diff --git a/HM_Task_1/HM_Task_1.ipynb b/HM_Task_1/HM_Task_1.ipynb new file mode 100644 index 0000000..9969684 --- /dev/null +++ b/HM_Task_1/HM_Task_1.ipynb @@ -0,0 +1,85 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# ВВЕДЕНИЕ В ВЫСШУЮ МАТЕМАТИКУ\n", + "## Практическое задание к `Уроку 1`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4. Задание (в программе):\n", + "Постройте на одном графике две кривые y(x) для функции двух переменной y(k,x)=cos(k∙x), взяв для одной кривой значение k=1, а для другой – любое другое k, не равное 1.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(1, 20, 200)\n", + "k1 = 1\n", + "k2 = 4\n", + "\n", + "plt.plot(x, np.cos(k1*x))\n", + "plt.plot(x, np.cos(k2*x))\n", + "plt.xlabel('x')\n", + "plt.ylabel('cos(kx)')\n", + "plt.grid(True)\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/HM_Task_1/P(3).jpg b/HM_Task_1/P(3).jpg new file mode 100644 index 0000000..80e8534 Binary files /dev/null and b/HM_Task_1/P(3).jpg differ diff --git a/HM_Task_1/P1,2(1).jpg b/HM_Task_1/P1,2(1).jpg new file mode 100644 index 0000000..b82fc0f Binary files /dev/null and b/HM_Task_1/P1,2(1).jpg differ diff --git a/HM_Task_1/P2(2).jpg b/HM_Task_1/P2(2).jpg new file mode 100644 index 0000000..9a9c543 Binary files /dev/null and b/HM_Task_1/P2(2).jpg differ diff --git a/HM_Task_2-3/HM_Task_2.ipynb b/HM_Task_2-3/HM_Task_2.ipynb new file mode 100644 index 0000000..a176237 --- /dev/null +++ b/HM_Task_2-3/HM_Task_2.ipynb @@ -0,0 +1,486 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# ВВЕДЕНИЕ В ВЫСШУЮ МАТЕМАТИКУ\n", + "****************\n", + "## Практическое задание к `Уроку 2`" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import math\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "from pylab import *\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1. Задание\n", + "Даны два вектора в трехмерном пространстве: (20,20,20) и (0,0,-20)\n", + "- 1)\tНайдите их сумму. (на листочке)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`Ответ:`\n", + "\n", + "$r_1=\\left(\\begin{array}{crl}20\\\\20\\\\20\\end{array}\\right)\\;; \\quad r_2=\\left(\\begin{array}{crl}0\\\\0\\\\-20\\end{array}\\right)\\;; \\\\\n", + "r_1 + r_2 = \\left(\\begin{array}{crl}20+0\\\\20+0\\\\20-20\\end{array}\\right) = \\left(\\begin{array}{crl}20\\\\20\\\\0\\end{array}\\right)$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- 2)\tНапишите код на Python, реализующий расчет длины вектора, заданного его координатами. (в программе)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Длина вектора: 28.284271247461902\n" + ] + } + ], + "source": [ + "r1 = np.array([20,20,20])\n", + "r2 = np.array([0,0,-20])\n", + "r3 = r1+r2\n", + "\n", + "def calculate_vector_length(coordinates):\n", + " length = (coordinates[0]**2 + coordinates[1]**2 + coordinates[2]**2)**(0.5)\n", + " return length\n", + "\n", + "print(f'Длина вектора: {calculate_vector_length(r3)}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2. Задание (на листочке)\n", + "Почему прямые не кажутся перпендикулярными? (см.ролик)" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`Ответ:` \n", + "\n", + "Условие перпендикулярности этих двух прямых соблюдено.\n", + "\n", + "Отображение угла искажается размерностью координатной сетки по осям `x` и `y`\n", + "\n", + "Для корректного отображения можно настроить график с помощью метода `plt.axes().set_aspect(1)`" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-5,5,21)\n", + "y = 3 *x+1\n", + "y2 = (-1/3)*x+1\n", + "\n", + "plt.plot(x,y)\n", + "plt.plot(x,y2)\n", + "plt.axes().set_aspect(1)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3. Задание (в программе)\n", + "Напишите код на Python, реализующий построение графиков:\n", + "- 1\tокружности,\n", + "- 2\tэллипса,\n", + "- 3\tгиперболы." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "t=np.linspace(0,2*np.pi,100)\n", + "k=1\n", + "h=2\n", + "r=2\n", + "plt.axes().set_aspect(1)\n", + "plt.plot(np.cos(t)*r+k,np.sin(t)*r+h,'r--')\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "t=np.linspace(0,2*np.pi,100)\n", + "k=10\n", + "h=10\n", + "a=8\n", + "b=4\n", + "plt.axes().set_aspect(1)\n", + "plt.plot(np.cos(t)*a+k,np.sin(t)*b+h,'g-')\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "t=np.linspace(-1,1,100)\n", + "k=1/2\n", + "a=2\n", + "b=2\n", + "\n", + "plt.axes().set_aspect(1)\n", + "plt.plot(t**2*a+k,t,'g-')\n", + "plt.plot(-t**2*b-k,-t,'r-')\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "*****************" + ] + }, + { + "cell_type": "code", + "execution_count": 192, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-40, 40, 48)\n", + "y = np.linspace(-40, 40, 48)\n", + "h=1\n", + "k=1\n", + "r=3\n", + "plt.plot(h + np.cos(x) * r, k + np.sin(y) * r)\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.axes().set_aspect(1)\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4. Задание (на листочке)\n", + "1) Пусть задана плоскость $Ax + Bx + Cz + D = 0$ \n", + "\n", + "Напишите уравнение плоскости, параллельной данной и проходящей через начало координат.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`Ответ:`\n", + "\n", + "- Для того, чтобы плоскости были параллельны, должно выполняться условие равенства коэффициентов `A, B, C`, задающих вектор нормали к плоскости\n", + "- Плоскость будет проходить через начало координат (0.0.0) если приравнять коэффициент `D` к нулю " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2) Пусть задана плоскость: $A_1x + B_1y + C_1z + D_1 = 0$\n", + "и прямая: \n", + "\n", + " $\\frac{x-x_1}{x_2-x_1}=\\frac{y-y_1}{y_2-y_1} = \\frac{z-z_1}{z_2-z_1}$\n", + " \n", + "Как узнать, принадлежит прямая плоскости или нет?\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`Ответ:`\n", + "\n", + "Прямая принадлежит плоскости, если две точки прямой принадлежат этой плоскости или, если она имеет общую точку с плоскостью и параллельна прямой, лежащей в этой плоскости\n", + "\n", + "Таким образом будет выполняться равенство\n", + "\n", + "$A(x-x_1)+B(y-y_1)+C(z-z_1)=0 \\\\\n", + "A(x-x_2)+B(y-y_2)+C(z-z_2)=0$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 5. Задание (в программе)\n", + "- 1)\tНарисуйте трехмерный график двух параллельных плоскостей." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = figure()\n", + "ax = Axes3D(fig)\n", + "X = np.arange(-5, 5, 0.5)\n", + "Y = np.arange(-5, 5, 0.5)\n", + "A = 2\n", + "B = 3\n", + "C = 0\n", + "D = 150\n", + "X, Y = np.meshgrid(X,Y)\n", + "Z1 = A*X + B*Y + D\n", + "Z2 = A*X + B*Y\n", + "ax.plot_wireframe(X, Y, Z1)\n", + "ax.plot_wireframe(X, Y, Z2)\n", + "ax.scatter(0, 0, 0, 'z', 50, 'red')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- 2)\tНарисуйте трехмерный график двух любых поверхностей второго порядка." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = figure()\n", + "ax = Axes3D(fig)\n", + "X = np.arange(-5, 5, 0.5)\n", + "Y = np.arange(-5, 5, 0.5)\n", + "A = 2\n", + "B = 3\n", + "C = 0\n", + "D = 150\n", + "X, Y = np.meshgrid(X,Y)\n", + "Z1 = A*X**2 + B*Y**2 + A*X + B*Y + D\n", + "Z2 = - A*X**2 - B*Y**2 - A*X - B*Y - D\n", + "ax.plot_wireframe(X, Y, Z1)\n", + "ax.plot_wireframe(X, Y, Z2)\n", + "ax.scatter(0, 0, 0, 'z', 50, 'red')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "******************" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ], + "text/plain": [ + " Угол, град. sin cos tan\n", + "0 30 0.5 0.87 0.58\n", + "1 45 0.71 0.71 1.0\n", + "2 60 0.87 0.5 1.7\n", + "3 90 1.0 6.1e-17 1.6e+16\n", + "4 180 1.2e-16 -1.0 -1.2e-16" + ] + }, + "execution_count": 124, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def toFixed(numObj, digits=2):\n", + " return f\"{numObj:.