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@ischurov
Created February 23, 2022 17:14
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{
"cells": [
{
"cell_type": "markdown",
"id": "considerable-comedy",
"metadata": {},
"source": [
"## Наука о данных\n",
"### Совместный бакалавриат ВШЭ-РЭШ, 2021-2022 учебный год\n",
"_Илья Щуров_\n",
"\n",
"[Страница курса](http://math-info.hse.ru/s21/j)"
]
},
{
"cell_type": "markdown",
"id": "dying-easter",
"metadata": {},
"source": [
"### broadcasting в numpy"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "sustainable-quarter",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "defensive-chain",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([11, 22, 33])"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([1, 2, 3]) + np.array([10, 20, 30])"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "obvious-mongolia",
"metadata": {},
"outputs": [
{
"ename": "ValueError",
"evalue": "operands could not be broadcast together with shapes (3,) (2,) ",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m/var/folders/h2/9nyrt4p55kq6pdvqg02_zmj40000gn/T/ipykernel_60584/3514204344.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,) (2,) "
]
}
],
"source": [
"np.array([1, 2, 3]) + np.array([10, 20])"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "broadband-stretch",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([11, 12, 13])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([1, 2, 3]) + np.array([10])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "worst-rocket",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([11, 12, 13])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([1, 2, 3]) + 10"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "infrared-quarterly",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([11, 12, 13])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([1, 2, 3]) + np.array([10, 10, 10])"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "removable-buying",
"metadata": {},
"outputs": [],
"source": [
"M = np.array([[1, 2, 3],\n",
" [5, 6, 7]])"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "nasty-payday",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[2, 3, 4],\n",
" [6, 7, 8]])"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M + 1"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "cooked-passage",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1, 2, 3],\n",
" [5, 6, 7]])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "portable-booking",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[11, 22, 33],\n",
" [15, 26, 37]])"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M + np.array([10, 20, 30])"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "frozen-northwest",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 10, 40, 90],\n",
" [ 50, 120, 210]])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M * np.array([10, 20, 30])"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "orange-france",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[11, 22, 33],\n",
" [15, 26, 37]])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M + np.array([[10, 20, 30]])"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "indirect-alaska",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1, 2, 3],\n",
" [5, 6, 7]])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "polish-keeping",
"metadata": {},
"outputs": [],
"source": [
"P = np.array([1, 2])\n",
"v = np.array([4, 2])"
]
},
{
"cell_type": "markdown",
"id": "concrete-guard",
"metadata": {},
"source": [
"Хочу нарисовать прямую, проходящую через точку $P$ и содержащую вектор $v$.\n",
"\n",
"$$\\{P + tv \\mid t \\in \\mathbb R\\}$$"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "brave-revision",
"metadata": {},
"outputs": [],
"source": [
"t = np.linspace(-4, 4, 101)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "classical-assignment",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "unique-hypothesis",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-16. , -8. ],\n",
" [-15.68, -7.84],\n",
" [-15.36, -7.68],\n",
" [-15.04, -7.52],\n",
" [-14.72, -7.36],\n",
" [-14.4 , -7.2 ],\n",
" [-14.08, -7.04],\n",
" [-13.76, -6.88],\n",
" [-13.44, -6.72],\n",
" [-13.12, -6.56],\n",
" [-12.8 , -6.4 ],\n",
" [-12.48, -6.24],\n",
" [-12.16, -6.08],\n",
" [-11.84, -5.92],\n",
" [-11.52, -5.76],\n",
" [-11.2 , -5.6 ],\n",
" [-10.88, -5.44],\n",
" [-10.56, -5.28],\n",
" [-10.24, -5.12],\n",
" [ -9.92, -4.96],\n",
" [ -9.6 , -4.8 ],\n",
" [ -9.28, -4.64],\n",
" [ -8.96, -4.48],\n",
" [ -8.64, -4.32],\n",
" [ -8.32, -4.16],\n",
" [ -8. , -4. ],\n",
" [ -7.68, -3.84],\n",
" [ -7.36, -3.68],\n",
" [ -7.04, -3.52],\n",
" [ -6.72, -3.36],\n",
