(",", ".") + + variant = "2" # your variant + name = "Барсуков Максим" # your name + + values = make_table(values) + print_table(values) + template_handler = TemplateHandler(variant, name) + process(values, template_handler, True) diff --git a/3 теорвер/дз/2/19.1/result.pdf b/3 теорвер/дз/2/19.1/result.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7ff2b837e6356b7f2cecfcfb3262205cbea4f336 GIT binary patch literal 177074 zcmd?RXH-<(^CsG;fQpC-kqnX~3zDOvy>l(?y@3#mTa82JtKRPfn;!)P4-6F8nT1xyp9oTK?Osp7BMu$j*GfU@9pu-#Wwb 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