{digits}}\"\n", + " \n", + "for item in df['sin']:\n", + " df.loc[df['sin']==item,'sin']=toFixed(item)\n", + "for item in df['cos']:\n", + " df.loc[df['cos']==item,'cos']=toFixed(item)\n", + "for item in df['tan']:\n", + " df.loc[df['tan']==item,'tan']=toFixed(item) \n", + "df" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Задание 2\n", + "Нарисуйте график функции: \n", + "\n", + "$y = k \\cdot cos(x-a)+b$" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-5, 5, 201)\n", + "k = [1,2,3]\n", + "a = [1,2,2]\n", + "b = [2,2,2]\n", + "\n", + "plt.plot(x, k[0]*cos(x-a[0])+b[0], 'g--', dashes=[8,4,2,4],label=r'k=1; a=1; b=2;')\n", + "plt.plot(x, k[1]*cos(x-a[1])+b[1], 'b--',label=r'k=2; a=2; b=2;')\n", + "plt.plot(x, k[2]*cos(x-a[2])+b[2], 'r',label=r'k=3; a=2; b=2;')\n", + "plt.xlabel('x',fontsize=14)\n", + "plt.ylabel('y',fontsize=14)\n", + "plt.title(r'$\\ y=cos(x-a)+b$',fontsize=16)\n", + "plt.grid(True)\n", + "plt.legend(fontsize=12)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Задание 3\n", + "- 1 Докажите, что при ортогональном преобразовании сохраняется расстояние между точками." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Преобразование координат" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$X=(x-a)\\cdot cos \\alpha +(y-b)\\cdot sin \\alpha$\n", + "\n", + "$Y=-(x-a)\\cdot sin \\alpha +(y-b)\\cdot cos \\alpha$" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0,5,21)\n", + "y = (x-2)**2 + 1\n", + "\n", + "a=1\n", + "b=2\n", + "s = pi/2\n", + "\n", + "X = (x-a)*cos(s) + (y-b)*sin(s)\n", + "Y = -(x-a)*sin(s) + (y-b)*cos(s)\n", + "\n", + "fig, ax = plt.subplots(nrows=1, ncols=2)\n", + "ax1, ax2 = ax.flatten()\n", + "ax1.plot(x, y)\n", + "ax1.plot(x[5], y[5], 'ro')\n", + "ax1.annotate('$M_1$', xy=(x[5], y[5]+0.5))\n", + "ax1.plot(x[20], y[20], 'ro')\n", + "ax1.annotate('$M_2$', xy=(x[20]-0.5, y[20]-0.5))\n", + "ax1.set_title('$xy$')\n", + "ax2.plot(X, Y)\n", + "ax2.plot(X[5], Y[5], 'ro')\n", + "ax2.annotate('$M\\'_1$', xy=(X[5], Y[5]+0.5))\n", + "ax2.plot(X[20], Y[20], 'ro')\n", + "ax2.annotate('$M\\'_2$', xy=(X[20]-0.5, Y[20]+0.5))\n", + "ax2.set_title('$XY$')\n", + "\n", + "fig.set_size_inches(8, 2)\n", + "plt.subplots_adjust(wspace=0.3, hspace=0.3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Подтвердим выполнение признаков ортогонального преобразования:\n", + "\n", + "$a_{11}^2 + a_{21}^2 = 1 \\\\\n", + "a_{12}^2 + a_{22}^2 = 1 \\\\\n", + "a_{11} a_{12} + a_{21} a_{22} = 0$" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " a(11)^2 + a(21)^2 = 1.0\n", + " a(12)^2 + a(22)^2 = 1.0\n", + " a(11) a(12) + a(21) a(22) = 0\n" + ] + } + ], + "source": [ + "print(f' a(11)^2 + a(21)^2 = {(cos(s))**2 + (sin(s))**2}')\n", + "print(f\" a(12)^2 + a(22)^2 = {(sin(s))**2 + (cos(s))**2}\")\n", + "print(f\" a(11) a(12) + a(21) a(22) = {int(cos(s)*sin(s) + sin(s)*cos(s))}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Докажем равенство отрезков $M_1M_2 = M'_1M'_2$" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "M (1,2) = 85.25390625\n", + "M'(1,2) = 85.25390625\n" + ] + } + ], + "source": [ + "print(f'M (1,2) = {((x[20]-x[5])**2 + (y[20]-y[5])**2)}')\n", + "print(f'M\\'(1,2) = {((X[20]-X[5])**2 + (Y[20]-Y[5])**2)}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Задание 4\n", + "- 1 Напишите код, который будет переводить полярные координаты (R,a) в декартовы (x,y)." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Используем полярные координаты: R = 1.0000000000000002, a = 0.3173325912716963\n", + "\n", + "Конвертируем в декартовы координаты...\n", + "Результат: x = 0.9500711177409457, y = 0.3120334456984872\n", + "\n", + "Конвертируем обратно в полярные координаты...\n", + "Результат: R = 1.0000000000000002, a = 0.3173325912716964\n" + ] + } + ], + "source": [ + "x = np.linspace(0, 2*pi, 100)\n", + "y1 = sin(x)**2+cos(x)**2\n", + "\n", + "def to_dec(radius, angle):\n", + " x_c = radius*cos(angle)\n", + " y_c = radius*sin(angle)\n", + " return x_c, y_c\n", + "\n", + "def to_polar(x, y):\n", + " rad = sqrt(x**2 + y**2)\n", + " angle = arcsin(y)\n", + " return rad, angle\n", + "\n", + "print(f'Используем полярные координаты: R = {y1[5]}, a = {x[5]}\\n')\n", + "print('Конвертируем в декартовы координаты...')\n", + "converted_1 = to_dec(y1[5],x[5])\n", + "print(f'Результат: x = {converted_1[0]}, y = {converted_1[1]}\\n')\n", + "print('Конвертируем обратно в полярные координаты...')\n", + "converted_2 = to_polar(converted_1[0],converted_1[1])\n", + "print(f'Результат: R = {converted_2[0]}, a = {converted_2[1]}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- 2 Напишите код, который будет рисовать график окружности в полярных координатах." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0, 2*pi, 100)\n", + "y1 = sin(x)**2+cos(x)**2\n", + "y2 = sin(x)**2+cos(x)**2-0.4\n", + "y3 = sin(x)**2+cos(x)**2-0.2\n", + "y4 = sin(x)**2+cos(x)**2+0.2\n", + "y5 = sin(x)**2+cos(x)**2+0.4\n", + "plt.polar(x, y1, 'bo', x, y2, x, y3, x, y4, x, y5)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- 3 Напишите код, который будет рисовать график прямой линии в полярных координатах." + ] + }, + { + "cell_type": "code", + "execution_count": 140, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0, 8*pi, 9)\n", + "y1 = sin(x-pi)+1\n", + "plt.polar(x, y1)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Задание 5\n", + "\n", + "- 1 Решите систему уравнений:\n", + "\n", + "$y=x^2-1 \\\\\n", + "exp(x)+x(1-y)=1$" + ] + }, + { + "cell_type": "code", + "execution_count": 201, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\Nickel\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in true_divide\n", + " This is separate from the ipykernel package so we can avoid doing imports until\n" + ] + }, + { + "data": { + "image/png": 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3iqVRhGctH34mkhCEEK5p66/w/U0QEAa3/gKRLS/o7a/M2Eigrzf3XxpnpwBdj8xDEEK4nKi9M2HsMKjeEG7/9YKTwZLMw8zesJ9/ecjWmOdLWghCCNdRVgK/PEGzzZ9YS1Fc9QUEhF7QR9hsmpd+ziAqLIDbPGx563ORhCCEcA0Fh2HCTbBjPjtjBhF73een3cvgXKat3cva3Tm8OawNAb6et4Dd2UhCEEI4v/3rYfy1kLcfBn9M5tE6xFYgGRSVlPHqL5toWTeUQW3r2SFQ12a8D0Ep5a2UWqWU+sl0LEIIJ5QxDT7tDaXFcMuMCxpWeqqvFu1gz7HjPNWvOV4euoDd2RhPCMD9QIbpIIQQTsZWBqkvWRPOasfDqDkQnVjhjztSUMz/UrdySXxtujbx7CUqzsRoQlBKRQNXAJ+ajEMI4WTyD8A3g2Huf6Ht9XDzzxAaVamPfPe3LRScKOWJy2WJijNRWmtzhSs1EXgZqAY8rLXuf5pjRgGjACIjIxNTUlIqVFZ+fj4hIZ41+UTq7Bncrc5hx9JpseF1fEoL2BJ3B9lRvf5xzIXWObvAxlMLjnNRtA83t3TNYaaV+Z6Tk5PTtNZJ5zxQa23kBvQHPii/3xP46VzvSUxM1BWVmppa4fe6KqmzZ3CbOpeVaT3vda2fC9f63fZa71t3xkMvtM63fblct3hmht6fe7ySQZpTme8ZWKHP47xscpRRN2CgUqofEACEKqW+1VqPMBiTEMKEgsMw5Q7YOhtaDoEB71zw/IIzmbf5IL9m7OexvvHUrnbmHdOEwWGnWusngCcAlFI9sS4ZSTIQwtNs+x1+uAsKD0O/1619DKpok5qSMhvP/7SB+jWDuLV7gyr5THcm8xCEEGaUFMFv/4ElH0CtpjA8Beq2rdIivl2SxZYD+XxyYxL+PjIJ7VycIiForecAcwyHIYRwlOx0mDwSDmyADiOh9/+BX1CVFnGkoJi3Zm/morha9Gpeu0o/2105RUIQQngImw2WvA+//R8EVreWrI7rbZei3py9iYLiMp7t38Kj90m+EJIQhBCOcSQTpt4HO+ZDfH+r4zjYPhPEMvblMm7pTm