{ "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": 2, "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": 3, "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": 4, "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": 10, "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": 11, "id": "d5ec6dd6-5afe-4317-8e5d-6bd0758862da", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 2.0125 -2.285 6.18 ]\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": 23, "id": "bf0b4a30-96d5-458c-9573-0ab8af6b5442", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 23, "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": 24, "id": "4d764cd1-9718-41de-87f1-e0def0e718b1", "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", "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": 94, "id": "96ac0ab5-7bb3-41fe-a934-45bb6b3302a6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 94, "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": 96, "id": "911adf10-f562-4d8c-a359-7809b1e71bf4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 96, "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": 113, "id": "170e18d8-81b4-4d0e-b37d-458b3beb51ec", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " s + 2\n", "---------------\n", "3 s^2 + 4 s + 5\n", "\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": 114, "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": 125, "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": 25, "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": 63, "id": "d2298a3b-60a2-4ab2-8ac0-2c4332869bd3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 63, "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": 64, "id": "afd3fd86-2b0d-4710-ba4a-07c9ed9b2a26", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 64, "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": 65, "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": 66, "id": "e8070f2d-8ea6-4847-9a31-80abf7cc3dfb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 66, "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": 67, "id": "0ba1595e-03a1-4c7e-96d5-102f7344d345", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 67, "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", "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": 71, "id": "84f59b4e-b39b-4f60-bdf1-ac1effd90187", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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": 102, "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": 100, "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": 101, "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": 103, "id": "4bb193da-9117-4bf1-8597-83930c0b8f58", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 1$" ], "text/plain": [ "1" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Предел\n", "sympy.limit(sympy.sin(x)/x, x, 0)" ] }, { "cell_type": "code", "execution_count": 104, "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": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Производная\n", "sympy.diff(sympy.tan(x), x)" ] }, { "cell_type": "code", "execution_count": 106, "id": "0e58739b-d00c-48f4-ad62-5fd0ebd736f3", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 2$" ], "text/plain": [ "2" ] }, "execution_count": 106, "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": 107, "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": 107, "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": "3.12.6" } }, "nbformat": 4, "nbformat_minor": 5 }