" [ -6.4 , -3.2 ],\n",
" [ -6.08, -3.04],\n",
" [ -5.76, -2.88],\n",
" [ -5.44, -2.72],\n",
" [ -5.12, -2.56],\n",
" [ -4.8 , -2.4 ],\n",
" [ -4.48, -2.24],\n",
" [ -4.16, -2.08],\n",
" [ -3.84, -1.92],\n",
" [ -3.52, -1.76],\n",
" [ -3.2 , -1.6 ],\n",
" [ -2.88, -1.44],\n",
" [ -2.56, -1.28],\n",
" [ -2.24, -1.12],\n",
" [ -1.92, -0.96],\n",
" [ -1.6 , -0.8 ],\n",
" [ -1.28, -0.64],\n",
" [ -0.96, -0.48],\n",
" [ -0.64, -0.32],\n",
" [ -0.32, -0.16],\n",
" [ 0. , 0. ],\n",
" [ 0.32, 0.16],\n",
" [ 0.64, 0.32],\n",
" [ 0.96, 0.48],\n",
" [ 1.28, 0.64],\n",
" [ 1.6 , 0.8 ],\n",
" [ 1.92, 0.96],\n",
" [ 2.24, 1.12],\n",
" [ 2.56, 1.28],\n",
" [ 2.88, 1.44],\n",
" [ 3.2 , 1.6 ],\n",
" [ 3.52, 1.76],\n",
" [ 3.84, 1.92],\n",
" [ 4.16, 2.08],\n",
" [ 4.48, 2.24],\n",
" [ 4.8 , 2.4 ],\n",
" [ 5.12, 2.56],\n",
" [ 5.44, 2.72],\n",
" [ 5.76, 2.88],\n",
" [ 6.08, 3.04],\n",
" [ 6.4 , 3.2 ],\n",
" [ 6.72, 3.36],\n",
" [ 7.04, 3.52],\n",
" [ 7.36, 3.68],\n",
" [ 7.68, 3.84],\n",
" [ 8. , 4. ],\n",
" [ 8.32, 4.16],\n",
" [ 8.64, 4.32],\n",
" [ 8.96, 4.48],\n",
" [ 9.28, 4.64],\n",
" [ 9.6 , 4.8 ],\n",
" [ 9.92, 4.96],\n",
" [ 10.24, 5.12],\n",
" [ 10.56, 5.28],\n",
" [ 10.88, 5.44],\n",
" [ 11.2 , 5.6 ],\n",
" [ 11.52, 5.76],\n",
" [ 11.84, 5.92],\n",
" [ 12.16, 6.08],\n",
" [ 12.48, 6.24],\n",
" [ 12.8 , 6.4 ],\n",
" [ 13.12, 6.56],\n",
" [ 13.44, 6.72],\n",
" [ 13.76, 6.88],\n",
" [ 14.08, 7.04],\n",
" [ 14.4 , 7.2 ],\n",
" [ 14.72, 7.36],\n",
" [ 15.04, 7.52],\n",
" [ 15.36, 7.68],\n",
" [ 15.68, 7.84],\n",
" [ 16. , 8. ]])"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t.reshape(-1, 1) * v"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "personal-shame",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11bcda050>]"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"line = P + t.reshape(-1, 1) * v\n",
"plt.plot(line[:, 0], line[:, 1])\n",
"plt.plot(P[0], P[1], 'o')\n",
"plt.plot([P[0], P[0] + v[0]], [P[1], P[1] + v[1]], lw=5)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "noted-entrance",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(4,)"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([1, 2, 3, 10]).shape"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "adapted-fossil",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(2, 3)"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([[1, 2, 3],\n",
" [10, 20, 30]\n",
" ]).shape"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "patent-electric",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(3,)"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([1, 2, 3]).shape"
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "flush-horizon",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1, 3)"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([[1, 2, 3]]).shape"
]
},
{
"cell_type": "code",
"execution_count": 45,
"id": "comic-sleeping",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(4, 3)"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([[1, 2, 3],\n",
" [1, 2, 3],\n",
" [1, 2, 3],\n",
" [1, 2, 3]\n",
" ]).shape"
]
},
{
"cell_type": "code",
"execution_count": 48,
"id": "subtle-banks",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(3, 1)"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([[1], [2], [3]]).shape"
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "frozen-nursing",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(3, 2)"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([[1, 1], [2, 2], [3, 3]]).shape"
]
},
{
"cell_type": "code",
"execution_count": 58,
"id": "periodic-impact",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(101, 1)"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t.reshape(-1, 1).shape"
]
},
{
"cell_type": "code",
"execution_count": 65,
"id": "premium-nirvana",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(2,)"
]
},
"execution_count": 65,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([1, 2]).shape"
]
},
{
"cell_type": "code",
"execution_count": 66,
"id": "robust-there",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1, 2)"
]
},
"execution_count": 66,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([[1, 2]]).shape"
]
},
{
"cell_type": "code",
"execution_count": 50,
"id": "fifth-wisdom",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-15. , -6. ],\n",
" [-14.68, -5.84],\n",
" [-14.36, -5.68],\n",
" [-14.04, -5.52],\n",
" [-13.72, -5.36],\n",
" [-13.4 , -5.2 ],\n",
" [-13.08, -5.04],\n",
" [-12.76, -4.88],\n",
" [-12.44, -4.72],\n",
" [-12.12, -4.56],\n",
" [-11.8 , -4.4 ],\n",
" [-11.48, -4.24],\n",
" [-11.16, -4.08],\n",
" [-10.84, -3.92],\n",
" [-10.52, -3.76],\n",
" [-10.2 , -3.6 ],\n",
" [ -9.88, -3.44],\n",
" [ -9.56, -3.28],\n",