7s0oC4yGp2KcMdSUIQQtiXrQyWfAi/vwDevjDwPWh3Q5V1HJ9Ka81/pq0nLNCXB3vJTmgXQhKCEMJ+DmTAj3fDnjRo2heueBPC7Luo3C/p2SzJPMLzg1oRFuRr17LcjSQEIUTVKy2GBW/BvNes+QRDP4NWQ+3WKjipqKSMF3/OIL5ONYZ3iLFrWe7onAlBKXUPMFZrfdQB8QghXF3WYpj+b2sEUauhcPmrdusrONWYeZnsPnqccSM74ePtDGt3upbzaSHUAZYrpVYCnwMzy6dCCyHEn/IPwOxnYc14CIuBa8dDfD+HFb/zcCHvp27lioQoujaW1Uwr4pwpVGv9NBAHfAbcDGxRSr2klGps59iEEK7AVgbLPoH3kmDdROj+b7h7qUOTgdaa56atx8dL8Uz/Fg4r192cVx+C1lorpbKBbKAUqA5MVErN1lo/as8AhRBObNdy6/JQ9lpoeLG19ESE40f2zN6wn983HuDpK5pTJ0zWK6qo8+lDuA+4CTiEtW/BI1rrEqWUF7AFkIQghKc5tsuaXLbue6gWZW1233Kw3TuNT6ewuJT/TNtAs8hq3NS1gcPLdyfn00KoBQzRWmf99UmttU0p9Y/9C4QQbuxEnjV6aPH71uOLHoLuD4K/uclf//t9K3uOHWfCnV3wlY7kSjlnQtBaP3uW12TrSyE8ga0MVn0Dv78IBQcgYRhc+iyEmx3aufVAPp/Mz2Ro+2g6NKhhNBZ3IPMQhBBnpjVsmgG/P28NI43pbK1KWom9jasuNM2zP6YT6OvNE/1kW8yqIAlBCHF6mXPgt+dhzwqo0Qiu/hJaDDLST3A6U9fsZdG2wzw/qBW1QlxzW0xnIwlBCPF3u5ZZHcY75kNoNAx4F9peZ61D5CQKSzQvTM+gdXQY13WMNR2O2zCWEJRSAcA8wL88jola69Gm4hHC4+1Jg7mvwuZfIDgC+v4XEm8GX+cbxjl5SzGH8kv57KYkvL2co8XiDky2EE4Al2it85VSvsACpdQMrfUSgzEJ4XmyFltrDm37DQLCrc7ijneAf4jpyE5r5c6j/LazlBu61Kd1dLjpcNyKyT2VNZBf/tC3/GaXJTF+3bCfiRtP0LOnPT5dCBektdVHMO91yFpgtQh6PQdJt1XZ5vb2UFxq44lJ66geoHikTzPT4bgdZXJZIqWUN5AGNAHe11o/dppjRgGjACIjIxNTUlIuuJzJW4qZuq2Efyf60zrCc7pN8vPzCQlxzl959iJ1PgddRq1Dy4jdOZnQvM2c8KvBztgh7Iu6DJu383fMTt1WzOQtJdzRXNOlvnzP5ys5OTlNa510ruOMJoQ/glAqHJgC3Ku1Tj/TcUlJSXrFihUX/PknSstIfnkmyjeAmQ/2IMTfM5LCnDlz6OlhzSKp8xkUF8CqsdaG9ke3Q3h96P4AtL0efJw/EQBsO5jP5W/Pp3eLSK6ulyvf8wVQSp1XQnCKaX1a62PAHKCvPT7f38ebW1r5szfnOK/P3GSPIoRwTnnZ1oihN1vAjEcgqCZc/RXctwqSbnWZZGCzaZ6YvI4AXy9GD5TF6+zF5CijCKBEa31MKRUI9AL+a6/y4qp7c1OXBny1eAcD2kSRWF9mNQo3pTXsXg7LP4X1U6CsBOKvgK73Qkwnp5lHcCG+W7GLZduP8MqQBGpXC2CD6YDclMlrJ1HAV+X9CF7A91rrn+xZ4CN9mjF7w34em7SO6fd1x9/H257FCeFYxQXW8tPLP4HsdeBXzRo22ulOqOm6q9UfyC3ipZ8z6NyoBtfILmh2ZXKU0VqgnSPLDPb34cXBrbj5i+W8//tW/n2ZjFIQri+wcA/MeBxWj4MTOVC7pbV3cethRhedqyqjp67nRKmNl4e0Rrlg68aVeEbv6l/0bFabIe3q8cGcbVyeEEXzKOcdYifEGZUch4yfYNU3dNo+F7x8ocWV0OF2iO3skpeFTmfW+mxmpGfzSJ9mNKwVbDoct+dxCQHgmf4tmLv5II9PWsvku7rJTEfhGrS2ZhOv+hbSJ1utgbBYtje4noZDR0O1SNMRVqljhcU89UM68XWqMapHI9PheASnGGXkaNWD/XhuYEvW7M7hi4XbTYcjxNnl7YeF78IHneHTS2FNCjTrCzdOhfvXkNVgmNslA4Dnpq7naEExr1/dRvY5cBCPbCEA9G8dxY+r9/D6rE1cEl+bRhGeNclFOLkTebBxOqRPgq2/gS6D6I4w4B1rZ7KAMNMR2tXM9dn8sHov918aR6t67l1XZ+KxCUEpxYuDE7jsrXk8NGENE+/sKpeOhFklRbBlFqRPhM0zobQIwmKs4aJtrzeyV7EJRwqKeWrKOlpEhXJ3chPT4XgUj00IAJGhAfzflS25P2U1Y+Zl8q+erjs0T7ioshLYPhfWTYKNP8GJXAiqBe1ugISrrFaBl2ddLhk9dT05x0v4+tZO+Pl4Vt1N8+iEADCwTV1mrs/mrdmbSY6PIL6OjDoSdlZcaK0smjHNWmq6KAf8Q6H5AGg1FBpeDN6e+b/mz+v2MW3NXh7q3ZQWdeX/RUfzzH91f6GU4vkrW7Fs+zz+/d0afri7m/wqEVXv+FHrMlDGNKtPoPQ4BFaHZldA8/7Q+FKn3HfAkQ7ln+DpH9JJqBfGndJaN8LjEwJAzRB/XhqcwKhv0njv9y08JBPWRGVpDYe3Wn0Cm2dC1kKwlUK1utBuhNUaqN/NY1sCp9Ja88wP6eQXlcqoIoPkX2O5y1rWYWj7aD6Ys41Lm0fSNkY23hAXqKTI2ltg8ywrERwtH9Ic0Ry63APNB0Lddh7XJ3A+flq7jxnp2TzatxnN6rj+7GpXJQnhL54d0IJF2w7x0PermX7fRQT4ylpH4iy0hkNbrI1mtv1udQ6XFIJPIDTsAV3vgSa9oXp905E6tX05x3n6h3TaxIQz6iKZgGaSJIS/CAv05b9DW3Pj58t4beYmnukvy+yKU+Tus078mXOtRJC313o+vL41NLRpH2jQHXwDjYbpKmw2zUPfr6GkzMbb17TFRy4VGSUJ4RQ9mkYwonMsny/cziXxtenWpJbpkIRJx4/BzsXWyT9zDhzcaD0fWAMaXWyNCGrUE2o0NBejC/t0QSaLth3mv0MTZK0iJyAJ4TSe7NecRdsO8+/vVzPj/h7UCPYzHZJwlLxsyFpkJYGsxbA/HdDgEwD1u0Lb66wEEJkgfQGVlL4nh9dmbqJvyzoMS5JlrZ2BJITTCPLz4d1r2zHkg0U8OnEtn9yYKMvuuiOtrY7frEXWyX/nIjiSab3mGwTRHaDn41YiiO7o8cNCq9Lx4jLuT1lFjWA/Xh6SIP9/OQmTO6bFAF8DdQAbMEZr/Y6peE7Vql4Yj/ZtxgvTM/h26U5u6Cwdgy7v+DHYuwr2rIDdadbfgoPWa4HVIbaLta1kbFeIag3evmbjdWMv/ryBbQcL+Pa2TlSXFrjTMNlCKAUe0lqvVEpVA9KUUrO11k6zO96t3Royb8shXvhpA50a1qBppAyHcxllJdblnj1pf578D23+8/VaTa0RQNFJVgugVjO5BOQgv2Xs59slOxl5UUO6x0kfnTMxuWPaPmBf+f08pVQGUA+cZ7tULy/FG1e34fJ35nHf+FX8cHc3GYrqjMpK4fAWiIgn7Fg6fPYS7FtjLQ4HEBwB9ZIgYRhEJ0Ld9hAo80xMOJBXxKMT19I8KpSH+8gEUGejtNamY0Ap1QCYB7TSWuee8tooYBRAZGRkYkpKSoXKyM/PJySkYktcrzlYyltpJ+hd34frm/tX6DNMqEydnZVPST7BBVmE5O8guGB7+d8svG3FLOk0htKcfSTsHU9uaFNyQ5uSV60pRQG13WYHsdNxle/ZpjVvpZ1g45EynusaSL2QirfIXKXOVakydU5OTk7TWied6zjjncpKqRBgEvDAqckAQGs9BhgDkJSUpHv27FmhcubMmUNF39sTOBawni8W7mB4clsuiXeNzUgqU2fjbGVWB2/2Oti/3rr8s3895Oz685jA6hDZClr2hqg2dG7ahzlLVxN27QN40gr6rvI9fzBnK+sObeL5Qa24vpJ9cq5S56rkiDobTQhKKV+sZDBWaz3ZZCzn8vjl8SzJPMLDE9Yy4/6LiAyVESdVorTYOvEf2gQHN5f/3WTNAC49bh2jvKFWHMR0sjp96yRAZEuoFuXWv/zdybLtR3hj1mb6t45iRKdY0+GIMzA5ykgBnwEZWus3TcVxvvx9vHlveFsGvLeQe8etYtzITjKr8kIUF1idugdPnvDL7x/dbi36dlJotLURTIPu1q//yJYQES9DPl3Y4fwT3Dt+JTHVA2WIqZMz2ULoBtwArFNKrS5/7kmt9c8GYzqrJrWr8fKQBB74bjWvzdrEE5c3Nx2ScykugCPbrV/8R7aV/y1/nLvnz+OUN9RoBBHNrFU/I5pZo35qNQV/z7ou7O5sNs2D36/haGEJn9/VgWoBMpTXmZkcZbQAcLmfCoPa1WP5jiN8PDeTpPo16N3CNfoTqoTW1rr+x3Zav+yPZFq3w+V/87P/fnxwhHXib9gDajS2fvnXamY95yNjzz3Bh3O3MW/zQV4c3IqWdT2pZ8c1Ge9UdkXP9G/Bmt3H/lgVNaZGkOmQqobWUHDIOuHn7LT+HttV/nen1aFbnP/394TUsU7wTXpZ6/nUaFR+a+j2G8GLs1uaeZg3Zm1iQJu6XNdR+g1cgSSECgjw9eaD6xK54r353DV2JRPu7OIa8xOKciFvH+TutW55eyFnj3WiP3nyP9mRe1JAOITHQM3G1ho+4bHW4+oNoXoDucQjTutQ/gnuHb+K+jWDpd/AhUhCqKDYmkG8OawtI79ewQvTN/DCoARzwdhs1hIMeXv/crLfR/zmlZD1ZnkS2AfFef98b1BN6yQfEQ9xl5Wf8MtvYTEQIPvaigtTZtM8+N1qco6X8OUtHQnxl9OMq5BvqhJ6t4jkjh6N+HheJh0a1ODKtvWq7sO1hqJjkH/AuhUcgPyDkL//lPvlf/86UgfAy4dw33DwbQi1m1t79oZGQWg9a7hmaJT1V9btF1XsjVk1qu2SAAATu0lEQVSbmL/lEK8MSaBFXflB4UokIVTSw32asWrnMR6ftI7mUaFnX++ouBAKD1u340eg8Ih1zb7ggHVSzz9Yfv+AdaIvK/7nZ3j5WJ21wREQEmkNywyJhNC61q1alPU3OIIl8+Z73OQdYdaMdfv4YM42hneM4VrpN3A5khAqqvzk7lt4mI+75vD6j4uZ8dlsYpPCCSjJ+eeJv/Dwn2vrnOrUk3ztFuX3a1uPT94Prm3NzpVF2IQT2rI/j4cnrKFtTDjPDWxpOhxRAZ6bEGw2OJFrXZYpyrGWRv7b/ZzTPz55v+zEHx9VHXgRoAxYBDqwOiqwhnV9PjQa6rSBoOrW45O3k68H1ZSTvHB5uUUljPomjUA/bz4c0R5/HxcYZCH+wTMSwrJPaLP6a9jInyf5olzgLAv7KS9r2GRAmDXSJiDMuu5+8nFgOATVKj+pWyf3yRuP88j0nYzs1JTHL493VO2EMMpm0/z7u9XsOlLI2Ns7ERUm/VKuyjMSQkkhXrYSCK1vdbCePMEHhv/9hP/Xx34hF/yrfUgEpB3y5qO522hRN5SBberaqUJCOI+3f9vCrxkHeG5ACzo1qmk6HFEJnpEQut3PqpI2DulgHT2gJZv35/HoxDU0jgiW2ZnCrU1bs5d3f9vCVYnR3NS1gelwRCXJhesq5ufjxQfXJ1I9yI9RX6dxIO8MHclCuLg1u47x8IQ1dGhQnRcHt5LJZ25AEoIdRFTz55MbkzhSUMyor9MoKikzHZIQVSo7p4iRX68gopo/H41IlE5kNyEJwU5a1Qvj7WvbWmseTViDzWZ+ZzohqsLx4jJGfr2CghOlfHZTB2qGuM4uguLsJCHYUZ+WdXi8bzzT1+7jrV83n/sNQjg5m03z8IQ1pO/N4d3h7WhW5ywTMYXL8YxOZYNG9WjEtoP5vPf7VhpFBDO4XbTpkISosFdnbmL6un082S+eS5t70NLvHsJoC0Ep9blS6oBSKt1kHPaklOKFQQl0aVSTxyauY9n2I6ZDEqJCvlmSxUdztzGicywjL2pkOhxhB6YvGX0J9DUcg935+Xjx4Yj2RNcI5PavlrNl/2lWHRXCif2WsZ/RP6ZzaXxtnhvQUkYUuSmjCUFrPQ/wiJ/M4UF+fHVLR/x9vbnp82Vk58hwVOEa1uw6xj3jVtGybhjvXddO9hJ3Y0prs6NflFINgJ+01q3O8PooYBRAZGRkYkpKSoXKyc/PJyTE/GYuWbllvLy0iFqBiic7BRLka79fWs5SZ0eSOletg4U2nl9yHD9vxdOdAwj3d45kIN/zhUlOTk7TWied80CttdEb0ABIP59jExMTdUWlpqZW+L1Vbf7mg7rJk9P1NR8v0kUlpXYrx5nq7ChS56pzILdI93wtVbd+bqbesj/PLmVUlHzPFwZYoc/jHOsc6d7DdI+rxWtXtWFJ5hH+/f0aymSOgnAyuUUlf1za/PzmDjSp7Vm/xj2VDDs1ZFC7ehzIK+KlnzcSGuDLSzL1XziJopIybv9yBVsO5PHJjUkk1q9uOiThIEYTglJqPNATqKWU2g2M1lp/ZjImRxrVozHHCkv4YM42QgN8ePzyeEkKwqiSMhv3jFvJ8qwjvHNtO3o2q206JOFARhOC1nq4yfKdwSN9mpF/opSP52VSLcCHey6JMx2S8FA2m+axSWv5NeMAzw9qJcu3eyC5ZGSYUornBrQkv6iU12dtJsTfh5u7NTQdlvAwWmue/jGdySv38FDvptzQub7pkIQBkhCcgJeX4tWrWlNQXMpz0zYQ5O/DsKQY02EJD6G15rmp6xm3dCf/6tmYey5pYjokYYiMMnISPt5evDu8HT2aRvDYpLVMWLHLdEjCA2iteWF6Bl8tzmLkRQ15tE8z6cfyYJIQnIi/jzdjbkike5NaPDppLRPTdpsOSbgxrTWv/LKRzxZs5+auDXiyX3NJBh5OEoKTCfD15pMbk+jepBaPTFwjSUHYhdaaN2Zt5uO5mYzoHMvoAS0kGQhJCM5IkoKwJ601L/2cwf9StzK8Ywz/N1DmwAiLJAQndTIpdGtsJYVxS3eaDkm4AZtN8+yP6/lkvnWZ6MVBCXh5STIQFkkITizA15tPb0oiuVltnpyyjo/nbjMdknBhZTbNo5PW8s2SLO64uBGjB7SQZCD+RhKCkwvw9eajEYn0bx3FyzM28sasTScXBRTivJWU2Xjgu9VMTNvNA73ieLyvzIoX/yTzEFyAn48X71zbjhB/