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zmr{`Xk=9uQ3_y8{&@10Cq_r?g%X%Zj`rF}`^O2*`N6k_onnxa6dIf7VKNqCEq$)YV%G4q_O^dR4d9rVM)hTb$}$JDsC&AzYD}q3+bww zGl;UzGtcBol=SGzTakd;9Sb8(1`KqtneJ(%{0MBpHxvdF!4FL;!Rfn(S>1uk-f4ieaLI7nHBl)7j0V?4{YI>D9eax6wf`+?AJFicrc{G7~cj z!BDBLcoP{|`-RAVYbJ$WMYPwz39f=NGlSP|fV6q#gT2JU49HlSNQb92s66a2MXKe5 z2GlgU529eZv3v6?%)&2hS`q?QJ4L`yY51x`* zdv7LO*FBwu`v|S`LvBVP zFLe`Gt!74n!(jRypE!vfGE?daHhz?$;}3@SzF&66wKtQ|hH5M)y{AHWp-9|d&N5cD zAmM;sPgrPmAshk`{B}zsmGD?+TUNZFKO-}A2cmR#8o%f+6P5R`y8&gW+*$TgkxYHU zO?sthfLGzMX5p{8>hq(to6Qttm16_i;ldFg%0N7v-=%XX56sc(tU67HQ)}$7~ zFuYf88Ib#g1H&`}x^YVer6B*qeFrjx?A@zis7|Wdy1h1K$4v36@bFCw_O=!dqoE7Saijmv-7NTzVg{va~5-FL$b{FN%8I zaT$(&SXNP$MY_53gx==gcSC|T;SD|!8hYh7pd|OB03tk{(r#AUq^1odap-JQ7}pAX zY#ZIz3oS^3T3Z}0pbq)W+nql(Rf}0D6Bd0NA%zB7*_0ZecF(QOsTHIP`5e0@Q$!1U zn*HioIF5hGnPP@;+gZ4ND`JLBtrZ;)w+W(E?4zHUwB`dQLdE<)T5`U*aA^@RK}`|c z0F3uV8E7mVBUwAw?_P7DK370vhZ{5%&aoTgF=sZyq_lqPbL9CNL}Y-PzYiXl4pY|w zK}jfihjlyEb#YX3nL|>Lo7;A5@@Dp!OdU=@Ty*Q}{?MB-8S?IFM*S1Z$j7J@xk|*3 z3nWtA^olWe0F~}LBdj;()u#I9^lNB+`A~-QnHx2fZ(TkFB6j~7{BXPWFBrH9~L)TrX8N+Nq~TK z!15VQvlU|h5kLtVjX-3gcziH%7zsBAA#yZw`K~Bi;$o>#1h?f<0zdPyJxA>q1rUZr zm$=}nY5_YEunyeWv9J+WmP}6-N+ZC+M%a6o5$9KiY-<4rJ~z@h{)e*_4XLmQ&_AQ7A-$D9B`Etn0Y zfU@p72#nB`Z*fVA+3e-_R`S|i5$t9Fpn?Gfz`&;kInGhMdBrAk!Xsz_+q@aRc3>)f zpCl^4k|b&>VGRp2Rb`Kq_RcDv@jUMIcPp{kZo-@2|1-!l|KITc5A2WrGxNmaT>> print(round(123.456,1)) + 123.5 +>>> print(round(123.456,0)) + 123.0 +``` +Данные результаты имеют тип float. Первое выражение округляет до одного знака после запятой, второе — до целого числа. +Попробуем выполнить следующую инструкцию: +```py +>>> print(round(123.456)) + 123 +``` +Полученный результат имеет тип int. + +#### п. 2.2. +Функция __range__ – создание последовательности целых чисел с заданным шагом или, по умолчанию, с шагом 1. +```py +>>> gg=range(76,123,9) +>>> print(gg) + range(76, 123, 9) +``` +Обратим внимание, что эта инструкция создает, так называемый, _«итерируемый объект»_ класса __range__. Чтобы увидеть получившуюся преобразуем его в список. +```py +>>> print(list(gg)) + [76, 85, 94, 103, 112, 121] +``` +Также возможно вызвать функцию __range__ с одним аргументом. +```py +>>> print(list(range(23))) + [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22] +``` +Мы получили объект, который содержит последовательность целых чисел от 0 до 22(включительно) с шагом 1. + +#### п. 2.3. +Функция __zip__ – создание общего объекта, элементами которого являются кортежи, составленные из элементов двух или более объектов-последовательностей. +```py +>>> qq = ['Зеленкина', 'Криви', 'Цветкова', 'Капитонов'] +>>> print(qq) + ['Зеленкина', 'Криви', 'Цветкова', 'Капитонов'] +>>> ff = zip(gg, qq) +>>> print(ff) + +>>> result_tuple = tuple(ff) +>>> print(result_tuple) + ((76, 'Зеленкина'), (85, 'Криви'), (94, 'Цветкова'), (103, 'Капитонов')) +``` +Количество элементов в ff равно минимальной длине из исходных списков gg и qq, то есть длине списка qq. +Проверим, можно ли к объекту ff обращаться с указанием индекса. + +```py +>>> print(result_tuple[0]) + (76, 'Зеленкина') +>>> print(result_tuple[2]) + (94, 'Цветкова') +``` +К объекту ff можно обращаться с указанием индекса. + +#### п. 