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zgxFwar)QK_tc05{Knv#zA;tnBf8xW4n)E>>)6|y40TaB1e4x1&>=N6Wrkh_U+$e-J zLqntHSljkb0IPE)0*%L7X9pP=pFn<{09eT$m@5RM!rk%*IegocJZ|LyN3U>d@S0?x zRVUKBc0eo!(-rqKF6IaW=LppSwe?OtH8Y#AWzUFo1f(YeYN)(gxp~*J7p*}z&qmF8 zT-=tr`f}=QA*9o3P>cn-zkd3~aICOP6bc4rZm^Fg<$2Tq+3R3^eBjH3=@#Rk^{tIR zF{N?$$1{!T}a^n}dXXkDP+C(_q|sb+J4w9pzi7jdg%wt@-#|1?qn_0nukC6#9Uz{oy_IEenOYrhvs! zVWy9G2Mrb|UNhcv*l|mE#8SZy1}=qkxjQCO;$e<(50!t4}z<*7qy>EKNTx8LP;W7T1wo!-GX&x|leR zMjVNJ3ZyExU5AN|jY0K%op>> import os +>>> os.chdir('C:\\MPEI\\PO_ASY\\BerezhkovGit\\python-labs\\Tema4') +``` +## 2. Стандартные функции. +2.1 Функция round – округление числа с заданной точностью: +```py +>>> help(round) +Help on built-in function round in module builtins: + +round(number, ndigits=None) + Round a number to a given precision in decimal digits. + + The return value is an integer if ndigits is omitted or None. Otherwise + the return value has the same type as the number. ndigits may be negative. + +>>> round(123.456,1) +123.5 +>>> round(123.456,0) +123.0 +>>> type(round(123.456,0)) + +>>> round(123.456) +123 +>>> type(round(123.456)) + +``` +2.2 Функция range: +```py +>>> gg=range(76,123,9) +>>> gg +range(76, 123, 9) +>>> list(gg) +[76, 85, 94, 103, 112, 121] +>>> range(23) +range(0, 23) +>>> 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] +``` +Объект с какими значениями получится в этом случае? Каковы границы диапазона? Какой шаг? + +Значения: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22] + +Границы: [0, 23) + +Шаг: 1 + +2.3 Функция zip: +```py +>>> qq=['Berezhkov','Stepanischev','Tabolin','Krishtul'] +>>> ff=zip(gg,qq) +>>> fff = tuple(ff) +>>> print(fff) +((76, 'Berezhkov'), (85, 'Stepanischev'), (94, 'Tabolin'), (103, 'Krishtul')) +>>> print(len(fff)) +4 +>>> len(gg), len(qq) +(6, 4) +>>> ff[0] +Traceback (most recent call last): + File "", line 1, in + ff[0] +TypeError: 'zip' object is not subscriptable +``` +Невозможно обратиться с указанием индекса, потому что объект является итерируемым. + +2.4 Функция eval: +```py +>>> fff=float(input('коэффициент усиления=')); dan=eval('5*fff-156') +коэффициент усиления=3 +>>> dan +-141.0 +``` +2.5 Функция exec: +```py +>>> exec(input('введите инструкции:')) +введите инструкции:perem=-123.456;gg=round(abs(perem)+98,3) +>>> gg +221.456 +``` +2.6 Функции abs, pow, max, min, sum, divmod, len, map: +```py +>>> abs(-13) +13 +>>> pow(2,4) +16 +>>> max(42,54,33) +54 +>>> min(1,3,5) +1 +>>> sum([1,2,3]) +6 +>>> divmod(5,3) +(1, 2) +>>> +>>> len(range(9)) +9 +>>> r = map(lambda x: round(x) * (-1), [12.1245, 14.125234, 534.222]) +>>> list(r) +[-12, -14, -534] +``` +## 3. Функции из стандартного модуля math. +```py +>>> import math +>>> 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', 'fma', '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. + +>>> math.factorial(5) +120 +``` +3.1 Функции sin, acos, degrees, radians, exp, log, log10, sqrt, ceil, floor, pi: +```py +>>> math.sin(90) +0.8939966636005579 +>>> math.acos(0) +1.5707963267948966 +>>> math.degrees(math.pi) +180.0 +>>> math.radians(180) +3.141592653589793 +>>> math.exp(4) +54.598150033144236 +>>> math.log(10) +2.302585092994046 +>>> math.log10(100) +2.0 +>>> math.sqrt(16) +4.0 +>>> math.ceil(3.14) +4 +>>> math.floor(3.14) +3 +>>> math.pi +3.141592653589793 +``` +3.2 Вычисление значения функции sin(2π/7+e0.23 ): +```py +>>> math.sin((2*math.pi/7) + math.exp(0.23)) +0.8334902641414562 +``` +## 4. Функции из модуля cmath: +```py +>>> import cmath +>>> 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'] +>>> cmath.sqrt(1.2-0.5j) +(1.118033988749895-0.22360679774997896j) +>>> cmath.phase(1-0.5j) +-0.4636476090008061 +``` +## 5. Стандартный модуль random. +```py +>>> import random +>>> 