H977fSt5RaU8219+3YnzU1hcyt1jV5K66SCPXx7PnRc3Nh2ScFKSEFyEt5fi5SEJhPj78OmC7eQeL+GVoa3x85FGnjizIwXF3PrlctbuPsZLgxO4rlOs6ZCEE5OE4EKUUjx1RXPCg3x5fdZmDuaf4IPr21MtwNd0aMIJ7T5ayI2fL2P30eN8OCKRPi3rmA5JODn5eelilFLcc0kcr13VmsXbDjPs4yXsz5XtOMXfbczOZeiHiziUd4Jvb+skyUCcF0kILurqpBg+v7kDOw8XMPj9hWzen2c6JOEk5m4+yNUfLgZgwp1d6diwhuGIhKuQhODCejSN4Ls7ulBi01z14SIWbDlkOiRh2NeLd3DLF8uoVz2QyXd1o1mdaqZDEi7EaEJQSvVVSm1SSm1VSj1uMhZX1apeGFPu6kpUWCA3fbGMLxZul2GpHqi0zMboH9N59sf1JDerzcR/daVeeKDpsISLMZYQlFLewPvA5UALYLhSqoWpeFxZdPUgJt3VleRmtfnPtA08MXkdxaU202EJByks0dz21Yo/Viwdc2MSIf4yXkRcOJP/ajoCW7XWmQBKqRTgSmCDwZhcVoi/D2NuSOSN2Zt4P3UbmQcLGNFIWgrubvP+PP5v8XEOFR3n5SEJDO8ow0pFxZlMCPWAvy76vxvoZCgWt+DlpXikTzxNI6vx6MS1bM3WxMQfpV2sbJLujqat2cujE9fiq2DcyM7SeSwqTZm63qyUuhroo7W+vfzxDUBHrfW9pxw3ChgFEBkZmZiSklKh8vLz8wkJCalc0C5kR04Z7608zrFixbXxfvSK9fGIpQo84XsutWkmbCpmZlYpceFe3BRXRnRN967zqTzhez5VZeqcnJycprVOOtdxJlsIu4G/7hMZDew99SCt9RhgDEBSUpLu2bNnhQqbM2cOFX2vq4oISmXK3hDGZhzgmE9NXhma4PaT2Nz9e87OKeK+lFUsyyr8Y1ObRQvmuXWdT8fdv+fTcUSdTSaE5UCcUqohsAe4FrjOYDxuJ9hXMeaGJMbMz+S1mZvI2JfLe9e1o2XdMNOhiQqYtT6bRyetpbjUxtvXtGVQu3qmQxJuxtgoI611KXAPMBPIAL7XWq83FY+78vJS3HlxY8bd3on8E6UMen8hH8/dhs0mHc6uoqikjGd+SGfUN2nEVA/ip3u7SzIQdmF0bJrW+mfgZ5MxeIpOjWoy84EePDF5HS/P2EjqpgO8OawtdWWsulPbmJ3L/eNXs2l/HqN6NOLhy5rJgobCbuRflgepHuzHhyPa8+pVrVm3O4e+b8/jx9V7ZCKbEyops/Heb1sY8N4CDhcU89WtHXmyX3NJBsKuZPaKh1FKMSwphk4Na/Dgd6u5P2U109bs5flBrYgKk9aCM8jYl8vDE9awfm8uA9rU5T8DW1Ij2M90WMIDyM8ND1W/ZjDf39GFp/o1Z8HWQ1z25jzGLs2SvgWDTpSW8c6vVqtgf24RH41oz3vD20kyEA4jLQQP5uPtxcgejbisZSRPTF7HU1PS+XH1Xl4anECT2p41xtu0BVsO8eyP6WQeKpBWgTBGWgiC+jWDGXt7J/47NIGN+3Lp+/Y8XvhpA7lFJaZDc3vZOUXcPW4lIz5bSpnWfHFLB2kVCGOkhSAAq2/hmg6xXNo8ktdnbuKzhdv5YfUeHu0bz1Xto2X/5ipWVFLGFwt38L/ft1Bq0zzYqyl3XNyIAF9v06EJDyYJQfxNrRB/Xhnamus6xfLc1PU8OnEt3y7J4rG+8XRrUst0eC6vzKb5YdUe3pi1ib05RVwaX5vRA1oSWzPIdGhCSEIQp9c6OpyJd3blh9V7eG3mJq7/dCndmtTkkT7xtI0JNx2ey9FaM2/LIV6ZsZGMfbm0jg7j9WFt6NpYkqxwHpIQxBl5eSmGtI+mX0IUY5fu5P3UrQx6fyF9WkbyYO+mxNcJNR2i09NaM3fzQd77fStpWUeJqRHIu8Pb0T8hSi7DCacjCUGcU4CvN7d1b8g1HWL4bP52Ppmfycz180luFsG/ejahQ4PqHrGS6oWw2TS/Zuznf6lbWbs7h7phATx/ZUuGdYjB30f6CYRzkoQgzluIvw/394rjpq71+WZxFl8s2sGwjxfTPjacOy9uzKXNI/H28F+9hcWlTFm1h68W7WDz/nxiawTx36EJDG4XLbOMhdOThCAuWHiQH/deGsftFzViQtouxszLZNQ3adQLD+S6TrFcnRRN7WoBpsN0qJ2HC/l68Q6+X7GL3KJSWtYN5c1hbRjYpi4+3pIIhGuQhCAqLNDPmxu7NOC6jrHM2rCfsUuzeG3mJt6avZk+LetwTYcYujau6bYnxIITpcxcn83klXtYuO0Q3krRt1Udbu7agMT6chlNuB5JCKLSfLy96JcQRb+EKDIP5jN+2U4mpO1m+rp91Arxo19CFAPb1KV9bHWX70gtKbOxJPMwU1bt4Zf0bAqLy4ipEch9l8QxvGMsdcI8q2Uk3IskBFGlGkWE8NQVLXjosmbM2XSQaWv28t3yXXy9OIu6YQH0ahFJcrPadG5Uk0A/1+hczS0qYc6mg/y6YT+pmw6QV1RKNX8frmxblyHto0mS1oBwE5IQhF0E+HrTt1Ud+raqQ/6JUmZvyGb62n1MWLGbrxdn4e/jRedGNbkorhZJDWrQsm4ovk5yael4cRkrdx5lSeZhlmYeYdWuo5SUaWoG+3F5qzr0ah5Jj6YRMqtYuB0jCUEpdTXwHNAc6Ki1XmEiDuEYIf4+DG4XzeB20RSVlLF8xxFSNx4kddMBXpieAUCArxeto8NJrF+dlnVDaRpZjQY1g+0+MqeopIwt+/PZsC+H9XtzSd+Tw7o9OZSUabwUJNQL49buDendPJJ2sdU9fhSVcG+mWgjpwBDgY0PlC0MCfL25KC6Ci+IieHZAC7JzikjLOmrddh7lk3mZlJYvwe3jpWhYK5jGESFEhQcQFRZAnbBA6oQGUD3Il2B/H+vm5/23jmutNTZtDQHNOV7CscISco6XcKSgmN1Hj7PraCG7jhRa948U/lFesJ83zaNCubV7Qzo3qklS/epUC/A18t9JCBOMJAStdQYg110FdcICuKJ1FFe0jgKsX+zbDuazZX8+m/fnWbcDeczbcpDC4rIzfo6ftxc2rSmzafQvZ9+VtXqQLzE1gmgRFUq/hDq0rBtGi6hQYmsEuXyntxCV4fR9CEqpUcCo8of5SqlNFfyoWsChqonKZUidTyMLWO2YWBxFvmfPUJk61z+fg+yWEJRSvwJ1TvPSU1rrH8/3c7TWY4AxVRDPCq11UmU/x5VInT2D1NkzOKLOdksIWute9vpsIYQQVc85xvkJIYQwzkhCUEoNVkrtBroA05VSMx1QbKUvO7kgqbNnkDp7BrvXWWmt7V2GEEIIFyCXjIQQQgCSEIQQQpTzqISglHpNKbVRKbVWKTVFKeX2mwMrpa5WSq1XStmUUm47TE8p1VcptUkptVUp9bjpeBxBKfW5UuqAUirddCyOoJSKUUqlKqUyyv9N3286JntTSgUopZYppdaU1/k/9izPoxICMBtopbVuDWwGnjAcjyOcXCZknulA7EUp5Q28D1wOtACGK6VamI3KIb4E+poOwoFKgYe01s2BzsDdHvA9nwAu0Vq3AdoCfZVSne1VmEclBK31LK11afnDJUC0yXgcQWudobWu6OxuV9ER2Kq1ztRaFwMpwJWGY7I7rfU84IjpOBxFa71Pa72y/H4ekAHUMxuVfWlLfvlD3/Kb3UYCeVRCOMWtwAzTQYgqUQ/Y9ZfHu3HzE4WnU0o1ANoBS81GYn9KKW+l1GrgADBba223Ojv9WkYX6nyWzFBKPYXV/BzryNjspaqWCXFhp1uRTsZTuymlVAgwCXhAa51rOh5701qXAW3L+zynKKVaaa3t0m/kdgnhXEtmKKVuAvoDl2o3mYQhy4SwG4j5y+NoYK+hWIQdKaV8sZLBWK31ZNPxOJLW+phSag5Wv5FdEoJHXTJSSvUFHgMGaq0LTccjqsxyIE4p1VAp5QdcC0w1HJOoYspaL/8zIENr/abpeBxBKRVxcjSkUioQ6AVstFd5HpUQgP8B1YDZSqnVSqmPTAdkb4aWCXGo8oEC9wAzsToav9darzcblf0ppcYDi4FmSqndSqnbTMdkZ92AG4BLyv//Xa2U6mc6KDuLAlKVUmuxfvjM1lr/ZK/CZOkKIYQQgOe1EIQQQpyBJAQhhBCAJAQhhBDlJCEIIYQAJCEIIYQoJwlBCCEEIAlBCCFEOUkIQlSCUqpD+f4aAUqp4PI161uZjkuIipCJaUJUklLqBSAACAR2a61fNhySEBUiCUGISipfP2k5UAR0LV+dUgiXI5eMhKi8GkAI1jpZAYZjEaLCpIUgRCUppaZi7dLWEIjSWt9jOCQhKsTt9kMQwpGUUjcCpVrrceV7Oy9SSl2itf7ddGxCXChpIQghhACkD0EIIUQ5SQhCCCEASQhCCCHKSUIQQggBSEIQQghRThKCEEIIQBKCEEKIcv8PJSF46Wg4JcoAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.618145573085454 5.854686241866959\n" + ] + } + ], + "source": [ + "x = np.linspace(-2, 3, 201)\n", + "plt.plot(x, x**2 - 1)\n", + "plt.plot(x, (np.exp(x) + x - 1)/x)\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.ylim(-1,8) \n", + "plt.grid(True)\n", + "plt.show()\n", + "\n", + "\n", + "\n", + "def equations(p):\n", + " x, y = p\n", + " return (y - x**2 + 1, np.exp(x) + x - x*y - 1)\n", + "\n", + "x1, y1 = fsolve(equations, (3, 3))\n", + " \n", + "print (x1, y1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- 2 Решите систему уравнений и неравенств:\n", + "\n", + "$y=x^2-1 \\\\\n", + "exp(x)+x(1-y)>1$" + ] + }, + { + "cell_type": "code", + "execution_count": 202, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-7.216800630079581e-36 -1.0\n" + ] + } + ], + "source": [ + "def equations2(p):\n", + " x, y = p\n", + " return (y - x**2 + 1, np.exp(x) + x - x*y > 1)\n", + "\n", + "x1, y1 = fsolve(equations2, (0, 0))\n", + " \n", + "print (x1, y1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/HM_Task_4 + bonus/HM_Task_4.ipynb b/HM_Task_4 + bonus/HM_Task_4.ipynb new file mode 100644 index 0000000..930e9d7 --- /dev/null +++ b/HM_Task_4 + bonus/HM_Task_4.ipynb @@ -0,0 +1,555 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# ВВЕДЕНИЕ В ВЫСШУЮ МАТЕМАТИКУ\n", + "****************" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Практическое задание к `Уроку 4`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Задание 1\n", + "Напишите код, моделирующий выпадение поля в рулетке (с учетом поля зеро)." + ] + }, + { + "cell_type": "code", + "execution_count": 109, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from numpy import (pi,sin,arcsin,cos,arccos,tan,sqrt,exp)\n", + "import itertools as it\n", + "import math\n", + "from math import factorial\n", + "import matplotlib.pyplot as plt\n", + "import pandas as pd\n", + "from pylab import *\n", + "import warnings\n", + "warnings.filterwarnings('ignore')\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Бросок 1: число - 21\n", + "Бросок 2: число - 16\n", + "Бросок 3: число - 15\n", + "Бросок 4: число - 3\n", + "Бросок 5: число - 21\n", + "Бросок 6: число - 0\n", + "Бросок 7: число - 17\n", + "Бросок 8: число - 4\n", + "Бросок 9: число - 9\n", + "Бросок 10: число - 15\n" + ] + } + ], + "source": [ + "# Рулетка Белое + Черное + зеро = 37/37 (0ю36)\n", + "N = 10 # число игр\n", + "\n", + "for i in range(N):\n", + " X = np.random.randint(0,37)\n", + " print(f'Бросок {i+1}: число - {X}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Задание 2\n", + "- 1)\tНапишите код, проверяющий любую из теорем сложения или умножения вероятности на примере рулетки или подбрасывания монетки.