" [ -9.24, -3.12],\n",
" [ -8.92, -2.96],\n",
" [ -8.6 , -2.8 ],\n",
" [ -8.28, -2.64],\n",
" [ -7.96, -2.48],\n",
" [ -7.64, -2.32],\n",
" [ -7.32, -2.16],\n",
" [ -7. , -2. ],\n",
" [ -6.68, -1.84],\n",
" [ -6.36, -1.68],\n",
" [ -6.04, -1.52],\n",
" [ -5.72, -1.36],\n",
" [ -5.4 , -1.2 ],\n",
" [ -5.08, -1.04],\n",
" [ -4.76, -0.88],\n",
" [ -4.44, -0.72],\n",
" [ -4.12, -0.56],\n",
" [ -3.8 , -0.4 ],\n",
" [ -3.48, -0.24],\n",
" [ -3.16, -0.08],\n",
" [ -2.84, 0.08],\n",
" [ -2.52, 0.24],\n",
" [ -2.2 , 0.4 ],\n",
" [ -1.88, 0.56],\n",
" [ -1.56, 0.72],\n",
" [ -1.24, 0.88],\n",
" [ -0.92, 1.04],\n",
" [ -0.6 , 1.2 ],\n",
" [ -0.28, 1.36],\n",
" [ 0.04, 1.52],\n",
" [ 0.36, 1.68],\n",
" [ 0.68, 1.84],\n",
" [ 1. , 2. ],\n",
" [ 1.32, 2.16],\n",
" [ 1.64, 2.32],\n",
" [ 1.96, 2.48],\n",
" [ 2.28, 2.64],\n",
" [ 2.6 , 2.8 ],\n",
" [ 2.92, 2.96],\n",
" [ 3.24, 3.12],\n",
" [ 3.56, 3.28],\n",
" [ 3.88, 3.44],\n",
" [ 4.2 , 3.6 ],\n",
" [ 4.52, 3.76],\n",
" [ 4.84, 3.92],\n",
" [ 5.16, 4.08],\n",
" [ 5.48, 4.24],\n",
" [ 5.8 , 4.4 ],\n",
" [ 6.12, 4.56],\n",
" [ 6.44, 4.72],\n",
" [ 6.76, 4.88],\n",
" [ 7.08, 5.04],\n",
" [ 7.4 , 5.2 ],\n",
" [ 7.72, 5.36],\n",
" [ 8.04, 5.52],\n",
" [ 8.36, 5.68],\n",
" [ 8.68, 5.84],\n",
" [ 9. , 6. ],\n",
" [ 9.32, 6.16],\n",
" [ 9.64, 6.32],\n",
" [ 9.96, 6.48],\n",
" [ 10.28, 6.64],\n",
" [ 10.6 , 6.8 ],\n",
" [ 10.92, 6.96],\n",
" [ 11.24, 7.12],\n",
" [ 11.56, 7.28],\n",
" [ 11.88, 7.44],\n",
" [ 12.2 , 7.6 ],\n",
" [ 12.52, 7.76],\n",
" [ 12.84, 7.92],\n",
" [ 13.16, 8.08],\n",
" [ 13.48, 8.24],\n",
" [ 13.8 , 8.4 ],\n",
" [ 14.12, 8.56],\n",
" [ 14.44, 8.72],\n",
" [ 14.76, 8.88],\n",
" [ 15.08, 9.04],\n",
" [ 15.4 , 9.2 ],\n",
" [ 15.72, 9.36],\n",
" [ 16.04, 9.52],\n",
" [ 16.36, 9.68],\n",
" [ 16.68, 9.84],\n",
" [ 17. , 10. ]])"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"P + t.reshape(-1, 1) * v"
]
},
{
"cell_type": "code",
"execution_count": 51,
"id": "organized-bookmark",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(2,)"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"P.shape"
]
},
{
"cell_type": "code",
"execution_count": 54,
"id": "hispanic-facial",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(101,)"
]
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t.shape"
]
},
{
"cell_type": "code",
"execution_count": 52,
"id": "consecutive-runner",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(101, 1)"
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t.reshape(-1, 1).shape"
]
},
{
"cell_type": "code",
"execution_count": 53,
"id": "assumed-peoples",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(2,)"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v.shape"
]
},
{
"cell_type": "markdown",
"id": "weird-portrait",
"metadata": {},
"source": [
"```\n",
" 101, 1\n",
" 2\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 56,
"id": "precise-industry",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(3, 2, 3)"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([[\n",
" [1, 2, 3],\n",
" [2, 3, 4]\n",
" ],\n",
" [\n",
" [10, 20, 30],\n",
" [100, 200, 300]\n",
" ],\n",
" [\n",
" [11, 22, 33],\n",
" [100, 200, 300]\n",
" ],\n",
" ]).shape"
]
},
{
"cell_type": "code",
"execution_count": 85,
"id": "criminal-faculty",
"metadata": {},
"outputs": [],
"source": [
"from scipy.optimize import fmin, root"
]
},
{
"cell_type": "code",
"execution_count": 70,
"id": "selective-economy",
"metadata": {},
"outputs": [],
"source": [
"from ipywidgets import interact"
]
},
{
"cell_type": "code",
"execution_count": 75,
"id": "legendary-kentucky",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.])"
]
},
"execution_count": 75,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"root(f, 0.2).x"
]
},
{
"cell_type": "code",
"execution_count": 80,
"id": "adult-single",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "e41956e209804804a8304e74d0692317",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"interactive(children=(FloatSlider(value=0.0, description='initial_value', max=3.0, min=-3.0), FloatSlider(valu…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def f(x, a):\n",
" return x ** 2 - a\n",
"\n",
"@interact(initial_value=(-3., 3.), a=(-3., 3.))\n",
"def find_root(initial_value, a):\n",
" r = root(f, initial_value, args=(a,)).x\n",
" x = np.linspace(-2, 2)\n",
" plt.plot(x, f(x, a))\n",
" plt.plot([r], [0], 'o')\n",
" plt.plot([-2, 2], [0, 0])\n"
]
},
{
"cell_type": "code",
"execution_count": 84,
"id": "tough-aviation",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"False"
]
},
"execution_count": 84,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"root(f, 0.2, args=(-1,)).success"
]
},
{
"cell_type": "code",
"execution_count": 90,