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', '_parse_args', '_pi', '_random', '_repeat', '_sha512', '_sin', '_sqrt', '_test', '_test_generator', '_urandom', 'betavariate', 'binomialvariate', 'choice', 'choices', 'expovariate', 'gammavariate', 'gauss', 'getrandbits', 'getstate', 'lognormvariate', 'main', '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. + +random.seed() +random.random() # вещественное число от 0.0 до 1.0 +0.022635313373460364 +random.uniform(5, 15) # вещественное число от 5.0 до 15.0 +5.363612111162993 +random.randint(1, 100) # целое число от 1 до 100 +2 +random.gauss(0, 1) # mu - среднее значение, sigma - стандартное отклонение +0.8104264223845308 +random.choice([1, 2, 3, 4]) # случайный выбор элемента из списка, кортежа, строки и т.д. +1 +Num = [1, 2, 3, 4] +random.shuffle(Num) +Num +[2, 1, 4, 3] +random.sample(Num, 2) # случайный выбор двух элементов из Num +[3, 1] +random.betavariate(2, 5) # случайное число с плавающей точкой на основе бета-распределения +0.3506592878950909 +random.gammavariate(2, 1) # случайное число с плавающей точкой на основе гамма-распределения +3.755676054491517 +``` +## 6. Функции из модуля time. +```py +>>> import time +>>> 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() +>>> c2=time.time()-c1 +>>> c1 +1761120933.7341516 +>>> c2 +5.980855703353882 +>>> dat=time.gmtime() +>>> dat +time.struct_time(tm_year=2025, tm_mon=10, tm_mday=22, tm_hour=8, tm_min=16, tm_sec=5, tm_wday=2, tm_yday=295, tm_isdst=0) +>>> dat.tm_mon +10 +>>> time.asctime((2025, 10, 13, 20, 13, 54, 1, 345, 0)) #год, месяц, день, час, минута, секунда, день недели, день года, летнее время +'Tue Oct 13 20:13:54 2025' +>>> time.ctime(time.time()) +'Wed Oct 22 11:19:57 2025' +>>> time.mktime((2025, 12, 25, 15, 30, 0, 0, 0, 0)) +1766665800.0 +``` +## 7. Графические функции. +```py +>>> import pylab +>>> x=list(range(-3,55,4)) +>>> t=list(range(15)) +>>> pylab.plot(t,x) #Создание графика в оперативной памяти +[] +>>> pylab.title('Первый график') +Text(0.5, 1.0, 'Первый график') +>>> pylab.xlabel('время') +Text(0.5, 0, 'время') +>>> pylab.ylabel('сигнал') +Text(0, 0.5, 'сигнал') +>>> pylab.show() #Отображение графика на экране +``` +Отображение графика: + + +```py +>>> X1=[12,6,8,10,7]; X2=[5,7,9,11,13] +>>> pylab.plot(X1) +[] +>>> pylab.plot(X2) +[] +>>> pylab.show() +``` +Отображение графика: + + +```py +>>> region=['Центр','Урал','Сибирь','Юг'] #Метки для диаграммы +>>> naselen=[65,12,23,17] # Значения для диаграммы +>>> pylab.pie(naselen,labels=region) #Создание диаграммы в памяти +([, , , ], [Text(-0.191013134139045, 1.0832885038559115, 'Центр'), Text(-0.861328292412156, -0.6841882582231001, 'Урал'), Text(0.04429273995539947, -1.0991078896938387, 'Сибирь'), Text(0.9873750693480946, -0.48486129194837324, 'Юг')]) +>>> pylab.show() #Отображение диаграммы +``` +Отображение диаграммы: + + +```py +>>> pylab.bar(region, naselen) + +>>> pylab.title('Население по регионам') +Text(0.5, 1.0, 'Население по регионам') +>>> pylab.ylabel('Население (млн)') +Text(0, 0.5, 'Население (млн)') +>>> pylab.show() +``` +Отбражение диаграммы: + + +```py +>>> pylab.hist(naselen) +(array([2., 0., 1., 0., 0., 0., 0., 0., 0., 1.]), array([12. , 17.3, 22.6, 27.9, 33.2, 38.5, 43.8, 49.1, 54.4, 59.7, 65. ]), ) +>>> pylab.title('Гистограмма распределения населения') +Text(0.5, 1.0, 'Гистограмма распределения населения') +>>> pylab.xlabel('Население (млн)') +Text(0.5, 0, 'Население (млн)') +>>> pylab.ylabel('Частота') +Text(0, 0.5, 'Частота') +>>> pylab.show() +``` +Отображение гистограммы: + +## 8. Статистический модуль statistics. +```py +>>> import statistics +>>> numbers = [1,2,3,4,5,6,7,8,9] +>>> statistics.mean(numbers) +5 +>>> statistics.median(numbers) +5 +>>> a = [-1,-2,-3,-4,-5,-6,-7,-8,-9] +>>> statistics.correlation(numbers, a) +-1.0 +``` \ No newline at end of file