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Сумма вероятностей каждого из событий = 1.0\n" + ] + } + ], + "source": [ + "red = [32,19,21,25,34,27,36,30,23,5,16,1,14,9,18,7,12,3]\n", + "black = [15,4,2,17,6,13,11,8,10,24,33,20,31,22,29,28,35,26]\n", + "zero = [0]\n", + "\n", + "S = len(red) + len(black) + len(zero) # Количество вариантов\n", + "\n", + "P_red = len(red)/S # Вероятность выпадения красного\n", + "P_black = len(black)/S # Вероятность выпадения черного\n", + "P_zero = len(zero)/S # Вероятность выпадения зеро\n", + "\n", + "print(f'Сумма вероятностей каждого из событий = {P_red + P_black + P_zero}')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Вероятность выпадения двух шариков на красное = 0.22352081811541274\n" + ] + } + ], + "source": [ + "# Если бросать на одну рулетку сразу 2 шарика и посчитать вероятность, что оба упадут на красное,\n", + "# то будет действовать закон умножения вероятностей\n", + "\n", + "P_double_red = P_red * (P_red - 1/S)\n", + "\n", + "print(f'Вероятность выпадения двух шариков на красное = {P_double_red}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- 2)\tСгенерируйте десять выборок случайных чисел х0, …, х9.\n", + "и постройте гистограмму распределения случайной суммы х0+х1+ …+ х9." + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": {}, + "outputs": [], + "source": [ + "def make_sum_dataset(size):\n", + " x = [] \n", + " for i in range(size):\n", + " x.append(np.sum(np.random.rand(10))) # Добавляет сумму из 10 случайных чисел к списку, длиной N\n", + " return x\n", + "\n", + "x = make_sum_dataset(10000)" + ] + }, + { + "cell_type": "code", + "execution_count": 96, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mu = 4.996014746023304, D = 0.8317610368910837, std = 0.9120093403529833\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "mu = np.mean(x) # Среднее\n", + "D = np.var(x) # Дисперсия\n", + "std = np.std(x) # Среднеквадратичное отклонение\n", + "print(f'mu = {mu}, D = {D}, std = {std}')\n", + "\n", + "num_bins = 40\n", + "n, bins, patches = plt.hist(x, num_bins, density=1, facecolor='b', alpha=0.5)\n", + "y = mlab.normpdf(bins, mu, std)\n", + "plt.plot(bins, y, 'r--')\n", + "plt.xlabel('Sum x0...x9 ')\n", + "plt.ylabel('Probability')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Задание 3\n", + "\n", + "- 1)\tДополните код Монте-Карло последовательности независимых испытаний расчетом соответствующих вероятностей (через биномиальное распределение) \n", + "и сравните результаты.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Последовательность независимых испытаний:\n", + "\n", + "$\\\\\n", + "P_n(k) = C_n^kp^kq^{n-k}=C_n^k\\frac{1}{2^n} \\\\\n", + "C_n^k=\\frac{n!}{k!(n-k)!}$" + ] + }, + { + "cell_type": "code", + "execution_count": 107, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k = 4, n = 10,\n", + "- k/n = 0.4,\n", + "- C_n_k = 210.0,\n", + "- Pn_k = 0.205078125\n", + "\n" + ] + } + ], + "source": [ + "# Используем пример с подбрасыванием монеты\n", + "\n", + "def compute_P(k, n):\n", + " a = np.random.randint(0, 2, n)\n", + " b = np.random.randint(0, 2, n)\n", + " c = np.random.randint(0, 2, n)\n", + " d = np.random.randint(0, 2, n)\n", + " x = a + b + c + d\n", + " for i in range(0, n):\n", + " if x[i] == 2:\n", + " k = k + 1 \n", + " C_n_k = factorial(n)/(factorial(k)*factorial(n-k)) # Расчет вероятности с помощью формулы Бернулли\n", + " Pn_K = C_n_k/2**n\n", + " return k, n, C_n_k, Pn_K\n", + "\n", + "k, n, C_n_k, Pn_K = compute_P(0, 10)\n", + "print(f'k = {k}, n = {n},\\n- k/n = {k/n},\\n- C_n_k = {C_n_k},\\n- Pn_k = {C_n_k/2**n}')\n", + "print()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- 2)\tПовторите расчеты биномиальных коэффициентов и вероятностей k успехов в последовательности из n независимых испытаний, взяв другие значения n и k." + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "metadata": {}, + "outputs": [], + "source": [ + "def create_p_dataset(n_0, n_max):\n", + " k, n, C_n_k, Pn_k = [], [], [], []\n", + "\n", + " for i in range(n_0,n_max):\n", + " k_tmp, n_tmp, C_n_k_tmp, Pn_k_tmp = compute_P(0, i)\n", + " k.append(k_tmp)\n", + " n.append(n_tmp)\n", + " C_n_k.append(C_n_k_tmp)\n", + " Pn_k.append(Pn_k_tmp)\n", + " \n", + " df = pd.DataFrame(n, columns=['n'])\n", + " df['k'], df['Pn_k'], df['C_n_k'] = k, Pn_k, C_n_k\n", + " df['k/n'] = df['k']/df['n']\n", + " return df" + ] + }, + { + "cell_type": "code", + "execution_count": 115, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(nrows=2, ncols=2)\n", + "ax1, ax2, ax3, ax4 = ax.flatten()\n", + "ax1.plot(df['n'], df['k'])\n", + "ax1.set_xlabel('$n$', fontsize=14)\n", + "ax1.set_ylabel('$k$', fontsize=14)\n", + "\n", + "ax2.plot(df['n'], df['Pn_k'])\n", + "ax2.set_xlabel('$n$',fontsize=14)\n", + "ax2.set_ylabel('$P_n(k)$',fontsize=14)\n", + "\n", + "ax3.scatter(df['n'], df['C_n_k'])\n", + "ax3.set_xlabel('$n$',fontsize=14)\n", + "ax3.set_ylabel('$C_n^k$',fontsize=14)\n", + "ax3.set_yscale('log')\n", + "\n", + "ax4.plot(df['n'], df['k/n'])\n", + "ax4.set_xlabel('$n$',fontsize=14)\n", + "ax4.set_ylabel('$k/n$',fontsize=14)\n", + "# ax4.set_aspect(1)\n", + "\n", + "\n", + "fig.set_size_inches(14, 6)\n", + "plt.subplots_adjust(wspace=0.3, hspace=0.3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Задание 4\n", + "Из урока по комбинаторике повторите расчеты, сгенерировав возможные варианты перестановок для других значений n и k" + ] + }, + { + "cell_type": "code", + "execution_count": 110, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Combinations for \"9hjk0\", n:5, k:4 = 5\n", + "Permutations for \"9hjk0\", n:5, k:4 = 120\n", + "Product for \"9hjk0\", n:5, k:4 = 625\n" + ] + } + ], + "source": [ + "text = '9hjk0'\n", + "key = 4\n", + "d1, d2, d3 = list(it.combinations(text, key)), list(it.permutations(text, key)), list(it.product(text, repeat=key))\n", + "print(f'Combinations for \\\"{text}\\\", n:{len(text)}, k:{key} = {len(d1)}')\n", + "print(f'Permutations for \\\"{text}\\\", n:{len(text)}, k:{key} = {len(d2)}')\n", + "print(f'Product for \\\"{text}\\\", n:{len(text)}, k:{key} = {len(d3)}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Задание 5\n", + "Дополните код расчетом коэффициента корреляции x и y по формуле\n", + "### $R = \\frac{\\sum(x_i-x_m)(y_i-y_m)}{\\sqrt{\\sum(x_i-x_m)^2 \\sum (y_i-y_m)^2}}$ " + ] + }, + { + "cell_type": "code", + "execution_count": 111, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a = 0.744682681103492, b = 0.1335863671443964\n", + "a1 = 0.7446826811034917, b1 = 0.13358636714439678\n", + "corr 1 = 0.9203860952988462\n", + "corr 2 = [0.9203861 1. ]\n" + ] + }, + { + "data": { + "image/png": 