"id": "anonymous-cornell",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "d15e7c3a06954b7e9b60ad47601e1dca",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"interactive(children=(FloatSlider(value=0.0, description='initial_value', max=3.0, min=-3.0), FloatSlider(valu…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def f(x, a):\n",
" return x ** 3 - a * x\n",
"\n",
"\n",
"@interact(initial_value=(-3., 3.), a=(-3., 3.))\n",
"def find_min(initial_value, a):\n",
" x_min, y_min = fmin(f, initial_value, args=(a,), full_output=True)[:2]\n",
" x = np.linspace(-2, 2)\n",
" plt.plot(x, f(x, a))\n",
" plt.plot([x_min], [y_min], 'o')\n",
" #plt.plot([-2, 2], [0, 0])"
]
},
{
"cell_type": "code",
"execution_count": 91,
"id": "signed-restaurant",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Collecting plotly\n",
" Downloading plotly-5.6.0-py2.py3-none-any.whl (27.7 MB)\n",
" |████████████████████████████████| 27.7 MB 5.4 MB/s \n",
"\u001b[?25hRequirement already satisfied: six in /Users/user/miniconda3/envs/py3.10/lib/python3.10/site-packages (from plotly) (1.16.0)\n",
"Collecting tenacity>=6.2.0\n",
" Downloading tenacity-8.0.1-py3-none-any.whl (24 kB)\n",
"Installing collected packages: tenacity, plotly\n",
"Successfully installed plotly-5.6.0 tenacity-8.0.1\n",
"Note: you may need to restart the kernel to use updated packages.\n"
]
}
],
"source": [
"%pip install plotly"
]
},
{
"cell_type": "code",
"execution_count": 92,
"id": "periodic-swing",
"metadata": {},
"outputs": [],
"source": [
"from plotly import graph_objects as go"
]
},
{
"cell_type": "code",
"execution_count": 93,
"id": "ahead-generation",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" <script type=\"text/javascript\">\n",
" window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
" if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
" if (typeof require !== 'undefined') {\n",
" require.undef(\"plotly\");\n",
" define('plotly', function(require, exports, module) {\n",
" /**\n",
"* plotly.js v2.9.0\n",
"* Copyright 2012-2022, Plotly, Inc.\n",
"* All rights reserved.\n",
"* Licensed under the MIT license\n",
"*/\n",
"!function(t){if(\"object\"==typeof exports&&\"undefined\"!=typeof module)module.exports=t();else if(\"function\"==typeof define&&define.amd)define([],t);else{(\"undefined\"!=typeof window?window:\"undefined\"!=typeof global?global:\"undefined\"!=typeof self?self:this).Plotly=t()}}((function(){return function t(e,r,n){function i(o,s){if(!r[o]){if(!e[o]){var l=\"function\"==typeof require&&require;if(!s&&l)return l(o,!0);if(a)return a(o,!0);var c=new Error(\"Cannot find module '\"+o+\"'\");throw c.code=\"MODULE_NOT_FOUND\",c}var u=r[o]={exports:{}};e[o][0].call(u.exports,(function(t){return i(e[o][1][t]||t)}),u,u.exports,t,e,r,n)}return r[o].exports}for(var a=\"function\"==typeof require&&require,o=0;o<n.length;o++)i(n[o]);return i}({1:[function(t,e,r){\"use strict\";var n=t(\"../src/lib\"),i={\"X,X div\":'direction:ltr;font-family:\"Open Sans\",verdana,arial,sans-serif;margin:0;padding:0;',\"X input,X button\":'font-family:\"Open Sans\",verdana,arial,sans-serif;',\"X input:focus,X 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0);display:none;opacity:0;z-index:1001;pointer-events:none;top:110%;right:50%;\",\"X [data-title]:hover:before,X [data-title]:hover:after\":\"display:block;opacity:1;\",\"X [data-title]:before\":'content:\"\";position:absolute;background:transparent;border:6px solid transparent;z-index:1002;margin-top:-12px;border-bottom-color:#69738a;margin-right:-6px;',\"X [data-title]:after\":\"content:attr(data-title);background:#69738a;color:#fff;padding:8px 10px;font-size:12px;line-height:12px;white-space:nowrap;margin-right:-18px;border-radius:2px;\",\"X .vertical [data-title]:before,X .vertical [data-title]:after\":\"top:0%;right:200%;\",\"X .vertical [data-title]:before\":\"border:6px solid transparent;border-left-color:#69738a;margin-top:8px;margin-right:-30px;\",\"X .select-outline\":\"fill:none;stroke-width:1;shape-rendering:crispEdges;\",\"X .select-outline-1\":\"stroke:#fff;\",\"X .select-outline-2\":\"stroke:#000;stroke-dasharray:2px 2px;\",Y:'font-family:\"Open 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strict\";e.exports=t(\"../src/traces/bar\")},{\"../src/traces/bar\":656}],4:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/barpolar\")},{\"../src/traces/barpolar\":669}],5:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/box\")},{\"../src/traces/box\":679}],6:[function(t,e,r){\"use