2.4. +Функция __eval__ – вычисление значения выражения, корректно записанного на языке Python и представленного в виде символьной строки. +```py +>>> fff=float(input('коэффициент усиления=')); dan=eval('5*fff-156') +>>> print(fff, dan) + коэффициент усиления=3 + 3.0 -141.0 +``` + +#### п. 2.5. +Похожая на __eval__ функция __exec__ – чтение и выполнение объекта-аргумента функции. Напишем и выполним код по инструкции: +```py +>>> exec(input('введите инструкции:')) + введите инструкции:perem=-123.456;gg=round(abs(perem)+98,3) +``` +Убедимся, что появился числовой объект с именем gg и со значением 221.456. +```py +>>> gg + 221.456 +>>> perem + -123.456 +``` + +#### п. 2.6. +Самостоятельно изучим и попробуем применить функции abs, pow, max, min, sum, divmod, len, map. +```py +>>> print(abs(-7.5)) + 7.5 +>>> print(pow(3, 4)) + 81 +>>> numbers = [5, 2, 8, 1] +>>> print(max(numbers)) + 8 +>>> print(min(numbers)) + 1 +>>> print(sum(numbers)) + 16 +>>> a, b = divmod(17, 5) +>>> print(a, b) + 3 2 +>>> text = "Hello" +>>> print('len("Hello") =', len(text)) + 5 +numbers = [1, 2, 3, 4] +text_numbers = list(map(str, numbers)) +print(text_numbers) + ['1', '2', '3', '4'] +``` + +## 3. Модуль math. +Функции из стандартного модуля __math__ – совокупность разнообразных математических функций. Загрум модуль math с помощью инструкции. Затем узнаем содержание модуля с помощью +функции _dir_. Изучим функцию расчета факториала __factorial__ с помощью функции __help__ и попробуем использовать эту функцию. +_Обращение к функциям из импортированного модуля осуществляется с указанием имени модуля, по образцу: <имя модуля>.<имя функции>(<аргументы функции>)_ +```py +>>> import math +>>> print(dir(math)) + ['__doc__', '__loader__', '__name__', '__package__', '__spec__', 'acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh', 'cbrt', 'ceil', 'comb', 'copysign', 'cos', 'cosh', 'degrees', 'dist', 'e', 'erf', 'erfc', 'exp', 'exp2', 'expm1', 'fabs', 'factorial', 'floor', 'fmod', 'frexp', 'fsum', 'gamma', 'gcd', 'hypot', 'inf', 'isclose', 'isfinite', 'isinf', 'isnan', 'isqrt', 'lcm', 'ldexp', 'lgamma', 'log', 'log10', 'log1p', 'log2', 'modf', 'nan', 'nextafter', 'perm', 'pi', 'pow', 'prod', 'radians', 'remainder', 'sin', 'sinh', 'sqrt', 'sumprod', 'tan', 'tanh', 'tau', 'trunc', 'ulp'] +>>> help(math.factorial) + Help on built-in function factorial in module math: + factorial(n, /) + Find n!. + Raise a ValueError if x is negative or non-integral. +>>> print(math.factorial(5)) + 120 +``` +Аналогичным образом изучим и попробуем применить некоторые другие функции из этого модуля: _sin, acos, degrees, radians, exp, log, log10, sqrt, ceil, floor, pi._ +```py +>>> import math +>>> print(math.factorial(5)) + 120 +>>> print(math.sin(math.pi/2)) + 1.0 +>>> print(math.acos(0.5)) + 1.0471975511965979 +>>> print(math.degrees(math.pi)) + 180.0 +>>> print(math.radians(180)) + 3.141592653589793 +>>> print(math.exp(1)) + 2.718281828459045 +>>> print(math.log(100)) + 4.605170185988092 +>>> print(math.log10(100)) + 2.0 +>>> print(math.sqrt(25)) + 5.0 +>>> print(math.ceil(4.2)) + 5 +>>> print(math.floor(4.9)) + 4 +>>> print(math.pi) + 3.141592653589793 +``` +Решение