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98k3n9G7faeTJ6PnyXy2HJ86DWw+G956GEb/wxgyOuiKvAgFidxHmk1CfFJxzxwKTgULgLjObFOGa8cAVgAFvmtmZYZZJJBHR+uSBmGsQMna+/NoP4eVr4a2HobCDN14w/JfQuWe6S5Y2WhntCS0UnHOFwK3A0cBKYL5zbrqZLW1xzQDgUmCEma13zu0SVnlEkhWpT37EpJlRAyHWYrK0WfexFwZvTvXOPT70ZzDil9BZ/+tpZbQnzCeFg4HlZvYRgHNuKjAGWNrimp8At5rZegAz+zLE8ogELtpdpAPmTDwitYVppeWg6bAdN3L9rv9lj8/+7YXBIefDiF9Bl15pLWMm0cpoT5ihUAJ81uLrlcAhra4ZCOCcm4PXxXSFmT0XYplEApWpd5dNg6bd6z7nynbTOGXryzR8WsCHe53BXiddBl12TWv5MpFWRnucRZhTHcgHO3cqMNrMftz49Q+Ag83sohbX/AeoBcYDuwGzgcFmVtnqs84DzgPo1avXsKlTpyZUpqqqKjp3Tt1GXZlAdQ7X3FW13Pd2DTUN37zWvgDOGdye4X2iH+wetNZ1vrZ8Bd+ve5JTCl/CcDxUfwS3151IXcfuXF8W3jbWqaR/2/EZNWrUQjMrbeu6MJ8UVgK7t/h6N2BVhGvmmVkt8LFzbhkwAJjf8iIzmwJMASgtLbVYe7zE0tb+MLlIdU5OW/PWy4BBGTC3vbnOG1bC7OsZbvdDITxcP4rb6sawGm8mkdtiOfPvQf+2wxFmKMwHBjjn+gMVwOlA65lF04AzgPuccz3wupM+CrFMIr75nbcebVFYKhdCtd+6Fp7+NbxxP5jxTLsjuWbTCayixzbXpbtbSzJfaKFgZnXOuQuBGXjjBfeY2TvOuT8DC8xseuP3jnHOLQXqgQlmtjasMonEI5nzD1K2EGrjanjlBg6dfw84gwO/D4f/Gj4uZP0TSyDPB00lfqGuUzCzZ4BnWr12eYs/G/C/jf+JZJRk5q2HfkTk15/DKzfCwnuhvpYveo2i92nXw079ABg79Jty5POgqcRP21yIRJHMzKLQFkJVfemFwYK7ob4WDjgDDv81y976lN6NgdBE20lLIhQKIlEkM2898KmqVWtgzo0w/26o3wr7n+51E3Xfq/GCTxP7XJFWFAoiUSQzbz2whVCbvoI5k2H+XVC3BYaMh5G/aREGbdPOnxIPhYJIDIl2wSS9EGrTWph7E7x+J9RuhiGnemHQY0Bc5dDOnxIvhYJISBIKlM3rYO7N8PoUqNnEZyXH8Zs1xzJvfnf6fPAZE0bvENdnhj7g3UhPI7lDoSASp1AawM3r4NVb4bW/Q00V7HcSL+5yDhe+UJ3UXX4qdv7U00hu0XkKkjZN5xD0n/g0IybN3O6840zk96xm36orYdaVMPkAmH0dfOsIuGAunHovl79an/T+/tEGtoNcxKZzCHKLQkHSIvDGNUUCawC3bPDOQL5xf+/Esz1Hwk/nwPh/QK9BQDB3+bEOBwqKziHILeo+krRIVV930JJuALdshNfugFdv8YJhnxNg5G+h9/7bXZrstNambq7q2noKnaPeLJQzHjJ1p1hJjJ4UJC2y9e4y4e6YrV97h9vcOARm/RX2GAHnvwynPxgxECC5u/yWT2IA9WbN7w06dFPxNCKpoycFSYtsvbuMe/3B1q+9mURzb4bq9TDwWCibCH2Genfy98+MOmCdzLTWsJ/EWg+2nzyshFnvrdHsoxygUJC0SHRxl9+ZP2FNkfTdUG+tgvl3wpyboHodDDjGC4OSYc3lS2YH1raE+SQWqeyPL6zgqnFDFAQ5QKEgaZHIXbDfhnTuqloeeDG8KZIxG+qaTd7q4zmTYfNa+NZRUHYp7PbN2SbTFlVwySNvUt/qgKvq2noueeRNLn54cdJBFuaTWLaOB4k/CgVJm3jvgv02Ro+/X0t17fYNbqiNVs1mWHCPtz/RpjWw1xFeGOx+8DaXNQVb60Bo0vR6skEW5nnD2ToeJP4oFCRr+G2M1m6J3OCG0mjVVsOCe+GVG2DTl7BnmRcGfQ+NeHmkYIsmmSAL87zhbB0PEn8UCpI1/DZG3Tu6iMEQaKNVuwUW3ueFQdXn0P9wKLsf9hge823xBlMyQRbW1tlhPoVI+rU5JdU5d6FzbqdUFEYkFr9TH08eWBTeFMnaLfDaFLjpQHjut9D9W3DO03D2U20GAsQfTIkGWZirxccOLeGqcUMo6VaMA0q6FWuQOYf4eVLYFZjvnHsDuAeY0XhimkjKdSwqaL5D7VZcxBUn7rddYzS8TxGD9h0UbNdJ3VZ44x8w+2/w9SroOxzGTfGeEOIQ7S775GElPL6wIpC771TsRaQDfHJXm6FgZn9wzl0GHAP8CLjFOfcIcLeZfRh2AUVg+4YOYFNNHVdMfyfibJ3AGq26Glj0gBcGG1fC7ofCSbdD/5HgXNwfF6uvv3SPnQMJMs0OkmT4GlMwM3POfQ58DtQBOwGPOeeeN7PfhFlAEYjc0NXWG5XVtcC2d8PdgviBdTWw+EGYfT1s+Ax2OxjG3Ax7jkooDFqKFlhBBZlmB0ky2gwF59wvgLOBr4C7gAlmVuucKwA+ABQKEjo/DVp1bT1/euodChrqWPfc04ndbdfXwuJ/eTuWVq6AklL43o2w15FJh0GqaHaQJMPP3kc9gHFmNtrMHjWzWgAzawBOCLV0Io38NmjrN9eydos177z6q4cXM/TP/217oLW+Ft54AG4eBk/9AnboAd9/DH78grcALUsCAbQXkSTHz5jC5TG+926wxRGJLNIArV/rN9dGH2itr4O3HvY2q1v/MfQ+EL57DQwc3WYQZOppY2GuUZDcp3UKkhVaNnSRukbast1Aa30dvP2Yd5bBuo9g1/3h9Idg7+/6eirQaWOSqxQKktEi3Y1HCwYHxJorvaqyGhrq4e3HvTBYuxx6DYHTHoR9jo+riyiTZ/gosCQZCgVJCz9dL9Eat2hdSIbXdx7p+wU08IMub8BtV8BX78Mu+8H4B7xDbgriP1Ykk2f4ZHJgSeZTKEjK+b2Tjda4NZ0i1lrTqWK/f3wxm+q81xwNHF/wGr8qeoJv1VZAwSA49X7Y98SEwqBJJs/wyeTAksynUJCU83snG60RazpFLNLq37FDS+i24QMqd9yLBc/exw+2TmXvgpVs7LIXjL4XBo1NKgyaZPL+P5kcWJL5dBynpJzfO9lojVjTXjsR995paKDHmrmMnXcaf6m9jr132YH5w67j+Jqr6f/PDoy4pjyQfYAyef8fTUmVZOhJQVLO751srLvx7Vb/msG7T0H5JAZ/8TZ0HwDj7mJa3SFc+uRSqmtrgGAHXTN1/x9NSZVkKBQk5fx2vfhq3Mxg2TNQfhV8vgR23ot397mYfcdfBgWFXDtpZtYOuiazDiJTA0syn0JBUi6eO9mojZsZvP+cFwar34Sd+sPYO2DIqXwx+xX2LfC6T8IYdE3FojVNK5V0UShIWiR8J2sGH/zXC4NVi6DbHjDmNtj/NCjc/p9z0IOuqWqsNa1U0iXUgWbn3LHOuWXOueXOuYkxrjvFOWfOudJo10ieM4MPnoe7joR/jYfNa+HEm+GihTD0+xEDAYIfdI3VWAdJ00olXUJ7UnDOFQK3AkcDK/EO6pluZktbXdcF+AXwWlhlkSxmBh/O9J4MVs6HrrvD9ybDAWdCu/Ztvj3oQddUNdaaVirpEmb30cHAcjP7CMA5NxUYAyxtdd3/AdcAvw6xLJJtzOCjci8MPnsNdtwNTrgBDjzLVxi0FOSga6oa60xeByG5zYV1sqZz7hTgWDP7cePXPwAOMbMLW1wzFPiDmZ3snCsHfm1mCyJ81nnAeQC9evUaNnXq1ITKVFVVRefOnRN6b7bKujqb0a1yCf0+eYhuG5aypUN3VvQ9ldW9j8IKira5dO6qWh5/39squ3tHx8kDixjepyjpOkf73Kbv3fd2DTUN31zfvgDOGdy++ZqgxCpHa1n39xwA1Tk+o0aNWmhmbXbRh/mkEGl3seYEajyk5wbgnLY+yMymAFMASktLraysLKEClZeXk+h7M0Eis16yqs4fz/aeDD6dA116w3HX0fGgHzKwXQcGtrp02qIKHnhxCdW13j+ptVuMB96tZ9C+g+jGBwnXOdbnjh1aQhkwKEVbZpcBv/N5bVb9PQdEdQ5HmKGwEti9xde7AatafN0FGAyUO293yl2B6c65EyM9LeS7nJ6i+MkcLww+mQ2dd/XOMzjobCjqGPUtsQZ8/3po4vMn/Mz60RoAyWVhhsJ8YIBzrj9QAZwOnNn0TTPbgHeqGwCxuo8kR6cofvoqlF8JH78MnXvBsZNg2DlQ1Hb/fOwB307bvBbPE5Zm/Ui+Cy0UzKzOOXchMAMoBO4xs3ecc38GFpjZ9LB+di6Kp7Fq2Qju3NFxWdeKzAqOz16HWVfCR7OgU08YfSUM+xG038H3R/gd8I33CSva5xY4R/+JCZ77LJJFQl2nYGbPmNlAM9vLzP7a+NrlkQLBzMry9Slh2qIKRkyaSf+JTzNi0syIG7ZFm90SrRGsqKzG8PrEL31iSSCbwCVt5QJ4YBzcfbS3JcUxf4FfvgWH/TyuQAD/6w/iXVcQ6XPB25m16dznjPl9ioRAu6SmWetGPFqjE1YjmBIrF8I/T/EWnq1eDEf9CX71Fgy/KO4wgG+ehJrOVoDou5TG2x3UevfTwginsaX99ykSIm1zkWZ+xwr8LsLKqD7xijegfBJ8MAOKd4Ij/wgHnwcdEp9G2Lo7qN4MB4zap2dc3UEGjJg0M+LvsOVAcv+JT0csh8YYJFcpFNIsnkbcz6yXjFgJu2qxFwbvPwsdu8ERl8Eh50OHLkl/dKQQNeDBeSso3WPn7X4/kRaBNfEzgysjfp8iKaTuozTzO1bgV6oOWIk4DrL6LXjoTJgyElbMhVF/gF8tgcN/HUggQPQQNYjYpdOyOyiStrqCdGCN5BuFQpoF3ei07hPv3tEFfiJY63GQLhuW0Wna2fD378Anr0DZ77wwGDkBOu4Y2M+F2GEZa5xgzsQjIq6mjPW+pvdm6glrImFQ91GatTVWkMgq5pbdTOXl5ZQF3IA1deHs7Vbwy3ZPcFzh62y0Ym6sG8ezHcZxQdeDGNuxa6A/s8mE0Xtz8cOLibQ5S1tPV4mML4AWq0l+USgEKNHDV6I1Opm6irnThg+4pehxTih8ja+tmMl1J3F33XfZSGfYQKhlHDu0hAWfruPBeSu2CQY/T1fJji+I5AOFQkAiNeATHn2TPz31DpWbaxNa9JRxq5jXLIPySTzX4Uk2WwduqRvDnXXHs4FtZxOFXca/jB1C6R47J/QEBd7vNdITQ9avEBcJgEIhIJEa8NoGY/3mWiCxO9GMmV761Qfw0tWw5DEo2oHlA87l7PcOYXVdp6hvCbuMiXbpNL2v/8SnI3ZBaaqp5DuFQkD8NCbx3omGcZRkXHfXXy2Hl6+BJY9Cu44w4hcw/BcM7NSD3zZ+VqTyJVPGVNFUU5HIFAoBidbItFZRWc1elz5DvRklbTTMQR60Etf4xNoP4eVr4a2HobCDtw3F8F9C557NlzTdcbf+3GTKmIx493vSITYikSkUAhJrELO1+saDjdrqUgryKElf4xPrPoKXr4M3p0JhERz6MxjxS+i8S9TPbXrvn556p7mrrEO71M50bh1MTfs9tSxfa0Ef0ymSKxQKAYnUOPrRVpdSUNMhY45PrP/EezJY/JAXBoecDyN+BV16+f78LbXfHEVWWV2b0pk8iQ7Ia6qpyPYUCgFr2TiCd/xcWweepmJwM1L31m5uDb/Z4Sm4uRxcIRz8E/j2xdBl17g+O92zpDJmQF4kBygUAhRtX55C55q7jCJJxeBmy+6tPnzFhe2mcUrhSxRaAZT+Py8MduyT0Genu1HWoLFIcBQKAYrWCNabUVxUGHG8IejBzdYzjI7vW08ZXldJcfVqNr94DcfXvQDOsbLfePY86TLomtzdfKyDaf4wbQmz3lsTWL99pBlUGjQWCY72PgpQtDvTpv1ymjZla+sMgERFOpvhvrdreG7uQnj6Eka/+F1Ospm0/5+zaX/xm+x5zh1JBwLEPpjmn/NWtHlWhF/Rzp4AQt/vSSRf6EkhQLHuWFMxqNm6+2oX1vMl3Hl6AAAOd0lEQVSzgn9zxH9nevF/4Pe9HUu79Q305zbV65JH3ozZTQbJjTXEGruYM/GIUPd7EskXCoUApXuaY1P3VU/Wc0G7p/h+4YsUUs/jdYdz2iWTYad+of3ssUNLuPjhxXGVM17pHrsQyQcKhYClc5rjfl23MnbTI5xV+ALtqOeJ+u9wc/1YGrr247QQA6GJ3wV8iQ4Aa0BZJHwaU8gFVWtgxu+ZVncBPyp8jv80HMaRNdfxm7rz+cL1StmAa7SxhZaSGQDWgTci4dOTQjbb9BXMmQzz74K6LbQbMp7ne/6QG+ZsZVVlNSWNs49S9eQSqfts1D49A5t9lO7uOZF8oFDIRpvWwtyb4PU7oXYzDDkVRv4GegzgaODo73xzaXl5eUqLFnb3mVYhi4RLoRCiRA/diWrzOph7M7w+BWo2weCTYeRvoefA4AotInlNoRCSQE9N27wOXr0VXvs71FTBfid5YbDLPkEXW0TynEIhJIHsB1RdCfNug3m3w9aNMGisFwa9BoVQYhERhUJokppTv2WDFwSv3gZbN8C+34ORE2HXwQGXUkRkWwqFAEQaO0hoTv2WjfDaHfDqLV4w7HOC92TQe/8QSy8i8g2FQpKijR2cPKyExxdW+NukbevXXhjMvQW2VMLex0HZROh9QKqqISICKBSSFm3sYNZ7a7hq3JDYs4+2fu3NJJp7M1Svh4HHemHQZ2iKayEi4lEoJCnW2EHUOfVbq2D+nTDnJqheBwOO8cKgZFjIpRURiU2hkKS4xg5qNnmrj+dMhs1r4VtHQdmlsFtpCkoqItK2UPc+cs4d65xb5pxb7pybGOH7/+ucW+qce8s596Jzbo8wyxMGX/vx1Gz2uogmHwDPX+6NFZz7PJz1uAJBRDJKaE8KzrlC4FbgaGAlMN85N93Mlra4bBFQamabnXMXANcAp4VVpjDE3I+nthoW3AOv3AibvoQ9y7wng76HprXMIiLRhNl9dDCw3Mw+AnDOTQXGAM2hYGazWlw/DzgrxPKEZruxg9otMO8OeOVvUPUF9D8cyu6HPYanr5AiIj44a+OkrIQ/2LlTgGPN7MeNX/8AOMTMLoxy/S3A52b2lwjfOw84D6BXr17Dpk6dmlCZqqqq6Ny5c0Lv9aOgvobeq5+n74rH6FCzjvXdBvNJvzPY0C3cRWdzV9Xy+Pu1rN1idO/oOHlgEcP7FAHh1zkTqc75QXWOz6hRoxaaWZv91WE+KbgIr0VMIOfcWUApMDLS981sCjAFoLS01MrKyhIqUHl5OYm+N6a6rfDGP2D23+DrVdB3OIy6lJ36H85Owf+0bUxbVMEDLy6hutb71a7dYjzwbj2D9h3E2KEl4dU5g6nO+UF1DkeYobAS2L3F17sBq1pf5Jw7Cvg9MNLMtoZYnuDV1cCiB7ww2LgSdj8UTrod+o8EFykTg5fsHkuB7+QqIlktzFCYDwxwzvUHKoDTgTNbXuCcGwr8Ha+b6csQyxKsuhpY/CDMvh42fMbanQ7k/4rO5d8fDKTPmgYmjF7VZsMaVGOczB5Lge7kKiI5IbRQMLM659yFwAygELjHzN5xzv0ZWGBm04Frgc7Ao867s15hZieGVaZEtGy8d+9axOR932Xox3fBhhVQUsrcQZdx7is7Ul3bAPhrWINsjJM5tziQnVxFJKeEuk7BzJ4xs4FmtpeZ/bXxtcsbAwEzO8rMepnZgY3/ZVwgXPrEEr6o/