strict\";e.exports=t(\"../src/components/calendars\")},{\"../src/components/calendars\":364}],7:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/candlestick\")},{\"../src/traces/candlestick\":688}],8:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/carpet\")},{\"../src/traces/carpet\":707}],9:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/choropleth\")},{\"../src/traces/choropleth\":721}],10:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/choroplethmapbox\")},{\"../src/traces/choroplethmapbox\":728}],11:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/cone\")},{\"../src/traces/cone\":734}],12:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/contour\")},{\"../src/traces/contour\":749}],13:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/contourcarpet\")},{\"../src/traces/contourcarpet\":760}],14:[function(t,e,r){\"use strict\";e.exports=t(\"../src/core\")},{\"../src/core\":481}],15:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/densitymapbox\")},{\"../src/traces/densitymapbox\":768}],16:[function(t,e,r){\"use strict\";e.exports=t(\"../src/transforms/filter\")},{\"../src/transforms/filter\":1115}],17:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/funnel\")},{\"../src/traces/funnel\":778}],18:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/funnelarea\")},{\"../src/traces/funnelarea\":787}],19:[function(t,e,r){\"use strict\";e.exports=t(\"../src/transforms/groupby\")},{\"../src/transforms/groupby\":1116}],20:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/heatmap\")},{\"../src/traces/heatmap\":800}],21:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/heatmapgl\")},{\"../src/traces/heatmapgl\":811}],22:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/histogram\")},{\"../src/traces/histogram\":823}],23:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/histogram2d\")},{\"../src/traces/histogram2d\":829}],24:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/histogram2dcontour\")},{\"../src/traces/histogram2dcontour\":833}],25:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/icicle\")},{\"../src/traces/icicle\":839}],26:[function(t,e,r){\"use strict\";e.exports=t(\"../src/traces/image\")},{\"../src/traces/image\":852}],27:[function(t,e,r){\"use strict\";var n=t(\"./core\");n.register([t(\"./bar\"),t(\"./box\"),t(\"./heatmap\"),t(\"./histogram\"),t(\"./histogram2d\"),t(\"./histogram2dcontour\"),t(\"./contour\"),t(\"./scatterternary\"),t(\"./violin\"),t(\"./funnel\"),t(\"./waterfall\"),t(\"./image\"),t(\"./pie\"),t(\"./sunburst\"),t(\"./treemap\"),t(\"./icicle\"),t(\"./funnelarea\"),t(\"./scatter3d\"),t(\"./surface\"),t(\"./isosurface\"),t(\"./volume\"),t(\"./mesh3d\"),t(\"./cone\"),t(\"./streamtube\"),t(\"./scattergeo\"),t(\"./choropleth\"),t(\"./scattergl\"),t(\"./splom\"),t(\"./pointcloud\"),t(\"./heatmapgl\"),t(\"./parcoords\"),t(\"./parcats\"),t(\"./scattermapbox\"),t(\"./choroplethmapbox\"),t(\"./densitymapbox\"),t(\"./sankey\"),t(\"./indicator\"),t(\"./table\"),t(\"./carpet\"),t(\"./scattercarpet\"),t(\"./contourcarpet\"),t(\"./ohlc\"),t(\"./candlestick\"),t(\"./scatterpolar\"),t(\"./scatterpolargl\"),t(\"./barpolar\"),t(\"./scattersmith\"),t(\"./aggregate\"),t(\"./filter\"),t(\"./groupby\"),t(\"./sort\"),t(\"./calendars\")]),e.exports=n},{\"./aggregate\":2,\"./bar\":3,\"./barpolar\":4,\"./box\":5,\"./calendars\":6,\"./candlestick\":7,\"./carpet\":8,\"./choropleth\":9,\"./choroplethmapbox\":10,\"./cone\":11,\"./contour\":12,\"./contourcarpet\":13,\"./core\":14,\"./densitymapbox\":15,\"./filter\":16,\"./funnel\":17,\"./funnelarea\":18,\"./groupby\":19,\"./heatmap\":20,\"./heatmapgl\":21,\"./histogram\":22,\"./histogram2d\":23,\"./histogram2dcontour\":24,\"./icicle\":25,\"./image\":26,\"./indicator\":28,\"./isosurface\":29,\"./mesh3d\":30,\"./ohlc\":31,\"./parcats\":32,\"./parcoords\":33,\"./pie\":34,\"./pointcloud\":35,\"./sankey\":36,\"./scatter3d\":37,\"./scattercarpet\":38,\"./scattergeo\":39,\"./scattergl\":40,\"./scattermapbox\":41,\"./scatterpolar\":42,\"./scatterpolargl\":43,\"./scattersmith\":44,\"./scatterternary\":45,\"./sort\":46,\"./splom\":47,\"./streamtube\":48,\"./sunburst\":49,\"./surface\":50,\"./table\":51,\"./treemap\":52,\"./violin\":53,\"./volume\":54,\"./waterfall\":55}],28:[function(t,e,r){\"use 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r=L(8/(3*y)),i=e/r;return[t/(r*(1-n(i)/y)),i]},gt.invert=function(t,e){var r=2-n(e)/L(2*y/3);return[t*L(6*y)/(2*r),d(e)*S((4-r*r)/3)]},mt.invert=function(t,e){var r=L(y*(4+y))/2;return[t*r/(1+L(1-e*e*(4+y)/(4*y))),e*r/2]},vt.invert=function(t,e){var r=e*L((4+y)/y)/2,n=S(r),i=o(n);return[t/(2/L(y*(4+y))*(1+i)),S((n+r*(i+2))/(2+x))]},yt.invert=function(t,e){var r=L(2+y),n=e*r/2;return[r*t/(1+o(n)),n]},xt.invert=function(t,e){var r=1+x,n=L(r/2);return[2*t*n/(1+o(e*=n)),S((e+g(e))/r)]};var bt=3+2*w;function _t(t,e){var r=g(t/=2),n=o(t),a=L(o(e)),s=o(e/=2),l=g(e)/(s+w*n*a),u=L(2/(1+l*l)),f=L((w*s+(n+r)*a)/(w*s+(n-r)*a));return[bt*(u*(f-1/f)-2*c(f)),bt*(u*l*(f+1/f)-2*i(l))]}_t.invert=function(t,e){if(!