примера sin(2π/7+e0.23 ): +```py +>>> result = math.sin(2 * math.pi / 7 + math.exp(0.23)) +>>> print(result) + 0.8334902641414562 +``` + +## 4. Модуль cmath. +Функции из модуля __cmath__ – совокупность функций для работы с комплексными числами. +Начнём с импорта модуля, затем отобразим его атрибуты и изучим функцию для извлечения квадратного корня из комплексного числа и и функцию расчета фазы. +```py +>>> import cmath +>>> print(dir(cmath)) + ['__doc__', '__loader__', '__name__', '__package__', '__spec__', 'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh', 'cos', 'cosh', 'e', 'exp', 'inf', 'infj', 'isclose', 'isfinite', 'isinf', 'isnan', 'log', 'log10', 'nan', 'nanj', 'phase', 'pi', 'polar', 'rect', 'sin', 'sinh', 'sqrt', 'tan', 'tanh', 'tau'] +>>> print(cmath.sqrt(1.2-0.5j)) + (1.118033988749895-0.22360679774997896j) +>>> print(cmath.phase(1-0.5j)) + -0.4636476090008061 +``` + +## 5. Модуль random. +Стандартный модуль __random__ – совокупность функций для выполнения операций с псевдослучайными числами и выборками. +```py +>>> import random +>>> print(dir(random)) + ['BPF', 'LOG4', 'NV_MAGICCONST', 'RECIP_BPF', 'Random', 'SG_MAGICCONST', 'SystemRandom', 'TWOPI', '_ONE', '_Sequence', '__all__', '__builtins__', '__cached__', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__spec__', '_accumulate', '_acos', '_bisect', '_ceil', '_cos', '_e', '_exp', '_fabs', '_floor', '_index', '_inst', '_isfinite', '_lgamma', '_log', '_log2', '_os', '_pi', '_random', '_repeat', '_sha512', '_sin', '_sqrt', '_test', '_test_generator', '_urandom', '_warn', 'betavariate', 'binomialvariate', 'choice', 'choices', 'expovariate', 'gammavariate', 'gauss', 'getrandbits', 'getstate', 'lognormvariate', 'normalvariate', 'paretovariate', 'randbytes', 'randint', 'random', 'randrange', 'sample', 'seed', 'setstate', 'shuffle', 'triangular', 'uniform', 'vonmisesvariate', 'weibullvariate'] +>>> help(random.seed) + Help on method seed in module random: + + seed(a=None, version=2) method of random.Random instance + Initialize internal state from a seed. + + The only supported seed types are None, int, float, + str, bytes, and bytearray. + + None or no argument seeds from current time or from an operating + system specific randomness source if available. + + If *a* is an int, all bits are used. + + For version 2 (the default), all of the bits are used if *a* is a str, + bytes, or bytearray. For version 1 (provided for reproducing random + sequences from older versions of Python), the algorithm for str and + bytes generates a narrower range of seeds. +>>> print(random.seed()) + None +``` + +Далее самостоятельно изучим и попробуем применить следующие функции: +```py +>>> import random +>>> random.seed(42) +>>> print(random.random()) + 0.6394267984578837 +>>> print(random.uniform(10, 20)) + 10.25010755222667 +>>> print(random.randint(1, 6)) + 3 +>>> print(random.gauss(0, 1)) + 0.017593105583573694 + +>>> fruits = ["яблоко", "банан", "апельсин", "киви"] +>>> print(random.choice(fruits)) + яблоко +>>> cards = ["Туз", "Король", "Дама", "Валет"] +>>> random.shuffle(cards) +>>> print(cards) + ['Валет', 'Король', 'Дама', 'Туз'] +>>> numbers = list(range(1, 