JpTCsv5Z/XPGLr4cta7rvD9x+DHLzBhUc/mQGjS1LBGE6sxjlcy5xYntZOriOQkrWiO4W/PLeX4hplc2H4a/Qq+4K2G/vyx5hzerz6MOQOOBBJrWINsjJM5tziZpwwRyU0KhUjq62DJo9xf/Uf6F33B2w39OLfmEl5sOAhwuA1bmi/ttkMR6zfXbvcRsRrWoBvjRM8tnjB67226scD/U4aI5CaFQksN9bDkMXj5Gli7nLrCfpy39WL+21BKyxm2TY33tEUVVG2p2+5jigpdzIY1UxrjZJ4yRCQ3KRTAC4N3noSXroav3odd9oPxD/DOlqHMfvId7/uNHDBqn56A15jWNmy/9KJT+3YxG9ZMaowTfcoQkdyU36HQ0ABLn4Tyq+GrZbDLIDj1ftj3RCgoYCywYEUlD85b0bzqzoDHF1ZQusfOUccANlRv353UmhpjEclE+RkKDQ3w7r+9MFjzLvTcB065FwaNhYJtJ2TNem/Ndsuwm2YKaaBWRHJNqFNSM441wNJ/wx3fhkfPAauHk++GC+bC4HHbBQLEnimUzHRQEZFMlD9PCh/OonTBxbDpE+g+AMbd1RgEhTHf1rW4iMoI3UFdi4syamxARCQI+RMKVV9Q0FADJ02BIae0GQZNom1htHFLLdMWVWhsQERySv6EwpBTmb+2JyMPODKut1VGWIMA0GD42ppCG86JSDbJnzGFgkLM59NBS7EGjdvamqJpm4yKymqMb/Y4mraoIu5yiIikQv6EQoIiDSa3FGtriiD3OBIRSQWFQhvGDi3hqnFDKIwyuBDrSUIbzolItlEo+DB2aAnXjz8g7umn0QJD6xhEJFMpFHxqemIo6VaMA3baoYgO7Qq4+OHFjJg0M+I4gdYxiEi2yZ/ZRwFomn7q95AcrWMQkWyjUEhAPCeWaR2DiGQTdR8lQAPIIpKrFAoJ0ACyiOQqhUICNIAsIrkqr8YU5q6q5feTZiY96BtpAHnUPj25dsYyLn54sQaURSRr5U0oTFtUwX1v11DT4H0dbcaQXy0HkP3ORhIRyXR503107YxlzYHQJKgtJ7SdhYjkirwJhTBnDGk2kojkirwJhTBnDGk2kojkirwJhQmj96Z9q9oGNWNIs5FEJFfkTSiMHVrCOYPbN+9dVNKtmKvGDQlkILj1vkhBfraISCrlzewjgOF9ivjdmWWhfLa2sxCRXJA3TwoiItI2hYKIiDRTKIiISLO8GlMIapsLEZFcFeqTgnPuWOfcMufccufcxAjf7+Cce7jx+6855/qFVZambS4qKqsxvtmKItKJaSIi+Sq0UHDOFQK3At8FBgFnOOcGtbrsXGC9mX0LuAG4OqzyhLnNhYhIrgjzSeFgYLmZfWRmNcBUYEyra8YA9zf++THgSOecC6Mw2opCRKRtYYZCCfBZi69XNr4W8RozqwM2AN3DKIy2ohARaVuYA82R7vgtgWtwzp0HnAfQq1cvysvL4y7M8X3ruXejUdvwzY9sX+C9nsjnZYuqqqqcrl8kqnN+UJ3DEWYorAR2b/H1bsCqKNesdM61A7oC61p/kJlNAaYAlJaWWllZWdyFKQP41/M8vaIwr2YflZeXk8jvK5upzvlBdQ5HmKEwHxjgnOsPVACnA2e2umY6cDbwKnAKMNPMtntSCEqY21yIiOSC0ELBzOqccxcCM4BC4B4ze8c592dggZlNB+4GHnDOLcd7Qjg9rPKIiEjbQl28ZmbPAM+0eu3yFn/eApwaZhlERMQ/bXMhIiLNFAoiItJMoSAiIs1ciJN9QuGcWwN8muDbewBfBVicbKA65wfVOT8kU+c9zKxnWxdlXSgkwzm3wMxK012OVFKd84PqnB9SUWd1H4mISDOFgoiINMu3UJiS7gKkgeqcH1Tn/BB6nfNqTEFERGLLtycFERGJISdDIZOOAU0VH3X+X+fcUufcW865F51ze6SjnEFqq84trjvFOWfOuayfqeKnzs658Y1/1+845/6V6jIGzce/7b7OuVnOuUWN/76PS0c5g+Kcu8c596Vz7u0o33fOuZsafx9vOecOCrQAZpZT/+FtvvchsCfQHngTGNTqmp8BdzT++XTg4XSXOwV1HgXs0PjnC/Khzo3XdQFeBuYBpekudwr+ngcAi4CdGr/eJd3lTkGdpwAXNP55EPBJusudZJ0PBw4C3o7y/eOAZ/HOozkUeC3In5+LTwoZdQxoirRZZzObZWabG7+ch3e+RTbz8/cM8H/ANcCWVBYuJH7q/BPgVjNbD2BmX6a4jEHzU2cDdmz8c1e2P7clq5jZy0Q4V6aFMcA/zDMP6Oac6x3Uz8/FUMioY0BTxE+dWzoX704jm7VZZ+fcUGB3M/tPKgsWIj9/zwOBgc65Oc65ec65Y1NWunD4qfMVwFnOuZV4uzJflJqipU28/7/HJdSts9MksGNAs4jv+jjnzgJKgZGhlih8MevsnCsAbgDOSVWBUsDP33M7vC6kMrynwdnOucFmVhly2cLip85nAPeZ2fXOucPwzmgZbGYN4RcvLUJtv3LxSSGeY0CJdQxoFvFTZ5xzRwG/B040s60pKltY2qpzF2AwUO6c+wSv73V6lg82+/23/W8zqzWzj4FleCGRrfzU+VzgEQAzexXoiLdHUK7y9f97onIxFJqPAXXOtccbSJ7e6pqmY0AhBceApkCbdW7sSvk7XiBkez8ztFFnM9tgZj3MrJ+Z9cMbRznRzBakp7iB8PNvexrepAKccz3wupM+Smkpg+WnziuAIwGcc/vihcKalJYytaYDP2ychXQosMHMVgf14TnXfWR5eAyozzpfC3QGHm0cU19hZiemrdBJ8lnnnOKzzjOAY5xzS4F6YIKZrU1fqZPjs86XAHc65y7G60Y5J5tv8pxzD+F1//VoHCf5I1AEYGZ34I2bHAcsBzYDPwr052fx705ERAKWi91HIiKSIIWCiIg0UyiIiEgzhYKIiDRTKIiISDOFgoiINFMoiIhIM4WCSJKcc//TuK99R+dcp8ZzDAanu1wiidDiNZEAOOf+gre9QjGw0syuSnORRBKiUBAJQOO+PPPxzm0Ybmb1aS6SSELUfSQSjJ3x9pbqgvfEIJKV9KQgEgDn3HS8U8H6A73N7MI0F0kkITm3S6pIqjnnfgjUmdm/nHOFwFzn3BFmNjPdZROJl54URESkmcYURESkmUJBRESaKRRERKSZQkFERJopFEREpJlCQUREmikURESkmUJBRESa/X+4YgIc0NHQowAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "n = 100\n", + "r = 0.7\n", + "x = np.random.rand(n)\n", + "y = r*x + (1 - r) * np.random.rand(n)\n", + "plt.plot(x, y, 'o')\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.grid(True)\n", + "\n", + "a = (np.sum(x)*np.sum(y) - n*np.sum(x*y))/(np.sum(x)*np.sum(x) - n*np.sum(x*x))\n", + "b = (np.sum(y) - a* np.sum(x))/n\n", + "\n", + "corr_1 = (np.sum((x-np.mean(x))*(y-np.mean(y))))/sqrt(np.sum((x-np.mean(x))**2)*np.sum((y-np.mean(y))**2))\n", + "corr_2 = np.corrcoef(x,y)\n", + "\n", + "A = np.vstack([x, np.ones(len(x))]).T\n", + "a1, b1 = np.linalg.lstsq(A, y)[0]\n", + "print(f'a = {a}, b = {b}')\n", + "print(f'a1 = {a1}, b1 = {b1}')\n", + "print(f'corr 1 = {corr_1}\\ncorr 2 = {corr_2[1]}')\n", + "plt.plot([0, 1], [b, a + b])\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git "a/HM_Task_4 + bonus/\320\240\320\265\321\210\320\265\320\275\320\270\320\265 \320\267\320\260\320\264\320\260\321\207\320\270 \320\221\321\216\321\204\321\204\320\276\320\275\320\260.ipynb" "b/HM_Task_4 + bonus/\320\240\320\265\321\210\320\265\320\275\320\270\320\265 \320\267\320\260\320\264\320\260\321\207\320\270 \320\221\321\216\321\204\321\204\320\276\320\275\320\260.ipynb" new file mode 100644 index 0000000..1e1a71c --- /dev/null +++ "b/HM_Task_4 + bonus/\320\240\320\265\321\210\320\265\320\275\320\270\320\265 \320\267\320\260\320\264\320\260\321\207\320\270 \320\221\321\216\321\204\321\204\320\276\320\275\320\260.ipynb" @@ -0,0 +1,878 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Решение задачи Бюффона:\n", + " - Иголку длиной L мм наудачу бросают на разлинованную бумагу, где расстояние между соседними линиями = A мм.\n", + " - С какой вероятностью упавшая иголка пересечет линию бумаги?" + ] + }, + { + "cell_type": "code", + "execution_count": 241, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from numpy import (linspace,logspace,zeros,ones,outer,meshgrid,\n", + " pi,sin,arcsin,cos,arccos,tan,sqrt,exp)\n", + "import matplotlib.pyplot as plt\n", + "import math\n", + "import pandas as pd\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "from pylab import *\n", + "from scipy.optimize import fsolve\n", + "plt.style.use('fivethirtyeight')\n", + "%matplotlib inline\n", + "import warnings\n", + "warnings.filterwarnings('ignore')" + ] + }, + { + "cell_type": "code", + "execution_count": 242, + "metadata": {}, + "outputs": [], + "source": [ + "A = 100 # Расстояние между линиями\n", + "L = 40 # Длина иглы" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Проверим работу зависимостей на одном броске с заданными параметрами" + ] + }, + { + "cell_type": "code", + "execution_count": 243, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(-100, 100)" + ] + }, + "execution_count": 243, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "C = A/4 # Изначальное расстояние от начала иглы до линии (-a/2 ... a/2) \n", + "angle = pi/4 # Угол поворота иглы (0 ... pi) \n", + "\n", + "x1 = 0\n", + "x2 = L*cos(angle)\n", + "y1 = C\n", + "y2 = L*sin(angle)+y1\n", + "\n", + "plt.plot([-A,2*A],[A/2,A/2], color ='blue', linewidth=0.75, linestyle =\"--\")\n", + "plt.plot([-A,2*A],[0,0], color ='red', linewidth=0.75, linestyle =\"--\")\n", + "plt.plot([-A,2*A],[-A/2,-A/2], color ='blue', linewidth=0.75, linestyle =\"--\") \n", + "plt.plot([x1,x2],[y1,y2], 'r')\n", + "plt.ylim(-A,A)\n", + "plt.xlim(-A,A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Параметры броска:" + ] + }, + { + "cell_type": "code", + "execution_count": 244, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x2-x1: 28.284271247461902\n", + "y2-y1: 28.284271247461902\n", + "R: 40.0\n", + "h: 25.0\n", + "L*sin(angle): 28.284271247461902\n", + "h < L*sin(a) ? True\n" + ] + } + ], + "source": [ + "print(f'x2-x1: {x2-x1}') # X\n", + "print(f'y2-y1: {y2-y1}') # Y\n", + "print(f'R: {sqrt((x2-x1)**2+(y2-y1)**2)}') # R\n", + "print(f'h: {A/2-y1}')\n", + "print(f'L*sin(angle): {L*sin(angle)}')\n", + "print(f'h < L*sin(a) ? {A/2-y1" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "N = 30\n", + "C = np.random.uniform(-A/2, A/2, N) # Изначальное расстояние от начала иглы до линии (-a/2 ... a/2) \n", + "angle = np.random.uniform(0, pi, N)\n", + "count = 0\n", + "\n", + "def is_crossed(A, L, C, angle):\n", + " \n", + " if A/2-C" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# A = 100 , L = 40\n", + "x = linspace(0,pi,1000)\n", + "plt.plot(x,L*sin(x), 'r') # L*sin(angle) = C\n", + "plt.scatter(angle,A/2-C) # A/2-C = h\n", + "plt.xlabel('angle x (0...pi)',fontsize=14)\n", + "plt.ylabel('Distance (C, h)',fontsize=14)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Вероятность того, что иголка пересечет нить, будет равна отношению площади фигуры под графиком к площади прямоугольника." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Теперь сгенерируем 100 000 бросков и проанализируем параметры" + ] + }, + { + "cell_type": "code", + "execution_count": 233, + "metadata": {}, + "outputs": [], + "source": [ + "A = 100 # Расстояние между линиями\n", + "L = 100 # Длина иглы\n", + "\n", + "N = 100000\n", + "C = np.random.uniform(-A/2, A/2, N) # Изначальное расстояние от начала иглы до линии (-a/2 ... a/2) \n", + "angle = np.random.uniform(0, pi, N)\n", + "count = 0\n", + "cn = []\n", + "nn = []\n", + "yy = []\n", + "\n", + "for i in range(N):\n", + " x1 = 0\n", + " x2 = L*cos(angle)[i]\n", + " y1 = C[i]\n", + " y2 = L*sin(angle)[i]+y1\n", + " if A/2-C[i]" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Произошло 63719 пересечений из 100000 бросков\n", + "Среднее ожидание для последних 50000.0 событий: 0.6366374351638979\n", + "Pi Cross = 3.1415064957284873\n" + ] + } + ], + "source": [ + "cn_pi = np.divide(2,cn)\n", + "plt.figure(figsize=(14,4))\n", + "plt.plot(nn,cn_pi,linewidth=2)\n", + "plt.plot([N-N*1.01,N*1.03],[cn_pi[N-1],cn_pi[N-1]], color ='red', linewidth=0.75, linestyle =\"--\")\n", + "\n", + "P = cn_pi[int(N/2):]\n", + "\n", + "plt.xlabel('№ броска',fontsize=14)\n", + "plt.ylabel('Pi Cross',fontsize=14)\n", + "plt.ylim(2.9,3.4)\n", + "plt.xlim(N-N*1.01,N*1.03)\n", + "plt.show() \n", + "print(f'Произошло {count} пересечений из {N} бросков')\n", + "print(f'Среднее ожидание для последних {N/2} событий: {np.mean(cn[int(N/2):])}')\n", + "print(f'Pi Cross = {np.mean(P)}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Гистограмма распределения расстояния от кончика иглы до ближайшей линии (при случайном угле бросания):" + ] + }, + { + "cell_type": "code", + "execution_count": 236, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mu = 33.7123064025261, D = 566.1974445251878, std = 23.79490375112259\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# A = 100, L = 100\n", + "# yy - координата кончика иглы c учетом угла поворота (y2) = L*sin(angle)+y1\n", + "\n", + "dist_1 = np.abs(np.subtract(np.abs(A/2), np.abs(yy))) # Абсолютное расстояние от кончика до ближайшей линии\n", + "# dist_1 = np.subtract(np.abs(A/2), np.abs(yy))\n", + "\n", + "num_bins = 50\n", + "n, bins, patches = plt.hist(dist_1, num_bins, density=1, facecolor='b', alpha=0.5)\n", + "\n", + "plt.xlabel('Расстояние от иглы до ближайшей линии')\n", + "plt.ylabel('Плотность распределения')\n", + "\n", + "mu = np.mean(dist_1) # Среднее\n", + "D = np.var(dist_1) # Дисперсия\n", + "std = np.std(dist_1) # Среднеквадратичное отклонение\n", + "print(f'mu = {mu}, D = {D}, std = {std}')\n", + "y = mlab.normpdf(bins, mu, std)\n", + "plt.plot(bins, y, 'r--')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Зависимость вероятности от начальных условий" + ] + }, + { + "cell_type": "code", + "execution_count": 238, + "metadata": {}, + "outputs": [], + "source": [ + "def func(L, A, N=1000):\n", + " C = np.random.uniform(-A/2, A/2, N) # Изначальное расстояние от начала иглы до линии (-a/2 ... a/2) \n", + " angle = np.random.uniform(0, pi/2, N)\n", + " count = 0\n", + " cn = []\n", + " nn = []\n", + "\n", + " for i in range(N):\n", + " x1 = 0\n", + " x2 = L*cos(angle)[i]\n", + " y1 = C[i]\n", + " y2 = L*sin(angle)[i]+y1\n", + " if A/2-C[i]\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
Длина иглы (L)Расстояние между линиями (A)Вероятность (P)
040400.622554
140500.544626
240600.430251
340700.346651
440800.323327
540900.249817
6401000.243603
7401100.231423
8401200.192077
9401300.212575
10401400.179365
11401500.164695
1250400.728317
1350500.633791
1450600.566064
1550700.440326
1650800.425583
1750900.329401
18501000.316428
19501100.288828
20501200.294491
21501300.230204
22501400.217535
23501500.234084
2460400.776536
2560500.761208
2660600.664171
2760700.527353
2860800.471080
2960900.373388
30601000.385029
31601100.344530
32601200.295321
33601300.301339
34601400.271689
35601500.216505
3670400.818032
3770500.780770
3870600.710011
3970700.627744
4070800.574248
4170900.492760
42701000.445870
43701100.415609
44701200.365906
45701300.358169
46701400.326138
47701500.306215
\n", + "" + ], + "text/plain": [ + " Длина иглы (L) Расстояние между линиями (A) Вероятность (P)\n", + "0 40 40 0.622554\n", + "1 40 50 0.544626\n", + "2 40 60 0.430251\n", + "3 40 70 0.346651\n", + "4 40 80 0.323327\n", + "5 40 90 0.249817\n", + "6 40 100 0.243603\n", + "7 40 110 0.231423\n", + "8 40 120 0.192077\n", + "9 40 130 0.212575\n", + "10 40 140 0.179365\n", + "11 40 150 0.164695\n", + "12 50 40 0.728317\n", + "13 50 50 0.633791\n", + "14 50 60 0.566064\n", + "15 50 70 0.440326\n", + "16 50 80 0.425583\n", + "17 50 90 0.329401\n", + "18 50 100 0.316428\n", + "19 50 110 0.288828\n", + "20 50 120 0.294491\n", + "21 50 130 0.230204\n", + "22 50 140 0.217535\n", + "23 50 150 0.234084\n", + "24 60 40 0.776536\n", + "25 60 50 0.761208\n", + "26 60 60 0.664171\n", + "27 60 70 0.527353\n", + "28 60 80 0.471080\n", + "29 60 90 0.373388\n", + "30 60 100 0.385029\n", + "31 60 110 0.344530\n", + "32 60 120 0.295321\n", + "33 60 130 0.301339\n", + "34 60 140 0.271689\n", + "35 60 150 0.216505\n", + "36 70 40 0.818032\n", + "37 70 50 0.780770\n", + "38 70 60 0.710011\n", + "39 70 70 0.627744\n", + "40 70 80 0.574248\n", + "41 70 90 0.492760\n", + "42 70 100 0.445870\n", + "43 70 110 0.415609\n", + "44 70 120 0.365906\n", + "45 70 130 0.358169\n", + "46 70 140 0.326138\n", + "47 70 150 0.306215" + ] + }, + "execution_count": 239, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "needle_len_min = 40\n", + "needle_len_max = 80\n", + "lines_min = 40\n", + "lines_max = 160\n", + "needle_len = []\n", + "line_width = []\n", + "P = []\n", + "\n", + "for i in range (needle_len_min, needle_len_max, 10):\n", + " for j in range (lines_min, lines_max, 10):\n", + " needle_len.append(i)\n", + " line_width.append(j)\n", + " P.append(np.mean(func(i, j)))\n", + "df = pd.DataFrame(needle_len, columns=['Длина иглы (L)'])\n", + "df['Расстояние между линиями (A)'], df['Вероятность (P)'] = line_width, P\n", + "df" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# $\\pi$ " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.14159265358" + ] + } + ], + "source": [ + "import string as str\n", + "s = 'Это я знаю и помню прекрасно, пи многие знаки мне лишни, напрасны'\n", + "s = s.replace(',', \"\")\n", + "b = s.split(' ')\n", + "for i in range(len(b)):\n", + " print(len(b[i]),end = '')\n", + " if i==0:\n", + " print('.',end = '')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}