(r=D.invert(t/1.2,1.065*e)))return null;var r,a=r[0],s=r[1],l=20;t/=bt,e/=bt;do{var h=a/2,p=s/2,d=g(h),m=o(h),y=g(p),b=o(p),T=o(s),k=L(T),A=y/(b+w*m*k),M=A*A,S=L(2/(1+M)),E=(w*b+(m+d)*k)/(w*b+(m-d)*k),C=L(E),P=C-1/C,I=C+1/C,O=S*P-2*c(C)-t,z=S*A*I-2*i(A)-e,R=y&&_*k*d*M/y,F=(w*m*b+k)/(2*(b+w*m*k)*(b+w*m*k)*k),B=-.5*A*S*S*S,N=B*R,j=B*F,U=(U=2*b+w*k*(m-d))*U*C,V=(w*m*b*k+T)/U,H=-w*d*y/(k*U),q=P*N-2*V/C+S*(V+V/E),G=P*j-2*H/C+S*(H+H/E),Y=A*I*N-2*R/(1+M)+S*I*R+S*A*(V-V/E),W=A*I*j-2*F/(1+M)+S*I*F+S*A*(H-H/E),X=G*Y-W*q;if(!X)break;var Z=(z*G-O*W)/X,J=(O*Y-z*q)/X;a-=Z,s=u(-x,f(x,s-J))}while((n(Z)>v||n(J)>v)&&--l>0);return n(n(s)-x)<v?[0,s]:l&&[a,s]};var wt=o(35*M);function Tt(t,e){var r=m(e/2);return[t*wt*L(1-r*r),(1+wt)*r]}function kt(t,e){var r=e/2,n=o(r);return[2*t/T*o(e)*n*n,T*m(r)]}function At(t){var e=1-t,r=i(y,0)[0]-i(-y,0)[0],n=L(2*(i(0,x)[1]-i(0,-x)[1])/r);function i(r,n){var i=o(n),a=g(n);return[i/(e+t*i)*r,e*n+t*a]}function a(t,e){var r=i(t,e);return[r[0]*n,r[1]/n]}function s(t){return a(0,t)[1]}return a.invert=function(r,i){var a=V(s,i);return[r/n*(t+e/o(a)),a]},a}function Mt(t){return[t[0]/2,S(m(t[1]/2*M))*A]}function St(t){return[2*t[0],2*i(g(t[1]*M))*A]}function Et(t,r){var i=2*y/r,s=t*t;function l(r,l){var c=e.geoAzimuthalEquidistantRaw(r,l),u=c[0],f=c[1],h=u*u+f*f;if(h>s){var d=L(h),m=a(f,u),b=i*p(m/i),_=m-b,w=t*o(_),T=(t*g(_)-_*g(w))/(x-w),k=Lt(_,T),A=(y-t)/Ct(k,w,y);u=d;var M,S=50;do{u-=M=(t+Ct(k,w,u)*A-d)/(k(u)*A)}while(n(M)>v&&--S>0);f=_*g(u),u<x&&(f-=T*(u-x));var E=g(b),C=o(b);c[0]=u*C-f*E,c[1]=u*E+f*C}return c}return l.invert=function(r,l){var c=r*r+l*l;if(c>s){var u=L(c),f=a(l,r),h=i*p(f/i),d=f-h;r=u*o(d),l=u*g(d);for(var m=r-x,v=g(r),b=l/v,_=r<x?1/0:0,w=10;;){var T=t*g(b),k=t*o(b),A=g(k),M=x-k,S=(T-b*A)/M,E=Lt(b,S);if(n(_)<1e-12||!--w)break;b-=_=(b*v-S*m-l)/(v-2*m*(M*(k+b*T*o(k)-A)-T*(T-b*A))/(M*M))}r=(u=t+Ct(E,k,r)*(y-t)/Ct(E,k,y))*o(f=h+b),l=u*g(f)}return e.geoAzimuthalEquidistantRaw.invert(r,l)},l}function Lt(t,e){return function(r){var n=t*o(r);return r<x&&(n-=e),L(1+n*n)}}function 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float fontSize, charStep, em, align, baseline;\\n\\t\\t\\tuniform vec4 viewport;\\n\\t\\t\\tuniform vec4 color;\\n\\t\\t\\tuniform vec2 atlasSize, atlasDim, scale, translate, positionOffset;\\n\\t\\t\\tvarying vec2 charCoord, charId;\\n\\t\\t\\tvarying float charWidth;\\n\\t\\t\\tvarying vec4 fontColor;\\n\\t\\t\\tvoid main () {\\n\\t\\t\\t\\tvec2 offset = floor(em * (vec2(align + charOffset, baseline)\\n\\t\\t\\t\\t\\t+ vec2(positionOffset.x, -positionOffset.y)))\\n\\t\\t\\t\\t\\t/ (viewport.zw * scale.xy);\\n\\n\\t\\t\\t\\tvec2 position = (position + translate) * scale;\\n\\t\\t\\t\\tposition += offset * scale;\\n\\n\\t\\t\\t\\tcharCoord = position * viewport.zw + viewport.xy;\\n\\n\\t\\t\\t\\tgl_Position = vec4(position * 2. - 1., 0, 1);\\n\\n\\t\\t\\t\\tgl_PointSize = charStep;\\n\\n\\t\\t\\t\\tcharId.x = mod(char, atlasDim.x);\\n\\t\\t\\t\\tcharId.y = floor(char / atlasDim.x);\\n\\n\\t\\t\\t\\tcharWidth = width * em;\\n\\n\\t\\t\\t\\tfontColor = color / 255.;\\n\\t\\t\\t}\",frag:\"\\n\\t\\t\\tprecision highp float;\\n\\t\\t\\tuniform float fontSize, charStep, opacity;\\n\\t\\t\\tuniform vec2 atlasSize;\\n\\t\\t\\tuniform vec4 viewport;\\n\\t\\t\\tuniform sampler2D atlas;\\n\\t\\t\\tvarying vec4 fontColor;\\n\\t\\t\\tvarying vec2 charCoord, charId;\\n\\t\\t\\tvarying float charWidth;\\n\\n\\t\\t\\tfloat lightness(vec4 color) {\\n\\t\\t\\t\\treturn color.r * 0.299 + color.g * 0.587 + color.b * 0.114;\\n\\t\\t\\t}\\n\\n\\t\\t\\tvoid main () {\\n\\t\\t\\t\\tvec2 uv = gl_FragCoord.xy - charCoord + charStep * .5;\\n\\t\\t\\t\\tfloat halfCharStep = floor(charStep * .5 + .5);\\n\\n\\t\\t\\t\\t// invert y and shift by 1px (FF expecially needs that)\\n\\t\\t\\t\\tuv.y = charStep - uv.y;\\n\\n\\t\\t\\t\\t// ignore points outside of character bounding box\\n\\t\\t\\t\\tfloat halfCharWidth = ceil(charWidth * .5);\\n\\t\\t\\t\\tif (floor(uv.x) > halfCharStep + halfCharWidth ||\\n\\t\\t\\t\\t\\tfloor(uv.x) < halfCharStep - halfCharWidth) return;\\n\\n\\t\\t\\t\\tuv += charId * charStep;\\n\\t\\t\\t\\tuv = uv / atlasSize;\\n\\n\\t\\t\\t\\tvec4 color = fontColor;\\n\\t\\t\\t\\tvec4 mask = texture2D(atlas, uv);\\n\\n\\t\\t\\t\\tfloat maskY = lightness(mask);\\n\\t\\t\\t\\t// float colorY = lightness(color);\\n\\t\\t\\t\\tcolor.a *= maskY;\\n\\t\\t\\t\\tcolor.a *= opacity;\\n\\n\\t\\t\\t\\t// color.a += .1;\\n\\n\\t\\t\\t\\t// antialiasing, see yiq color space y-channel formula\\n\\t\\t\\t\\t// color.rgb += (1. - color.rgb) * (1. - mask.rgb);\\n\\n\\t\\t\\t\\tgl_FragColor = color;\\n\\t\\t\\t}\"});return{regl:t,draw:e,atlas:{}}},T.prototype.update=function(t){var e=this;if(\"string\"==typeof t)t={text:t};else if(!t)return;null!