{ "cells": [ { "cell_type": "markdown", "id": "b2ad1576-587b-4147-b4be-271289c03b72", "metadata": {}, "source": [ "# Вычисления. Часть 2\n", "\n", "Для решение многих вычислительных задач существует модуль `scipy`.\n", "\n", "## Численное решение уравнений\n", "### В случае одной переменной" ] }, { "cell_type": "code", "execution_count": 1, "id": "4896027a-b4fc-49f6-b903-e86f07bf9c08", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x = [-1.5]\n" ] } ], "source": [ "import scipy.optimize\n", "\n", "def foo(x):\n", " y = 4*x+6\n", " return y\n", "\n", "# Найдем решение foo(x) = 0\n", "# с начальным приближением x = 0\n", "optobj = scipy.optimize.root(foo, 0)\n", "\n", "if optobj.success:\n", " print(\"x = \", optobj.x)" ] }, { "cell_type": "markdown", "id": "cd04811d-2c5e-4208-89ae-0dab540e02d5", "metadata": {}, "source": [ "### Совместное решение системы уравнений" ] }, { "cell_type": "code", "execution_count": 2, "id": "94b1220b-d763-4156-aef0-6e25b71c2b9d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x = [ 1.73205081 -1.15470054]\n" ] } ], "source": [ "import scipy.optimize\n", "\n", "def func(d):\n", " x,y = d\n", " f1 = 2*x + 3*y\n", " f2 = -x**2 + 3\n", " return (f1,f2)\n", "\n", "# Найдем решение foo(x,y) = 0\n", "# с начальным приближением x = 5, y = 5\n", "optobj = scipy.optimize.root(func, (5,5))\n", "\n", "if optobj.success:\n", " print(\"x = \", optobj.x)" ] }, { "cell_type": "markdown", "id": "09ba4acb-dff3-4938-8b73-e106aa31285a", "metadata": {}, "source": [ "## Минимизация функции" ] }, { "cell_type": "code", "execution_count": 3, "id": "657ae838-265a-4cf5-8ec6-5d3399627761", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x = [0.99999991 0.99999979]\n" ] } ], "source": [ "import scipy.optimize\n", "\n", "def f(c):\n", " x, y = c\n", " return 0.5*(1 - x)**2 + (y - x**2)**2\n", "\n", "\n", "# Выполним минимизацию f(x,y) -> min\n", "# с начальным приближением x = 2, y = -1\n", "optobj = scipy.optimize.minimize(f, [2, -1])\n", "\n", "if optobj.success:\n", " print(\"x = \", optobj.x)" ] }, { "cell_type": "markdown", "id": "1f04865e-adde-48b0-abaa-07222466779d", "metadata": {}, "source": [ "## Решение системы линейных уравнений" ] }, { "cell_type": "code", "execution_count": 4, "id": "9fa74ec0-e7ca-4186-b34b-9a617a734c82", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.07299771 -0.23112712 0.16181287]\n" ] } ], "source": [ "import numpy as np\n", "import scipy.linalg\n", "\n", "# Решаем систему Ax=B\n", "\n", "# Переопределенная система\n", "m = [[ 1, 3, 4],\n", " [ 2, -3, 1],\n", " [ -3, -4, 8],\n", " [1.1, 2.9, 4.1]]\n", "A = np.array(m)\n", "\n", "B = np.array([ 0. , 1. , 2. , 0.1])\n", "\n", "# Решение методом наименьших квадратов\n", "x, res, rnk, s = scipy.linalg.lstsq(A,B)\n", "\n", "print(x)" ] }, { "cell_type": "markdown", "id": "d5671882-b34f-4619-921a-2f6b43c299d8", "metadata": {}, "source": [ "Функция возвращает кортеж, важнейшие поля: значение, сумма ошибок и эффективный ранг матрицы.\n", "\n", "## Поиск оптимальных параметров" ] }, { "cell_type": "code", "execution_count": 5, "id": "d5ec6dd6-5afe-4317-8e5d-6bd0758862da", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 2.0125 -2.28500001 6.18000001]\n" ] } ], "source": [ "import scipy.optimize\n", "\n", "def foo(x, a, b, c):\n", " return a*x**2+b*x+c\n", "\n", "xdata = [0,2,4,6]\n", "ydata = [6.1,9.9,29,65]\n", "\n", "popt, pcov = scipy.optimize.curve_fit(foo, xdata, ydata)\n", "\n", "print(popt)" ] }, { "cell_type": "markdown", "id": "68582683-8566-4063-a545-b06c70f2698b", "metadata": {}, "source": [ "Аргумент `bounds` метода `curve_fit` принимает кортеж из двух списков - минимальные и максимальные ограничения для