51)) +>>> print(random.sample(numbers, 5)) + [3, 2, 6, 14, 15] +>>> print(random.betavariate(2, 5)) + 0.3918844780644009 +>>> print(random.gammavariate(2, 1)) + 2.219353519271194 +>>> print(random.randint(100, 999)) + 703 +>>> print(random.uniform(-5, 5)) + -2.218092917693373 +``` + +Создадим список с 4 случайными значениями, подчиняющимися, соответственно, равномерному, нормальному, бета и гамма: +```py +random_values = [random.uniform(0, 1), random.gauss(0, 1), random.betavariate(2, 5), random.gammavariate(2, 1)] +print(random_values) + [0.869300320792934, 0.5479616463399781, 0.33952976689383546, 0.5704217216825608] +``` + +## 6. Модуль time. +Функции из модуля __time__ – работа с календарем и со временем. +```py +>>> import time +>>> print(dir(time)) + ['_STRUCT_TM_ITEMS', '__doc__', '__loader__', '__name__', '__package__', '__spec__', 'altzone', 'asctime', 'ctime', 'daylight', 'get_clock_info', 'gmtime', 'localtime', 'mktime', 'monotonic', 'monotonic_ns', 'perf_counter', 'perf_counter_ns', 'process_time', 'process_time_ns', 'sleep', 'strftime', 'strptime', 'struct_time', 'thread_time', 'thread_time_ns', 'time', 'time_ns', 'timezone', 'tzname'] +>>> c1=time.time() +>>> print(c1) + 1757970835.4250033 +``` +Изучим функцию __time__, возвращающую время в секундах, прошедшее с начала эпохи, за которое обычно принимается 1.01.1970г. +```py +>>> c2=time.time()-c1 +>>> print(c2) + 0.022925376892089844 +``` +Теперь изучим функцию __gmtime__. +```py +>>> dat=time.gmtime() +>>> print(dat) + time.struct_time(tm_year=2025, tm_mon=9, tm_mday=15, tm_hour=21, tm_min=16, tm_sec=35, tm_wday=0, tm_yday=258, tm_isdst=0) +>>> print(dat.tm_mon) + 9 +``` +__ Функция localtime()__ - местное время: +```py +>>> local_time = time.localtime() +>>> print(local_time.tm_year) + 2025 +>>> print(local_time.tm_mon) + 9 +>>> print(local_time.tm_mday) + 18 +>>> print(local_time.tm_hour) + 10 +>>> print(local_time.tm_min) + 11 +>>> print(local_time.tm_sec) + 12 +``` +__Функция asctime()__ - ппреобразование представления времени из кортежа в строку: +```py +time_str = time.asctime(local_time) +print(time_str) + Thu Sep 18 10:22:12 2025 +``` +__Функция ctime()__ - преобразование времени в секундах, прошедшего с начала эпохи, в строку: +```py +>>> current_seconds = time.time() +>>> print(current_seconds) + 1758180132.4304066 +>>> time_from_seconds = time.ctime(current_seconds) +>>> print(time_from_seconds) + Thu Sep 18 10:22:12 2025 +``` + +__Функция sleep()__ - прерывание работы программы на заданное время: +```py +>>> print("Начинаем отсчет...") +>>> for i in range(3, 0, -1): +>>> print(f"{i}...") +>>> time.sleep(2) +>>> print("Запуск!") +``` +Вывод программы: +```py +Начинаем отсчет... +3... +2... +1... +Запуск! +``` +Числа выводлись через 2 секунды. + +__Функция mktime()__ - преобразование времени из типа кортежа или struct_time в число секунд с начала эпохи. +```py +>>> seconds_from_struct = time.mktime(local_time) +>>> print(seconds_from_struct) + 1758180480.0 +``` +Обратное преобразование из секунд в местное время осуществляется той же функцией localtime(): +```py +>>> print(time.localtime(c1)) + time.struct_time(tm_year=2025, tm_mon=9, tm_mday=18, tm_hour=10, tm_min=29, tm_sec=52, tm_wday=3, tm_yday=261, tm_isdst=0) +``` + +## 