=(t=i(t,{position:\"position positions coord coords coordinates\",font:\"font fontFace fontface typeface cssFont css-font family fontFamily\",fontSize:\"fontSize fontsize size font-size\",text:\"text texts chars characters value values symbols\",align:\"align alignment textAlign textbaseline\",baseline:\"baseline textBaseline textbaseline\",direction:\"dir direction textDirection\",color:\"color colour fill fill-color fillColor textColor textcolor\",kerning:\"kerning kern\",range:\"range dataBox\",viewport:\"vp viewport viewBox viewbox viewPort\",opacity:\"opacity alpha transparency visible visibility opaque\",offset:\"offset positionOffset padding shift indent indentation\"},!0)).opacity&&(Array.isArray(t.opacity)?this.opacity=t.opacity.map((function(t){return parseFloat(t)})):this.opacity=parseFloat(t.opacity)),null!=t.viewport&&(this.viewport=f(t.viewport),this.viewportArray=[this.viewport.x,this.viewport.y,this.viewport.width,this.viewport.height]),null==this.viewport&&(this.viewport={x:0,y:0,width:this.gl.drawingBufferWidth,height:this.gl.drawingBufferHeight},this.viewportArray=[this.viewport.x,this.viewport.y,this.viewport.width,this.viewport.height]),null!=t.kerning&&(this.kerning=t.kerning),null!=t.offset&&(\"number\"==typeof t.offset&&(t.offset=[t.offset,0]),this.positionOffset=y(t.offset)),t.direction&&(this.direction=t.direction),t.range&&(this.range=t.range,this.scale=[1/(t.range[2]-t.range[0]),1/(t.range[3]-t.range[1])],this.translate=[-t.range[0],-t.range[1]]),t.scale&&(this.scale=t.scale),t.translate&&(this.translate=t.translate),this.scale||(this.scale=[1/this.viewport.width,1/this.viewport.height]),this.translate||(this.translate=[0,0]),this.font.length||t.font||(t.font=T.baseFontSize+\"px sans-serif\");var r,a=!1,o=!1;if(t.font&&(Array.isArray(t.font)?t.font:[t.font]).forEach((function(t,r){if(\"string\"==typeof t)try{t=n.parse(t)}catch(e){t=n.parse(T.baseFontSize+\"px \"+t)}else t=n.parse(n.stringify(t));var i=n.stringify({size:T.baseFontSize,family:t.family,stretch:_?t.stretch:void 0,variant:t.variant,weight:t.weight,style:t.style}),s=p(t.size),l=Math.round(s[0]*d(s[1]));if(l!==e.fontSize[r]&&(o=!0,e.fontSize[r]=l),!(e.font[r]&&i==e.font[r].baseString||(a=!0,e.font[r]=T.fonts[i],e.font[r]))){var c=t.family.join(\", \"),u=[t.style];t.style!=t.variant&&u.push(t.variant),t.variant!=t.weight&&u.push(t.weight),_&&t.weight!=t.stretch&&u.push(t.stretch),e.font[r]={baseString:i,family:c,weight:t.weight,stretch:t.stretch,style:t.style,variant:t.variant,width:{},kerning:{},metrics:v(c,{origin:\"top\",fontSize:T.baseFontSize,fontStyle:u.join(\" \")})},T.fonts[i]=e.font[r]}})),(a||o)&&this.font.forEach((function(r,i){var a=n.stringify({size:e.fontSize[i],family:r.family,stretch:_?r.stretch:void 0,variant:r.variant,weight:r.weight,style:r.style});if(e.fontAtlas[i]=e.shader.atlas[a],!e.fontAtlas[i]){var o=r.metrics;e.shader.atlas[a]=e.fontAtlas[i]={fontString:a,step:2*Math.ceil(e.fontSize[i]*o.bottom*.5),em:e.fontSize[i],cols:0,rows:0,height:0,width:0,chars:[],ids:{},texture:e.regl.texture()}}null==t.text&&(t.text=e.text)})),\"string\"==typeof t.text&&t.position&&t.position.length>2){for(var s=Array(.5*t.position.length),h=0;h<s.length;h++)s[h]=t.text;t.text=s}if(null!=t.text||a){if(this.textOffsets=[0],Array.isArray(t.text)){this.count=t.text[0].length,this.counts=[this.count];for(var b=1;b<t.text.length;b++)this.textOffsets[b]=this.textOffsets[b-1]+t.text[b-1].length,this.count+=t.text[b].length,this.counts.push(t.text[b].length);this.text=t.text.join(\"\")}else this.text=t.text,this.count=this.text.length,this.counts=[this.count];r=[],this.font.forEach((function(t,n){T.atlasContext.font=t.baseString;for(var i=e.fontAtlas[n],a=0;a<e.text.length;a++){var o=e.text.charAt(a);if(null==i.ids[o]&&(i.ids[o]=i.chars.length,i.chars.push(o),r.push(o)),null==t.width[o]&&(t.width[o]=T.atlasContext.measureText(o).width/T.baseFontSize,e.kerning)){var s=[];for(var l in t.width)s.push(l+o,o+l);m(t.kerning,g(t.family,{pairs:s}))}}}))}if(t.position)if(t.position.length>2){for(var w=!t.position[0].length,k=u.mallocFloat(2*this.count),A=0,M=0;A<this.counts.length;A++){var S=this.counts[A];if(w)for(var E=0;E<S;E++)k[M++]=t.position[2*A],k[M++]=t.position[2*A+1];else for(var L=0;L<S;L++)k[M++]=t.position[A][0],k[M++]=t.position[A][1]}this.position.call?this.position({type:\"float\",data:k}):this.position=this.regl.buffer({type:\"float\",data:k}),u.freeFloat(k)}else this.position.destroy&&this.position.destroy(),this.position={constant:t.position};if(t.text||a){var