значений каждой из переменных." ] }, { "cell_type": "markdown", "id": "83cbc807-1748-4500-8dbb-d2955161df9b", "metadata": {}, "source": [ "## Фильтрация сигнала" ] }, { "cell_type": "code", "execution_count": 6, "id": "bf0b4a30-96d5-458c-9573-0ab8af6b5442", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import signal\n", "\n", "# Исходный сигнал\n", "t = np.linspace(0,8*np.pi,800)\n", "data = t+4*np.sin(t)*np.random.random(800)\n", "\n", "#Фильтр Баттерворта\n", "\n", "fs = 5 # Частота сигнала герцах\n", "fc = 0.05 # Частота отсечения\n", "# Частота в единицах отсчетов\n", "# (одна для НЧ и ВЧ или кортеж из двух для полосового и режекторного фильтра)\n", "w = fc / (fs / 2)\n", "# Синтез НЧ фильтра 5-го порядка \n", "b, a = signal.butter(3, w, 'low')\n", "filtered = signal.filtfilt(b, a, data)\n", "plt.plot(data)\n", "plt.plot(filtered)" ] }, { "cell_type": "markdown", "id": "d2ebcb74-4152-488f-b0bc-5303042e50fd", "metadata": {}, "source": [ "## Сглаживание апериодического сигнала" ] }, { "cell_type": "code", "execution_count": 7, "id": "4d764cd1-9718-41de-87f1-e0def0e718b1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "a = np.r_[np.arange(0,30,1),np.zeros((40,))+30,np.arange(30,60,1)]\n", "\n", "plt.plot(a)\n", "\n", "noise_a = a + np.random.random_sample(100)*16-8\n", "\n", "plt.plot(noise_a)\n", "\n", "def smooth(data, window_len = 10, tails = \"odd\"):\n", " lead_0 = data[0]\n", " lead = data[window_len//2-1:0:-1]\n", " tail_0 = data[-1]\n", " tail = data[-2:-window_len//2-2:-1]\n", " if tails == \"odd\":\n", " ds = np.r_[2*lead_0-lead, data , 2*tail_0-tail]\n", " else:\n", " ds = np.r_[lead, data , tail]\n", " w = np.hanning(window_len)\n", " return np.convolve(w/w.sum(), ds, mode='valid')\n", "\n", "plt.plot(smooth(noise_a, 40, tails = \"odd\"))" ] }, { "cell_type": "markdown", "id": "d0fa66ba-d87f-4bda-9a61-e4f79c7f53c7", "metadata": {}, "source": [ "## Анализ спектра сигнала\n", "\n", "Будем разлагать значения сигнала на сетке в спектр с помощью быстрого преобразования Фурье." ] }, { "cell_type": "code", "execution_count": 8, "id": "96ac0ab5-7bb3-41fe-a934-45bb6b3302a6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.fftpack import fft\n", "\n", "x = np.linspace(0.0, 2, 600)\n", "y = np.sin(15.0 * 2.0*np.pi*x) + np.sin(20.0 * 2.0*np.pi*x)\n", "\n", "plt.plot(y)" ] }, { "cell_type": "code", "execution_count": 9, "id": "911adf10-f562-4d8c-a359-7809b1e71bf4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "yf = fft(y)\n", "\n", "plt.plot(np.abs(yf)[0:50])" ] }, { "cell_type": "markdown", "id": "a8d61eb8-d372-432e-8486-dc7fe825287d", "metadata": {}, "source": [ "## Расчет передаточной фукнции" ] }, { "cell_type": "code", "execution_count": 14, "id": "170e18d8-81b4-4d0e-b37d-458b3beb51ec", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ": sys[3]\n", "Inputs (1): ['u[0]']\n", "Outputs (1): ['y[0]']\n", "\n", " s + 2\n", " ---------------\n", " 3 s^2 + 4 s + 5\n" ] } ], "source": [ "import control as ct\n", "import matplotlib.pyplot as plt\n", "\n", "num= [1., 2.]\n", "den= [3., 4., 5.]\n", "w= ct.tf(num, den)\n", "print(w)" ] }, { "cell_type": "markdown", "id": "d8c7d539-34d5-41cb-965c-1710645005f5", "metadata": {}, "source": [ "### Реакция на изменение уровня и импульс входного сигнала" ] }, { "cell_type": "code", "execution_count": 15, "id": "ec3d8702-a9ac-4f18-b67c-4b8fda2831cd", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x,y=ct.step_response(w)\n", "plt.plot(x,y)\n", "x,y=ct.impulse_response(w)\n", "plt.plot(x,y)\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0625ab45-6d4e-49a4-a251-7db05cc3ea45", "metadata": {}, "source": [ "### Амплитудно-частотная характеристика" ] }, { "cell_type": "code", "execution_count": 16, "id": "2be350d9-f23c-4bf8-a465-49f7d5f74382", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "omega = np.logspace(-2, 2, 500)\n", "response = ct.frequency_response(w, omega)\n", "ct.bode_plot(w, initial_phase=0)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "182ceaa5-a716-4492-b076-fd941945c55c", "metadata": {}, "source": [ "## Интерполяция\n", "\n", "Будем рассматривать случаи получения функции в неявном виде.