7. Графические функции. +Импортируем модуль с инструкцией. Создадим два списка, один из которых будет содержать значения сигнала x, а другой – моменты времени измерения значений сигнала t. После этого введем инструкции создания и отображения графика x(t): +```py +import pylab +x=list(range(-3,55,4)) +t=list(range(15)) +pylab.plot(t, x) +pylab.title('Первый график') +pylab.xlabel('время') +pylab.ylabel('сигнал') +pylab.show() +``` +Мы полчили: + + +Изучим содержание окна с появившимся графиком и сохраним график в текущем каталоге в файле с именем __Ris1__. +Рассмотрим способ построения нескольких графиков на одном рисунке. Для этого создадим два списка: +```py +>>> X1=[12,6,8,10,7] +>>> X2=[5,7,9,11,13] +>>> pylab.plot(X1) +>>> pylab.plot(X2) +>>> pylab.show() +``` + + +Теперь изучим возможность построения круговой диаграммы: +```py +>>> region=['Центр','Урал','Сибирь','Юг'] +>>> naselen=[65,12,23,17] +>>> pylab.pie(naselen,labels=region) +>> pylab.show() +``` + +Самостоятельно изучим и попробуем применить функции __hist__ и __bar__ для построения гистограмм и столбиковых диаграмм. +__hist__ +```py +>>>> import matplotlib.pyplot as plt +>>> assessments = [3, 4, 5, 3, 4, 5, 5, 4, 3, 2, 4, 5, 3, 4, 5, 4, 3, 5, 4, 3] +>>> plt.hist(assessments, bins=5, color='lightblue', edgecolor='black') +>>> plt.xlabel('Оценки') +>>> plt.ylabel('Количество студентов') +>>> plt.title('Распределение оценок студентов') +>>> plt.show() +``` + + +__bar__ +```py +>>> fruits = ['Яблоки', 'Бананы', 'Апельсины', 'Груши'] +>>> count = [25, 30, 15, 20] +>>> color = ['red', 'yellow', 'orange', 'green'] +>>> plt.bar(fruits, count, color=color) +>>> plt.ylabel('Количество') +>>> plt.title('Любимые фрукты') +>>> plt.show() +``` + + +__statistics__ +Изучим состав статистического модуля __statistics__: +```py +>>> import statistics +>> print(dir(statistics)) + ['Counter', 'Decimal', 'Fraction', 'LinearRegression', 'NormalDist', 'StatisticsError', '_SQRT2', '__all__', '__annotations__', '__builtins__', '__cached__', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__spec__', '_coerce', '_convert', '_decimal_sqrt_of_frac', '_exact_ratio', '_fail_neg', '_float_sqrt_of_frac', '_integer_sqrt_of_frac_rto', '_isfinite', '_mean_stdev', '_normal_dist_inv_cdf', '_rank', '_sqrt_bit_width', '_ss', '_sum', 'bisect_left', 'bisect_right', 'correlation', 'count', 'covariance', 'defaultdict', 'erf', 'exp', 'fabs', 'fmean', 'fsum', 'geometric_mean', 'groupby', 'harmonic_mean', 'hypot', 'itemgetter', 'linear_regression', 'log', 'math', 'mean', 'median', 'median_grouped', 'median_high', 'median_low', 'mode', 'multimode', 'namedtuple', 'numbers', 'pstdev', 'pvariance', 'quantiles', 'random', 'reduce', 'repeat', 'sqrt', 'stdev', 'sumprod', 'sys', 'tau', 'variance'] +``` +Рассмотрим три функции: +```py +>>> data = [1, 2, 3, 4, 5, 5, 6] +>>> print("Mean:", statistics.mean(data)) +>>> print("Median:", statistics.median(data)) +>>> print("Mode:", statistics.mode(data)) +>>> print("Stdev:", statistics.stdev(data)) + Mean: 3.7142857142857144 + Median: 4 + Mode: 5 + Stdev: 1.7994708216848747 +``` + +## Завершение работы.