C=u.mallocUint8(this.count),P=u.mallocFloat(2*this.count);this.textWidth=[];for(var I=0,O=0;I<this.counts.length;I++){for(var z=this.counts[I],D=this.font[I]||this.font[0],R=this.fontAtlas[I]||this.fontAtlas[0],F=0;F<z;F++){var B=this.text.charAt(O),N=this.text.charAt(O-1);if(C[O]=R.ids[B],P[2*O]=D.width[B],F){var j=P[2*O-2],U=P[2*O],V=P[2*O-1]+.5*j+.5*U;if(this.kerning){var H=D.kerning[N+B];H&&(V+=.001*H)}P[2*O+1]=V}else P[2*O+1]=.5*P[2*O];O++}this.textWidth.push(P.length?.5*P[2*O-2]+P[2*O-1]:0)}t.align||(t.align=this.align),this.charBuffer({data:C,type:\"uint8\",usage:\"stream\"}),this.sizeBuffer({data:P,type:\"float\",usage:\"stream\"}),u.freeUint8(C),u.freeFloat(P),r.length&&this.font.forEach((function(t,r){var n=e.fontAtlas[r],i=n.step,a=Math.floor(T.maxAtlasSize/i),o=Math.min(a,n.chars.length),s=Math.ceil(n.chars.length/o),l=x(o*i),u=x(s*i);n.width=l,n.height=u,n.rows=s,n.cols=o,n.em&&n.texture({data:c({canvas:T.atlasCanvas,font:n.fontString,chars:n.chars,shape:[l,u],step:[i,i]})})}))}if(t.align&&(this.align=t.align,this.alignOffset=this.textWidth.map((function(t,r){var n=Array.isArray(e.align)?e.align.length>1?e.align[r]:e.align[0]:e.align;if(\"number\"==typeof n)return n;switch(n){case\"right\":case\"end\":return-t;case\"center\":case\"centre\":case\"middle\":return.5*-t}return 0}))),null==this.baseline&&null==t.baseline&&(t.baseline=0),null!=t.baseline&&(this.baseline=t.baseline,Array.isArray(this.baseline)||(this.baseline=[this.baseline]),this.baselineOffset=this.baseline.map((function(t,r){var n=(e.font[r]||e.font[0]).metrics,i=0;return i+=.5*n.bottom,i+=\"number\"==typeof t?t-n.baseline:-n[t],i*=-1}))),null!=t.color)if(t.color||(t.color=\"transparent\"),\"string\"!=typeof t.color&&isNaN(t.color)){var q;if(\"number\"==typeof t.color[0]&&t.color.length>this.counts.length){var G=t.color.length;q=u.mallocUint8(G);for(var Y=(t.color.subarray||t.color.slice).bind(t.color),W=0;W<G;W+=4)q.set(l(Y(W,W+4),\"uint8\"),W)}else{var X=t.color.length;q=u.mallocUint8(4*X);for(var Z=0;Z<X;Z++)q.set(l(t.color[Z]||0,\"uint8\"),4*Z)}this.color=q}else this.color=l(t.color,\"uint8\");if(t.position||t.text||t.color||t.baseline||t.align||t.font||t.offset||t.opacity)if(this.color.length>4||this.baselineOffset.length>1||this.align&&this.align.length>1||this.fontAtlas.length>1||this.positionOffset.length>2){var J=Math.max(.5*this.position.length||0,.25*this.color.length||0,this.baselineOffset.length||0,this.alignOffset.length||0,this.font.length||0,this.opacity.length||0,.5*this.positionOffset.length||0);this.batch=Array(J);for(var K=0;K<this.batch.length;K++)this.batch[K]={count:this.counts.length>1?this.counts[K]:this.counts[0],offset:this.textOffsets.length>1?this.textOffsets[K]:this.textOffsets[0],color:this.color?this.color.length<=4?this.color:this.color.subarray(4*K,4*K+4):[0,0,0,255],opacity:Array.isArray(this.opacity)?this.opacity[K]:this.opacity,baseline:null!=this.baselineOffset[K]?this.baselineOffset[K]:this.baselineOffset[0],align:this.align?null!=this.alignOffset[K]?this.alignOffset[K]:this.alignOffset[0]:0,atlas:this.fontAtlas[K]||this.fontAtlas[0],positionOffset:this.positionOffset.length>2?this.positionOffset.subarray(2*K,2*K+2):this.positionOffset}}else this.count?this.batch=[{count:this.count,offset:0,color:this.color||[0,0,0,255],opacity:Array.isArray(this.opacity)?this.opacity[0]:this.opacity,baseline:this.baselineOffset[0],align:this.alignOffset?this.alignOffset[0]:0,atlas:this.fontAtlas[0],positionOffset:this.positionOffset}]:this.batch=[]},T.prototype.destroy=function(){},T.prototype.kerning=!0,T.prototype.position={constant:new Float32Array(2)},T.prototype.translate=null,T.prototype.scale=null,T.prototype.font=null,T.prototype.text=\"\",T.prototype.positionOffset=[0,0],T.prototype.opacity=1,T.prototype.color=new Uint8Array([0,0,0,255]),T.prototype.alignOffset=[0,0],T.maxAtlasSize=1024,T.atlasCanvas=document.createElement(\"canvas\"),T.atlasContext=T.atlasCanvas.getContext(\"2d\",{alpha:!1}),T.baseFontSize=64,T.fonts={},e.exports=T},{\"bit-twiddle\":81,\"color-normalize\":89,\"css-font\":99,\"detect-kerning\":125,\"es6-weak-map\":183,\"flatten-vertex-data\":191,\"font-atlas\":192,\"font-measure\":193,\"gl-util/context\":226,\"is-plain-obj\":236,\"object-assign\":247,\"parse-rect\":249,\"parse-unit\":251,\"pick-by-alias\":253,regl:283,\"to-px\":314,\"typedarray-pool\":327}],226:[function(t,e,r){(function(r){(function(){\"use strict\";var n=t(\"pick-by-alias\");function i(t){if(t.container)if(t.container==document.body)document.body.style.width||(t.canvas.width=t.width||t.pixelRatio*r.innerWidth),document.body.style.height||(t.canvas.height=t.height||t.pixelRatio*r.innerHeight);else{var 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