\n", " \n", "### В случае одной переменной" ] }, { "cell_type": "code", "execution_count": 17, "id": "ea15f662-e688-4f55-8252-17d01afc993c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-2.8000000000000003\n" ] } ], "source": [ "import scipy.interpolate\n", "x = np.arange(0, 10)\n", "y = 2*x**3-16*x**2\n", "foo = scipy.interpolate.interp1d(x, y)\n", "\n", "print(foo(0.2))" ] }, { "cell_type": "markdown", "id": "11adf1a1-9650-4807-bb2d-e47f20e52640", "metadata": {}, "source": [ "### В случае нескольких переменных на регулярной сетке" ] }, { "cell_type": "code", "execution_count": 18, "id": "d2298a3b-60a2-4ab2-8ac0-2c4332869bd3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.interpolate import RegularGridInterpolator, LinearNDInterpolator\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "def func(x, y):\n", " return 8*x**2-y**3\n", "\n", "xi = np.arange(-5,5,0.2)\n", "yi = np.arange(-2,2,0.1)\n", "\n", "grid_x, grid_y = np.meshgrid(xi, yi, indexing='ij')\n", "\n", "#Прямой расчет на сетке\n", "data = func(grid_x, grid_y)\n", "\n", "# Интерполяция\n", "foo = RegularGridInterpolator((xi,yi),data)\n", "\n", "# исходное поле\n", "plt.imshow(func(grid_x, grid_y), extent=[-5,5,-2,2], origin='lower')\n", "\n", "# точки\n", "plt.scatter(grid_x, grid_y, s=1, c ='red')" ] }, { "cell_type": "code", "execution_count": 19, "id": "afd3fd86-2b0d-4710-ba4a-07c9ed9b2a26", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# результат интерполяции\n", "plt.imshow(foo((grid_x, grid_y)), extent=[-5,5,-2,2], origin='lower')" ] }, { "cell_type": "markdown", "id": "8f09a0a3-c4c0-4f35-898a-52c1be9ee2cf", "metadata": {}, "source": [ "### В случае нескольких переменных на случайных точках" ] }, { "cell_type": "code", "execution_count": 20, "id": "96de80c2-196c-4c00-8674-77a5fece4372", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Нерегулярная сетка\n", "xs = np.random.uniform(-5, 5, 50)\n", "ys = np.random.uniform(-2, 2, 50)\n", "\n", "#Значение в точках\n", "values = func(xs, ys)\n", "\n", "# исходное поле\n", "plt.imshow(func(grid_x, grid_y), extent=[-5,5,-2,2], origin='lower')\n", "\n", "# точки\n", "plt.scatter(xs, ys, s=1, c ='red')\n", "\n", "# Линейная интерполяция на нерегулярной сетке\n", "baz = scipy.interpolate.LinearNDInterpolator(np.rollaxis(np.array([xs,ys]), 1), values)" ] }, { "cell_type": "code", "execution_count": 21, "id": "e8070f2d-8ea6-4847-9a31-80abf7cc3dfb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# результат интерполяции\n", "plt.imshow(baz((grid_x, grid_y)), extent=[-5,5,-2,2], origin='lower')" ] }, { "cell_type": "markdown", "id": "b709ff02-fa9e-4a9d-8546-ee417a911bba", "metadata": {}, "source": [ "### Кригинг\n", "\n", "Отличие от других методов интерполяции — наилучшее линейное несмещенное предсказание промежуточных значений. В `scipy` криггинга нет, но он есть в пакете `pykrige`. " ] }, { "cell_type": "code", "execution_count": 24, "id": "0ba1595e-03a1-4c7e-96d5-102f7344d345", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from pykrige.uk import UniversalKriging\n", "\n", "# Значения в точках : x, y, value\n", "data = np.array([[0.3, 1.2, 0.47],\n", " [1.9, 0.6, 0.56],\n", " [1.1, 3.2, 0.74],\n", " [3.3, 4.4, 1.47],\n", " [4.7, 3.8, 1.74]])\n", "\n", "xi = np.arange(0.0, 5.5, 0.5)\n", "yi = np.arange(0.0, 5.5, 0.5)\n", "\n", "# Подготовка объекта кригинга\n", "UK = UniversalKriging(data[:, 0], data[:, 1], data[:, 2],\n", " variogram_model='linear',\n", " drift_terms=['regional_linear'])\n", "\n", "# Кригинг\n", "z, ss = UK.execute('grid', xi, yi)\n", "\n", "grid_x, grid_y = np.meshgrid(xi, yi, indexing='ij')\n", "\n", "plt.scatter(data[:, 0], data[:, 1], c = 'red')\n", "plt.imshow(z, origin='lower')" ] }, { "cell_type": "markdown", "id": "6132ae61-6fea-4085-9ef1-a741dbe49d2d", "metadata": {}, "source": [ "## Построение функции плотности распределения" ] }, { "cell_type": "code", "execution_count": 25, "id": "84f59b4e-b39b-4f60-bdf1-ac1effd90187", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import stats\n", "\n", "# data - массив измерений\n", "# В данном примере одномерный, но многомерные тоже поддерживаются\n", "\n", "t = np.linspace(0,4*np.pi,800)\n", "data = t+4*np.sin(t)*np.random.random(800)\n", "\n", "kde = stats.gaussian_kde(data)\n", "\n", "x_grid = np.linspace(min(data),max(data), 1000)\n", "\n", "kde_vals = kde.evaluate(x_grid)\n", "\n", "plt.hist(data, bins=50, density=True)\n", "plt.plot(x_grid,kde_vals)" ] }, { "cell_type": "markdown", "id": "13f6f2a6-5b39-4e0d-b7ba-7dfdbe071ace", "metadata": {}, "source": [ "## Символьные вычисления\n", "\n", "Помимо численных расчетов для Python существует достаточно простая система символьной математики `sympy`." ] }, { "cell_type": "code", "execution_count": 26, "id": "a536fb06-d88f-4e95-adc2-039558f745e0", "metadata": {}, "outputs": [], "source": [ "import sympy\n", "from sympy import oo, Symbol\n", "\n", "x = sympy.Symbol('x')\n", "y = sympy.Symbol('y')\n", "\n", "# Важно! eq не значение выражения справа,\n", "# а специальный объект типа sympy.equation" ] }, { "cell_type": "code", "execution_count": 27, "id": "4ab201df-4c17-4d17-b403-65cb9219df40", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "11.0000000000000\n" ] } ], "source": [ "eq = y**2+x\n", "\n", "print(eq.subs(x,2).subs(y,3).evalf())" ] }, { "cell_type": "code", "execution_count": 28, "id": "bad3b542-2afd-403f-877b-6d7787b7ac80", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-1/(x + 2) + 1/(x + 1)\n" ] } ], "source": [ "eq2 = 1/( (x + 2)*(x + 1) )\n", "\n", "print(sympy.apart(eq2, x))" ] }, { "cell_type": "code", "execution_count": 29, "id": "4bb193da-9117-4bf1-8597-83930c0b8f58", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 1$" ], "text/plain": [ "1" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Предел\n", "sympy.limit(sympy.sin(x)/x, x, 0)" ] }, { "cell_type": "code", "execution_count": 30, "id": "f97dceed-bb8b-4856-8f36-07e23bea5a74", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\tan^{2}{\\left(x \\right)} + 1$" ], "text/plain": [ "tan(x)**2 + 1" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Производная\n", "sympy.diff(sympy.tan(x), x)" ] }, { "cell_type": "code", "execution_count": 31, "id": "0e58739b-d00c-48f4-ad62-5fd0ebd736f3", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 2$" ], "text/plain": [ "2" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Сумма ряда\n", "i = sympy.Symbol('i')\n", "sympy.summation(1/2**i, (i, 0, oo))" ] }, { "cell_type": "code", "execution_count": 32, "id": "19700398-06b7-486a-9f31-2de9c92d9768", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle x^{2} + \\cosh{\\left(x \\right)}$" ], "text/plain": [ "x**2 + cosh(x)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Первообразная\n", "sympy.integrate(2*x + sympy.sinh(x), x)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.7" } }, "nbformat": 4, "nbformat_minor": 5 }